A Boundary Element Method For Kinked Crack In Transversely Isotropic Rock Material Of Infinite Domain

Abstract

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.

巖體材料的各向異性導致其中的光滑裂紋在擴展后會變為折線裂紋。對于折線裂紋,其折線處裂紋面外法線方向不惟一,不能用連續單元離散。為此,在光滑裂紋問題方法的基礎上,引入4種新的不連續單元來離散折線處裂紋面,建立了適用于折線裂紋問題的對偶邊界元方法,該方法基于橫觀各向同性基本解。算例驗證表明,該方法具有較好的精度。最后用該方法分析了橫觀各向同性巖體中的折線裂紋,得到了該類裂紋的應力強度因子。當裂紋面上作用法向均布力,橫觀各向同性巖體介質中的矩形光滑裂紋發生彎折時,折線兩側的裂紋面在張開時存在抑制效應,從而導致折線裂紋裂尖應力強度因子小于原光滑裂紋。同時還發現,隨裂紋面的逐漸彎折,其裂紋面對各向同性面的傾角發生變化,因此,其裂尖斷裂特性還受到巖體各向異性的影響。