To study the seismic performance, a physical model of the retaining wall for this planar sliding landslide was built. The top and bottom vibration cylinders can drive the overall vertical vibration of the model. The test device also includes an electro-hydraulic servo loading device, a monitoring device and corresponding control software (Shan et al., 2022; Zheng et al., 2021), as shown in Figure 1. The cylinders are equipped with force sensors. Considering the convenience of testing and the limitations in the size of the test instrument, the ratio of similarity between this model and the actual scenario was obtained based on similarity theory. This test mainly involved five similarity ratios; namely, geometric similarity ratio C _L , gravity similarity ratio C _γ , acceleration similarity ratio C _a , stress similarity ratio C _σ , and force similarity ratio C _F . Considering the equipment size and the convenience of research, the geometric similarity ratio was set as 10. The unit weight similarity ratio was preliminarily determined as 0.955. The acceleration similarity ratio was taken as 1 due to the same self-weight stress field.

This test mainly involves simulating the soil layer, bedrock and fabricated retaining wall, in which the fabricated retaining wall includes a grid steel frame and shotcrete as shown in Figure 2. Prepare suitably similar materials according to the above similarity ratio. Through the proportioning test, the compressive strength of bedrock model material is 2.33 MPa, and the compressive strength of retaining wall model material is 2.98 MPa. Three prefabricated retaining walls were made for test, and the thickness of vertical plate was 150 mm, 200 mm and 300 mm, respectively. In order to minimize the influence of rigid boundary in the vibration direction on the dynamic response of the structure, 5 mm thick polystyrene foam plates were placed on the side wall and bottom of the model box to reduce the reflection of vibration waves. The amplitude is selected as 1 mm, the vibration frequency is set as 2 Hz, 4 Hz, 6 Hz, 8 Hz, 10 Hz, and the vibration times are 100 times each. The size of geometric model can be shown in Figure 2. The model before loading can be presented in Figure 3.

To investigate the dynamic behavior of retaining walls with varying thicknesses under different frequency vibration loads, this paper focuses on the damage evolution process of retaining walls with thicknesses of 150 mm, 200 mm, and 300 mm subjected to vibration frequencies of 2 Hz, 4 Hz, 6 Hz, 8 Hz, and 10 Hz, respectively. The corresponding results are depicted in Figures 4–6.

Figure 4 illustrates the damage evolution of the 200 mm thickness retaining wall across various loading frequencies. It is important to note that the number of vibrations at different frequencies is consistently 100 times. At very small vibration frequencies, the inclination of the vertical plate is minimal, resulting in less force applied to the retaining wall. Consequently, surface cracks are small, primarily concentrated at the bottom of the vertical plate. The impact on the backfill behind the retaining wall is negligible at these low frequencies. As the frequency increases, the backfill soil exerts gradually escalating pressure on the retaining wall, leading to a step-by-step augmentation of retaining force. Consequently, the vertical plate of the retaining wall becomes unstable due to varying forces at different positions, and cracks at the bottom of the vertical plate expand in tandem with the frequency increase. Figure 5 depicts the damage evolution of the retaining wall with a thickness of 300 mm under varying frequency loads. It is crucial to highlight that the damage characteristics of the 300 mm thick retaining wall are considerably milder in comparison to those of the 200 mm thick retaining wall. When the frequency of loading is low, the impact on the retaining wall and its backfill is small. As the frequency of loading increases, the surface shear force exerted on the retaining wall experiences a gradual augmentation, resulting in different shear action on the specimen surface. Concurrently, cracks located at the bottom of the retaining wall expand proportionally with the increase in frequency, contributing to the progressive instability of the retaining wall. Figure 6 illustrates the damage evolution of a retaining wall with a thickness of 150 mm at loading frequencies of 2 Hz, 4 Hz, 6 Hz, 8 Hz, and 10 Hz. It is crucial to highlight that the damage characteristics of the 150 mm thick retaining wall differ significantly from those of the 200 mm and 300 mm thick retaining walls. As the vibration frequency increases, the backfill exerts a progressively escalating soil pressure on the retaining wall’s surface. This results in a gradual tilting of the retaining wall and the incremental expansion of cracks at its base, ultimately pushing the retaining wall into an unstable state.

The failure characteristics of retaining wall with different vertical plate thicknesses after loading can be presented in Figure 7. It can be seen that the thickness of retaining wall significantly affects its failure pattern. Specifically, when the thickness of the retaining wall is 150 mm, a significant breaking phenomenon occurs, and the straight wall is broken very seriously. When the thickness is 200 mm, block failure occurs in the retaining wall. However, when the thickness of the retaining wall is 300 mm, the shape of the retaining wall is relatively complete, and the peeling phenomenon occurs only in the local area.

Figure 8 shows the soil pressure distribution of initial value, peak value and final value on the vertical plate. The distribution mode is with an “S” shape of peak and final value, while an “C” shape of initial value. Generally speaking, the peak stress is greater than the initial and final values. The Earth pressure at 1002 is relatively high, which is consistent with the test. The stress of the 2001 is relatively high, which may be due to nonlinear phenomena of soils and the soil–structure interface during shaking, especially for higher intensities, may also affect the dynamic Earth pressure. These recorded Earth pressures may be biased to some extent by the response of the Earth pressure cells.

As the main purpose of the results of the numerical simulation was to study the dynamic response for stress, strain and displacement of the prefabricated retaining wall and not to pursue a high degree of consistency with the physical model. Therefore, the Vrancea wave can be used in the numerical simulation. The numerical model is numbered as RWS-1, which is mainly composed of prefabricated retaining wall, sliding bed and sliding body. The connecting plate of the retaining wall is designed on the front side of vertical plate. The connecting plate is equipped with bolt holes, and the bottom plate is equipped with grooves and bolt holes. The solid segment of the vertical plate is inserted into the groove of the bottom plate, and is connected to the bottom plate through the bolt hole of the connecting plate. The parameters of model are shown in Table 1. The natural slope of the landslide is about 23°, the dip angle of the sliding surface is 20°, and the longitudinal length of the model is 2 m. The retaining wall is made of concrete with strength of C30. Its density is 2.385 t/m³, elastic modulus is 30,000 MPa and Poisson’s ratio is 0.2. The density of bolts is 7.8 t/m³. The elastic modulus of the bolt is 201,000 MPa and the Poisson’s ratio is 0.3. Four-node linear tetrahedral element is adopted on the bolt. Concrete is modeled by plastic damage constitutive model. The plastic damage constitutive model is used to simulate the concrete, and the Drucker-Prager model is used to simulate the sliding body and bedrock, which are set as 8-node hexahedron linear reduction integral units. The density of sliding bed is 24.5 g/cm³, Young’s modulus is 13,770 MPa, and Poisson’s ratio is 0.25. The density of sliding body is 19.8 g/cm³, Young’s modulus is 1001.7 MPa, and Poisson’s ratio is 0.35. The sliding bed and sliding body are set as 8-node hexahedron linear reduction integral units (Ren et al., 2023). Five monitoring points (P110, P746, P841, P142, and P284) of the model RWS-1 vertical plate are selected for analysis. The model and the location diagram of monitoring point are shown in Figure 9.

The contact surface is set to Explicit, and the slip formula is finite slip. The normal of the contact surface is defined as hard contact. The tangential penalty friction formula is given to allow certain elastic slip, and the friction coefficient is 0.5. The normal of the bolt-concrete contact surface is defined as hard contact, and the friction coefficient is defined as 0.7 under the penalty contact type defined in tangential direction. To reduce the iteration and convergence problems in the calculation process, this paper uses explicit integration algorithm to define the acceleration—time amplitude curve, and input the seismic action in the form of seismic waves into the defined boundary conditions. The bottom and four sides of the slide bed are constrained by unidirectional hinge support. Vrancea seismic wave is selected in this simulation as the representative waveform. In order to save calculation time, it is compressed to 3.5 s, and the acceleration remains unchanged. The acceleration curve is shown in Figure 10. There are two analysis steps in the calculation. In the first analysis step, only gravity is applied from 0 to 0.5 s. In the second analysis step, seismic waves are applied from 0.5 to 4.0 s.

The stress contour plot of each component of model RWS-1 retaining wall at 4.0 s is shown in Figure 11. It can be seen from Figure 11A that the stress at the joint between the vertical plate and the bolt is maximum, about 3.30 MPa. The stress on both sides of the embedded section is relatively large, about 0.55–0.83 MPa. Figure 11B shows that the maximum stress of the retaining wall base is about 4.51 MPa, which is mainly distributed in the bolt hole, the connection between the vertical plate and the bottom plate, and the front side of the bottom plate. In Figure 11C, the maximum stress of the bolt is distributed in the middle of the bolt, about 54.54 MPa, and the stress at both ends of the bolt decreases gradually. Overall, the stress of the vertical plate is less than that of the bottom plate, and the stress of the bolt is much greater than that of the vertical plate and the bottom plate. It shows that under the action of earthquake, the stress concentration of this kind of precast retaining wall appears at the connection nodes. Due to the relatively large stiffness of bolts and baseplate, the connection between vertical plate and baseplate is prone to damage.

The displacement contour of each component of the model RWS-1 retaining wall at 4.0 s is shown in Figure 12. As shown in Figure 12A, the vertical plate rotates, and the upper part moves more than the lower part. The maximum displacement of the plate is about 40 mm at the top, and the minimum displacement is about 0.4 mm at the embedded segment. As shown in Figure 12B, the minimum displacement of the baseplate is distributed in the groove, and gradually increase toward the front end and the rear end of the baseplate. As shown in Figure 12C, The displacement of bolts is small, ranging from 0.64 mm to 0.72 mm, and the maximum displacement of the bolt is located at the top part. It indicates that under the action of vibration load, the displacement of fabricated retaining wall is mainly rotation, and slight sliding.

The node P142 at the assembly node of the model (Figure 13) is selected for research, and the stress-strain and stress-displacement curves are shown in Figures 13, 14. As shown in Figure 13A, the stress - strain curve of point P142 in 0–4.0 s is complicated due to the randomness of seismic action. The curve is amplified in different periods as shown in Figures 13B–D. Amplify the stress-strain curve of 0.5–1.5 s, as shown in Figure 14B, the curve is mainly in series “V” shape, and the nonlinearity and hysteresis are not obvious. As shown in Figure 14C, the curve of stress-strain is “V” -shaped stacking during 1.5–3.0 s. As shown in Figure 13D, the curve of stress-strain in the period of 3.0–4.0 s is mainly triangular, showing obvious nonlinearity and hysteresis at some moment.

As shown in Figure 14, the stress-displacement curve reflects the variation characteristics of point P142 under earthquake action. It can be seen that in the first 0–0.5 s, the displacement of the point is basically 0 under the action of gravity only, and the stress at this point is compressive stress due to earth pressure. From 0.5 s, the displacement gradually increases under the action of earthquake. During 0.5–1.4 s, the compressive stress decreases to 0 gradually, and the displacement is 0–1.5 mm. During 1.4–2.7 s, the stress is mainly tensile stress with small value, and the displacement is 1.5–4.0 mm. During 2.7–4.0 s, the displacement of the point is about 4.0–7.0 mm, and the stress changes into compressive stress. With the increase of seismic action time, the rate of displacement increases gradually.

The stress time history curve of all the monitoring points is shown in Figure 15. As can be seen from Figure 15, points P142 and P284 are located at the assembly nodes of retaining wall. From 0 to 0.5 s, the stress of P110, P746 and P841 in the middle and upper part of the vertical slab is small, but increases slightly with the increase of depth, which is consistent with the distribution law of earth pressure. In order to balance the upper earth pressure, the compressive stress of P142 and P284 is larger during 0–0.5 s. From 0.5 s to 4.0 s, the stress changes of P110, P746, and P841 in the middle and upper parts of the vertical slab are relatively small under earthquake action. During 0.5–1.5 s, the compressive stress of P142 at the assembly joint gradually decreases, the tensile stress appears during 1.5–2.8 s, and then converts into compressive stress during 2.8–4.0 s and gradually increases. At point P284, the compressive stress first increases and then decreases during 0.5–1.5 s, the tensile stress appears during 1.5–2.5 s, and the compressive stress increases gradually during 2.5–4.0 s. The change trend of P284 is similar to that of P142, and the stress value is greater than that of P142. In summary, the closer to the assembly node, the greater the compressive stress.

The concrete strength grades of RW-M1, RW-M2, RW-M3, and RW-M4 are C20, C25, C30, and C40 respectively, and other parameters are the same. When Vrancea seismic wave is input, the calculation results of stress distribution of vertical slab with different concrete strength at 4.0 s are shown in Figure 16. It can be seen that the stress at the top of the vertical plate is almost zero, and the stress at the bottom is maximum. The bottom stress of vertical slab with concrete strength of C20 (RW-M1), C25 (RW-M2), C30 (RW-M3) and C40 (RW-M4) is 0.185 MPa, 0.5 MPa, 0.165 MPa, and 0.35 MPa respectively. Therefore, the strength of concrete significantly affects the stress of the vertical plate.

The displacement of vertical slabs with different concrete strength at 4.0 s is shown in Figure 17. As shown in Figure 17, it is noted that the displacement of vertical plate includes translation and rotation. The top displacement is the largest and the bottom is the smallest. The displacement distribution curve is basically straight. The displacement at the top of the vertical slab with concrete strength C25 is the largest, as well as the inclination. The displacement at the top of the vertical slab with concrete strength C30 and C40 decreases to about 0.8 mm, the inclination of the vertical slab decreases as well. Displacement of vertical plate with strength C20 is between of C25 and C30.

The vertical plate thickness of models RW-M6, RW-M3, and RW-M5 is 150 mm, 200 mm, and 300 mm respectively. The influence of thickness on plate stress, displacement and acceleration under seismic action is analyzed. The stress distribution curve of vertical plates with different thicknesses at 4.0 s is shown in Figure 18. It can be seen from the figure that the stress at the top of the vertical plate is tensile stress with small magnitude, and gradually transforms downward into compressive stress, which is relatively large. The compressive stress at the bottom vertical plate increases with the increase of the vertical plate thickness. The thicker the vertical plate is, the greater the stiffness is, and the smoother the stress distribution curve is.

As shown in Figure 19, the overall displacement is less than 0.9 mm, and the upper displacement is larger. The greater the thickness of the vertical plate, the greater the horizontal displacement at the top. When the thickness of the vertical plate is 150 mm and 200 mm, the slope of the embedded section is smaller than that of the free section due to the limitation of the bottom plate. When the thickness of vertical plate is 300 mm, the stiffness is larger, and the slope of embedded section is the same as free section, which is greater than that of 150 mm and 200 mm.

The acceleration distribution curves of vertical plates with different thicknesses at 4.0 s are shown in Figure 20. As shown in Figure 20, when the thickness of the vertical plate is 150 mm and 200 mm, the acceleration is almost zero compared with 300 mm. When the thickness of vertical plate is 150 mm, 200 mm and 300 mm, the inflection points are 4, 2, and 1 respectively. In general, with the increase of vertical plate thickness, the number of inflection point of acceleration distribution curve decreases gradually, and the acceleration of embedded section at the bottom of vertical plate increases gradually.

To study the influence of the embedded depth of vertical slab on the mechanical properties of retaining wall, models RW-M9, RW-M3, RW-M10, and RW-M11 were designed, with embedded depths of 180 mm, 200 mm, 220 mm, and 250 mm respectively. The stress distribution curves corresponding to different embedded depths of vertical plates at 4.0 s are shown in Figure 21. It can be seen from Figure 21 that the upper stress of the four models is close to zero, and the compressive stress at the bottom of the model gradually increases with the increase of the embedding depth. When the embedding depth is 250 mm, the compressive stress at the bottom increases significantly, and the tensile stress occurs at the connecting plate.

The vertical plate displacement distribution of models with different embedding depths at 4.0 s is shown in Figure 22. As shown in Figure 22, if the embedding depth of the vertical plate is small, the overall inclination of the vertical plate is large. When the embedding depth is 250 mm, the inclination direction of the embedding section is opposite to that of the free section, which is related to the tensile stress produced there, and the embedding section significantly reduces the slope of the free section.