考虑填土侧向变形的地震土压力计算方法
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摘要
地震土压力评价是挡土墙抗震设计的关键问题之一。以往的研究结果表明,挡墙上地震土压力的大小及分布与墙体的侧向位移或者墙后填土的侧向变形密切相关。经典的物部-冈部地震土压力公式可计算填土处于主动与被动状态的极限平衡条件下的土压力,未考虑挡墙侧向位移或填土侧向变形对土压力的影响。在研究土压力系数随应变增量比变化规律的基础上,本文指出土压力系数与挡土墙位移量之间不存在唯一性关系,发现正常固结填土的土压力系数与以应变增量比表述的填土侧向应变约束条件之间具有良好的唯一性,揭示了压剪耦合效应是土压力形成的物理本质;基于上述的唯一性关系和中间土楔等概念,提出了可考虑填土侧向变形的地震土压力实用计算方法,并通过土压力模型试验结果初步验证了该方法的合理性。
Evaluation of seismic earth pressure is one of the key items in the earthquake-resistant design of retaining structures.Previous studies indicate that seismic earth pressure is closely related to the lateral deformation of the backfill.Classic Mononobe-Okabe earth pressure theories can be used to compute the earth pressure at the active and passive limit states only,ignoring the effect of lateral deformation on earth pressure change.In this paper,the variation of earth pressure coefficient with the strain increment ratio is investigated.The earth pressure coefficient is experimentally confirmed to have no unique relationship with the wall displacement,but it has a unique one with the strain increment ratio.The compression-dilatancy coupling effect is found to be responsible for the dependency of the earth pressure change on the strain increment ratio and also the lateral strain constraint of the backfill.From this finding and new concept of intermediate soil wedge,a new method is then developed for the evaluation of the seismic earth pressure under any lateral deformation.Furthermore,Its essential effectiveness is preliminarily checked through comparing the calculated results with model test data.
Evaluation of seismic earth pressure is one of the key items in the earthquake-resistant design of retaining structures.Previous studies indicate that seismic earth pressure is closely related to the lateral deformation of the backfill.Classic Mononobe-Okabe earth pressure theories can be used to compute the earth pressure at the active and passive limit states only,ignoring the effect of lateral deformation on earth pressure change.In this paper,the variation of earth pressure coefficient with the strain increment ratio is investigated.The earth pressure coefficient is experimentally confirmed to have no unique relationship with the wall displacement,but it has a unique one with the strain increment ratio.The compression-dilatancy coupling effect is found to be responsible for the dependency of the earth pressure change on the strain increment ratio and also the lateral strain constraint of the backfill.From this finding and new concept of intermediate soil wedge,a new method is then developed for the evaluation of the seismic earth pressure under any lateral deformation.Furthermore,Its essential effectiveness is preliminarily checked through comparing the calculated results with model test data.
引文
[1]Mononobe N,Matsuo H.On the determination of earth pres-sure during earthquakes[A]∥Proceedings of the 6th WorldEngineering Congress[C].Tokyo:[s.n.],Japan,1929,(9):177-185.
[2]Okabe S.General theory on earth pressure and seismic stabilityof retaining walls and dams[J].Journal of the Japanese Societyof Civil Engineering,1924,10(6):1277-1323.
[3]Morrison E E,Ebeling R M.Limit equilibrium computation ofdynamic passive earth pressure[J].Canadian GeotechnicalJournal,1995,32:481-487.
[4]Kumar J.Seismic passive earth pressure coefficients for sands[J].Canadian Geotechnical Journal,2001,38(4):876-881.
[5]Subba Rao K S,Choudhury D S.Seismic passive earth pres-sures in soils[J].Journal of Geotechnical and Geoenvironmen-tal Engineering,2005,131(1):131-135.
[6]Kumar J,Chitikela.Seismic passive earth pressure coefficientsusing the method of characteristics[J].Canadian GeotechnicalJournal,2002,39:463-471.
[7]Cheng Y M.Seismic lateral earth pressure coefficients for c-Φsoils by slip line method[J].Computers and Geotechnics,2003,30:661-670.
[8]Prakash S,Saran S.Static and dynamic earth pressures behindretaining walls[A]∥Proceedings of the 3rd Symposium onEarthquake Engineering[C].Roorkee,India:University of Ro-orkee,1966,277-288.
[9]Prakash S,Basavanna B M.Earth pressure distribution behindretaining walls during earthquake[A]∥Proceedings of the 4thWorld Conference on Earthquake Engineering[C].Santiago:[s.n.],Chile,1969,133-148.
[10]Das B M,Puri V K.Static and dynamic active earth pressure[J].Geotechnical and Geological Engineering,1996,14:353～366.
[11]Chen W F.Limit analysis and soil plasticity.Developments ingeotechnical engineering[M].Amsterdam,The Netherlands:Elsevier,1975.
[12]Chen W F,Liu X L.Limit analysis in soil mechanics[M].De-velopments in geotechnical engineering,52[G].Amsterdam,The Netherlands,Elsevier:1990:477.
[13]Soubra A H.Static and seismic passive earth pressure coeffi-cients on rigid retaining structures[J].Canadian GeotechnicalJournal,2000,37(2):463-478.
[14]Matsuo H.Experimental study on the distribution of earthpressure acting on a vertical wall during earthquakes[J].Journal of the Japan Society of Civil Engineers,1941,27(2):211-230.
[15]Matsuo H,Ohara S.Lateral earth pressure and stability ofquay walls during earthquakes[A]∥Proceedings of 2ndWorld Conference on Earthquake Engineering[C].Tokyo:[s.n.],Japan,1960,1:165-183.
[16]Ishii Y.,Arai H,Tsuchida H.Lateral earth pressure in anearthquake[A]∥Proceedings of the 2nd World Conference onEarthquake Engineering[C].Tokyo:[s.n.],Japan,1960,1:211-230.
[17]Ichihara M,Matsuzawa H.Earth pressure during earthquake[J].Soils and Foundations,1973,13(4):75-86.
[18]Sherif M,Ishibashi I,Lee C D.Earth pressures against rigidretaining walls[J].Journal of geotechnical engineering,ASCE,1982,108(GT5):679-695.
[19]Sherif M A,Fang Y S.Dynamic earth pressures on walls rota-ting about the top[J].Soils and foundations,1984,24(4):109-117.
[20]Ishibashi I,Fang Y S.Dynamic earth pressures with differentwall movement modes[J].Soils and Foundations,1987,27(4),11-22.
[21]Seed H B,Whitman R V.Design of earth retaining structuresfor dynamic loads[A]∥Proc.ASCE Specialty Conference onlateral stresses in the ground and design of earth retainingstructures[C].[S.l]:Cornell University,USA,1970,103-147.
[22]Shakya D A.Engineering solutions for the displacement ofrigid retaining walls subjected to earthquake loads[D].[S.l]:University of Missouri-Rolla,USA,1987:1-115.
[23]Prakash S,Wu Y,Rafnsson E A.On Seismic design displace-ments of rigid retaining walls[A]∥Proceedings of the 3rd In-ternational Conference on Recent Advances in GeotechnicalEngineering and Soil Dynamics[C].St.Louis,MO,III:[s.n.]:1183-1192
[24]Iai S.Rigid and flexible retaining walls during Kobe earth-quake[A]∥Proceedings of the 4th International Conferenceon Case Histories in Geotechnical Engineering,St.Louis,MO.,March 8-12,CD-ROM,SOA-4,108-127.
[25]Wu Y.Displacement-based analysis and design of rigid retai-ning walls during earthquakes[D].USA:University of Mis-souri-Rolla,1999:1-223.
[26]Psarropoulosa P N,Klonarisb G,Gazetasa G.Seismic earthpressures on rigid and flexible retaining walls[J].Soil Dynam-ics and Earthquake Engineering,2005,25,795-809.
[27]Maleki S,Mahjoubi S.A New Approach for estimating theseismic soil pressure on retaining walls[J].Transaction A:Civil Engineering,2010,17(4):273-284.
[28]Zhang J M,Shamoto Y,Tokimatsu K.Evaluation of earthpressure under any lateral deformation[J].Soils and Founda-tions,1998,38(1):15-33.
[29]Terzaghi K.Large retaining wall tests[J].Engineering NewsRecord,1934,112:136–140.
[30]Fang Y S,Chen T J,Wu B F.Passive earth pressures with va-rious wall movements[J].Journal of Geotechnical Engineer-ing,1994,120(8):1 307–1 323.
[31]Fnaf Y S,Ho Y C,Chen T J.Passive earth pressure with crit-ical state concept[J].Journal of Geotechnical and Geoenvir-onmental Engineering,2002,127(3):248-257.
[32]Zhang J M,Shamoto Y,Tokimatsu K.Seismic earth pressuretheory for retaining walls under any lateral displacement[J].Soils and Foundations,1998,38(2):143-163.
[33]Zhang J M.Cyclic Critical Stress State Theory of Sand withIts Application to Geotechnical Problems[R].Research Re-port of Tokyo Institute of Technology,Tokyo,1997:78-100.
[34]Gudehus G,Goldscheoder M,Winter H.Mechanical proper-ties of sand and clay and numerical integration methods:somesources of errors and bounds of accuracy[A]∥G udehus.Fi-nite elements in geomechanics[C].Balkema,Rotterdam,1977,121-150.
[35]Chu J,Lo S-C R.Asymptotic behavior of a granular soil instrain path testing[J].Geotechnique,1994,44(1):65–82.
[36]Asaka Y,Tokimatsu K,Iwasaki K,et al.A simple stress-strain relation based on stress-path behavior in strain-pathcontrolled triaxial tests[J].Soils and foundations,2003,43(2):55-68.
[37]宋飞.考虑侧向变形的各向异性填土土压力计算方法及试验研究[D].北京:清华大学,2009:152-165.Song Fei.Evaluation and experimental study of earth pressurefor anisotropic sand under any lateral deformation[D].Bei-jing:Tsinghua University,2009:152-165.
[38]张建民,宋飞.砂土的压剪效应与渐近状态准则[J].岩土工程学报,2008,30(2):166–171.Zhang Jian-Min,Song Fei.Compression-dilatancy couplingeffect and asymptotic state criterion of sand[J].ChineseJournal of Geotechnical Engineering,2008,30(2):166–171.
[39]Terzaghi K.Theoretical Soil Mechanics[M].Wiley,NewYork.1943.
[40]Sherif M A,Fang Y S,Sherif R I.Kaand K0behind rotatingand non-yielding walls[J].Journal of Geotechnical Engineer-ing,ASCE,1984,110(1):41-56.
[41]宋飞,张建民.平动模式下刚性挡墙被动侧土压力计算方法[A]∥中国土木工程学会第十届土力学及岩土工程学术会议论文集(下册)[C].重庆:[s.n.],2007:447-451.Song Fei,Zhang Jian-Min.Earth pressure at the passive sideagainst rigid retaining wall under translational mode[A]∥Proceedings of the 10th Chinese National Conference on SoilMechanics and Geotechnical Engineering[C].Chongqi:[s.n.],2007:447-451.
[42]Song F,Zhang J M.Evaluation of Seismic Earth Pressures atthe Passive Side[A]∥Proceedings of the 14th World Confer-ence on Earthquake Engineering[G].Beijing,:[s.n.],2008,CD:14-04-02-0122.
[43]Zhang J M,Shamoto Y,Tokimatsu K.Seismic earth pressureagainst basement wall[A]∥Proceedings of the 8th Interna-tional Conference on Soil Dynamics and Earthquake Engineer-ing[C].Istanbul,Turkey:1997.
[44]Zhang J M,Shamoto Y,Tokimatsu K.Earth pressures on rig-id walls during earthquakes[J].ASCE Geotechnical SpecialPublication,1998,75(2):1053-1070.
[45]Zhang G,Zhang J M.Simplified Methods for dynamic soil andsemi-berried structure interaction[A]∥Proceedings of 4th In-ternational Conference on Advances in Geotechnical Earth-quake Engineering and Soil Dynamics[C].[S.l.]:San Diego,CA,USA,2001:345-350.
[46]Zhang J M,Song F,Li D.Effect of strain localization on seis-mic active earth pressures[J].Journal of Geotechnical andGeoenvironmental Engineering,ASCE,2010,136(7):999-1003.
[47]宋飞,张建民.考虑挡墙位移效应的被动侧土压力计算方法[J].岩土力学,2011.32(1):151-157.Song Fei,Zhang Jian-min.Evaluation of earth pressure at thepassive side considering wall displacement effect[J].Rock andSoil Mechanics 2011.32(1):151-157.
[48]宋飞,张建民.考虑侧向变形的各向异性砂土土压力试验研究[J].岩石力学与工程学报,2009,28(9):1884-1895.Song Fei,Zhang Jian-Min.Investigation of earth pressure foranisotropic sand considering wall movement[J].Chinese Jour-nal of Rock Mechanics and Engineering,2009,28(9):1884-1895.
[49]宋飞,张建民.各向异性砂土渐近状态试验研究[J].岩土工程学报,2010,32(4):551-561.Song Fei,Zhang Jian-min.Experimental study of asymptoticbehavior of anisotropic sand[J].Chinese Journal of Geotech-nical Engineering,2010,32(4):551-561.
[50]宋飞,张建民,刘超.各向异性砂土K0试验研究[J].岩土力学,2010,31(12):3727-3732.Song Fei,Zhang Jian-Min,LIU Chao.Experimental study ofK0for anisotropic sand[J].Rock and Soil Mechanics,2010,31(12):3727-3732.
[51]宋飞,张建民.各向异性砂土主动侧土压力计算方法[J].岩土力学,2011,32(4):1029-1034.Song Fei,Zhang Jian-Min.Evaluation of earth pressure at theactive side for anisotropic sand[J].Rock and Soil Mechanics,2011,32(4):1029-1034.
[52]Song F,Zhang J M.Zhang L Y.Evaluation of earth pressuresagainst rigid retaining structures with RTT mode[J].Ad-vanced Materials Research,2011,168:200-205.
[53]Song F,Zhang J M.Estimation of seismic earth pressures a-gainst rigid retaining structures with rotation mode[J].TheOpen Civil Engineering Journal,2011,5:52-58.
[54]Zhang J M,Shamoto Y.Total stress change during cyclicloading under K0conditions[A]∥Proceedings of the 3rd In-ternational Conference on Recent Advances in GeotechnicalEarthquake Engineering and Soil Dynamics[C].Missouri:[s.n.],USA,1995:1,18.
[55]Zhang J M,Shamoto Y,Tokimatsu K.Total lateral stresschange in saturated sand after liquefaction under differentstrain constraints[A]∥Proceedings of the 11th World Con-ference on Earthquake Engineering[C].Mexico,1996:1053.
[56]Zhang J M,Shamoto Y,Sato M.Dynamic soil and water pres-sures against quay walls[A]∥Proceedings,98’IS Centrifuge[C].Tokyo:[s.n.],1998,154-159.
[57]Fang Y S,Ishibashi I.Static earth pressures with various wallmovements[J].Journal of Geotechnical Engineering,1986,112(3):317–333.
[58]Matsuo M,Kenmochi S,Yagi H.Experimental study on earthpressure of retaining wall by field tests[J].Soils and Founda-tions,1978,18(3):27-41.
[2]Okabe S.General theory on earth pressure and seismic stabilityof retaining walls and dams[J].Journal of the Japanese Societyof Civil Engineering,1924,10(6):1277-1323.
[3]Morrison E E,Ebeling R M.Limit equilibrium computation ofdynamic passive earth pressure[J].Canadian GeotechnicalJournal,1995,32:481-487.
[4]Kumar J.Seismic passive earth pressure coefficients for sands[J].Canadian Geotechnical Journal,2001,38(4):876-881.
[5]Subba Rao K S,Choudhury D S.Seismic passive earth pres-sures in soils[J].Journal of Geotechnical and Geoenvironmen-tal Engineering,2005,131(1):131-135.
[6]Kumar J,Chitikela.Seismic passive earth pressure coefficientsusing the method of characteristics[J].Canadian GeotechnicalJournal,2002,39:463-471.
[7]Cheng Y M.Seismic lateral earth pressure coefficients for c-Φsoils by slip line method[J].Computers and Geotechnics,2003,30:661-670.
[8]Prakash S,Saran S.Static and dynamic earth pressures behindretaining walls[A]∥Proceedings of the 3rd Symposium onEarthquake Engineering[C].Roorkee,India:University of Ro-orkee,1966,277-288.
[9]Prakash S,Basavanna B M.Earth pressure distribution behindretaining walls during earthquake[A]∥Proceedings of the 4thWorld Conference on Earthquake Engineering[C].Santiago:[s.n.],Chile,1969,133-148.
[10]Das B M,Puri V K.Static and dynamic active earth pressure[J].Geotechnical and Geological Engineering,1996,14:353～366.
[11]Chen W F.Limit analysis and soil plasticity.Developments ingeotechnical engineering[M].Amsterdam,The Netherlands:Elsevier,1975.
[12]Chen W F,Liu X L.Limit analysis in soil mechanics[M].De-velopments in geotechnical engineering,52[G].Amsterdam,The Netherlands,Elsevier:1990:477.
[13]Soubra A H.Static and seismic passive earth pressure coeffi-cients on rigid retaining structures[J].Canadian GeotechnicalJournal,2000,37(2):463-478.
[14]Matsuo H.Experimental study on the distribution of earthpressure acting on a vertical wall during earthquakes[J].Journal of the Japan Society of Civil Engineers,1941,27(2):211-230.
[15]Matsuo H,Ohara S.Lateral earth pressure and stability ofquay walls during earthquakes[A]∥Proceedings of 2ndWorld Conference on Earthquake Engineering[C].Tokyo:[s.n.],Japan,1960,1:165-183.
[16]Ishii Y.,Arai H,Tsuchida H.Lateral earth pressure in anearthquake[A]∥Proceedings of the 2nd World Conference onEarthquake Engineering[C].Tokyo:[s.n.],Japan,1960,1:211-230.
[17]Ichihara M,Matsuzawa H.Earth pressure during earthquake[J].Soils and Foundations,1973,13(4):75-86.
[18]Sherif M,Ishibashi I,Lee C D.Earth pressures against rigidretaining walls[J].Journal of geotechnical engineering,ASCE,1982,108(GT5):679-695.
[19]Sherif M A,Fang Y S.Dynamic earth pressures on walls rota-ting about the top[J].Soils and foundations,1984,24(4):109-117.
[20]Ishibashi I,Fang Y S.Dynamic earth pressures with differentwall movement modes[J].Soils and Foundations,1987,27(4),11-22.
[21]Seed H B,Whitman R V.Design of earth retaining structuresfor dynamic loads[A]∥Proc.ASCE Specialty Conference onlateral stresses in the ground and design of earth retainingstructures[C].[S.l]:Cornell University,USA,1970,103-147.
[22]Shakya D A.Engineering solutions for the displacement ofrigid retaining walls subjected to earthquake loads[D].[S.l]:University of Missouri-Rolla,USA,1987:1-115.
[23]Prakash S,Wu Y,Rafnsson E A.On Seismic design displace-ments of rigid retaining walls[A]∥Proceedings of the 3rd In-ternational Conference on Recent Advances in GeotechnicalEngineering and Soil Dynamics[C].St.Louis,MO,III:[s.n.]:1183-1192
[24]Iai S.Rigid and flexible retaining walls during Kobe earth-quake[A]∥Proceedings of the 4th International Conferenceon Case Histories in Geotechnical Engineering,St.Louis,MO.,March 8-12,CD-ROM,SOA-4,108-127.
[25]Wu Y.Displacement-based analysis and design of rigid retai-ning walls during earthquakes[D].USA:University of Mis-souri-Rolla,1999:1-223.
[26]Psarropoulosa P N,Klonarisb G,Gazetasa G.Seismic earthpressures on rigid and flexible retaining walls[J].Soil Dynam-ics and Earthquake Engineering,2005,25,795-809.
[27]Maleki S,Mahjoubi S.A New Approach for estimating theseismic soil pressure on retaining walls[J].Transaction A:Civil Engineering,2010,17(4):273-284.
[28]Zhang J M,Shamoto Y,Tokimatsu K.Evaluation of earthpressure under any lateral deformation[J].Soils and Founda-tions,1998,38(1):15-33.
[29]Terzaghi K.Large retaining wall tests[J].Engineering NewsRecord,1934,112:136–140.
[30]Fang Y S,Chen T J,Wu B F.Passive earth pressures with va-rious wall movements[J].Journal of Geotechnical Engineer-ing,1994,120(8):1 307–1 323.
[31]Fnaf Y S,Ho Y C,Chen T J.Passive earth pressure with crit-ical state concept[J].Journal of Geotechnical and Geoenvir-onmental Engineering,2002,127(3):248-257.
[32]Zhang J M,Shamoto Y,Tokimatsu K.Seismic earth pressuretheory for retaining walls under any lateral displacement[J].Soils and Foundations,1998,38(2):143-163.
[33]Zhang J M.Cyclic Critical Stress State Theory of Sand withIts Application to Geotechnical Problems[R].Research Re-port of Tokyo Institute of Technology,Tokyo,1997:78-100.
[34]Gudehus G,Goldscheoder M,Winter H.Mechanical proper-ties of sand and clay and numerical integration methods:somesources of errors and bounds of accuracy[A]∥G udehus.Fi-nite elements in geomechanics[C].Balkema,Rotterdam,1977,121-150.
[35]Chu J,Lo S-C R.Asymptotic behavior of a granular soil instrain path testing[J].Geotechnique,1994,44(1):65–82.
[36]Asaka Y,Tokimatsu K,Iwasaki K,et al.A simple stress-strain relation based on stress-path behavior in strain-pathcontrolled triaxial tests[J].Soils and foundations,2003,43(2):55-68.
[37]宋飞.考虑侧向变形的各向异性填土土压力计算方法及试验研究[D].北京:清华大学,2009:152-165.Song Fei.Evaluation and experimental study of earth pressurefor anisotropic sand under any lateral deformation[D].Bei-jing:Tsinghua University,2009:152-165.
[38]张建民,宋飞.砂土的压剪效应与渐近状态准则[J].岩土工程学报,2008,30(2):166–171.Zhang Jian-Min,Song Fei.Compression-dilatancy couplingeffect and asymptotic state criterion of sand[J].ChineseJournal of Geotechnical Engineering,2008,30(2):166–171.
[39]Terzaghi K.Theoretical Soil Mechanics[M].Wiley,NewYork.1943.
[40]Sherif M A,Fang Y S,Sherif R I.Kaand K0behind rotatingand non-yielding walls[J].Journal of Geotechnical Engineer-ing,ASCE,1984,110(1):41-56.
[41]宋飞,张建民.平动模式下刚性挡墙被动侧土压力计算方法[A]∥中国土木工程学会第十届土力学及岩土工程学术会议论文集(下册)[C].重庆:[s.n.],2007:447-451.Song Fei,Zhang Jian-Min.Earth pressure at the passive sideagainst rigid retaining wall under translational mode[A]∥Proceedings of the 10th Chinese National Conference on SoilMechanics and Geotechnical Engineering[C].Chongqi:[s.n.],2007:447-451.
[42]Song F,Zhang J M.Evaluation of Seismic Earth Pressures atthe Passive Side[A]∥Proceedings of the 14th World Confer-ence on Earthquake Engineering[G].Beijing,:[s.n.],2008,CD:14-04-02-0122.
[43]Zhang J M,Shamoto Y,Tokimatsu K.Seismic earth pressureagainst basement wall[A]∥Proceedings of the 8th Interna-tional Conference on Soil Dynamics and Earthquake Engineer-ing[C].Istanbul,Turkey:1997.
[44]Zhang J M,Shamoto Y,Tokimatsu K.Earth pressures on rig-id walls during earthquakes[J].ASCE Geotechnical SpecialPublication,1998,75(2):1053-1070.
[45]Zhang G,Zhang J M.Simplified Methods for dynamic soil andsemi-berried structure interaction[A]∥Proceedings of 4th In-ternational Conference on Advances in Geotechnical Earth-quake Engineering and Soil Dynamics[C].[S.l.]:San Diego,CA,USA,2001:345-350.
[46]Zhang J M,Song F,Li D.Effect of strain localization on seis-mic active earth pressures[J].Journal of Geotechnical andGeoenvironmental Engineering,ASCE,2010,136(7):999-1003.
[47]宋飞,张建民.考虑挡墙位移效应的被动侧土压力计算方法[J].岩土力学,2011.32(1):151-157.Song Fei,Zhang Jian-min.Evaluation of earth pressure at thepassive side considering wall displacement effect[J].Rock andSoil Mechanics 2011.32(1):151-157.
[48]宋飞,张建民.考虑侧向变形的各向异性砂土土压力试验研究[J].岩石力学与工程学报,2009,28(9):1884-1895.Song Fei,Zhang Jian-Min.Investigation of earth pressure foranisotropic sand considering wall movement[J].Chinese Jour-nal of Rock Mechanics and Engineering,2009,28(9):1884-1895.
[49]宋飞,张建民.各向异性砂土渐近状态试验研究[J].岩土工程学报,2010,32(4):551-561.Song Fei,Zhang Jian-min.Experimental study of asymptoticbehavior of anisotropic sand[J].Chinese Journal of Geotech-nical Engineering,2010,32(4):551-561.
[50]宋飞,张建民,刘超.各向异性砂土K0试验研究[J].岩土力学,2010,31(12):3727-3732.Song Fei,Zhang Jian-Min,LIU Chao.Experimental study ofK0for anisotropic sand[J].Rock and Soil Mechanics,2010,31(12):3727-3732.
[51]宋飞,张建民.各向异性砂土主动侧土压力计算方法[J].岩土力学,2011,32(4):1029-1034.Song Fei,Zhang Jian-Min.Evaluation of earth pressure at theactive side for anisotropic sand[J].Rock and Soil Mechanics,2011,32(4):1029-1034.
[52]Song F,Zhang J M.Zhang L Y.Evaluation of earth pressuresagainst rigid retaining structures with RTT mode[J].Ad-vanced Materials Research,2011,168:200-205.
[53]Song F,Zhang J M.Estimation of seismic earth pressures a-gainst rigid retaining structures with rotation mode[J].TheOpen Civil Engineering Journal,2011,5:52-58.
[54]Zhang J M,Shamoto Y.Total stress change during cyclicloading under K0conditions[A]∥Proceedings of the 3rd In-ternational Conference on Recent Advances in GeotechnicalEarthquake Engineering and Soil Dynamics[C].Missouri:[s.n.],USA,1995:1,18.
[55]Zhang J M,Shamoto Y,Tokimatsu K.Total lateral stresschange in saturated sand after liquefaction under differentstrain constraints[A]∥Proceedings of the 11th World Con-ference on Earthquake Engineering[C].Mexico,1996:1053.
[56]Zhang J M,Shamoto Y,Sato M.Dynamic soil and water pres-sures against quay walls[A]∥Proceedings,98’IS Centrifuge[C].Tokyo:[s.n.],1998,154-159.
[57]Fang Y S,Ishibashi I.Static earth pressures with various wallmovements[J].Journal of Geotechnical Engineering,1986,112(3):317–333.
[58]Matsuo M,Kenmochi S,Yagi H.Experimental study on earthpressure of retaining wall by field tests[J].Soils and Founda-tions,1978,18(3):27-41.
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