CAJ | 학술논문

石油开采和非常规天然气开采等领域经常遇到页岩、砂岩等沉积岩，这类岩石材料往往具有正交各向异性特征。采用扩展有限元方法研究了正交各向异性岩体裂纹扩展问题，并基于Matlab平台编写了数值计算程序Betaxfem2D。将由复变函数法得到的裂纹尖端渐进位移场作为裂尖位移增强函数，用相互作用积分法计算混合模式应力强度因子，采用修改后的最大周向拉应力扩展准则确定裂纹扩展方向。与传统有限元方法的对比表明，扩展有限元方法达到相同计算精度需要的自由度少，节省计算机时。分别采用扩展有限元程序和传统有限元程序模拟了岩石试件4点弯曲试验，二者所得结果一致。数值试验表明：随着正交材料坐标系与空间坐标系夹角α的增大，裂纹扩展方向角?按照周期为?的近似正弦函数的规律变化；保持剪切模量和泊松比不变时，正弦函数的值域随着弹性模量比值E1/E2的减小而缩小，但相位基本保持不变；研究沉积岩断裂力学问题时，岩石的正交各向异性特征不可忽略。
석유개채화비상규천연기개채등영역경상우도혈암、사암등침적암，저류암석재료왕왕구유정교각향이성특정。채용확전유한원방법연구료정교각향이성암체렬문확전문제，병기우Matlab평태편사료수치계산정서Betaxfem2D。장유복변함수법득도적렬문첨단점진위이장작위렬첨위이증강함수，용상호작용적분법계산혼합모식응력강도인자，채용수개후적최대주향랍응력확전준칙학정렬문확전방향。여전통유한원방법적대비표명，확전유한원방법체도상동계산정도수요적자유도소，절성계산궤시。분별채용확전유한원정서화전통유한원정서모의료암석시건4점만곡시험，이자소득결과일치。수치시험표명：수착정교재료좌표계여공간좌표계협각α적증대，렬문확전방향각?안조주기위?적근사정현함수적규률변화；보지전절모량화박송비불변시，정현함수적치역수착탄성모량비치E1/E2적감소이축소，단상위기본보지불변；연구침적암단렬역학문제시，암석적정교각향이성특정불가홀략。
Sedimentary rocks such as shale and sandstone are very common in the fields of oil and unconventional gas drilling;and they are often characterized by orthotropy. The extended finite element method is used for crack propagation analysis of orthotropic rock mass and a Matlab program Betaxfem2D has been developed. Asymptotic crack tip displacement fields deduced by function of complex variable method are adopted as the crack tip displacement enrichment function;and mixed mode stress intensity factors are calculated by the interaction integral (M-integral) method. Besides, a modified maximum circumferential tensile stress criterion is adopted to determine crack propagation direction. Compared with conventional finite element method (FEM), the results show that the extended finite element method needs less DOFs and less computer resources to achieve the same calculation accuracy. The extended finite element method program developed by this paper and the conventional FEM program are used to simulate the 4-point bending test of rock sample, and both of them show the same results. Numerical experiments show that crack propagation direction angle ?varies according to an approximate sine function with a period of π with the increase of α, i.e. the angle between the orthotropic material coordinate and the space coordinate. Besides, when shear modulus and Poisson ratio remain constant;the range of the sine function shrinks with the decrease of the ratio of the elasticity moduli E1/E2, but the phase basically remains unchanged. So, the orthotropy of rock cannot be neglected when dealing with the fracture mechanics problems of sedimentary rock.