**2.2 Buckling failure**

The second mechanism is the buckling instability under the interaction of axial and lateral loads, and piles acting as beam-columns under both axial and lateral loading [32–35]. Bhattacharya [35] argued this failure mechanism and suggested piles become laterally unsupported in the liquefiable zone during strong shaking which the axial load applied on pile and the soil around the pile liquefies loses of its stiffness and strength. Next, the piles act as unsupported long slender columns, and soils cannot support the corresponding action. Buckling failure depends on the geometrical properties of the member (i.e. slenderness ratio). The buckling mechanism is in the length of in touch with liquefied soil. The lateral loads for structural elements, due to slope movement increase lateral spread displacement demands, which in can cause plastic hinge to form and reducing the buckling load.

Extensive research has been carried out on the buckling instability of pile in liquefied soils. One early method for the stability of beams on elastic foundations proposed by Hetenyi [36] may be the base of the buckling analysis of pile foundations. The lateral loads, due to inertia or lateral spreading, could increase the lateral deflection of pile and thus reduce the buckling load [35]. On the other hand, there will always be confining pressure around the pile even if the soil has fully liquefied, and it could provide some lateral support to the pile and increase the buckling load [37]. As observed by Bhattacharya et al. [24], Knappett and Madabhushi [32], and Zhang et al. [38], buckling failure of the end-bearing pile normally occurs when the soil is fully liquefied. And pile buckling in partially liquefied soil would require a higher buckling load than that in the fully liquefied soil. In other words, when predicting the critical buckling load of pile in liquefiable soils, only the soil that has fully been liquefied needs to be considered. Zhang et al. [38] found that the critical buckling load of piles in liquefied soils increases with the increase of soil relative density and flexural rigidity of the pile and decreases with the increase of initial geometric imperfections of the pile and pier height. Shanker et al. [39] proposed an analytic method to predict the critical buckling load of pile under partial to full loss of lateral support.

#### **2.3 Dynamic failure (bending–buckling)**

A collapse of pile-supported structures in liquefiable deposits may occur under the combined action of lateral load and axial load. Bhattacharya et al. [37] included the dynamics failure on the combined axial and lateral loads on a pile foundation. In this mechanism, piles are subjected to both axial and lateral loads during seismic shaking and piles act like beam-column members (**Figure 6**).

As a result of this combination (axial- and lateral-loading) on piles during a seismic liquefaction-induced event, the influence of the axial load, P, in piles causes a loss of lateral stiffness (y is the lateral displacement) until the axial load

#### **Figure 6.**

*Schematic of the effect of bending–buckling interaction on the response of pile foundation [40].*

approaches the critical value (P=Pcr). The loss of lateral stiffness in association with the axial load (i.e., pile deflection), Δ, is dominated by the excessive moment caused by the P-Δ effect (see Section 3.3.1). Subsequently, the large deflection of the beam may then induce plasticity in the beam resulting in an early failure. The same failure point of the pile is also possible when bending moment reaches Mp and pile continues to deflect without any additional loading.

Dash et al. [40] investigated the importance of bending–buckling interaction in seismic design of piles in liquefiable soils using numerical techniques. They concluded that if a pile is designed for bending and buckling criteria separately and safe for these individual design criteria, it may fail due to their combined effect. Recently, this is also suggested by Zhang et al. [41] to consider the buckling mechanism together with the effect of lateral load. It is hence important for the designers to consider a possible boundary for safe design to avoid failure of the pile.
