A new closed-form solution for circular openings modeled by the Unified Strength Theory and radius-dependent Young’s modulus

Advances in Civil Engineering

Fan³

et al. 2018

is paper aims to estimate the stability of the water-resistant strata between the tunnel and the small-medium-sized concealed cavity filled with high-pressurized water or other fillings at optional position around tunnel through solving the double-hole problem. e analytical method to identify the critical water-resistant thickness is proposed based on the Schwarz alternating method and Griffith strength criterion, and the program to calculate the critical thickness was prepared according to this method using mathematical software. Parametric study of the critical thickness indicates that the critical water-resistant thickness will increase with the buried depth of the tunnel and cavity size; the lateral pressure coefficient has more complicated influence on the critical thickness, which is affected by cavity position; when the cavity is filled with sand or gravel, the critical water-resistant thickness will decrease with the increase of the filling pressure; and when the cavity is filled with the high-pressurized water, the critical thickness will decrease as the water pressure initially and increase afterwards. e analytical result of the critical thickness is consistent with that obtained by numerical simulation using the user-defined program based on FLAC 3D , demonstrating the rationality and feasibility of the proposed method in this study.

Section: Discussionmentioning

confidence: 99%

Using the Schwarz Alternating Method to Identify Critical Water‐Resistant Thickness between Tunnel and Concealed Cavity

Guo

Advances in Civil Engineering

Fan³

et al. 2018

“…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%

“…Based on the twin shear yield criterion, the unified strength theory is established by considering the influence of all the stress components and intermediate principal stress on the material yield failure [19][20][21][22]24]. e UST is a series of yield criteria and failure criteria, which can be adopted for most materials.…”

Section: Unified Strength Eory (Ust)mentioning

confidence: 99%

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

Mao

Advances in Civil Engineering

et al. 2018

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.

Rock Mechanics and Its Applications in Civil, Mining, and Petroleum Engineering

“…The elastic-plastic analytical solutions for the stress and displacement around a circular opening in the rock mass at great depth are required in a widely variety for the preliminary design such as tunnels, shafts, and boreholes (Zhang et al 2012). A great number of the closed-form solutions based on different strength criteria for an axisymmetric circular opening in an infinite medium subjected to a hydrostatic in-situ stress have been presented.…”

Section: Introductionmentioning

confidence: 99%

A New Insight for the Effect of Strength Criterion on the Stress and Displacement around a Circular Opening

Changguang¹,

Zhu²,

Gao³

2014

A unified formula for three strength criteria as the Mohr-Coulomb criterion, generalized Matsuoka-Nakai criterion, and Circumscribed Drucker-Prager criterion is presented under the plane strain state and is used to obtain the unified analytical solutions for the stress and displacement of a circular opening. The influence of strength criterion is discussed. The results show that the application of the unified formula is very convenient; the effect of strength criterion is significant.