탄성영역이 없는 J2-경계면 소성모델 = J2-bounding Surface Plasticity Model with Zero Elastic Region

다국어 초록 (Multilingual Abstract)

Soil plasticity models for cyclic and dynamic loads are essential in non-linear numerical analysis of geotechnical structures. While a single yield surface model shows a linear behavior for cyclic loads, J2-bounding surface plasticity model with zero elastic region can effectively simulate a nonlinearity of the ground response with the same material properties. The radius of the yield surface inside the boundary surface converged to 0 to make the elastic region disappear, and plastic hardening modulus and dilatancy define plastic strain increment. This paper presents the stress-strain incremental equation of the developed model, and derives plastic hardening modulus for the hyperbolic model. The comparative analyses of the triaxial compression test and the shallow foundation under the cyclic load can show stable numerical convergence, consistency with the theoretical solution, and hysteresis behavior. In addition, plastic hardening modulus for the modified hyperbolic function is presented, and a methodology to estimate model variables conforming 1D equivalent linear model is proposed for numerical modeling of the multi-dimensional behavior of the ground.

국문 초록 (Abstract)

반복하중이나 동적하중에 대한 지반의 소성모델은 지반구조물의 비선형 수치해석에 매우 중요하다. 단일 항복면 모델은 반복하중에 대해 선형적 거동을 보이는 반면, 개발된 탄성영역이 없는 J2-경계면 소성모델은 동일한 물성치로 효과적으로 지반의 비선형성을 모사할 수 있다. 경계면 내부 항복면의 반경을 0으로 수렴시켜 탄성영역이 사라지도록 수식화하고, 소성경화 계수과 팽창률을 이용하여 소성변형 증분을 정의하였다. 개발된 모델의 응력-변형률 증분식을 제시하고, 쌍곡선 모델에 대한 소성경화 계수를 유도하였다. 삼축압축조건과 얕은기초의 반복하중에 대한 비교해석은 개발된 모델의 안정적인 수렴성, 이론식과의 일치성, 그리고 이력경로을 보여 주었다. 또한, 수정된 쌍곡선함수에 대한 소성경화 계수를 제시하여, 1차원 등가선형모델에 부합하는 모델변수 산정법을 제안하여 지반의 다차원 거동을 모델링할 수 있도록 하였다.

참고문헌 (Reference)

1 신호성, "불포화지반에 대한 열-수리-역학 거동의 수식화" 한국지반공학회 27 (27): 75-83, 2011

2 Terzaghi, K, "Theoretical Soil Mechanics" Wiley 1943

3 Prager, W., "The theory of plasticity-A survey of recent achievements" 169 (169): 41-57, 1955

4 d’Onofrio, A., "Strain rate dependent behavior of a natural stiff clay" Elsevier 39 (39): 69-82, 1999

5 Ishihara, K, "Soil behaviour in earthquake geotechnics" Oxford science publications 1996

6 Pisanò, F., "Simulating stiffness degradation and damping in soils via a simple visco-elastic-plastic model" Elsevier 63 : 98-109, 2014

7 Anastasopoulos, I., "Simplified constitutive model for simulation of cyclic response of shallow foundations : Validation against laboratory tests" ASCE 137 (137): 1154-1168, 2011

8 Hardin, B. O., "Shear modulus and damping in soils-design equations and curves" ASCE 98 (98): 667-692, 1972

9 Dafalias, Y. F., "SANISAND-Z : Zero elastic range sand plasticity model" ICE 66 (66): 999-1013, 2016

10 Yu, H. S., "Plasticity and geotechnics" Springer 2006

11 Borja, R. I., "Non-linear ground response at Lotung LSST site" ASCE 125 (125): 187-197, 1999

12 Borja, R. I., "Multiaxial cyclic plasticity model for clays" ASCE 120 (120): 1051-1070, 1994

13 Restrepo, D., "Multiaxial cyclic plasticity in accordance with 1D hyperbolic models and Masing criteria" Wiley 42 (42): 2095-2108, 2018

14 Roscoe, K. H., "Mechanical behaviour of an idealized ‘wet’ clay" 1 : 47-54, 1963

15 Kondner, R. L., "Hyperbolic stress-strain response : cohesive soils" ASCE 89 (89): 115-143, 1963

16 Kramer, S. L, "Geotechnical earthquake engineering" Prentice-Hall 1996

17 Yang, B., "Experimental investigation and empirical model on damping properties of rock under multistage cyclic loading" Elsevier 163 : 107557-, 2022

18 Masing, G., "Eignespannungen und Verfestigung beim Messing" 332-335, 1926

19 Dafalias, Y. F., "Cyclic loading for materials with a vanishing elastic region" Elsevier 41 (41): 293-302, 1977

20 Simo, J. C., "Consistent tangent operators for rate-independent elastoplasticity" Elsevier 48 (48): 101-118, 1985

21 Stewart, J. P., "Benchmarking of non-linear geotechnical ground response analysis procedures" Pacific earthquake engineering research center 2008

22 Shin, H., "An implicit joint-continuum model for the hydro-mechanical analysis of fractured rock masses" Elsevier 119 : 140-148, 2019

23 Yu, H. S., "A unified plasticity model for cyclic behaviour of clay and sand" Elsevier 34 (34): 97-114, 2007

24 Been, K., "A state parameter for sands" ICE 35 (35): 99-112, 1985

25 Dafalias, Y. F., "A model of nonlinearly hardening materials for complex loading" Springer 21 (21): 173-192, 1975