循环荷载下软粘土一维非线性固结理论研究
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摘要
非线性是软粘土重要特性之一，而循环荷载是实际工程常见的一种荷载形式，但现有关于循环荷载作用下软粘土的非线性固结理论研究却很少。本文对低频循环荷载作用下考虑软粘土渗透性和压缩性随时间变化的单层地基一维非线性固结理论作了较深入的研究。
首先，基于Davis等(1965)提出的固结过程中土体渗透性和压缩性同步减小的假定，获得了常见循环荷载(如梯形、三角形、矩形等)下单层地基的一维非线性固结问题的解析解。
其次，对于所得的循环荷载下的非线性固结解，分别采用将其特例情况下的解与目前已有的解析解进行对比以及与相应的数值解进行对比的方法作了验证。
最后，根据所得解通过编程计算，分析了循环荷载作用下单层地基的一维非线性固结特性、影响因素以及平均固结度、有效应力和超静孔压的发展规律。
本文所给出的考虑土体压缩性和渗透性变化的低频梯形荷载下软粘土一维非线性固结解析解，是目前关于土体小应变非线性固结问题最完整的理论解。现有一维非线性固结解均为该解析解的特例，而且只要将加载参数适当变化，该解即可分别转化为三角形、矩形等循环荷载形式下的一维非线性固结解析解。
Although nonlinear characteristic is one of the important properties of soft clay and cyclic loading is one of the loading types common in practical engineering, there seems no study made on nonlinear theory for one-dimensional consolidation of soft clay under cyclic loading. In this thesis, based on the previous work available, a careful study was made on one-dimensional consolidation theory of soft clay under low-frequency cyclic loading with permeability and compressibility varying with time.
Firstly, analytical solutions were developed for one-dimensional nonlinear consolidation of soil under some common types of cyclic loading such as trapezoidal cyclic loading, triangular cyclic loading and rectangular cyclic loading, based on the assumption proposed by Davis et al. (1965) that the decrease in permeability is proportional to the decrease in compressibility during the consolidation process of soil.
Secondly, the obtained nonlinear analytical solutions were verilied through comparing them with the known analytical solution corresponding to special cases and with semi-analytical solution respectively.
Finally, computer program was developed corresponding to the solutions obtained, and the nonlinear consolidation behavior of soft clay under cyclic loading, the influence of some parameters, and the law of development of the average degree of consolidation, the effective stress and the excess pore water pressure were investigated.
It has been shown that the analytical solution presented herein for one-dimensional nonlinear consolidation of soil under trapezoidal cyclic loading considering the variation of permeability and compressibility of soil with time is the most perfect solution so far available for small-strain and nonlinear consolidation of soil, and all the known solutions for nonlinear consolidation of soil are the special cases of this solution. By altering the related parameters, this solution can also be deduced into the ones corresponding to simpler cyclic loading such as triangular loading, rectangular loading, etc.
首先，基于Davis等(1965)提出的固结过程中土体渗透性和压缩性同步减小的假定，获得了常见循环荷载(如梯形、三角形、矩形等)下单层地基的一维非线性固结问题的解析解。
其次，对于所得的循环荷载下的非线性固结解，分别采用将其特例情况下的解与目前已有的解析解进行对比以及与相应的数值解进行对比的方法作了验证。
最后，根据所得解通过编程计算，分析了循环荷载作用下单层地基的一维非线性固结特性、影响因素以及平均固结度、有效应力和超静孔压的发展规律。
本文所给出的考虑土体压缩性和渗透性变化的低频梯形荷载下软粘土一维非线性固结解析解，是目前关于土体小应变非线性固结问题最完整的理论解。现有一维非线性固结解均为该解析解的特例，而且只要将加载参数适当变化，该解即可分别转化为三角形、矩形等循环荷载形式下的一维非线性固结解析解。
Although nonlinear characteristic is one of the important properties of soft clay and cyclic loading is one of the loading types common in practical engineering, there seems no study made on nonlinear theory for one-dimensional consolidation of soft clay under cyclic loading. In this thesis, based on the previous work available, a careful study was made on one-dimensional consolidation theory of soft clay under low-frequency cyclic loading with permeability and compressibility varying with time.
Firstly, analytical solutions were developed for one-dimensional nonlinear consolidation of soil under some common types of cyclic loading such as trapezoidal cyclic loading, triangular cyclic loading and rectangular cyclic loading, based on the assumption proposed by Davis et al. (1965) that the decrease in permeability is proportional to the decrease in compressibility during the consolidation process of soil.
Secondly, the obtained nonlinear analytical solutions were verilied through comparing them with the known analytical solution corresponding to special cases and with semi-analytical solution respectively.
Finally, computer program was developed corresponding to the solutions obtained, and the nonlinear consolidation behavior of soft clay under cyclic loading, the influence of some parameters, and the law of development of the average degree of consolidation, the effective stress and the excess pore water pressure were investigated.
It has been shown that the analytical solution presented herein for one-dimensional nonlinear consolidation of soil under trapezoidal cyclic loading considering the variation of permeability and compressibility of soil with time is the most perfect solution so far available for small-strain and nonlinear consolidation of soil, and all the known solutions for nonlinear consolidation of soil are the special cases of this solution. By altering the related parameters, this solution can also be deduced into the ones corresponding to simpler cyclic loading such as triangular loading, rectangular loading, etc.
引文
[1] 黄文熙(1983)．土的工程性质．北京：水利电力出版社．
[2] Schiffman R L, Stein J R (1970). One-dimensional Consolidation of Layered System. Journal of the Soil Mechanics and Foundation Division ASCE, 96(SM4): 1499～1504.
[3] 栾茂田，钱令希(1992)．层状饱和土体一维固结分析．岩土力学，13(4)：45～56
[4] 谢康和(1994)．双层地基一维固结理论及其应用．岩土工程学报，16(5)：26～38．
[5] 谢康和，潘秋元(1995)．变荷载下任意层地基一维固结理论．岩土工程学报，17(5)：80～85．
[6] Lee P K K, Xie K H, Cheung Y K (1992). A Study on One Dimensional Consolidation of Layered Systems. International Journal of Numerical and Analytical Methods in Geomechanics, 16: 815～831.
[7] Xie K H, Xie X Y, Gao X (1999). Theory of one-dimensional consolidation of two-layered soil with partially drained boundaries. Computers and Geotechnics, 24: 265～278.
[8] 陈剑洲，朱向荣，谢康和，潘秋元，曾国熙(1996)．One Dimensional Consolidation of Soft Clay Under Trapezoidal Cyclic Loading. Second International Conference on Soft Soil Engineering: 211-216.
[9] 蔡袁强，徐长节，袁海明(2001)．任意荷载下成层粘弹性地基的一维固结．应用数学和力学，Vol．22，No．3：307-313．
[10] 蔡袁强，徐长节，丁狄刚(1998)．循环荷载下成层饱水地基的一维固结．振动工程学报，Vol．11，No．2：194-193．
[11] 谢康和, S. Guo, 李冰和, 曾国熙(1997). A Theory of Consolidation for Soil Exhibiting Rheological Characteristics under Cyclic Loading. Computer Methods and Advances in Geomechanics: 1053-1058.
[12] 杨丹，吴世明，陈龙珠(1992)．循环荷载下饱和粘土的一维粘弹塑性解答．水利学报，No．5：52-58．
[13] 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．岩土力学，24(5)，849-853．
[14] 周建(2000)．循环荷载作用下饱和软粘土的孔压模型．工程勘察，No．4：7-9．
[15] 周建，龚晓南，李剑强(2000)，循环荷载作用下饱和软粘土特性试验研究．工业建筑，Vol．30，No．11：43-47．
[16] 周建，龚晓南(2000)．循环荷载作用下饱和软粘土应变软化研究．土木工程学报，Vol．33，No．5：75-78．
[17] 许才军，周洪波(1998)．不排水循环荷载作用下饱和软粘土的孔压增长模型．勘察科学技术，No．3：3-7．
[18] 许才军，周洪波(1997)．上海地区循环不排水作用下饱和软粘土孔隙水压力模型的
建立．岩土工程师，Vol．9，No．4：7-11．
[19] 赵小林(1989)．循环荷载及循环等应变幅作用下砂土孔隙水压力的变化规律．工程勘察，No．3：11-14．
[20] 候永峰，张航，周建，龚晓南(2001)．循环荷载作用下复合地基沉降分析．工业建筑，Vol．31，No．6：40-42．
[21] 候永峰，张航，周建，龚晓南(2001)．循环荷载作用下水泥复合土变形性状试验研究．岩土工程学报，Vol．23，No．3：288-291．
[22] H.B. Seed, C.K. Chan (1961). Effect of Duration of Stress Application on Soil Deformation under Repeated Loading, Proceeding, 5th International Congress on Soil Mechanics and Foundations: 341-345.
[23] 蒋军(2000)．循环荷载作用下粘土及含砂芯复合试件性状试验研究．浙江大学博士学位论文．
[24] 章克凌，陶振宇(1994)．饱和粘土在循环荷载作用下的孔压预测．岩土力学，Vol．15，No．3：9-17．
[25] Duncan J M (1993). Limitations of conventional analysis of consolidation settlement. Journal of Geoteclmical Engineering ASCE, 119(9): 1333～1359.
[26] Davis E H, Raymond G P (1965). A non-linear theory of consolidation. Geotechnique, 15(2): 161～173.
[27] Xie, K.H. & C.J. Leo (1999). An Investigation into the Nonlinear Consolidation of Layered Soft Soils. Research Report CE11, School of Civil Engineering and Environment, UWS, Nepean, Australia.
[28] 李冰河，谢康和，应宏伟，曾国熙(1999)．初始有效应力沿深度变化的非线性一维固结半解析解．土木工程学报，32(6)：47～52．
[29] 李冰河，谢康和，应宏伟，曾国熙(1999)．变荷载下软粘土非线性一维固结半解析解．岩土工程学报，21(3)：288～293．
[30] 李冰河，谢永利，谢康和，曾国熙(1999)．软粘土非线性一维固结半解析解．西安公路交通大学学报，19(1)：24～29．
[31] Xie K H, Li B H, Li Q L (1996). A nonlinear theory of consolidation under time-dependent loading. In: Proceedings of 2nd International Conference on Soft Soil Engineering. Nanjing, 27-30, 193～196.
[32] 李冰河(1999)．成层饱和软粘土地基大应变固结理论研究【博士学位论文】．浙江大学．
[33] Mesri G, Rokhsar A (1974). Consolidation of normally consolidated clay[J], J of SMFD, ASCE, GT8: 889-903.
[34] Mesri G, Choi Y K (1985). Settlement analysis of embank -ments on soft clays[J], J. of Geotechnical Engi-neering, ASCE, 111,441-464.
[35] Mesri G.,Tavenas F (1983). Discussion of Permeability and consolidation of normally consolidated soils" by Y H Huang and V P Drenevich [J], Journal of the Geotechnical Engineering Div., ASCE,109(GT6): 873-878.
[36] Tavenas F.,Jean P.,Leblond R, et al (1983). The perme-ability of natural soft clays,Part Ⅱ Permeability Characteristics[J], Canadian Geotechnical Journal, 20(4): 645-660.
[37] Xie K.H., Xie X.Y., Jiang W (2002). A study on one dimensional nonlinear consolidation of double- layered soil[J]. Computers and Geotechnics, 29(2): 151-168.
[38] 谢康和，郑辉，李冰河，刘兴旺(2003)．变荷载下成层地基一维非线性固结分析，浙江大学学报(工学报)，37(4)，426-431．
[39] Xie K. H., Leo C. J (1999). A study on one dimensional nonlinear consolidation of soft soils. Research report[R], UWS, Nepean,Australia, School of Civic Engineering and Environment.
[2] Schiffman R L, Stein J R (1970). One-dimensional Consolidation of Layered System. Journal of the Soil Mechanics and Foundation Division ASCE, 96(SM4): 1499～1504.
[3] 栾茂田，钱令希(1992)．层状饱和土体一维固结分析．岩土力学，13(4)：45～56
[4] 谢康和(1994)．双层地基一维固结理论及其应用．岩土工程学报，16(5)：26～38．
[5] 谢康和，潘秋元(1995)．变荷载下任意层地基一维固结理论．岩土工程学报，17(5)：80～85．
[6] Lee P K K, Xie K H, Cheung Y K (1992). A Study on One Dimensional Consolidation of Layered Systems. International Journal of Numerical and Analytical Methods in Geomechanics, 16: 815～831.
[7] Xie K H, Xie X Y, Gao X (1999). Theory of one-dimensional consolidation of two-layered soil with partially drained boundaries. Computers and Geotechnics, 24: 265～278.
[8] 陈剑洲，朱向荣，谢康和，潘秋元，曾国熙(1996)．One Dimensional Consolidation of Soft Clay Under Trapezoidal Cyclic Loading. Second International Conference on Soft Soil Engineering: 211-216.
[9] 蔡袁强，徐长节，袁海明(2001)．任意荷载下成层粘弹性地基的一维固结．应用数学和力学，Vol．22，No．3：307-313．
[10] 蔡袁强，徐长节，丁狄刚(1998)．循环荷载下成层饱水地基的一维固结．振动工程学报，Vol．11，No．2：194-193．
[11] 谢康和, S. Guo, 李冰和, 曾国熙(1997). A Theory of Consolidation for Soil Exhibiting Rheological Characteristics under Cyclic Loading. Computer Methods and Advances in Geomechanics: 1053-1058.
[12] 杨丹，吴世明，陈龙珠(1992)．循环荷载下饱和粘土的一维粘弹塑性解答．水利学报，No．5：52-58．
[13] 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．岩土力学，24(5)，849-853．
[14] 周建(2000)．循环荷载作用下饱和软粘土的孔压模型．工程勘察，No．4：7-9．
[15] 周建，龚晓南，李剑强(2000)，循环荷载作用下饱和软粘土特性试验研究．工业建筑，Vol．30，No．11：43-47．
[16] 周建，龚晓南(2000)．循环荷载作用下饱和软粘土应变软化研究．土木工程学报，Vol．33，No．5：75-78．
[17] 许才军，周洪波(1998)．不排水循环荷载作用下饱和软粘土的孔压增长模型．勘察科学技术，No．3：3-7．
[18] 许才军，周洪波(1997)．上海地区循环不排水作用下饱和软粘土孔隙水压力模型的
建立．岩土工程师，Vol．9，No．4：7-11．
[19] 赵小林(1989)．循环荷载及循环等应变幅作用下砂土孔隙水压力的变化规律．工程勘察，No．3：11-14．
[20] 候永峰，张航，周建，龚晓南(2001)．循环荷载作用下复合地基沉降分析．工业建筑，Vol．31，No．6：40-42．
[21] 候永峰，张航，周建，龚晓南(2001)．循环荷载作用下水泥复合土变形性状试验研究．岩土工程学报，Vol．23，No．3：288-291．
[22] H.B. Seed, C.K. Chan (1961). Effect of Duration of Stress Application on Soil Deformation under Repeated Loading, Proceeding, 5th International Congress on Soil Mechanics and Foundations: 341-345.
[23] 蒋军(2000)．循环荷载作用下粘土及含砂芯复合试件性状试验研究．浙江大学博士学位论文．
[24] 章克凌，陶振宇(1994)．饱和粘土在循环荷载作用下的孔压预测．岩土力学，Vol．15，No．3：9-17．
[25] Duncan J M (1993). Limitations of conventional analysis of consolidation settlement. Journal of Geoteclmical Engineering ASCE, 119(9): 1333～1359.
[26] Davis E H, Raymond G P (1965). A non-linear theory of consolidation. Geotechnique, 15(2): 161～173.
[27] Xie, K.H. & C.J. Leo (1999). An Investigation into the Nonlinear Consolidation of Layered Soft Soils. Research Report CE11, School of Civil Engineering and Environment, UWS, Nepean, Australia.
[28] 李冰河，谢康和，应宏伟，曾国熙(1999)．初始有效应力沿深度变化的非线性一维固结半解析解．土木工程学报，32(6)：47～52．
[29] 李冰河，谢康和，应宏伟，曾国熙(1999)．变荷载下软粘土非线性一维固结半解析解．岩土工程学报，21(3)：288～293．
[30] 李冰河，谢永利，谢康和，曾国熙(1999)．软粘土非线性一维固结半解析解．西安公路交通大学学报，19(1)：24～29．
[31] Xie K H, Li B H, Li Q L (1996). A nonlinear theory of consolidation under time-dependent loading. In: Proceedings of 2nd International Conference on Soft Soil Engineering. Nanjing, 27-30, 193～196.
[32] 李冰河(1999)．成层饱和软粘土地基大应变固结理论研究【博士学位论文】．浙江大学．
[33] Mesri G, Rokhsar A (1974). Consolidation of normally consolidated clay[J], J of SMFD, ASCE, GT8: 889-903.
[34] Mesri G, Choi Y K (1985). Settlement analysis of embank -ments on soft clays[J], J. of Geotechnical Engi-neering, ASCE, 111,441-464.
[35] Mesri G.,Tavenas F (1983). Discussion of Permeability and consolidation of normally consolidated soils" by Y H Huang and V P Drenevich [J], Journal of the Geotechnical Engineering Div., ASCE,109(GT6): 873-878.
[36] Tavenas F.,Jean P.,Leblond R, et al (1983). The perme-ability of natural soft clays,Part Ⅱ Permeability Characteristics[J], Canadian Geotechnical Journal, 20(4): 645-660.
[37] Xie K.H., Xie X.Y., Jiang W (2002). A study on one dimensional nonlinear consolidation of double- layered soil[J]. Computers and Geotechnics, 29(2): 151-168.
[38] 谢康和，郑辉，李冰河，刘兴旺(2003)．变荷载下成层地基一维非线性固结分析，浙江大学学报(工学报)，37(4)，426-431．
[39] Xie K. H., Leo C. J (1999). A study on one dimensional nonlinear consolidation of soft soils. Research report[R], UWS, Nepean,Australia, School of Civic Engineering and Environment.