Mechanisms of pile-soil stress and deformation in excavations under the coupled effects of excavation disturbance and extreme rainfall infiltration

Abstract

Under the increasingly frequent extreme rainfall events, deep excavations are subjected to complex coupled effects of excavation-induced disturbance and rainfall infiltration, making it essential to clarify the deformation mechanisms of surrounding soils and retaining structures. In this study, a typical metro foundation pit in Zhengzhou was selected as the research object. By integrating field monitoring data with ABAQUS finite-element simulations, the deformation response and mechanical evolution of the pile–soil system under the combined influence of staged excavation and extreme rainfall infiltration were systematically investigated. The results indicate that rainfall infiltration leads to significant pore-water pressure accumulation, while the downward migration of the wetting front continuously reduces the effective stress and shear strength of the mid-to-deep soils. This process weakens the passive resistance at the pile toe and induces the downward movement of the primary deformation zone. The bending moment distribution of the retaining piles evolves from a “coexisting positive–negative moment” pattern to a “positive-moment dominant” mode, and the horizontal displacement at the pile toe changes from negative to positive, revealing a coupled mechanism involving deep-soil softening and arching loss. A mechanical chain of rainfall infiltration, pore-pressure evolution, stress redistribution, and pile–soil deformation is established to explain how extreme rainfall amplifies excavation-induced effects through dual pathways of mid-to-deep soil softening and accelerated seepage. Based on these findings, a prevention framework of source reduction, structural enhancement, and process control is proposed to improve the safety and resilience of deep excavations under extreme climatic conditions.

Introduction

In recent years, with the rapid development of urban infrastructure, deep excavations have become increasingly common in densely populated urban areas¹. As a crucial component of underground construction, deep foundation pits involve large-scale soil disturbance and complex environmental loading during excavation, which can easily induce ground surface settlement, retaining-structure instability, and other safety problems^2,3. Staged excavation, as a widely adopted construction technique, gradually removes the overburden and alters the in-situ stress state of the surrounding soils, leading to stress release and redistribution that may cause lateral pile displacement, soil settlement, and heaving⁴. Meanwhile, under extreme climatic conditions, heavy rainfall events^5,6 can result in a sharp rise in pore-water pressure and a rapid reduction in matric suction, thereby weakening the shear strength of unsaturated soils. The downward migration of the wetting front from the surface to deeper strata further aggravates soil softening and deformation risks^7,8. Therefore, understanding the pile–soil deformation mechanisms of deep excavations under extreme rainfall is of great theoretical and practical significance.

Previous studies have investigated the deformation mechanisms and structural responses of foundation pits under excavation-induced disturbance. Liu et al.⁹ revealed the relationship between excavation depth, basal heave, and surface settlement. Li et al.¹⁰ analyzed the evolution of the elasto-plastic failure mechanism of retaining structures during staged excavation in soft soils. Lan et al.¹¹ explained the deformation and load transfer mechanism of double-row piles from the perspective of soil arching effects. Song et al.¹² demonstrated that the influence of excavation on surface deformation decays spatially based on long-term monitoring data. Hu et al.¹³, using a Biot-type seepage–stress coupling model, found that the maximum vertical displacement during excavation mainly occurs near the diaphragm wall. Mao et al.¹⁴ emphasized that excavation-induced unloading leads to additional deformation and internal force increases in adjacent tunnels. These studies have laid the theoretical and practical foundation for understanding the influence of excavation disturbance. However, most research focuses on the “excavation-only” condition, and few studies have addressed the coupled evolution of pile–soil systems under rainfall infiltration. In particular, quantitative analyses of pile toe resistance degradation, migration of the controlling deformation zone, and redistribution of bending moments in retaining piles remain insufficient.

On the other hand, recent studies have gradually paid attention to the influence of rainfall infiltration on excavation deformation and stability. It has been shown that rainfall-induced seepage interacts with excavation-induced unloading, resulting in complex coupling between soil stress states and retaining-structure responses^{15,16,17,18,19,20}. Wang et al.²¹ identified the stratified characteristics of moisture profiles under different rainfall patterns. Zhang et al.²² pointed out that the combined effects of rainfall and excavation amplify structural deformation but did not systematically explore the spatiotemporal evolution of the wetting front and its engineering implications. Kim et al.²³ highlighted that surface settlement during rainfall is highly sensitive to groundwater table variations. Wang et al.²⁴ reported that rainfall infiltration causes a rapid rise in surface pore pressure and an overall decrease in the surrounding soil pore pressure but did not elucidate the underlying pile–soil interaction mechanism. Wang et al.²⁵ observed enhanced additional deformation of both retaining structures and ground surfaces under rainstorms but confined their analysis to the deformation phenomena. Although these studies have confirmed the significance of rainfall infiltration in excavation responses, most of them remain at the macroscopic level, focusing on pore pressure variation and global deformation. The nonlinear coupling mechanism governing the mechanical evolution of the pile–soil system under combined rainfall infiltration and excavation disturbance has not been comprehensively investigated. In particular, the redistribution of bending moments in retaining piles, the transformation of the pile toe passive zone from a constrained to a softened state, and the downward migration of the controlling deformation zone with the wetting-front advancement have not yet been fully revealed.

In view of the above research gaps, this study focuses on a typical deep excavation project during the “7·20” extreme rainfall event in Zhengzhou. By integrating field monitoring data with numerical simulations, the paper systematically investigates the stress and deformation mechanisms of the pile–soil system under the coupled effects of staged excavation and extreme rainfall infiltration. The main contributions of this work are as follows. First, the progressive downward migration of the controlling deformation zone under the combined influence of excavation disturbance and rainfall infiltration is revealed and quantitatively correlated with the advancement of the wetting front. Second, the key mechanism of pile toe horizontal displacement reversal—from negative to positive—is identified and explained, clarifying the intrinsic relationship between the loss of passive resistance in deep soils and the accumulation of excess pore-water pressure. Third, a redistribution pattern of bending moments in the retaining piles is proposed, evolving from “coexisting positive–negative moments” to “positive-moment dominance,” thereby elucidating the amplification process of internal forces in the structure under extreme rainfall. Finally, a deformation–instability framework for the pile–soil system under coupled excavation and rainfall conditions is established, providing a theoretical reference and engineering guidance for the design and disaster prevention of deep excavations in regions prone to extreme climatic events.

Methods

Study area and meteorological data

Putian West Station is located at the intersection of Shangdu Road and Boxue Road in Jinshui District, Zhengzhou City, Henan Province, China, and is aligned along Boxue Road in the east–west direction. The station is an underground two-level island-type station constructed by the cut-and-cover method, designed for parallel interchange with the under-construction Line 3 of the Zhengzhou Metro. The main structure of the station is approximately 304 m in length, with a standard section width of 21 m and a platform width of 12 m. The excavation depth of the standard section is about 16.93 m. The main structure consists of a two-span rectangular frame with a full external waterproofing system. Together with the retaining structure, it forms a composite supporting system. The station is situated in the alluvial–proluvial plain of the Yellow River, and the subsurface stratigraphy, revealed by site investigation, consists—from top to bottom—of miscellaneous fill, silty clay, silty sand, and silty clay layers, as illustrated in Fig. 1.

Fig. 1

Geological cross-section of the project site.

The study area lies in the southern part of the North China Plain, within the lower reaches of the Yellow River, and spans the Yellow and Huai River basins. The region is characterized by a warm temperate continental monsoon climate, with precipitation decreasing from south to north²⁶. The highest recorded annual rainfall occurred in 2021, reaching 1571 mm, with an extraordinary rainstorm event on July 19, 2021. Between 16:00 and 17:00 on July 20, 2021, the hourly rainfall intensity reached 201.9 mm/h, far exceeding the “extraordinary rainfall” threshold defined in the national standard GB/T 28,592–2012. The cumulative precipitation between July 17 and July 22 totaled 798.8 mm²⁷, surpassing the local mean annual rainfall of 640.8 mm.

Foundation pit structure and monitoring layout

The excavation began on June 28, 2021, adopting a staged and zoned cut-and-cover approach. As shown in Fig. 2, the entire foundation pit was divided into three excavation zones: Zone A (excavation depth = 5 m), Zone B (13 m), and Zone C (17 m). Nine inclinometers were installed along one side of the pit (Fig. 3), each with a measurement accuracy of 0.02 mm/500 m. On the opposite side, surface settlement points were arranged at 5 m intervals from the pit edge, where a precision level instrument was used to monitor ground settlements outside the pit. The monitoring layout is summarized in Table 1.

Fig. 2

Layout of monitoring points.

Fig. 3

Inclinometer instrumentation. (a) On-site inclinometer casing, (b) Inclinometer probe.

Table 1 Zoning of foundation pit monitoring points.

To maintain pit stability, dewatering was conducted within the excavation using a large-diameter well-point system that lowered the groundwater table to approximately 1 m below the pit bottom. Observation wells were installed around the pit to dynamically monitor the groundwater variations inside and outside the excavation, allowing timely countermeasures to prevent instability or abnormal deformation in case of anomalies.

Ground surface settlement monitoring results are presented in Table 2. Before rainfall, the settlement values at all monitoring points were relatively small, ranging from − 0.3 cm to − 1.8 cm, with the maximum settlement occurring 5 m from the pit edge. After the rainfall, settlements increased significantly, with the maximum reaching − 4.65 cm. Compared with pre-rainfall conditions, post-rainfall settlements increased by approximately two to three times, indicating that extreme rainfall markedly intensified ground deformation. All monitoring points exhibited a consistent trend: larger settlements occurred near the pit, gradually decreasing with distance.

Table 2 Monitoring data of ground surface settlement outside the foundation pit.

The average lateral pile displacements at five monitoring points in Zones A, B, and C were compared and analyzed. As shown in Fig. 4, the maximum displacement in Zone A was 0.234 cm, located at a depth of − 5 to − 10 m; in Zone B, the maximum displacement reached 0.496 cm at − 11 to − 13 m; and in Zone C, it increased to 0.616 cm at − 12 to − 15 m. All three zones exhibited a progressive downward shift of the deformation zone with the advancement of rainfall infiltration. The maximum displacement point migrated toward the pile toe as rainfall continued. Owing to its greater excavation depth, Zone C displayed the most pronounced displacement response and the highest structural safety risk.

Fig. 4

Lateral displacement monitoring of support piles.

Numerical model establishment

In this study, the finite element software ABAQUS was employed to establish a numerical model for systematically analysing the coupled effects of staged excavation and extreme rainfall infiltration. To accurately simulate the interaction between the retaining piles and the surrounding soil, a surface-to-surface contact approach was adopted to define the pile–soil interface, allowing realistic representation of the relative displacement and stress transfer between the two media. This interface configuration effectively captures the shear stress transfer and potential slip behaviour along the pile–soil contact under excavation and rainfall infiltration conditions.

Normal contact behaviour was defined as “hard contact”, which permits separation but prevents interpenetration between the pile and soil surfaces. Tangential contact was governed by a Coulomb friction model, ensuring the effective transfer of side friction and passive resistance at the pile toe. During rainfall infiltration, pore-water pressure variations were transmitted through the contact surface via coupled pore-pressure degrees of freedom, thereby maintaining hydraulic continuity across the interface.

To minimise boundary effects, the overall model dimensions were set to 100 m in length, 9 m in width, and 75 m in height. The retaining piles were modelled using three-dimensional eight-node solid elements (C3D8R) to capture bending, shear, and axial deformation behaviours comprehensively. Each pile had a diameter of 1.0 m, spacing of 1.5 m, and length of 25 m. The pile material was assumed to be linearly elastic, with an elastic modulus of 3.0 × 10¹⁰ Pa and a Poisson’s ratio of 0.2. During post-processing, the bending moment distribution along the pile depth was obtained by integrating the element stress output from ABAQUS over the pile cross-section.

The retaining structure was simulated as a series of continuously arranged solid piles with the same geometric and material parameters. The surrounding soil was modelled using the Mohr–Coulomb elastoplastic constitutive model, whose shear strength criterion is expressed as:

$$f = \Gamma - c - \sigma^{\prime} \tan \phi \leqslant 0$$

where $\Gamma$ is the shear stress, c is the cohesion, $\phi$ is the internal friction angle, and σ′ is the effective normal stress.The Mohr–Coulomb model itself is defined in the deviatoric stress space and is primarily used to describe the soil strength criterion and plastic flow behavior. It does not directly simulate the variation of pore-water pressure.

In the seepage–consolidation coupled analysis, the temporal and spatial evolution of pore-water pressure during rainfall infiltration was calculated using the Van Genuchten model. The effective stress was then obtained through the following relationship:

$$\sigma^{\prime} = \sigma - u$$

where $\sigma^{\prime}$ is the effective stress, $\sigma$ is the total stress, and u is the pore-water pressure.It can therefore be concluded that the evolution of pore-water pressure during rainfall infiltration directly modifies the Mohr–Coulomb strength function through the effective stress principle, thereby capturing the degradation of soil strength associated with changes in the seepage field.

The rainfall infiltration process was simulated using the Van Genuchten model to describe the soil–water characteristic curve and the hydraulic conductivity function, as expressed by the following equations:

$$\theta (h) = {\theta _r} + \frac{{{\theta _s} - {\theta _r}}}{{{{[1 + {{(\alpha |h|)}^n}]}^m}}},m = 1 - \frac{1}{n}$$

$$k(h) = {k_s} \cdot \frac{{{{\{ 1 - {{(\alpha |h|)}^{n - 1}}{{[1 + {{(\alpha |h|)}^n}]}^{ - m}}\} }^2}}}{{{{[1 + {{(\alpha |h|)}^n}]}^{m/2}}}}$$

where $\theta$ is the volumetric water content, $\theta_{s}$ and $\theta_{r}$ are the saturated and residual volumetric water contents, respectively, $\alpha$ and n are empirical fitting parameters, and k represents the hydraulic conductivity.

The Mohr–Coulomb model was adopted for the soil because its parameters can be readily obtained and directly correspond to conventional geotechnical investigation results. It has been widely applied in analyzing pile–soil interaction and deformation characteristics in deep excavations. However, the model cannot fully capture the complex effects of suction loss, stiffness degradation, and strain softening that occur in unsaturated soils during rainfall infiltration, and it is therefore a simplified representation compared with more advanced unsaturated soil models such as the Barcelona Basic Model (BBM) and Hypoplastic Model. Since the primary objective of this study is to reveal the overall stress and deformation mechanisms of the pile–soil system under the coupled effects of staged excavation and extreme rainfall infiltration, the Mohr–Coulomb model is considered adequate for this purpose. Future studies will incorporate field measurements and unsaturated constitutive models to further improve the accuracy of simulations under extreme climatic conditions.

The extreme rainfall process was simulated in the model by applying a time-dependent infiltration flux at the top surface. The Van Genuchten model was employed to characterize the soil–water characteristic curve (SWCC) and the permeability function of the in-situ silty clay, thereby capturing the dynamic evolution of pore-water pressure and the advancement of the wetting front during rainfall infiltration^28,29. The obtained SWCC curve is consistent with the typical behaviour of low-permeability cohesive soils, reasonably describing the transition of soil from unsaturated to saturated states under rainfall, and reflecting the rapid attenuation of matric suction and the gradual increase of permeability in shallow and intermediate layers.

The rainfall intensity was set to 20 mm/h, referring to the measured data from the “7·20” Zhengzhou extreme rainfall event and the classification of torrential rainfall in the national standard GB/T 28,592 − 2012. Three rainfall durations of 24 h, 48 h, and 72 h were simulated. Considering that actual rainstorms often exhibit stage-wise enhancement and temporal fluctuations in intensity, a constant rainfall intensity was adopted to eliminate the influence of varying rainfall patterns and to highlight the essential effects of excavation–rainfall coupling. This assumption is reasonable for mechanistic analysis but has certain limitations. Future work will incorporate field-measured rainfall curves to perform sensitivity analyses and further evaluate the pile–soil system’s response under different rainfall intensities and durations.

The physical and mechanical parameters of each soil layer and retaining component are listed in Table 3, and the finite-element mesh contains approximately 45,100 elements and 53,166 nodes, as shown in Fig. 5.

Table 3 Physical and mechanical parameters of soil layers and structural elements.

Fig. 5

Numerical model layout.

Model validation

To verify the reliability of the numerical model, a comparative analysis was conducted between the simulated results and field measurements of surface settlement outside the excavation and the lateral displacement of the retaining piles before and after extreme rainfall. Figure 6 compares the simulated and measured ground surface settlements at monitoring point 25, while Fig. 7 presents the comparison of lateral pile displacements along depth at monitoring point 19. The results indicate that the simulated displacement trends agree well with the observed data, with overall discrepancies within 5%, demonstrating that the established numerical model possesses high accuracy and strong engineering applicability. Therefore, further mechanical mechanism analyses can be reasonably carried out based on the validated model to elucidate the pile–soil response mechanisms and influencing factors under the coupled effects of staged excavation and extreme rainfall infiltration.

Fig. 6

Comparison between measured and simulated ground surface settlement outside the pit in Zone C.

Fig. 7

Comparison between measured and simulated lateral displacement of retaining piles in Zone C.

Due to monitoring limitations, complete field data for pore-water pressure and pile bending moments were not available for this project, and thus direct validation of these simulated results was not feasible. However, previous studies have shown that the Mohr–Coulomb model combined with a seepage–consolidation coupling approach can reasonably predict pore-pressure evolution and pile–soil internal force distribution under excavation–rainfall conditions, with prediction trends highly consistent with those obtained in this study^28,29. Consequently, despite certain limitations, the multi-index comparison and literature-based corroboration adopted in this research ensure the rationality and reliability of the numerical simulation results.

Results

Deformation characteristics and mechanisms of soils inside and outside the excavation

Soil deformation is a key indicator for evaluating the stability and safety of deep excavation projects. The uplift inside the pit and the settlement outside the pit intuitively reflect the stress release characteristics during the excavation process³⁰. The ground surface settlement outside the excavation is shown in Fig. 8. Influenced by staged excavation, the settlement profiles in Zones A, B, and C exhibit typical “trough-shaped” distributions, with maximum settlements generally occurring at approximately 9 m from the pit edge. This is primarily due to the constraint of the retaining structure on the vertical displacement near the pit wall, which transfers stress release and shear concentration to slightly farther regions, forming a settlement concentration zone. The settlement magnitude increases with excavation depth: the maximum settlement reaches − 0.71 cm in Zone A, − 1.26 cm in Zone B, and − 1.86 cm in Zone C, indicating that deeper excavation induces stronger disturbance and consequently more significant surface responses³¹.

Fig. 8

Ground surface settlement outside the excavation.

As extreme rainfall continues, the settlement magnitude in all three zones increases, with the settlement curves showing a downward trend in the near-field region and flattening in the far-field area. Prolonged heavy rainfall leads to continuous accumulation of pore-water pressure and a significant reduction in effective stress, which intensifies soil softening and consolidation deformation³². In Zone A, the peak settlement remains around 3 m from the pit edge, corresponding to the stress redistribution region where the constraint of the retaining structure weakens gradually. The reduction in shear strength in this area causes concentrated deformation release, and the peak settlement increases from − 1.86 cm to − 2.24 cm within 3 days of rainfall. In Zone B, the peak settlement occurs adjacent to the pit wall, where the soil disturbance is more severe, the seepage path is shorter, and the hydraulic gradient is steeper. This region is highly sensitive to infiltration and deformation accumulation, with settlement increasing from − 2.71 cm to − 3.01 cm over 3 days of rainfall. Zone C exhibits the most pronounced rainfall response, with peak settlement rising sharply from − 1.86 cm to − 4.65 cm, an increase exceeding 150%. As rainfall duration increases, the location of maximum settlement shifts closer to the retaining structure, which can be attributed to higher pore-pressure accumulation capacity in deeper strata and progressive shear softening near the pile toe³³.

The vertical deformation of the soil surface inside the excavation is illustrated in Fig. 9. At different excavation depths, the uplift within the pit shows a distinct symmetric pattern characterized by “central heave with gradual reduction toward both sides.” The retaining systems on both sides constrain the adjacent soil, limiting vertical displacement and concentrating rebound deformation in the central area of the pit bottom. The maximum uplift in Zone A is approximately 0.93 cm, concentrated within 3.5 m of the pit center. In Zone B, the maximum uplift increases to 1.33 cm, with the influence range extending to 6.5 m, while in Zone C, the uplift reaches 2.11 cm, expanding the affected zone to more than 8.5 m around the pit center. The overall deformation magnitude and influence range both increase with excavation depth, mainly because excavation releases stress at the pit bottom, leading to structural degradation of the soil and accumulation of elastic strain, which results in more pronounced heave responses³⁴.

Fig. 9

Ground surface uplift inside the excavation.

Under continuous extreme rainfall, the central uplift in all three zones shows a clear attenuation trend, while the deformation at the edges lags and changes only slightly. In Zone A, the maximum uplift decreases from 0.93 cm to 0.42 cm after 3 days of rainfall, a reduction of over 55%. In Zone B, the uplift decreases from 1.33 cm to 0.77 cm (42.1% reduction), and in Zone C, it declines from 2.11 cm to 1.01 cm (52.1% reduction). Although Zone A exhibits smaller deformation, its attenuation is the most significant due to rapid softening and structural breakdown of the shallow fill under heavy rainfall. Zone B shows a relatively stable deformation trend, reflecting the buffering and resilience of the intermediate soil layer to seepage disturbance. In contrast, Zone C displays the largest deformation amplitude, where pore-pressure transmission and structural degradation in deep soil layers exhibit clear hysteresis and cumulative effects, leading to greater deformation potential and longer duration.

Evolution of pore water pressure

According to Terzaghi’s effective stress principle, rainfall infiltration significantly increases pore-water pressure, thereby weakening soil strength and reducing overall stability³⁵. Analyzing the evolution of pore-water pressure helps to elucidate the stress redistribution mechanism within the soil profile from shallow to deep layers during rainfall. To capture this process, Zone C—where rainfall-induced deformation is most pronounced—was selected for detailed analysis. As shown in Fig. 10, before rainfall, the pore-pressure contours exhibit a typical stratified horizontal distribution, with pore pressure gradually increasing with depth. The upper zone is dominated by negative pore pressure (matric suction) due to unsaturated conditions, while the lower zone is fully saturated and governed by hydrostatic pressure. The pore-pressure field is generally symmetric inside and outside the pit, indicating that no significant seepage disturbance had yet occurred.

Fig. 10

Variation of pore water pressure under extreme rainfall.

After one day of rainfall, the negative pore pressure in the shallow layer rises rapidly as rainfall infiltration reduces matric suction. Pore pressure near the slope and around the retaining piles increases significantly, and localized ponding begins to appear near the surface boundaries. After two days of rainfall, the overall pore pressure level continues to rise, and the area with densely spaced contours expands. Seepage disturbance intensifies near the pit wall and pile sides, indicating that the subsurface flow structure is undergoing reconstruction. By the third day, pore pressure continues to accumulate and propagate downward; the maximum pressure at the pit bottom exceeds 380 kPa, and the infiltration depth extends beyond 60 m. The pore-pressure difference between both sides of the retaining structure increases further, forming new seepage pathways between the pile sides and the slope, and a localized excess pore-pressure zone develops near the pile toe.

To further investigate the pore-pressure response, a vertical section located 10 m away from the pit edge was analyzed. This section, being relatively undisturbed by the retaining structure, represents the intrinsic response of the in-situ soil. Before rainfall, the section shows the typical suction profile of unsaturated soil, with a surface pore pressure of − 208.3 kPa gradually increasing with depth, turning positive at approximately − 27 m. After one day of rainfall, the surface suction decreases, and the pore pressure increases to − 105.1 kPa. After three days, the surface pore pressure further increases to − 75.6 kPa, indicating that the shallow layer approaches saturation. The downward migration of the wetting front causes the pore pressure at − 15 m to rise from − 41.7 kPa to 44.1 kPa, marking a transition from unsaturated to saturated conditions. Meanwhile, continued water accumulation elevates pore pressure in the deep saturated zone, with the pressure at 30 m depth increasing from 26.7 kPa to 133.7 kPa, indicating localized buildup of excess pore pressure.

Although the direct percolation effect of rainfall is generally limited to shallow layers in low-permeability silty clay, the results of this study indicate a notable pore pressure increase and deformation response at mid-to-deep depths. This phenomenon is not attributed to the direct infiltration of rainfall but rather to the coupled hydraulic–mechanical response triggered by excavation unloading and surface infiltration.During extreme rainfall, the rapid loss of matric suction in the shallow zone alters the stress equilibrium and induces pore pressure redistribution throughout the soil mass. Meanwhile, the excavation-induced stress release promotes hydraulic connectivity between the shallow wetting front and the deeper stress-relaxed zone, leading to a delayed but continuous propagation of excess pore pressure toward the mid-to-deep layers. This coupled mechanism—comprising stress transfer, suction dissipation, and seepage-induced pressure migration—explains the observed deep response even in silty clay with low permeability.Similar deep hydraulic responses under combined excavation and rainfall conditions have also been reported in previous studies^36,37,38, supporting the rationality of the present model predictions.

Characteristics of seepage pathways and flow velocity distribution

The propagation path and velocity of water flow within the soil not only determine the timing of pore-pressure accumulation and dissipation but also influence the local stress redistribution, the degree of soil softening, and the hydraulic load acting on the retaining structure^39,40. To further reveal the dynamic behavior of the seepage process, flow velocity cloud maps (FLVEL) were extracted from the numerical simulations to illustrate the spatial distribution and temporal evolution of seepage under extreme rainfall conditions. As shown in Fig. 11, the flow velocity within the soil generally increases progressively with the duration of rainfall. The maximum velocity rises from approximately 5.7 × 10⁻³ m/s on the first day to 2.26 × 10⁻² m/s on the third day—an increase of more than threefold. High-velocity zones are primarily distributed in the near-surface layer, behind the retaining piles, and above the slope, forming typical preferential flow channels. The flow vectors gradually evolve from an initially vertical downward infiltration to a tilted inward flow pattern, exhibiting a distinct transition from vertical to lateral migration.

Fig. 11

Variation of rainwater seepage velocity in soil under extreme rainfall.

After one day of rainfall, seepage mainly concentrates in the shallow surface layer, where both the affected range and flow velocity remain limited. Only sparse downward infiltration bands are observed near the ground surface and at the pile tops, corresponding to the initial stage of negative pore-pressure release, with the deeper layers not yet responding significantly. After two days, the shallow layer becomes nearly saturated, and flow velocity increases markedly. A high-velocity zone develops behind the retaining piles, and the seepage pathway begins to converge toward the interior of the pit. Continuous flow paths appear within the intermediate soil layers, indicating that the infiltration process has entered an accelerated stage. By the third day, the high-velocity zones expand further, with the flow field becoming highly concentrated behind the piles, at the pit bottom, and along the slope, forming continuous seepage channels that penetrate through the soil mass.

Displacement response characteristics of retaining piles

As shown in Fig. 12, the lateral displacement profiles of the retaining piles in Zones A, B, and C under dry (no-rainfall) conditions exhibit clear regularity with increasing excavation depth.

Fig. 12

Lateral displacement of support piles.

In Zone A, the maximum displacement of the retaining pile is only + 0.021 cm, with a small overall deformation concentrated mainly in the upper-to-middle part of the pile. The displacement direction slightly deflects inward toward the pit. In Zone B, the maximum displacement reaches + 0.232 cm, concentrated between depths of − 10 m to − 18 m, indicating that the middle weak soil layer is strongly affected by unloading disturbance. In Zone C, with an excavation depth of 17 m, the maximum displacement increases markedly to + 1.053 cm, and the main deformation zone shifts downward to − 12 to − 16 m. The displacement magnitude and concentration in Zone C greatly exceed those in Zones A and B, indicating that the excavation-induced disturbance intensifies with increasing depth.

From the deformation distribution trend, the limited deformation in Zone A is primarily attributed to the fact that shallow excavation does not significantly weaken the lateral support capacity of the deeper soil, and the pile maintains good end restraint. In contrast, Zones B and C, with larger excavation depths and wider unloading ranges, experience substantial disturbance to the original stress structure of the middle and deep soils. The release of active earth pressure leads to a concentrated displacement zone, intensifying the overall inward deflection of the piles. This effect is particularly evident in Zone C, where the deformation exhibits a monotonic one-way inward shift, suggesting that the deep soil can no longer provide sufficient passive resistance under strong unloading disturbance. As the excavation depth increases, the amplitude of pile deformation enlarges significantly, and the primary deformation zone gradually migrates downward, indicating that deep-layer unloading disturbance is a key factor driving pile deformation.

Under extreme rainfall, the retaining piles in all three zones show a pronounced inward lateral displacement response. With increasing rainfall duration, the maximum pile displacement continues to grow, and the inflection point of the displacement curve shifts downward, demonstrating that rainfall progressively affects deeper parts of the pile. In the early rainfall stage, the rapid loss of matric suction in the shallow soil and the sharp rise in pore-water pressure cause a sudden increase in lateral earth pressure, which becomes the dominant source of horizontal loading on the pile. As rainfall continues, the lateral deformation of the piles shows a clear evolution pattern of “top-down expansion with the main deformation zone migrating downward”, indicating that the downward movement of the wetting front softens the deep soil and reduces its effective stress, thereby weakening the passive resistance provided by the deep strata around the pile.

In terms of displacement magnitude, the maximum pile displacement in Zone C occurs at − 12 m, reaching 1.895 cm, far exceeding that in Zone B (0.956 cm) and Zone A (0.518 cm), confirming that Zone C responds most strongly to rainfall. Regarding the depth of the dominant deformation zone, the displacement peak in Zone C is concentrated at − 9 to − 14 m, while in Zone B it lies at − 11 to − 13 m, and in Zone A at − 5 to − 10 m, reflecting that the depth of the main deformation zone is closely related to excavation depth, soil permeability, and the advancement rate of the wetting front. In terms of deformation mode, the upper portion of the pile in Zone A moves inward toward the pit, while the lower portion deflects slightly outward, representing a composite effect of increased active earth pressure in the shallow zone and reduced passive resistance in the deep zone. In contrast, the piles in Zones B and C exhibit a persistent one-directional inward displacement, especially in Zone C, where the pile toe displacement changes from negative to positive after three days of rainfall, indicating that the deep soil that originally provided passive resistance has transformed from a constrained zone into a softened zone, and the overall pile deformation pattern has fundamentally changed.

The reversal of the pile toe displacement from negative to positive under rainfall results from the combined effects of pore-pressure accumulation, effective stress reduction, and weakening of the soil arching effect. As rainfall infiltration continues, the downward-advancing wetting front significantly elevates pore pressure near the pile toe and continuously reduces the effective stress, leading to softening and a decrease in shear strength of the deep soil. Consequently, the passive resistance at the pile toe is weakened. Meanwhile, the hydraulic gradient induced by infiltration drives seepage flow toward the pit bottom, further diminishing the stress-arching effect and causing a redistribution of lateral earth pressure. Under this combined influence, the constraint capacity at the pile toe gradually diminishes, resulting in a directional reversal of horizontal displacement—from negative to positive—reflecting the transition of the passive zone from a “constrained” to a “softened” state.

All three zones experience a progressive response from shallow to deep layers under extreme rainfall disturbance. However, Zone C, with the greatest excavation depth and the longest rainfall infiltration path, exhibits the largest displacement magnitude and the deepest structural response, indicating a significantly higher risk of lateral deformation in deep excavations subjected to extreme rainfall.

Distribution of bending moments in retaining piles

Bending moment, as a key parameter reflecting the internal force state of retaining piles, is directly influenced by the combined effects of soil stress redistribution, variation in structural stiffness, and groundwater seepage disturbance^41,42,43. Therefore, it is necessary to systematically analyze the distribution characteristics and response mechanisms of bending moments under different excavation conditions and extreme rainfall events.

As shown in Fig. 13, the bending moment of the pile in Zone A exhibits a typical “S-shaped” distribution. The maximum positive moment is + 65.70 kN·m at a depth of − 7 m, while the maximum negative moment is − 120.68 kN·m at − 21 m. This indicates that the pile behavior is mainly governed by active earth pressure acting on the upper–middle portion and passive soil resistance in the lower part, with the mechanical response still concentrated in the shallow layers. In Zone B, the positive bending moment rises sharply to + 261.89 kN·m at − 10 m, nearly three times higher than that in the shallower excavation stage, suggesting that the exposed pile length increases and the unloading of active soil intensifies, expanding the structural deformation zone. Meanwhile, the negative moment at the pile toe decreases to − 47.89 kN·m, reflecting a decline in the deep-soil restraint capacity and an upward shift of the inflection point, with structural response becoming concentrated in the upper portion. In Zone C, the positive bending moment reaches a maximum of + 303.78 kN·m at − 14 m, while the negative moment further weakens to − 28.74 kN·m, indicating near-decoupling of the pile toe resistance and a downward migration of the dominant deformation zone from the mid–upper section to the mid–lower section, where the deep soil gradually loses its load-bearing control.

Fig. 13

Bending moment variation of pit support piles.

Under extreme rainfall, the piles in all three zones exhibit a significant increase in bending moment, accompanied by progressive redistribution of internal forces.

In Zone A, after 1 day of rainfall, the upper segment of the pile deflects inward toward the pit, and the maximum positive moment rises rapidly to + 155.66 kN·m, an increase of approximately 130% compared with pre-rainfall conditions. Simultaneously, the negative moment at the pile toe decreases to − 80.96 kN·m, indicating a marked reduction in toe restraint due to rainfall infiltration. After 3 days of rainfall, the positive moment further increases to + 233.44 kN·m, and the moment envelope expands noticeably, with the inflection point shifting upward. The combined effects of wetting front advancement, excess pore-pressure accumulation, and soil softening reduce effective stress, thereby altering the passive resistance distribution. The location of the maximum negative moment moves upward from − 21 m to − 20 m, suggesting gradual degradation of deep-soil constraint due to stress reconstruction.

In Zone B, after 1 day of rainfall, the positive moment at − 10 m increases sharply to + 304.56 kN·m, while the negative moment decreases drastically to − 0.29 kN·m, indicating a notable loss of passive resistance and an initial internal force redistribution. After 2 days, as the wetting front continues to descend, the positive moment expands to + 337.6 kN·m, and the zero-moment point moves upward, with a re-emerging negative moment (–21.78 kN·m) observed at − 24 m. By the third day, the maximum positive moment peaks at + 381.68 kN·m, and the negative moment at − 25 m recovers slightly to − 28.7 kN·m, resulting in a nearly symmetrical moment envelope. Compared with Zone A, Zone B exhibits a higher positive moment peak and an earlier recovery of the pile toe negative moment, mainly due to its greater excavation depth, deeper rainfall influence, and steeper hydraulic gradient.

In Zone C, the bending moment response under extreme rainfall is the most dramatic. After 1 day, the maximum positive moment increases sharply from + 303.78 kN·m to + 354.07 kN·m, while the negative moment reduces to − 22.61 kN·m, accompanied by a clear upward shift of the zero-moment point. After 2 days, the intensified seepage leads to further expansion of the upper–middle positive moment to + 438.0 kN·m, and the negative moment at the pile toe decreases to − 6.12 kN·m, indicating that pore-pressure buildup reduces the deep-soil bearing capacity and weakens toe resistance. After 3 days, the maximum positive moment reaches + 516.0 kN·m, approximately 70% higher than before rainfall. The negative moment at the pile toe vanishes and transforms into a positive value, revealing that the passive zone at the pile toe has evolved from a load-bearing region into a softened control zone.

A comparative analysis of the three zones under extreme rainfall indicates that the magnitude of the bending moment response increases significantly with both excavation depth and rainfall intensity.Zone A exhibits a relatively small bending moment with deformation concentrated in the upper and middle sections, dominated by positive bending. Zone B demonstrates a more intense response, showing a dual-peak stress redistribution pattern. Zone C shows a strong concentration of positive bending moments and complete decoupling of pile toe resistance, forming a critical risk state characterized by downward migration of the bending-moment peak zone and disappearance of the negative-moment region under extreme rainfall.

Coupled mechanism and mitigation of pile–soil deformation

Mechanism of pile–soil deformation under coupled excavation and rainfall effects

As illustrated in Fig. 14, the coupled effects of staged excavation unloading and extreme rainfall infiltration result in a complex interactive deformation and stress transfer process within the pile–soil system. Rainfall infiltrates from the ground surface downward, rapidly saturating the shallow soil layer. The sudden reduction in matric suction and the sharp increase in pore-water pressure lead to the formation of a surface softening zone. Meanwhile, as the wetting front progressively advances to deeper layers, both effective stress and shear strength in the mid-to-deep soils continuously decline.

Fig. 14

Schematic diagram of foundation pit deformation.

The passive resistance of the soil along the pit wall is weakened by rainfall infiltration, causing the retaining piles to deflect inward due to the combined effects of increased lateral earth pressure and reduced toe restraint. Numerical simulations and field monitoring data from Zones A, B, and C consistently demonstrate that the dominant deformation zone of the retaining piles gradually migrates downward with increasing excavation depth—evolving from shallow bending to pronounced deep deflection and pile toe uplift. The arching effect at the pit bottom gradually diminishes as internal stress redistributes, leading to stress concentration behind the pile and at the toe of the slope.

Simultaneously, the seepage flow pattern transitions from an initially vertical downward infiltration to an inclined inward trajectory toward the pit, promoting soil particle rearrangement and pore-water migration, thereby intensifying soil deformation. Ultimately, the coupling of excavation disturbance and extreme rainfall infiltration leads to a severe degradation of pile toe resistance and a substantial increase in structural instability risk.

The results indicate that extreme rainfall not only disturbs the shallow soil rapidly but also, through the downward migration of the wetting front, significantly weakens the bearing capacity of the mid-to-deep soils and amplifies the stress redistribution effects induced by excavation unloading. Excavation releases the in-situ stress and reduces lateral earth pressure, causing inward displacement of the pile and shifting the main bearing role to the passive zone at the pit bottom. Rainfall infiltration leads to a rapid loss of matric suction in the shallow layer and gradual accumulation of pore-water pressure in the mid-to-deep layers, continuously reducing effective stress. Meanwhile, seepage paths increasingly concentrate behind the pile and at the pit bottom, altering the hydraulic gradient field.

The coupled action of excavation and rainfall infiltration softens the mid-to-deep soils and accelerates the degradation of passive resistance at the pile toe, resulting in the reversal of pile toe displacement from negative to positive, redistribution of pile bending moments, and a marked increase in overall deformation and instability risk.

Based on these findings, a mechanical evolution framework of the pile–soil system under coupled excavation–rainfall conditions is proposed, as shown in Fig. 15. The framework elucidates the internal mechanical chain of “rainfall → pore-pressure evolution → stress redistribution → pile–soil deformation.” It further reveals that extreme rainfall amplifies excavation-induced disturbances through two primary pathways: softening of the mid-to-deep soil layers and acceleration of seepage flow paths, both of which synergistically magnify the deformation and failure potential of deep excavations.

Fig. 15

Framework of the deformation mechanism of the pile–soil system under coupled excavation–rainfall effects.

Mitigation strategies for pile–soil deformation under coupled excavation–rainfall effects

The preceding analyses indicate that the coupled influence of extreme rainfall and excavation amplifies foundation pit risks through three principal mechanisms: the rapid loss of shallow matric suction induces surface softening and potential sliding; the accumulation of pore-water pressure in the mid-to-deep layers weakens the passive bearing capacity at the pile toe, resulting in the reversal of horizontal displacement; and the redistribution of pile bending moments magnifies internal structural stresses.

Accordingly, mitigation measures should follow the overall strategy of “source reduction, structural enhancement, and process control.” This approach aims to simultaneously suppress pore-pressure buildup caused by rainfall infiltration, strengthen the load-bearing capacity of the pile–soil system, and achieve dynamic regulation through monitoring and management.

1 Source reduction — waterproofing and drainage measures:

To minimize the risk of rapid pore-pressure rise and water accumulation in the foundation pit under extreme rainfall, infiltration and drainage should be controlled at the source. In terms of waterproofing, a scientifically designed water-retaining berm should be constructed around the pit, with its layout optimized according to pit elevation, surrounding terrain, and nearby river or drainage conditions to reduce surface runoff infiltration. The outer soil can be treated with a concrete surface layer or crack grouting, while the slope surface can be reinforced with shotcrete, mesh anchoring, or soil-nailing walls to improve overall impermeability. In terms of drainage, sump wells and well-point dewatering systems should be installed inside the pit to lower the groundwater level in a timely manner. Peripheral drainage ditches and pipelines should be arranged around the pit to provide efficient discharge routes during rainfall. These measures can effectively mitigate pore-pressure accumulation and are critical in preventing failure of the passive zone at the pile toe.

2 Structural enhancement — optimization and reinforcement of retaining systems:

To counteract the degradation of passive resistance at the pile toe and the redistribution of bending moments, the structural capacity must be enhanced. From a design perspective, the pile diameter and length should be appropriately increased to improve vertical bearing and lateral resistance, while pile spacing should be optimized according to pit geometry and geological conditions to avoid localized stress concentration. For pile toe reinforcement, grouting or base enlargement can be applied in the toe region, or a water-resistant reinforcement layer can be introduced to increase shear strength and delay the reversal of pile toe displacement from negative to positive. A structure–drainage coupling approach can also be adopted by integrating permeable materials or drainage layers around the retaining structure, forming a coordinated “structure–seepage” system that alleviates bending-moment amplification effects.

3 Process control — monitoring and early-warning systems:

Given the abrupt and dynamic nature of coupled rainfall–excavation interactions, establishing a real-time monitoring and early-warning system is essential. Continuous monitoring should include key indicators such as pore-water pressure, lateral pile displacement, pile bending moment, and ground settlement. Threshold-based warning mechanisms should be implemented to trigger immediate stabilization or dewatering interventions once monitoring data exceed predefined limits. During extreme rainfall events, monitoring frequency should be increased to enhance responsiveness. Such proactive control measures transform passive response into active prevention, thereby significantly improving the resilience and safety of foundation pit systems under extreme climatic conditions.

Discussion

This study, integrating field monitoring data and numerical simulations, revealed the complex response mechanisms of the pile–soil system in deep excavations under the coupled effects of staged excavation and extreme rainfall infiltration. Compared with previous studies that focused solely on excavation disturbance or isolated rainfall conditions, this work further quantified the downward migration of the dominant deformation zone with the advance of the wetting front and elucidated the intrinsic relationship between the reversal of pile toe displacement and the accumulation of pore-water pressure. Several points merit further discussion.

Existing studies have primarily concentrated on shallow pore-pressure responses and slope stability issues. However, the present results demonstrate that the strength degradation of mid-to-deep soils driven by the downward movement of the wetting front is the key factor leading to the loss of passive resistance at the pile toe. This finding extends the depth of understanding of rainfall–excavation interactions and highlights the coupled evolution between deep pore pressure and passive reaction forces.

The simulation results indicate that the distribution of pile bending moments evolves from a pattern of “coexisting positive and negative moments” to one dominated by positive moments. The underlying mechanism lies in the loss of passive support from deep soils due to rainfall infiltration. This stress redistribution mode has rarely been reported in previous literature and provides a new theoretical perspective for understanding the failure pathways of pile–soil systems under extreme climatic conditions.

The results also show that relying solely on the passive resistance at the pile toe to counteract lateral displacement carries significant failure risks under extreme rainfall. Therefore, mitigation strategies should emphasize a coordinated system of source reduction, structural enhancement, and process control—including optimization of waterproofing and drainage systems, reinforcement of the pile toe, and integration of real-time monitoring and early-warning mechanisms—to improve the overall resilience of deep excavations.

In this study, the Mohr–Coulomb model was employed to describe soil behavior, which, while computationally efficient, cannot fully capture the suction loss and stress-dependent stiffness degradation characteristics of unsaturated soils. Future work should incorporate more advanced unsaturated constitutive models and integrate complete field measurements of pore-water pressure and pile bending moments to achieve more accurate validation of the nonlinear coupled rainfall–excavation effects. In addition, the influence of varying rainfall patterns (e.g., impulsive or intermittent rainfall) on the pile–soil interaction should be further explored in subsequent research to provide a more comprehensive understanding of the system’s long-term behavior under extreme climatic events.

Conclusions

Based on field monitoring data and finite-element numerical simulations, this study systematically investigated the stress–deformation characteristics of soil and retaining structures in deep foundation pits subjected to the coupled effects of staged excavation disturbance and extreme rainfall infiltration. The findings provide theoretical support and practical guidance for deep excavations under extreme climatic conditions. The main conclusions are as follows:

• (1) Under the coupled effects of staged excavation and extreme rainfall, deformation inside and outside the foundation pit was significantly intensified, showing a “top-to-bottom expansion” pattern. During the early stage of rainfall, the suction of the shallow soil rapidly decreased and the effective stress declined, causing deformation to propagate downward. As the wetting front advanced vertically, the deeper soils softened, resulting in pronounced inward displacement of both internal and external soils. The largest deformation occurred in Zone C, revealing that excavation depth, rainfall intensity, and seepage pathways jointly govern the deformation behavior.

• (2) Extreme rainfall infiltration led to a remarkable redistribution of pore-water pressure and seepage velocity fields, showing a progressive evolution from shallow to deep layers. The simulation results indicate that pore pressure in the shallow soil rose rapidly, while the deep seepage responded with a delay, producing a sharp hydraulic-gradient increase around the pit. Initially, high-velocity seepage was concentrated near the upper soil interface, then gradually extended downward over time. Localized zones of seepage convergence and stress concentration developed, substantially reducing the shear strength of the soil and amplifying the structural response.

• (3) The lateral deformation of retaining piles increased markedly with excavation depth, and the main deformation zone gradually migrated toward the pile toe. Deep-layer unloading disturbance was identified as a key factor driving pile deformation. Under the combined influence of excavation and rainfall, the displacement pattern evolved toward a continuous inward deflection. In deep excavations, rainfall-induced softening of the middle and lower soils reduced passive resistance, causing the pile toe displacement to reverse from negative to positive, thus indicating a tendency toward deep-seated instability.

• (4) Under the coupled effects of staged excavation and extreme rainfall, the bending-moment response of retaining piles exhibited a pronounced amplification. As excavation proceeded, the exposed length of the upper pile increased, the unloading of the active zone intensified, and the mid-depth bending moment grew rapidly while the inflection point moved downward, accompanied by significant degradation of pile-toe resistance. With rainfall infiltration, the positive bending moment expanded rapidly, the envelope broadened, and the inflection point shifted upward, whereas the negative bending moment at the pile toe weakened or even reversed to positive. This behavior indicates that the constraint capacity of the pile toe was greatly reduced due to deep-soil softening and pore-pressure accumulation.

• (5) This study established a mechanical chain of rainfall infiltration, pore-pressure evolution, stress redistribution, and pile–soil deformation, revealing the overall instability mechanism of deep foundation pits under coupled excavation–rainfall conditions. Based on these findings, a three-level mitigation framework of “source attenuation, structural reinforcement, and process control” is proposed. Optimizing the drainage system, strengthening the pile-toe zone, and implementing real-time monitoring and early-warning measures can effectively mitigate rainfall-induced hazards and enhance the safety and resilience of deep excavations under extreme weather conditions.