考虑剪胀及软化的洞室围岩弹塑性分析的统一解

基于俞茂宏统一强度理论，考虑某些材料屈服后的强度衰减(塑性软化)和体积膨胀的特点，用弹性-塑性软化-塑性残余三线性应力-应变模型推导出了洞室围岩塑性残余区半径、塑性软化区半径、洞周边位移、围岩内任一点应力及围岩压力的解析表达式，给出了洞室围岩所处应力状态的判别式。得出的解答具有广泛意义，著名的Kastner公式、Airey公式和现有的一些结果为其特例。通过实例分析了剪胀、软化及不同强度模型对结果的影响。该结果在洞室围岩稳定性分析和加固等方面具有一定的工程实用价值。

Unified Elastoplastic Solution for Surrounding Rocks of Openings with Consideration of Material Dilatancy and Softening

Based on the unified strength theory proposed by Yu Maohong and by considering the behaviors of strength reduction and volume dilatancy for some materials after yielding,that is plastic-softening,the analytical equations for calculating the radius of plastoesidual and plastic-softening zones as well as the displacements around openings are proposed according to the elastic-softening-residual plastic triple linear stress-strain model. At the same time,the equations of stress state for surrounding rocks are also given in the general form. The famous Kastner equation,the Airey equation and the other existing solutions may be taken as special cases of the proposed solution. In the mean time,the influences of shearing dilatancy,softening and different strength models on the results are also analyzed. The results of this paper have an important value in stability analysis of engineering practice and in reinforcement of surrounding rocks.