대한토목학회논문집 (KSCE Journal of Civil and Environmental Engineering Research)

  • 제43권4호
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  • Pages.469-476
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  • 2023
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  • 1015-6348(pISSN)
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  • 2799-9629(eISSN)
대한토목학회 (Korean Society of Civil Engeneers)
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탄성영역이 없는 J2-경계면 소성모델

J2-bounding Surface Plasticity Model with Zero Elastic Region

  • 신호성 (울산대학교 건설환경공학부) ;
  • 오세붕 (영남대학교 건설시스템공학과) ;
  • 김재민 (전남대학교 토목공학과)
  • 투고 : 2023.01.19
  • 심사 : 2023.05.10
  • 발행 : 2023.08.01
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초록

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.

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.

키워드

과제정보

본 연구는 한국연구재단 중견연구자지원사업(NRF-2022R1A2C200823612)과 한국수력원자력(주) 해오름동맹출연사업(원전지역 특화연구)의 지원으로 수행되었으며, 이에 깊은 감사를 드립니다.

참고문헌

  1. Anastasopoulos, I., Gelagoti, F. and Kourkoulis, R. (2011). "Simplified constitutive model for simulation of cyclic response of shallow foundations: Validation against laboratory tests." Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 137, No. 12, pp. 1154-1168, https://doi.org/10.1061/(ASCE)GT.1943-5606.0000534.
  2. Been, K. and Jefferies, M. G. (1985). "A state parameter for sands." Geotechnique, ICE, Vol. 35, No. 2, pp. 99-112, https://doi.org/10.1680/geot.1985.35.2.99.
  3. Borja, R. I. and Amies, A. P. (1994). "Multiaxial cyclic plasticity model for clays." Journal of Geotechnical Engineering, ASCE, Vol. 120, No. 9, pp. 1051-1070, https://doi.org/10.1061/(ASCE)0733-9410(1994)120:6(1051).
  4. Borja, R. I., Chao, H. Y., Montans, F. J. and Lin, C. H. (1999). "Non-linear ground response at Lotung LSST site." Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 125, No. 3, pp. 187-197, https://doi.org/10.1061/(ASCE)1090-0241(1999)125:3(187).
  5. Dafalias, Y. F. and Popov, E. P. (1975). "A model of nonlinearly hardening materials for complex loading." Acta Mechanica, Springer, Vol. 21, No. 3, pp. 173-192. https://doi.org/10.1007/BF01181053
  6. Dafalias, Y. F. and Popov, E. P. (1977). "Cyclic loading for materials with a vanishing elastic region." Nuclear Engineering and Design, Elsevier, Vol. 41, No. 2, pp. 293-302, https://doi.org/10.1016/0029-5493(77)90117-0.
  7. Dafalias, Y. F. and Taiebat, M. (2016). "SANISAND-Z: Zero elastic range sand plasticity model." Geotechnique, ICE, Vol. 66, No. 12, pp. 999-1013, https://doi.org/10.1680/jgeot.15.P.271.
  8. d'Onofrio, A., Silvestri, D. and Vinale, F. (1999). "Strain rate dependent behavior of a natural stiff clay." Soils and Foundations, Elsevier, Vol. 39, No. 2, pp. 69-82, https://doi.org/10.3208/sandf.39.2_69.
  9. Hardin, B. O. and Drnevich, V. P. (1972). "Shear modulus and damping in soils-design equations and curves." Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 98, No. 7, pp.667-692, https://doi.org/10.1061/JSFEAQ.0001760.
  10. Ishihara, K. (1996). Soil behaviour in earthquake geotechnics, Oxford science publications, South East England, UK.
  11. Kondner, R. L. (1963). "Hyperbolic stress-strain response: cohesive soils." Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 89, No. 1, pp. 115-143, https://doi.org/10.1061/JSFEAQ.0000479.
  12. Kramer, S. L. (1996). Geotechnical earthquake engineering, Prentice-Hall.
  13. Masing, G. (1926). Eignespannungen und Verfestigung beim Messing, 2nd International Congress on Applied Mechanics, Switzerland, pp. 332-335.
  14. Pisano, F. and Jeremic, B. (2014). "Simulating stiffness degradation and damping in soils via a simple visco-elastic-plastic model." Soil Dynamics and Earthquake Engineering, Elsevier, Vol. 63, pp. 98-109, https://doi.org/10.1016/j.soildyn.2014.02.014.
  15. Prager, W. (1955). "The theory of plasticity - A survey of recent achievements." Proceedings of the Institution of Mechanical Engineers, Vol. 169, No. 1, pp. 41-57, https://doi.org/10.1243/PIME_PROC_1955_169_015_02.
  16. Restrepo, D. and Taborda, R. (2018). "Multiaxial cyclic plasticity in accordance with 1D hyperbolic models and Masing criteria." International Journal for Numerical and Analytical Methods in Geomechanics, Wiley, Vol. 42, No. 17, pp. 2095-2108, https://doi.org/10.1002/nag.2845.
  17. Roscoe, K. H. and Schofield, A. N. (1963). "Mechanical behaviour of an idealized 'wet' clay." Proceedings of 3rd European Conference on Soil Mechanics and Foundation Engineering, Wiesbaden, Germany, Vol. 1, pp. 47-54.
  18. Shin, H. (2011). "Formulation of fully coupled THM behavior in unsaturated soil." Journal of the Korean Geotechnical Society, KGS, Vol. 27, No. 3, pp. 75-83, https://doi.org/10.7843/kgs.2011.27.3.075 (in Korean).
  19. Shin, H. and Santamarina, J. (2019). "An implicit joint-continuum model for the hydro-mechanical analysis of fractured rock masses." International Journal of Rock Mechanics and Mining Sciences, Elsevier, Vol. 119, pp. 140-148, https://doi.org/10.1016/j.ijrmms.2019.04.006.
  20. Simo, J. C. and Taylor, R. L. (1985). "Consistent tangent operators for rate-independent elastoplasticity." Computer Methods in Applied Mechanics and Engineering, Elsevier, Vol. 48, No. 1, pp. 101-118, https://doi.org/10.1016/0045-7825(85)90070-2.
  21. Stewart, J. P., Kwok, A. O. L., Hashash, Y. M. A., Matasovic, N., Pyke, R., Wang, Z. L. and Yang, Z. (2008). Benchmarking of non-linear geotechnical ground response analysis procedures, Pacific earthquake engineering research center.
  22. Terzaghi, K. (1943). Theoretical Soil Mechanics, Wiley.
  23. Yang, B., He, M., Zhang, Z., Zhu, J. and Chen, Y. (2022). "Experimental investigation and empirical model on damping properties of rock under multistage cyclic loading." Soil Dynamics and Earthquake Engineering, Elsevier, Vol. 163, 107557, https://doi.org/10.1016/j.soildyn.2022.107557.
  24. Yu, H. S. (2006). Plasticity and geotechnics, Springer.
  25. Yu, H. S., Khong, C. and Wang, J. (2007). "A unified plasticity model for cyclic behaviour of clay and sand." Mechanics Research Communications, Elsevier, Vol. 34, No. 2, pp. 97-114, https://doi.org/10.1016/j.mechrescom.2006.06.010.