岩体脆性破裂失稳临界应力特征重正化群研究  

Study on the Critical Stress State of Brittle Failure of Rock Based on Renormalization Group Theory

作　　者：薛雷[1] 孙强[2] 王媛媛[3] 王四巍[4] 李国梁[1] 泮晓华[1] 

机构地区：[1]中国科学院地质与地球物理研究所,中国科学院工程地质力学重点实验室,北京100029 [2]中国矿业大学资源与地球科学学院,江苏徐州221116 [3]中国科学院遥感与数字地球研究所,北京100094 [4]华北水利水电大学,岩土工程与水工结构研究院,河南郑州450045

出　　处：《应用基础与工程科学学报》2013年第4期710-724,共15页Journal of Basic Science and Engineering

基　　金：中国科学院工程地质力学重点实验室开放基金(KLEG201106);中国博士后科学基金资助项目(2012M520376);国家自然科学基金资助项目(41302233;41030750)

摘　　要：岩体通常是由节理和岩桥组成,大量岩体工程破坏和失稳多是由于系统中较硬介质突然脆性破坏所致.把岩体脆性破坏过程看作一个逾渗相变过程,假定岩体细观微元体强度服从Weibull分布,基于系统在逾渗阈值处有尺度不变的性质,利用重正化群方法在求得一维和二维条件下系统逾渗阈值的基础上,首次研究了三维重正化群条件下岩体脆性破坏在逾渗阈值附近的临界特性,为相关问题三维重正化群研究提供了解析解参考,并揭示了如下规律:(1)维数一定时,逾渗阈值p*随着形状参数m的增大呈减小趋势;当形状参数m一定且m较小时,逾渗阈值p*随着维数增加而降低;当形状参数m一定且m较大时,逾渗阈值p*随着维数增加呈逐渐增大趋势.(2)形状参数m一定时,关联临界指数ν随着维数增加呈降低趋势;维数为1时,关联临界指数ν随着形状参数m的增大呈衰减趋势,而对于二维、三维的情况,其随着形状参数m的增大基本呈增大趋势.(3)对于一维、二维情况而言,体积膨胀点与峰值强度点所对应的应力之比σcd/σf随着形状参数m的增大呈减小趋势,三维则正好相反,σcd/σf随着形状参数m的增大呈增大趋势.特别需要指出的是,在维数、形状参数m一定时,σcd/σf为定值,说明对于特定的岩石破裂过程,其膨胀点处应力与峰值应力之间存在某种联系,可能遵循一定的规律,这对于宏观岩石破裂现象(诸如边坡失稳、岩爆、地震等)的预测具有一定的启示意义.Rock mass usually is composed of joints and rock bridges, many failure cases of rock mass engineering were induced by the sudden brittle failure of rock bridges. In this paper, the percolation model of brittle failure was established firstly and supposing the strength distribution of rock obeyed weibull function, then the percolation thresholds of one-dimension and two- dimension models were computed by the renormalization group methods. Furthermore, the critical state features of the three-dimension percolation model were studied for the first time and the results indicated ： （ 1 ） with the dimension of renormalization group fixed, the percolation threshold p＂ decreases when the shape parameter m increases;with m fixed and it is smaller,p ＊ decreases when the dimension of renormalization group increases;with m fixed and it is larger, p ＊ increases when the dimension of renormalization group increases; （2） with m fixed, the correlative length index v decreases with the increasing dimension of renormalization group. For one-dimension renormalization group, correlative length index v decreases with the increasing re;For two-dimension and three-dimension renormalization group, the index v increases with the increasing m; （ 3 ） For one-dimension and two-dimension renormalization group, the stress ratio between volume dilatant point and peak point, σcd/σf, decreases with the increasing m; however, for three-dimension renormalization group, σcd/σf increases with the increasing m. Especially speaking, with the dimension of renormalization group and m fixed, σcd/σf is a definite value,which means that there exists a certain law between the stress at the expansion point and peak stress in the process of rock failure. Maybe it has certain significance for the forecast of the macro rock rupture phenomena（ such as slope instability, rock burst, earthquake, etc. ）.

关 键 词：脆性破坏 WEIBULL分布 重正化群 应力转移机制 

分 类 号：TU452[建筑科学—岩土工程]