岩石损伤统计本构模型研究

Study on the Rock Statistical Damage Constitutive Model

摘要: 从岩石微裂隙等缺陷及随机分布的特点出发，建立岩石损伤统计本构模型，其核心在于科学地选取反映损伤程度的岩石微元强度度量方法、岩石内部损伤随机分布的形式以及模型参数。首先基于Lemaitre应变等价性假说建立了三维应力作用下岩石损伤本构方程，讨论了常用的M-C等3个岩石强度准则和Weibull分布等5个岩石微元强度概率模型。然后基于H-B强度准则和幂函数分布建立了岩石的损伤统计本构模型，并给出了相关参数的确定方法，借助引用的实例验证了本文所建模型和参数确定方法的有效性，最后建议了下一步研究的重点方向。

Abstract: To establish a rock statistical damage constitutive model taking the defects such as the rock mi-cro-cracks and the characteristics of their random distribution into account, the vital steps are to select a method scientifically to measure the rock micro-strength, which is capable of reflecting its damage conditions; as well as the pattern of randomly distributed damage in rock and the deter-mination of the model parameters. Firstly, a damage constitutive equation for rock under three dimensional stress conditions is established, in terms of the Lemaitre’s hypothesis of strain equi-valence; then discussions are presented in detail to address the frequently employed rock strength criterions such as M-C strength criterion and the rock micro-element strength probability models such as Weibull probability distribution. Based on the H-B criteria and the power function distribution, a statistical damage constitutive model for rock is proposed, and the method of de-termination for the relative model parameters is suggested; Furthermore, a case study is intro-duced to testify the validity of the constitutive model and the method to obtain the parameters which are proposed in this paper; at last, suggestions on the further research and its method are addressed.