• Geomechanics and Engineering
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• v.8 no.3
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• pp.323-359
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• 2015

This paper presents an elasto-plastic model for determination of the ground response curve of a circular underwater tunnel excavated in elastic-strain softening rock mass compatible with a nonlinear Hoek-Brown yield criterion. The finite difference method (FDM) was used to propose a new solution to calculate pore water pressure, stress, and strain distributions on periphery of circular tunnels in axisymmetric and plain strain conditions. In the proposed solution, a modified non-radial flow pattern, for the hydraulic analysis, is utilized. To evaluate the effect of gravitational loads and variations of pore water pressure, the equations concerning different directions around the tunnel (crown, wall, and floor) are derived. Regarding the strain-softening behavior of the rock mass, the stepwise method is executed for the plastic zone in which parameters of strength, dilatancy, stresses, strains, and deformation are different from their elasto-plastic boundary values as compared to the tunnel boundary values. Besides, the analytical equations are developed for the elastic zone. The accuracy and application of the proposed method is demonstrated by a number of examples. The results present the effects of seepage body forces, gravitational loads and dilatancy angle on ground response curve appropriately.

• Geomechanics and Engineering
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• v.21 no.2
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• pp.215-226
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• 2020

The magnitude and distribution of tunnel deformation were widely discussed topics in tunnel engineering. In this paper, a three-dimensional (3D) finite element program was used for the analysis of various horseshoe-shaped opening expressway tunnels under different geologies. Two rock material models - Mohr-Coulomb and Hoek-Brown were executed in the process of analyses; and the results show that the magnitude and distribution of tunnel deformation were close by these two models. The tunnel deformation behaviors were relevant to many factors such as cross-sections and geological conditions; but the geology was the major factor to the normalized longitudinal deformation profile (LDP). If the time-dependent factors were neglected, the maximum displacements were located at the distance of 3 to 4 tunnel diameters behind the excavation face. The ratios of displacement at the excavation face to the maximum displacement were around 1/3 to 1/2. In general, the weaker the rock mass, the larger the ratio. The displacements in front of the excavation face were decreased with the increasement of distance. At the distance of 1.0 to 1.5 tunnel diameter, the displacements were reduced to one-tenth of the maximum displacement.

• Geomechanics and Engineering
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• v.18 no.3
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• pp.225-234
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• 2019

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass is investigated, which is compatible with Mohr-Coulomb and generalized Hoek-Brown failure criteria. Based on finite difference method, plastic region is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium and compatibility equations, the material parameters of the rock or soil mass are assumed to be the same in each ring. For the strain-softening behavior, the strength parameters are assumed to be a linear function of deviatoric plastic strain (${\gamma}p^*$) for each ring. Increments of stress and strain for each ring are calculated with the finite difference method. Assumptions of large-strain for soil mass and small-strain for rock mass are adopted, respectively. A new numerical stepwise approach for limited pressure and plastic radius are obtained. Comparisons are conducted to validate the correctness of the proposed approach with Vesic's solution (1972). The results show that the perfectly elasto-plastic model may underestimate the displacement and stresses in cavity expansion than strain-softening coefficient considered. The results of limit expansion pressure based on the generalised H-B failure criterion are less than those obtained based on the M-C failure criterion.

• Geomechanics and Engineering
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• v.22 no.4
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• pp.277-290
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• 2020

This paper presents an elastic-plastic solution for the circular tunnel of elastic-strain softening behavior considering the pressure-dependent Young's modulus and the nonlinear dilatancy. The proposed solution is verified by the results of the field measuring and numerical simulation from a practical project, and a published closed-form analysis solution. The influence of each factor is discussed in detail, and the ability of Young's modulus and dilatancy characterizing the mechanical response of surrounding rock is investigated. It is found that, in low levels of support pressure, adopting the constant Young's modulus model will seriously misestimate the surrounding rock deformation. Using the constant dilatancy model will underestimate the surrounding rock deformation. When adopting the constant dilatancy model, as the dilation angle increases, the range of the plastic region increases, and the surrounding rock deformation weakens. When adopting the nonlinear dilatancy, the plastic region range and the surrounding rock deformation are the largest. The surrounding rock deformation using pressure-dependent Young's modulus model is between those resulted from two constant Young's modulus models. The constant α of pressuredependent Young's modulus model is the main factor affecting the tunnel displacement. The influence of α using a constant dilatancy model is much more apparent than that using a nonlinear dilatancy model.

• Journal of the Korean Geotechnical Society
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• v.18 no.5
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• pp.99-108
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• 2002

The nonlinear-brittle-plastic model derived from experiments as well as elastic and elasto-plastic models was applied to the analysis of the rock damaged zone around a highly stressed circular tunnel. The depths of stress redistribution and disturbed zone as well as the characteristic behaviors predicted from each numerical model were compared, As the magnitudes and stress differences of in situ stresses increased, influences of stress redistribution and stress disturbance on un(tiled region of rock mass also intensified. As a result, larger stress redistribution and disturbed zone as well as greater deviatoric stress and displacement were obtained by the nonlinear-brittle-plastic model rather than other conventional models such as elasto-plastic and elastic models. from such results, it was concluded that as the magnitudes and stress differences of in situ stresses increased, larger rock damaged zone might be predicted by the nonlinear-brittle-plastic model. Therefore, it is thought that the damage analysis may be indispensable far highly stressed tunnels.

• Geomechanics and Engineering
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• v.24 no.4
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• pp.307-321
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• 2021

In an earlier publication (Serrano et al. 2014), the theoretical basis for evaluating the shear strength in rock joints was presented and used to derive an equation that governs the relationship between tangential and normal stresses on the joint during slippage between the joint faces. In this paper, the theoretical equation is applied to two non-linear failure criteria by using non-associated flow laws, including the modified Hoek and Brown and modified Mohr-Coulomb equations. The theoretical model considers the geometric dilatancy, the instantaneous friction angle, and a parameter that considers joint surface roughness as dependent variables. This model uses a similar equation structure to the empirical law that was proposed by Barton in 1973. However, a good correlation with the empirical values and, therefore, Barton's equation is necessary to incorporate a non-associated flow law that governs breakage processes in rock masses and becomes more significant in highly fractured media, which can be induced in a rock joint. A linear law of dilatancy is used to assess the importance of the non-associated flow to obtain very close values for different roughness states, so the best results are obtained for null material dilatancy, which considers significant changes that correspond to soft rock masses or altered zones of weakness.

• Geomechanics and Engineering
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• v.11 no.3
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• pp.439-455
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• 2016

This paper presented solutions of displacement and stress for a circular opening which is reinforced with grouted rock bolt. It satisfies the Mohr-Coulomb (M-C) or generalized Hoek-Brown (H-B) failure criterion, and exhibits elastic-brittle-plastic or strain-softening behavior. The numerical stepwise produce for strain-softening rock mass reinforced with grouted rock bolt was developed with non-associative flow rules and two segments piecewise linear functions related to a principle strain-dependent plastic parameter, to model the transition from peak to residual strength. Three models of the interaction mechanism between grouted rock bolt and surrounding rock proposed by Fahimifar and Soroush (2005) were adopted. Based on the axial symmetrical plane strain assumption, the theoretical solution of the displacement and stress were proposed for a circular tunnel excavated in elastic-brittle-plastic and strain-softening rock mass compatible with M-C or generalized H-B failure criterion, which is reinforced with grouted rock bolt. It showed that Fahimifar and Soroush's (2005) solution is a special case of the proposed solution for n = 0.5. Further, the proposed method is validated through example comparison calculated by MATLAB programming. Meanwhile, some particular examples for M-C or generalized H-B failure criterion have been conducted, and parametric studies were carried out to highlight the influence of different parameters (e.g., the very good, average and very poor rock mass). The results showed that, stress field in plastic region of surrounding rock with considering the supporting effectiveness of the grouted rock bolt is more than that without considering the effectiveness of the grouted rock bolt, and the convergence and plastic radius are reduced.