• 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.

• 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.

• Tunnel and Underground Space
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• v.7 no.4
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• pp.323-333
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• 1997

A rock mass is usually classified by the results of geological survey and laboratory tests on rock specimens in order to obtain the adequate properties for the numerical analysis. For these purposes a rock mass strength is estimated based on the empirical criterion proposed by Hoek and Brown and a modulus of deformation is taken with the empirical relations developed by Bieniawski, Serafim and Pereira. In addition, the $K_o$ value which is the ratio of the horizontal stress to the vertical stress is one of the most important input data in the numerical analysis. Its role on a tunnel stability analysis could be verified with the numerical results taken by a finite difference code or a distinct element code. However, a deduced value used to be applied for the $K_o$ value in most of tunnel designs, even though the patterns of stress tensor are variable with regions and depths. Thus in situ stresses were measured by a hydraulic fracturing technique on several tunnel sites and applied directly to the tunnel design for the enhancement of its precision. With those informations on in situ stresses, the safe design should be obtained economically on the road or subway tunnels.

• Computers and Concrete
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• v.31 no.5
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• pp.443-455
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• 2023

This is a research analyses on the bearing capacity at a pile tip embedded in rock. The aim is to propose a shape coefficient for an analytical solution and to investigate the influence of the plastic flow law on the problem. For this purpose, the finite difference method is used to analyze the bearing capacity of various types and states of rock masses, assuming the Hoek & Brown failure criterion, by considering both plane strain and an axisymmetric model. Different geometrical configurations were adopted for this analysis. First, the axisymmetric numerical results were compared with those obtained from the plane strain analytical solution. Then the pile shape influence on the bearing capacity was studied. A shape factor is now proposed. Furthermore, an evaluation was done on the influence of the plastic flow law on the pile tip bearing capacity. Associative flow and non-associative flow with null dilatancy were considered, resulting in a proposed correlation. A total of 324 cases were simulated, performing a sensitivity analysis on the results and using the graphic output of vertical displacement and maximum principal stress to understand how the failure mechanism occurs in the numerical model.

• The Journal of Engineering Geology
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• v.29 no.2
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• pp.85-97
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• 2019

It can be observed that steep slopes ($65^{\circ}$ to $80^{\circ}$) consist of rock masses were kept stable for a long time. In rock-mass slopes with similar ground condition, steeper slopes than 1 : 0.5 ($63^{\circ}$) may be applied if the discontinuities of rock-mass slope are distributed in a direction favorable to the stability of the slope. In making a decision the angle of the slope, if the preliminary rock mass conditions applicable to steep slope are quantitatively setup, they may be used as guidance in design practice. In this study, the above rock mass was defined as a good continuum rock mass and the quantitative setup criterion range was proposed using RMR, SMR and GSI classifications for the purpose of providing engineering standard for good continuum rock mass conditions. The methods of study are as follows. The stable slope at steep slopes ($65^{\circ}$ to $80^{\circ}$) for each rock type was selected as the study area, and RMR, SMR and GSI were classified to reflect the face mapping results. The results were reviewed by applying the calculated shear strength to the stable analysis of the current state of rock mass slope using the Hoek-Brown failure criterion. It is intended to verify the validity of the preliminary criterion as a rock mass condition that remains stable on a steep slope. Based on the analysis and review by the above research method, it was analyzed that a good continuum rock mass slope can be set to Basic RMR ${\geq}50$ (45 in sedimentary rock), GSI and SMR ${\geq}45$. The safety factor of the LEM is between Fs = 14.08 and 67.50 (average 32.9), and the displacement of the FEM is 0.13 to 0.64 mm (average 0.27 mm). This can be seen as a result of quantitative representation and verification of the stability of a good continuum rock mass slope that has been maintained stable for a long period of time with steep slopes ($65^{\circ}$ to $80^{\circ}$). The setup guideline for a good continuum rock mass slope will be able to establish a more detailed setup standard when the data are accumulated, and it is also a further study project. If stable even on steep slopes of 1 : 0.1 to 0.3, the upper limit of steep slopes is 1 : 0.3 with reference to the overseas design standards and report, thus giving the benefit of ensuring economic and eco-friendlyness. Also, the development of excavation technology and plantation technology and various eco-friendly slope design techniques will help overcome psychological anxiety and rapid weathering and relaxation due to steep slope construction.

• 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.

• Geomechanics and Engineering
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• v.31 no.5
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• pp.461-476
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• 2022

Research studies on the scale effect on triaxial strength of intact rocks are scarce, being more common those in uniaxial strength. In this paper, the authors present and briefly interpret the peak and residual strength trends on a series of triaxial tests on different size specimens (30 mm to 84 mm diameter) of an intact granitic rock at confinements ranging from 0 to 15 MPa. Peak strength tends to grow from smaller to standard-size samples (54 mm) and then diminishes for larger values at low confinement. However, a slight change in strength is observed at higher confinements. Residual strength is observed to be much less size-dependent. Additionally, this study introduces preliminary modelling approaches of these laboratory observations with the help of three-dimensional particle flow code (PFC3D) simulations based on bonded particle models (BPM). Based on previous studies, two modelling approaches have been followed. In the first one, the maximum and minimum particle diameter (D_max and D_min) are kept constant irrespective of the sample size, whereas in the second one, the resolution (number of particles within the sample or ϕ_v) was kept constant. Neither of these approaches properly represent the observations in actual laboratory tests, even if both of them show some interesting capabilities reported in this document. Eventually, some suggestions are provided to proceed towards improving modelling approaches to represent observed scale effects.

• 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.