A three-dimensional (3D) analytical solution for the ultimate side shear resistance of rock-socketed shafts

Abstract

This paper presents a new analytical solution to the ultimate side shear resistance τsf of rock socketed shafts with consideration of three-dimensional (3D) strength and shaft sidewall roughness. Specifically, the shaft sidewall profile is simplified as triangular asperities and micro-mechanical analysis is performed on the shear behavior of one representative asperity. A 3D version of the Hoek-Brown (HB) criterion for rock mass and the equilibrium equations in a cylindrical coordinate system are first utilized to derive the governing equations. Then the governing equations are solved by using the method of characteristics. Finally, the τsf is obtained by considering the constant normal stiffness condition and the relative displacement of the rock mass due to sliding along the shaft-rock mass interface. Twenty-four (24) model and field test shafts with measured τsf are collected for analysis to verify the proposed solution. The results indicate that the predicted τsf values are in good agreement with the measured τsf values. Extensive parametric studies are also conducted to investigate the effects of rock mass properties, shaft dimensions, and sidewall roughness parameters on the ultimate side shear resistance factor αf (the ratio of τsf to the unconfined compressive strength of intact rock σc) of rock socketed shafts. The results indicate that the αf increases with rock constant mi, geological strength index (GSI) and asperity half chord length λ, but decreases with shaft diameter B, σc and disturbance D. Furthermore, the αf first increases and then decreases with the asperity inclination angle δ, resulting in an optimum asperity inclination angle δOp. Therefore, it is important to reduce the disturbance of rock mass from construction and select a proper asperity inclination angle when designing a rock socketed shaft.