Dilation angle variations in plastic zone around tunnels in rocks-constant or variable dilation parameter

Abstract

Dilation angle is a significant parameter needed for numerical simulation of tunnels. Even though dilation parameter is physically variable and dependent on confinement and experienced shear plastic strain based on the existing dilation models, numerical simulations of tunnels and underground openings with constant dilation parameter usually lead to satisfactory results in practical use. This study aims to find out why constant dilation angle is enough under practical conditions to simulate numerically tunnels and underground excavations in spite of the fact that dilation angle is variable in laboratory and experimental scale. With this aim, this work studies how mobilized dilation angle varies in a plastic zone surrounding a tunnel. For the circular tunnel under uniform in situ stress field, the stepwise finite difference approximation analytical solution considering strain softening rock mass behavior with mobilized dilation angle was used to study how mobilized dilation angle varies in plastic zone around tunnel under very different conditions. In practical conditions determined in this study, dilative behavior of all over the plastic zone around the tunnel can be approximated to constant dilation angle in the middle region of the plastic zone. Moreover, the plastic zone displacements for mobilized and constant dilation angle models are compared with each other. Further investigation under more general non-uniform in situ stress conditions and non-circular tunnels is performed by using the commercial finite difference software to numerically simulate the Mine-by experimental tunnel of AECL (Atomic Energy of Canada Limited) and the arched tunnel. Although the Mine-by and arched tunnels were numerically simulated based on the mobilized dilation angle model, the variability associated with dilation angle around the simulated Mine-by and arched tunnels is insignificant, and dilation angle is approximately constant in the plastic zone.

摘要

扩容角是隧道数值模拟中一个重要的参数。 虽然现有扩容模型表明扩容参数是变量, 与约束有关且经受剪切应变, 但利用常数扩容参数对隧道和地下孔洞进行数值模拟, 在实际应用中可以得到令人满意的结果。 本研究旨在查明为什么在实验室和试验过程中, 扩容角为变量, 而在实际上隧道和地下采挖的数值模拟过程中可以用常数进行模拟。 研究了隧道塑性区扩容角的变化情况。 对于具有均匀原位应力场的圆形隧道, 采用考虑应变软化岩体行为的梯度有限差分近似解析解研究了在不同条件下, 移动扩容角在隧道周围塑性区的变化规律。 在本研究确定的实际条件下, 隧道周围塑性区全部的扩容行为可以近似为塑性区中部的恒定扩容角。 此外, 比较了移动扩容角模型和定扩容角模型的塑性区位移。 利用商用有限差分软件对 AECL (加拿大原子能有限公司) 的矿山试验隧道和拱形隧道进行了数值模拟, 对非均匀应力条件和非圆形隧道进行了进一步研究。 虽然在移动扩容角模型的基础上对矿山及拱形巷道进行了数值模拟, 但模拟矿山及拱形巷道周围的扩容角变化不明显, 塑性区扩容角近似恒定。