Abstract
Abstract This paper focuses on the stability analysis of tunnel structures with a circular hollow section based on the with a strain-degradation model using unified strength theory. A simplified numerical approach is proposed for analyzing the elasto-plastic behavior of surrounding rocks. A constitutive equation is proposed based on the unified strength theory and the strain degradation behavior was taken into account as well with deviatoric plastic strain chosen as the degradation parameter. Meanwhile, the plastic potential function can be obtained with the associated flow rule, by which the surrounding rocks can be classified as plastic zone and elastic zone. The solution in plastic zones adopted the differential method subdividing surrounding rock into infinitesimal concentric annuli, in which the radial stresses decrease monotonically with a decrease in radial coordinate. The relationship of the increment of stresses and the increment of strains in adjacent annuli can be derived from equilibrium, constitutive and geometrical equations. The numerical solution of each annulus is calculated from the outmost annulus at the elastic-plastic interface. In addition, the impact of the intermediate principal stress factor and the critical degradation parameter on the solution, and the factors of influence on plastic radius are discussed.
Highlights
Analysis of stresses and displacements around circular hollow sections in isotropic rock masses has been one of the critical issues in civil engineering
The radial displacement u of the brittle-plastic model reaches the largest 0.76m, but the radial stress decreases contrarily. These comparative results indicate that smaller plastic zone is likely formed in rock masses when incorporating the effect of strain degradation which might correspondingly result in larger instability potential
6 Conclusions In this study, a new method of elasto-plastic analysis based on the unified strength strain degradation model is proposed and the influences of the correlated parameters on the plastic solution are studied
Summary
Analysis of stresses and displacements around circular hollow sections in isotropic rock masses has been one of the critical issues in civil engineering. A literature review has shown that theoretical analysis methods of ground reaction curves for underground openings excavated in elastic-plastic materials are diversified and have been fully developed (Alonso et al 2003, Brown et al 1983, Carranza-Torres and Fairhurst 1999, 2000, Chen et al 1999, Duncan Fama 1993, Pan and Edwin 1996, Park and Kim 2006, Sharan 2003, 2005, 2008) Those numerical methods provide an accurate prediction of the displacements around a circular opening in the elastic-perfectly plastic rock mass and propose analytical solutions for practical applications. The studies on the circular openings based on the UST have been implemented, and the stresses and displacements of the plastic zone were given (Ma et al 2009, and Zhang et al 2010) They neglected the influences of the degradation of strength parameters leading a limitation to the materials with strain softening. The parametric analyses are performed to quantify the influences of the intermediate principal stress on the critical deviatoric plastic strain, strength parameters and supporting pressure in the plastic zone
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