基于非线性渗流定律的软土一维固结理论研究
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摘要
大量的室内试验和现场沉降观测资料均表明软粘土中的渗流会出现偏离达西定律的现象,然而目前现有的大多数固结理论均采用达西定律来描述土中的渗流,对基于非线性渗流(或称非达西渗流)定律的软土固结理论的研究目前并不多见,尤其是对考虑非达西渗流定律的成层地基非线性固结理论研究更为不足。鉴于此,本文分别基于Slepicka指数形式渗流定律和Hansbo所提出的非达西渗流模型采用有限差分法及半解析法对软土一维线性及非线性固结理论展开较系统深入的研究,详细的分析了考虑非达西渗流的软土一维固结性状。主要的研究内容和创新工作如下：
1.考虑实际中的变荷载,建立了考虑两种常用的非达西渗流模型的软土地基一维固结问题的控制方程,并分别采用有限差分法和半解析法对其进行数值求解。然后将两种方法计算的固结曲线进行对比,验证了两种数值计算结果的可靠性。在此基础上,详细分析了两种非达西渗流模型中的参数、土层厚度、荷载的大小以及加载速率等对非达西渗流模型下软土地基一维固结性状的影响。2.考虑实际中的变荷载及天然地基的成层性,对考虑两种常用的非达西渗流模型的成层地基一维固结问题展开了系统的研究。首先对考虑两种非达西渗流模型的双层地基
一维线性固结采用有限差分法进行求解,而对考虑两种非达西渗流模型的多层地基一维线性固结则采用半解析方法进行求解。然后将两种方法得到的双层地基固结曲线进行对比,验证了计算结果的可靠性。进而详细地分析讨论了两种非达西渗流模型中的参数、荷载大小、土层厚度、双层地基上、下土层相对压缩性、相对渗透性以及相对厚度对双层地基固结性状的影响,并给出了考虑两种常用的非达西渗流模型的多层地基一维固结计算实例。
3.考虑实际中的变荷载及自重应力沿深度的不同分布形式,引入经典的土体孔隙比与渗透系数、土体孔隙比与有效应力之间的非线性关系,对考虑两种常用的非达西渗流模型的软土地基一维非线性固结问题分别采用差分法和半解析法进行求解。将两种方法得到的固结曲线进行对比,验证了数值计算的可靠性。在此基础上,系统地分析了两种非达西渗流模型中的参数、压缩指数和渗透指数的比值、荷载大小、土层厚度、自重应力的分布形式对软土地基一维非线性固结性状的影响。
Numerous experiments and settlement measurements have shown that the water flow in soft soils may deviate from Darcy's law. However, few researches on consolidation theory for soft soils with non-Darcian flow have been reported, especially on non-linear consolidation theory of layed-soil with non-Darcian flow. Therefore, this dissertation systematically studies one-dimensional linear and non-linear consolidation theory with exponential flow law and non-Darcian flow model proposed by Hansbo by finite difference method and semi-analytical method, and one-dimensional consolidation behaviour of soft soils with two common non-Darcian flow models is analyzed in detail. The main original works are as follows:
1. Considering time-dependent loading in actual engineering, the differential equations governing one-dimensional consolidation with two common non-Darcian flow models are developed, and the numerical solutions are obtained respectively by finite difference method and semi-analytical method. The consolidation curves obtained by both methods are compared, and the reliability of numerical results is testified. On this basis, the influences of parameters in two common non-Darcian flow models, the thickness of soil layer, the value of external loading and the loading rate on consolidation behavior with non-Darcian flow models are analyzed in detail.
2. Considering time-dependent loading and layered distribution of soils in natural foundation, one-dimensional consolidation theory for layered soils with two common non-Darcian flow models is systematically studied. Firstly the problem of one-dimensional consolidation of double-layered soil with two common non-Darcian flow models is solved by finite difference method, and that of multi-layered soils is solved by semi-analytical method. Then consolidation curves of double-layered soil with two common non-Darcian flow models obtained by both numerical methods are plotted together to show the correctness of numerical results. Further more, the influences of parameters of two common non-Darcian flow models, the value of external loading, the total thickness of double-layered soils, relative permeability, relative compressibility and relative thickness of double-layered soils on the consolidation behavior of the double-layered soils are discussed in detail.
3. Considering time-dependent loading and different distribution types of self-weight stress and incorporating the nonlinear relationship between void ratio and permeability coefficient as well as that between void ratio and effective stress, the differential equations governing one-dimensional non-linear consolidation with two common non-Darcian flow models are solved by finite difference menthod and semi-analytical method, respectively. The reliability of numerical results is verified by comparing the consolidation curves obtained by both numerical methods. The influence of parameters of non-Darcian flow models, the ratio of compression index to permeability index, the value of external loading, the thickness of soil layer and the distribution type of self-weight stress on nonlinear consolidation behavior with two common non-Darcian flow models are systematically discussed.
1.考虑实际中的变荷载,建立了考虑两种常用的非达西渗流模型的软土地基一维固结问题的控制方程,并分别采用有限差分法和半解析法对其进行数值求解。然后将两种方法计算的固结曲线进行对比,验证了两种数值计算结果的可靠性。在此基础上,详细分析了两种非达西渗流模型中的参数、土层厚度、荷载的大小以及加载速率等对非达西渗流模型下软土地基一维固结性状的影响。2.考虑实际中的变荷载及天然地基的成层性,对考虑两种常用的非达西渗流模型的成层地基一维固结问题展开了系统的研究。首先对考虑两种非达西渗流模型的双层地基
一维线性固结采用有限差分法进行求解,而对考虑两种非达西渗流模型的多层地基一维线性固结则采用半解析方法进行求解。然后将两种方法得到的双层地基固结曲线进行对比,验证了计算结果的可靠性。进而详细地分析讨论了两种非达西渗流模型中的参数、荷载大小、土层厚度、双层地基上、下土层相对压缩性、相对渗透性以及相对厚度对双层地基固结性状的影响,并给出了考虑两种常用的非达西渗流模型的多层地基一维固结计算实例。
3.考虑实际中的变荷载及自重应力沿深度的不同分布形式,引入经典的土体孔隙比与渗透系数、土体孔隙比与有效应力之间的非线性关系,对考虑两种常用的非达西渗流模型的软土地基一维非线性固结问题分别采用差分法和半解析法进行求解。将两种方法得到的固结曲线进行对比,验证了数值计算的可靠性。在此基础上,系统地分析了两种非达西渗流模型中的参数、压缩指数和渗透指数的比值、荷载大小、土层厚度、自重应力的分布形式对软土地基一维非线性固结性状的影响。
Numerous experiments and settlement measurements have shown that the water flow in soft soils may deviate from Darcy's law. However, few researches on consolidation theory for soft soils with non-Darcian flow have been reported, especially on non-linear consolidation theory of layed-soil with non-Darcian flow. Therefore, this dissertation systematically studies one-dimensional linear and non-linear consolidation theory with exponential flow law and non-Darcian flow model proposed by Hansbo by finite difference method and semi-analytical method, and one-dimensional consolidation behaviour of soft soils with two common non-Darcian flow models is analyzed in detail. The main original works are as follows:
1. Considering time-dependent loading in actual engineering, the differential equations governing one-dimensional consolidation with two common non-Darcian flow models are developed, and the numerical solutions are obtained respectively by finite difference method and semi-analytical method. The consolidation curves obtained by both methods are compared, and the reliability of numerical results is testified. On this basis, the influences of parameters in two common non-Darcian flow models, the thickness of soil layer, the value of external loading and the loading rate on consolidation behavior with non-Darcian flow models are analyzed in detail.
2. Considering time-dependent loading and layered distribution of soils in natural foundation, one-dimensional consolidation theory for layered soils with two common non-Darcian flow models is systematically studied. Firstly the problem of one-dimensional consolidation of double-layered soil with two common non-Darcian flow models is solved by finite difference method, and that of multi-layered soils is solved by semi-analytical method. Then consolidation curves of double-layered soil with two common non-Darcian flow models obtained by both numerical methods are plotted together to show the correctness of numerical results. Further more, the influences of parameters of two common non-Darcian flow models, the value of external loading, the total thickness of double-layered soils, relative permeability, relative compressibility and relative thickness of double-layered soils on the consolidation behavior of the double-layered soils are discussed in detail.
3. Considering time-dependent loading and different distribution types of self-weight stress and incorporating the nonlinear relationship between void ratio and permeability coefficient as well as that between void ratio and effective stress, the differential equations governing one-dimensional non-linear consolidation with two common non-Darcian flow models are solved by finite difference menthod and semi-analytical method, respectively. The reliability of numerical results is verified by comparing the consolidation curves obtained by both numerical methods. The influence of parameters of non-Darcian flow models, the ratio of compression index to permeability index, the value of external loading, the thickness of soil layer and the distribution type of self-weight stress on nonlinear consolidation behavior with two common non-Darcian flow models are systematically discussed.
引文
[1]Abbott M B. One dimensional consolidation of multi-layered soils[J]. Geotechnique,1960,10(4): 151-165.
[2]Barden L, Berry P L. Consolidation of normally consolidated clay[J]. Journal of the Soil M echanics and Foundation Division, ASCE,1965,91 (SM5):15-35.
[3]Barden L. Consolidation of clay with non-linear viscosity[J]. Geotechnique,1965,15(4):321-344.
[4]Cargill K W. Prediction of Consolidation of Very Soft Soil[J]. Journal of Geotechnical Engineering, ASCE,1984,110(6):775-795.
[5]Cherubini C, Vacca G, Giasi C I. Modeling non-Darcian flow in one-dimensional consolidation[J]. Computers and Geotechnics,1988,6(4):247-264.
[6]Chopra M B, Dargush G F. Finite-element analysis of time-dependent large-deformation problems[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1992,16(2):101-130.
[7]Davis E H, Raymond G P. A non-linear theory of consolidation [J]. Geotechnique,1965,15 (2): 161-173.
[8]Desai C S, Saxena S K. Consolidation analysis of layered anisotropic foundations [J]. International Journal for Numerical and Analytical Methods in Geomechanics,1977,1(1):5-23.
[9]Dubin B, Moulin G. Influence of a critical gradient on the consolidation of clays[C]. Consolidation of soils:testing and evaluation (STP 892). West Conshochen(PA):ASTM,1986:354-377.
[10]Duncan J M. Limitation of conventional analysis of consolidation settlement[J]. Journal of the Soil Mechanics and Foundation Division, ASCE,1993,119(9):1333-1359.
[11]Duncan J M, Rajot J P, Perrone V J. Coupled analysis of consolidation and secondary compression[C].Proc. of the 2nd Int. Conf. on Soft Engineering,1, Nanjing, China,1996:3-27.
[12]Elnaggar H A, Krizek R J. Effect of non-Darcian flow on time rate of consolidation [J]. Journal of the Franklin Institute,1973,296(5):323-337.
[13]Garlanger J E. The consolidation of soils exhibiting creep under constant effective stress[J]. Geotechnique,1972,22(1):71-78.
[14]Geng X Y, Xu C J, Cai Y Q. Non-linear consolidation analysis of soil with variable compressibility and permeability under cyclic loadings[J]. International Journal for Numerical and Analytical Methods in eomechanics,2006,30(8):803-821.
[15]Gibson R E, England G L, Hussey M J L. The theory of one-dimensional consolidation of saturated clays:Ⅰ. Finite non-linear consolidation of thin homogeneous layers[J]. Geotechnique,1967,17(3): 261-273.
[16]Gibson R E, Schiffman R L, Cargill K W. The theory of one-dimensional consolidation of saturated clays:Ⅱ. Finite non-linear consolidation of thick homogeneous layers[J]. Canadian Geotechnical Journal,1981,18(2):280-293.
[17]Gray H. Simultaneous consolidation of contiguous layers of unlike compressible soils[J]. Trans. ASCE, 1945,110:1327-1356.
[18]Hansbo S. Consolidation of clay with special reference to influence of vertical drains[C]. Swedish Geotechnical Institute Proceeding. Stockholm:Swedish Geotechnical Institute,1960,18:45-50.
[19]Hansbo S. Aspects of vertical drain design:Darcian or non-Darcian flow[J]. Geotechnique,1997,47(5): 983-992.
[20]Hansbo S. Consolidation equation valid for both Darcian and non-Darcian flow[J]. Geotechnique,2001, 51(1):51-54.
[21]Hansbo S. Deviation from Darcy's law observed in one-dimensional consolidation [J]. Geotechnique, 2003,53(6):601-605.
[22]Huerta A, Rodriguez A. Numerical analysis of nonlinear large-strain consolidation and filling[J]. Computers and structures,1992,44:357-365.
[23]Imai G, Tang Y X. A constitutive equation of one-dimensional consolidation derived from interconnected test[J]. Soil and Foundations,1992,32(2):83-96.
[24]King F H. Principles and conditions of the movement of ground water[R]. U.S.:United States Geological Survey,1898.
[25]Kutilek M. Non-Darcian Flow of Water in Soils—Laminar Region:A Review[J]. Developments in Soil Science,1972,2:327-340.
[26]Lee P K K, Xie K H, Cheung Y K. A study on one-dimensional consolidation of layered systems[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1992,16:815-831.
[27]Lee K, Choa V, Lee S H, Quek S H. Constant rate of strain consolidation of Singapore marine clay Source[J]. Geotechnique,1993,43(3):471-488.
[28]Lekha K R, Krishnaswamy N R, Basak P. Consolidation of clays for variable permeability and compressibility[J] Journal of Geotechnical and Geoenvironmental Engineering, ASCE,2003,129(11): 1001-1009.
[29]Mesri G, Rokhsar A. Theory of consolidation for clays[J]. Journal of the Soil Mechanics and Foundation Division, ASCE,1974, GT8:889-903.
[30]Mesri G, Choiy Y K. Settlement analysis of embankments on soft clays [J]. Journal of the Soil Mechanics and Foundation Division, ASCE,1985,111 (4):441-464.
[31]Mesri G, Tavena S F. Discussion of permeability and consolidation of normally consolidated soils [J]. Journal of the Soil Mechanics and Foundation Division, ASCE,1983,109 (GT6):873-878.
[32]Miller R J, Low P E. Threshold gradient for water flow in clay systems[J]. Soil Science Society of American Journal,1963,27(6):605-609.
[33]Monte J L, Krizek R J. One-dimensional mathematical model for large-strain consolidation [J]. Geotechnique,1976,26(3):495-510.
[34]Morris P H. Analytical Solutions of Linear Finite-Strain One-Dimensional Consolidation[J].Journal of Geotechnical & Geoenvironmental Engineering,2002,128(4):319-325.
[35]Olsen H W. Osmosis:a cause of apparent deviation from Darcy's law[J]. Canadian Geotechnical Journal,1985,22(2):238-241.
[36]Olson R E. Consolidation under time dependent loading[J]. Journal of Geotechnical Engineering, ASCE,1977,103(1):55-60.
[37]Pascal F, Pascal H, Murray D W. Consolidation with threshold gradients[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1981,5(3):247-261.
[38]Poskitt T J. The consolidation of saturated clay with variable permeability and compressibility [J]. Geotechnique,1969,19(2):234-252.
[39]Pyrah I C. One-dimensional consolidation of layered soils[J]. Geotechnique,1996,46(3):555-560.
[40]Schiffman R L. Consolidation of soil under time-dependent loading and varying permeability [J]. Highway Research Board Proceedings,1958,37:584-617.
[41]Schiffman R L, Stein J R. One-dimensional consolidation of layered systems[J]. Journal of Soil Mechanics and Foundations, ASCE,1970,96(4):1499-1504.
[42]Schiffman R L, Gibson R E. Consolidation of nonhomogeneous clay layers [J]. Journal of the Soil Mechanics andFoundations Division, ASCE,1964,90(5):1-30.
[43]Schmidt J D, Westmann R A. Consolidation of porous media with non-Darcy flow[J]. Journal of the Engineering Mechanics Division,1973, EM6:1201-1216.
[44]Skempton A W, Bjerrum L A. Contribution to the settlement analysis of foundations on clay[J]. Geotechique,1957,7(4):168-178.
[45]Slepicka F. Contribution to the solution of the filtration law[C]. International union of Geodesy and Geophysics, Commission of Subterranean Waters. Finland:[s.n.],1960:245-258.
[46]Swartzendruber D. Modification of darcy's law for the flow of water in soils[J]. Soil Science,1962, 93(1):22-29.
[47]Tan T S, Scott R F. Finite strain consolidation—a study of convection[J]. Soils and Foundations,1988, 28(3):64-74.
[48]Tavenas F, Jean P, Leblond P, Leroueil S. The permeability of natural soft clays[J]. Part Ⅰ:methods of laboratory permeability measurements. Canadian Geotechnical Journal,1983(a),20(4):629-644.
[49]Tavenas F, Leblond P, Jean P, Leroueil S. The permeability of natural soft clays. Part Ⅱ:Permeability characteristics[J].Canadian Geotechnical Journal,1983(b),20(4):645-659.
[50]Taylor D W, Merchant W. A theory of clay consolidation accounting for secondary compression [J]. Journal of Mathematics and Physics,1940,19(3):167-185.
[51]Teh C I, Nie X Y. Coupled consolidation theory with non-Darcian flow[J]. Computers and Geotechnics, 2002,29(3):169-209.
[52]Thomas C, Sheahan M. Experimental Verification of CRS Consolidation Theory[J]. Journal of Geotechnical and Geoenvironmental Engineering,1997,123(5):430-437.
[53]Townsend F C, Mc Vay M C. SOA:Large strain consolidation prediction [J]. Journal of Geotechnical Engineering, ASCE,1990,116 (2):222-243.
[54]Weber W G Performance of embankments constructed over peat[J]. Journal of Soil Mechanics and Foundation Division, ASCE,1969,95(1):53-76.
[55]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, China,1996:193-198.
[56]Xie K H, Guo S, Li B H, Zeng G X. A theory of consolidation for soils exhibiting rheological characteristics under cyclic loading[C]. Proceedings of the 9th International Conference on Computer Methods and Advances in Geomechanics 2, Wuhan, China,1997:1053-1058.
[57]Xie K H, Xie X Y, Jiang W. A study on one dimensional nonlinear consolidation of double-layered soil[J]. Computers andGeotechnics,2002,29(2):151-168.
[58]Xie K H, Leo C J. Analytical solutions of one-dimensional large strain consolidation of saturated and homogeneous clays[J]. Computers and Geotechnics,2004,31(4):301-314.
[59]Xie K H, Wang K, Wang Y L, Li C X. Analytical solution for one-dimensional consolidation of clayey soils with a threshold gradient[J]. Computers and Geotechnics,2010,37(4):487-493.
[60]Zhu G F, Yin J H. Consolidation of soil under depth-dependent ramp load[J]. Canadian Geotechnical Journal,1998,35(2):344-350.
[61]Zhu G, Yin J H. Consolidation of double soil layers under depth-dependent ramp load[J]. Canadian Geotechnical Journal,1999,49(3):415-421.
[62]Zhuang Y C, Xie K H, Li X B. Nonlinear analysis of consolidation with variable compressibility and permeability[J]. Journal of Zhejiang University SCIENCE,2005,6A(3):181-187.
[63]陈根媛.多层地基的一维固结计算方法与砂井地基计算的改进建议[J].水利水运科学研究,1984(2)：1-13.
[64]陈铁林,陈生水,周成,沈珠江.粘土的流变特性分析[J].岩土工程学报,2001,23(3)：279-283.
[65]陈宗基.固结及次时间效应的单向问题[J].土木工程学报,1958,5(1),1-9.
[66]邓英尔,谢和平,黄润秋,刘慈群.饱和粘土非线性渗流规律与径向固结[J]应用数学和力学,2007,28(11)：1272-1280.
[67]邓英尔,刘慈群.两相流体非线性渗流模型及其应用[J].应用数学和力学,2003,24(10)：1049-1056.
[68]邓岳保,谢康和.互补算法在一维非线性固结求解中的应用[J].岩土力学,2011,32(9)：2656-2662.
[69]鄂建,陈刚,孙爱荣.考虑低速非Darcy渗流的饱和黏性土一维固结分析[J].岩土工程学报,2009,31(7)：1115-1119.
[70]洪振舜.大变形固结计算模型及定解条件的探讨[J].河海大学学报(自然科学版),1988,16(5)：103-111.
[71]洪振舜.吹填土的一维大变形固结计算模型[J].河海大学学报(自然科学版),1987,15(6)：27-36.
[72]黄文熙.土的工程性质[M].北京：水利电力出版社,1983.
[73]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.
[74]蓝柳和,谢康和.成层软粘土地基粘弹性一维固结半解析解[J].土木工程学报,2003,36(4)：105-110.
[75]蓝柳和.成层软粘土地基非线性流变固结性状研究[D].杭州：浙江大学,2002.
[76]李冰河,谢康和,应宏伟,曾国熙.变荷载下软粘土非线性一维固结半解析解[J].岩土工程学报,1999(a),21(3),288-293.
[77]李冰河,谢康和,应宏伟,曾国熙.初始有效应力沿深度变化的非线性一维固结半解析解[J].土木工程学报,1999(b),32(6)：47-52.
[78]李西斌.软土流变固结理论与试验研究[D].杭州：浙江大学,2005.
[79]李作勤.粘土固结变形的时间性[J].岩土工程学报,1992,14(6),60-67。
[80]陆金甫,关治.偏微分方程数值解法[M].北京：清华大学出版社,2004.
[81]刘慈群.有起始比降固结问题的近似解[J].岩土工程学报,1982,4(3)：107-109.
[82]刘忠玉,刘忠广,马崇武.考虑起始水力梯度时饱和黏土的一维固结[J].郑州大学学报(工学版),2006,27(3)：21-24.
[83]刘忠玉,杨荣根.考虑起始水力梯度时双层地基的一维固结[J].合肥工业大学学报(自然科学版),2006,29(5)：568-572.
[84]刘忠玉,孙丽云,乐金朝,马崇武.基于非Darcy渗流的饱和黏土一维固结理论[J].岩石力学与工程学报,2009,28(5)：973-979.
[85]刘忠玉,纠永志,乐金朝,孙丽云.基于非Darcy渗流的饱和黏土一维非线性固结分析[J].岩石力学与工程学报,2010,29(11)：2348-2355.
[86]栾茂田,钱令希.层状饱和土体一维固结分析[J].岩土力学,1992,13(4)：45-56.
[87]门福录.粘土固结与次时间效应单维问题的近似解[J].水利学报,1963,(1)：44-51.
[88]齐添.软土一维非线性固结理论与试验对比研究[D].杭州：浙江大学,2008.
[89]齐添,谢康和,胡安峰,张智卿.萧山黏土非达西渗流性状的试验研究[J].浙江大学学报(工学版),2007,41(6)：1023-1028.
[90]施建勇,杨立昂,赵维炳,刘永新.考虑土体非线性特性的一维固结理论研究[J].河海大学学报(自然科学版),2001,29(1)：1—5.
[91]夏建中,江雯,谢康和.成层非均质地基一维固结方程半解析求解[J].中国公路学报,2006,19(3)：8-11.
[92]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.
[93]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.
[94]谢康和,郑辉,李冰河,刘兴旺.变荷载下成层地基一维非线性固结分析[J].浙江大学学报(工学版),2003(a),37(4)：426-431.
[95]谢康和,郑辉,Leo C J变荷载下饱和软黏土一维大应变固结解析理论[J].水利学报,2003(b), 34(10)：6-13.
[96]谢康和,庄迎春,李西斌.萧山饱和软粘土的渗透性试验研究[J].岩土工程学报,2005,27(5)：591-594.
[97]谢海澜,武强,赵增敏,金晓丽,李娟.考虑非达西流的弱透水层固结计算[J].岩土力学,2007,28(5)：1061-1065.
[98]谢新宇,朱向荣,谢康和,潘秋元.饱和土体一维大变形固结理论新进展[J].岩土工程学报,1997,19(4)：30-37.
[99]谢新宇,张继发,曾国熙.半无限体地基一维非线性大变形固结解析分析方法研究[J].水利学报,2002,33(7)：16-22.
[100]薛定锷.多孔介质中的渗流物理[M].王鸿勋,译.北京：石油工业出版社,1984.
[101]王坤.考虑起始比降的软土地基一维固结理论研究[D].杭州：浙江大学,2011.
[102]赵维炳.广义Voigt模型模拟的饱和土体一维固结理论及其应用[J].岩土工程学报,1989,11(5),78-85。
[103]郑辉.软粘土地基大应变非线性流变固结理论研究[D].杭州：浙江大学,2004.
[2]Barden L, Berry P L. Consolidation of normally consolidated clay[J]. Journal of the Soil M echanics and Foundation Division, ASCE,1965,91 (SM5):15-35.
[3]Barden L. Consolidation of clay with non-linear viscosity[J]. Geotechnique,1965,15(4):321-344.
[4]Cargill K W. Prediction of Consolidation of Very Soft Soil[J]. Journal of Geotechnical Engineering, ASCE,1984,110(6):775-795.
[5]Cherubini C, Vacca G, Giasi C I. Modeling non-Darcian flow in one-dimensional consolidation[J]. Computers and Geotechnics,1988,6(4):247-264.
[6]Chopra M B, Dargush G F. Finite-element analysis of time-dependent large-deformation problems[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1992,16(2):101-130.
[7]Davis E H, Raymond G P. A non-linear theory of consolidation [J]. Geotechnique,1965,15 (2): 161-173.
[8]Desai C S, Saxena S K. Consolidation analysis of layered anisotropic foundations [J]. International Journal for Numerical and Analytical Methods in Geomechanics,1977,1(1):5-23.
[9]Dubin B, Moulin G. Influence of a critical gradient on the consolidation of clays[C]. Consolidation of soils:testing and evaluation (STP 892). West Conshochen(PA):ASTM,1986:354-377.
[10]Duncan J M. Limitation of conventional analysis of consolidation settlement[J]. Journal of the Soil Mechanics and Foundation Division, ASCE,1993,119(9):1333-1359.
[11]Duncan J M, Rajot J P, Perrone V J. Coupled analysis of consolidation and secondary compression[C].Proc. of the 2nd Int. Conf. on Soft Engineering,1, Nanjing, China,1996:3-27.
[12]Elnaggar H A, Krizek R J. Effect of non-Darcian flow on time rate of consolidation [J]. Journal of the Franklin Institute,1973,296(5):323-337.
[13]Garlanger J E. The consolidation of soils exhibiting creep under constant effective stress[J]. Geotechnique,1972,22(1):71-78.
[14]Geng X Y, Xu C J, Cai Y Q. Non-linear consolidation analysis of soil with variable compressibility and permeability under cyclic loadings[J]. International Journal for Numerical and Analytical Methods in eomechanics,2006,30(8):803-821.
[15]Gibson R E, England G L, Hussey M J L. The theory of one-dimensional consolidation of saturated clays:Ⅰ. Finite non-linear consolidation of thin homogeneous layers[J]. Geotechnique,1967,17(3): 261-273.
[16]Gibson R E, Schiffman R L, Cargill K W. The theory of one-dimensional consolidation of saturated clays:Ⅱ. Finite non-linear consolidation of thick homogeneous layers[J]. Canadian Geotechnical Journal,1981,18(2):280-293.
[17]Gray H. Simultaneous consolidation of contiguous layers of unlike compressible soils[J]. Trans. ASCE, 1945,110:1327-1356.
[18]Hansbo S. Consolidation of clay with special reference to influence of vertical drains[C]. Swedish Geotechnical Institute Proceeding. Stockholm:Swedish Geotechnical Institute,1960,18:45-50.
[19]Hansbo S. Aspects of vertical drain design:Darcian or non-Darcian flow[J]. Geotechnique,1997,47(5): 983-992.
[20]Hansbo S. Consolidation equation valid for both Darcian and non-Darcian flow[J]. Geotechnique,2001, 51(1):51-54.
[21]Hansbo S. Deviation from Darcy's law observed in one-dimensional consolidation [J]. Geotechnique, 2003,53(6):601-605.
[22]Huerta A, Rodriguez A. Numerical analysis of nonlinear large-strain consolidation and filling[J]. Computers and structures,1992,44:357-365.
[23]Imai G, Tang Y X. A constitutive equation of one-dimensional consolidation derived from interconnected test[J]. Soil and Foundations,1992,32(2):83-96.
[24]King F H. Principles and conditions of the movement of ground water[R]. U.S.:United States Geological Survey,1898.
[25]Kutilek M. Non-Darcian Flow of Water in Soils—Laminar Region:A Review[J]. Developments in Soil Science,1972,2:327-340.
[26]Lee P K K, Xie K H, Cheung Y K. A study on one-dimensional consolidation of layered systems[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1992,16:815-831.
[27]Lee K, Choa V, Lee S H, Quek S H. Constant rate of strain consolidation of Singapore marine clay Source[J]. Geotechnique,1993,43(3):471-488.
[28]Lekha K R, Krishnaswamy N R, Basak P. Consolidation of clays for variable permeability and compressibility[J] Journal of Geotechnical and Geoenvironmental Engineering, ASCE,2003,129(11): 1001-1009.
[29]Mesri G, Rokhsar A. Theory of consolidation for clays[J]. Journal of the Soil Mechanics and Foundation Division, ASCE,1974, GT8:889-903.
[30]Mesri G, Choiy Y K. Settlement analysis of embankments on soft clays [J]. Journal of the Soil Mechanics and Foundation Division, ASCE,1985,111 (4):441-464.
[31]Mesri G, Tavena S F. Discussion of permeability and consolidation of normally consolidated soils [J]. Journal of the Soil Mechanics and Foundation Division, ASCE,1983,109 (GT6):873-878.
[32]Miller R J, Low P E. Threshold gradient for water flow in clay systems[J]. Soil Science Society of American Journal,1963,27(6):605-609.
[33]Monte J L, Krizek R J. One-dimensional mathematical model for large-strain consolidation [J]. Geotechnique,1976,26(3):495-510.
[34]Morris P H. Analytical Solutions of Linear Finite-Strain One-Dimensional Consolidation[J].Journal of Geotechnical & Geoenvironmental Engineering,2002,128(4):319-325.
[35]Olsen H W. Osmosis:a cause of apparent deviation from Darcy's law[J]. Canadian Geotechnical Journal,1985,22(2):238-241.
[36]Olson R E. Consolidation under time dependent loading[J]. Journal of Geotechnical Engineering, ASCE,1977,103(1):55-60.
[37]Pascal F, Pascal H, Murray D W. Consolidation with threshold gradients[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1981,5(3):247-261.
[38]Poskitt T J. The consolidation of saturated clay with variable permeability and compressibility [J]. Geotechnique,1969,19(2):234-252.
[39]Pyrah I C. One-dimensional consolidation of layered soils[J]. Geotechnique,1996,46(3):555-560.
[40]Schiffman R L. Consolidation of soil under time-dependent loading and varying permeability [J]. Highway Research Board Proceedings,1958,37:584-617.
[41]Schiffman R L, Stein J R. One-dimensional consolidation of layered systems[J]. Journal of Soil Mechanics and Foundations, ASCE,1970,96(4):1499-1504.
[42]Schiffman R L, Gibson R E. Consolidation of nonhomogeneous clay layers [J]. Journal of the Soil Mechanics andFoundations Division, ASCE,1964,90(5):1-30.
[43]Schmidt J D, Westmann R A. Consolidation of porous media with non-Darcy flow[J]. Journal of the Engineering Mechanics Division,1973, EM6:1201-1216.
[44]Skempton A W, Bjerrum L A. Contribution to the settlement analysis of foundations on clay[J]. Geotechique,1957,7(4):168-178.
[45]Slepicka F. Contribution to the solution of the filtration law[C]. International union of Geodesy and Geophysics, Commission of Subterranean Waters. Finland:[s.n.],1960:245-258.
[46]Swartzendruber D. Modification of darcy's law for the flow of water in soils[J]. Soil Science,1962, 93(1):22-29.
[47]Tan T S, Scott R F. Finite strain consolidation—a study of convection[J]. Soils and Foundations,1988, 28(3):64-74.
[48]Tavenas F, Jean P, Leblond P, Leroueil S. The permeability of natural soft clays[J]. Part Ⅰ:methods of laboratory permeability measurements. Canadian Geotechnical Journal,1983(a),20(4):629-644.
[49]Tavenas F, Leblond P, Jean P, Leroueil S. The permeability of natural soft clays. Part Ⅱ:Permeability characteristics[J].Canadian Geotechnical Journal,1983(b),20(4):645-659.
[50]Taylor D W, Merchant W. A theory of clay consolidation accounting for secondary compression [J]. Journal of Mathematics and Physics,1940,19(3):167-185.
[51]Teh C I, Nie X Y. Coupled consolidation theory with non-Darcian flow[J]. Computers and Geotechnics, 2002,29(3):169-209.
[52]Thomas C, Sheahan M. Experimental Verification of CRS Consolidation Theory[J]. Journal of Geotechnical and Geoenvironmental Engineering,1997,123(5):430-437.
[53]Townsend F C, Mc Vay M C. SOA:Large strain consolidation prediction [J]. Journal of Geotechnical Engineering, ASCE,1990,116 (2):222-243.
[54]Weber W G Performance of embankments constructed over peat[J]. Journal of Soil Mechanics and Foundation Division, ASCE,1969,95(1):53-76.
[55]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, China,1996:193-198.
[56]Xie K H, Guo S, Li B H, Zeng G X. A theory of consolidation for soils exhibiting rheological characteristics under cyclic loading[C]. Proceedings of the 9th International Conference on Computer Methods and Advances in Geomechanics 2, Wuhan, China,1997:1053-1058.
[57]Xie K H, Xie X Y, Jiang W. A study on one dimensional nonlinear consolidation of double-layered soil[J]. Computers andGeotechnics,2002,29(2):151-168.
[58]Xie K H, Leo C J. Analytical solutions of one-dimensional large strain consolidation of saturated and homogeneous clays[J]. Computers and Geotechnics,2004,31(4):301-314.
[59]Xie K H, Wang K, Wang Y L, Li C X. Analytical solution for one-dimensional consolidation of clayey soils with a threshold gradient[J]. Computers and Geotechnics,2010,37(4):487-493.
[60]Zhu G F, Yin J H. Consolidation of soil under depth-dependent ramp load[J]. Canadian Geotechnical Journal,1998,35(2):344-350.
[61]Zhu G, Yin J H. Consolidation of double soil layers under depth-dependent ramp load[J]. Canadian Geotechnical Journal,1999,49(3):415-421.
[62]Zhuang Y C, Xie K H, Li X B. Nonlinear analysis of consolidation with variable compressibility and permeability[J]. Journal of Zhejiang University SCIENCE,2005,6A(3):181-187.
[63]陈根媛.多层地基的一维固结计算方法与砂井地基计算的改进建议[J].水利水运科学研究,1984(2)：1-13.
[64]陈铁林,陈生水,周成,沈珠江.粘土的流变特性分析[J].岩土工程学报,2001,23(3)：279-283.
[65]陈宗基.固结及次时间效应的单向问题[J].土木工程学报,1958,5(1),1-9.
[66]邓英尔,谢和平,黄润秋,刘慈群.饱和粘土非线性渗流规律与径向固结[J]应用数学和力学,2007,28(11)：1272-1280.
[67]邓英尔,刘慈群.两相流体非线性渗流模型及其应用[J].应用数学和力学,2003,24(10)：1049-1056.
[68]邓岳保,谢康和.互补算法在一维非线性固结求解中的应用[J].岩土力学,2011,32(9)：2656-2662.
[69]鄂建,陈刚,孙爱荣.考虑低速非Darcy渗流的饱和黏性土一维固结分析[J].岩土工程学报,2009,31(7)：1115-1119.
[70]洪振舜.大变形固结计算模型及定解条件的探讨[J].河海大学学报(自然科学版),1988,16(5)：103-111.
[71]洪振舜.吹填土的一维大变形固结计算模型[J].河海大学学报(自然科学版),1987,15(6)：27-36.
[72]黄文熙.土的工程性质[M].北京：水利电力出版社,1983.
[73]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.
[74]蓝柳和,谢康和.成层软粘土地基粘弹性一维固结半解析解[J].土木工程学报,2003,36(4)：105-110.
[75]蓝柳和.成层软粘土地基非线性流变固结性状研究[D].杭州：浙江大学,2002.
[76]李冰河,谢康和,应宏伟,曾国熙.变荷载下软粘土非线性一维固结半解析解[J].岩土工程学报,1999(a),21(3),288-293.
[77]李冰河,谢康和,应宏伟,曾国熙.初始有效应力沿深度变化的非线性一维固结半解析解[J].土木工程学报,1999(b),32(6)：47-52.
[78]李西斌.软土流变固结理论与试验研究[D].杭州：浙江大学,2005.
[79]李作勤.粘土固结变形的时间性[J].岩土工程学报,1992,14(6),60-67。
[80]陆金甫,关治.偏微分方程数值解法[M].北京：清华大学出版社,2004.
[81]刘慈群.有起始比降固结问题的近似解[J].岩土工程学报,1982,4(3)：107-109.
[82]刘忠玉,刘忠广,马崇武.考虑起始水力梯度时饱和黏土的一维固结[J].郑州大学学报(工学版),2006,27(3)：21-24.
[83]刘忠玉,杨荣根.考虑起始水力梯度时双层地基的一维固结[J].合肥工业大学学报(自然科学版),2006,29(5)：568-572.
[84]刘忠玉,孙丽云,乐金朝,马崇武.基于非Darcy渗流的饱和黏土一维固结理论[J].岩石力学与工程学报,2009,28(5)：973-979.
[85]刘忠玉,纠永志,乐金朝,孙丽云.基于非Darcy渗流的饱和黏土一维非线性固结分析[J].岩石力学与工程学报,2010,29(11)：2348-2355.
[86]栾茂田,钱令希.层状饱和土体一维固结分析[J].岩土力学,1992,13(4)：45-56.
[87]门福录.粘土固结与次时间效应单维问题的近似解[J].水利学报,1963,(1)：44-51.
[88]齐添.软土一维非线性固结理论与试验对比研究[D].杭州：浙江大学,2008.
[89]齐添,谢康和,胡安峰,张智卿.萧山黏土非达西渗流性状的试验研究[J].浙江大学学报(工学版),2007,41(6)：1023-1028.
[90]施建勇,杨立昂,赵维炳,刘永新.考虑土体非线性特性的一维固结理论研究[J].河海大学学报(自然科学版),2001,29(1)：1—5.
[91]夏建中,江雯,谢康和.成层非均质地基一维固结方程半解析求解[J].中国公路学报,2006,19(3)：8-11.
[92]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.
[93]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.
[94]谢康和,郑辉,李冰河,刘兴旺.变荷载下成层地基一维非线性固结分析[J].浙江大学学报(工学版),2003(a),37(4)：426-431.
[95]谢康和,郑辉,Leo C J变荷载下饱和软黏土一维大应变固结解析理论[J].水利学报,2003(b), 34(10)：6-13.
[96]谢康和,庄迎春,李西斌.萧山饱和软粘土的渗透性试验研究[J].岩土工程学报,2005,27(5)：591-594.
[97]谢海澜,武强,赵增敏,金晓丽,李娟.考虑非达西流的弱透水层固结计算[J].岩土力学,2007,28(5)：1061-1065.
[98]谢新宇,朱向荣,谢康和,潘秋元.饱和土体一维大变形固结理论新进展[J].岩土工程学报,1997,19(4)：30-37.
[99]谢新宇,张继发,曾国熙.半无限体地基一维非线性大变形固结解析分析方法研究[J].水利学报,2002,33(7)：16-22.
[100]薛定锷.多孔介质中的渗流物理[M].王鸿勋,译.北京：石油工业出版社,1984.
[101]王坤.考虑起始比降的软土地基一维固结理论研究[D].杭州：浙江大学,2011.
[102]赵维炳.广义Voigt模型模拟的饱和土体一维固结理论及其应用[J].岩土工程学报,1989,11(5),78-85。
[103]郑辉.软粘土地基大应变非线性流变固结理论研究[D].杭州：浙江大学,2004.