基于复变函数的圆形水平冻结壁弹性分析与设计

为了获得非均匀荷载作用下圆形水平冻结壁与围岩的应力-位移场分布规律，考虑冻结壁与围岩相互作用及开挖卸荷作用，建立了符合实际施工情况的水平冻结壁弹性力学模型。利用复变函数方法，推导出弹性冻结壁与围岩的应力和位移解析解；讨论了基于Tresca和Mises准则的冻结壁厚度设计方法。结果表明：弹性模量比(β)、冻结壁外内径比(ξ)和侧压力系数(λ)对冻结壁与围岩的应力和位移变化影响显著；冻结壁内外缘环向应力差及45°方向最大剪应力与β正相关；β与ξ交互影响冻结壁应力和位移，β越大，ξ影响越显著，ξ>2.4后，β、ξ影响均不显著；0.4<λ<2.4时，冻结壁处于完全受压状态；β越大，围岩作用越弱，冻结壁厚度设计越大，Mises准则条件下冻结壁设计厚度比Tresca准则下小。

Elastic analysis and design of circular horizontal frozen wall based on interactionbetween frozen wall and surrounding rock

For the purpose of obtaining the law of stress-displacement distribution in circular horizontal frozen wall under non-uniformly distributed load,a mechanical model,conformed to the practical construction situation,was established,considering the interaction between frozen wall and surrounding rock,and the influence of unloading during excavation.Its elastic analytical expressions of stress and displacement were deduced by complex function method.The thickness design of frozen wall based on Tresca and Mises yield criterion were discussed.The results show that the ratio of elasticity modulus between frozen wall and surrounding rock (β),the diameter ratio of frozen wall (ξ),and lateral pressure coefficient (λ) have remarkable effects on stress and displacement in frozen wall and surrounding rock.The greater the β,the greater the pressure difference between the inner and outer surface of frozen wall,the higher the maximum shearing stress in 45 degrees.β and ξ have reciprocal effect on the stress and displacement of frozen wall,the influence of ξ becomes greater with the growth of β,after ξ>2.4,the influence of β and ξ decrease;while 0.4<λ<2.4,frozen wall and surrounding rock are all in compression state.The greater the β,the bigger the thickness of frozen wall,and the thickness deduced by using Mises yield criterion is thinner than Tresca result.