Seismic Failure Mechanisms of Concrete Pile Groups in Layered Soft Soil Profiles

Abstract

So far, little attention has been paid to the investigation on the seismic failure mechanisms of flexible concrete pile groups embedded in the layered soft soil profiles considering the material non-linearities of soil and concrete piles. The purpose of this study is to investigate seismic failure mechanism models of flexible concrete piles with varied groups in silt layered loose sand profiles under horizontal strong ground motions. Three-dimensional finite element models of the pile–soil interaction systems, which include nonlinearities of soil and concrete piles as well as coupling interactions between the piles and soil, were created for Models I, II, and III of the soil domains, encompassing 1x1, 2x2, and 3x3 flexible pile groups with diameters of 0.80 m and 1.0 m. Model I consists of a homogenous sand layer and a bedrock, Models II and III are composed of a five-layered domain with homogeneous sand and silt soil layers of different thicknesses. The linear elastic perfectly plastic constitutive model with a Mohr–Coulomb failure criterion is considered to represent the behavior of the soil layers, and the Concrete Damage Plasticity (CDP) model is used for the nonlinear behavior of the concrete piles. The interactions between the soil and the pile surfaces are modeled by defining tangential and normal contact behaviors. The models were analyzed for the scaled acceleration records of the 1999 Düzce and Kocaeli earthquakes, considering peak ground accelerations of 0.25 g, 0.50 g, and 0.75 g. The numerical results indicated that failure mechanisms of flexible concrete groups occur near the silt layers, and the silt layers have led to a significant increase in the spread area of the damaged zone and the number of damaged elements.

1. Introduction

Piles, the vertical structural elements of deep foundations, find widespread applications in supporting various engineering structures, including transmission towers, high-rise buildings, dams, bridges, heavy oil tanks, wind turbines, offshore structures, machine foundations, and earth retaining structures. Pile foundations can be categorized into two types: long (flexible) and short, depending on their length-to-diameter ratio (L/D). Piles with L/D ratios between 10 and 30 are referred to as flexible piles [1]. Short piles tend to exhibit rigid behavior when subjected to strong ground motions, whereas long piles demonstrate flexible behavior. Long piles are typically designed in groups. The capacity of pile groups is influenced by several factors, including the characteristics of the individual piles, the properties of the soil layers, the interactions occurring at the pile–soil interface, as well as the nature and magnitude of applied loads [2]. In addition to the vertical load-bearing capacity of pile groups under static loads and machine-induced vibrations, their lateral capacity becomes particularly critical when subjected to strong earthquake ground motions. Inadequate lateral capacity can result in seismic-induced failure to pile groups.

The failures of pile foundations have been extensively observed during earthquakes such as North Ridge 1994, Kobe 1995, Kocaeli 1999, Chi-chi 1999, Bhuj 2001, Chile 2010, and Japan 2011 [3]. As a result, the seismic behavior of pile foundations under the influence of strong ground motion has garnered significant attention from researchers. Some of the theoretical and experimental studies on the behavior of piles under earthquake effects are mentioned below. The behaviors of laterally loaded single and group piles were first investigated by Chang [4], Poulos [5], and Randolph [6]. Ettouney et al. [7] developed a semi-analytical solution for the dynamic behavior of vertical pile groups, which included pile–soil–pile dynamic interactions and a linear plane strain continuum soil model. Gazetas and Dobry [8] proposed a procedure for estimating the lateral response of flexible piles embedded in a layered soil deposit under harmonic head loading. Lee et al. [9] determined the static behavior of an axially loaded single pile in layered soil in terms of effective stresses, using a rigorous elastic load transfer theory.

Wu and Finn [10,11] conducted an examination on both the elastic and nonlinear behaviors of pile foundations using the finite element method in both the frequency and time domains. Mylonakis and Gazetas [12] developed simplified analytical models to assess the lateral harmonic response of single piles and pile groups in layered soil. They utilized a dynamic Winkler formulation based on frequency-dependent springs and dashpots. Finn [2] presented an assessment of standard engineering practices for predicting the response of pile foundations within layered weak soil profiles during earthquakes. This assessment was based on findings derived from field tests, model pile centrifuge experiments, and extensive nonlinear dynamic analyses. Liyanapathirana and Poulos [13] proposed a numerical model to analyze the seismic lateral response of piles in weak soils, accounting for reductions in soil stiffness and strength, as well as material nonlinearity. Yang and Jeremic [14] investigated the effects of layering on the lateral loading behavior of a single pile in elastic-plastic soils. Brandenberg et al. [15] developed material models for soil-structure interaction within the open-source finite-element modeling platform OpenSees. These models were compared with the results obtained from two dynamic centrifuge model tests of pile systems in soft soil profiles. Banerjee et al. [16] explored the seismic impacts on fixed-head and end-bearing piles installed through single layer of soft clay, combining centrifuge testing with numerical modeling techniques. Tang and Ling [17] conducted shake-table tests to investigate the failure behavior of a reinforced-concrete elevated cap pile foundation during soil liquefaction.

Lin et al. [18] examined the interaction between laterally loaded piles and the surrounding soil, simultaneously measuring the compressive soil–pile interaction pressures, lateral movements along the pile length, and the distribution of soil pressure. Liu et al. [19] determine the dynamic response of pile groups partially embedded in layered saturated soil under a harmonic horizontal load applied at the pile cap, utilizing a combination of Novak’s thin-layer and the transfer matrix methods. Zhang et al. [20] delved into the influence of variations in seismic ground motions on the seismic bending moment response of fixed-head and end-bearing piles installed through soft clay in a single layer. Kaneko et al. [21] presented an analytical static simulation technique that accounts for multiple factors such as the nonlinear characteristics of pile load deformation, rotational stiffness dependence on axial load at the pile head, and nonlinear behavior of soil springs with the pile group effect. The authors emphasized the significance of accounting for these nonlinear behaviors of piles and soil when simulating the pile failure process. Lopez Jimenez et al. [22] explored the effects of multiple variables—such as soil relative density, pile length, pile modeling type, and earthquake predominant frequency—on pile and rigid inclusion systems embedded in soft soils. Turello et al. [23] addressed the issue of lateral loading on pile groups by employing embedded beam elements featuring elasto-plastic interaction interfaces, allowing for the accurate representation of the nonlinear soil behavior around the piles.

Keawsawasvong and Ukritchon [24] thoroughly examined the influence of overburden stress factors on the undrained capacity of laterally loaded piles under combined horizontal static load and moment. Anoyatis and Mylonakis [25] introduced an analytical elastic continuum model focused on the settlement of end-bearing piles situated in a two-layer soil system above a rigid stratum. Rajeswari and Sarkar [3] conducted a detailed 3D numerical investigation using the open-source finite element software OpenSees (https://en.wikipedia.org/wiki/OpenSees) to explore the response of a pile embedded in both single-layer and two-layered soil profiles. Wang et al. [1] presented a mechanism model to predict the lateral behavior of monopiles in soft clay, considering various length-to-diameter ratios, encompassing flexible, semi-rigid, and rigid piles. Shahbazi et al. [26] conducted an extensive full-scale shake table testing program involving two helical pile groups with pinned head and fixed head connections, aiming to enhance the understanding of the dynamic characteristics of soil–pile group–structure systems. Liu et al. [27] implemented quasi-static tests to investigate the impact of pile-group and cap-rotation effects on the seismic failure mechanisms of partially embedded bridge foundations in sand layers. Rajeswari and Sarkar [28] examined the behavior of single piles with varying batter angles and slenderness ratios under lateral soil movements, utilizing the beam on non-linear Winkler foundation concept. Zhang et al. [29] conducted shake-table tests and accompanied pseudo-static analyses to explore how lateral loads affect the buckling failure of an end-bearing pile partially embedded in a saturated sand layer.

Ebadi-Jamkhaneh et al. [30] acquired insights into the seismic behavior of a soil–pile system within soft soil using three-dimensional finite element analysis. Fattah et al. [31] conducted a series of laboratory tests to measure both vertical and horizontal displacements of pile foundations in a single layer subjected to dynamic loads. Ali and Aggour [32] carried out 3D finite element analyses of pile groups to assess the axial dynamic response and efficiency of these pile groups under vertical harmonic loading. Saadatinezhad et al. [33] conducted an investigation into the behavior of non-connected piled raft foundations filled with a layer of compacted soil subjected to earthquake loading, utilizing a three-dimensional finite element model validated against centrifuge test results. Garala and Madabhushi [34] implemented centrifuge tests to investigate the influence of pile spacing on the dynamic behavior of pile groups embedded in two-layered soil profiles. Tran et al. [35] conducted both numerical and experimental examinations on the soil–pile interface properties in the lateral direction, particularly in sand soils subjected to earthquake forces.

Basack et al. [36] investigated the experimental and numerical behaviors of pile–soil interaction under cyclic lateral loads, focusing on loose sands. Radhima et al. [37] explored the effects of both soil (material) and pile–soil interface (geometric) non-linearities on the response of linear pile groups within a single layer under static and dynamic harmonic loadings. Ye and Ai [38] delved into the dynamic response of a pile embedded in layered transversely isotropic unsaturated poroelastic media subjected to vertical external excitations, employing a coupling of finite element and boundary element methods. Timurağaoğlu et al. [39] conducted numerical examinations of the dynamic p–y curves in group piles, considering the nonlinear behavior of soil with a kinematic hardening model. Fansuri et al. [40] prepared a study to investigate the impact of soil–pile interaction on the seismic responses of both the piles and the surrounding soil. The authors considered various influential factors, including axial loading, ground inclination, pile spacing, and diameter. Zafar et al. [41] employed experimental and numerical approaches to explore vertical dynamic pile-to-pile interactions in floating piles embedded within cohesionless soils. Lee and Do [42] proposed a novel concept of a group suction pile designed to enhance the inadequate horizontal resistance offered by a single suction pile. Zou et al. [43] presented a coupled dynamic interaction model that considers the interaction between unsaturated surrounding soil and partially embedded piles under combined loads, utilizing a three-dimensional multiphase viscoelastic continuum and one-dimensional beam theory. Jia et al. [44] conducted 1-g shaking table tests involving a 2x2 pile group embedded in sloping soft soils with a crust to examine the seismic behaviors and failure mechanisms of the pile groups. Hu et al. [45] proposed a probability density evolution method, combined with a stochastic ground motion model, for the stochastic seismic response of reinforced concrete single piles.

The literature review above summarizes numerous studies conducted on the static and dynamic behaviors of vertically and laterally loaded pile–soil interaction systems in both single and layered soil domains. These studies utilized laboratory testing, field-based investigations, and theoretical analyses including analytical and numerical modeling. They have significantly contributed to the understanding of soil–pile interaction. However, relatively little attention has been given to the investigation of seismic failure mechanisms in concrete flexible pile groups embedded in layered soft soil profiles, considering material non-linearities of soil and concrete piles, as well as geometric nonlinearity at the soil–pile interface. This paper focuses on determining the seismic failure mechanisms of single and group piles embedded in homogeneous silt layered loose sand profiles, considering material and geometric nonlinearities under strong earthquake effects. The study begins by presenting the pile damages experienced during earthquakes and introduces material nonlinear models for soil domain and concrete piles. Subsequently, 3D finite element models of the pile–soil interaction systems are developed, and the seismic failure mechanisms of both single and group piles situated within homogeneous silt layered loose sand profiles are investigated for different pile configurations and strong ground motion scenarios.

2. Damage to Concrete Pile Foundations during Earthquakes

Pile foundations are commonly employed in seismic regions characterized by loose to medium-dense soil profiles. The structural damage experienced by pile foundations during earthquakes is influenced by various factors, including the stiffness of the pile, the properties of the surrounding soil, the interaction between the soil and the pile, and the specific characteristics of the seismic events. Piles exposed to intense ground motions may exhibit damage in the form of bending, buckling, and settlement, as highlighted in studies by Bhattacharya et al. [46] and Rostami et al. [47]. Bending damage commonly arises from the lateral spreading of soil due to transverse or lateral seismic loads or from the inertia of the superstructure. Conversely, buckling damage occurs when the restraining effect of the surrounding soil decreases under both axial and lateral loadings, often influenced by the slenderness ratio of the piles [46,47].

Pile damage typically occurs in proximity to the pile head and at the bottom, as well as near interfaces between layers with significant differences in stiffness and between liquefied and non-liquefied layers. Extensive instances of pile damage at the interface between soft and stiff layers have been observed in earthquakes such as the 1964 Niigata, 1971 San Fernando, 1989 Loma Prieta, and 1995 Kobe earthquakes [48,49,50,51,52]. Figure 1 presents some visual examples of real and scaled concrete piles extracted from the soil after earthquakes.

3. Material Models for Concrete Pile and Soil Domain

Concrete Damage Plasticity (CDP) model proposed by Lubliner et al. [55] are considered to account for the nonlinear behavior of the concrete piles in this study. Figure 2 illustrates the uniaxial tensile and compressive behaviors of the CDP model. The tensile and compressive stresses, σ_to and σ_cu, are defined as follows:

$${\mathsf{\sigma }}_{\mathrm{to}}=\left(1-{\mathrm{d}}_{\mathrm{t}}\right){\mathrm{E}}_0\left({\mathsf{\epsilon }}_{\mathrm{t}}-{\mathsf{\epsilon }}_{\mathrm{t}}^{\mathrm{pl}}\right)$$

(1)

$${\mathsf{\sigma }}_{\mathrm{cu}}=\left(1-{\mathrm{d}}_{\mathrm{c}}\right){\mathrm{E}}_0\left({\mathsf{\epsilon }}_{\mathrm{c}}-{\mathsf{\epsilon }}_{\mathrm{c}}^{\mathrm{pl}}\right)$$

(2)

where ${\mathrm{E}}_0$ represents the initial modulus of elasticity, ${\mathsf{\epsilon }}_{\mathrm{c}}$ and ${\mathsf{\epsilon }}_{\mathrm{t}}$ stand for the total strains in compressive and tensile conditions, ${\mathsf{\epsilon }}_{\mathrm{c}}^{\mathrm{pl}}$ and ${\mathsf{\epsilon }}_{\mathrm{t}}^{\mathrm{pl}}$ denote the equivalent plastic strains in compressive and tensile conditions, and ${\mathrm{d}}_{\mathrm{c}}$ and ${\mathrm{d}}_{\mathrm{t}}$ represent the compressive and tensile damage parameters [56]. These damage parameters can range from 0 (indicating no damage) to 1.0 (representing full damage).

Table 1. Material properties for concrete piles.

Properties	Concrete
Elasticity Modulus (MPa)	27,000
Density (kg/m3)	2500
Poisson’s ratio	0.20

provides the selected material properties for the concrete piles. Figure 3 displays the stress–strain curves in tension and compression, as well as the damage parameters in relation to the corresponding strains for the concrete piles. In Figure 3a,b, blue color represents elastic behavior, red and green colors represent inelastic behavior.

Three different soil domain profiles, denoted as Models I, II, and III in Figure 4, have been chosen for the nonlinear seismic analyses. Model I comprises a homogeneous sand layer atop a bedrock, whereas both Model II and Model III consist of five-layered domains with varying thicknesses of homogeneous sand and silt soil layers. The layer thicknesses in the soil profile models are illustrated in Figure 4. The total depth of the soil profile is set at 30 m, with the combined thickness of the soil layers and bedrock being 20 m and 10 m, respectively. Notably, Model III incorporates thicker silt layers compared to Model II. The elastic modulus values for the sand and silt soil layers are specified as 40 MPa and 13 MPa, respectively. To represent the behavior of the soil layers in the nonlinear analyses, a linear elastic perfectly plastic constitutive model with a Mohr–Coulomb failure criterion has been employed. The Mohr–Coulomb plasticity model uses a smooth flow potential that has a hyperbolic shape in the meridional stress plane and a piecewise elliptic shape in the deviatoric stress plane. Additionally, to account for material hardening behavior, it assumes isotropic cohesion hardening [56]. The mechanical properties of the soil layers are detailed in

Table 2. Material properties for the soil layers in Models I, II and III [59].

Layer	Density (kg/m3)	Modulus of Elasticity (MPa)	Poisson’s Ratio	Cohesion (MPa)	Friction Angle (deg)	Dilatation Angle (deg)	Shear Wave Velocity (m/s)
Layer 1 (Sand)	1800	40	0.25	0.00	36	5	298
Layer 2 (Silt)	1800	13	0.30	0.00	36	5	167
Bedrock	2500	3500	0.35	2.55	38	0	2277

. Since the behavior of the bedrock is assumed to be perfectly rigid, the dilatation angle was selected as zero in the analyses [58].

4. Finite Element Models of the Selected Pile–Soil Interaction Systems

Overall, 1x1, 2x2, and 3x3 pile groups have been selected to determine seismic failure mechanisms of the flexible concrete piles (Figure 5). Based on the studies in the literature, the pile diameters (D) have been determined as 0.8 m and 1.0 m, the pile length (L) is 20 m, and the spacing between the piles (s) is 3.0 m. The length-to-diameter (L/D) ratios for the piles with the diameters of 0.8 m and 1.0 m are 25 and 20, respectively. Since the L/D ratios of the selected piles fall within the range of 10 < L/D ≤ 30, they are referred to as flexible piles [1]. Nine 3D finite element models created for Models I, II, and III of the soil domains, taking into account the 1x1, 2x2, and 3x3 pile groups, are presented in Figure 6. The depth and diameter of the soil domain are selected as 30 m and 40 m, respectively [60]. Finite element models of soil domain and piles consist of standard, first-order, eight-noded hexagonal ‘brick’-type elements (C3D8R). These elements are surrounded by eight-noded hexagonal ‘infinite’ elements (CIN3D8), properly reproducing the wave radiation in the dynamic problem. A relatively fine mesh was adopted for the pile and a coarser mesh was adopted for the soil medium.

The accuracy of a numerical simulation of seismic wave propagation in a dynamic soil-structure interaction problem is controlled by two main parameters [8,61,62,63]: (i) the grid spacing (height) of element (h), (ii) the length of time step t. The maximum grid spacing should not be larger than h < V_s,min/(10f_max), where V_s,min is the minimum shear wave velocity, and f_max is the maximum frequency of the soil stratum due to vertically propagating (horizontal polarized) shear waves. The height of soil element was taken as 0.50 m in the finite element models. The time step ∆t needs to be limited to ∆t < h/V_s,min. The time step was chosen as 0.001 s in the nonlinear analyses.

This study accounts for material non-linearity in both concrete piles and the soil domain, as well as geometric non-linearity at the pile–soil interaction interfaces. The top surface of the soil domain is treated as a free surface, allowing unrestricted displacements in all directions. In contrast, the bottom surface of the bedrock is considered to be fixed. In the finite element models, the horizontal movements of the concrete pile groups on the surface have been equalized using the diaphragm model. It is assumed that both the soil and the pile move in the same manner at the bottom end of the pile. To ensure this alignment, a tie contact has been established between the bottom end of the pile and the soil. Infinite elements are employed to enable wave radiation along the lateral sides of the numerical models. The interaction between the soil and the pile surfaces is simulated by defining tangential and normal contact behaviors. Within the finite element models, master and slave surfaces are designated [56]. The master surface corresponds to the exterior surface of the pile, while the slave surface represents the interior surface of the soil, extruded to match the precise dimensions of the pile. Tangential contact between these two surfaces is defined using a friction coefficient of 0.33. Frictional contact is considered at pile–shaft interfaces, while zero friction is assumed at the pile tip.

5. Seismic Failure Mechanisms of Concrete Pile Groups

Three-dimensional finite element models of the pile–soil interaction system were developed for Models I, II, and III of the soil domains. These models were aimed at determining the seismic failure mechanisms of flexible concrete pile groups embedded in layered soft soil profiles. These models included 1x1, 2x2, and 3x3 pile groups, each with diameters of 1.0 m and 0.80 m. Geostatic analyses of the finite element models under gravity loads were performed prior to the earthquake analyses. It was observed that the stresses obtained from the numerical geostatic analysis are close to the analytical solutions.

The correct seismic input represents one of the most important parameters for the design of structures, especially for those located in high seismicity areas [64]. The strong ground motion records of the 1999 Düzce and Kocaeli earthquakes were selected according to the characteristics of the soil domain profiles in Table 2. The selected earthquake records were applied horizontally onto all nodes at the bottom part of the finite element models. Torsional loads were not considered in the analyses.

Table 3. The characteristics of the selected earthquakes [65].

Event	Record Seq.	Station	Date	Rrup (km)	Magnitude	PGA (g)	Shear Wave Velocity (m/s)
Düzce	1602	Bolu	12 November 1999	12.04	7.14	1.01	293.57
Kocaeli	1147	Ambarlı	17 August 1999	69.62	7.51	0.253	175.00

provides a summary of the characteristics of the 1999 Kocaeli and Düzce earthquakes, while Figure 7 illustrates the original acceleration records and Arias intensities of these earthquakes. The earthquake records were scaled to achieve identical peak acceleration values which are 0.25 g, 0.50 g, and 0.75 g, using DEEPSOIL V7 software [63]. DEEPSOIL V7 [63] provides the user the option to linearly scale the selected original input motion. The user has two options for scaling: scale the original motion by a specified factor or scale the original motion to a specified maximum acceleration. The option to scale the original motion to a specified maximum acceleration option was used for the acceleration records of the 1999 Kocaeli and Düzce earthquakes.

A total of 108 nonlinear seismic analyses were performed considering both single pile and pile groups to investigate the failure mechanisms of flexible concrete piles in layered soft soil zones. Each analysis took an average of one day. Therefore, in order to make the calculations more efficient and faster, the most effective 6 s duration of each record was selected by considering the Arias intensities. After taking the most effective 6 s duration, each analysis took an average of 6 h to complete. Nonlinear seismic analyses were performed using the Full Newton-Raphson method with a time increment of 0.001 s. It is well known that soil layers and concrete piles have different damping ratios. In this study, an average damping ratio of 5% was chosen for the nonlinear seismic analysis of the pile–soil interaction system considering the behaviors of the soil layers and concrete piles. The 1st and 50th frequencies of the pile–soil interaction system were considered for the calculation of Rayleigh damping coefficients corresponding to the 5% average damping ratio.

To evaluate and compare the failure behavior of the concrete piles, the maximum tensile (principal) stresses were considered. Cracks initiate when the tensile stress reaches predefined limit values in Figure 3. The scale bars in the figures below illustrate the tensile damage ratios of each element, represented by different colors. The blue color indicates zero damage (dt = 0), while red corresponds to full damage (dt = 1). The damage of the finite element model is generally consistent with the experimental results when the tensile damage factors are greater than 0.90. In the figures below, a tensile damage parameter, dt, is set to 0.94, which means that areas colored in red indicate that at least 94% of the element body is damaged. The pile failures below are compared considering the damage parameter value of 0.94. The figures below depict the distributions of the maximum tensile damage (DAMAGET) at the conclusion of the total duration of the earthquake records.

The seismic failure mechanisms of single pile (1x1) and pile (2x2 and 3x3) groups with diameters of 0.80 m and 1.0 m in Models I, II, and III in Figure 6 are presented separately for the peak ground accelerations of 0.25 g, 0.50 g, and 0.75 g in Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13. Figure 8 illustrates the distributions of the maximum tensile damage ratios and the number of damaged elements in Models I, II, and III for the 0.80 m diameter single pile (1x1) configuration under the Düzce and Kocaeli earthquakes. Similarly, Figure 9 presents the same graphics for the 1.0 m diameter single pile (1x1) configuration. In Model I, minor damage is visible in a restricted area for both 0.80 m and 1.0 m diameters. However, substantial damage is evident in the single pile element of Model II, particularly in locations with soft soil silt layers. Model II exhibits more pronounced damage distribution than Model I. In Model III, characterized by a larger coverage of the soft ground layer compared to Models I and II, there is an escalation in both the distribution and severity of damage, encompassing a broader region. It is generally observed that damages decrease as the pile diameter increases across all pile–soil interaction models with a single pile (1x1) configuration. Additionally, there are observed increases in both the distribution and quantity of damaged elements with the escalation of the silt layer thickness.

The seismic failure mechanisms of concrete piles, each with a diameter of 0.80 m arranged in a four-pile configuration (2x2), are depicted in Figure 10 for Models I, II, and III. Correspondingly, damage distributions for models featuring a 1.0 m pile diameter are illustrated in Figure 11. In Model I, employing a 2x2 pile configuration, negligible damage is observed for both the Düzce and Kocaeli earthquakes at the 0.25 g and 0.50 g accelerations. However, indications of minor damage begin to emerge at an acceleration of 0.75 g. In Model II, the onset of damage becomes apparent within the piles, and with the escalation of earthquake accelerations, there are concurrent increases in both the size of damaged areas and the count of damaged elements. In Model III, as the thickness of the silt layer increases, considerable rises are observed in both the spread of damage within the piles and the quantity of damaged elements. It can be generally stated that the damage propagation predominantly occurs in regions near the silt layers. Additionally, Figure 10 and Figure 11 reveal a higher number of damaged elements in piles with a 0.80 m diameter compared to those with the diameter of 1.0 m. This disparity arises from the larger diameter, which enhances the bearing capacity, deformation behavior, durability, and overall performance of the piles.

Figure 12 displays the damage distributions of piles with a diameter of 0.80 m in Models I, II, and III employing a nine-pile configuration (3x3). Meanwhile, Figure 13 illustrates the damage distributions of piles with a 1.0 m diameter across the same models. In Model I, the damage distribution and count of damaged elements within the pile group (3x3) remain notably limited, exhibiting a slight increase corresponding to higher peak ground acceleration values. Conversely, in Model II, damages intensify in proximity to the silt layers and exhibit a corresponding escalation with the increasing peak ground acceleration. In Model III, characterized by a more extensive silt layer, there is a substantial increase in both the damaged area and the count of damaged elements. These extents notably surpass those observed in both Model I and Model II.

6. Conclusions

The seismic failure mechanisms of single (1x1) piles, as well as grouped configurations (2x2 and 3x3) with the dimensions of 0.80 m and 1.0 m, situated within homogeneous silt layered loose sand profiles, have undergone extensive investigation. This comprehensive exploration encompasses considerations of material and geometric nonlinearities, diverse models of pile–soil interaction, and the varying effects of peak ground accelerations. The results obtained from this study are summarized below.

• The presence of the soft silt layer has markedly expanded the area affected by damage and increased the count of damaged elements. Furthermore, the thickness of the soft silt layer has notably influenced both the scope and intensity of the damaged zone within the piles. The greatest extent of damage is observed in Model III, where the soft silt layers are the thickest. Additionally, Model II exhibits more damage compared to Model I.
• The peak ground accelerations have emerged as a crucial parameter in the onset of damage. Minimal damage is observed at 0.25 g, while the most extensive damage occurs at an acceleration of 0.75 g.
• The distribution of damage and the count of damaged elements resulting from the Kocaeli earthquake have shown a relatively higher impact compared to those caused by the Düzce earthquake.
• An increase in pile diameter correlates with a decrease in both the distribution of damaged areas and the count of damaged elements. Models featuring a 1.0 m pile diameter exhibited less damage compared to those with a 0.80 m pile diameter.
• The damages to both single and grouped pile elements were primarily concentrated near the lower and upper junction points where the sand and silt layers intersect.