中文摘要：

针对深埋圆形洞室,用半径时变函数模拟断面开挖过程,引入空间影响系数对力学模型进行修正以考虑纵向开挖影响。当岩体模拟为任一黏弹性材料时,将方程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,利用围岩与支护接触条件建立关于支护力的积分方程。当取Boltzmann黏弹模型时,求解积分方程得到支护力的确切表达,并可求得开挖过程及任意时刻支护后应力、位移分段解析表达。算例分析表明,纵向推进速度越大,位移越大;断面开挖较快时纵向推进速度对位移的影响越显著。最终洞型和纵向推进速度均相同时,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。文中导出的解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,该方法也适用于其它黏弹模型岩体的施工分析。

英文摘要：

The tunnel excavation and support are continuous processes.A time-varying function of radius is established to simulate the excavation process of a circular tunnel.The general solutions of stresses and displacements of viscoelastic rock mass with elastic support during construction are derived by the Laplace transformation method,which contains the undetermined supporting force.An integral equation for the supporting force is established based on the contact conditions between the rock mass and the support.By means of Boltzmann viscoelastic model,the supporting force can be calculated exactly.The example shows that the displacement is larger when the longitudinal excavation velocity is higher.Besides,the effect of the longitudinal excavation is more clear when the cross-section is excavated faster.If the final tunnel is in the same size and supported immediately at the finishing time but excavated with different velocities,the displacement of cases with high velocity is larger at the beginning and smaller after some time.The final steady displacement is also smaller when excavated faster,but the displacement occurring after supporting is larger.The solutions can be employed to calculate the displacements and stresses of arbitrary time-varying radius.The proposed method is suitable for the analysis of other viscoelastic models.