强夯的物质点法模拟及其能量转化规律分析
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摘要
提出大应力范围内的密度相关土体本构模型,适用于分析强夯等作用下的土体变形问题。对刚柔接触算法进行了修正,用物质点法结合提出的本构模拟了强夯过程。与其他数值模拟将荷载假设为三角形应力波作为输入荷载不同,通过输入夯锤与土体的碰撞速度实现加载。模拟结果与承德机场4标段某处试验数据进行了对照,吻合较好。提出强夯过程中的能量转化率的概念,对能量转化的规律进行了研究,为研究强夯问题提供了新视角。模拟分析表明,能量转化率的提高不总意味着每击夯沉量的提高,因为能量在较大范围的扩散可能导致高能量转化率下的低夯沉量;剪切变形过程中吸收较多的塑性应变能,可能会使体积压缩变形吸收的塑性应变能向局部集中。通过数值模拟还发现,重锤低落时的能量转化率高于轻锤高落,一般可产生更大的夯沉量。
A density-dependent soil constitutive model for large stress range is proposed for the analysis of large deformation of soil subjected to high stresses under dynamic compaction. A rigid-flexible contact algorithm is further developed and the material point method combined with the proposed constitutive model is used to simulate the dynamic compaction process. In contrast to some previous numerical simulations, in which the input load is assumed to be a triangular stress wave, the loading procedure here is achieved by controlling the collision speed between the hammer and the soil. The computed results are in good agreement with the experimental data on the construction site of Chengde Airport. A new concept, the "energy conversion rate" in the process of dynamic compaction, is introduced, and the laws of energy conversion are studied, which provides a new perspective on the study of dynamic compaction. The numerical simulations indicate that an increase in the energy conversion rate does not necessarily mean an increase of the crater depth per impact, since the distribution of energy in a larger domain may result in a lower crater depth under a high energy conversion rate. A greater shear plastic strain energy absorbtion may contribute to a local concentration of the absorbed plastic strain energy in volume compression of soil. It is also found that the energy conversion rate under low drop of a heavy hammer is higher than that under high drop of a light hammer, and consequently produces in general a larger crater depth.
A density-dependent soil constitutive model for large stress range is proposed for the analysis of large deformation of soil subjected to high stresses under dynamic compaction. A rigid-flexible contact algorithm is further developed and the material point method combined with the proposed constitutive model is used to simulate the dynamic compaction process. In contrast to some previous numerical simulations, in which the input load is assumed to be a triangular stress wave, the loading procedure here is achieved by controlling the collision speed between the hammer and the soil. The computed results are in good agreement with the experimental data on the construction site of Chengde Airport. A new concept, the "energy conversion rate" in the process of dynamic compaction, is introduced, and the laws of energy conversion are studied, which provides a new perspective on the study of dynamic compaction. The numerical simulations indicate that an increase in the energy conversion rate does not necessarily mean an increase of the crater depth per impact, since the distribution of energy in a larger domain may result in a lower crater depth under a high energy conversion rate. A greater shear plastic strain energy absorbtion may contribute to a local concentration of the absorbed plastic strain energy in volume compression of soil. It is also found that the energy conversion rate under low drop of a heavy hammer is higher than that under high drop of a light hammer, and consequently produces in general a larger crater depth.
引文
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[12]张北战,姚仰平,方雨菲.填土地基强夯加固效果研究[J].地震工程学报,2015,37(7):30-34.(ZHANG Bei-zhan,YAO Yang-ping,FANG Yu-fei.Reinforcement effect of dynamic compaction on a backfilled foundation[J].China Earthquake Engineering Journal,2015,37(7):30-34.(in Chinese))
[13]THILAKASIRI H S,GUNARATNE M,MULLINS G,et al.Investigation of impact stresses induced in laboratory dynamic compaction of soft soils[J].International Journal for Numerical&Analytical Methods in Geomechanics,2015,20(10):753-767.
[14]姚仰平,张北战.基于体应变的强夯加固范围研究[J].岩土力学,2016,37(9):2663-2671.(YAO Yang-ping,ZHANG Bei-zhan.Reinforcement range of dynamic compaction based on volumetric strain[J].Rock and Soil Mechanics,2016,37(9):2663-2671.(in Chinese))
[15]向泽华,胡焕校,吴高权.强夯作用下土体动力特性的数值模拟[J].水资源与水工程学报,2015(6):207-211.(XIANG Ze-hua,HU Huan-xiao,WU Gao-quan.Numerical simulation of dynamic characteristics of soil under role of strong compaction[J].Journal of Water Resources and Water Engineering,2015(6):207-211.(in Chinese))
[16]EBRAHIMIAN B.Numerical simulation of soil compaction by impact using smoothed particle hydrodynamics(SPH)method[C]//International Conference on Modeling,Simulation and Applied Optimization.Sharjah,2009.
[17]PASDARPOUR M,GHAZAVI M,TESHNEHLAB M,et al.Optimal design of soil dynamic compaction using genetic algorithm and fuzzy system[J].Soil Dynamics&Earthquake Engineering,2009,29(7):1103-1112.
[18]贾敏才,吴邵海,叶建忠.基于三维离散元法的强夯动力响应研究[J].湖南大学学报(自然科学版),2015(3):70-76.(JIA Min-cai,WU Shao-hai,YE Jian-zhong.Discrete element modeling of dynamic compaction in granular soils using PFC3D[J].Journal of Hunan University Natural Sciences,2015(3):70-76.(in Chinese))
[19]张雄,廉艳平,刘岩,等.物质点法[M].北京:清华大学出版社,2013:38-102.(ZHANG Xiong,LIANYan-ping,LIU Yan.Material point method[M].Beijing:Tsinghua University Press,Beijing,2013:38-102.(in Chinese))
[20]SULSKY D,CHEN Z,SCHREYER H L.A particle method for history-dependent materials[J].Computer Methods in Applied Mechanics&Engineering,1993,118(1/2):179-196.
[21]HARLOW F.A machine calculation method for hydrodynamic problems[R].Los Alamos:Los Alamos Scientific Laboratory,1955.
[22]DAWSON J M.Particle simulation of plasmas[J].Review of Modern Physics,1983,55(55):403.
[23]BRACKBILL J U,RUPPEL H M.FLIP:a method for adaptively zoned,particle-in-cell calculations of fluid flows in two dimensions[J].Journal of Computational Physics,1986,65(2):314-343.
[24]BARDENHAGEN S G,KOBER E M.The generalized interpolation material point method[J].Computer Modeling in Engineering&Sciences,2004,5(6):477-495.
[25]ZHANG D Z,MA X,GIGUERE P T.Material point method enhanced by modified gradient of shape function[J].Journal of Computational Physics,2011,230(16):6379-6398.
[26]SO?OWSKI W T,SLOAN S W,KANTY P T,et al.Numerical simulation of a small scale dynamic replacement stone column creation experiment[C]//International Conference on Particle-based Methods-Fundamentals and Applications.Stuttagrt,2013:522-533.
[27]王钟琦,邓祥林.强夯机理及其环境影响[C]//中国土木工程学会土力学及基础工程学术会议论文选集.北京,1983.(WANG Zhong-qi,DENG Xiang-lin.Dynamic mechanism and its environmental impact[C]//Selected Works of the Conference of Soil Mechanics and Basic Engineering of China Civil Engineering Society.Beijing,1983.(in Chinese))
[28]WANG Z Q,DENG X I.Mechanism of dynamic consolidation and its environmental effects[C]//First International Conference on Case Histories in Geotechnical Engineering.St Louis,1984.
[29]孔令伟,袁建新.强夯的边界接触应力与沉降特性研究[J].岩土工程学报,1998,20(2):86-92.(KONG Ling-wei,YUAN Jian-xin.Study on surface contact stress and settlement properties during dynamic consolidation[J].Chinese Jounal of Geotechnical Engineering,1998,20(2):86-92.(in Chinese))
[30]SULSKY D,ZHEN S,SCHREYER H L.Application of a particle-in-cell method to solid mechanics[J].Computer Physics Communications,1995,87(1):236-252.
[31]孙玉进.岩土大变形问题的物质点法研究[D].北京:清华大学,2017:21-51.(SUN Yu-jin.Research on geotechnical problems involving extremely large deformation using the material point methoed[D].Beijing:Tsinghua University,2017:21-51.(in Chinese))
[32]孙玉进,宋二祥.大位移滑坡形态的物质点法模拟[J].岩土工程学报,2015,37(7):1218-1225.(SUN Yu-jin,SONGEr-xiang.Simulation of large-displacement landslide by material point method[J].Chinese Journal of Geotechnical Engineering,2015,37(7):1218-1225.(in Chinese))
[33]廉艳平,张帆,刘岩,等.物质点法的理论和应用[J].力学进展,2013,43(2):237-264.(LIAN Yan-ping,ZHANGFan,LIU Yan,et al.Material point method and its applications.Advances in Mechanics,2013,43(2):237-264.(in Chinese))
[34]黄鹏.金属及岩土冲击动力学问题的物质点法研究[D].北京:清华大学,2010:99-102.(HUANG Peng.Material point method for metal and soil impact dynamics problems[D].Beijing:Tsinghua University,2010:99-102.(in Chinese))
[35]AL-KAFAJI I K J.Formulation of a Dynamic Material Point Method(MPM)for Geomechanical Problems[D].Stuttgart:Uni Stuttgart-Universit?tsbibliothek,2013.
[36]CUNDALL P A.Explicit finite-difference methods in geomechanics[J].Numerical Methods in Geomechanics,1976,1:132-150.
[37]BAUER E.Calibration of a comprehensive hypoplastic model for granular materials[J].Soils and Foundations,1996,36(1):13-26.
[38]SCHANZ T,VERMEER P A,BONNIER P G.The hardening soil model:formulation and verification[C]//Beyond 2000 in Computational Geotechnics.Amsterdam,1999:281-296.
[39]HERLE I,GUDEHUS G.Determination of parameters of a hypoplastic constitutive model from properties of grain assemblies[J].International Journal for Numerical&Analytical Methods in Geomechanics,2015,4(5):461-486.
[40]MAYNE P W,JONES J S.Impact stresses during dynamic compaction[J].Journal of Geotechnical Engineering,1983,109(10):1342-1346.
[41]PORAN C J,RODRIGUEZ J A.Impact behaviour of sand[J].Soils&Foundations,1992,32(4):81-92.
[2]MENARD L,BROISE Y.Theoretical and practical aspects of dynamic consolidation[J].Géotechnique,1975,25(1):3-18.
[3]CHOW Y K,YONG D M,YONG K Y,et al.Dynamic compaction analysis[J].Journal of Geotechnical Engineering,1992,118(8):1141-1157.
[4]CHOW Y K,YONG D M,YONG K Y,et al.Dynamic compaction of loose sand deposits[J].Soils&Foundations,1992,32(4):93-106.
[5]钱家欢,帅方生.边界元法在地基强夯加固中的应用[J].中国科学:数学物理学天文学技术科学,1987(3):107-114.(QIAN Jia-huan,SHUAI Fang-sheng.Application of boundary element method in dynamic compaction reinforcement of foundation[J].Scientia Sinica,1987(3):107-114.(in Chinese))
[6]孔令伟,袁建新.强夯时地基土的应力场分布特征及应用[J].岩土力学,1999,20(3):13-19.(KONG Ling-wei,YUAN Jian-xin.Stress field distribution characteristics and applications of foundation soil during dynamic compaction[J].Rock and Soil Mechanics,1999,20(3):13-19.(in Chinese))
[7]蒋鹏,李荣强,孔德坊.强夯大变形冲击碰撞数值分析[J].岩土工程学报,2000,22(2):222-226.(JIANG Peng,LI Rong-qiang,KONG De-fang.Numerical analysis of large deformation impact and collision properties during dynamic compaction[J].Chinese Jounal of Geotechnical Engineering,2000,22(2):222-226.(in Chinese))
[8]PAN J L,SELBY A R.Simulation of dynamic compaction of loose granular soils[J].Advances in Engineering Software,2002,33(7):631-640.
[9]杨建国,彭文轩,刘东燕.强夯法加固的主要设计参数研究[J].岩土力学,2004,25(8):1335-1339.(YANG Jian-guo PENG Wen-xuan,LIU Dong-yan.Research of choosing tamping factors for dynamic consolidation method[J].Rock and Soil Mechanics,2004,25(8):1335-1339.(in Chinese))
[10]蔡袁强,陈仁伟,徐长节.强夯加固机理的大变形数值分析[J].浙江大学学报(工学版),2005,39(1):65-69.(CAIYuan-qiang,CHEN Ren-wei,XU Chang-jie.Numerical analysis of dynamic compaction using large deformation theory[J].Journal of Zhejiang University(Engineering Science),2005,39(1):65-69.(in Chinese))
[11]付乐.工程碎石土基本力学特性与强夯加固机理研究[D].北京:北京科技大学,2015:77-93.(FU Le.Research on the basic mechanical properties of engineering gravelly soil and dynamic compaction strengthening mechanism[D].Beijing:University of Science and Technology Beijing,2015:77-93.(in Chinese))
[12]张北战,姚仰平,方雨菲.填土地基强夯加固效果研究[J].地震工程学报,2015,37(7):30-34.(ZHANG Bei-zhan,YAO Yang-ping,FANG Yu-fei.Reinforcement effect of dynamic compaction on a backfilled foundation[J].China Earthquake Engineering Journal,2015,37(7):30-34.(in Chinese))
[13]THILAKASIRI H S,GUNARATNE M,MULLINS G,et al.Investigation of impact stresses induced in laboratory dynamic compaction of soft soils[J].International Journal for Numerical&Analytical Methods in Geomechanics,2015,20(10):753-767.
[14]姚仰平,张北战.基于体应变的强夯加固范围研究[J].岩土力学,2016,37(9):2663-2671.(YAO Yang-ping,ZHANG Bei-zhan.Reinforcement range of dynamic compaction based on volumetric strain[J].Rock and Soil Mechanics,2016,37(9):2663-2671.(in Chinese))
[15]向泽华,胡焕校,吴高权.强夯作用下土体动力特性的数值模拟[J].水资源与水工程学报,2015(6):207-211.(XIANG Ze-hua,HU Huan-xiao,WU Gao-quan.Numerical simulation of dynamic characteristics of soil under role of strong compaction[J].Journal of Water Resources and Water Engineering,2015(6):207-211.(in Chinese))
[16]EBRAHIMIAN B.Numerical simulation of soil compaction by impact using smoothed particle hydrodynamics(SPH)method[C]//International Conference on Modeling,Simulation and Applied Optimization.Sharjah,2009.
[17]PASDARPOUR M,GHAZAVI M,TESHNEHLAB M,et al.Optimal design of soil dynamic compaction using genetic algorithm and fuzzy system[J].Soil Dynamics&Earthquake Engineering,2009,29(7):1103-1112.
[18]贾敏才,吴邵海,叶建忠.基于三维离散元法的强夯动力响应研究[J].湖南大学学报(自然科学版),2015(3):70-76.(JIA Min-cai,WU Shao-hai,YE Jian-zhong.Discrete element modeling of dynamic compaction in granular soils using PFC3D[J].Journal of Hunan University Natural Sciences,2015(3):70-76.(in Chinese))
[19]张雄,廉艳平,刘岩,等.物质点法[M].北京:清华大学出版社,2013:38-102.(ZHANG Xiong,LIANYan-ping,LIU Yan.Material point method[M].Beijing:Tsinghua University Press,Beijing,2013:38-102.(in Chinese))
[20]SULSKY D,CHEN Z,SCHREYER H L.A particle method for history-dependent materials[J].Computer Methods in Applied Mechanics&Engineering,1993,118(1/2):179-196.
[21]HARLOW F.A machine calculation method for hydrodynamic problems[R].Los Alamos:Los Alamos Scientific Laboratory,1955.
[22]DAWSON J M.Particle simulation of plasmas[J].Review of Modern Physics,1983,55(55):403.
[23]BRACKBILL J U,RUPPEL H M.FLIP:a method for adaptively zoned,particle-in-cell calculations of fluid flows in two dimensions[J].Journal of Computational Physics,1986,65(2):314-343.
[24]BARDENHAGEN S G,KOBER E M.The generalized interpolation material point method[J].Computer Modeling in Engineering&Sciences,2004,5(6):477-495.
[25]ZHANG D Z,MA X,GIGUERE P T.Material point method enhanced by modified gradient of shape function[J].Journal of Computational Physics,2011,230(16):6379-6398.
[26]SO?OWSKI W T,SLOAN S W,KANTY P T,et al.Numerical simulation of a small scale dynamic replacement stone column creation experiment[C]//International Conference on Particle-based Methods-Fundamentals and Applications.Stuttagrt,2013:522-533.
[27]王钟琦,邓祥林.强夯机理及其环境影响[C]//中国土木工程学会土力学及基础工程学术会议论文选集.北京,1983.(WANG Zhong-qi,DENG Xiang-lin.Dynamic mechanism and its environmental impact[C]//Selected Works of the Conference of Soil Mechanics and Basic Engineering of China Civil Engineering Society.Beijing,1983.(in Chinese))
[28]WANG Z Q,DENG X I.Mechanism of dynamic consolidation and its environmental effects[C]//First International Conference on Case Histories in Geotechnical Engineering.St Louis,1984.
[29]孔令伟,袁建新.强夯的边界接触应力与沉降特性研究[J].岩土工程学报,1998,20(2):86-92.(KONG Ling-wei,YUAN Jian-xin.Study on surface contact stress and settlement properties during dynamic consolidation[J].Chinese Jounal of Geotechnical Engineering,1998,20(2):86-92.(in Chinese))
[30]SULSKY D,ZHEN S,SCHREYER H L.Application of a particle-in-cell method to solid mechanics[J].Computer Physics Communications,1995,87(1):236-252.
[31]孙玉进.岩土大变形问题的物质点法研究[D].北京:清华大学,2017:21-51.(SUN Yu-jin.Research on geotechnical problems involving extremely large deformation using the material point methoed[D].Beijing:Tsinghua University,2017:21-51.(in Chinese))
[32]孙玉进,宋二祥.大位移滑坡形态的物质点法模拟[J].岩土工程学报,2015,37(7):1218-1225.(SUN Yu-jin,SONGEr-xiang.Simulation of large-displacement landslide by material point method[J].Chinese Journal of Geotechnical Engineering,2015,37(7):1218-1225.(in Chinese))
[33]廉艳平,张帆,刘岩,等.物质点法的理论和应用[J].力学进展,2013,43(2):237-264.(LIAN Yan-ping,ZHANGFan,LIU Yan,et al.Material point method and its applications.Advances in Mechanics,2013,43(2):237-264.(in Chinese))
[34]黄鹏.金属及岩土冲击动力学问题的物质点法研究[D].北京:清华大学,2010:99-102.(HUANG Peng.Material point method for metal and soil impact dynamics problems[D].Beijing:Tsinghua University,2010:99-102.(in Chinese))
[35]AL-KAFAJI I K J.Formulation of a Dynamic Material Point Method(MPM)for Geomechanical Problems[D].Stuttgart:Uni Stuttgart-Universit?tsbibliothek,2013.
[36]CUNDALL P A.Explicit finite-difference methods in geomechanics[J].Numerical Methods in Geomechanics,1976,1:132-150.
[37]BAUER E.Calibration of a comprehensive hypoplastic model for granular materials[J].Soils and Foundations,1996,36(1):13-26.
[38]SCHANZ T,VERMEER P A,BONNIER P G.The hardening soil model:formulation and verification[C]//Beyond 2000 in Computational Geotechnics.Amsterdam,1999:281-296.
[39]HERLE I,GUDEHUS G.Determination of parameters of a hypoplastic constitutive model from properties of grain assemblies[J].International Journal for Numerical&Analytical Methods in Geomechanics,2015,4(5):461-486.
[40]MAYNE P W,JONES J S.Impact stresses during dynamic compaction[J].Journal of Geotechnical Engineering,1983,109(10):1342-1346.
[41]PORAN C J,RODRIGUEZ J A.Impact behaviour of sand[J].Soils&Foundations,1992,32(4):81-92.