挡土墙抗震设计中两个重要问题的研究
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摘要
公路工程在我国国民经济中正在发挥越来越重要的作用。近十几年来，通车里程迅速增加，技术等级大幅度提高，公路桥梁和隧道建设取得显著成果。从国内外大量地震的震害中能够看到，现代公路工程仍然十分脆弱，在地震中容易遭受破坏，影响甚至中断交通，还会给震后救灾工作带来极大困难。公路工程的震害表明，挡土结构的地震破坏，往往是造成道路受损、桥梁破坏的主要原因之一。受各种条件限制，挡土墙的抗震验算，仍普遍采用拟静力法(以下简称静力法)。地震惯性力和地震土压力的确定方法，是目前挡土结构的抗震分析中有待深入研究改进的课题。我国现行《公路工程抗震设计规范》(JTJ 004-89)已使用十多年。在这期间，我国公路工程建设高速增长，科学技术有了长足发展，公路建设的规模大大超过此前。规范的部分内容已落后于时代、落后于地震工程科学技术的发展，不能很好的满足我国的公路工程的建设和发展。为此，迫切需要更新，采用更先进、成熟的理论和方法。结合规范JTJ 004—89的修编，本文在总结已有研究成果的基础上，主要研究了挡土墙和桥台地震惯性力沿高度分布的规律，粘性填土的地震土压力计算和计算公式的简化，以及在公路工程抗震设计规范中将挡土墙和桥台的抗震设计归入一章的问题，具体包括如下5项工作。
1．综合评述国内外公路工程抗震设计规范中地震作用计算方法以及地震土压力计算方法的演进历史及现状，详细分析我国现行公路工程抗震设计规范中挡土墙和桥台的抗震验算方法，指出存在的问题和解决这些问题的必要性。
2．选用针对地震烈度6、7、8、9合成的总共18条地震动时程，选取具有代表性的6个不同高度的挡土墙以及2个不同高度的桥台模型，利用波动有限元法既有程序分析地震反应，研究水平地震加速度沿高度的分布规律。数值结果显示，重力式挡土结构刚度很大，地震加速度反应在水平方向差异很小，可看作是同步的，可取中心线上各点最大加速度来描述静力法中地震作用沿高度的变化规律。在沿墙高度方向，加速度分布不是呈直线变化，比较复杂，总的变化趋势大体一致。从挡墙底部开始，最大地震加速度并不马上随高度的增加而增大，直至高度达到挡墙总高度的1／2—2／3处才开始比较迅速的增加，至项部达到最大值，约为底部的1.1-2.0倍。高挡墙(高度25米)自振周期长，对近处小震放大不明显，除此以外，
中国地震局工程力学研究所硕士学位论文
顶部放大都在14倍以上。放大倍数，随挡墙总高度的增大，呈渐增的趋势，
只有个别的超过1名倍(大于1.9的占2.1%，大于1.8的占35%)。根据这
些规律性的认识，本文建议了两种挡土结构水平地震作用沿相对墙高(高
度与挡墙总高度的比)分布系数，一种折线型、一种曲线型，最大值均取
1 .8。
3.规范JTJ 00牛se-89规定当挡土墙高度大于12米时才考虑加速度沿墙
高的放大效应，可能不够安全。本文计算结果表明，高度高7米、9米的挡
土墙和高度6米、8米的扩大基础桥台的地震加速度反应在顶部也会有约
1，5一1.6倍的放大。为了安全，本文建议改以6米为界限，墙高小于6米的
可以不考虑地震惯性力沿墙高的增大。
4.基于广义库仑基本理论的最近研究成果叫’]，整理、推导了粘性填
土地震主动土压力和被动土压力的计算表达式，得出了考虑填土为粘性土、
填土表面作用均布荷载、填土表面有一定坡度的地震土压力解析解。导出
的计算公式很复杂，应用到实际工程、采纳到规范中，仍有一定难度。在
分析粘性土地震土压力对计算公式中各因素敏感性的基础上，采用厂十。型
思路，部分吸收M一O法的优点，借鉴Seed一Whi加an对M一O公式简化思想，
本文提出了两种简易工程计算式。结合具体算例，将第一种简化算式与国
内外多种计算公式的结果进行了比较，将第二种简化算式与现行水运工程
抗震设计规范的粘性土地震土压力计算式的结果进行了对比，说明了本文
建议公式的适用性和工程应用价值。此外，还简单地讨论了本文方法在一
些复杂问题地震土压力计算中的应用。
5.现行公路工程抗震设计规范中将挡土墙和桥台的验算分放在两章考
虑，分别按各自的公式计算，造成一定的不方便。本文从挡土结构承受地
震作用和地震土压力两个方面分析，强调了这两类结构验算的共性，将挡
土墙和桥台的抗震验算统一了起来，并建议在规范修编中列入一章。
最后，对本文工作进行了总结，并提出了有待今后继续研究的三个问题。
Highway system plays a more and more important role in the national economy. In the past ten odd years, a great progress has been made in highway construction. The total length of road, the length of good quality highway, number of the bridges and tunnels are all increased and increasing remarkably. Seismic damage of highway system caused in strong earthquake worldwide indicated that modern Highway system is still vulnerable, it may be damaged extensively and slow down so much as shut down the local traffic, which always makes big troubles for rescue in a past earthquake situation. The earthquake damage of Highway system shows that the failure of retaining structures is sometimes one of the main causes of road damage and bridge collapse. The pseudo-static method (static method in brief) is now currently adopted in seismic analysis of retaining structures for some well known limitation. The study on seismic inertia and seismic soil pressure is a significant task to be deeply treated with and improved in the s
tatic analysis of retaining structures. The currently used Chinese Earthquake Resistant Design Code for Highway Construction (JTJ 004-89) was issued a dozen years ago. During this period. Highway construction increased very fast in China and the scale was much larger than ever before, while the technology was developed quite great. Some contents of the code now have dropped behind the progress of science and technology and the development of the epoch and can not meet the requirement of the development of highway construction any longer. Therefore the code needs to be updated by some more advanced and mature theories and approaches. On basis of a review of the recent achievements, the distribution of the lateral seismic inertia force along the height of retaining wall and/or bridge abutment, and the calculation of the seismic soil pressure of cohesive backfill are treated with in this paper, for the revision of Chinese Earthquake Resistant Design Code for Highway Construction, and a suggestion to combine sei
smic design of retaining wall and of bridge abutment together into one chapter from the past in two chapters in the previous version is also worked out. The main contents are summarized as follows:
1. The evolution, state of the art and the developing trend of the lateral
seismic inertia force calculation for retaining wall and/or bridge abutment and the calculation of the seismic cohesive backfill soil pressure are reviewed. The approaches of seismic analysis of retaining walls and bridge abutments in the current Highway codes of China are studied in detail and the shortcomings in the analysis procedure and the necessity of further improvements to them are pointed out.
2. Total 18 simulated acceleration time histories for Intensity 6, 7, 8 and 9 are adopted as inputs, 6 typical retaining walls heights and 2 bridge abutments with difference are selected as the structural models of soil-structure system, the seismic responses of the system and the horizontal variation of the maximum response accelerations at different height levels are analyzed by means of a wave propagation finite element program. The numerical results show that the horizontal variation of response acceleration of gravity retaining wall is quite small since its lateral rigidity is large enough, the response at a given height level can be considered as the same, the maximum accelerations at different heights on the central vertical line can describe the distribution of earthquake load along the wall height in static analysis very well. The acceleration changes along the height direction nonlinearly with a little bit complicated pattern, and the changing patterns, in general, are similar. The acceleration does not increase immediately after the wall height is getting taller from the bottom of the retaining wall, and it starts to increase rapidly with the height level at a height of half to two thirds of the total wall height. It gets a maximum amplification value of 1.1 to 2.0 at the top of the wall. The ratios between accel
1．综合评述国内外公路工程抗震设计规范中地震作用计算方法以及地震土压力计算方法的演进历史及现状，详细分析我国现行公路工程抗震设计规范中挡土墙和桥台的抗震验算方法，指出存在的问题和解决这些问题的必要性。
2．选用针对地震烈度6、7、8、9合成的总共18条地震动时程，选取具有代表性的6个不同高度的挡土墙以及2个不同高度的桥台模型，利用波动有限元法既有程序分析地震反应，研究水平地震加速度沿高度的分布规律。数值结果显示，重力式挡土结构刚度很大，地震加速度反应在水平方向差异很小，可看作是同步的，可取中心线上各点最大加速度来描述静力法中地震作用沿高度的变化规律。在沿墙高度方向，加速度分布不是呈直线变化，比较复杂，总的变化趋势大体一致。从挡墙底部开始，最大地震加速度并不马上随高度的增加而增大，直至高度达到挡墙总高度的1／2—2／3处才开始比较迅速的增加，至项部达到最大值，约为底部的1.1-2.0倍。高挡墙(高度25米)自振周期长，对近处小震放大不明显，除此以外，
中国地震局工程力学研究所硕士学位论文
顶部放大都在14倍以上。放大倍数，随挡墙总高度的增大，呈渐增的趋势，
只有个别的超过1名倍(大于1.9的占2.1%，大于1.8的占35%)。根据这
些规律性的认识，本文建议了两种挡土结构水平地震作用沿相对墙高(高
度与挡墙总高度的比)分布系数，一种折线型、一种曲线型，最大值均取
1 .8。
3.规范JTJ 00牛se-89规定当挡土墙高度大于12米时才考虑加速度沿墙
高的放大效应，可能不够安全。本文计算结果表明，高度高7米、9米的挡
土墙和高度6米、8米的扩大基础桥台的地震加速度反应在顶部也会有约
1，5一1.6倍的放大。为了安全，本文建议改以6米为界限，墙高小于6米的
可以不考虑地震惯性力沿墙高的增大。
4.基于广义库仑基本理论的最近研究成果叫’]，整理、推导了粘性填
土地震主动土压力和被动土压力的计算表达式，得出了考虑填土为粘性土、
填土表面作用均布荷载、填土表面有一定坡度的地震土压力解析解。导出
的计算公式很复杂，应用到实际工程、采纳到规范中，仍有一定难度。在
分析粘性土地震土压力对计算公式中各因素敏感性的基础上，采用厂十。型
思路，部分吸收M一O法的优点，借鉴Seed一Whi加an对M一O公式简化思想，
本文提出了两种简易工程计算式。结合具体算例，将第一种简化算式与国
内外多种计算公式的结果进行了比较，将第二种简化算式与现行水运工程
抗震设计规范的粘性土地震土压力计算式的结果进行了对比，说明了本文
建议公式的适用性和工程应用价值。此外，还简单地讨论了本文方法在一
些复杂问题地震土压力计算中的应用。
5.现行公路工程抗震设计规范中将挡土墙和桥台的验算分放在两章考
虑，分别按各自的公式计算，造成一定的不方便。本文从挡土结构承受地
震作用和地震土压力两个方面分析，强调了这两类结构验算的共性，将挡
土墙和桥台的抗震验算统一了起来，并建议在规范修编中列入一章。
最后，对本文工作进行了总结，并提出了有待今后继续研究的三个问题。
Highway system plays a more and more important role in the national economy. In the past ten odd years, a great progress has been made in highway construction. The total length of road, the length of good quality highway, number of the bridges and tunnels are all increased and increasing remarkably. Seismic damage of highway system caused in strong earthquake worldwide indicated that modern Highway system is still vulnerable, it may be damaged extensively and slow down so much as shut down the local traffic, which always makes big troubles for rescue in a past earthquake situation. The earthquake damage of Highway system shows that the failure of retaining structures is sometimes one of the main causes of road damage and bridge collapse. The pseudo-static method (static method in brief) is now currently adopted in seismic analysis of retaining structures for some well known limitation. The study on seismic inertia and seismic soil pressure is a significant task to be deeply treated with and improved in the s
tatic analysis of retaining structures. The currently used Chinese Earthquake Resistant Design Code for Highway Construction (JTJ 004-89) was issued a dozen years ago. During this period. Highway construction increased very fast in China and the scale was much larger than ever before, while the technology was developed quite great. Some contents of the code now have dropped behind the progress of science and technology and the development of the epoch and can not meet the requirement of the development of highway construction any longer. Therefore the code needs to be updated by some more advanced and mature theories and approaches. On basis of a review of the recent achievements, the distribution of the lateral seismic inertia force along the height of retaining wall and/or bridge abutment, and the calculation of the seismic soil pressure of cohesive backfill are treated with in this paper, for the revision of Chinese Earthquake Resistant Design Code for Highway Construction, and a suggestion to combine sei
smic design of retaining wall and of bridge abutment together into one chapter from the past in two chapters in the previous version is also worked out. The main contents are summarized as follows:
1. The evolution, state of the art and the developing trend of the lateral
seismic inertia force calculation for retaining wall and/or bridge abutment and the calculation of the seismic cohesive backfill soil pressure are reviewed. The approaches of seismic analysis of retaining walls and bridge abutments in the current Highway codes of China are studied in detail and the shortcomings in the analysis procedure and the necessity of further improvements to them are pointed out.
2. Total 18 simulated acceleration time histories for Intensity 6, 7, 8 and 9 are adopted as inputs, 6 typical retaining walls heights and 2 bridge abutments with difference are selected as the structural models of soil-structure system, the seismic responses of the system and the horizontal variation of the maximum response accelerations at different height levels are analyzed by means of a wave propagation finite element program. The numerical results show that the horizontal variation of response acceleration of gravity retaining wall is quite small since its lateral rigidity is large enough, the response at a given height level can be considered as the same, the maximum accelerations at different heights on the central vertical line can describe the distribution of earthquake load along the wall height in static analysis very well. The acceleration changes along the height direction nonlinearly with a little bit complicated pattern, and the changing patterns, in general, are similar. The acceleration does not increase immediately after the wall height is getting taller from the bottom of the retaining wall, and it starts to increase rapidly with the height level at a height of half to two thirds of the total wall height. It gets a maximum amplification value of 1.1 to 2.0 at the top of the wall. The ratios between accel
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[50]张徽正，九二一地震地质调查报告，经济部‘中央’地质调查所，2000
[51]张克绪、谢君斐，土动力学．地震出版社，1989
[52]赵恒惠，挡土墙后粘性土填土的土压力计算，岩土工程学报，1983，第5卷，第1期
[53]赵振东，地震灾害与防御，中国地震工程力学研究所研究生参考教材(试行稿)，2001
[54]中国地震局检测预报司，中国大陆地震灾害损失评估汇编(1996～2000)，地震出版社，2001
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[62]周正华，地基土介质阻尼和辐射阻尼的数值模拟，工学博士学位论文，中过地震局工程力学研究所，2000
[63]朱大勇、钱七虎、姜弘道，挡土结构中土体被动临界滑动场及被动土压力的数值计算，2000，第11期
[64] Abdul-Hamid Soubra, Borut.Macuh, Active and passive earth pressure coefficients by a kinematical approach, Geotechnical Engineering 155, April 2002, Issue 2, 119-131
[65] AbduI-Hamid Soubra, Member, ASCE, and Pierre Regenass, Three-dimensional passive earth pressures by Kinematical approach, Journal of geotechnieal and geoenvironmental engineering, ASCE, November 2000, 969-978
[66] Adel M Bekal, K.P George, Finite element analysis of reinforced retaining walls subjected to seismic loading, 12WCEE 2000,0842
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[68] A.L.Simonelli, C.Viggiani, Some remarks on retaining wall design under conditions, Earthuake Engineering, Tenth World Conference, 1992,1665-1670
[69] Anestis S.Veletsos, Member, ASCE, and Adel H.Youman, Associate, ASCE, Dynamic response of cantilever retaining walls, ASCE, February 1997 161-172
[70] Azm S.Al-Homoud, Robert V.Whitman, Evaluating tilt of gravity retaining walls during earthquakes, Earthuake Engineering, Tenth World Conference, 1992, 16831688
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[74] Farrokh Nadim, A.M.ASCE, Robert V.Whitman, F, ASCE, Seismically induced movement of retaining walls, Journal of Geotechnical engineering, Vol.109, No.7, July 1983, 915-931
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[76] Hagop N.Nazarian, Asadour H.Hadjian, Members, ASCE, Earthquake-induce lateral soil pressures on structures, Journal of the geotechnical engineering division, ASCE, September 1979,1049-1066
[77] Mikio Futaki, Osamu Sakaguchi, Behavior of the cantilever retaining wall under seismic loadings, Earthuake Engineering, Tenth World Conference, 1992,1667-1682
[78] M.M.Dewoolkar, A.T.Stadler, S.N.Batiste, H.Y.Ko, R.Y.S.Pak, Dynamic centrifuge experiment on a cantilever retaining wall, Third International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics April 2-7, 1995, 1 Vol.Ⅲ, St.Louis, Missouri, Paper No.2.14, 1117-1121
[79] Ramiro A Sofrronie, Colin A Taylor, Paul G Greening, Seismic resistant retaining walls reinforced soil, 12WCEE 2000, 2029
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[81] Shamsher Prakash, Yingwei Wu, Eyjolfur Arni Rafnsson, On seismic design displacements of rigid retaining walls, Third International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, April 2-7, 1995, Vol. Ⅲ, St.Louis, Missouri, Paper No.4.19, 1183-1192
[82] S.P.G.Madabhushi, X.Zeng, Associate Member, ASCE, Seismic response of gravity quay walls. □: centrifuge modeling, Journal of geoteehnical and geoenvironmental engineering, ASCE, may 1998, 418-427
[83] V.silvestri, Ashok K.Chugh, D.R.Phatak, Lateral earth pressure problem of cohesive backfill with inclined surface, Journal of geotechnical and geoenvironmental engineering, ASCE, June 1999, 536-538
[84] W.D.Liam, Guoxi Wu, N.Yoshida, Seismic response of sbeet pile walls, Earthuake Engineering, Tenth World Conference, 1992, 1689-1694
[85] X.Zeng, Associate member, ASCE, and R.S.Steedman, Rotating block method for seismic displacement of gravity walls, Journal of geoteclmical and geoenvironmental engineering, ASCE,August 2000, 709-717
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[87] Yingwei WU, Shamsher Prakash, Seismic displacements of rigid retaining walls on submergence.
12WCEE 2000, 0562
[88] Yung-Show Fang. Ying-Chieh Ho. Tsang-Jiang Chen, Passive earth pressure with critical state concept. Journal of geotechnical and geoenvironmental engineering, ASCE, August 2002. 651-659
[89] Z.H.Mazindrani, M.H.Ganjali. Lateral earth pressure problem of cohesive with inclined suuface. Journal of geotechnical and geoenvironmental engineering, ASCE, February 1997,110-112
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[49]岳祖润、彭胤宗、张师德，压实粘性填土挡土墙土压力离心模型试验，岩土工程学报，1992，第14卷，第6期
[50]张徽正，九二一地震地质调查报告，经济部‘中央’地质调查所，2000
[51]张克绪、谢君斐，土动力学．地震出版社，1989
[52]赵恒惠，挡土墙后粘性土填土的土压力计算，岩土工程学报，1983，第5卷，第1期
[53]赵振东，地震灾害与防御，中国地震工程力学研究所研究生参考教材(试行稿)，2001
[54]中国地震局检测预报司，中国大陆地震灾害损失评估汇编(1996～2000)，地震出版社，2001
[55]中国赴日地震考察团，日本阪神大地震考察，地震出版社，1995，
[56]中华人民共和国电力行业标准，水工建筑物抗震设计规范(DL 5073-2000)，中国电力出版社，2001
[57]中华人民共和国国家标准，建筑抗震设计规范(GB 50011-2001)，中国建筑工业出版社，2001
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[61]周应英、任美龙，刚性挡土墙主动土压力的实验研究，岩土工程学报，1990，第12卷，第2期
[62]周正华，地基土介质阻尼和辐射阻尼的数值模拟，工学博士学位论文，中过地震局工程力学研究所，2000
[63]朱大勇、钱七虎、姜弘道，挡土结构中土体被动临界滑动场及被动土压力的数值计算，2000，第11期
[64] Abdul-Hamid Soubra, Borut.Macuh, Active and passive earth pressure coefficients by a kinematical approach, Geotechnical Engineering 155, April 2002, Issue 2, 119-131
[65] AbduI-Hamid Soubra, Member, ASCE, and Pierre Regenass, Three-dimensional passive earth pressures by Kinematical approach, Journal of geotechnieal and geoenvironmental engineering, ASCE, November 2000, 969-978
[66] Adel M Bekal, K.P George, Finite element analysis of reinforced retaining walls subjected to seismic loading, 12WCEE 2000,0842
[67] Ahmed-W.M.Elgamal, Sreenivas Alampalli, Earthquake response of retaining walls: Full scale testing and computational analysis, Earthuake Engineering, Tenth World Conference, 1992,1671-1676
[68] A.L.Simonelli, C.Viggiani, Some remarks on retaining wall design under conditions, Earthuake Engineering, Tenth World Conference, 1992,1665-1670
[69] Anestis S.Veletsos, Member, ASCE, and Adel H.Youman, Associate, ASCE, Dynamic response of cantilever retaining walls, ASCE, February 1997 161-172
[70] Azm S.Al-Homoud, Robert V.Whitman, Evaluating tilt of gravity retaining walls during earthquakes, Earthuake Engineering, Tenth World Conference, 1992, 16831688
[71] Ernesto Cascone, Simone Lo Grasso, Michele Maugeri, Dynamic dodel tests on L-shaped gravity retaining wails, 12WCEE 2000, 2445
[72] Farhang Ostadan, Willian H.White, Lateral seismic soil pressure an updated approach, US-Japan SSI Workshop, September 22-23, 1998
[73] Forrokh Nadim, S.Ihara, A.Pecker, E.A.Pafnsson, General report-session Ⅳ dynamic earth pressures and design of earth retaining structures, Third International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, April 2-7, 1995, Vol. Ⅲ, St.Louis, Missouri, 1193-1196
[74] Farrokh Nadim, A.M.ASCE, Robert V.Whitman, F, ASCE, Seismically induced movement of retaining walls, Journal of Geotechnical engineering, Vol.109, No.7, July 1983, 915-931
[75] Gregory N.Richardson, A.MASCE, Kkenneth L.Lee, M.ACES, Seismic design of reinforced earth walls, Jouranal of the geoteshnical engineering division, Vol. 101, No.GT2, February 1975, 167-189
[76] Hagop N.Nazarian, Asadour H.Hadjian, Members, ASCE, Earthquake-induce lateral soil pressures on structures, Journal of the geotechnical engineering division, ASCE, September 1979,1049-1066
[77] Mikio Futaki, Osamu Sakaguchi, Behavior of the cantilever retaining wall under seismic loadings, Earthuake Engineering, Tenth World Conference, 1992,1667-1682
[78] M.M.Dewoolkar, A.T.Stadler, S.N.Batiste, H.Y.Ko, R.Y.S.Pak, Dynamic centrifuge experiment on a cantilever retaining wall, Third International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics April 2-7, 1995, 1 Vol.Ⅲ, St.Louis, Missouri, Paper No.2.14, 1117-1121
[79] Ramiro A Sofrronie, Colin A Taylor, Paul G Greening, Seismic resistant retaining walls reinforced soil, 12WCEE 2000, 2029
[80] R.V.Whitman, Seismic design of earth retaining structures(state of the art paper), Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, March 11-15. 1991, St.Louis, Missouri, Paper No.SOA6, 1767-1778
[81] Shamsher Prakash, Yingwei Wu, Eyjolfur Arni Rafnsson, On seismic design displacements of rigid retaining walls, Third International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, April 2-7, 1995, Vol. Ⅲ, St.Louis, Missouri, Paper No.4.19, 1183-1192
[82] S.P.G.Madabhushi, X.Zeng, Associate Member, ASCE, Seismic response of gravity quay walls. □: centrifuge modeling, Journal of geoteehnical and geoenvironmental engineering, ASCE, may 1998, 418-427
[83] V.silvestri, Ashok K.Chugh, D.R.Phatak, Lateral earth pressure problem of cohesive backfill with inclined surface, Journal of geotechnical and geoenvironmental engineering, ASCE, June 1999, 536-538
[84] W.D.Liam, Guoxi Wu, N.Yoshida, Seismic response of sbeet pile walls, Earthuake Engineering, Tenth World Conference, 1992, 1689-1694
[85] X.Zeng, Associate member, ASCE, and R.S.Steedman, Rotating block method for seismic displacement of gravity walls, Journal of geoteclmical and geoenvironmental engineering, ASCE,August 2000, 709-717
[86] X.Zeng, Associate Member, ASCE, Seismic response of gravity quay walls. Ⅰ: centrifuge modeling, Journal of geotechnical and geoenvironmental engineering, ASCE, may 1999, 406-417
[87] Yingwei WU, Shamsher Prakash, Seismic displacements of rigid retaining walls on submergence.
12WCEE 2000, 0562
[88] Yung-Show Fang. Ying-Chieh Ho. Tsang-Jiang Chen, Passive earth pressure with critical state concept. Journal of geotechnical and geoenvironmental engineering, ASCE, August 2002. 651-659
[89] Z.H.Mazindrani, M.H.Ganjali. Lateral earth pressure problem of cohesive with inclined suuface. Journal of geotechnical and geoenvironmental engineering, ASCE, February 1997,110-112