Dynamic numerical analysis of liquefiable silty fine sand reinforced by gravel pile

Abstract

Silty fine sand is prone to liquefaction under the action of earthquake. The research on the reinforcement method of silty fine sand foundation is the key to earthquake prevention and disaster reduction. This paper takes the Zhulong river section of the main canal of Xixiayuan irrigation area as the research object, and the cross section model of the canal is established by FLAC 3D software. Considering the dynamic hydraulic coupling effect of soil, the mechanism and effect of anti-liquefaction reinforcement of gravel pile are explored. Research findings demonstrate that stone columns exert a significant influence on the displacement of the main water conveyance canal and its foundation. Under seismic loading, the unreinforced model exhibited pronounced plastic horizontal displacement and upward heave displacement at the toe of the canal embankment. In contrast, the reinforced model showed a marked reduction in plastic horizontal displacement and the complete elimination of upward heave. Significant pore pressure increases occurred at the base of the canal embankment and at the embankment toe in the unreinforced model, triggering initial liquefaction at the embankment toe. The liquefied zone rapidly expanded to within 3 m below the ground surface, exhibiting clear liquefaction phenomena. The installation of stone columns created effective drainage pathways, facilitating the downward drainage of pore water from the liquefiable silty fine sand layer. This resulted in substantially reduced pore pressures at the embankment base and toe, accompanied by a decrease in the pore pressure ratio. Only localized liquefaction zones were observed at the embankment toe and between the stone columns near the sand surface. These findings indicate that stone columns effectively mitigate the seismic-induced buildup of pore water pressure, thereby enhancing the liquefaction resistance of the engineering structure. The research findings hold significance for silt liquefaction prevention and control in the main canal project of the Xixiayuan Irrigation Area.

1 Introduction

The 1964 Niigata earthquake in Japan, the 1970 Tokai earthquake, the 1976 Tangshan earthquake, the 1999 and Taiwan Chi-Chi earthquake, the 2008 Wenchuan earthquake and other major earthquakes with a magnitude of 7 or more have experienced sand spraying and water gushing. The liquefaction of the site has caused a large number of casualties (Bhattacharya et al., 2014; Wang et al., 2010; Wu et al., 2010; Earthquakes in China over the last, 2022). On 6 February2023, a double strong earthquake occurred in Turkey, which caused serious site liquefaction. Typical liquefaction damage forms, such as sand spraying, ground lateral displacement, foundation settlement and foundation loss of bearing capacity, caused serious damage to buildings and casualties (Huang and Yu, 2013; Chen et al., 2024). On 18 December2023, an earthquake in Jishishan County, Linxia Prefecture, Gansu Province, triggered a large-scale liquefaction slip disaster of 2.5 km long under the loess tableland landform of the second terrace of Jintian Village and Caotan Village, about 20 km from the epicenter. It buried 51 houses in two villages and killed more than 20 people (Taftsoglou et al., 2023). The engineering geological disasters induced by site liquefaction under earthquake are becoming more and more serious, which is a key problem in the field of earthquake resistance and disaster prevention and mitigation (Wang et al., 2024).

Liquefied soils cover granular soils such as saturated and unsaturated sandy soils, Silt, loess, etc. In addition, saturated coarse gravelly soils, rockfill materials, and relatively dense sandy soils may also be liquefied in the presence of high-intensity vibrations and poor drainage conditions (Wang, 2021; Mele et al., 2023; Guo et al., 2022; Ma et al., 2023). Among them, sand-powder mixed soils such as silty sand and sandy silt are the most common liquefied soils (Xu et al., 2022). The reinforcement methods of liquefaction site include dynamic compaction method, compaction sand pile method, gravel pile method, grouting method and so on. Among them, the gravel pile construction is simple, the material is convenient, the cost is low, and it is widely used in the project. The gravel pile has good permeability and large stiffness relative to the foundation soil, so it can play the role of drainage and stiffness constraints, thereby improving the liquefaction resistance of the liquefiable site.

At present, domestic and foreign scholars have carried out research on seismic liquefaction of gravel pile reinforcement through field investigation, physical model test, numerical simulation and other methods (Do et al., 2016; Madhav and Krishna, 2008; Yasuda et al., 2012). Chen et al. summarized the cases of anti-liquefaction foundation treatment in 8 strong earthquakes, and found that the anti-liquefaction effect of granular drainage piles such as sand compaction pile method and gravel pile method was obvious (Chen et al., 2015). Bayati et al. carried out shaking table tests of gravel piles to reinforce loose and extremely loose saturated sand. The results show that gravel piles can effectively reduce the maximum settlement and pore water pressure ratio, and the gravel piles in loose sand have a greater effect on reducing pore water pressure than very loose sand. (Bayati and Bagheripour, 2018). Cui et al. studied the seismic performance, liquefaction process and reinforcement mechanism of earth-rock dam foundation through shaking table test and numerical simulation. The results show that raft and gravel pile significantly alleviate uneven settlement and cracking through various reinforcement mechanisms such as support effect, drainage effect and stiffness improvement effect (Cui, 2023). Complementing these mechanism studies, Shenthan et al. developed an analytical methodology to evaluate the effectiveness of composite stone columns in silty soils, specifically quantifying the role of drainage in pore pressure dissipation (Shenthan et al., 2004). In terms of numerical simulation, Kouhdaragh and Ashrafi provided a clear methodological reference for modeling soil-structure interaction under liquefaction conditions using the Finite Element Method (FEM) and the Mohr-Coulomb model, which offers crucial insights for establishing dynamic numerical models of gravel pile-reinforced foundations (Kouhdaragh and Ashrafi, 2024). Building on advanced modeling techniques, Forcellini and Tarantino utilized 3D numerical modeling to analyze stone columns as a mitigation technique for earthquake-induced lateral spreading, demonstrating their efficacy in reducing ground deformation (Forcellini and Tarantino, 2014). Yang et al. used numerical simulation software to simulate the reinforcement effect of gravel pile on liquefied sand foundation of main canal. The results show that gravel pile can effectively reduce the excess pore water pressure, and its drainage and compaction effect can effectively eliminate the site liquefaction phenomenon (Yang et al., 2014). Zou et al. conducted a numerical simulation of the model test of gravel pile reinforced saturated sand site. The results show that the gravel pile has a significant effect on the anti-liquefaction performance of the soil and effectively improves the peak shear stress ratio of the soil (Zou and Wang, 2019). Regarding engineering practice and validation, Moazafarbaygi and Asghari-Kaljahi assessed regional liquefaction potential based on field SPT data and empirical methods, highlighting the importance of calibrating numerical analysis results with measurable field indicators and widely accepted empirical criteria to enhance the reliability and practicality of conclusions (Moazafarbaygi and Asghari-Kaljahi, 2024). Meng et al. evaluated the treatment effect of compacted gravel pile through standard penetration test, heavy dynamic penetration test and composite foundation load test, and reviewed the bearing capacity of the foundation after treatment (Meng, 2024).

However, despite these advances, the drainage effect of gravel pile material—acting as a granular medium—is highly complicated under dynamic action. There are still many dynamic characteristics, such as the coupling of deformation, effective stress, and pore pressure changes in gravel pile-reinforced liquefied foundations, that remain to be fully understood.

Therefore, this paper takes the Zhulong River section of the main canal of the Xixiayuan irrigation area as the research object. Using FLAC 3D numerical simulation software, this study simulates the reinforcement effect of the liquefied stratum and analyzes the dynamic response and seepage field evolution of the site. The research results aim to promote the continuous development and improvement of the seismic theory of liquefaction site reinforcement.

2 Overview of the study area

The Zhulong river section of the main canal of Xixiayuan irrigation area is relatively straight. The elevation of the river bottom 105.20 m, which is flat. The elevation of the left bank embankment is 109.2 m, and the width of the embankment is about 3.1 m. The elevation of the right bank embankment is 110.5 m, and the width of the embankment is about 7.1 m. According to the drilling, the first layer is sandy loam layer thickness of 1.6 m, layer bottom elevation of 103.6 m. The second layer is the silty fine sand layer with a thickness of 2.8 m and a bottom elevation of 101.8 m. The third layer is light silty loam with a thickness of 1.4 m and a bottom elevation of 99.4 m. The fourth layer is a heavy silty loam layer with a thickness of 7.3 m and a bottom elevation of 92.1 m (Figure 1).

During the investigation, the groundwater depth is about 4 m in the silty fine sand layer, which is the pore phreatic water of Quaternary loose layer.According to the 《China ground motion parameter zoning map GB18306-2015》, the peak acceleration of ground motion in the study area is 0.1 g, and the characteristic period of basic ground motion acceleration response spectrum of class II site is 0.40. The basic intensity of earthquake in the study area is VII degree, and the seismic design standard of channels and hydraulic structures is based on the basic intensity of earthquake VII degree.

3 Model building and calculation process

3.1 Calculation model

In order to explore the effect and mechanism of gravel pile reinforcement, the dynamic calculation of two groups of channel models before and after gravel pile reinforcement was carried out. According to the field investigation and the actual situation of the project, adhering to the general principles of dynamic numerical simulation, the calculation model is established. Rationale for Model Dimensions: The height of the model is 12.8 m (Z-axis direction, from the model bottom to the canal embankment top), the distance from the bottom of the model to the ground surface is 9 m. The length of the model is 175 m (X-axis direction),This lateral extent was specifically selected to satisfy wave propagation requirements, placing the artificial boundaries sufficiently far from the central region of interest to minimize the interference of reflected waves, and the width of the model is 1 m (Y-axis direction). This choice represents a plane strain simplification, allowing for an accurate capture of the cross-sectional dynamic behavior of the linear canal structure while optimizing computational efficiency.The unreinforced model includes a dam and six layers of soil (Figure 2a). In addition to the soil layer, the reinforcement model also includes two parts: gravel pile and compacted sand between piles. Therefore, the gravel piles are mainly arranged at the bottom of the channel and the slope platform outside the embankment to the bottom of the slope.Based on the engineering requirements for drainage capacity and stiffness, the designed pile diameter is 1 m, the pile length is 8.0 m, and the pile spacing is 2 m. (The reinforcement model is shown in Figure 2b).

FIGURE 1

FIGURE 2

3.2 Loading waveform and loading boundary

The selection of seismic wave is the key to carry out the dynamic calculation of engineering structure. In the current stage of engineering seismic dynamic simulation, the selected seismic waves mainly include: ①strong earthquake records that have occurred in the site; ②representative typical strong earthquake records; ③artificial simulation to generate seismic waves. In this paper, considering the effective duration of seismic waves, spectral characteristics, seismic peak intensity, seismic characteristic period grouping and site category of engineering construction, horizontal and vertical natural seismic waves suitable for engineering site conditions and fortification intensity are selected from the PEER Ground Motion Database Center. In the process of numerical analysis, in order to ensure the accuracy of the dynamic calculation results and reproducibility, the grid size should be less than 1/10-1/8 of the wavelength. Therefore, the selected seismic waves are filtered by seismosignal software to ensure that the mesh size meets the calculation requirements.

The free field boundary is used to simulate the effect of the infinite site around the model. The input mode of the dynamic load is the velocity time history (Figure 3). The input motion is applied at the model base, which is treated as the engineering bedrock interface. Apply an 80-s time history of horizontal loading along the X-direction at the model base, comprising 40 s of seismic excitation followed by 40 s of excess pore water pressure dissipation.The mechanical damping adopts local damping, and the local damping coefficient is 0.157. In the calculation, it is assumed that the soil of the channel foundation is completely saturated, the bottom of the foundation is regarded as the undrained boundary, and the top of the foundation is the free drained boundary.

FIGURE 3

3.3 Material constitutive model and parameter selection

The model fine sand layer and sand between piles are the main liquefied soil layers, which are simulated by Finn model, and other rock and soil bodies are simulated by Mohr-Coulomb model. Finn model is a liquefaction constitutive model built in Flac3D software. This model integrates the Byrne equation (1991) (Byrne, 1991) which describes the plastic volumetric strain increment into the Mohr-Coulomb model. Based on the elastic-plastic analysis, it is assumed that the rise of dynamic pore pressure is related to the plastic volumetric strain increment. The fused Finn-Byrne equation is as follows:

In the formula: is the volume strain, is the shear strain, and are the input parameters, and the relationship between them is as follows:

There exists the following relationship between Parameter C₁ and the relative density Dr of sandy soil:

Additionally, an empirical correlation exists between relative density (Dr) and the normalized standard penetration resistance (N1).

Furthermore, there exists a definite empirical relationship between the relative density and the standard penetration blow count:

The calculation parameters of the model are selected according to the results of field standard penetration test and indoor static and dynamic test. The physical and mechanical parameters of each soil are shown in Table 1.

3.4 Layout of model monitoring points

Monitoring points were selected at horizontal offsets of 27.5 m, 50 m, 75 m, 100 m, 125 m, and 150 m from the left boundary of the model, with vertical positions at ground surface and subsurface depths of 1.5 m, 2.5 m, 3.5 m, 5 m, and 7 m below grade. A total of 36 monitoring points were used to monitor the response of displacement, acceleration, pore pressure ratio and other parameters of the model. The location and number of monitoring points are shown in Figure 4.

FIGURE 4

4 Analysis of dynamic response results

4.1 Displacement

After 40 s of seismic wave loading, the displacement nephogram of the two groups of models before and after reinforcement is shown in Figure 5. As evidenced in Figures 5a,b, significant horizontal displacements were concentrated near the toe of the right canal embankment and within adjacent off-channel areas. The maximum horizontal displacement reached 0.20 m in the unreinforced case. Following stone column reinforcement, displacements along the main trunk canal decreased substantially, with peak values reduced to 0.03 m. Vertical displacement contours (Figures 5c,d) reveal pronounced settlement of 0.22 m in the embankment zone prior to ground improvement. Post-reinforcement, embankment crest settlements diminished significantly, with maximum values declining to 0.12 m.

FIGURE 5

Time-history curves of ground surface displacements before and after reinforcement are presented in Figure 6. These demonstrate that the displacement response of the main trunk canal foundation increased monotonically with seismic duration, with primary accumulation occurring during the initial seismic phase due to higher acceleration amplitudes. Following attenuation of seismic accelerations, deformation rates decreased substantially, resulting in permanent seismic deformations at analysis termination.Comparative analysis of Figures 6a,b reveals significant permanent horizontal displacements deviating from baseline in the unreinforced model, which were effectively mitigated in the reinforced case. Specifically, maximum horizontal displacement at the right embankment toe reached 0.19 m under unreinforced conditions - approximately twice that of the left counterpart (0.095 m). Post-stone-column installation reduced maximum displacements to 0.06 m (left) and 0.05 m (right) at respective toes.

FIGURE 6

Figures 6c,d indicate that the unreinforced model, dominated by soil liquefaction effects, exhibited maximum vertical heave of 0.007 m at the inner slope toe (x = 50 m) and 0.002 m at channel centerline. Reinforcement eliminated heave at left slope toe and channel surface while reducing vertical deformations at right toe. The unreinforced foundation displayed compressive heave deformation patterns both inside and outside the embankment, attributed to liquefaction-induced slope instability characterized by seismic subsidence and tensile cracking at the crest, combined with lateral spreading and compressive heaving at the toe. In contrast, stone columns with substantially higher stiffness than surrounding soil developed a coupled horizontal-vertical resistance mechanism that effectively suppressed these failure modes.

4.2 Pore water pressure

Figure 7 presents the pore water pressure contour plot under static loading conditions. Results indicate a linear decrease in pore water pressure with increasing elevation, reaching a maximum value of 90.0 kPa. The horizontal alignment of equipotential lines confirms a hydrostatic pressure distribution.

FIGURE 7

With the input of seismic waves, the pore water pressure of the main water conveyance line increases significantly. Figure 8 reveals non-uniform distribution of pore water pressure equipotential lines in the unreinforced model due to topographic effects of the canal embankment. At t = 40 s of seismic loading, the peak value reached 125 kPa within the sandy stratum beneath the right high embankment. Following stone column reinforcement, vertical hydraulic conduits formed by the columns facilitated drainage of pore water from liquefiable silty sand layers toward deeper zones. By t = 40 s, pore pressures at the embankment base and toe decreased by approximately 7.2% compared to the unreinforced case. Notably, synergistic drainage between stone columns and surrounding sand led to pore water accumulation at the model base, increasing hydraulic gradients in this region. The stone column system effectively dissipated seismically induced excess pore pressures through enhanced foundation drainage capacity. Concurrently, preferential flow along column-soil interfaces triggered localized pore pressure buildup at the basal layer.

FIGURE 8

4.3 Pore pressure ratio

The pore pressure ratio (r_u) refers to the ratio of the pore water pressure increment (Δu) to the initial vertical effective stress (σ_v0), which can be expressed as:

When the pore pressure ratio is equal to 1, the soil can be considered to be in a liquefied state. Taking the center point c1 as an example, the time history curve of the pore pressure ratio at this point is shown in Figure 9. It can be seen from the diagram that the pore pressure ratio at the center of the channel before reinforcement increases obviously with the seismic input, and then fluctuates up and down. The maximum value of the pore pressure ratio is 1.2, indicating that the liquefaction phenomenon occurs at the center of the channel. The variation law of pore pressure ratio at the center of the channel after reinforcement is consistent, but the fluctuation amplitude is obviously reduced, and the maximum pore pressure ratio at the center of the channel after reinforcement is 1.07.

FIGURE 9

With the input of seismic waves, the pore pressure ratio at different elevations is also different. Taking the different elevation measuring points in the center of the channel as an example, the time history curve of the pore pressure ratio of each monitoring point is shown in Figure 10. It can be observed that under earthquake loading, the pore pressure ratio (r_u) in the shallow layers is significantly higher than that in the deep layers, reaching its peak near the surface. This vertical distribution is scientifically attributed to two mechanisms: first, the initial effective overburden stress (σ_v0) decreases as the depth decreases, naturally elevating the ratio; second, the excess pore water pressure generated in deeper liquefied strata migrates upward, leading to an accumulation effect in the shallow layers. Comparing the distribution of pore pressure ratio before and after reinforcement, it can be seen that the pore pressure ratio of the reinforced model decreases significantly in the elevation range of more than 11 m. The pore pressure ratio increases obviously at the elevation of 11 m. This is due to the reason that the gravel pile and the sand between the piles move the water in the upper part of the model downward, which is manifested in the decrease of the pore pressure ratio in the upper 5 m and the increase of the pore pressure ratio in the range below 5 m.

FIGURE 10

4.4 Liquefaction zone

Under the action of earthquake, some soil reaches the critical state of liquefaction (the pore pressure ratio is still less than 1), that is, the strength of soil decreases, but still retains a certain bearing capacity, which is called quasi-liquefaction phenomenon. Referring to the existing research, the pore pressure ratio exceeding 0.8 is used as the criterion of quasi-liquefaction, and the development of liquefaction zone is dynamically marked in the model (Dong et al., 2015; Li et al., 2024; Zou, 2019; Fan et al., 2024).

Considering that no active drainage measures (e.g., pumping) were implemented in the gravel pile reinforced foundation, identical hydraulic boundary conditions were applied to both reinforced and unreinforced models. By solely adjusting the parameters of the piles and inter-pile sand to simulate reinforcement effects, significant differences manifested in the liquefaction zone distribution between the two models.

The cloud distribution of the liquefaction zone under an earthquake with a duration ranging from 1 to 40 s is depicted in Figure 10 for both unreinforced and reinforced models. From the diagram, it can be seen that at the initial stage of seismic wave loading (within the first 3 s), the liquefaction phenomenon of the unreinforced model first occurs at the foot of the embankment, and the liquefaction range reaches the bottom of the fine sand layer (liquefaction layer) within 3 m below the surface. With continued loading under high acceleration in the first 5 s, the liquefaction front propagated progressively, exhibiting non-monotonic expansion patterns at the ground surface and embankment toe locations governed by seismic phase variations. In contrast, the reinforced model shows minimal liquefaction development at the same loading stage, with liquefaction confined to the embankment toe and sand surface between piles, but no significant deepening.

The analysis indicates that the higher seismic acceleration in the initial 5 s promotes more pronounced liquefaction in the unreinforced case; however, after 5 s, as acceleration decays, the liquefaction area expansion is limited. Although the central area of the channel in the unreinforced model is not the peak area of excess pore water pressure, the initial effective stress there is relatively low, resulting in a pore pressure ratio of 0.8–1.0 and triggering local liquefaction. On the contrary, although the excess pore water pressure at the bottom of the right dam of the unreinforced model is the highest, its effective stress is significantly higher, so the pore pressure ratio is less than 0.8 and no liquefaction occurs.

The effective drainage function of the gravel piles and the sand between piles in the reinforced model slows the accumulation of pore water pressure, thereby preventing the expansion of liquefaction zones. The specific analysis is as follows: In the early stage of seismic wave loading on the reinforced model, liquefaction areas appear at the toe of the embankment and on the surface of the sand between the piles. However, as the seismic waves continue to be input, the liquefaction areas do not develop further. This is because the effective drainage function of the gravel piles and the sand between them reduces the pore water pressure at the surface of the channel, thereby significantly reducing the liquefaction phenomenon of the water conveyance channel and improving the seismic performance of the project.

4.5 Mechanism of anti - liquefaction reinforcement of gravel piles

The mechanism of gravel pile reinforcement for liquefiable silty-fine sand foundation is mainly reflected in two aspects: stiffness constraint and drainage dissipation. Under the action of seismic cyclic loading, the silty-fine sand generates excess pore water pressure due to the shear shrinkage effect, which in turn leads to liquefaction and instability. Gravel piles are composed of high-strength granular materials, and their shear modulus can reach 146 MPa, much higher than the 18.9 MPa of the surrounding silty-fine sand, resulting in a significant stiffness difference. This high stiffness characteristic enables them to play a “skeleton” role in the foundation, effectively suppressing the lateral flow and uneven bulging of the soil. Numerical simulation results show that after the installation of gravel piles, the maximum horizontal displacement of the foundation decreases from 0.2 m to 0.03 m, and the vertical deformation changes from destructive heave to controllable overall settlement, significantly improving the dynamic stability of the foundation.

Meanwhile, gravel piles have excellent drainage performance, which can accelerate the dissipation of excess pore water pressure and prevent it from accumulating to the liquefaction critical state. The permeability coefficient of the pile body is as high as the order of 1e-1 cm/s^-1, which has an obvious advantage compared with silty fine sand (about 5e-5 cm/s^-1), forming an efficient vertical drainage channel at the pile - soil interface. Under the boundary conditions of free drainage at the top and impermeability at the bottom, pore water is rapidly drained downward along the pile body under dynamic loads, creating a favorable hydraulic gradient. The simulation results show that after reinforcement, the pore pressure ratio at the monitoring point decreases from 0.97 to 0.43, a decrease of more than 55%, and it basically dissipates completely within 40 s after the earthquake. The liquefaction area is effectively limited, showing a benign response characteristic of “local transient liquefaction rapid recovery”.

The stiffness constraint and drainage dissipation mechanism do not exist in isolation but form a unified system of mutual promotion and synergistic action. Thanks to its high - stiffness characteristics, the gravel pile significantly enhances the anti-deformation ability of the water conveyance channel and effectively suppresses the development of plastic strain in the soil. The composite drainage channel formed by the gravel pile and the sand between the piles efficiently drains pore water and weakens the accumulation of excess hydrostatic pore pressure caused by dynamic loads. The synergistic action of the two fundamentally suppresses the liquefaction deformation of the foundation and greatly improves the dynamic stability of the project. Through the dual paths of mechanical constraint and hydraulic drainage, the gravel pile fundamentally improves the anti - liquefaction ability of the silty fine sand foundation and has broad application prospects in the seismic reinforcement of water conservancy projects.

5 Discussion

5.1 Analysis of displacement and deformation

The numerical simulation results indicate distinct differences in deformation characteristics before and after reinforcement. For the unreinforced model, soil liquefaction leads to pronounced plastic horizontal displacement, reaching a maximum of 0.20 m at the embankment toe, and obvious vertical uplift displacement of 0.22 m near the dam toe. In contrast, the gravel pile reinforcement substantially alters this behavior. The plastic horizontal displacement is reduced to a peak value of 0.03 m, and the uplift displacement disappears completely. Although localized settlement (maximum 0.12 m) occurs in the middle of the channel, this controlled vertical deformation replaces the more destructive uplift and lateral spreading observed in the unreinforced case.

5.2 Pore pressure regulation and liquefaction mitigation

The mitigation mechanism relies on the hydraulic properties of the gravel piles. Simulation results show that under seismic action, the unreinforced model experiences a rapid increase in pore water pressure at the embankment bottom and dam toe, resulting in extensive liquefaction. However, in the reinforced model, the gravel piles form effective vertical drainage channels together with the inter-pile sand. This structure facilitates the downward dissipation of pore water from the liquefiable silty fine sand layer. Consequently, the pore pressures and pore pressure ratios at the embankment base and toe are significantly reduced, effectively suppressing the occurrence of liquefaction.

5.3 Mechanism of seismic performance enhancement

Mechanism of Seismic Performance Enhancement The improvement in seismic performance is attributed to the coupling effect of dynamic and hydraulic factors. In the unreinforced model, liquefaction initiates at the embankment toe and rapidly expands to within 3 m below the ground surface. Conversely, the reinforced model limits liquefaction to localized zones at the embankment toe and inter-pile sand surface during the early shaking stage, preventing further progression. By simultaneously reducing plastic deformation and promoting efficient pore water drainage, gravel piles demonstrate prominent effectiveness in treating foundation liquefaction.

6 Conclusion

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