摘要
针对两向不等压巷道围岩塑性区的解析问题,使用应力构造法求解时,巷道围岩塑性区以外的弹性区应力被主观地认为与围岩弹性应力状态下的应力在形式上一致。这虽然明显不合理,但在侧压系数为1的某个邻域内,应力构造法的准确度较高;只是在该邻域以外,其仅能确保围岩水平(或竖向)轴上塑性区半径的精度,其余位置并不准确,甚至偏差很大。同时,以侧压系数为1的特例为基准,将依据近似隐式法得到的围岩塑性区半径与基于成熟轴对称平面应变理论的相应解析解进行对比,可以发现前者存在较大理论误差。为改进上述不足,以应力构造法为基础确定围岩水平(或竖向)轴上塑性区半径;再结合近似隐式法能够较好反映塑性区形态一般变化规律的优势,以近似隐式法为基础确定塑性区的形状;最后,依据相似原理,相对准确地给出了两向不等压巷道围岩塑性区的近似解析范围。将该理论应用于工程实例的分析计算,并以数值模拟结果为基准就各算法的准确性问题进行了对比分析,结果表明:上述算法不仅消除了近似隐式法在侧压系数为1时的理论误差;还克服了应力构造法无法反映塑性区一般形态变化规律的缺陷。该算法与数值模拟的结果比较接近,可代替数值模拟进行两向不等压巷道围岩塑性区的近似求解。
In order to obtain the solution of plastic zone in roadway surrounding rock under unequal compression in two directions,the stress of elastic zone beyond plastic zone in roadway surrounding rock is subjectively considered to be the formally same with that of elastic surrounding rock while stress constructing method is used,which is obviously unreasonable.The accuracy of stress constructing method is relatively high in a neighborhood of the lateral pressure coefficient 1,while outside the neighborhood,only the plastic zone radius on horizontal(or vertical) axis can be ensured,radii on the rest locations are not accurate,or even wildly inaccurate.Meanwhile,based on the special lateral pressure coefficients 1,the radius of surrounding rock plastic zone obtained by approximate implicit method has a big error deviation contrasted with the corresponding analytical solution of the mature axisymmetric plane strain theory.In order to improve the shortcomings above,the surrounding rock plastic zone of non-uniform stress field on horizontal(or vertical) axis is derived based on stress constructing method.Then the plastic zone shape is determined by approximate implicit method because the evolution law for general shape of circular roadway plastic zone can be well reflected by this method.Finally,the approximate radius of plastic zone in surrounding rock under unequal compression in two directions is relatively accurately presented by using the similar principles.On the basis of the application of the above theory to the analysis of an engineering example and the numerical simulation results,the accuracy of each algorithm is compared and analyzed.The results show that the proposed method above not only eliminates the theoretical error of the approximate implicit method for the lateral pressure coefficient 1,but also overcomes the defect of that stress constructing method can not reflect the evolution law for the general shape of circular roadway plastic zone.The solution is fairly close to the results calculated by the numerical simulation,which can be used for the approximation on the plastic zone in roadway surrounding rock under unequal compression in two directions instead of numerical simulation.
作者
董海龙
高全臣
张赵
陈汝博
刘娜
DONG Hailong;GAO Quanchen;ZHANG Zhao;CHEN Rubo;LIU Na(School of Mechanics&Civil Engineering,China University of Mining&Technology(Beijing),Beijing 100083,China)
出处
《煤炭学报》
EI
CAS
CSCD
北大核心
2019年第11期3360-3368,共9页
Journal of China Coal Society
基金
中央高校基本科研业务费专项基金资助项目(2010YL01)
关键词
两向不等压
围岩塑性区
应力构造法
近似隐式法
数值模拟
unequal compression in two directions
surrounding rock plastic zone
stress constructing method
approximate implicit method
numerical simulation
