# Numerical investigation of the effect of non-plastic fines on the behavior of an embankment on liquefiable soil subjected to earthquake

Chedid Saade, Zheng Li, Sandra Escoffier, Luc Thorel

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Chedid Saade, Zheng Li, Sandra Escoffier, Luc Thorel. Numerical investigation of the effect of non-plastic fines on the behavior of an embankment on liquefiable soil subjected to earthquake. Soil Dynamics and Earthquake Engineering, 2025, 196, pp.109427. 10.1016/j.soildyn.2025.109427. hal-05516663

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# Numerical investigation of the effect of non-plastic fines on the behavior of an embankment on liquefiable soil subjected to earthquake

Chedid Saade<sup>1,*</sup>, Zheng Li<sup>1</sup>, Sandra Escoffier, Luc Thorel<sup>1</sup>

Laboratoire Centrifugeuses Géotechniques (CG), Département Géotechnique, Environnement, Risques Naturels et Science de la Terre (GERS), Université Gustave Eiffel, Allée des Ponts et Chaussées, CS 5004, 44344, Bouguenais, France

## ARTICLE INFO

Dataset link: 10.57745/FLR3HY, 10.57745/KV AGUH

**Keywords:**

Numerical modeling

Embankment

Soil liquefaction

Non-plastic fines

## ABSTRACT

This study presents a numerical investigation of the effects of non-plastic fines on the behavior of an embankment constructed on liquefiable soil. The numerical models, developed using OpenSees FEM platform and the PM4Sand constitutive model, simulate centrifuge tests of a homogeneous embankment constructed on liquefiable soil, with different fines contents ($f_c$ = 0%, $f_c$ = 5%, and $f_c$ = 10%). The numerical models were subjected to both small (PGA=0.1 g) and high amplitude (PGA=0.2 g) base shakings. The performance of these numerical models was validated against the experimental results of centrifuge tests in terms of excess pore pressure, acceleration response and embankment deformation. Additionally, the effect of fines on soil liquefaction was examined using the validated numerical models. The results indicate that the presence of non-plastic fines increases the liquefaction resistance and significantly reduces the settlement of the embankment crest. The addition of non-plastic fines exhibits an improving and reinforcing effect on the liquefiable soil.

## 1. Introduction

Earth dams, levees and embankments play an important role in the development of infrastructures and are considered the oldest construction forms in civil engineering, used for multiple purposes: transportation, irrigation or production of electricity. Their failure can lead to catastrophic disasters and significant loss of life and facilities [1]. Dam failures characterized by cracks, large settlements, or internal erosion can occur under dynamic loadings [2] even for embankments located in low to medium seismic zones [3–5]. Due to earthquakes, the failure and deformations of these structures can appear in different patterns of deformation [1,6,7]. These failures could be due directly to the earthquake, but also due to the liquefaction of soil ground induced by earthquakes [8].

Numerical modeling or simulation of soil liquefaction is frequently used in the geotechnical earthquake engineering community to understand its effect on the embankment response. In numerical simulations, both simplified approaches and direct nonlinear analyses in the time domain are employed to examine earthquake-induced behavior [9]. Nonlinear analyses, commonly used to study the response of embankments subjected to earthquakes, are typically performed using the finite element method (FEM) [10–12] or finite difference method (FDM) [13–16]. These analyses incorporate advanced constitutive models capable of capturing the complex behavior of liquefied soil. The main

objectives of these numerical simulations are to predict the behavior and the failure mechanisms of embankment due to earthquake-induced liquefaction. A reasonable prediction of deformation and damage is considered an essential key to seismic safety and remediation decisions for embankments. To have a more accurate and realistic prediction of this complex phenomenon, many constitutive models have been proposed and used in the simulation of liquefaction-related problems. Many previous numerical studies have focused on soil liquefaction and especially the effect of the liquefaction on the embankment behavior. Some representative examples of these studies are summarized in Table 1, which includes details on the simulation codes, constitutive models and the key model dimensions.

For the nonlinear deformation analyses in time domain, the numerical platform and the constitutive law were considered as the two main components [9]. The simulation platform and the constitutive model are used to solve the coupled solid–fluid governing equations and to correctly reproduce the behavior of the soil, respectively. Elgamal et al. [17] tried to reproduce the centrifuge results of Adalier et al. [18] using a self-developed solid–fluid coupled finite element code with a multi-yield surface constitutive model. The numerical results and the experimental results in this study show a divergence in excess pore pressures at the central part and a divergence in deformation. Then Aydingun and Adalier [10] re-performed the simulation

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: chedid.saade@univ-eiffel.fr, chedid97@gmail.com (C. Saade), zheng.li@univ-eiffel.fr (Z. Li), sandra.escoffier@univ-eiffel.fr (S. Escoffier), luc.thorel@univ-eiffel.fr (L. Thorel).</footnote>
List of symbols

<table><tr><td>A</td><td>CRR<sub>SS</sub> - N<sub>eq</sub> curve fitting parameter</td></tr><tr><td>a<sub>max</sub></td><td>Maximum amplitude acceleration</td></tr><tr><td>b</td><td>Active fines fraction</td></tr><tr><td>B</td><td>CRR<sub>SS</sub> - N<sub>eq</sub> curve fitting parameter</td></tr><tr><td>C</td><td>CRR<sub>SS</sub> - N<sub>eq</sub> curve fitting parameter</td></tr><tr><td>CRR<sub>SS</sub></td><td>Cyclic resistance ratio of simple shear test</td></tr><tr><td>CRR<sub>TX</sub></td><td>Cyclic resistance ratio of cyclic triaxial test</td></tr><tr><td>c<sub>z</sub></td><td>Fabric effect parameter</td></tr><tr><td>D</td><td>CRR<sub>SS</sub> - N<sub>eq</sub> curve fitting parameter</td></tr><tr><td>D<sub>r</sub></td><td>Global relative density</td></tr><tr><td>D<sub>50</sub></td><td>Mean particle diameter</td></tr><tr><td>EPP</td><td>Excess pore pressure</td></tr><tr><td>e</td><td>Global void ratio</td></tr><tr><td>e<sub>g</sub></td><td>Intergranular void ratio</td></tr><tr><td>e<sub>g</sub><sup>*</sup></td><td>Equivalent intergranular void ratio</td></tr><tr><td>e<sub>max</sub></td><td>Maximum void ratio</td></tr><tr><td>e<sub>min</sub></td><td>Minimum Void ratio</td></tr><tr><td>f<sub>c</sub></td><td>Fines content</td></tr><tr><td>t</td><td>Time</td></tr><tr><td>t<sub>2</sub></td><td>Start time of decreasing stage of permeability</td></tr><tr><td>t<sub>3</sub></td><td>End time of decreasing stage of permeability</td></tr><tr><td>G<sub>max</sub></td><td>Maximum shear modulus</td></tr><tr><td>G<sub>o</sub></td><td>Shear modulus coefficient</td></tr><tr><td>G<sub>s</sub></td><td>Specific gravity</td></tr><tr><td>g</td><td>Earth gravity</td></tr><tr><td>H</td><td>Prototype height of embankment</td></tr><tr><td>h<sub>po</sub></td><td>Contraction rate parameter</td></tr><tr><td>h<sub>o</sub></td><td>Secondary input parameter that adjusts the ratio of plastic modulus to elastic modulus</td></tr><tr><td>k</td><td>Permeability</td></tr><tr><td>k<sub>f</sub></td><td>Initial permeability</td></tr><tr><td>k<sub>b</sub></td><td>Permeability in excess pore pressure build up stage</td></tr><tr><td>k<sub>d</sub></td><td>Permeability in excess pore pressure decreasing stage</td></tr><tr><td>k<sub>f</sub></td><td>Permeability in liquefaction stage</td></tr><tr><td>K<sub>0</sub></td><td>Lateral earth pressure coefficient</td></tr><tr><td>L</td><td>Prototype width of the embankment base</td></tr><tr><td>N</td><td>Number of cycles required for liquefaction</td></tr><tr><td>ρ<sub>A</sub></td><td>Atmospheric pressure</td></tr><tr><td>ρ'</td><td>Mean effective stress</td></tr><tr><td>Q</td><td>Bolton's constant in PM4Sand model</td></tr><tr><td>R</td><td>Bolton's constant in PM4Sand model</td></tr><tr><td>r<sub>u</sub></td><td>Excess pore water pressure ratio</td></tr><tr><td>X</td><td>Horizontal position</td></tr><tr><td>Y</td><td>Vertical position</td></tr><tr><td>α</td><td>Constant controls the variation of excess pore pressure</td></tr><tr><td>α<sub>2</sub></td><td>Constant controls the variation of excess pore pressure</td></tr><tr><td>β<sub>1</sub></td><td>Constant controls the variation of excess pore pressure</td></tr><tr><td>β<sub>2</sub></td><td>Constant controls the variation of excess pore pressure</td></tr><tr><td>ν</td><td>Poisson's ratio</td></tr><tr><td>ρ<sub>sat</sub></td><td>Saturated density of the soil</td></tr></table>

<table><tr><td>ρ<sub>dmin</sub></td><td>Minimum dry density</td></tr><tr><td>ρ<sub>dmax</sub></td><td>Maximum dry density</td></tr><tr><td>σ'<sub>h</sub></td><td>Initial horizontal effective stress</td></tr><tr><td>σ<sub>v</sub></td><td>Initial vertical stress</td></tr><tr><td>σ'<sub>v</sub></td><td>Initial vertical effective stress</td></tr><tr><td>τ</td><td>Shear stress</td></tr><tr><td>φ</td><td>Critical state friction angle</td></tr></table>

by using Pastor-Zienkiewicz Mark III model for liquefiable soil and Mohr-coulomb model for the embankment. This constitutive model was integrated with the Diana-Swandine II finite element program. The numerical model results such as acceleration, excess pore pressure and liquefaction-induced deformation behaviors were compared satisfactorily with the centrifuge tests. However, in the zones below the centerline of the embankment, significant discrepancies were found in pore pressures and vertical deformations. Bhatnagar et al. [11] used PLAXIS with UBC3D-PLM (UBCSAND) constitutive model to simulate a 3D model of an earth dam resting on liquefiable soil taking into consideration some remedial measures. The limitations of the simulation were observed in the tendency to produce a limited strain development and the inability to capture the variation of relative density under loading cycles [9].

Recently, PM4Sand constitutive model was used widely and successfully to simulate the soil liquefaction [24,25] and study the effect of liquefaction on the behavior of dams [15,16,26,27], traffic embankments [20], structures with shallow foundation [28], tunnels in liquefiable soil [29] or offshore pipelines [30]. PM4Sand is a model that describes the plasticity of sand controlled by the stress ratio related to the critical state and the boundary surface [31]. PM4Sand model can predict the behavior of soil under cyclic loading for various relative densities [32]. It has been shown that the numerical model with PM4Sand model was able to reproduce correctly the responses in terms of accelerations and excess pore pressures [16,28,33]. PM4Sand is also recognized by the United States Society on Dams (USSD) as one of the constitutive models used for the seismic analysis of embankments, dams, and levees, and it has been extensively validated against centrifuge experimental results [9]. However, there are still some limitations in the prediction of the settlement and the generation pattern of excess pore pressure. To improve the predictions of pore pressure generation, Shahir et al. [34] introduced the concept of variable permeability as a function of excess pore pressure, a concept that was later adopted by Dinesh et al. [16] and Basu et al. [33].

These existing numerical studies on embankments resting on liquefiable ground or soil layers show that when the liquefaction happened at the ground level, huge settlements and lateral displacements in the embankment were observed. In addition, these studies have focused on the behavior of embankments under various soil ground profiles, embankment geometries, and remediation methods, none of these studies have examined the response of embankments subjected to liquefaction taking into account the presence of fines particles in the liquefiable soil. However, in the liquefied sites, such as the Kocaeli earthquake (1999) [35], Chi-Chi earthquake (1999) [36] and Darfield earthquake (2010) [37], the liquefaction had happened in the soil containing fines where significant damage was caused. As a result, the effect of fines on soil liquefaction has become increasingly apparent in recent years, and researchers have shifted their focus from studying the behavior of clean soils to investigating the liquefaction potential of soils containing fines. However, the effect of fines content on the liquefaction response, typically studied through experimental laboratory tests, remains unclear. Previous studies introduce various concepts and comparison criteria, such as global void ratio, intergranular void ratio, and sample preparation, to better understand the impact of fines. It has been shown that as fines content increases, the liquefaction resistance of silty sand could
<table><caption>**Table 1**
Some of the previous numerical simulations of a homogeneous embankment.</caption><thead><tr><th rowspan="2">Studies</th><th rowspan="2">Simulation code</th><th colspan="2">Constitutive model</th><th colspan="3">Prototype dimensions</th></tr><tr><th>Embankment</th><th>Foundation</th><th>L<sup>a</sup> (m)</th><th>H<sup>b</sup> (m)</th><th>Slope<sup>c</sup> (-)</th></tr></thead><tbody><tr><td>Elgamal et al. [17]</td><td>FE Program</td><td>Multi-yield surface</td><td>Multi-yield surface</td><td>14.7</td><td>4.5</td><td>1/1</td></tr><tr><td>Aydingun and Adalier [10]</td><td>Diana Swandyne</td><td>Mohr Coulomb</td><td>Pastor Zienkiewicz</td><td>14.7</td><td>4.5</td><td>1/1</td></tr><tr><td>Bhatnagar et al. [11]</td><td>Plaxis 3D</td><td>UBC3D-PLM</td><td>UBC3D-PLM</td><td>14.7</td><td>4.5</td><td>1/1</td></tr><tr><td>Boulanger et al. [19]</td><td>FLAC 7</td><td>PM4Sand</td><td>PM4Sand</td><td>60</td><td>28</td><td>1/2</td></tr><tr><td>Rapti et al. [12]</td><td>Code-Aster</td><td>ECP</td><td>ECP</td><td>74</td><td>9</td><td>1/3</td></tr><tr><td>Oblak et al. [20]</td><td>FLAC 2D</td><td>Mohr Coulomb</td><td>PM4Sand</td><td>6<br>12<br>24</td><td>2<br>4<br>6<br>8</td><td>1/2</td></tr><tr><td>Shahbodagh et al. [7]<br>Oka et al. [21]</td><td>LIQCA2-D11</td><td>Cyclic elastoplastic</td><td>Cyclic elastoplastic</td><td>30</td><td>6</td><td>1/2</td></tr><tr><td>Gu et al. [22]</td><td>DBLEAVES</td><td>Cyclic Mobility</td><td>Cyclic Mobility</td><td>23</td><td>6</td><td>1/1.5</td></tr><tr><td>Dinesh et al. [16]</td><td>FLAC 2D</td><td>Mohr Coulomb</td><td>PM4Sand</td><td>14.7</td><td>4.5</td><td>1/1</td></tr><tr><td>Saade et al. [23]</td><td>OpenSees</td><td>Drucker Prager</td><td>PM4Sand</td><td>21</td><td>6</td><td>1/1.5</td></tr></tbody></table>

Note:

a Prototype width of base of embankment;

b Prototype height of embankment in prototype model;

c Slope of embankment (Vertical/Horizontal).

<table><caption>**Table 2**
Properties of materials used in the model [40,48].</caption><thead><tr><th>Material</th><th>D<sub>50</sub> (μm)</th><th>e<sub>min</sub></th><th>e<sub>max</sub></th><th>G<sub>s</sub></th><th>ρ<sub>dmin</sub> (g/cm<sup>3</sup>)</th><th>ρ<sub>dmax</sub> (g/cm<sup>3</sup>)</th></tr></thead><tbody><tr><td>Hostun HN31</td><td>350</td><td>0.656</td><td>1.000</td><td>2.65</td><td>1.33</td><td>1.6</td></tr><tr><td>Fine C500</td><td>6</td><td>-</td><td>-</td><td>2.65</td><td>-</td><td>-</td></tr></tbody></table>

increase [38–40] or decrease [38,41–46]. Although some studies used the same soil [40,45], experimental results and conclusions remain contradictory due to differences in the basis of comparison. Even when applying the same basis of comparison to different soil types [44,47], the contradictions persist. Therefore, it is essential to focus again on the influence of the fines on the soil liquefaction and also its influence on the behavior of the embankment.

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Grain size distribution curves of clean sand (Hostun HN31) and sand mixtures (HN31+C500).</figcaption></figure>

This study aims to provide more insight through numerical modeling into the effect of non-plastic fines on the liquefaction response and embankment behavior. The general objective of these numerical simulations is to reproduce correctly the centrifuge tests (scale 1/60) of embankment constructed on liquefiable soil [23,49] and to further highlight the effect of the presence of non-plastic fines in the liquefiable silty soil. This paper first presents the details of the numerical model including the constitutive model calibration and the procedure of the numerical simulation. The numerical models were validated by comparing numerical results with experimental findings of Saade et al. [50,51]. At the same time, numerical observations focused on the effect of non-plastic fines were discussed in terms of pore pressures, accelerations, and displacements.

## 2. Numerical modeling

In this study, the numerical simulations were performed on the platform – “Open System for Earthquake Engineering Simulation” [52], which is a well-known and open-source Finite Element Method (FEM) based code. Three numerical models with three fines contents (0%, 5% and 10%) were constructed. This section provides a detailed description of the FEM mesh, boundary conditions, constitutive laws, and the calibration of constitutive model parameters.

### 2.1. Geometry and dimensions

The geometry of the centrifuge model in prototype scale is shown in Fig. 2(a). The numerical model is created exactly based on the prototype of the centrifuge tests of Saade et al. [23] and Saade et al. [49] (Fig. 2(a)) and it represents an embankment of 6 m in height resting on a liquefiable soil with 9 m in depth.

### 2.2. Model materials

The embankment, which has a relative density of 80%, was prepared with clean Hostun sand (Table 2) using air-pluviation. The medium dense liquefiable layer ($e_g = 0.83$) was constructed with a
<figure><img src="image_5.png" /><figcaption>Fig. 2. Geometry and dimensions of the (a) centrifuge model and (b) numerical model (Dimensions in meters at prototype scale).</figcaption></figure>

mixture of Hostun sand HN31 and non-plastic fines C500 (Table 2) using under-compaction method proposed by Ladd [53]. Three mixtures of HN31-C500 fines contents of 0%, 5%, and 10% were used in the experimental campaign [49]. These mixtures, characterized by a mean diameter ratio ($D_{50}/d_{50}$) exceeding 6.5 [54] and fines contents below the transition fines content ($f_{cth}$ = 20%, estimated by Zhu et al. [40]), are classified as sand-dominant. The grain size distribution curves of the different used mixtures are presented in Fig. 1

## 2.3. FEM mesh and boundary conditions

The FEM mesh of the numerical models is shown in Fig. 2(b). the liquefiable soil and embankment were modeled using 4-node quadrilateral SSPquadUP elements in plane strain condition [55]. There were 1728 elements and 756 elements for the liquefiable ground and the

embankment, respectively. The boundary conditions in the numerical models represent the real conditions of the rigid container used in the dynamic centrifuge tests. The nodes at the base were fixed both horizontally (in the X direction) and vertically (in the Y direction), while the lateral sides were fixed only horizontally. the liquefiable soil and embankment surfaces were assigned drained conditions (marked by a blue dashed line), while the bottom and lateral sides were assigned with undrained conditions.

A mesh sensitivity analysis was conducted by comparing the calculated acceleration, the build-up of excess pore pressure, and settlements using different mesh sizes (0.25 m, 0.5 m, 0.75 m, and 1.0 m) in a free-field model without the embankment. Since soil liquefaction occurs only in the saturated soil ground, the mesh sensitivity analysis of the free field soil ground can guarantee an accurate and correct simulation of the soil liquefaction in the model. This analysis was performed for
a liquefiable soil with 0% fines, subjected to a small-amplitude input signal. The results showed that the 0.25 m, 0.5 m, and 0.75 m meshes produced similar values in terms of acceleration, excess pore pressure, and settlements, as presented in Fig. 3. According to the results of the mesh sensitivity analysis, 0.5 m mesh size provides an optimized balance between the computational accuracy and the computational time. Therefore, the mesh size ≈0.5 m is selected in the numerical simulations in this study.

## 2.4. Constitutive model and parameter calibration

### 2.4.1. Liquefiable soil

In this study, PM4Sand constitutive law developed by Boulanger [56], Boulanger and Ziotopoulou [26] and Boulanger and Ziotopoulou [57] was used to model the behavior of liquefiable soil. This model describes the plasticity of sand, controlled by the stress ratio related to the critical state and the bounding surface [31]. The PM4Sand model offers the ability to predict soil behavior under cyclic loading across a range of relative densities. PM4Sand model requires 27 input parameters, which consist of 6 primary parameters and 21 secondary parameters [57]. The primary parameters include the relative density ($D_r$), small-strain shear modulus coefficient ($G_o$), contraction rate parameter ($h_{po}$), atmospheric pressure ($p_A$), and two “flags” parameters (“FirstCall” and “PostShake”). To estimate $G_o$, several methods can be employed, including empirical correlations with SPT or CPT tests during field tests or laboratory element tests such as the bender element test. In this study, $G_o$ was estimated directly using the equations proposed by Azeiteiro et al. [58] and Kassas [28] for clean Hostun HN31 sand. Additionally, $h_{po}$ was calibrated against experimental results in terms of the cyclic resistance curve ($CRR_{SS} - N_{eq}$) of the sand. The secondary parameters can either be left as their default values or calibrated against laboratory test data [57]. For this study, the parameter $h_o$, which adjusts the ratio of the plastic modulus to the elastic modulus, was set to 0.3 for all models with different fines contents. This value is close to the default value proposed by Boulanger and Ziotopoulou [57] and was calculated based on the global relative density of the model with 0% of fines. Meanwhile, the other secondary input parameters were kept as their default values. The main parameters of PM4Sand model used in this study for different fines content are summarized in Table 3.

For the model parameters of PM4Sand which are not dependent on the sample preparation method i.e. $\phi$, $Q$ and $R$, the values were estimated from the literature studies. For clean HN31, the values proposed by Kassas [28] were adopted (see Table 3). The two constants of Bolton ($Q$ and $R$) related to the critical state of the soils were estimated from the experimental results of Gobbi [45] and Zhu et al. [40]. These constants can be obtained by fitting the results of Gobbi [45] related to the HN31-C500 mixture with the empirical equation (Eq. (1)) proposed by Bolton [59]. Fig. 4 shows the data points of the critical state obtained from the experimental studies of Gobbi [45] and Zhu et al. [40]. The values of $Q$ and $R$ were then obtained by fitting Eq. (1) with the experimental results. It has been shown from Fig. 4 that the presence of non-plastic fines has a significant influence on the confining pressure and relative density relationship.

$$D_r = \frac{R}{Q - \ln \frac{100(1+2K_0)}{3} \frac{p'}{p_A}} \quad (1)$$

The initial permeability $k$ was estimated using Eq. (2) proposed by Kassas [28] for clean HN31 sand. According to Khan et al. [60], the permeability of silty sand decreases with a high rate when fines content increases up to 20%. Therefore, the initial permeability for clean HN31 (Eq. (2)) was decreased for the fines content $f_c = 5\%$ and $f_c = 10\%$ with a reduced factor equal to 5 and 10, respectively.

$$k = 2.92 \times 10^{-3} \times \frac{e^3}{(1 + e)} \quad (2)$$

The equation for the shear modulus coefficient $G_o$ is derived from the empirical equation for the maximum shear modulus proposed by Azeiteiro et al. [58]. Fig. 5 presents a comparison between the maximum shear modulus obtained from the experimental results of Gobbi [45] for different fines contents and that obtained using the empirical equation Eq. (3), in terms of the equivalent intergranular void ratio. Eq. (3) corresponds to the empirical equation of Azeiteiro et al. [58], modified by replacing the global void ratio with the equivalent intergranular void ratio introduced by Thevanayagam [61]. This comparison shows the consistency between the experimental result of Gobbi [45] and Eq. (3). Therefore, the shear modulus coefficient $G_o$ was determined using the empirical equation proposed by Kassas [28] but with the equivalent intergranular void ratio $e_g^*$ instead of the global void ratio $e$.

$$G_{\max}(kPa) = 29300 \frac{(2.97 - e_g^*)^2}{1 + e_g^*} \left(\frac{p'}{100}\right)^{0.49} \quad (3)$$

Additionally, the secondary parameter $c_z$ which is related to the fabric effect [57] was taken 50 to simulate the effects of fines ($f_c = 5\%$ and $f_c = 10\%$) instead of the default value 250 which is used for the clean sand model. It was found that the value of $c_z = 250$ leads a rapid build-up of the excess pore pressure at the beginning of the shaking for the silty sand with 5% and 10% non-plastic fines. Due to the presence of non-plastic fines, the initial fabric of the silty sand could be different from the clean sand. By testing different values, an optimized value of $c_z = 50$ was found, with which the rapid generation of excess pore pressure at the beginning of dynamic shaking can be effectively reduced and controlled.

According to the literature [62–65], the sample preparation method affects the liquefaction resistance. Therefore, the contraction rate parameter $h_{po}$, which plays an important role in stimulating the liquefaction resistance of sand under cyclic loading, has to be calibrated carefully by taking into account the effects of the sample preparation method and the effects of fines content. The calibration of $h_{po}$ was carried out against the experimental data of $CRR_{SS} - N_{eq}$ curve of sand mixtures (Hostun HN31 with C500) prepared by the moist tamping method. For the $CRR_{SS} - N_{eq}$ curve, since the direct data of undrained cyclic simple shear test of mixture sand (HN31-C500) with undercompaction method was rare, thus the experimental data has to be obtained indirectly from triaxial cyclic test. Therefore, the isotropically consolidated undrained cyclic triaxial tests on medium dense ($D_r = 50\%$) and dense ($D_r = 80\%$) sand mixture of Gobbi [45], Gobbi et al. [66] and Gobbi et al. [67] were converted to undrained simple shear $CRR_{SS} - N_{eq}$ curves by Eq. (4) [68]:

$$CRR_{SS} = \frac{1 + 2K_0}{3} CRR_{TX} \quad (4)$$

where $CRR_{SS}$ is the cyclic resistance ratio in simple shear form; $CRR_{TX}$ is the cyclic resistance ratio of cyclic triaxial test; $K_0$ is the lateral pressure coefficient for simple shear test.

An empirical equation Eq. (5) was used to fit the converted undrained simple shear $CRR_{SS} - N_{eq}$ data. Eq. (5) is based on the equation originally in terms of global void ratio $e$ proposed by Kassas et al. [69], with modified parameters.

$$CRR_{SS} = (A e + B) N_{eq}^{(C e + D)} \quad (5)$$

The fitting parameters related to the studied fine contents are listed in Table 3. Fig. 6 shows the $CRR_{SS} - N_{eq}$ curves fitted with the experimental results of Gobbi [45] for different global relative densities ($D_r = 50\%$ and $D_r = 80\%$) and for fines content 0%, 5% and 10%. The dashed $CRR_{SS} - N_{eq}$ curves presented in Fig. 6, obtained from the empirical equations by considering the global void ratio related to the centrifuge model, were used in the calibration process.

The calibration of $h_{po}$ was performed numerically by simulating the simple shear test, which was carried out on a single element
<figure><img src="image_6.png" /><figcaption>Fig. 3. Mesh sensitivity analysis of the liquefiable ground: Acceleration, excess pore pressure, and settlement response.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. Fitting of the empirical equation of the critical state proposed by Bolton [59] with the experimental results of Gobbi [45] of different fines content (0%, 5% and 10%).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 5. Comparison between the maximum shear modulus obtained from the experimental results of Gobbi [45] for different fines contents and that obtained using the empirical equation in terms of the equivalent intergranular void ratio.</figcaption></figure>
<table><caption>**Table 3**
Parameters used in the numerical models of different fines content.</caption><thead><tr><th rowspan="2">Parameter</th><th rowspan="2"></th><th rowspan="2"></th><th colspan="3">Value</th></tr><tr><th>f<sub>c</sub> = 0%</th><th>f<sub>c</sub> = 5%</th><th>f<sub>c</sub> = 10%</th></tr></thead><tbody><tr><td>Intergranular void ratio</td><td>[-]</td><td>e<sub>g</sub><sup>(1)</sup> = (e + f<sub>c</sub>)/(1 - f<sub>c</sub>)</td><td>0.83</td><td>0.83</td><td>0.83</td></tr><tr><td>Minimum void ratio</td><td>[-]</td><td>e<sub>min</sub></td><td>0.656</td><td>0.580</td><td>0.482</td></tr><tr><td>Maximum void ratio</td><td>[-]</td><td>e<sub>max</sub></td><td>1.000</td><td>1.050</td><td>1.162</td></tr><tr><td>Global void ratio</td><td>[-]</td><td>e</td><td>0.83</td><td>0.74</td><td>0.65</td></tr><tr><td>Global relative density</td><td>[%]</td><td>D<sub>t</sub> = <sup>e<sub>min</sub> - e</sup>&frasl;<sub>e<sub>max</sub> - e<sub>min</sub></sub></td><td>50</td><td>66</td><td>76</td></tr><tr><td>Equivalent intergranular void ratio</td><td>[-]</td><td>e<sub>g</sub><sup>(2)</sup> = <sup>(e + (1 - b)f<sub>c</sub>)</sup>&frasl;<sub>(1 - (1 - b)f<sub>c</sub>)</sub></td><td>-</td><td>0.82</td><td>0.80</td></tr><tr><td>Shear modulus coefficient</td><td>[-]</td><td>G<sub>o</sub> = 293 <sup>(2.97 - e<sub>g</sub><sup>2</sup>)</sup>&frasl;<sub>(1 + e<sub>g</sub><sup>2</sup>)</sub></td><td>712</td><td>742</td><td>769</td></tr><tr><td>Critical state friction angle</td><td>[°]</td><td>φ</td><td>33.8</td><td>33.8</td><td>33.8</td></tr><tr><td>Atmospheric pressure</td><td>[kPa]</td><td>P<sub>λ</sub></td><td>101.3</td><td>101.3</td><td>101.3</td></tr><tr><td>Lateral earth pressure</td><td>[-]</td><td>K<sub>0</sub> = 1 - sin φ</td><td>0.44</td><td>0.44</td><td>0.44</td></tr><tr><td>Poisson's ratio</td><td>[-]</td><td>ν = <sup>k<sub>0</sub></sup>&frasl;<sub>1 + K<sub>0</sub></sub></td><td>0.3</td><td>0.3</td><td>0.3</td></tr><tr><td>Bolton's Constant</td><td>[-]</td><td>Q</td><td>8.4</td><td>8.4</td><td>11</td></tr><tr><td>Bolton's Constant</td><td>[-]</td><td>R</td><td>0.78</td><td>1.24</td><td>3.5</td></tr><tr><td>Permeability</td><td>[m/s]</td><td>k</td><td>9.68 × 10<sup>-4</sup></td><td>1.94 × 10<sup>-4</sup></td><td>9.68 × 10<sup>-5</sup></td></tr><tr><td>Contraction rate parameter</td><td>[-]</td><td>h<sub>po</sub></td><td>0.07</td><td>0.3</td><td>1.0</td></tr><tr><td>Modulus ratio</td><td>[-]</td><td>h<sub>o</sub></td><td>0.3</td><td>0.3</td><td>0.3</td></tr><tr><td>Permeability variable</td><td>[-]</td><td>α</td><td>1.2</td><td>1.2</td><td>1.2</td></tr><tr><td>Permeability variable</td><td>[-]</td><td>a<sub>2</sub></td><td>40</td><td>13</td><td>6</td></tr><tr><td>Permeability variable</td><td>[-]</td><td>β</td><td>1</td><td>1</td><td>1</td></tr><tr><td>Permeability variable</td><td>[-]</td><td>β<sub>2</sub></td><td>1</td><td>1</td><td>1</td></tr><tr><td>Strain levels control parameter</td><td>[-]</td><td>c<sub>z</sub></td><td>250</td><td>50</td><td>50</td></tr><tr><td>CRR<sub>SS</sub> - N<sub>eq</sub> curve fit parameter</td><td>[-]</td><td>A</td><td>-1.119</td><td>-1.21</td><td>-1.19</td></tr><tr><td>CRR<sub>SS</sub> - N<sub>eq</sub> curve fit parameter</td><td>[-]</td><td>B</td><td>1.14</td><td>1.15</td><td>1.08</td></tr><tr><td>CRR<sub>SS</sub> - N<sub>eq</sub> curve fit parameter</td><td>[-]</td><td>C</td><td>0.24</td><td>0.28</td><td>0.32</td></tr><tr><td>CRR<sub>SS</sub> - N<sub>eq</sub> curve fit parameter</td><td>[-]</td><td>D</td><td>-0.44</td><td>-0.39</td><td>-0.44</td></tr></tbody></table>

(1) Thevanayagam [41].

(2) Thevanayagam [41]; with b, active fines fraction $b = (e_{max} - e_{min})/(1 + e/f_{cth})$ [45]

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Fitting of cyclic resistance ratio versus the number of cycles for liquefaction equation with the experimental results of Gobbi [45] for different fines content: (a) 0% (b) 5% and (c) 10%.</figcaption></figure>

(SSPquadUP) under the initial effective vertical stress $\sigma'_v = 100$ kPa. The optimized value of $h_{po}$ was presented in Table 3. The results of the undrained simple shear test with a cyclic stress ratio equal to 0.15 are shown in Fig. 7 for the fines content used in the experiments. The criteria used to determine liquefaction during the calibration process in this study are based on thresholds [28,70]. For the medium-dense sample (case of $f_c = 0$%), full liquefaction was considered to be triggered when the excess pore pressure reached 98% of the initial vertical effective stress, as indicated by red stars in Fig. 7. In the case of the dense samples (cases of $f_c = 5\%$ and $f_c = 10\%$), the soil does not necessarily liquefy with a complete loss of effective stress when cyclic mobility occurs. Therefore, for these cases, liquefaction was defined as the onset of cyclic mobility combined with the excess pore pressure reaching 80% of the initial vertical effective stress, as marked by black stars in Fig. 7.

Additionally, the calibration results for different cyclic resistance ratios (CRR<sub>SS</sub> - N<sub>eq</sub> curves) are shown in Fig. 8 for the fines contents studied in the centrifuge tests ($f_c = 0\%$, $f_c = 5\%$ and $f_c = 10\%$). It is shown that the calibration fits well with the curve globally. As previously mentioned, these curves were derived from the experimental

results of Gobbi [45], which were based on a constant global relative density. However, in this study, they were analyzed considering the three mixtures ($f_c = 0\%$, $f_c = 5\%$ and $f_c = 10\%$) at a constant intergranular void ratio ($e_g = 0.83$). Fig. 8 clearly shows that the addition of non-plastic fines increases the liquefaction resistance of the sand-fines mixture when using the intergranular void ratio as the basis for comparison.

### 2.4.2. Embankment

For the embankment soil, Drucker-Prager model was adopted. As it was reported by Saade et al. [23], the centrifuge model was saturated at 1 g with viscous fluid and the fluid content decreased from around 27% (after 1 g saturation) to 3.5% in the centrifuge. As a result of the unsaturated state of the embankment, the cohesion and strength of the embankment soil increased especially when viscous fluid was used in the centrifuge test [23]. Therefore, in this study the peak friction angle 38°, the bulk modulus 173 kPa and the shear modulus 76 kPa were assumed as the parameters of the Drucker-Prager model for the unsaturated embankment soil according to Chen and Saleeb [71]. The cohesion of soil was set at 65 kPa to fit the settlement of
<figure><img src="image_10.png" /><figcaption>Fig. 7. Single element simulation of undrained simple shear test with a cyclic stress ratio 0.15 under initial vertical stress $\sigma_v$ = 100 kPa for different fines content $f_c$ = 0%, $f_c$ = 5% and $f_c$ = 10%.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 8. Calibration of PM4Sand constitutive model: comparison of simulation results with empirical $CRR_{SS} - N_{eq}$ curves for different fines content $f_c$ = 0%, $f_c$ = 5% and $f_c$ = 10%.</figcaption></figure>

the embankment in case of clean sand used in the liquefiable layer and during the high-amplitude signal [23].

## 2.5. Procedure of numerical simulation

The numerical simulation was conducted on the FEM platform OpenSees – Version 3.2.2 64-Bit [52]. Three numerical models with different fines contents were constructed, and the simulation was performed in three steps. Firstly, the consolidation of the model was performed. At this stage, all elements’ material properties were switched to elastic. The material properties were switched from elastic to plastic and the “Update FirstCall” is activated, then a “plastic gravity analysis” step was performed to initialize the internal variables and to reach

the initial stress state of the model. After the consolidation, the whole model was subjected to dynamic shaking by “UniformExcitation” [72]. The numerical models were excited by a 1D horizontal sinusoidal base shaking consisting of 20 full cycles with a dominant frequency of 1.5 Hz and a signal amplitude of 0.1 g in prototype scale (Fig. 9). The actual signal recorded at the base of the container during the centrifuge tests was used as the input in the numerical simulations.

During the dynamic excitation, 3.0% of Rayleigh damping was applied. The damping parameters were calculated with two modal frequencies i.e. 2.7 Hz and 6.7 Hz. These two frequencies were estimated by modal analysis with the elastic material properties listed in Table 3. The 3.0% damping ratio was kept constant for the models with different fines contents. Boulanger and Ziotopoulou [57] recommended a 0.5% damping ratio for the Rayleigh damping to control the numerical noise during the dynamic integration in FLAC 7.0 [73]. For the numerical simulation using constitutive models with high non-linearity such as PM4Sand, a certain small amount of Rayleigh damping could be helpful for the convergence of the simulation. In this study, in OpenSees FEM platform, a comparative analysis was conducted by using different damping ratios of 0.5% and 3.0%, and no significant differences were observed in terms of acceleration, excess pore pressure, or settlements.

To properly model the variation of the excess pore pressure, the permeability in the numerical model varied in two different stages: first, during the base shaking; and second, during the dissipation of excess pore pressure after shaking. During base shaking, the procedure proposed by Shahir et al. [34] was adopted. The permeability was updated at each step according to Eq. (6), by which the permeability varied according to the excess pore pressure ratio [16,33,34].

$$k = \begin{cases} k_b = k_i (1 + (\alpha - 1)r_u^{\beta_1}) & (\text{if } r_u < 0.95) \\ k_i = \alpha k_i & (\text{if } r_u \ge 0.95) \end{cases} \qquad (6)$$

where $k_i$ is the initial permeability of the soil; $k_b$ is the permeability during the build-up of pore pressure ($r_u < 0.95$); $k_i$ is the permeability during liquefaction ($r_u \ge 0.95$). The two constants $\alpha$ and $\beta_1$ were taken as 1.2 and 1.0, respectively, as they were proposed by Basu et al. [33] for clean Hostun HN31 sand.

After the shaking, the “PostShake flag” in PM4Sand model was activated. It has been reported in the literature that the influence of
<figure><img src="image_12.png" /><figcaption>Fig. 9. The input signal (prototype scale) recorded during centrifuge tests and used in the numerical simulation: (a) Small-amplitude signal (with target amplitude $a_{max}$ = 0.1 g) and (b) High-amplitude signal (with target amplitude $a_{max}$ = 0.2 g).</figcaption></figure>

the permeability and the value of the permeability coefficient on the post-liquefaction is not clear [74,75]. It has been suggested by Shahir et al. [74] that permeability decreases before the excess pore pressure dissipation. It is also recommended by Tobita [76] that the permeability should decrease to a certain value lower than its initial value during the dissipation process. Therefore, Eq. (7) was used for the reduction of permeability, which starts at the middle of the last cycle of the input signal ($t_2$ = 18.1 s) and ends at the last cycle ($t_3$ = 18.7 s) as presented in Fig. 9. This equation is based on the one proposed by Shahir et al. [74] taking into account the reduction of permeability by a constant factor of $\alpha_2$.

$$k_d = \frac{k_i}{\alpha_2}(1 + (\alpha_2 - 1)\left(\frac{t-t_2}{t_3-t_2}\right)^{\beta_2}) \quad (7)$$

where $k_d$ is the permeability in the decreasing stage; $t_2$ and $t_3$ are the start and end time of the decreasing stage, respectively. The optimized values of $\alpha_2$ and $\beta_2$ were found to have the best fit with the experimental results during the dissipation stage and the values are listed in Table 3.

### 3. Initial states of the simulation

The initial states of the three numerical models (0%, 5% and 10%) are similar in terms of initial pore pressure profiles and stress distributions. Therefore, in this part, only the initial state of the numerical model with fines 0% is presented as the representative.

Fig. 10 shows the initial pore pressure profiles obtained from the theoretical calculation, the experimental measurement after the in-flight consolidation and the numerical simulation after the consolidation stage. The pore pressure profiles were compared under the embankment and under the free liquefiable soil. The experimental measurement agreed well with the theoretical calculation and the numerical simulation. The theoretical profile was calculated by assuming an absolute dry state of the embankment, with the water level exactly at the surface of the liquefiable soil. However, during the centrifuge test,

the embankment was in an unsaturated state (with an estimated fluid content of around 3.5%). At the interface between the embankment and the liquefiable soil, the actual water level in the center of the embankment was slightly higher than that of the surface of the liquefiable soil. This effect was observed after consolidation in both the experimental measurement and the numerical simulation, as shown in Fig. 10.

Generally, the stress in the centrifuge model is difficult to measure. However, with the help of numerical models, the distribution of initial stress, especially the shear stress distribution in the model, can be easily investigated. Fig. 11(a), (b) and (c) show the initial effective vertical, horizontal and shear stresses. It has been shown that shear stress (≥10 kPa) concentrated beneath the slope of the embankment, while the central zone and the zones under the free surface of the liquefiable soil exhibited negligible initial shear stress (≤2 kPa).

### 4. Validation of the numerical models: Effect of non-plastic fines on liquefaction behavior

The performance of the numerical models was validated by comparing the numerical results with the experimental data [50,51] in terms of excess pore pressure, acceleration response and vertical displacements. It is important to note that the experimental tests were conducted following the program in Table 4.

<table><caption>Table 4
Experimental program of the centrifuge tests [49].</caption><thead><tr><th>Test ID</th><th>Fines content f<sub>c</sub> (%)</th><th>Shake 1 (S1)</th><th>Shake 2 (S2)</th><th>Shake 3 (S3)</th><th>Shake 4 (S4)</th><th>Shake 5 (S5)</th></tr></thead><tbody><tr><td>Emb_0</td><td>0</td><td><strong>0.1 g</strong></td><td>0.1 g</td><td>0.1 g</td><td><strong>0.2 g</strong></td><td>0.2 g</td></tr><tr><td>Emb_5</td><td>5</td><td><strong>0.1 g</strong></td><td>0.1 g</td><td>0.1 g</td><td><strong>0.2 g</strong></td><td>0.2 g</td></tr><tr><td>Emb_10</td><td>10</td><td><strong>0.1 g</strong></td><td>0.1 g</td><td>0.1 g</td><td><strong>0.2 g</strong></td><td>0.2 g</td></tr></tbody></table>

The models were first subjected to three successive small-amplitude signals (0.1 g), followed by two high-amplitude signals (0.2 g). The
<figure><img src="image_13.png" /><figcaption>Fig. 10. Comparison of the initial pore pressures recorded in all the centrifuge models with those computed by the numerical model.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 11. Distribution of the initial vertical (a) and horizontal (b) effective stress and (c) the shear stress in the numerical model.</figcaption></figure>

numerical results of models subjected to small amplitude signals (0.1 g) were compared to the first shake (S1) of the experimental program. By assuming that the first three small-amplitude signals had minimal impact on the centrifuge tests [77], the numerical results obtained from the models subjected to high-amplitude signals (0.2 g) were compared to the fourth shake (S4) of the experimental program.

4.1. Excess pore pressure ratio

Figs. 12 and 13 show the comparison of the excess pore pressure recorded during centrifuge tests and those computed from the numerical models during small-amplitude signal (0.1 g) and high-amplitude signal (0.2 g), respectively.
<figure><img src="image_15.png" /><figcaption>**Fig. 12.** Comparison of the excess pore pressure profiles calculated from the numerical models (0%, 5% and 10%) and recorded during centrifuge tests (0%, 5% and 10%) under the embankment (P3, P5, P9 and P10) and the free surface of the liquefiable soil (P12 and P13) during small-amplitude signal ($a_{max}$ = 0.1 g).</figcaption></figure>

The numerical models capture well the build-up pore pressure, as shown in Figs. 12 and 13, under the free surface of the liquefiable soil (P12 and P13) and under the embankment (P3 and P5). During centrifuge tests, the pore pressure increased and reached its maximum value after several cycles, this behavior was also reproduced by the numerical models. The maximum excess pore pressure in the centrifuge tests was predicted in an acceptable range by the numerical models with differences less than 30% observed especially at the bottom positions where liquefaction did not happen. The largest discrepancies were observed in the model with 0% during high-amplitude signal, where the numerical models overestimated the excess pore pressure. This overestimation is attributed to the effect of the three initial small-amplitude signals generated before the high-amplitude signal. Liquefaction observed in the centrifuge model with 0% fines, due to the small-amplitude signal, is higher than in the models with 5% and 10% fines. This slight difference could affect the liquefiable soil, resulting in a higher resistance of the liquefiable layer, as reported by Saade [77]. Additionally, at position P13 under the free surface of the liquefiable soil, where liquefaction was detected in the experimental tests, the numerical results are consistent with the experimental observations.

Significant discrepancies were observed at the interface between the embankment and the liquefiable soil (P5) and the zone near the embankment toes (P10), which could be linked to the simulation of the embankment in its unsaturated state. These limitations, particularly at the interface, may be attributed to its inability to accurately simulate the changes in pore pressure as the soil transitions from a fully saturated state (in the liquefiable layer) to a partially saturated state (in the embankment). Furthermore, the numerical models can predict the dissipation of excess pore pressure generated during the applied signal using the variable permeability for the dissipation stage presented proposed by Shahir et al. [34], as shown in Figs. 12 and 13.

After verifying the excess pore pressures calculated, the distributions of the excess pore pressure ratios in models with different fine contents were presented in Fig. 14(a) and (b), corresponding to the end ($t = 18.26$ s) of the signal of small amplitude and signal of high amplitude, respectively. The liquefied zones, highlighted in yellow (Fig. 14) are observed under the free surface of the liquefiable soil and were extended from the embankment toes to the free surface of the liquefiable soil.
<figure><img src="image_16.png" /><figcaption>**Fig. 13.** Comparison of the excess pore pressure profiles calculated from the numerical models (0%,5% and 10%) and recorded during centrifuge tests (0%,5% and 10%) under the embankment (P3, P5, P9 and P10) and the free surface of the liquefiable soil (P12 and P13) during high-amplitude signal ($a_{max}$ = 0.2 g).</figcaption></figure>

However, under the embankment, the excess pore pressure ratios did not reach the unit value, therefore the liquefaction did not happen under the embankment during either the small-amplitude and high-amplitude signals. These numerical results are consistent with experimental observations, showing that the numerical model predicted in a good way the initiation of liquefaction and the resulting liquefied zones based on excess pore pressures.

The effect of the addition of non-plastic fines was highlighted by comparing the computed results of the numerical models with different fine content (0%,5%, and 10%). At the end ($t = 18.26$ s) of both the small-amplitude (Fig. 14(a)) and high-amplitude (Fig. 14(b)) signals, the lateral and depth extents of the liquefied zone decreased with increasing fines content. For example, in the model with 0% of fines subjected to the high-amplitude signal, liquefaction extended to a depth of approximately 6 m, while in the model with 5% and 10% fines, liquefaction did not exceed a depth of 5 and 4 m, respectively. Therefore, the numerical simulations reproduce the observations of Saade et al. [49], showing that the extent of liquefied zones decreases as the fines content increases. This indicates that the liquefaction resistance of the

soil increases with higher fine content when the intergranular void ratio is used as a basis for comparison.

## 4.2. Acceleration response

Figs. 15 and 16 show the time-histories of acceleration at different positions under the embankment (A2, A3 and A4) and under the free surface of the liquefiable soil (A15, A16 and A17), during the small-amplitude and high-amplitude signals. The comparison of the acceleration was also quantitatively evaluated with Anderson's Goodness of Fit [78,79] criteria (noted in Figs. 15 and 16). These criteria give each computed acceleration a score classified between excellent fit (marked with A), good fit (marked with B), fair fit (marked with C), and poor fit (marked with D). Overall, the computed acceleration time histories can reproduce well the acceleration measured in the centrifuge tests for all the models in the embankment and the liquefiable soil layer. The computed scores at the different positions in the model are classified between good and excellent fit for the numerical models subjected to both the small and high amplitude signals.
<figure><img src="image_17.png" /><figcaption>**Fig. 14.** The model deformation and the distribution of excess pore pressure ratio at the end of shaking (t = 18.26 s) of the model three numerical model (0%, 5% and 10% of non-plastic fines) subjected to (a) small-amplitude ($a_{max}$ = 0.1 g) and (b) high-amplitude signal ($a_{max}$ = 0.2 g).</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig. 15. Comparison of the acceleration time histories calculated from the numerical models (0%,5% and 10%) and recorded during centrifuge tests (0%,5% and 10%) under the embankment (A2, A3 and A4) and the free surface of the liquefiable soil (A15, A16 and A17) during small-amplitude signal ($a_{max}$ = 0.1 g).</figcaption></figure>

In addition, under the central part of the embankment (A2, A3 and A4), under the embankment toes (A12, A13) and at the bottom of the model (A15 and A16), a symmetrical acceleration profile is observed in both the centrifuge and the numerical models for the cases with 0%, 5% and 10% of fines and subjected to both small-amplitude and high-amplitude signals. The computed numerical accelerations match the experimental results in the central part and under the embankment toes and at the bottom of all the models, where liquefaction did not occur as reported by Saade et al. [23,49].

The numerical models well captured the liquefaction phenomenon of the surface of the liquefiable soil (A17). For the model 0% and 5% of fines subjected to a small-amplitude signal (Fig. 15), there is a decrease in the acceleration amplitude in the negative direction after around 4 and 5 cycles respectively. These decreases correspond

to the non-transmissibility of shear waves in the negative direction, which is related to the initiation of liquefaction. These observations are consistent with the experimental results recorded during centrifuge tests. With the increase of the non-plastic fines content up to 10%, at the same position A17, both the numerical and experimental results manifest a symmetric acceleration profile and soil liquefaction did not occur in this circumstance. As it was explained in Fig. 8, the addition of non-plastic fines increases the liquefaction resistance of the sand-fines mixture using the intergranular void ratio as a basis of comparison. The reinforcing effect of the non-plastic fines in reducing the liquefaction potential is confirmed by both experimental results and these numerical simulations.
<figure><img src="image_19.png" /><figcaption>**Fig. 16.** Comparison of the acceleration time histories calculated from the numerical models (0%,5% and 10%) and recorded during centrifuge tests (0%,5% and 10%) under the embankment (A2, A3 and A4) and the free surface of the liquefiable soil (A15, A16 and A17) during high-amplitude signal ($a_{max}$ = 0.2 g).</figcaption></figure>

With the high-amplitude signal, the acceleration time histories at the free surface of the liquefiable soil (A14 and A17) from the numerical model are comparable to those recorded during centrifuge, characterized by the asymmetric response for the model with 0% and 5% of fines. Some differences are observed at position A17 under the free surface of the liquefiable soil, particularly during the high-amplitude signal. These differences are characterized by an underestimation of the acceleration amplitude in the positive direction. These underestimations, observed especially after the initiation of the liquefaction, could be attributed to the inability of the numerical model to reproduce properly the de-liquefaction spikes [80] observed in the centrifuge models, as well as to the effect of the three initial

small-amplitude signals generated during centrifuge models before the high-amplitude signal.

Spectrum analysis of the numerical acceleration was also carried out to investigate the effect of non-plastic fines on the liquefaction observed under the free surface of the liquefiable soil at position A17. The results in Fig. 17 were calculated by Stockwell-transform spectrograms [81] of the acceleration at position A17 for the models with 0%, 5%, and 10% of fines subjected to small-amplitude and high-amplitude signals. These time-frequency analyses were performed to identify the initiation of the liquefaction [82,83]. The high-frequency contents in the calculated acceleration appeared first and then vanished, indicating the initiation of liquefaction. For the models subjected to small-amplitude signal (Fig. 17(a)), the time-frequency analysis revealed that liquefaction occurred
<figure><img src="image_20.png" /><figcaption>Fig. 17. Stockwell-transform spectrograms of the acceleration under the free surface of the liquefiable soil (A17) calculated from the numerical models (0%,5% and 10%) subjected to (a) small-amplitude (0.1 g) and (c) high amplitude (0.2 g) signals.</figcaption></figure>

at approximately 9 s for the model with 0% of fines. However, for the models with 5% and 10% fines, no liquefaction was detected at acceleration A17. This does not exclude the possibility that liquefaction occurred at a shallower depth. For the models subjected to high-amplitude signal (Fig. 17(b)), the time at which liquefaction occurred increased from 5 s with 0% of fines to 8 s and 11 s with 5% and 10% of fines, respectively. However, the high-frequency components did not completely vanish in the models with 5% and 10% of fines compared to the model with 0% of fines. These detected frequencies correspond to the positive and negative spikes observed in the experimental centrifuge tests and are attributed to the dilative behavior of the soil [80]. Therefore, the time required to initiate liquefaction increases with fines content, which is consistent with the experimental observations of Saade et al. [49]. This indicates that liquefaction becomes more difficult to initiate with the addition of non-plastic fines while maintaining a constant intergranular void ratio.

## 5. Performance validation of the numerical models: Effect of non-plastic fines on the response of the embankment

The performance of the numerical models was also verified in terms of model deformation. The model deformation pattern at the end of shaking (t = 18.26 s) from the numerical model was presented previously in Fig. 14 for different fines content and different input amplitudes. The computed deformation pattern, characterized by a crest settlement and lateral displacement of the embankment toes followed by heaving at the surface of the liquefiable soil, was close to the experimental observations [23,49]. In addition, Fig. 18 shows the comparison of the settlement of the embankment crest recorded during centrifuge tests for the model 0%, 5%, and 10% of fines and subjected to small and high amplitude signals. Fig. 18(a) shows that the numerical model models qualitatively capture the embankment crest settlement during shaking, with significant overestimation. Despite the calculated overestimation, the numerical models effectively reproduce the influence of fines on the crest settlements of the embankment. As shown in Figs. 14(a) and 18(a), at the end of the shaking (t = 18.26 s), the crest settlement was reduced from approximately 0.26 m (around 0.1 m in the centrifuge test) with 0% of fines to around 0.18 m (around 0.03 m in the centrifuge test) with 5% and 10% of fines. The crest settlement was significantly reduced when non-plastic fines were added to the liquefiable soil, which is consistent with the experimental observations.

For the models subjected to high amplitude signal (Figs. 18(b) and 14(b)), the numerical models capture the effect of the presence of non-plastic fines, which is similar to what has been observed with the models subjected to the small-amplitude signal. A significant reduction in crest settlement was observed numerically, decreasing from 0.72 m with 0% of fines to 0.58 m with 5% and 10% of fines during the high-amplitude signal. By comparing the experimental and the numerical results during the high-amplitude signal, significant discrepancies were observed with the models with 5% and 10% of fines. At position D3, near the toes of the embankment (Fig. 14(a)), the vertical displacement shows a reduction in the calculated heave as the fines content increases. It is important to note that the observed heave was not detectable by the potentiometer at D3 in the experimental tests. This limitation is attributed to the self-weight of the sensor, which can alter and reduce the heaving of the soil. Consequently, the experimental measurements at this position are not suitable for direct comparison with the numerical model.

It is important to note that the embankment was modeled using the Drucker-Prager constitutive model, and its calibration involved selecting the soil cohesion to match the obtained crest settlement of the embankment of the model 0% directly subjected to high amplitude signal [49]. However, this approach resulted in a significant overestimation and notable discrepancies between the numerical and experimental results of the model 0% subjected to small-amplitude signal and the models 5% and 10%. These results highlight that the chosen cohesion during the calibration of the Drucker-Prager model does not accurately simulate the correct quantitative results. These observations suggest that exploring an alternative constitutive law for the embankment could potentially lead to more accurate results in terms of vertical displacements. Despite the differences observed quantitatively between the experimental and numerical results, the numerical models still can capture the reduction of the settlements when non-plastic fines were introduced to the liquefiable soil.

## 6. Conclusion

In this study, numerical modeling was carried out based on the centrifuge experiment tests of an embankment constructed on liquefiable soil. The numerical modeling exploited an advanced constitutive model – PM4Sand to capture the complex behavior of soil under liquefaction conditions and the presence of non-plastic fines was taken into consideration. The performance of the numerical models was then
<figure><img src="image_21.png" /><figcaption>Fig. 18. Crest settlement recorded during centrifuge tests and computed from the numerical models (0%,5% and 10%) with (a) 0.1 g and (c) 0.2 g shakes. (The settlement of the 0% of fines model under the high-amplitude signal is missed during the test).</figcaption></figure>

validated against the experimental centrifuge tests in terms of excess pore pressures, acceleration responses and vertical displacement of the embankment. The effect of non-plastic fines was also investigated and discussed by the comparison of the numerical results with the experimental observations and the following conclusions can be drawn:

* The numerical models effectively captured the build-up of excess pore pressure during centrifuge tests under both small-amplitude (0.1 g) and high-amplitude (0.2 g) inputs. The comparison of the predicted maximum excess pore pressures and the experimental records were in an acceptable range. The highest discrepancies were observed at the interface between the embankment and the liquefiable soil, due to the challenges in simulating the transition from fully saturated to partially saturated conditions. In addition, the models accurately predicted liquefaction, particularly under free surface of the liquefiable soil, where liquefaction was detected during centrifuge tests. Furthermore, the models successfully simulated the dissipation of excess pore pressure during the dissipation stage.

* The numerical model reproduced correctly the impact of non-plastic fines on excess pore pressure ratios. The addition of fines led to a reduction in the extent of liquefied zones in both the lateral direction and the depth during both small and high-amplitude signals. During the high-amplitude signal, the depth of the liquefied zones decreased from approximately 6 m in the model with 0% fines to around 4 m when fines were added in the liquefiable layer. The reduction in the extension of the liquefied zones indicates that the addition of non-plastic fines increased the liquefaction resistance of the soil.

* The numerical models reproduce well the acceleration time-histories observed during centrifuge tests subjected to both small-amplitude (0.1 g) and high-amplitude (0.2 g) signals. The models also successfully capture the liquefaction phenomenon, showing that liquefaction did not occur beneath the embankment, however it was triggered under the free surface of the liquefiable soil. Some differences were observed in the liquefied areas, especially during the high-amplitude signal, when the numerical model was compared to the experimental test subjected to three small-amplitude signals in its loading history.

* The effect of fines on the acceleration response was also studied using the validated numerical models. A comparison of these

models with varying fines content indicates that the time for liquefaction initiation at the position beneath the free surface of the liquefiable soil increases with the increasing of the fines content, during both the small and high amplitude signals. The numerical models show that the presence of non-plastic fines has restricted and retarded the initiation of liquefaction.

* The numerical models were validated against experimental results in terms of embankment deformation. Both numerical and experimental results showed a deformation pattern characterized by crest settlement and lateral displacement of the embankment toes. The numerical models qualitatively captured the impact of fines content on the embankment crest settlement under both small and high amplitude signals, showing that the addition of non-plastic fines led to a significant reduction in crest settlement, which is consistent with the experimental observations. However, significant overestimation was observed in the numerical predictions of vertical displacement. This overestimation was linked to the calibration of the Drucker–Prager model, suggesting that exploring an alternative constitutive law for the embankment may improve the accuracy of vertical displacement results.

### CRediT authorship contribution statement

**Chedid Saade:** Writing – original draft, Visualization, Validation, Formal analysis. **Zheng Li:** Writing – review & editing, Supervision, Investigation, Conceptualization. **Sandra Escoffier:** Writing – review & editing, Supervision, Investigation, Conceptualization. **Luc Thorel:** Writing – review & editing, Supervision, Investigation, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

The authors express gratitude to the University Gustave Eiffel and the Région Pays de la Loire for their financial support. The authors would like to extend thanks for the valuable support and assistance provided by the centrifuge team, including both the technicians and the researchers.
## Data availability

The experimental data used in this article are available in open-access datasets:

* Saade, C., Li, Z., Escoffier, S. and Thorel, L. (2025). Centrifuge modelling database for dynamic response of homogeneous embankments resting on liquefiable clean sand layer subjected to a series of dynamic excitations. *Recherche Data Gouv*, V1. Doi:10.57745/FLR3HY

* Saade, C., Li, Z., Escoffier, S. and Thorel, L. (2025). Centrifuge modelling database for dynamic response of homogeneous embankments resting on liquefiable sand layer containing fines. *Recherche Data Gouv*, V1. Doi:10.57745/KVAGUH.

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