连续排水边界下梯形循环荷载作用的一维固结解析解
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摘要
针对现有固结问题中边界排水面存在孔压突变为零的问题,引入连续排水边界条件,基于该边界推导了考虑任意荷载作用的连续排水边界条件,并在此基础上建立了一维均质地基固结模型,求得其无量纲化的一般解答。将梯形循环荷载的傅里叶级数展开式的各项分别代入固结一般解答中,最后运用叠加原理将所求得的固结解答叠加,即是连续排水边界下梯形循环荷载作用的一维固结解析解。将本文梯形循环荷载退化为骤加荷载,并和已有文献进行对比,验证了所求解析解的合理性。通过参数分析,研究了界面参数和梯形循环荷载对固结性状的影响。
Aiming at the contradiction between the initial condition and the boundary condition in the existing consolidation problem, a continuous drainage boundary is introduced, and a continuous drainage boundary condition considering the arbitrary loadings is deduced on the basis of it, a one-dimensional consolidation model of the foundation under arbitrary loadings is established, and its dimensionless general answer was obtained. Then the Fourier series expansion of the trapezoidal cyclic loadings is substituted into the consolidation analysis. Finally, the superposition principle is used to superimpose the obtained consolidation solution, which is the one-dimensional consolidation analytical solution of trapezoidal cyclic loading under a continuous drainage boundary. The trapezoidal loading is reduced to a sudden load and compared with the existing literature to verify the rationality of the solution. The influence of interface parameters and trapezoidal cyclic loadings on the consolidation behavior was studied by parametric analysis.
Aiming at the contradiction between the initial condition and the boundary condition in the existing consolidation problem, a continuous drainage boundary is introduced, and a continuous drainage boundary condition considering the arbitrary loadings is deduced on the basis of it, a one-dimensional consolidation model of the foundation under arbitrary loadings is established, and its dimensionless general answer was obtained. Then the Fourier series expansion of the trapezoidal cyclic loadings is substituted into the consolidation analysis. Finally, the superposition principle is used to superimpose the obtained consolidation solution, which is the one-dimensional consolidation analytical solution of trapezoidal cyclic loading under a continuous drainage boundary. The trapezoidal loading is reduced to a sudden load and compared with the existing literature to verify the rationality of the solution. The influence of interface parameters and trapezoidal cyclic loadings on the consolidation behavior was studied by parametric analysis.
引文
[1]Schiffman R L.Consolidation of soil under time-dependent loadings and varying permeability[J].Proceedings,Highway Research Board,Washington,1958,37:584-617.
[2]Wilson N,Elgohary M.Consolidation of soils under cyclic loadings[J].Canadian Geotechnical Journal,1974,11(3):420-423.
[3]Alonso E E,Krizek R J.Randomness of settlement rate under stochastic loadings[J].Journal of the Geotechnical Engineering Division ASCE,1974,100:1211-1226.
[4]Balighm M,Levadoux J.Consolidation theory of cyclic loadings[J].Journal of Geotechnical Engineering Division ASCE,1978,104(4):415-431.
[5]Favaretti M,Soranzo M.A simplified consolidation theory in cyclic loadings conditions[C].International Symposium on Compression and Consolidation of Clayey Soils,A.A.Balkema:Rotterdam,The Netherlands,1995:405-409.
[6]Rahal M A,Vuez A R.Analysis of settlement and pore pressure induced by cyclic loadings of Soil[J].Journal of Geotechnical and Geoenvironmental Engineering,ASCE,1998,124(12):1208-1210.
[7]吴世明,陈龙珠,杨丹.周期荷载作用下饱和粘土的一维固结[J].浙江大学学报:工学版,1988,22(5):60-70.Wu Shiming Chen Longzhu Yang Dan.1-Dconsolidation of saturated clays under cyclic loadings[J].Journal of Zhejiang University(Engineering Science),1988,22(5):60-70.(in Chinese)
[8]杨峻,蔡袁强,吴世明.循环荷载作用下双层地基的一维固结[J].浙江大学学报:工学版,1996,30(3):319-326.Yang Jun,Cai Yuanqiang,Wu Shiming.One dimensional consolidation of double-layered ground under cyclic loadings[J].Journal of Zhejiang University(Engineering Science),1996,30(3),319-326.(in Chinese)
[9]蒋军,陈龙珠.长期循环荷载作用下粘土的一维沉降[J].岩土工程学报,2001,23(3):366-369.Jiang Jun,Chen Longzhu.One-dimensional settlement due to long-term cyclic loadings[J].Chinese Journal of Geotechnical Engineering,2001,23(3):366-369.(in Chinese)
[10]梁旭,蔡袁强,吴世明.半透水边界饱和土层在循环荷载作用下的一维固结分析[J].水利学报,2002,31(7):31-36.Liang Xu,Cai Yuanqiang,Wu Shiming.1-Dconsolidation analysis of saturated soil with semi-pervious boundaries under cyclie loadings[J].Shui Li Xue Bao,2002,31(7):31-36.(in Chinese)
[11]关山海,谢康和,胡安峰.低频循环荷载下地基一维固结性状分析[J].岩土力学,2003,24(5):849-853.Guan Shanhai,Xie Kanghe,Hu Anfeng.Analysis of one-dimensional consolidation behavior of soils under low-frequency cyclic loadings[J].Rock and Soil Mechanics,2003,24(5):849-853.(in Chinese)
[12]李西斌,谢康和,王奎华,等.双面半透水边界饱和土层在循环荷载作用下的一维粘弹性固结解析解[J].工程力学,2004,21(5):103―108,99.Li Xibin,Xie Kanghe,Wang Kuihua,et al.Analytical solution of 1-D visco-elastic consolidation consolidation of soils with impeded boundaries under cyclic loadings[J].Engineering Mechanics,2004,21(5):103-108,99.(in Chinese)
[13]庄迎春,胡安峰,谢康和.循环荷载下软土的一维固结分析[J].土木工程学报,2005,38(9):109-114.Zhuang Yingchun,Hu Anfeng,Xie Kanghe.An analysis of one dimensional consolidation of soft clay under cyclic loadingsing[J].China Civil Engineering Journal2005,38(9):109-114.(in Chinese)
[14]谢康和,周瑾,董亚钦.循环荷载作用下地基一维非线性固结解析解[J].岩石力学与工程学报,2006,25(1):21-26.Xie Kanghe,Zhou Jin,Dong Yaqin,Analytical solution for one dimensional nonlinear consolidation of soil under cyclic loadings[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(1):21-26.(in Chinese)
[15]胡亚元.梯形周期荷载作用下软基路堤的一维沉降研究[J].工程力学,2010,27(12):114-118.Hu Yayuan.Study on the 1D settlement of road embankment on soft clay under trapezoidal periodic loading[J].Engineering Mechanics,2010,27(12):114-118.(in Chinese)
[16]Lei G H,Fu C W,Ng C W W.Vertical-drain consolidation using stone columns:An analytical solution with an impeded drainage boundary under multi-ramp loadings[J].Geotextiles&Geomembranes,2016,44(1):122-131.
[17]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(增刊1):11-17.He Lijun,Wu Lisong,Zhang Tao,et al.The average degree of consolidation about soil layer thickness changing with time based on continuous drainage boundary[J].Engineering Mechanics,2016,33(Suppl1):11-17.(in Chinese)
[18]Ho L,Fatahi B.Analytical solution for the twodimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading[J].Computers&Geotechnics,2015,67:1-16.
[19]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 onedimensional consolidation equation and its solution based on asymmetric continuous drainage boundary[J].Chinese Journal of Geotechnical Engineering,2011,33(1):28-31.(in Chinese)
[2]Wilson N,Elgohary M.Consolidation of soils under cyclic loadings[J].Canadian Geotechnical Journal,1974,11(3):420-423.
[3]Alonso E E,Krizek R J.Randomness of settlement rate under stochastic loadings[J].Journal of the Geotechnical Engineering Division ASCE,1974,100:1211-1226.
[4]Balighm M,Levadoux J.Consolidation theory of cyclic loadings[J].Journal of Geotechnical Engineering Division ASCE,1978,104(4):415-431.
[5]Favaretti M,Soranzo M.A simplified consolidation theory in cyclic loadings conditions[C].International Symposium on Compression and Consolidation of Clayey Soils,A.A.Balkema:Rotterdam,The Netherlands,1995:405-409.
[6]Rahal M A,Vuez A R.Analysis of settlement and pore pressure induced by cyclic loadings of Soil[J].Journal of Geotechnical and Geoenvironmental Engineering,ASCE,1998,124(12):1208-1210.
[7]吴世明,陈龙珠,杨丹.周期荷载作用下饱和粘土的一维固结[J].浙江大学学报:工学版,1988,22(5):60-70.Wu Shiming Chen Longzhu Yang Dan.1-Dconsolidation of saturated clays under cyclic loadings[J].Journal of Zhejiang University(Engineering Science),1988,22(5):60-70.(in Chinese)
[8]杨峻,蔡袁强,吴世明.循环荷载作用下双层地基的一维固结[J].浙江大学学报:工学版,1996,30(3):319-326.Yang Jun,Cai Yuanqiang,Wu Shiming.One dimensional consolidation of double-layered ground under cyclic loadings[J].Journal of Zhejiang University(Engineering Science),1996,30(3),319-326.(in Chinese)
[9]蒋军,陈龙珠.长期循环荷载作用下粘土的一维沉降[J].岩土工程学报,2001,23(3):366-369.Jiang Jun,Chen Longzhu.One-dimensional settlement due to long-term cyclic loadings[J].Chinese Journal of Geotechnical Engineering,2001,23(3):366-369.(in Chinese)
[10]梁旭,蔡袁强,吴世明.半透水边界饱和土层在循环荷载作用下的一维固结分析[J].水利学报,2002,31(7):31-36.Liang Xu,Cai Yuanqiang,Wu Shiming.1-Dconsolidation analysis of saturated soil with semi-pervious boundaries under cyclie loadings[J].Shui Li Xue Bao,2002,31(7):31-36.(in Chinese)
[11]关山海,谢康和,胡安峰.低频循环荷载下地基一维固结性状分析[J].岩土力学,2003,24(5):849-853.Guan Shanhai,Xie Kanghe,Hu Anfeng.Analysis of one-dimensional consolidation behavior of soils under low-frequency cyclic loadings[J].Rock and Soil Mechanics,2003,24(5):849-853.(in Chinese)
[12]李西斌,谢康和,王奎华,等.双面半透水边界饱和土层在循环荷载作用下的一维粘弹性固结解析解[J].工程力学,2004,21(5):103―108,99.Li Xibin,Xie Kanghe,Wang Kuihua,et al.Analytical solution of 1-D visco-elastic consolidation consolidation of soils with impeded boundaries under cyclic loadings[J].Engineering Mechanics,2004,21(5):103-108,99.(in Chinese)
[13]庄迎春,胡安峰,谢康和.循环荷载下软土的一维固结分析[J].土木工程学报,2005,38(9):109-114.Zhuang Yingchun,Hu Anfeng,Xie Kanghe.An analysis of one dimensional consolidation of soft clay under cyclic loadingsing[J].China Civil Engineering Journal2005,38(9):109-114.(in Chinese)
[14]谢康和,周瑾,董亚钦.循环荷载作用下地基一维非线性固结解析解[J].岩石力学与工程学报,2006,25(1):21-26.Xie Kanghe,Zhou Jin,Dong Yaqin,Analytical solution for one dimensional nonlinear consolidation of soil under cyclic loadings[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(1):21-26.(in Chinese)
[15]胡亚元.梯形周期荷载作用下软基路堤的一维沉降研究[J].工程力学,2010,27(12):114-118.Hu Yayuan.Study on the 1D settlement of road embankment on soft clay under trapezoidal periodic loading[J].Engineering Mechanics,2010,27(12):114-118.(in Chinese)
[16]Lei G H,Fu C W,Ng C W W.Vertical-drain consolidation using stone columns:An analytical solution with an impeded drainage boundary under multi-ramp loadings[J].Geotextiles&Geomembranes,2016,44(1):122-131.
[17]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(增刊1):11-17.He Lijun,Wu Lisong,Zhang Tao,et al.The average degree of consolidation about soil layer thickness changing with time based on continuous drainage boundary[J].Engineering Mechanics,2016,33(Suppl1):11-17.(in Chinese)
[18]Ho L,Fatahi B.Analytical solution for the twodimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading[J].Computers&Geotechnics,2015,67:1-16.
[19]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 onedimensional consolidation equation and its solution based on asymmetric continuous drainage boundary[J].Chinese Journal of Geotechnical Engineering,2011,33(1):28-31.(in Chinese)
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