Experimental evaluation of the surcharge and loading shape on lateral earth pressure for retaining walls in coarse-grained gravel and sandy soils

Abstract

The present study examines the parameters affecting drift due to soil reaction and the effects of factors such as the loading plate shape and soil type on the performance of retaining walls. The laboratory experiments were conducted with soil particle sizes of 0.249, 1.18, and 15 mm and three foundation shapes: circular, square, and rectangular - all with the same cross-section. The experimental results indicate the effect of soil particle size and shape on the lateral force. Soil with larger particles requires higher surcharge pressure to achieve the same settlement compared to other cases, and this will cause higher horizontal pressure on the wall. For the first tested soil, a settlement of 5 cm occurs with circular, square, and rectangular loading plates at pressures of 484 kPa, 416 kPa, and 594 kPa, respectively. However, a similar settlement occurs in the second soil at pressures of 165 kPa, 154 kPa, and 148 kPa, respectively. A third soil with different loading plates yields negligible pressure for a settlement of 5 cm. It was found that the maximum stress and strain occur in the backfill with the first soil with the maximum particle size and with circular, square, and rectangular plates at 60%, 84%, and 84% of the embankment height from the wall foot, respectively. Moreover, the maximum horizontal stress in this soil with circular, square, and rectangular foundations was estimated as 0.48%, 0.68%, and 0.48% of the vertical stress for a 5 cm settlement, respectively.

Keywords:

retaining wall

lateral force

settlement

backfill

surcharge

1 Introduction

Retaining walls are used to support vertical and inclined slopes of soil along roads and highways, and other locations where lateral support is needed [1, 2]. Evaluation of the pressure distribution on a retaining wall due to the loading of the backfill behind the wall and its point of application is very important for the safe and economical design of geotechnical structures, especially retaining walls [3, 4].

Coulomb (1776) and Rankine (1857) developed earth pressure theories that have been widely used by civil engineers to calculate pressure on retaining walls so that with these calculations, is assumed that the backfill is in an equilibrium state [5, 6]. Coulomb's earth pressure theory is based on the force equilibrium of a non-cohesive soil sliding wedge behind the rigid retaining wall. In contrast, Rankine's theory is based on the ultimate stress at any point in the semi-infinite non-cohesive soil mass [2]. Earth pressure obtained by Coulomb's and Rankine's theory show a linear increase with increasing depth, which is like the distribution of earth pressure under translational movement (state T) of the retaining wall. Many studies show that the earth pressures applied to retaining walls are non-linear like Tsagareli [7], Narain et al. [8], Matsuo et al. [9], Sherif and Fang [10], Fang and Ishibashi [11], Chang [12], Take and Valsangkar [13], O’Neal and Hagerty [14], Tang et al. [15], Patel and Deb [3], Huang et al. [16],

Many researchers have presented formulas to evaluate active earth pressure under wall movement [17–22]. Sekkel and Meghachou [23] observed that the failure surface is different for continuous and discontinuous wall movements. Hu et al. [24] found that when the soil is infinite, earth pressure approaches Coulomb's active earth pressure values by increasing the ratio of the width to the height of the backfill. Horizontal pressure is nonlinearly distributed for limited soils. Considering the shear stress between soil layers as well as the effect of soil arching, the point of action of the resultant active earth pressure exceeds that from the Coulomb solution. Also, the application point of the resultant active pressure from the method presented by Fan et al. [25] was obtained from 0.25H to 0.49H by changing the wall movement modes due to soil arching.

Several researchers investigated active earth pressure about soil arching [26–31]. Goel and Patra [19] provided a diagram for correcting the active earth pressure coefficient and height of the force's point of action from the base of the wall. Rao et al. [32] showed that increasing the wall-soil friction reduces the active earth pressure on the rigid retaining wall. The analysis by Khosravi et al. [33] revealed that the maximum stresses do not occur at the wall toe but at a distance away from it. The results presented by Chen et al. [5] showed that the active earth pressure for a confined width decreases due to arching. Also, the inclination angle of the slip plane in non-cohesive soil yielded close agreement to Coulomb's solution. Using the arching theory, Joshi et al. [34] showed that the lateral earth pressure coefficient decreases with increasing the depth for a narrow retaining wall. This behavior is a consequence of soil arching and the mobilization of the wall-soil friction angle along the side walls.

Various factors affect earth pressure on the retaining wall and its point of application, such as compaction during the construction [35], the percentage of fine particles [36], internal friction angle of the soil, unit weight of backfill, wall-soil friction angle, wall-back inclination and backfill [2], the rigidity of the wall, the distance of the loading plate from the facing panel [37], wall back roughness, and inclination [6]. Given the diversity and multiplicity of factors affecting the soil-retaining wall interaction and the complexity of their relationship, methods to easily estimate the retaining wall's behavior are not readily available.

Investigating the critical levels of sandy soils regarding soil loading (the level where the surcharge produces the greatest lateral force) has been considered before, but there is a lack of knowledge of the effect of important factors, including different soil conditions (change in soil type) that makes such an investigation challenging. Loading (change in the shape of the loading plate), instability of the backfill behind the retaining wall, and the lateral earth pressure are important considerations in the present research. By conducting a series of laboratory experiments, the present study investigates the lateral force behind a retaining wall under dynamic surcharge and the force's point of action in different conditions. Three types of soils and three foundation shapes (circular, square, and rectangular) are used as design variables.

2 Materials and Methods

A physical model was constructed to investigate the lateral earth pressure on the retaining wall, and the effective parameters were investigated as well. The following sections describe backfill specifications, the experimental model, and the loading system.

2.1 Backfill specifications

This study considers three types of soils with grain sizes of 0.24 mm, 1.18 mm, and 15 mm as the backfill materials. The physical properties of these materials, known as GP, SP, and SP in the Unified Soil Classification System (USCS), are summarized in Table 1. Also, the particle size distributions associated with backfill materials according to ASTM D 6913-04 are depicted in Fig. 1 [38].

Table 1
Physical properties of the backfill materials.
Description	Soil 1	Soil 2	Soil 3	Test standard
Medium grain size, D50 (mm) Uniformity coefficient, Cu Curvature coefficient, Cc Specific gravity, Gs Moisture content (%) Friction angle using direct shear test Soil unit weight (Kg/m3)	15 1.6 0.97 3.1 0 46 1870	1.18 5 0.61 2.9 0 40 1780	0.249 3.39 1.03 2.69 0 28 1450	ASTM D 422 and ASTM D 2487 ASTM D 422 and ASTM D 2487 ASTM D 422 and ASTM D 2487 ASTM D 854 - ASTM D 3080 ASTM D 4254-16
Classification (USCS)	GP	SP	SP	ASTM D 422 and ASTM D 2487

Fig. 1

Particle size distribution of backfill materials.

2.2 The experimental model

To investigate the retaining wall behavior and perform the desired experiments, a test box with flat surfaces and internal dimensions of 160 cm×47 cm in the plane and 120 cm in height was used. A photograph of the experimental setup is shown in Fig. 2. The frame of the test box was made of steel with a thickness of 8 mm. A transparent Plexiglass sheet with a thickness of 10 mm was used on the front face of the model to allow observation of the soil deformation during the tests and to facilitate data collection. Steel belts restrained the front side of the model to prevent the bending of the Plexiglass plate.

To maintain the backfill for recording the horizontal soil displacements, a wall model was constructed based on the specifications of the real wall on a reduced scale of 1/10 from four Teflon blocks with a height of 15 cm, width of 47 cm, thickness of 5 cm and flexural rigidity (EI) of 264 KNm2/m. A load cell was installed at the center of each block (at Z = 11.5, 28.5, 44.5, and 60 cm, where Z is the distance from the center of each block to the soil surface) to measure the earth pressure on the panels, and the data was collected with a data logger. In addition, the horizontal displacement of each panel was measured. Figure 3 shows a schematic view of the test setup.

Fig. 2

Photograph of the test box used.

Fig. 3

Schematic view of the test setup.

A hydraulic jack with a maximum capacity of 2 tons and an accuracy of ± 0.01% applied the load to the backfill through different loading plates with almost the same cross-section and a transitional speed of less than 2 mm/min. A pressure gauge was used to measure the pressure applied to the foundation through the jack. It should be noted that depending on the backfill reaction, the applicable load level changes from one experiment to another [38]. For applying a uniform load through the loading plate, the plates were fixed, there was no possibility of tilting, and the foundation was rigid. Dynamic loads were applied to the horizontal surface of the backfill through a circular loading plate with a diameter of 32 cm, a square plate with a side length of 28 cm, and a rectangular plate with a length of 40 cm and width of 20 cm, all of which have a thickness of 2 cm.

Nine experiments were conducted to investigate the effect of soil particle size (medium grain sizes of 0.24 mm, 1.18 mm, and 15 mm) and loading plate shape (circle, square, and rectangle) on the lateral earth pressure exerted on the retaining wall. In each experiment, the other parameters were held constant to examine a specific parameter. To perform the corresponding experiments, the backfill was constructed from five 15 cm-thick layers to reach a final height of 72 cm, and the soil was compacted manually using a metal pounder.

According to ASTM D1556-07, soil density was measured in certain samples to assess the backfill compaction. To attain the desired conditions, several tests were conducted to standardize the compactions, equalize the compaction energy resulting from the pounder impacts for each layer, and ultimately produce nearly identical backfill in all models. The loading was performed after filling the test box; the displacement of the blocks and the lateral earth pressure were recorded. Table 2 lists the testing conditions for the various experiments. Listed in Table 2 are the soil type, plate shape, maximum settlement, surcharge pressure, and lateral force. Maximum surcharge pressure is the maximum pressure applied by the hydraulic jack during loading. The maximum lateral force is the maximum lateral force applied to the load cells (each load cell is located in the center of each block).

Table 2
Maximum surcharge pressure and lateral force applied to the retaining wall under different test conditions.
Soil type	Loading plate shape	Maximum settlement (cm)	Maximum surcharge pressure (kN)	Maximum lateral force (N)
Soil 1 Soil 1 Soil 1 Soil 2 Soil 2 Soil 2 Soil 3 Soil 3	Circular Square Rectangular Circular Square Rectangular Circular Square	5 5 5 6 6 6 14 14	484.47 415.10 593.66 189.06 189.76 178.10 59.08 47.44	187.85 220.29 229.20 168.73 166.58 217.23 206.67 194.70
Soil 3	Rectangular	SP	SP	205.36

3 Results and Discussion

The thrust applied to the retaining wall is the sum of the forces due to the weight of the backfill behind the wall and the surcharge applied to the backfill surface. Figure 4 depicts an example of the load cell data recording where Part A represents the lateral force due to the weight of the soil behind the wall; Part B describes the lateral force during the loading stage; Part C represents the lateral force after the jack is turned off and is actually the residual stress generated in the backfill; and Part D shows the unloading stage. The shapes presented in this study are obtained based on Part B of the variation of the lateral forces. As evident from Fig. 4, the load initially increases before reaching a more-or-less steady value. Then, during the loading stage, the force increases significantly until it reaches a new stable condition. At this time (Part C), the jack has been turned off, and the stresses at that time are a combination of backfill weight and jack-induced stress. Finally, in Part D, unloading is performed, and the stress rapidly decreases to a slightly lower value.

Fig. 4

The lateral force variation over time.

3.1 The effect of foundation shape on the backfill with soil 1

This section investigates the effect of surcharge shape on the magnitude and distribution of the lateral force applied to the retaining wall with soil 1. The variation of lateral force applied to the center of the blocks is plotted in Fig. 5 with the surcharge pressure at all loading stages and for all shapes. As can be seen, the surcharge pressure applied to the soil surface takes on its highest and lowest values for circular and rectangular foundations, respectively. These pressure changes can be attributed to the foundation shape perimeter and shear. Since the circular foundation has a smaller perimeter compared to other shapes, it results in a lower shear force and requires higher jack pressure to achieve the same settlement. The opposite is true for the case of a rectangular foundation, which has the largest perimeter among the three shapes.

Fig. 5

Variations of the lateral force versus the surcharge pressure at different depths of backfill for soil 1 (settlement from 1 to 5 cm), (a) Z = 11.5 cm, (b) Z = 28.5 cm, (c) Z = 44.5 cm, and (d) Z = 60 cm.

Due to the nature of backfill and particles locking to each other, the maximum lateral force occurs in the upper layer of the soil (Z = 11.5cm, Z = 28.5cm), and the force magnitude decreases with increasing depth (Figs. 5a and 5b). As shown in Fig. 5, the slope of lateral force changes with surcharge pressure is almost constant at each depth and decreases with increasing depth. The active pressure coefficient decreases with the increase in depth. For a settlement of 5 cm, the lateral force associated with the square, rectangular, and circular foundations at a depth of 60 cm decreases by 58%, 53%, and 39% compared to that at a depth of 11.5 cm, respectively. This further indicates a more uniform stress distribution generated deep in the soil with a circular foundation.

Figure 6 depicts the lateral force distribution with soil depth associated with backfills for circular, square, and rectangular surcharges.

Fig. 6

The lateral force distribution for soil 1 with (a) circular, (b) square, and (c) rectangular surcharge (settlement from 1 to 5 cm).

As observed in Fig. 6a, the lateral force on the wall with the circular surcharge plate increases up to a depth of 28.5 cm from the soil surface and then decreases to the foot of the wall. This indicates that due to the shear strength of soil and the interlocking of particles, no failure has yet occurred at the corresponding depth, and the failure line has not reached that location. Also, Fig. 6a shows that the lateral earth pressure increases with increasing loading intensity. In addition, the maximum lateral force is estimated to be 0.48% of the force due to surcharge pressure. Its point of action, independent of the input acceleration, is located at 60% of the backfill height from the wall foot. It was also found that increasing the surcharge pressure does not affect the position of the maximum lateral force.

The lateral force applied to the wall increases by 29% in depth for a settlement of 1 cm, which is mainly due to the static pressure associated with soil weight. However, for a settlement of 5 cm, there is a 39% reduction in the lateral force, indicating that the forces due to dynamic surcharge overcome those due to soil weight with increasing depth. It can be understood from Fig. 6b that at lower load intensities (to 226 kPa), the square surcharge plate behaved similarly to the circular one. However, with increasing load intensity, the lateral earth pressure distribution with soil depth is almost linear, and the lateral force on the wall decreases linearly as the depth increases. The maximum lateral force is 0.68% of the force due to the surcharge pressure and at 84% of the backfill height from the wall foot. With this surcharge, the lateral force has undergone 17% and 58% decreases in depth for settlement amounts of 1 and 5 cm, respectively.

With a rectangular surcharge plate (Fig. 6c) with the onset of loading (q = 24 kPa), the lateral force on the wall is approximately the same for different soil depths, indicating equal dynamic and static lateral forces. However, as the loading intensity increases, the lateral force sharply decreases to a depth of 28.5 cm, then increases to a depth of 44.5 cm, and subsequently decreases again (q = 47 kPa,178 kPa). With continued loading and elastic settlement of the soil, lateral force changes with the depth of the soil decreases continuously (q = 297 kPa, 594 kPa). The maximum lateral force was 0.48% of the force due to surcharge pressure and occurs at 84% of the backfill height from the foot of the wall. Also, the lateral force reduction with respect to the soil (Z = 11.5cm, F = 229N, Z = 60cm, F = 108N) was achieved as 53% for a settlement of 5 cm.

In general, lateral earth pressure increases with increasing loading intensity (Fig. 6). With increasing pressure, the soil becomes stronger due to compaction, and its elastic behavior improves. By doubling the surcharge pressure, the lateral earth pressure may more than triple. This is mainly because as the surcharge pressure increases, more particles are locked together, the soil approaches a solid state, and the granulation effect decreases due to increasing surcharge pressure. As seen in Fig. 6, the maximum lateral earth pressure depth was estimated to be 28.5 cm for circular foundations and 11.5 cm for rectangular and square foundations. The depth of maximum lateral earth pressure depends on the foundation shape.

Fig. 7

Variation of the lateral force with depth for soil 1 with (a) circular, (b) square, and (c) rectangular foundations (settlement from 1 to 5 cm).

According to Fig. 7a, for a circular surcharge plate and with increasing surcharge pressure, the lateral force increases linearly at any depth with a constant slope. This indicates a uniform stress distribution at any soil depth. For the upper soil level (Z = 11.5cm), the slope of lateral force changes against the surcharge pressure is the largest. However, in backfills with a square surcharge plate (Fig. 7b), the increasing lateral force with surcharge pressure shows almost the same behavior at all depths except for 11.5 cm. Also, at the soil surface, there will be a sudden increase in lateral force with respect to surcharge pressure. In backfills with rectangular surcharge plates (Fig. 7c), the trend of lateral force changes with surcharge pressure is almost the same as for the square with similar behaviors at three different depths. According to Fig. 7, as the jack settles and sinks deeper into the ground, more force is damped, and the lateral force on the wall at the upper level differs significantly from the lower ones. Most of the surcharge pressure at the upper level is applied to the wall as a lateral force.

3.2 The effect of foundation shape on backfill with soil 2

Figure 8 displays the variation of lateral force with respect to the surcharge pressure at different loading stages of backfill with soil 2. As with backfill with soil 1, the maximum and minimum surcharge pressures are associated with the circular and rectangular foundations for the same soil settlement, respectively. However, the surcharge pressure values are lower due to the physical nature of the soil and the fineness of the particles (Fig. 8 compared to Fig. 5). It was found that with the penetration of the loading plate into the backfill and the elastic settlement, the highest values of lateral force applied to the wall occur at a depth of 28.5 cm (Fig. 8b). According to Fig. 8, the lateral force decreases with increasing depth, and this trend is the same for all foundations.

Fig. 8

Variations of the lateral force with the surcharge pressure at different depths of backfill with soil 2, (a) Z = 11.5 cm, (b) Z = 28.5 cm, (c) Z = 44.5 cm, and (d) Z = 60 cm (settlements ranged from 1 to 6 cm).

According to Fig. 8, the slope of lateral force changes with respect to the surcharge pressure, which was found to be almost the same for all foundations at different depths. This indicates that the increasing lateral force is almost the same at different heights. This behavior can be attributed to the physical structure of the backfill. Also, from Fig. 8, it is seen that with a rectangular surcharge plate, a greater lateral force is applied to the blocks for the same settlement compared to the circular and square surcharge plates.

A diagram of the lateral force applied to the center of the blocks is plotted in Fig. 9 for the soil 2 backfill with circular, square, and rectangular loading plates. According to these diagrams, it can be concluded that the lateral force variation with soil depth is the same for surcharges with different shapes and increases to a depth of 28.5 cm and then decreases. The graphs drawn in Fig. 9 show that for backfills with circular, square, and rectangular loading plates, the maximum lateral force is estimated as 1.1%, 1.1%, and 1.5% of the force due to the surcharge pressure, respectively, and occurs at 60% of the backfill height from the foot of the wall. Lateral force changes in depth for a circular surcharge plate have been found to increase by 248% and decrease by 6.5% at the 1- and 6-cm settlements, respectively. However, these changes were evaluated as an increase of 261% and a decrease of 1.2% for square and an increase of 84%, and a reduction of 0.1% for rectangular surcharges plate, respectively. These trends can be attributed to the footing shape and type of backfill.

Fig. 9

The lateral force distribution in backfill 2 with (a) circular, (b) square, and (c) rectangular surcharge plate (settlement ranged from 1 to 6 cm).

As illustrated by Fig. 9, the lateral force changes with respect to depth are almost the same for the backfill with different loading plates, and the lateral force is higher for the case of a rectangular surcharge.

Fig. 10

Variation of the lateral force with depth in backfill 2 with (a) circular, (b) square, and (c) rectangular foundations (settlement ranged from 1 to 6 cm).

As observed from Fig. 10, the slope of lateral force variation with surcharge pressure is almost the same up to a pressure of ~ 106 kPa for the circle and 107 kPa for the square) in two backfills with circular and square shapes at different soil depths and the lateral force increases with a greater slope, which can be attributed to soil compaction and the effect of foundation shape on the backfill performance. The lateral forces applied at different soil levels converge after passing a certain pressure value (106 kPa for the circle, 107 kPa for the square, and 119 kPa for the rectangle). However, at a depth of 28.5 cm, a sharp increase is observed in the lateral force compared to those at other depths. This further indicates that the surcharge pressure with soil 2 is transmitted to greater depths with less damp than for backfill with soil 1, and the difference between lateral force and surcharge pressure at soil levels is much smaller (Fig. 10 compared to Fig. 7).

3.3 The effect of foundation shape on the backfill with soil 3

The effects of surcharge shape on the magnitude and distribution of the lateral force applied to the retaining wall in Fig. 11 illustrates that the surcharge pressure provides little difference in the backfill for the three foundation shapes. Thus, lateral force changes caused by surcharge pressure are very slight for various foundation shapes and at different soil depths. This difference is very small near the soil surface (Z = 11.5cm) and increases slightly with the continuation of the loading process and higher soil compaction.

Fig. 11

Variations of the lateral force versus the surcharge pressure at different depths of backfill 3, (a) Z = 11.5 cm, (b) Z = 28.5 cm, (c) Z = 44.5 cm, and (d) Z = 60 cm (settlement ranged from 1 to 14 cm).

As seen in Fig. 12, with the third soil type, the square and circular foundations have similar behavior, and the rectangular plate leads to an increased stress value in the soil depth (Z = 44.5, 60 cm). Depending on the type of backfill, the lateral force distribution will be such that the maximum lateral force for the three types of foundation shapes occurs in the middle layers of the soil.

Fig. 12

The lateral force distribution with backfill 3 with (a) circular, (b) square, and (c) rectangular surcharge (settlement from 1 to 14 cm).

The lateral forces with soil depth are depicted in Fig. 12 for the three types of foundations. It is seen that the trend of these changes is similar for square and circular foundations, and the maximum lateral force occurs at a depth of 28.5 cm. However, the rectangular foundation behaves similarly to the other two foundation shapes up to a settlement of 6 cm. The continuation of the loading process causes the transfer of the maximum lateral force to a greater depth (Z = 35 cm). Due to the loose nature of the backfill, the maximum lateral force associated with the three shapes of the foundation are slightly different (4.4%, 5.2%, and 5.1%) of the surcharge-induced force at the corresponding depth for the circular, square, and rectangular foundations, respectively. The maximum lateral force in the square and circular foundations occurs at 60%, while that of the rectangular one is obtained at 51% of the backfill height from the wall foot. The lateral force changes with depth show a decrease and an increase of 74% and 31%, 19% and 27%, 17% and 35% for circular, square, and rectangular foundations and for 1 and 14 cm settlements, respectively. Moreover, the lateral force changes with soil depth will undergo further increases with an increment in the loading intensity.

Fig. 13

Variation of the lateral force as for the surcharge pressure and soil depth in backfill 3 with (a) circular, (b) square, and (c) rectangular foundations.

As observed from Fig. 13, for foundations with square and circular shapes that experienced the maximum lateral force at a depth of 28.5 cm, a sharp decrease occurs in this force at the soil depth of 44.5 cm. However, for a rectangular foundation, a gradual reduction in lateral force occurs at a depth of 44.5 cm compared to that of 28.5 cm. The lateral forces applied to the soil surfaces at Z = 11.5 cm with this type of backfill for the three foundation shapes are slightly different.

4 Conclusions

In this study, the effects of loading plate shapes and soil type were investigated for their impact on lateral forces behind a retaining wall at different depths. The results indicated that with increasing soil particle size, the surcharge pressure applied by the jack and, consequently, the lateral force on the retaining wall increase for the same settlement compared to the fine-grained soils.

The present results showed that the earth pressure distribution with depth is not linear, and its maximum values occur at different soil depths depending on the type of soil and foundation shape. The maximum stress and strain values for the backfill created with soil 1 and with circular, square, and rectangular loading plates were observed in 60, 84, and 84% of the backfill height from the wall foot, respectively. In the case of the backfill with soil 2, these maximum values were found to occur at 60% of the height from the foot of the wall for all three foundation shapes. However, for the third soil type with circular and square foundations, the maximum lateral force occurs at 60% of the backfill height. In contrast, for backfill with a rectangular foundation, the continuation of the loading process causes the transfer of maximum lateral force to greater soil depths. One observes the maximum lateral force at 51% of the backfill height from the wall foot. In addition, the lateral force changes with respect to the soil depth will increase, and the active force coefficient decreases with increasing depth.

The present achievements illustrated that the maximum lateral force for backfill with soil 1, soil 2, and soil 3 are 0.48, 0.68, and 0.48%, 1.1, 1.1 and 1.5%, 4.4, 5.2, and 5.1% of the force due to the surcharge for the circular, square and rectangular foundations, respectively. One of the main factors in the safe design and construction of retaining walls is the quantitative and qualitative knowledge of the lateral force applied to them. Understanding the rate of lateral force changes with the surcharge pressure according to the soil depth and also knowing the increasing-decreasing behavior of the lateral force in the soil depth, with different foundation shapes and different types of soil, is a useful help in comprehension of the behavior of the retaining wall during the loading of the soil behind the wall is that in this way it is possible to recognize and strengthen the containment of the soil at critical levels.

Author Contribution

Conceptualization: All authors; Methodology: All authors, Software: Fatemeh Moala and Javad Ahadiyan, Validation: Fatemeh Moala and Javad Ahadiyan, Formal Analysis: All authors, Investigation: All authors, Resources: All authors, Data Curation: Fatemeh Moala and Javad Ahadiyan, Writing—Original Draft Preparation: All authors, Writing—Review and Editing: All authors, Visualization: All authors, Supervision: Javad Ahadiyan and Masoud Oulapour, Project Administration: Javad Ahadiyan and Masoud Oulapour, Funding Acquisition Javad Ahadiyan and Masoud Oulapour, All authors have read and agreed to the published version of the manuscript.

Funding:

This work was supported by the Shahid Chamran University of Ahvaz and Khuzestan Water and Power Authority.

Data Availability

All data generated or analysed during this study are available from the corresponding authors on request.

Acknowledgments:

The authors are grateful to the Research Council of the Shahid Chamran University of Ahvaz, and the Center of Excellence of the Network Improvement and Maintenance for their valuable support.

Conflicts of Interest:

The authors declare no conflicts of interest.

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Yes