砂土剪胀软化、剪缩硬化统一本构的显式计算
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摘要
密实砂土通常表现出常压下剪胀软化特性、高压下剪缩硬化特性,不同的力学特性对岩土体受荷力学行为的演化有着重要影响。构建能够反映剪胀软化、剪缩硬化特性的本构模型并且实现其数值模拟计算,则是分析剪胀软化材料的受荷响应特征以及完善岩土体渐进破坏理论所要解决的一个重要科学问题。研究中首先对已构建的能够反映密实砂土相关力学特性的砂土统一本构模型进行描述,分析该模型的数值计算关键问题。基于显式方法进行模型应力积分程序的二次开发,应力积分过程中采用应变空间中的加卸载准则并对模型破坏面进行光滑处理以满足计算过程中的加卸载判断以及塑性应变方向的确定。通过计算实例验证了显式方法能够克服剪胀、软化问题的计算难点,可以实现对剪胀软化、剪缩硬化材料的力学行为分析计算。
Dense sand normally exhibits shear dilatancy softening under normal pressure and shear shrinkage hardening under high pressure. Therefore, unified model of sand and its numerical implementation is an important scientific problem for describing the loading response of dilatancy softening material, and it will also promote the progressive failure theory. In this study, the unified model of sand which reflects the mechanical properties of dense sand under normal and high pressure is firstly described, and then the key problem of numerical calculation for the model is analyzed. By using the explicit method, the secondary development of stress integration program is carried out. In the process of stress integration, loading-unloading criterion within strain space and smoothed failure surface are used for satisfying the judgment of loading condition and determination of plastic strain direction. An example is given to prove that the explicit method can overcome the difficulties in calculation for dilatancy and softening. This method shows a good way to analyze the mechanical behavior for materials with dilatancy softening and shrinkage hardening characteristics.
Dense sand normally exhibits shear dilatancy softening under normal pressure and shear shrinkage hardening under high pressure. Therefore, unified model of sand and its numerical implementation is an important scientific problem for describing the loading response of dilatancy softening material, and it will also promote the progressive failure theory. In this study, the unified model of sand which reflects the mechanical properties of dense sand under normal and high pressure is firstly described, and then the key problem of numerical calculation for the model is analyzed. By using the explicit method, the secondary development of stress integration program is carried out. In the process of stress integration, loading-unloading criterion within strain space and smoothed failure surface are used for satisfying the judgment of loading condition and determination of plastic strain direction. An example is given to prove that the explicit method can overcome the difficulties in calculation for dilatancy and softening. This method shows a good way to analyze the mechanical behavior for materials with dilatancy softening and shrinkage hardening characteristics.
引文
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[29]GAO Z W,ZHAO J D.Strain localization and fabric evolution in sand[J].International Journal of Solids&Structures,2013,50(22-23):3634-3648.
[2]YAO Y P,SUN D A,LUO T.A critical state model for sands dependent on stress and density[J].International Journal for Numerical and Analytical Methods in Geomechanics,2004,28(4):323-337.
[3]YAO Y P,SUN D A,MATSUOKA H.A unified constitutive model for both clay and sand with hardening parameter independent on stress path[J].Computers and Geotechnics,2008,35(2):210-222.
[4]张卫华,赵成刚,傅方.基于相变状态的非饱和砂土边界面本构模型[J].应用力学学报,2015,32(5):724-730.ZHANG Wei-hua,ZHAO Cheng-gang,FU Fang.The bounding-surface constitutive model for unsaturated sands based on the phase transformation state[J].Chinese Journal of Applied Mechanics,2015,32(5):724-730.
[5]CHAVEZ C,ALONSO E E.A constitutive model for crushed granular aggregates which includes suction effects[J].Soils and Foundations,2003,43(4):215-227.
[6]SALIM W,INDRARATNA B.A new elastoplastic constitutive model for coarse granular aggregates incorporating particle breakage[J].Canadian Geotechnical Journal,2004,41(4):657-671.
[7]SUN D,HUANG W,SHENG D,et al.An elastoplastic model for granular materials exhibiting particle crushing[J].Key Engineering Materials,2007,340-341(36):1273-1278.
[8]YAO Y P,YAMAMOTO H,WANG N D.Constitutive model considering sand crushing[J].Soils and Foundations,2008,48(4):603-608.
[9]HU W,YIN Z Y,DANO C,et al.A constitutive model for granular materials considering grain breakage[J].Science China-Technological Sciences,2011,54(8):2188-2196.
[10]冯兆祥,吉林,卓家寿.考虑材料应变软化的非线性有限元的改进变Kp法[J].解放军理工大学学报(自然科学版),2005,6(4):56-61.FENG Zhao-xiang,JI Lin,ZHUO Jia-shou.Improved variational Kp method of nonlinear FE considering strain-softening of material[J].Journal of PLAUniversity of Science and Technology,2005,6(4):56-61.
[11]彭芳乐,李福林,白晓宇.针对砂土应变软化强非线性问题的动态松弛有限元法研究[J].岩土力学,2012,33(2):33-37.PENG Fang-le,LI Fu-lin,BAI Xiao-yu.A dynamic relaxation-finite element method for strong nonlinearity caused by post-peak strain softening of sands[J].Rock and Soil Mechanics,2012,33(2):33-37.
[12]陆勇,周国庆,顾欢达.高低压下不同力学特性的砂土统一模型[J].岩土力学,2018,39(2):614-620.LU Yong,ZHOU Guo-qing,GU Huan-da.Unified model of sand with different mechanical characteristics under high and low pressures[J].Rock and Soil Mechanics,2018,39(2):614-620.
[13]SCHOFIELD A,WROTH P.Critical state soil mechanics[M].London:Mc Graw-Hill,1968.
[14]陆勇,周国庆,顾欢达.常压至高压下砂土强度、变形特性试验研究[J].岩石力学与工程学报,2016,35(11):2369-2376.LU Yong,ZHOU Guo-qing,GU Huan-da.Experimental study of strength and deformation characteristics of sand under different pressures[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(11):2369-2376.
[15]罗汀,姚仰平,侯伟.土的本构关系[M].北京:人民交通出版社,2010.LUO Ting,YAO Yang-ping,HOU Wei.Constitutive law of soil[M].Beijing:China Communications Press,2008.
[16]姚仰平,余亚妮.基于统一硬化参数的砂土临界状态本构模型[J].岩土工程学报,2011,33(12):1827-1832.YAO Yang-ping,YU Ya-ni.Extended critical state constitutive model for sand based on unified hardening parameter[J].Chinses Journal of Geomechnical Engineering,2011,33(12):1827-1832.
[17]RIEMER M F,SEED R B.Factors affecting apparent position of steady-state line[J].Journal of Geotechnical and Geoenvironmental Engineering,1997,123(3):281-288.
[18]LI X S,WANG Y.Linear representation of steady-state line for sand[J].Journal of Geotechnical and Geoenvironmental Engineering,1998,124(12):1215-1217.
[19]殷有泉.非线性有限元基础[M].北京:北京大学出版社,2007.YIN You-quan.Nonlinear finite element basis[M].Beijing:Peking University press,2007.
[20]ABBO A J,SLOAN S W.A smooth hyperbolic approximation to the Mohr-Coulomb yield criterion[J].Computers&Structures,1995,54(3):427-441.
[21]KLISINSKI M.Degradation and plastic deformation of concrete[D].Poland:IFTR Rep,1985.
[22]SHENG D,SLOAN S W,YU H S.Aspects of finite element implementation of critical state models[J].Computational Mechanics,2000,26(2):185-196.
[23]赵冰,李宁,盛国刚.软化岩土介质的应变局部化研究进展[J].岩土力学,2005,26(3):494-499.ZHAO Bing,LI Ning,SHENG Guo-gang.Recent development of strain localization of softening geo-materials[J].Rock and Soil Mechanics,2005,26(3):494-499.
[24]薛海斌,党发宁,尹小涛,等.基于动力学和材料软化特性的边坡渐进破坏特征研究[J].岩土力学,2016,37(8):2238-2246.XUE Hai-bin,DANG Fa-ning,YIN Xiao-tao,et al.Progressive failure characteristics of slopes considering strain-softening behavior of geotechnical materials and dynamics[J].Rock and Soil Mechanics,2016,37(8):2238-2246.
[25]施维成,朱俊高,刘汉龙.中主应力对砾石料变形和强度的影响[J].岩土工程学报,2008,30(10):1449-1453.SHI Wei-cheng,ZHU Jun-gao,LIU Han-long.Influence of intermediate principal stress on deformation and strength of gravel[J].Chinese Journal of Geotechnical Engineering,2008,30(10):1449-1453.
[26]肖杨,刘汉龙,陈育民.砂土中主应力与内摩擦角统一关系研究[J].岩土工程学报,2012,34(6):1102-1108.XIAO Yang,LIU Han-long,CHEN Yu-min.Unified relationship between intermediate principal stress and internal friction angle for sand[J].Chinese Journal of Geotechnical Engineering,2012,34(6):1102-1108.
[27]HALL S A,BORNERT M,DESRUES J,et al.Discrete and continuum analysis of localised deformation in sand using X-ray CT and volumetric digital image correlation[J].Geotechnique,2010,60(5):11-20.
[28]GUO N,ZHAO J D.Multiscale insights into classical geomechanics problems[J].International Journal for Numerical&Analytical Methods in Geomechanics,2016,40(3):367-390.
[29]GAO Z W,ZHAO J D.Strain localization and fabric evolution in sand[J].International Journal of Solids&Structures,2013,50(22-23):3634-3648.