Introduction

Numerous studies have shown that catastrophic landslides triggered by earthquakes account for a significant proportion of earthquake-induced disasters (e.g., Parise and Jibson 2000; Jibson et al. 2007; Hsieh and Lee 2011). Earthquake-induced landslides of soft clayey slopes have also been widely reported, such as the Government Hill and Turnagain Heights landslides triggered by the 1964 Alaska earthquake (Seed 1968; Updike et al. 1988), the Sainte-Thecle and Saint-Adelphe landslides induced by the 1988 Saguenay earthquake in Canada (Lefebvre et al. 1992). As a preventive measure in stabilizing slopes, anti-slide piles have been used successfully in many slopes consisting of different soil or rock types, which can transfer the sliding thrust induced by landslide to rock or more stable soil layers at greater depths (e.g., Chen and Martin 2002; Zeng and Liang 2002; Won et al. 2005; Stamatopoulos et al. 2009 Zhang et al. 2017a, 2024; Nguyen et al. 2018; Olgun et al. 2019; Mao et al. 2019; Wang et al. 2024; Yenginar and Olgun 2023).

Compared to rock or cohesionless soil slopes (e.g., Lin and Wang 2006; Zhao et al. 2020; Yan et al. 2020; Zhang et al. 2020, 2021a; Su et al. 2021; Xu et al. 2022; Liu et al. 2022; Xie et al. 2022; Zhou et al. 2023; Zheng et al. 2024; Peng et al. 2024), the seismic model tests performed on soft cohesive soil slopes with or without reinforcement are relatively scarce; the relevant experimental studies using centrifuge set-up are briefly introduced herein. The seismic responses of five clayey embankment slopes were experimentally investigated by Kutter et al. (1989), in which the influences of earthquake intensity on the acceleration amplification factor and slope failure pattern were discussed. A series of seismic model tests on soil-nailing-reinforced steep cutting slope of unsaturated silty clay were performed by Zhang et al. (2001), observing that the seismic deformation behavior and failure mechanism of the soil-nailed slope were influenced significantly by the nail spacing, nail length and inclination of slope; similar findings were observed by Wang et al. (2010) who also experimentally explored the seismic responses of nail-reinforced and unreinforced cohesive soil slopes. The seismic behavior of cohesive soil slope reinforced by single pile was experimentally examined by Wang and Zhang (2014), in which the displacement and acceleration of the slope, as well as the displacement and bending moment of the stabilizing pile, were analyzed. Park and Kutter (2015) experimentally explore the static and seismic failure mechanisms of moderately to highly sensitive clay slopes, and found that the slip surfaces of the sensitive clay slopes under seismic loading tended to reach deeper depths and yielded a more diffused shear band than that under static load. Tarazona et al. (2020) experimentally explored the seismic behavior of kaolin clay canyons with three different sloping angles (15°, 30° and 45°, respectively), and the influences of terrain condition, input motion frequency and amplitude were examined. Soriano Camelo et al. (2021, 2022) experimentally investigated the seismic response of gently inclined slopes (3° and 6° inclination angles) of soft clay, analyzing the acceleration response and lateral displacement of the slopes subjected to a suite of sinusoidal waves and scaled realistic motions with different amplitudes and intensities. To date, some experiments have been performed to investigate the seismic behavior of clayey slope with and without reinforcement; however, these studies seldom involve the use of piles with different configurations. Hence, to better understand the reinforcement effect of pile on clayey slope subjected to seismic shaking, further experimental studies are still needed.

On the other hand, numerical approaches have been widely employed to investigate the seismic response of clayey slopes. Biscontin and Pestana (2006) performed a series of dynamic finite element analyses to investigate the seismic response of submarine clayey slope, finding that the ground motions with lower frequency content, longer duration tended to cause more significant excess pore pressure and larger permanent deformation of the slope; besides, the earthquake-induced deformations of very gentle clayey slopes (e.g. inclination angle of 2.5°) could be also considerable. Zhou et al. (2017) proposed a disturbance-dependent soil constitutive model for describing nonlinear behavior of sensitive clays subjected to dynamic loads, which was incorporated in the QUIVER code to perform one-dimensional seismic parametric analyses on generic clay slopes with varying sloping angles. Using the two-dimensional finite difference software FLAC, Karray et al. (2018) conducted both pseudo-static and dynamic analyses on homogeneous clayey slopes under seismic shakings, and safety factors and failure surfaces of the slopes were obtained from these analyses, which were also compared with the relevant 1-g model test results. By employing cyclic elastoplastic constitutive model to depict the dynamic behavior of saturated soft clay and updated Lagrange technology, Mi and Wang (2021) proposed a numerical simulation procedure to analyze the dynamic sliding process of submarine soft clay slope under seismic load using ABAQUS. In addition, some other simplified methods have also been employed to examine the seismic behavior of slope, such as limit equilibrium method (LEM) (e.g., Rodríguez-Ochoa et al. 2015a; Nian et al. 2019) in which the earthquake-induced force was generally accounted for using the pseudo-static method, and Newmark sliding block method to evaluate the accumulated displacement of a slope during an earthquake (Grelle et al. 2011; Yang et al. 2021). As can be seen, although there are some numerical and simplified approaches employed to investigate the seismic stability of clayey slope, the effect of reinforcement measure such as using anti-slide piles is not accounted for.

As can be summarized from the above descriptions, most of the previous experimental and numerical analyses focused on the seismic responses of rock or cohesionless soil slopes; the relevant studies on the response of piled clayey slope, especially considering pile group of varying configurations, are significantly insufficient. Considering that the dynamic behavior of soil and dynamic soil-structure interaction are highly dependent on the soil type, the seismic performance of seldom investigated pile-reinforced clayey slope is largely unknown. Hence, some relevant investigations are needed to well understand the behavior of pile-reinforced clayey slope under seismic shakings. In this study, a series of 1-g shaking table tests were performed to investigate the seismic performance of pile-reinforced clayey slope subjected to far-field ground motions, taking into account the variations in pile configuration and ground motion parameters. Subsequently, the rationality of three-dimensional (3D) dynamic finite element (FE) analyses were validated by the experimental results; moreover, a suite of numerical parametric analyses were conducted to for further extended investigations, from which some viable suggestions on using anti-slide piles to improve the seismic stability of inclined soft clay ground can be drawn.

Test material and methodology

Test model construction

The earthquake model tests were performed using the 1-g shaking table set-up at the Wuhan University of Technology. The clay slurry was mixed in a de-airing chamber containing Malaysia kaolin clay powder and water in a mass ratio of 1:1.2 for around 4 h. To prevent the leakage of clay slurry, a flexible and thin rubber bag was placed inside the shear box with internal dimensions of 900 mm (length) × 600 mm (width) × 400 mm (height). The clay slurry was then placed into the rubber bag, with a lightweight wooden mold to form the shape of the slope. The clay slurry was then subjected to 1-g consolidation process for about 14 days to stabilize the settlement at clay surface and pore water pressures at selected positions. The basic properties of the clay sample are listed in Table 1. In small-scale model tests, to satisfy all the similarity conditions is extremely challenging and often unfeasible. In this study, with reference to previous 1-g shaking table tests (Meymand 1998; Liu et al. 2017; Wu et al. 2022; Haeri et al. 2023; Jia et al. 2023; Pan et al. 2023), the key similarity ratios of geometric parameters, initial stress conditions and dynamic characteristics are designed according to the Buckingham π theorem, as shown in Table 2. Notwithstanding some unavoidable inconsistencies between the prototype and model materials, the present 1-g shaking table tests can provide useful findings revealing the influencing trends of some important factors, which can also be employed to validate a reliable numerical analysis procedure for extended investigations.

As Fig. 1 shows, three types of pile configuration were employed, namely 1 × 2 single-row piles, 2 × 2 double-row piles, and 2 × 2 pile-cap system, with a pile spacing of 64 mm (4 times the pile diameter). The model piles were gradually inserted into the fully consolidated soft clay bed. The model piles were made of thin-walled aluminum alloy tubes with a length of 320 mm (16 m prototype), a wall thickness of 3 mm (0.15 m prototype), and an outer diameter of 16 mm (0.8 m prototype), the basic properties of pile are shown in Table 3. The pile cap was made of a rectangular aluminum block with dimensions of 128 mm × 128 mm × 20 mm, which was rigidly connected to the model piles by welding, as shown in Fig. 2.

Fig. 1
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Layout of 1-g shaking table model test (number in bracket denotes prototype size). (a) three-dimensional view of pile reinforcement model; (b) elevational view of the model

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Table 1 Basic parameters of the soft clay
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Fig. 2
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The model of 2 × 2 pile-cap system in shaking table test. (a) photo of pile cap; (b) schematic diagram

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Table 2 Similarity ratio relationships adopted in present 1-g shaking table test
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Table 3 Basic properties of pile
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Instrumentation and input ground motions

As shown in Fig. 2, several full-bridge strain gauges (strain gauges S1-S7,with sensitivity coefficient of ± 1%) were attached to the anti-slide piles to measure the respective bending moment responses during the seismic shakings. A total of 7 horizontal accelerometers, namely A1 ~ A7, were installed at different locations to measure the acceleration response of the test model. Displacements at the locations of accelerometers were obtained by performing the double integration computations of acceleration versus time. Besides, to monitor the pore water pressure changes during the consolidation stage and the seismic shakings, two pore water pressure transducers (PPT) were installed within the clay sample.

In the model tests, a series of sinusoidal waves with frequencies of 1.0 Hz, 3.5 Hz and 7 Hz and peak values of 0.05 g and 0.1 g were employed as the input ground motions, as shown in Fig. 3. It is noted that peak accelerations of 0.05 g and 0.1 g respectively correspond to the seismic intensity levels 6 and 7 specified in the Chinese code for seismic design of buildings (NSPRC 2010); model scale frequencies ranging from 1 to 7 Hz correspond to prototype frequencies ranging approximately from 0.15 to 1 Hz, which fall within the dominant frequency range of typical far-field ground motions. Unless otherwise stated, the test results presented in the next section are in model scale.

Fig. 3
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Input ground motions in shaking table model test (frequencies are 1 Hz, 3.5 Hz and 7 Hz, PBA denotes peak base acceleration)

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Experimental results

Slope failure phenomenon

For peak base acceleration (PBA) equal to 0.05 g, all the slopes with and without pile reinforcement are generally stable throughout the seismic shakings, regardless of the shaking frequencies. For PBA equal to 0.1 g, as demonstrated in Fig. 4(a) and 4(b), after the seismic shakings obvious slope slide occurs for the unreinforced and 1 × 2 single-row-pile reinforced slope models. For the slope models reinforced by 2 × 2 double-row piles and pile-cap system, such slope slides are not observed, as Fig. 4(c) and 4(d) show; however, the piles generally become tilted due to downslope kinematic force imposed by the clays. Hence, for pile-reinforced clayey slope, the seismic stability of which is highly dependent on the pile reinforcement configuration.

Fig. 4
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Photos of test samples after seismic shaking (PBA = 0.1 g, frequency = 1 Hz). (a) unreinforced slope; (b) slope reinforced with 1×2 single-row piles; (c) slope reinforced with 2×2 double-row piles; (d) slope reinforced with 2×2 pile-cap system

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Acceleration response

Typical measured acceleration time histories at different locations of slope are presented in Fig. 5, in which the accelerations of the slope toe, slope middle and slope top are measured by the accelerometers A4, A5 and A6 respectively. As can be seen, for all of the test models, the accelerations experienced at different locations of slope are clearly larger than that excited at the slope model base, indicating the evident amplification effect of soft clay on seismic ground motions (Tinawi et al. 1993; Mayoral et al. 2009; Banerjee et al. 2014; Garala and Madabhushi 2019; Soriano Camelo et al. 2022). Moreover, the acceleration responses of the unreinforced slope are relatively more significant.

The acceleration amplification factor in this study is defined as the ratio of the peak acceleration experienced at a selected location to that excited at the model base. Figure 6 gives the detailed comparison curves of acceleration amplification factor for slope models without and with different pile reinforcement configurations, in which h/H represents the relative height; it is defined as the ratio of the height of a certain measuring point to the total height of the slope, measured from the slope toe. As can be seen, for all the scenarios considered, the acceleration amplification factor along the slope surface gradually increases with the increasing elevation. In comparison, the amplification effect of slope surface is more significant for shaking frequency equal to 7 Hz than that involving the other two frequencies; the acceleration responses of slopes reinforced by anti-slide piles are suppressed in different degrees compared with the unreinforced slope. For shaking frequency equal to 7 Hz and PBA = 0.05 g, the acceleration amplification factor at slope top for the unreinforced slope is 2.83, while that associated with the pile reinforcement configurations of 1 × 2 single-row piles, 2 × 2 double-row piles, and 2 × 2 pile-cap system are respectively 10%, 15% and 20% smaller.

Fig. 5
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Acceleration time histories at different positions of slopes reinforced by different anti slide piles (PBA = 0.1 g, frequency = 3.5 Hz). (a) unreinforced slope; (b) slope reinforced with 1 × 2 single-row piles; (c) slope reinforced with 2 × 2 double-row piles; (d) slope reinforced with 2 × 2 pile-cap system

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Fig. 6
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Plots of acceleration amplification factor for slopes reinforced by different anti slide piles (h/H denotes relative height). (a) frequency=1 Hz, PBA=0.05 g; (b) frequency=3.5 Hz, PBA=0.05 g; (c) frequency=7 Hz, PBA=0.05 g; (d) frequency=1 Hz, PBA=0.1 g; (e) frequency=3.5 Hz, PBA=0.1 g; (f) frequency=7 Hz, PBA=0.1 g

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Maximum relative displacement

Figure 7 presents the maximum relative displacements at different locations of the slope surface. The maximum relative displacement is defined as the maximum value of relative displacement between a monitoring point and model base during a specific seismic shaking, along the horizontal shaking direction. As can be seen from Fig. 7, for the same ground motion intensity, the maximum relative displacements of the slopes reinforced by anti-sliding piles are significantly smaller compared to that of unreinforced slope, which tend to be evidently influenced by the shaking frequency and intensity. For PBA equal to 0.1 g and shaking frequency equal to 1 Hz, the maximum relative displacement experienced at the top of unreinforced slope is the about 3 cm, while that associated with 2 × 2 pile-cap system is 42% smaller.

Fig. 7
figure 7

Maximum relative displacements of slope after seismic shakings. (a) frequency=1 Hz, PBA=0.05 g; (b) frequency=3.5 Hz, PBA=0.05 g; (c) frequency=7 Hz, PBA=0.05 g; (d) frequency=1 Hz, PBA=0.1 g; (e) frequency=3.5 Hz, PBA=0.1 g; (f) frequency=7 Hz, PBA=0.1 g

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Typical excess pore water pressure response

Two pore pressure transducers, namely PPT-1 and PPT-2 located respectively at depths of 140 mm (7 m prototype depth) and 280 mm (14 m prototype depth) below the clay surface in shaking table model tests, respectively, were employed to monitor the excess pore water pressure response in the clay during seismic shakings.

Figures 8 and 9 respectively present the typical time histories of excess pore water pressure for both unreinforced clay slope and clay slope reinforced with pile-cap system subjected to different seismic shakings. As can be seen, although there are some local discrepancies, the variation trends of excess pore water pressure are generally comparable between unreinforced and reinforced clay slopes; under the same seismic loadings, the excess pore water pressures generated in the reinforced clay slope are slightly smaller, indicating that the excess pore water pressure response in clay slope is not significantly influenced by pile reinforcement. Moreover, the variations in excess pore water pressure tend to be more evident for a deeper depth or a stronger shaking intensity, which become relatively less significant with the shaking frequency changing from 1 Hz to 7 Hz; this decreasing trend is consistent with that shown in Fig. 7 of maximum relative displacement of slope involving different shaking frequencies. However, in all the test cases, due to the low permeability of saturated kaolin clay and its insensitivity of volumetric change to horizontal seismic shakings, the accumulated excess pore water pressures are rather low compared to the respective hydrostatic pressures. Hence, the effects of excess pore water pressure accumulation and dissipation are relatively insignificant for the kaolin clay bed subjected to small to medium seismic shakings.

Fig. 8
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Typical PPT readings during different ground motions for the unreinforced clay slope. (a) frequency=1 Hz, PBA=0.05 g; (b) frequency=3.5 Hz, PBA=0.05 g; (c) frequency=7 Hz, PBA=0.05 g; (d) frequency=1 Hz, PBA=0.1 g; (e) frequency=3.5 Hz, PBA=0.1 g; (f) frequency=7 Hz, PBA=0.1 g

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Fig. 9
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Typical PPT readings during different ground motions for the clay slope reinforced with 2 × 2 pile-cap system. (a) frequency=1 Hz, PBA=0.05 g; (b) frequency=3.5 Hz, PBA=0.05 g; (c) frequency=7 Hz, PBA=0.05 g; (d) frequency=1 Hz, PBA=0.1 g; (e) frequency=3.5 Hz, PBA=0.1 g; (f) frequency=7 Hz, PBA=0.1 g

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Typical pile bending moment response

The focus of this study is mainly placed on the seismic response of slope. In this section, the seismic bending moment response of the pile-cap system is presented. Figure 10 presents the maximum pile bending moment profiles for both the frontal and rear piles, where the frontal and rear piles are differentiated as nearer to the slope top and toe, respectively. The maxium pile bending moment profile refers to the instantaneous pile bending moment profile at the instant when the uppermost strain gauge attains its maximum value. As can be seen, the seismic pile bending moment can be considerably influenced by both shaking frequency and intensity. For the shaking frequency equal to 1 Hz and PBA increasing from 0.05 g to 0.1 g, the corresponding maximum bending moments of the frontal pile are 0.53 N·m and 1.08 N·m, while that for the rear pile are approxiametly 31% and 27% smaller, respectively. Hence, for the clayey slope reinforced by the 2 × 2 pile-cap system, the frontal piles bear significantly more downward thrust load during the seismic shakings.

In addition, regardless of the frontal or rear piles, the pile bending moments are the largest in the case of 1 Hz compared to other two frequencies. This is consistent with the findings shown in Fig. 7, which demonstrates that the relative displacements between the slope surface and model base are also the largest for the shaking frequency of 1 Hz. Hence, the seismic bending moment response of pile is more dependent on the downward thrust of the clayey slope rather than the motion intensity experienced at the slope surface.

Fig. 10
figure 10

Maximum pile bending moment profiles for the 2 × 2 pile-cap system. (a) frequency=1 Hz, PBA=0.05 g; (b) frequency=3.5 Hz, PBA=0.05 g; (c) frequency=7 Hz, PBA=0.05 g; (d) frequency=1 Hz, PBA=0.1 g; (e) frequency=3.5 Hz, PBA=0.1 g; (f) frequency=7 Hz, PBA=0.1 g

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Finite element modelling procedure and validation

Geometric modelling information

To further understand the seismic response of pile-reinforced clayey slope, it is necessary to extend the work via reliable numerical simulations. Three-dimensional (3D) simulations are performed using the finite element (FE) software ABAQUS. Considering the geometric symmetry of the test models along the shaking direction, haft 3D FE models can be established for improving computational efficiency, as illustrated in Fig. 11. The soil finite element model adopts solid elements with a mesh type of C3D8R (8-node linear brick element with reduced integration); the pile foundation adopts a hybrid modeling method, using which the pile bending moments can be conveniently extracted from the embedded beam elements of element type B31 (three-dimensional linear beam element) (Banerjee et al. 2014; Zhang et al. 2017b, c).

The seismic waves are applied at the bottom of the model, and the normal directions of two vertical boundaries parallel to the shaking direction are fixed. To minimize the boundary reflection effect, the distance between the lateral boundaries (left and right sides) of the slope models are appropriately extended. Besides, as also adopted in many previous studies (Banerjee et al. 2014; Tsinidis et al. 2016) to replicate a free-field ground motion condition, the two lateral boundaries of each extended part, which are perpendicular to the shaking direction, are constrained to ensure that nodes at the same elevations have the consistent motions.

Fig. 11
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Semi-symmetrical finite element models of the slopes. (a) unreinforced slope; (b) slope reinforced with 1×2 single-row piles; (c) slope reinforced with 2×2 double-row piles; (d) slope reinforced with 2×2 pile-cap system

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Constitutive modelling of soft clay and pile

As demonstrated in Fig. 12, the dynamic behavior of the soft clay is depicted using a hyperbolic-hysteretic constitutive model that is initially proposed by Banerjee et al. (2014), which has been successfully employed to numerically analyze the seismic interaction between clay and various structures (Zhang et al. 2021b; Liu and Zhang 2019); the basic parameters used in this model are listed in Table 1. More detailed information on this model can be found in the study of Banerjee et al. (2014). The ideal linear elastic model is selected for pile and cap involved in this section. In addition, hard-contact and penalty friction algorithms are used to model the behavior of the soil-pile interface, and frictional angle along the interface is taken as 0.8 times that of the clay (e.g., Lin et al. 2023). Rayleigh damping coefficients are applied to the individual piles and pile-cap system, corresponding to a damping ratio of 5% with respect to the first two fundamental frequencies of them.

Fig. 12
figure 12

Schematic diagram of the hyperbolic-hysteretic constitutive soil model

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Validation analysis

Figure 13 exemplifies the comparison between the computed and measured acceleration amplification factors of slope reinforced by the pile-cap-system. As can be seen, the computed and measured acceleration amplification factors at different elevations are generally comparable, and the overall trends of them are quite similar, with the averaged difference generally less than 10%.

Figure 14 plots the corresponding computed and measured maximum pile bending moment profiles involving different shaking frequencies. As can be seen, although there are some discrepancies between each other, the overall distribution trends of computed and measured bending moments are favorably consistent, with the averaged differences of about 4%, 5% and 8% for shaking frequencies of 1 Hz, 3.5 Hz and 7 Hz, respectively.

The above favorable comparisons between numerical simulation and 1-g shaking table test results confirm that the present 3D FE method can be reliably employed to analyze the pile-reinforced soft clayey slope subjected to ground motions. In the subsequent section, this numerical simulation procedure will be adopted for a suite of numerical parametric analyses for extended investigations.

Fig. 13
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Comparison of the measured and computed acceleration amplification factors (PBA = 0.1 g). (a) 1 Hz; (b) 3.5 Hz; (c) 7 Hz

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Fig. 14
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Comparison of the measured and computed maximum bending moment profiles of rear pile for different shaking frequencies (PBA = 0.1 g). (a) 1 Hz; (b) 3.5 Hz; (c) 7 Hz

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Numerical parametric analysis

From the model test results, the reinforcement effect of pile-cap system on the clay slope is more significant, and this type of pile configuration is employed in the present parametric analysis. As Fig. 15 shows, using the experimental model of 2 × 2 pile-cap system as a basis, a series of 3D FE models are established according to the prototype dimensions. The piles in the 2 × 2 pile-cap system are modelled by an equivalent elastic-plastic model (Zhang et al. 2021b), while the rest of the modelling details is the same as that introduced in the preceding section. The basic properties of pile used in parametric analysis are shown in Table 4, and the pile cap share the same elastic properties of pile.

Table 4 Basic properties of pile used in parametric analysis
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Figure 16 (a)-(c) show the three types of ground motions employed in this section, and the response spectra corresponding to a peak acceleration of 0.06 g are plotted in Fig. 16 (d). The dominant frequencies of these three types of ground motions are all about 1 Hz, representing the typical ground motions that can be experienced at a far field. Detailed information on these ground motions can be found in the study of Zhang and Liu (2018). Furthermore, to investigate the influence of ground motion intensity, each of these base motions was scaled into four ground motions with peak values of 0.03 g, 0.06 g, 0.12 g and 0.24 g.

Fig. 15
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Schematic layout of anti-slide pile reinforced slope model with varying length and installation location of pile

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Fig. 16
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Input ground motions adopted in the parametric analysis. (a) Sumatra type; (b) Landers type; (c) Chi-Chi type; (d) response spectra (PBA=0.06 g, 5% damping)

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Influence of ground motion intensity

Figure 17 demonstrates the yield zone contours of both unreinforced slope and reinforced slope with 2 × 2 pile-cap system at the instant when the pile attains its maximum bending moment, where a shear strain of 0.137% is adopted as the threshold value above which evident plastic deformation of clay is initiated (Banerjee 2010; Banerjee et al. 2014). It should be noted that, for shear strains larger than 0.137%, the shear stress of clay can continually increase against the shear strain; the failure state of clay is reached until the clay experiences its peak shear stress (i.e. shear strength), which normally corresponds to a shear strain larger than 2% for Malaysian kaolin clay. As can be seen, with the increasing ground motion intensity, the yield zone of slope tends to gradually expand for both the unreinforced and reinforced slopes, while the yield zone of slope reinforced by the 2 × 2 pile-cap system is significantly alleviated. For example, for PBA equal to 0.06 g, evident slope failure can be observed from Fig. 17(b) for the unreinforced slope with a maximum shear strain of about 2.36%, while the yield zone is mainly localized around the slope top for the reinforced slope with a maximum shear strain of about 0.45%, indicating that the 2 × 2 pile-cap system has a satisfactory performance in stabilizing the clayey slope subjected to seismic shakings. Figure 18 also presents the typical plastic strain contours of pile-cap system subjected to different-intensity ground motions. As can be seen, for PBA equal to 0.03–0.06 g, plastic deformation of pile is negligible; for PBA equal to 0.12 g, evident plastic deformations can be observed at both the top and lower part of the pile. This suggests that pile-cap system installed in clay slope can be damaged under strong ground motions, and the vulnerable locations appear to be the pile top and lower part of pile.

In the subsequent parts of this study, the influences of several important factors on the acceleration amplification factor and maximum relative displacement of slope are discussed.

Fig. 17
figure 17

Yield zone contours of clayey slope at the instant when the frontal pile attains its maximum bending moment, under different-PBA Sumatra-type ground motions (ε denotes shear strain). (a) PBA=0.03 g (unreinforced slope); (b) PBA=0.06 g (unreinforced slope); (c) PBA=0.12 g (unreinforced slope); (d) PBA=0.03 g (reinforced slope); (e) PBA=0.06 g (reinforced slope); (f) PBA=0.12 g (reinforced slope)

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Fig. 18
figure 18

Equivalent plastic strain (PEEQ) contours of pile-cap system after seismic shakings (EpIp = 6.03 × 105 kNm2, Sumatra waves). (a) PBA=0.03 g; (b) PBA=0.06 g; (c) PBA=0.12 g

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Figure 19 plots the acceleration amplification factors and maximum relative displacement distributions of the slope surface (denoted as ag and Sd in this study, respectively), subjected to Sumatra type ground motions with different PBAs. As consistent with the model test results, both the acceleration amplification factor and maximum relative displacement generally tend to increase nonlinearly with the increasing elevation of the monitoring point. Acceleration amplification factors tend to have decreasing trends with the increasing PBA, regardless of the location of monitoring point, indicating that clay damping ratio gradually becomes more significant with the increasing ground motion intensity.

As Fig. 20 shows, for the three types of ground motions, the amplification factor and maximum relative displacement at slope top tend to gradually decrease and increase with the increasing ground motion intensity, respectively, which can be well represented by best-fit lines with maximum prediction errors less than 20%.

Fig. 19
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Plots of acceleration amplification factor and maximum relative displacement of slope surface (Sumatra-type ground motions). (a) acceleration amplification factor; (b) maximum relative displacement

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Fig. 20
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Influence of PBA on the acceleration amplification factor and maximum relative displacement experienced at slope top. (a) acceleration amplification factor; (b) maximum relative displacement

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Influence of pile flexural rigidity

Five different pile flexural rigidities ranging from 1.01 × 105 to 1.41 × 106 kN·m2 are considered in this study to explore the influence of pile flexural rigidity (denoted as EpIp in this study) on the seismic response of the pile-reinforced clayey slope. As Fig. 21 shows, the larger is the pile flexural rigidity, the smaller are both the acceleration amplification factor and maximum relative displacement of the slope; however, the variation in pile flexural rigidity has no influence on the increasing trends of both amplification factor and maximum relative displacement against the relative height.

Figure 22 illustrates that both the acceleration amplification factor and maximum relative displacement of the slope top against pile flexural rigidity exhibit a slightly decreasing trend. This is reasonable because the pile with a larger flexural rigidity generally has a better performance in resisting the lateral deformation of slope. Besides, for the three types of ground motions, the acceleration amplification factors and maximum relative displacement at the slope top against pile flexural rigidity can be well represented by respective best-fit lines with the maximum prediction errors less than 15%.

Fig. 21
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Plots of acceleration amplification factor and maximum relative displacement of slope surface for different pile flexural rigidities (Sumatra-type ground motion, PBA = 0.12 g). (a) acceleration amplification factor; (b) maximum relative displacement

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Fig. 22
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Influence of pile flexural rigidity on the acceleration amplification factor and maximum relative displacement experienced at slope top (PBA = 0.12 g). (a) acceleration amplification factor; (b) maximum relative displacement

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Influence of pile length

The influence of pile length is considered by varying the embedment depth of pile while the average vertical distance between pile top and slope surface is kept as 2 m. Six different pile embedment depths, viz. Le/h0 = 1, 1.2, 1.6, 2, 2.4 and 2.8, are considered in this subsection, in which Le and h0 denote average embedment depth of pile and vertical distance between the pile-surrounded slope surface and slope toe, respectively. As Fig. 23 shows, compared with the unreinforced slope, the acceleration amplification factor and maximum relative displacement of slope surface with the 2 × 2 pile-cap system are evidently smaller, which tend to gradually decrease with the increasing pile length. In comparison with the unreinforced slope, for Le/h0 = 1, 1.2, 1.6, 2, 2.4 and 2.8, the averaged acceleration amplification factors of slope surface are respectively 8%, 11%, 17%, 23%, 28% and 32% smaller, and the averaged maximum relative displacements of slope surface are respectively 9%, 13%,17%, 22%, 26% and 30% smaller. In addition, as Fig. 24 shows, with the increasing pile length, the successive differences in reductions of both acceleration amplification factor and maximum relative displacement of slope appear to be initially increasing and then decreasing. As indicated in Fig. 24, a selection of pile length with average embedment depth of 2 h0 is more suitable, which can well balance the reinforcement effect on slope and consumption of pile material.

As Fig. 25 shows, for the three types of ground motions, the amplification factor and maximum relative displacement at slope top tend to gradually decrease with the increasing pile length, and their decreasing trends can be well represented by the respective best-fit lines with the maximum prediction errors less than 15%.

Fig. 23
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Plots of acceleration amplification factor and maximum relative displacement of slope surface for different pile lengths (Sumatra-type ground motion, PBA = 0.12 g). (a) acceleration amplification factor; (b) maximum relative displacement

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Fig. 24
figure 24

Successive differences in reductions of acceleration amplification factor and maximum relative displacement of slope surface for different pile lengths (Sumatra-type ground motion, PBA = 0.12 g)

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Fig. 25
figure 25

Influence of pile length on the acceleration amplification factor and maximum relative displacement experienced at slope top (PBA = 0.12 g). (a) acceleration amplification factor; (b) maximum relative displacement

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Influence of pile installation location

To explore the influence of pile installation location, denoted as xp/X in this study, on the seismic response of the pile-reinforced clay slope, five different xp/X values ranging from 0.3 to 0.7 are considered. As demonstrated in Fig. 15, xp represents the horizontal distance between the center of pile cap and slope toe, and X represents the horizontal distance between slope toe and top.

The plots of acceleration amplification factor and maximum relative displacement of slope surface are exemplified in Fig. 26. As can be seen, compared with the unreinforced slope, the acceleration amplification factors and maximum relative displacements at different monitoring points can be influenced by the pile installation location to varying degrees. Compared to the acceleration amplification factor, the distribution of maximum relative displacement along the slope surface is more sensitive to the variation of pile installation location. In comparison with the unreinforced slope, for xp/X = 0.3, 0.4, 0.45, 0.6 and 0.7, the averaged acceleration amplification factors of slope surface are respectively 19%, 30%, 32%, 16% and 12% smaller, and the averaged maximum relative displacements of slope surface are respectively 22%, 32%, 23%, 21% and 19% smaller, indicating that the installation location corresponding to xp/X = 0.4 is the most efficient for improving the seismic stability of clayey slope.

Fig. 26
figure 26

Plots of acceleration amplification factor and maximum relative displacement of slope surface for different pile locations (Sumatra-type ground motions, PBA = 0.12 g, xp/X represents the pile installation location). (a) acceleration amplification factor; (b) maximum relative displacement

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Conclusions

A series of shaking table model tests were carried out to investigate the seismic responses of clayey slopes reinforced by anti-sliding piles with different configurations. Moreover, a suite of extended 3D FE analyses were performed to further investigate the effects of some important factors on the seismic performance of clayey slope reinforced by pile-cap system, these factors mainly being ground motion intensity, pile flexural rigidity, pile length and pile installation location. The following main conclusions can be drawn:

(1) The 1-g shaking table tests suggest that the soft clay tends to significantly amplify the seismic motions, especially at the location of slope top. Compared with the unreinforced slope, the use of anti-slide piles can evidently reduce the acceleration amplification factor and maximum relative displacement responses of the slope surface due to seismic shakings. Among the different pile configurations considered, the reinforcement effect of the pile-cap system is the most significant, which can substantially reduce the seismic response of the slope and hence improve its seismic stability. For PBA not exceeding 0.1 g, the excess pore water pressure of clay during seismic shakings increases with the increasing seismic intensity or clay depth, but tends to decrease with the increasing shaking frequency; nevertheless, the accumulation or dissipation of excess pore water pressure is quite insignificant compared to the respective hydrostatic pressures.

(2) The acceleration amplification factors and maximum relative displacements for all monitoring points at the slope surface generally increase nonlinearly with the increasing elevation, regardless of the configurations of anti-slide piles. The maximum relative displacements of monitoring points increase significantly with the increasing ground motion intensity while the corresponding acceleration amplification factors tend to have the decreasing trends. For the slope reinforced by the 2 × 2 pile-cap system, the frontal piles (nearer to the slope top) tend to experience considerably larger downward thrust force than the rear piles, suggesting a shadowing effect existing within the pile group.

(3) The extended numerical parametric studies suggest that, in addition to the pile group configuration, the flexural rigidity, length and installation location of pile also have substantial effects on the seismic response of clayey slope reinforced by pile-cap system. With the increasing pile flexural rigidity, both the acceleration amplification factor and maximum relative displacement of slope surface tend to have decreasing trends; for pile flexural rigidity larger than around 6.03×105 kN·m2, the decreasing trends become negligible. Moreover, a pile length with an average embedment depth of 2 h0 and installation location corresponding to xp/X = 0.4 are found to be favorably efficient for improving the seismic performance of clayey slope reinforced by the pile-cap system.

Nevertheless, only relatively stiff piles and moderate far-field ground motions are considered in the present 1-g shaking table tests, and the variations in geometric configuration of clayey slope are not accounted for in both the experimental and numerical investigations. Some more factors can be considered in a future study to systematically investigate the elastic-plastic behavior, stability and failure evolution pattern of the piled clayey slope subjected to strong ground motions.