“…The safety of the soil-pile -bridge system is a primary concern in the engineering practice (Gerolymos et al, 2008;Cubrinovski et al, 2014;Qu et al, 2018a;Qu et al, 2018b;Qu et al, 2019). Liquefaction-induced lateral displacement has caused much damage to the piled abutment of bridges in the past earthquakes, such as the 1991 Costa Rica Earthquake, the 2011 Christchurch earthquake, and the 2011 Great East Japan earthquake (Gerolymos et al, 2008;Cubrinovski et al, 2014; National Institute for Land and Infrastructure Management of Japan, Public Works Research Institute of Japan, 2014; Tazohb et al, 2008;Xu et al, 2023). It is reported that the inclined piles are more effective than vertical piles in restricting lateral displacements of superstructures subjected to liquefaction induced lateral displacement.…”