75504
2712-8172
Magazine of Civil Engineering
19
1
141
2026
RAR
RUS
14101-14101
56703453300
0000-0002-4149-4348
Peter the Great St. Petersburg Polytechnic University
Feshin
Aleksandr
feshin_ao@spbstu.ru
St. Petersburg, Russian Federation
57212553296
0000-0003-2722-5552
Peter the Great St. Petersburg Polytechnic University,
Polyukhovich
Maxim
St. Petersburg, Russian Federation
57210916868
0000-0002-8392-1790
Peter the Great St. Petersburg Polytechnic University
Logvinova
Yulia
logvinova_yuv@spbstu.ru
St. Petersburg, Russian Federation
Burlov
Vyacheslav
Barskov
Victor
viktorbarskov@ntcmtt.ru
0000-0002-4101-878X
Technological University of Havana "José Antonio Echeverría"
Arzola-Ruiz
Jose
josearzolaruiz1945@gmail.com
Havana, Cuba
Peter the Great Saint Petersburg Polytechnic University
Castro
Jose
jose.castro.lozano@hotmail.com
Polytechnicheskay, 29
Electric power system functioning in conditions of extreme weather events in the presence of distributed generation based on renewable energy sources
Significant number of accidents in electric power systems are caused by the effects of extreme weather events. In such conditions, providing consumers with electric energy is especially important. This study is devoted to solving this problem, in which a decision-making model has been developed that takes into account distributed generation based on renewable energy sources. The proposed model is a procedure for optimizing the established electric power mode. Optimization is performed using a genetic algorithm. The regulated parameters are the active capacities of electric power plants, the voltage on the busbars of generators of these stations, and the transformation coefficients. The values of these parameters are determined in case of disconnection of one and two overhead power lines using the example of a modified IEEE-39 circuit. The results show that distributed generation makes it possible to provide full power supply to consumers in a larger number of these emergencies (by 13.2 % and 27.2 %, respectively). With the most optimal location and generation capacity based on renewable energy sources, full power supply to consumers is achieved in 100 % and 98.3 % of emergency situations, respectively. The proposed decision-making model has a high potential to expand its functionality.
1.Introduction
Electric power industry occupies a special place in human economic activity, since the supply of electric energy is critically necessary in all areas of the economy: industry, agriculture, transport, healthcare, etc. In addition, a significant part of the total consumption of electric energy is occupied by household consumers.
Extreme weather events have an impact on all areas of human activity [1]. Electric power facilities are also affected by these phenomena [2–4]. Since the main task of the complex is to supply consumers with electric energy, the issue of ensuring reliable and uninterrupted power supply becomes even more urgent in conditions of extreme events.
Electric power systems (EPS) contain many elements, one of which is overhead power lines (OHPL). Due to the significant length of overhead lines, more than other elements of the EPS are adversely affected by extreme weather events. The impact of these phenomena can lead to an emergency shutdown of one or more overhead lines, which, in turn, may be accompanied by a disruption in the supply of electrical energy to consumers.
Centralized restoration of power supply requires repair of damaged network infrastructure, which, in some cases, may take a long time. Therefore, a common method is the temporary use of backup power circuits and backup sources of electrical energy, which makes it possible to fully or partially restore supply to consumers. At the same time, an important circumstance should be noted: even in an emergency state, the parameters of the electric power mode, as a rule, must be within strictly defined limits.
Based on the information and statistics available to the author's team on the EPS of the Republic of Cuba, an analysis of the threats of power supply disruption was performed. As a result, risk factors have been identified that can lead to emergency disturbances in the operation of the EPS. Extreme weather events are among these factors:
hurricanes and severe storms; high probability of damage to the electric grid infrastructure, massive power outages, long-term repairs of the EPS infrastructure;
high ambient temperature; overheating of equipment, increased electrical loads of equipment, damage to OHPL supports due to thermal expansion of materials and reduced structural strength; increased boom sag of OHPL wires;
heavy rains, which can lead, among other things, to floods and landslides; falling OHPL poles due to soil erosion, damage to underground utilities, flooding of power grid infrastructure, power outages.
From 1980 to 2024, 112 major accidents occurred in the EPS of the Republic of Cuba, disabling more than half of consumers and causing significant economic and technological damage. At the same time, in 97 cases, the interruption in the electricity supply to consumers was more than a day. The causes of these accidents were:
high ambient temperature – 23 cases (20.5 %);
thunderstorm events – 19 cases (17 %);
floods – 9 cases (8 %);
complex of adverse events (hurricanes/storms and floods) – 34 cases (30.4 %);
complex of adverse events (thunderstorms and floods) – 2 cases (1.8 %);
hurricanes/storms – 1 case (0.9 %);
other reasons (equipment wear, personnel error during repair work, etc.) – 24 cases (21.4 %).
Presented results show that 78.6 % of accidents in the EPS of the Republic of Cuba occurred as a result of exposure to extreme weather events. This resulted in broken wires and falling OHPL supports, flooding of substations, overload of the electrical network due to abnormally high temperatures, and short circuits.
Functioning of EPS in conditions of extreme weather events is characterized by the concept of resilience, which is defined as the ability of EPS to withstand extreme events and recover quickly after these events [5]. Resilience measures can be divided into short-term or operational, which are applied in a relatively short time interval (several days or weeks), including an extreme weather event, and long-term, which are aimed at reducing the vulnerability of EPS to future events [5, 6]. The optimal functioning of EPS in conditions of exposure to extreme weather events is possible if a high level of resilience is ensured and the volume of disconnected electrical energy is reduced among consumers. This issue is of interest among researchers and is considered by them as an optimization problem.
In [7], the solution of the noted problem is performed by determining the optimal composition, capacity, and location of virtual power plants. The virtual station includes generating sources based on renewable energy sources (RES), energy storage systems based on rechargeable batteries and electric vehicles (it is assumed that the latter will operate in the power supply mode in the event of an accident). The problem is solved using the IEEE-118 distribution scheme using the "black widow" optimization algorithm. The determination of the optimal composition, capacity, and location of virtual power plants is also discussed in [8–11]. The following optimization algorithms are used in these works, the effectiveness of which is tested in IEEE test distribution schemes: the spotted hyena algorithm, IEEE-34 scheme [8]; a hybrid algorithm based on the algorithms "herd of krill" and "pack of gray wolves", IEEE-33 scheme [9]; the hunting prey algorithm, IEEE-85 scheme [10]; hybrid algorithm based on the "krill herd" and "sine-cosine" algorithms, IEEE-69 scheme [11].
Method for increasing the resilience of an electric distribution network, which is formulated as a multi-criteria optimization model, was proposed in [12]. The paper describes in detail the mathematical part of the model, in which the nonlinear components are linearized, and the penalty components are introduced into the objective function. Optimization is performed using the GUROBI software product. The efficiency check was performed in the IEEE-123 test distribution circuit. The developed method is proposed as an assistant to dispatching personnel when making decisions in conditions of extreme weather events.
In [13], it was proposed to optimize the location of charging stations for electric vehicles. A joint solution algorithm is used that combines the Voronoi diagram and the particle swarm optimization algorithm. Testing of the developed algorithm is carried out in the IEEE-39 distribution scheme.
Solution to the optimization problem, taking into account energy storage systems and the individual characteristics of consumer load schedules, is presented in [14]. The particle swarm optimization algorithm is used, testing is performed in the IEEE-33 distribution scheme.
The articles [15, 16] consider the issue of increasing resilience by determining the optimal topology of the electrical network. In [17], in order to increase resilience, it is proposed to determine the optimal composition of power transmission lines that should be laid underground. In these studies, optimization is performed using a genetic algorithm [15], the "Column & Constraint Generation" algorithm based on decomposition [17], and the HiGHS software product [16].
In order to increase resilience in operation [18], a solution is proposed, in which OHPL supports are reinforced and distributed and mobile energy sources are placed. In [19], RES-based sources and battery-based energy storage systems are considered for this purpose. In these studies, the CPLEX software product is used to find the optimal solution. The approaches presented in the papers were tested in IEEE-33 distribution schemes [18, 19] and modified IEEE-118 [19].
In [20], measures such as strengthening OHPL supports and placing distributed energy sources and energy storage systems are considered to solve the optimization problem. The problem is solved using a genetic algorithm. The article [21] uses a particle swarm optimization algorithm and examines the reinforcement of OHPL supports. It is worth noting that [21] additionally takes into account the influence of the state of wind turbines, and in the study [22], when solving the optimization problem, the random nature of power generation by RES-based generating sources is taken into account. The solutions proposed in [20, 21] were tested in the IEEE-69 distribution scheme (a modified scheme is used in [21]).
In the work cycle [23, 24], attention was paid to strengthening and modernizing OHPL supports, pruning bushes and trees, and commissioning backup generating sources. These studies use, among other things, the greedy search algorithm [23] and the "Progressive Hedging" decomposition algorithm [24]. The operation of the proposed models is shown on the test schemes EPRI [23], IEEE-34 [24], and IEEE-123 [24].
It is important to note that the solution of the noted optimization problem is also performed using machine learning algorithms. Increasing the resilience of systems and distribution networks is considered in [25–27]. In [28], a decision support system is presented for managing the demand for electrical energy in distribution networks. In [29], it is predicted that wind power plants will generate power, which has a serious impact on the resilience of the system and the reliability of electricity supply to consumers.
The result of the optimization algorithm is the values of the variables, at which the best value of the objective function is achieved. Based on the analysis of the literature and [30], it can be concluded that researchers use as such variables: reduction or restoration of the load volume (i.e., forced disconnection of electrical energy from some consumers or restoration of their power supply); the capacity of distributed energy sources (including RES-based ones); location and capacity of mobile energy sources, energy storage systems, reactive power compensation systems; the location of electric vehicles and the capacity of their batteries; the condition of devices that change the topology of the electrical network (on or off); variables that characterize the condition of operational repair teams; and some others.
Statistics on accidents in the EPS of the Republic of Cuba and a number of countries (for example, [1–4] and others), as well as the interest of researchers in increasing the resilience of EPS, emphasize the urgency of the problem of optimal functioning of EPS in conditions of extreme weather events. The results obtained in this work are new and complement the above studies. These results include the following. Firstly, the paper considers the EPS scheme, rather than the scheme of the distribution network, that is, the study was carried out on a larger scale. Secondly, since the EPS scheme is being considered, the work uses a new set of variables for which the best value of the objective function is achieved. Thirdly, the implemented model makes it possible to determine the values of these variables practically for the current electric power mode.
The task of optimizing the current electric power mode can be formulated as follows. It is necessary to determine the values of regulated (independent or optimized) operating and circuit parameters, which will ensure the fullest possible supply of electric energy to consumers. The optimization problem is conditional because it contains constraints in the form of equalities and inequalities.
The noted task was solved by the team of authors, who developed a decision-making model for the optimal functioning of EPS under the influence of extreme weather events. This paper is devoted to the development of this model, which will allow taking into account the availability of distributed energy sources based on RES when making decisions.
Thus, the purpose of this study is to evaluate the effectiveness of integration into EPS of distributed generation based on RES to fully provide consumers with electric energy under the influence of extreme weather events. Such phenomena include high ambient temperature and phenomena that lead to OHPL shutdown (hurricanes, storms, and others). In accordance with the purpose of the study, the following tasks are formulated:
perform accounting in a distributed generation decision-making model based on RES;
in the EPS test scheme, determine the optimal RES-based generation capacity and location for various emergency scenarios;
in the EPS test scheme, consider the uniform distribution of RES-based generation for various emergency scenarios;
to evaluate the effectiveness of the solutions obtained for the full provision of electric energy to consumers.
2.Methods
The developed decision-making model is a procedure for optimizing the steady-state electric power mode, which makes it possible to determine the values of regulated operating and circuit parameters, at which the minimum value of the objective function is achieved.
The following parameters are accepted as regulated parameters: active capacities of centralized power supply stations, voltage modules on the busbars of generators of these stations, transformation coefficients of step-down transformers.
Optimization task is solved taking into account two types of constraints. Constraints in the form of equalities represent a system of nonlinear equations of the steady-state electric power mode, the solution of which is performed by the Newton method. These equations relate all the operating and circuit parameters of EPS to each other. Restrictions in the form of inequalities are imposed on the regulated variables, as well as on the currents flowing in the OHPL and on the voltages in the EPS nodes.
The dependence of the form is considered as an objective function:
where is the number of OHPL that take into account restrictions on the amount of current flowing; is the number of EPS nodes that take into account restrictions on the amount of voltage; is the number of EPS nodes that require a full supply of electrical energy to consumers; is the amount of OHPL current exceeding the maximum limit number is the amount of if the voltage in the node with the number exceeds the minimum or maximum limit; is the relative value of the current value of the consumed active power in the node with the number
Thus, the objective function takes into account both the current power consumption values and limitations in the form of inequalities. In the optimal mode, OHPL currents and EPS node voltages should be within the specified limits, so the first two components of the objective function will be zero. When consumers are fully supplied with electric energy, Therefore, in this case, the minimum value of the objective function, regardless of the EPS scheme and the set of optimized parameters, is a constant value and is –1.
Distributed generation based on RES is taken into account in the model when forming a system of nonlinear equations of the steady-state electric power mode. The paper considers two accounting methods. The first one is focused on determining the optimal location (among the consumption nodes) and generation capacity during the current emergency event. In this case, it is assumed that each consumption node has generation capacity (the maximum value of which is 50% of the load capacity), which is included in the list of adjustable parameters. The second method considers the uniform distribution of generation in the consumption nodes.
Let us make an important remark about the above. The lists of regulated parameters and constraints in the form of inequalities adopted in the work are not strictly defined and can be expanded. The lists selected in the work are designed and allow us to show the fundamental possibility of solving the optimization problem. Taking into account additional parameters and restrictions in the algorithm will not lead to significant difficulties.
Optimization of the mode in the developed decision-making model is performed using a genetic algorithm. This algorithm, as follows from the literature review, is used by researchers to solve such problems, since, due to its stochastic nature, it supports a variety of possible solutions and allows for various constraints. This article does not compare the effectiveness of solving the optimization problem using different methods, as this study addresses a different goal. Such a comparison could be performed as part of a continuation and development of this research.
Let us note one more fact. Earlier it was said that the objective function has a known minimum value –1. However, the set of values of the regulated parameters, at which this minimum is achieved, is not the only one. In other words, the minimum of the objective function is not a point, but a certain surface. Due to the stochastic nature of the genetic algorithm, solving the same problem generally leads to different sets of values of the regulated parameters. Thus, among the many solutions, you should choose the one that best suits the current properties and technical characteristics of the equipment. Another possible method, which does not require the marked choice, is to take into account additional components in the expression of the objective function, which will change the form of the function so that it will have obvious extremum points (for example, such a component may be the loss of active power in an electrical network). In this paper, these features are not considered – as noted earlier, the fundamental possibility of solving the optimization problem is shown.
3.Results and Discussion
Testing of the new version of the decision-making model was performed in a modified IEEE-39 scheme, in which the structure and values of the parameters were changed. The structural changes are as follows: three transformers that are not connected to generating sources have been replaced by OHPL; a step-down transformer has been added to each consumption node. The EPS diagram obtained in this way is shown in Fig. 1.
Figure 1. EPS schematic diagram.
This circuit contains 56 nodes, of which 17 are load-bearing (represented as a ZIP model), 9 are generating (represented as a PU model), and 29 are intermediate. The number of branches in the circuit is 64, of which 38 are OHPL, 17 are transformers connected to consumption nodes (LT), and 9 are transformers connected to generating sources (GT). The parameters of the same type of nodes and branches are the same and are presented in Table 1 ( are the nominal values of voltage, active power, and reactive power, respectively) and Table 2 ( are active and inductive resistance, active and reactive conductivity, respectively; is the transformation coefficient; is the limits of change in the transformation coefficient).
Table 1. Node parameters.
Node
Parameters
, kV
, MW
, Mvar
ZIP model
Loading
10
100
50
; ; ;
; ;
Generating
10.5
200
–
–
Intermediate
220
–
–
–
Table 2. Branch parameters.
Branch
Parameters
, Ω
, Ω
, µS
, µS
OHPL
7.5
42
–
270
–
–
LT
2
50.3
3.1
20.4
0.047826
±8x1.5 %
GT
0.7
26
4.6
21.3
0.043388
–
In the accepted formulation of the optimization problem, constraints in the form of inequalities are imposed on the currents flowing in the OHPL. The high ambient temperature leads to a decrease in the permissible OHPL current load, which is expressed in terms of a correction factor, the minimum value of which is 0.67, which corresponds to a temperature of +50 °C. Assuming these most severe conditions, we obtain that the maximum OHPL current limit is 536 A. The minimum and maximum limits for regulated parameters and voltages in EPS nodes are presented in Table 3.
Table 3. Limits of variable variation.
Variable
min
max
Active power, MW
50
200
Generator voltage, kV
10
11
Voltage in the intermediate nodes, kV
198
242
Voltage in the consumption nodes, kV
9
11
So, the effect of high ambient temperature is taken into account in the decision-making model by reducing the permissible OHPL current load. The effects of other extreme weather events that cause OHPL wires to break or supports to fall are taken into account in the model by disabling the corresponding OHPL. In this study, only two possible combinations are considered: disabling one OHPL (38 possible options) and disabling two OHPL (703 possible options). Disabling more OHPLS was not considered due to the increased computational and time costs incurred in sorting through all possible options (for example, when disabling three OHPL, there are 8436 possible options). Nevertheless, for the specific case of disabling several OHPL, the developed decision-making model allows us to determine the values of the regulated parameters corresponding to the most optimal mode of EPS operation. However, in the received mode, some of the electric energy consumers may be turned off.
Let's make an important point. In some of the considered variants, disabling OHPL leads to the separation of the EPS circuit into two independent subcircuits. In this case, the optimal mode is determined for the part of the circuit that contains node No 39, which is the basic balancing node.
Results for the case of disabling one OHPL are shown in Table 4. This table shows the number of shutdown options, in which consumers are fully supplied with electrical energy. In the case of optimal distribution of RES generation, the model solves the problem of determining the optimal location and power of generating sources in a given emergency situation. The uniform distribution of RES generation is taken into account by the presence of generation power consumption in the nodes, which ranges from 5 % to 20 % of the load capacity. The values shown in the columns with the distribution of RES generation take into account the number of options, in which the power supply to consumers is provided without RES.
Table 4. Calculation results when one OHPL is turned off.
Without RES
Optimal distribution of RES generation
Uniform distribution of RES generation
5 %
10 %
15 %
20 %
32 (84.2 %)
38 (100 %)
34 (89.5 %)
36 (94.7 %)
37 (97.4 %)
37 (97.4 %)
The data obtained show that the availability of RES-based generation contributes to a more complete supply of electric energy to consumers. With optimal distribution, full power supply to consumers is achieved in all emergency situations. However, such a solution is not universal, since the location and power of the generating source are determined for a specific emergency situation, with another emergency disturbance, the result will not be optimal. Therefore, in this formulation of the problem, the uniform distribution of RES generation is a more universal solution.
Similar results for the case of disabling two OHPL are presented in Table 5. These data also confirm the noted positive impact of RES generation on the power supply to consumers. However, in the case of disabling two OHPL, there is a decrease in the relative number of options, which indicates that there is no required minimum value of the objective function due to the concomitant aggravation of the EPS operating mode.
Table 5. Calculation results when two OHPL are disabled.
Without RES
Optimal distribution of RES generation
Uniform distribution of RES generation
5 %
10 %
15 %
20 %
450 (64 %)
691 (98.3 %)
517 (73.5 %)
585 (83.2 %)
625 (88.9 %)
641 (91.2 %)
With a uniform distribution of RES generation (10 %), three calculations were performed for the case of disconnection of one OHPL (3–4) and two OHPL (3–4 and 10–14). The average number of generations (iterations) required to obtain the minimum value of the objective function was 7 in the first case and 12 in the second. The convergence process for all cases is shown in Fig. 2 when one overhead line is disconnected and in Fig. 3 when two OHPL are disconnected. The results obtained demonstrate slower convergence to the solution in the case of disconnection of the two OHPL, which also indicates a more severe mode of EPS operation.
Figure 2. The process of convergence to the minimum
of the objective function when one OHPL is turned off.
Figure 3. The process of convergence to the minimum
of the objective function when two OHPL are disabled.
In the EPS scheme under consideration, the number of adjustable parameters is 35 (in the case of optimal RES generation distribution, the number of parameters is 52). Table 6 shows the values of some of these parameters for the above cases of disconnection of one OHPL (3–4) and two OHPL (3–4 and
10–14). The presented results confirm that the minimum of the objective function is generally achieved with different sets of values of the controlled parameters.
Table 6. Values of the regulated parameters.
Parameter
Disabling one OHPL (3–4)
Disabling two OHPL (3–4 и 10–14)
Calculation No 1
Calculation No 2
Calculation No 3
Calculation No 1
Calculation No 2
Calculation No 3
, MW
163.51
173.49
149.2
153.90
106.65
138.46
, MW
127.24
161.07
158.13
93.96
115.38
83.6
, MW
197.68
155.58
196.19
186.45
196.09
196.4
, kV
10.792
10.75
10.846
10.209
10.649
10.455
, kV
10.599
10.939
10.503
10.734
10.822
10.732
, kV
10.348
10.88
10.817
10.851
10.46
10.89
0.053437
0.043281
0.050879
0.051704
0.049305
0.048554
0.05008
0.047826
0.046433
0.044489
0.045767
0.045767
0.046433
0.044489
0.045119
0.045767
0.051704
0.043877
Results shown in Table 4 and Table 5 were obtained by iterating through all possible options for disabling one OHPL and two OHPL. Consider the case of disabling three (3–4, 10–14, 28–29), four (3–4, 10–14, 28–29, 14–15), and five (3–4, 10–14, 28–29, 14–15, 16–24) OHPL in a scheme with uniform distribution of generating sources based on RES (10 %). We will perform three calculations for each case. The average number of generations required to achieve the minimum value of the objective function was 21, 25, and 31, respectively. The process of convergence to the solution, which is defined in each case for the calculation with the largest number of generations, is shown in Fig. 4. The results show that each addition of a disabled OHPL leads to a heavier EPS mode.
Figure 4. The process of convergence to the solution.
Thus, the calculations performed confirm that in conditions of exposure to extreme weather events, distributed generation based on RES makes it possible in some cases to fully provide consumers with electric energy. The cases of disconnection of one and two OHPL were considered in the most detail. It follows from the results obtained that even a small distributed generation (5 % of the consumption capacity) can save the power supply to consumers in case of 2 additional accidents in the first case and 67 accidents in the second case. Solutions with optimal distribution of sources based on RES have the greatest efficiency in fully providing electric energy, but each such solution is designed for a specific emergency situation. For this reason, this result is generally not acceptable.
The results of this study are consistent with the results obtained by other authors (for example, [7, 9, 10]). These studies note that the optimal implementation of distributed energy sources, including those based on RES, significantly increases the resilience of the system and reduces the amount of electric energy that is not supplied to consumers.
4.Conclusions
The performed research allows us to conclude the following:
a decision-making model is proposed for the optimal functioning of EPS under the influence of extreme weather events, taking into account the availability of distributed energy sources based on RES;
the algorithms implemented in the model make it possible to account for various regulated variables, constraints and functions without significant difficulties, which determines the flexibility of the model and the possibility of obtaining scalable solutions (both for large EPS schemes and for electric distribution network schemes);
the application of the developed model to the modified IEEE-39 scheme made it possible to determine for a number of emergency situations the values of controlled variables, in which the full or maximum supply of electric energy to consumers is achieved;
uniform (or proportional to the volume of load power) distribution of RES generation in the consumption nodes is preferable to optimal, since it allows to preserve the power supply to consumers in a larger number of emergency situations;
an algorithm for solving the problem of optimal distribution of RES generation in consumption nodes in the event of a specific emergency can be used to develop an algorithm for solving a similar problem, but in the case of several emergencies.
10.34910/MCE.141.1
004.02
energy efficiency
optimal mode
machine learning
genetic algorithm
objective function
optimal allocation
extreme weather event
https://engstroy.spbstu.ru/article/2026.141.1/
RAR
RUS
14102-14102
Peter the Great Saint Petersburg Polytechnic University
Sabri
Mohanad Muaya
mohanad.m.sabri@gmail.com
Polytechnicheskay, 29
University of Technology
Fattah
Mohammed Y.
myf_1968@yahoo.com
Baghdad, Iraq
University of Technology
Abood
Ahmed
bce.20.32@grad.uotec
Baghdad, Iraq
University of Technology
Al-Adili
A.Sh.
Aqeeladili@hotmail.com
Baghdad, Iraq
Dynamic characteristics of machine foundation under harmonic loading on gypseous soil with various degrees of saturation
Most previous studies on collapsible soils have demonstrated considerable variability in reliability, primarily due to variations in testing procedures and sampling methods. Additionally, it has often employed static testing as its primary method of validation. However, as development continues, a gap remains in our understanding of how collapsible soil reacts to various dynamic stresses, including mechanical equipment, power stations, trains, roadways, and other dynamic loads. Conventional studies often fail to adequately represent real dynamic loading conditions. Accordingly, it is essential to investigate the response of gypseous soils to vibration and varying moisture content. This research aims to characterize the dynamic behavior of gypseous soil under different saturation states (unsaturated and saturated), subjected to harmonic loading at a relative density of 35%, with additional consideration of foundation depth and eccentric mass. The experimental program aims to establish a database that enables reliable correlations between wave attenuation and soil damping in gypseous soils. Results showed that the dynamic characteristics of gypseous soil increased by 50-52% with settlement, 3-6% with sorption stress, 47-68% with total stresses, 42-46% with acceleration, and 44-48% with vertical displacement as frequency increased. However, they decreased by 6-7% for settlement and total loads, 2-5% for acceleration, and 6-9% for vertical displacement when gypseous soil saturation rose to 60%. Saturation levels also influenced these increases, which ranged from 60% to 100% (149-150%) for settlement, 139-173% for total stresses, 50-51% for acceleration, and 52-54% for vertical displacement. Meanwhile, suction stress increased between 45% and 457% as the gypsum soil's saturation level reached 60%, then decreased between 100% and 104% as saturation increased above 60% but before reaching 100%.
10.34910/MCE.141.2
624.13
amplitude
dynamic behavior
dynamic characteristics
gypseous soil
harmonic loading
saturation degree
https://engstroy.spbstu.ru/article/2026.141.2/
RAR
RUS
14103-14103
0000-0002-3352-9010
University of Babylon
Al-Mashhadi
Samir
eng.samer.abdul@uobabylon.edu.iq
Hillah, Iraq
University of Babylon
Radhi
Mohammed Sattar
mat.mohammed.sattar@uobabylon.edu.iq
Hillah, Iraq
University of Babylon
Obead
Imad Habeeb
eng.imad.habeeb@uobabylon.edu.iq
Hillah, Iraq
0000-0002-5450-7312
National University of Malaysia
Al-Khafaji
Zainab
p123005@siswa.ukm.edu.my
Bangi, Malaysia
Babil Tower for Studies and Scientific Researches
Mohammed
Zainab Adel
Zoozadil97@gmail.com
Hillah, Iraq
Babil Tower for Studies and Scientific Researches
Jabr
Sarah Fadel
sara.fadeljaber97@gmail.com
Hillah, Iraq
Improvements of mechanical and physical features of cement mortar by nano Al2O3 and CaCO3 as additives
The current research aimed to investigate the impact of Al2O3 and CaCO3 nanoparticles on the properties of cement mortar. The research methodology primarily focused on preparing mortars using Al2O3 nanoparticles with a mean diameter of ~50 nm and CaCO3 nanoparticles with a particle size of 100 nm. These were utilized at three different substitution levels of 1, 3, and 5 % by weight of cement as binary blending materials. The mechanical and physical properties of the cement mortar (compressive strength, density) were tested after 7 and 28 days, while ultrasonic pulse velocity was tested after 28 days of water curing. The experimental results illustrated that utilizing Al2O3 nanoparticles improved the mortar’s compressive strength at an early age (7 days of curing) more than at 28 days, with 3 % substitution being the optimal proportion. Similarly, the use of CaCO3 nanoparticles as a binary blending mixture at substitution levels of 1, 3, and 5 % by cement weight improved the compressive strength at an early age (7 days of curing) more than at 28 days. The optimal proportion was again 3 %, with 87 and 40 % improvement for 7 and 28 days of curing, respectively. When comparing Al2O3 and CaCO3 nanoparticles, the latter yielded better results than Al2O3 nanoparticles for both early and later ages. The combined effect of substituting 1 and 3 % of Al2O3 and CaCO3 nanoparticles in cement mortar increased compressive strength by 28 and 74 % at 7 days of curing and by 30 and 42 % at 28 days of curing, respectively.
10.34910/MCE.141.3
69
cement mortar
Al2O3 nanoparticles
CaCO3 nanoparticles
compressive strength
density
ultrasonic pulse velocity
https://engstroy.spbstu.ru/article/2026.141.3/
RAR
RUS
14104-14104
57220745862
0000-0001-5985-8050
St. Petersburg State University of Architecture and Civil Engineering
Kovalchuk
Vlada
kovalchuk.vsk@gmail.com
St.Petersburg, Russia
LLC “GEOKEM”
Tsigelnyuk
Elena
etsygelnyuk@inbox.ru
St. Petersburg, Russian Federation
37099331400
0000-0003-0815-4621
St. Petersburg State University of Architecture and Civil Engineering
Korolev
Evgeniy
korolev@nocnt.ru
St. Petersburg, Russia
Cement paste stratification at critical cementing point
The relevance of this research is driven by the necessity to investigate and predict the technological parameters of grouting mixtures in conditions that closely resemble real-world scenarios. The subject of this study is a grouting compound used in well construction, which serves to ensure the adhesion between the casing and the formation, strengthen the borehole walls, and prevent the leakage of underground fluids. The objective is to develop a methodology for investigating the cement mixture formation based on both theoretical and empirical data, with the aim of most accurately representing the actual behavior of the grouting solution within the annulus of a wellbore. The authors have proposed a model for two types of cement mortar structures. A method for examining the sedimentation stability of cement mortars using a specially designed experimental setup and monitoring protocol is presented. The analysis of samples collected at the proposed site allows us to study changes in the density of cement slurry over time, while simulating the behavior of cement in the annulus during the first hour of pumping. The findings indicate a tendency towards thickening and hardening of the cement mixture, as well as highlight potential issues that may arise when the cement composition does not meet the requirements set by downhole conditions. The statistical analysis of measured data demonstrates good reproducibility with low error, allowing us to simulate deposition of cement under various conditions. The results and the proposed recommendations for improving cement stability will be of value to technical experts and researchers, enabling them to achieve the objectives of environmentally friendly, time-efficient, and economically viable well construction.
1.Introduction
During the construction of wells, cement-based formulations are primarily used, which must comply with the requirements outlined in relevant regulatory documents such as Russian State Standards GOST 1581-2019 and GOST 34532-2019, as well as API Specification 10A:2019 and API RP 10B-2-2024. These standards specify the type and range of properties for both cement paste and the resulting artificial stone. The main purpose of grouting mixtures is to fill the annular space between the casing and the borehole.
The problem of the lack of a homogeneous cement stone structure creates the need for a more detailed study of the issue of quality violations during well construction [1, 2]. The active stratification of the grouting composition by the depth of cementation negatively affects the quality of rock insulation and the tightness of the borehole, and also forms a highly porous cement stone, significantly reducing the operational lifespan of the well [3]. The appearance of water in the upper zones of the cementing sites is one of the observed consequences of uneven filling of annular space with cement paste during drilling. The aim of this study is to develop a technique for determining water separation in cement slurry, free from the shortcomings of the standard method, as well as identifying correlations with key factors influencing water separation in grouting mixtures.
It is known that the denser the packing of Portland cement particles, the higher the ability of cement paste to hold a certain volume of water. The cohesion of the structure is crucial when designing a cement mix with specified rheological properties. If the normal density of the cement paste is significantly exceeded, the particles do not come into direct contact with each other, as they are sufficiently removed and separated by layers of water. This type of system is sedimentationally unstable, leading to water separation. This process can also be described as the stratification of the cement dispersion system. Stratification occurs throughout the entire height, forming a material density gradient. Naturally, the density in the upper layers will be lower than in the deeper layers. This density gradient, after hardening, will naturally lead to differences in porosity and strength in the cement stone.
Water separation is a structural heterogeneity of the cement paste, and, as a result, a negative factor leading to the formation of a cement stone with gradients in its density and properties, particularly during the construction of deep boreholes, where there is a difference in the height of the cementing intervals. To eliminate this inhomogeneity, various methods have been proposed, including the introduction of filler additives such as chalk, quartz, clay, fly ash, asbestos, and others, which reduce water segregation (plasticizing and hydrophilic surfactants), as well as the use of aqueous solutions containing chloride and sodium carbonate [4–6].
The water-cement (W/C) ratio of a cement paste of normal density is dependent not only on the mineral composition of the clinker and the content and properties of mineral additives but also on the conditions, under which the structure forms. For normal Portland cement, this parameter is approximately 0.25 under hardening conditions. It is known that when filling borehole spaces with a grouting mixture, the initial W/C ratio specified may differ significantly from the actual concentration of the cement gel, depending on the depth of the mass distribution. By analogy with Boltzmann’s barometric formula [7], we can consider a problem regarding the effect of forces on a cement particle evenly surrounded by water in a state of equilibrium. In this case, the downward gravitational force will be balanced by the resistance forces of the medium and Archimedes. This model accurately describes the issue of uneven filling of the annulus of the well with cement slurry, followed by strata formation and possible absorption or migration of the cement mix into nearby heterogeneous formations. As a consequence, the resulting anisotropic cement rock will not meet the standards for high-quality isolation of the borehole from corrosive subsurface fluids (liquids and gases), which could lead to industrial incidents.
The analysis of standard requirements reveals that to assess the stability of grouting mixes (cement slurry or mortar) against sedimentation, the characteristic “water separation” is used, defined as the volume of water that separates. In this instance, a measuring cylinder with a capacity of 250 cm3 is employed, which significantly differs from the depth of the well being cemented. This disadvantage could be overcome by simulating the sedimentation process of cement-water systems. Nevertheless, addressing this issue involves overcoming challenges related to the interaction of settling particles and the formation of agglomerates, whose structure and properties vary significantly over time. Consequently, experimental statistical models have gained popularity, the production of which entails conducting experimental studies using equipment that avoids the shortcomings of known methods [8–10].
The rheological properties of cement slurry are influenced by various factors, including the concentration, average size, and volume distribution of cement particles. These factors also include the shape, structure, surface properties, and physical properties of the liquid and solid components [11, 12].
Additionally, water segregation in cement slurries is influenced by physical and chemical processes such as the sedimentation, aggregation, and hydration of cement particles. This process leads to the formation of a dispersed phase, which can be observed in the chemical equation for the hydration of tricalcium silicate , a major component of cement [13]:
(1)
It follows from this equation that the ratio of the volumes of the solid phases of the hydration products and the starting material is Some of these processes are considered in the standards for determining the water separation rate of a cement mix using a measuring cylinder [14]. A cement paste is placed in a cylinder and allowed to set for a specific period of time. After this, the stratification of the mixture is visually examined, and the extent of stratification is calculated based on the volume of water displaced in the upper portion of the cylinder [15–17]. However, this method of water separation measurement does not consider many geological, technical, and other significant factors, including the influence of external environmental conditions (geological characteristics of rocks in contact with cement), physical and mechanical parameters (pressure, temperature), and technological aspects of well construction (geometrical parameters of the well, construction method, type of flushing fluid, etc.).
The study [18] showed the technological limitations of the current standards for water separation analysis using a measuring glass cylinder in revealing the true picture of cement particle sedimentation in the annulus. The work also identified and described cracks and voids (migration pathways) that may be filled during cement injection.
W/C ratios are among the key cement parameters that affect the mixture characteristics and mechanical properties of grouting materials. Micro-cement compositions with W/C ratios ranging from 0.8:1 to 2:1 were examined in [19]. It was found that density, workability, rate of cement-stone formation, and bending and compressive strengths of cement stones gradually decreased with increasing W/C ratio. Conversely, the spreadability and fluidity of micro-cement mixes gradually increased.
A method for investigating the water separation properties of cement mixtures using low-field nuclear magnetic resonance (NMR) has been proposed in the study [20]. The findings indicate that the NMR technique in a weak magnetic field can be successfully employed not only to measure the extent of water separation, investigate the microstructure of cement materials but also to provide information on the concentrations of substances present in the separated water. Furthermore, it has been determined that the migration of a substantial amount of water from the porous structure of a maturing cement slurry gives rise to significant alterations and deterioration in the microstructure of the resulting cement stone.
To address the issue of static segregation, it is common practice to select formulations with the lowest possible W/C or water-binder ratio, as well as to utilize microsilica to reduce water segregation while maintaining the structural properties of the cement matrix in studies of high-performance mobile concrete mixes [21]. At the same time, it has been established that superplasticizers, which increase the flowability (workability) of the cement paste, adversely affect the mechanical characteristics of mortar mixtures and reduce the durability of molded cement products [22]. In order to explore the correlation between cement properties and the propensity of cement mixtures to water segregation, the authors of [23] discovered that with a lower specific surface area and higher alkali content, there is a greater tendency towards intensive water segregation.
The authors of [24] investigated the deposition of cement mixtures by visual observation, which revealed two stages of delamination: an initial phase of rapid water separation followed by a stage with a decreasing sedimentation rate, where the upper layer gradually became transparent.
In predicting the sedimentation of cement mixtures, the laws of suspension dynamics may be applied. Specifically, article [25] addresses the issue of particle sedimentation in a stationary fluid. The authors conclude that the concentration of solids in the flow and the density increase linearly with depth, while the pressure increase follows a weakly quadratic trend.
One of the most significant criteria for assessing the quality of concrete is the density of the concrete mixture. The researchers in [26] developed a method for determining the density of settling concrete suspensions by sampling from specific heights at different times. This study demonstrated that the characteristics of the concrete mixtures, including their uniformity and flowability, vary significantly depending on the height and time of sampling. Further research into the relationship between concrete mixture properties and their tendency to separate revealed that mixtures with a smaller specific surface area have a higher tendency for water displacement. It has also been shown that due to obvious separation, the water-to-cement ratio and phase content in the settled suspension layer do not match the initial concrete composition parameters.
The main limitation of previous studies is the significant gap between laboratory testing of grouting materials during the initial phase of cement-stone structure formation and the measurement of the state of the cement annulus after hardening in the borehole.
The classical approach to the sedimentation process involves determining the sedimentation rate of a particulate, which is influenced by the forces of Stokes and Archimedes, as well as the gravitational force of the Earth. However, the actual rate of deposition of grouting mixtures may differ from the calculated value, due to both assumptions made in determining the geometric properties of the particles, and the influence of adjacent particles [27]. The Lyashenko method has been used to study the constrained deposition rate of particles with different geometric shapes. However, this method has the disadvantage of relying solely on experimental measurements, which are used as the primary method for determining the properties of sedimentation. As mentioned above, and in other studies [28–30], completely experimental dependencies are used to calculate the parameters of suspended deposition.
The quality of grouting material cannot be determined solely based on average laboratory test results. In practice, there are always variations from the obtained results. Changes in mixing and injecting the mixture, composition of clinker, activity and normal density of cement, dosage of improving additives, and other technological and geological factors affecting the formation and hardening of the structure have an impact on the quality of well construction. To improve the quality of cementing operations, it is necessary to modernize existing laboratory methods for simulating borehole conditions.
In accordance with the objectives set by the authors, this paper presents the findings of a study on the sedimentation of cement particles and stratification of cement slurry prior to cement setting when it is injected into a borehole. A method has been devised to analyze the heterogeneity of cement matrix formation based on a density analysis of grouting mixture at various depths after a specific period of time. To implement the method for measuring cement slurry density, an experimental setup is proposed, and the process of sample preparation and experimentation is described in detail. The results obtained indicate consistent trends in the behavior of the cement mixture in simulated conditions of cement structure formation in a wellbore.
2.Materials and Methods
For the experiments, casing Portland cement I-50 brand similar to Portland cement I-G-CC-1 brand was used, which meets the requirements of GOST 1581-2019. The properties of the cement mixtures were investigated using methods specified in GOST 33213-2014, GOST 34532-2019, and GOST 30744-2001. Storage, preparation, labelling and sample preparation were conducted in accordance with GOST 30515-2013. The standard specifications and actual characteristics of the cement are presented in Table 1 below.
Table 1. Characteristics of the cement mixture with a W/C ratio of 0.5.
Physical and mechanical characteristics
GOST requirements
Actual performance
Bending strength, MPa at the age of 2 days, not less than MPa
2.7
3.1
Spreading capacity of cement paste, not less than mm
200
220
Bleeding capacity, no more than ml
8.7
2.5
Thickening time to consistency of 30 Bc, not less than min
90
320
To meet the requirements for pumpability and workability of standard grouting cement, it is common to use W/C = 0.44…0.5. However, for lightweight and heavyweight cements, this ratio can vary between 0.3 and 1.3. In this study, we will consider compositions with W/C = 0.5…1.0.
When discussing the structural and rheological properties of cement paste, the concept of water retention capacity is introduced [31–33]. This is the amount of water that is retained within the cement paste after it has been formed. The W/C ratio of a cement paste of normal density indicates at what water content the paste will form, without any separation of its components (phases). As the W/C increases, a more heterogeneous structure begins to form, with increased structural heterogeneity. To assess this heterogeneity, we utilize a modified version of the phase separation coefficient proposed by A.N. Bobryshev et al. [34, 35]. For cement pastes, this coefficient takes the following form:
(2)
where ‒ volume fraction of water for sedimentation-resistant cement paste; ‒ volume fraction of water of the studied composition.
For formula (2) must be converted to the form:
(3)
It is evident that structural heterogeneity is the origin of water separation (phase segregation), and at structural heterogeneity reaches its maximum (Fig. 1).
Figure 1. The dependence of the coefficient of uniformity on the W/C ratio.
As the proportion of water in a cement mixture increases, the distance between the cement particles also increases:
(4)
where and – unit surface and cement density.
Furthermore, the rate of increase in the thickness of the water layer increases proportionately Obviously, the natural process aims to minimize the potential energy of all particles in a dispersed system affected by the Earth’s gravitational field. The model, which allows assessing the influence of the main factors at the initial stage, is based on the classical effect of forces on a particle as well as the limitations of: 1) the absence of the influence of other particles, and 2) the absence of compaction of the particle sediment. A particle with a diameter in the initial state is surrounded by a layer of water of thickness and after sedimentation (steady state) – by a layer with thickness Let the height of the column where the suspension is located be and the area of the base In its initial state, this column will be divided into thin layers To reach a stable state for the particle in the first layer, that is the layer located immediately adjacent to the lower boundary, or bottom, requires that an equal distance be traversed. The particle in the second layer must traverse the distance to the interface with the first layer as well as the distance the first particle has already traversed – Thus, the total distance that particles in the second layer need to travel before reaching a stable position is equal to Similar reasoning applies to particles in any other layer, and their distance will be equal to (where is the layer index). These distances are related to sedimentation rates [36–38]:
(5)
where and – viscosity and density of the medium, in which occurs the sedimentation of particles with density – gravitational acceleration.
In this scenario, all particles, regardless of their position, will move an equal distance over time The motion of particles in the upper regions under the influence of gravity corresponds to the creation of a layer of liquid on the surface of the system. When determining the requirements for the thickness of the liquid layer, it is feasible to assess the geometric properties of the container used in a study on the distribution of fractions of the material in various states (Fig. 2).
a
b
Figure 2. The effect of column height on the distribution of types of mixture states at the relative height: a) ; b) .
The data presented in Fig. 2 illustrate that at low column heights, stratification of the mixture occurs more rapidly, specifically the formation of a stable layer of particle mixture and a layer of liquid. The time required to reach stratification is found to be proportional to the height ratio between the two containers under comparison (at ). Another implication of the model is the possibility of describing the structure of the mixture as a system composed of different compositional types. Based on the presented model, it is sufficient for there to be two such structural types.
Obviously, the model under consideration is a rather crude approximation. In actual mixtures, there would not be distinct boundaries between structures. Nevertheless, it allows us to fully assess both the origin of structural heterogeneity and the impact of various factors, including the depth of well cementing.
Using the presented model, we will determine mixture density as a feature characterizing cement paste’s structural characteristic at various depths. Let us imagine that the cement mixture consists of a three-phase system “cement – water – air”:
(6)
where – cement volume fraction; – water volume fraction; – air volume fraction.
Considering a hypothetical scenario where a cement particle is spherical in shape. At the initial point in time, the contribution from its hydration process can be disregarded, and the physical and chemical interaction results in the formation of a water adsorption layer on the surface of the cement particles. This adsorption layer differs significantly from the properties of freely flowing water (Fig. 3a). Regarding the model discussed previously, as well as the various phases that constitute the cement slurry, we can identify two main types of structures: 1. “cement – adsorbed water – free water;” 2. “cement – adsorbed water – free water – air” (Fig. 3b).
a
b
Figure 3. Cement structuring by two types of particle arrangement:
a) model of a cement particle surrounded by water; b) types of cement paste structures,
where – diameter of the cement particle; – thickness of the adsorbed water layer;
– thickness of the free water layer.
The geometric characteristics of each structural type are determined by a set of parameters, which are shown in Table 2.
Table 2. Parameters for the types of structures.
Type
Number of phases
Phases
Phase Parameters
Cement
Waterad
Waterw
Air
I
3
Cement, adsorbed water, free water
II
4
Cement, adsorbed water, free water, air
The values of the parameters presented are derived from literature sources [39–41]. Under the given conditions and we derive the following system of equations to calculate density according to type
(7)
For type II is valid therefore, we obtain a system of equations:
(8)
The density of the cement paste, taking into account and will be equal to:
(9)
where and – volume fractions of the corresponding types of structures:
The determination of and is only possible through solving the inverse problem. This involves using calculated and experimentally determined values Furthermore, the cement slurry for determination can be chosen at any depth within the pipe column.
In order to experimentally determine the variation in the density of the cement paste, a specialized experimental setup has been designed. The schematic diagram of this setup is shown in Fig. 4.
a
b
Figure 4. General view of the experimental installation for measuring the density
of the cement mixture: a – side view; b – spatial view, where 1 – pipeline; 2 – funnel;
3 – removable plug; 4, 5 and 6 – tees; 7, 8 and 9 – taps.
The device is a vertically positioned housing consisting of a pipeline (1) with a diameter of and a length of having a circular cross-section with a diameter that does not change in the axial direction of the pipeline. The body can be a metal or plastic pipe, industrial ceramics, plexiglass, or other material that simulates downhole conditions. A funnel (2) is fixed in the upper part of the housing for feeding the analyzed grouting mixture, and a removable plug (3) closes the bottom of the pipeline. At distances and from the pipe mouth, there are tees (4), (5), and (6), with taps (7), (8), and (9) connected to them. Depending on the simulated conditions, it is recommended to use at least three measuring taps. In addition, the height of the pipe column depends on the specific set conditions.
The proposed method for measuring the density of a grouting mixture is as follows. The upper edge of the stand is taken as the zero reference point, and subsequent measurements are counted down along the depth of filling the pipe column with cement paste. Cement mixture is prepared according to GOST 34532-2019. The prepared mixture is poured into a funnel to enter the pipeline, until it is completely filled with the test cement paste to the plug, after which it is tightly closed for sealing. The cement paste settles in the installation during the studied measurement time … – from 15 to 60 minutes. By alternately opening the ball valves connected through tees to the pipeline, samples are taken for further measurement of the density of the cement mixture by the weighing method. Using mathematical methods of experiment planning, two variable independent factors were selected: W/C ratio and sampling depth, on the basis of which a series of experiments were conducted. The experimental density is taken to be the arithmetic mean of the results of three measurements, the discrepancy between which should not exceed 200 kg/m3. Proper filling and opening of taps in a certain sequence helps to avoid the occurrence of air bags and water in the laboratory installation in order to obtain correct data. After the measurements, the pipe space is cleaned of the remaining cement paste by rinsing with water.
3.Results
After preparing cement slurry with various water-to-cement ratios, the initial specific gravity was measured under standard conditions. The results of the measurements of the specific gravities of grout mixtures at W/C = 0.5…1.0, and their associated errors, are presented in Table 3.
Table 3. Initial density of cement mixtures.
W/C ratio
0.5
0.6
0.7
0.8
0.9
1.0
Average initial density, kg/m3
1790
1710
1610
1550
1500
1420
Measurement error, %
8
8
7
6
6
5
After preparing the cement slurry and filling the mold, samples were collected in a volume of 100 mL from each height level, and their density was measured using an electronic balance and the weighting method. Based on the results from three measurements, an average value for density at each height and time point (from the start of setting) was calculated. The findings of the study are presented in Table 4.
If the setting time is less than 15 minutes, the cement paste with a high water-to-cement ratio does not form a densified structure, which can lead to inaccurate density readings. Therefore, any measurements taken with a hydration time of less than 15 minutes have been excluded from the table.
When conducting laboratory tests on the cement mixture with W/C = 0.5, measurements were taken at the installation 15 and 20 minutes after the beginning of the active growth of the setting and the lack of laminar leakage from the tap. With an increase in the W/C to 0.6, the mobility of the cement system increased, allowing for sampling after 30 and 40 minutes from the start of mixing.
Table 4. Experimental density of cement slurries, kg/m3.
W/C
Thickening time, min
Sampling depth, m
H1 = 0.5
H2 = 1.5
H3 = 2.5
0.5
T1 = 15
1730
1820
1900
T2 = 20
1700
1800
1870
0.6
T1 = 15
1610
1750
1800
T2 = 20
1600
1740
1780
T3 = 30
1600
1730
1770
T4 = 40
1590
1720
1770
0.7
T1 = 15
1550
1660
1740
T2 = 20
1550
1660
1730
T3 = 30
1540
1650
1720
T4 = 40
1530
1640
1720
T5 = 60
1520
1640
1710
0.8
T1 = 15
1500
1600
1690
T2 = 20
1490
1590
1650
T3 = 30
1480
1610
1680
T4 = 40
1470
1590
1650
T5 = 60
1460
1580
1640
0.9
T1 = 15
1460
1570
1620
T2 = 20
1460
1570
1610
T3 = 30
1450
1560
1610
T4 = 40
1450
1550
1600
T5 = 60
1440
1550
1590
1.0
T1 = 15
1360
1460
1540
T2 = 20
1350
1450
1530
T3 = 30
1340
1450
1520
T4 = 40
1330
1440
1520
T5 = 60
1320
1430
1500
Experimental data have shown that when using cement slurry with a water-to-cement ratio up to 0.6, it is important to carefully monitor the initial consistency, density, and setting time of the mixture in order to prevent premature thickening in the pipeline, which would prevent the extraction of samples of the material in liquid form. Later, the density results obtained for W/C ratios of 0.5 and 0.6 were not considered due to insufficient time measurements for further analysis.
It has been decided to divide the process of cement sedimentation and structure formation into three stages. In the first stage, the binder is sealed and pumped into the column, during which the most active phase of stratification occurs. The second stage, lasting from 15 minutes to 60 minutes, or the beginning of the setting of the cement mixture, reflects the main phase of structure formation. During the third stage, the cement slurry thickens until it has completely cured. The first stage is the most difficult to accurately measure due to high error and the short time period. Therefore, the most suitable stage for study is the structure formation of cement prior to its setting. Fig. 5 illustrates the kinetic curves of density versus time for W/C = 0.8.
Figure 5. Kinetic curves of density as a function of time, W/C = 0.8.
It has been observed that over time, there is a decrease in density at a certain height in the column, with a maximum reduction of 2.9 %. This can be attributed to the formation of hydration products from the cement paste, as water molecules surround the cement particles and fill the empty space. Due to the small error in density measurements at each time point between and we did not consider the effect of time on sedimentation stability for the grouting mixture for up to 60 minutes after mixing. Instead, we averaged the density values of the mixture at each height for further calculations.
The results obtained allowed us to identify several trends. As the W/C ratio increases, there is a general decrease in density due to an increase in the liquid phase of the suspension. Additionally, the lower the sample, the higher the density of the cement paste, indicating a deposition of the solid phase at greater depths and, consequently, a lower sedimentation stability of the mixture within the volume of the pipe.
The W/C ratio also significantly influences sedimentation. As one dives deeper into the cement mixture, the density increases. This pattern is typical for suspensions, as within 40 minutes of starting the mixing process, the heaviest fractions of cement are deposited at the base of a narrow cylinder.
To determine the relationship between the density of the cement mixture, the W/C ratio and depth, considering the effect of sedimentation, the actual W/C ratio was calculated at each measuring level, which was determined as a result of the sedimentation process:
(10)
where – mass of water, kg; – mass of cement, kg; – density of water and true density of cement, respectively, kg/m3; – density of cement paste, kg/m3 [38, 42].
For a mathematical analysis of the obtained density values and an understanding of the possibility of forecasting, based on experimental data, a graph was constructed-the surface of the dependence of W/C at the level and the density of cement paste on the depth of measurements at the initial W/C = 0.7…1.0 (Fig. 6).
a
b
Figure 6. The dependence of the physical parameters of the cement pastes on the sampling depth: a – dependence of density; b – dependence of the W/C ratio at the level of Hn.
Fig. 7 shows the dependencies of density and W/C at at the initial W/C = 0.8, representing projections of the surface graph onto corresponding planes of the Cartesian coordinate system.
Figure 7. Dependence of density and W/C steady at the H level.
Taking into account the surface density data obtained at H = 0 m, it should be noted that as a result of sedimentation of the cement composition, the density at the bottom of the column is 14–19 % higher than that at the surface. Thus, it is possible to present a general view of the equation obtained for the dependence of cement paste density on the total depth of the column:
(11)
where – density of cement paste at the level – actual W/C ratio calculated at the level
In order to study the stability of high-density suspensions and to test cement mixtures with W/C ratios of 0.5 and 0.6, plasticizing and/or retardant additives are recommended to be used when forming a mixture in order to solve the technical problem of well cementing under specified conditions. The results of laboratory measurements with W/C = 0.7…1.0 provide a significant level of reliability in simulating the rheology of the cement paste and offer a more accurate representation of the mixture’s behavior at various readings of hydrostatic pressure and gravitational loads.
4.Discussion
Solving the inverse problem, values of a combination of indicators for two types of structures were determined from the sampling depth with initial W/C = 0.7…1.0 (Fig. 8).
a
b
c
d
Figure 8. Dynamics of cement precipitation by two types of structures:
a – W/C = 0.7; b – W/C = 0.8; c – W/C = 0.9; d – W/C = 1.0.
Based on the calculations, it has been established that as the measurement depth increases, a phenomenon of inversion occurs, where one structural phase is replaced by a second. With increasing measurement depth, the proportion of a homogeneous structure of type I increases, while the proportion of air phase of structure type II decreases. This can be attributed to the effect of air displacement during constrained deposition of the cement slurry. It has also been determined that an increase in the water content of the cement paste leads to a structural inversion as the depth increases.
The dependencies follow the general form:
 
10.34910/MCE.141.4
691.535
casing cementing
structure formation
sedimentation
cement density
cement bleeding
cement segregation
solids settling
fluid loss
https://engstroy.spbstu.ru/article/2026.141.4/
RAR
RUS
14105-14105
Surveying Engineering, Technical Engineering College
Sabir
Sanarya
sanaohasan4@gmail.com
Baghdad, Iraq
Surveying Engineering, Technical Engineering College
Al-Baghdadi
Jasim
jasim76@gmail.com
Baghdad, Iraq
Surveying Engineering, Technical Engineering College
Hamdoon
Rana
ranamounjeo@mtu.edu.iq
Baghdad, Iraq
Videogrammetric method for measuring of concrete beam deformations under dynamic vertical loading
Many studies have examined their use in civil and close-range applications, including building structural monitoring due to advances in videogrammetric systems. However, the videogrammetric system's ability to reliably identify concrete beam dynamic deformations under vertical loads has not been fully studied. This study aims to examine the efficacy of the videogrammetric system in detecting the dynamic deformation of various concrete beams through the utilization of the videogrammetry technique. The researchers utilized PhotoModeler software to generate a three-dimensional stereo model of concrete beams. This was done both before and after applying a vertical load. The primary objective of this research is to determine the deflection values exhibited by these beams. The videogrammetric system employs a pair of stationary video cameras to record the dynamic deformations of loaded beams. This study involves the selection and calibration of two identical model video cameras, specifically the Canon IXUS. In the practical trials, three distinct types of concrete beam sections of identical length are employed. The beams possess cross-sectional dimensions of 10×13×300 cm and have been chosen with varying compositions. In the laboratory setting, the apparatus is utilized to apply a consistent load to each of the three beams. The video results are subsequently examined based on the civil design calculations. The study provides evidence that the utilization of videogrammetric system approaches enables accurate and efficient measurement of deformation in various types of concrete beams, achieving precision at the millimeter level. Based on the aforementioned findings, it is evident that this particular technique holds the potential for effective implementation and utilization in the context of conducting destructive inspections on critical civil structural components
1.Introduction
Extensive investigations have been conducted in recent years about the deformation of structural elements in civil engineering. Nevertheless, the measurement of structural deformation in the bulk of these studies was conducted using conventional equipment, such as a dial gauge. Several of these equipment items are characterized by high costs, whereas the remaining one lacks precision and is not specifically engineered for measuring or displaying dynamic deformation [1]. An excellent method for assessing the performance of a structure is to measure its displacement when subjected to operational loads. Nevertheless, measuring structural deformation with high precision is still challenging, especially in complicated structures [2]. The fatigue life of the structure can be reduced by fluctuating cyclic loading. Cracks are frequently observed as a result of fatigue failure in reinforced concrete structures [3]. Various imaging techniques, including laser scanners and digital photogrammetry, have demonstrated their effectiveness and accuracy in capturing deformations in both large and small areas subjected to static loading circumstances. Close-range photogrammetry (CRP) is widely recognised as a cost-effective, secure, and precise measuring method across various industries [4]. Videogrammetry is the technique used to acquire three-dimensional data of objects. It utilizes cameras to capture and analyse spatial data [5]. Videogrammetry, which involves determining the coordinates of object points using several video streams captured by camcorders, is an auspicious area of research that holds the capacity to surmount the constraints of current methodologies. A videogrammetric approach is automated and may produce high-quality results without the need for human intervention [6]. Recently, some studies have utilized a video camera and employed videogrammetry, a specialized branch of photogrammetry, to quantify the displacement of the oscillating bridge structure. Lidar has numerous advantages and a diverse range of applications in comparison to photogrammetry, particularly in accurately capturing the movements of objects in motion. The presence of objects makes it a desirable option as a 3D measurement tool [7, 8]. Multiple studies have suggested the potential of utilizing cameras and photogrammetric techniques to accurately quantify the movement of objects that can change shape in three dimensions [9–11]. For instance, the utilization of a high-resolution camcorder in digital photogrammetry on a shipyard enables the measurement of object points. This is done by using retro-reflective targets to provide accurate dimension checking and control [10]. To achieve precise calibration, a robust network geometry was established by capturing 8 images from 5 camera stations, some of which involved panning or rotating the camera axis [12]. Demonstrated that CRP may be employed in both static and dynamic modes. Furthermore, it emphasized the advantages of rapid measurements, comprehensive coverage, and non-contact, which were not possible with alternative methods. The researchers employed two Pulnix (TM-1020-15) digital cameras. Video cameras are used throughout the practical examinations. The cameras were fitted with a built-in ring lamp to provide uniform illumination for retroreflective targets. Moreover, numerous prior research has employed videogrammetric methods in industrial settings. A videogrammetric system with a large field of view, consisting of four cameras, was utilized to perform feature detection and matching, reconstruction of 3D coordinates and displacements, as well as computation of motion parameters. The experiments provided evidence that the suggested method achieved a high level of accuracy, with measurements of dynamic length accurate to within a margin of 0.5 mm [11].
The experiments tests showed that the four-camera video measurement system can accurately predict the position within a range of vision measuring 5000×5000 mm. Consequently, numerous researchers have successfully employed digital photogrammetric approaches to monitor deformations in structures and civil construction [13, 14]. In general, the digital photogrammetric method involves employing digital stereo images captured by a digital camera to monitor deflections in structures and civil elements. Digital photogrammetry offers numerous advantages compared to traditional tools when it comes to measuring deflection. Photogrammetry is a non-contact method that eliminates the need for manually reading dials and generates three-dimensional data. It takes measurements and generates visual recordings of the tests. It is particularly well-suited for conducting destructive testing since only a few inexpensive targets are lost or damaged, in contrast to the expensive Linear Variable Differential Transformers (LVDTs) or dial gauges [13]. For instance [15], photogrammetric techniques were used to evaluate various civil engineering materials. Two cameras with mirrors were used to analyse structures from a rear perspective. Additionally, photogrammetry was employed for on-site monitoring during load tests. Two distinct cameras were employed to capture images, and the results were compared toLVDTs displacement measures [16]. This study investigates the outcomes of utilizing photogrammetry to assess the distortions of bar and plate components in the steel structures of hoisting machines. It analyses the primary difficulties that arise during the processing of these components and suggests remedies to attain the necessary accuracy. The study suggested by [17] presents a novel videogrammetry technique to accurately measure the displacement of a vibration pre-stressed concrete bridge. The technique is applied in both daylight and day-night circumstances utilizing reflective targets. The investigation was carried out in two stages using four High-Definition (HD) video cameras. Additionally, [1] developed a unique transducer to measure the deformation of a high-speed shaking table. This was achieved by utilizing videogrammetric measurements with a high-speed CMOS camera. This study aimed to assess the precision of the shaking table's three-dimensional coordinates using the high-speed videogrammetric measurement method outlined. Based on the literature study, it is evident that digital photogrammetric and videogrammetric approaches are suitable for measuring and observing the changes in shape or structure in civil constructions. Previous studies have not examined the capability of utilizing the videogrammetric systems to identify deflections and the deformations in various types of steel beams subjected to the same load. Therefore, this study seeks to investigate the videogrammetric system's ability to detect deflections and deformations in different sections of steel beams under a dynamic uniform vertical load.
1.1.Mathematical Algorithm
The mathematical algorithm employed in videogrammetry encompasses the utilization of photogrammetric procedures, such as bundle correction, which relies on collinearity Equations (1) and (2). Bundle adjustment is a prevalent optimization technique that finds extensive application in the field of image processing.
Scene reconstruction is a fundamental aspect of computer vision and computer graphics [18]. The methodology involves the utilization of recorded picture coordinates as well as the consideration of external and internal factors. The intrinsic camera parameters, along with the object space coordinates of the seen points, are essential components in computer vision and image processing. The latter entities exert control over the resultant nonlinear system. The equations of collinearity serve as the fundamental basis for the proposed mathematical model and integrate the observed picture coordinates with the outside and internal camera parameters. The characteristics, as well as the object space coordinates, of the observed points were determined:
(1)
(2)
where are image coordinates of an object and a principal point respectively; rotation matrix according to angles : focal length of a camera; are ground coordinates of the object and principal point respectively.
1.2.Structural Concrete Beam Design
Three identical concrete beams were prepared and monitored for testing under emotional load. The length of the beams is 3200 mm and has a rectangular cross-section of 130×100 mm (Fig. 1a). Each type of concrete consists of a different ratio of mixtures, as the first specimen contains a mixture (1:2:4), which means one part of resistant cement two parts of fine sand and four parts of coarse gravel. The second specimen is the mixing ratio (1:3:6) one part of resistant cement, half a part of fine sand, and three parts of crushed gravel (crushed kashi). The third specimen is the mixing ratio (1:1:2), which is one part of resistant cement, one part of fine sand, and two parts of coarse gravel. The concrete used in the beams contains compressive design strength at 28 days and has a fair face. Note that the reason behind testing three concrete beams made from three different ratios of mixture is to make sure that the developed videogrammetric system can capture dynamic deformations of various types of concrete beams. Each girder is reinforced with two lower bars with a diameter of 12 mm and two top bars with a diameter of 12 (Fig. 1). Models have been tested on a testing machine.
c)
b)
a)
Figure 1. The tested concrete beam: a) longitudinal view; b) perspective view; c) cross-section.
2.Methods
Two non-metric Canon IXUS 185 cameras were used in the study. Additionally, engineering testing equipment manufacture was studied. The equipment is a 10-ton hydraulic jack. Three different concrete formulations have been used to make 10×13×300 cm concrete beams. Custom-made Light Emitting Diode (LED) gadget for video-frame synchronisation was used. The Topcon Total Station (GM 50 series) is used in surveying and construction. Our research relies on this equipment's exact three-dimensional ground coordinate and distance readings. The target was encoded in 10 pixels. Project management software creates targets. Print and attach captured objects. During processing, the project management software may recognise and detect targets in object photos. These targets' proportions depend on the camera's distance from captured items. This study attaches targets to industrial videogrammetric systems. These targets are likewise mounted on the systems' front of concrete beams' surfaces. Internet-accessible Virtual Dub software is free. This tool software breaks a movie into image sequences for many uses. Extract photos from the video. Software like PhotoModeler Scanner (PMS) creates precise 3D models from photos. This programme was integrated by Canadian business Eos Systems Inc. PMS has many uses. Many photogrammetric and videogrammetric applications include quantifying 3D points and creating 3D models. Using images or videos to analyse surfaces as shown in Fig. 2.
Figure 2. The chart showing the Research Methodology processing.
2.1.Video Camera Calibration
Through camera calibration, the focal length main point coordinates and radial and decentering lens distortions are determined to determine the camera's internal orientation parameters (IOPs). As [13] stated, camera characteristics largely affect relative photogrammetric measurements. The (IOPs) are calculated by linearizing collinearity equations for unknown parameters such as camera lens centre coordinates orientation , and lens distortion provides intermediate precision. Wide-angle cameras and accurate photogrammetric applications require and Also, least-squares methods are used to determine the decentering parameters and their affinity and shear properties Iterative computation estimates small constant corrections like the sensor chip's principle distance and principal point The collinearity models determine the target's 3D coordinates after obtaining parameter values. The calibration sheet has four coded targets and 96 grid dots (Fig. 2a). Each camera captured 12 videos. Each camera was photographed on Fig. 3a's calibration sheet. For calibration, each photo was taken from a different location and angle (Fig. 3b). The calibrating process for sheets frequently requires three movies from each corner. Capture video frames with Virtual Dub. The PMS programme then generates a report with the selected cameras' calibrated inner orientation parameters and camera calibration residuals Root Mean Square Error (RMSE). Information is in Table 1. Camera 1 had 0.102 pixels residuals and camera 2 0.112 pixels. Every calibration residual was below half a pixel. The lens distortion PMS calibration process has been employed to enhance the accuracy of picture coordinates. The study's camera parameters are Type (1) and type (2) cameras including the Canon IXUS 185.
(b)
(a)
Figure 3. (a) Single-sheet for camera calibration PhotoModeler User Manual, 2020;
(b) Twelve photos by every chosen camera were captured on the calibration sheet,
PhotoModeler User Manual, 2020.
Table 1. Camera calibration parameters of the two selected cameras.
Items
Camera Canon IXUS 185
Left camera
Right Camera
Focal length
7.51563 mm
7.493389 mm
(X0, Y0)
4.596474 mm × 2.596654 mm
4.503162 mm ×2.585972 mm
K1
4.735e-04
5.540e-04
K2
–2.907e-06
–6.138e-06
K3
0.000e+00
0.000e+00
P1
–3.9843e-04
–1.971e-04
P2
3.984e-04
1.372e-04
No. of photos
12
12
Overall RMSE
o.106
0.111
Maximum RMSE
0.322
0.266
2.2.Load Cell Calibration
A load cell is a measuring instrument utilized for the direct or indirect measurement of loads. There are different types of load cells available, namely hydraulic load cells, pneumatic load cells, and strain gauge load cells [19, 20]. Only pneumatic load cells were utilized in this paper. The steel beams were attached to an electrical indication device to measure the imposed load. The calibration was performed between the load cell and the indication. By utilizing varying weights of 5 kg, 10 kg, and 15 kg, as depicted in Fig. 4.
Figure 4. Load Cell Calibration steps.
2.3.Capturing and Processing Videos
After calibration, cameras are set at the right distance from objects. To generate perfect stereo films, the base-to-height ratio was about 1. As shown in Fig. 6, "base" is the horizontal distance between the two cameras' exposure stations, while "height" is the vertical distance between the cameras, the ground, and the subject taken by the camera. As mentioned, stereo recordings use two cameras along the same line to film objects simultaneously. The video parts were then analysed and manipulated on a computer. Uploading videos to Virtual Dub turned them into frames. The two contemporaneous stereo images from the left and right cameras were visually selected for processing. The PMS determines the tridimensional ( , and
) coordinates of test apparatus points. Fig. 6 shows the camera's position relative to the test apparatus's targets.
Figure 6. Study area and the equipment for this investigation.
2.4.Accuracy Assessment
This article employed an accuracy assessment to validate the outcomes of video measuring methodologies. The evaluation was conducted by examining the coordinates and extracting the horizontal distances between the points; where these points were fixed on the steel frame (yellow frame), as shown in Fig. 6. The technique involves recording the coordinates of 24 targets, with 12 points serving as a control and 12 points as a chick point. A total station (GM50) with an accuracy of 1 mm was utilized to find the precise 3D ground coordinates of the 24 target points. PMS software was used also to determine the 3D ground coordinates of the 12 checkpoints using the selected stereo images from the video frames. The accuracy assessment process was done by comparing the coordinates of the 12 checkpoints that were measured using the total station with the coordinates of the same points computed using PMS. Subsequently, the variance for each point was computed, followed by the calculation of the cumulative residual of all the points.
2.5.Determining the Target Points' Three-D Coordinates for Deflection Detection
To detect deflection, the team will put 11 10-pixel targets on reinforced concrete beams. To synchronise the camera, an LED light was attached to the steel frame (Fig. 10) before videotaping. TOPCON Total Station (GM50) accuracy (1 mm) The target points' 3D ground coordinates were measured before and after loading. Video measurement determined the target points' 3D positions. Thus, the two cameras recorded six videos of the thing. The video camera's detection is tested. Load-induced deflection of three similar reinforced concrete beams with varied mixture percentages The photos' stereo recordings were uploaded from both cameras before and after the application was installed to the PC for processing. Virtual Dub converted stereo. Videos for every situation in stereo frames. Optical synchronisation of stereo frames from left and right cameras allows PMS software to calculate target point 3D coordinates. Installed encrypted targets (fixed objects) were control points. 12 checkpoints (CPs) were established to provide data tracking and calculating coordinates for targets on steel frames and concrete beams under stresses.. Ensure the 3D coordinates are precise and free of artefacts.
Figure 8. Shows the distribution targets on the test device.
3.Results and Discussion
Accuracy Assessment Result
Important (error-free) 3D coordinates of target sites as measured using a total station were considered in section 6. The device used PMS to determine the 3D spatial placement of target points attached to the steel frame using stereo video images. The 3D spatial location of target points (PMS) findings were measured by the total station, as shown in Table 2.
Table 2. 3D GCP coordinates of fixed-on-a-steel-frame targets, measured, computed, and residuals.
No.
Observed (m) (Total Station)
Computed coordinates (with photo modeller) (m)
Differences between coordinates (m)
x
y
z
x
y
z
vx
vy
vz
1
104.6454
101.9679
30.9364
104.6414
101.9628
30.936
0.004
0.005
0.004
2
104.4009
102.2072
30.9474
104.4059
102.2134
30.9486
–0.005
–0.006
–0.001
3
104.1327
102.4848
30.9436
104.1355
102.4876
30.9416
–0.002
–0.002
0.002
4
103.8176
102.8082
30.9429
103.8189
102.8052
30.9427
–0.001
0.003
0.002
5
103.6078
103.0228
30.9389
103.6028
103.0178
30.9387
0.005
–0.005
–0.004
6
102.9734
103.6647
30.9374
102.9722
103.6632
30.9376
0.001
0.001
–0.002
7
102.7611
103.8751
30.9279
102.7639
103.8765
30.9268
–0.002
–0.001
0.001
8
102.4655
104.1763
30.9354
102.4645
104.175
30.9366
0.001
0.001
–0.001
9
102.2094
104.4314
30.9481
102.2078
104.4298
30.9473
0.002
0.002
–0.002
10
101.9559
104.689
30.9273
101.9492
104.6855
30.9275
–0.006
0.003
–0.002
11
101.7376
104.9028
31.0787
101.7361
104.9031
31.0747
0.001
–0.003
0.004
12
103.3112
103.3678
32.0807
103.3117
103.3648
32.0787
–0.005
0.003
0.003
RMSE
0.00313
0.00321
0.00258
Concrete Beam Deflection Results According to Applying Load
Three experiments were performed for each type of reinforced concrete beam of 3.2 m length utilizing a video imaging technology system to record two clips. 11 points for each type of concrete beam were determined using the four loading case weights. Tables following exhibit the length law in Equation (3) used to compute the lengths between every two coordinates of the same object point of no-load situation. According to load, these distances are concrete beam deviation values. At beam number one, the deviation value was high, notably in the bearing zone, as illustrated in Tables 3 and 4 and in Fig. 8. The concrete beam's natural high deflection, especially in the loading area, makes the video measurement system reliable for precise applications. Fig. 9 shows that the gradient in the deflection value of the second and third beams, which have significant resistance, decreases with concrete beam stiffness, verifying these readings. According to Table 5, the video imaging technology system's accuracy lies in sensing deflection values detected for small values (millimetres) and not in loading areas. Figs. 10–12 depict Tables 6 to 12.
(3)
Table 3. The three-dimensional coordinates of the targets that were installed on the first concrete beam were measured before and after loading 300 kg.
Point
Before loading (Zero Load)
After loading (300 Kg)
Deflection (m)
X₀ (m)
Y₀ (m)
Z₀ (m)
Xᴀ (m)
Yᴀ (m)
Zᴀ (m)
1
104.3971
102.3046
31.52695
104.3951
102.2966
31.51895
0.008
2
104.19
102.5238
31.52496
104.185
102.5168
31.51596
0.009
3
103.9855
102.7428
31.52421
103.9765
102.7358
31.51321
0.011
4
103.7807
102.9602
31.52325
103.7717
102.9522
31.51125
0.012
5
103.5734
103.1759
31.52564
103.5634
103.1669
31.51264
0.013
6
103.3636
103.3947
31.5255
103.3506
103.3867
31.5105
0.015
7
103.1502
103.6098
31.52291
103.1402
103.6008
31.50991
0.013
8
102.9399
103.82
31.52311
102.9309
103.812
31.51111
0.012
9
102.7266
104.0337
31.52465
102.7186
104.0277
31.51465
0.01
10
102.5201
104.2485
31.52768
102.5151
104.2415
31.51868
0.009
11
102.3093
104.4604
31.51998
102.3073
104.4524
31.51198
0.008
Table 4. The three-dimensional coordinates of the targets that were installed on the first concrete beam were measured before and after loading 600 kg.
Point
Before loading (Zero Load)
After loading (600 Kg)
Deflection (m)
X₀ (m)
Y₀ (m)
Z₀ (m)
Xᴀ (m)
Yᴀ (m)
Zᴀ (m)
1
104.3971
102.3046
31.52695
104.3831
102.2956
31.50995
0.017
2
104.19
102.5238
31.52496
104.173
102.5148
31.50596
0.019
3
103.9855
102.7428
31.52421
103.9655
102.7358
31.50321
0.021
4
103.7807
102.9602
31.52325
103.7587
102.9532
31.50025
0.023
5
103.5734
103.1759
31.52564
103.5504
103.1689
31.50164
0.024
6
103.3636
103.3947
31.5255
103.3396
103.3867
31.5005
0.025
7
103.1502
103.6098
31.52291
103.1282
103.6018
31.49991
0.023
8
102.9399
103.82
31.52311
102.9189
103.813
31.50111
0.022
9
102.7266
104.0337
31.52465
102.7066
104.0297
31.50465
0.02
10
102.5201
104.2485
31.52768
102.5031
104.2395
31.50868
0.019
11
102.3093
104.4604
31.51998
102.2953
104.4514
31.50298
0.017
Table 5. The three-dimensional coordinates of the targets that were installed on the first concrete beam were measured before and after loading 900 kg.
Point
Before loading (Zero Load)
After loading (900 Kg)
Deflection (m)
X₀ (m)
Y₀ (m)
Z₀ (m)
Xᴀ (m)
Yᴀ (m)
Zᴀ (m)
1
104.3971
102.3046
31.52695
104.3761
102.2876
31.49995
0.027
2
104.19
102.5238
31.52496
104.174
102.5008
31.49696
0.028
3
103.9855
102.7428
31.52421
103.9635
102.7218
31.49421
0.03
4
103.7807
102.9602
31.52325
103.7567
102.9392
31.49125
0.032
5
103.5734
103.1759
31.52564
103.5454
103.1559
31.49164
0.034
6
103.3636
103.3947
31.5255
103.3346
103.3727
31.4895
0.036
7
103.1502
103.6098
31.52291
103.1292
103.5838
31.48991
0.033
8
102.9399
103.82
31.52311
102.9169
103.799
31.49211
0.031
9
102.7266
104.0337
31.52465
102.7036
104.0127
31.49365
0.031
10
102.5201
104.2485
31.52768
102.5001
104.2275
31.49868
0.029
11
102.3093
104.4604
31.51998
102.2883
104.4434
31.49298
0.027
Figure 9. Beam1 deflection under 300, 600, and 900 kg vertical load.
Table 6. The three-dimensional coordinates of the targets that were installed on the second concrete beam were measured before and after loading 300 kg.
Point
Before loading (Zero Load)
After loading (300 kg)
Deflection (m)
X₀ (m)
Y₀ (m)
Z₀ (m)
Xᴀ (m)
Yᴀ (m)
Zᴀ (m)
1
104.3973
102.3037
31.527
104.3953
102.2977
31.521
0.006
2
104.191
102.5241
31.5238
104.189
102.5161
31.5158
0.008
3
103.9853
102.7429
31.5232
103.9802
102.7359
31.5142
0.009
4
103.7827
102.9622
31.5228
103.7747
102.9562
31.5128
0.01
5
103.5721
103.1734
31.5263
103.5630
103.1664
31.5153
0.011
6
103.363
103.3924
31.5237
103.3520
103.3834
31.5107
0.013
7
103.153
103.6116
10.34910/MCE.141.5
624.042
videogrammetry
3D coordinates
vertical loading
concrete beam
deformation
PhotoModeler software
https://engstroy.spbstu.ru/article/2026.141.5/
RAR
RUS
14106-14106
LGC for National Engineering School of Tunis (ENIT), University of Tunis El Manar
Tarkhani
Imeen
imeentarkhani16@gmail.com
Tunis, Tunisia
Military Academy of Fondouk Jedid; GESTE for National School of Engineers of Sfax, University of Sfax
Kammoun
Zied
kammounzied@yahoo.fr
Nabeul, Tunisia; Sfax, Tunisia
LGC for National Engineering School of Tunis (ENIT), University of Tunis El Manar; Military Academy of Fondouk Jedid
Trabelsi
Abderraouf
abederraouftrabelsi@gmail.com
Tunis, Tunisia; Nabeul, Tunisia
Faculty of Engineering, King Abdulaziz University
Smaoui
Hichem
hismaoui@yahoo.fr
Jeddah, Kingdom of Saudi Arabia
Properties of concrete incorporating treated prickly pear fibers
The integration of natural fibers into building materials is key to enhancing sustainability within the construction industry. However, vegetable fibers are known to undergo mechanical degradation over time when embedded in the alkaline environment of cementitious matrices. This study investigates the incorporation of prickly pear fibers into concrete, evaluating the efficacy of three surface treatments (epoxy, lime, and bitumen) over a curing period extending from 3 to 180 days. Results indicate that while untreated fibers reduce compressive strength, the applied treatments significantly mitigate this loss. Notably, epoxy-treated fiber concrete exhibited only an 11 % decrease in compressive strength at 28 days compared to ordinary concrete, eventually achieving a strength 53 % higher than that of untreated fiber concrete by 180 days. At the optimal dosage of 15 kg/m3, epoxy treatment enhanced 28-day flexural strength by 333 %, while lime treatment yielded a 229 % increase. Furthermore, whereas untreated fibers exhibited mechanical degradation after 28 days, treated fibers demonstrated sustained strength gains up to 180 days. Additionally, a fiber dosage of 40 kg/m3 substantially improved thermal performance, reducing conductivity by 40–45 % and increasing specific heat capacity by 22–24 %. These findings highlight the potential of treated prickly pear fibers as a viable, sustainable reinforcement for high-performance construction applications.
1.Introduction
Plant fibers are increasingly incorporated into cementitious materials owing to their renewability, biodegradability, low embodied energy, and near carbon-neutral life cycle [1]. Beyond these environmental benefits, their low density and cost-competitiveness relative to synthetic fibers make them attractive for lightweight, sustainable construction [2, 3]. Numerous plant-based reinforcements – including straw, date palm, Stipa tenacissima (Alfa), bamboo, sisal, coconut shell, and Ampelodesmos mauritanicus (Diss) – have been evaluated in concrete and mortar composites [4–12]. A consistent finding across the literature is a reduction in composite density, primarily due to the lower intrinsic density of lignocellulosic materials compared to mineral aggregates. In parallel, several studies report enhanced thermophysical performance, specifically reductions in thermal conductivity, diffusivity, and effusivity, alongside increased specific heat capacity. These effects are attributed both to the low intrinsic thermal conductivity of plant fibers and the additional porosity introduced within the matrix [1].
Mechanical performance is highly dependent on fiber morphology, dosage, dispersion, and the quality of the fiber–matrix interface. Although compressive strength often declines with increasing fiber content – largely due to higher porosity and interfacial weaknesses – improvements in flexural strength, splitting tensile strength, and post-cracking toughness are frequently observed. Alfa fiber-reinforced concrete, for example, exhibited reduced compressive strength at high dosages, yet flexural and tensile strengths peaked at 15 kg/m3, accompanied by improved ballistic resistance [13]. Similarly, incorporating 50 mm maguey fibers pretreated with calcium oxide (0.9 % by cement weight) increased compressive, flexural, and tensile strengths by 13.4, 17.4, and 1.5 %, respectively, while boosting the modulus of elasticity by 53.8 % [14]. In ultra-high-performance concrete, sisal fibers (6–18 mm, 1–3 % by volume) had negligible effects on compressive strength but successfully transitioned the failure mode from brittle to ductile; at a 2 % volume fraction, flexural strength and toughness increased by 16.7 and 540 %, respectively [15]. Comparable trends were observed with palm leaf sheath fibers, whereas banana fibers led to performance losses attributed to inadequate interfacial bonding [16].
Among various lignocellulosic reinforcements, prickly pear fibers exhibit significant structural and thermal potential. In lightweight concrete, their incorporation reduced density by approximately 25 % and thermal conductivity by 42 %, while increasing flexural strength by 170 %; compressive strength remained above 22 MPa, thereby meeting structural-grade requirements [17]. In high-strength concrete, density reductions of up to 30 % and thermal conductivity decreases of 50 % were reported, with compressive strengths ranging from 41 to 59 MPa and flexural strength gains reaching 35 % at 28 days [18]. Furthermore, improved impact resistance and toughness highlight their suitability for both conventional and high-performance systems.
Despite these advantages, long-term durability remains a critical challenge. Plant fibers consist primarily of cellulose, hemicellulose, and lignin, all of which are susceptible to degradation in the highly alkaline cementitious environment (pH > 12). Alkaline hydrolysis of hemicellulose and lignin, partial depolymerization of cellulose chains, and the diffusion of pore solution toward the fiber surface progressively weaken the lignocellulosic structure. Moreover, the precipitation of hydration products within the lumen and cell walls promotes stiffening and embrittlement, while cyclic swelling and shrinkage of the hydrophilic fibers under fluctuating moisture conditions induce interfacial microcracking [19, 20]. Collectively, these mechanisms compromise long-term strength and toughness.
To mitigate degradation and enhance fiber–matrix compatibility, several pretreatment strategies have been explored. Lime treatment of palm nut shells increased 28-day compressive strength by 10 %, whereas polyvinyl alcohol (PVA) primarily reduced water absorption without providing mechanical benefits [21]. Boiling and linseed oil coating of Diss fibers improved tensile behavior and delayed crack initiation [22]. A 60-minute Ca(OH)2 treatment of date palm fibers enhanced flexural strength by removing inhibitory extractives and promoting interfacial bonding [23]. Mineral and organic coatings have also been investigated to control dimensional instability: oil impregnation reduced drying shrinkage in wood-based composites by 43.6 %, while lime coatings improved compatibility more effectively than cement [24]. Paraffin wax coatings acted as hydrophobic barriers to optimize moisture exchange, whereas prolonged pre-wetting (48 h) reduced performance due to diminished suction capacity [25]. In straw-reinforced sand concrete, hot water treatment provided the most balanced improvement (a 30 % increase in flexural strength), while gasoil minimized shrinkage and waste oil adversely affected dimensional stability despite strength gains [26].
While various treatments have been evaluated for different plant fibers, research on prickly pear fibers remains limited, with existing studies primarily focused on hot-water treatments and assessments restricted to 28 days of age. The present study aims to fill this gap by evaluating the impact of three coating-based treatments – resin, lime solution, and bitumen – on the mechanical (compressive and flexural), physical (density), and thermal (conductivity) behavior of prickly pear fiber-reinforced concrete. The analysis extends to 180 days to evaluate the evolution of properties beyond standard curing ages. Treated and untreated composites are compared to identify the most effective method for enhancing interfacial stability and mitigating alkaline-induced degradation.
2.Materials and Methods
The development of sustainable construction materials often involves either the optimization of the binder [27] or the reinforcement of the matrix with agricultural residues [28]. In the present study, the focus is placed on the incorporation of cactus fiber sheets as a natural reinforcement within a standardized concrete matrix. All materials and experimental procedures followed the international standards prevailing in the region of study to ensure technical consistency. The binder used is a Portland cement manufactured according to EN 197-1 specifications. The mechanical characterization of the concrete was performed according to the EN 12390 series, specifically EN 12390-1 for specimen geometry (16×32 cm cylinders) and EN 12390-6 for splitting tensile strength. The following subsections describe the aggregate and binder properties, the fiber treatments, the concrete mix design, and the experimental techniques applied.
2.1.Aggregate and Binder Properties
The binder is a CEM I 42.5 Portland cement, with a density of 3.15 g/cm3, a compactness of 0.574, and a Blaine specific surface area of 346.6 m2/kg. The fine aggregate is a 0/2 mm sand extracted from the Borj Hfaiedh quarry. Its measured sand equivalent (SE = 81, NF P18-597) confirms a high level of cleanliness. The coarse aggregate is a 4/12 mm gravel obtained from the Jbel Ressas quarry. The sand exhibits an apparent density of 1650 kg/m3 and an absolute density of 2510 kg/m3, while the gravel presents an apparent density of 1560 kg/m3 and an absolute density of 2521 kg/m3. The particle size distributions of the aggregates (Fig. 1) were determined by dry sieving, a methodology consistent with the characterization of alternative and conventional granular materials [29, 30]. According to EN 12620, the sand is classified by its fineness modulus, which was calculated as 1.85, identifying it as a fine sand. The coarse aggregate is classified as a 4/12 mm class gravel, with a maximum particle size of 12.5 mm, as confirmed by the grading analysis. These classifications are essential for ensuring an optimal granular skeleton and for monitoring the water demand of the cementitious matrix.
Figure 1. Particle size distribution curves for sand and gravel.
2.2.Fibers
Opuntia ficus-indica, commonly known as the prickly pear cactus, is prevalent in Africa, the Americas, and the Mediterranean basin [31]. This species is characterized by its stems, referred to as “cladodes” or “nopalitos,” which fulfill the function of leaves [32]. Upon the decay of an Opuntia trunk or cladode, the outer layer gradually decomposes, exposing an underlying structure composed of multiple fibrous layers arranged in a honeycomb-like pattern, as illustrated in Fig. 2.
Figure 2. Dead prickly pear cladode.
The fibers used in this study were sourced from naturally dead cladodes and trunks and manually cut into 5 × 5 cm pieces. According to Mannai et al. [33], Opuntia ficus-indica fibers exhibit a chemical composition of approximately 53.6 % cellulose, 4.8 % lignin, and 10.9 % hemicellulose. While the relatively high cellulose content is favorable for mechanical performance, the presence of lignin and hemicellulose – components known to be chemically unstable in highly alkaline environments such as Portland cement – raises concerns regarding potential degradation over time when the fibers are embedded in cementitious matrices. This consideration motivates the use of protective surface treatments aimed at improving their durability within concrete. In addition to their chemical characteristics, the mechanical behavior of Opuntia fibers displays significant variability in the literature, as highlighted in [34]. This dispersion is mainly attributed to differences in extraction methods, environmental factors, and particularly the maturity of the cladodes. Reported tensile elastic modulus values range from 0.15 to 2.93 GPa, while tensile strengths vary between 1 and 27 MPa, with the highest values generally obtained from older cladodes where the lignocellulosic network is more developed.
The treatments applied in this study involved coating the fibers with lime, epoxy, or bitumen, as illustrated in Fig. 3. Consequently, the study examined five distinct types of concrete: ordinary concrete (OC) serving as the control; concrete reinforced with untreated prickly pear fibers (UTFC); and concretes reinforced with lime-treated (LFC), epoxy-treated (EFC), and bitumen-treated (BFC) prickly pear fibers. The lime treatment involved immersing the fibers in a lime solution for 30 seconds, followed by drying for 24 hours. This process aims to improve the bond between the fibers and the cementitious matrix. The bitumen treatment entailed immersing the fibers in bitumen heated to 160 °C, followed by drying at ambient temperature to allow the bitumen to solidify. The epoxy treatment involved coating the fibers with an epoxy resin, which acts as a binding agent that encapsulates the fibers. The objective of the bitumen and epoxy treatments is mainly to enhance the moisture protection of the fibers and, consequently, to improve their resistance to the alkaline environment.
a b c d
Figure 3. Untreated (a), epoxy (b), bitumen (c), and lime (d) treated fibers.
The densities of the concrete samples incorporating prickly pear fibers varied depending on the treatment applied. The untreated fibers had a density of 571 kg/m3. While fiber density increased slightly with treatment, the maximum increase remained below 5 %. Consequently, the density variation of the fibers was neglected in the concrete mix design.
a b
c d
Figure 4. SEM of untreated (a), epoxy (b), bitumen (c), and lime (d) treated fibers.
Fig. 4 presents Scanning Electron Microscopy (SEM) images of both treated and untreated prickly pear fibers. The SEM image of the untreated fiber reveals a fibrous structure with loosely attached impurities and plant residues. In the case of the lime-treated fiber, a thin layer of lime is visible, coating the fibers and filling the gaps between them, resulting in a granular surface texture. The bitumen-treated fiber appears coated with a smooth, continuous layer of bitumen that obscures the natural surface features. The SEM image of the epoxy-treated fiber shows a uniform, smooth epoxy resin coating that encapsulates the fibers, effectively covering the natural surface texture and filling the inter-fiber spaces, with fewer visible microfibrils.
2.3.Elaboration of the Concrete
The baseline formulation (C0) was designed using the Dreux–Gorisse method to achieve a specific target consistency and strength class. The mix proportions, which resulted in a constant water-to-cement (W/C) ratio of 0.4375, are detailed in Table 1. The fibers were incorporated as a volumetric replacement for the aggregates, maintaining a constant sand-to-gravel volume ratio. Any variation in fiber density resulting from the different treatments was considered negligible and was therefore not accounted for during the mix design process. Consequently, five different fiber dosages were evaluated: 5, 10, 15, 20, and 40 kg/m3 (Table 1).
Table 1. Composition of concrete (kg/m3).
Designation
C0
C5
C10
C15
C20
C40
Gravel
1175
1161
1146
1132
1118
1060
Sand
646
638
630
622
613
581
Cement
400
400
400
400
400
400
Water
175
175
175
175
175
175
Fibers
0
5
10
15
20
40
The untreated and lime-treated fibers were pre-saturated with water before mixing to prevent them from absorbing water from the fresh concrete. This step was unnecessary for the epoxy- and bitumen-treated fibers, as their treatment effectively prevents water absorption. Following the mixing process, which ensured a random distribution of the fibers, three specimens of each concrete composition were prepared for each test. The specimens were demolded 24 hours after casting.
2.4.Experimental Techniques
The workability of fresh concrete was assessed using the slump test, in accordance with the aforementioned EN 12350-2. Compressive and flexural tests were performed on cubic (15 × 15 × 15 cm) and prismatic (7 × 7 × 28 cm) specimens, respectively, using a universal testing machine (Fig. 5). As previously specified, splitting tensile strength was determined on the 16 × 32 cm cylindrical specimens. These tests were performed at curing ages of 3, 7, 28, 90, and 180 days to assess the strength evolution of the concrete over time.
a b c
Figure 5. Experimental setup for compression (a), flexural (b), and splitting tensile (c).
Thermal conductivity, diffusivity, and specific heat were measured using a Fox 314 calorimeter, following the ASTM C518 and ISO 8301 standards.
3.Results and Discussion
Workability and Densities
Fig. 6 presents the effect of fiber type and treatment on the workability of the concrete. The reference OC exhibits a slump of 11.0 cm. At a low dosage of 5 kg/m3, untreated fibers slightly reduce the slump to 10.8 cm, while bitumen-, lime-, and epoxy-treated fibers result in values of 11.1, 11.2, and 10.9 cm, respectively. These variations indicate that fiber treatments modify the fresh behavior of the mix, likely due to differences in fiber morphology and the quality of the fiber–matrix interface induced by each treatment.
Figure 6. Workability of concrete.
As the fiber content increases, an overall improvement in workability is observed. At 40 kg/m3, slump values reach 11.3 cm for UTFC, 11.6 cm for BFC, 11.8 cm for LFC, and 11.5 cm for EFC, confirming that the lime treatment provides the greatest enhancement, followed by bitumen and epoxy, while untreated fibers remain the least effective. Despite these changes, all mixtures maintain an S3 consistency class, indicating that the addition of treated or untreated fibers does not compromise the required workability level.
Figure 7. Density of concrete.
Fig. 7 shows that the incorporation of plant fibers leads to a measurable decrease in concrete density. The reference concrete exhibits a density of 2399 kg/m3. At a low dosage of 5 kg/m3, the density decreases slightly, reaching 2363–2365 kg/m3 depending on the fiber treatment, which corresponds to a reduction of about 1.5 %. Increasing the fiber dosage amplifies this effect: at 40 kg/m3, densities range from 2231 to 2244 kg/m3, representing a reduction of approximately 7 % compared to the reference mix. This decrease is primarily attributed to the partial replacement of dense mineral aggregates with fibers of significantly lower density.
Compressive Strength
Fig. 8 presents the evolution of compressive strength at 3, 7, 28, 90, and 180 days for the different concrete formulations. The reference concrete exhibits strengths of 36.3 MPa at 28 days, increasing to 37.5 MPa at 90 days and 38.5 MPa at 180 days, reflecting the expected hydration of the cement matrix over time.
Figure 8. Compressive strength at different ages (Sdmax = 0.8 MPa).
For all fiber dosages and treatments, the incorporation of plant fibers leads to a reduction in compressive strength compared to the reference mix. At low dosages, this reduction remains limited, but it becomes more pronounced at higher fiber contents. At a dosage of 40 kg/m3, UTFC exhibits a 28-day strength of 28.5 MPa, corresponding to a reduction of approximately 21.5 % relative to OC. The effect of fiber treatment is clearly observable: LFC reaches 28.8 MPa (a ≈ 20 % reduction), BFC reaches 29.8 MPa (a ≈ 17 % reduction), while EFC achieves the highest value, 32.2 MPa, representing only an 11 % strength loss at 28 days. These results confirm that surface conditioning of the fibers mitigates the mechanical performance loss caused by fiber addition.
Strength evolution over time further highlights the contrasting behavior between untreated and treated fibers. For UTFC at 40 kg/m3, strength continues to decrease beyond 28 days, reaching 25.0 MPa at 90 days and 22.7 MPa at 180 days, corresponding to reductions of 33 and 41 % relative to OC. This progressive deterioration suggests fiber degradation within the alkaline cementitious environment. In contrast, concretes incorporating treated fibers exhibit strength gains between 28 and 180 days, similar to the trend observed in OC. At 90 and 180 days, reductions relative to the reference mix range from 21 % for LFC to 17–18 % for BFC and only 9.5–10.5 % for EFC. The long-term improvement observed for treated mixes confirms that fiber treatments enhance durability and stabilize fiber–matrix interactions, preventing the degradation observed in untreated fibers.
The microstructural observations obtained through optical microscopy (Fig. 9) reinforce the mechanical results by illustrating the distinct behaviors of treated and untreated fibers within the cementitious matrix. In specimens containing untreated fibers, several degradation features are apparent. Figs. 9d to 9f show interfacial gaps and fiber–matrix detachment, indicating insufficient adhesion and early debonding. Adjacent voids and the altered morphology of the fibers provide evidence of moisture-driven swelling and subsequent shrinkage, mechanisms known to promote fiber–matrix debonding, as documented in several studies [35–38]. In Fig. 9g, the fiber appears partially cracked and separated from the surrounding matrix, while Fig. 9h shows a longitudinal subdivision of the fiber into individual microfilaments located within a void. Notably, matrix cracking is not observed in these regions, confirming that degradation primarily affects the fibers and their interface rather than the cement paste itself. These mechanisms explain the progressive loss of mechanical performance observed between 28 and 180 days.
a b c d
e f g h
Figure 9. An image of concrete with fibers treated by bitumen (a), microscopic images fibers treated by bitumen in concrete (b, c), an image of concrete with untreated fibers (d),
microscopic images of untreated fibers in concrete (e–h).
In contrast, treated fibers exhibit markedly improved interfacial behavior. Figs. 9a to 9c show continuous, well-bonded interfaces without visible detachment or voids. The protective coating limits water ingress and reduces direct exposure to the alkaline pore solution, thereby preventing swelling-induced stresses and preserving interfacial integrity. These stabilized fiber–matrix interactions directly correlate with the improved and sustained compressive strength development observed beyond 28 days in concretes incorporating treated fibers.
Flexural Strength
The flexural strength results at 3, 7, 28, 90, and 180 days for all mixtures and fiber treatments are presented in Fig. 10. The reference concrete (C0) exhibits a flexural strength of 2.8 MPa at 28 days, increasing slightly to 2.85 MPa at 90 days and 2.92 MPa at 180 days. The introduction of plant fibers significantly improves flexural performance, with the magnitude of enhancement depending on fiber dosage and treatment.
At the lowest dosage (C5), the 28-day flexural strength increases to 7.9–9.7 MPa depending on the treatment, which corresponds to improvements of approximately 180 to 245 % relative to C0. In this case, lime treatment yields the lowest strength values – slightly higher than those of untreated fibers – whereas bitumen and epoxy treatments achieve considerably greater gains. The C15 mixtures exhibit the highest flexural strengths across all curing ages, with 28-day values ranging from 9.2 MPa for lime-treated fibers to 12.1 MPa for epoxy-treated fibers, representing increases of approximately 229 to 333 % relative to the C0. This dosage consistently maximizes the efficiency of fiber incorporation, irrespective of the treatment applied.
At the highest dosage (C40), flexural strengths at 28 days remain markedly higher than those of the C0, with values of 7.6 MPa for untreated fibers, 7.7 MPa for lime treatment, 8.2 MPa for bitumen treatment, and 10.7 MPa for epoxy treatment. Although these absolute values are slightly lower than those at C15, the same hierarchy among treatments is observed, with epoxy remaining the most effective and lime providing the lowest improvement.
Figure 10. Flexural strength results (Sdmax = 0.45 MPa).
a b c
d e
Figure 11. Flexural test: a – OC, b – UTFC, c – BFC, d – LFC, e – EFC.
Post-failure observations presented in Fig. 11 further support these results. The C0 exhibits brittle fracture and complete separation once the maximum load is reached, which is characteristic of unreinforced cementitious materials. In contrast, fiber-reinforced specimens retain partial integrity after failure due to fibers bridging the cracked surfaces and maintaining residual load transfer. This bridging mechanism, widely reported in the literature for cementitious composites incorporating natural fibers [5, 17], explains the substantial increase in flexural strength observed despite the reduction in compressive strength.
Fig. 12 shows SEM images of crack zones in specimens incorporating bitumen-treated fibers. The images reveal fibers fully coated with bitumen and embedded within a continuous and cohesive interface, with no visible separation between the coating and the surrounding cement matrix. These results are consistent with the optical microscopy observations (Fig. 9) and confirm that the protective coating stabilizes the fiber–matrix interface, enhances stress transfer after matrix cracking, and contributes to the sustained flexural performance for up to 180 days.
a b
Figure 12. SEM of concrete with fibers treated by bitumen:
a – concrete and fibers, b – concrete and fiber interface.
The evolution of the flexural strength relative to the compressive strength provides further insight into the mechanical behavior of the fiber-reinforced concrete. According to Ahmed et al. [39], the relationship between the flexural tensile strength and the compressive strength is frequently expressed in the literature as a power equation in the form Several standards provide formulas for this relationship in the form For instance, AS 3600 and CSA-A23.3 specify while the ACI 363-92 standard proposes a different equation: [40]. Fig. 13 presents the flexural tensile strength as a function of the compressive strength for the current study.
Figure 13. Flexural and compressive strength relationship.
The experimental results exhibit a clear increasing trend of flexural strength relative to compressive strength. A power-law regression performed on the experimental dataset of the fibrous concrete specimens (treated and untreated) yielded the following relationship:
(1)
The exponent obtained from this regression (1.533) is significantly higher than the value implicitly assumed in current design standards (0.5), indicating that the flexural strength of fibrous concrete increases at a faster rate than predicted by code-based formulations. This behavior reflects the dominant role of the reinforcement and matrix modification mechanisms under flexural loading.
Fig. 13 further shows that the fibrous concrete specimens subjected to epoxy and bitumen treatments are located in the upper-right region of the diagram, corresponding to the highest flexural and compressive strength values. This indicates that these two treatments are the most effective in enhancing overall mechanical performance, particularly in flexure. This superior behavior can be attributed to the improved crack-bridging efficiency of the fibers, combined with enhanced fiber–matrix interaction and reduced microcrack propagation due to the presence of epoxy or bitumen. By contrast, the non-fibrous concrete is represented by a single data point located in the lower region of the figure, lying very close to the AS 3600 prediction curve. This observation confirms that, in the absence of fiber reinforcement, the standard code-based relationship remains applicable within the investigated strength range.
Overall, the deviation of the fibrous and treated concretes from the normative predictions highlights the limitations of existing flexural–compressive strength relationships when applied to modified concretes. The proposed empirical relationship should therefore be interpreted as representative of fibrous concrete behavior within the investigated domain, with epoxy and bitumen treatments playing a key role in achieving superior flexural performance.
Splitting Tensile Strength
Fig. 14 shows the evolution of the splitting tensile strength. The values at 28, 90, and 180 days – points at which mechanical properties stabilize – allow for a direct comparison. The C0 records 2.18, 2.22, and 2.27 MPa at these ages. Incorporating fibers significantly enhances tensile performance, with the maximum improvement obtained at a dosage of 15 kg/m3. At 28 days, C15 exhibits tensile strengths of 7.84 MPa with untreated fibers, 7.47 MPa with lime-treated fibers, 9.28 MPa with bitumen-treated fibers, and 9.82 MPa with epoxy-treated fibers. These values correspond to increases of approximately 260, 243, 326, and 350 % relative to the C0. At later ages, untreated fibers show a decline in tensile strength (5.45 MPa at 90 days and 4.68 MPa at 180 days), whereas lime-, bitumen-, and epoxy-treated fibers maintain or improve their performance, reaching up to 11.17 MPa at 180 days with epoxy treatment. Increasing the fiber dosage to 40 kg/m3 reduces tensile strength relative to C15 but still yields values higher than those of the C0. At 28 days, C40 reaches 6.14 MPa for untreated fibers, 6.21 MPa for lime-treated fibers, 6.69 MPa for bitumen-treated fibers, and 8.64 MPa for epoxy-treated fibers. This confirms that excessive fiber content induces fiber clustering and matrix discontinuities, limiting mechanical efficiency [41].
Figure 14. Splitting tensile test results.
The failure patterns support the mechanical observations. The C0 splits abruptly into two detached halves, whereas the fiber-reinforced specimens remain connected after testing, with the cracks bridged by fibers. Manual separation reveals fracture surfaces containing randomly distributed prickly pear fibers (Fig. 15), most of which underwent fracture rather than pullout. This indicates strong fiber–matrix adhesion, particularly in the treated-fiber mixtures.
a b c d
Figure 15. Splitting tensile test results: a – OC, b – EFC, c – LFC, d – BFC.
Thermal Characteristics
This section examines the influence of prickly pear fibers and their surface treatments on the thermal behavior of concrete. Three fundamental properties are considered: thermal conductivity, specific heat capacity, and thermal diffusivity. These parameters are intrinsically linked to the microstructure of cementitious composites and are affected by the addition of low-conductivity plant fibers.
3.5.1. Thermal conductivity
Thermal conductivity governs the heat transfer capacity of cementitious composites and is strongly influenced by microstructural variables such as moisture content, aggregate volume fraction, pore connectivity, and the nature of the embedded inclusions. Fig. 16 reports the evolution of thermal conductivity as a function of fiber dosage and surface treatment. A monotonic reduction is observed with increasing fiber content, with values decreasing from 1.91 W/(m·K) for the reference mixture to a range of 1.04–1.14 W/(m·K) at 40 kg/m3, depending on the treatment; this corresponds to a decrease of approximately 40–45 %. Given that common mineral aggregates exhibit conductivities between 1.16 and 8.6 W/(m·K) [42], such reductions are consistent with the replacement of higher-conductivity constituents with materials of lower intrinsic conductivity.
The decrease in effective conductivity can be explained by considering the microstructural role of the fibers. Materials with low intrinsic conductivity or highly porous internal structures act as insulating inclusions that alter the topology of conduction pathways. With an intrinsic conductivity of approximately 0.057 W/(m·K) and a naturally porous morphology, prickly pear fibers reduce the continuity of solid heat transfer routes within the matrix and, therefore, behave as thermally insulating inclusions.
To assess these experimental results, they were compared with classical homogenization models formulated for isotropic two-phase composites. The cementitious matrix is considered the continuous phase with conductivity while the prickly pear fibers constitute the dispersed phase with conductivity and respective volume fractions and satisfying Under these assumptions, the extremal estimates of effective conductivity are provided by the Voigt and Reuss bounds [43]:
(2)
(3)
Eqs. (2) and (3) represent the maximal conductivity corresponding to a parallel-phase configuration and the minimal conductivity associated with a series configuration, respectively. Although these idealized morphologies are not strictly representative of the present composite, they provide an essential admissible interval for assessing the effective thermal behavior. A more physically constrained prediction is given by the Hashin–Shtrikman bounds, which are derived from variational principles and are applicable to isotropic composites with arbitrarily shaped inclusions [44]:
(4)
(5)
These bounds (Eqs. (4) and (5)) define the narrowest theoretically admissible interval for the effective conductivity of an isotropic two-phase material. The measured values remain well below the Voigt limit while staying above the Reuss bound; however, in several cases, they lie below the Hashin–Shtrikman lower limit. This departure indicates that the actual microstructure – featuring elongated pores, anisotropic fiber arrangements, and potentially a third interfacial phase – creates a higher thermal tortuosity than assumed in classical isotropic models.
The slightly higher conductivities measured for the treated fibers are consistent with improved interfacial bonding. Enhanced adhesion reduces the volume of interfacial air voids – the conductivity of which is extremely low – increasing the continuity of solid heat transfer paths and, consequently, raising the effective thermal conductivity.
Figure 16. Thermal conductivity of concrete incorporating treated fibers (Sdmax = 0.015 W/(m.K)).
3.5.2. Specific heat
Specific heat capacity represents the amount of heat required to increase the temperature of a unit mass by one degree [40]. In cementitious materials, this property depends on the thermal behavior of the constituent solid phases. Prickly pear fibers contain high fractions of cellulose, hemicellulose, and lignin, which exhibit greater heat capacities than mineral aggregates. Their cellular microstructure, rich in voids and capable of retaining bound water, also contributes to increasing the heat storage capacity of the composite.
Fig. 17 shows that the incorporation of fibers leads to a systematic increase in the specific heat capacity for all treatment types. When considering only the reinforced mixtures (5–40 kg/m3), the evolution of with fiber dosage is quasi-linear. This behavior is consistent with a progressive increase in the volumetric fraction of organic phases, whose intrinsic heat capacity is significantly higher than that of the mineral matrix. At 40 kg/m3, the specific heat capacity rises by approximately 22–24 % compared to the C0.
Differences between treatment types follow a consistent hierarchy across all dosages. EFC systematically exhibits the highest values, with an increase of approximately 1–3 % relative to UTFC. This enhancement is primarily linked to the stabilization of the fiber surface by the epoxy coating, which prevents fiber degradation and preserves a durable and continuous contact with the cement matrix. LFC shows slightly lower values, typically within 0.5–2 % lower than those of EFC, reflecting the partial mineralization induced by the lime treatment and the improved compatibility of the fibers with the surrounding matrix. UTFC presents the lowest cp values among the reinforced mixtures. This is attributed to the absence of surface modification, which results in weaker fiber–matrix adhesion and a less efficient contribution of the fibers to the overall thermal storage capacity. Collectively, the results indicate that both fiber dosage and surface treatment contribute to variations in the specific heat capacity of the composite, with the dominant effect being associated with the fiber fraction.
Figure 17. Specific heat of concrete incorporating treated fibers (Sdmax = 4.5 J/(kg.K)).
3.5.3. Thermal diffusivity
Thermal diffusivity α quantifies the rate at which heat propagates through a material and is defined as:
(6)
where represents the thermal conductivity (W/(m.K)), is the density (kg/m3), and is the specific heat capacity (J/(kg·K)).
Figure 18. Thermal diffusivity of concrete incorporating treated fibers (Sdmax = 4×10–9 m2/s).
Fig. 18 shows that thermal diffusivity decreases consistently with increasing fiber content, regardless of the treatment applied. The C0 presents a diffusivity of 0.50 mm2/s. At 40 kg/m3, the values decrease to 0.41 mm2/s for UTFC, 0.40 mm2/s for BFC, 0.40 mm2/s for EFC, and 0.39 mm2/s for LFC, representing reductions of approximately 18–22 %.
This reduction stems primarily from microstructural modifications induced by the fibers and their treatments. The dominant factor is the marked decrease in thermal conductivity the fibers and their internal air cavities lower the effective conductivity of the composite by about 40–45 % at 40 kg/m3, directly reducing the numerator of A secondary effect arises from changes in the volumetric heat capacity fiber incorporation increases by roughly 22–24 % while slightly reducing the bulk density (≈7 %), which increases the denominator of α and contributes further to the decrease in diffusivity. Although the reduction in density alone would tend to raise the combined effect of reduced conductivity and increased heat capacity overrides this tendency, producing the observed decline.
Differences among treatments remain limited but systematic. Epoxy- and bitumen-treated fibers lead to the lowest diffusivities at equivalent dosages, followed by lime-treated fibers, which slightly outperform untreated ones at higher fiber contents. These distinctions reflect the influence of surface treatments on fiber integrity and interfacial contact: epoxy and bitumen create more stable coatings that limit interfacial voids and maintain the insulating character of the fibers, whereas lime treatment induces partial mineralization that modifies thermal behavior to a lesser extent. The overall decrease in diffusivity shows that the presence of prickly pear fibers enhances the material’s thermal inertia by simultaneously restricting heat transfer and increasing its heat storage capacity.
4.Conclusion
This study investigated the long-term mechanical and thermal performance of concrete reinforced with prickly pear fibers, comparing untreated fibers with three coatings: epoxy, bitumen, and lime. The following findings highlight the main contributions of this research:
Surface conditioning of the fibers significantly mitigates the loss of compressive strength; notably, the epoxy treatment limits the 28-day reduction to only 11 %, compared to a 21.5 % loss for untreated fibers at a dosage of 40 kg/m3.
Long-term durability is critically enhanced by these treatments. While untreated fibers degrade in the alkaline cementitious environment (reaching a 41 % strength loss at 180 days), treated fibers maintain stable performance, with strength reductions relative to the reference mix limited to
10.5–21 % at the same age.
An optimal dosage of 15 kg/m3 maximizes mechanical efficiency, yielding peak increases in flexural and splitting tensile strengths at 28 days of up to 333 and 350 %, respectively (obtained with epoxy-treated fibers).
High fiber content (40 kg/m3) leads to a relative decline in mechanical performance compared to the 15 kg/m3 dosage due to fiber clustering and matrix discontinuities; however, values remain significantly higher than those of the plain reference concrete (0 kg/m3) in both flexural and tensile strength.
Thermal properties are substantially improved with increasing fiber content. A dosage of 40 kg/m3 achieves a 40–45 % reduction in thermal conductivity and a 22–24 % increase in specific heat capacity. This enhancement is driven by the higher volumetric fraction of organic phases, with epoxy-treated concrete showing the highest thermal storage capacity due to stabilized fiber-matrix adhesion.
In summary, pretreating prickly pear fibers – particularly with epoxy – overcomes the durability limitations typically associated with natural fibers, offering a high-performance, sustainable alternative with reliable long-term properties.
10.34910/MCE.141.6
624
concrete
prickly pear
fiber
treatment
long-term
strength
mechanical properties
thermal properties
https://engstroy.spbstu.ru/article/2026.141.6/
RAR
RUS
14107-14107
Civil Engineering Department, Al-Nahrain University
Mohammed
Mohammed Jumaah
st.Mohammed.g.m.f@nahrainuniv.edu.iq
Baghdad, Iraq
Civil Engineering Department, Al-Nahrain University
Al-Azzawi
Adel
dr_adel_azzawi@yahoo.com
Baghdad, Iraq
Finite element analysis of the effect reinforced concrete beams under pure torsion strengthened by SIFCON jacketing with different fiber types
In recent years, emphasis has been made on studying the effect and behavior of beams under pure torsion, which required the emergence of different types of strengthening. Because of concrete's poor tensile strength, fiber can be added with high or low percentages. This paper aimed to study the torsional behavior of reinforced concrete beams and the jacketing technique. Reinforced beams were strengthened using a layer of Slurry Infiltrated Fiber Concrete (SIFCON) and with different types of fiber. SIFCON is a special type of fiber concrete that contains a high percentage of fiber. It is an effective substance used for repair and strengthening. The finite element (FE) method through ABAQUS software is carried out to test seven samples previously tested experimentally. Reasonable agreement was acquired between the ultimate torque and angle of twist of FE numerical models and found experimentally, in which the value of the mean and coefficient of variations were 0.998 and 0.247 %, respectively for the ultimate torque, whilst for the angle of twist, the value of the mean and coefficient of variation were 0.945 and 3.823 %, respectively. The effect of increasing longitudinal reinforcement ratio is found to be higher for torsional unreinforced beams and marginal for other beams for the selected range of reinforcement ratio or diameter (8 to 12 mm bar diameter). The effect of thickness of the SIFCON layer on the behavior is found to be higher for steel fiber SIFCON and lower for hybrid fiber SIFCON jacketing. The effect of hybrid fiber on behavior is studied.
10.34910/MCE.141.7
624
pure torsion
slurry infiltrated fiber concrete
SIFCON
strengthening layer
hybrid fibers
finite element.
https://engstroy.spbstu.ru/article/2026.141.7/
RAR
RUS
14108-14108
57194619278
0000-0001-7065-3726
Don State Technical University
Manzhilevskaya
Svetlana
smanzhilevskaya@yandex.ru
Rostov-on-Don, Russian Federation
Dust atlas of construction works in point-pattern housing development
With the development of megacities, active construction is becoming a key factor in the deterioration of atmospheric air quality due to the release of fine particulate matter, such as PM0.5–PM10. These particles pose a significant environmental risk. Given the increasing demand for dense urban development, issues of air purification and environmental stability are coming to the fore. A thorough understanding of the physical and chemical characteristics of dust is fundamental to developing and implementing dust protection measures on construction sites, including the selection of suitable dust collectors. A new approach has been developed for the analysis of dust particles generated by construction work at various urban sites. As part of this approach, a dust atlas has been created that organizes and classifies the diverse types of construction dust, detailing their physical and chemical characteristics. The atlas is based on a unique methodology that enables the identification and description of the main properties of each type of dust encountered during construction operations. Each type of dust studied in this research was assigned its own specification, which includes both the analysis methodology and the identified characteristics of the dust. Documentation related to dust testing contains all the necessary information, including the type of dust, the method of data collection, the time of measurement, the materials used, and the results of dust analysis. For the study, dust samples were taken from the air during construction processes. The study of dust on construction sites revealed that particle size varies significantly, a phenomenon that cannot be attributed solely to measurement errors. These variations in dust particle size can be attributed both to the specific nature of the work performed and to external conditions, including changes in humidity and wind intensity.
1.Introduction
Studies by Lumens & Spi [1] have shown an inextricable link between construction activity and dust formation. Dust particles in the air pose a serious threat to health, so their monitoring requires close attention [2]. At every stage of the construction process, whether it is the initial construction phase, its operation or dismantling, it is necessary to use resources efficiently and ensure personnel protection. An integrated approach to dust suppression plays a key role in ensuring environmental and industrial safety. From the start of preparatory work to the final cleaning of the site, it is critically important to comply with environmental regulations and safety requirements. The introduction of dust control methods is becoming a prerequisite for the protection of both humans and the ecosystem as a whole.
The construction industry makes a significant contribution to urban air pollution. Concreting, stone processing, preparation of building mixes and other operations on construction sites lead to the formation of microscopic dust particles. These particles, ranging in size from PM0.5 to PM10, pose a serious threat to health [3, 4]. They are particularly dangerous for construction workers and residents of the surrounding areas because if they enter the respiratory tract, they can provoke the development of various lung diseases. Loading of materials, excavation, plastering, and delivery of building materials – all these processes exacerbate the problem of air pollution in urbanized areas [5].
In 2016, Deborah Dickerson identified that construction activities, including drilling, excavation, and loading and unloading operations, are a source of significant dust pollution [6]. Ming Hu has established the equivalent risks for office staff and construction personnel during construction activities [7]. In 2017, a scientific group led by Jiang Zuo documented the negative effects of atmospheric dust pollution on the health of both office workers and construction workers [8]. It is necessary to create and use comprehensive monitoring and management methods to ensure the security of workers on construction sites, where dust pollution is widespread [9].
Protecting the population from the negative effects of construction work is becoming a critically important task in modern cities [10, 11]. A team of researchers led by Zezhou Wu has developed innovative ways to control dust on construction sites, which is especially important when building in cramped urban environments [12]. Experiments by a group of scientists led by Qiming Luo have revealed a serious problem: during construction operations, such as mixing concrete, processing it and working with marble, large-scale air pollution occurs [13]. The most alarming situation is observed when cutting bricks – the concentration of fine particles PM2.5 and PM10 reaches values 60–100 times higher than the NAAQS (National Ambient Air Quality Standards) standards [14]. This problem is becoming particularly acute against the background of growing urbanization and increasing urban population density.
The problem of the spread of particulate matter in confined urban spaces has become the subject of close attention from the scientific community [15, 16]. A notable breakthrough in this area was made by a group led by Zhang Yisheng, who applied a combined research method: they combined computer simulations with experiments in a wind tunnel to study the behavior of dust on construction sites [17]. Successful results in solving the problem of air pollution caused by dust particles have been achieved by international scientific teams, including specialists from the USA, China, European countries, Korea, and the UK [18–21]. This innovative approach has allowed for a deeper understanding of the mechanisms of movement of construction dust in dense urban areas, which is especially important for megacities with high population density.
The problem of construction dust control has attracted the attention of many scientists who have proposed various solutions. Thus, a study by Sang-Woo Han and colleagues presented a hybrid model based on receptors for monitoring dust pollution [22]. Studying the characteristics of dust emissions during construction, the Bo Yu team analyzed their time parameters, intensity and concentration [23]. Optimization of the construction site layout using the MOPSO algorithm was proposed in Guowu Tao's work as a way to reduce dust pollution [24]. Special attention was paid to the protection of vulnerable groups of the population – Zachary M. Klaver and co-authors evaluated the effectiveness of HEPA PAF filters for air purification in the homes of elderly people living near construction sites [25].
The danger of construction dust to human health is confirmed by numerous scientific studies [26]. The Matthew Dietrich team has found that the chemical composition of dust particles entering the premises from construction sites poses serious risks to the public [27]. The specialists from the Russian Federation have also been actively studying this problem. A group of Russian scientists, including N. Sergina, D. Borovkov, V. Azarov, and A. Strelyaeva, discovered large-scale environmental violations during point-pattern housing development, especially in the context of air pollution by fine dust [28–31]. In densely populated urban areas, the problem of managing construction sites and controlling dust emissions is acute. The study revealed serious shortcomings in the implementation of anti-dust measures on construction sites.
The lack of a clear pollution control system in dense urban areas requires urgent measures and close attention from responsible authorities.
A deep understanding of the physical and chemical characteristics of dust from construction work is the basis for the development and implementation of dust suppression measures on construction sites, including the selection of suitable dust collectors. Solving this problem requires the development of a new approach to the analysis of dust particles generated as a result of construction work at various sites in the city. As part of this approach, a dust atlas has been created that systematizes and classifies various types of construction dust according to their physical and chemical characteristics.
2.Materials and Methods
Rostov-on-Don is a rapidly developing metropolis. The construction of new buildings and other structures is always an integral part of urban infrastructure development. Today, a large number of different residential complexes have been built in Rostov-on-Don, and this list is constantly growing. Rostov-on-Don is the largest city in southern Russia and the eleventh most populous city in the Russian Federation. In recent years, the city has experienced an unfavorable environmental situation to breathe polluted air. Air pollution is often observed at construction sites, primarily caused by emissions of inorganic dust. This dust, containing up to 70 % silicon dioxide, is found in various materials such as chamotte and cement, as well as in industrial waste. Dust with a silicon dioxide content of more than 70 % was also found in dinas. There is also an environmental threat at construction sites from suspended particles and nitrogen dioxide released during the construction process. Sources of dust emissions into the atmosphere at construction sites include: construction machinery (e.g., transportation, loading, and unloading of bulk materials); building materials (e.g., gypsum, cement, sand); and construction processes (e.g., cutting gas blocks, mixing plaster, and mortar). The construction site of the 11-floor residential building (Fig. 1) is one of the typical examples of point-pattern housing development in a megacity.
Figure 1. Schemes of the research site: 1–3 – sampling points at the construction site.
This construction site was chosen as a research object because, according to the data from the developed map of the distribution of suspended matter concentrations near point-pattern housing development construction sites in Rostov-on-Don (Fig. 2), it was located in an area with the highest dust levels. Here, dust samples were taken at the construction site during construction. The construction dust sampling was carried out during excavation, foundation installation, and bulk materials handling.
Figure 2. Distribution of suspended matter concentrations
near point-of-construction facilities in Rostov-on-Don.
The study used two main devices to collect samples: a portable particle counter, Handheld 3016 by Lighthouse Worldwide Solutions (Medford, OR, USA), featuring 0.3 µm sensitivity, and a PU-3E/12 electric respirator by Ximko (Moscow, Russia). The respirator was used to detect dust and aerosol levels in the air with AFA VP aerosol filters having an active area of 10 cm2 in both working and residential environments, as shown in Fig. 3.
(a)
(b)
(c)
Figure 3. Devices used in sampling: (a) Handheld 3016 particle counter;
(b) PU-3E/12 electric respirator; (c) AFA aerosol filters by Krezol (Voronezh, Russia).
Dust particles filtered from various zones of the construction site were mixed to form a representative sample. The excess volume of the selected material was intensively homogenized, after which it was reduced to the required amount, thereby increasing the reliability of the analysis.
During sampling, special AFA filters were used to monitor aerosol particles in gaseous media and the atmosphere. Calibration and verification of measurement accuracy were carried out using the WIN-SFV32 v1.0 software package integrated with an electronic respirator. The filter elements were made using PVC-based fibers. The IRA-10 holders manufactured by the Russian company Krezol in Voronezh were used as retaining structures. The analysis of the collected samples was carried out using the methods for determining the concentration of pollutants in the air of the Russian Federation. According to the GOST R 58577-2019 standard [32], the sampling time for air samples to measure instantaneous concentrations at each control point was set to 20 minutes. The pretreatment of AFA type filters included their daily exposure in a desiccator containing calcium chloride as a moisture absorber. The filters were kept in open packages. After that, each sample was extracted using tweezers and weighed on a scale with a precision of 0.1 mg. The obtained weight data and the identification number were recorded on a paper package, into which the filter was then placed. An open filter holder was used to determine the dust concentration in the air. A filter, previously weighed to a constant weight, was placed in it. The prepared filters were stored in a room with a normal temperature, where there was no possibility of contamination. Before carrying out the weighing procedure, the filters delivered from the sampling site were left in the laboratory room for 24 hours. The process of weighing the dried samples was carried out several times until the weight became stable. During the dust particle sampling process, key characteristics of the air-dust mixture were measured, including humidity (%), temperature (°C), and flow rate (cm/sec).
The dust concentration was determined by the following formula
(1)
where is the mass of dust trapped on the filter, determined by the gravimetric method as the difference between the mass of the filter after sampling and that of the clean filter before sampling, in milligrams; is the volume of the sample of air (gas) passed through the filter, in cubic meters.
The value of each sample was adjusted to normal conditions and calculated using the following formula
(2)
where is the volume of the selected gas emissions sample, m3; is the atmospheric pressure during sampling, kPa; is the gas temperature at the aspirator during sampling, °C; is the volume of the selected dust sample, m3; is the vacuum at the aspirator, kPa.
During sampling, the environment was characterized by moderate temperatures around 25 °C, with relatively dry air showing 30–40 % humidity. A steady 5-meter-per-second breeze was present, while no rain or artificial moisture sources were detected throughout the duration.
The selected samples were sent to a scientific laboratory to determine the physical and chemical characteristics of construction dust according to the following parameters: morphological analysis of particles, dispersion, specific surface area, density (bulk, free-state, and dense-packing densities), surcharge angle, adhesion, abrasiveness, electrical resistivity, chemical composition, hygroscopicity, and wettability. The devices used to determine the physical and chemical characteristics of construction dust are shown in Fig. 4. Table 2 shows the device specifications.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
Figure 4. Devices used to determine the physico-chemical characteristics of construction dust:
(a) TDS/pH-metr PH-986 analyzer by Hanna instruments (Germany); (b) MBS-10 stereoscopic microscope by LZOS (Moscow, Russia); (c) Versa 3D DualBeam electron-ion (bi-beam) microscope by FEI Company (Hillsboro, OR, USA); (d) PSKh-10 instrument by PSH (Moscow, Russia); (e) Pycnomatic Evo gas-weighing balloon by POROTEC (Germany); (f) SSL1 orbital shaker by Stual (Germany); (g) SWТ-3М density analyzer by Emerging technologies corporate group (Russia); (h) ALC-80d4 digital weighing scale by Acculab (USA); (i) 80-2S sedimentator
by Armed (Russia); (j) UT58B multimeter by UNI-T (China).
The process of studying the physical and chemical characteristics of construction dust took place in the following sequence.
Morphological analysis of construction dust particles was performed using an MBS-10 stereomicroscope equipped with a photodetector, which made it possible to obtain images magnified 200–2000 times. The resulting photographs were processed using the "Dust 1" software package, which made it possible to calculate the area occupied by the particles and determine their geometric shape based on these data. This technique relies on microscopic examination and photographic recording of dust particle sizes, followed by digital processing. The pH level in the dust samples was measured using a TDS/pH-meter PH-986 analyzer, which can measure pH and detect mineral particles.
The Versa 3D scanning electron microscope, which allows for detailed elemental analysis, was used to analyze the chemical state of construction dust. Using the software "STATISTICA 12.6," the data obtained during the analysis are visualized. The use of scanning transmission electron microscopy technology in combination with a suite of detectors (ETD, CBS, STEM) in high vacuum conditions made it possible to study the chemical elements in dust particles in detail and obtain their clear, highly detailed images. The mass percentage of component B for each chemical element was also determined.
The dispersion of construction dust was studied using a logarithmically normal distribution [33, 34]. Both theoretical models and experimental data were used to describe the characteristics of dust particles. In the presented results, the key parameters were the mass fraction percentage (g) of particles and their median diameter measured in microns. It is important to note that for cases of a logarithmically normal distribution, it is necessary not only to specify the median diameter of the particles but also to include the value of the standard deviation of the diameters
(3)
where particles with sizes and represent the threshold values at which the total mass of small fractions reaches 16 % and 84 % of the total mass of the dust suspension, respectively. These patterns have been confirmed by studies [35, 36].
The specific surface area indicator (cm2/g) was determined using a PSKh-10 instrument. This indicator characterizes the specific surface area of the material, expressed in square centimeters per gram. The measurement is based on recording the time interval, during which a given amount of air passes through a sample of material.
The Pycnomatic Evo gas-type pycnometer was used to determine the density (kg/m3). It is important to determine the mass-volume characteristics of construction dust. One of the key parameters is bulk density, an indicator that reflects the ratio of the mass of a substance to the space it occupies, including voids between individual elements. Measurements are carried out using two methods. The first method involves determining the density of the material in its free state ( kg/m3), where the sample is simply filled into a measuring container. The second method involves pre-compaction of the substance using special equipment – a laboratory SSL1 orbital shaker – which makes it possible to obtain the densest packing of particles ( kg/m3).
The surcharge angle ( degrees) of construction dust was measured using a SWТ-3М density analyzer. When the dust sample is poured, a cone-shaped mound is formed. The phenomenon under study is characterized by a static angle of collapse ( degrees), an indicator that determines the slope between the base and the side surface of the formed figure. This angle was also measured during the experiment.
The breaking strength of the dust layer, adhesion ( Pa), was measured using a special technique with the aid of an ALC-80d4 digital weighing scale. The procedure begins by loading a dust sample into an air intake syringe, where the material is sealed at a pressure of 0.5 bar. The creation of a vacuum is ensured by hermetically closing the syringe. The breaking force ( g) is determined at the moment the integrity of the dust layer is violated during the reverse movement of the piston. A quantitative estimate of the tensile strength of the layer ( g/cm2) is calculated using an appropriate mathematical expression that takes into account the experimentally obtained data
(4)
where is the weight of the device with dust particles, g; is the transverse square of the dust layer at its cut-off point, cm2.
Information on the classification of dust in construction according to its adhesion properties is shown in Table 1.
Table 1. Adhesion degrees of construction dust.
Adhesion degree
The breaking strength, Pa
Non-stick
˂60
Baseline
60–300
Average
300–600
Strong
600
A special technique utilizing a steel capsule is employed to measure the coefficient of abrasiveness, which characterizes the ability of dust to abrade materials. The experiment is based on determining the difference in weight of the test container before and after exposure to dust particles. The testing process comprises several stages: first, the test container with a screw cap is weighed using an ALC-80d4 digital scale, then the dust sample is filled into it. Next, the container is placed in a laboratory 80-2S sedimentator, where, during rotation, mechanical interaction occurs between the dust particles and the inner surface of the container. The final weighing enables the recording of a decrease in mass of the steel container, based on which the desired dust abrasiveness index is calculated using a specific formula
(5)
where is the reduction of capsule weight, kg; is the constant that is established based on comparison with known materials that have the greatest similarity.
A special technique was used to determine the electrical resistivity (Ω×m) of dust particles. The UT58B multimeter was used to measure current and resistance in an electrical circuit. At the first stage, the base resistance between the copper conductors was recorded. The experiment was carried out with controlled temperature and voltage parameters. The key point was to find the distance between the conductors, at which the circuit was closed. After that, a sample of dusty material was inserted into the point, where the circuit was closed, and the resistance measurement procedure was repeated to obtain new measurements taking into account the influence of dust. After that, the electrical resistivity of dust particles was calculated using the appropriate mathematical expression.
After that, the electrical resistance of dust particles per unit volume was calculated using the appropriate mathematical expression
(6)
where is the dust resistance, Ω; is the conductor square, m2; is the gap separating a pair of electrically conductive copper elements, m; is set voltage, V; is the electric current intensity, A.
Special measurements were conducted to study the ability of dust to absorb atmospheric moisture. The process involved sequential weighing of samples: first in a completely dry state, and then with a gradual increase in ambient humidity. The most important parameter of the study was the equilibrium humidity of the dust (%), which indicates the percentage of moisture contained in a substance at a given relative humidity (%). This key indicator was calculated for each sample after all measurements using a special formula
(7)
where is the volume of dust particles that have reached the point of equilibrium in moisture saturation, g; is the weight of dried dust particles, g.
This method made it possible to study in detail the hygroscopic properties of dust particles – their ability to absorb water from the environment.
The ability to control pollution through humidification and wet dust collection largely depends on the wettability (Wet, %), which characterizes the interaction of particles with water. The film flotation method is used to measure this characteristic. The procedure includes several steps: first, identical amounts of dust samples are weighed, which are then placed in an aqueous medium. After light mixing, a part of the material settles. The final stage consists of filtration, drying, and weighing of the settled particles. The final wettability index is calculated as the ratio of the mass of the sediment to the mass of dust initially introduced. This parameter is crucial in assessing the effectiveness of hydraulic removal of dust pollution. Experimental measurements make it possible to classify dust particles according to their wettability. When 80–100 % of the particles settle, a high level of wettability is observed. An intermediate value in the range of 30–80 % indicates an average degree of interaction with moisture. If the amount of settled particles does not exceed 30 %, this indicates a low wettability of the dust.
3.Results
The dust particles produced during the construction of point-pattern development, not exceeding 150 microns, are divided into several categories.
The smallest elements belong to medium-dispersed particles of 0.5–10 microns in size, which have specific intermediate properties. The larger fractions are represented by fine dust (10–50 microns), which can be viewed with low magnification under a microscope due to its slow settling. The largest particles belong to coarse dust (50–150 microns) – they are easily distinguishable to the naked eye and are characterized by rapid deposition in the air. This four-step classification covers the entire spectrum of dust pollution encountered during construction work.
Microscopic studies have shown interesting features of construction dust. Its particles are characterized by solidity and do not form clusters. They stand out for their black color and hardness, and their surface is distinguished by its brilliance. Externally, these opaque elements resemble stone fragments with pointed edges.
Dimensional characteristics make it possible to divide dust particles into categories. Electron microscopy is necessary to study the smallest particles (less than 0.1 microns) that constantly perform Brownian motion. However, larger particles (0.1–20 microns) can be viewed using a conventional microscope; this fine dust is characterized by slow settling.
The structure of dust particles shows a significant variety of shapes. The formation of construction dust is dominated by particles with a rough, irregular structure, which is typical for crushed solids, as shown in Fig. 5.
(a)
(b)
Figure 5. Images of dust particles obtained by microscopic scanning:
(a) cement dust; (b) gypsum dust.
However, it is also possible to detect elements in the dust that have a fibrous or lamellar structure due to their crystalline nature [37].
The morphological analysis of construction dust helped to distinguish three main categories of particles, differing in their spatial characteristics. Some of them are plate formations with predominant sizes in two planes. Another type includes particles with a uniform size distribution along all axes – they can have the shape of both ideal and deformed spheres or polyhedra. It is interesting to note that when such particles combine into larger formations, the resulting clusters exhibit significant morphological diversity. The latter category includes one-dimensional structures, which are elongated objects represented by fibrous, needle-like, and prismatic particle shapes.
Depending on the production method, the particles acquire different geometries. Grinding creates pointed elements, while attrition forms rounded edges. The most dangerous materials are those with cutting edges, whether it is hard quartz, glass, or metal dust. Plastic substances like clay, plaster, and cement carry less risk due to their soft structure.
A whole range of oxide compounds can be detected in the composition of the dust generated during the construction of point-pattern housing developments. It is based on substances such as sodium and potassium oxides, as well as sulfur compounds in the form of SO2 and SO3. A significant proportion is occupied by metal oxides – iron (Fe2O3), manganese (MnO), magnesium (MgO), and aluminum (Al2O3). In addition, phosphorus-containing components are present in the form of P2O5, silicon-containing components are SiO2, and calcium compounds are CaO.
After analyzing the results obtained from studying the physical and chemical characteristics of construction dust from point-pattern housing developments in the laboratory, a compact dust atlas was created that systematizes dust particles of various sizes that occur in the construction industry. An individual specification has been compiled for each type of dust pollution, containing detailed information in tabulated form, shown in Figs. 6 and 7.
Figure 6. Specification of suspended particles formed during cement production and processing.
Figure 7. Specification of suspended particles formed during welding of the building frame.
The documentation includes information on sample collection methods, time parameters, materials involved, and a detailed analysis of dust characteristics. An important part of the project was the formation of a classifier of construction dust with a detailed description of its chemical and physical characteristics, as well as the methodology for their determination. All data are structured as a single information complex with a simple and intuitive navigation system.
Based on a comparative analysis of the data obtained in Rostov-on-Don and the data presented in the works of researchers [7, 14, 17, 18–21], it can be concluded that studies of the morphological and chemical parameters of dust from construction activities are often scattered. There is no systematic approach to capturing and structuring data on dust pollution, nor is there a consistent application of this data in practice to develop design and technical solutions for controlling pollution on construction sites for future construction projects. The advantage of the proposed system for determining dust pollution parameters on a construction site is its unified approach, as areas of concentrated development have their own climatic characteristics, and a dust atlas must be developed for each specific construction project.
4.Discussion
When participating in tenders and contractual prices for contractors involved in point-pattern housing development can gain significant advantages over competitors by applying data from the dust atlas of a model of a construction site or developing a dust atlas for a specific construction project. This can be achieved by including rational methods in projects of protecting the air environment from pollution and competent organization of construction work that minimizes the negative impact on the environment, knowing the list of works to be carried out on the urban area construction site and what building materials and mechanisms will be used [38].
Rationally selected dust collecting equipment helps not only to reduce costs but also to increase the profitability of point developments by reducing the environmental costs of combating and cleaning the territory and atmospheric air of the urban environment from dust pollution from point-pattern construction. The selection of dust collecting equipment requires a detailed analysis of the polluting components and their characteristics. Before installing a new dust collection system, it is important to conduct a comprehensive survey of the area, where point-pattern housing development will be implemented, including measurements of background concentrations of harmful substances, analysis of dust dispersion, assessment of temperature conditions and humidity levels, as well as dust pollution that will be generated during construction work.
It is difficult for an inexperienced contractor to independently choose the optimal solution that takes into account both the economic component and the cleaning efficiency. The physical and chemical characteristics and volume of pollutants directly affect the technical requirements for the equipment to be installed.
The proposed methodology for developing a dust atlas that takes into account the characteristics of dust for the construction of a specific point development facility will make it possible to optimize and control dust emissions at the construction site of an urban area located near the construction industry. Manufacturers often overestimate the efficiency of dust collection systems, especially when they claim performance above 98 %. It is necessary to conduct a full analysis of construction work with respect to dust before evaluating the declared characteristics of cleaning equipment and analyzing manufacturing companies' statements about their effectiveness. It is important to keep in mind that equipment testing is usually carried out on typical dust in the laboratory, so the actual efficiency may vary significantly when working with particles of different sizes and densities, as well as at different temperatures and humidity conditions.
There are many criteria to consider when choosing a cleaning system. Humidity parameters, temperature conditions of the gas environment, as well as spatial constraints for equipment installation, play a key role. It is necessary to take into account the consumption of water resources and wastewater disposal methods. The nature and characteristics of the pollutant are essential, including the resistance of particles to air flows, their dimensions and density in the medium. The difference between 99 % and 99.9 % efficiency indicators is minimal. However, if we consider this difference from the point of view of the ability to suppress and reduce the concentration of dust pollution, then the difference can be tenfold. When choosing equipment, its cost and installation location play a key role. These criteria are closely linked and require integrated assessment. In conditions of limited space, it is often necessary to give preference to compact but expensive installations, although there are equally efficient and more economical alternatives of a larger size. The specifics of the location of the facility also affect the choice – for hard-to-reach areas and cramped construction sites, more advanced and expensive equipment may be needed. There is no universal solution – each case requires individual consideration of all parameters. Making the best decision involves a thorough analysis of both technical characteristics and economic feasibility. It is necessary to study all aspects in detail, since the obvious choice at first glance may not be the most rational.
Choosing the most cost-effective dust control equipment requires an analysis of certain economic and technical indicators.
Equipment utilization rate shows the ratio of the time of the actual operation of the machine for a certain period of time to the duration of this period
(8)
where is the actual operation time of the dust control equipment on the construction site, months; is the overall time spent by the equipment on the construction site.
The value of the equipment utilization rate for periodically used equipment in technological operations ranges from 0.05 to 0.1. The continuously operating installations have since part of the time is spent on maintenance and repair work. Under these conditions, the choice of equipment will depend on the actual parameters of the abrasiveness of the dust which will be deleted by this equipment.
Profitability of equipment is the ratio of the useful return of the equipment for a certain period to the total cost of the equipment for the same period
(9)
Let us consider the economic effect of the introduction of a wet dust collector at a construction site. Prior to its installation, the company incurred significant costs. They included expenses for dust control: regular humidification, cleaning, cleaning and updating of work clothes. In addition, the company was losing funds due to frequent sick leave. All these costs form a basic amount of money that can be saved after installing the dust collection equipment with the technical characteristics of dust collection that correspond to the data of the analysis of the physical and chemical characteristics of the dust, which will be deleted by this equipment.
The total costs associated with the operation and maintenance of dust collection systems can be calculated by this expression
(10)
where is the cost of consumed electricity; is he cost of consumables (for example, filter media that is periodically replaced, water); is the cost of equipment repair, payment of maintenance personnel for repairs, tools necessary for maintenance during operation of the equipment; is the costs of depreciation that reduce the cost of equipment due to its wear and tear.
When choosing efficient equipment, The rational selection of equipment, taking into account the data of the dust atlas, reduces these costs.
Assessment of the financial benefits of upgrading the facility using technical means
(11)
The total economic benefit accumulated over the entire period of operation of the technical means is
(12)
The assessment of the economic efficiency of the equipment reflects the ratio between the total operating costs and the initial cost of the technical means and takes into account all costs during use
(13)
where is the cost of buying or renting equipment.
The equipment cost coefficient is the percentage ratio of the cost of the machine to the amount of costs
(14)
As the service life of increases, there is a significant increase in the indicator, reflecting operating costs, which can reach values from 50 to 100. This leads to the fact that the share of depreciation charges in the structure of total expenses shows a tendency to decrease.
Based on the collected information on the physical and chemical characteristics of construction dust, presented in a dust atlas, the calculation and selection of optimal dust collection equipment for a point-pattern housing development facility – an 11-storey residential complex – was carried out. Tables 2 and 3 show the initial parameters and the final calculation results. The analysis included a comparison of several installations with identical cleaning and performance indicators, shown in Fig. 8, but differing in operational characteristics and maintenance costs. The information obtained on the dust composition made it possible to adjust the calculations and optimize the choice of equipment, taking into account technical and economic factors.
(a)
(b)
Figure 8. Dust collecting equipment for the construction site:
(a) vehicle-mounted water mist cannon atomizer sprayer Fog Elefante 70 by INDROBASE (Italy);
(b) WLP 500 dust suppression system by WLP (Italy).
Table 2. Initial data and parameters for assessing the economic feasibility of using dust cleaning systems.
No.
Initial data
Units
Fog Elefante 70
WLP 500
1
KU
USD
1 323.81
1 632.45
2
UR
USD
1 224.34
1 224.34
3
tOP
Months
6
6
4
CEN
USD
271.39
46.93
5
CER
USD
336.69
73.46
6
tACTUAL
Months
4
4
7
CCS
USD
38.26
20.41
8
CDE
USD
12.24
26.12
Table 3. The results of the calculation of the feasibility study.
No.
Indicators
Fog Elefante 70
WLP 500
1
KU
0.67
0.67
2
CTOTAL
658.59 USD
166.92 USD
3
P
1.85
7.3
4
E
563.19 USD
1 065.17 USD
5
KEF
0.49
0.1
6
KEC
201
977
When choosing dust-collecting equipment, the key role is played by its efficiency indicators, including productivity and durability, which in turn depends on the characteristics of the dust emissions, with which it operates. A rational decision on the purchase of equipment can be made by analyzing the total cost of transportation, maintenance, and repair during the entire period of use. An individual calculation of operating costs for a specific case allows us to assess the economic feasibility of introducing equipment into the production process and make the best choice in terms of financial costs.
A study of previous work on the formation of dust particles in construction sites [4, 39] revealed both common features and discrepancies with the data we obtained. Our work focused on a detailed study of the chemical composition and physical properties of dust pollutants that occur during construction work. The main goal was to find effective methods of controlling dust emissions to protect the ecology of urban airspace and protect the health of residents whose homes are located near point-pattern housing developments. In our study, we did not limit ourselves to the chemical analysis of construction dust but also studied in detail its dispersed characteristics. In point-pattern housing developments, this analysis technique shows the most accurate results in determining the properties of dust particles, surpassing traditional methods for estimating dust emissions on construction sites. Of particular value is the fact that we measured the concentration of dust, its chemical composition, density, surcharge angle, adhesion, abrasiveness, electrical resistivity, hygroscopicity, and wettability for each individual type of construction work. Thanks to this, the created dust pollution atlases can be effectively used in a variety of situations – from the construction of new buildings to the reconstruction of existing facilities and even during repair activities. In this scientific work, the main focus was on the study of particulate matter, although the analysis of silica particles is equally important in assessing construction emissions. It is noteworthy that the degree of harmful effects of dust pollution on construction sites is largely determined by the concentration of silica in the dust. It is worth noting that the conducted research is not without certain drawbacks, and the study of the silica component remains a promising area for further scientific research in the field of construction dust pollution.
5.Conclusions
The physical and chemical characteristics of construction dust, including its size, shape, composition, and electrical charge, determine the degree of its impact on the environment and human health. Fine particles ranging in size from PM0.5 to PM10, which are formed during construction work, are particularly dangerous. Their influence extends to both workers and residents of the surrounding areas. The ability of particles to stay in the air for a long time and penetrate deep into the respiratory tract directly depends on their size. This parameter also determines their chemical activity and electrostatic properties. Therefore, measuring the size of dust particles on construction sites is crucial for assessing potential harm to health and developing protective measures.
In modern cities undergoing rapid development, it is critically important to control air quality, especially in the context of construction activities. Throughout the entire life cycle of a building, from construction to dismantling, there is a constant impact of dust pollution on the environment. The scientific community, both internationally and locally, pays increased attention to environmental degradation caused by dust pollutants. When designing new facilities, it is necessary to take into account research data on parti
10.34910/MCE.141.8
69.058.4
point-pattern housing development
construction dust
dust atlas
dust protection measures
https://engstroy.spbstu.ru/article/2026.141.8/
RAR
RUS
14109-14109
57215535887
Lomonosov Moscow State University
Klochkov
Michael
m.klo4koff@yandex.ru
Moscow, Russia
57189646401
0000-0001-9148-2815
Volgograd State Technical University
Pshenichkina
Valeria
vap_hm@list.ru
Volgograd, Russian Federation
7202396806
0000-0002-7098-5998
Volgograd State Agricultural University
Nikolaev
Anatoliy
anpetr40@yandex.ru
Volgograd, Russia
57170472500
0000-0002-1027-1811
Volgograd State Agricultural University
Klochkov
Yury
Klotchkov@bk.ru
Volgograd, Russia
55235780600
0000-0001-9234-7287
Volgograd State Agricultural University
Vakhnina
Olga
ovahnina@bk.ru
Volgograd, Russia
Comparison of single-field and three-field fem in nonlinear shell calculations
On the basis of physical equations of deformation theory of plasticity using Kirchhoff–Lava hypothesis, matrix dependences between columns of forces and moments and columns of deformations and curvatures of the shell midface are determined at the loading step. As a finite element, a quadrilateral fragment of the shell midface with nodal unknowns in the form of: increments of displacements and their derivatives; increments of deformations and increments of curvatures; increments of forces and increments of moments were used. To approximate the required quantities, the following expressions are adopted: bicubic functions with elements of Hermite polynomials of the third degree for displacements; bilinear functions for deformation and force parameters. To obtain the stiffness matrix of the finite element, the nonlinear Lagrangian functional on the loading step was used with an additional condition: the real work of the difference of forces determined using their direct approximation and using approximating expressions for displacements, on deformations and curvatures of the loading step must be equal to zero. Minimisation of the functional by nodal unknowns provides three systems of equations, the solution of which determines the stiffness matrix of the finite element used to calculate the displacement fields. The force and deformation parameters at the discretisation nodes of the shell are determined from the displacements found. Case studies show the effectiveness of using a three-field finite element method (FEM) technique compared to using FEM in the displacement method formulation (single-field technique).
1.Introduction
Definition of the object of study. Structures consisting of shells and their fragments are now increasingly used in various fields. These include hangars, warehouses, domes and slabs, tanks, bunkers, cisterns, pipelines and others. The worldwide trend aimed at significant reduction of material intensity of systems and objects actualises the problem of determining the stress-strain state (SSS) of structures in the form of shells and their fragments in a physically nonlinear formulation.
Assumption within the regulated limits of the plastic stage of the applied material of structures allows to reduce the overall material intensity of structures, including those consisting of shells.
Literature review. The developed theory of solid body deformation [1–4] turned out to be theoretically unrealisable in the practice of engineering calculations of real structures, which led to the development of numerical methods for solving the equations of solid body deformation mechanics [5–9]. At the present stage of development of structural mechanics and computer science, the main tool for investigating the SSS of shell structures beyond the elastic limit is numerical finite element method (FEM). In spite of the considerable volume of publications on this subject [10–15] and the availability of foreign (ANSYS, ABAQUS, NASTRAN, etc.) and domestic (PRIIS, LIRA, etc.) finite element computational systems, the problem of finding the most optimal formulations of the FEM for the calculation of shell structures in a physically nonlinear setting remains quite relevant. It is known that the FEM in the form of the displacement method is the most widespread at present, but it does not lack the disadvantages associated with the use of only one field of unknowns – the displacement field. The mixed variant of the FEM with kinematic and force fields of unknowns [16–23], as well as the FEM variant with three fields of unknowns [24, 25], are becoming the most promising.
Purpose and objectives of the study. In this paper, the three-field variant of the mixed FEM is applied to the calculation of shells under elastic-plastic deformation and the finite element solutions obtained on its basis are compared with the solutions obtained using the FEM in the formulation of the displacement method in a physically nonlinear setting.
2.Materials and Methods
In order to realise the three-field variant of the mixed FEM in a physically nonlinear formulation, it is first of all necessary to formulate the corresponding nonlinear three-field functional. For this purpose, we introduce the following matrix notations: is matrix-string of longitudinal forces and bending moments and their increments at the loading step, respectively; is matrix-string of deformation increments and curvature increments at the midpoint of the shell structure surface at the loading step; is matrix-string of step increments of displacement vector components; are matrix-string of external surface load vector components and their step increments, respectively.
The increments of longitudinal forces and increments of bending moments at the loading step can be expressed through the increments of deformation and increments of curvature using the following relations:
(1)
(2)
where and are matrices obtained by numerically finding definite integrals; are the increments of the contravariant components of the stress tensor at the loading step.
The plasticity matrix included in (1) and (2) is composed on the basis of the relationships of the deformation theory of plasticity [4], represented in a curvilinear coordinate system by the expression:
(3)
where are components of the deformation deviator; are intensity of deformations and stresses; is stress deviator; are first invariants of strain and stress tensors; are covariant and contravariant components of the metric tensor.
The increments of deformations in an arbitrary layer at a loading step are determined by differentiating (3) in the following general form:
(4)
The partial derivatives included in (4) were determined by the relations:
(5)
where is modulus of elasticity; is coefficient of transverse deformation.
The derivatives of the ratio of strain and stress intensities included in (5) are determined by the expressions:
(6)
where are tangent and secant modules of the deformation diagram;
Using (4), (5), (6) a matrix dependence is formed:
(7)
where
Matrix determined by matrix inversion
Taking into account the above, the matrix relationship is written:
(8)
where
Taking into account (1) and (2), the following matrix relation can be composed as follows:
(9)
where
If we use a four-node fragment of its midface [24] with nodes as a discretisation element of the shell structure, the increments of longitudinal forces and increments of bending moments at the loading step can be expressed through their nodal values by means of bilinear relationships:
(10)
where are local coordinates used to organise the procedure of numerical integration by Gauss quadrature;
Here, is understood as or On the basis of (10), a matrix dependence can be compiled:
(11)
where is a quasi-diagonal matrix, on the main diagonal of which the row matrices
Taking into account the notations introduced above and (1)–(11), the nonlinear mixed functional can be written in the following form:
(12)
The column of increments of deformations and curvatures of the medial surface of the shell structure included in (12) can be expressed similarly to (11) through their nodal values:
(13)
and can be represented by the Cauchy relations for thin shells [26] by a matrix product:
(14)
The column of step increments of the components of the displacement vector of a point of the centre surface of the shell structure can be interpolated through the nodal values of the component increments by means of products of Hermite polynomials of the third degree:
(15)
where is a quasi-diagonal matrix containing matrix-rows of polynomial Hermite functions; and are columns of kinematic nodal unknowns at the loading step in local and global coordinate systems, respectively, and is the transition matrix from column to column
The relation (14) taking into account (15) will take the form:
(16)
where
Here, means or and and are curvilinear global coordinates.
The functional (12) taking into account (8)–(11) and (13)–(16) can be transformed to the form:
(17)
For convenience of further calculations, we introduce the following matrix notations:
(18)
The functional (17) taking into account (18) can be written in the following form:
(19)
By successively minimising (19) by and we can obtain the following system of matrix equations:
(20)
To solve the system (20), we can use the substitution method. For this purpose, from the first and second equations (20), it is necessary to express the force and deformation step nodal unknowns:
(21)
By substituting (21) into the third equation (20), the following matrix equation can be obtained:
(22)
or in a more convenient form:
(23)
where is the stiffness matrix of the used four-node discretisation element of the three-field variant of the mixed FEM at one of the successive loading steps; is the column of step forces; is the Newton–Raphson correction at the loading step.
To obtain the stiffness matrix of the finite element at the loading step, a numerical integration procedure was applied using the Gauss method for the area of the mid-surface and the Simpson formula when integrating over the shell thickness.
The global stiffness matrix of the shell structure is composed of a four-node discretisation element by means of an index matrix formed according to the accepted boundary conditions of the calculated shell [27].
In order to verify the above algorithm for the calculation of shell structures in a physically nonlinear formulation, a comparative analysis of finite element solutions obtained using the developed variant of the mixed FEM with the solutions obtained on the basis of the FEM in the formulation of the displacement method was performed.
3. Results and Discussion
Example 1. As an example, a fragment of an elliptical cylinder made of duralumin alloy with the ratio of ellipse parameters of cross-section = 5, loaded with internal pressure of intensity = 6·10–3 MPa, was calculated. The calculation scheme of the shell is shown in Fig. 1. The following initial data were used: = 1.5 m; = 0.3 m; = 0.01 m; = 0.01 m; = 7.49·104 MPa; = 0.32. The deformation diagram was assumed as a two-linked broken line defined by the formula:
where
Figure 1. Calculation diagram of an elliptical cylinder.
The calculations were performed in two variants: in the first variant, the above three-field mixed FEM algorithm in a physically nonlinear formulation was implemented; in the second variant, the FEM algorithm in the formulation of the displacement method was used. The results of the variant calculations are presented in tabular form. The tables show the numerical values of normal stresses in the rigid embedment and at the free end of the shell, as well as the values of bending moment (for the first variant of calculation) when varying the degree of refinement of the discretisation grid and the number of loading steps.
Tables 1–3 present the results of the first variant of calculation at successive densification of the mesh of nodes 41×2, 51×2, and 61×2 depending on the number of stages of successive loading.
The selected design scheme allows to calculate the values of physical bending moment in the rigid embedment (Fig. 2):
Figure 2. Section of the shell by the plane ZOY.
It is also obvious that the bending moment at the free end of the elliptical cylinder, as well as the stresses, must be equal to zero.
The rightmost column of Tables 1–3 shows the above-mentioned analytical values of the controlled strength parameters of the shell SSS.
Table 1. Values of controlled SSS parameters at 41×2 node grid.
Point coordinates, y, m; z, m
Stress σ, MPa, moment, M22, N·m
Number of loading steps
Analytical solution
22
52
82
102
0.0;
0.3
347.3
347.5
347.6
347.6
–
-346.7
–347.1
–347.1
–347.1
–
70.74
70.55
70.22
70.16
70.20
1.5;
0.0
–0.192
–0.190
–0.190
–0.191
–
–0.137
–0.136
–0.136
–0.136
–
0.0687
0.0681
0.0681
0.0685
0.000
0.0005
0.0005
0.0005
0.0005
0.000
Table 2. Values of controlled SSS parameters at 51×2 node grid.
Point coordinates, y, m; z, m
Stress σ, MPa, moment, M22, N·m
Number of loading steps
Analytical solution
22
52
82
102
0.0;
0.3
347.4
347.6
347.6
347.6
–
–346.7
–347.1
-347.2
–347.2
–
70.87
70.36
70.32
70.29
70.20
1.5;
0.0
–0.0708
–0.0682
–0.0679
–0.0683
–
–0.0533
–0.0514
–0.0511
–0.0515
–
0.0273
0.0266
0.0265
0.0266
0.000
0.0004
0.0004
0.0004
0.0004
0.000
Table 3. Values of controlled SSS parameters at 61×2 node grid.
Point coordinates, y, m; z, m
Stress σ, MPa, moment, M22, N·m
Number of loading steps
Analytical solution
22
52
82
102
0.0;
0.3
347.5
347.6
347.7
347.7
–
–346.7
–347.1
–347.2
–347.2
–
71.03
70.50
70.37
70.33
70.20
1.5;
0.0
–0.0295
–0.0298
–0.0299
–0.0297
–
–0.0223
–0.0225
–0.0225
–0.0224
–
0.0119
0.0120
0.0120
0.0120
0.000
0.0003
0.0003
0.0003
0.0003
0.000
As follows from the analysis of the data given in Tables 1–3, the three-field version of the mixed FEM in the physically nonlinear formulation demonstrates stable convergence of the computational process, both when the discretisation grid is reduced and when the number of successive loading stages is increased. In addition, the numerical values of the bending moment in the rigid embedment and at the free end practically coincide with their analytical values, which is also a proof of the correctness and high degree of accuracy of finite element solutions obtained by using the developed three-field mixed FEM in the physically nonlinear formulation.
If the classical FEM formulation of the displacement method is applied to the solution of this problem, the results of finite element solutions will be quite different from the above-mentioned ones. For example, Table 4 shows the results of the FEM calculation of an elliptical cylinder in the form of the displacement method with a 61×2 node grid.
Table 4. Stress values of elliptical cylinder FEM in the form of displacement method with 61×2 node grid.
Point coordinates, y, m; z, m
Stress σ22, MPa
Number of loading steps
Analytical solution
22
52
82
102
0.0;
0.3
304.1
274.6
120.3
276.0
–
–303.8
–274.3
–112.7
–275.8
–
1.5;
0.0
–76.44
–66.17
–140.8
–62.41
–
358.4
323.2
330.2
319.4
–
270.7
250.8
246.4
248.9
0.000
As follows from the analysis of Table 4, there is no convergence of the computational process when the number of successive loading steps is increased. In addition, the stresses at the free end of the shell reach unacceptably high values, although they should be equal to zero.
Obviously, when using the FEM in the formulation of the displacement method in physically nonlinear calculations of shells with significant curvature of the medial surface, a much more significant refinement of the discretisation grid is required. Tables 5–7 show the results of elliptical cylinder calculations with 81×2, 101×2, and 121×2 node grids, respectively.
Table 5. Stress values of elliptical cylinder FEM in the form of displacement method with 81×2 node grid.
Point coordinates, y, m; z, m
Stress σ22, MPa
Number of loading steps
Analytical solution
22
52
82
102
0.0;
0.3
343.9
302.9
369.0
264.1
–
–343.4
–302.2
–370.4
–263.0
–
1.5;
0.0
–66.74
–59.54
–32.91
–56.99
–
278.5
259.7
253.6
248.7
–
213.8
178.8
176.7
156.3
0.000
Table 6. Stress values of elliptical cylinder FEM in the form of displacement method with 101×2 node grid.
Point coordinates, y, m; z, m
Stress σ22, MPa
Number of loading steps
Analytical solution
22
52
82
102
0.0;
0.3
345.0
345.2
344.2
341.6
–
–344.5
–344.8
–343.8
–341.2
–
1.5;
0.0
–47.34
–47.49
–47.21
–46.41
–
227.5
227.7
227.2
225.6
–
114.9
115.2
114.6
112.9
0.000
Table 7. Stress values of elliptical cylinder FEM in the form of displacement method with 121×2 node grid.
Point coordinates, y, m; z, m
Stress σ22, MPa
Number of loading steps
Analytical solution
22
52
82
102
0.0;
0.3
346.3
346.6
346.6
346.6
–
–345.8
–346.1
–346.1
–346.1
–
1.5;
0.0
–37.30
–37.41
–37.43
–37.44
–
145.1
145.6
145.7
145.8
–
69.49
69.74
69.80
69.81
0.000
Analysing the tabulated values of normal stresses in Table 5 shows that for 81×2 node grid, there is also no convergence of the computational process as the number of sequential loading steps increases and the stresses at the free end have unacceptably high values.
For 101×2 node grid in rigid embedment (Table 6), satisfactory convergence of the computational process is observed. However, the stresses at the free end have unacceptably high values.
With a 121×2 node grid (Table 7), the values of stresses in the rigid embedment remain almost unchanged and coincide with the values of stresses in the rigid embedment obtained using the three-field version of mixed FEM (Tables 1–3). However, at the free end, the normal stresses still remain very far from zero values, which requires further refinement of the discretisation grid.
Table 8 shows the calculation results of the elliptical cylinder at 201×2 node grid. As can be seen from the analysis of the tabular data, a steady convergence of the computational process is observed in the rigid termination as the number of successive loading steps increases. At the free end of the shell, the stress values have decreased but still remain quite far from zero values.
Table 8. Stress values of elliptical cylinder FEM in the form of displacement method with 201×2 node grid.
Point coordinates, y, m; z, m
Stress σ22, MPa
Number of loading steps
Analytical solution
22
52
82
102
0.0;
0.3
347.2
347.5
347.6
347.6
–
–346.8
–347.0
–347.1
–347.1
–
1.5;
0.0
–17.44
–17.49
–17.50
–17.51
–
40.28
40.41
40.44
40.45
–
16.31
16.37
16.38
16.38
0.000
In addition, it should be noted that when using the traditional formulation of the FEM in the form of the displacement method, the problem of obtaining the numerical value of the bending moment in the rigid embedment arises. To solve this problem, a graphical method can be applied to calculate the bending moment value from the normal stress epiphysis in the rigid embedment, plotted at fixed points of vertical coordinate along the normal to the medial surface of the shell.
Fig. 3 shows the normal stress epiphysis in the rigid embedment with a 201×2 node grid plotted at 9 node points along the surface normal. For convenience of further calculations, the epyure was divided into elementary figures and the centres of gravity in each figure were found. Then, the forces were calculated as the areas of each of the figures. Moments were calculated as products of forces by the corresponding arms
Figure 3. Normal stress diagram in a rigid termination.
The resultant moment can be obtained by summing the moments :
After performing the above calculations, the resultant torque is obtained as follows:
The calculation error was:
Obviously, when building a more detailed stress diagram, for example, by dividing it by height into 17 points, the calculation error can be reduced. However, the error of 0.92 % obtained by dividing the stress diagram into 9 points along the section height is quite acceptable for engineering calculations.
Calculation example 2: A fragment of an elliptical ring with the ratio of ellipse parameters = 6, loaded on the right side with a linear load of intensity = 25 kN/m uniformly distributed along the formations and having a hinged support on the left side, was calculated (Fig. 4). The following initial data were used: = 1.2 m; = 0.2 m; = 0.008 m; = 0.01 m. The physical characteristics of the material and the deformation diagram were taken from the previous calculation example. A reactive force equal to the applied nodal load occurs at the hinge points Thus, the normal stresses at points and must be equal. The equality of the normal stresses at points and can serve as an additional criterion for the correctness of the numerical values of the normal stresses obtained as a result of the solution.
Figure 4. Calculation diagram of an elliptical ring.
The calculations, as in the previous example, were performed in two variants: the first variant used the developed three-field mixed four-node discretisation element; the second variant used a finite element whose stiffness matrix was composed in the formulation of the displacement method. The results of the first variant of the calculation are summarised in Tables 9 and 10. Table 9 shows the values of normal stresses on the inner and outer surfaces of the shell at the points of application of a given load and at the points of hinge support depending on the density of the discretisation grid at a fixed number of loading steps equal to 22.
Table 9. Stress values of the first calculation variant depending on the size of the discretisation grid.
Point coordinates, y, m; t, m
Stress σ22, MPa
Sampling grid
10.34910/MCE.141.9
539.3
three-field finite element method
nonlinear mixed functional
kinematic unknowns
force unknowns
deformation unknowns
https://engstroy.spbstu.ru/article/2026.141.9/
RAR
RUS
14110-14110
0000-0002-0644-2657
Islamic Azad University
Beigi
Mohsen
mohsenbeigi59@gmail.com
Semnan, Iran
Adaptive cost-constrained optimization of concrete mixtures using machine learning-guided genetic algorithms
This study presents an adaptive framework for optimizing high-performance concrete mixtures by integrating machine learning with a genetic algorithm under cost constraints. An experimental dataset was used to train an XGBoost model, which accurately predicts 28-day compressive strength. The trained machine learning model was embedded as the objective function within the genetic algorithm to maximize compressive strength while incorporating cost limitations defined by user-provided unit prices and budget. Unlike most previous studies that treat cost and strength as two separate objectives in multi-objective formulations, this work introduces cost as a constraint and strength as the sole optimization objective, thereby simplifying the decision-making process. To bridge the gap between theory and practice, an Android application was developed. The application enables users to input real-time material prices and budget limits, which are transmitted to a server hosting the machine learning model and genetic algorithm. The server computes optimized mix proportions and returns both the predicted compressive strength and the optimal design to the user interface. The proposed adaptive optimization framework was shown to effectively adjust to market price fluctuations and varying budget scenarios, providing a practical and flexible solution for real-world applications. Furthermore, the single-objective formulation ensures a unique optimal solution, avoiding the complexity of selecting among multiple Pareto-optimal alternatives.
1.Introduction
Concrete is one of the most widely used construction materials due to its versatility, durability, and cost-effectiveness. It is a composite material composed primarily of cement, aggregates, water, and chemical admixtures. Cement acts as the binding agent, holding the mixture together, while aggregates contribute to bulk and significantly influence the mechanical and durability properties of both fresh and hardened concrete. Water facilitates the hydration of cement and affects the porosity, strength, and durability of the hardened material. Chemical admixtures are employed to regulate physical properties and improve workability and performance [1, 2].
The 28-day compressive strength of concrete is a critical performance indicator in both research and practice. It is affected by multiple factors including mix proportions, water-to-cement ratio, curing conditions, and the properties of individual components. Accurate prediction of this property is essential for ensuring safety, performance, and compliance with standards [3, 4].
Cost is another significant factor in concrete production. Raw material expenses, such as cement, aggregates, and admixtures, can constitute more than half of the total production cost. Rising material prices, particularly for cement, can substantially impact project budgets. Optimizing concrete mixtures with supplementary materials like fly ash or slag can reduce costs while maintaining or enhancing performance [5, 6].
However, compressive strength and production cost are generally conflicting objectives, since an increase in strength is often associated with higher costs, and vice versa. In many studies, this trade-off has been addressed through multi-objective optimization approaches, where compressive strength and cost are treated as two separate objectives to be optimized simultaneously 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[7–17].
Predicting concrete compressive strength is a complex task due to nonlinear relationships between input variables, such as mix proportions and curing conditions, and output variables. Traditional empirical models often fall short in capturing these interactions. Machine learning techniques, such as extreme gradient boosting and artificial neural networks, have demonstrated high accuracy in estimating compressive strength, effectively managing complex datasets and improving prediction reliability [18, 19].
Integrating genetic algorithms with machine learning models has proven highly effective for optimizing concrete mix designs to achieve maximum compressive strength under specified constraints. Genetic algorithm explores vast solution spaces and identifies optimal solutions by mimicking natural selection. When combined with machine learning models predicting compressive strength, genetic algorithms can fine-tune mix proportions for enhanced performance. Studies have demonstrated that integrating machine learning estimators with genetic algorithms enables optimization of concrete mixtures, balancing strength, cost, and durability under quality constraints [20, 21].
In this study, an experimental dataset was employed to develop a machine learning model for predicting the 28-day compressive strength of concrete. The trained model was subsequently coupled with a genetic algorithm to optimize concrete mixture proportions subject to both technical and economic constraints. In contrast to previous studies, construction cost is not formulated as a secondary optimization objective; instead, it is explicitly imposed as a constraint. This formulation allows market price fluctuations to be flexibly incorporated into the optimization framework. By enabling users to specify material unit prices and a maximum allowable budget, the proposed approach ensures that compressive strength is maximized while strictly satisfying the prescribed cost limitation.
The novelty of this work lies in two main aspects. First, the optimization problem is formulated as a single-objective genetic algorithm, where the objective function is the compressive strength predicted by the machine learning model, while cost and proportional limitations are treated as constraints. This design offers a more flexible and practical framework compared to traditional multi-objective approaches. Second, to facilitate real-world application, an Android application was developed that allows users to input unit prices and budget information. These inputs are transmitted to a server hosting the machine learning model and genetic algorithm, which computes the optimal mixture proportions and returns the results to the application (Fig. 1). This user-oriented design makes the framework not only technically innovative but also highly accessible for practical decision-making in concrete mix design.
Figure 1. Schematic representation of the developed framework.
2.Materials and Methods
2.1.Problem Formulation
The present study addresses the optimization of high-performance concrete mixture proportions using a single-objective genetic algorithm. The objective function (cost function) is to maximize the 28-day compressive strength predicted by a trained machine learning model:
(1)
where represents the output of the machine learning model and the input variables (all in kg/m3) the concrete constituents as defined in Table 1.
Table 1. Concrete components, specific gravities, and constraint ratios.
Component
Symbol
Specific Gravity (kg/m³)
Min Ratio
Max Ratio
Notes / Constraint Type
Cement
X1
3.15
—
—
Part of binder
Slag
X2
2.80
0
0.61
Slag-to-binder ratio
Fly Ash
X3
2.50
0
0.61
Fly Ash-to-binder ratio
Water
X4
1.00
0.23
0.90
Water-to-binder ratio
Superplasticizer
X5
1.35
0
0.13
SP-to-cement ratio
Coarse Aggregate
X6
2.50
1.18
5.62
Coarse-to-binder ratio
Fine Aggregate
X7
2.65
0.35
0.54
Fine-to-total aggregate ratio
The genetic algorithm aims to determine the optimal mixture proportions under a set of general, proportional, and cost constraints.
2.1.1. Volume constraint
The total volume of the concrete mixture must equal 1 m3, enforced using the specific gravities of each component:
(2)
This ensures that the genetic algorithm-generated mixture corresponds to a physically feasible 1 m3 concrete volume.
2.1.2. Ratio constraints
To maintain logical and practical mixture proportions, the ratio constraints listed in Table 1 are imposed [16].
2.1.3. Cost constraint
A user-defined budget constraint is introduced as an innovative aspect of this study. The user specifies the unit price (per kg) for each material and the maximum allowable budget is ensures that the optimized mixture maximizes compressive strength without exceeding the user’s budget.
2.2.Implementation
2.2.1. Framework description
As illustrated in Fig. 2, the proposed framework operates as follows. The user, through an Android application, inputs the unit prices of the concrete constituents (cement, slag, fly ash, water, superplasticizer, coarse aggregate, and fine aggregate) along with the maximum allowable budget. This information is transmitted to a web server via an API. On the server, a machine learning model – trained on an experimental dataset – is hosted to predict the 28-day compressive strength of concrete for given inputs through Simultaneously, a genetic algorithm is implemented on the server, where the output of the machine learning model serves as the fitness function to be maximized. The genetic algorithm searches for optimal mixture proportions while satisfying the volume constraint, ratio constraints (e.g., water-to-binder ratio, slag-to-binder ratio, fly ash-to-binder ratio, coarse-to-total aggregate ratio, fine-to-binder ratio, and superplasticizer-to-cement ratio), and the budget.
Finally, the genetic algorithm computes the optimal values of that maximize the predicted compressive strength while ensuring that all constraints are satisfied. The optimized mix proportions are then returned to the Android application, enabling the user to conveniently view and utilize the results without requiring advanced knowledge of optimization methods.
Figure 2. Framework of the proposed methodology.
2.2.2. Modeling
In this study, a dataset of 425 samples of high-performance concrete was employed for developing the machine learning model. The input features consisted of seven variables – cement, slag, fly ash, water, superplasticizer, coarse aggregate, and fine aggregate – while the output variable was the 28-day compressive strength. The experimental data were originally obtained from the program reported by Yeh [22], in which ASTM Type I Portland cement was used. Aggregate properties were described qualitatively, indicating that the coarse aggregate consisted of crushed natural stone with a maximum size of 10 mm, whereas the fine aggregate was washed river sand with a fineness modulus of approximately 3 mm. This dataset provided sufficient diversity to capture the variability in mixture proportions and their influence on compressive strength.
To incorporate economic considerations, an additional column representing the cost of each mixture was computed using unit prices ($/kg) for all constituents: cement (0.11), slag (0.06), fly ash (0.055), water (0.000024), superplasticizer (2.94), coarse aggregate (0.01), and fine aggregate (0.006). Descriptive statistics for the dataset used in this study are presented in Table 2. The distributions of the input variables compressive strength and cost are shown in Fig. 3, illustrating the range and variability of the experimental data.
Table 2. Descriptive statistics for the concrete dataset.
mean
std
min
25 %
50 %
75 %
max
Cement
265.44
104.67
102.00
160.20
261.00
323.70
540.00
Slag
86.29
87.83
0.00
0.00
94.70
160.50
359.40
Fly Ash
62.80
66.23
0.00
0.00
60.00
120.00
200.10
Water
183.06
19.33
121.80
171.00
185.00
193.30
247.00
Superplasticizer
7.00
5.39
0.00
0.00
7.80
10.30
32.20
Coarse Aggregate
956.06
83.80
801.00
882.60
953.20
1013.20
1145.00
Fine Aggregate
764.38
73.12
594.00
712.00
769.30
811.50
992.60
Compressive Strength
36.75
14.71
8.54
26.23
33.76
44.39
81.75
Cost
72.55
19.05
34.93
59.24
72.07
83.67
166.86
Figure 3. Histograms of input and output variables used in the study.
The correlation map (Fig. 4) displays the pairwise Pearson correlation coefficients between the main concrete mix variables and cost. Strong positive correlations are observed between superplasticizer and cost, compressive strength and cement, and compressive strength and cost, indicating that higher amounts of superplasticizer and cement lead to increased compressive strength and higher overall cost 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[23–26].
Figure 4. Correlation map of concrete mix variables and cost.
Three different machine learning models were considered: extreme gradient boosting [19], multilayer perceptron neural network [27], and random forest [28]. To ensure robust evaluation, a 10-fold cross-validation approach was employed during training. Model performance was compared using the mean squared error metric.
2.2.3. Optimization
Genetic algorithm is an evolutionary optimization technique inspired by the process of natural selection [29]. It operates by encoding potential solutions, known as chromosomes, and evolving them over successive generations to find the optimal solution. In the present study, each chromosome represents a possible concrete mixture, defined by the seven input variables (cement, slag, fly ash, water, superplasticizer, coarse aggregate, and fine aggregate). The fitness of each chromosome is evaluated using the trained machine learning model, which predicts the 28-day compressive strength, while budget and proportional constraints are simultaneously enforced. As illustrated in Fig. 5, the genetic algorithm applies selection to retain high-performing chromosomes, crossover to recombine parent solutions, and mutation to introduce diversity and avoid premature convergence. Through iterative search of the solution space, the genetic algorithm gradually improves the population until the optimal mix proportions that maximize compressive strength without exceeding the budget are obtained.
Figure 5. Schematic representation of the genetic algorithm framework.
2.2.4. Implementation and deployment
After the machine learning model was trained and saved, it was deployed on the PythonAnywhere hosting platform. Along with the trained model, the genetic algorithm code was also implemented on the same host. To enable practical use, an Android application was developed using App Inventor, through which users could provide unit prices of concrete components and the maximum allowable budget. These inputs were transmitted via an API to the server. The Flask framework was employed to handle communication, ensuring efficient transfer of requests and responses between the application and the server. On the server side, the genetic algorithm utilized the user-provided information together with the trained machine learning model to compute the optimal mix proportions The optimization process was carried out with the objective of maximizing compressive strength without exceeding the specified budget. Finally, the computed optimal proportions and the corresponding compressive strength were returned to the Android application through the API, enabling the user to conveniently access and interpret the results.
3.Results and Discussion
< >Modeling Results
Metrics and hyperparameters
Value
max_depth
4
n_estimators
500
Mean Squared Error
17.56
Root Mean Squared Error
4.19
Mean Absolute Error
2.82
R-squared
0.93
< >Genetic Algorithm
Figure 6. Pseudocode of the server-side implementation of the genetic algorithm integrated
with the trained machine learning model and Flask framework.
< >Practical Implementation
Figure 7. Schematic representation of the developed framework integrating
the Android application with the Flask-based server on PythonAnywhere.
In Fig. 8, the essential App Inventor blocks required for developing the Android application are illustrated. Two groups of blocks can be observed. The blocks on the left are responsible for sending the input information provided by the user – including the unit prices of concrete components and the maximum allowable budget – to the server. The blocks on the right handle the response received from the server, which contains the optimized mixture proportions of the seven components within the specified budget. Additionally, these blocks display the corresponding 28-day compressive strength predicted by the trained machine learning model for the optimized mixture design.
Figure 8. App Inventor blocks used in the Android application.
4.Conclusion
In this study, a machine learning-guided optimization framework was developed to design cost-effective and high-performance concrete mixtures. An XGBoost model was trained on an experimental dataset of 425 samples to accurately predict the 28-day compressive strength of concrete. The trained model was then integrated with a genetic algorithm to optimize mixture proportions under adaptive cost constraints, allowing flexible consideration of varying market conditions. Unlike conventional multi-objective approaches that simultaneously optimize strength and cost, this study formulated the problem as a single-objective optimization with compressive strength maximization, while cost was incorporated as a constraint. This approach enables practical adaptability while ensuring budget limits are not exceeded.
To bridge the gap between theory and practice, an Android application was developed using App Inventor. The application allows users to input unit prices of components and defines budget limits, which are then transmitted to a server hosting the machine learning model and genetic algorithm implemented via Flask. The server computes optimized mixture proportions and returns both the mix design and predicted compressive strength to the user interface. This practical implementation demonstrates the usability of the framework even for non-expert users, supporting data-driven decision-making in construction material design.
An important advantage of the proposed framework lies in its adaptability to real-world economic conditions. In scenarios where market prices of materials fluctuate, the system can seamlessly adjust optimization results according to updated unit prices. Similarly, when project budgets vary – ranging from generous allocations to highly cost-sensitive cases – the framework can readily adapt to provide optimized designs that meet the specified financial constraints. This flexibility makes the proposed approach highly practical and valuable for real construction applications where both material costs and budget availability are inherently dynamic.
Moreover, unlike multi-objective approaches that typically generate a large set of non-dominated solutions (Pareto front), which may cause confusion for practitioners in selecting the most suitable mix design, the single-objective formulation adopted here provides a unique optimal solution. This simplifies the decision-making process by directly identifying the best mix design under the specified budget, thereby enhancing the usability of the framework in practical scenarios.
Workability, commonly quantified by slump, is a critical performance requirement for concrete mixtures, as it directly affects placing, compaction, and overall constructability, particularly in high-strength concrete. Future work may extend the proposed framework by incorporating concrete workability as a constraint rather than as an additional optimization objective. This can be achieved by developing a dedicated machine learning model to predict slump based on mixture proportions. During the optimization process, the objective function would remain the maximization of compressive strength, while a minimum target slump value would be imposed as a constraint. Such a constrained optimization strategy would ensure that the optimized concrete mixtures achieve high strength while maintaining adequate workability, thereby enhancing the practical applicability of the proposed framework.
10.34910/MCE.141.10
666.972:004.8
concrete mix optimization
machine learning
genetic algorithm
compressive strength prediction
cost constraint
android application
https://engstroy.spbstu.ru/article/2026.141.10/