Elasto-plastic coupling analysis of circular openings in elasto-brittle-plastic rock mass

Zhang, Q.; Jiang, Binsong; Wu, Xianshuai; Zhang, H.Q.; Han, Lijun

doi:10.1016/j.tafmec.2012.06.008

Cited by 43 publications

(22 citation statements)

References 23 publications

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“…The emerging conditions of the two parts can be described in accordance to two conditions: a) when the stress of the surrounding rock does not reach the plastic condition, the deformation is considered to be in the elastic state, and b) when the stress reaches and exceed the plastic yield condition (that is, when no deformation occurs and when the stress decreases at the same time), the deformation is considered to be in the fractured region. For convenience of analysis, the stress-strain curve of the actual rock is replaced by the fold line in Fig Stress-strain curves for elastic-brittle rocks [26] The plane strain problem requires the deformation of long roadway to be completed instantaneously. In fact, the deformation of the surrounding rock is gradually carried out.…”

Section: Mechanical Modelmentioning

confidence: 99%

“…In the final state of the surrounding rock, the fractured region and the elastic region are formed, and the stress components and the displacement can be expressed as follows [8,26].…”

Section: Deformation Analysis Of Broken Rock In the Final Statementioning

confidence: 99%

“…The displacement contact condition is replaced by Eq. (26), that is, the fourth equation of Eq. (13):…”

Section: Initial Plastic Zone Stress and Relative Displacement Of Surmentioning

confidence: 99%

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Analytical solution of circular tunnel in elastic-viscoplastic rock mass

Wang

Jiang

Zhang

et al. 2019

Lat. Am. j. solids struct.

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This paper deals with a deep circular tunnel excavated in infinite homogeneous and isotropic elastoviscoplastic rock mass subjected to a hydrostatic initial stresses. The tunnel is divided into the initial plastic, viscoplastic, and elastic zones. By combining the generalized Bingham model with Mohr-Coulomb yield criteria, analytical solutions of the circular tunnel are derived with the consideration of non-associated flow rule and elasto-viscoplasticity. The initial plastic zone is defined as the instantaneous change of rock mass excavation. Based on the initial plastic zone, the stresses in viscoplastic zone are transferred to the deep surrounding rock with time due to the initial earth stresses. The results are compared with the elastic-brittle solution at static conditions, and the solutions of this paper are validated. Moreover, the presented results shows that the stress and displacement of the surrounding rock varies with time, and the solutions can be obtained at different instants of time.

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Section: Mechanical Modelmentioning

confidence: 99%

“…In the final state of the surrounding rock, the fractured region and the elastic region are formed, and the stress components and the displacement can be expressed as follows [8,26].…”

Section: Deformation Analysis Of Broken Rock In the Final Statementioning

confidence: 99%

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Analytical solution of circular tunnel in elastic-viscoplastic rock mass

Wang

Jiang

Zhang

et al. 2019

Lat. Am. j. solids struct.

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“…It is generally believed that the plastic deformation satisfies the nonassociated flow rule, determined by the plastic potential function [8,10,11,22]. e plastic potential function f and the yield function F ′ have the same expression form.…”

Section: Definition Of Dilatancy Coefficientmentioning

confidence: 99%

A New Unified Solution for Circular Tunnel Based on a Four‐Stage Constitutive Model considering the Intermediate Principal Stress

Chen

Mao

Chen

et al. 2018

Advances in Civil Engineering

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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. e 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. e numerical simulation has been used to verify the correctness of the EPSDM. e 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 strainsoftening 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.

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“…As described in the former paper [30], the MBPM supposes that the rock mass experiences elasto-perfectlyplastic deformation and brittle-failure in each spherical shell. The material deterioration process only occurs in the brittle-failure process.…”

Section: Restrictive Condition In the Post-failure Regionmentioning

confidence: 99%

Analytical Strain-softening Solutions of a spherical cavity

Zhang

Quan

et al. 2018

Lat. Am. j. solids struct.

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This paper deals with a spherical cavity excavated in infinite homogeneous and isotropic strain-softening rock mass subjected to a hydrostatic initial Displacements and stresses distributions are two of the most important information for underground engineering, for that it can provide a theoretical foundation for geotechnical engineering optimism design and stability evaluation. In past few years, many scholars have developed series of (semi-)analytical and numerical solutions for circular openings and spherical cavities. . However, most of those solutions are based on the common elasto-perfectly-plastic and elasto-brittle-plastic models, because those solutions can be easily obtained using simple mathematical methods. However, most of the geotechnical materials display strain-softening behavior in the post-failure region. Therefore, the normally used elasto-perfectly plastic model and elasto-brittleplastic model can't well represent the actual failure process. Brown et al. were the earliest ones to analyze the stresses and displacements of circular openings excavated in the strain-softening rock mass. But, the assumption of constant elastic strain in the plastic region, which should obey the generalized Hooke's law, leads to a poor accuracy of the results. And Wang points out that Brown et al.'s solution is difficult to predict the plastic radius [11]. Carranza-Torres and Fairhurst's solution for H-B rock mass, which is based on the so-called self-similarity of H-B criterion, is theoretically rigorous. But, it seems rather complicated for practical use and is applicable only to the As we see, all of the solutions for strain-softening rock mass are based on semi-analytical and numerical method, no analytical solutions are available. Additionally, most of the indoor and field tests show that material properties of rock mass change during the failure process, not only strength parameters but also elastic parameters, i.e. Yong's modulus and Poisson's ratio. This is the so-called elasto-plastic coupling effect. Generally speaking, the effect of Young's modulus is analyzed in two ways. One is the pressure-dependent Young's modulus model (PDM) [26][27], the progressive failure process may be more significant. However, the two models can hardly be solved with analytical method. Considering the different tensile and compressive Young's modulus, Luo et al. obtained the closed-form solutions of spherical cavities in elastobrittle-plastic rock mass [28]. The difficulty of analytical methods for strain-softening rock mass is the coupling effect between softening index and material properties. In view of this, the Multi-step Brittle-Plastic model (MBPM) is proposed to solve the stress, strain, and displacement in the post-failure region for the spherical cavity. Moreover, the deterioration process of elastic parameters and strength parameters are also considered.

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Elasto-plastic coupling analysis of circular openings in elasto-brittle-plastic rock mass

Cited by 43 publications

References 23 publications

Analytical solution of circular tunnel in elastic-viscoplastic rock mass

Analytical solution of circular tunnel in elastic-viscoplastic rock mass

A New Unified Solution for Circular Tunnel Based on a Four‐Stage Constitutive Model considering the Intermediate Principal Stress

Analytical Strain-softening Solutions of a spherical cavity

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