连续排水边界条件下线性加载地基一维固结解析解
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摘要
基于瞬时加载下的连续排水边界条件,推导出任意荷载连续排水边界条件,建立了任意荷载连续排水边界条件下线性加载一维固结方程。利用有限正弦傅里叶变换,求解出其解析解,通过公式退化和有限元成果对比分析,对该文解答的正确性进行了验证。在不同加载速率和界面参数的条件下,分析了加载速率和界面排水参数对孔压和平均固结度的影响。结果表明:加载速率对固结影响较为显著,加载速率越大,孔压消散越为迅速;当加载速率趋于无穷大时,线性加载退化为瞬时加载;随着界面参数的增大,孔压消散明显,地基固结增快;当界面参数趋于无穷大时,排水边界退化为完全排水边界。工程中,在界面参数或堆载时间确定时,对选择合适的堆载时间或界面参数保证地基稳定性和提高工程效益具有一定参考意义。
Based on the instantaneous loading with continuous drainage boundary conditions, a continuous drainage boundary condition under arbitrary loading is derived. The one-dimensional consolidation equation of linear loading is established under the continuous drainage boundary conditions under arbitrary loading. Using the finite Fourier sine transformation method, the analytical solution is presented. The effectiveness of the solution is demonstrated by formula degradation and a comparison with finite element analysis results. The influence of the loading rate and interface parameters on the excess pore-water pressure and consolidation degree is discussed. The results show that the loading rate has a significant effect on consolidation, and that the greater is the loading rate,the faster the excess pore-water pressure dissipates. When the loading rate approaches to infinity, linear loading degradation is instantaneous loading. With the increase of the interface parameters, the excess pore-water pressure dissipates and the consolidation increases rapidly. When the interface parameter approaches to infinity, the drainage boundary degenerates into a complete permeable boundary. In engineering practice, when the interface parameters(or surcharge time) are determined, it is of certain significance to select suitable loading time(or interface parameters) to ensure the stability of foundation and to increase engineering benefits.
Based on the instantaneous loading with continuous drainage boundary conditions, a continuous drainage boundary condition under arbitrary loading is derived. The one-dimensional consolidation equation of linear loading is established under the continuous drainage boundary conditions under arbitrary loading. Using the finite Fourier sine transformation method, the analytical solution is presented. The effectiveness of the solution is demonstrated by formula degradation and a comparison with finite element analysis results. The influence of the loading rate and interface parameters on the excess pore-water pressure and consolidation degree is discussed. The results show that the loading rate has a significant effect on consolidation, and that the greater is the loading rate,the faster the excess pore-water pressure dissipates. When the loading rate approaches to infinity, linear loading degradation is instantaneous loading. With the increase of the interface parameters, the excess pore-water pressure dissipates and the consolidation increases rapidly. When the interface parameter approaches to infinity, the drainage boundary degenerates into a complete permeable boundary. In engineering practice, when the interface parameters(or surcharge time) are determined, it is of certain significance to select suitable loading time(or interface parameters) to ensure the stability of foundation and to increase engineering benefits.
引文
[1]Terzaghi K.Erdbaumechanik auf bodenphysikalischer grundlage[M].Wien:Fanz Deuticke,1925:399.
[2]Gray H.Simultaneous consolidation of contiguous layers of unlike compressible soils[J].Transactions of the American Society of Civil Engineering,1945,110:1327-1356.
[3]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 Guoxiong,Xia Jun,Mei Ling.Terzaghi's one-dimensional consolidation equation and its solution based on asymmetric continuous drainage bXound@ary[J].Chinese Journal of Geotechnical Engineering,2011,33(1):28-31.(in Chinese)
[4]Mei G X,Chen Q M.Solution of Terzaghi one-dimensional consolidation equation with general boundary conditions[J].Journal of Central South University,2013,20(8):2239-2244.
[5]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 Yun,Mei Guoxiong,Mei Ling.Generalized continuous drainage boundary applied in one-dimensional consolidation theory[J].Journal of Nanjing University of Technology(Natural Science),2010,32(6):54-58.(in Chinese)
[6]蔡烽,何利军,周小鹏,等.连续排水边界下成层地基一维固结问题的有限元分析[J].中南大学学报:自然科学版,2013,44(1):315-323.Cai Feng,He Lijun,Zhou Xiaopeng,et al.Finite element analysis of one-dimensional consolidation problem with continuous drainage boundaries in layered ground[J].Journal of Central South University(Natural Science),2013,44(1):315-323.(in Chinese)
[7]蔡烽,何利军,周小鹏,等.连续排水边界下一维固结不排水对称面的有限元分析[J].岩土工程学报,2012,34(11):2141-2147.Cai Feng,He Lijun,Zhou Xiaopeng,et al.Finite element analysis of one-dimensional consolidation of undrained symmetric plane under continuous drainage boundary[J].Chinese Journal of Geotechnical Engineering,2012,34 (11):2141-2147.(in Chinese)
[8]蔡烽,何利军,张青青,等.考虑土体自重的不排水对称面有限元分析[J].浙江大学学报(工学版),2013,47(12):2132-2140.Cai Feng,He Lijun,Zhang Qingqing,et al.Finite element analysis of undrained symmetry plane with self-weight[J].Journal of Zhejiang University(Natural Science),2013,47(12):2132-2140.(in Chinese)
[9]Liu J C,Lei G H.One-dimensional consolidation of layered soils with exponentially time-growing drainage boundaries[J].Computers and Geotechnics,2013,54(10):202-209.
[10]何利军,吴立松,张涛,等.基于连续边界条件的土层厚度随时间变化的平均固结度研究[J].工程力学,2016,33(6):11-17.He Lijun,Wu Lisong,Zhang Tao,et al.Study on the average consolidation of soil thickness based on continuous boundary conditions[J].Engineering Mechanics,2016,33(6):11-17.(in Chinese)
[11]Wu W,Zong M,El Naggar M H,et al.Analytical solution for one-dimensional consolidation of double-layered soil with exponentially time-growing drainage boundary[J].International Journal of Distributed Sensor Networks,2018,14(10):1550147718806716.
[12]Schiffman R.Consolidation of soil under time-dependent loading and varying permeability[J].Proceedings,Highway Research Board,1958,37:584-617.
[13]Lei G H,Zheng Q,Ng C W W,et al.An analytical solution for consolidation with vertical drains under multi-ramp loading[J].Géotechnique,2015,65(7):531-547.
[14]Xie K H,Xia C Q,An R,et al.A study on the one-dimensional consolidation of double-layered structured soils[J].Computers and Geotechnics,2016,73:189-198.
[15]Wilson N E,Elgohary M M.Consolidation of soils under cyclic loading[J].Canadian Geotechnical Journal,1974,11(3):420-423.
[16]Alonso E E,Krizek R J.Randomness of settlement rate under stochastic load[J].Journal of the Geotechnical Engineering Division,ASCE,1974,100(EM6):1211-1226.
[17]Xie K H,Li B H,Li Q L.A nonlinear theory of consolidation under time-dependent loading[C].Proceedings of 2nd International Conference on Soft Soil Engineering,Nanjing:Hohai University Press,1996:193-196.
[18]Hu A F,Xia C Q,Cui J,et al.Nonlinear consolidation analysis of natural structured clays under time-dependent loading[J].International Journal of Geomechanics,2017,18(2):04017140.
[19]Favaretti M,Soranzo M.A simplified consolidation theory in cyclic loading conditions[C].International Symposium on Compression and Consolidation of Clayey Soils,A.A.Balkema:Rotterdam,The Netherlands,1995:405-409.
[20]王小雯,张建民.随机波浪作用下饱和砂质海床弹塑性动力响应规律[J].工程力学,2018,35(6):240-248,256.Wang Xiaowen,Zhang Jianmin.Elastoplastic dynamic behaviors of saturated sandy seabed under random[J].Engineering Mechanics,2018,35(6):240-248,256.(in Chinese)
[21]Chen J Z,Zhu X R,Xie K H,et al.One dimensional consolidation of soft clay under trapezoidal cyclic loading[C].Proceedings of 2nd International Conference on Soft Soil Engineering,Nanjing:Hohai University Press,1996:211-216.
[22]Pzul M,Sahu R.One dimensional consolidation under cyclic loading[J].International Journal of Geotechnical Engineering,2013,6(3):395-401.
[23]Ho L,Fatahi B.Analytical solution for the two-dimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading[J].Computers and Geotechnics,2015,67:1-16.
[24]Feng J X,Ni P P,Mei G X.One-dimensional self-weight consolidation with continuous drainage boundary conditions:Solution and application to clay-drain reclamation[J].International Journal for Numerical and Analytical Methods in Geomechanics,2019,43(8):1634-1652.
[25]黄文熙.土的工程性质[M].北京:水利水电出版社,1983:138-139.Huang Wenxi.Engineering properties of soil[M].Beijing:Hydraulic and Hydroelectricity Press,1983:138-139.(in Chinese)
[26]徐书平,刘祖德,鲍华,等.堆载预压过程中的地基稳定性计算方法[J].岩土力学,2005,26(6):955-958.Xu Shuping,Liu Zude,Bao Hua,et al.Calculation methods of foundation stability in process of preloading[J].Rock&Soil Mechanics,2005,26(6):955-958.(in Chinese)
[2]Gray H.Simultaneous consolidation of contiguous layers of unlike compressible soils[J].Transactions of the American Society of Civil Engineering,1945,110:1327-1356.
[3]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 Guoxiong,Xia Jun,Mei Ling.Terzaghi's one-dimensional consolidation equation and its solution based on asymmetric continuous drainage bXound@ary[J].Chinese Journal of Geotechnical Engineering,2011,33(1):28-31.(in Chinese)
[4]Mei G X,Chen Q M.Solution of Terzaghi one-dimensional consolidation equation with general boundary conditions[J].Journal of Central South University,2013,20(8):2239-2244.
[5]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 Yun,Mei Guoxiong,Mei Ling.Generalized continuous drainage boundary applied in one-dimensional consolidation theory[J].Journal of Nanjing University of Technology(Natural Science),2010,32(6):54-58.(in Chinese)
[6]蔡烽,何利军,周小鹏,等.连续排水边界下成层地基一维固结问题的有限元分析[J].中南大学学报:自然科学版,2013,44(1):315-323.Cai Feng,He Lijun,Zhou Xiaopeng,et al.Finite element analysis of one-dimensional consolidation problem with continuous drainage boundaries in layered ground[J].Journal of Central South University(Natural Science),2013,44(1):315-323.(in Chinese)
[7]蔡烽,何利军,周小鹏,等.连续排水边界下一维固结不排水对称面的有限元分析[J].岩土工程学报,2012,34(11):2141-2147.Cai Feng,He Lijun,Zhou Xiaopeng,et al.Finite element analysis of one-dimensional consolidation of undrained symmetric plane under continuous drainage boundary[J].Chinese Journal of Geotechnical Engineering,2012,34 (11):2141-2147.(in Chinese)
[8]蔡烽,何利军,张青青,等.考虑土体自重的不排水对称面有限元分析[J].浙江大学学报(工学版),2013,47(12):2132-2140.Cai Feng,He Lijun,Zhang Qingqing,et al.Finite element analysis of undrained symmetry plane with self-weight[J].Journal of Zhejiang University(Natural Science),2013,47(12):2132-2140.(in Chinese)
[9]Liu J C,Lei G H.One-dimensional consolidation of layered soils with exponentially time-growing drainage boundaries[J].Computers and Geotechnics,2013,54(10):202-209.
[10]何利军,吴立松,张涛,等.基于连续边界条件的土层厚度随时间变化的平均固结度研究[J].工程力学,2016,33(6):11-17.He Lijun,Wu Lisong,Zhang Tao,et al.Study on the average consolidation of soil thickness based on continuous boundary conditions[J].Engineering Mechanics,2016,33(6):11-17.(in Chinese)
[11]Wu W,Zong M,El Naggar M H,et al.Analytical solution for one-dimensional consolidation of double-layered soil with exponentially time-growing drainage boundary[J].International Journal of Distributed Sensor Networks,2018,14(10):1550147718806716.
[12]Schiffman R.Consolidation of soil under time-dependent loading and varying permeability[J].Proceedings,Highway Research Board,1958,37:584-617.
[13]Lei G H,Zheng Q,Ng C W W,et al.An analytical solution for consolidation with vertical drains under multi-ramp loading[J].Géotechnique,2015,65(7):531-547.
[14]Xie K H,Xia C Q,An R,et al.A study on the one-dimensional consolidation of double-layered structured soils[J].Computers and Geotechnics,2016,73:189-198.
[15]Wilson N E,Elgohary M M.Consolidation of soils under cyclic loading[J].Canadian Geotechnical Journal,1974,11(3):420-423.
[16]Alonso E E,Krizek R J.Randomness of settlement rate under stochastic load[J].Journal of the Geotechnical Engineering Division,ASCE,1974,100(EM6):1211-1226.
[17]Xie K H,Li B H,Li Q L.A nonlinear theory of consolidation under time-dependent loading[C].Proceedings of 2nd International Conference on Soft Soil Engineering,Nanjing:Hohai University Press,1996:193-196.
[18]Hu A F,Xia C Q,Cui J,et al.Nonlinear consolidation analysis of natural structured clays under time-dependent loading[J].International Journal of Geomechanics,2017,18(2):04017140.
[19]Favaretti M,Soranzo M.A simplified consolidation theory in cyclic loading conditions[C].International Symposium on Compression and Consolidation of Clayey Soils,A.A.Balkema:Rotterdam,The Netherlands,1995:405-409.
[20]王小雯,张建民.随机波浪作用下饱和砂质海床弹塑性动力响应规律[J].工程力学,2018,35(6):240-248,256.Wang Xiaowen,Zhang Jianmin.Elastoplastic dynamic behaviors of saturated sandy seabed under random[J].Engineering Mechanics,2018,35(6):240-248,256.(in Chinese)
[21]Chen J Z,Zhu X R,Xie K H,et al.One dimensional consolidation of soft clay under trapezoidal cyclic loading[C].Proceedings of 2nd International Conference on Soft Soil Engineering,Nanjing:Hohai University Press,1996:211-216.
[22]Pzul M,Sahu R.One dimensional consolidation under cyclic loading[J].International Journal of Geotechnical Engineering,2013,6(3):395-401.
[23]Ho L,Fatahi B.Analytical solution for the two-dimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading[J].Computers and Geotechnics,2015,67:1-16.
[24]Feng J X,Ni P P,Mei G X.One-dimensional self-weight consolidation with continuous drainage boundary conditions:Solution and application to clay-drain reclamation[J].International Journal for Numerical and Analytical Methods in Geomechanics,2019,43(8):1634-1652.
[25]黄文熙.土的工程性质[M].北京:水利水电出版社,1983:138-139.Huang Wenxi.Engineering properties of soil[M].Beijing:Hydraulic and Hydroelectricity Press,1983:138-139.(in Chinese)
[26]徐书平,刘祖德,鲍华,等.堆载预压过程中的地基稳定性计算方法[J].岩土力学,2005,26(6):955-958.Xu Shuping,Liu Zude,Bao Hua,et al.Calculation methods of foundation stability in process of preloading[J].Rock&Soil Mechanics,2005,26(6):955-958.(in Chinese)
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