• 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.

• Proceedings of the Korean Geotechical Society Conference
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• 2009.03a
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• pp.58-63
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• 2009

Biaxial compression test was conducted on a transversely isotropic synthetic jointed rock model for the understanding of the fracture behaviors of a sedimentary or metamorphic rocks with well developed bedding or foliation in uni-direction. The joint angles employed for the model are 30, 45, and 60 degrees to the horizontal, and the synthetic rock mass was made of early strength cement. From the biaxial compression test, initiation propagation of tensile cracks at norm to the joint angle was found. The propagated tensile cracks eventually developed rock blocks, which was dislodged from the rock mass. Furthermore, the propagation process of the tensile cracks varies with joint angle: lower joint angle model shows more stable and progressive tensile crack propagation. The experiment results were validated from the simulation by using discrete element method PFC 2D. From the simulation, as has been observed from the test, a rock mass with lower joint angle produces wider damage region and rock block by tensile cracks. In addition, a rock model with lower joint angle shows a progressive tensile cracks generation around the opening from the investigation of the interacted tensile cracks.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2005.03a
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• pp.47-51
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• 2005

If a structure is founded on the ground saturated with pore water, then the ground should be modeled as a saturated two-phase porous medium for accurate earthquake response analysis. In this study, an axisymmetric transmitting boundary hyperelement is developed for modeling of far field of the ground using u-U formulation for water-saturated transversely isotropic layered stratum. The developed hyperelement is verified by comparing the dynamic stiffness of rigid circular foundation on water-saturated isotropic layered stratum with the case of using equivalent single-phase medium model.

• Structural Engineering and Mechanics
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• v.30 no.4
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• pp.501-512
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• 2008

The axisymmetric problem of a functionally graded annular plate is considered by extending the theory of functionally graded materials plates suggested by Mian and Spencer (1998). In particular, their expansion formula for displacements is adopted and the hypothesis that the material parameters can vary along the thickness direction in an arbitrary continuous fashion is retained. However, their analysis is extended here in two aspects. First, the material is assumed to be transversely isotropic, rather than isotropic. Second, the plate is no longer tractions-free on the top and bottom surfaces, but subject to uniform loads applied on the surfaces. The elasticity solutions are given for a uniformly loaded annular plate of functionally graded materials for a total of six different boundary conditions. Numerical results are given for a simply supported functionally graded annular plate, and good agreement with those by the classical plate theory is obtained.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2006.03a
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• pp.345-350
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• 2006

If a structure is founded on the ground saturated with pore water, then the ground should be modeled as a saturated two-phase porous medium for accurate earthquake response analysis. In this study, a 3-dimensional transmitting boundary is developed for modeling of far field using u-U formulation for water-saturated transversely isotropic layered stratum. The developed transmitting boundary is verified by comparing the dynamic stiffness of rigid square foundation on water-saturated isotropic layered stratum with the case of using equivalent single-phase medium model.

• Journal of the Earthquake Engineering Society of Korea
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• v.13 no.6
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• pp.67-86
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• 2009

In this study, a 3D transmitting boundary in water-saturated transversely isotropic soil strata has been developed based on u-w formulation for application to general 3D analysis. Behavior in the far field region is expanded in the Fourier series, and dynamic stiffness for each term is obtained based on the u-w formulation. Transformation of the dynamic stiffness is presented to combine the transmitting boundary with the 3D finite elements for the near field region formulated in a 3D Cartesian coordinate system. The developed transmitting boundary is verified through a comparison of the dynamic behavior of a rigid circular foundation with the results from the existing numerical method. In addition, the developed transmitting boundary is applied to the analysis of the dynamic behavior of rigid foundations of diverse shapes, and the effects of the level of the groundwater table on the dynamic stiffness of a rigid rectangular foundation in the water-saturated transversely isotropic layered stratum are studied.

• 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.

• 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.

• Geomechanics and Engineering
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• v.29 no.1
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• pp.53-63
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• 2022

Simplified analytical solutions are developed for the dynamic analyses of an axially loaded pile foundation embedded in a transverse-isotropic, fluid-filled, poro-visco-elastic soil with rigid substratum. The pile is modeled as a viscoelastic Rayleigh-Love rod, while the surrounding soil is regarded as a transversely isotropic, liquid-saturated, viscoelastic, porous medium of which the mechanical behavior is represented by the Boer's poroelastic media model and the fractional derivative model. Upon the separation of variables, the frequency-domain responses for the impedance function of the pile top, and the vertical displacement and the axial force along the pile shaft are gained. Then by virtue of the convolution theorem and the inverse Fourier transform, the time-domain velocity response of the pile head is derived. The presented solutions are validated, compared to the existing solution, the finite element model (FEM) results, and the field test data. Parametric analyses are made to show the effect of the soil anisotropy and the excitation frequency on the pile-soil dynamic responses.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.5
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• pp.521-532
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• 2007

Elastic wave propagations in the semi-infinite transversely isotropic cylinder under various kinds of longitudinal impact loads are analyzed using the axisymmetric finite element method and Houbolt time-integration scheme. For which the finite element program is newly constructed and verified through the comparison of present numerical results with those by other researchers. E-type glass-epoxy composite cylinders with different fiber volume fractions are adopted and studied in detail with dynamic responses of the isotropic cylinder. Three dimensional wave motions are given in graphic form to show the realistic view of the wave propagation. Nondimensionalized dynamic characteristic variables which relate the size of finite element mesh, the time step, and the wave speed are presented for obtaining accurate and stable numerical results.