Hoek-Brown准则的多项式近似解法

Approximate Solution of Hoek-Brown Criterion Using Polynomial Equation

Hoek-Brown岩体破坏准则已在全世界范围内的岩土工程中广泛应用,它综合考虑了岩体结构、岩块强度、应力状态等多方面的影响。基于通用的Hoek-Brown准则,引入Lambe变量和既时摩擦角,将其转化为Mohr-Coulomb破坏准则的形式,得到用Mohr-Coulomb破坏准则形式表示的隐式函数Hoek-Brown准则。为求得隐式函数的近似解,采用三次和四次多项式进行拟合,得到了n为0.5及0.65时的近似解以及Hoek-Brown破坏应力圆的Mohr包络线,并给出了各不同多项式拟合公式的误差分布。经分析对比,考虑到精度和工程的适用性,最终选用四次多项式进行拟合。最后结合一嵌岩桩嵌岩段极限摩阻力工程实例,并给出了该算法求解的具体过程。

The Hoek-Brown failure criterion for rock masses is widely accepted and has been applied in a large number of projects around the world, in which it has taken the rock structure, rock strength, stress status and so on into account. Based on the general Hoek-Brown criterion, its Mohr-Coulomb criterion form was obtained by introdu- cing Lambe parameters and instantaneous friction angle. Then the implicit equation of Hoek-Brown using Mohr-Cou- lomb criterion was given. The approximate solutions for the implicit equation were solved using cube and quartic poly- nomial equations, when n is O. 5 and O. 65 respectively and the Mohr failure envelope for Hoek-Brown failure circle has been obtained. The error distribution for different solution was shown. Considering the accuracy and engineering applicability, the quartic polynomial equation was selected. Finally, combined with a rock-socketed pile, the calcula- tion process was given.