• Tunnel and Underground Space
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• v.14 no.5
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• pp.339-344
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• 2004

Variation of horizontal to vertical stress ratio of transversely isotropic rock caused by erosion was studied by numerical analysis. Influence of transversely isotropic was less than 5% for isotropic case. Difference between stresses obtained by numerical analysis and theoretical solution was small when initial stress ratio was small and the difference increased as erosion depth increased. Stress ratios diverged from initial ones as depth increased. An equation to determine stress ratio considering erosion according to the analyses was suggested.

• Tunnel and Underground Space
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• v.11 no.1
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• pp.59-63
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• 2001

The total number of elastic constants of an anisotropic body is 9 and thus it is very difficult to measure these constants experimentally. The number of elastic constants can be reduced if a rock or rock mass is regarded as isotropic or transversely isotropic material. Since only 4 stress-strain relationships can be obtained, it is theoretically impossible to determine all 5 constants from a single uniaxial compression teat. Lekhnitskii overcame this problem by suggesting the fifth equation based on laboratory tests. But his equation is theoretically wrong and does not agree with experimental results. This paper describes the stress-strain relationships and the independent/dependent elastic constants of an anisotropic mass and suggests a testing mothed to determine 5 independent elastic constants for a transversely isotropic rock.

• Tunnel and Underground Space
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• v.15 no.4 s.57
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• pp.288-295
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• 2005

Many mechanical defects originated from various geological causes make rock mass exhibit anisotropic characteristics. Understanding how the stress distribution occurs in anisotropic rock mass is, therefore, very important for the design of footings on rock and rock structures. In this study, the patterns of elastic stress distribution, developed by acting line load on the surface, in transversely isotropic was investigated. The influence of joint stiffness, joint spacing, and dip angle on the stress distribution was examined. By assuming the Mohr-Coulomb criterion as joint slip condition, the development of joint slip zone was also 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.

• Tunnel and Underground Space
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• v.15 no.6 s.59
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• pp.391-399
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• 2005

In this study, stress difference between isotropic and transversely isotropic rock mass, and planar principal stresses at the periphery of the tunnel in the rock with various ratio of anisotropy were determined theoretically. Stress differences between isotropic and anisotropic calculations at crown. side walls and floor of a tunnel with assumed stress states were analyzed and compare each other by $FLAC^{2D}$, a finite differential element method. As a result, magnitude and direction of principal stresses in the case of ignoring anisotropy were different from those of anisotropic cases, whatever the stress state was. Stress difference increased as the ratio of anisotropy increased. Direction or anisotropy affected stress difference, especially in the cases of anisotropic directions of $45^{\circ}\;and\;135^{\circ}$ of counterclockwise from x direction.

• 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.

• Journal of the Korean Society for Nondestructive Testing
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• v.21 no.3
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• pp.269-276
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• 2001

Ultrasonic testing of composite materials is much more difficult than that of isotropic materials, because of the beam skew phenomenon caused by their elastic anisotropy. An established analytical method exists for elastic wave propagation in anisotropic media as a result of previous research efforts. Yet, due to the complexity of the analytical method, solution of real problems must resort to the numerical method. In this work, analytical solutions have first been obtained for the wavefield due to a point source in a unidirectional fiber-reinforced composite, which may be modeled as transversely isotropic. Then, the corresponding numerical solutions have been obtained using the mass-spring lattice model(MSLM). The two solutions have agreed well with each other. Other problems such as reflection from free boundaries and scattering from cracks have also been solved numerically, and the results have been investigated from the viewpoint of wave mechanics. The numerical model whose validity has been confirmed by this work will be of great use in simulating ultrasonic testing of composite materials.

• Journal of the Korean Society for Nondestructive Testing
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• v.26 no.1
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• pp.30-39
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• 2006

Feasibility is studied for an application of the mass-spring lattice model (MSLM), a numerical model previously developed for unidirectional composites, to the numerical simulation of ultrasonic inspection of austenitic welds modeled as transversely isotropic. Fundamental wave processes, such as propagation, reflection, refraction, and diffraction of ultrasonic waves in such an inspection are simulated using the MSLM. All numerical results show excellent agreement with the analytical results. Further, a simplified model of austenitic weld inspection has been successfully simulated using the MSLM. In conclusion, a great potential of the MSLM in numerically simulating ultrasonic inspections of austenitic welds has been manifested in this work, though significant further efforts will be required to develop a model with field practicality.

• The Journal of Engineering Geology
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• v.33 no.4
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• pp.573-586
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• 2023

Joints or weak planes can induce anisotropy in the strength and deformability of fractured rock masses. Comprehending this anisotropic behavior is crucial to engineering geology. This study used plaster as a friction material to mold specimens with a single joint. The strength and deformability of the specimens were measured in true triaxial compression tests. The measured results were compared with three-dimensional numerical analysis based on the distinct element method, conducted under identical conditions, to assess the reliability of the modeled values. The numerical results highlight that the principal stress conditions in the field, in conjunction with joint orientations, are crucial factors to the study of the strength and deformability of fractured rock masses. The strength of a transversely isotropic rock mass derived numerically considering changes in the dip angle of the joint notably increases as the intermediate principal stress increases. This increment varies depending on the dip of the joint. Moreover, the interplay between the dip direction of the joint and the two horizontal principal stress directions dictates the strength of the transversely isotropic rock mass. For a rock mass with two joint sets, the set with the steeper dip angle governs the overall strength. If a rock bridge effect occurs owing to the limited continuity of one of the joint sets, the orientation of the set with longer continuity dominates the strength of the entire rock mass. Although conventional three-dimensional failure criteria for fractured rock masses have limited applicability in the field, supplementing them with numerical analysis proves highly beneficial.

• Tunnel and Underground Space
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• v.26 no.5
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• pp.363-374
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• 2016

All five independent elastic constants of a transversely isotropic rock sometimes need to be determined from a single specimen. Saint-Venant approximation has been widely used for a long time in the analysis of single specimen test. This paper has proven how this empirical equation can be mathematically transformed into a form of the apparent Young's modulus based on theory of elasticity. The transformed equation is a monotonous function on anisotropic angle and can be useful in the analysis of the in-situ stress measurement in an anisotropic rock mass. The estimations of data in literatures have shown that the measured values of $G^2$ are uniform on anisotropic angles and smaller than that of Saint-Venant's case. This decrement may be caused by sliding of the interface of strata and the decrement rate is inferred to relate well with the combination of bonding condition of strata and strength of rock material. Accumulation of these kinds of studies in the future enables to define the decrement and to determine elastic constants of a transversely isotropic rock from a single specimen from modifying Saint-Venant approximation.