基于特征应力的正常固结土三维弹塑性本构模型
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摘要
在特征应力空间中,Drucker-Prager形式的强度准则可以合理描述岩土类材料的真三维强度特性,即特征应力具有以各向同性形式的表达式描述岩土类材料各向异性力学特性的功能。在特征应力空间中,利用插值函数法直接提出了正常固结土的新的屈服函数,结合笔者已在特征应力空间中提出的塑性势函数,直接建立了正常固结土的真三维弹塑性本构模型。模型只有7个材料参数,每个参数均具有明确的物理意义,可利用室内试验简单确定。通过模型功能分析以及与文献中试验结果的对比验证表明,本文模型可简单合理地描述正常固结土的真三维变形与强度特性,并且可简化为修正剑桥模型。
The strength criterion in the characteristic stress space, whose form is the same as that of the Drucker-Prager strength criterion, can describe the true three-dimensional strength of geomaterials. In other words, the isotropic function in the characteristic stress space can describe the anisotropic mechanical properties of the geomaterials. In the characteristic stress space, a new yield function is proposed for the normally consolidated soils on the basis of the interpolation function method. By using the plastic potential function from the authors' previous researches, a true 3D elastoplastic constitutive model for normally consolidated soils is directly established in the characteristic stress space. There are only 7 parameters in the proposed model. All the parameters have clear physical meanings and can be easily determined through laboratory tests. The proposed model is analyzed through model simulations and is verified using the soil data available in the literatures. These results demonstrate that the proposed model can simply and reasonably describe the characteristics of the true three-dimensional strength and deformation of normally consolidated soils and can be degenerated to the modified Cam-clay model.
The strength criterion in the characteristic stress space, whose form is the same as that of the Drucker-Prager strength criterion, can describe the true three-dimensional strength of geomaterials. In other words, the isotropic function in the characteristic stress space can describe the anisotropic mechanical properties of the geomaterials. In the characteristic stress space, a new yield function is proposed for the normally consolidated soils on the basis of the interpolation function method. By using the plastic potential function from the authors' previous researches, a true 3D elastoplastic constitutive model for normally consolidated soils is directly established in the characteristic stress space. There are only 7 parameters in the proposed model. All the parameters have clear physical meanings and can be easily determined through laboratory tests. The proposed model is analyzed through model simulations and is verified using the soil data available in the literatures. These results demonstrate that the proposed model can simply and reasonably describe the characteristics of the true three-dimensional strength and deformation of normally consolidated soils and can be degenerated to the modified Cam-clay model.
引文
[1]WOOD D M.Soil behaviour and critical state soil mechanics[M].Cambridge:Cambridge University Press,1990.
[2]ROSCO K H,SCHOFIELD A N,WROTH C P.On the yielding of soils[J].Géotechnique,1958,8:22-53.
[3]ROSCOE K H,BURLAND J B.On the generalized stress-strain behavior of an ideal wet clay[M].Cambridge:Cambridge University Press,1968:535-609.
[4]WROTH C P,HOULSBY G T.Soil mechanics-property characterization and analysis procedures[C]//Proceedings of the 11th International Conference on Soil Mechanics and Foundation Engineering.San Francisco,1985:1-55.
[5]ZIENKIEWICZ O C,PANDE G N.Some useful forms of isotropic yield surface for soil and rock mechanics[C]//Finite Elements in Geomechnaics.London,1977:179-190.
[6]HASHIGUCHI K.A proposal of the simplest convex-conical surface for soils[J].Soils and Foundations,2002,42(3):107-113.
[7]XIAO Y,LIU H L,LIANG R Y.Modified Cam-clay model incorporating unified nonlinear strength criterion[J].Science China Technological Sciences,2011,54(4):805-10.
[8]TSIAMPOUSI A,ZDRAVKOVIC L,POTTS D M.A new Hvorslev surface for critical state type unsaturated and saturated constitutive models[J].Computers and Geotechnics,2013,48:156-166.
[9]CHAKRABORTY T,SALGADO R,LOUKIDIS D.Atwo-surface plasticity model for clay[J].Computers and Geotechnics,2013,49:170-190.
[10]SUTHARSAN T,MUHUNTHAN B,LIU Y.Development and implementation of a constitutive model for unsaturated sands[J].International Journal of Geomechanics,ASCE,2017,17(11):4017103.
[11]YAO Y P,WANG N D.Transformed stress method for generalizing soil constitutive models[J].Journal of Engineering Mechanics,ASCE,2014,140(3):614-629.
[12]YAO Y P,SUN D A.Application of Lade's criterion to Cam-clay model[J].Journal of Engineering Mechanics,ASCE.2000,126(1):112-119.
[13]孙德安,姚仰平.基于SMP准则的双屈服面弹塑性模型的三维化[J].岩土工程学报,1999,21(5):631-634.(SUNDe-an,YAO Yang-ping.Generalization of elasto-plastic model with two yield surfaces based on SMP criterion[J].Chinese Journal of Geotechnical Engineering,1999,21(5):631-634.(in Chinese))
[14]姚仰平,路德春,周安楠,等.广义非线性强度理论及其变换应力空间[J].中国科学(E辑),2004,34(11):1283-1299.(YAO Yang-ping,LU De-chun,ZHOU An-nan,et al.Generalized non-linear strength theory and transformed stress space[J].Science in China(Series E),2004,34(11):1283-1299.(in Chinese))
[15]LADE P V,DUNCAN J M.Elasto-plastic stress-strain theory for cohesionless soil[J].Journal of Geotechnical Engineering Division,1975,101(10):1037-1053.
[16]LADE P V.Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces[J].International Journal of Solids and Structures,1977,13(11):1019-1035.
[17]LADE P V,KIM M K.Single hardening constitutive model for frictional materials:II yield critirion and plastic work contours[J].Computers and Geotechnics,1988,6(1):13-30.
[18]DESAI C S.A general basis for yield,failure and potential functions in plasticity[J].International Journal for Numerical and Analytical Methods in Geomechanics,1980,4:361-75.
[19]DESAI C S,SOMASUNDARAM S,FRANTZISKONIS G.A hierarchical approach for constitutive modelling of geologic materials[J].International Journal for Numerical and Analytical Methods in Geomechanics,1986,10:225-257.
[20]MATSUOKA H,NAKAI T.Stress-deformation and strength characteristics of soil under three different principal stresses[J].Proceedings of JSCE,1974,232:59-70.
[21]NAKAI T,MIHARA Y.A new mechanical quantity for soils and its application to elastoplastic constitutive models[J].Soils and Foundations,1984,24(2):82-94.
[22]NAKAI T,MATSUOKA H.A generalized elastoplastic constitutive model for clay in three-dimensional stresses[J].Soils and Foundations,1986,26(3):81-98.
[23]NAKAI T,SHAHIN H M,KIKIUMOTO M,et al.A simple and unified three-dimensional model to describe various characteristics of soils[J].Soils and Foundations,2011,51(6):1149-1168.
[24]CHOWDHURY E Q,NAKAI T.Consequences of the tij-concept and a new modeling approach[J].Computers and Geotechnics,1998,23(3):131-164.
[25]LU D C,MA C,DU X L,et al.Development of a new nonlinear unified strength theory for geomaterials based on the characteristic stress concept[J].International Journal of Geomechanics,ASCE,2016,17(2):04016058.
[26]MA C,LU D C,DU X L,et al.Developing a 3D elastoplastic constitutive model for soils:a new approach based on characteristic stress[J].Computers and Geotechnics,2017,86:129-140.
[27]路德春,曹胜涛,程星磊,等.欠固结土的弹塑性本构模型[J].土木工程学报,2010,43(增刊2):320-326.(LUDe-chun,CAO Sheng-tao,CHENG Xing-lei,et al.An elastoplastic constitutive model for under consolidated clay[J].China Civil Engineering Journal,2010,43(S2):320-326.(in Chinese))
[28]NAKAI T,MATSUOKA H,OKUNO N,et al.True triaxial tests on normally consolidated clay and analysis of the observed shear behavior using elastoplastic constitutive models[J].Soils and Foundations,1986,26(4):67-78.
[29]LADE P V,MUSANTE H M.Three-dimensional behavior of remolded clay[J].Journal of Geotechnical and Geoenvironmental Engineering,1978,104(2):193-20.
[2]ROSCO K H,SCHOFIELD A N,WROTH C P.On the yielding of soils[J].Géotechnique,1958,8:22-53.
[3]ROSCOE K H,BURLAND J B.On the generalized stress-strain behavior of an ideal wet clay[M].Cambridge:Cambridge University Press,1968:535-609.
[4]WROTH C P,HOULSBY G T.Soil mechanics-property characterization and analysis procedures[C]//Proceedings of the 11th International Conference on Soil Mechanics and Foundation Engineering.San Francisco,1985:1-55.
[5]ZIENKIEWICZ O C,PANDE G N.Some useful forms of isotropic yield surface for soil and rock mechanics[C]//Finite Elements in Geomechnaics.London,1977:179-190.
[6]HASHIGUCHI K.A proposal of the simplest convex-conical surface for soils[J].Soils and Foundations,2002,42(3):107-113.
[7]XIAO Y,LIU H L,LIANG R Y.Modified Cam-clay model incorporating unified nonlinear strength criterion[J].Science China Technological Sciences,2011,54(4):805-10.
[8]TSIAMPOUSI A,ZDRAVKOVIC L,POTTS D M.A new Hvorslev surface for critical state type unsaturated and saturated constitutive models[J].Computers and Geotechnics,2013,48:156-166.
[9]CHAKRABORTY T,SALGADO R,LOUKIDIS D.Atwo-surface plasticity model for clay[J].Computers and Geotechnics,2013,49:170-190.
[10]SUTHARSAN T,MUHUNTHAN B,LIU Y.Development and implementation of a constitutive model for unsaturated sands[J].International Journal of Geomechanics,ASCE,2017,17(11):4017103.
[11]YAO Y P,WANG N D.Transformed stress method for generalizing soil constitutive models[J].Journal of Engineering Mechanics,ASCE,2014,140(3):614-629.
[12]YAO Y P,SUN D A.Application of Lade's criterion to Cam-clay model[J].Journal of Engineering Mechanics,ASCE.2000,126(1):112-119.
[13]孙德安,姚仰平.基于SMP准则的双屈服面弹塑性模型的三维化[J].岩土工程学报,1999,21(5):631-634.(SUNDe-an,YAO Yang-ping.Generalization of elasto-plastic model with two yield surfaces based on SMP criterion[J].Chinese Journal of Geotechnical Engineering,1999,21(5):631-634.(in Chinese))
[14]姚仰平,路德春,周安楠,等.广义非线性强度理论及其变换应力空间[J].中国科学(E辑),2004,34(11):1283-1299.(YAO Yang-ping,LU De-chun,ZHOU An-nan,et al.Generalized non-linear strength theory and transformed stress space[J].Science in China(Series E),2004,34(11):1283-1299.(in Chinese))
[15]LADE P V,DUNCAN J M.Elasto-plastic stress-strain theory for cohesionless soil[J].Journal of Geotechnical Engineering Division,1975,101(10):1037-1053.
[16]LADE P V.Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces[J].International Journal of Solids and Structures,1977,13(11):1019-1035.
[17]LADE P V,KIM M K.Single hardening constitutive model for frictional materials:II yield critirion and plastic work contours[J].Computers and Geotechnics,1988,6(1):13-30.
[18]DESAI C S.A general basis for yield,failure and potential functions in plasticity[J].International Journal for Numerical and Analytical Methods in Geomechanics,1980,4:361-75.
[19]DESAI C S,SOMASUNDARAM S,FRANTZISKONIS G.A hierarchical approach for constitutive modelling of geologic materials[J].International Journal for Numerical and Analytical Methods in Geomechanics,1986,10:225-257.
[20]MATSUOKA H,NAKAI T.Stress-deformation and strength characteristics of soil under three different principal stresses[J].Proceedings of JSCE,1974,232:59-70.
[21]NAKAI T,MIHARA Y.A new mechanical quantity for soils and its application to elastoplastic constitutive models[J].Soils and Foundations,1984,24(2):82-94.
[22]NAKAI T,MATSUOKA H.A generalized elastoplastic constitutive model for clay in three-dimensional stresses[J].Soils and Foundations,1986,26(3):81-98.
[23]NAKAI T,SHAHIN H M,KIKIUMOTO M,et al.A simple and unified three-dimensional model to describe various characteristics of soils[J].Soils and Foundations,2011,51(6):1149-1168.
[24]CHOWDHURY E Q,NAKAI T.Consequences of the tij-concept and a new modeling approach[J].Computers and Geotechnics,1998,23(3):131-164.
[25]LU D C,MA C,DU X L,et al.Development of a new nonlinear unified strength theory for geomaterials based on the characteristic stress concept[J].International Journal of Geomechanics,ASCE,2016,17(2):04016058.
[26]MA C,LU D C,DU X L,et al.Developing a 3D elastoplastic constitutive model for soils:a new approach based on characteristic stress[J].Computers and Geotechnics,2017,86:129-140.
[27]路德春,曹胜涛,程星磊,等.欠固结土的弹塑性本构模型[J].土木工程学报,2010,43(增刊2):320-326.(LUDe-chun,CAO Sheng-tao,CHENG Xing-lei,et al.An elastoplastic constitutive model for under consolidated clay[J].China Civil Engineering Journal,2010,43(S2):320-326.(in Chinese))
[28]NAKAI T,MATSUOKA H,OKUNO N,et al.True triaxial tests on normally consolidated clay and analysis of the observed shear behavior using elastoplastic constitutive models[J].Soils and Foundations,1986,26(4):67-78.
[29]LADE P V,MUSANTE H M.Three-dimensional behavior of remolded clay[J].Journal of Geotechnical and Geoenvironmental Engineering,1978,104(2):193-20.