**2. Pile failure**

Piles are a particular type of deep foundation generally constructed to support heavily loaded structures to transfer the loads from superstructures to the deeper layers of soil, relying on both skin friction and tip resistance [19]. Piles are also used in seismic-prone zones comprising loose to medium-dense sandy soil or soft clay. However, during earthquake shaking when the soil around the pile loses much of its stiffness and strength due to liquefaction, the pile will act like a long laterally unsupported column and could buckle under the high axial load from the superstructure, affecting the foundations. Collapse and damage of pile-supported structures due to liquefaction have been observed after many major earthquakes [2–4]. The observations from many historic cases indicated that the failure of foundations occurred at unexpected locations (see **Figure 4**).

During earthquakes, the response of pile-supported structures to liquefiable soils would depend of the stiffness of the pile foundation type, the response of the soil surrounding the pile, and the soil-pile interaction effects. The analysis of this response requires accurate characterisation of the interaction effects include the inertial loading exerted by the superstructure and the kinematic loading induced by the soil surrounding the pile. **Figure 5** illustrates four critical stages of loading on the piles during a seismic liquefaction-induced event.

**Figure 4.** *(a), (b) Buildings in Niigata city and (c) Building in Kobe city [12].*

**Figure 5.**

Before, or just at the onset of the earthquake, the axial load on the piles can be estimated based on static equilibrium. Upon commencement of the seismic vibration, and before the excess pore water pressure build-up, this axial compressive load may increase/decrease further due to the inertial effect of the superstructure (due to oscillation of superstructure) and the kinematic effects of the soil flow past the foundation (due to ground movement). This change in loading can be transient (during the vibration, due to the dynamic effects of the soil mass) and residual (after the vibration, due to soil flow, often known as "lateral spreading" [21]). However, at this stage, with pore water pressure built up (at full liquefaction, the excess pore water pressures reach the overburden vertical effective stress), the soil loses its strength and stiffness, and the pile acts as an unsupported slender columns over the liquefied depth. Most of the efforts have been made to greatly improve understanding of pile failure mechanism due to liquefaction [20–24]. Two plausible mechanisms of pile failure: bending (due to inertia of the superstructure and/or kinematic loads due to lateral soil pressure) and buckling (due to axial load), have been studied in detail separately. However, dynamic failure (bending–buckling interaction) of a pile foundation may also occur in a seismically liquefiable soil deposits and lead to failure of the structure.
