| 正交各向异性岩体裂纹扩展的扩展有限元方法研究 |
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| 引用本文： | 师 访,高 峰,杨玉贵.正交各向异性岩体裂纹扩展的扩展有限元方法研究[J].岩土力学,2014,35(4):1203-1210. |
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| 作者姓名： | 师 访 高 峰 杨玉贵 |
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| 作者单位： | 1. 中国矿业大学 深部岩土力学与地下工程国家重点实验室，江苏 徐州 221116；2. 中国矿业大学 力学与建筑工程学院，江苏 徐州 221116 |
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| 基金项目： | 国家重点基础研究发展计划(973)项目(No. 2011CB201205)；江苏省普通高校研究生科研创新计划基金(No. CXZZ13_0922)。 |
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| 摘 要： | 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。
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| 关 键 词： | 扩展有限元法 裂纹 正交各向异性 断裂力学 |
| 收稿时间： | 2013-09-10 |
Application of extended finite element method to study crack propagation problems of orthotropic rock mass |
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| SHI Fang,GAO Feng,YANG Yu-gui.Application of extended finite element method to study crack propagation problems of orthotropic rock mass[J].Rock and Soil Mechanics,2014,35(4):1203-1210. |
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| Authors: | SHI Fang GAO Feng YANG Yu-gui |
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| Institution: | 1. State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China; 2. School of Mechanics & Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China |
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| Abstract: | 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. |
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| Keywords: | extended finite element method crack orthotropy mechanics of fracture |
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