This test scheme is based on the geocell retaining wall structure developed by Prerana et al. (2025), Sedaght and Ghalandarzadeh (2023) during the Yan’an Airport relocation project. Yan’an Airport is located in the heart of the Loess Plateau, characterized by a thick accumulation of loess layers with a loose and porous structure. It is situated at the intersection of multiple active fault zones, resulting in relatively high seismic intensity and significant risks of geological disasters such as landslides and collapses. The shaking table tests were performed at the Lanzhou Institute of Seismology, China Earthquake Administration, using a shaking table with dimensions of 4 m × 6 m, featuring three directions and six degrees of freedom, as shown in Figure 1. The normal operating frequency range of the shaking table was 0.1–70 Hz. A rigid model box with interior dimensions of 2.8 m × 1.46 m × 1.8 m (length × width × height) was utilized. The side walls on the left and right were made of transparent acrylic, allowing observations of the model’s state changes during vibration. The front and rear walls were composed of steel plates, and a layer of foam board (thickness = 5 cm) was strategically placed at each end of the model box to absorb seismic waves and mitigate the impact of reflected waves. The tested model is geometrically similar to the prototype; thus, material similarity for fillers and reinforcement materials was not considered. This may lead to certain differences in the mechanical performance of the geocell retaining walls compared to the prototype. Nevertheless, this test remains highly valuable for investigating the dynamic response characteristics of geocell retaining walls under seismic conditions.

The model materials utilized in this study included loess, quartz sand, geocells, and steel connectors.

The model comprises two components: the foundation and slope. The foundation, with dimensions of 2.7 m (length) × 1.46 m (width) × 0.2 m (height), was constructed by compacting loess to a density of 1,600 kg/m³. The slope was composed of a geocell-reinforced retaining wall and the backfill slope. The retaining wall was constructed using 16 layers of geocells, which were filled with filler using a layered filling method. Each layer was compacted to a height of 10 cm. The geocells and the slope filler were both composed of quartz sand. The slope’s dimensions are as follows: a height of 1.6 m, width of 1.46 m, and a slope ratio of 1:0.25.

The test measurements encompass acceleration, geocell strain, slope displacement, and slope top settlement. A total of 19 acceleration monitoring points were arranged in four columns, numbered sequentially as A₁ to A₁₉.Strain measuring points were strategically placed on the inner walls of the geocells to obtain the geocell strain. Five settlement monitoring points were placed at the top of the model, with a spacing of 283 mm between adjacent points, as shown in Figure 4a. The noncontact 3D optical measurement system by XTDIC was employed to assess the displacement of the retaining wall, with the measuring points arranged, as shown in Figure 4b.

This test utilized three distinct types of load waveforms: EI-Centro, Wolong, and Sin waves. The initial amplitude was set at 0.1 g, and increased in 0.1 g increments, as shown in Table 2. Following the completion of loading for each level of seismic waves, a sinusoidal sweep frequency excitation with an amplitude of 0.05 g, a frequency range spanning from 1 to 50 Hz, and a duration of 235 s was applied. This excitation served to evaluate the dynamic characteristics of the model and partially mitigate the residual deformation induced during the vibration process, as shown in Figure 5. To comply with seismic design specifications (Song et al., 2016), the acceleration amplitude was based on the seismic wave in the X-direction when bidirectional XZ seismic waves were applied, and the amplitude of the seismic wave in the Z-direction was set at 65% of the amplitude of the seismic wave in the X-direction.

To analyze the effects of seismic wave amplitudes on the dynamic response of retaining walls, the EI-Centro wave in the X-direction was used as an example. The study focuses on conditions with amplitudes of 0.1 g, 0.3 g, 0.5 g, 0.7 g, and 1.0 g.

As illustrated in Figure 6, the variation of peak value of horizontal displacement along elevation under different amplitudes. As demonstrated, when the amplitude is less than 0.5 g, the peak value of horizontal displacement changes approximately linearly along the elevation. When the amplitude exceeds 0.7 g, the peak value of horizontal displacement gradually increases with the increase of the amplitude, and the trend of change along the elevation is first increasing and then decreasing, and the maximum value of displacement peak appears at the 15th layer geocell position. Due to the vibration density settlement of the packing inside the geocell under the action of earthquake, lateral expansion deformation occurs, resulting in the geocell stretching and tensile stress. This tensile stress exerts lateral binding force on the packing inside the geocell, that is, the lateral confinement pressure of the geocell effectively limits the lateral movement of the packing, resulting in the increase of the stiffness of the packing, and the upper retaining wall structure is affected by the free surface on both sides. The displacement increases with the increase of the amplitude, which also indicates that the interaction mechanism between the geocell and the filler has an important influence on the seismic performance of the retaining wall structure.

The lateral confinement pressure of the geocell on the filler can be calculated according to Equations 1–3 (Wang et al., 2024; GB50011-2010, 2010; Rajagopal et al., 1999): σ g = 2 M t D ε ε c 1 − ε 1 (1) D ε = D 0 1 − ε 1 (2) ε c = 1 − 1 − ε 1 1 − ε 1 (3) where σ g denotes the lateral confinement pressure of the geocell, M _t signifies the stiffness of the geocell strip, ε c is the circumferential strain of the geocell, D ε represents the equivalent diameter of the geocell under the circumferential strain ε c , D ₀ is the initial equivalent diameter of the geocell, and ε 1 is the axial strain of the geocell.

As illustrated in Figure 7, the variation of lateral confinement pressure of geocell along elevation under different amplitudes. As demonstrated, when the amplitude is less than 0.3 g, the lateral confinement pressure of the wall and the wall size is similar, and it changes approximately linearly along the elevation. When the amplitude exceeds 0.5 g, the lateral confinement pressure under geocell confinement increases significantly. Because of the significant nonlinear characteristics of quartz sand packing, when the amplitude is small, the interparticle friction makes the particles in a static state, so the lateral confinement pressure under geocell confinement is small. With the increase of the amplitude, the particles overcome the friction between the particles and produce shear slip, and the packing gradually sinks, resulting in greater tensile strain on the cell. In addition, the lateral confinement pressure of the wall compartment is greater than that of the wall physical chamber, and the maximum lateral confinement pressure of the wall compartment appears in the area below 850 mm elevation, while the lateral confinement pressure of the wall physical chamber appears at the top of the wall. Since the wall compartment is at the free surface, its deformation is not restricted and it can be fully developed, resulting in a larger lateral confinement pressure of the wall compartment. The deformation of the wall structure chamber is restricted by the surrounding geocell and the packing material, so the lateral confinement pressure of the cell is small.

As illustrated in Figure 8, the variation of the acceleration amplification coefficient along elevation under different amplitudes. As demonstrated,the acceleration amplification factors at both columns of monitoring points exhibit an elevation amplification effect across various amplitudes. Specifically, the acceleration amplification coefficient at the first column of monitoring points demonstrates a three-stage trend of “increase-decrease-increase” along the elevation, whereas the second column shows a two-stage trend of “decrease-increase”. Overall, the acceleration amplification coefficient varies rhythmically with increasing amplitude, generally trending downward. This trend is attributed to the gradual compaction of the filler due to shear slip as seismic conditions accumulate. Once the amplitude reaches a certain threshold, the filler ceases to experience shear slip, predominantly undergoing inter-particle shear friction. Consequently, slope damping and shear modulus increase, leading to heightened seismic energy attenuation and a decreasing trend in the acceleration amplification coefficient.

As illustrated in Figure 9, the horizontal variation pattern of slope top settlement under varying amplitudes. As demonstrated, the slope top settlement initially decreases and then increases horizontally across different amplitudes, with the maximum value occurring at the wall geocell location. Additionally, as the amplitude increases, the slope top settlement gradually augments. The differential settlement value, Δx/H (settlement value/wall height), serves as an indicator of settlement magnitude. Upon completion of vibration at an amplitude of 0.9 g, the maximum settlement reaches 9.5 mm, representing 0.593% of the wall height. This value is significantly lower than the 2% of wall height recommended by the AASHTO (WU, 2019) standard, highlighting the effective settlement suppression capability of the geocell retaining wall.

In conclusion, when the seismic amplitude exceeds 0.5 g (corresponding to a seismic intensity greater than VI), it becomes necessary to install additional tie bars at positions 3H/16 and 1H/2 to enhance the stability of the retaining wall.

To analyze the effects of seismic wave direction on the dynamic response of retaining walls, the EI-Centro waves with amplitudes of 0.4 g in the X,Z and XZ directions were used as examples for investigation.

As demonstrated in Figures 12a–d, the variation patterns of geocell lateral confinement pressure, acceleration amplification factor, horizontal displacement peak and slope roof settlement under different directions. As demonstrated, the lateral confinement pressure of the geocell, the acceleration amplification factor and the settlement of the slope top are all larger in the x-direction vibration, while the peak value of the horizontal displacement is larger in the XZ direction vibration. On the whole, among the three vibration directions, the dynamic response of the retaining wall under X and XZ vibration is more significant, and the influence of X vibration is more prominent. Therefore, in the seismic design, we should pay attention to the role of X vibration and take it as the main design basis.

To analyze the effects of seismic wave types on the dynamic responses of retaining walls, the unidirectional EI-Centro, Wolong, and Sin waves were used as examples for investigation with amplitudes equal to 0.4 g in the X-direction.

As demonstrated in Figures 13a–d, the variation of geocell lateral confinement pressure, acceleration amplification factor, peak of horizontal displacement and settlement of slope top under different wave patterns. As demonstrated, geocell lateral confinement pressure, acceleration amplification factor and slope top settlement all exhibit significant dynamic response of the retaining wall under the action of natural seismic waves. This is due to the complex composition of natural seismic waves, including multiple frequency and amplitude components and wide frequency band, which have large energy and will induce complex dynamic response when interacting with the structure. However, the frequency and amplitude of the sine wave are relatively fixed, and the interaction process with the structure is relatively simple, resulting in a small dynamic response of the retaining wall. However, the peak of horizontal displacement is larger under the action of sine wave, because the retaining wall is easy to resonate with the specific frequency of sine wave, resulting in a larger displacement response.

In summary, the dynamic response of the geocell retaining wall is more significant under the action of natural seismic waves, which is mainly due to the characteristics of wide spectrum and uneven energy distribution of natural seismic waves, and its influence on the dynamic response of the structure is more complex and significant. Therefore, the effect of natural seismic waves should be considered in seismic design.

A numerical model was developed using the FLAC^3D.6.0 software program, with its dimensions shown in Figure 16. The slope ratio was 1:0.25. Contact surfaces were established between the fillers, which obey the Mohr–Coulomb criterion. In accordance with the findings of preceding studies (Krishnaraj et al., 2023; Li S. H. et al., 2021), an elastoplastic constitutive relationship was adopted for the geocell, gravel, and sand. The yield criterion employed was the Mohr–Coulomb criterion, a suitable model for describing the mechanical behavior of geotechnical materials. The numerical model employs a viscous boundary condition at the bottom and free-field boundaries surrounding it. Local damping was selected, with a damping coefficient of 0.158. The seismic input consisted of the EI-Centro wave with a peak acceleration of 0.4 g, applied in the X direction.

To verify the accuracy of the numerical simulation, a numerical model with the same size as the shaking table model test was established. Parameter Settings, test conditions, test elements, monitoring point layout, monitoring indicators and seismic wave selection in the numerical model were all set according to the shaking table test conditions, as shown in Figure 17. The numerical simulation results are similar to the shaking table test results and their variation rules, which shows that the numerical simulation results are accurate and reliable.

According to the provisions in the existing norms (Steudle, 2014), the slope ratio of the retaining wall is generally 1:0.25 ∼ 1:0.75, and the slope ratio of 1:0.2, 1:0.3, 1:0.4, 1:0.5 and 1:0.6 is selected for research.

As demonstrated in Figures 18a–d, the variation of geocell lateral confinement pressure, permanent horizontal displacement, acceleration amplification factor and slope top settlement under different slope ratios. As demonstrated, with the decrease of the slope ratio, the above four indexes gradually decrease, and the stability of the retaining wall is significantly improved, which is because the center of gravity of the wall moves down with the decrease of the slope ratio, and the anti-overturning ability is enhanced. At the same time, the stress distribution in the interior of the geogrid is more uniform, reducing the phenomenon of stress concentration, so as to absorb and disperse seismic energy more effectively, reduce the impact on the wall, and improve the seismic performance. In addition, when the slope ratio decreases from 1:0.2 to 1:0.3, the dynamic response increases significantly, while when the slope ratio exceeds 1:0.3, the increase is relatively gentle. This is because when the retaining wall is steeper, the wall stiffness is larger, the natural vibration frequency is higher, and it is easy to resonate with the seismic wave frequency. At the same time, the contact area between the filler and the geocell is small, and the friction is limited, resulting in a significant increase in dynamic response. The easy-going slope ratio decreases, the wall stiffness decreases, the natural vibration frequency decreases, the resonance effect weakens, the contact area between the packing and the geocell increases, the friction is enhanced, and the interaction is more stable, thus inhibiting the increase of the dynamic response.

In summary, the downslope ratio of seismic action has a significant effect on the stability of the slope. With the decrease of slope ratio, the stability of slope is improved significantly, and the seismic resistance is enhanced. However, too small slope ratio will lead to the increase of retaining wall area, resulting in waste of resources. Therefore, considering the economy and seismic performance, it is suggested that the slope ratio of retaining wall should be prefered to be about 1:0.3 to meet the seismic demand while saving resources.

To analyze the influence of the height to width ratio of retaining wall (retaining wall height H/retaining wall thickness B), the retaining wall height remained unchanged, and the retaining wall thickness was studied with 1, 2, 3, 4 and 5 geocell thickness.

As demonstrated in Figures 19a–d, the variation laws of geocell lateral confinement pressure, permanent horizontal displacement, acceleration amplification factor and hilltop settlement under different aspect ratios. As can be seen from the figure, with the decrease of the aspect ratio, the above four indicators are gradually reduced, and the stability of the retaining wall is improved. This is because the overall stiffness of the retaining wall is significantly increased with the decrease of the aspect ratio, and it can better resist the deformation and displacement under the action of earthquake. At the same time, the anti-overturning moment and shear section area of the wall increase, which can more effectively resist the overturning force and shear force generated by the earthquake, thus improving the anti-overturning and shear stability of the wall, so the stability is enhanced. In addition, when the ratio of height to width is large, the deflection of the retaining wall itself is large, and the wall appears as a convex parabola shape. The maximum value of permanent horizontal displacement and lateral confinement pressure of the geocell appears at about H/3 away from the bottom of the wall, which is because the position of the resultant point of earth pressure is about H/3 away from the bottom of the wall, and the bottom of the retaining wall is constrained by the foundation friction force. Therefore, under the combined action of earth pressure and bottom friction, the wall forms a convex parabola form. With the increase of the thickness of the retaining wall, the weight and flexural stiffness of the retaining wall also increase, and the deformation of the wall changes. When the height to width ratio is 1.4, the wall body almost shifts, which is because with the increase of the width of the retaining wall, its deformation characteristics gradually approach from the characteristics of the flexible retaining wall to the characteristics of the rigid retaining wall, so its bending deformation decreases.

In conclusion, the aspect ratio is closely related to the stability of slope under earthquake action. As the aspect ratio decreases, the seismic performance increases. It should be pointed out that although blindly increasing the thickness of the retaining wall can improve the stability, it has limited effect on deformation control, and will significantly increase the project cost and reduce the construction efficiency. Therefore, on the premise of meeting the requirements of seismic fortification, it is recommended that the aspect ratio should be preferred at about 1.8 to achieve the balance between economy and seismic performance.