基于极限分析的桩端岩层冲切分析

 岩溶区桩基桩端岩层易发生冲切破坏。针对岩溶区岩体特点引进Hoek-Brown非线性岩石破坏强度准则，并推导得其剪应力的二次抛物线型表达式。基于极限分析上限法原理，确定冲切破坏体的功能方程，并通过变分求极值原理获得冲切破坏体的母线方程，进一步通过微分得到桩端岩层抗冲切安全厚度计算公式。结合岩溶区桩基实践，分析抗冲切安全厚度影响因素的取值范围并进行参数分析，结果表明：(1) 冲切破坏体上下直径比d1/d随岩体地质力学分类指标RMR值的增大呈非线性减小，说明岩体质量好的岩溶顶板其冲切所形成的锥形旋转体底部直径小，反之，旋转体底部直径大；(2) 根据不同的d1/d及RMR值，初始冲切角 为24°～42°；(3) 厚径比h/d随RMR的增大呈非线性减小，表明岩体质量越好，所需安全厚度也越小；在岩体质量较好(RMR＞65)的情况下，h/d基本在2.5以下。

PUNCHING ANALYSIS OF ROCK AT PILE TIP BASE ON LIMIT ANALYSIS

The rock stratum at pile tip is prone to punching failare for pile foundation in karst region. The Hoek-Brown nonlinear rock strength criterion has been introduced according to the characteristics of rock mass in the karst region；and then the shear stress of quadratic parabolic expression was obtained. The work-energy equation of punching failure body was established using limit analysis method. Then the generatrix equation of punching failure body was obtained through the variational extremum principle. Furthermore，the calculation formula of safe thickness for the rock stratum anti-punching failure was obtained by differential equation. Combined with the practice of pile foundation in karst area，the value range of main resistant punching shear safety thickness factors affecting were analyzed. Parameter analysis shows that：(1) The top and bottom diameter ratio d1/d of punching failure body decreased nonlinearly along with the increase of RMR value；in other words the bottom conical rotor diameter of punching failure which formed by the good karst roof of rock mass quality is small. Conversely，the greater the diameter at the bottom of the body of revolution. (2) According to the different d1/d and RMR values，the ranges of initial punching angle is between 24°–42°. (3) The ratio of thickness to diameter h/d decreases nonlinearly along with the increase of RMR. That is to say the better the rock mass quality，the smaller the safe thickness. When the rock mass quality is good(RMR＞65)，the safety thickness h/d is lower than 2.5.