岩质隧道施工过程变形时空问题的位移释放系数法

岩质隧道施工过程变形具有显著的成洞时间效应与开挖面空间效应。由于应力释放率与施工过程参数、围岩力学性态等的关系难以量化，应力释放系数法在解析岩质隧道施工过程变形问题时存在局限性。为描述岩质隧道与时间、空间相关的复杂的施工力学过程，假设围岩为Burgers体和Drucker-Prager组合模型。利用弹性-黏弹性对应原理与非关联流动法则建立无支护隧道变形解，采用位移释放系数法描述隧道施工过程变形的时空效应。获得的2维平面应变无支护隧道最大径向位移的数学函数形式与Manh解一致；当不考虑时间因素时，本文解可退化为Park解。通过与既有数值解和解析解对比，验证了本文解的正确有效性。进而分析隧道时空变形曲线，包括隧道蠕变特征曲线、围岩变形径向分布曲线和隧道纵剖面变形曲线，得到关于黏聚力、内摩擦角、扩容角与延迟时间等参数的敏感性规律。结果表明：随着时间推移或纵向距离的增大，隧道变形非线性递增；随着围岩深度的增加，隧道变形递减，隧道变形和塑性区半径均为黏聚力与内摩擦角的非线性递减函数；围岩扩容加剧了隧道变形；延迟时间控制了隧道变形的时程规律；隧道时空变形对介入参数的敏感性与其物理意义一致。位移释放系数法成功描述了岩质隧道施工过程变形的时空效应，可为施工过程提供理论指导。

Displacement Release Coefficient Method for Spatiotemporal Deformations of Rocky Tunnels During Construction

The spatiotemporal effects of deformations of rocky tunnels are significant during the construction. Stress release coefficient method is not applicable to study the deformations of rocky tunnels because of the limited advance knowledge of the quantitative connection between the stress release rate and the parameters associated with the construction process and the surrounding rock properties. In order to investigate spatiotemporal deformations of rocky tunnels during construction, the combination model of Burgers body and Drucker-Prager criterion is applied to characterize the mechanical properties of surrounding rock. The closed-form solutions of tunnel''s deformation are derived by using the correspondence principle of elasticity-viscoelasticity and the non-associated flow rule. The displacement release coefficient method is introduced to describe spatiotemporal deformations of the surrounding rock during the construction of rocky tunnels. The maximum short term radial displacement corresponding to plane strain analysis of a tunnel cross section has the similar function formations as the Manh solutions. Moreover, the present solutions reduce to the Park solutions when the time effect is neglected. The correctness and effectiveness of the present solutions are verified by comparing the previous numerical/analytical solutions and the present solutions. Finally, spatiotemporal deformations curves of rocky tunnels, which includes creep characteristic curve of tunnel, radial distribution curve of tunnel''s deformation and longitudinal deformation profile of tunnel, are analyzed with considering the effects of different parameters, such as cohesive, internal friction angle, dilation angle and retardation time. The results show that the deformation of tunnel nonlinearly increases with the increase of time and longitudinal distance, but decreases as the depth of surrounding rock increases. The deformation of tunnel is the nonlinear decreasing function of cohesive and internal friction angle as well as the radius of plastic zone. The dilation of rock increases the deformation of tunnel. Besides, the retardation time determines the time history of tunnel''s deformation. Effects of incorporated parameters on spatiotemporal deformations of rocky tunnels are consistent with their physical meanings. Displacement release coefficient method successfully describes the spatiotemporal deformations of rocky tunnels, which provides the theoretical guidance for the construction of rocky tunnels.