Numerical Insights into Tunnel Excavation Effects on Pile-Supported Embankment in Soft Clay: A Comparison Between Consolidated and Unconsolidated Conditions

Abstract

This study examines the influence of adjacent tunnel excavation on pile-supported embankment in soft clay under both unconsolidated and long-term consolidated conditions. A comprehensive three-dimensional numerical model was developed to simulate the coupled hydro-mechanical interaction between the embankment, piles, and surrounding ground. The soft clay behaviour was described using a hypoplastic constitutive model enhanced with intergranular strain theory to capture stress-dependent stiffness, dilatancy, and degradation under loading. Three tunnel alignments relative to the pile foundation alongside the pile shaft (S), near the pile toe (T), and beneath the pile toe (B) were analyzed to evaluate deformation and load transfer mechanisms. Results indicate that tunnelling induces significant differential settlements, with maximum values of 0.49%, 0.20%, and 0.45% for Cases S, T, and B, respectively. Consolidation substantially reduced both surface and pile settlements while improving subgrade stiffness and load-carrying performance. The maximum bending moment in the leading pile reached 142 kNm at Z/Lp = 0.56 under unconsolidated conditions and decreased following consolidation. The findings highlight the critical role of tunnel depth and consolidation state in controlling deformation, stress redistribution, and structural safety of pile-supported embankment during tunnelling activities.

1. Introduction

The rapid development of underground transportation infrastructure has emerged as a practical solution to mitigate urban traffic congestion [1,2,3]. In China, the accelerated expansion of high-speed railway (HSR) networks has necessitated extensive use of underground structures, making tunnel construction in close proximity to railway subgrades increasingly inevitable. In recent years, numerous tunnelling projects have been executed beneath active railway systems, increasing concerns regarding their potential effects on operational stability [4,5,6,7]. Such excavations inevitably disturb the in-situ stress field, resulting in non-uniform ground deformation and differential settlement within the subgrade [8,9,10]. Given that high-speed railway operations impose strict serviceability criteria with an allowable track deformation limit of only 2 mm according to the High-Speed Railway Design Specification [11], a rigorous assessment of tunnelling-induced deformation mechanisms in the railway foundation is of critical engineering importance [12,13]. The interaction between tunnels and pile-supported systems has been extensively explored through field monitoring, centrifuge modelling, and numerical analyses to explain the underlying mechanisms of soil–structure interaction [14,15,16,17,18,19,20,21,22,23]. Pang et al. [16] reported notable variations in axial load and bending moment along bridge pier piles subjected to nearby shield tunnelling in Singapore. Selemetas [24] conducted one of the earliest systematic evaluations of tunnel-induced pile response, comparing analytical and field-based assessment techniques during the Channel Tunnel Rail Link project in Essex, UK. Building on these pioneering observations, various researchers [25,26,27,28,29] extended the understanding of pile behaviour through advanced numerical models, revealing that the relative position of the tunnel with respect to pile length is an important factor controlling settlement magnitude and the redistribution of load transfer during tunnelling. With the rising need for tunnelling in underground transportation systems and pile-supported embankment for highways and HSR driven by population growth, constructing a tunnel in proximity to a pile-supported embankment is inevitable [30,31]. Despite these efforts, studies addressing pile-supported embankment, a critical substructure in HSR systems, remain extremely limited. Among the few available contributions, Lin et al. [7] proposed an analytical approach for estimating the influence of tunnelling on embankment performance, though consolidation effects were not considered. The detrimental effects of excavations and tunnelling on nearby structures such as tunnels [32], bridge piles [33], and railway subgrades [34] have also been well documented, highlighting the complex stress redistribution induced by underground construction. However, the majority of previous research has neglected the influence of subgrade consolidation, despite its significant role in governing deformation and stiffness evolution in soft ground. Addressing this gap, the present study employs three-dimensional finite element analysis to comprehensively evaluate the effects of adjacent tunnelling on pile-supported embankment in soft clay under both consolidated and unconsolidated conditions. In this study, the “unconsolidated” condition refers to the short-term state of the subgrade immediately after the completion of the pile-supported embankment construction. The novelty of this research lies in the explicit incorporation of time-dependent consolidation effects in assessing tunnelling-induced responses, thereby capturing the coupled hydro-mechanical behaviour of soft clays often ignored in prior work. Unlike earlier studies that primarily investigated isolated piles or pile groups, this research provides an integrated examination of tunnel–embankment–pile interaction, focusing on tunnel depth relative to pile length influences settlement distribution and load transfer mechanisms. By employing a detailed finite element model calibrated against experimental data, the study advances understanding of the stability and serviceability performance of pile-supported embankment subjected to nearby tunnelling in soft ground conditions.

2. Establishment of the Three-Dimensional Computational Framework

2.1. Representation of Geometrical Features Within the Numerical Analysis

This investigation examines the behaviour of pile-supported embankment subjected to adjacent tunnel excavation in soft clay. Two distinct ground conditions were considered to assess the time-dependent influence of consolidation on the soil–structure interaction. The embankment and pile installation were simulated using a fully coupled consolidation formulation, and each construction stage generated excess pore pressures in the soft clay consistent with undrained loading. No time was permitted for pore pressure dissipation following the completion of the final embankment lift. As a result, the initial condition for tunnelling in the unconsolidated scenario corresponds to a soil state characterized by elevated excess pore pressures, reduced effective stresses, and correspondingly low stiffness. This represents the practical situation in which tunnelling proceeds soon after embankment formation, before significant consolidation has occurred. In contrast, the “long-term consolidated” condition was modelled by allowing pore pressures to dissipate fully prior to tunnel excavation, producing a stiffer and more stable subgrade. This distinction enables a direct comparison of tunnelling effects under short-term undrained and long-term consolidated ground responses. A comprehensive three-dimensional finite element model was established in Abaqus to realistically simulate the coupled hydro-mechanical interaction between the embankment, piles, and surrounding soft clay. The coupled consolidation formulation was implemented to capture excess pore pressure evolution, dissipation, and the associated ground deformation during tunnel advancement. Comparative analyses between the consolidated and unconsolidated cases were performed to quantify their influence on the deformation patterns, settlement characteristics, and load transfer mechanisms within the pile-supported embankment tunnel system. Two primary behavioural aspects, settlement characteristics and load transfer mechanisms, were examined under varying tunnelling depths. Three representative tunnel alignments relative to the pile foundations were analyzed: excavation alongside the pile shaft (case S), adjacent to the pile toe (case T), and directly beneath the pile toe (case B).

The geometric configurations of these scenarios are illustrated in Figure 1a–c, which present the transverse sections of the pile-supported embankment tunnel interaction domain. The embankment was modelled with a height of 6 m, a top width of 14 m, and side slopes of 1V:1.5H, founded on a soft clay deposit. The supporting foundation comprised bored piles of 0.5 m diameter and 20 m embedded length, arranged in a square grid with 2.5 m centre-to-centre spacing. For the simulated longitudinal section, 224 piles were modelled (Figure 2), each connected to a 1.5 m × 1.5 m × 0.3 m reinforced concrete cap to ensure realistic load transfer between the embankment and the pile group. A 6 m diameter tunnel was excavated adjacent to the embankment, maintaining a 2 m offset between its periphery and the nearest pile, thereby capturing the critical interaction between tunnelling-induced ground loss and the composite pile-supported embankment system.

2.2. Finite Element Discretization, Initial Stress Generation, and Boundary Conditions

For each simulation scenario, the three-dimensional geometry of the pile-supported embankment, as described previously, was discretized into a finite element mesh using Abaqus. Figure 3 presents the mesh configuration for Case S, illustrating the spatial discretization of the soil domain, piles, and embankment structure. The model dimensions were 116 m × 40 m × 35 m in the global x, y, and z directions, respectively, ensuring that boundary effects were negligible throughout the analysis domain. To ensure numerical stability and accuracy, particular attention was given to the finite element mesh density around the piles, tunnel, and embankment–soil interface [35]. The sensitivity of the numerical results to the mesh size was examined, and it was determined that a mesh element width of 1.5 m, approximately 50 times the shear band thickness, provided the optimal balance without compromising the stability of the analysis [36]. A finer mesh was applied around the piled raft and tunnel, where larger shear strains were anticipated, while a progressively coarser mesh was used at greater distances from the pile-supported embankment and the tunnel. The minimum element size around the pile and tunnel was selected to be less than 0.25d_p (where d_p is the pile diameter), which satisfies widely accepted recommendations for capturing pile-soil interaction and tunnelling-induced deformation fields. The mesh comprised approximately 142,304 solid elements and 272,105 nodes, providing sufficient refinement to capture stress gradients around the piles and the tunnel.

The soil medium was represented using eight-node hexahedral elements (C3D8P type) capable of simulating fully coupled pore pressure-displacement behaviour, with three translational degrees of freedom and three pore pressure degrees of freedom per node. A mesh convergence check was performed by comparing results with a finer mesh (approximately 1.7 times the element count), and differences in crest settlement, maximum bending moment, and pile head load remained within 3–5%, confirming that the adopted mesh configuration is rational and capable of accurately capturing the soil–structure interaction mechanisms examined in this study.

The embankment fill and pile caps were modelled using eight-node linear brick elements, assuming full compatibility at the pile-cap interface to allow continuous load transfer. At the base of the mesh, all translational degrees of freedom were fixed to simulate a rigid boundary, while along the vertical sides, horizontal movement normal to each boundary was restricted to prevent lateral distortion while allowing vertical deformation. A hydraulic boundary condition with zero pore water pressure was imposed at the ground surface. In this research, the contact algorithm in Abaqus incorporating finite sliding was utilized to accurately simulate the behaviour of the pile-supported embankment system. A Coulomb frictional model was adopted to characterize the frictional interaction between the piles, diaphragm wall, geogrid, and subgrade soil. The model was defined with specific parameters, including a friction coefficient (μ) of 0.35 and a limiting displacement (γ_lim) of 5 mm [25,37].

The initial in situ stress field was generated under self-weight using a saturated unit weight of 16.5 kN/m³, with horizontal stresses established according to the coefficient of earth pressure at rest, K₀. The pore water pressure increased linearly with depth, ensuring hydrostatic equilibrium prior to loading. After initial equilibrium was achieved, pile installation was simulated sequentially, activating 14 piles per row as shown in Figure 2, followed by the activation of the embankment elements. The embankment was constructed in six successive lifts, each 1 m thick, to replicate the staged construction process and to capture time-dependent settlement behaviour. Once the embankment reached equilibrium, tunnel excavation was initiated and progressed incrementally along the tunnel axis. In the numerical simulations, the tunnel advancement process was represented using two complementary mechanisms: (i) element deactivation within the designated tunnel volume to simulate material removal and (ii) application of inward boundary displacements along the tunnel periphery to reproduce ground loss effects, corresponding to a controlled volume loss of 2%. To simulate dewatering during excavation, a fully coupled effective stress analysis was used in Abaqus. As each set of elements was deactivated, the pore water pressure distribution was automatically updated. To maintain face stability during excavation, zero-displacement constraints were imposed at the tunnel face of each excavation step.

The tunnel was modelled using an equivalent volume loss method, where inward radial displacements were applied along the tunnel boundary to reproduce the ground deformation typically observed during shield tunnelling. This approach follows established numerical practice for assessing tunnelling effects on adjacent piled structures and has been validated against centrifuge and field observations in similar studies [15,18]. The method allows the analysis to focus on the far-field deformation pattern and the associated stress redistribution that govern pile–soil interaction without requiring detailed modelling of shield operation, face pressure, annular grouting, grout curing, or lining installation stages. However, the approach does not reproduce explicit soil–lining contact behaviour or the temporary gaps that may develop around a real lining. While this may affect local stress conditions immediately adjacent to the tunnel, its influence on global ground movement and deeper pile response is limited. This modelling strategy enables a robust evaluation of soil–structure interaction mechanisms, ensuring numerical stability and realistic replication of field-scale tunnelling effects beneath pile-supported embankment.

2.3. Constitutive Model and Material Parameters Adopted in the Numerical Simulations

The hypoplastic parameters used for the soft kaolin clay were adopted from Hong et al. [38], who calibrated the model against comprehensive laboratory tests including triaxial compression, isotropic compression, swelling, and cyclic shear loading. Their parameter set has been widely used in simulating soil–pile interaction problems involving kaolin and has been validated through centrifuge experiments. Since the present study adopts the same clay type and similar stress paths during embankment loading and tunnelling-induced unloading, the parameter set is fully consistent with benchmark studies and ensures realistic reproduction of clay stiffness degradation, stress dependency, and volumetric behaviour. The formulation adopted in this study was based on the hypoplastic clay model originally proposed by Mašín [39] and subsequently enhanced through the intergranular strain concept to improve its predictive capability under complex stress paths. The model incorporates key material constants c₁, c₂, and the scalar factor a which together define the shape and curvature of the stress–strain envelope. To accurately describe the stress-dependent stiffness evolution, two scalar functions were introduced: the barotropy factor (fₛ), which accounts for the influence of mean effective stress, and the pyknotropy factor (f_d), which represents the effect of density or the overconsolidation ratio in clayey soils. A linear isotropic normal compression line was included to capture density variation with stress history, while parameters R, β_r, χ, m_R, and m_T from the intergranular strain theory [40] were embedded into the hypoplastic framework to govern small-strain stiffness and cyclic degradation. Detailed theoretical background and parameter definitions can be found in the studies by Niemunis and Herle [40] and Mašín and Herle [41]. For the present analysis, kaolin clay was selected as the representative soft subgrade material due to its well-documented physical and mechanical characteristics. This material has been extensively investigated through microstructural studies [38], hydraulic and seepage analyses [42], and compressive and shear testing [43]. Its established consistency and reproducibility have made kaolin a benchmark soil in experimental and numerical investigations of soil–pile interaction [44,45]. The hypoplastic parameters used in this study were adopted from Hong et al. [38]. To assess the influence of these parameters on tunnelling-induced responses, a parametric sensitivity study was carried out focusing on three key parameters: m_R, which controls the initial shear modulus upon strain-path reversal; β_r which governs the rate of stiffness degradation with strain and χ, which controls stiffness degradation under large strains. For each parameter, the baseline value (taken from Hong et al. [38] and used throughout this study) was independently varied by ±20%, while all other parameters were kept constant. For computational efficiency, the sensitivity analysis was conducted for the most critical configuration (Case S under unconsolidated conditions), which produces the largest deformation response, and the maximum surface settlement above the tunnel was monitored as the primary indicator. The parametric runs followed a one-factor-at-a-time approach. The results indicate that increasing m_R, which represents higher small-strain stiffness, leads to a reduction in surface settlement. In contrast, increasing β_r, corresponding to a faster rate of stiffness degradation with strain, results in increased settlement. Variations in χ exhibit a similar directional effect to β_r, although the magnitude of change is slightly smaller for an equivalent percentage variation. Overall, while the absolute settlement values show moderate sensitivity to these small-strain and degradation parameters, the qualitative trends and the fundamental response mechanisms discussed in Section 3 remain unchanged. This confirms the reliability of the parameter set proposed by Hong et al. [38] for representing kaolin clay behaviour in the present analysis. Further verification was performed by comparing the model response with field observations reported by Cai et al. [46]. confirming its reliability for simulating soft clay behaviour under excavation-induced stress redistribution. All model parameters are provided in

Table 1. Model parameters of kaolin clay adopted in the parametric study.

Description	Parameter
Effective angle of shearing resistance at critical state: ϕ’	22°
Parameter controlling the slope of the isotropic normal compression line in the ln(1 + e) versus lnp plane, λ*	0.11
Parameter controlling the slope of the isotropic normal compression line in the ln(1 + e) versus lnp plane, κ*	0.026
Parameter controlling the position of the isotropic normal compression line in the ln(1 + e)–ln p plane, N	1.36
Parameter controlling the shear stiffness at medium- to large- strain levels, r	0.65
Parameter controlling initial shear modulus upon 180° strain path reversal, mR	14
Parameter controlling initial shear modulus upon 90° strain path reversal, mT	11
Size of elastic range, R	1 × 10−5
Parameter controlling the rate of degradation of the stiffness with strain βr	0.1
Parameter controlling degradation rate of stiffness with strain χ	0.7
Initial void ratio, e	1.0
Dry density (kg/m3)	1136
Coefficient of permeability, k (m/s)	1 × 10−9

.

The embankment fill was represented as silty clay, modelled using an elasto-plastic Mohr–Coulomb formulation to capture its shear strength and deformation characteristics. The adopted parameters were mass density (ρ) = 2200 kg/m³, friction angle (f′) = 31, cohesion (c′) = 3 kPa, elastic modulus (E) = 60 MPa, and Poisson’s ratio (n) = 0.3, consistent with data reported by Yan et al. [47]. The piles and raft were assumed to behave as linearly elastic materials, characterized by a Young’s modulus of 35 GPa, Poisson’s ratio of 0.25, and a unit weight of 24 kN/m³. This assumption is justified because the structural components were designed to remain within the serviceability range of stress and strain during all stages of loading.

The adopted combination of hypoplastic modelling for soft clay, Mohr–Coulomb formulation for embankment fill, and linear elasticity for concrete components provided a robust and realistic representation of the complex soil–structure interaction mechanisms governing the performance of the pile-supported embankment during tunnel excavation.

2.4. Validation of Numerical Model Using Field Data

To further validate the model parameters, a comparison was made with field test data reported by Cai et al. [46] on a pile-supported embankment along the Wuhan–Guangzhou high-speed railway in China. The soil profile at the site consisted of a soft clay layer (4.5–10.7 m), overlying a cobbly soil layer (10.7–14.2 m), and underlain by a silty clay layer (14.2–25.1 m). The embankment was supported by piles of 0.5 m diameter, spaced 2.5 m centre to centre, with square pile caps (1.5 m × 1.5 m × 0.3 m). The total embankment height was 6.0 m. These dimensions were adopted in the numerical model to ensure consistency. Figure 4a shows the comparison of measured and FEM-computed settlement during embankment construction. It is important to note that although the embankment was designed to be 6.0 m high, the settlement data reported and compared here correspond to the first 5.0 m of construction. The settlement patterns from both the simulation and field measurements showed strong consistency, indicating that the initial settlement rate during the first 3 m of embankment construction was greater than that observed in the final 2 m. Figure 4b presents the lateral ground movement (near the pile located at the toe of the embankment) along normalized depth (Z/L_p) obtained from field measurement and the finite element analysis after the completion of embankment construction. The maximum lateral displacement from field measurements occurs within the soft soil layer at a depth of 8 m, with a value of 5.4 mm. In contrast, the computed results show the maximum lateral movement near the pile head. Despite this discrepancy near the ground surface, both the measured and computed results show good agreement at greater depths. To quantify model accuracy, statistical error index Root Mean Square Error (RMSE) was calculated for the settlement and lateral movement comparison. The calculated RMSE values for settlement and lateral movement were 2.8 mm and 0.6 mm, respectively. The RMSE implies close agreement between measured and numerical results. The computed results agree well with the measured data, particularly in capturing the magnitude and trend of settlement development. This validation indicates that the hypoplastic clay model with intergranular strain can reliably reproduce field behaviour of pile-supported embankment.

3. Results and Discussion of Computed Results

3.1. Settlement Mechanism in Pile-Supported Embankment During the Progression of Tunnelling

3.1.1. Induced Settlements at the Crest and Sloping Sides of the Embankment

Since the aim of this study is to compare the performance of the pile-supported embankment under adjacent tunnelling activities, this section explores the impact of tunnel excavation on the settlement of both the crest and sloping sides of the embankment both immediately after the construction of the pile embankment and after its long-term settlement. The study compares the differential settlement observed under long-term consolidation and unconsolidated conditions. Following the construction of the embankment, its self-weight leads to settlements at both the crest and the sloping sides. When tunnel excavation is carried out adjacent to the pile-supported embankment, this can exacerbate differential settlements, particularly between the embankment crest and its sloping sides. Figure 5 presents the normalized settlement profiles of the embankment crest and sloping sides for three distinct cases (S, T, and B) under long-term consolidation and unconsolidated conditions. The settlement values are taken from the mid-section of the embankment in the transverse direction, with both induced settlement and distance in the transverse direction normalized by the pile diameter and tunnel diameter, respectively. The results indicate that tunnel excavation induces differential settlements in all three cases, with the crest and sloping sides nearest the tunnel experiencing greater settlement relative to those farther away. A comparative analysis reveals that the differential settlement under unconsolidated conditions is significantly higher than that under consolidated conditions, particularly in Case T.

This behaviour can be attributed to the combined effects of pile settlement beneath the embankment and ground movement caused by stress release during tunnelling. In the unconsolidated condition, the embankment and subgrade have not fully stabilized, and the soil skeleton is still undergoing primary consolidation, making the system more susceptible to additional displacements from tunnelling. Conversely, after long-term consolidation, the stiffness of the subgrade increases due to enhanced effective stress and reduced excess pore water pressure. As a result, once tunnelling commences, the more rigid subgrade in the consolidated condition is able to better resist deformation, leading to smaller settlements compared to the unconsolidated condition. The piles closest to the tunnel still experience greater ground movement and shear strain, but the stabilized soil system mitigates the magnitude of settlement. This highlights the importance of considering consolidation effects when evaluating tunnelling impacts on pile-supported embankment. The maximum magnitudes of differential settlement of 0.49% (29.4 mm), 0.20% (12.0 mm), and 0.45% (27.0 mm) were computed under consolidated conditions in the S, T, and B cases, respectively. These values highlight that, although the settlements are presented as normalized percentages for comparative purposes, the absolute magnitudes remain well above the 2 mm deformation tolerance stipulated for high-speed railway track smoothness. This comparison highlights the necessity of careful assessment of tunnelling-induced deformation when such excavations are conducted in close proximity to HSR embankments.

3.1.2. Development Subgrade Surface Settlement

The pile-supported embankment was constructed over soft ground, and surface settlement was induced due to adjacent tunnel excavation. Figure 6 illustrates the development of surface settlement in the embankment after the completion of tunnelling under three scenarios (S, T, and B) for both long-term consolidation and unconsolidated conditions.

A comparison of the three cases shows that, in the S and T scenarios, the maximum surface settlement occurs directly above the tunnel axis. When focusing only on the settlement at the vertical axis of the tunnel, the shallow tunnel in the S case induces the largest settlement, whereas the deep tunnel in the B case results in the smallest settlement. However, when examining the complete surface settlement profile beneath the embankment including the crest and both side slopes an opposite trend is observed: the B case exhibits the largest overall settlement, while the S case shows the smallest. This contrast arises from the influence of the pile group beneath the embankment. Because the settlement beneath a pile-supported system is governed not only by ground loss around the tunnel but also by pile–soil interaction, the settlement mechanism differs from that observed at the ground surface above the tunnel. In the B case, the deeper tunnel intersects with longer pile shafts and results in larger ground movement near the lower portion of the piles, leading to increased pile settlement that is transferred to the embankment. In contrast, in the S case, the tunnel is shallower and interacts with only the pile heads, where the stiffness is higher, resulting in a smaller settlement response beneath the embankment despite a larger settlement directly above the tunnel.

When comparing long-term consolidation and unconsolidation conditions, it is observed that the surface settlements in the S and T cases are smaller under long-term consolidation. This reduction is attributed to the increase in subgrade stiffness after consolidation, as excess pore pressure dissipates and effective stress increases. The stiffer soil is able to resist the additional deformation caused by tunnelling, thereby reducing the transmitted settlement to the embankment. However, in the B case, the settlements remain nearly identical for both consolidated and unconsolidated conditions. This is because tunnelling at a deeper horizon predominantly affects the lower portions of the piles, where the settlement response is governed more by pile–soil interaction than by changes in subgrade stiffness at the ground surface. As a result, long-term consolidation has little influence on mitigating surface settlement in the B case. These findings highlight that surface settlements in pile-supported embankment are governed by two competing mechanisms (i) ground loss around the tunnel (driving vertical-axis settlement) and (ii) pile–soil interaction (governing settlement transmission to the embankment). The relative dominance of these mechanisms depends on tunnel depth, pile length, and the stiffness of the subgrade.

3.1.3. Induced Pile Settlement

To investigate pile settlement induced by tunnel construction, a transverse cross-sectional slice of the embankment was selected along the central axis, where piles were labelled P1 to P14 from left to right. Figure 7a,b compare the normalized pile settlements after tunnelling under long-term consolidation and unconsolidated conditions for cases S, T, and B. The settlement values were normalized by the pile diameter (d_p). As discussed in previous sections, under both consolidated and unconsolidated conditions in all three cases (S, T, and B), pile P1 which is closest to the tunnel exhibited the maximum settlement, and settlement progressively decreased as the distance from the tunnel increased. Among the three scenarios, pile settlements were smallest in Case S and increased progressively through Case T, reaching the largest values in Case B at corresponding positions. This behaviour is governed by the relative depth of tunnelling with respect to pile length. In Case S, the shallow tunnel intersects only the upper portion of the pile shaft.

Tunnelling-induced stress relief and ground movement reduce shaft resistance, causing limited pile settlement until sufficient end-bearing resistance is mobilized. In contrast, in Cases T and B, deeper tunnelling subjects a much larger portion of the pile to ground movement and shear strain. In Cases T and B, where the tunnel is located adjacent to and beneath the pile toe, respectively, tunnel-induced stress release affects the entire pile length, substantially reducing both shaft resistance and end-bearing capacity. To reach equilibrium, the piles must undergo larger downward displacement to mobilize additional resistance, resulting in greater settlement. This mechanism explains why pile settlements increase with tunnel depth and aligns with the findings of Lu et al. (2020) [15]. Because the embankment is pile-supported, its surface settlement pattern closely corresponds to the deformation characteristics of the underlying piles.

A comparison between consolidated and unconsolidated conditions shows that pile settlements are smaller under long-term consolidation. After consolidation, the dissipation of excess pore water pressure increases effective stress in the subgrade, which enhances soil stiffness and load-transfer capacity along both the shaft and the pile toe. The stiffened subgrade better resists tunnel-induced ground deformation, thereby limiting additional pile settlement. In contrast, under unconsolidated conditions, the soil skeleton remains soft and compressible, making the piles more susceptible to downward movement. This explains, particularly in Cases S and T, that the settlement differences between piles are more pronounced under unconsolidated conditions, which subsequently results in a larger embankment settlement compared to the consolidated scenario.

3.1.4. Induced Lateral Movement of Piles

Tunnel excavation inevitably induces stress relief in the surrounding soil, resulting in ground movement toward the tunnel. Consequently, tunnels cause not only vertical settlement of the ground and piles, but also lateral pile displacement. To examine this behaviour, three representative piles were selected: P1 (the pile closest to the tunnel), P7 (located near the mid-width of the embankment), and P14 (the farthest pile). Figure 8a–c present the lateral displacement profiles of these piles under both long-term consolidated and unconsolidated conditions, where displacement toward the tunnel is considered positive. For both consolidation conditions, P1 consistently moves laterally toward the tunnel after excavation, whereas the influence on P7 and P14 is negligible due to their larger offset distance and reduced stress disturbance. In Cases T and B, where the tunnel is positioned adjacent to and beneath the pile toe, respectively, the maximum lateral displacement of P1 develops at the pile toe. This response is governed by ground movement toward the tunnel induced by stress release in the deep soil layer. Noticeable lateral movement also occurs at the pile head due to the overburden pressure of the embankment, which promotes pile bending under reduced confinement. In Case S, where the tunnel intersects the pile shaft, the maximum lateral displacement coincides with the tunnel axis, reflecting stress relaxation occurring at that specific depth.

A comparison between consolidated and unconsolidated scenarios shows that although the deformation pattern remains similar, the magnitude of lateral displacement is consistently larger under long-term consolidation. This is attributed to the increase in soil stiffness after consolidation, which reduces compressibility but enhances shear transfer to the pile. As a result, once tunnelling commences, the stiffer ground mobilizes greater horizontal stress redistribution, increasing lateral pile bending compared to the unconsolidated case.

3.2. Load Transfer Mechanism in Pile-Supported Embankment During the Progression of Tunnelling

3.2.1. Variation in Pile–Soil Stress Ratio

To examine the evolution of load transfer between the piles and the surrounding soil during tunnel advancement, three representative piles, P1, P7, and P14, were selected, as described in Section 3.1.4. Figure 9a–c present the variation in the pile–soil stress ratio for these piles under S, T, and B working conditions, respectively, plotted against the normalized tunnel advancement distance (in terms of tunnel diameter, D) from the monitored embankment section. Under both long-term consolidated and unconsolidated conditions, all three piles exhibited a broadly similar trend across the S, T, and B cases, indicating a systematic response of the pile-supported embankment to tunnel-induced stress disturbance. After embankment construction, due to soil arching, P1 initially carried a greater proportion of the vertical load relative to the surrounding soil. In the S case, where the tunnel was excavated adjacent to the pile shaft, the pile–soil stress ratio of P1 increased progressively as the tunnel approached. This behaviour is attributed to the relative movement between the pile and soil: the surrounding soil experienced greater settlement than the pile, while the pile toe remained supported by deeper soil layers that were not directly influenced by tunnel-induced stress release. Consequently, a higher portion of the embankment load was transferred to the pile, resulting in an increasing pile–soil stress ratio. This also indicates that the embankment surface settlement was smallest for Case S among the three configurations. In contrast, under the T and B cases where the tunnel was excavated near and below the pile toe the pile–soil stress ratio of P1 decreased as the tunnel face approached (i.e., at y/D = 0.0). The stress carried by the pile reduced because the stress release at deeper soil layers compromised toe resistance and allowed greater pile settlement. Once the tunnel passed P1, a slight rebound in the pile-soil stress ratio was observed, reflecting partial recovery of the load transfer mechanism due to changes in pile–soil contact conditions and post-excavation reconsolidation of the soil. Overall, the results demonstrate that tunnelling near or beneath the pile toe leads to more pronounced reductions in pile capacity compared to tunnelling at the pile shaft. Figure 9b shows the response of P7, located at the mid-width of the embankment. Prior to tunnel excavation, P7 carried a larger load than P1 due to its position beneath the embankment, where arching intensity is the highest. For all S, T, and B configurations, the pile-soil stress ratio of P7 increased continuously with tunnel advancement. This trend indicates that settlements near the tunnel face were greater than those in the central region, causing more load to be redirected to piles farther from the tunnel. Accordingly, the embankment surface above P7 experienced significantly smaller deformation compared to the area immediately above the tunnel. Pile P14, the farthest from the tunnel, exhibited a similar increasing trend in pile–soil stress ratio, but with a smaller magnitude than P7, as can be seen in Figure 9c. Its response also confirms the progressive redistribution of load away from the tunnel–pile interaction zone toward piles located in stiffer and less disturbed soil. The increase in pile–soil stress ratio for piles P7 and P14 was more pronounced under consolidated conditions, where the stiffer soil mass allowed more efficient transfer of load to the piles as settlement gradients developed.

3.2.2. Changes in Load Distribution in Axial Direction Along Piles

Figure 10a–c present the axial load distribution of piles P1, P7, and P14 after tunnel completion for Cases S, T, and B, respectively. Due to the arching effect of the embankment, the central pile (P7) carried a greater proportion of the vertical load, while P1 and P14 located beneath the embankment slope supported comparatively smaller loads.

For pile P1 in Case S, where the tunnel was excavated near the pile shaft, the axial load initially increased along the upper portion of the pile (up to Z/L_p = 0.6) and subsequently decreased at the lower portion and toe of the pile. This behaviour implies a transition from negative skin friction in the upper portion caused by soil settlement exceeding pile settlement to positive shaft resistance at greater depth. Because the pile toe remained supported by undisturbed soil, toe resistance was increased, allowing the pile to mobilize additional shaft resistance to maintain load equilibrium. Consequently, the head load of the pile increased significantly after tunnelling. In Case T, where the tunnel was located adjacent to the pile toe, a similar trend was observed; however, the neutral plane shifted downward to approximately Z/L_p = 0.8. The shifting of the neutral plane indicates that negative shaft resistance extended over a larger portion of the pile length. Owing to reduction in confining stresses around the pile toe, end-bearing resistance decreased. Therefore, the pile had to settle to mobilize shaft resistance for equilibrium. This resulted in a substantial redistribution of axial load compared to Case S. On the other hand, in Case B, where the tunnel is constructed directly beneath the pile toe, the axial load profile remained similar to the pre-tunnelling condition, but the magnitude increased noticeably along the entire pile length. The ground movement due to tunnelling-induced stress release led to a more mobilization of shaft resistance and end-bearing resistance.

For P7 and P14, located at greater distances from the tunnel-induced disturbance zone, negligible changes in axial load were observed across all three cases. The soil surrounding these piles experienced limited stress relief, meaning both shaft resistance and toe support remained largely unchanged. These observations are consistent with the pile–soil stress ratio trends discussed previously. As the tunnel approaches P1, the pile–soil stress ratio increases due to differential settlement and downward migration of the neutral plane. In deeper tunnel scenarios (Cases T and B), the reduction in toe confinement enhances negative skin friction and forces a larger portion of the embankment load to be transferred into the pile head. This explains deeper tunnels cause greater axial load redistribution despite smaller changes in settlement at the embankment surface.

When comparing consolidated and unconsolidated conditions, axial load redistribution is consistently more pronounced after long-term consolidation. Higher subgrade stiffness enhances shear transfer into the pile, resulting in greater mobilization of negative skin friction and deeper neutral plane positions. Under unconsolidated conditions, the softer ground accommodates a larger proportion of the tunnel-induced deformation, reducing drag load and limiting changes in axial load.

From a design perspective, these findings highlight that deep tunnelling beneath pile-supported embankment can significantly alter load transfer mechanisms, particularly after long-term consolidation. To ensure serviceability, measures such as increasing pile length, enhancing toe confinement, or applying toe protection (e.g., base grouting or enlarged pile bases) should be considered in projects involving deep tunnelling adjacent to pile foundations.

3.2.3. Bending Moment Along Pile Lengths

After completion of the pile-supported embankment, the piles located beneath the embankment slopes develop bending moments due to lateral soil displacement generated by the self-weight of the embankment. Subsequent tunnel excavation acts as a stress-relief process that induces ground movement toward the tunnel, further increasing lateral pile deformation and bending demand. Figure 11a–c presents the bending moment distribution along piles P1, P7, and P14 for Cases S, T, and B under both long-term consolidated and unconsolidated conditions. Positive bending moments indicate curvature toward the tunnel, whereas negative values represent curvature away from the tunnel. Under long-term consolidated conditions, pile P1 exhibits a maximum positive bending moment of approximately 77 kNm at Z/L_p = 0.21 due to lateral displacement behind the slope. At the pile head, the rotational restraint provided by the pile cap induces a counteracting negative moment of magnitude 38 kNm. In Case S, where the tunnel excavated adjacent to the pile shaft, the bending demand increases significantly after tunnelling. The pre-tunnelling positive moment decreases progressively, transitions to negative curvature at Z/L_p = 0.35, and reaches a peak negative bending moment of 142 kNm at Z/L_p = 0.56.

This behaviour corresponds to stress release around the tunnel face, which induces lateral soil movement toward the tunnel and induces reverse bending in the pile. With increasing depth beyond the tunnel axis, the bending moment gradually recovers and changes sign, eventually producing a secondary peak of positive curvature (approximately 126 kNm) at Z/L_p = 0.8.

A comparison with unconsolidated conditions shows similar deformation patterns; however, the magnitudes are consistently larger in the unconsolidated case. Due to lower soil stiffness, stress relaxation propagates farther into the surrounding ground, generating larger horizontal displacements and greater pile curvature. This also aligns with larger surface settlements observed under unconsolidated conditions. In Case T, where the tunnel is located near the pile toe, the maximum bending moment shifts toward the toe region. As the lower portion of the pile experiences lateral soil movement toward the tunnel, concave deformation develops on the tunnel-facing side, and the bending moment reaches its peak near the excavation plane. Case B exhibits a similar trend, but with slightly smaller peaks due to increased stand-off distance and reduced stress disturbance at the shaft level. For piles P7 and P14, the influence of tunnelling is minimal. Their bending moment profiles show only minor deviations from the pre-tunnelling state because the tunnel-induced stress release does not significantly affect soil stiffness or lateral movement at their locations. This confirms that pile bending response attenuates rapidly with increasing offset from the tunnel disturbance zone. From a design perspective, the results demonstrate that tunnel depth and position relative to the pile govern the distribution and magnitude of bending moments. When tunnels pass close to the pile shaft or toe, additional bending reinforcement or increased pile flexural stiffness may be required to limit structural demand. In addition, long-term consolidation stiffens the subgrade, reducing bending deformation but increasing drag forces; therefore, embankment–pile–tunnel interaction analysis should consider both time-dependent soil behaviour and tunnel alignment to ensure serviceability performance.

4. Limitation of the Study

While the developed three-dimensional numerical model provides valuable insights into the interaction between tunnelling and pile-supported embankment, certain simplifications should be acknowledged. The tunnel advancement was represented using an equivalent volume loss method, which does not explicitly capture the influence of face pressure, grouting behaviour, or segmental lining installation. The soil profile was modelled as uniform soft clay governed by a calibrated hypoplastic model, whereas natural deposits often exhibit spatial variability and anisotropic stiffness that may lead to different deformation characteristics. The model also does not incorporate installation-induced effects on piles, such as disturbance or excess pore pressure generation during construction. In addition, the analysis focused solely on static loading, and potential interactions with dynamic loads from high-speed train operation were not included. These simplifications do not affect the comparative trends revealed in this study but should be considered when applying the results to specific field conditions.

5. Engineering-Oriented Implications for Real Project Applications

The findings of this study provide several engineering insights relevant to the planning and execution of tunnelling works adjacent to pile-supported embankment in soft clay. First, shallow tunnels (Case S) induce the largest settlement directly above the tunnel but impose comparatively smaller global embankment deformation due to limited disturbance along the pile length. Conversely, deeper tunnels intersecting the lower pile shaft or toe (Cases T and B) generate greater pile settlement and significant changes in load-transfer mechanisms, which are critical for design. Therefore, tunnel alignment relative to pile length should be carefully evaluated during preliminary planning to minimize impacts on both vertical and lateral pile responses. Second, the results highlight the importance of ground consolidation prior to tunnelling. Long-term consolidation significantly reduces both surface and pile settlements and mitigates changes in stress redistribution. For embankments constructed on soft ground, tunnelling should ideally be excavated after substantial consolidation has occurred or be accompanied by acceleration measures (e.g., preloading, prefabricated vertical drains). Third, deep tunnelling beneath the pile toe leads to reductions in toe confinement and increases in drag load, especially after consolidation. In such cases, piles may require design adaptations such as increased embedment length, enlarged bases, or toe stiffening through base grouting. The integration of settlement, axial load, and bending moment responses presented in this study offers engineers a more comprehensive understanding of the deformation mechanisms, enabling better-informed decisions on monitoring, mitigation, and structural protection strategies.

6. Conclusions

This study investigates the effects of tunnel excavation on pile-supported embankment in stiff clay under both long-term consolidated and unconsolidated conditions. The cases are defined based on the relative position of the tunnel to the piles: S, T, and B correspond to scenarios where the tunnel is excavated near the pile shaft, adjacent to the pile toe, and beneath the pile toe, respectively. Based on the computational results, the following conclusions can be drawn:

• Tunnel excavation induced notable differential settlements between the crest and slopes of the embankment, with maximum values of 0.49%, 0.20%, and 0.45% for the S, T, and B cases, respectively, under long-term consolidated conditions. The settlements were substantially higher under unconsolidated conditions due to lower subgrade stiffness.
• The maximum subgrade settlement occurred above the tunnel axis, being largest in the S case (shallow tunnel) and smallest in the B case (deep tunnel). However, when considering the entire embankment, overall settlement was greatest in case B because of enhanced ground movement around the longer pile shafts.
• Pile P1, located closest to the tunnel, experienced the largest settlement in all scenarios, with settlements increasing progressively from case S to case B. Long-term consolidation reduced pile settlement magnitudes by enhancing effective stress and subgrade stiffness, resulting in smaller differential movements.
• The pile–soil stress ratio of P1 increased in Case S as the tunnel approached but decreased sharply in Cases T and B due to loss of toe confinement. In contrast, piles farther from the tunnel (e.g., P7, P14) exhibited a stress ratio increase of up to 20–25% under consolidated conditions, indicating load redistribution away from the tunnel zone.
• Deeper tunnelling substantially altered the axial load distribution along the piles, particularly in Cases T and B, where the neutral plane shifted downward from Z/Lp = 0.6 to 0.8, indicating extended negative skin friction zones. The axial load along P1 increased by nearly 120% after tunnel completion due to enhanced drag load effects.
• The maximum bending moment in pile P1 reached approximately 142 kNm at Z/Lp = 0.56 in Case S under unconsolidated conditions, compared with 77 kNm before tunnelling. Consolidation reduced bending deformation but increased load transfer and drag, emphasizing the importance of considering tunnel depth and time-dependent soil stiffness in design.
• The influence of tunnelling reduced rapidly with increasing offset from the excavation zone; piles beyond approximately 2D from the tunnel axis experienced negligible settlement or bending change. These findings suggest that deeper tunnels (Case B) predominantly affect the lower pile portions, while shallow tunnels (Case S) control surface deformation and crest settlement behaviour.