# Numerical Simulation of Piles in a Liquefied Slope Using a Modified Soil-Pile Interface Model
## 1 Introduction  
Liquefaction under seismic loads has caused severe damage to various structures due to the loss of strength and stiffness of the liquefied ground [1, 2]. In particular, liquefaction of sloping ground induces more dangerous conditions, resulting in the lateral spreading of soil in the downslope direction [3, 4, 5]. Pile foundations in waterfront structures are typically installed on slopes, and the liquefaction potential is high in recently formed reclaimed or sedimentary grounds near the coast or river [6, 7, 8, 9]. Therefore, the liquefaction of slopes can cause significant damage to pile structures and should be properly simulated by considering the soil-pile interaction on liquefied slopes. In order to predict liquefaction-induced damage, studies were conducted based on the statistical analysis of reported liquefaction damage data. [PERSON] and [PERSON] [10] and [PERSON] et al. [11] proposed empirical formulas for the lateral spread displacement under free-face and gentle slope conditions based on a multilinear regression method. [PERSON] [12] proposed an empirical formula for the lateral load on piles during liquefaction based on back-analyses of pile damage during the 1995 Kobe earthquake. Experimental approaches have been carried out to simulate piles in liquefied ground. [PERSON] et al. [13] proposed a uniform lateral load on piles for a liquefied layer based on centrifuge model experiments with piles embedded in a liquefied ground with a 2-degreeinclination. [PERSON] et al. [14] suggested a linearly distributed lateral load on piles for a liquefied layer, which was identical to the total stress of the ground based on shaking table tests. A method for applying lateral design load along a pile length was found to predict the maximum bending moment of the pile due to liquefaction [15; 16]. However, using this method, it is difficult to consider displacement variations within liquefiable soil layers, and it tends to overestimate the pile head displacement [17]. To address this limitation, the \(p\)-\(y\) spring method was proposed, which varies the soil reaction according to the relative displacement between the pile and soil. The \(p\)-\(y\) curve, which is the most widely adopted nonlinear spring representing the horizontal interaction between a pile and the ground [18; 19; 20], was proposed to capture the nonlinear horizontal resistance behavior of the ground when a pile head is subjected to a horizontal load. These curves are independently connected for each element of the pile. When considering the liquefied soil conditions, reducing the ultimate resistance [21; 22] or changing the shape of the \(p\)-\(y\) curve [23; 24] were proposed. The \(p\)-\(y\) method assumes independent nonlinear springs for each sub-layer of the ground, which requires a separate estimation of the final deformation shape for each liquefied ground layer. However, the ground responses of a finite slope, including excess pore pressure and deformation, are significantly influenced by the horizontal and vertical interactions within the liquefied ground. For a rigorous analysis, it is necessary to model the entire ground behavior and define the interaction between the liquefied soil and pile elements. Some researchers conducted numerical studies on piles in liquefied ground. Considering the effect of liquefaction on soil-pile interaction, a method of simply reducing the friction angle of the interface spring was adopted. However, the level of reduction in friction angle is somewhat arbitrary. [PERSON] [25] and [PERSON] et al. [26] proposed 70% and 60% of the friction angle of non-liquefied ground, respectively. [PERSON] et al. [27] and [PERSON] et al. [28] proposed a reduction of 5 degrees less than the maximum friction angle. However, it is crucial to recognize that these methods have limitations in accurately capturing a significant phenomenon: the rapid weakening of soil strength resulting from slope liquefaction.