Analysis of the Dynamic Behavior of Multi-Layered Soil Grounds

Abstract

The ground consists of many layers of soil with different properties. The propagation speed and path of seismic waves are affected by different soil layers. It is necessary to understand that layered soil exhibits different dynamic behaviors and responses under the action of seismic waves. This study utilized weathered soil and silica sand as materials to create multi-layered soil conditions with varying degrees of compaction. By conducting a 1 g shaking-table test on multi-layered soil, the interactions and influences between different soil layers under different earthquake conditions were observed. The approach of our numerical analysis aimed to complement the experimental results and provide an in-depth understanding of the dynamic behavior of multi-layered soil surfaces during seismic events. The acceleration results achieved with the ABAQUS and DEEPSOIL models for multi-layered soil were in good agreement with the experimental results. By comparing the stress–strain curves, the deformation mechanisms under different constitutive models in the numerical analysis were studied. The results of this study show that the amplification effect of seismic waves is related to the number of soil layers and the degree of compaction of the soil layers. This indicates that multi-layered soil ground and the behavior of the soil layers play an important role in the propagation and impact of seismic waves, and this amplification effect is of great significance in the design of actual seismic disaster risk assessments.

1. Introduction

Earthquakes are one of the most common natural disasters on Earth and are extremely destructive. Earthquakes cause seismic waves to propagate through the Earth’s crust, with numerous effects on its soil and foundations, such as seismic wave amplification, earthquake-induced liquefaction, and effects on infrastructure, which have been modeled in various studies [1]. Earthquakes propagate seismic waves in soil, and different types and layers of soil have different effects on the propagation and response of seismic waves. Therefore, to assess the stability and safety of the ground during earthquakes, an in-depth understanding of the response behavior of multi-layered soils is required.

A lot of studies have been conducted using 1 g shaking-table test and numerical analysis methods for single-layer soil [2,3,4,5,6,7,8,9]. For multi-layered soil grounds, 1 g shaking-table tests are designed to simulate the interactions between different soil layers under seismic conditions and the effects of earthquakes on buildings and infrastructure. The following are some studies related to multi-layered soil. Bretschneider et al. (2016) demonstrated the amplification effect that occurs in multiple soil layers by performing centrifuge tests on three soil layers. The results they obtained comprised only experimental data, and because the field size was too small, it could not reflect the amplification effect well [10]. Adampira and Derakhshandi (2019) combined 1 g shaking-table tests and the numerical analysis program OpenSees to evaluate the seismic behavior of the liquefiable sub-layer and its impact on the seismic ground response [11]. Jin et al. (2022) conducted 1 g shaking-table tests to study the dynamic behaviors of multi-layered soil, but the established soil layer only had two layers and they used soil layers of the same material, which cannot represent multi-layered soil well [12]. Namdar et al. (2021) used ABAQUS to conduct a modeling analysis on single-layer soil and three-layer soil to verify the interactions between multiple layers, but their findings were not supported by experimental data [13]. Özener et al. (2012) investigated the liquefaction mechanism of layered sand through shaking-table tests and numerical analysis [14]. Verma et al. (2020) used the finite-element software CyclicTP to analyze the dynamic response of the foundation of a layered homogeneous soil system [15]. Yang et al. (2023) used a 1 g shaking table to study the improvement and liquefaction of drainage piles in a layered soil model [16]. Wang et al. (2022) studied the seismic responses of abutment models under different soil types through large-scale shaking-table tests and numerical simulations, analyzing the dynamic response under three soil types (silty clay, clay–gravel layer, pure gravel soil) [17]. Modoni et al. (2018) investigated how compaction affects the behavior of gravel embankments under seismic conditions [18]. Ferić et al. (2023) measured the performance parameters of permeable concrete by changing the mixture ratio of eleven types of concrete, controlling the size of the aggregate and four degrees of compaction [19]. Ren et al. (2024) compared the effects of tier offset, soil density, and reinforcement layout on the seismic response of tiered reinforced soil retaining walls (TRS-RWs) through numerical analysis [20].

Conducting a 1 g shaking-table test combined with numerical analysis enables the examination of how seismic waves travel through various soil layers. This approach helps in understanding the intricate patterns and characteristics of seismic wave propagation within multi-layered soil systems. Seismic waves may be amplified or attenuated in multiple layers of soil, depending on the nature and structure of the soil layers. Through dynamic analysis, the amplification effect or energy loss of different soil layers on seismic waves can be quantified, and the response of multi-layered soil grounds to seismic waves can be evaluated. Also, through the dynamic analysis of seismic waves, the vibration characteristics of different soil layers can be predicted, providing a scientific basis for the design of seismic disaster prevention measures.

Thus far, although numerous studies have explored the seismic response of multi-layered soil sites, there remains a significant gap in comprehensive research focused specifically on purely multi-layered soil sites. This gap restricts our understanding of the dynamic properties of such sites and hampers thorough seismic risk assessments in earthquake engineering and infrastructure planning. Despite the extensive literature, the detailed interaction mechanisms within purely multi-layered soil structures under seismic conditions are not well understood. Therefore, our study aims to fill this critical gap by providing an in-depth investigation into the seismic behavior of these specific soil configurations, thereby highlighting the novelty and importance of our research.

2. Materials and Methods

2.1. Soil Properties

The weathered soil used in this study was sourced from a cut slope at a construction site in Ulju-gun, Ulsan Metropolitan City, and underwent comprehensive physical property analyses. These analyses included specific gravity, grain size distribution, Standard Proctor, and relative density tests. The results indicated a specific gravity of 2.69, with maximum and minimum dry unit weights of 18.27 kN/m³ and 12.43 kN/m³, respectively. The optimum moisture content was determined to be 12.5%, and Atterberg limit tests classified the soil as non-plastic (NP) with a plasticity index (PI) of 0. The maximum and minimum void ratios were found to be 1.123 and 0.443, respectively. The soil had a fines content of 10.8%, resulting in a Unified Soil Classification System (USCS) designation of SW-SM. For the dynamic model testing, a specimen was prepared from soil that passed through the No. 4 sieve, with approximately 1% of the original sample being retained on the No. 4 sieve.

Table 1. Geotechnical index properties of the weathered soil used in this study.

Parameter	Value	Parameter	Value
Gs	2.69	emax	1.12
Plasticity index (%)	3.7	emin	0.44
Cc	3.57	Cu	9.28
USCS	SW-SM	D50 (mm)	1.09

presents the geotechnical index properties of the weathered soil utilized in the 1 g shaking-table test.

The silica sand investigated in this study displayed specific characteristics: a specific gravity of 2.65, a friction angle measuring 38 degrees, and maximum and minimum void ratios of 1.06 and 0.64, respectively. Its coefficient of curvature (Cc) stood at 1.03, while the coefficient of uniformity (Cu) was measured at 1.76. This silica sand is classified as SP in the Unified Soil Classification System and has a median particle size (D50) of 0.235 mm. The reason for using weathered soil and silica sand is that the characteristics of the two are quite different, allowing the dynamic characteristics of the site to be more clearly observed.

Table 2. Geotechnical index properties of silica sand used in this study.

Parameter	Value	Parameter	Value
Gs	2.65	emax	1.06
Friction angle	38	emin	0.64
Cc	1.03	Cu	1.76
USCS	SP	D50 (mm)	0.235

presents the geotechnical index properties of the silica sand used in the 1 g shaking-table test.

2.2. The 1 g Shaking-Table Test

2.2.1. Experimental Equipment

In the study of multi-layered soil behavior, a 1 g shaking table offers a controlled setting for simulating seismic events and examining the dynamic response of layered soils. This study employed various experimental components to explore soil dynamics. Figure 1 depicts a schematic diagram of the 1 g shaking-table test system, serving as the central component for conducting experiments and grasping the dynamic properties of the multi-layered soils. The key equipment included the 1 g shaking-table test equipment system, a laminar shear box, a data logger, and an accelerometer. These specialized tools facilitated the replication of ground motions, while the use of the 1 g shaking table enabled analysis with the aim of comprehending the behavior and stability of multi-layered soil under diverse dynamic conditions. The experimental system utilized in this study aligns with that used by Kim et al., 2020 [21].

The laminar shear box comprised 12 independently movable aluminum frames, simulating infinitely expanding ground boundary conditions for horizontal shear motion, as depicted in Figure 2a. The dimensions of the aluminum frames were 2000 mm (W) × 600 mm (L) × 600 mm (H), with each frame having a thickness of 4.5 cm and an approximate frame spacing of 0.5 cm. Data logging involved measuring and recording physical or electrical parameters over time. In this study, seismic acceleration was captured using ARF-20A acceleration transducers, capable of measuring up to 20 m/s². The data logger we employed was the 24-channel SDL-350R model, compatible with ARF-20A, offering a data storage interval of up to 0.005 s. Visuals of the data logger and accelerometer used are shown in Figure 2b,c.

2.2.2. Experimental Method

To evaluate the fundamental behavior of the ground, Hachinohe and Ofunato waves corresponding to a Peak Ground Acceleration of 0.3 g were utilized. Additionally, we employed an artificial seismic wave synthesized from the Gyeongju-Pohang earthquake using empirical Green’s function based on Kori Nuclear Power Plant raw data, with a Peak Ground Acceleration of 0.1 g. This artificial seismic wave, known for its diverse periodic components leading to high amplification, was specifically chosen to evaluate boundary condition effects under such amplification. Notably, the Hachinohe wave exhibits long-period characteristics, while the Ofunato wave is characterized by short-period dynamics. Our reason for selecting these seismic waves was to compare the different seismic waves of long and short periods, which allowed us to more clearly compare the dynamic characteristics between the soil layers. Figure 3 illustrates the waveform diagram of the seismic waves employed in this study.

2.2.3. Test Design

To capture the dynamic behavior of the site, a 1 g shaking-table test was conducted. In order to better compare the amplification characteristics and dynamic responses between soil layers, the flat-ground experiment was divided into four groups, which were named Cases 1, 2, 3, and 4. Case 4 was used as a case study to illustrate the preparation and setup of the experiment. First of all, the weathered soil was placed in the laminar shear box with a compaction degree of 90% of the thickness of five centimeters, and a total of four layers were laid. Then, weathered soil with a thickness of 5 cm and a compaction degree of 90% was placed in the laminar shear box. Finally, the silica sand was naturally placed in the laminar box with a thickness of five centimeters. This meticulous arrangement ensured a uniform soil distribution throughout the box and facilitated the installation of accelerometers within the designated soil layers.

Four experiments were designed to obtain experimental results. The specific parameters are shown in Table 3.

• Case 1: Naturally falling silica sand, with a height of 0.6 m;
• Case 2: Weathered soil with a compaction degree of 90% and a height of 0.6 m;
• Case 3: The lower part is weathered soil with a compaction degree of 90%, and the upper part is naturally falling silica sand; each layer is 0.3 m;
• Case 4: The lower part is weathered soil with a compaction degree of 90%, the middle part is weathered soil with a compaction degree of 80%, and the upper part is naturally falling silica sand; each layer is 0.2 m.

Table 3. Descriptions of the soil layers for each case.

Case	Soil Type	Depth	Description
1	Silica sand	0.6 m	Loose
2	Weathered soil A	0.6 m	Very dense
3	Silica sand	0.3 m	Loose
	Weathered soil A	0.3 m	Very dense
4	Silica sand	0.2 m	Loose
	Weathered soil B	0.2 m	Dense
	Weathered soil A	0.2 m	Very dense

Table 3. Descriptions of the soil layers for each case.

Case	Soil Type	Depth	Description
1	Silica sand	0.6 m	Loose
2	Weathered soil A	0.6 m	Very dense
3	Silica sand	0.3 m	Loose
	Weathered soil A	0.3 m	Very dense
4	Silica sand	0.2 m	Loose
	Weathered soil B	0.2 m	Dense
	Weathered soil A	0.2 m	Very dense

Figure 4 depicts the experimental design for each soil layer, including the placement of the accelerometers. Through these four experiments, the different behaviors of the soil layers were measured. The type of soil and the height of the soil can be referred to Figure 3.

2.3. Numerical Analysis

Numerical analysis is essential for assessing the feasibility and accuracy insights in the analysis of multi-layered soil models. It facilitates the simulation of complex interactions within these systems, providing valuable data between the layers of the site, which can be used in understanding soil behavior, predicting deformations, and optimizing designs. In this study, the numerical analysis programs DEEPSOIL V7.0 and ABAQUS 6.14 were used to supplement the experimental results.

2.3.1. DEEPSOIL Program

DEEPSOIL is a one-dimensional (1D) seismic site response analysis program; it focuses on simulating the effects of seismic events on soil in the vertical direction. This one-dimensional approach allows for a detailed analysis of the interaction of soil layers along the depth of the soil profile [23].

In this study, four models were established in DEEPSOIL, and their cross-sectional diagrams are shown in Figure 5. The position of the derived results in DEEPSOIL (white circle) was completely consistent with that of the experimental design (Figure 4).

The constitutive model employed was the Darendeli mode lIn DEEPSOIL. The Darendeli model characteristically correlates soil properties, such as shear wave velocity, with fundamental parameters like density, effective confining pressure, and plasticity index [24]. It is used in seismic site response analysis to estimate soil stiffness, which is crucial for understanding how structures respond to ground motions during earthquakes. The empirical formula for the Darendeli model is

$$\frac{\mathrm{G}}{{\mathrm{G}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}=\frac{1}{1+{\left(\frac{\gamma }{{\gamma }_{\mathrm{r}}}\right)}^a},$$

(1)

where $\mathrm{G}=$ shear modulus; ${\mathrm{G}}_{\mathrm{m}\mathrm{a}\mathrm{x}}=$ small-strain shear modulus; $\gamma =$ shear strain; ${\gamma }_{\mathrm{r}}=$ reference strain; $a=$ curvature coefficient.

In the DEEPSOIL modeling, the basic parameters required are thickness, unit weight, shear wave velocity, effective vertical stress, and shear strength. Among these, effective vertical stress is related to the unit weight of the soil and the depth of the soil layer.

According to the empirical formula proposed by Seed and Idriss [25] and illustrated in the following expression, shear wave velocity is related to soil depth and soil density. K₂ can be considered to be determined mainly by the void ratio or relative density and the strain amplitude of the motion.

$${\mathrm{V}}_{\mathrm{s}}=\sqrt{\frac{1000K_2{\left({\sigma }_m^{\prime }\right)}^{0.5}}{\rho }},$$

(2)

where ${\mathrm{V}}_{\mathrm{s}}=$ shear wave velocity (m/s), ${\sigma }_{\mathrm{m}}^{\prime }=$ effective vertical stress, and $\gamma =$ soil density (kg/m³).

Based on the DEEPSOIL User Manual, shear strength is related to the shear wave velocity and soil density. Shear strength can be expressed as

$${\mathrm{C}}_{{\mathrm{v}}_{\mathsf{\delta }}}=\mathsf{\rho }{\mathrm{V}}_{\mathrm{s}}^2·0.8·0.1\%,$$

(3)

where ${\mathrm{V}}_{\mathrm{s}}=$ shear wave velocity (m/s), $\mathsf{\rho }=$ soil density (kg/m³).

2.3.2. Finite-Element Analysis

ABAQUS is a formidable finite-element analysis software that enjoys widespread adoption in the simulation and analysis of soil behavior. In the realm of multi-layered soil modeling, ABAQUS boasts numerous advantages. Firstly, it provides sophisticated constitutive models to capture the behavior of soils under varying loading conditions. ABAQUS allows for the creation of realistic soil layering configurations, enabling engineers to simulate the response of multi-layered soil profiles to seismic, geotechnical loading. Additionally, ABAQUS offers robust meshing capabilities to discretize complex soil geometries efficiently, ensuring the accurate representation of soil layer interfaces and boundary conditions.

In this study, multi-layered models were constructed within ABAQUS. Artificial seismic waves, Hachinohe seismic waves, and Ofunato seismic waves were applied at the base of each model to mirror conditions akin to those in the 1 g shaking-table test. The chosen constitutive model, the Mohr–Coulomb model, offers a straightforward yet robust representation of soil strength, encompassing critical factors such as cohesion and frictional resistance. The Mohr–Coulomb model accurately captures the shear behavior of soils under diverse loading scenarios.

Table 4. Soil input parameters used in ABAQUS (weathered soil A).

Parameter	Value	Parameter	Value
Density (kg/m3)	2000	Young’s modulus (MPa)	20
Poisson’s ratio	0.3	Cohesion yield stress (kN)	10
Internal Friction angle (°)	27	Dilatancy angle (°)	25
Damping (alpha)	0.9256	Damping (beta)	3.265 × 10−3

outlines the parameters specific to the weathered soil A employed in the ABAQUS simulations.

The model was divided into a mesh with a size of 0.05 × 0.05 m, which was the best mesh size obtained after multiple mesh-size tests. The infinite boundary section utilized CINPE4 elements, establishing a 2D framework bounded solely horizontally and vertically. Dynamic analysis was conducted with a fixed time increment of 0.001 s. Notably, the bottom boundary solely experienced horizontal acceleration and lacked vertical motion capacity. To mitigate boundary effects on the model analysis outcomes, both boundary sides were reconfigured as infinite boundaries, aligning their conditions as closely as feasible with those of the laminar shear box, as shown in Figure 6a. Figure 6b,c show the acceleration–time results and shear stress results.

3. Results and Discussion

In this section, we compare and analyze the numerical analysis results with the experiments results in Section 2. The setup of the numerical analysis is consistent with the acceleration setup of the experiment in Figure 4. A dynamic response analysis of the multi-layered soil sites under different seismic waves was conducted using acceleration–time history, Peak Ground Acceleration (PGA), Spectral Acceleration (SA), and stress–strain data. The results from the horizontally placed accelerometers (e.g., ACC 3, 4, and 5 in Case 1) validate the accuracy of the experimental results, further demonstrating the value of the laminar shear box in seismic response analysis. The results from the vertically placed accelerometers (e.g., ACC 1, 2, 3, and 4 in Case 3) illustrate the different dynamic responses to seismic wave acceleration in multi-layered soil. Due to the presence of various periodic components in artificial seismic waves, significant amplification can occur. Therefore, this study primarily presents results based on artificial seismic waves. The following is a comparison and discussion of the results obtained in this study.

3.1. Acceleration–Time History

Due to the very small time intervals of the acceleration data, a random selection of portions of the acceleration data was compared in order to clearly identify differences between the experimental and numerical analysis data. Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 present partial acceleration–time history graphs of the artificial seismic waves from the 1 g shaking-table experiments and numerical analysis.

Firstly, Figure 7 presents the experimental results from the 1 g shaking-table tests conducted across the four cases. The results indicate minimal differences among several points at the top of the experimental cases, with overlapping acceleration–time history graphs. This strongly indicates that the laminar shear box can effectively neglect boundary effects. Similar results are also demonstrated in the numerical analysis. However, for the sake of brevity, only the experimental data are presented here.

Figure 8 shows the partial acceleration–time history graphs for Case 1 (silica sand). The ABAQUS results exhibit the highest acceleration amplification, followed by the experimental results, and DEEPSOIL shows the smallest amplification. Overall, the results from the numerical analysis closely match those from the experiments.

Figure 9 shows the partial acceleration–time history graphs for Case 2 (weathered soil A). The ABAQUS results exhibit the highest acceleration amplification, followed by DEEPSOIL, and the experimental results show the smallest amplification. Moreover, the amplification in weathered soil is greater than that in silica sand.

Figure 10 shows the partial acceleration–time history graphs for Case 3 (silica sand and weathered soil A). It is observed that the acceleration amplification in weathered soil is greater, with the distance between ACC 3 and ACC 4 being smaller than that between ACC 1 and ACC 2. According to Figure 10d, ABAQUS and DEEPSOIL show similar levels of acceleration amplification, with the experimental results exhibiting the smallest amplification. The DEEPSOIL and ABAQUS results are closer to the experimental results.

Figure 11 shows the partial acceleration–time history graphs for Case 4 (silica sand and weathered soil A, B). The ABAQUS results are closer to the experimental results. Additionally, it is observed that the acceleration amplification in silica sand is smaller, with the distance between ACC 1, 2, 3, and 4 being smaller than that between ACC 5 and ACC 6.

Overall, combining the results from the four cases, the laminar shear box demonstrates the ability to neglect boundary effects, providing strong support for its practical application. According to the results from our numerical analysis and experiments, there is an amplification effect in acceleration from the bottom to the top of the seismic wave. Both the numerical analysis and experimental data from Figure 8, Figure 9, Figure 10 and Figure 11a–c demonstrate amplification effects in acceleration from the bottom to the surface. It can be observed that seismic waves typically amplify acceleration more rapidly in denser weathered soil compared to less dense silica sand. This is because denser weathered soil usually possesses higher compaction and strength, allowing for more efficient propagation of seismic waves. On the other hand, less dense silica sand may have larger inter-particle voids, leading to greater impedance during the propagation of seismic waves and slower acceleration amplification. The graphs in Figure 8, Figure 9, Figure 10 and Figure 11d do not fully overlap. The agreement between ABAQUS and the experimental results was higher than that between DEEPSOIL and the experimental results. This discrepancy arose from differences in computational methods between the numerical analysis software, as the experiments were based on intervals determined by accelerometer measurements; ABAQUS used a fixed incremental step, with each analysis step spaced at the same time interval as the accelerometer measurement experiment, which was 0.001 s. DEEPSOIL used a nonlinear time-delay system to obtain seismic responses by solving a soil dynamic response equation. This is why the DEEPSOIL results are not quite in line with the ABAQUS results.

3.2. Peak Ground Acceleration

Peak Ground Acceleration (PGA) can serve as an indicator of the maximum ground-shaking experienced during an earthquake. Analyzing the PGA in multi-layered soil profiles involves considering the response of each soil layer to seismic waves and their interaction with adjacent layers. Layer thickness influences the amplification or attenuation of ground motion. Figure 12 shows the Peak Ground Acceleration (PGA) graphs derived from the acceleration–time history graphs.

In Figure 12a, the PGA of the DEEPSOIL results is generally lower than that of the experimental and ABAQUS results. However, in Figure 12b–d, the PGA of the DEEPSOIL results tends to be higher compared to those of the experimental and ABAQUS results. This is attributed to the effective amplification of DEEPSOIL on weathered soil. Additionally, the densely bound particles in weathered soil contribute to a higher velocity of acoustic wave propagation, facilitating rapid acceleration amplification. The PGA of the experimental and ABAQUS results shows closer agreement.

Different soil layers exhibit distinct amplification characteristics. Areas with softer or thicker soil layers may experience higher PGA due to greater amplification of the seismic waves. Overall, analyzing PGA in multi-layered soil profiles requires consideration of various soil properties and wave propagation mechanisms.

3.3. Spectral Acceleration

Spectral Acceleration (SA) refers to the acceleration response spectrum at various frequencies experienced during seismic events when seismic waves pass through layers of different soil properties. The SA values at each frequency are influenced by the impedance contrast between soil layers, as well as the resonance frequencies and damping characteristics of individual layers. In multi-layered soil profiles, the SA distribution can vary spatially due to the complex interactions of seismic waves with the soil layers, resulting in the amplification or attenuation of ground motion at different frequencies across the site. Understanding the SA characteristics in multi-layered soil profiles is essential for seismic hazard assessment and site-specific ground motion prediction. Figure 13, Figure 14, Figure 15 and Figure 16 show the Spectral Acceleration (SA) of the artificial seismic waves in Case 1, 2, 3, and 4.

In Figure 13, the DEEPSOIL and ABAQUS results show comparable Spectral Accelerations (SAs), with DEEPSOIL closely matching the SA at ACC 2 and ACC 3, attributed to the inherent frequency of the silica sand layer. Post earthquake, significant settlement in the DEEPSOIL model’s nonlinear constitutive and computational modes led to an amplified position SA. For ACC 1, the experimental and numerical results align well. By comparing the results in Figure 14, DEEPSOIL yields slightly higher results than the ABAQUS and experimental results. Moreover, the natural frequencies of the soil layers in the numerical analysis are generally consistent, with the experimental soil layer frequencies slightly exceeding those of the numerical analysis. This is attributed to the inclusion of the laminar shear box’s mass in the experiment, adjusted through calculations to approximately 12.5 Hz, closely matching the numerical analysis. In the weathered soil case, comparing Figure 15a–c, DEEPSOIL and ABAQUS exhibit highly similar Spectral Accelerations, slightly higher than the experimental SA. Comparing Figure 15d, the numerical analysis closely matches the experimental SA. In the weathered soil layer, comparing Figure 16a–c, DEEPSOIL closely matches the experimental Spectral Accelerations, slightly exceeding ABAQUS. Comparing Figure 16d, the numerical analysis closely matches the experimental Spectral Accelerations.

The Spectral Acceleration (SA) during earthquakes varies due to soil types and properties. In silica sand layers, seismic waves’ energy is more easily absorbed and amplified due to the lower soil density and shear wave velocity, resulting in higher SA within a certain frequency range. In contrast, in weathered soil layers, the higher soil density and shear wave velocity lead to less damping and the amplification of seismic wave propagation, resulting in relatively lower SA within the same frequency range. Therefore, silica sand layers may experience greater seismic responses, while weathered soil layers may experience relatively smaller seismic responses.

3.4. Stress–Strain Curves

Figure 17 illustrates the stress–strain curves for the artificial seismic waves in Cases 1, 2, 3, and 4. In the numerical analysis, DEEPSOIL used the Darendeli nonlinear constitutive model; this model characterizes soil behavior by incorporating nonlinearity, hysteresis, and strain rate effects. ABAQUS employs the Mohr–Coulomb plasticity model for simulating the behavior of soils under various loading conditions.

By comparing the stress–strain characteristics of the numerical analysis, it can be observed that in Case 1, the stress–strain values are greater than those in the other three cases. Case 2 exhibits the lowest stress and strain values, followed by Case 3 and then Case 4, indicating a progressive increase in the stress–strain response. However, the stress–strain behavior observed in the Mohr–Coulomb model closely resembles that observed with the Darendeli model, with no significant differences noted overall. Silica sand typically has a lower density and shear wave velocity, thus it experiences larger strains during seismic wave propagation. Additionally, due to its lower strength and stability, silica sand may be more susceptible to stress induced by earthquakes, resulting in greater deformation and strain. The stress–strain relationship in the Mohr–Coulomb model exhibits linearity, while the elastic modulus in the Darendeli model demonstrates a nonlinear relationship, although the hysteresis loop is not significant. This is because the seismic waves are not particularly strong, and the shear strength of the soil layer is large enough.

4. Conclusions

In this study, the dynamic responses of four multi-layered soil cases under different seismic waves w studied according to numerical analysis and 1 g shaking-table test methods, and the interactions and influences between the different soil layers were analyzed. A preliminary understanding of the dynamic characteristics of multi-layered soil models under seismic conditions has been achieved, serving as a good reference for future studies involving more soil layers. Derived from a synthesis of experimental observations and numerical analysis, the following conclusions emerge from this study:

• The laminar shear box effectively mitigates boundary effects, indicating a positive signal for subsequent 1 g shaking-table tests using laminar shear boxes.
• In the acceleration–time history graphs and PGA graphs, there is an amplification effect of acceleration from bottom to surface. Denser weathered soil typically exhibits faster acceleration amplification due to its higher strength, indicating that a greater soil density results in larger acceleration amplification.
• Spectral Acceleration (SA) during seismic varies depending on soil types and properties. In silica sand layers, seismic wave energy is more easily absorbed and amplified, resulting in higher Spectral Acceleration within a certain frequency range. In contrast, in weathered soil layers, Spectral Acceleration is relatively lower within the same frequency range. Therefore, less-dense soil layers may experience larger seismic responses, while denser soil layers may experience relatively smaller seismic responses.
• The acceleration–time history graphs and Spectral Acceleration graphs of the numerical analysis and experimental results show very close agreement. This indicates successful modeling simulation in replicating the scenarios in the experiments, providing valuable guidance for subsequent modeling analyses.
• Stress–strain curves from DEEPSOIL and ABAQUS were compared, revealing linear stress–strain relationships in the Mohr–Coulomb model and nonlinear stress–strain relationships in the Darendeli model. While there are some differences between the Darendeli and Mohr–Coulomb models, these differences are acceptable. This area requires further refinement in future experiments.
• This paper also has some limitations, such as that it does not address the issue of how to obtain the dynamic behavior of an actual site because the size of the actual site will be much larger than that used in an experiment. Also, tests with experimental models that are not only flat but also include more complex slopes and models of various shapes need to be conducted in the future. Next, various types of large-scale models will be verified in combination with similarity law and centrifuge tests to simulate the dynamic behavior of the prototype in this study.