Seismic response comparison of various geogrid reinforced earth-retaining walls: based on shaking table and 3D FE analysis | Scientific Reports

Oct 15, 2024

Scientific Reports volume 14, Article number: 24168 (2024) Cite this article

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The performance of various geogrid earth-retaining walls integrated with a non-cohesion granular backfill for reducing earth pressure has been investigated through small-scale shaking table tests and full-scale 3D finite element analysis. This purpose involved a series of physical modeling tests involving different earth-retaining walls (0.83 cm, height 7.5 cm, thickness, and length 1 m) and arrangements of full-scale 3D finite element analysis (5 m, height, 0.3 m, thickness, and length 6 m). This research investigates and designs hollow prefabricated concrete panels, gravity-type stone masonry, and reinforcement concrete (GRE) walls. It also displays comparative studies such as the top displacement of the wall, deflection of the wall, lateral pressure of the wall, settlement of the backfill, and vertical settlement of the foundation across the height of the (GRE) walls. The understanding and findings based on shaking table experiments and FE simulations have been used to develop a critical model for estimating earthquake-induced displacement (GRE) walls. The validity of the proposed FE simulation model has also been examined in the shaking table experiment and the FE simulation results. Based on the findings, the hollow prefabricated concrete panels were the most practical alternative due to their lower deflection and displacement. The observation also found that the hollow prefabricated (GER) wall is the most viable option, as the backfill surface settlement and lateral pressure decreased with the inclusion of geogrid reinforcement.

Geogrid earth-retaining walls are often used in geotechnical engineering to resist the lateral earth pressure exerted by the backfills they hold in place. Earth pressure is the primary component that influences the seismic design of geogrid earth-retaining walls1,2. By decreasing the lateral stress, optimizing the design and minimizing the project cost is possible. This paper aims to design various geogrid-reinforced earth-retaining walls with granular backfill, geogrid-reinforcement soil, and hollow precast concrete panels. Numerous researchers have investigated the earth-retaining walls during prior earthquakes3,4. The 2005 Pakistan earthquake (0.6 g, maximum recorded peak ground acceleration, PGA) caused significant damage to earth-retaining structures, bridges, and highways near the epicenter, along with excessive sliding and deformation of traditional earth-retaining walls. Due to the 2019 assault earthquake, which measured a maximum peak ground acceleration of 0.4 g, the earth-retaining wall experienced significant displacement and rotation5,6.

Different experimental methods have attempted to reduce the lateral earth pressure by mixing the backfill with geogrid materials. The use of geogrid7,8 and steel strips9,10 have been well documented as ways to reduce the lateral earth pressure behind an earth-retaining wall. All these materials positively decreased the lateral earth pressure under seismic conditions and shaking table test conditions. However, the seismic conditions and properties of these materials with the backfill can be challenging for geotechnical engineers11.

Connecting a geogrid backfill material with rigid connections to a retaining wall is an efficient way to reduce the lateral pressure on a non-yielding retaining wall, especially where there is a surcharge on the edge of the wall embankment10,11. Generally, when a geogrid backfill is connected to an earth-retaining wall, the effect of lateral stress decreases, and the stability of the earth-retaining wall becomes more assured12,13. This type of geogrid earth-retaining wall also reduces the volume of excavation and the concrete used compared to a wall having no wall-facing panels14. This means that the practical use of this retaining wall is becoming increasingly popular in different countries15,16,17.

Finite element (FE) numerical modeling tests have shown that a geogrid earth-retaining wall can decrease the lateral earth pressure and settlement of the backfill. Lam Tawari et al. 2021 evaluated the use of five input earthquake motions earth-retaining walls in a simulation of a cantilever earth-retaining wall constructed using the 2D finite element analysis program Abaqus. Besides the decrease in the lateral displacement and lateral earth pressure of the earth-retaining wall, they observed important tensile and compressive stresses on the faces of the wall just above the mid-height of the wall. Another study investigated the behavior of a geogrid rigid earth-retaining wall with three earthquake input motions using a numerical code18,19. They showed that increasing the acceleration of the input motion from the top toward the bottom of the wall significantly decreased the lateral displacement and lateral pressure in the seismic condition. Determined the optimum rate of decrease in the earth pressure and the shape of the failure mechanism20. They also reported that the stability of a retaining wall with geogrid depended on the soil interface.

The results of an FE study and tests comparing gravity-type and rigid retaining walls revealed that the gravity-type of earth-retaining walls substantially affected backfill pressure21,22. A detailed analytical analysis of the seismic performance of gravity-type retaining walls23 concentrated on the significance of wall height during earth shackling. The finite element (FE) method was employed to investigate the passive response of a gravity-type concrete retaining wall. The study revealed that the size of the failure domain was observed to increase with the application of base excitation24. Hokelekli Emin25 determined that a nonlinear distribution of backfill pressure behind an earth-retaining wall could be calibrated using finite element (FE) analysis. Several studies have used shaking tables and FE analysis on miniature retaining wall models to better comprehend the force that dynamic backfill places on the wall and its various failure mechanisms26. They discovered that the backfill soil may significantly impact the seismic performance of geogrid earth-retaining walls. Estimating earthquake-induced displacement of earth-retaining walls is critical to current performance-based seismic design26. Munoz H. et al.27 modified the Newmark sliding block model to forecast earthquake-induced retaining wall movement. Nimbalkar, Sanjay, and Deepankar Choudhury22,28 found a nonlinear dynamic soil pressure along the basement wall height and that the typical MO technique yields conservative seismic force estimates when evaluating retaining walls numerically.

To investigate the seismic behavior of geogrid-reinforced earth-retaining walls, researchers have employed a combination of experimental shaking table tests and advanced finite element (FE) simulations29,30. These tests provide direct measurements of essential parameters such as displacements and forces, enabling a better understanding of the unique response characteristics exhibited by geogrid-reinforced earth-retaining walls. On the other hand, FE simulations simulate the complex interaction between the soil, wall structure, and backfill material, allowing for a more detailed analysis of internal forces, displacement patterns, and stress distribution within the retaining wall system31. By combining the insights from experimental tests and numerical simulations, researchers can gain comprehensive knowledge of retaining walls' dynamic behavior and failure mechanisms, contributing to improved design practices and enhanced seismic performance32,33,34. Despite the significant progress in studying the seismic performance of various types of (GRE) walls, there remains a considerable research gap in understanding displacement behavior and backfill stability, specifically retaining walls35,36. Precast reinforcing concrete pale walls have gained popularity due to their unique design and construction techniques, which involve limited connection points between the facing panels and the backfill materials37,38.

The interaction mechanism of an earth-retaining wall with a geogrid the numerical modeling and shaking table experiments with various geogrid earth-retaining walls showed that using a hollow prefabricate retaining wall effectively reduced the top displacement, backfill settlement, and the earth's lateral pressure on the wall. However, accurate evaluation under the seismic conditions of using various geogrid earth-retaining walls and their role in the lateral earth moment has not been the focus of numerical modeling and shaking table experiments. The current study used a series of physical experiments and numerical modeling tests on various earth-retaining walls with a connected geogrid backfill. The behavior of the various earth-retaining walls with geogrid backfill was evaluated in the active seismic conditions. In addition, influencing earthquake forces such as the effect of the width, height, and location of the geogrid from the bottom of the wall, the distance from the surface of the slope, and the role of backfill at the edge of the wall have been investigated in physical modeling tests. (Table 1). Therefore, the researchers assumed the possibility of achieving that goal. These groups can keep their strength regardless of geographic location, although the effect of the factors may vary from country to country. Table 1 demonstrates the factors affecting the seismic performance of (GRE) walls in developing and developed countries.

Accurate assessment of earthquake-induced actions on (GRE) walls is important for ensuring their satisfactory performance during a design-level seismic event10. Several researchers performed full-scale experimental investigations and scaled-down models of earth-retaining structures to understand their seismic behavior. Full-scale experiments can effectively replicate the seismic behaviour of earth-retaining structures. However, full-scale experiments are limited to ground accelerations and backfill types. Moreover, full-scale experiments are costly and require a longer time for construction than scaled-down models. Hence, a detailed parametric investigation of full-scale earth-retaining structure models is complicated30.

Utilizing the shaking table facility at The University of Engineering and Technology, Taxila, Pakistan, shaking table experiments were conducted on models of scaled-down earth-retaining walls, as shown in Fig. 2. The shaking table platform measured 1 m by 1 m and could support a maximum of 1,500 kg of weight. With a maximal stroke capacity, the shaking table has two actuators that can generate uni-directional or bi-directional base excitations. It is important to mention that only un-directional x-axis base excitation was examined in this investigation. The hydraulic pump system provided power and regulated the actuators' motion. 1.0 gal was the maximal horizontal acceleration, and 0.1–50 Hz was the operating frequency.

The similitude rules of the various physical and mechanical variables were exported by p theorems of Bockinghamin dimensional analysis theories to study the seismic response characteristics of the GRE wall and the granular backfill soil. According to the wall and soil characteristics, basic physical variables must be confirmed in the similitude rule. The three basic physical variables of the model walls were length, elasticity modulus, and acceleration, and the three fundamental physical variables of the model soils were shear wave velocity, density, and acceleration. Then, two different similarity ratios for the model wall and granular backfill soil the model soils were deduced. According to the test purpose of the geogrid reinforced earth-retaining wall, we should obey the similitude ratio of the model wall, but the effect of time must be considered due to the increase and dissipation of the excess pore water pressure in the saturated ground. Hence, the time-similitude ratio of the model wall was determined by the time-similitude ratio of the model soil. According to the Froude constant (Wr) of the p theorem, the gravity similitude rule was applied, and the Froude constant can be represented by the shear wave velocity of soil (Ne). The question is used for simulation text parameters for reduced-scale experiments, shown in Eqs. (1)–(3). In Table 2, the scale factor so fall parameters were confirmed according to the similarity rule of these parameters: granular soil, the geometric scale factor, and the scale factor of the wall.

The measurements of the several walls in the GRE were 0.83 m (L), 0.83 m (H), and 7.5 cm (t). Figures 1, 2, and 3 show the model's details. These walls were constructed using hollow precast panels, reinforced concrete, and stone masonry; the details are shown in Table 3. The concrete had small gravel particles as its coarse aggregate and fine sand as its fine aggregate. The material mixing ratio makes it possible to create an appropriate elastic modulus for the materials, as shown by the similitude requirement of SE in Table 2. The elastic modulus values for the prototype model are illustrated in Table 2.

Overview of 3D model precast hollow concrete structural components of (GRE) wall.

Complete overview of conventional gravity-type stone masonry wall.

Complete overview of conventional reinforcement concrete (GRE) wall.

In the experimental setup, a compact and unified subsoil layer was positioned at the container's base to minimize water infiltration from the surrounding backfill soil. An impermeable membrane enclosed the backfill, which consisted of sand, silt, gravel, and clay, in the container. The backfill soil was obtained from the site. The grain composition curve of the backfill soil can be seen in Fig. 4, and its parameters are described in Table 2. In the test model, the backfill soil had a unit weight, as shown in Table 2, and a relative density of 55%, which may be considered low for port field constructions. Therefore, the prototype is designed to backfill soil in moderately compacted conditions. The water table of the backfill soil was situated under the land's surface. The length of the reinforced soil and the distance beyond the reinforced zone were sufficient to examine the backfill soil settlements thoroughly. Figure 5 displays the measurements of the test models.

Grain composition curve of the backfill soil.

Modeling of the backfill and backfill geogrid reinforcement.

The geogrid constructed of low-strength plastic was chosen based on the similitude criteria, as shown in Fig. 5. At a strain of 2%, the geogrid exhibited a tensile force, as shown in Table 3, corresponding to the prototype model's tensile force. The geogrid layers were arranged horizontally in the reinforced zone. The spacing between the reinforcements was 0.166 m, and the length of the reinforcements was 0.7 m, which was equal to the height of the wall. The geogrid layers were partially immersed inside the wall, forming what is referred to as the geogrid roots. The reinforced earth-retaining wall backfill was built using five layers, each height 0.166 m apart.

The model backfill was constructed using the water sedimentation technique, as described by39. The test models required the backfill soil to be regulated at a relative density of 55%. The relative density of 55% was achieved by precisely regulating the dry backfill material in the test container to satisfy the required specifications. The specific calculation method for determining the total volume of dry backfill soil is as follows: firstly, the soil used for testing must be dry and composed of granules. Secondly, the natural void ratio can be determined based on the relative density and the backfill soil's maximum and minimum void ratios. This allows us to calculate the solid volume (VS) and pore volume (VV) of the backfill soil in the container. Thirdly, since the backfill soil in the pack backfill car is loose, we can determine the solid volume (VS) of a pack backfill soil car based on the maximum void ratio of the backfill soil. Finally, we can determine the number of pack backfill soil cars required to meet the backfill soil volume of the test container.

Figure 6 displays the schematics of the test models and test equipment within the laminar shear container. The geogrid-reinforced earth-retaining wall (GRE) is also shown in Fig. 6. Three horizontal accelerometers were explicitly inserted into the strengthened backfill material labeled A1, A2, and A3. Three laser displacement meters (L1, L2, and L3) were mounted on a single batten and secured by a steel frame to measure the displacement movements of the (GRE) walls. Three laser displacement meters (SD1, SD2, and SD3) were used to measure the settling of the surfaces of the backfill materials in the reinforced zone. Three pressure gauges were inserted into the backfill to measure the excessive pressures exerted inside the reinforced zone. Three strain gauges were affixed to the surfaces of the geogrids, with two strain gauges placed on one side of each layer to measure the dynamic stresses of the geogrids. Photographs taken during the installation of the test setup are shown in Fig. 6.

Shaking table test models, geogrid reinforced earth-retaining wall.

Finite element (FE) analysis was conducted on three-dimensional models of (GRE) walls to examine their seismic response. A parametric study was carried out to investigate and analyze the seismic response of three distinct earth-retaining walls, namely SM-W (5 m), GS-W (5 m), and RC-W (5 m), about the impacts of hollow precast concrete, second gravity-type, and third reinforcement concrete panel (GRE) wall. The FE analysis results were utilized in nonlinear dynamic analyses to comprehend the seismic response of the model better. Therefore, the input base accelerations, also known as accelerograms, have been scaled to be 0.4 g times the peak ground acceleration (PGA)6. The responses of the (GRE) walls to stress distribution, deflection of the wall, acceleration across the wall height, wall displacement, lateral wall pressure, and backfill settlement have all been analyzed based on the results of finite element computations. The numerical modeling showed that the boundary conditions, zone dimensions, and property assignment significantly impact the seismic response behavior of these types of structures; they perform a significant role in the model simulations. The connections between (1) the bottom of the foundation dirt being fixed in both the horizontal and vertical dimensions, (2) the two sides of the foundation soil, and (3) the left side of the retained soil being attached only in the horizontal direction. ABAQUS's acceleration and displacement-controlled boundary option established the FE model's confines5,40.

This study uses three different types of materials to create the Abaqus FE model for analysis, as shown in Table 3. The wire element feature was utilized to build the steel reinforcement and geogrid, and the (CDP) model of concrete-damaged plasticity was used to build the model's facing panels. The Mohr–Coulomb material (MC) model has been utilized to construct the backfill and simulate the constitutive behavior backfill. The plane strain conditions have been assumed to have contributed to creating the 3D model28,31. The seismic loading was applied to the foundation of the FE model by using acceleration along the x-axis. An explicit central difference integration rule and several steps are used in Abaqus' dynamic explicit analyses to address boundary conditions concerns.

The study uses three different (GRE) walls for simulation: a hollow precast concrete panel, gravity-type, and reinforcement concrete (GRE) wall. Figures 1, 2, and 3 show the geometry specification details. The numerical model depicts an idealized repeating unit that is 1 m wide and runs along the length of the wall, consisting of panels that are 5 m tall. The steel reinforcement rebar is positioned at a vertical spacing of 250 mm rebar stripe and is 150 mm wide by 14 mm thick; these are standard dimensions for hollow precast concrete GRE walls. The numerical model depicts a wall measuring 5 m in height and comprising six modules stretching along its length. L = 1 m represents the reinforced zone's length, equivalent to 5 m for the wall height H. The wall of each panel is 1 m in length, as shown in Fig. 1. The gravity-type and reinforcement concrete (GRE) wall running length is 6 m and height is 5 m, as shown in Figs. 2 and 3.

A detailed parametric investigation has been carried out for granular backfill soil types to understand the role of backfill in the overall seismic performance of the (GRE) wall. The mechanical properties of the backfill materials are shown in Tables 4 and 5. The granular backfill materials for the parametric FE analysis studies. According to research by Allen and Bathurst5, wall performance is influenced by the reinforcement global stiffness, which is calculated by dividing the wall height (H) by the total reinforcement stiffness from all reinforcement layers. For instance, while all other parameters stay the same, wall reinforcement loads will rise with increased global reinforcement stiffness. Based on data from full-scale instrumented earth-retaining reinforced soil walls under operating settings, Allen and Bathurst7 found a range of 35-380 MPa for global stiffness, 43 MPa, and reinforcement stiffness 56 (Table 4). These walls were determined to be of inextensible reinforcement. The maximum reinforcement stresses in the present investigation were less than 0.03% for all instances and layers, significantly below the steel yield strain of 0.2%. In contrast, Bakr et al.9 reported up to 0.08% stresses after construction on a monitored 17 m high production (GRE) wall. The maximum strains computed in this paper for the steel straps were about 0.2%, which is at the low end of values measured in actual geogrid retaining walls and well below the 1% strain that is recommended to keep these systems at working stress levels39 and to ensure adequate margins of safety against tensile failure8.

The peak plane strain friction angles most accurately characterize the shear strength of the granular soils. Determining plane strain friction angles for granular soil is possible using a "plane strain" test apparatus, consisting of a block of soil between two frictionless parallel plates that inhibit deformations at the plate boundaries that occur out of the plane. Therefore, the soil is constrained by this testing apparatus in a manner analogous to the y–z boundaries implemented in the numerical model utilized in this research. For compact granular soils, the peak friction angles calculated using plain strain tests are greater in magnitude than the values obtained using triaxial tests. By applying the correlation between triaxial tests and the maximal plane strain friction angle of 4432, it is possible to determine that 38 represents the latter. This value is typical for granular fill materials of superior quality specified by AASHTO3 for use in earth-retaining walls. A value of cohesion C = 1 kPa was selected to ensure numerical stability at the soil zone (top) free boundaries during construction5. The length of the backfill reinforced zone is about L = 4 m, which is 5H, where H is the wall height, as shown in Fig. 5. The numerical simulations did not include any surcharge at the top boundary of the model. The Mohr–Coulomb (MC) material model was used to simulate the constitutive behavior of granular backfill.

Several investigations34 simulated backfill pre and post-yield behavior using the MC material model. It should be noted herein that the post-yield behavior of soil could also be simulated by providing an extension to the MC material model35. Consequently, the MC model of granular backfills has been applied to the results of the FE investigations in this study. Song36 has presented details of the MC material model and calibrations using triaxial test results. The triaxial test outcomes, namely the hardening and softening behaviors obtained from the calibrated MC material model, were compared to the laboratory triaxial results of granular backfills. The specification of MC material modeling, calibrations of the post-yield response of backfill using triaxial test data, and modeling of Rayleigh damping of backfill in an investigation40. This study modeled the geogrid mesh used for backfill reinforcing with wire components in Abaqus31. Thin reinforcing geogrid are layered into the backfill soil for structural support. It is possible to determine a limit for the geogrid components' tensile failure strain, and these components can give either under tension or under compression. The shear behavior at the geogrid-soil interface is characterized by a nonlinear shear failure wrapping that shifts in shape depending on the confining pressure. The geogrid components' characteristics are shown in Table 5, which provides a summary to replicate the geogrid's primary and secondary reinforcement layers. The geogrid layers were arranged horizontally in the reinforced zone. The geogrid embedded in the backfill layer and the geogrid length were the same as the backfill material. The geogrid soil was constructed with five layers, as shown in Fig. 6, where the distance of each layer was 1 m.

The reduction factor connected the interfaces' modulus and friction angle characteristics to the nearby soil. This number was set to 0.6 for the facing-soil interface, and for the soil-reinforcement interface, it was set to 0.52. The facing-soil interface was supposed to be smooth and non-dilatant. Still, the soil-reinforcement interface was assumed to be rough and given the same dilatancy angle as the nearby soil. The soil and interface characteristics employed here were chosen based on Damians et al.14 and Yu et al.37 experience with 2D modeling of steel mesh reinforced walls. For the base scenario, the friction coefficient was assumed to be = 0.4, which is at the low end for steel strips5,8, and a cautious (safe) estimate for design with ribbed steel strips1. The horizontal joint between adjacent panels was chosen based on its mechanical characteristics to convert bearing pads with internal cavities and grooved geometry into zones of continuous thin solid rectangular strips with equivalent one-dimensional compressive stiffness. The material used for base case models' joints is the same as a row of high-density bearing pads23 (Table 6).

The Abaqus FE program has been used to simulate the concrete, and the CDP model of concrete-damaged plasticity has been used. Numerous researchers have utilized the CDP model to study the constitutive behavior of concrete27,40. The CDP model uses the following formulation in Eqs. (4) and (5) to characterize concrete's constitutive behavior under compression and tension.

The tensile and compressive stress variables are indicated by Mt and Mc, respectively. The £tvs and £cvs are the tensile and compressive plastic strain equivalents. The initial undamaged elastic modulus, denoted by the (K0vs), has been calculated based on the strain and stress response of a uniaxial compressive strength test performed on concrete41. Plastic strains are the dependent variables in the damage equation27. Lubliner et al.42 created the first version of the CDP model's yield function, which was later revised by Lee and Fenves43. The Abaqus/Explicit User's Manual44 has information on the CDP yield function. The eccentricity and the dilation angle control the plastic potential process, measured at the deviatoric stress plane.

Table 2 displays the material characteristics considered using the CDP model to model concrete. Carreira and Chu9 proposed a method for generating the stress–strain response of concrete with a characteristic strength (Sfc) of 30 MPa. When the stresses in concrete reach a level greater than 0.3 Sfc, it was hypothesized that the material would begin to act in-elastically (when subjected to compression). When subjected to uniaxial stress, the fracture energy approach predicted the concrete's tensile behavior45. A linear softening model has been used to predict the tensile failure of concrete. We used Eqs. (6) and (7) to figure out Bf, which stands for the tensile strength of the concrete, and Jg, which stands for the fracture energy. Both the concrete compressive strength (Sfc) and the maximum aggregate size (ag) have been used in the process of determining the Bf and the Jg, respectively41,44.

The numerical modeling showed that the boundary conditions, zone dimensions, and property assignment significantly impact the facing behavior of these types of walls; they perform a significant role in the model simulations. All elements of the finite element mesh were 10-noded hexahedra, including the zones used to simulate the interfaces of dissimilar materials. The finite element mesh had 13,128 elements and 14,888 nodes. The connections between (1) the bottom of the foundation dirt being fixed in both the horizontal and vertical dimensions, (2) the two sides of the foundation soil, and (3) the left side of the retained soil being attached only in the horizontal direction. ABAQUS's acceleration- and displacement-controlled boundary option established the FE model's confines. The FE model is based on a pinned support that allows horizontal x-axis motion but imposes y-axis limitations.8,30. In addition, geostatic stresses have been established in the backfill and foundation zones. The primary goal of providing a detailed description of the geostatic pressures was to verify the accuracy of the FE values and the distribution of the forces.13. The x-axis acceleration was used to apply the seismic loading to the FE model's base. The vertical movement of the domain boundaries was uncontrolled in both the front foundation zone and the rear foundation and retained fill zones. Choosing the wall-facing distance from the domain's rear boundary was a pragmatic compromise to reduce the impact of far-field boundaries on wall-facing deformations and runtime.

The primary goal of providing a detailed description of the geostatic pressures was to verify the accuracy of the FE analysis and the distribution of the forces.31. The foundation, situated at a depth of 2 m below the wall, was determined to be sufficiently distant to have little impact on numerical results in a practical context. The vertical y–z boundaries were fixed in the cross-plane (x) direction. Hence, the soil and panel y–z boundaries in the vertical (y) direction were free to move. The domain boundaries at the front of the foundation zone and the back of the foundation and retained fill zones were free to move in the vertical direction. The seismic loading was applied to the base of the finite element (FE) model using acceleration along the x-axis. The vertical mobility of the domain boundaries was uncontrolled in both the front foundation zone and the retained fill zones. The boundaries of the model were constrained regarding all degrees of freedom system (Dof's)40.

Mesh sensitivity analyses were performed to investigate mesh size influence on the earth-retaining wall's seismic response. Except for the steel reinforcement, the FE model was modeled using plane strain elements with reduced integration and hourglass control (CPE4R). A beam element (B31) was used to mesh the steel reinforcement (rebar)40. Numerous scholars have investigated the impact of mesh size on structural response and noted that the findings of finite element analysis exhibit a high degree of sensitivity to changes in mesh size. Additionally, it has been shown that selecting an optimal mesh size may lead to more precise finite element (FE) results while reducing computing time16,20. During the FE investigations conducted by Tiwari et al.40, it was discovered that the backfill near the (ER) wall stem and the heel slab significantly impacted the earth-retaining wall's seismic response.

Consequently, mesh sensitivity assessments have been conducted to evaluate the effects of varying mesh sizes on the accuracy of the computational model at the points of contact between the earth-retaining wall and the backfill material, as shown in Fig. 7a. The mesh sensitivity assessments were carried out by altering the mesh sizes of the stem and heel of the model. A medium-dense mesh was used for the finite element analysis to reduce the shear-locking effects. The mesh sensitivity studies have used four different mesh sizes: 25 mm, 50 mm, 75 mm, and 100 mm. Mesh sensitivity analyses were conducted using the FE model. A minor distinction has been observed between the outcomes of various model mesh sizes. A 25 mm mesh size was chosen based on mesh sensitivity analyses for the comprehensive FE investigations.

Mesh sensitivity and backfill domain size analysis for (ER) wall model.

The outcomes of FE simulations may be greatly influenced by boundary conditions5,28. A thorough parametric analysis was conducted on various backfill domain lengths behind the wall-facing panels to determine the ideal length. Four (GRE) models with backfill domain lengths of 4 m, 5 m, 7 m, and 8 m were considered for the domain size investigation. In place of backfill, granular soil has been utilized in the three earth-retaining models. The backfill was modeled using the MC model. A spring and dashpot system representing the FE software Abaqus illustrated boundary conditions40. For the backfill domain size investigation, the input base excitation for the nonlinear time history finite element analyses was the Taft accelerogram (United States Station). The relative displacement time history at the summit of the earth-retaining wall, as observed from various backfill domain lengths, is depicted in Fig. 7b. Higher active state displacement was observed in the (GRE) with backfill domains of 8 m, 7 m, and 5 m in length compared to the (GRE) with a backfill domain of 4 m. This difference can be attributed to the greater reflection of stress waves from the boundaries of the 8 m and 7 m long backfill domains, respectively. The computational time for the earth-retaining wall with backfill domains measuring 7 m and 8 m was considerably greater than that of the wall with 5 m and 4 m long.

FE study on (GRE) wall models estimates earthquake-induced displacement. FE investigations on full-scale (GRE) wall models need FE simulation and constitutive modeling competence. A force-based displacement check model has been proposed to estimate the maximal earthquake-induced elastic displacement (£max) of the (GRE) retaining wall with granular backfill. Figure 8 depicts the (GRE) wall considered during formulation development. The height and thickness of the (GRE) wall are respectively denoted by ''h'' and ''wt''.

Input estimating (GRE) wall maximum elastic seismic displacement.

Determine the body force at the (GRE) wall's unit height.

Backfill dynamic pressure coefficient according to the Mononobe–Okabe method.

Dynamic soil pressure at the base of the (GRE) wall

Utilize the (SAE) to represent a triangular load per (GRE) retaining wall unit width.

Determine the greatest possible movement caused by the inertia of the (GRE) wall.

Calculate the maximum displacement caused by dynamic soil pressure.

Determine the utmost elastic displacement exhibited by the (GRE) wall.

Figure 8. depicts the seismic body force (M1CD) on the (GRE) wall stem and the dynamic soil force per unit width of the wall (M2CD) along the wall height (assuming a triangular distribution). It supports a homogeneous, horizontal, granular backfill behind it, and it should be highlighted. The backfill contact angle (ø) has been considered to be ø /2. The MO equation has been used to predict the seismic pressure behind the (GRE) wall stem33. The pseudo-static pressure on the (GRE) wall stem is calculated using the MO equation and grows linearly with wall depth. The pseudo-static lateral pressure coefficient (\({S}_{AE}\)) was calculated to be 100% Sh. Equation (6) calculates the seismic force (SEA) along the (GRE) wall height.

Where AFH is the backfill's horizontal acceleration amplification. The formulation utilized to determine the maximum displacement resulting from the wall inertia forces (\({\text{\pounds }1}_{max}\)) has been computed as follows: the variables used in this context are E, representing Young's modulus of the (GRE) wall; I, representing the moment of inertia of the facing panels; backfill, representing the unit weight of the backfill, kh, representing the horizontal seismic coefficient, and Wwall, representing the weight of the model. The calculation of \({(\text{\pounds }2}_{max})\), which represents the maximum displacement resulting from seismic active pressure of backfill, has been determined utilizing the subsequent formulation: The equation \({(M2}_{CD}\)) = \({S}_{AE}\) Indicates the seismic force per unit of wall breadth. After computing £1max and £2max, these values can be used to determine the utmost displacement at the model's apex. The process for estimating the earthquake-induced elastic displacement of the (GRE) wall with granular backfill is illustrated in detail in Eqs. (8) to (14).

In this work, the authors conducted reduce-scale shaking table experiments with GRE wall model results to validate the capabilities of the current FE modeling technique. A 3D plane strain FE analysis model of the full-scale wall model has been created using the FE modeling method. The backfill was modeled using the MC material model, and all wall models were modeled using the CDP materials. Analyses of nonlinear time histories have been carried out with the help of the dynamic explicit scheme that the FE program Abaqus provides. It is important to note that the recorded displacement time history of the earthquake shaking base was utilized to construct the input base excitation for the FE models. Simulation reduce-scale experiments results correlate very well with the FE analysis model. The seismic force of the prototype structures connects instead well40. This indicates the current FE modeling technique can reproduce the seismic response of (GRE) walls in a virtual environment in an accurate manner.

This research explores the seismic behavior of (GRE) walls using reduced-scale shaking table experiments and FE analysis under earthquake conditions equivalent to those utilized in the analysis's base movements. The various base excitations with different amplitudes and frequencies were used as the basis for the model's initial movements. The strength of these stimulations was gradually raised from low peak acceleration amplitudes for brief periods to high peak acceleration amplitudes for a specific time. It is depicted that the time history of acceleration was applied to the model for evaluation. Considering the seismic wave characteristics of the ground motions, three seismic waves were used in the FE analysis, which included one near-field seismic wave in (SM wave), one far-field seismic wave in EI Centro (EI-wave), and one middle-far-field seismic wave in Taft (TA-wave) in the United States as shown in figure 9A. Acceleration recordings and Fourier spectra from near-fault, far-field, and mid-far-field grounds characteristics are shown in Table 7.

The recordings of seismic ground motion acceleration are classified into three types: (a) TA-wave, (b)SM-wave, and (c) EI-wave6,7.

The baseline model parameters were sourced from the study conducted by Yu et al. (48), which focused on modeling the instrumented reinforcement wall at the Public Works Department (PWD) in Pakistan, as documented by6. To establish a higher confidence level in the 3D model created for this investigation, the authors and their colleagues reexamined the deflection and lateral pressure toe load observed and numerically predicted in a previous study43. The situation of reinforcement concrete and Gravity-type (GRE) walls after an earthquake is depicted in Fig. 10a, b. The 3D numerical and reduce-scale results agree reasonably with the physical system's complexity. In this study, using the reduce-scale experiments and 3D FE model, it was determined that increasing the structural elastic modulus from its initial value improved the overall accord between measured and predicted values. Yu et al.45 reported the 2D numerical model results using the program FLAC 2D, and the authors performed the 3D modeling using the program ABAQUS. The disadvantage of the 2D approach is that discontinuous reinforcement loads must be regarded as continuous elements along the plane of strain (x). These challenges (GRE) walls have variable horizontal spacing between reinforcement backfill layers, such as the Minnow Creek wall in the United States, as studied by34.

(a) Conventional reinforcement concrete wall: (b) Conventional gravity-type stone masonry wall (case study)

The results obtained from analyzing various parameters related to hollow precast walls SM-W, gravity-type GS-W, and reinforcement concrete rigid RC-W (GRE) walls under seismic loading conditions are discussed in this section. The results include lateral pressure of the wall, settlement of the backfill soil, backfill lateral pressure, vertical settlement of the foundation, deflection of the wall, and displacement of the wall. The experiments provide valuable insights by comparing the results with the FE model; we gain valuable insights into the behavior and performance of these different GRE wall types, allowing overall effectiveness in mitigating the effects of seismic events.

The lateral pressure distributions at different earth-retaining walls with displacement changes are shown in Fig. 11. From the Figure, it can be seen that the lateral pressure increases with an increase in the height of the wall and changes into a concave curve. As the height of the earth-retaining wall increased, the lateral pressure gradually increased from the top to the bottom of the wall. The reduction rate of the lateral pressure at the upper part of the retaining wall was significantly larger than at the lower part of the retaining wall, owing to the larger displacement of the upper part of the retaining wall compared to the lower part. The lateral pressure at the bottom part of the wall was slightly greater than the lateral pressure given at the top of the wall. In explanation of this finding, during rotation of the GRE wall, the principal stress is deflected, as the soil layer at the top of the wall (which has a larger displacement) is subjected to additional shear stress by the soil layer at the bottom of the wall (which has a smaller displacement), causing the earth pressure at the top of the wall to decrease and the earth pressure at the bottom to increase.

Lateral pressure of the wall (A) lateral pressure of wall, (B) vertical pressure of the wall.

The distribution of the vertical wall pressure of the walls (SM-W, GS-W, and CR-W) walls under seismic loading conditions. The physical experiments on the vertical pressure of the walls reveal significant variations in vertical pressure distribution along the height of the walls. Figure 11B demonstrates that SM-W has better results with lower negative vertical pressure than GS-W and CR-W, indicating that the bottom of the wall has the highest vertical pressure.

To evaluate the effectiveness of the geogrid on the backfill settlement, two LVDTs, SD1 near the wall, SD2 mid, and SD3 far from the wall, were installed on the backfill. Figure 12 shows the vertical settlement of the backfill at LVDT. As seen, compared to the reduce-scale test, the connection of the backfill to the wall decreased the vertical settlement of the backfill in all tests. As expected, the physical modeling test that performed best in reducing the lateral earth moment (SM-W) showed the lowest vertical displacement. In this test, the backfill geogrid connected to the back part of the wall controlled the backfill soil, resulting in less settlement. The same trend was observed for tests with RC-W. The presence of the geogrid decreased the vertical settlement in all tests, as shown in Fig. 12. In these tests, test results (SM-W = 15 mm RC-W = 15 cm, GS-W = 5 kPa, same backfill condition) performed best in decreasing the settlement. However, the vertical settlement of the backfill at the GS-W did not show a similar trend. The backfill experienced vertical settlement at the GS-W, which was very high due to self-weight and the type of wall. It was important in the physical modeling tests to match the required wall displacement to achieve active conditions. Figure 12 shows the failure moment of backfills in some tests.

Settlement of the backfill soil.

A detailed reduce-scale experiment of the lateral pressure distribution in the backfill of SM-W, GS-W, and RC-W GRE walls under seismic loading conditions. The analysis of lateral pressure distribution along the height of the backfill soil revealed distinct patterns. The lateral backfill pressures were predominantly lower, around one-third of the wall's height, and transitioned to positive values after the mid-level. The SM-W and RC-W exhibited similar performance in terms of lateral pressure resistance. Figure 13a demonstrated that these walls were subjected to primarily lower lateral pressures at one-third of their height, suggesting their capacity to endure and resist lateral forces. On the contrary, GS-W exhibited high lateral pressure. This alternating pattern suggests potential instability and oscillation in the lateral response of GS-W. The ability of SM-W and GM-W to withstand and resist lateral forces, as indicated by predominantly negative lateral pressures, these backfills demonstrate their capacity to distribute and resist lateral forces exerted on them effectively. The findings emphasize the advantages of SM-W and RC-W regarding lower lateral pressure.

Lateral pressure of the backfill (A) lateral pressure of backfill, (B) vertical pressure of the backfill.

A comprehensive experiment of the vertical backfill pressure of the SM-W, GS-W, and RC-W walls under seismic loading conditions. The analysis of backfill vertical pressure revealed that the pressure decreased with the backfill's depth and the soil's nature. As the depth below the foundation increased, the vertical earth pressure exerted on the backfill decreased. This observation suggests that the depth below the foundation significantly influences vertical pressure distribution in the backfill. Furthermore, the findings indicated that backfill height also influences the vertical pressure. Figure 13b illustrates and accentuates the benefits of SM-W and RC-W regarding decreased vertical pressure. On the contrary, the alternating high negative vertical pressure was observed in the bottom of the GS-W backfill.

Figure 14 presents a detailed experiment investigation of the deflection on the height of the earth-retaining wall. The findings indicate that the wall's height increased, its deflection increased, and it became highest at the top of the wall. The amount of deflection in the (SM-W) wall grew from lowest to highest as the wall rose in height. It indicates that the upper area of the wall experiences the highest deflection. Similar deflection behavior in GS-W and RC-W (GRE) walls is depicted in Fig. 14. However, the deflection distribution behavior in the (SM-W) wall differed from that of the GS-W and RC-W. The findings display the continuous deflection in the earth-retaining walls after 0.2 m of wall height, whereas they display the progressive rise in deflection with the wall's height. Their research emphasized the importance of accurate prediction and control of deflection to ensure the stability and performance of (GRE) walls under seismic forces. Nevertheless, there were notable differences in the deflection distribution patterns between SM-W, GS-W, and CR-W walls. The distributions of wall deflection, namely SM-W (42 mm, 90 mm, and 170 mm), GS-W (52 mm, 120 mm, and 225 mm), and RC-W (50 mm, 105 mm, and 210 mm) are measured, respectively.

Deflection of the wall.

Figure 15 shows the moment-displacement behavior of a GRE wall with a geogrid backfill soil. The behavior of the GRE walls in both the at-rest and active conditions over 9 tests (SM-W, GS-W, and RC-W) can be compared in this Figure. The behavior of the retaining wall with SM-W in the active condition differed from that of a wall with a GS-W and RC-W. As stated, to change the GRE wall's seismic input motion from at-rest to active, the GS-W wall was allowed to maximum displacement up to 40 mm in increments of 1 mm. This lateral displacement of the SM-W wall differs from GS-W and RC-W; therefore, the influence of the backfill soil for determining an effect of the SM-W and RC-W on the lateral displacement was greater than for the SM-W wall. Generally, it was observed that the double SM-W wall model significantly decreased the lateral displacement of the wall. This decrease enabled the GRE wall to become more stable. Figure 15 shows that tests SM-W (bottom = 2 mm, top = 10 mm), SM-W-18 (bottom = 10 mm, top = 40 mm), and RC-W (bottom = 4 mm, top = 18 mm), SM-W wall model performed best for decreasing the displacement in the various seismic input motion. Note that an increase in the height of the wall influences the wall displacement by increasing the top displacement. Figure 15 compares the top displacement for all tests' various seismic input motions.

Top displacement of the wall.

A detailed and rigorous FE investigation has been performed to understand the GRE walls' seismic response. As mentioned in part. Third, the influence of different-facing panels and cohesionless backfills on the seismic response of the GRE walls was studied by performing nonlinear time history FE analyses on GRE walls.

Figure 16A detailed analysis of the lateral pressure distribution on (SM-W, GS-W, and CR-W) under seismic loading conditions. The lateral wall pressures were predominantly positive up to the middle height of the wall and gradually approached slightly low values towards the top. When comparing the performance of the different wall types, SM-W and CR-W demonstrated better stability and resistance to lateral pressure than GS-W. The passive deformation of earth pressure mainly affects the earth-retaining wall for the passive state. According to Coulomb's law, passive earth pressure, calculated by the pressure theory, is the limit earth pressure, which is generally more biased than the earth pressure on the retaining wall. Our analysis aligns with their observations, as SM-W and CR-W demonstrated better stability and resistance to lateral pressure than GS-W. Additionally,40 investigated earth-retaining walls' behavior under seismic conditions and analyzed their response to lateral pressures. Our results corroborate their findings, as we observed similar patterns in the distribution of lateral pressures along the height of the walls. Furthermore, our analysis, which further supports to the lateral pressure of SM-W, is superior when compared to GS-W and CR-W.

Lateral pressure of the wall (A) lateral pressure of wall, (B) vertical pressure of the wall.

The distribution of vertical pressure of wall (SM-W, GS-W, and CR-W) walls under seismic loading conditions. Analysis of vertical pressure reveals significant variations in vertical pressure distribution along the height of the walls. Figure 16B demonstrates that SM-W has better results with lower negative vertical pressure than GS-W and CR-W, indicating superior resistance to vertical pressure. These findings are consistent with the results obtained in a previous study by Ling et al., 2005, highlighting the influence of wall height on vertical pressure distribution. Our study further confirms the importance of considering wall height as a crucial factor in designing earth-retaining walls. Comparing our results with previous researchers is crucial to validate our findings and contribute to the existing body of knowledge21,28. By examining the literature, we can identify similar trends and patterns in the behavior of different wall types under seismic loading conditions, confirming the reliability of our analysis and experiments and gaining a broader perspective35.

Figure 17 compares seismic settlement recordings of the backfill surfaces (SM-W, GS-W, and RC-W) caused by the ground motions of TA-wave, EI-wave, and SM-wave. The settlements are caused by the ground motions of the three ground motions. The surface settlements of (SM-W, GS-W, and RC-W) in the reinforced zone of the SM-W and RC-W (GRE) wall were much smaller than the surface settlements of GS-W in the reinforced zone of the earth-retaining wall as shown in the Figure; furthermore, the backfill surface settlements of SM-W in the (GRE) wall were also much smaller than the backfill surface settlements of the GS-W (GRE) wall. Particularly under the ground motions from the far and middle-far fields, the backfill surface settlement of the SM-W and RC-W models was only approximately half that of the GS-W model. The settlements of SM-W in the reinforced zone of the (GRE) wall were close to the settlements of RC-W in the (GER) wall, which was because the positions were located in the backfill reinforced zones of the backfill material; however, they were much smaller than the backfill surface settlements of GS-W in the (GRE) wall. The results showed that the existence of the geogrid could effectively decrease seismic settlements of the SM-W and RC-W backfill surfaces and provide seismic settlement resistance abilities for the (GRE) wall. The settlements increase with time and distance from the face and are greater for geogrid strip materials that are more extensible. The maximum settlement of walls SM-W (12 mm, 20 mm, and 17 mm), GS-W (27 mm, 39 mm, and 33 mm), and RC-W (18 mm, 23 mm, and 21 mm) is approximately, respectively. The finding demonstrates that for each (GRE) wall case in each plot, the minimum settlements are close to the connections, consistent with the soil drooping over the reinforcement geogrid mesh as previously described.

Settlement of the backfill soil.

A detailed FE analysis of the lateral pressure distribution in the backfill of SM-W, GS-W, and RC-W walls under seismic loading conditions. The analysis of lateral pressure distribution along the height of the backfill soil revealed distinct patterns. The lateral backfill pressures were predominantly lower, around one-third of the wall's height, and transitioned to positive values after the mid-level. The SM-W and RC-W exhibited similar performance in terms of lateral pressure resistance. Figure 18A demonstrated that these walls were subjected to primarily lower lateral pressures at one-third of their height, suggesting their capacity to endure and resist lateral forces. On the contrary, GS-W exhibited high lateral pressure. This alternating pattern suggests potential instability and oscillation in the lateral response of GS-W. The comparison allows us to gain insights into the behavior of backfill lateral pressure and its impact on the stability and seismic performance of backfill. The SM-W wall demonstrates its capacity to effectively distribute and resist lateral forces exerted on it. On the contrary, the alternating positive lateral pressures observed gradually increase from top to bottom, and the maximum lateral pressure in the bottom of the backfill.

Lateral pressure of the wall (A) lateral pressure of backfill, (B) vertical pressure of the backfill.

A comprehensive FE analysis of the vertical backfill pressure of the SM-W, GS-W, and RC-W walls under seismic loading conditions. The analysis of backfill vertical pressure revealed that the pressure decreased with the depth of the backfill and types of backfill soil. As the height of the backfill layers increased, the vertical earth pressure exerted on the backfill in the bottom increased. This observation suggests that the backfill height significantly influences vertical pressure distribution in the backfill. Furthermore, the findings indicated that backfill height also influences the foundation pressure. A higher vertical ground pressure on the backfill resulted from a higher backfill height. Figure 18B illustrates the vertical pressure of SM-W, RC-W, and GS-W. On the contrary, the alternating high negative vertical pressure observed in RC-W and GS-W suggests potential instability in its vertical pressure response.

Figure 19 presents a detailed experiment investigation of the deflection on the height of the earth-retaining wall. The findings indicate that the wall's height increased, its deflection increased, and it became highest at the top of the wall. The amount of deflection in the (SM-W) wall grew from lowest to highest as the wall rose in height. It indicates that the upper area of the wall experiences the highest deflection. Similar deflection behavior in GS-W and RC-W (GRE) walls is depicted in Fig. 19. However, the deflection distribution behavior in the (SM-W) wall differed from that of the GS-W and RC-W. The findings display the continuous deflection in the earth-retaining walls after 0.2 m of wall height, whereas they display the progressive rise in deflection with the wall's height. Their research emphasized the importance of accurate prediction and control of deflection to ensure the stability and performance of (GRE) walls under seismic forces. Nevertheless, there were notable differences in the deflection distribution patterns between SM-W, GS-W, and CR-W walls. The distributions of wall deflection, namely SM-W (42 mm, 90 mm, and 170 mm), GS-W (52 mm, 120 mm, and 225 mm), and RC-W (50 mm, 105 mm, and 210 mm) are measured, respectively.

Deflection of the wall.

Figure 20 illustrates the calculated vertical settlement of the foundation and the vertical pressure the facing wall panel exerts on the base case footing. The data points with open symbols show that the toe load pressures differ throughout the wall's running length. A two-dimensional model cannot identify this small three-dimensional impact. Because the distributions of foundation vertical settlement at the same three places were not practically discernible, they were not depicted to prevent visual clutter. The vertical toe pressure exceeds the pressure resulting from the panels' self-weight (the footing load factor) owing to a down-drag on both the rear of the (GRE) wall panels and the foundation. This suggests that wall height and depth below the foundation influence the foundation's vertical settlement. The GS-W wall's self-weight differs from that of the other walls analyzed, and the vertical settlement is larger than that of the other two walls analyzed. An increase in the self-weight of the wall affects the foundation settlement considerably due to the overturning moment generated by the lateral pressure developed from the backfill. The vertical settlement of the foundation progressively changes; the vertical settlement is larger at various spots throughout the wall's running length. Figure 20 shows that the vertical settlement at the same positions on the (GRE) wall is SM-W (8 mm, 14 mm, and 13 mm), GS-W (23 mm, 31and 28 mm), and RC-W (15 mm, 21 mm, and 20 mm), respectively. Finally, the findings show that the vertical settlement of the SM-W wall foundation is meager due to the wall's self-weight compared to the other walls. GS-W, RC-W.

Vertical settlement of the foundation.

A seismic input motion was applied to the (GRE) wall to compare the lateral displacement of hollow precast concrete SM-W and reinforcement rigid concrete and gravity-type stone masonry SM-W and RC-W. The lateral displacement of each type of wall was measured and plotted against the wall's height, as illustrated below. The curves represent the lateral displacement values for the same heights of (GRE) walls SM-W, GS-W, and RC-W. The (GRE) wall's lateral displacement increased linearly with height. Notably, GS-W, a 5 m tall gravity-type (GRE) wall, exhibited a more significant maximum lateral displacement than the SM-W and RC-W, which had a lower displacement value. This is attributed to the fact that SM-W displays lower levels of lateral displacement, as illustrated below. The lateral displacement of the hollow precast concrete wall SM-W was observed to be approximately 30% lower than that of the reinforcement rigid concrete and stone masonry (GRE) walls RC-W and GS-W. These findings are supported by physical experiment results demonstrating a reduction in incremental active lateral displacement to values under seismic loadings, such as the numerical simulation highlighted in models and tests. The behavior of SM-W is consistent with the lower lateral displacement depicted in Fig. 21 at the same location. However, the study found that the RC-W and GS-W lateral displacement compression was much higher, which aligns with the findings of Ling et al.21.

Displacement of the wall.

The present study focused on the effectiveness of connecting the GRE wall to decrease the lateral earth moment on the wall. A total of 9 physical reduce-scale tests and full-scale finite element analyses were prepared, and the behavior of (GER) walls was evaluated under seismic conditions. This research compared the worldwide performance of conventional and prefabricated (GER) walls under seismic conditions. Several conclusions were drawn from the results of the present study.

The physical reduced-scale tests and FE analysis results revealed that the deflection level on the bottom of the valve stems in SM-W decreased by about 40%, and the displacement reduced by 30–40%. Owing to the reduction in deflection level, it is concluded that SM-W is significantly more stable than RC-W and GS-W (GER) walls in terms of seismic response. The deflection distribution and top displacement in (GER) walls increased with the height and maximum displacement at the top.

The experimental testing and finite element analysis findings concluded that the settlements of the backfill surface were contingent upon the presence of geogrid reinforcement in the backfill. The geogrid can significantly reduce the seismic settling of the backfill surfaces. The settling of the backfill surface in the reinforced zones of SM-W and RC-W (GRE) was much less than in the GS-W reinforced zone. The geogrid enhanced the seismic settlement resistance of the GRE walls.

The pressure development level in the backfill material was determined by the appearance time length of seismic waves with high acceleration values and the depth of the test places in the backfill material. Because geogrids were lighter and more flexible mesh structures than soils, they successfully reduced vertical pressure development and backfill settlement dissipation.

Both physical reduced-scale testing and finite element (FE) analysis demonstrated that the displacement of the (GRE) wall impacted the distribution of lateral pressure and the position of the resulting pressure. There was a direct relationship between the lateral pressure distribution and the displacement of the wall. The highest lateral pressure was seen near the base of the GRE walls and backfill, which was directly connected to the displacement of the wall.

The drop in pressure against backfill settlement was found to be quite comparable to the decrease in pressure against wall displacement. This demonstrates that the wall's movement was directly influenced by the pressure exerted by the backfill and its settlement at the wall's edge.

The novel configuration exhibits enhanced seismic resistance and improved cost-effectiveness by substantially reducing bottom bar thickness (25%) and precast wall volume (40%). The wall system can be rapidly assembled with minimal physical exertion. Overall, the precast concrete (GRE) wall demonstrated superior performance in terms of stability and efficiency when compared to the conventional (GRE) retaining wall. According to the comparative study, prefabricated concrete (GRE) walls outperformed conventional earth-retaining walls in regions with elevated seismic activity. The (GRE) walls are considered thick and non-bending from a geotechnical engineering viewpoint. Hence, they can resist the seismic passive earth pressure force development when moving toward the backfill soil. However, this circumstance is crucial for the stability of embedded (GRE) walls and the structural design of (GRE) wall types. Additional research is necessary to understand these critical geotechnical structures' seismic resilience comprehensively.

The datasets generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request.

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This work was supported by Supported by the Science and Technology Research Program of the Institute of Mountain Hazards and Environment, CAS (IMHE-ZDRW-01), and the National Natural Science Foundation of China, China (Grant numbers: 42077275& 42271086), and the Special project of Basic Research-Key project, Yunnan (Grant numbers: 202301AS070039).

Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu, 610299, China

Muhammad Akbar, Pan Huali & Ou Guoqiang

University of Chinese Academy of Sciences, Beijing, 100049, China

Muhammad Akbar

Institute of International Rivers and Eco-Security, Yunnan University, South Section, East Outer Ring Road, Chenggong District, Kunming, 650500, Yunnan, China

Jiangcheng Huang

Department of Civil Engineering, University of Engineering and Technology Taxila, Rawalpindi, Pakistan

Muhammad Usman Arshid & Qaiser uz Zaman Khan

Department of Structural Engineering, Faculty of Civil Engineering, Doctoral School, Akademicka 2, Silesian University of Technology, Akademicka Street 5, 44-100, Gliwice, Poland

Bilal Ahmed

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Study conception and design: Research Concept, MA, Methodology, MA data collection: MA, B, A software, MA, supervision, PH, OU, Funding Source, PH, OU, Project Admiration, PH, OU, Draft manuscript preparation: MA PH, Review and editing M.U.A, Q, Z, K. All authors reviewed the results and approved the final version of the manuscript.

Correspondence to Pan Huali.

The authors declare no competing interests.

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Akbar, M., Huali, P., Huang, J. et al. Seismic response comparison of various geogrid reinforced earth-retaining walls: based on shaking table and 3D FE analysis. Sci Rep 14, 24168 (2024). https://doi.org/10.1038/s41598-024-64203-4

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Received: 27 November 2023

Accepted: 06 June 2024

Published: 15 October 2024

DOI: https://doi.org/10.1038/s41598-024-64203-4

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