基于渗流与应力耦合的防渗墙与坝体相互作用研究
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摘要
在国内大规模实施的土石坝除险加固工程建设中，封闭式坝体混凝土防渗墙得到了大量应用。由于土体固结影响及所承受的荷载形式不同，封闭式坝体防渗墙的承载性状及其与坝体的相互作用规律，与一般土石围堰中的堰体防渗墙或深厚覆盖层中的坝基防渗墙均有明显区别。目前针对土石坝加固工程中增建封闭式坝体防渗墙的情况，关于墙体应力变形及其对坝坡稳定影响的研究很少。此外，关于防渗墙与坝体相互作用的研究方法方面，很少有考虑渗流与应力耦合作用的研究。然而土石坝中存在典型的流固耦合作用，考虑渗流与应力耦合是防渗墙与土石坝相互作用研究方法进一步发展的必然要求。
针对上述问题，本文以土石坝加固工程中增建的封闭式坝体防渗墙为研究对象，通过全面分析土石坝加固工程中增建混凝土防渗墙的实际工程条件，建立了同时考虑墙-土接触、渗流与应力耦合共同作用的耦合数值模型。在系统研究防渗墙与坝体相互作用机理的基础上，探讨混凝土防渗墙在不同工程条件下的承载性状、适用性及其对坝坡稳定的影响。本文研究成果对于土石坝加固工程中合理、安全、经济地进行应用混凝土防渗墙具有重要意义，主要研究成果和结论如下。
首次针对土石坝加固工程中增建封闭式坝体防渗墙的情况，提出了防渗墙与坝体相互作用的耦合数值模拟方法，实现了同时考虑墙-土接触、渗流与应力耦合共同作用的模拟，并通过典型算例对数值模拟结果进行了验证。通过对比分析是否考虑渗流与应力耦合作用对防渗墙应力、坝体应力场和渗流场的影响，说明简单忽略渗流与应力耦合作用会导致墙体应力计算结果明显偏小。
基于渗流与应力耦合计算，系统研究了混凝土防渗墙与坝体相互作用机理与规律，并在此基础上进一步分析了封闭式坝体混凝土防渗墙在不同工程条件下的承载性状及其适用性。正常蓄水工况下，封闭式坝体防渗墙主要承受墙体前后水头差引起的水平荷载作用。刚性混凝土墙以拉应力作用为主，且最大拉应力较大，而塑性混凝土墙则整体处于受压状态。不同坝体填筑材料、坝基透水性能及基岩强度等因素对刚性混凝土墙的应力影响明显，而对塑性混凝土墙的应力影响则相对较小。
通过对增建防渗墙前后坝体应力场和渗流场变化的分析，系统研究了增建混凝土防渗墙对土石坝上、下游坝坡稳定的影响。建设防渗墙后，下游坝坡稳定安全系数增加，而上游坝坡的稳定安全系数则有所降低。
The closed cut-off wall was widely used in the reinforcement projects ofearth-rock dam. As the influences of consolidation and the load-type were different,the bearing characteristics of closed cut-off wall and the interaction law between thedam and wall were quite different compared with the wall in the cofferdam or in thedeep covering layer. At present, researches on the stress-strain of the wall and itsinfluences on slope stability were very few when building closed cut-off wall in thereinforcement works of earth-rock dam. Beyond this, seepage-stress coupling wasrarely considered in the research on the interaction between the dam and wall.However, seepage-stress coupling definitely existed in the earth-rock dam. Theseepage-stress coupling should be considered in the study with the furtherdevelopment of the study on interaction between the dam and wall.
According the above problems, the closed cut-off wall built in the reinforcementproject of earth-rock dam was selected as the study object in this paper. Bycomprehensively analyzing the project conditions of building cut-off wall in theearth-rock dam, the numerical model was established. The contacts of wall-damtogether with the coupling of seepage-stress were taken into account in the model.Based on the systematic study of the interaction between the wall and dam, thebearing characteristics, applicability of the cut-off wall and its influences on slopestability were discussed. The research achievements of this paper can be useful inbuilding a scientific, safety and economical cut-off wall. The main achievements andresults are as follows.
For the situation of building closed cut-off wall in the earth-rock dam, thenumerical simulation method of modeling the interaction of the wall and dam wasproposed. The wall-dam coupling and seepage-stress coupling were considered in themodel, and the results of the numerical modeling were verified by a typical theoreticalformula calculation. According to the comparative analysis, the wall stress wasobviously smaller when the seepage-stress coupling effect was ignored.
Basing on the calculation of seepage-stress coupling, the mechanisms and therules of the interaction between the cut-off wall and the dam were systematicallyresearched, the bearing characteristics and availability of the closed cut-off wall underdifferent conditions was also analyzed. In the condition of normal storage level, theclosed cut-off wall was mainly bearing the horizontal stress which was caused by thehydraulic head of upstream and downstream. The rigid concrete cut-off wall was mainly bearing tensile stress, while the plastic concrete cut-off wall bearing completepressure stress. The stress of the rigid concrete cut-off wall was obviously influencedby the dam material, seepage characteristics and strength of bed rock while the stressof the plastic wall was rarely influenced.
According to the changes of the stress field and the seepage field when buildinga cut-off wall, the affect of the cut-off wall on the slope stability was systematicallyresearched. The stability safety factor of downstream slope increased while theupstream slope decreased after building a cut-off wall.
针对上述问题，本文以土石坝加固工程中增建的封闭式坝体防渗墙为研究对象，通过全面分析土石坝加固工程中增建混凝土防渗墙的实际工程条件，建立了同时考虑墙-土接触、渗流与应力耦合共同作用的耦合数值模型。在系统研究防渗墙与坝体相互作用机理的基础上，探讨混凝土防渗墙在不同工程条件下的承载性状、适用性及其对坝坡稳定的影响。本文研究成果对于土石坝加固工程中合理、安全、经济地进行应用混凝土防渗墙具有重要意义，主要研究成果和结论如下。
首次针对土石坝加固工程中增建封闭式坝体防渗墙的情况，提出了防渗墙与坝体相互作用的耦合数值模拟方法，实现了同时考虑墙-土接触、渗流与应力耦合共同作用的模拟，并通过典型算例对数值模拟结果进行了验证。通过对比分析是否考虑渗流与应力耦合作用对防渗墙应力、坝体应力场和渗流场的影响，说明简单忽略渗流与应力耦合作用会导致墙体应力计算结果明显偏小。
基于渗流与应力耦合计算，系统研究了混凝土防渗墙与坝体相互作用机理与规律，并在此基础上进一步分析了封闭式坝体混凝土防渗墙在不同工程条件下的承载性状及其适用性。正常蓄水工况下，封闭式坝体防渗墙主要承受墙体前后水头差引起的水平荷载作用。刚性混凝土墙以拉应力作用为主，且最大拉应力较大，而塑性混凝土墙则整体处于受压状态。不同坝体填筑材料、坝基透水性能及基岩强度等因素对刚性混凝土墙的应力影响明显，而对塑性混凝土墙的应力影响则相对较小。
通过对增建防渗墙前后坝体应力场和渗流场变化的分析，系统研究了增建混凝土防渗墙对土石坝上、下游坝坡稳定的影响。建设防渗墙后，下游坝坡稳定安全系数增加，而上游坝坡的稳定安全系数则有所降低。
The closed cut-off wall was widely used in the reinforcement projects ofearth-rock dam. As the influences of consolidation and the load-type were different,the bearing characteristics of closed cut-off wall and the interaction law between thedam and wall were quite different compared with the wall in the cofferdam or in thedeep covering layer. At present, researches on the stress-strain of the wall and itsinfluences on slope stability were very few when building closed cut-off wall in thereinforcement works of earth-rock dam. Beyond this, seepage-stress coupling wasrarely considered in the research on the interaction between the dam and wall.However, seepage-stress coupling definitely existed in the earth-rock dam. Theseepage-stress coupling should be considered in the study with the furtherdevelopment of the study on interaction between the dam and wall.
According the above problems, the closed cut-off wall built in the reinforcementproject of earth-rock dam was selected as the study object in this paper. Bycomprehensively analyzing the project conditions of building cut-off wall in theearth-rock dam, the numerical model was established. The contacts of wall-damtogether with the coupling of seepage-stress were taken into account in the model.Based on the systematic study of the interaction between the wall and dam, thebearing characteristics, applicability of the cut-off wall and its influences on slopestability were discussed. The research achievements of this paper can be useful inbuilding a scientific, safety and economical cut-off wall. The main achievements andresults are as follows.
For the situation of building closed cut-off wall in the earth-rock dam, thenumerical simulation method of modeling the interaction of the wall and dam wasproposed. The wall-dam coupling and seepage-stress coupling were considered in themodel, and the results of the numerical modeling were verified by a typical theoreticalformula calculation. According to the comparative analysis, the wall stress wasobviously smaller when the seepage-stress coupling effect was ignored.
Basing on the calculation of seepage-stress coupling, the mechanisms and therules of the interaction between the cut-off wall and the dam were systematicallyresearched, the bearing characteristics and availability of the closed cut-off wall underdifferent conditions was also analyzed. In the condition of normal storage level, theclosed cut-off wall was mainly bearing the horizontal stress which was caused by thehydraulic head of upstream and downstream. The rigid concrete cut-off wall was mainly bearing tensile stress, while the plastic concrete cut-off wall bearing completepressure stress. The stress of the rigid concrete cut-off wall was obviously influencedby the dam material, seepage characteristics and strength of bed rock while the stressof the plastic wall was rarely influenced.
According to the changes of the stress field and the seepage field when buildinga cut-off wall, the affect of the cut-off wall on the slope stability was systematicallyresearched. The stability safety factor of downstream slope increased while theupstream slope decreased after building a cut-off wall.
引文
[1]王清友，孙万功，熊欢.塑性混凝土防渗墙[M].北京:中国水利水电出版社,2008.
[2]沈珠江,左元明.三峡工程二期混凝土防渗墙围堰初步设计方案的应力应变计算[J].长江科学院院报.1987(3):31-37.
[3] Oscar Dascal.Behaviour of the Manicouagan3cutoff[J]. Canadian GeotechnicalJournal.1979,11(1).
[4]王旭芳，郑旭荣，杨春鸣.土石坝渗流研究进展[J].山西建筑.2008.34（31）：25-26.
[5] Westergaard H M. Water pressures on dams during earthquakes[J]. Trans Amer.Soc Civ. Eng.,98(1933):418-433.
[6]居荣初，曾心传.弹性结构与液体的耦联振动理论[M].地震出版社，1983.
[7] Terzaghi K. Theoretical soil mechanics[M]. Wiley, New York,1943.
[8] Biot M A. General theory of three dimensional consolidation [J]. J. App l. Phys.1941,12:155～164.
[9] Biot M A. General solution of the equation of elasticity and consolidation for aporous material[J]. J. App l. M ech.1956,78:91～96.
[10] Biot M A. Theory of elasticity and consolidation for a porous anisotropic solid[J]. J. App l. Phys.1954,26:182.
[11] Biot M A. Mechanics of deformation and acoustic propagation in porousmedia[J]. J. App l. Phys.1962,33:1482.
[12] Lubinski A. Theory of elasticity for porous bodies displaying a strong porestructure[J]. Proc.2nd U. S. National Congress of Applied Mechanics.1954:247～256.
[13] Geertsman J. A remark on the analogy between thermo-elasticity and theelasticity of saturated porous media[J]. J. Mech. Phys. solids,1957,6:13～16.
[14] Zienkiewicz O C and Shiomi T. Dynamic behaviour of saturated porous media:the generalized Biot formulation and its numerical solution [J]. Int. J. Num.and Analy. Meth. in Geomech.1984,8:71～96.
[15] Oda. M. Permeability tensor for discontinuous rock masses. Geotechnique.1985(4)
[16] Noorlshad J. Coupled thermal-hydraulic-mechanical phenomena In saturatedFractured porous. Numberical approach. J. Geoph. Res.1989(B12)
[17] Savage W Z and Bradock W A. A model for hydro static consolidation of pierreshale[J]. Int. J. Rock M ech. M in.Sci.&Geomech. A bstr.1991,28:345～354.
[18] ZIENKIEWICZ O C, CHAN A H C, PASTOR M, et al. Static and dynamicbehaviour of soils: a rational approach to quantitative solutions(Ⅰ). Fullysaturated problem[C]//Proceedings of the Royal society of London.[S. l.]:[s.n.],1990:285-309.
[19] ZIENKIEWICZ O C, XIE Y M, SCHREFLER B A, et al. Static and dynamicbehaviour of soils: a rational approach to quantitative solutions(Ⅱ).Semisaturated problems[C]//Proceedings of the Royal society of London.[S.l.]:[s. n.],1990:311-321.
[20] LI X K, ZIENKIEWICZ O C, XIE Y. A numerical model for immiscibletwo-phase fluid flow in a porous medium and its time domain solution[J].International Journal for Numerical Methods in Engineering,1990,30(6):1195-1212.
[21] Schreer B A, Zhan X. A fully coupled model for water flow and air flow indeformable porous media[J]. Water Resources Research,1993,29:155-167.
[22] Fredlund, Rahardjo. Soil mechanics for unsaturated soils[M]. New York:Willey and Sons inc,1993.
[23] OLIVELLA S, CARRERA J, GENS A. et al. Non-isothermal multiphase flowof brine and gas through saline media[J]. Transport in Porous Media,1994,15:271-293
[24] Thomas H R, He Y. Analysis of coupled heat moisture and air flow in adeformable unsaturated soil[J]. Geotechnique,1995,45(4):677-689.
[25]李培超，孔祥言，卢德唐.饱和多孔介质流固耦合渗流的数学模型[J].水动力学研究与进展A辑，2003(4):419-426.
[26] Bolzon G, Schreer B A. Zienkiewicz O C. Elastoplastic soil constitutive lawsgeneralized to partially saturated states[J]. Geotechnique,1996,46:279-289.
[27]褚卫江，徐卫亚，苏静波.变形多孔介质流固耦合模型及数值模拟研究[J].工程力学，2007,24（9）:0056-0064.
[28]殷宗泽，凌华.非饱和土一维固结简化计算[J].岩土工程学报，2007，29(5):633-637.
[29]殷宗泽.土工原理[M].北京:中国水利水电出版社，2007:354-364.
[30]曹雪山，殷宗泽.非饱和土二维固结简化计算的研究[J].岩土力学，2009，30(9):2575-2580.
[31] Sandu R. S, Wilson E. L. Finite element analysis of seepage in elasticmedia[J].J.Eng.Mesh.Div.ASCE.1969,95(3):641-652.
[32] Christian John T，Boehmer Jan Willem. Plane strain consolidation by finiteelements[J]. J. Soil Mech. Founmd. Div. ASCE，1970，96(4)：1435～1457
[33]沈珠江.用有限单元法计算软土地基的固结变形[J].水利水运科技情报，1977，（1）:7-23.
[34]张洪武,钟万勰,钱令希.土体固结分析的一种有效算法[J].计算结构力学及其应用,1991,8(4):389.
[35]张洪武,钟万勰,钱令希.饱和土壤固结分析的算法研究[J].力学与实践,1993,15(1):20～22.
[36]王媛.多孔介质渗流与应力的耦合计算方法[J].工程勘察，1995(2):33-37.
[37]杨林德，杨志锡.各向异性饱和土体的渗流耦合分析和数值模拟[J].岩石力学与工程学报.2002，21(10):1447-1451.
[38]陈庆中，冯星梅.应力场、渗流场、流场耦合系统定边值定初值问题的变分原理[J].岩石力学与工程学报，1999，18(5):550-553.
[39]陈庆中，张弥，冯星梅.应力场、渗流场、流场耦合系统问题[J].工程力学，2000，17(6):53-58.
[40]陈庆中，张弥，冯星梅.对Biot固结方程的再认识[J].工程力学，2001，18(6):124-133.
[41]罗晓辉.深基坑开挖渗流与应力耦合分析[J].工程勘察，1996(6)：37～41.
[42]柴军瑞，仵彦卿.均质土坝渗流场与应力场耦合分析的数学模型[J].陕西水力发电，1997，13（3）：4-7.
[43]王晓鸿，仵彦卿.渗流场-应力场耦合分析.[J].勘察科学技术，1998，（4）：3-6.
[44]刘建军，耿万东.地下水渗流的流固耦合理论及数值方法[J].勘察科学技术.2000(4):7-10.
[45]李锡夔,朴光虎,邓子辰.考虑固结效应的结构—土壤相互作用分析及其有限元解[J].计算结构力学及其应用,1990,7(3):1～11.
[46]平扬，白世伟，徐燕萍.深基坑工程渗流一应力耦合分析数值模拟研究[J].岩土力学，200122(1):37-41.
[47]徐则民，黄润秋，许模等.基于水-力耦合理论超深隧道围岩渗透性预测[J].成都理工学院学报，2001，28(2)：130-134.
[48]毛昶熙，李吉庆，段祥宝.渗流作用下土坡圆弧滑动有限元计算[J].岩土工程学报，2001，23(6):746-752.
[49]柴军瑞，李守义.大柳树水利枢纽坝区渗流场与应力场耦合分析[J].岩石力学与工程学报.2002,21(s2):2322-2325.
[50]柴军瑞，李守义.三峡库区泄滩滑坡渗流场与应力场耦合分析[J].岩石力学与工程学报，2004（8）:1280-1284.
[51]张玉军.饱和-非饱和介质水-应力耦合的研究[J].岩石力学与工程学报，2005，24(17):3045-3051.
[52]张玉军.热-水-应力耦合弹塑性二维有限元程序的开发与应用尝试[J].岩土力学,2005,26(2):169-174.
[53]张玉军.核废料处置概念库近场热-水-应力耦合二维有限元模拟[J].岩土工程学报,2006,28(9):1053-1058.
[54]张玉军.热-水-应力耦合条件下三项因素对核素迁移影响的有限元分析[J].岩土力学,2008,29(10):1599-2605.
[55]张玉军，张维庆.双重孔隙介质THMM耦合模型及其有限元分析[J].力学学报,2010,42(4):660-669.
[56]江益敏，陈页开，韩大建等.降雨入渗对边坡稳定影响的实例分析[J].岩石力学与工程学报.2004,23(6):920-924.
[57]周家文，徐卫亚，邓俊晔等.降雨入渗条件下边坡的稳定性分析[J].水利学报.2008,39(9):1066-1073.
[58]张芳枝，陈晓平.非饱和堤岸的渗流特征及其稳定性研究[J].岩土力学，2011,32（5）:1561-1567.
[59] Swift G. W. and kiel O. G.: The Predietion of Gas well performance includingthe effect of Non-Darcy flow，J. Pet. Tech. July.1961,791-798, Trans AIMEVol225.
[60] Rowan G, Clegg M W. An Approximate Method for Non-Darcy Radial GasFlow, AIME,1964,?96.
[61] Dranchuk P. M. and Flores J. Non-Darey Transient Radial gas Flow ThroughPorous media. SPEJ. apr.1975.
[62] Holditch S. A. and Morse S. A. The Effects on Non-Darcy Flow on theBehavior of Hydraulically Fractured Gas well. J. P. T. Oct.1976:1169-1179.
[63] Guppy K. H. Non-Darcy Flow in wells with a Finite Conductivity VerticalFracture，Ph. D. Dissertation. Stanford University, June.1980.
[64] K. H Guppy, Heber Cinco-Ley, and Henry J. Ramey Jr. Effect of Non-DareyFlow on the Constant Pressure Production of Fractured Wells. SPEJ Vol21No3. June,1981.
[65]孟宪麒.狭槽渗流模型试验的若干经验介绍[J].中国水利.1957(9):45-53.
[66]毛昶熙.三向电拟试验与渗流研究，南京水利科学研究所.1963.
[67]毛昶熙,李祖贻.渗流三向电拟试验的电解液模型，水利水运科学研究.1981（3）:1-15.
[68]速宝玉，赵坚，张祝添等.正置模型在尾矿坝空间渗流场电模拟试验中的应用[J].金属矿山.1994,213(3):27-29.
[69]刘昌军，丁留谦，吴梦喜等.双层堤基管涌溃堤砂槽模型试验及渗流场特点研究[J].水利水电技术.2007,38(2):40-43.
[70]陈壁宏.单刺墙边墩对称连接段渗流计算解析解法与数值解法[J].华北水利水电.1985(9):14-19.
[71]吴昌瑜.解析元素法及其在水工渗流问题中的应用研究[J].长江科学院院报.1990(2):65-72.
[72]童磊,谢康和,卢萌盟等.半无限含水层中带衬砌隧洞渗流解析研究[J].岩土力学.2011,32(1):304-308.
[73]毛昶熙.水工渗流发展与坝工建设[J].人民长江,1986(12):32-39.
[74]李思慎,谢红.丹江口左联土石坝渗流问题研究[J].水利水电技术.1994(7):57-61.
[75]任大春,吴昌瑜,朱国胜.三峡二期围堰饱和-非饱和渗流分析.长江科学院院报.1997,14(2):44-47.
[76] Chapuis R P. Controlling the quality of groundwater parameters: someexamples[J].Canadian Geotechnical Journal,2001(32):172-177.
[77] Robert P, Chapuis, Djaouida Chenaf. A user’s approach to assess numericalcodes for saturated and unsat-urated seepage conditions[J]. CanadianGeotechnical Journal,2001,38:1113-1126.
[78]毛昶熙,段祥宝,蔡金榜等.堤防非稳定渗流几个关键值的经验公式[J].水利学报.2004(1):52-56.
[79]沈振中,张鑫,陆希等.西藏老虎嘴水电站左岸渗流控制优化[J].水利学报.2006,37(10):1230-1234.
[80]任杰，沈振中，王谊等.哈达山水利枢纽右岸三维渗流场特性研究[J].水利水运工程学报.2010(3):89-94.
[81]段伟，骆原，陈珂等.黄壁庄水库副坝渗流及防渗墙应力分析[J].水利水电技术.2011,33(5):124-127.
[82]郑秀培.土石坝地基混凝土防渗墙设计与计算[M].北京:水利电力出版社,1979.
[83]张文正,杨端仪,徐泽平.三峡工程二期混凝土防渗墙围堰的应力和变形计算[J].长江科学院院报.1987(3):15-21.
[84] Duncan J M, et al. Stress-strain and Bulk Modulus Parameters for finiteElement Analysis of stresses and Movements in soil Masses，Report No.VCB/GT/80-01, University of California,1980.
[85] Duncan J M, et al. FEADAM: A Computer Program for Finite ElementAnalysis of Dam. Report No.VCB/GT/80-02, University of California,1980.
[86]张小平,包承纲,张劲松.三峡工程二期围堰防渗墙变形规律及运行状况分析[J].水利学报.2000(9):91-96.
[87]王刚,张建民,濮家骝.坝基混凝土防渗墙应力位移影响因素分析[J].土木工程学报.2006,39(4):73-77.
[88]熊欢,王清友,高希章,等.沙湾水电站一期围堰塑性混凝土防渗墙应力变形分析[J].水力发电学报,2010,29(2):197－203.
[89]高莲士,郁琼华.高土石坝与基础防渗墙的应力变形分析[J].岩土工程学报.1983,5(2):73-86.
[90]陈慧远.土石坝坝基混凝土防渗墙的应力和变形[J].水利学报.1990(4):11-21.
[91]沈新慧.防渗墙及周围土体的应力探讨[J].水利学报.1995(11):39-45.
[92]卢廷浩,汪荣大.瀑布沟土石坝防渗墙应力变形分析[J].河海大学学报.1998,26(2):41-44.
[93]郭诚谦.论混凝土防渗墙的应力特性[J].水力发电.1995(7):18-22.
[94]朱俊高,殷宗泽.高土石坝混凝土防渗墙弹塑性应力变形分析[J].水利学报.1997(7):19-23.
[95]陈剑,卢廷浩.结构型式及接触面参数对防渗墙应力变形的影响分析[J].水利水电技术.2003,34(11):33-36.
[96]孙明权,常跃.影响混凝土防渗墙内力及变形的因素分析[J].人民黄河,2006,28(4):65－68.
[97]郦能惠,米占宽,孙大伟.深覆盖层上面板堆石坝防渗墙应力变形性状影响因素的研究[J].岩土工程学报.2007,29(1):26-31.
[98]介玉新,周厚德.防渗墙的弯矩计算[J].岩石力学与工程学报,2009,28(6):1213－1219.
[99]陈祖煜.土质边坡稳定分析--原理·方法·程序.北京：中国水利水电出版社.2003.
[100] Fellenius W. Erdstatisch Berechnungen, Berlin W Ernst and revised edition,1939.
[101] Bishop A W. The use of the slip circle in the stability analysis of slopes.Geotechnique,1955,5(1):7-17.
[102] Janbu N. Application of composite slip surfaces for stability analysis.Proceedings of European Conference on Stability of Earth Slopes, Sweden,1954,3:43-49.
[103] Lowe J?, Karaflath L. Stability of earth dams upon drawdown. Proceedingsof the1st International Panamer Conference on Soils Mechanics,1960,Mexico City2,537-552.
[104] U S Army, Corps of Engineers. Stability of slopes and foundations,Engineering Manual, Visckburg, Miss,1967.
[105] Morgenstern N R, Price V. The analysis of stability of general slip surfaces.Geotechnique,1965,15(1):79-93.
[106] Spencer E. A method of analysis of the stability of embankments assumingparallel inter-slice forces. Geotechnique,1967,17:11-26.
[107] Sarma S K. Stability analysis of embankments and slopes. Geotechnique,1973,23(3):423-33
[108] anbu N. Slope stability computations. Embankment Dam Engineering,1973,47-86.
[109]钱家欢,殷宗泽.土工原理与计算[M].北京:中国水利水电出版社.1996.
[110] Fredlund D G, Krahn J. Comparison of slope stability analysis methodsanalysis. Canadian Geotechnique Journal.1977,14:429-439.
[111] Chen Zuyu, Morgenstern N R. Extensions to the generalized method of slicesfor stability analysis. Canadian Geotechnique Journal,1983,20(1):104-119.
[112]王成华,夏绪勇,李广信.边坡稳定分析中的临界滑动面搜索方法述评[J].四川建筑科学研究.2002,28(3):34-39.
[113] Lefebvre G·STABR user’s manual[M].Dept.of Civil Engineering,The Univ.ofCalifornia at Berkeley,1971.
[114] Siegel R A.Computer analysis of general slope stability problems [M]. Res.Report No. JHRP-75-8,Engineering Experiment Station,Purdue University,West Lafayette, Ind.1975.
[115]江见鲸.土建工程常见程序选编[M].北京:水利电力出版社,1987
[116] Nguyen V U. Determination of critical slope failure surfaces[J]. J. Geotech.Engineering. ASCE,1985,111(2):238-250.
[117] Revilla J, Castillo E. The calculus of variations applied to stability of slopes.Geotechnique,1977,27(1):1-11.
[118] Castillo E,Revilla J.The calculus of variations and the stability of slopes[A].Proc.9th Int.Conf.on SoilMech.and Found.Engng.[C].1977,Vol.2:25-30.
[119] Ramamurthy T,Narayan C G P,Bhatkar V P.Variational method for slopestability analysis[A].Proc.9th Int.Conf.on Soil Mech.and Found. Engng.[C].1977, Vol.3:139-142.
[120] Baker R, Gaber M. Theoretical analysis of the stability of slopes.Geotechnique,1978,28(4):395-411.
[121] Celestino T B,Duncan J M.Simplified search for non-circular slip surface[A].Proc,10th Int. Conf. on Soil Mech. and Found.Engrg.[C]. A. A. Balkema,Rotterdam, The Netherlands,1981,3:391-394.
[122] Arai K, Tagyo K.Determination of noncircular slip surface giving theminimum factor of safety in slope stability analysis[J]. Soils andFounddations,1985,25(1):43-51.
[123]阎中华.均质土坝与非均质土坝稳定安全系数极值分布规律及电算程序简介[J].水利水电技术,1983,(7).
[124]周文通.最优化方法在土坝稳定分析中的应用[J].土石坝工程,1984,(2).
[125]孙君实.条分法的数值分析[J].岩土工程学报,1984,6(2):1-12.
[126] Boutrop A W, Lovell C W. Search technique in slope stability analysis.Engineering Geology,1980,16(1):51-61.
[127] Siegel R A, Kovacs W D, Lovell C W. Random surface generation in stabilityanalysis. Journal of Geotechnical Engineering,1981,107(7):996-1002.
[128] Greco V R. Efficient Monte-Carlo technique for locating critical slip surface.Journal of Geotechnical Engineering,1996,122(7):517-525.
[129] Abdallah I H, Waleed F H, Sarada K S. Global search method for locatinggeneral slip surface using Monte Carlo techniques. Journal of Geotechnicaland Geoenvironmental Engineering,2001,127:688-698.
[130] Giam S K, Donald I B. Determination of critical slip surfaces for slopes viastress-strain calculations. Proceedings of the5th Australia-New ZealandConference Geomechanics, Sydney,1988,461-464.
[131] Zou J, Z，Williams D J，Xiong W L. Search for critical slip surfaces based onfinite element method. Canadian Geotechnical Journal.1995,32:233-246.
[132] Pham H T A, Fredlund D G, Xiong W L. The application of dynamicprogramming to slope stability analysis. Canadian Geotechnical Journal,2003,40(4):830-847.
[133] Yamagami T, Ueta Y. Search for critical slip lines in finite element stressfields by dynamic programming. Proceedings of the6th InternationalConference on Numerical methods in Geomechanics, Innsbruck,1988,1347-1352.
[134] Naylor D J. Finite element and slope stability. Numerical Methods inGeomechnics. D. Reidel Publishing Company, Dordrecht, Holland,1982.
[135] Kim J Y, Lee S R. An improve search strategy for the critical slip surfaceusing finite element stress fields. Computers and Geotechnics,1997,22(4):295-313.
[136]邵龙潭,韩国城.堆石坝边坡稳定分析的一种方法[J].大连理工大学学报,1994,34(3):365-369.
[137] Fredlund D G, Scoular R E G. Using limit equilibrium concepts in finiteelement slope stability analysis. Proceedings of the International Symposiumon Slope Stability Engineering, Rotterdam, Balkema,1999,31-47.
[138]邵龙潭,唐洪祥,韩国城.有限元边坡稳定分析方法及应用[J].计算力学学报,2001,18(1):81-87.
[139]王成华,夏绪勇,李广信.基于应力场的土坡临界滑动面的蚂蚁算法搜索技术[J].岩石力学与工程学报,2003,22(5):823-829.
[140]王成华,夏绪勇,李广信.基于应力场的土坡临界滑动面的遗传算法搜索[J].清华大学学报,2004,44(3):425-428.
[141]殷宗泽,吕擎峰.圆弧滑动有限元土坡稳定分析.岩土力学,2005,26(10):1525-1529.
[142] Zienkiewicz O C, Humpheson C, Lewis R W. Associated and Non-associatedVisco-plasticity and Plasticity in Soil Mechanics [J]. Geotechnique,1975,25(4):671~689.
[143] Ugai K. A method of calculation of total factor of safety of slope byelastic-plastic FEM. Soils and Foundations,1989,29(2):190-195.
[144] Ugai K, Leshchinsky D. Three-dimensional limit equilibrium and finiteelement analysis. Soils and Foundations,1995,35(4):1-7.
[145]迟世春,关立军.应用强度折减有限元法分析土坡稳定的适应性.哈尔滨工业大学学报,2005,37(9):1298-1302.
[146] Manzari M T, Nour M A. Significance of soil dilatancy in slope stabilityanalysis[J]. Jouranal of Geotechnique and Geoenvironmental Engineering,2000,126(1):75-80.
[147]赵尚毅,郑颖人,时卫民等.用有限元强度折减法求边坡稳定安全系数[J].岩土工程学报,2002,24(3):343-346.
[148]张鲁渝,郑颖人,赵尚毅等.有限元强度折减系数法计算土坡稳定安全系数的精度研究[J].水利学报,2003(1):21-27.
[149]郑颖人,赵尚毅.有限元强度折减法在土坡和岩坡中的应用.岩石力学与工程学报,2004,23(19):3381-3388.
[150]张培文,陈祖煜.剪胀角对求解边坡稳定的安全系数的影响[J].岩土力学,2004,25(11):1757-1760.
[151] Matsui T, San K C. Finite element slope stability analysis by shear strengthreduction technique. Soils and Foundations,1992,32(1):59-70.
[152]宋二祥.土工结构安全系数的有限元计算[J].岩土工程学报,1997,19(2):1-7.
[153]连镇营,韩国城,孔宪京.强度折减有限元法研究开挖边坡的稳定性[J].岩土工程学报,2001,23(4):407-411.
[154]连镇营.基坑工程三维有限元数值分析中若干问题的研究[D].大连:大连理工大学,2001.
[155]栾茂田,武亚军,年延凯.强度折减有限元法中边坡失稳的塑性区判据及其应用.防灾减灾工程学报,2003,23(3):1-8.
[156]武亚军.基坑工程中土与支护结构相互作用及边坡稳定性的数值分析[D].大连:大连理工大学,2003.
[157]赵尚毅,郑颖人,张玉芳.有限元强度折减法中边坡失稳的判据探讨.岩土力学,2005,26(2):332-326.
[158]张学言,闫澍旺.岩土塑性力学基础[M].天津：天津大学出版社,2004.
[159] ABAQUS Documentation [CP/DK]. ABAQUS Theory Manual (Version6.10),2010.
[160]陈卫忠,伍国军,贾善坡. ABAQUS在隧道及地下工程中的应用[M].北京：中国水利水电出版社,2010.
[161]赵杰.边坡稳定有限元分析方法中若干应用问题研究[D].大连：大连理工大学,2006.
[162] ABAQUS Documentation [CP/DK]. ABAQUS Theory Manual (Version6.10),2010.
[163]费康，张建伟. ABAQUS在岩土工程中的应用[M].北京：中国水利水电出版社,2010.
[2]沈珠江,左元明.三峡工程二期混凝土防渗墙围堰初步设计方案的应力应变计算[J].长江科学院院报.1987(3):31-37.
[3] Oscar Dascal.Behaviour of the Manicouagan3cutoff[J]. Canadian GeotechnicalJournal.1979,11(1).
[4]王旭芳，郑旭荣，杨春鸣.土石坝渗流研究进展[J].山西建筑.2008.34（31）：25-26.
[5] Westergaard H M. Water pressures on dams during earthquakes[J]. Trans Amer.Soc Civ. Eng.,98(1933):418-433.
[6]居荣初，曾心传.弹性结构与液体的耦联振动理论[M].地震出版社，1983.
[7] Terzaghi K. Theoretical soil mechanics[M]. Wiley, New York,1943.
[8] Biot M A. General theory of three dimensional consolidation [J]. J. App l. Phys.1941,12:155～164.
[9] Biot M A. General solution of the equation of elasticity and consolidation for aporous material[J]. J. App l. M ech.1956,78:91～96.
[10] Biot M A. Theory of elasticity and consolidation for a porous anisotropic solid[J]. J. App l. Phys.1954,26:182.
[11] Biot M A. Mechanics of deformation and acoustic propagation in porousmedia[J]. J. App l. Phys.1962,33:1482.
[12] Lubinski A. Theory of elasticity for porous bodies displaying a strong porestructure[J]. Proc.2nd U. S. National Congress of Applied Mechanics.1954:247～256.
[13] Geertsman J. A remark on the analogy between thermo-elasticity and theelasticity of saturated porous media[J]. J. Mech. Phys. solids,1957,6:13～16.
[14] Zienkiewicz O C and Shiomi T. Dynamic behaviour of saturated porous media:the generalized Biot formulation and its numerical solution [J]. Int. J. Num.and Analy. Meth. in Geomech.1984,8:71～96.
[15] Oda. M. Permeability tensor for discontinuous rock masses. Geotechnique.1985(4)
[16] Noorlshad J. Coupled thermal-hydraulic-mechanical phenomena In saturatedFractured porous. Numberical approach. J. Geoph. Res.1989(B12)
[17] Savage W Z and Bradock W A. A model for hydro static consolidation of pierreshale[J]. Int. J. Rock M ech. M in.Sci.&Geomech. A bstr.1991,28:345～354.
[18] ZIENKIEWICZ O C, CHAN A H C, PASTOR M, et al. Static and dynamicbehaviour of soils: a rational approach to quantitative solutions(Ⅰ). Fullysaturated problem[C]//Proceedings of the Royal society of London.[S. l.]:[s.n.],1990:285-309.
[19] ZIENKIEWICZ O C, XIE Y M, SCHREFLER B A, et al. Static and dynamicbehaviour of soils: a rational approach to quantitative solutions(Ⅱ).Semisaturated problems[C]//Proceedings of the Royal society of London.[S.l.]:[s. n.],1990:311-321.
[20] LI X K, ZIENKIEWICZ O C, XIE Y. A numerical model for immiscibletwo-phase fluid flow in a porous medium and its time domain solution[J].International Journal for Numerical Methods in Engineering,1990,30(6):1195-1212.
[21] Schreer B A, Zhan X. A fully coupled model for water flow and air flow indeformable porous media[J]. Water Resources Research,1993,29:155-167.
[22] Fredlund, Rahardjo. Soil mechanics for unsaturated soils[M]. New York:Willey and Sons inc,1993.
[23] OLIVELLA S, CARRERA J, GENS A. et al. Non-isothermal multiphase flowof brine and gas through saline media[J]. Transport in Porous Media,1994,15:271-293
[24] Thomas H R, He Y. Analysis of coupled heat moisture and air flow in adeformable unsaturated soil[J]. Geotechnique,1995,45(4):677-689.
[25]李培超，孔祥言，卢德唐.饱和多孔介质流固耦合渗流的数学模型[J].水动力学研究与进展A辑，2003(4):419-426.
[26] Bolzon G, Schreer B A. Zienkiewicz O C. Elastoplastic soil constitutive lawsgeneralized to partially saturated states[J]. Geotechnique,1996,46:279-289.
[27]褚卫江，徐卫亚，苏静波.变形多孔介质流固耦合模型及数值模拟研究[J].工程力学，2007,24（9）:0056-0064.
[28]殷宗泽，凌华.非饱和土一维固结简化计算[J].岩土工程学报，2007，29(5):633-637.
[29]殷宗泽.土工原理[M].北京:中国水利水电出版社，2007:354-364.
[30]曹雪山，殷宗泽.非饱和土二维固结简化计算的研究[J].岩土力学，2009，30(9):2575-2580.
[31] Sandu R. S, Wilson E. L. Finite element analysis of seepage in elasticmedia[J].J.Eng.Mesh.Div.ASCE.1969,95(3):641-652.
[32] Christian John T，Boehmer Jan Willem. Plane strain consolidation by finiteelements[J]. J. Soil Mech. Founmd. Div. ASCE，1970，96(4)：1435～1457
[33]沈珠江.用有限单元法计算软土地基的固结变形[J].水利水运科技情报，1977，（1）:7-23.
[34]张洪武,钟万勰,钱令希.土体固结分析的一种有效算法[J].计算结构力学及其应用,1991,8(4):389.
[35]张洪武,钟万勰,钱令希.饱和土壤固结分析的算法研究[J].力学与实践,1993,15(1):20～22.
[36]王媛.多孔介质渗流与应力的耦合计算方法[J].工程勘察，1995(2):33-37.
[37]杨林德，杨志锡.各向异性饱和土体的渗流耦合分析和数值模拟[J].岩石力学与工程学报.2002，21(10):1447-1451.
[38]陈庆中，冯星梅.应力场、渗流场、流场耦合系统定边值定初值问题的变分原理[J].岩石力学与工程学报，1999，18(5):550-553.
[39]陈庆中，张弥，冯星梅.应力场、渗流场、流场耦合系统问题[J].工程力学，2000，17(6):53-58.
[40]陈庆中，张弥，冯星梅.对Biot固结方程的再认识[J].工程力学，2001，18(6):124-133.
[41]罗晓辉.深基坑开挖渗流与应力耦合分析[J].工程勘察，1996(6)：37～41.
[42]柴军瑞，仵彦卿.均质土坝渗流场与应力场耦合分析的数学模型[J].陕西水力发电，1997，13（3）：4-7.
[43]王晓鸿，仵彦卿.渗流场-应力场耦合分析.[J].勘察科学技术，1998，（4）：3-6.
[44]刘建军，耿万东.地下水渗流的流固耦合理论及数值方法[J].勘察科学技术.2000(4):7-10.
[45]李锡夔,朴光虎,邓子辰.考虑固结效应的结构—土壤相互作用分析及其有限元解[J].计算结构力学及其应用,1990,7(3):1～11.
[46]平扬，白世伟，徐燕萍.深基坑工程渗流一应力耦合分析数值模拟研究[J].岩土力学，200122(1):37-41.
[47]徐则民，黄润秋，许模等.基于水-力耦合理论超深隧道围岩渗透性预测[J].成都理工学院学报，2001，28(2)：130-134.
[48]毛昶熙，李吉庆，段祥宝.渗流作用下土坡圆弧滑动有限元计算[J].岩土工程学报，2001，23(6):746-752.
[49]柴军瑞，李守义.大柳树水利枢纽坝区渗流场与应力场耦合分析[J].岩石力学与工程学报.2002,21(s2):2322-2325.
[50]柴军瑞，李守义.三峡库区泄滩滑坡渗流场与应力场耦合分析[J].岩石力学与工程学报，2004（8）:1280-1284.
[51]张玉军.饱和-非饱和介质水-应力耦合的研究[J].岩石力学与工程学报，2005，24(17):3045-3051.
[52]张玉军.热-水-应力耦合弹塑性二维有限元程序的开发与应用尝试[J].岩土力学,2005,26(2):169-174.
[53]张玉军.核废料处置概念库近场热-水-应力耦合二维有限元模拟[J].岩土工程学报,2006,28(9):1053-1058.
[54]张玉军.热-水-应力耦合条件下三项因素对核素迁移影响的有限元分析[J].岩土力学,2008,29(10):1599-2605.
[55]张玉军，张维庆.双重孔隙介质THMM耦合模型及其有限元分析[J].力学学报,2010,42(4):660-669.
[56]江益敏，陈页开，韩大建等.降雨入渗对边坡稳定影响的实例分析[J].岩石力学与工程学报.2004,23(6):920-924.
[57]周家文，徐卫亚，邓俊晔等.降雨入渗条件下边坡的稳定性分析[J].水利学报.2008,39(9):1066-1073.
[58]张芳枝，陈晓平.非饱和堤岸的渗流特征及其稳定性研究[J].岩土力学，2011,32（5）:1561-1567.
[59] Swift G. W. and kiel O. G.: The Predietion of Gas well performance includingthe effect of Non-Darcy flow，J. Pet. Tech. July.1961,791-798, Trans AIMEVol225.
[60] Rowan G, Clegg M W. An Approximate Method for Non-Darcy Radial GasFlow, AIME,1964,?96.
[61] Dranchuk P. M. and Flores J. Non-Darey Transient Radial gas Flow ThroughPorous media. SPEJ. apr.1975.
[62] Holditch S. A. and Morse S. A. The Effects on Non-Darcy Flow on theBehavior of Hydraulically Fractured Gas well. J. P. T. Oct.1976:1169-1179.
[63] Guppy K. H. Non-Darcy Flow in wells with a Finite Conductivity VerticalFracture，Ph. D. Dissertation. Stanford University, June.1980.
[64] K. H Guppy, Heber Cinco-Ley, and Henry J. Ramey Jr. Effect of Non-DareyFlow on the Constant Pressure Production of Fractured Wells. SPEJ Vol21No3. June,1981.
[65]孟宪麒.狭槽渗流模型试验的若干经验介绍[J].中国水利.1957(9):45-53.
[66]毛昶熙.三向电拟试验与渗流研究，南京水利科学研究所.1963.
[67]毛昶熙,李祖贻.渗流三向电拟试验的电解液模型，水利水运科学研究.1981（3）:1-15.
[68]速宝玉，赵坚，张祝添等.正置模型在尾矿坝空间渗流场电模拟试验中的应用[J].金属矿山.1994,213(3):27-29.
[69]刘昌军，丁留谦，吴梦喜等.双层堤基管涌溃堤砂槽模型试验及渗流场特点研究[J].水利水电技术.2007,38(2):40-43.
[70]陈壁宏.单刺墙边墩对称连接段渗流计算解析解法与数值解法[J].华北水利水电.1985(9):14-19.
[71]吴昌瑜.解析元素法及其在水工渗流问题中的应用研究[J].长江科学院院报.1990(2):65-72.
[72]童磊,谢康和,卢萌盟等.半无限含水层中带衬砌隧洞渗流解析研究[J].岩土力学.2011,32(1):304-308.
[73]毛昶熙.水工渗流发展与坝工建设[J].人民长江,1986(12):32-39.
[74]李思慎,谢红.丹江口左联土石坝渗流问题研究[J].水利水电技术.1994(7):57-61.
[75]任大春,吴昌瑜,朱国胜.三峡二期围堰饱和-非饱和渗流分析.长江科学院院报.1997,14(2):44-47.
[76] Chapuis R P. Controlling the quality of groundwater parameters: someexamples[J].Canadian Geotechnical Journal,2001(32):172-177.
[77] Robert P, Chapuis, Djaouida Chenaf. A user’s approach to assess numericalcodes for saturated and unsat-urated seepage conditions[J]. CanadianGeotechnical Journal,2001,38:1113-1126.
[78]毛昶熙,段祥宝,蔡金榜等.堤防非稳定渗流几个关键值的经验公式[J].水利学报.2004(1):52-56.
[79]沈振中,张鑫,陆希等.西藏老虎嘴水电站左岸渗流控制优化[J].水利学报.2006,37(10):1230-1234.
[80]任杰，沈振中，王谊等.哈达山水利枢纽右岸三维渗流场特性研究[J].水利水运工程学报.2010(3):89-94.
[81]段伟，骆原，陈珂等.黄壁庄水库副坝渗流及防渗墙应力分析[J].水利水电技术.2011,33(5):124-127.
[82]郑秀培.土石坝地基混凝土防渗墙设计与计算[M].北京:水利电力出版社,1979.
[83]张文正,杨端仪,徐泽平.三峡工程二期混凝土防渗墙围堰的应力和变形计算[J].长江科学院院报.1987(3):15-21.
[84] Duncan J M, et al. Stress-strain and Bulk Modulus Parameters for finiteElement Analysis of stresses and Movements in soil Masses，Report No.VCB/GT/80-01, University of California,1980.
[85] Duncan J M, et al. FEADAM: A Computer Program for Finite ElementAnalysis of Dam. Report No.VCB/GT/80-02, University of California,1980.
[86]张小平,包承纲,张劲松.三峡工程二期围堰防渗墙变形规律及运行状况分析[J].水利学报.2000(9):91-96.
[87]王刚,张建民,濮家骝.坝基混凝土防渗墙应力位移影响因素分析[J].土木工程学报.2006,39(4):73-77.
[88]熊欢,王清友,高希章,等.沙湾水电站一期围堰塑性混凝土防渗墙应力变形分析[J].水力发电学报,2010,29(2):197－203.
[89]高莲士,郁琼华.高土石坝与基础防渗墙的应力变形分析[J].岩土工程学报.1983,5(2):73-86.
[90]陈慧远.土石坝坝基混凝土防渗墙的应力和变形[J].水利学报.1990(4):11-21.
[91]沈新慧.防渗墙及周围土体的应力探讨[J].水利学报.1995(11):39-45.
[92]卢廷浩,汪荣大.瀑布沟土石坝防渗墙应力变形分析[J].河海大学学报.1998,26(2):41-44.
[93]郭诚谦.论混凝土防渗墙的应力特性[J].水力发电.1995(7):18-22.
[94]朱俊高,殷宗泽.高土石坝混凝土防渗墙弹塑性应力变形分析[J].水利学报.1997(7):19-23.
[95]陈剑,卢廷浩.结构型式及接触面参数对防渗墙应力变形的影响分析[J].水利水电技术.2003,34(11):33-36.
[96]孙明权,常跃.影响混凝土防渗墙内力及变形的因素分析[J].人民黄河,2006,28(4):65－68.
[97]郦能惠,米占宽,孙大伟.深覆盖层上面板堆石坝防渗墙应力变形性状影响因素的研究[J].岩土工程学报.2007,29(1):26-31.
[98]介玉新,周厚德.防渗墙的弯矩计算[J].岩石力学与工程学报,2009,28(6):1213－1219.
[99]陈祖煜.土质边坡稳定分析--原理·方法·程序.北京：中国水利水电出版社.2003.
[100] Fellenius W. Erdstatisch Berechnungen, Berlin W Ernst and revised edition,1939.
[101] Bishop A W. The use of the slip circle in the stability analysis of slopes.Geotechnique,1955,5(1):7-17.
[102] Janbu N. Application of composite slip surfaces for stability analysis.Proceedings of European Conference on Stability of Earth Slopes, Sweden,1954,3:43-49.
[103] Lowe J?, Karaflath L. Stability of earth dams upon drawdown. Proceedingsof the1st International Panamer Conference on Soils Mechanics,1960,Mexico City2,537-552.
[104] U S Army, Corps of Engineers. Stability of slopes and foundations,Engineering Manual, Visckburg, Miss,1967.
[105] Morgenstern N R, Price V. The analysis of stability of general slip surfaces.Geotechnique,1965,15(1):79-93.
[106] Spencer E. A method of analysis of the stability of embankments assumingparallel inter-slice forces. Geotechnique,1967,17:11-26.
[107] Sarma S K. Stability analysis of embankments and slopes. Geotechnique,1973,23(3):423-33
[108] anbu N. Slope stability computations. Embankment Dam Engineering,1973,47-86.
[109]钱家欢,殷宗泽.土工原理与计算[M].北京:中国水利水电出版社.1996.
[110] Fredlund D G, Krahn J. Comparison of slope stability analysis methodsanalysis. Canadian Geotechnique Journal.1977,14:429-439.
[111] Chen Zuyu, Morgenstern N R. Extensions to the generalized method of slicesfor stability analysis. Canadian Geotechnique Journal,1983,20(1):104-119.
[112]王成华,夏绪勇,李广信.边坡稳定分析中的临界滑动面搜索方法述评[J].四川建筑科学研究.2002,28(3):34-39.
[113] Lefebvre G·STABR user’s manual[M].Dept.of Civil Engineering,The Univ.ofCalifornia at Berkeley,1971.
[114] Siegel R A.Computer analysis of general slope stability problems [M]. Res.Report No. JHRP-75-8,Engineering Experiment Station,Purdue University,West Lafayette, Ind.1975.
[115]江见鲸.土建工程常见程序选编[M].北京:水利电力出版社,1987
[116] Nguyen V U. Determination of critical slope failure surfaces[J]. J. Geotech.Engineering. ASCE,1985,111(2):238-250.
[117] Revilla J, Castillo E. The calculus of variations applied to stability of slopes.Geotechnique,1977,27(1):1-11.
[118] Castillo E,Revilla J.The calculus of variations and the stability of slopes[A].Proc.9th Int.Conf.on SoilMech.and Found.Engng.[C].1977,Vol.2:25-30.
[119] Ramamurthy T,Narayan C G P,Bhatkar V P.Variational method for slopestability analysis[A].Proc.9th Int.Conf.on Soil Mech.and Found. Engng.[C].1977, Vol.3:139-142.
[120] Baker R, Gaber M. Theoretical analysis of the stability of slopes.Geotechnique,1978,28(4):395-411.
[121] Celestino T B,Duncan J M.Simplified search for non-circular slip surface[A].Proc,10th Int. Conf. on Soil Mech. and Found.Engrg.[C]. A. A. Balkema,Rotterdam, The Netherlands,1981,3:391-394.
[122] Arai K, Tagyo K.Determination of noncircular slip surface giving theminimum factor of safety in slope stability analysis[J]. Soils andFounddations,1985,25(1):43-51.
[123]阎中华.均质土坝与非均质土坝稳定安全系数极值分布规律及电算程序简介[J].水利水电技术,1983,(7).
[124]周文通.最优化方法在土坝稳定分析中的应用[J].土石坝工程,1984,(2).
[125]孙君实.条分法的数值分析[J].岩土工程学报,1984,6(2):1-12.
[126] Boutrop A W, Lovell C W. Search technique in slope stability analysis.Engineering Geology,1980,16(1):51-61.
[127] Siegel R A, Kovacs W D, Lovell C W. Random surface generation in stabilityanalysis. Journal of Geotechnical Engineering,1981,107(7):996-1002.
[128] Greco V R. Efficient Monte-Carlo technique for locating critical slip surface.Journal of Geotechnical Engineering,1996,122(7):517-525.
[129] Abdallah I H, Waleed F H, Sarada K S. Global search method for locatinggeneral slip surface using Monte Carlo techniques. Journal of Geotechnicaland Geoenvironmental Engineering,2001,127:688-698.
[130] Giam S K, Donald I B. Determination of critical slip surfaces for slopes viastress-strain calculations. Proceedings of the5th Australia-New ZealandConference Geomechanics, Sydney,1988,461-464.
[131] Zou J, Z，Williams D J，Xiong W L. Search for critical slip surfaces based onfinite element method. Canadian Geotechnical Journal.1995,32:233-246.
[132] Pham H T A, Fredlund D G, Xiong W L. The application of dynamicprogramming to slope stability analysis. Canadian Geotechnical Journal,2003,40(4):830-847.
[133] Yamagami T, Ueta Y. Search for critical slip lines in finite element stressfields by dynamic programming. Proceedings of the6th InternationalConference on Numerical methods in Geomechanics, Innsbruck,1988,1347-1352.
[134] Naylor D J. Finite element and slope stability. Numerical Methods inGeomechnics. D. Reidel Publishing Company, Dordrecht, Holland,1982.
[135] Kim J Y, Lee S R. An improve search strategy for the critical slip surfaceusing finite element stress fields. Computers and Geotechnics,1997,22(4):295-313.
[136]邵龙潭,韩国城.堆石坝边坡稳定分析的一种方法[J].大连理工大学学报,1994,34(3):365-369.
[137] Fredlund D G, Scoular R E G. Using limit equilibrium concepts in finiteelement slope stability analysis. Proceedings of the International Symposiumon Slope Stability Engineering, Rotterdam, Balkema,1999,31-47.
[138]邵龙潭,唐洪祥,韩国城.有限元边坡稳定分析方法及应用[J].计算力学学报,2001,18(1):81-87.
[139]王成华,夏绪勇,李广信.基于应力场的土坡临界滑动面的蚂蚁算法搜索技术[J].岩石力学与工程学报,2003,22(5):823-829.
[140]王成华,夏绪勇,李广信.基于应力场的土坡临界滑动面的遗传算法搜索[J].清华大学学报,2004,44(3):425-428.
[141]殷宗泽,吕擎峰.圆弧滑动有限元土坡稳定分析.岩土力学,2005,26(10):1525-1529.
[142] Zienkiewicz O C, Humpheson C, Lewis R W. Associated and Non-associatedVisco-plasticity and Plasticity in Soil Mechanics [J]. Geotechnique,1975,25(4):671~689.
[143] Ugai K. A method of calculation of total factor of safety of slope byelastic-plastic FEM. Soils and Foundations,1989,29(2):190-195.
[144] Ugai K, Leshchinsky D. Three-dimensional limit equilibrium and finiteelement analysis. Soils and Foundations,1995,35(4):1-7.
[145]迟世春,关立军.应用强度折减有限元法分析土坡稳定的适应性.哈尔滨工业大学学报,2005,37(9):1298-1302.
[146] Manzari M T, Nour M A. Significance of soil dilatancy in slope stabilityanalysis[J]. Jouranal of Geotechnique and Geoenvironmental Engineering,2000,126(1):75-80.
[147]赵尚毅,郑颖人,时卫民等.用有限元强度折减法求边坡稳定安全系数[J].岩土工程学报,2002,24(3):343-346.
[148]张鲁渝,郑颖人,赵尚毅等.有限元强度折减系数法计算土坡稳定安全系数的精度研究[J].水利学报,2003(1):21-27.
[149]郑颖人,赵尚毅.有限元强度折减法在土坡和岩坡中的应用.岩石力学与工程学报,2004,23(19):3381-3388.
[150]张培文,陈祖煜.剪胀角对求解边坡稳定的安全系数的影响[J].岩土力学,2004,25(11):1757-1760.
[151] Matsui T, San K C. Finite element slope stability analysis by shear strengthreduction technique. Soils and Foundations,1992,32(1):59-70.
[152]宋二祥.土工结构安全系数的有限元计算[J].岩土工程学报,1997,19(2):1-7.
[153]连镇营,韩国城,孔宪京.强度折减有限元法研究开挖边坡的稳定性[J].岩土工程学报,2001,23(4):407-411.
[154]连镇营.基坑工程三维有限元数值分析中若干问题的研究[D].大连:大连理工大学,2001.
[155]栾茂田,武亚军,年延凯.强度折减有限元法中边坡失稳的塑性区判据及其应用.防灾减灾工程学报,2003,23(3):1-8.
[156]武亚军.基坑工程中土与支护结构相互作用及边坡稳定性的数值分析[D].大连:大连理工大学,2003.
[157]赵尚毅,郑颖人,张玉芳.有限元强度折减法中边坡失稳的判据探讨.岩土力学,2005,26(2):332-326.
[158]张学言,闫澍旺.岩土塑性力学基础[M].天津：天津大学出版社,2004.
[159] ABAQUS Documentation [CP/DK]. ABAQUS Theory Manual (Version6.10),2010.
[160]陈卫忠,伍国军,贾善坡. ABAQUS在隧道及地下工程中的应用[M].北京：中国水利水电出版社,2010.
[161]赵杰.边坡稳定有限元分析方法中若干应用问题研究[D].大连：大连理工大学,2006.
[162] ABAQUS Documentation [CP/DK]. ABAQUS Theory Manual (Version6.10),2010.
[163]费康，张建伟. ABAQUS在岩土工程中的应用[M].北京：中国水利水电出版社,2010.