基于应变能密度理论的岩石破裂数值模拟方法研究

Study of numerical simulation method of rock fracture based on strain energy density theory

采用双线性应变软化本构模型结合能量耗散原理建立了损伤本构方程,并通过应变能密度理论建立了细观单元岩石破坏的能量判别准则。当某一单元所存储的应变能超过某固定值时,单元进入损伤状态,同时单元的损伤程度随着能量耗散的增加而增加,损伤单元的材料属性也随之改变,直到变为具有一定残余强度的单元。随着荷载增加,单元损伤的程度变大,当单元储存的应变能超过所建立的能量判别准则时,定义单元破坏,随着破坏单元的数目不断增多,破坏单元相互连通形成宏观裂纹,实现了利用线性计算完成非线性计算的过程,避免了数值计算在单元断裂时的奇异性,模拟了岩石的峰后破裂行为。对上述算法利用FLAC中的FISH语言开发了岩石破裂化计算程序,并将该程序成功应用于巴西劈裂和中间裂隙拉伸试验的破裂模拟过程中,其模拟结果与相应的理论和试验结果吻合较好,说明该方法对于模拟岩石破裂过程的正确性和可行性。

For the nonlinear fracture phenomena of rock,many numerical methods are carried out for study,but the numerical simulation methods for cracked rock are still being studied.Therefore,this paper combines the bilinear strain softening constitutive model with energy dissipation principle to establish damage constitutive equations;and through the strain energy density theory,energy failure criterion of mesoscopic element is established.When the strain energy of an element stored exceeds a fixed value,the element comes into damage situation and the damage degree increases with the increasing of energy dissipation.Simultaneously,the material properties of the damaged element change until it becomes the element with residual strength.As load increases,the element＇s damage degree increases.When the strain energy of the element stored exceeds the established value of the energy criterion,the element gets into fracture.With the increasing of fractured elements,macro-crack generates.This method implements linear calculation instead of the process of nonlinear computation,avoids the singularity of the numerical calculation in element fracture,and simulates the post-peak fracture behaviour of rock.The algorithm can be used to develop a rock fracture process computer program by the FISH language in the fast Lagrangian analysis of continual（FLAC）.This program is successfully applied to the simulation of Brazilian splitting and tensile test with cracks.The simulation results agree well with the experimental results.It indicates that the simulation method of rock failure process is correct and feasible.