变参数土层一维固结的半解析解
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摘要
基于直接模态摄动法方法,提出了变参数土层一维固结方程的半解析解。该方法利用均匀土层一维固结方程的特征值和固有函数,将变参数土层的固结微分方程转化为代数方程,从而得到变参数土层的特征值和固有函数,计算结果具有两阶以上精度。在此基础上进一步导出了超孔隙水压力和沉降随时间变化的计算公式。该文建议的方法对土层性质的变化规律没有特殊要求,不仅适用于层状土层,也适用于土介质物理特性沿深度不均匀变化的土层,从而为各类变参数土层的一维固结分析提供一种有效的计算手段。通过算例,表明这一方法简单实用,且具有良好的精度。
Based on direct mode perturbation method,a new approach is developed to analyze one-dimensional consolidation equation of soil layers with variable properties.The new method has at least second-order precision.The eigenvalues and eigenfunctions of the homogeneous soil layers are used to simplify the solution of differential equation of one-dimension consolidation of nonhomogeneous soil layers.As the result,a set of algebraic equations are obtained,and it will be solved for semi-analytic solution of one-dimensional consolidation equation.According to the semi-analytic solution of eigenvalues and eigenfunctions of the nonhomogeneous soil layers,the formulae of excess pore water pressure and settlement are derived,which vary with time.Using the proposed method,there is no restriction on the variation soil layer properties with depth.It can be applied to the layered homogeneous soil,as well as any other soil layers with property varying with depth in any form.The results of numerical examples show that the method is simple,practicable and accurate.
Based on direct mode perturbation method,a new approach is developed to analyze one-dimensional consolidation equation of soil layers with variable properties.The new method has at least second-order precision.The eigenvalues and eigenfunctions of the homogeneous soil layers are used to simplify the solution of differential equation of one-dimension consolidation of nonhomogeneous soil layers.As the result,a set of algebraic equations are obtained,and it will be solved for semi-analytic solution of one-dimensional consolidation equation.According to the semi-analytic solution of eigenvalues and eigenfunctions of the nonhomogeneous soil layers,the formulae of excess pore water pressure and settlement are derived,which vary with time.Using the proposed method,there is no restriction on the variation soil layer properties with depth.It can be applied to the layered homogeneous soil,as well as any other soil layers with property varying with depth in any form.The results of numerical examples show that the method is simple,practicable and accurate.
引文
[1]Gray H.Simultaneous consolidation of contiguous layers of unlike compressible soils[J].Transactions,ASCE,1945,110:1327―1356.
[2]Schiffman R L,Stein J R.One-dimensional consolidation of layered system[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1970,96(4):1499―1504.
[3]Lee P K K,Xie K H,Cheung Y K.A study on one dimension consolidation of layered systems[J].International Journal for Numerical and Analytical Methods in Geomechanics,1992,16:815―831.
[4]谢康和.双层地基一维固结理论与应用[J].岩土工程学报,1994,16(5):24―35.Xie Kanghe.Theory of one dimensional consolidation of double-layered ground and its applications[J].Chinese Journal of Geotechnical Engineering,1994,16(5):24―35.(in Chinese)
[5]谢康和,潘秋元.变荷载下任意层地基一维固结理论[J].岩土工程学报,1995,17(5):80―85.Xie Kanghe,Pan Qiuyuan.Theory of one dimensional consolidation of multi-layered soil under varied load[J].Chinese Journal of Geotechnical Engineering,1995,17(5):80―85.(in Chinese)
[6]徐长节,蔡袁强,吴世明.任意荷载下成层弹性地基的一维固结[J].土木工程学报,1999,32(4):57―63.Xu Changjie,Cai Yuanqiang,Wu Shiming.One dimensional consolidation of layered elastic soils under arbitrary loading[J].China Civil Engineering Journal,1999,32(4):57―63.(in Chinese)
[7]Schiffman R L,Gibson R E.Consolidation of non-homogeneous clay layers[J].Journal of soil mechanics and foundation division,ASCE,1964,90(SM5):1―30.
[8]方晔,徐长节,蔡袁强.Gibson地基的一维固结解[J].岩土力学,2003,24(6):913―916.Fang Ye,Xu Changjie,Cai Yuanqiang.One dimensional consolidation of elastic Gibson soils[J].Rock and Soil Mechanics,2003,24(6):913―916.(in Chinese)
[9]江雯,谢康和,夏建中.压缩模量随深度线性变化的软粘土地基一维固结解析解[J].科技通报,2003,19(6):452―460.Jiang Wen,Xie Kanghe,Xia Jianzhong.Analytical solution to1-D consolidation of soft clay with modulus of compressibility varying linearly along depth[J].Bulletin of Science and Technology,2003,19(6):452―456.(in Chinese)
[10]夏建中,江雯,谢康和.成层非均质地基一维固结方程的半解析求解[J].中国公路学报,2006,19(3):8―11.Xia Jianzhong,Jiang Wen,Xie Kanghe.Semi-analytical solution to one-dimensional consolidation equation of layered non-homogeneous sub-grade[J].China Journal of Highway and Transport,2006,19(3):8―11.(in Chinese)
[11]楼梦麟.变参数土层的动力特性和地震反应分析[J].同济大学学报,1997,25(2):155―160.Lou Menglin.Dynamic analysis for modal characteristics and seismic response of soil layer with variable properties[J].Journal of Tongji University,1997,25(2):155―160.(in Chinese)
[12]李广信.高等土力学[M].北京:清华大学出版社2004.Li Guangxin.Advanced soil mechanics[M].Beijing:Tsinghua University Press,2004.(in Chinese)
[13]William B B.An improved perturbation technique for eigenvalues of continuous system[J].Communications in Applied Numerical Methods,1991,7:103―110.
[14]陈塑寰.结构振动分析的矩阵摄动理论[M].重庆:重庆出版社,1991.Chen Suhuan.Matrix perturbation theory in structural dynamics[M].Chongqing:Chongqing Press,1991.(in Chinese)
[2]Schiffman R L,Stein J R.One-dimensional consolidation of layered system[J].Journal of the Soil Mechanics and Foundations Division,ASCE,1970,96(4):1499―1504.
[3]Lee P K K,Xie K H,Cheung Y K.A study on one dimension consolidation of layered systems[J].International Journal for Numerical and Analytical Methods in Geomechanics,1992,16:815―831.
[4]谢康和.双层地基一维固结理论与应用[J].岩土工程学报,1994,16(5):24―35.Xie Kanghe.Theory of one dimensional consolidation of double-layered ground and its applications[J].Chinese Journal of Geotechnical Engineering,1994,16(5):24―35.(in Chinese)
[5]谢康和,潘秋元.变荷载下任意层地基一维固结理论[J].岩土工程学报,1995,17(5):80―85.Xie Kanghe,Pan Qiuyuan.Theory of one dimensional consolidation of multi-layered soil under varied load[J].Chinese Journal of Geotechnical Engineering,1995,17(5):80―85.(in Chinese)
[6]徐长节,蔡袁强,吴世明.任意荷载下成层弹性地基的一维固结[J].土木工程学报,1999,32(4):57―63.Xu Changjie,Cai Yuanqiang,Wu Shiming.One dimensional consolidation of layered elastic soils under arbitrary loading[J].China Civil Engineering Journal,1999,32(4):57―63.(in Chinese)
[7]Schiffman R L,Gibson R E.Consolidation of non-homogeneous clay layers[J].Journal of soil mechanics and foundation division,ASCE,1964,90(SM5):1―30.
[8]方晔,徐长节,蔡袁强.Gibson地基的一维固结解[J].岩土力学,2003,24(6):913―916.Fang Ye,Xu Changjie,Cai Yuanqiang.One dimensional consolidation of elastic Gibson soils[J].Rock and Soil Mechanics,2003,24(6):913―916.(in Chinese)
[9]江雯,谢康和,夏建中.压缩模量随深度线性变化的软粘土地基一维固结解析解[J].科技通报,2003,19(6):452―460.Jiang Wen,Xie Kanghe,Xia Jianzhong.Analytical solution to1-D consolidation of soft clay with modulus of compressibility varying linearly along depth[J].Bulletin of Science and Technology,2003,19(6):452―456.(in Chinese)
[10]夏建中,江雯,谢康和.成层非均质地基一维固结方程的半解析求解[J].中国公路学报,2006,19(3):8―11.Xia Jianzhong,Jiang Wen,Xie Kanghe.Semi-analytical solution to one-dimensional consolidation equation of layered non-homogeneous sub-grade[J].China Journal of Highway and Transport,2006,19(3):8―11.(in Chinese)
[11]楼梦麟.变参数土层的动力特性和地震反应分析[J].同济大学学报,1997,25(2):155―160.Lou Menglin.Dynamic analysis for modal characteristics and seismic response of soil layer with variable properties[J].Journal of Tongji University,1997,25(2):155―160.(in Chinese)
[12]李广信.高等土力学[M].北京:清华大学出版社2004.Li Guangxin.Advanced soil mechanics[M].Beijing:Tsinghua University Press,2004.(in Chinese)
[13]William B B.An improved perturbation technique for eigenvalues of continuous system[J].Communications in Applied Numerical Methods,1991,7:103―110.
[14]陈塑寰.结构振动分析的矩阵摄动理论[M].重庆:重庆出版社,1991.Chen Suhuan.Matrix perturbation theory in structural dynamics[M].Chongqing:Chongqing Press,1991.(in Chinese)
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