变荷载下连续排水边界黏弹性地基一维固结性状分析
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摘要
在考虑软黏土流变特性的基础上,结合工程实际,引入连续排水边界条件,建立了变荷载下连续排水边界黏弹性地基一维固结模型。通过分离变量法与常数变易法,求得了变荷载作用及连续排水边界条件下的饱和软黏土一维固结模型的解析解,进一步研究了透水边界条件和土体参数对超孔隙水压力、有效应力的影响。研究结果表明:上下边界透水性的不同会直接影响超孔隙水压力的变化;越靠近透水性大的边界处的土体固结速度越快,且随着其离排水边界的距离减小,对固结速度的影响逐渐增大;另外,软土层的渗透系数、Kelvin体弹簧的弹性模量和黏滞系数等对土颗粒间的有效应力影响较大。
Considering the rheological properties of soft clay and the engineering practice, the continuous boundary condition is applied to construct a one-dimensional consolidation model for viscoelastic foundation under time-dependent loading condition. The analytic solution for one-dimensional consolidation of saturated soft clay under time-dependent loading and continuous drainage boundary is solved by using separation of variables and variation of constants methods. Furthermore, influences of boundary conditions and soil parameters on excess pore water pressure and effective stress are studied. It is found that the variation of excess pore water pressure is directly influenced by permeability of upper-and lower-boundary. The consolidation rate is larger at the location closer to the boundary with higher permeability, and with decreasing the distance from drainage boundary, the influence on consolidation rate increases gradually. Moreover, the effective stress is significantly influenced by permeability coefficient, elastic modulus of Kelvin model and viscosity coefficient.
Considering the rheological properties of soft clay and the engineering practice, the continuous boundary condition is applied to construct a one-dimensional consolidation model for viscoelastic foundation under time-dependent loading condition. The analytic solution for one-dimensional consolidation of saturated soft clay under time-dependent loading and continuous drainage boundary is solved by using separation of variables and variation of constants methods. Furthermore, influences of boundary conditions and soil parameters on excess pore water pressure and effective stress are studied. It is found that the variation of excess pore water pressure is directly influenced by permeability of upper-and lower-boundary. The consolidation rate is larger at the location closer to the boundary with higher permeability, and with decreasing the distance from drainage boundary, the influence on consolidation rate increases gradually. Moreover, the effective stress is significantly influenced by permeability coefficient, elastic modulus of Kelvin model and viscosity coefficient.
引文
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[10]王少媚,夏森炜,蒋军.循环荷载作用下黏弹性地基一维固结性状研究[J].岩土力学,2008,29(2):470-474.WANG Shao-mei,XIA Sen-wei,JIANG Jun.Study on one-dimensional consolidation behavior of saturated clay under cyclic loading[J].Rock and Soil Mechanics,2008,29(2):470-474.
[11]QIN A,SUN D,TAN Y.Semi-analytical solution to one-dimensional consolidation in unsaturated soils[J].Applied Mathematics and Mechanics in English,2010,29(2):215-226.
[12]QIN A,SUN D,ZHANG J.Semi-analytical solution to one-dimensional consolidation for viscoelastic unsaturated soils[J].Computers&Geotechnics,2014,62(10):110-117.
[13]郑昱,梅国雄,梅岭.广义连续排水边界在一维固结问题中的应用[J].南京工业大学学报(自然科学版),2010,32(6):54-58.ZHENG Yu,MEI Guo-xiong,MEI Ling.Generalized continuous drainage boundary applied in one-dimensional consolidation theory[J].Journal of Nanjing University of Technology(Natural Science Edition),2010,32(6):54-58.
[14]梅国雄,夏君,梅岭.基于不对称连续排水边界的太沙基一维固结方程及其解答[J].岩土工程学报,2011,33(1):28-31.MEI Guo-xiong,XIA Jun,MEI Ling.Terzaghi’s onedimensional consolidation equation and its solution based on asymmetric continuous drainage boundary[J].Chinese Journal of Geotechnical Engineering,2011,33(1):28-31.
[15]张磊,孙树林.变荷载下双曲线模型修正土体一维固结理论[J].岩石力学与工程学报,2007,26(增刊2):4306-4310.ZHANG Lei,SUN Shu-lin.One-dimensional consolidation theory based on hyperbola model under time-dependent loading for saturated soil[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(Suppl.2):4306-4310.
[16]梁俊奇,王庆东.常系数非齐次线性微分方程的一个简捷解法[J].高等数学研究,2002,5(2):14-16.LIANG Jun-qi,WANG Qing-dong.A simple method for solving nonhomogeneous linear differential equations with constant coefficients[J].Journal of Higher Mathematics,2002,5(2):14-16.
[17]周文渊,闪黎,宋新江,等.等加载速率下软土固结特性试验研究[J].南水北调与水利科技,2015,13(4):695-698.ZHOU Wen-yuan,SHAN Li,SONG Xin-jiang,et al.research on consolidation test of soft clay under constant loading rate[J].South-to-North Water Transfers and Water Science&Technology,2015,13(4):695-698.
[18]李学伟,宋小金,车法.粉质黏土地基超孔隙水压力消散规律研究[J].中外公路,2014,34(2):86-89.LI Xue-wei,SONG Xiao-jin,CHE Fa.Study on dissipation law of excess pore water pressure in silty clay ground[J].Journal of China&Foreign Highways,2014,34(2):86-89.
[2]门福录.黏土固结与次时间效应单维问题的近似解[J].水利学报,1963(1):44-63.MENG Fu-lu.An approximate solution to the unidimensional problem of clay consolidation and subtime effects[J].Journal of Hydraulic Engineering,1963(1):44-63.
[3]王盛源.变荷载下的黏弹性体一维固结问题[J].水利水运科学研究,1981(2):10-17.WANG Sheng-yuan.One-dimensional consolidation of viscoelastic body under variable load[J].Water Resources and Hydropower Engineering,1981(2):10-17.
[4]赵维炳.广义Voigt模型模拟的饱水土体一维固结理论及其应用[J].岩土工程学报,1989,11(5):78-85.ZHAO Wei-bin.One-dimensional consolidation theory of saturated soil with generalized Voigt model simulation and its application[J].Chinese Journal of Geotechnical Engineering,1989,11(5):78-85.
[5]李冰河,谢康和,应宏伟,等.变荷载下软黏土非线性一维固结半解析解[J].岩土工程学报,1999,21(3):288-293.LI Bing-he,XIE Kang-he,YING Hong-wei,et al.Semi-analytical solution of one dimensional non-linear consolidation of soft clay under time-dependent loading[J].Chinese Journal of Geotechnical Engineering,1999,21(3):288-293.
[6]蔡袁强,徐长节,袁海明.任意荷载下成层黏弹性地基的一维固结[J].应用数学和力学,2001,(3):307-313.CAI Yuan-qiang,XU Chang-jie,YUAN Hai-ming.One-dimensional consolidation of layered viscoelastic foundations under arbitrary loading[J].Applied Mathematics and Mechanics,2001,(3):307-313.
[7]蔡袁强,粱旭,郑灶锋,等.半透水边界的黏弹性土层在循环荷载下的一维固结[J].土木工程学报,2003,36(8):86-90.CAI Yuan-qiang,LIANG Xu,ZHENG Zhao-feng,et al.One-dimensional consolidation of viscoelastic soil layer with semi-permeable boundary under cyclic loadings[J].Chinese Journal of Civil Engineering,2003,36(8):86-90.
[8]LEO C J,XIE K H.An efficient solution of onedimensional consolidation of layered soft soils with time effects[C]//Proceedings of 10th International Conference Oncomputer Methods and Advances in Geomechanics.Tucson:[s.n.],2001.1791-4.
[9]XIE K H,XIE X Y,LI X B.Analytical theory for one-dimensional consolidation of clayey soils exhibiting rheological characteristics under time-dependent loading[J].International Journal for Numerical&Analytical Methods in Geomechanics,2008,32(14):1833-1855.
[10]王少媚,夏森炜,蒋军.循环荷载作用下黏弹性地基一维固结性状研究[J].岩土力学,2008,29(2):470-474.WANG Shao-mei,XIA Sen-wei,JIANG Jun.Study on one-dimensional consolidation behavior of saturated clay under cyclic loading[J].Rock and Soil Mechanics,2008,29(2):470-474.
[11]QIN A,SUN D,TAN Y.Semi-analytical solution to one-dimensional consolidation in unsaturated soils[J].Applied Mathematics and Mechanics in English,2010,29(2):215-226.
[12]QIN A,SUN D,ZHANG J.Semi-analytical solution to one-dimensional consolidation for viscoelastic unsaturated soils[J].Computers&Geotechnics,2014,62(10):110-117.
[13]郑昱,梅国雄,梅岭.广义连续排水边界在一维固结问题中的应用[J].南京工业大学学报(自然科学版),2010,32(6):54-58.ZHENG Yu,MEI Guo-xiong,MEI Ling.Generalized continuous drainage boundary applied in one-dimensional consolidation theory[J].Journal of Nanjing University of Technology(Natural Science Edition),2010,32(6):54-58.
[14]梅国雄,夏君,梅岭.基于不对称连续排水边界的太沙基一维固结方程及其解答[J].岩土工程学报,2011,33(1):28-31.MEI Guo-xiong,XIA Jun,MEI Ling.Terzaghi’s onedimensional consolidation equation and its solution based on asymmetric continuous drainage boundary[J].Chinese Journal of Geotechnical Engineering,2011,33(1):28-31.
[15]张磊,孙树林.变荷载下双曲线模型修正土体一维固结理论[J].岩石力学与工程学报,2007,26(增刊2):4306-4310.ZHANG Lei,SUN Shu-lin.One-dimensional consolidation theory based on hyperbola model under time-dependent loading for saturated soil[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(Suppl.2):4306-4310.
[16]梁俊奇,王庆东.常系数非齐次线性微分方程的一个简捷解法[J].高等数学研究,2002,5(2):14-16.LIANG Jun-qi,WANG Qing-dong.A simple method for solving nonhomogeneous linear differential equations with constant coefficients[J].Journal of Higher Mathematics,2002,5(2):14-16.
[17]周文渊,闪黎,宋新江,等.等加载速率下软土固结特性试验研究[J].南水北调与水利科技,2015,13(4):695-698.ZHOU Wen-yuan,SHAN Li,SONG Xin-jiang,et al.research on consolidation test of soft clay under constant loading rate[J].South-to-North Water Transfers and Water Science&Technology,2015,13(4):695-698.
[18]李学伟,宋小金,车法.粉质黏土地基超孔隙水压力消散规律研究[J].中外公路,2014,34(2):86-89.LI Xue-wei,SONG Xiao-jin,CHE Fa.Study on dissipation law of excess pore water pressure in silty clay ground[J].Journal of China&Foreign Highways,2014,34(2):86-89.
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