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地下洞室的开挖与支护是逐步的连续过程。对具有流变效应的粘弹性岩体,流变时效与施工效应发生耦合,变形与时间相关。针对深埋圆形洞室的施工,用半径时变函数模拟断面开挖过程。当岩体模拟为任一粘弹性材料时,将方程进行拉普拉斯变换求得位移通解,逆变换后代入边界条件确定待定函数,最终得到用洞周面力表达的围岩应力、位移统一解。区分开挖与支护时段,将半径时变函数、洞周面力不同表达式代入,利用支护后围岩与弹性支护接触条件建立关于支护力的Volterra积分方程。当岩石模拟为Boltzmann粘弹模型时,代入材料参数可求解积分方程得到支护力的确切表达,并进一步求得开挖过程及任意时刻支护后应力、位移分段解析表达式。表达式和算例分析表明:加支护后的径向位移增长呈指数形式变化且最终稳定于某一数值。最终洞型相同时,采用不同断面开挖速度且挖完立即支护时,开挖较快的情况位移变化较剧烈,而支护后最终稳定位移较小;但是,相应支护阶段产生的位移较大,支护力也较大。文中给出的方法可用于计算圆形洞室半径任意开挖并加支护后的应力、位移,适用于任一粘弹模型岩体的施工分析。
Underground caverns excavation and support is a gradual continuous process. For viscoelastic rock mass with rheological effect, rheological aging and construction effect are coupled, and the deformation is related to time. Aiming at the construction of deep circular cavern, the time-varying function of radius is used to simulate the section excavation process. When the rock mass is simulated as any viscoelastic material, Laplace transform is used to obtain the displacement general solution. After the inverse transformation, the boundary conditions are used to determine the undetermined function. Finally, the stress of the surrounding rock expressed by the circumferential force of the hole is obtained, and the displacement is uniform solution. Differentiating the excavation and support periods, different expressions of time varying functions of radius and surrounding forces of the cave are substituted into each other. Volterra integral equations for supporting forces are established by using contact conditions between surrounding rock and elastic support. When the rock is modeled as Boltzmann viscoelastic model, the exact expression of support force can be obtained by solving the integral equation by substituting the material parameters, and the analytical expressions of the stress and displacement after excavation process can be obtained. The analysis of the expressions and examples shows that the radial displacement increases with the change of exponential form and finally stabilizes at a certain value. When the final hole type is the same, when the excavation speed of different sections is used and the immediate support is excavated, the displacement changes more rapidly when the excavation is faster and the final stable displacement after supporting is smaller. However, the displacement caused by the corresponding support phase Larger, supporting force is also larger. The method given in this paper can be used to calculate the stress and displacement of a circular cavern with arbitrary excavation and reinforcement, which is suitable for the construction analysis of any viscoelastic model rock mass.