考虑颗粒破碎效应的堆石料静动力本构模型
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摘要
为合理反映颗粒破碎对堆石料力学特性的影响,基于试验结果分析,得出了堆石料在压缩和剪切作用下的颗粒破碎特性规律。通过引入压缩破碎和剪切破碎的相关参数,借鉴已有本构模型的合理定义,吸收临界状态理论和边界面理论的优点,发展了考虑颗粒破碎和状态相关的堆石料静动力统一弹塑性本构模型,并阐述了模型参数的确定方法。该模型不仅能够反映堆石料在静力荷载作用下的低压剪胀、高压剪缩、应变软化和硬化等特性,还能够反映在循环荷载作用下应力-应变的滞回特性和残余变形的累积效应。最后为验证模型的合理性,分别对堆石料的静力三轴和循环三轴试验进行了数值模拟预测,结果表明:模型预测与试验数据吻合良好,所提出的本构模型能够合理地描述颗粒破碎对堆石料静动力变形特性的影响。
In order to reasonably reflect the influence of particle breakage on the mechanical properties of the rockfill material, it is obtained by the analysis of the test results that the particle breakage characteristics of the rockfill material under the compression and shear. By introducing the related parameters in the compression breakage and shear breakage, some reasonable definitions of the existing constitutive models are used. Taking the advantages on the critical state theory and the boundary surface theory, a unified constitutive model is developed considering the particle breakage and state parameter, and the determination method of model parameters is described. The model can reflect not only the low pressure dilatancy, high pressure shear shrinkage, strain softening and hardening phenomenon of the rockfill material under the static loading, but also the stress-strain hysteresis characteristics and the cumulative effect of residual deformation under the cyclic loading. Finally, in order to verify the reasonability of the model, the static triaxial and cyclic triaxial tests of rockfill material are carried out. The results show that the model prediction is in good agreement with the experimental data, and the constitutive model can reasonably describe the impact of particle breakage on the static and dynamic deformation characteristics of the rockfill material.
In order to reasonably reflect the influence of particle breakage on the mechanical properties of the rockfill material, it is obtained by the analysis of the test results that the particle breakage characteristics of the rockfill material under the compression and shear. By introducing the related parameters in the compression breakage and shear breakage, some reasonable definitions of the existing constitutive models are used. Taking the advantages on the critical state theory and the boundary surface theory, a unified constitutive model is developed considering the particle breakage and state parameter, and the determination method of model parameters is described. The model can reflect not only the low pressure dilatancy, high pressure shear shrinkage, strain softening and hardening phenomenon of the rockfill material under the static loading, but also the stress-strain hysteresis characteristics and the cumulative effect of residual deformation under the cyclic loading. Finally, in order to verify the reasonability of the model, the static triaxial and cyclic triaxial tests of rockfill material are carried out. The results show that the model prediction is in good agreement with the experimental data, and the constitutive model can reasonably describe the impact of particle breakage on the static and dynamic deformation characteristics of the rockfill material.
引文
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[16]DAFALIAS Y F.Bounding surface plasticity I:mathematical foundation and hypoplasticity[J].Journal of Engineering Mechanics,1986,112(9):966-987.
[17]WANG Z L.Bounding surface hypoplasticity model for granular soils and its applications[D].Les Angeles:University of California,1990.
[18]吴兴征.堆石料的静动力本构模型及其在混凝土面板堆石坝中的应用[D].大连:大连理工大学,2001.WU Xing-zheng.The static and dynamic constitutive model of rockfill materials and its application in concrete face rockfill dam[D].Dalian:Dalian University of Technology,2001.
[19]杨光.复杂应力条件下堆石料的静动力特性与本构模型研究[D].北京:清华大学,2009.YANG Guang.Study on static-dynamic behavior and constitutive model of rockfill materials under complex stress conditions[D].Beijing:Tsinghua University,2009.
[20]张幸幸.堆石料弹塑性循环本构模型研究及应用[D].北京:清华大学,2015.ZHANG Xing-xing.Research on cyclic elasto-plastic constitutive model for rockfill materials and its application[D].Beijing:Tsinghua University,2015.
[21]WANG Z L,DAFALIAS Y F,SHEN C K.Bounding surface hypoplasticity model for sand[J].Journal of Engineering Mechanics,1990,116(5):983-1001.
[22]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.
[23]LI X S,DAFALLIAS Y S.Dilatancy for cohensionless soils[J].Geotechnique,2000,50(4):449-460.
[24]LI X S.A sand model with state-dependent dilatancy[J].Geotechnique,2002,52(3):173-186.
[25]张建民.砂土动力学若干基本理论探究[J].岩土工程学报,2012,34(1):1-50.ZHANG Jian-min.New advances in basic theories of sand dynamics[J].Chinese Journal of Geotechnical Engineering,2012,34(1):1-50.
[26]张建民,罗刚.考虑可逆与不可逆剪胀的粗粒土动本构模型[J].岩土工程学报,2005,27(2):178-184.ZHANG Jian-min,LUO Gang.A new cyclic constitutive model for granular soil considering reversible and irreversible dilatancy[J].Chinese Journal of Geotechnical Engineering,2005,27(2):178-184.
[27]罗刚.粒状土的可逆性和不可逆性变形规律与循环本构模型研究[D].北京:清华大学,2004.LUO Gang.Studies on reversible and irreversible cyclic deformation and constitutive model for granular soils[D].Beijing:Tsinghua University,2014.
[28]王刚.砂土液化大变形的物理机制与本构模型研究[D].北京:清华大学,2005.WANG Gang.Research on physical fundamentals and constitutive model of large poat-liquefaciton deformation of sand[D].Beijing:Tsinghua University,2005.
[29]王刚,张建民.砂土液化大变形的弹塑性循环本构模型[J].岩土工程学报,2007,29(1):51-59.WANG Gang,ZHANG Jian-min.A cyclic elasto-plasticity constitutive model for evaluating large liquefaction-induced deformation of sand[J].Chinese Journal of Geotechnical Engineering,2007,29(1):51-59.
[30]ZHANG J M,WANG G.Large post-liquefaction deformation of sand,part I:physical mechanism,constitutive description and numerical algorithm[J].Acta Geotechnica,2012,7(2):69-113.
[31]WANG R.Single piles in liquefiable ground:seismic response and numerical analysis methods[M].Berlin:Springer Verlag Berlin Heidelberg,2016.
[32]WANG R,ZHANG J M,Wang G.A unified plasticity model for large post-liquefaction shear deformation of sand[J].Computers and Geotechnics,2014,59:54-66.
[33]清华大学水利系.南渡江迈湾水利枢纽工程黏土心墙堆石坝筑坝材料试验报告[R].北京:清华大学水利系,2017.Department of Water Resources,Tsinghua University.The test report on the material of the in CWRD in the Nandu river[D].Beijing:Department of Water Resources,Tsinghua University,2017.
[34]GUDEHUS G.A comprehensive constitutive equation for granular materials[J].Soils and Foundations,1996,36(1):1-12.
[35]BAUER E.Calibration of a comprehensive hypoplastic model for granular materials[J].Soils and Foundations,1996,36(1):13-26.
[36]陈生水,傅中志,韩华强,等.一个考虑颗粒破碎的堆石料弹塑性本构模型[J].岩土工程学报,2011,33(10):1489-1495.CHEN Sheng-shui,FU Zhong-zhi,HAN Hua-qiang,et al.An elastoplastic model for rockfill materials considering particle breakage[J].Chinese Journal of Geotechnical Engineering,2011,33(10):1489-1495.
[37]EINAV I.Breakage mechanics-part I:theory[J].Journal of the Mechanics and Physics of Solids,2007,55(6):1274-1297.
[38]杨光,张丙印,于玉贞,等.不同应力路径下粗粒料的颗粒破碎试验研究[J].水利学报,2010,41(3):338-342.YANG Guang,ZHANG Bing-yin,YU Yu-zhen.An experimental study on particle breakage of coarse-grained materials under various stress paths[J].Journal of Hydraulic Engineering,2010,41(3):338-342.
[39]HARDIN B O.Crushing of soil particles[J].Journal of Geotechnical Engineering,1985,111(10):1177-1192.
[40]BEEN K,JEFFERIES M G.State parameter for sands[J].Geotechnique,1985,35(2):99-112.
[2]朱晟.土石坝震害与抗震安全[J].水利水电学报,2011,30(6):40-51.ZHU Sheng.Earthquake-induced damage and aseismic safety of earth-rock dam[J].Journal of Hydroelectric Engineering,2011,30(6):40-51.
[3]尹振宇,许强,胡伟.考虑颗粒破碎效应的粒状材料本构研究:进展及发展[J].岩土工程学报,2012,34(12):2170-2180.YIN Zhen-yu,XU Qiang,HU Wei.Constitutive relations for granular materials considering particle crushing:review and development[J].Chinese Journal of Geotechnical Engineering,2012,34(12):2170-2180.
[4]SUN D A,HUANG W X,SHENG D C,et al.An elastoplastic model for granular materials exhibiting particle crushing[J].Key Engineering Materials,2007,340/341(2):1273-1278.
[5]YAO Y P,YAMAMOTO H,WANG N D.Constitutive model considering sand crushing[J].Soils and Foundations,2008,48(4):603-608.
[6]孙吉主,罗新文.考虑剪胀性与状态相关的钙质砂双屈服面模型研究[J].岩石力学与工程学报,2006,25(10):2145-2149.SUN Ji-zhu,LUO Xin-wen.Study on a two-yield surface model with consideration of state-dependent dilatancy for calcareous sand[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(10):2145-2149.
[7]米占宽,李国英,陈铁林.考虑颗粒破碎的堆石料本构模型[J].岩土工程学报,2007,29(12):1865-1869.MI Zhan-kuan,LI Guo-ying,CHEN Tie-lin.Constitutive model for rockfill material considering grain crushing[J].Chinese Journal of Geotechnical Engineering,2007,29(12):1865-1869.
[8]RUSSELL A R,KHALILI N.A bounding surface plasticity model for sands exhibiting particle crushing[J].Canadian Geotechnical Journal,2004,41(6):1179-1192.
[9]刘恩龙,覃燕林,陈生水,等.堆石料的临界状态探讨[J].水利学报,2012,43(5):505-511.LIU En-long,TAN Yan-lin,CHEN Sheng-shui,et al.Investigation on critical state of rockfill materials[J].Journal of Hydraulic Engineering,2012,43(5):505-511.
[10]DAOUADJI A,HICHER P,RAHMA A.An elastoplastic model for granular materials taking into account grain breakage[J].European Journal of Mechanics-A/Soilds,2001,20(1):113-137.
[11]HU W,YIN Z Y,DANO C,et al.A constitutive model for granular materials considering particle crushing[J].Science in China(Series E),2011,54(8):2188-2196.
[12]孔亮,郑颖人,姚仰平.基于广义塑性力学的土体次加载面循环塑性模型(Ⅰ):理论与模型[J].岩土力学,2003,24(2):141-145.KONG Liang,ZHENG Ying-ren,YAO Yang-ping.Subloading surface cyclic plastic model for soil based on generalized plasticity(Ⅰ):theory and model[J].Rock and Soil Mechanics,2003,24(2):141-145.
[13]孔亮,郑颖人,姚仰平.基于广义塑性力学的土体次加载面循环塑性模型(Ⅱ):本构方程与验证[J].岩土力学,2003,24(3):349-354.KONG Liang,ZHENG Ying-ren,YAO Yang-ping.Subloading surface cyclic plastic model for soil based on Generalized plasticity(Ⅱ):constitutive equation and identification[J].Rock and Soil Mechanics,2003,24(3):349-354.
[14]刘恩龙,陈生水,李国英,等.循环荷载作用下考虑颗粒破碎的堆石体本构模型[J].岩土力学,2012,33(7):1972-1978.LIU En-long,CHEN Sheng-shui,LI Guo-ying,et al.Aconstitutive model for rockfill materials incorporating grain crushing under cyclic loading[J].Rock and Soil Mechanics,2012,33(7):1972-1978.
[15]陈生水,彭成,傅中志.基于广义塑性理论的堆石料动力本构模型研究[J].岩土工程学报,2012,34(11):1961-1968.CHEN Sheng-shui,PENG Cheng,FU Zhong-zhi.Dynamic constitutive model for rockfill materials based on generalized plasticity theory[J].Chinese Journal of Geotechnical Engineering,2012,34(11):1961-1968.
[16]DAFALIAS Y F.Bounding surface plasticity I:mathematical foundation and hypoplasticity[J].Journal of Engineering Mechanics,1986,112(9):966-987.
[17]WANG Z L.Bounding surface hypoplasticity model for granular soils and its applications[D].Les Angeles:University of California,1990.
[18]吴兴征.堆石料的静动力本构模型及其在混凝土面板堆石坝中的应用[D].大连:大连理工大学,2001.WU Xing-zheng.The static and dynamic constitutive model of rockfill materials and its application in concrete face rockfill dam[D].Dalian:Dalian University of Technology,2001.
[19]杨光.复杂应力条件下堆石料的静动力特性与本构模型研究[D].北京:清华大学,2009.YANG Guang.Study on static-dynamic behavior and constitutive model of rockfill materials under complex stress conditions[D].Beijing:Tsinghua University,2009.
[20]张幸幸.堆石料弹塑性循环本构模型研究及应用[D].北京:清华大学,2015.ZHANG Xing-xing.Research on cyclic elasto-plastic constitutive model for rockfill materials and its application[D].Beijing:Tsinghua University,2015.
[21]WANG Z L,DAFALIAS Y F,SHEN C K.Bounding surface hypoplasticity model for sand[J].Journal of Engineering Mechanics,1990,116(5):983-1001.
[22]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.
[23]LI X S,DAFALLIAS Y S.Dilatancy for cohensionless soils[J].Geotechnique,2000,50(4):449-460.
[24]LI X S.A sand model with state-dependent dilatancy[J].Geotechnique,2002,52(3):173-186.
[25]张建民.砂土动力学若干基本理论探究[J].岩土工程学报,2012,34(1):1-50.ZHANG Jian-min.New advances in basic theories of sand dynamics[J].Chinese Journal of Geotechnical Engineering,2012,34(1):1-50.
[26]张建民,罗刚.考虑可逆与不可逆剪胀的粗粒土动本构模型[J].岩土工程学报,2005,27(2):178-184.ZHANG Jian-min,LUO Gang.A new cyclic constitutive model for granular soil considering reversible and irreversible dilatancy[J].Chinese Journal of Geotechnical Engineering,2005,27(2):178-184.
[27]罗刚.粒状土的可逆性和不可逆性变形规律与循环本构模型研究[D].北京:清华大学,2004.LUO Gang.Studies on reversible and irreversible cyclic deformation and constitutive model for granular soils[D].Beijing:Tsinghua University,2014.
[28]王刚.砂土液化大变形的物理机制与本构模型研究[D].北京:清华大学,2005.WANG Gang.Research on physical fundamentals and constitutive model of large poat-liquefaciton deformation of sand[D].Beijing:Tsinghua University,2005.
[29]王刚,张建民.砂土液化大变形的弹塑性循环本构模型[J].岩土工程学报,2007,29(1):51-59.WANG Gang,ZHANG Jian-min.A cyclic elasto-plasticity constitutive model for evaluating large liquefaction-induced deformation of sand[J].Chinese Journal of Geotechnical Engineering,2007,29(1):51-59.
[30]ZHANG J M,WANG G.Large post-liquefaction deformation of sand,part I:physical mechanism,constitutive description and numerical algorithm[J].Acta Geotechnica,2012,7(2):69-113.
[31]WANG R.Single piles in liquefiable ground:seismic response and numerical analysis methods[M].Berlin:Springer Verlag Berlin Heidelberg,2016.
[32]WANG R,ZHANG J M,Wang G.A unified plasticity model for large post-liquefaction shear deformation of sand[J].Computers and Geotechnics,2014,59:54-66.
[33]清华大学水利系.南渡江迈湾水利枢纽工程黏土心墙堆石坝筑坝材料试验报告[R].北京:清华大学水利系,2017.Department of Water Resources,Tsinghua University.The test report on the material of the in CWRD in the Nandu river[D].Beijing:Department of Water Resources,Tsinghua University,2017.
[34]GUDEHUS G.A comprehensive constitutive equation for granular materials[J].Soils and Foundations,1996,36(1):1-12.
[35]BAUER E.Calibration of a comprehensive hypoplastic model for granular materials[J].Soils and Foundations,1996,36(1):13-26.
[36]陈生水,傅中志,韩华强,等.一个考虑颗粒破碎的堆石料弹塑性本构模型[J].岩土工程学报,2011,33(10):1489-1495.CHEN Sheng-shui,FU Zhong-zhi,HAN Hua-qiang,et al.An elastoplastic model for rockfill materials considering particle breakage[J].Chinese Journal of Geotechnical Engineering,2011,33(10):1489-1495.
[37]EINAV I.Breakage mechanics-part I:theory[J].Journal of the Mechanics and Physics of Solids,2007,55(6):1274-1297.
[38]杨光,张丙印,于玉贞,等.不同应力路径下粗粒料的颗粒破碎试验研究[J].水利学报,2010,41(3):338-342.YANG Guang,ZHANG Bing-yin,YU Yu-zhen.An experimental study on particle breakage of coarse-grained materials under various stress paths[J].Journal of Hydraulic Engineering,2010,41(3):338-342.
[39]HARDIN B O.Crushing of soil particles[J].Journal of Geotechnical Engineering,1985,111(10):1177-1192.
[40]BEEN K,JEFFERIES M G.State parameter for sands[J].Geotechnique,1985,35(2):99-112.