한국지반공학회논문집 (Journal of the Korean Geotechnical Society)

  • 제22권9호
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  • Pages.45-59
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  • 2006
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  • 1229-2427(pISSN)
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  • 2288-646X(eISSN)
한국지반공학회 (Korean Geotechnical Society)
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Implicit 수치적분 방법을 이용한 조립토에 관한 구성방정식의 수행

Implicit Numerical Integration of Two-surface Plasticity Model for Coarse-grained Soils

  • Choi, Chang-Ho (Geotechnical Engineering Research Dept., Korea Institute of Construction Technology)
  • 발행 : 2006.09.30
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⟨ 이전 논문 다음 논문 ⟩

초록

탄소성 구성방정식은 주로 미분방적식(rate equation)으로 이루어져 있기 때문에 유한요소법 등을 이용한 지반구조물 해석시 미분방정식들에 대한 수치적분을 수행할 수 있는 방법이 필요하다. 구조물의 거동을 해석할시 미분방정식들을 위한 적분방법은 해석결과의 정확성과 유한요소법 모델링의 안전성에 큰 영향을 미치고 있다. 본 논문에서는 최근에 개발되어 사용되고 있는 흙에 관한 구성모델인 "Two-surface soil plasticity model (Manzari and Dafalias 1997)"을 Implicit return-mapping 수치적분방법을 이용하여 실행하는 과정을 제시한다. 본 연구에서 사용된 수치적분방법은 Closest-Point-Projection Method(CPPM) 방법으로 탄성 예측자-소성 교정자(elastic predictor-plastic corrector) 개념을 Implicit Backward Euler방법으로 체계화 시킨 알고리듬이다. 본 연구에서 수행한 "Two-surface soil plasticity model"은 조립토의 비선형거동을 해석하며, Bounding surface 개념 및 비선형 등방경화와 이동경화법칙을 사용하는 모델이다. 본 연구는 CPPM 방법이 정확하고 안정되며 유용한 수치적분을 수행할 수 있는 알고리듬이라는 것을 제시한다. 또한, CPPM 알고리듬은 구성방정식의 해를 반복적으로 해석하는 동안 "Consistent tangent operator $d{\sigma}/d{\varepsilon}$"를 제공하므로, 비선형 유한요소 해석이 2차(quadratic convergence rate)의 수렴 조건을 만족하는데 기여한다는 것을 보여준다.

The successful performance of any numerical geotechnical simulation depends on the accuracy and efficiency of the numerical implementation of constitutive model used to simulate the stress-strain (constitutive) response of the soil. The corner stone of the numerical implementation of constitutive models is the numerical integration of the incremental form of soil-plasticity constitutive equations over a discrete sequence of time steps. In this paper a well known two-surface soil plasticity model is implemented using a generalized implicit return mapping algorithm to arbitrary convex yield surfaces referred to as the Closest-Point-Projection method (CPPM). The two-surface model describes the nonlinear behavior of coarse-grained materials by incorporating a bounding surface concept together with isotropic and kinematic hardening as well as fabric formulation to account for the effect of fabric formation on the unloading response. In the course of investigating the performance of the CPPM integration method, it is proven that the algorithm is an accurate, robust, and efficient integration technique useful in finite element contexts. It is also shown that the algorithm produces a consistent tangent operator $\frac{d\sigma}{d\varepsilon}$ during the iterative process with quadratic convergence rate of the global iteration process.

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