【作者】 徐小敏；

【导师】 周小平； 张永兴；

【作者基本信息】 重庆大学 ， 岩土工程， 2007， 硕士

【摘要】 由细观力学与宏观唯象学理论相结合所建立的裂隙岩体损伤本构模型,既能反映材料内部的微观结构,又能说明其宏观力学性能。本文拟在细观力学Gibbs自由能函数的基础上,结合断裂力学、经典塑性力学和连续介质的热力学等,建立了弹性损伤本构模型和弹塑性损伤耦合本构模型。主要研究工作为:①通过对栖霞山矿地质构造的研究,根据赤平极射投影原理,判断了X断裂,确定了地应力的方位和倾角。并据此在-625 m中段主巷道内进行取样工作,根据凯泽效应,进行岩石的声发射实验,得到了原岩地应力。另外,室内常规实验为后续的计算分析提供了所需的岩石力学参数。②从Gibbs自由能函数出发,通过Legendre变换得到了应变空间表示的Helmholtz自由能函数,进而根据正交性原理,得到了三维弹性损伤本构方程。同时,运用断裂准则,分别确定了拉、压应力作用下平行分布裂纹和均匀分布裂纹的弹性损伤演化规律。③将岩石峰前的应力-应变关系分为三个阶段分别考虑:1)在弹性初始损伤阶段,采用第三章的弹性损伤本构方程;2)在弹塑性初始损伤阶段,结合经典塑性力学和连续介质的热力学,得到了考虑损伤的弹塑性应变能和塑性乘子,并考虑等温过程,引入塑性流动法则,得到了弹塑性初始损伤本构方程。同时,根据裂纹的弯折扩展确定了损伤门槛值。3)在弹塑性损伤耦合阶段,将总的应力率和应变率分解为弹性、塑性和损伤三部分,引入塑性流动法则和共轭力表示的损伤演化方程,根据一致性条件,求得塑性乘子和损伤乘子,从而得到三维弹塑性损伤耦合阶段的非线性增量本构方程。④退化三维模型为平变应变状态下的弹塑性损伤耦合本构模型,分别进行了单轴压缩和双轴压缩问题的验证,理论预测曲线与实验应力-应变曲线吻合较好。运用ANSYS 9.0,分别计算分析了在理想弹塑性模型和本文弹塑性损伤耦合本构模型下-625 m中段主巷道断面的的平面应变问题。结果表明,损伤模型较理想弹塑性模型更符合实际情况。更多还原

【Abstract】 The damage constitutive model, which is established through the combination of micromechanics and macroscopical phenomenology, can both reflect the micro-structures of the material, and explain its macroscopic mechanical behaviors. Based on micromechanical Gibbs free energy function, as well as fracture mechanics, classic plastic mechanics and continuum thermodynamics, an elastic damage constitutive model and an elastic-plastic constitutive model coupled with damage are obtained. The specific work including:①From research on geological structure of QiXiaShan mine by using equatorial horizon projection principle, the dips of ground stress are determined through the judgment of the X failure. Thus, specimen was picked up in the main roadway in 625 meters depth below ground level according to the determination. And the original ground stress was tested through Kaiser acoustic emissional experiments. In addition, indoor conventional experiments provided necessary parameters to numerical simulations.②Helmholtz free energy function in the strain space is deduced through Legendre transformation from Gibbs energy function. Three dimensional elastic damage constitutive equations are acquired based upon orthogonality principle. Meanwhile, the elastic damage evolution laws are given for both parallel and uniformly distributed microcracks under both tension and compression respectively by using fracture criterion.③The pre-peak stress-strain relationship is divided into three stages: Firstly, the elastic damage constitutive equations given in chapter three are adopted for elastic stage only with initial damage. Secondly, by taking classic plastic mechanics and continuum thermodynamics into account, the elastic-plastic strain energy including initial damage and plastic multiplicator are derived for elastic-plastic stage. Then, the elastic-plastic constitutive equations considering initial damage are gained by importing plastic flow rule and isothermal assumption. Threshold value is determined according to the kink expanding of microcracks. Lastly, the total stress rate and strain rate are resolved into three parts as elastic, plastic and damage ones. According to consistent condition, plastic and damage multiplicators are calculated by introducing plastic flow rule and damage evolution equation denoted by conjugated force. The three dimensional nonlinear incremental constitutive equations for the stage of elastic-plastic coupled with damage are developed.④The elastic-plastic constitutive model coupled with damage under plane strain condition is obtained. Identifications, both on uniaxial and bioaxial compressions, have shown good consistency with the experimental curves of stress-strain. The main roadway in 625 meters depth below ground level under plane strain condition is studied through numerical simulation using ANSYS 9.0. Comparison is drawn between the elastic-plastic constitutive model coupled with damage and the ideal elastic-plastic one, and the former is more accord with actual situation.更多还原