电阻网法求解固结问题研究
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摘要
土体固结问题的研究一直是岩土工程研究的热点之一,且取得了许多研究成果。本文在前人工作的基础上引入基于Liebmann原理的电阻网法,同时运用电元件及运算电路方法分别对土体固结问题进行了研究。
基于现有的理论成果,首先运用电阻网法对饱和土均质及层状地基的一维固结问题进行了分析和讨论,编制了相应的考虑初始孔压非均布、外荷载随时间变化的Matlab求解程序,并与已有的解析解进行了对比,验证了本文方法及程序的正确性。同时,讨论了影响电阻网法求解计算结果的因素,并提出了优化程序的量化指标。利用Matlab求解程序分析了某双层地基的一维固结问题,并讨论了某三层地基随土层厚度、压缩模量及渗透系数变化对固结性状的影响。
然后,运用电阻网法及对应的Matlab求解程序对均质地基的二维固结问题进行了分析。由于多维固结问题解析解求解计算的复杂性,本文仅与前人的理论成果进行了对比,进一步论证了本文方法的可行。最后,本文探讨了电元件及相应运算电路在求解固结问题的应用,尝试运用电路模拟固结问题的可行性。
本文首次将电路及相关理论引入土体固结问题的研究之中,使两者的共性得到关联,为研究土体固结性状问题提供了新的思路和方向,进一步发展和完善了固结理论。
Study on the problem of soil consolidation has been always a research hotspot in Geotechnical Engineering, there are many results on the issue so far. In this paper, the electrical components, related operational circuit and the resistance network method which based on Liebmann's principle were introduced to study on the consolidation problem.
The resistance network method was used to study on one-dimensional homogeneous soil and layered foundation consolidation problems in this paper. Computation programs, considering the arbitrary distribution of initial pore pressure and the time-dependent loading condition, were developed by using Matlab programming. The reliability of the programs was verified through the comparisons with available analytical solutions. The factors which can be affected the simulation solutions were also analyzed and the quantitative indicators which use for the optimization procedure were proposed. Secondly, the resistance network method and the related program were applied to analyze the one-dimensional consolidation of double-layered soil problems. The consolidation behavior of a three-layer foundation was studied with the thickness, compression modulus and the permeability coefficient of the soil varying.
Then, the homogeneous two-dimensional consolidation behavior of soil was analyzed by using resistance network method. The reliability of the programs was further confirmed through comparisons with available theoretical solutions as the analytical solutions being complex and inconvenient to apply. Finally, the electrical components and related operational circuit were applied to the consolidation problem.
The circuit and related theory were introduced into the study on the problem of soil consolidation firstly which linked the similarities between the two. It provides a new way to study the consolidation problems of soil. This develops the consolidation theory and makes it more perfect.
基于现有的理论成果,首先运用电阻网法对饱和土均质及层状地基的一维固结问题进行了分析和讨论,编制了相应的考虑初始孔压非均布、外荷载随时间变化的Matlab求解程序,并与已有的解析解进行了对比,验证了本文方法及程序的正确性。同时,讨论了影响电阻网法求解计算结果的因素,并提出了优化程序的量化指标。利用Matlab求解程序分析了某双层地基的一维固结问题,并讨论了某三层地基随土层厚度、压缩模量及渗透系数变化对固结性状的影响。
然后,运用电阻网法及对应的Matlab求解程序对均质地基的二维固结问题进行了分析。由于多维固结问题解析解求解计算的复杂性,本文仅与前人的理论成果进行了对比,进一步论证了本文方法的可行。最后,本文探讨了电元件及相应运算电路在求解固结问题的应用,尝试运用电路模拟固结问题的可行性。
本文首次将电路及相关理论引入土体固结问题的研究之中,使两者的共性得到关联,为研究土体固结性状问题提供了新的思路和方向,进一步发展和完善了固结理论。
Study on the problem of soil consolidation has been always a research hotspot in Geotechnical Engineering, there are many results on the issue so far. In this paper, the electrical components, related operational circuit and the resistance network method which based on Liebmann's principle were introduced to study on the consolidation problem.
The resistance network method was used to study on one-dimensional homogeneous soil and layered foundation consolidation problems in this paper. Computation programs, considering the arbitrary distribution of initial pore pressure and the time-dependent loading condition, were developed by using Matlab programming. The reliability of the programs was verified through the comparisons with available analytical solutions. The factors which can be affected the simulation solutions were also analyzed and the quantitative indicators which use for the optimization procedure were proposed. Secondly, the resistance network method and the related program were applied to analyze the one-dimensional consolidation of double-layered soil problems. The consolidation behavior of a three-layer foundation was studied with the thickness, compression modulus and the permeability coefficient of the soil varying.
Then, the homogeneous two-dimensional consolidation behavior of soil was analyzed by using resistance network method. The reliability of the programs was further confirmed through comparisons with available theoretical solutions as the analytical solutions being complex and inconvenient to apply. Finally, the electrical components and related operational circuit were applied to the consolidation problem.
The circuit and related theory were introduced into the study on the problem of soil consolidation firstly which linked the similarities between the two. It provides a new way to study the consolidation problems of soil. This develops the consolidation theory and makes it more perfect.
引文
Abbott M. B. (1960).One dimensional consolidation of multi-layered soils[J]. Geotechnique,10(4): 151-165.
Aboshi H., Yoshikum. H., Maruyama. S. (1970). Constant loading rate of cosolidation test[J]. Soils and Foundations,10(1):43-56.
Alonso E. E., Krizek. R. J. (1974). Randomness of settlement rate under stochastic load[J]. Journal of Engineering Mechanics Division, ASCE,100(6):1211-1226.
Baligh M. M., Levadoux. J. N. (1978). Consolidation theory of cyclic loading[J]. Journal of Geotechnical Engineering Division, ASCE,104(4):415-431.
Barden L. (1969). Time dependent deformation of normally consolidated clays and peats[J]. Journal of Soil Mechanics and Foundations, ASCE,95(1):1-31.
Barden L. (1965). Consolidation of clay with non-linear viscosity[J]. Geotechnique.15(4):345-362.
Barden L. Berry. P. L. (1965). Consolidation of normally consolidated clay[J]. Journal of Soil Mechanics and Foundations, ASCE,91(5):15-35.
Berry P. L., Wilkinson W. B. (1969). The radial consolidation of clay soils[J]. Geotechnique,19(2): 253-284.
Bjerrum L. (1967). Engineering geology of Norwegian normally consolidated marine clays as related to settlements of buildings[J]. Geotechnique,17(2):83-118.
Biot M. A., Willis D.G. (1957). The elastic coefficient of a theory of consolidation[J].Transactions, Journal of Applied Mechanics, ASME,79:594-601.
Chen J Z, Zhu X R, Xie K H, Pan Q Y, Zeng G X. (1996). One dimensional consolidation of soft clay under trapezoidal cyclic loading[A]. Proceedings of the second International Conference on Soft Soil Engineering[C]. Nanjing:[s.n.],211-216.
Davis E. H., Polus. H. G. (1972). Rate of settlement under two-and-three dimensional conditions. Geotechnique,22(1):95-114.
Favaretti M., Soranzo M. (1995). A simplified consolidation theory in cyclic loading conditions[J]. Proceedings of International Symposium on Compression and Consolidation of Clayey Soils. Janpan, (1):405-409.
Karplus W J. (1955). The use of electronic analogue computers with resistance network analogues[J]. British Journal of Applied Physics,6(10):356-357.
Korthals J P. (1959). Use of an electronic analogue computer with resistance network analogues [J]. British Journal of Applied Physics,10(4):176-180.
Lee P.K., Xie K H., Cheung Y.K. (1992). A study on one dimensional consolidation of layered systems[C]. Int.J.for Numerical and Analytical Methods in Gemechnics,16:15-31.
Leonards G.A., Altschaeffl A.G. (1964). Compressibility of clay[J]. Journal of Soil Mechanics and Foundations, ASCE,90(5):133-155.
Liebmann G. (1955). The solution of plane stress problems by an electrical analogue method[J]. British Journal of Applied Physics,6(5):145-157.
Liebmann G. (1955). The solution of transient heat flow and heat transfer problems by relaxation[J]. British Journal of Applied Physics,6(4):129-135.
Liebmann G. (1950). Solution of partial differential equations with a resistance network analogue[J]. British Journal of Applied Physics,1(4):92-103.
Liebmann G. (1954). Resistance network analogue with unequal meshes or subdivided meshes[J]. British Journal of Applied Physics,5:362-366.
Liebmann G. (1954). An improved experimental iteration method for use with resistance-network analogues[J]. British Journal of Applied Physics,5:32-35.
Mesri G. (1973). Coefficient of Secondary compression[J]. Journal of Geotechnical Engineering, ASCE, 99(1):123-137.
Mesri G. Rokhsar A. (1974). Theory of consolidation for clays[J].Journal of Geotechnical Engineering, ASCE,100(8):889-904.
Mesri G. Godlewski P.M. (1977). Time and stress compressibility interrelationship[J]. Journal of Geotechnical Engineering, ASCE,103(5):417-430.
Mesri G. Choi Y.K. (1985a). Settlement analysis of embankments on soft clays[J]. Journal of Geotechnical Engineering, ASCE,111(4):441-464.
Chen M.F., Lin Y.T. (2002). Static behavior and dynamic stability analysis of grooved rectangular aerostatic thrust bearings by modified resistance network method[J]. Tribology International,35(5): 329-338.
Olson R. E. (1977). Consolidation under time-dependent loading[J]. Journal of Geotechnical Engineering Divison, ASCE,103(1):55-60.
Robin Herbert. (1968). Time variant ground water flow by resistance network analogues[J].Journal of Hydrology,6(3):237-264
Schiffman R.L. (1958). Consolidation of soil under time-dependent loading and varying permeability[J]. Highway Research Board Proceedings,37:584-617.
Wilson N. E., Elgohary M M. (1974). Consolidation of soils under cyclic loading[J]. Canadian Geotechnical Journal,11(3):420-423
蔡袁强,徐长节(2001).任意荷载下成层粘弹性地基的一维固结[J].应用数学和力学.22(3)：307-313.
陈仁朋,周万欢,王宏志等(2005).用DQM求解成层地基一维非线性固结问题[J].计算力学学报.22(3)：330-315.
陈宗基(1985a).固结及次时间效应的单向问题[J].土木工程学报.5(1)：1-9.
陈宗基(1985b).粘土层沉陷(由于固结和次时间效应)[J].力学学报.2(1)：1-9.
陈根媛(1984).多层地基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,2：1-13.
B.A.弗洛林著,北京水利科学研究院译(1958).土体压密理论[M].北京：水利电力出版社.
龚晓南编著(1998).高等土力学[M].杭州：浙江大学出版社.
龚晓南(2000).土工计算机分析[M].北京：中国建筑工业出版社.
顾尧章,金波(1992).轴对称荷载下多层地基的Biot固结及其变形[J].工程力学,9(3)：81-94.
关山海,谢康和,胡安峰(2003).低频循环荷载下地基一维固结性状分析[J].岩土力学,24(5)：849-853.
胡亚元,王立忠(1998).多层地基二维Biot固结的理论解答[J].岩土工程学报,20(5)：17-21.
黄传志(1991).多维太沙基固结微分方程求解[J].岩土工程学报,13(1)：34-47.
黄文熙(1983).土的工程性质[M].北京：水利电力出版社.
江雯(2003).考虑软粘土渗透性和压缩性变化的一维固结理论研究[D].杭州：浙江大学硕士学位论文.
蓝柳和,谢康和(2003).半解析法在成层软粘土地基固结问题中的应用[J].岩石力学与工程学报,22(2)：327-331.
李冰河,王奎华,谢康和等(2002).软粘土非线性一维固结有限差分法分析[J].浙江大学学报(工学版),34(4)：376-381.
李西斌,谢康和(2005).循环荷载下半透水边界土层一维固结解析解[J].岩土力学,26(1)：155-159.
李志星,张季如(2007).饱和软粘土在循环荷载下的孔压数值分析[J].土工基础,21(2)：51-54.
李作勤(1992).粘土一维固结变形特性[J].岩土力学,13(2,3)：24-36.
刘连寿,王正清编著(1990).数学物理方法[M].北京：高等教育出版社.
栾茂田,钱令希(1992).层状饱和土体一维固结分析[J].岩土力学,13(4)：45-56.
罗嗣海(1997).层状地基的固结计算与固结特性[J].地球科学,22(2)：205-209.
潘晓东,蔡袁强,徐长节.张云峰(2006).循环荷载下粘弹性饱和土层的一维固结[J].岩土力学,27(2)：272-276.
齐添(2008).软土一维非线性固结理论与实验对比研究[D].杭州：浙江大学博士学位论文.
钱家欢,殷宗泽(1996).土工原理与计算(第二版)[M].北京：中国水利水电出版社.
秦曾煌主编(2004).电工学(第6版).北京：高等教育出版社.
马文淦(2009).计算物理学[M].北京：科学出版社.
毛昶熙(1981).电模拟试验与渗流研究[M].北京：水利出版社.
毛昶熙,陈平,李祖贻等(1991).裂隙岩体渗流计算方法研究[J].岩土工程学报,13(6)：38-42.
毛昶熙,段祥宝,李定方(1994).网络模型程序化及其应用[J].水利水运科学研究,3：197-208.
门福录(1963).粘土固结与次固结效应单维固结问题的近似解[J].水利学报,1：44-54.
李志星,张季如(2007).饱和软粘土在循环荷载下的孔压数值分析[J].土工基础,21(2)：51-54
沈珠江(2000).理论土力学[M].北京：中国水利水电出版社.
孙丽云,刘忠玉,乐金朝(2010).考虑非Darcy渗流时循环荷载下饱和粘土一维固结分析[J].岩土力学,31(增刊1)：62-67.
童幺华(2009).一维有限变形固结控制方程的解析解探讨[D].长沙：湖南大学硕士学位论文.
王宏志,陈仁朋,周万欢等(2004).双层地基一维非线性固结的DQM解[J].水利学报,4：8-14.
王立忠,陈云敏(1996).饱和弹性半空间在低频谐和集中力下的积分形式解[J].水利学报,2：84-88.
王志亮(2004).无网格法在静载下土体二维固结问题中的应用[J].岩土工程学报,26(1):152-154.
魏汝龙(1987).软粘土的强度和变形[M].北京：中国建筑工业出版社.
问延煦、施建勇(2003)Terzaghi一维固结理论研究综述[J].西部探矿工程,15(2)：1-4.
吴世明,陈龙珠,杨丹(1988).周期荷载作用下饱和粘土的一维固结[J].浙江大学学报,22(5)：60-70.
谢康和(1994).双层地基一维固结理论及应用[J].岩土工程学报,16(5)：24-35.
谢康和,潘秋元(1995).变荷载下任意层地基一维固结理论[J].岩土工程学报,17(5)：80-85.
谢康和,郑辉,李冰河等(1995).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),37(4)：426-431.
谢康和,周健(2002).岩土工程有限元分析理论与应用[M].北京：科学出版社.
谢康和,周瑾,董亚钦(2006).循环荷载作用下地基一维非线性固结问题解析解[J].岩石力学与工程学报.25(1)：21-26
谢松高(1991).层状土地下水非稳定流水平排水电阻网络模拟[J].水利学报,9：1-6.
徐瑞,黄兆东,阎凤玉(2008)Matlab2007科学计算与工程分析[M].北京：科学出版社.
徐栓海,薛伟(1998).矿区疏干地下水三维流与二维流对比研究[J].煤田地址与勘探,26(3)：38-42.
阎澍旺(1984).二维及三维太沙基方程的解法[J].岩土工程学报,6(3)：86-94.
杨丹,吴世明(1992).循环荷载下饱和粘土的一维粘弹塑性解答[J].水利学报,5：52-58.
杨峻,蔡袁强,吴世明(1996).循环荷载作用下双层地基的一维固结[J].浙江大学学报(自然科学版),30(3)：319-326.
叶挺秀,张伯尧(2008).电工电子学[M].北京：高等教育出版社.
袁坚敏,谢康和(2005).双层地基一维非线性固结性状分析[J].科技通报,21(4)：471-475.
赵维炳(1989).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,11(5)：78-85.
折学森(1996).二维太沙基固结微分方程求解[J].西安公路交通大学学报,16(1)：8-12.
朱百里,沈珠江(1990).计算土力学[M].上海：科学技术出版社.
朱承高等编(2004).电工学概论[M].北京：高等教育出版社.
庄迎春,胡安峰,谢康和(2005).循环荷载作用下软土的一维固结分析[J].土木工程学报,38(9)：109-114.
Aboshi H., Yoshikum. H., Maruyama. S. (1970). Constant loading rate of cosolidation test[J]. Soils and Foundations,10(1):43-56.
Alonso E. E., Krizek. R. J. (1974). Randomness of settlement rate under stochastic load[J]. Journal of Engineering Mechanics Division, ASCE,100(6):1211-1226.
Baligh M. M., Levadoux. J. N. (1978). Consolidation theory of cyclic loading[J]. Journal of Geotechnical Engineering Division, ASCE,104(4):415-431.
Barden L. (1969). Time dependent deformation of normally consolidated clays and peats[J]. Journal of Soil Mechanics and Foundations, ASCE,95(1):1-31.
Barden L. (1965). Consolidation of clay with non-linear viscosity[J]. Geotechnique.15(4):345-362.
Barden L. Berry. P. L. (1965). Consolidation of normally consolidated clay[J]. Journal of Soil Mechanics and Foundations, ASCE,91(5):15-35.
Berry P. L., Wilkinson W. B. (1969). The radial consolidation of clay soils[J]. Geotechnique,19(2): 253-284.
Bjerrum L. (1967). Engineering geology of Norwegian normally consolidated marine clays as related to settlements of buildings[J]. Geotechnique,17(2):83-118.
Biot M. A., Willis D.G. (1957). The elastic coefficient of a theory of consolidation[J].Transactions, Journal of Applied Mechanics, ASME,79:594-601.
Chen J Z, Zhu X R, Xie K H, Pan Q Y, Zeng G X. (1996). One dimensional consolidation of soft clay under trapezoidal cyclic loading[A]. Proceedings of the second International Conference on Soft Soil Engineering[C]. Nanjing:[s.n.],211-216.
Davis E. H., Polus. H. G. (1972). Rate of settlement under two-and-three dimensional conditions. Geotechnique,22(1):95-114.
Favaretti M., Soranzo M. (1995). A simplified consolidation theory in cyclic loading conditions[J]. Proceedings of International Symposium on Compression and Consolidation of Clayey Soils. Janpan, (1):405-409.
Karplus W J. (1955). The use of electronic analogue computers with resistance network analogues[J]. British Journal of Applied Physics,6(10):356-357.
Korthals J P. (1959). Use of an electronic analogue computer with resistance network analogues [J]. British Journal of Applied Physics,10(4):176-180.
Lee P.K., Xie K H., Cheung Y.K. (1992). A study on one dimensional consolidation of layered systems[C]. Int.J.for Numerical and Analytical Methods in Gemechnics,16:15-31.
Leonards G.A., Altschaeffl A.G. (1964). Compressibility of clay[J]. Journal of Soil Mechanics and Foundations, ASCE,90(5):133-155.
Liebmann G. (1955). The solution of plane stress problems by an electrical analogue method[J]. British Journal of Applied Physics,6(5):145-157.
Liebmann G. (1955). The solution of transient heat flow and heat transfer problems by relaxation[J]. British Journal of Applied Physics,6(4):129-135.
Liebmann G. (1950). Solution of partial differential equations with a resistance network analogue[J]. British Journal of Applied Physics,1(4):92-103.
Liebmann G. (1954). Resistance network analogue with unequal meshes or subdivided meshes[J]. British Journal of Applied Physics,5:362-366.
Liebmann G. (1954). An improved experimental iteration method for use with resistance-network analogues[J]. British Journal of Applied Physics,5:32-35.
Mesri G. (1973). Coefficient of Secondary compression[J]. Journal of Geotechnical Engineering, ASCE, 99(1):123-137.
Mesri G. Rokhsar A. (1974). Theory of consolidation for clays[J].Journal of Geotechnical Engineering, ASCE,100(8):889-904.
Mesri G. Godlewski P.M. (1977). Time and stress compressibility interrelationship[J]. Journal of Geotechnical Engineering, ASCE,103(5):417-430.
Mesri G. Choi Y.K. (1985a). Settlement analysis of embankments on soft clays[J]. Journal of Geotechnical Engineering, ASCE,111(4):441-464.
Chen M.F., Lin Y.T. (2002). Static behavior and dynamic stability analysis of grooved rectangular aerostatic thrust bearings by modified resistance network method[J]. Tribology International,35(5): 329-338.
Olson R. E. (1977). Consolidation under time-dependent loading[J]. Journal of Geotechnical Engineering Divison, ASCE,103(1):55-60.
Robin Herbert. (1968). Time variant ground water flow by resistance network analogues[J].Journal of Hydrology,6(3):237-264
Schiffman R.L. (1958). Consolidation of soil under time-dependent loading and varying permeability[J]. Highway Research Board Proceedings,37:584-617.
Wilson N. E., Elgohary M M. (1974). Consolidation of soils under cyclic loading[J]. Canadian Geotechnical Journal,11(3):420-423
蔡袁强,徐长节(2001).任意荷载下成层粘弹性地基的一维固结[J].应用数学和力学.22(3)：307-313.
陈仁朋,周万欢,王宏志等(2005).用DQM求解成层地基一维非线性固结问题[J].计算力学学报.22(3)：330-315.
陈宗基(1985a).固结及次时间效应的单向问题[J].土木工程学报.5(1)：1-9.
陈宗基(1985b).粘土层沉陷(由于固结和次时间效应)[J].力学学报.2(1)：1-9.
陈根媛(1984).多层地基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,2：1-13.
B.A.弗洛林著,北京水利科学研究院译(1958).土体压密理论[M].北京：水利电力出版社.
龚晓南编著(1998).高等土力学[M].杭州：浙江大学出版社.
龚晓南(2000).土工计算机分析[M].北京：中国建筑工业出版社.
顾尧章,金波(1992).轴对称荷载下多层地基的Biot固结及其变形[J].工程力学,9(3)：81-94.
关山海,谢康和,胡安峰(2003).低频循环荷载下地基一维固结性状分析[J].岩土力学,24(5)：849-853.
胡亚元,王立忠(1998).多层地基二维Biot固结的理论解答[J].岩土工程学报,20(5)：17-21.
黄传志(1991).多维太沙基固结微分方程求解[J].岩土工程学报,13(1)：34-47.
黄文熙(1983).土的工程性质[M].北京：水利电力出版社.
江雯(2003).考虑软粘土渗透性和压缩性变化的一维固结理论研究[D].杭州：浙江大学硕士学位论文.
蓝柳和,谢康和(2003).半解析法在成层软粘土地基固结问题中的应用[J].岩石力学与工程学报,22(2)：327-331.
李冰河,王奎华,谢康和等(2002).软粘土非线性一维固结有限差分法分析[J].浙江大学学报(工学版),34(4)：376-381.
李西斌,谢康和(2005).循环荷载下半透水边界土层一维固结解析解[J].岩土力学,26(1)：155-159.
李志星,张季如(2007).饱和软粘土在循环荷载下的孔压数值分析[J].土工基础,21(2)：51-54.
李作勤(1992).粘土一维固结变形特性[J].岩土力学,13(2,3)：24-36.
刘连寿,王正清编著(1990).数学物理方法[M].北京：高等教育出版社.
栾茂田,钱令希(1992).层状饱和土体一维固结分析[J].岩土力学,13(4)：45-56.
罗嗣海(1997).层状地基的固结计算与固结特性[J].地球科学,22(2)：205-209.
潘晓东,蔡袁强,徐长节.张云峰(2006).循环荷载下粘弹性饱和土层的一维固结[J].岩土力学,27(2)：272-276.
齐添(2008).软土一维非线性固结理论与实验对比研究[D].杭州：浙江大学博士学位论文.
钱家欢,殷宗泽(1996).土工原理与计算(第二版)[M].北京：中国水利水电出版社.
秦曾煌主编(2004).电工学(第6版).北京：高等教育出版社.
马文淦(2009).计算物理学[M].北京：科学出版社.
毛昶熙(1981).电模拟试验与渗流研究[M].北京：水利出版社.
毛昶熙,陈平,李祖贻等(1991).裂隙岩体渗流计算方法研究[J].岩土工程学报,13(6)：38-42.
毛昶熙,段祥宝,李定方(1994).网络模型程序化及其应用[J].水利水运科学研究,3：197-208.
门福录(1963).粘土固结与次固结效应单维固结问题的近似解[J].水利学报,1：44-54.
李志星,张季如(2007).饱和软粘土在循环荷载下的孔压数值分析[J].土工基础,21(2)：51-54
沈珠江(2000).理论土力学[M].北京：中国水利水电出版社.
孙丽云,刘忠玉,乐金朝(2010).考虑非Darcy渗流时循环荷载下饱和粘土一维固结分析[J].岩土力学,31(增刊1)：62-67.
童幺华(2009).一维有限变形固结控制方程的解析解探讨[D].长沙：湖南大学硕士学位论文.
王宏志,陈仁朋,周万欢等(2004).双层地基一维非线性固结的DQM解[J].水利学报,4：8-14.
王立忠,陈云敏(1996).饱和弹性半空间在低频谐和集中力下的积分形式解[J].水利学报,2：84-88.
王志亮(2004).无网格法在静载下土体二维固结问题中的应用[J].岩土工程学报,26(1):152-154.
魏汝龙(1987).软粘土的强度和变形[M].北京：中国建筑工业出版社.
问延煦、施建勇(2003)Terzaghi一维固结理论研究综述[J].西部探矿工程,15(2)：1-4.
吴世明,陈龙珠,杨丹(1988).周期荷载作用下饱和粘土的一维固结[J].浙江大学学报,22(5)：60-70.
谢康和(1994).双层地基一维固结理论及应用[J].岩土工程学报,16(5)：24-35.
谢康和,潘秋元(1995).变荷载下任意层地基一维固结理论[J].岩土工程学报,17(5)：80-85.
谢康和,郑辉,李冰河等(1995).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),37(4)：426-431.
谢康和,周健(2002).岩土工程有限元分析理论与应用[M].北京：科学出版社.
谢康和,周瑾,董亚钦(2006).循环荷载作用下地基一维非线性固结问题解析解[J].岩石力学与工程学报.25(1)：21-26
谢松高(1991).层状土地下水非稳定流水平排水电阻网络模拟[J].水利学报,9：1-6.
徐瑞,黄兆东,阎凤玉(2008)Matlab2007科学计算与工程分析[M].北京：科学出版社.
徐栓海,薛伟(1998).矿区疏干地下水三维流与二维流对比研究[J].煤田地址与勘探,26(3)：38-42.
阎澍旺(1984).二维及三维太沙基方程的解法[J].岩土工程学报,6(3)：86-94.
杨丹,吴世明(1992).循环荷载下饱和粘土的一维粘弹塑性解答[J].水利学报,5：52-58.
杨峻,蔡袁强,吴世明(1996).循环荷载作用下双层地基的一维固结[J].浙江大学学报(自然科学版),30(3)：319-326.
叶挺秀,张伯尧(2008).电工电子学[M].北京：高等教育出版社.
袁坚敏,谢康和(2005).双层地基一维非线性固结性状分析[J].科技通报,21(4)：471-475.
赵维炳(1989).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,11(5)：78-85.
折学森(1996).二维太沙基固结微分方程求解[J].西安公路交通大学学报,16(1)：8-12.
朱百里,沈珠江(1990).计算土力学[M].上海：科学技术出版社.
朱承高等编(2004).电工学概论[M].北京：高等教育出版社.
庄迎春,胡安峰,谢康和(2005).循环荷载作用下软土的一维固结分析[J].土木工程学报,38(9)：109-114.