粘土中圆形隧道上限解的研究

Research on the Upper Bound Solution of Circle Tunnel in Clay

根据极限分析上限理论,基于Davis等人提出的隧道垮落模型,提出了剪切区参数α等于1时的新的隧道垮落模型。由不可压缩性条件和速度连续性条件求出了剪切区速度和间断线表达式,计算了该模型间断线上能量耗损、剪切区能量耗损和总外力所做的功。利用功能原理,求出了稳定率的表达式,并计算了相应的稳定率。从求解结果来看,所得上限解小于Davis等人的结果,因而该上限解将更接近真实解。从与实验结果比较来看,该上限解位于实验值附近,能与实验结果比较好地吻合,从而说明该模型更加接近真实隧道垮落情形。该上限解可为隧道支护提供理论依据。

Base on Daris at al tunnel failure model and the upper bound theory of plastic limit analysis, a new parameter aequal to 1, governing size of shear zone of tunnel failure model was put forward. The velocity of shear zone and formula of line of discontinuity was applied in using incompressibility condition and velocity continuity condition, deducing energy dissipated on the line of discontinuity, energy dissipated within shear zone and total the work done by the outside force of the model Expres- sion of stability ratios got by applying conversation of energy theory, from the result standpoint, the upper bound solution is smaller than Davis et al the results, thus the upper bound solution to be closer the real solution. From the standpoint of the ex- perimental results comparison, the upper bound solution is located nearby the experimental value, which can agree with experi- mental results, thus the model is closer the real failure tunnel. The upper bound solution would provide the theory basis of the tunnel support.