• Tunnel and Underground Space
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• v.21 no.3
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• pp.174-180
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• 2011

An anisotropic version of Mohr-Coulomb failure criterion is proposed in order to provide a strength criterion for transversely isotropic rock. The concept of fabric tensor introduced by Pietruszczak & Mroz (2001) is employed to define the friction angle and cohesion as scalar functions of the fabric tensors. The anisotroy in these two strength parameters are calculated in association with the consideration of the relative rotation between the principal stress coordinate and the principal material triad. The critical plane on which the anisotropic function maximized is found by an optimization technique based on the Lagrange multiplier method. To demonstrate the performance of the anisotropic failure criterion, conventional triaxial tests on the samples having various inclinations of weakness plane are simulated and the resulting triaxial strength and dip angle of failure plane are discussed.

• Tunnel and Underground Space
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• v.17 no.2 s.67
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• pp.119-127
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• 2007

Based on the critical plane approach, a methodology far predicting the anisotropic strength ot transversely isotropic rock is Proposed. It is assumed that the rock failure is governed by Hoek-Brown failure criterion. In order to establish an anisotropic failure function, Mohr envelope equivalent to the original Hoek-Brown criterion is used and the strength parameters m, s are expressed as scalar functions of orientation. The conjugate gradient method, which is one of the robust optimization techniques, is applied to the failure function for searching the orientation giving the maximum value of the anisotropic function. While most of the existing anisotropic strength models can be applied only when the stress condition is the same as that of conventional triaxial compression test, the proposed model can be applied to the general 3-dimensional stress conditions. Through the simulation of triaxial compression tests for transversely isotropic rock sample, the validity of the proposed method is investigated by comparing the predicted triaxial strengths and inclinations of failure plane.

• Tunnel and Underground Space
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• v.10 no.2
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• pp.165-172
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• 2000

When tunnels or underground structures are constructed in anisotropic rock mass, designers and constructors have to consider the anisotropic characteristics in rock mass because their physical and mechanical properties are depended on the anisotropic angles(${\beta}$). In this study, therefore, we have first investigated the mechanical behavior of the gneiss specimen from lab. tests, and then have analysed the behavior of specimens for to the transversely isotropic model in elastic medium using the FLAC program. The results of this study were summarized as follows; 1) In the result of the variation tests, in general, the properties of strength were depended on the angle of inclination in spite of the hard rock. And except for the shear strength test, the lowest and peak stress were appeared at 60$^{\circ}$ and 90$^{\circ}$respectively. 2) The results of specimen modeling analysis using FDM well indicated the mechanical behaviors of the specimen of transversely isotropic model.

• Tunnel and Underground Space
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• v.26 no.2
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• pp.100-109
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• 2016

This study suggests three spatial distribution functions of strength parameters, which can be adopted in the derivation of failure conditions for transversely isotropic rocks. All three proposed functions, which are the oblate spheroidal function, the exponential function, and the function based on the directional projection of the strength parameter tensor, consist of two model parameters. With assumption that the cohesion and friction angle can be described by the proposed distribution functions, the transversely isotropic Mohr-Coulomb criterion is formulated and used as a failure condition in the simulation of the conventional triaxial tests. The simulation results confirm that the failure criteria incorporating the proposed distribution functions could reproduce the general trend in the variations of the axial stress at failure and the directions of failure planes with varying inclination of the weankness planes and confining pressure. Among three distribution functions, the function based on the directional projection of the strength parameter tensor yields the highest axial strength, while the axial strength estimated by the oblate spheroidal distribution function is the lowest.

• Journal of the Korean Geotechnical Society
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• v.18 no.5
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• pp.133-141
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• 2002

Isotropic rock and anisotropic rock have different tensile strength which has the greatest influence on rock failure. In this study, elastic modulus of anisotropic rock is obtained through uniaxial compression test, and tensile strength and tension failure behavior are analyzed through indirect tensile strength test. Stress concentration factor of a specimen at the center is obtained from anisotropic elastic modulus and strain by indirect tensile strength test. Theoretical solutions for tensile strength of isotropic and anisotropic rock are compared. Stress concentration factor of anisotropic rock is either higher or lower than isotropic rock depending on the inclination angle of bedding plane. The use of stress concentration factor of isotropic rock resulted in overestimation or underestimation of tensile strength.

• Tunnel and Underground Space
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• v.12 no.4
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• pp.237-247
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• 2002

A total of 18 stress measurements were performed in the rock and rock-like blocks in the laboratory to estimate the influence of anisotropy in rock. Full scale overcoring equipment, which consists of a coring machine and a biaxial loading system by flat jacks, was developed to simulate the in-situ rock stress condition in the laboratory By comparing the isotropic analysis with the anisotropic analysis in measuring the stress, conclusions have been drawn as to the influence of anisotropy. The maximum difference between the isotropic and the anisotropic analysis was 34% and it was shown that the stress measurement considering the anisotropy was needed. To confirm the validity of the observed data, a diagnostic analysis of stress relief curve by overcoring was conducted using the three dimensional finite difference program, FLAC 3D.

• Tunnel and Underground Space
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• v.20 no.6
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• pp.455-464
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• 2010

The variations of the uniaxial compressive strength, the strains and the elastic constants with respect to the angle of anisotropy are analyzed in order to investigate the characteristics of a transversely isotropic rock experimentally. Total 35 specimens of 7 different angles from a large block of rhyolite presenting the flow structure obviously are used in tests. This study is composed of two reports; the elastic constants are mainly analyzed for the every individual angle in the report No. 1 and they will be discussed synthetically in the report No. 2. From the specimens of 0 and 90 degree, 4 independent elastic constants which can directly be obtained without the help of any other suggested equations, may be referred to the true values. Data variation in the strain measurements differs on the angle is analyzed. That of small angle specimens tends higher than that of large angle specimens. The relation of apparent Young’s modulus and angle is found to be M- or U-shaped. For small angle specimens, Saint-Venant approximation cannot be applied successfully on account of showing the non-monotonous increase, and E1 is analyzed out of the true value range. In the specimen of $\phi$ = 75, the deviation of strain measurement and strength are smallest and 4 all constants are analyzed in the true value range. Therefore, specimen of the angle of around 75 may become preferable if only one specimen should be used in test of a transversely isotropic rock.

• Tunnel and Underground Space
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• v.11 no.1
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• pp.72-78
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• 2001

A method to determine elastic constants for transversely isotropic rock using a single uniaxial compression test was proposed by Kim(1995). However, some problems were found when this method was applied. We derived two different equations in determination of elastic constants using V$\sub$12/ and V$\sub$21/ and performed uniaxial compression tests for two specimens whose angles between transversely isotropic plane and horizontal plane are 30$^{\circ}C$ and 65$^{\circ}C$. The anisotropic elastic constants should be calculated with different equations depend on the angle. If the anisotropic angle is lower than 45$^{\circ}$, V$\sub$21/ may be used. However, if the anisotropic angle is higher than 45$^{\circ}$, V$\sub$12/ may be used.

• Tunnel and Underground Space
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• v.23 no.5
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• pp.383-391
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• 2013

A number of true triaxial tests on rock samples have been conducted since the late 1960 and their results strongly suggest that the intermediate principal stress has a considerable effect on rock strength. Based on these experimental evidence, various 3-D rock failure criteria accounting for the effect of the intermediate principal stress have been proposed. Most of the 3-D failure criteria, however, are focused on the phenomenological description of the rock strength from the true triaxial tests, so that the associated strength parameters have little physical meaning. In order to confirm the likelihood that the intermediate principal stress dependency of rock strength is related to the presence of weak planes and their distribution to the preferred orientation, true triaxial tests are simulated with the transversely isotropic rock model. The conventional Mohr-Coulomb criterion is extended to its anisotropic version by incorporating the concept of microstructure tensor. With the anisotropic Mohr-Coulomb criterion, the critical plane approach is applied to calculate the strength of the transversely isotropic rock model and the orientation of the fracture plane. This investigation hints that the spatial distribution of microstructural planes with respect to the principal stress triad is closely related to the intermediate principal stress dependency of rock strength.

• Tunnel and Underground Space
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• v.18 no.4
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• pp.252-262
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• 2008

In the uniaxial compressive test of a single specimen of transversely isotropic rock, its 5 independent elastic constants can not be defined since maximum 4 independent strain measurements are available theoretically. In order to solve this problem, one equation proposed by Saint Venant in 19C and confirmed by Lekhnitskii through the test experiences has been used for long time. Accordign to authors' experiences, however, this equation turned out to give erroneous elastic constants in some cases. Three new equations are suggested and their compatibilities are discussed in this paper. As the results of the analyses of the models, Lekhnitskii's suggested equation is effective for the specimen with the high dip angle whereas it results in the large erred output for that with dip angle less than $25{\sim}30$. It was found that the effectivenesses of three suggested equations and their compatibilities are subject to the dip angle and not to the amounts of elastic constants. Guide map to the selection of the compatible one of those suggested equations is presented as a result of the study.