*The Dynamic Behaviour of Pile Foundations in Seismically Liquefiable Soils: Failure… DOI: http://dx.doi.org/10.5772/intechopen.94936*

Bhattacharya et al. [33] collated 15 case histories of pile earthquake performance and classified them according to their Euler buckling load when the soil was fully liquefied. In most of the cases where the axial load in the pile was 50% or more of the buckling loads, the foundation suffered significant damage.

Based on these observations, the failure of pile foundations occurred in both laterally spreading ground and in level ground where no lateral spreading would be anticipated. The cracks observed were near the bottom and at interfaces between liquefied and non-liquefied layers and often at the pile head. Additionally, severe damage had also formed at the boundaries of the liquefiable and non-liquefiable layers and at various depths between. The plastic hinge formation occurred at the boundaries of the liquefiable and non-liquefiable layers and at various depths.

## **3.2 Laboratory testing**

Laboratory studies are also critical to elucidate the failure mechanisms and the behaviour of soil–pile interaction in liquefiable soils and its relevant fundamental parameters such as relative density, confining pressure, shear strength, frequency content and amplitude, damping ratio, pile bending moment, and deformed shape of the soil profile. Therefore, while the aim of the work presented in this section is to review and provide well-interpreted field of the dynamic response of piles by different physical model tests that can be used to evaluate analytical procedures and design methods. Many studies have investigated the seismic response of pile, soil and superstructure using shake-table experiments [58–63], dynamic centrifuge experiments [19, 64, 65], and full-scale field tests that utilise blast-induced liquefaction [66, 67]. The requirements for a model container for carrying out seismic soil-structure interactions (SSI) at 1-g (shaking table) and N-g (geotechnical centrifuge at N times earth's gravity) are well introduced in [68].

#### *3.2.1 Shaking table tests*

Iwasaki et al., [69] used a shaking table to estimate the liquefaction potential by using fundamental properties of the soil. Meymand [70] carried out a set of soil-pile interaction tests using the large shaking table operated by U.C. Berkeley. It was reported that damping for the single piles computed from 10 to 20%. Yao et al., [71] highlighted that the transient state prior to soil liquefaction was important in the design of piles due to dynamic earth pressure showed peak response in this state. Tokimatsu et al. [72] investigated pile under the combination of inertial and kinematic forces and reported that the pile foundation response depends on the time period of the ground as well as the superstructure. Cubrinovski et al. [73] discussed the behaviour of pile foundations under lateral spreading. Chau et al. [74] suggested that seismic pounding between the laterally compressed soil and the pile near the pile cap level can be one of the probable causes of pile damages. Motamed & Towhata [75] carried out a series of 1 g small-scale shake table model tests on a 3 × 3 pile group located behind a sheet-pile quay wall. It reported that fixed-end mitigating sheet pile can reduce the bending moment of pile. This is depended on the pile position within the group [76]. Gao et al. [61] studied the dynamic interactive behaviour of soil–pile foundations in liquefying ground under different shaking frequency and amplitude. They reported that the frequency of motion does not have a significant effect on the pile and soil response; however, these responses depend on the shaking amplitude. Besides, Lombardi & Bhattacharya [34] concluded that natural frequency of pile foundation decreases due to liquefaction; also they found that the damping ratio may increase due to liquefaction in excess of 20% (**Figure 7**).

**193**

*The Dynamic Behaviour of Pile Foundations in Seismically Liquefiable Soils: Failure…*

A similar observation was reported by Tang and Ling [62] and Tang et al. [63], which conducted a shaking table experiment to investigate the dynamic behaviour of a reinforced-concrete (RC) elevated cap pile foundation during (and prior to) soil liquefaction. These works indicated decreasing the frequency and increasing the amplitude of earthquake excitation. Next to this, Chen et al. [77] suggested that the seismic response of the soil and structure depends on input motion with richer low frequency components. On the other hand, Su et al. [58] document thicker pile having higher displacement. Likewise, the work performed by Liu et al. [78] was demonstrated that pile group bending moment was able to increase dramatically as the diameter increases. Four large laminar-box shaking table experiments used by Ebeido et al. [59] to examine pile response due to the mechanism of liquefaction-induced lateral spreading. They concluded that the highest pile lateral loads occurred at the initial stages of lateral deformation. Zhang et al. [41] reported that a pile collapsed due to buckling instability, which

Similar to the shaking table test, centrifuge test enables to address liquefaction, lateral spreading, and their effect on pile foundations by the simulation of gravityinduced stress conditions in scale models of soil structures at N times earth's gravity. Conceptually, this technique consists of the linear dimensions in the model soil by a factor 1/N and the confining stress is identical by a factor of unity. Thus, scale models law to simulate the behaviour of full-scale earth structures by reduced scale

Several experimental studies have investigated of piles subject to liquefaction by using centrifuge method testing. McVay et al. [79] analysed the behaviour of the laterally loaded on pile group in sand with different pile group models. They reported that by changing the size of the group, there was no change in the group's lateral resistance, but only was a function of row position. Wilson [80] and Wilson et al. [81] performed dynamic centrifuge tests on the soil-pile interaction (**Figure 8**), which was directly obtained from the observed p-y response through back analysis of a single pile. This analyse presented the first dynamic characterisa-

*DOI: http://dx.doi.org/10.5772/intechopen.94936*

*(a) The shaking table test and (b) elevation view of test [34].*

happened after the soil fully liquefied.

and provide data applicable to full-scale problems [68].

tion of p–y behaviour of pile foundations in liquefying sand.

*3.2.2 Centrifuge tests*

**Figure 7.**

*The Dynamic Behaviour of Pile Foundations in Seismically Liquefiable Soils: Failure… DOI: http://dx.doi.org/10.5772/intechopen.94936*

**Figure 7.** *(a) The shaking table test and (b) elevation view of test [34].*

A similar observation was reported by Tang and Ling [62] and Tang et al. [63], which conducted a shaking table experiment to investigate the dynamic behaviour of a reinforced-concrete (RC) elevated cap pile foundation during (and prior to) soil liquefaction. These works indicated decreasing the frequency and increasing the amplitude of earthquake excitation. Next to this, Chen et al. [77] suggested that the seismic response of the soil and structure depends on input motion with richer low frequency components. On the other hand, Su et al. [58] document thicker pile having higher displacement. Likewise, the work performed by Liu et al. [78] was demonstrated that pile group bending moment was able to increase dramatically as the diameter increases. Four large laminar-box shaking table experiments used by Ebeido et al. [59] to examine pile response due to the mechanism of liquefaction-induced lateral spreading. They concluded that the highest pile lateral loads occurred at the initial stages of lateral deformation. Zhang et al. [41] reported that a pile collapsed due to buckling instability, which happened after the soil fully liquefied.

### *3.2.2 Centrifuge tests*

Similar to the shaking table test, centrifuge test enables to address liquefaction, lateral spreading, and their effect on pile foundations by the simulation of gravityinduced stress conditions in scale models of soil structures at N times earth's gravity. Conceptually, this technique consists of the linear dimensions in the model soil by a factor 1/N and the confining stress is identical by a factor of unity. Thus, scale models law to simulate the behaviour of full-scale earth structures by reduced scale and provide data applicable to full-scale problems [68].

Several experimental studies have investigated of piles subject to liquefaction by using centrifuge method testing. McVay et al. [79] analysed the behaviour of the laterally loaded on pile group in sand with different pile group models. They reported that by changing the size of the group, there was no change in the group's lateral resistance, but only was a function of row position. Wilson [80] and Wilson et al. [81] performed dynamic centrifuge tests on the soil-pile interaction (**Figure 8**), which was directly obtained from the observed p-y response through back analysis of a single pile. This analyse presented the first dynamic characterisation of p–y behaviour of pile foundations in liquefying sand.

#### **Figure 8.**

*Layout of the centrifuge test setup by Wilson [80].*

Abdoun et al. [82] estimated the peak subgrade reaction values in liquefiable sand from centrifuge tests and concluded that the largest free head pile bending moment occurred at the boundary between the liquefied and non-liquefied strata. Similarly, a large displacement due to the liquefaction of the backfill soil was observed between the rubble mound and the bearing stratum, which produced a large bending moment at the top of the pile [83]. Brandenberg et al. [84] conducted various aspects of bending failure mechanism. In contrast, Bhattacharya et al. [85] proposed buckling instability failure mechanism as a new theory of pile failure mechanism verified by dynamic centrifuge tests. Another experiment concluded that an increase in excess pore pressure around and beneath end-bearing piles might induce the instability failure caused by liquefaction [86]. A similar observation was reported to clarify the buckling instability failure mechanism by Knappett and Madabhushi [32]. Recently, Garala et al. [19] conducted unexplored aspects of kinematic pile bending.

### **3.3 Numerical modelling**

The numerical simulation tools have been prominent for analysing liquefaction problems in the light of potential disadvantages of physical models used in experimental simulation. This section presents different numerical platforms used in modelling of pile foundations under dynamic loading and their capabilities and limitations. Review of the recent relevant works delineates the important aspects of the seismic analysis of piles in liquefiable soils.

Numerical modelling can be divided into three categories: Beam on nonlinear Winkler Foundation (BNWF) approach with the proposed p–y curves, twodimensional numerical modelling and the full three-dimensionality of model. Due to computationally complex and time-consuming of two- and three-dimensional numerical modelling, most of the researchers prefer to use the pseudo-static analyse is based on Winkler method for the seismic analysis of pile foundations. Winkler models are approximately capable of predicting maximum lateral displacement and maximum bending moment of pile foundations in liquefied soils. However, it is not able to simulate the prototype model accurately because it is difficult to estimate the accurate values for the springs and dashpots coefficients, which considerably change over time, especially during strong shaking.

**195**

**Figure 9.**

*Method of pile analysis using p-y curves, Dash et al. [87].*

*The Dynamic Behaviour of Pile Foundations in Seismically Liquefiable Soils: Failure…*

The beam-on-nonlinear-Winkler-foundation (BNWF) method (also known as p-y method or Winkler method) is widely used in the modelling of soil–pile–structure interaction due to its simplicity in modelling and computational efficiency. This method is based on the hypothesis that the reaction exerted by the soil at a given depth on the pile shaft is proportional to the relative pile–soil lateral deflection. In the BNWF method, soil-pile interactions are modelled by a set of nonlinear soil springs, whereas the horizontal responses are analysed using p-y spring, for simulating shaft friction controlling vertical loading characteristics by t-z spring and end-bearing at the bottom of the piles responses are represented via the q-z spring (**Figure 9**). Each spring can be defined by means of a non-linear relationship between the soil reaction (per unit length of the pile) p and the corresponding relative soil–pile displacement. This method is based on the beam on elastic foundation approach of Hetényi [36] and Winkler [88]. The p–y curves have been used to model the reaction of the foundation with consideration of inertial effects and seismic soil–pile interaction. Guidelines for the p – y curves as prescribed by current codes of practice are based on the works of Matlock [89] for soft clay, Reese [90] for cohesionless soils and Cox et al. [91] and O'Neill and Murchison [92] for sand, published by API [93] and DNV [94]. A different approach based on the assumption that the liquefied soil behaves like soft clay applied to account for the effects of liquefaction on the p–y curves, which is known as "residual strength" method [95]. However, applications of these curves were developed from a number of field tests with relatively few inherent limitations. Therefore, numerous works have been carried out to evaluate p–y curves for laterally loaded piles in liquefiable soils, such as Dobry et al. [96], Yasuda et al., [97], Sivathayalan and Vaid [98] and Rollins et al. [99]. Subsequently, the p–y method was extended to liquefiable soils by applying a "p multiplier" [96, 100], which is a reduction factor (mp). Combining the force- and displacement-based methods,

*DOI: http://dx.doi.org/10.5772/intechopen.94936*

*3.3.1 p–y curves*

*The Dynamic Behaviour of Pile Foundations in Seismically Liquefiable Soils: Failure… DOI: http://dx.doi.org/10.5772/intechopen.94936*

#### *3.3.1 p–y curves*

The beam-on-nonlinear-Winkler-foundation (BNWF) method (also known as p-y method or Winkler method) is widely used in the modelling of soil–pile–structure interaction due to its simplicity in modelling and computational efficiency. This method is based on the hypothesis that the reaction exerted by the soil at a given depth on the pile shaft is proportional to the relative pile–soil lateral deflection. In the BNWF method, soil-pile interactions are modelled by a set of nonlinear soil springs, whereas the horizontal responses are analysed using p-y spring, for simulating shaft friction controlling vertical loading characteristics by t-z spring and end-bearing at the bottom of the piles responses are represented via the q-z spring (**Figure 9**). Each spring can be defined by means of a non-linear relationship between the soil reaction (per unit length of the pile) p and the corresponding relative soil–pile displacement.

This method is based on the beam on elastic foundation approach of Hetényi [36] and Winkler [88]. The p–y curves have been used to model the reaction of the foundation with consideration of inertial effects and seismic soil–pile interaction. Guidelines for the p – y curves as prescribed by current codes of practice are based on the works of Matlock [89] for soft clay, Reese [90] for cohesionless soils and Cox et al. [91] and O'Neill and Murchison [92] for sand, published by API [93] and DNV [94]. A different approach based on the assumption that the liquefied soil behaves like soft clay applied to account for the effects of liquefaction on the p–y curves, which is known as "residual strength" method [95]. However, applications of these curves were developed from a number of field tests with relatively few inherent limitations. Therefore, numerous works have been carried out to evaluate p–y curves for laterally loaded piles in liquefiable soils, such as Dobry et al. [96], Yasuda et al., [97], Sivathayalan and Vaid [98] and Rollins et al. [99]. Subsequently, the p–y method was extended to liquefiable soils by applying a "p multiplier" [96, 100], which is a reduction factor (mp). Combining the force- and displacement-based methods,

**Figure 9.** *Method of pile analysis using p-y curves, Dash et al. [87].*

Cubrinovski et al. [100] proposed to use limit pressures for non-liquefied crust layers and linear springs with a "stiffness degradation factor" (known as the p-multiplier) for liquefied layers during liquefaction-induced lateral spreading. Several analyses of the full-scale tests [81, 101–103] conducted and observed the actual shape of postcyclic stress–strain response of liquefied soils. They suggested an S-curve shape of the "p–y" curve for liquefied soil. Similarly, the post-liquefaction behaviour of sands observed in element tests by [104, 105]. Lombardi et al. [106] and Dash et al. [107] adopted a new set of p–y curves that can be obtained by modifying the conventional p–y curves (for non-liquefied soils) in such a way that replicates the strain hardening behaviour with practically-zero stiffness at low strain.
