Mesh sensitivity analysis of the solution to hydraulic fracture problems based on a smeared crack model

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.