模型边界对圆形隧道开挖引起地表沉降的影响分析

Influence of model boundary on ground settlement caused by excavation of a circular tunnel

为明确圆形隧道开挖引起地表沉降分析所需模型边界尺寸,采用理论分析与数值模拟方法研究模型底边界与水平边界尺寸对圆形隧道开挖引起地表沉降的影响。理论分析采用Bobet、Park及Verruijt法,数值模拟采用弹性与弹塑性本构模型。研究结果表明:随着模型底边界尺寸增大,圆形隧道拱顶在地表的映射点由沉降逐渐转为隆起,当模型底部为半空间无限体时,圆形隧道拱顶在地表映射点无限隆起,这种现象显然有悖于工程实际;当模型底边界存在下卧硬质层时,如果下卧硬质层土的弹性模量是上覆土的5倍,则可将下卧硬质层土作为模型底边界条件;模型水平边界尺寸与底边界尺寸以及隧道半径关系密切,随着模型底边界尺寸以及隧道半径的增大,模型水平边界尺寸近似线性增加。

To explicate the size of model boundary required for the analysis of ground settlement caused by circular tunnel excavation, the influences of the sizes of bottom boundary and horizontal boundary of the model on the ground settlement caused by a circular tunnel excavation were studied by the theoretical analysis and the numerical simulation. The Bobet, Park and Verruijt methods were adopted in the process of the theoretical analysis. The elastic and elastoplastic constitutive models were adopted in the process of the numerical simulation. The results of research showed that the mapping point of the circular tunnel vault on the ground surface gradually changed from settlement to uplift as the size of the model bottom boundary increased. When the model bottom was a half-space infinite body, the mapping point of the circular tunnel vault on the ground surface bulged infinitely. This phenomenon was obviously contrary to engineering reality. When there was an underlying hard layer at the model bottom boundary, if the elastic modulus of the underlying hard layer was 5 times that of the overlying soil, the underlying hard layer could be used as the bottom boundary condition of the model. The size of the model horizontal boundary was closely related to the size of the model bottom boundary and the tunnel radius. The size of the model horizontal boundary increased approximately linearly with the increased of the size of the model bottom boundary and the tunnel radius.