基于相场法的花岗岩弹塑性损伤模型及其细观力学行为研究

Study on the mesoscopic fracture behaviors of granite based on the elastoplastic phase-field model

花岗岩的细观非均质性对其损伤破坏行为有着重要影响。基于热力学原理和力与能量平衡方程,在经典相场模型框架内引入适合岩石类材料的非关联塑性本构关系,构建弹塑性相场模型,通过与解析解和试验数据对比,验证了其正确性和可靠性。在此基础上,采用数字图像处理建立符合真实细观结构的花岗岩非均质数值模型,并对其三轴压缩试验进行数值模拟,在细观尺度预测其宏观力学行为以及分析岩石裂纹扩展机制。研究结果表明:通过与试验数据和传统弹脆性相场模拟结果对比,建立的基于花岗岩真实细观结构的弹塑性相场模型可以很好地捕捉其宏观非线性力学行为;花岗岩的内部裂纹的起裂、扩展以及局部应力场的分布会受到矿物颗粒的力学性质、几何形状及分布的影响。该研究方法为今后研究岩石多尺度损伤破坏问题提供一种简单有效的途径,对评价地下工程中围岩力学性质有着重要的工程实践意义。

The mesoscopic heterogeneity of granite has an important influence on its damage and failure behavior.In this paper,an elastoplastic phase-field model is established based on the thermodynamic principle as well as the balance equations of forces and energy,and the non-associative plastic constitutive relationship suitable for rock-like materials within the framework of the classical phase field model is introduced.By comparing with the analytical solution and experimental data,the accuracy and reliability of the elastoplastic phase-field model are verified.Furthermore,a heterogeneous numerical model reflecting the real mesostructure of granite is established by digital image processing.The triaxial compression test of granite is numerically simulated,and the macroscopic mechanical behavior and the crack propagation mechanism of rock is analyzed at the mesoscale.The results show that compared with the experimental data and the traditional elastic-brittle phase-field methods,the elastoplastic phase-field model based on the real mesostructure of granite is capable of well capturing its macroscopic nonlinear mechanical behavior.The initiation and propagation of internal cracks in granite and the distribution of local stress field are affected by the mechanical properties,geometric shape and distribution of mineral particles.The research method of this paper provides a simple and effective way to study the multi-scale damage and failure of rock in the future,and it has important engineering practical significance for evaluating the mechanical properties of surrounding rock in underground engineering.