线弹性半无限体中开挖引起围岩位移与参数关系的相似方法研究

摘要

Based on the derived general expression for the displacement of a point in a surrounding rock mass caused by excavating under the action of self-weight volume forces from similarity theory,by means of dimensional analysis,and comparing with the results of the numeral simulations,an empirical formula of parametric ratios expressed in geometric,physical and mechanical parameters is proposed,which shows the quantitative relationships between the displacement of a point in a surrounding rock mass caused by excavating in a linearly elastic semi-infinite body and any one of the parameters,including the specific weight of a rock material,the modulus of elasticity for the material,the size of a cross section of a tunnel and the distance from the earth surface to the center of the cross section.And the conditions under which the formula holds and its applications are discussed,and the methods for use it are given.A main conclusion says that,in the case that the geometric similarity law is not completely satisfied,under the given other conditions the displacement of a point in the rock mass surrounding a tunnel is proportional to the product of the distance from the center of cross section to the earth surface and the size of the cross section and is independent of the shape of the cross section.%根据用相似理论导出的、在自重体积力作用下开挖引起围岩位移的一般关系式，借助于量纲分析，并与数值模拟结果比较，给出了在线弹性半无限体中开挖引起围岩位移与岩石材料的单位体重、弹性模量及开挖几何条件的定量关系，并讨论了这种定量关系成立的条件及使用方法。所得到的一个重要结论是，在不完全满足几何相似律和所给定的其他条件下，巷道围岩中一点的位移与其横断面尺寸和几何中心（或形心）到地表的距离的乘积成正比。