Elastoplastic Analysis of Circular Tunnel Based on Drucker–Prager Criterion

According to the strain-softening characteristics of rock mass, an ideal elastic strain-softening model is developed, and the surrounding rock of tunnels is subdivided into the plastic broken zone, plastic strain-softening zone, and elastic zone. Based on the generalized spatially mobilized plane criterion, an elastic-plastic analytical solution of a circular tunnel is derived. The effects of intermediate principal stress, strain softening, and dilatancy are considered in the unified solution. The stress, displacement, and plastic zone radius of surrounding rock based on the SMP criterion are compared with those based on the Mohr–Coulomb criterion. Furthermore, the effects of parameters such as the softening modulus, dilatancy angle, and internal friction angle on the deformation and stress of tunnels are discussed. It has been found that the larger the dilatancy angle is, the larger the plastic zone displacement and the radius of the broken zone are. The larger the internal friction angle, the smaller the sizes of the plastic zone, the strain-softening zone, and the broken zone are. The deformation of surrounding rock in the broken zone is more sensitive to the internal friction angle than that in the strain-softening zone. The unified solution based on the SMP criterion provides a well understanding for the elastic-plastic state of tunnels, which can be the guidance for tunnel excavations and support designs.

“…According to equation (10), the expression of the cohesive force in the strain-softening zone can be obtained:…”

Section: Stress and Displacement In The Plastic Strain-softeningmentioning

confidence: 99%

“…Radius of the Plastic Broken Zone. According to equation (10), the residual cohesion c * at the interface between the strain-softening zone and the broken zone can be expressed as…”

Section: Radius Of the Strain-softening Zonementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Unified Solution for Circular Tunnels Based on Generalized SMP Criterion considering the Strain Softening and Dilatancy

Guo

Pan

et al. 2019

“…However, the above three sets of criteria ignore this effect, leading to several limitations in engineering applications. Even though several researchers deem the Drucker-Prager criterion as the failure condition of rock strength when studying the response behaviour of a rock mass, they put the same amount of emphasis on it in studying the impact of both the minimum and maximum principal stress [12,13]. Yu and He [14] have advanced a unified strength criterion (USC) that will be utilized to depict the reaction conduct of rock mass in this study.…”

Section: Introductionmentioning

confidence: 99%

Unified Analytical Solutions of Circular Tunnel Excavated in an Elastic‐Brittle‐Plastic Rock Mass considering Blast‐Induced Damage and Dead Weight Loading

Cao

Chen

et al. 2021

Stress and deformation around circular tunnel are crucial for optimizing the support system and evaluating the tunnel stability. The damage zone induced by blasting or mechanical excavation can dramatically influence the support design and methods because the self-weight of broken rock mass at the roof of the tunnel can exert a high pressure on the support system, leading to the support system instability due to the overload. This paper presents a new closed-form solution for analyzing the stress and deformation of deep circular tunnel excavated in elastic-brittle rock mass with the consideration of the rock gravity and damage zone by using the unified strength criterion. A new modified equilibrium equation in the fracture zone is used to determine the stress and the radius of fracture zone. The correctness of the solution is also verified by comparison with the numerical simulation results. The results illustrate that the rock gravity, damage zone radius, and intermediate principal stress have an extremely important influence on the ground response. The tunnel surface convergence and damage zone radius with the consideration of the gravity are obviously larger than those without consideration of the gravity. The rock gravity effect under the high intermediate principal stress gradually weakens, illustrating that the intermediate principal stress is beneficial to tunnel stability. Large deformation instability of the tunnel is dependent on the extension of damage zone. The larger the radius of damage zone, the larger both fracture range and tunnel surface deformation. The proposed solution in this study is novel and can be used to assess the ground convergence for different scenarios and to optimize the support system during the early design stage of the tunnel.

“…Although various exact solutions or numerical solutions have been proposed in the above works, the influence of intermediate principal stress was ignored in the strength criteria, which has significant effect on the mechanical behaviors of surrounding rock [13][14][15]. erefore, the yield criteria considering intermediate principal stress were gradually adopted to investigate the elastoplastic solutions of tunnel surrounding rock and achieved significant results, such as Drucker-Prager (D-P) criterion [16,17], the unified strength theory [18][19][20][21][22], and Lade-Duncan (L-D) criterion [23]. However, the assumption of axisymmetric in situ stress field is still introduced to calculate the elastoplastic solution of rock mass, which is not in line with the actual stress state under most circumstances [24].…”

Section: Introductionmentioning

confidence: 99%

Elastoplastic Analysis for Circular Tunnel Based on Modified Lade Criterion considering Strain Softening and Dilatancy

Deng

Wang

Zou

2021

Modified Lade criterion can not only describe the strength properties of many kinds of rocks well but also has simple and practical parameters. Although the elastoplastic solution of circular tunnel has been extensively investigated, the method based on modified Lade criterion considering the effect of the intermediate principal stress, strain-softening behavior, and dilatancy has not yet been studied. In this paper, a new numerical procedure based on modified Lade criterion is proposed to calculate the elastoplastic solutions for surrounding rock of the circular tunnel. The comparisons of stress, displacement, and plastic zone radius are carried out between the presented method and published literatures under axisymmetric and nonaxisymmetric original in situ stress field. Finally, a series of parametric analyses are executed and discussed. It can be concluded that the lateral pressure coefficient, λ, influences both the size of plastic zone and the development direction. The plastic zone radius shows a negative power function change with increasing critical deviatoric plastic strain and increases slightly with increasing dilation angle, ψ.