Keywords

9.1 Introduction

Pile foundations are usually recommended where the soil strata are weak at shallow depth and soil has a very low bearing capacity to transfer the load from the superstructure. Centrifuge modelling of pile response to lateral spreading on different pile foundation models such as end-bearing piles, floating piles, single pile and pile groups with and without pile cap in two- and three-layer liquefiable soil has been reported by Abdoun et al. [1, 2], and the results showed that the bending moment depends on the depth of liquefiable soil and shallow non-liquefiable layers. The maximum bending moment in the pile is due to the presence of a shallow non-liquefiable layer showing passive mode failure. The centrifuge data also shows increased moment due to the presence of pile cap by soil densification around the piles and the maximum bending moment occurs at the bottom of the liquefiable layer at the end of shaking in a three-layered soil for end-bearing piles. The behaviour of piles under earthquake loading in liquefiable soil is complex because of the gradual buildup of pore pressure and the corresponding decrease in strength and stiffness.

Basavanagowda et al. [3] have reported that for a pile group subjected to different earthquake loading, the largest value of bending moment at any time during shaking has been observed at the interface of the liquefied and non-liquefied layers as the soil loses its confining pressure. In the case of sloping ground where lateral spreading can be a major concern for pile foundation, downward movement of the non-liquefied crust has the potential to develop a large bending moment leading to substantial damage due to lateral spreading and also due to inertial loads transmitted to piles [4,5,6,7]. Lateral spreading is recognized to be a major concern for pile foundations in sloping grounds when a thick non-liquefied soil layer overlies a liquefied soil layer, and piles are embedded in competent non-liquefiable soil layer below the liquefied soil [8].

Rao et al. [9] using 3D FD analysis investigated the behaviour of pile foundations in loose soil and reported that PGA and deflection at the top of the pile in liquefied soil are more compared to non-liquefiable soils. Hazzar et al. [10] used 3D FD analysis to investigate the influence of vertical load on the lateral response of piles in sand and clay, and they reported that the lateral response of piles does not vary considerably with the vertical load in sandy soils, especially in the loose state. In fact, the scope of previous attempts examining the problem of pile foundation is limited to the behaviour of piles installed in homogenous sandy or clayey soils. Little work has been devoted to the behaviour of piles in homogenous or layered soils which are often encountered in many geotechnical sites. Moreover, mechanisms regarding the influence of liquefiable soils in layered soils may be quite different from those of piles in ideal homogenous situations.

Earthquakes impose lateral loads in the piles through lateral spreading. Structurally, piles are long slender columns with lateral support from the surrounding soil. If unsupported, these columns will fail in buckling instability and not due to the crushing of pile material [11]. In addition, piles can also fail by bending or shear and failure of soil (i.e., excessive settlement). Further, these failure mechanisms may interact with each other. In order to understand this phenomenon of failure of piles in liquefiable soils, the present study investigates the possible causes of the failure of pile foundations.

9.2 Numerical Modelling

The 3D finite difference (FD) FLAC3D [4] was used to study the behaviour of piles under the 2001 Bhuj earthquake ground motion. The complete 3D geometric model was used to represent the coupled soil-pile system.

The stress-strain behaviour of soil-strata is considered as elasto-plastic in nature, and the most extensively used Mohr–Coulomb constitutive model was selected to model non-liquefiable layer, and the Byrne [12] constitutive model is chosen to model liquefiable sand layer. The parameters required to effectively define soil behaviour are the elastic bulk modulus (K), elastic shear modulus (G), density (ρ), angle of internal friction (Φ) and cohesion (C).

9.2.1 Validation Study for Static Loading

Before analysing the pile behaviour under seismic loading, the applicability of the model was verified by evaluating the pile response under lateral loading from the FD half model of Hazzar et al. [10]. The soil block consists of a single layer of very dense sand. The pile length is 10 m having a diameter of 1 m. Soil thickness is considered as 16 m. The Geotechnical properties of soil strata and the pile used in the analysis are summarized in Table 9.1.

Table 9.1 Soil properties used for the static analysis [4]
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Figure 9.1 shows the general layout and meshing of the FLAC 3D model used for the analysis of the soil-pile system. Lateral load was applied gradually at the pile head till the lateral deflection of the pile reaches 100 mm without any vertical load. Figure 9.2 shows the lateral displacement of the pile due to the applied lateral load. It is observed that, as lateral load increases, lateral displacement of the pile increases. The results of the present study are compared with Hazzar et al. [10] and are indicated in Fig. 9.2. The results obtained are in close agreement with the results reported.

Fig. 9.1
A general layout for the analysis of the soil-pile system denotes pile, loading direction, pile length, and pile diameter. A meshing FLAC 3 D model denotes zone and S E L geometry using color coding.

General layout and meshing of FLAC 3D model

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Fig. 9.2
A line graph depicts the lateral load on the pile in kilo newton versus the lateral displacement of the pile in millimeters for Lassaad et.al 2007 and the present study FLAC 3 D. The lateral load on the pile trended in increasing order for both cases.

Lateral load versus lateral displacement of pile

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9.2.2 Validation Study for Dynamic Loading

The applicability of the adopted FLAC 3-D model was verified for dynamic loading by studying the pile response from the published centrifuge model studies. Abdoun et al. [2] reported the response of a 10 m long and 0.6 m diameter pile embedded in a three-layered strata consisting of non-liquefiable sand (slightly cemented sand) of 2 m thickness at the top and bottom, liquefiable sand (Nevada sand) layer extending to a depth of 6 m in between as shown in Fig. 4a. Soil-pile-pile cap model developed in the present study using FLAC 3D is shown in Fig. 4b. The geotechnical properties of soil layers in the model are summarized in Table 9.2. The dimensions of the pile cap are 2.5 m × 2.5 m made out of aluminium having a thickness of 0.5 m firmly connected to the pile made of polyetherimide rod. The water table is introduced at the ground surface. Byrne (1991) and Mohr–Coulomb constitutive models are adopted to model liquefiable and non-liquefiable sand layers, respectively. The soil model was subjected to harmonic motion of 0.3 g acceleration as shown in Fig. 9.3 at the base of the model. The frequency of harmonic motion was 2Hz. The normal and shear stiffness values calculated using Eqs. (9.1) and (9.2) are 64 × 107 N/m and 57.6 × 107 N/m, respectively. The interaction between soil and the pile cap obtained by Eq. (9.5) is found to be 897.3 × 108 N/m. The variation in bending moment along the depth between the centrifuge study and FLAC 3D modelling is shown in Fig. 9.5. The FLAC 3D results are in accordance with the results reported by Abdoun et al. [1].

Table 9.2 Properties of soil and pile [13, 14]
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Fig. 9.3
A graph of acceleration in g versus time in seconds depicts harmonic motion.

Harmonic motion

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Fig. 9.4
A schematic illustration of model units denotes Nevada sand sandwiched between slightly cemented sand layers. It denotes input motion, S G 1 to S G 6, and L V D T 1 to L V D T 4. A model of FLAC 3 D denotes zone and S E L geometry using color codes.

a Centrifuge model used by Abdoun et al. [2] and b model developed in the present study

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Fig. 9.5
A graph depicts depth below G L in meters versus pile bending moment in kilonewton meter for Abdoun et.al 2003 and present study FLAC 3D.

Comparison between present FLAC 3D and centrifuge study data of Abdoun et al. [2]

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9.3 Parametric Studies

In this section, a pile is modelled in FLAC3D [15] which is a 3D “explicit finite difference program” that performs “Lagrangian analysis” for engineering mechanics computation. A free-headed pile of length 9 m and diameter 0.6 m is modelled in a soil grid of 15 m × 15 m × 10 m dimension consisting of three layers in which top and bottom 2 m thickness is slightly cemented sand (SCS), and in between 6 m Nevada sand (Nsand) layer in level ground condition and ground having a slope of 2° with the horizontal is considered. The water table is introduced at the ground level. The properties of Nsand, SCS and pile are tabulated in Table 9.2.

9.3.1 Modelling Procedure

The coordinate axes for the FLAC 3D model are located with the origin at the bottom and z-axis oriented along the pile axes and downward. The top of model, at z = 10 m, is a free surface. The base of the model, at z = 0 m, is fixed in x, y and z directions, and roller boundaries are provided on the sides of the model and further increase in the dimension of the soil block will not affect the results.

Pile was modelled as the collection of pile structural elements (pileSELs). PileSELs are two-noded finite elements having six degrees of freedom per node. The elastic bulk modulus (Kp), elastic shear modulus (Gp) and density of pile (ρp) are the three parameters used to define pile material behaviour.

9.3.2 Soil-Pile Interface Model

The pile was divided into 32 segments and as the pile capacity is a function of skin friction resistance along the pile shaft and the end-bearing capacity at the pile tip, skin friction resistance is modelled through normal and shear coupling springs, and these springs transfer forces and motions between the soil grid, pile and pile cap. These springs are non-linear, and the normal and shear behaviour at the interface is both cohesive and frictional (Table 9.3).

Table 9.3 Soil-pile interface properties [IS:2911(Part 1, Sec4)-1985 and Timoshenko and Goodier [16]]
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The interactions are represented by normal stiffness (Kn) and shear stiffness (Ks) as per Timoshenko and Goodier [16] and are given as follows:

$${\text{Normal stiffness}},K_n = \frac{{4{\text{Gr}}}}{1 - \mu }$$
(9.1)
$${\text{Shear stiffness}}, \, K_s = \frac{{32\left( {1 - \mu } \right)Gr}}{7 - 8\mu }$$
(9.2)

where G = Shear modulus of soil (N/m)

r0 = Radius of pile (m) and

µ = Poisson’s ratio of soil (N/m).

The bulk modulus (K) and shear modulus (G) were calculated using the following equations:

$${{K}} = \frac{E}{{3\left( {1 - 2\mu } \right)}}$$
(9.3)
$${{G}} = \frac{E}{{3\left( {1 + \mu } \right)}}$$
(9.4)

Using Eqs. (9.1) and (9.2), the values of normal stiffness and shear stiffness obtained are 6.4 × 106 N/m and 5.76 × 106 N/m, respectively.

In dynamic analysis, free field boundary conditions are provided to reduce the reflection of input waves thereby simulating the field conditions. The default model of hysteresis damping was chosen.

The interaction between soil and the pile cap is represented through the normal spring stiffness and shear spring stiffness calculated using the equation:

$${K}_{n}={K}_{s}=\frac{K+\frac{4}{3}G}{{\Delta Z}_{\mathrm{min}}}$$
(9.5)

To study the response of the pile in liquefiable soils for level ground and sloping ground, Bhuj ground motion (2001) of 0.106g peak ground acceleration shown in Fig. 9.6 is considered.

Fig. 9.6
A trend graph depicts acceleration in g versus time in seconds. The acceleration is very high and very low, between 30 and 60 seconds.

2001 Bhuj earthquake ground motion

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9.4 Results and Discussions

The soil-pile model properties considered by Abdoun et al. [2] consist of top and bottom 2 m thick non-liquefiable sand (SCS) and in between 6 m thickness of liquefiable sand (Nsand). Three cases of soil model (Case A, Case B and Case C) were considered both in level ground and sloping ground, and the pile is embedded at the centre of the soil block. The 2001 Bhuj earthquake ground motion (Fig. 9.6) is applied at the base of the model.

9.4.1 Soil-Pile Interaction in Level Ground

9.4.1.1 Case A: Non-liquefiable Crust Overlies Liquefiable Soil, and Pile is Embedded in Non-liquefiable Soil Below the Liquefiable Soil

The typical layered system configuration is shown in Fig. 7a. The pile is supported at the top and bottom non-liquefiable layers which act as fixed support for the pile. Due to the applied dynamic load, pore water pressure builds up in the soil model and as a result pore pressure ratio reaches a value of 1 as shown in Fig. 7b causing the sand (Nsand) to liquefy. The lateral displacement of the pile top reaches a value of 46 mm and tends to zero at the tip of the pile as shown in Fig 7c. The liquefaction of sand (middle layer) resulted in exerting maximum bending moment in the pile at the top and bottom interface. The maximum bending moment at the top interface is 30 kNm and negative moment of 20.5 kNm at the bottom interface as shown in Fig 7d. The vertical settlement of the pile tip is observed to be 0.79 mm due to the self-weight of the pile itself as there is no axial load on the pile under the earthquake loading.

Fig. 9.7
A schematic illustration of a layered system denoting N sand sandwiched between S C S. 1 meter of pile is above the G L, and 1 meter of pile is below the S C S. Three graphs depict depth below G L in meters versus P W P ratio, pile lateral displacement in millimeters, and pile bending moment in kilonewton meters.

Profiles of a layered configuration, b pore pressure ratio, c lateral displacement and d bending moment for Case A in level ground condition

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9.4.1.2 Case B: The Top Non-liquefiable Layer is Absent, and the Pile is Embedded in Non-liquefiable Soil Below the Liquefiable Soil

When the top non-liquefiable layer is absent (Fig. 9.8a), the pile will be unsupported at the top and supported at the bottom (1 m into the non-liquefiable layer), thereby it behaves like a cantilever beam supported by the non-liquefiable soil.

Fig. 9.8
A schematic illustration of a layered system denoting N sand above S C S. 1 meter of pile is above the G L, and 1 meter of pile is below the S C S. Three graphs depict depth below G L in meters versus P W P ratio, pile lateral displacement in millimeters, and pile bending moment in kilonewton meters.

Profiles of a layered configuration, b pore pressure ratio, c pile lateral displacement and d pile bending moment for Case B in level ground condition

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The dynamic load applied at the base of the model develops pore water pressure resulting in a pore pressure ratio of 1 in liquefiable sand (Nsand) (Fig. 9.8b). As a result, the lateral displacement of the pile is found to be 26 mm at the top as shown in Fig. 9.8c, and becomes zero at the tip of the pile. The maximum bending moment induced in the pile is 9.3 kNm at 2 m depth and the fixity of the pile in the non-liquefied crust yields a negative moment of 6.1 kNm at the bottom interface of 8 m below the ground as shown in Fig. 9.8d. Further, in the absence of vertical load, the vertical settlement of the pile tip is 0.64 mm.

9.4.1.3 Case C: Thin Non-liquefiable Crust is Overlaid by Liquefiable Soil, and the Pile Tip Rests on Liquefiable Soil

In this case, the pile is embedded completely in liquefiable soil (Fig. 9.9a), and it is simply supported by the soil surrounding the pile as there is no support at the top and bottom of the pile. The pore pressure develops in the soil due to dynamic load, the pore pressure ratio attains a value of 1 and the lateral displacement of the pile top is found to be 12 mm as shown in Fig. 9.9c. Figure 9.9d shows the bending moment induced in the pile due to the liquefied soil exerting lateral pressure similar to the laterally loaded pile. Further, due to self-weight of the pile during shaking, it has shown a vertical settlement of 1.05 mm.

Fig. 9.9
A schematic illustration of a layered system denoting N sand above S C S. 1 meter of pile is above the ground level. Three graphs depict depth below G L in meters versus P W P ratio, pile lateral displacement in millimeters, and pile bending moment in kilonewton meters.

Profiles of a layered configuration, b pore pressure ratio, c pile lateral displacement and d pile bending moment for Case C in level ground condition

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9.4.2 Soil-Pile Interaction in Sloping Ground

The current understanding of pile failure is based on the bending mechanism where lateral loads due to slope movements induce bending in the pile. The permanent lateral deformation is reported to be the main source of distress in piles. To simulate the effect of sloping ground on the pile response, the soil profile considered above was provided with a gentle slope of 2° with respect to the horizontal as shown in Fig. 9.10a.

Fig. 9.10
A schematic illustration of a layered system in 2 degrees of sloped ground denoting N sand sandwiched between S C S. Three graphs depict depth below G L in meters versus P W P ratio, pile lateral displacement in millimeters, and pile bending moment in kilonewton meters.

Profiles of a layered configuration, b pore pressure ratio, c pile lateral displacement and d pile bending moment for Case A in sloping ground condition

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9.4.2.1 Case A: Non-liquefiable Crust Overlies Liquefiable Soil, and Pile is Embedded in Non-liquefiable Soil Below the Liquefiable Soil

Figure 9.10a shows the schematic of the soil-pile model. The pile is embedded at the centre of the soil block wherein the top and bottom 2 m is of slightly cemented sand and at the middle 6 m is of Nevada sand (Nsand) forming a total thickness of soil profile as 10 m on one side and by providing gentle slope of 2°, the thickness on the other side of the model is 10.52 m. When the tip of the pile is embedded sufficiently into the non-liquefiable layer, as the dynamic load is applied, the pore pressure ratio reaches a value of 1 resulting in liquefaction of sand (Nsand), thereby the lateral displacement of the pile is 121 mm at the ground level and reduces to zero at the tip of the pile.

Further at the interface of liquefiable and non-liquefiable soils, the maximum bending moment is observed to be 40 kNm and −21 kNm at the top and bottom interface, respectively. The settlement of pile tip under the absence of axial load is 1.02 mm is more in sloping ground compared to level ground.

9.4.2.2 Case B: The Top Non-liquefiable Layer is Absent, and the Pile is Embedded in Non-liquefiable Soil Below the Liquefiable Soil

When the top non-liquefiable layer is absent (Fig. 9.11a), the pore pressure ratio reaches 1 (Fig. 9.11b) resulting in the liquefaction of Nsand. Figure 9.11c shows the maximum lateral pile top displacement of 89 mm and the maximum bending moment of 22 kNm is developed at 2 m depth and has attained a negative value of 20 kNm at the bottom interface (Fig. 9.11d). The pile tip has shown vertical settlement of 1.305 mm which is more in sloping ground compared to level ground.

Fig. 9.11
A schematic illustration of a layered system in 2 degrees of sloped ground denoting N sand and S C S. Three graphs depict depth below G L in meters versus P W P ratio, pile lateral displacement in millimeters, and pile bending moment in kilonewton meters.

Profiles of a layered configuration, b pore pressure ratio, c pile lateral displacement and d pile bending moment for Case B in sloping ground condition

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9.4.2.3 Case C: When Thin Non-liquefiable Crust is Overlaid by Liquefied Soil, and Pile Tip Rests on Liquefied Soil

Figure 9.12a shows the schematic of a layered system in sloping ground. As a result of the pore pressure ratio reaching a value of 1, the complete liquefaction of Nsand exerts a lateral load on the pile, thereby the lateral displacement of the pile top is 53 mm and the maximum bending moment attained is 16 kNm at 7 m depth. The vertical settlement of the pile is found to be 1.4 mm which is more compared to level ground.

Fig. 9.12
A schematic illustration of a layered system in 2 degrees of sloped ground. Three graphs depict depth below G L in meters versus P W P ratio, pile lateral displacement in millimeters, and pile bending moment in kilonewton meters.

Profiles of a layered configuration, b pore pressure ratio, c pile lateral displacement and d pile bending moment for Case C in sloping ground condition

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Figure 9.13a–c shows the comparison between the displacement values and Fig. 9.14a–c shows the comparison between bending moment values in level and sloping ground for all three cases which clearly represents that in the case of sloping ground, vulnerability is very severe in terms of increased displacement and bending moments in the pile.

Fig. 9.13
Three line graphs depict depth below G L in meters versus pile lateral displacement millimeters for level ground and sloping ground for cases A, B, and C, respectively.

Comparison of pile lateral displacement with depth for all three cases

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Fig. 9.14
Three line graphs depict depth below G L in meters versus pile bending moment in kilonewton meters for level ground and sloping ground for cases A, B, and C, respectively.

Comparison of pile bending moment with depth for all three cases

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9.5 Conclusions

The numerical analysis was performed for a pile resting in liquefiable soils using FLAC 3D. The results were presented in terms of pore pressure ratio, displacement and bending moment.

From the present study, the following conclusions are drawn:

  1. 1.

    The maximum values of bending moment during dynamic loading have been observed at the interface between liquefiable and non-liquefiable soils.

  2. 2.

    Pile displacement is maximum at the top and reduces gradually towards the bottom and tends to zero at the tip of the pile.

  3. 3.

    When the top non-liquefiable layer is absent, liquefaction of Nevada sand exerts lateral pressure on the pile and the pile starts to behave like a cantilever beam thereby reduction in pile displacement and bending moment sets up.

  4. 4.

    Pile has shown increased displacement and bending moment under sloping ground compared to level ground in the three cases discussed.

  5. 5.

    If the pile is not founded on the non-liquefiable hard layer below the liquefiable layer, liquefied soil can exert lateral pressure on the pile in a manner similar to a laterally loaded pile in level and sloping ground. Also, the vertical settlement can be the cause of the failure of piles.

The results of the present study are restricted to the analysis of a single pile embedded in liquefiable level and sloping ground in the absence of vertical load. However, the analysis of the pile behaviour for different ground sloping angles considering the parameters such as slenderness ratio of pile, inertial and kinematic loading deserves further study.