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建立了求解自然裂纹和水力裂纹扩展的扩展有限元法,对裂纹附近区域的节点采用广义形函数,并采用线增函数消除混合单元,以提高裂纹附近的精度。引入水力劈裂的非耦合模型,即假设裂纹中的水压力为均布力;用砂浆法(线段-线段接触法)结合增广型拉格朗日乘子法处理受压裂纹段的接触条件。并通过算例分析了以下内容:计算了受压裂纹和裂纹面分布均布水压力的水力裂纹的应力强度因子,并与解析解进行了比较,结果表明,提出的方法具有很高的精度;模拟了水力裂纹对自然裂纹面的影响,并分析了自然裂纹面上的接触力和接触状态。
An extended finite element method for solving natural and hydraulic crack propagation was established. The generalized shape function was adopted for the nodes in the vicinity of the crack, and the mixed element was eliminated by linearly increasing function to improve the accuracy near the crack. The non-coupling model of hydraulic fracturing is introduced, that is, the water pressure in the crack is assumed to be uniform. The mortar method (line segment-line contact method) and the augmented Lagrange multiplier method are used to deal with the contact conditions . And an example is given to analyze the following contents: The stress intensity factor of hydraulic crack with uniform distribution of compressive crack and crack surface distribution is calculated and compared with analytical solution. The results show that the proposed method has high precision. The influence of hydraulic crack on natural crack surface is simulated, and the contact force and contact condition on natural crack surface are analyzed.