• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2006년도 춘계 학술발표회 논문집
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• pp.286-300
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• 2006

Nonlinear cross-anisotropic properties of soil is critical for exact numerical simulation. Theoretically, initial cross-anisotropic properties can be evaluated from triaxial tests with bender element tests, and nonlinear cross-anisotropic properties over initial strain level cannot be evaluated from triaxial tests. In this study, a supposed condition among nonlinear cross-anisotropic properties is suggested to calculate nonlinear cross-anisotropic properties from triaxial tests. Maximum strain and incremental strain energy are applied to combine triaxial test results and theoretical normalized shear modulus curve, respectively Based on combined results, nonlinear cross-anisotropic properties are calculated. Numerical simulation for triaxial tests Is carried out to verify the applicability of the supposed condition with calculated cross-anisotropic properties and simplified nonlinear cross-anisotropic model.

• 한국터널지하공간학회 논문집
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• 제6권4호
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• pp.291-302
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• 2004

발파압력이 발파공 주위 암반에 발생시키는 암반손상을 연속체 손상역학과 사용자 부프로그램을 이용한 수치해석을 통하여 분석하였다. 암반의 이방성 특성을 적용한 이방성 발파압력을 산출하였으며, 이를 이용하여 이방성 암반손상을 분석하였다. 또한 등방성 암반손상에 대해서도 분석하였다. 자연 암반이 가지고 있는 초기손상을 함께 고려하여 암반손상을 분석하였다. 등방성 암반손상의 매개변수 분석결과, 발파압력과 탄성계수가 암반손상에 가장 크게 영향을 미쳤다. 또한 이방성 암반손상의 매개변수 분석결과, 발파압력이 이방성 암반손상에 가장 크게 영향을 미쳤으나 탄생계수는 이방성 암반손상에 크게 영향을 미치지 않음을 알 수 있었다. 등방성과 이방성 암반손상을 등방성 암반손상과 비교한 결과, 이방성 암반의 수평방향 암반손상이 약 34% 증가 하였고 수직방향은 12% 감소하는 결과를 얻을 수 있었다. 등방성 암반에 대한 밀장전 조건과 디커플링장전 조건하에 발파로 인한 암반손상을 비교한 결과, 밀장전 조건의 암반손상이 디커플링장전 조건보다 약30배 정도 크게 나타났으며, 밀장전 조건의 발파압력은 디커플링장전 조건보다 10배 이상 큼을 알 수 있었다.

• Geomechanics and Engineering
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• 제25권4호
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• pp.303-315
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• 2021

A rigorous and generic similarity solution is developed for assessment of the undrained expansion responses of a cylindrical cavity expansion in K₀-consolidated anisotropic soils. A K₀-consolidated anisotropic modified Cam-clay (K₀-AMCC) model that can represent the initial stress anisotropy and the effects of stress-induced anisotropy is used to model the soil behaviors during cavity expansion. All the seven basic unknowns, the three stress components, the pore water pressure, the particle velocity, the specific volume and the hardening parameter, are reduced to the functions of a dimensionless radial coordinate and are taken as coupled variables to formulate the problem. The governing equations are formulated by making use of the equilibrium equation, the constitutive equation, the consistency condition, the continuity condition and the undrained condition, which are then solved as an initial value problem. The proposed rigorous similarity solution is compared with some well-documented rigorous solutions to validate the solution and to highlight the special expansion responses in anisotropic soils. The results reveal that the present solution can yield more predictions for cavity expansion problems in soils with initial anisotropic stresses.

• 지구물리와물리탐사
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• 제11권2호
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• pp.153-160
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• 2008

실제 매질에서 전파하는 파의 거동을 묘사하기 위하여 탄성파 모델링을 수행한다. 일반적으로 실제매질은 반무한 매질이나 컴퓨터를 이용한 수치모델링에서 반무한 매질을 표현하기는 쉽지 않다. 따라서, 유한한 크기의 모형을 가정하며, 이 경우 모형의 좌우 및 하부 경계는 가상의 경계이므로 이로부터 반사되는 인위적인 반사파들은 적절한 경계조건을 도입하여 제거되어야 한다. 최근 들어 등방성 매질 뿐 아니라 이방성 매질에 대한 연구가 증가하면서 이방성 매질에서의 경계를 적절히 표현해 줄 수 있는 방법이 필요하게 되었다. 본 연구에서는 등방성 매질의 탄성파 모델링에서 가장 많이 이용되는 스펀지 경계조건, Clayton과 Engquist가 제안한 흡수경계조건, Higdon의 흡수경계조건 세 방법을 이방성 매질에 적용할 수 있도록 변형한 후 다양한 포아송의 비를 갖는 모형에 적용함으로써 세 경계조건의 특성을 분석해 보았다. Clayton과 Engquist의 흡수경계조건은 등방성 매질에서 포아송의 비가 클 때 불안정한 모습을 보이는데, 이방성 매질에서도 역시 같은 결과를 보여주었다. 스펀지 경계조건은 등방성 매질과 이방성 매질에서 매우 좋은 결과를 보여주었지만, 컴퓨터 메모리나 계산시간을 고려하였을 때 비효율적이다. 이에 반해 Higdon이 제안한 경계조건은 필요로 하는 컴퓨터 메모리와 계산시간이 적을 뿐 아니라 큰 각도로 입사되는 파에 의해 발생하는 반사파까지 효과적으로 제거하였다. 따라서 포아송의 비가 비교적 크게 나타나는 이방성 매질에서는 계산상의 효율성 등을 고려할 때 Higdon의 흡수경계조건이 적합할 것으로 생각된다.

• Geomechanics and Engineering
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• 제19권2호
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• pp.141-151
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• 2019

A novel theoretical solution is presented for created (zero initial radius) cavity expansion problem based on CamClay model and considers the effect of initial anisotropic in-situ stress and drained conditions. Here the strain of this theoretical solution is small deformation in elastic region and large deformation in plastic region. The works for cylindrical and spherical cavities expanding in drained condition from zero initial radius are investigated. Most of the conventional solutions were based on the isotropic and undrained condition, however, the initial stress state of natural soil mass is anisotropy by soil deposition history, and drained cavity expansion calculation is closer to actual engineering in permeable soil mass. Finally, the parametric study is presented in order to the engineering significance of this work.

• 대한수학회보
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• 제58권2호
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• pp.365-384
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• 2021

Let A be an expansive dilation on ℝn, and p(·) : ℝn → (0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. Let Hp(·)A (ℝn) be the variable anisotropic Hardy space defined via the non-tangential grand maximal function. In this paper, the author obtains the boundedness of anisotropic convolutional ��-type Calderón-Zygmund operators from Hp(·)A (ℝn) to Lp(·) (ℝn) or from Hp(·)A (ℝn) to itself. In addition, the author also obtains the duality between Hp(·)A (ℝn) and the anisotropic Campanato spaces with variable exponents.

• 한국지구물리탐사학회:학술대회논문집
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• 한국지구물리탐사학회 2003년도 Proceedings of the international symposium on the fusion technology
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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.

• 대한수학회지
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• 제58권5호
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• pp.1109-1129
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• 2021

This paper considers an anisotropic polytropic infiltration equation with a source term $$u_t={\sum\limits_{i=1}^{N}}{\frac{{\partial}}{{\partial}x_i}}\(a_1(x){\mid}u{\mid}^{{\alpha}_i}{\mid}u_{x_i}{\mid}^{p_i-2}u_{x_i}\)+f(x,t,u)$$, where p_i > 1, α_i > 0, a_i(x) ≥ 0. The existence of weak solution is proved by parabolically regularized method. Based on local integrability $u_{x_i}{\in}W_{loc}^{1,p_i}(\Omega)$, the stability of weak solutions is proved without boundary value condition by the weak characteristic function method. One of the essential characteristics of an anisotropic equation different from an isotropic equation is found originally.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2002년도 봄 학술발표회 논문집
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• pp.41-48
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• 2002

The fact that nonlinearity and anisotropy of soil should be considered for the proper estimation of soil deformation has been recongnized for a long time. In this study, a new stiffness model which can reflect both nonlinearity and anisotropy is proposed. Nonlinearity is simulated by Ramberg-Osgood model and anisotropy is modeled with the cross-anisotropic elasticity. Analysis results with the developed model compared with those from analyses using linear isotropic model, linear anisotropic model, and nonlinear isotropic model. In the triaxial compression like condition, the effects of nonlinearity on the vertical strain are significant, but soil anisotropy does not affect the vertical strain. In 1-dimensional deformation condition, however, both nonlinearity and anisotropy of soil influence the final magnitude of the vertical strain. Also the increase of poisson's ratio magnifies the effect of anisotropy on the vertical strain in this condition.

• 대한수학회보
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• 제47권2호
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• pp.231-249
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• 2010

Asymptotic behavior of three-dimensional mixed, periodic and rotating magnetohydrodynamic system is investigated as the Rossby number goes to zero. The system presents the difficulty to be singular and mixed, that is hyperbolic in the vertical direction and parabolic in the horizontal one. The divergence free condition and the spectral properties of the penalization operator are crucial in the proofs. The main tools are the energy method, the Schochet's method and products laws in anisotropic Sobolev spaces.