Abstract
Based on the triaxial test, the elasto-perfectly plastic strain-softening damage model (EPSDM) is proposed as a new four-stage constitutive model. Compared with traditional models, such as the elasto-brittle-plastic model (EBM), elasto-strain-softening model (ESM), elasto-perfectly plastic model (EPM), and elasto-peak plastic-brittle plastic model (EPBM), this model incorporates both the plastic bearing capacity and strain-softening characteristics of rock mass. Moreover, a new closed-form solution of the circular tunnel is presented for the stress and displacement distribution, and a plastic shear strain increment is introduced to define the critical condition where the strain-softening zone begins to occur. The new analysis solution obtained in this paper is a series of results rather than one specific solution; hence, it is suitable for a wide range of rock masses and engineering structures. The numerical simulation has been used to verify the correctness of the EPSDM. The parametric studies are also conducted to investigate the effects of supporting resistance, residual cohesion, dilation angle, strain-softening coefficient, plastic shear strain increment, and yield parameter on the result. It is shown that when the supporting resistance is fully released, both the post-peak failure radii and surface displacement could be summarized as EBM > EPBM > ESM > EPSDM > EPM; the dilation angle in the damage zone had the highest influence on the surface displacement, whereas the dilation angle in the perfectly plastic zone had the lowest influence; the strain-softening coefficient had the most significant effect on the damage zone radii; the EPSDM is recommended as the optimum model for support design and stability evaluation of the circular tunnel excavated in the perfectly plastic strain-softening rock mass.
Highlights
The plane strain of circular holes is a relatively simple problem, it can provide effective theoretical basis for the support parameter design and stability evaluation of surrounding rock in underground engineering. erefore, it has been widely applied in the tunnel, coal mine shaft construction, oil extraction, coal gas penetration, and other projects.In the early stage, the elastoplastic analysis of the circular tunnel was first proposed by Fenner and corrected by Kastner
The shallow rock mass is still in the triaxial stress state under the effect of the supporting structure after tunnel excavation. en, the yield strength of rock mass increased due to the influence of intermediate principal stress, which in turn would affect the stress and deformation of surrounding rock. erefore, intermediate principal stress is crucial for tunnel design [15, 16]. e unified strength theory (UST) considers the impact of all stress components on material yield failure under different stress states and is applicable to a variety of Advances in Civil Engineering σ1 – σ3 σ1 – σ3 σ1 – σ3 σ1 – σ3
When Δc∗ increases from 0.0001 to 0.0005, Rp/a, Rs/a, and Rc/a are, respectively, reduced to 5.72%, 11.92%, and 10.08%; u0/a is reduced to 16.67%. e above data show that Δc∗ has a crucial in uence on the post-peak failure radii and surface displacement. e plastic bearing capacity of rock mass gradually increases with the increasing Δc∗
Summary
The plane strain of circular holes is a relatively simple problem, it can provide effective theoretical basis for the support parameter design and stability evaluation of surrounding rock in underground engineering. erefore, it has been widely applied in the tunnel, coal mine shaft construction, oil extraction, coal gas penetration, and other projects. The elastoplastic analysis of the circular tunnel was first proposed by Fenner and corrected by Kastner Both of them regarded the rock mass as a perfectly elastoplastic material. A large number of rock masses firstly showed the strain-softening characteristics after the peak plastic zone and entered the residual flow stage. Erefore, according to the total stress-strain curve, the elasto-perfectly plastic strain-softening damage model (EPSDM) was proposed in this paper and applied to the engineering practice. The EPSDM includes all the features of the EPM, EBM, ESM, and EPBM and can be transformed into the above four models under certain conditions It can be regarded as a unified constitutive model. Based on the triaxial test, the elasto-perfectly plastic strain-softening damage model (EPSDM) is proposed as a new four-stage constitutive model.
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