粘弹性岩体中支护圆形洞室施工过程的解析分析

Analytical analysis of supporting circular tunnel construction in viscoelastic rock mass

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。

Tunnel excavation and supporting are continuous processes.The time related deformation is due to rheologic behavior of rock mass and construction process.Time-varying function of radius is established to simulate the circular tunnel excavation process.The stresses and displacement general solutions of viscoelastic rock mass with elastic support during construction are derived by Laplace transformation method,which contains the undetermined supporting force.Volterra integral equation of supporting force is established by substituting different radius excavation function and surface force of excavation and supporting stage into the contact conditions.For Boltzmann viscoelastic model,supporting force can be calculated exactly.The expression and example show that radial displacement after supporting is increased with exponential form and stabilized to one value.If final tunnel is the same size and supported immediately in the finish time but excavated with different velocity,the displacement of cases with high velocity is larger in the beginning and smaller after some time.The final steady displacement is also smaller when excavated faster,but the displacement occurred after supporting is larger.The solutions can be calculated for cases with arbitrary time-varying radius and the method is applicable for the analysis of other viscoelastic models.