# Lateral Loading of a Rock-Socketed Pile Using the Strain Wedge Model Based on Hoek-Brown Criterion
## 1 Introduction  
The lateral load from upper structures could be transferred to bedrock via rock-socketed pile based on the interaction between the pile and the surrounding rock mass. As a special pile foundation, the rock-socketed pile has the characteristics of high bearing capacity, small pile group effect, and rapid settlement convergence. These characteristics meet the requirements of the bearing capacity of high-rise buildings, long-span bridges, ports, and offshore oil drilling platforms. To date, it has been customary practice to adopt the techniques developed for laterally loaded piles in the soil to analyze the bearing capacity of laterally loaded rock-socketed piles [1; 2; 3]. However, the method used to analyze the lateral bearing capacity of the pile in hard clay cannot fully consider the characteristics of the rock due to the difference between rock mass and soil [4; 5]. The few studies published about the load transfer process in rock-socketed piles under lateral loading are made based on numerical methods and fields tests, and theoretical analysis. According to [PERSON] et al. [4], the calculation methods for the lateral bearing capacity of rock-socketed piles can be divided into two categories: (1) elastic or elastoplastic continuum method; (2) subgrade reaction method. [PERSON] et al. [6; 7] used the finite element method to study flexible and rigid rock-socketed piles and proposed an analytical solution for predicting the lateral bearing capacity and displacement of the rock-socketed pile. It is proposed that the lateral resistance of a rock-socketed pile is mainly composed of the lateral friction resistance of the pile-rock interface and the compressive strength of the rock in front of the pile. However, [PERSON] [8] believed that this method was only suitable for a low load (20-30% bearing capacity), and it was not suitable for a higher load. [PERSON] et al. [5] used the elastic-plastic continuum method to predict the load-displacement response of rock-socketed piles under lateral loads. Assuming that the overlying soil layer is continuously distributed, the deformation modulus of soil and rock varies linearly with depth, and the deformation modulus of the rock remains unchanged at the tip of the shaft. Based on the method of Hoek-Brown strength criterion, the calculation method of rock ultimate bearing capacity is proposed. [PERSON] et al. [9] extended [PERSON]'s method to multi-layered soil or rock conditions. The yield of the soil and the decrease in pile stiffness due to cracking were considered in the method. The elastic or elastoplastic continuum method can better reflect the continuity of the rock mass around the pile and is more in line with the actual situation. However, it cannot be applied to the rock, which is complex, nonlinear, and anisotropic, around the pile  
[PERSON]. [10] analyzed a single rock-socketed pile under lateral load using the \(p\)-\(y\) curve method (Figure 1). Based on the Winkel beam on elastic foundation, the rock-shaft lateral interaction was replaced by a series of discrete, nonlinear springs. The relationship between lateral displacement and lateral load had been established. The ultimate lateral resistance of rock mass and the initial stiffness of the \(p\)-\(y\) curve were briefly analyzed. Moreover, the change of pile stiffness when the concrete cracked had also been analyzed. Some researchers [4; 11; 12] put forward a hyperbolic \(p\)-\(y\) curve of rock-socketed pile suitable for weathered rock based on field and laboratory tests combined with finite element analysis. The rock mass joint conditions, RQD value and core strength were considered. Moreover, the proposed model was verified by field tests. [PERSON] et al. [13] analyzed the lateral bearing characteristics of a single pile in soft calcareous sandstone through field tests and believed that the \(p\)-\(y\) curve model in soft rock proposed by [PERSON] could not describe the pile behavior well in this case.