无限域横观各向同性岩体介质中折线裂纹边界元方法

A boundary element method for kinked crack in transversely isotropic rock material of infinite domain

岩体材料的各向异性导致其中的光滑裂纹在扩展后会变为折线裂纹。对于折线裂纹,其折线处裂纹面外法线方向不惟一,不能用连续单元离散。为此,在光滑裂纹问题方法的基础上,引入4种新的不连续单元来离散折线处裂纹面,建立了适用于折线裂纹问题的对偶边界元方法,该方法基于横观各向同性基本解。算例验证表明,该方法具有较好的精度。最后用该方法分析了横观各向同性岩体中的折线裂纹,得到了该类裂纹的应力强度因子。当裂纹面上作用法向均布力,横观各向同性岩体介质中的矩形光滑裂纹发生弯折时,折线两侧的裂纹面在张开时存在抑制效应,从而导致折线裂纹裂尖应力强度因子小于原光滑裂纹。同时还发现,随裂纹面的逐渐弯折,其裂纹面对各向同性面的倾角发生变化,因此,其裂尖断裂特性还受到岩体各向异性的影响。

In rock material, the smooth crack mostly becomes kinked crack during its growth due to the anisotropy of rock material. For the kinked crack, the outer normal direction of the crack surface at the kinked line is not unique, so the continuous element is not feasible to discrete the crack surface near the kinked line. Therefore four types of new discontinuous element are employed for the kinked crack. A dual boundary element method（DBEM） based on the method suited for the smooth crack problem is proposed to deal with the kinked crack problem. The numerical verification shows that the results calculated with the present method are in very good agreement with those with the primary method for the smooth crack problem. Furthermore, the proposed method is used to analyze the kinked crack in transversely isotropic rock material of infinite domain. The stress intensity factor（SIF） is obtained. The rectangular smooth crack in transversely isotropic rock material bends. The crack opening of both crack surfaces at two sides of the kinked line has mutual inhibiting effect due to the crack surface subjected to uniformly-distributed normal load. The dip angle between the crack surface and the isotropy plane changes as the crack surface bends gradually. It is found that the fracture behavior of the kinked crack is also affected by the anisotropy of the rock material.