弥散裂缝模型水力压裂数值方法的网格敏感性分析

Mesh Sensitivity Analysis of the Solution to Hydraulic Fracture Problems Based on a Smeared Crack Model

在非线性岩土/石力学问题中，网格质量是影响计算结果的一个重要因素.本文分析了弥散裂缝模型水力压裂数值求解方法中单元高宽比（AR）对计算结果的影响.材料的弹性部分采用线弹性和多孔弹性两种本构关系，屈服和破坏准则采用 Drucker -Prager（DP）和 Mohr -Coulomb（MC）两种模型.通过综合分析，无论采用何种本构关系，均存在网格敏感性问题.当裂缝的传播方向已知时，可以将单元的 AR 值控制在2.8~8.0之间，以避免弥散裂缝模型的网格敏感性问题，并得到稳定的结果.如果裂缝传播方向未知，建议使用线弹性本构关系和 DP 或者 MC 塑性模型，同时建议 AR 的取值为1.0.

Mesh quality is an important factor that affects the simulation results in nonlinear soil /rock mechanic problems.The effect of aspect ratio of element （AR）on calculation was analyzed in numerical solution of hydraulic fracture for the smeared crack model.Elasticity was measured by adopting the porous elastic （PE）and linear elastic （LE）constitutive models.Regarding to material yielding and failure,both the Drucker-Prager （DP）and Mohr-Coulomb （MC）models were considered.Based on a comprehensive analysis,it is concluded that no matter which constitutive model is adopted,there always exists mesh sensitivity.If the direction of fracture propagation is known,the AR should be between 2.8 and 8.0 to obtain stable results.If the direction is unknown,it is recommended that the LE constitutive model as well as the MC /DP plasticity model should be used together with the AR equal to 1.0.