土石坝多点输入地震反应分析及相关方法研究
|
摘要
对于大尺度的土石坝等结构物由于其与外部围岩的接触面上各点的运动不同步而需进行多点输入地震反应分析的研究，1969年M.Dibaj和J.Penzien最早开始对此课题研究。由于土石坝在地震作用下的失效形式包括累积损伤破坏和过大的永久位移，本文从累积损伤和永久位移两方面研究土石坝多点输入相对单点输入地震反应有何不同，即多点效应如何，因此与多点输入分析相关的损伤值和永久位移的计算方法也在研究之列。本文的多点输入为顺河向和竖向的双向输入，附带研究了单点输入时双向地震动相关程度对反应的影响。本文在总结回顾过去工作的基础上，主要开展了如下6个方面的工作。
1、提出了基于动剪应力极值的土体损伤值计算方法。以往计算土体在不规则的动剪应力作用下的损伤值根据的是动剪应力的峰值，在时域内多点输入分析中，由于差动力的的存在，使得时程后段动剪应力不穿零而在一侧做幅度不大的波动，基于峰值的损伤值计算特别过高地估计了这段剪应力的破坏作用，过高的程度还随延时增加而增加。新方法克服了这一缺点，使得评价多点输入地震破坏作用更加合理。
2、提出了对人工合成地震动进行速度归零化的观点和方法。以往人工合成的地震波在地震结束时即地震加速度恒为零时速度不为零，这与合成地震动是“模拟输入点从静止到运动再到静止的运动过程”这一要求不一致，同时导致时域内多点输入分析时差动力过大以至算出的损伤值过大，于是本文提出了简易的地震动速度归零化方法并分析了其合理性。
3、完善了计算地震作用下土石坝的永久位移的等价节点力法中等价节点力的计算方法。本文认为多点输入的永久位移包括两部分，一是由累积损伤引起的，二是由地基永久位移附带的。经计算，第二部分相对较小可以忽略。而多点输入由累积损伤引起的永久位移可采用等价节点力法，水平面和最大静剪应力面两种等价节点力法中等价节点力的计算方法都在本文得到完善。
4、研究了时域内地震动的多点效应。若同时进行了多点地震动速度归零化和采用基于极值的损伤值计算方法，对于100米高的土石坝，多点输入与单点输入反应十分接近。对于240米高的超大型土石坝，坝体内永久位移和损伤值较大的部位多点输入的反应量较小，这是多点输入反应的特点或说多点效应。另外，多点效应也包括坝基部位的最大动剪应力和损伤值偏大这一效应。多点地震动的同步性越差，如地震波视波速越小，多点效应就越明显。用内差法合成的地震动输入情况下多点效应弱一些，但仍能体现多点效应。
5、研究了频域内地震动的多点效应，并对计算过程进行了一定程度的简化，即只需要计算输入地震动功率谱矩阵从大到小排列的前4个特征值所对应的地震动的动力反应。频域内多点效应与时域内有不一致的地方，即对于240米高的超大型坝，
摘要
对于竖向永久位移最大的坝顶部位和损伤值原本就比较高的坝顶及斜坡部位，频域内
多点输入比单点输入的永久位移和损伤值反应要大些。不一致的原因在于频域内多点
作用是通过拟静应力实现的。拟静力法假设了地基位移引起坝体内节点产生位移的过
程是不需要时间的，‘这不符合实际。因此建议多点效应以时域内的为准。
6、研究了单点输入时水平和竖向的相关程度与反应的关系。对于240米高的超
大型土石坝，相关程度越小，坝顶竖向永久位移和易破坏单元的损伤值越大，当竖向
与水平向地震动强度接近时，这一规律更明显。时域和频域内这一规律是一致的。
本文的多点输入地震反应的结论可供土石坝抗震设计时参考，提出的新方法以及
进一步完善后的原方法可应用到岩土工程相关领域，基于不规则动应力极值的损伤值
计算方法有应用到机械等其它领域的前景。
Multi-Point Input Method is necessary in Seismic Response Analysis of large scale earth dam, because the points move unsynchronously on the interface between the structure and surrounding rock, and the researching task was initiated by M. Dibaj and J. Penzien in 1969. Whether the earth dam lapses in Seismic Response Analysis is mainly judged by two criterion, the Damage Value and the permanent displacement, so the difference of response between Multi-Point Input and One-Point Input, that is the Multi-Point Effect, is also checked by this two criterion. Therewith the method to calculate Damage Value and permanent displacement is studied too. The Multi-Point Input is two directional, one direction is along river, and another is vertical. By way of parenthesis, In One-Point Input Method the relation is studied between the response and the correlative coefficient of horizontal and vertical earthquake wave. After reviewing the past work, 6 aspects of researching is developed as following:
1. A more reasonable method to calculate soil's Damage Value is advanced, which bases on extrema of irregular dynamic shear stress. Previously it bases on peaks of shear
stress to calculate Damage Value, but by this method the destructive action of Multi-Point Inputted earthquake is overestimated, especially in the second half section of responding shear stress' time history the shear stress caused mainly by differential force undulate slightly on one side of its zero line. Moreover the overestimated Damage Value increases along with the Delayed Time. The new method overcomes the old methods' shortcoming.
2. The idea and method to velocity-zeroize artifical accelerations is put forward. The precious method to simulate earthquake accelerations is not perfect because the points on the interface still move according to the simulated acceleration when the points' motion ends, which is obviously a paradox. If the points' velocity is not zeroized, soil's Damage Value based on shear stress's peaks or extrema is overestimated in Multi-Point Input Analysis. The new method's rationality is analyzed.
3. The way to calculate the Equivalent Joint-force is consummated in the Equivalent Joint-force Method to calculate dam's permanent displacement caused by earthquake. It's thought that dam's permanent displacement by Multi-Point Input includes two parts, the first is caused by the Accumulated Damage, while the second is incidental to the basement's permanent displacement. Based on computation, the second part can be neglected because it is relatively small. The permanent displacement caused by Accumulated Damage is calculated in Equivalent Joint-force Method, while the way to calculate the Equivalent Joint-force is consummated, both in the Equivalent Joint-force
Method of Horizontal Face and Maximal Static Shear Stress Face.
4. The Multi-Point Effect in time domain is studied. If the inputted accelerations are velocity-zeroized and the Damage Value is calculated according to shear stress' extrema, as to 100-meter-high earth dam, Multi-Point Effect is not distinct; But as to 240-meter-high earth dam, in the part where permanent displacement and Damage Value is originally bigger the response is less tenser than that by One-Point Input, and in the part near basement the maximal shear stress and Damage Value is bigger, that is the Multi-Point Effect in time domain. Weaker the synchronicity of inputted accelerations is, for example, smaller the velocity of earthquake wave is, stronger the Multi-Point Effect is. The Multi-Point Effect with input of the artificial earthquake acceleration simulated by Interpolation Method is weaker than that of the directly simulated acceleration.
5. The Multi-Point Effect in frequency domain is studied, and the analytical procedure is simplified to some extent, that is, the responding data is accurate enough only with the input according to the first four degressively arranged eigenvalue of earthquake power spectrum matrix. There are disaccordant conclusions of Multi-Point Input Analys
1、提出了基于动剪应力极值的土体损伤值计算方法。以往计算土体在不规则的动剪应力作用下的损伤值根据的是动剪应力的峰值，在时域内多点输入分析中，由于差动力的的存在，使得时程后段动剪应力不穿零而在一侧做幅度不大的波动，基于峰值的损伤值计算特别过高地估计了这段剪应力的破坏作用，过高的程度还随延时增加而增加。新方法克服了这一缺点，使得评价多点输入地震破坏作用更加合理。
2、提出了对人工合成地震动进行速度归零化的观点和方法。以往人工合成的地震波在地震结束时即地震加速度恒为零时速度不为零，这与合成地震动是“模拟输入点从静止到运动再到静止的运动过程”这一要求不一致，同时导致时域内多点输入分析时差动力过大以至算出的损伤值过大，于是本文提出了简易的地震动速度归零化方法并分析了其合理性。
3、完善了计算地震作用下土石坝的永久位移的等价节点力法中等价节点力的计算方法。本文认为多点输入的永久位移包括两部分，一是由累积损伤引起的，二是由地基永久位移附带的。经计算，第二部分相对较小可以忽略。而多点输入由累积损伤引起的永久位移可采用等价节点力法，水平面和最大静剪应力面两种等价节点力法中等价节点力的计算方法都在本文得到完善。
4、研究了时域内地震动的多点效应。若同时进行了多点地震动速度归零化和采用基于极值的损伤值计算方法，对于100米高的土石坝，多点输入与单点输入反应十分接近。对于240米高的超大型土石坝，坝体内永久位移和损伤值较大的部位多点输入的反应量较小，这是多点输入反应的特点或说多点效应。另外，多点效应也包括坝基部位的最大动剪应力和损伤值偏大这一效应。多点地震动的同步性越差，如地震波视波速越小，多点效应就越明显。用内差法合成的地震动输入情况下多点效应弱一些，但仍能体现多点效应。
5、研究了频域内地震动的多点效应，并对计算过程进行了一定程度的简化，即只需要计算输入地震动功率谱矩阵从大到小排列的前4个特征值所对应的地震动的动力反应。频域内多点效应与时域内有不一致的地方，即对于240米高的超大型坝，
摘要
对于竖向永久位移最大的坝顶部位和损伤值原本就比较高的坝顶及斜坡部位，频域内
多点输入比单点输入的永久位移和损伤值反应要大些。不一致的原因在于频域内多点
作用是通过拟静应力实现的。拟静力法假设了地基位移引起坝体内节点产生位移的过
程是不需要时间的，‘这不符合实际。因此建议多点效应以时域内的为准。
6、研究了单点输入时水平和竖向的相关程度与反应的关系。对于240米高的超
大型土石坝，相关程度越小，坝顶竖向永久位移和易破坏单元的损伤值越大，当竖向
与水平向地震动强度接近时，这一规律更明显。时域和频域内这一规律是一致的。
本文的多点输入地震反应的结论可供土石坝抗震设计时参考，提出的新方法以及
进一步完善后的原方法可应用到岩土工程相关领域，基于不规则动应力极值的损伤值
计算方法有应用到机械等其它领域的前景。
Multi-Point Input Method is necessary in Seismic Response Analysis of large scale earth dam, because the points move unsynchronously on the interface between the structure and surrounding rock, and the researching task was initiated by M. Dibaj and J. Penzien in 1969. Whether the earth dam lapses in Seismic Response Analysis is mainly judged by two criterion, the Damage Value and the permanent displacement, so the difference of response between Multi-Point Input and One-Point Input, that is the Multi-Point Effect, is also checked by this two criterion. Therewith the method to calculate Damage Value and permanent displacement is studied too. The Multi-Point Input is two directional, one direction is along river, and another is vertical. By way of parenthesis, In One-Point Input Method the relation is studied between the response and the correlative coefficient of horizontal and vertical earthquake wave. After reviewing the past work, 6 aspects of researching is developed as following:
1. A more reasonable method to calculate soil's Damage Value is advanced, which bases on extrema of irregular dynamic shear stress. Previously it bases on peaks of shear
stress to calculate Damage Value, but by this method the destructive action of Multi-Point Inputted earthquake is overestimated, especially in the second half section of responding shear stress' time history the shear stress caused mainly by differential force undulate slightly on one side of its zero line. Moreover the overestimated Damage Value increases along with the Delayed Time. The new method overcomes the old methods' shortcoming.
2. The idea and method to velocity-zeroize artifical accelerations is put forward. The precious method to simulate earthquake accelerations is not perfect because the points on the interface still move according to the simulated acceleration when the points' motion ends, which is obviously a paradox. If the points' velocity is not zeroized, soil's Damage Value based on shear stress's peaks or extrema is overestimated in Multi-Point Input Analysis. The new method's rationality is analyzed.
3. The way to calculate the Equivalent Joint-force is consummated in the Equivalent Joint-force Method to calculate dam's permanent displacement caused by earthquake. It's thought that dam's permanent displacement by Multi-Point Input includes two parts, the first is caused by the Accumulated Damage, while the second is incidental to the basement's permanent displacement. Based on computation, the second part can be neglected because it is relatively small. The permanent displacement caused by Accumulated Damage is calculated in Equivalent Joint-force Method, while the way to calculate the Equivalent Joint-force is consummated, both in the Equivalent Joint-force
Method of Horizontal Face and Maximal Static Shear Stress Face.
4. The Multi-Point Effect in time domain is studied. If the inputted accelerations are velocity-zeroized and the Damage Value is calculated according to shear stress' extrema, as to 100-meter-high earth dam, Multi-Point Effect is not distinct; But as to 240-meter-high earth dam, in the part where permanent displacement and Damage Value is originally bigger the response is less tenser than that by One-Point Input, and in the part near basement the maximal shear stress and Damage Value is bigger, that is the Multi-Point Effect in time domain. Weaker the synchronicity of inputted accelerations is, for example, smaller the velocity of earthquake wave is, stronger the Multi-Point Effect is. The Multi-Point Effect with input of the artificial earthquake acceleration simulated by Interpolation Method is weaker than that of the directly simulated acceleration.
5. The Multi-Point Effect in frequency domain is studied, and the analytical procedure is simplified to some extent, that is, the responding data is accurate enough only with the input according to the first four degressively arranged eigenvalue of earthquake power spectrum matrix. There are disaccordant conclusions of Multi-Point Input Analys
引文
[001]蒋国澄，近代高土石坝结构的重要进展[A]，高土石坝筑坝关键技术问题研究成果汇编[C]，第二册，水利水电科学研究院，1986
[002]顾淦臣编著，土石坝地震工程[M]，南京：河海大学出版社，南京：1989，
[003]刘文廷，土石坝地基随机地震反应分析[D]，[博士学位论文]，大连：大连理工大学，1993
[004]Seed, H. B., Lessons from the performance of earth dams during earthquake[J], Dams and earthquake, London, 1981
[005]Feng, Q. M., Hu, .X., Spatial Correlation of Earthquake Motion and Its Effect on Structural Response[A], Proc. Of US-PRC, Bilateral Workshop on Earthquake Engineering[C], Vol. 1, A-5, Beijing,1982
[006]钱家欢，殷宗泽主编．土工原理与计算[M]．北京：中国水利水电出版社，1996
[007]周健、白冰，徐建平编著，土动力学理论与计算[M]，北京：中国建筑工业出版社。2001，116～118
[008]田景元，孙树林，刘汉龙，隧洞围岩中岩块稳定动力学分析[J]，河海大学学报，2002，30(2)，81～84
[009]Mononobe, H.A., et al., Seismic stability of the earth dam[A], Proc, 2nd Congress of Large Dams[C], Washington DC, Ⅳ, 1936.
[010]Martin, G.R., The response of earth dams to earthquakes[D], Ph.D Thesis, University of California, Berkeley, 1965.
[011]Gazetas, G., Shear vibrations of vertically inhomogeneous earth dams to earthquake[J], Int, J. Num. Anal. Mech. Geomech., Vol.6, No.4,1981.
[012]Clough, R.W., and Chopra, A. K., Earthquake stress analysis in earth dams[J], ASCE, Vol.92, No.EM2,1966.
[013]Duncan, J,M., Chang, C.Y., Non-linear Analysis of Stress and Strain in Soils[J], ASCE, Vol.96, No. SM5, 1970
[014]Seed, H. Bolton and Lee, Kenneth L. and Idriss, I. M., Analysis of Sheffield Dam Failure[J], ASCE, 1969, 95 (SM6), 1453～1490.
[015]Hardin, B.O., and Denevich, V. P., Shear Moduls and Damping in Soil: Measurements and parameter effects [J], ASCE, 1972, 98 (SM6), 603-624.
[016]Hardin, B.O., and Denevieh, V. P., Shear Moduls and Damping in Soil: Design Equations and Curves [J], ASCE, 1972, 98(SM7), 667-692.
[017]Idriss, I. M., Lysmer. J., Huang, R., and Seed, H. B., QUAD-4: A Computer program for Evaluating the Seismic Response of Soil Structures by Variable Damping Finite Element procedures. [A],No.EERC73-16[R], College of Engineering Univ. of California, Berkeley, Calif., July, 1973
[018]K.Pyke, Nonlinear soil Models for irregular Cyclic Loadings[J], ASCE, 1979, 105. (GT6) ,715～726
[019]Abdel-Ghaffar, A. M.; Ail-Siong Koh, Longitudinal Vibration of Non-homogeneous Earth
Dams, [J], EESD, 1981,9 (3)
[020]Abdel-Ghaffar, A. M., Ail-Siong Koh, Earthquake-Induced Longitudinal Strains and Stresses in Nonhomogeneous Earth Dams[J], EESD, 1981,9 (6)
[021]钱家欢，卢盛松，郭志平，土坝动力分析(有限元法)的几点改进[J]，华东水利学院学报，1982，10(1)，14～27
[022]Seed, H. B., and Lee, K. L., Liquefaction of Saturated Sands During Cyclic Loading[J], ASCE, 1966, 92(SM6), 105～134
[023]Peacock, W. H., Seed, H.B., Sand Liquefaction under Cyclic Loading Simple Shear Conditions[J], ASCE, 1968, 94 (SM3), 689～708
[024]Finn, W. D. L., et al., Sand Liquefaction in Triaxial and Simple Shear Tests[A], Soil Mechanics Research Report Series No. 11[R], University of British Columbia, Vancounver, Canada, Aug., 1969
[025]Ishihara, K., and Li, S. I., Liquefaction of Saturated Sand in Triaxial Torsion Shear Test,[J], Soil and Foundations, Tokyo, Japan, 1972, 12(3), 19～39
[026]Seed, H. B., and Idriss, I. M., Simplified Procedure for evaluating Soil Liquefaction Potential[J], ASCE, 1971, 97 (SM9), 1249～1273
[027]Martin G. B., Finn W. D. L., Seed H. B., Fundamentals of Liquefaction under cyclic loading [J]. ASCE, 1975, 101(GT5), 423～438
[028]Ishihara, K., and Yasuda, S., Sand Liquefaction Due to irregular Excitation[J]. Soil and Foundations, Tokyo, Japan, 1972, 12 (4), 65～77
[029]Anniaki M and Lee K. L, Equivalent Uniform Cycle Concept for Soil Dynamics[J], ASCE, 1997, 103(GT106),549～569
[030]Seed H.B et al, Dynamic Analysis of The Slide in the Lower San Fernando Dam during the Earthquake of February 9, 1971[J]. ASCE, 1975, 101(GT9), 889～911
[031]陈玉田，王淑云、吴旭光，，土坝的非线性动力分析[J]，华东水利学院学报，1980，8(4)，1～26
[032]张克绪，饱和砂土的液化应力条件[J]，地震工程与工程震动，1984，4(1)，99～108
[023]Finn, W. D. L., Lee, K. L. , Martin, G. R., An effective Stress model for Liquefaction[J], 1977, ASCE, GT6
[034]沈珠江，饱和砂土的动力渗透变形计算[J]，水利学报，1980(2)
[035]Lee. K. L., et al. Earthquake Induced Settlements in Saturated Sands[J], ASCE,1974,100 (GT4)
[036]Yasuhara K. Approximate Prediction of Soil Deformation under Drained-Repeated Loading[J], Soil and Foundations, 1953, 23(2)
[037]Ohara Set al, Study on the Settlement of Saturated Clay Layer induced by Cyclic Shear Stress[J]. Soils and Foundation, 1988,28(3)
[038]Yasuhara K. Recompression of Normally Consolidated Clay after Cyclic Loading[J], Soil and Foundations, 1983, 23(2)
[039]Seed, H. B., and Chart, C,K:, Clay Strength under Earthquake Loading condition[J], ASCE, 1966, 92(SM)
[040]Thiers, G. R., and Seed, H. B., Strength and Stress-Strain Characteristics of Clays Subjected to Seismic Loading Condition[J], Vibration Effects of Earthquake On Soil and Foundation, 1969
[041]Lee L. K., Seismic Permanent Deformation in earth dams [D], Mechanics and Structure Department School of Engineering and Applied science University of California Los Angles, California, December, 1974
[042]石兆吉，郁寿松，软土震陷计算中若干问题的讨论[J]，地震工程与工程振动，1986，6 (4)，92～97
[043]Newmark, N, M., Effect of earthquake on dams and embankments[J], Geo. Vol.15, 1965
[044]Franldin, A.G., and Chang, F.K., Earthquake resistance of earth and rock fill dam: permanent displacement of earth embankments by Newmark sliding block analysis[A], Misc. paper S-71-17, Report 5, U.S. Army Engineer[R], WES, 1977
[045]Makdisi, F.I., and Seed, H.B., Simplified procedure for estimating dam and embankment earthquake-induced deformations[J], ASCE, GT, 1978, Vol. 104 (7), pp.849～868.
[046]渡边启行，动的解析-Ⅰ，动的解析方法[J]，大，No．87，1979，pp．46～64
[047]陈生水，沈珠江，强震区域堆石坝的地震永久变形分析[J]，河海大学学报，1990，(2)
[048]Serif. N., Seed, H. B., Makdisi. F. I., and Chang, C, K, Earthquake induced deformation of earth dams[A], Report No. EERC76-4[R], University of California, Berkeley, 1976.
[049]谢君斐，石兆吉，郁寿松等，液化危害性分析[J]。地震工程与工程振动，1998(1)，61～77
[050]Taniguehi, E., Whitman, R. V., and Man', W. A., Prediction of earthquake induced deformation of earth dams[J], Soils and Foundation, 1983, 23(4), 126～132
[051]张克绪，李明宰，常向前，地震引起的土坝永久变形分析[J]，地震工程与工程振动，1989，9(1)，91～100
[052]刘汉龙，陆兆溱，钱家欢，土石坝地震永久变形分析[J]，河海大学学报，1996，24(1)，91～96
[053]郭兴文，王德信，燕立群，谢能刚，于玉莽，水布垭混凝土面板堆石坝地震永久变形分析[J]，河海大学学报，2001，29(6)，56～60
[054]冯启民，地震动随机理论[J]，世界地震工程，1986(3)，11～16
[055]汪闻韶，王钟宁，不同地震波输入对土石坝动力反应的影响[A]，全国土工建筑及地基抗震会议论文集[C]，西安，1986。
[056]Franldin, A,G., Chang, F. K., Permanent displacement of embankment by Newmark sliding block analysis[A], Report of U.S. Army Water Exp. Stat.[R], 1977, S-17～17
[057]Isbihara, K.., Yasuda, S, Sand liquation under random earthquake loading conditions[A], Int. Pro. Of 5th WCEE[C]., 1973.
[058]沈智刚等，随机荷载下砂土的动力反应[J]，国外地震工程，1980，(3)，52～56。
[059]谢定义，巫志辉，不规则动荷脉冲波对砂土液化特性的影响[J]，岩土工程学报，1987，9(4)，1～12
[060]Housner, G.W., Characteristics of strong.motion earthquakes[J], BSSA, Vol.37, No. 1; 1947.
[061]Singh,. M.P., Khatua, T. P., Stochastic. seismic prediction of earth dams[A], Proe. Of
Earthquake Engineering and Soil Dynamics Specialty Conference[C], ASCE, 1978.
[062]Gazetas, G., et al, random vibration analysis for the seismic response of earth dam[J], Geotechnique, Vol.31, No.2, 1981, pp.261～277.
[063]Gazetas, G., et al., Stochastic estimation of the nonlinear response of earth dam to strong earthquake[J], Soil Dynamics and Earthquake Engineering, Vol. 1, No. 1,1982, pp,39～46.
[064]Gasparini, D.A., et al., Random vibration analysis of finite element models of earth dam[A], Soil Dynamics and Earthquake Engineering Conference[C], Southampton, 1982.
[065]吴再光，韩国城，林皋，非线性土层随机地震反应分析的等价线性方法[J]，水利学报，1988(8)，68～73。
[066]吴再光，韩国城，林皋，非线性土层随机地震反应的概率平均等价线性方法[J]，岩土工程学报，1989，11(4)，9～16。
[067]吴再光，土层随机地震反应的一种改进算法[J]，振动工程学报，1990，3(1)56～59
[068]Wu Zaiguang, Lin Gao, Han Guocheng. Nonstationary stochastic seismic response analysis for nonlinear soil foundation[A], Proc of Vibration Engineering Conference[C], Wuhan-Chongqing, 1990.6.
[069]吴再光，考虑土料参数变异性的土层地震反应分析[J]，水利学报，1991(10)，1～6
[070]吴再光，土层非平稳有效应力随机地震反应分析[J]，水利学报，1991，(9)，25～30
[071]林家浩，(平稳)随机地震响应的确定性算法[J]．地震工程与工程震动，1985，5(1)，89～93
[072]林家浩，非平稳随机地震响应的精确高效算法[J]，地震工程与工程震动，1993，13(1)，24～29
[073]曾心传，秦小军，土层对地震的随机反应分析[J]，地震工程与工程震动，1998，18(3)，27～29
[074]门玉明，黄义，刘增荣，场地土的随机地震反应分析[J]，工程地质学报，2001，9(1)，68～73
[075]Ishihara, k., and Yasuda, S., Sand liquefaction under random Earthquake Loading Condition[A], Proceedings, fifth World Conference on Earthquake Engineering, Rome, Italy, 1972
[076]Christian, J., T., Probabilistic Soil Dynamics, State-of-the Art[J], ASCE, 1980, 106 (GT4), 385～397
[077]Whitman., R. V., Evaluation Calculated Risk in Geotechnical Engineering[J], ASCE, 1984, 110(GT2), 145～188
[078]Haldar., A., et al, Probabilistic Evaluation of Liquefaction Potential[J], ASCE, 1979, 102 (GT2), 145～163
[079]吴再光，韩国城，林皋，砂土地震液化概率分析[J]，大连理工学院学报，1988，27(2)，111～118
[080]吴再光，韩国城，林皋，随机地震作用下砂土液化概率分析[J]，岩土工程学报，1990，12(5)，1～8
[081]Lin,J.S., Risk assessments of the earthquake induced permanent displacement in earth dams[A], Proc. Of 8th WCEE[C],1984.
[082]Lin, J. S., Whitman, R.V., Earthquake induced displacement of sliding blocks[J], ASCE, GT,1986, 112(1);pp.44～59.
[083]吴再光，韩国城，林皋，土石坝地震永久变形的危险性分析[J]，岩土工程学报，1991，13(2)，13～20
[084]吴再光，韩国城，面板堆石坝地震塑性滑移的概率分析[A]，第六届全国土力学及基础工程学术讨论会议论文集[C]，同济大学出版社，1991。
[085]吴再光，韩国城，随机地震作用下高桩码头岸坡永久变形分析[J]，岩土工程学报，1991，13(3)
[086]吴再光，韩国城，粉土海堤随机地震反应及振陷变形分析[A]，首届全国岩土力学与工程青年工作者学术讨论会论文集[C]，浙江大学出版社，1992。
[087]刘汉龙，随机地震作用下地基及土坝永久变形分析[J]，岩土工程学报，1996．，18(3)，19～27
[088]刘汉龙，陆兆溱，钱家欢，土石坝非线性随机反应及动力可靠度分析[J]，河海大学学报，1996，24(3)，86～91
[089]陆绍俊，土石坝永久变形决策分析法研究，岩土工程学报[J]，1998，20(1)，80～83
[090]Dibaj M., Penzien J., Response of Earths Dams to Travelling Seismic Waves[J], ASCE, 1969(SM2),
[091]驹田广野，林正夫，北原义浩。进行性地震入力波考虑三次元震动应答解析[J]，土木学会论文报告集，1977，No．261，77～92
[092]沈珠江，徐志英，考虑行进波的土工建筑物地震反应分析[J]，水利学报，1983(11)37～43。
[093]楼梦麟，林皋，重力坝地震行进波反应分析[J]，水利学报，1984(5)，26～32．
[094]Wemen,. S.,D., et al., Structural Response to traveling .Seismic wave[J]s, ASCE, Vol.105, No.ST12,1979
[095]Chen, H.Q., et al., effect of Seismic Traveling Waves on the Response of Arch Dam[A], Proc. China-US Workshop on Earthquake Behavior of Arch Dam[C], Beijing, China, 1987.
[096]Penzien, J.,Watable, M., Characteristics of 3-Dimensional earthquake ground motion[J], EESD.,1975, Vol.3.
[097]Kubo, T.,Penzien, J., Analysis of 3-D Strong Ground Motion Along Principal Axes San Fernando Earthquake [J], EESD, 1976, Vol.7, No.3, pp.265～278.
[098]李宏男，地震动各分量间的谱矩阵[A]，全国第三届随机振动学术交流会论文集[C]，泰安，1991．8，pp．321～326
[099]Hadiam, A., On the Correlation of the Components of Strong Ground Motion[J], part 2,, BSSA,1981.
[100]黄玉平，双向水平地震动的空间相关性[J]，哈尔滨建筑工程学院学报，Vol．3，1987，10～14
[101]Housner, G.W, Interaction of Building and ground During an earthquake[J], BSSA, Vol.47, No.3,1957
[102]刘浩吾，何发祥，拱坝行波输入的动力分析和抗震设计[J]，水利学报，1990(9)，26～35
[103]沈强，沈珠江，一种考虑地震波传播方式的堤坝三维动力分析法[J]，水利水电科学研究，1987(4)，．47～57。
[104]Harichandran, Estimating the spatial variation of earthquake ground motion from dense array recording[J], Structural Safety,. Vol. 10, 1991, pp.219～234.
[105]Zerva, A., Shinozuka, M., stochastic differential ground motion[J], Struetural Safety, Vol. 10,
1991, pp. 129～144
[106]Ellis,G.W., Cakmak, A. S., Effect of spatial variability on ARMA modeling of ground motion[J], Structural Safety, Vol. 10,1991, 181～192.
[107]K. Kanai, Semi-empirical Formula for the Seismic Characteristics of Ground[A], Bull. Earthquake Res[C]. Inst. Univ. Tokyo, Vol.35, 1957
[108]H. Tajimi, A Statistical Method of Determining the Maximum Response of a Building Structure During an Earthquake[A], Proc.2nd, WCEE[C], 1960
[109]胡聿贤，周锡元，弹性体系在平稳和非平稳化地面运动下的反应[A]，中国科学院土木建筑研究所地震工程研究报告集[R]，第一集，科学出版社，1962
[110]金家和，胡聿贤、周锡元，关于“弹性体系在平稳和非平稳化地面运动下的反应”一文的讨论[A]，中国科学院土木建筑研究所地震工程研究报告集[R]，第二集，科学出版社，1965
[111]屈铁军，地面运动的空间变化特征研究及地下管线地震反应分析[D]，[博士学位论文]，哈尔滨：国家地震局工程力学研究所，1995，81～85，163～167
[112]Kureghian, A.D., Crempien, J., An evolutionary model for earthquake ground motion[J], Structural Safety, 1989, No.6, 235～246
[113]Saragoni, G.R.., Hart. G.C. Simulation of Artificial earthquakes[J], Earthquake Eng. Structure Dynamics, 1974,2(3), 249～267
[114]Harichandrun R. S. , Vanmavcke, E. H., Stochastic variation of earthquake ground motion in space and time[J], ASCE, Vol. 112, No., EM2, 1986,2.
[115]H.Hao. Effects of Spatial Variation of Ground Motions on Large Multiply-Structure[A], Report No. UCB/EERC-89-06[R],1989
[116]王君杰，多点多维地震动随机模型及结构的反应谱分析方法[D]，[博士学位论文]，哈尔滨：国家地震局工程力学研究所，1995，13，20，84，112
[117]N.A.Abrahamson, J.E. Schneider and J.C. Stepp, Empirical Spatial Coherency Function for Application to Soil-Structure Interaction Analyses[J], Earthquake Spectra, Vol. 7, No. 1,1991
[118]C.H.Lob and S.G.Lin, Directionality and Simulation in Spatial Variation of Seismic waves[J], Eng. Struct.Vol.12, No.3, 1990,134～143
[119]C.H.Lob and Y.T.Yeh, Spatial Variation and Stochastic Modelling of Seismic Differential Ground Movement[J], EESD, Vol. 16, No.4,1988
[120]胡聿贤，地震工程学[M]，地震出版社，北京：1988，175～177．
[121]Nafi-Toksoz, M., Dainty, A. M., et al., Spatial Variation of Ground Motion due to Lateral Heterogeneity[J], Structural Safety, Vol. 10, 1991, pp. 53～78.
[122]Tassoulas., J. L., Roesset., J. M., Wave propagation in a rectangular valley[J], Structural Safety, Vol. 10, 1991, pp. 15～26,
[123]Sesma, F. J. S., Rosenblueth, E., Ground motion at Canyon of arbitrary shapes under incident SH wave[J], Int. J, Earthquake Eng. Structural Dyn, Vol. 7, No.5, 1979
[124]Abrahamson, N., Schneider, J. E, Spatial coherency of shear waves from the Lotung, Taiwan large scale seismic Test[J], Structural Safety, Vol. 10, 1991, pp. 145～162
[125]Someville , P, G., et al, Site-specific estimation of spatial incoherent of strong ground
motion[A], Proc. Earthquake Eng. Soil Dyn., Ⅱ[C], ASCE, Park city, UT, 1988.6,pp. 188～202
[126]星谷胜，石井清，栗田博昭，空间·时间分布特性有地震动[J]，土木学会论文报告集，1987，No．386，359～367
[127]Hao, H., C.S.Oliveira and J. Penzien., Multiple station ground motion processing and simulation based on SMART-1 array data[J], Nuclear Engineering and design, Vol. 111, 1989, pp. 293～310.
[128]屈铁军，王前信，空间相关的多点地震动合成(Ⅰ)基本公式[J]，地震工程与工程振动，1998，18(1)，8～15
[129]屈铁军，王前信，空间相关的多点地震动合成(Ⅱ)合成实例[J]，地震工程与工程振动，1998，18(2)，．25～32
[130]夏友柏，王华桥，张尚根，一种合成多点地震动时程的方法[J]，世界地震工程，2002，18(1)，119～122。
[131]屈铁军，王前信，多点地震输入反应分析研究的进展[J]，世界地震工程，1993(1)，
[132]王前信，伍国周，李云林，拱式结构对地震多点输入的反应[J]，地震工程与工程振动，1984，4(2)，49～81
[133]潘旦光，楼梦麟，范立础，多点输入下大跨度结构地震反应分析研究现状[J]。同济大学学报，2002，29(10)
[134]林家浩，任意多相干多激励随机响应[A]，大连理工大学工程力学研究所资料[R]，1990．4
[135]陈健云，林皋，多点输入随机地震动拱坝—地基体系反应分析[J]，世界地震工程，2000，16(3)40～43
[136]邱法维，钱稼茹，多点地震动输入下的拟动力实验方法[J]，地震工程与工程振动，1998，18(2)，38～47
[137]陈厚群，侯顺载，张力飞，朱栗武，拱坝多点输入动力反应试验研究[J]，水利学报，1995(8)，12～19
[138]田景元，刘汉龙，高玉锋，郭作美，状的模糊聚类及其优势方位的确定[J]，华东地质学院学报，
[139]庄表中，王行新编著．随机振动概论[M]．北京：地震出版社，1982，303～306．
[140]田景元，土坝地震多点输入反应[A]。见刘汉龙主编，土动力学与沿途地震工程[C]，北京：中国建筑工业出版社，2002，525～530
[141]朱伯芳，有限单元法原理与应用[M]北京：水利电力出版社，1979
[142]姜弘道，陈和群，有限单元法的程序设计[M]，北京：水利电力出版社，57～58
[143]刘汉龙，土体地震永久变形分析[D]，[博士学位论文]，南京：南京河海大学岩土工程研究所，1994
[144]张克绪，谢君斐，土动力学[M]，北京：地震出版社，1989，91～92
[145]田景元，刘汉龙，陈国兴，周云东，基于剪应力时程极值的损伤值等效转换及其在土石坝多点输入地震反应中的应用[J]，世界地震工程，2003，19(1)，128～135
[146]俞载道，曹国敖，随机振动理论及其应用[M]，上海：同济大学出版社，1988，
[147]徐士良，Fortarn常用算法程序集[M]，北京，清华大学出版社，1997，
[002]顾淦臣编著，土石坝地震工程[M]，南京：河海大学出版社，南京：1989，
[003]刘文廷，土石坝地基随机地震反应分析[D]，[博士学位论文]，大连：大连理工大学，1993
[004]Seed, H. B., Lessons from the performance of earth dams during earthquake[J], Dams and earthquake, London, 1981
[005]Feng, Q. M., Hu, .X., Spatial Correlation of Earthquake Motion and Its Effect on Structural Response[A], Proc. Of US-PRC, Bilateral Workshop on Earthquake Engineering[C], Vol. 1, A-5, Beijing,1982
[006]钱家欢，殷宗泽主编．土工原理与计算[M]．北京：中国水利水电出版社，1996
[007]周健、白冰，徐建平编著，土动力学理论与计算[M]，北京：中国建筑工业出版社。2001，116～118
[008]田景元，孙树林，刘汉龙，隧洞围岩中岩块稳定动力学分析[J]，河海大学学报，2002，30(2)，81～84
[009]Mononobe, H.A., et al., Seismic stability of the earth dam[A], Proc, 2nd Congress of Large Dams[C], Washington DC, Ⅳ, 1936.
[010]Martin, G.R., The response of earth dams to earthquakes[D], Ph.D Thesis, University of California, Berkeley, 1965.
[011]Gazetas, G., Shear vibrations of vertically inhomogeneous earth dams to earthquake[J], Int, J. Num. Anal. Mech. Geomech., Vol.6, No.4,1981.
[012]Clough, R.W., and Chopra, A. K., Earthquake stress analysis in earth dams[J], ASCE, Vol.92, No.EM2,1966.
[013]Duncan, J,M., Chang, C.Y., Non-linear Analysis of Stress and Strain in Soils[J], ASCE, Vol.96, No. SM5, 1970
[014]Seed, H. Bolton and Lee, Kenneth L. and Idriss, I. M., Analysis of Sheffield Dam Failure[J], ASCE, 1969, 95 (SM6), 1453～1490.
[015]Hardin, B.O., and Denevich, V. P., Shear Moduls and Damping in Soil: Measurements and parameter effects [J], ASCE, 1972, 98 (SM6), 603-624.
[016]Hardin, B.O., and Denevieh, V. P., Shear Moduls and Damping in Soil: Design Equations and Curves [J], ASCE, 1972, 98(SM7), 667-692.
[017]Idriss, I. M., Lysmer. J., Huang, R., and Seed, H. B., QUAD-4: A Computer program for Evaluating the Seismic Response of Soil Structures by Variable Damping Finite Element procedures. [A],No.EERC73-16[R], College of Engineering Univ. of California, Berkeley, Calif., July, 1973
[018]K.Pyke, Nonlinear soil Models for irregular Cyclic Loadings[J], ASCE, 1979, 105. (GT6) ,715～726
[019]Abdel-Ghaffar, A. M.; Ail-Siong Koh, Longitudinal Vibration of Non-homogeneous Earth
Dams, [J], EESD, 1981,9 (3)
[020]Abdel-Ghaffar, A. M., Ail-Siong Koh, Earthquake-Induced Longitudinal Strains and Stresses in Nonhomogeneous Earth Dams[J], EESD, 1981,9 (6)
[021]钱家欢，卢盛松，郭志平，土坝动力分析(有限元法)的几点改进[J]，华东水利学院学报，1982，10(1)，14～27
[022]Seed, H. B., and Lee, K. L., Liquefaction of Saturated Sands During Cyclic Loading[J], ASCE, 1966, 92(SM6), 105～134
[023]Peacock, W. H., Seed, H.B., Sand Liquefaction under Cyclic Loading Simple Shear Conditions[J], ASCE, 1968, 94 (SM3), 689～708
[024]Finn, W. D. L., et al., Sand Liquefaction in Triaxial and Simple Shear Tests[A], Soil Mechanics Research Report Series No. 11[R], University of British Columbia, Vancounver, Canada, Aug., 1969
[025]Ishihara, K., and Li, S. I., Liquefaction of Saturated Sand in Triaxial Torsion Shear Test,[J], Soil and Foundations, Tokyo, Japan, 1972, 12(3), 19～39
[026]Seed, H. B., and Idriss, I. M., Simplified Procedure for evaluating Soil Liquefaction Potential[J], ASCE, 1971, 97 (SM9), 1249～1273
[027]Martin G. B., Finn W. D. L., Seed H. B., Fundamentals of Liquefaction under cyclic loading [J]. ASCE, 1975, 101(GT5), 423～438
[028]Ishihara, K., and Yasuda, S., Sand Liquefaction Due to irregular Excitation[J]. Soil and Foundations, Tokyo, Japan, 1972, 12 (4), 65～77
[029]Anniaki M and Lee K. L, Equivalent Uniform Cycle Concept for Soil Dynamics[J], ASCE, 1997, 103(GT106),549～569
[030]Seed H.B et al, Dynamic Analysis of The Slide in the Lower San Fernando Dam during the Earthquake of February 9, 1971[J]. ASCE, 1975, 101(GT9), 889～911
[031]陈玉田，王淑云、吴旭光，，土坝的非线性动力分析[J]，华东水利学院学报，1980，8(4)，1～26
[032]张克绪，饱和砂土的液化应力条件[J]，地震工程与工程震动，1984，4(1)，99～108
[023]Finn, W. D. L., Lee, K. L. , Martin, G. R., An effective Stress model for Liquefaction[J], 1977, ASCE, GT6
[034]沈珠江，饱和砂土的动力渗透变形计算[J]，水利学报，1980(2)
[035]Lee. K. L., et al. Earthquake Induced Settlements in Saturated Sands[J], ASCE,1974,100 (GT4)
[036]Yasuhara K. Approximate Prediction of Soil Deformation under Drained-Repeated Loading[J], Soil and Foundations, 1953, 23(2)
[037]Ohara Set al, Study on the Settlement of Saturated Clay Layer induced by Cyclic Shear Stress[J]. Soils and Foundation, 1988,28(3)
[038]Yasuhara K. Recompression of Normally Consolidated Clay after Cyclic Loading[J], Soil and Foundations, 1983, 23(2)
[039]Seed, H. B., and Chart, C,K:, Clay Strength under Earthquake Loading condition[J], ASCE, 1966, 92(SM)
[040]Thiers, G. R., and Seed, H. B., Strength and Stress-Strain Characteristics of Clays Subjected to Seismic Loading Condition[J], Vibration Effects of Earthquake On Soil and Foundation, 1969
[041]Lee L. K., Seismic Permanent Deformation in earth dams [D], Mechanics and Structure Department School of Engineering and Applied science University of California Los Angles, California, December, 1974
[042]石兆吉，郁寿松，软土震陷计算中若干问题的讨论[J]，地震工程与工程振动，1986，6 (4)，92～97
[043]Newmark, N, M., Effect of earthquake on dams and embankments[J], Geo. Vol.15, 1965
[044]Franldin, A.G., and Chang, F.K., Earthquake resistance of earth and rock fill dam: permanent displacement of earth embankments by Newmark sliding block analysis[A], Misc. paper S-71-17, Report 5, U.S. Army Engineer[R], WES, 1977
[045]Makdisi, F.I., and Seed, H.B., Simplified procedure for estimating dam and embankment earthquake-induced deformations[J], ASCE, GT, 1978, Vol. 104 (7), pp.849～868.
[046]渡边启行，动的解析-Ⅰ，动的解析方法[J]，大，No．87，1979，pp．46～64
[047]陈生水，沈珠江，强震区域堆石坝的地震永久变形分析[J]，河海大学学报，1990，(2)
[048]Serif. N., Seed, H. B., Makdisi. F. I., and Chang, C, K, Earthquake induced deformation of earth dams[A], Report No. EERC76-4[R], University of California, Berkeley, 1976.
[049]谢君斐，石兆吉，郁寿松等，液化危害性分析[J]。地震工程与工程振动，1998(1)，61～77
[050]Taniguehi, E., Whitman, R. V., and Man', W. A., Prediction of earthquake induced deformation of earth dams[J], Soils and Foundation, 1983, 23(4), 126～132
[051]张克绪，李明宰，常向前，地震引起的土坝永久变形分析[J]，地震工程与工程振动，1989，9(1)，91～100
[052]刘汉龙，陆兆溱，钱家欢，土石坝地震永久变形分析[J]，河海大学学报，1996，24(1)，91～96
[053]郭兴文，王德信，燕立群，谢能刚，于玉莽，水布垭混凝土面板堆石坝地震永久变形分析[J]，河海大学学报，2001，29(6)，56～60
[054]冯启民，地震动随机理论[J]，世界地震工程，1986(3)，11～16
[055]汪闻韶，王钟宁，不同地震波输入对土石坝动力反应的影响[A]，全国土工建筑及地基抗震会议论文集[C]，西安，1986。
[056]Franldin, A,G., Chang, F. K., Permanent displacement of embankment by Newmark sliding block analysis[A], Report of U.S. Army Water Exp. Stat.[R], 1977, S-17～17
[057]Isbihara, K.., Yasuda, S, Sand liquation under random earthquake loading conditions[A], Int. Pro. Of 5th WCEE[C]., 1973.
[058]沈智刚等，随机荷载下砂土的动力反应[J]，国外地震工程，1980，(3)，52～56。
[059]谢定义，巫志辉，不规则动荷脉冲波对砂土液化特性的影响[J]，岩土工程学报，1987，9(4)，1～12
[060]Housner, G.W., Characteristics of strong.motion earthquakes[J], BSSA, Vol.37, No. 1; 1947.
[061]Singh,. M.P., Khatua, T. P., Stochastic. seismic prediction of earth dams[A], Proe. Of
Earthquake Engineering and Soil Dynamics Specialty Conference[C], ASCE, 1978.
[062]Gazetas, G., et al, random vibration analysis for the seismic response of earth dam[J], Geotechnique, Vol.31, No.2, 1981, pp.261～277.
[063]Gazetas, G., et al., Stochastic estimation of the nonlinear response of earth dam to strong earthquake[J], Soil Dynamics and Earthquake Engineering, Vol. 1, No. 1,1982, pp,39～46.
[064]Gasparini, D.A., et al., Random vibration analysis of finite element models of earth dam[A], Soil Dynamics and Earthquake Engineering Conference[C], Southampton, 1982.
[065]吴再光，韩国城，林皋，非线性土层随机地震反应分析的等价线性方法[J]，水利学报，1988(8)，68～73。
[066]吴再光，韩国城，林皋，非线性土层随机地震反应的概率平均等价线性方法[J]，岩土工程学报，1989，11(4)，9～16。
[067]吴再光，土层随机地震反应的一种改进算法[J]，振动工程学报，1990，3(1)56～59
[068]Wu Zaiguang, Lin Gao, Han Guocheng. Nonstationary stochastic seismic response analysis for nonlinear soil foundation[A], Proc of Vibration Engineering Conference[C], Wuhan-Chongqing, 1990.6.
[069]吴再光，考虑土料参数变异性的土层地震反应分析[J]，水利学报，1991(10)，1～6
[070]吴再光，土层非平稳有效应力随机地震反应分析[J]，水利学报，1991，(9)，25～30
[071]林家浩，(平稳)随机地震响应的确定性算法[J]．地震工程与工程震动，1985，5(1)，89～93
[072]林家浩，非平稳随机地震响应的精确高效算法[J]，地震工程与工程震动，1993，13(1)，24～29
[073]曾心传，秦小军，土层对地震的随机反应分析[J]，地震工程与工程震动，1998，18(3)，27～29
[074]门玉明，黄义，刘增荣，场地土的随机地震反应分析[J]，工程地质学报，2001，9(1)，68～73
[075]Ishihara, k., and Yasuda, S., Sand liquefaction under random Earthquake Loading Condition[A], Proceedings, fifth World Conference on Earthquake Engineering, Rome, Italy, 1972
[076]Christian, J., T., Probabilistic Soil Dynamics, State-of-the Art[J], ASCE, 1980, 106 (GT4), 385～397
[077]Whitman., R. V., Evaluation Calculated Risk in Geotechnical Engineering[J], ASCE, 1984, 110(GT2), 145～188
[078]Haldar., A., et al, Probabilistic Evaluation of Liquefaction Potential[J], ASCE, 1979, 102 (GT2), 145～163
[079]吴再光，韩国城，林皋，砂土地震液化概率分析[J]，大连理工学院学报，1988，27(2)，111～118
[080]吴再光，韩国城，林皋，随机地震作用下砂土液化概率分析[J]，岩土工程学报，1990，12(5)，1～8
[081]Lin,J.S., Risk assessments of the earthquake induced permanent displacement in earth dams[A], Proc. Of 8th WCEE[C],1984.
[082]Lin, J. S., Whitman, R.V., Earthquake induced displacement of sliding blocks[J], ASCE, GT,1986, 112(1);pp.44～59.
[083]吴再光，韩国城，林皋，土石坝地震永久变形的危险性分析[J]，岩土工程学报，1991，13(2)，13～20
[084]吴再光，韩国城，面板堆石坝地震塑性滑移的概率分析[A]，第六届全国土力学及基础工程学术讨论会议论文集[C]，同济大学出版社，1991。
[085]吴再光，韩国城，随机地震作用下高桩码头岸坡永久变形分析[J]，岩土工程学报，1991，13(3)
[086]吴再光，韩国城，粉土海堤随机地震反应及振陷变形分析[A]，首届全国岩土力学与工程青年工作者学术讨论会论文集[C]，浙江大学出版社，1992。
[087]刘汉龙，随机地震作用下地基及土坝永久变形分析[J]，岩土工程学报，1996．，18(3)，19～27
[088]刘汉龙，陆兆溱，钱家欢，土石坝非线性随机反应及动力可靠度分析[J]，河海大学学报，1996，24(3)，86～91
[089]陆绍俊，土石坝永久变形决策分析法研究，岩土工程学报[J]，1998，20(1)，80～83
[090]Dibaj M., Penzien J., Response of Earths Dams to Travelling Seismic Waves[J], ASCE, 1969(SM2),
[091]驹田广野，林正夫，北原义浩。进行性地震入力波考虑三次元震动应答解析[J]，土木学会论文报告集，1977，No．261，77～92
[092]沈珠江，徐志英，考虑行进波的土工建筑物地震反应分析[J]，水利学报，1983(11)37～43。
[093]楼梦麟，林皋，重力坝地震行进波反应分析[J]，水利学报，1984(5)，26～32．
[094]Wemen,. S.,D., et al., Structural Response to traveling .Seismic wave[J]s, ASCE, Vol.105, No.ST12,1979
[095]Chen, H.Q., et al., effect of Seismic Traveling Waves on the Response of Arch Dam[A], Proc. China-US Workshop on Earthquake Behavior of Arch Dam[C], Beijing, China, 1987.
[096]Penzien, J.,Watable, M., Characteristics of 3-Dimensional earthquake ground motion[J], EESD.,1975, Vol.3.
[097]Kubo, T.,Penzien, J., Analysis of 3-D Strong Ground Motion Along Principal Axes San Fernando Earthquake [J], EESD, 1976, Vol.7, No.3, pp.265～278.
[098]李宏男，地震动各分量间的谱矩阵[A]，全国第三届随机振动学术交流会论文集[C]，泰安，1991．8，pp．321～326
[099]Hadiam, A., On the Correlation of the Components of Strong Ground Motion[J], part 2,, BSSA,1981.
[100]黄玉平，双向水平地震动的空间相关性[J]，哈尔滨建筑工程学院学报，Vol．3，1987，10～14
[101]Housner, G.W, Interaction of Building and ground During an earthquake[J], BSSA, Vol.47, No.3,1957
[102]刘浩吾，何发祥，拱坝行波输入的动力分析和抗震设计[J]，水利学报，1990(9)，26～35
[103]沈强，沈珠江，一种考虑地震波传播方式的堤坝三维动力分析法[J]，水利水电科学研究，1987(4)，．47～57。
[104]Harichandran, Estimating the spatial variation of earthquake ground motion from dense array recording[J], Structural Safety,. Vol. 10, 1991, pp.219～234.
[105]Zerva, A., Shinozuka, M., stochastic differential ground motion[J], Struetural Safety, Vol. 10,
1991, pp. 129～144
[106]Ellis,G.W., Cakmak, A. S., Effect of spatial variability on ARMA modeling of ground motion[J], Structural Safety, Vol. 10,1991, 181～192.
[107]K. Kanai, Semi-empirical Formula for the Seismic Characteristics of Ground[A], Bull. Earthquake Res[C]. Inst. Univ. Tokyo, Vol.35, 1957
[108]H. Tajimi, A Statistical Method of Determining the Maximum Response of a Building Structure During an Earthquake[A], Proc.2nd, WCEE[C], 1960
[109]胡聿贤，周锡元，弹性体系在平稳和非平稳化地面运动下的反应[A]，中国科学院土木建筑研究所地震工程研究报告集[R]，第一集，科学出版社，1962
[110]金家和，胡聿贤、周锡元，关于“弹性体系在平稳和非平稳化地面运动下的反应”一文的讨论[A]，中国科学院土木建筑研究所地震工程研究报告集[R]，第二集，科学出版社，1965
[111]屈铁军，地面运动的空间变化特征研究及地下管线地震反应分析[D]，[博士学位论文]，哈尔滨：国家地震局工程力学研究所，1995，81～85，163～167
[112]Kureghian, A.D., Crempien, J., An evolutionary model for earthquake ground motion[J], Structural Safety, 1989, No.6, 235～246
[113]Saragoni, G.R.., Hart. G.C. Simulation of Artificial earthquakes[J], Earthquake Eng. Structure Dynamics, 1974,2(3), 249～267
[114]Harichandrun R. S. , Vanmavcke, E. H., Stochastic variation of earthquake ground motion in space and time[J], ASCE, Vol. 112, No., EM2, 1986,2.
[115]H.Hao. Effects of Spatial Variation of Ground Motions on Large Multiply-Structure[A], Report No. UCB/EERC-89-06[R],1989
[116]王君杰，多点多维地震动随机模型及结构的反应谱分析方法[D]，[博士学位论文]，哈尔滨：国家地震局工程力学研究所，1995，13，20，84，112
[117]N.A.Abrahamson, J.E. Schneider and J.C. Stepp, Empirical Spatial Coherency Function for Application to Soil-Structure Interaction Analyses[J], Earthquake Spectra, Vol. 7, No. 1,1991
[118]C.H.Lob and S.G.Lin, Directionality and Simulation in Spatial Variation of Seismic waves[J], Eng. Struct.Vol.12, No.3, 1990,134～143
[119]C.H.Lob and Y.T.Yeh, Spatial Variation and Stochastic Modelling of Seismic Differential Ground Movement[J], EESD, Vol. 16, No.4,1988
[120]胡聿贤，地震工程学[M]，地震出版社，北京：1988，175～177．
[121]Nafi-Toksoz, M., Dainty, A. M., et al., Spatial Variation of Ground Motion due to Lateral Heterogeneity[J], Structural Safety, Vol. 10, 1991, pp. 53～78.
[122]Tassoulas., J. L., Roesset., J. M., Wave propagation in a rectangular valley[J], Structural Safety, Vol. 10, 1991, pp. 15～26,
[123]Sesma, F. J. S., Rosenblueth, E., Ground motion at Canyon of arbitrary shapes under incident SH wave[J], Int. J, Earthquake Eng. Structural Dyn, Vol. 7, No.5, 1979
[124]Abrahamson, N., Schneider, J. E, Spatial coherency of shear waves from the Lotung, Taiwan large scale seismic Test[J], Structural Safety, Vol. 10, 1991, pp. 145～162
[125]Someville , P, G., et al, Site-specific estimation of spatial incoherent of strong ground
motion[A], Proc. Earthquake Eng. Soil Dyn., Ⅱ[C], ASCE, Park city, UT, 1988.6,pp. 188～202
[126]星谷胜，石井清，栗田博昭，空间·时间分布特性有地震动[J]，土木学会论文报告集，1987，No．386，359～367
[127]Hao, H., C.S.Oliveira and J. Penzien., Multiple station ground motion processing and simulation based on SMART-1 array data[J], Nuclear Engineering and design, Vol. 111, 1989, pp. 293～310.
[128]屈铁军，王前信，空间相关的多点地震动合成(Ⅰ)基本公式[J]，地震工程与工程振动，1998，18(1)，8～15
[129]屈铁军，王前信，空间相关的多点地震动合成(Ⅱ)合成实例[J]，地震工程与工程振动，1998，18(2)，．25～32
[130]夏友柏，王华桥，张尚根，一种合成多点地震动时程的方法[J]，世界地震工程，2002，18(1)，119～122。
[131]屈铁军，王前信，多点地震输入反应分析研究的进展[J]，世界地震工程，1993(1)，
[132]王前信，伍国周，李云林，拱式结构对地震多点输入的反应[J]，地震工程与工程振动，1984，4(2)，49～81
[133]潘旦光，楼梦麟，范立础，多点输入下大跨度结构地震反应分析研究现状[J]。同济大学学报，2002，29(10)
[134]林家浩，任意多相干多激励随机响应[A]，大连理工大学工程力学研究所资料[R]，1990．4
[135]陈健云，林皋，多点输入随机地震动拱坝—地基体系反应分析[J]，世界地震工程，2000，16(3)40～43
[136]邱法维，钱稼茹，多点地震动输入下的拟动力实验方法[J]，地震工程与工程振动，1998，18(2)，38～47
[137]陈厚群，侯顺载，张力飞，朱栗武，拱坝多点输入动力反应试验研究[J]，水利学报，1995(8)，12～19
[138]田景元，刘汉龙，高玉锋，郭作美，状的模糊聚类及其优势方位的确定[J]，华东地质学院学报，
[139]庄表中，王行新编著．随机振动概论[M]．北京：地震出版社，1982，303～306．
[140]田景元，土坝地震多点输入反应[A]。见刘汉龙主编，土动力学与沿途地震工程[C]，北京：中国建筑工业出版社，2002，525～530
[141]朱伯芳，有限单元法原理与应用[M]北京：水利电力出版社，1979
[142]姜弘道，陈和群，有限单元法的程序设计[M]，北京：水利电力出版社，57～58
[143]刘汉龙，土体地震永久变形分析[D]，[博士学位论文]，南京：南京河海大学岩土工程研究所，1994
[144]张克绪，谢君斐，土动力学[M]，北京：地震出版社，1989，91～92
[145]田景元，刘汉龙，陈国兴，周云东，基于剪应力时程极值的损伤值等效转换及其在土石坝多点输入地震反应中的应用[J]，世界地震工程，2003，19(1)，128～135
[146]俞载道，曹国敖，随机振动理论及其应用[M]，上海：同济大学出版社，1988，
[147]徐士良，Fortarn常用算法程序集[M]，北京，清华大学出版社，1997，