Abstract This paper presents a numerical finite strain solution for a circular tunnel in Mohr-Coulomb and generalized Hoek-Brown strain-softening rock masses. By approximating the differential equations with a difference method in the deformed coordinates, an efficient procedure is presented to calculate the displacements and stresses. The proposed solution is verified by another numerical method for both elasto-brittle-plastic and strain-softening finite strain examples. The parametric analysis indicates that (1) with the decrease in Young’s modulus of the residual region, the displacement increases, and the thickness of the softening region decreases. The displacement and the thickness of the softening and residual regions remain relatively stable when the deterioration coefficient of Young’s modulus is less than 0.01. (2) The displacement and the thickness of the softening and residual regions decrease with the increasing Poisson’s ratio, and increase with the increasing parameter α for the generalized Hoek-Brown rock mass. (3) With the increase in the in-situ stress, the dimensionless displacement of the tunnel wall increases and tends to 1.0, and the thicknesses of plastic and residual region first increase to their maximum values and then decrease. The finite strain solution is necessary for the displacement prediction and supporting design, rather than the small strain solution.

中文翻译：

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应变软化岩体中圆形隧道弹塑性耦合有限应变分析的简单数值程序

摘要 本文提出了Mohr-Coulomb 和广义Hoek-Brown 应变软化岩体中圆形隧道的数值有限应变解。通过在变形坐标中用差分法逼近微分方程，提出了一种计算位移和应力的有效程序。提出的解决方案通过弹脆塑性和应变软化有限应变示例的另一种数值方法进行验证。参数分析表明(1)随着残余区杨氏模量的减小，位移增大，软化区厚度减小。当杨氏模量劣化系数小于0.01时，软化区和残余区的位移和厚度保持相对稳定。(2) 对于广义Hoek-Brown 岩体，软化区和残余区的位移和厚度随着泊松比的增大而减小，随着参数α 的增大而增大。(3)随着地应力的增加，隧道壁无量纲位移增加并趋于1.0，塑性区和残余区的厚度先增加到最大值后减小。位移预测和支撑设计需要有限应变解，而不是小应变解。隧道壁无量纲位移增大并趋于1.0，塑性区和残余区的厚度先增大到最大值后减小。位移预测和支撑设计需要有限应变解，而不是小应变解。隧道壁无量纲位移增大并趋于1.0，塑性区和残余区的厚度先增大到最大值后减小。位移预测和支撑设计需要有限应变解，而不是小应变解。