基于三轴压缩试验的岩石统计损伤本构模型研究

发布时间：2018-04-02 01:02

本文选题：岩石　切入点：统计损伤本构模型　出处：《清华大学》2013年硕士论文

【摘要】：岩石等准脆性材料的本构关系一直是工程界十分关注的问题。本文结合统计强度理论和连续损伤理论建立了一种岩石统计损伤本构模型。与常规的损伤本构方程不同，本文分别基于统计强度理论和连续损伤理论导出了统计损伤演化方程和连续损伤演化方程，并在两种损伤演化方程中消去损伤变量后结合成为统计损伤本构方程，本构方程本身并不含有损伤变量。在统计损伤演化方程的建立过程中，需要引入微元强度满足的概率分布，以及微元应力水平的表达式。对于微元强度分布，本文引入了抗力常用的对数正态分布和Weibull分布。对于微元应力表达式，文本借鉴了岩土材料常用的M-C准则和D-P准则中的应力组合形式。在连续损伤演化方程的建立过程中，本文引入了线弹性Hooke定律。基于岩石三轴压缩试验，考虑到试验中实测的应力值和应变值并非真实值，本文建议将统计损伤本构方程中的真实应力、真实应变进行修正，建立了基于实测应力、实测应变的岩石统计损伤本构方程。对于单轴压缩情况，统计损伤本构方程是显式的，而对于三轴压缩情况，统计损伤本构方程是隐式的。本文建立的岩石统计损伤本构方程中含有两个统计参数，需要与岩石单轴、三轴压缩试验曲线匹配后拟合得出。本文主要介绍了统计参数确定的线性回归法和峰值点法，并通过优缺点对比后建议使用峰值点法。通过对建立的岩石统计损伤本构模型的数学意义和物理意义及其适用性进行讨论分析，可知该本构方程能较好地描述岩石材料的非线性力学行为，也能逼近材料的线弹性本构关系。对于岩石单轴压缩试验曲线的压密阶段，本文给出了岩石初始损伤的估计方法。通过基于不同分布类型、不同强度准则的统计损伤本构方程理论曲线与若干岩石单轴、三轴压缩试验曲线的对比分析，验证了本文建立的岩石统计损伤本构模型的合理性，，肯定了本文建议的统计参数确定方法以及本构方程的修正方法。比对结果显示，微元强度分布类型对统计损伤本构方程理论曲线的形态影响不大。对于单轴压缩或低围压三轴压缩情况，强度准则对统计损伤本构方程理论曲线的形态影响也不大。而对于高围压三轴压缩情况，D-P准则的表现要优于M-C准则。
[Abstract]:The constitutive relation of quasi brittle materials has been the focus problem in engineering field. Based on the statistical strength theory and continuum damage theory to establish a statistical damage constitutive model of rock. With the conventional damage constitutive equation, based on the statistical strength theory and continuum damage theory of damage evolution equation and continuous the damage evolution equation of statistics, and in two in the damage evolution equation of damage variable elimination combined with a statistical damage constitutive equation, the constitutive equation itself does not contain the damage variable.
In the process of establishing a statistical damage evolution equation, the probability distribution of the micro unit strength meet the need to introduce, and differential expression of stress level. The micro unit strength distribution, this paper introduces the commonly used resistance lognormal distribution and Weibull distribution. The differential stress expression, the text from the stress of combination of M-C and D-P criteria the geotechnical materials in common. In the continuous process of establishing damage evolution equation, this paper introduces the linear elastic Hooke law.
Three axial compression test of rock based on considering the measured value of stress and strain values are not real values, this thesis suggests the damage constitutive equation of the true stress true strain statistics, revised, established based on the measured stress, the damage constitutive equation of rock strain. For the uniaxial compression and the statistical damage constitutive equation is explicit, and for the three axial compression, the damage constitutive equation is implicit in the statistics.
Damage constitutive equation containing two statistical parameters of rock is established in this paper, with uniaxial and triaxial compression tests of the three curve fitting after matching. This paper mainly introduces the method of linear regression and peak point method to determine statistical parameters, and through comparing the advantages and disadvantages after the recommended peak point method.
The mathematical and physical meaning of damage constitutive model was analyzed and its applicability to rock establishment, the constitutive equation can describe the nonlinear mechanical behavior of rock material, also can approximate linear elastic material constitutive relationship for the uniaxial compression test curve of the compression phase, is given in this paper the estimation of initial damage of rock. Through different distribution types based on damage constitutive equation of the theoretical curve and some uniaxial strength criterion of different statistics, comparison and analysis of three axis compression test curve, verify the established rock damage constitutive model of rationality, affirmed the method to determine the statistical parameters proposed in this paper and the correction method of constitutive equations. Comparison results show that the intensity distribution of element types had little effect on morphology statistical damage constitutive equation theory for single axis curve. Compression or low confining pressure three axis compression, strength criterion has little effect on the shape of statistical damage constitutive equation, while for high confining pressure three axis compression, the performance of D-P criterion is better than M-C criterion.

【学位授予单位】：清华大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TU45

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