Hoek-Brown岩体非线性强度的线性化方法

廖异¹，曾祥国¹，符文熹²，刘卫国¹

(1. 四川大学 建筑与环境学院，四川 成都，610065；
2. 四川大学 水力学与山区河流开发保护国家重点实验室，四川 成都，610065)

摘 要：以瞬态摩擦角φ_i为中间变量详细推导Hoek-Brown准则的τ-σ关系。根据Hoek-Brown准则的τ-σ关系，推求Hoek-Brown准则下最小单元安全系数所对应的截面位置，并认为该截面为岩体发生临界破坏时的破坏面。根据岩体发生临界破坏时的破坏面位置以及作用于该面上的正应力和剪应力求得岩体在发生临界破坏时所受到的最小主应力σ₃。通过搜寻计算模型范围内每一种材料中所有单元临界破坏状态下的最小主应力σ₃找出每一种材料中最小主应力区间。采用最小二乘法推导通用Hoek-Brown准则在任意最小主应力区间范围内的等效Mohr-Coulomb参数。采用本文中建议的线性化方法和Hoek-Brown准则强度折减法对一边坡算例进行计算。结果表明：当每一种材料的最小主应力区间划分得越细，通过等效Mohr-Coulomb参数求得的边坡安全系数和破坏面位置与通过Hoek-Brown准则强度折减法获得的结果越接近。

关键词：Hoek-Brown准则；线性化；等效Mohr-Coulomb参数；安全系数；最小主应力区间

Linearization method of non-linear strength of Hoek-Brown rock mass

LIAO Yi¹, ZENG Xiang-guo¹, FU Wen-xi², LIU Wei-guo¹

(1. College of Architecture &Environment, Sichuan University, Chengdu 610065, China;
2. State Key Laboratory of Hydraulic and Mountain River Engineering,
School of Water Resource and Hydropower, Sichuan University, Chengdu 610065, China)

Abstract:The shear and normal stress relationship of the Hoek-Brown criterion was obtained by means of intermediate variable φ_i. The position of the section corresponding to the minimum safety factor of Hoek-Brown criterion could be obtained by means of the shear and normal stress relationship of the Hoek-Brown criterion. The section was considered as the failure plane at critical failure state. The minor principal stress σ₃ acting on the rock mass at critical failure state could be obtained on the basis of the position of failure plane and the value of the shear and normal stress acting on it. The interval of minor principal stress could be found by searching the minor principal stress σ₃ of all elements in each material in the range of calculation model. The equivalent Mohr-Coulomb parameters of the generalized Hoek-Brown failure criterion over an artificial interval might be expressed by the least square method. A slope example was analyzed by the linearization method of Hoek-Brown criterion and the Hoek-Brown strength reduction method respectively. The results indicate that when the actual Hoek-Brown strength curve of each material is divided finer, the slope safety factor and slip surface, based on the equivalent Mohr-Coulomb model, are very close to those obtained from the Hoek-Brown strength reduction.

Key words:Hoek-Brown criterion; linearization; equivalent Mohr-Coulomb parameters; safety factor; interval of minor principal stress