基于Weibull分布的高温高围压岩石统计损伤本构模型  

Statistical Damage Constitutive Model for Rocks Under High Temperature and High Confining Pressure Environments Based on the Weibull Distribution

作　　者：郑栋 戚承志 卢春生 班力壬 王东岳 候宇航 Zheng Dong;Qi Chengzhi;Lu Chunsheng;Ban Liren;Wang Dongyue;Hou Yuhang(School of Civil and Transportation Engineering,Beijing University of Civil Engineering and Architecture,Beijing 100044,China;School of Civil and Mechanical Engineering,Curtin University,Perth 6845,Australia)

机构地区：[1]北京建筑大学土木与交通工程学院,北京100044 [2]澳大利亚科廷大学土木与机械工程学院,西澳珀斯6845

出　　处：《市政技术》2024年第4期45-53,共9页Journal of Municipal Technology

基　　金：国家自然科学基金面上项目(12172036;517744018);长江学者和创新团队发展计划项目(PCSIRT;IRT_17R06)。

摘　　要：深部岩石通常处于高温及高围压环境中,深入研究深部岩石的本构关系对于深地矿产资源的开采、地热的高效利用以及岩体的稳定性分析等具有重要的理论和现实意义。为研究岩石在不同温度和围压作用下的静态三轴压缩破坏全过程本构关系,基于宏观唯象损伤力学的概念,从岩石的弹性模量随着温度变化的角度出发,得到了岩石在温度作用下的损伤表达式;又基于Weibull分布和修正的Mohr-Coulomb强度准则,将岩石细观均匀化,并结合统计损伤理论,得到了岩石在轴向压力作用下的统计损伤表达式;然后根据推广的应变等价性原理将两部分损伤耦合,得到了岩石在高温及轴压力作用下的岩石耦合损伤表达式。将所得的耦合损伤表达式结合考虑岩石残余应力的Lemaitre应变等价性假说以及有效应力原理,同时考虑岩石内部裂纹起裂阈值的影响,将本构模型分为阈值应变之前和阈值应变之后两部分,得到了一种分段函数形式的可反映高温及高围压影响的岩石统计损伤本构模型。为验证模型的适用性和准确性,分别将岩石在温度为25、200、400、600、800、1000℃和围压为0、10、20、30、40 MPa情况下的模型本构曲线与试验本构曲线进行了对比验证,对比结果较好,可以反映出岩石存在临界温度。在围压一定时,随着温度的升高,岩石的强度先增大后减小;在温度一定时,随着围压的升高,岩石的延性逐渐增强。Deep-seated rocks are typically found under high temperature and high confining pressure conditions.It has strong theoretical and practical significance to intensive research the constitutive relationship of deep-seated rocks for the exploration of deep-earth mineral resources,efficient utilization of geothermal energy,and stability analysis of rock masses.In order to investigate the constitutive relationship of rocks during the entire process of static triaxial compression under different temperature and confining pressure,based on the concept of macroscopic phenomenological damage mechanics,from the aspect of rock elastic modulus changing with temperature,an expression of rock damage under temperature effects was obtained.Furthermore,based on the Weibull distribution and modified Mohr-Coulomb strength criterion,rock mesoscopic was homogenized.Combined with the statistical damage theory,a statistical damage expression of rocks was obtained under axial pressure;Subsequently,based on the extended strain equivalence principle,the two parts of damage were coupled to yield a coupled damage expression of rocks under high temperature and axial pressure.Combined with the consideration of rock residual stress following Lemaitre's strain equivalence hypothesis and the principle of effective stress,this coupled damage expression was considered.At the same time,the influence of the threshold of crack initiation within rocks was taking into account.The constitutive model was divided into two parts of before and after the threshold strain.This resulted in a segmented function form of a statistical damage constitutive model for rocks that reflects the impact of high temperature and high confining pressure.To validate the applicability and accuracy of the model,the model's constitutive curves for rocks were compared with experimental constitutive curves under different conditions of temperature(25,200,400,600,800,1000℃)and confining pressure(0,10,20,30,40 MPa).The comparison results were favorable which indicated there is a c

关 键 词：统计损伤理论 岩石本构模型 WEIBULL分布 高围压 高温 阈值应变 

分 类 号：TU452[建筑科学—岩土工程] TD803[建筑科学—土工工程]