基于微观破损机理的胶结砂土三维本构模型研究
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摘要
在岩土破损力学和临界状态土力学框架内,遵循宏微观土力学的研究思路,建立了胶结砂土三维本构模型。定义与重塑砂土屈服面几何相似但尺寸扩大的胶结砂土屈服面;采用经三维离散元验证的Lade-Duncan强度准则作为临界状态强度面;基于胶结材料微观力学理论并结合三维离散元模拟结果,获得具有微观力学机制的胶结破损规律;将胶结破损规律引入到重塑砂土的硬化规律和流动法则,得到胶结砂土的硬化规律和流动法则。将该本构模型应用于人工制备胶结砂土室内常规三轴压缩试验和等平均应力真三轴试验的模拟,初步验证了该模型的适用性。
Based on the framework of breakage mechanics for geological materials and the critical-state soil mechanics, a three-dimensional(3-D) constitutive model for cemented sands is proposed following the research idea for macro-and micro-mechanical soil mechanics. A yield surface for reconstituted sands is improved for the cemented sands by enlarging the surface size. To consider the behaviors of shear strength in the 3-D space, the Lade-Duncan strength criterion, validated by simulations of 3-D distinct element method(DEM), is used as the critical-state strength surface. A degradation evolution for bond is obtained from 3-D DEM specimens based on the micro-mechanics theory for cemented materials and the simulated results of DEM. By introducing the degradation evolution for bond, the hardening law and flow rule for reconstituted sands are modified and applied for cemented sands. The proposed model is preliminarily verified by predicting the mechanical behaviors of artificially cemented sands in the conventional triaxial compression tests and true triaxial tests with constant mean stress.
Based on the framework of breakage mechanics for geological materials and the critical-state soil mechanics, a three-dimensional(3-D) constitutive model for cemented sands is proposed following the research idea for macro-and micro-mechanical soil mechanics. A yield surface for reconstituted sands is improved for the cemented sands by enlarging the surface size. To consider the behaviors of shear strength in the 3-D space, the Lade-Duncan strength criterion, validated by simulations of 3-D distinct element method(DEM), is used as the critical-state strength surface. A degradation evolution for bond is obtained from 3-D DEM specimens based on the micro-mechanics theory for cemented materials and the simulated results of DEM. By introducing the degradation evolution for bond, the hardening law and flow rule for reconstituted sands are modified and applied for cemented sands. The proposed model is preliminarily verified by predicting the mechanical behaviors of artificially cemented sands in the conventional triaxial compression tests and true triaxial tests with constant mean stress.
引文
[1]CUCCOVILLO T,COOP M R.On the mechanics of structured sands[J].Géotechnique,1999,49(6):741-760.
[2]MITCHELL J K,SOGA K.Fundamentals of soil behavior[M].3rd ed.Hoboken:John Wiley&Sons,2005.
[3]CONSOLI N C,DA FONSECA A V,SILVA S R,et al.Parameters controlling stiffness and strength of artificially cemented soils[J].Géotechnique,2012,62(2):177-183.
[4]沈珠江,章为民.损伤力学在土力学中的应用[C]//第三届全国岩土力学数值分析及解析方法讨论会.武汉,1988:47-51.(SHEN Zhu-jiang,ZHANG Wei-min.Application of damage mechanics in soil mechanics[C]//The 3rd Chinese Conference of Numerical Simulation and Analysis of Geomaterial.Wuhan,1988:47-51.(in Chinese))
[5]沈珠江.结构性黏土的弹塑性损伤模型[J].岩土工程学报,1993,15(3):21-28.(SHEN Zhu-jiang.The elastoplastic damage model of structural clay[J].Chinese Journal of Geotechnical Engineering,1993,15(3):21-28.(in Chinese))
[6]沈珠江.结构性黏土的非线损伤力学模型[J].水利水运科学研究,1993(3):247-255.(SHEN Zhu-jiang.A nonlinear damage model for structured clay[J].Hydro-Science and Engineering,1993(3):247-255.(in Chinese))
[7]沈珠江.结构性黏土的堆砌体模型[J].岩土力学,2000,21(1):1-4.(SHEN Zhu-jiang.A masonry model for structured clays[J].Rock and Soil Mechanics,2000,21(1):1-4.(in Chinese))
[8]沈珠江.岩土破损力学:理想脆弹塑性模型[J].岩土工程学报,2003,25(3):253-257.(SHEN Zhu-jiang.Breakage mechanics for geological materials:an ideal brittle-elasto-plastic model[J].Chinese Journal of Geotechnical Engineering,2003,25(3):253-257.(in Chinese))
[9]沈珠江,刘恩龙,陈铁林.岩土二元介质模型的一般应力应变关系[J].岩土工程学报,2005,27(5):489-494.(SHEN Zhu-jiang,LIU En-long,CHEN Tie-lin.Generalized stress-strain relationship of binary medium model for geological materials[J].Chinese Journal of Geotechnical Engineering.2005,27(5):489-494.(in Chinese))
[10]刘恩龙,罗开泰,张树祎.初始应力各向异性结构性土的二元介质模型[J].岩土力学,2013,34(11):310-3109.(LIU En-long,LUO Kai-tai,ZHANG Shu-yi.Binary medium model for structured soils with initial stress-induced anisotropy[J].Rock and Soil Mechanics,2013,34(11):3103-3109.(in Chinese))
[11]DESAI C S,TOTH J.Disturbed state constitutive modeling based on stress-strain and nondestructive behavior[J].International Journal of Solids and Structures,1996,33(11):1619-1650.
[12]DESAI C S.Disturbed state concept(DSC)for constitutive modeling of geologic materials and beyond[C]//Constitutive Modeling of Geomaterials.Springer,2013:27-45.
[13]吴刚.工程材料的扰动状态本构模型(I)——扰动状态概念及其理论基础[J].岩石力学与工程学报,2002,21(6):759-765.(WU Gang.Disturbed state constitution models of engineering material I:disturbed state concept and its theory principium[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(6):759-765.(in Chinese))
[14]吴刚.工程材料的扰动状态构模型(II)——基于扰动状态概念的有限元数值模拟[J].岩石力学与工程学报,2002,21(8):1107-1110.(WU Gang.Disturbed state constitution models of engineering material II:DSC-based numerical simulation of finite element method[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(8):1107-1110.(in Chinese))
[15]周成,沈珠江,陈生水,等.结构性土的次塑性扰动状态模型[J].岩土工程学报,2004,26(4):435-439.(ZHOU Cheng,SHEN Zhu-jiang,CHEN Sheng-shui,et al.A hypoplasticity disturbed state model for structured soils[J].Chinese Journal of Geotechnical Engineering,2004,26(4):435-439.(in Chinese))
[16]ATHUKORALA R,INDRARATNA B,VINOD J S.Disturbed state concept-based constitutive model for lignosulfonate-treated silty sand[J].International Journal of Geomechanics,2015,15(6):04015002.
[17]OURIA A.Disturbed state concept-based constitutive model for structured soils[J].International Journal of Geomechanics,2017,17(7):04017008.
[18]ABDULLA A A,KIOUSIS P D.Behavior of cemented sands II:modelling[J].International Journal for Numerical and Analytical Methods in Geomechanics,1998,21(8):549-568.
[19]HAERI S M,HAMIDI A.Constitutive modelling of cemented gravelly sands[J].Geomechanics and Geoengineering:An International Journal,2009,4(2):123-139.
[20]GENS A,NOVA R.Conceptual bases for a constitutive model for bonded soils and weak rocks[J].Geotechnical Engineering of Hard Soils-Soft Rocks,1993,1(1):485-494.
[21]NOVA R,CASTELLANZA R,TAMAGNINI C.A constitutive model for bonded geomaterials subject to mechanical and/or chemical degradation[J].International Journal for Numerical and Analytical Methods in Geomechanics,2003,27(9):705-732.
[22]YU H S,TAN S M,SCHNAID F.A critical state framework for modelling bonded geomaterials[J].Geomechanics and Geoengineering:An International Journal,2007,2(1):61-74.
[23]RAHIMI M,CHAN D,NOURI A.Bounding surface constitutive model for cemented sand under monotonic loading[J].International Journal of Geomechanics,2016,16(2):04015049.
[24]REDDY K R,SAXENA S K.Constitutive modeling of cemented sand[J].Mechanics of materials,1992,14(2):155-178.
[25]SUN D A,MATSUOKA H.An elastoplastic model for frictional and cohesive materials and its application to cemented sands[J].Mechanics of Cohesive-Frictional Materials,1999,4(6):525-543.
[26]蒋明镜,刘静德,孙渝刚.基于微观破损规律的结构性土本构模型[J].岩土工程学报,2013,35(6):1134-1139.(JIANG Ming-jing,LIU Jing-de,SUN Yu-gang.Constitutive model for structured soils based on microscopic damage law[J].Chinese Journal of Geotechnical Engineering,2013,35(6):1134-1139.(in Chinese))
[27]蒋明镜,周卫,刘静德,等.基于微观力学机制的各向异性结构性砂土的本构模型研究[J].岩土力学,2016,37(12):3347-3355.(JIANG Ming-jing,ZHOU Wei,LIU Jing-de,et al.A constitutive model for anisotropic structured sandy soil based on micromechanical mechanism[J].Rock and Soil Mechanics,2016,37(12):3347-3355.(in Chinese))
[28]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.
[29]ROSCOE K H,BURLAND J B.On the generalised stress-strain behaviour of wet clay[J].Engineering Plasticity,1968,535-609.
[30]张伏光.基于微观破损机理的结构性砂土三维本构模型研究[D].上海:同济大学,2017.(ZHANG Fu-guang.A study on the three-dimensional constitutive model for strctured sands based on the micro-mechanism of structure degradation[D].Shanghai:Tongji University,2017.(in Chinese))
[31]MATSUOKA H,NAKAI T.Stress-deformation and strength characteristics of soil under three different principal stresses[C]//Proceedings of Japanese Society of Civel Engineering.1974:59-70.
[32]杜修力,马超,路德春.岩土材料的非线性统一强度模型[J].力学学报,2014,46(3):389-397.(DU Xiu-li,MA Chao,LU De-chun.Nonlinear unified strength model of geomaterials[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(3):389-397.(in Chinese))
[33]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.
[34]MORTARA G.A yield criterion for isotropic and crossanisotropic cohesive-frictional materials[J].International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(9):953-977.
[35]BAGI K.An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies[J].Granular Matter,2005,7(1):31-43.
[36]孙渝刚.结构性砂土宏微观力学特性的试验研究与数值模拟[D].上海:同济大学,2012.(SUN Yu-gang.Experimental and numerical investigation on macro-and micro-mechanical behaviors of structural sands[D].Shanghai:Tongji University,2012.(in Chinese))
[37]ASAOKA A,NAKANO M,NODA T.Superloading yield surface concept for highly structured soil behaviour[J].Soils and Foundations,2000,40(2):99-110.
[38]ROUAINIA M,WOOD D M.A kinematic hardening constitutive model for natural clays with loss of structure[J].Géotechnique,2000,50(2):153-164.
[39]LIU M D,CARTER J P.A structured Cam Clay model[J].Canadian Geotechnical Journal,2002,39(6):1313-1332.
[40]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].Chinese Journal of Geotechnical Engineering,2011,33(12):1827-1832.(in Chinese))
[41]SUN D A,HUANG W X,YAO Y P.An experimental study of failure and softening in sand under three-dimensional stress condition[J].Granular Matter,2008,10(3):187-195.
[42]LI X S,DAFALIAS Y F.Dilatancy for cohesionless soils[J].Géotechnique,2000,50(4):449-460.
[43]YU H S.CASM:a unified state parameter model for clay and sand[J].International Journal for Numerical and Analytical Methods in Geomechanics,1998,22(8):621-653.
[44]WANG Y H,LEUNG S C.Characterization of cemented sand by experimental and numerical investigations[J].Journal of Geotechnical and Geoenvironmental Engineering,2008,134(7):992-1004.
[45]REDDY K R,SAXENA S K,BUDIMAN J S.Development of a true triaxiai testing apparatus[J].Geotechnical Testing Journal,1992,15(2):89-105.
[2]MITCHELL J K,SOGA K.Fundamentals of soil behavior[M].3rd ed.Hoboken:John Wiley&Sons,2005.
[3]CONSOLI N C,DA FONSECA A V,SILVA S R,et al.Parameters controlling stiffness and strength of artificially cemented soils[J].Géotechnique,2012,62(2):177-183.
[4]沈珠江,章为民.损伤力学在土力学中的应用[C]//第三届全国岩土力学数值分析及解析方法讨论会.武汉,1988:47-51.(SHEN Zhu-jiang,ZHANG Wei-min.Application of damage mechanics in soil mechanics[C]//The 3rd Chinese Conference of Numerical Simulation and Analysis of Geomaterial.Wuhan,1988:47-51.(in Chinese))
[5]沈珠江.结构性黏土的弹塑性损伤模型[J].岩土工程学报,1993,15(3):21-28.(SHEN Zhu-jiang.The elastoplastic damage model of structural clay[J].Chinese Journal of Geotechnical Engineering,1993,15(3):21-28.(in Chinese))
[6]沈珠江.结构性黏土的非线损伤力学模型[J].水利水运科学研究,1993(3):247-255.(SHEN Zhu-jiang.A nonlinear damage model for structured clay[J].Hydro-Science and Engineering,1993(3):247-255.(in Chinese))
[7]沈珠江.结构性黏土的堆砌体模型[J].岩土力学,2000,21(1):1-4.(SHEN Zhu-jiang.A masonry model for structured clays[J].Rock and Soil Mechanics,2000,21(1):1-4.(in Chinese))
[8]沈珠江.岩土破损力学:理想脆弹塑性模型[J].岩土工程学报,2003,25(3):253-257.(SHEN Zhu-jiang.Breakage mechanics for geological materials:an ideal brittle-elasto-plastic model[J].Chinese Journal of Geotechnical Engineering,2003,25(3):253-257.(in Chinese))
[9]沈珠江,刘恩龙,陈铁林.岩土二元介质模型的一般应力应变关系[J].岩土工程学报,2005,27(5):489-494.(SHEN Zhu-jiang,LIU En-long,CHEN Tie-lin.Generalized stress-strain relationship of binary medium model for geological materials[J].Chinese Journal of Geotechnical Engineering.2005,27(5):489-494.(in Chinese))
[10]刘恩龙,罗开泰,张树祎.初始应力各向异性结构性土的二元介质模型[J].岩土力学,2013,34(11):310-3109.(LIU En-long,LUO Kai-tai,ZHANG Shu-yi.Binary medium model for structured soils with initial stress-induced anisotropy[J].Rock and Soil Mechanics,2013,34(11):3103-3109.(in Chinese))
[11]DESAI C S,TOTH J.Disturbed state constitutive modeling based on stress-strain and nondestructive behavior[J].International Journal of Solids and Structures,1996,33(11):1619-1650.
[12]DESAI C S.Disturbed state concept(DSC)for constitutive modeling of geologic materials and beyond[C]//Constitutive Modeling of Geomaterials.Springer,2013:27-45.
[13]吴刚.工程材料的扰动状态本构模型(I)——扰动状态概念及其理论基础[J].岩石力学与工程学报,2002,21(6):759-765.(WU Gang.Disturbed state constitution models of engineering material I:disturbed state concept and its theory principium[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(6):759-765.(in Chinese))
[14]吴刚.工程材料的扰动状态构模型(II)——基于扰动状态概念的有限元数值模拟[J].岩石力学与工程学报,2002,21(8):1107-1110.(WU Gang.Disturbed state constitution models of engineering material II:DSC-based numerical simulation of finite element method[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(8):1107-1110.(in Chinese))
[15]周成,沈珠江,陈生水,等.结构性土的次塑性扰动状态模型[J].岩土工程学报,2004,26(4):435-439.(ZHOU Cheng,SHEN Zhu-jiang,CHEN Sheng-shui,et al.A hypoplasticity disturbed state model for structured soils[J].Chinese Journal of Geotechnical Engineering,2004,26(4):435-439.(in Chinese))
[16]ATHUKORALA R,INDRARATNA B,VINOD J S.Disturbed state concept-based constitutive model for lignosulfonate-treated silty sand[J].International Journal of Geomechanics,2015,15(6):04015002.
[17]OURIA A.Disturbed state concept-based constitutive model for structured soils[J].International Journal of Geomechanics,2017,17(7):04017008.
[18]ABDULLA A A,KIOUSIS P D.Behavior of cemented sands II:modelling[J].International Journal for Numerical and Analytical Methods in Geomechanics,1998,21(8):549-568.
[19]HAERI S M,HAMIDI A.Constitutive modelling of cemented gravelly sands[J].Geomechanics and Geoengineering:An International Journal,2009,4(2):123-139.
[20]GENS A,NOVA R.Conceptual bases for a constitutive model for bonded soils and weak rocks[J].Geotechnical Engineering of Hard Soils-Soft Rocks,1993,1(1):485-494.
[21]NOVA R,CASTELLANZA R,TAMAGNINI C.A constitutive model for bonded geomaterials subject to mechanical and/or chemical degradation[J].International Journal for Numerical and Analytical Methods in Geomechanics,2003,27(9):705-732.
[22]YU H S,TAN S M,SCHNAID F.A critical state framework for modelling bonded geomaterials[J].Geomechanics and Geoengineering:An International Journal,2007,2(1):61-74.
[23]RAHIMI M,CHAN D,NOURI A.Bounding surface constitutive model for cemented sand under monotonic loading[J].International Journal of Geomechanics,2016,16(2):04015049.
[24]REDDY K R,SAXENA S K.Constitutive modeling of cemented sand[J].Mechanics of materials,1992,14(2):155-178.
[25]SUN D A,MATSUOKA H.An elastoplastic model for frictional and cohesive materials and its application to cemented sands[J].Mechanics of Cohesive-Frictional Materials,1999,4(6):525-543.
[26]蒋明镜,刘静德,孙渝刚.基于微观破损规律的结构性土本构模型[J].岩土工程学报,2013,35(6):1134-1139.(JIANG Ming-jing,LIU Jing-de,SUN Yu-gang.Constitutive model for structured soils based on microscopic damage law[J].Chinese Journal of Geotechnical Engineering,2013,35(6):1134-1139.(in Chinese))
[27]蒋明镜,周卫,刘静德,等.基于微观力学机制的各向异性结构性砂土的本构模型研究[J].岩土力学,2016,37(12):3347-3355.(JIANG Ming-jing,ZHOU Wei,LIU Jing-de,et al.A constitutive model for anisotropic structured sandy soil based on micromechanical mechanism[J].Rock and Soil Mechanics,2016,37(12):3347-3355.(in Chinese))
[28]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.
[29]ROSCOE K H,BURLAND J B.On the generalised stress-strain behaviour of wet clay[J].Engineering Plasticity,1968,535-609.
[30]张伏光.基于微观破损机理的结构性砂土三维本构模型研究[D].上海:同济大学,2017.(ZHANG Fu-guang.A study on the three-dimensional constitutive model for strctured sands based on the micro-mechanism of structure degradation[D].Shanghai:Tongji University,2017.(in Chinese))
[31]MATSUOKA H,NAKAI T.Stress-deformation and strength characteristics of soil under three different principal stresses[C]//Proceedings of Japanese Society of Civel Engineering.1974:59-70.
[32]杜修力,马超,路德春.岩土材料的非线性统一强度模型[J].力学学报,2014,46(3):389-397.(DU Xiu-li,MA Chao,LU De-chun.Nonlinear unified strength model of geomaterials[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(3):389-397.(in Chinese))
[33]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.
[34]MORTARA G.A yield criterion for isotropic and crossanisotropic cohesive-frictional materials[J].International Journal for Numerical and Analytical Methods in Geomechanics,2010,34(9):953-977.
[35]BAGI K.An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies[J].Granular Matter,2005,7(1):31-43.
[36]孙渝刚.结构性砂土宏微观力学特性的试验研究与数值模拟[D].上海:同济大学,2012.(SUN Yu-gang.Experimental and numerical investigation on macro-and micro-mechanical behaviors of structural sands[D].Shanghai:Tongji University,2012.(in Chinese))
[37]ASAOKA A,NAKANO M,NODA T.Superloading yield surface concept for highly structured soil behaviour[J].Soils and Foundations,2000,40(2):99-110.
[38]ROUAINIA M,WOOD D M.A kinematic hardening constitutive model for natural clays with loss of structure[J].Géotechnique,2000,50(2):153-164.
[39]LIU M D,CARTER J P.A structured Cam Clay model[J].Canadian Geotechnical Journal,2002,39(6):1313-1332.
[40]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].Chinese Journal of Geotechnical Engineering,2011,33(12):1827-1832.(in Chinese))
[41]SUN D A,HUANG W X,YAO Y P.An experimental study of failure and softening in sand under three-dimensional stress condition[J].Granular Matter,2008,10(3):187-195.
[42]LI X S,DAFALIAS Y F.Dilatancy for cohesionless soils[J].Géotechnique,2000,50(4):449-460.
[43]YU H S.CASM:a unified state parameter model for clay and sand[J].International Journal for Numerical and Analytical Methods in Geomechanics,1998,22(8):621-653.
[44]WANG Y H,LEUNG S C.Characterization of cemented sand by experimental and numerical investigations[J].Journal of Geotechnical and Geoenvironmental Engineering,2008,134(7):992-1004.
[45]REDDY K R,SAXENA S K,BUDIMAN J S.Development of a true triaxiai testing apparatus[J].Geotechnical Testing Journal,1992,15(2):89-105.