岩石直接拉伸破坏过程及其分形特征的三维数值模拟研究

THREE-DIMENSIONAL NUMERICAL STUDY OF DIRECT TENSILE FRACTURE OF ROCK AND ASSOCIATED FRACTAL

通过建立带有残余强度的弹脆性拉伸损伤细观力学模型,运用并行有限元计算手段,模拟不同均匀程度的岩石试样在直接拉伸应力作用下的破坏演化过程,得到拉伸断裂位移–应力全过程曲线,并进行理论和试验对比分析验证。通过分析非均匀性对拉伸过程中非线性力学行为及断裂破坏形态,最后讨论了拉伸断裂破坏的分形特征。数值试验结果表明,非均匀程度对岩石直接拉伸破坏过程中的非线性行为有很重要的影响。岩石细观非均匀程度越高,宏观表现出的直接拉伸强度和初始弹性模量越高,破坏的脆性程度越强,但是残余变形能力和残余强度越低,断口表现出更为光滑的形态。三维空间的破坏分形分析表明,分形维数随着拉伸的进行而逐渐增加,当岩石完全拉伸断裂之后分形维数增加到一个恒定的最大值,而分形维数的变化情况同样反映了岩石的非均匀程度和脆性拉伸破坏程度。

A numerical mode is developed to simulate the completely failure process of rock subjected to direct tension with the aid of the parallel computing.The mechanical properties follow a certain distribution function,including elastic modulus,Poisson ratio and peak tensile strength.When the maximum tensile stress in the element meets its tensile strength,the element loses its bearing capacity and the elastic modulus will be reduced to a small value.Then the numerical model is proved to be efficient compared with the theoretical model,experimental results and other numerical models.Five specimens with different heterogeneities at meso-scopic level are undertaken direct tension test.The complete loading-displacement curves as well as the nonlinear mechanical behaviors are obtained.Numerical tests show that the rock specimens with higher homogeneities at meso-scopic level have the higher tensile strength,the higher initial elastic modulus at macroscopic level and show a more brittle failure and a lower residual strength.The surfaces of the fracture are rougher in the more heterogeneous rock specimens.The results of the fractal of the distribution of the failure elements（AE events） show that fractal dimensions increase with the increase of the tensile stress and will arrive to a certain value when the specimens are fractured totally.The fractal of the failure elements distribution represents the heterogeneity and the brittleness of different rocks.