• Journal of the Korean Geotechnical Society
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• v.17 no.5
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• pp.71-82
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• 2001

불포화토에 있어서 함수상태는 지반이 건조할수록 수축하고 습윤상태로 진행할수록 파괴에 이르게 하는 추가적인 입자간 응력을 발생시키며, 이러한 간극수와 흙입자 사이에 발생하는 현상을 규명하기 위해서는 정확한 모형화가 필요하다. 흙입자와 간극수 사이의 상호작용에서 흡입유발 유효응력(suction-induced effective stress)을 규명하기 위해 정규모형(regular packing)과 임의모형(random packing)이 적용될 수 있다. 최근의 연구결과에 따르면 흙은 흡입유발 유효응력과 밀접한 관계가 있으며, 흙의 비등방텐서(anisotropic tensor)를 구하기 위해 적용된 ALTERNAT 모델을 이용하여 구조텐서(fabric tensor)를 개략적으로 정의할 수 있다. Thornton의 임의모형 시뮬레이션은 구조텐서에 상응하는 파괴응력 상태를 포함하고 있으며, 미소역학 시뮬레이션을 통하여 구조텐서를 구하였다. 본 연구에서는 상기에 언급된 구형의 흙입자 모형에 대한 이론적 고찰이 수행되었고, ALTERNAT 모델을 적용한 간단한 비등방텐서의 결과를 구조텐서와 비교하였다. 본 연구결과 비등방텐서는 미소역학 시뮬레이션에 의한 구조텐서에 비해 약 20~40%정도 큰 값을 나타내었다.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2465-2470
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• 2007

We have analyzed the three-dimensional thermal conduction in anisotropic materials using nonsymmetric-Fourier transforms. And a complete theoretical treatment of the photothermal deflection spectroscopy has been performed for thermal conductivity measurement in anisotropic medium. Thermal conductivity tensor was determined by the deflection angle and phase angle with the relative position between the heating and probe beams. The influence of the parameters, such as modulation frequency of the heating beam, the thermal conductivity tensor, was investigated.

• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.150-155
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• 2003

Fractures in the form of micro cracks are commonly found in natural rocks. A rock behaves in a complex way due to fracture; in particular, the anisotropic strength of a rock material is significantly influenced by the presence of these fractures. Therefore, it is essential to understand the failure mechanism of a fractured rock. In this study, a fractured rock is formulated in terms of fabric tensor based on geometric and mechanical simplifications. In this way, position, density and shape of fractures can be determined by the fabric tensor so that rocks containing multi-fractures can successfully be modeled. Also an index to evaluate the degree of anisotropy of a fractured rock is proposed. Hence, anisotropic strength of a rock containing fractures under uniaxial compression condition is estimated through a series of numerical analyses for the multi-fractured model. Numerical investigations are carried out by varying the fracture angle from $0^{\circ}\;to\;90^{\circ}$ and relationship between uniaxial compression strength and the degree of anisotropy is investigated. By comparing anisotropic strength of numerical analysis with analytic solution, this study attempts to understand the failure mechanism of rock containing fractures.

• 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.

• Journal of Astronomy and Space Sciences
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• v.37 no.2
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• pp.131-142
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• 2020

As the laws of physics are expressed in a manner that makes their invariance under coordinate transformations manifest, they should be written in terms of tensors. Furthermore, tensors make manifest the characteristics and behaviors of electromagnetic fields through inhomogeneous, anisotropic, and compressible media. Electromagnetic fields are expressed completely in tensor form, F^αβ, which implies both electric field ${\overrightarrow{E}}$ and magnetic field ${\overrightarrow{B}}$ rather than separately in the vector fields. This study presents the Mathematica platform that generates and transforms a second-rank antisymmetric field-strength tensor F^αβ and whiskbroom pattern in Minkowski space. The platforms enhance the capabilities of students and researchers in tensor analysis and improves comprehension of the elegant features of complete structure in physics.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.3A
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• pp.309-316
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• 2010

This paper proposed a nonlocal anisotropic damage model to simulate the behavior of plain and reinforced concrete structures that are predominantly tensile and compressive load. This model based on continuum damage mechanics, used a symmetric second-order tensor as the damage variable. For quasi-brittle materials, such as concrete, the damage patterns were different in tension and in compression. These two damage states were modeled by damage evolution laws ensuring a damage tensor rate proportional to the total strain tensor in terms of principal components. To investigate the effectiveness of proposed model, the double edge notched specimen experimented by nooru-mohamed and reinforced concrete bending beam were analyzed using the implementation of the proposed model. As the results for the simulation, the nonlocal anisotropic damage model with an adequate control of rupture correctly represented the crack propagation for mixed mode fracture. In the structural failure of reinforced concrete bending beam, the proposed model can be showed up to a very high damage level and yielding of the reinforcements.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.736-740
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• 2007

It is not always convenient to consider isotropic meshes where the edge length depends on the orientation of the edge. It is desirable to go for anisotropic mesh strategy instead. There are many instances where the solution shows directional features such as great variations along certain directions with less significant changes along other ones. Anisotropic meshes considered to be worthy in these cases. By using anisotropic elements we can resolve the solution accurately with few elements. Many techniques have been used as a common feature that the shape, size and orientation of the triangle elements are controlled by specifying metric tensor. This paper attempts at clear understanding of the estimation and equidistribution of the error and discusses the parameters like reliability and effectivity of an anisotropic mesh in a mathematical manner. Also we study some of applications of anisotropic mesh.

• Journal of the Korean Geophysical Society
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• v.2 no.2
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• pp.123-134
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• 1999

Magnetotelluric responses may be affected by strong anisotropy of the high-conductivity layers (HCL) in the upper mantle or lower crust. We have studied two-dimensional anisotropy MT modelling to examine the effect of high anisotropic media. Electrical properties of a homogeneous anisotropic body are defined by a symmetric conductivity tensor and the problem is described by coupled diffusion equation in the frequency domain. In two-dimensional anisotropic environments, diagonal elements of the impedance tensor have higher values than those in isotropic environments. In some cases, TM mode phases reach more than 90°and apparent resistivities decrease for some frequency range because of telluric distortion. GB decomposition may be used to recover regional responses, but can be affected by the regional anisotropic effect. Considering these results, BC87 dataset was interpreted with a modified anisotropic model.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.13 no.5
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• pp.432-435
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• 2020

The elasticity tensor for water may be employed to model the fully saturated porous material. Mostly water is assumed to be incompressible with a bulk modulus, however, the upper and lower bounds of off-diagonal components of the elasticity tensor of porous materials filled with water are violated when the bulk modulus is relatively high. In many cases, the generalized Hill inequality describes the general bounds of Voigt and Reuss for eigenvalues, but the bounds for the component of elasticity tensor are more realistic because the principal axis of eigenvalues of two phases, matrix and water, are not coincident. Thus in this paper, for anisotropic material containing pores filled with water, the bounds for the component of elasticity tensor are expressed by the rule of mixture and the upper and lower bounds of fully saturated porous materials are violated for low porosity and high bulk modulus of water.

• Geomechanics and Engineering
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• v.5 no.1
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• pp.71-86
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• 2013

For rock materials, a transversely isotropic failure criterion established through the extended Lade-Duncan failure criterion incorporating an anisotropic state scalar parameter, which is a joint invariant of deviatoric microstructure fabric tensor and normalized deviatoric stress tensor, is verified with the results of triaxial compressive data on Tournemire shale. For torsional shear mode with $0{\leq}b{\leq}0.75$, rock shear strengths decrease with ${\alpha}$ increasing until the rock shear strength approaches minimum value at ${\alpha}{\approx}40^{\circ}$, and after this point, the rock shear strengths increase as ${\alpha}$ increases further. For the torsional shear mode with b > 0.75, rock shear strengths are almost constant for ${\alpha}{\leq}40^{\circ}$, but it increases with increase in ${\alpha}$ afterwards. The rock shear strength variation against ${\alpha}$ agrees with shear strength changing tendency of heavily OCR natural London Clays tested before. Prediction results show that the transversely isotropic failure criterion proposed in the paper is reasonable.