土石坝地震永久变形计算方法
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摘要
对于土石坝的地震永久变形,本文提出等效结点力-逐步软化有限元计算模型。首先根据坝体地震动力响应的非线性有限元分析确定各时段坝体单元可能发生的残余应变、振动孔隙水压力增量及累积振动孔隙水压力,以此对静变形模量和强度及静应力-应变关系进行修正,并应用于下一时段计算中;同时基于所确定的与上一时段地震作用所产生的潜在残余应变增量和静应力-应变关系确定地震作用相应的等效结点力。在每一时段末根据上述所确定的等效结点力和应力-应变关系,运用整体有限元分析确定坝休的残余变形增量,将各个时段计算所确定的残余位移累加得到地震作用后坝体的残余变形量。这种方法能够同时考虑地震惯性力效应和土的软化效应对土石坝地震永久变形的影响。
This paper presents a finite element procedure for evaluating seismically-induced permanent deformation of earth-rock dams.In the proposed procedure,both concepts of equivalent nodal forces and step-by-step gradually softening moduli are integrated together.The earthquake duration is divided into a certain number of time increments.And for each time increment the residual strain and dynamic pore water pressure which is likely induced during previous time increments under undrained condition are estimated on the basis of the stress condition obtained by the dynamic analysis and the empirical patterns of both residual strain and pore water pressure achieved experimentally.Then,the computed accumulative pore-water pressure at the end of each time increment is used directly to modify the static hyperbolic relationship between stress and strain which is to be used for the next time period.And at the same time,the equivalent nodal forces equivalent to incremental residual strain potential are defined.By using the modified stress-strain relationship,the incremental deformations are computed when the nodal forces equivalent to earthquake effect on the dam defined as above are imposed on the earth-rock dam.The computed incremental displacements of the earth-rock dam for each time increment are accumulated and the accumulative displacements can be regarded as approximation of the residual deformation which is to be initiated by earthquake shaking.In fact,the proposed numerical procedure has taken into consideration both the inertia effect and the softening effect of earthquake-induced loading on the permanent deformation of the earth-rock dam.
This paper presents a finite element procedure for evaluating seismically-induced permanent deformation of earth-rock dams.In the proposed procedure,both concepts of equivalent nodal forces and step-by-step gradually softening moduli are integrated together.The earthquake duration is divided into a certain number of time increments.And for each time increment the residual strain and dynamic pore water pressure which is likely induced during previous time increments under undrained condition are estimated on the basis of the stress condition obtained by the dynamic analysis and the empirical patterns of both residual strain and pore water pressure achieved experimentally.Then,the computed accumulative pore-water pressure at the end of each time increment is used directly to modify the static hyperbolic relationship between stress and strain which is to be used for the next time period.And at the same time,the equivalent nodal forces equivalent to incremental residual strain potential are defined.By using the modified stress-strain relationship,the incremental deformations are computed when the nodal forces equivalent to earthquake effect on the dam defined as above are imposed on the earth-rock dam.The computed incremental displacements of the earth-rock dam for each time increment are accumulated and the accumulative displacements can be regarded as approximation of the residual deformation which is to be initiated by earthquake shaking.In fact,the proposed numerical procedure has taken into consideration both the inertia effect and the softening effect of earthquake-induced loading on the permanent deformation of the earth-rock dam.
引文
[1]Newmark N M.Effects of earthquakes on dams and embankments[J].Geotechnique,1965,15(2):139~160.
[2]汪闻韶,金崇磐,王克成.土石坝的抗震计算和模型实验及原型观测[J].水利学报,1987,(12):1~15.WANG Wenshao,JIN Chongpan,WANG Kecheng.Aseismatic calculation,model and prototype experiments and field monitoring of earth-rock dams[J].Journal of Hydraulic Engineering,1987,(12):1~15.(in Chinese)
[3]迟世春,林皋,孔宪京.堆石料残余体应变对计算面板堆石坝永久变形的影响[J].水力发电学报,1998,(1):59~67.CHI Shichun,LIN Gao,KONG Xianjing.Influence of residual volumetric strain of rockfill material on calculated permanent deformation ofconcrete faced rockfill dams[J].Journal of Hydroelectric Engineering,1998,(1):59~67.(in Chinese)
[4]王玲玲,何蕴龙,费文平.水牛家心墙堆石坝地震永久变形及液化分析[J].岩土力学,2004,25(1):165~168.WANG Lingling,HE Yunlong,FEI Wenping.Analysis of earthquake induced liquetaction and permanent deformation of Shuiniujia centralcore rock-fill dam[J].Rock and Soil Mechanics,2004,25(1):165~168.(in Chinese)
[5]赵剑明,常亚屏,陈宁.高心墙堆石坝地震变形与稳定分析[J].岩土力学,2004,25(增2):423~428.ZHAO Jianming,CHANG Yaping,CHEN Ning.Study on earthquake-induced permanent deformation and dynamic stability of high corerockfill dam[J].Rock and Soil Mechanics.2004,25(Supp.2):423~428.(in Chinese)
[6]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.ZHANG Kexu,LI Mingzai,CHANG Xiangqian.Analysis of earthquake induced permanent deformations for earth dams[J].EarthquakeEngineering and Engineering Vibration,1989,9(1):91~100.(in Chinese)
[7]Kuwano J,Ishihara K,Haya H,et al.Analysis on permanent deformation of embankments caused by earthquakes[J].Soils andFoundations,1991,31(3):97~110.
[8]何广讷,杨斌.计算软土震陷的综合应变势法[A].栾茂田编.土动力学理论与实践[C].大连:大连理工大学出版社,1998,215~218.HE Guangne,YANG Bin.Comprehensive strain potential method for calculation of soft soil seismic deformation[A].LUAN Maotian,ed.,Soil Dynamics-from Theory to Practice[C].Dalian:Dalian University of Technology Press,1998,215~218.(in Chinese)
[9]钱家欢,曾力真,洪振舜.小浪底土坝地震后永久变形预估[J].水利水电科技进展,1993,13(4):70~72.QIAN Jiahuan,ZENG Lizhen,HONG Zhenshun.Prediction of earthquake-induced permanent deformation of Xiaolangdi soil dam[J].Advances in Science and Technology of Water Resources,1993,13(4):70~72.(in Chinese)
[10]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.LIU Hanlong,LU Zhaozhen,QIAN Jiahuan.Earthquake-induced permanent deformation of earth-rock dams[J].Journal of Hehai University(Natural Sciences),1996,24(1):91~96.(in Chinese)
[11]Seff N,Seed H B,Makdisi F I,et al.Earthquake induced deformations of earth dams[R].In:Report No.EERC 76-4,EarthquakeEngineering Research Centre,University of California,Berkeley,1976.
[12]沈珠江.一个计算砂土液化变形的等价粘弹性模式[A].中国土木工程学会第四届土力学及基础工程学术会议论文选集[C].北京:中国建筑工业出版社,1986,199~207.SHEN Zhujiang.An equivalent visco-elastic model for liquefaction deformation calculation of sand[A].Proceedings of the Fourth SoilMechanics and Foundation Engineering Conference of China Civil Engineering Society[C].Beijing:China Architecture and Building Press,1986,199~207.(in Chinese)
[13]Taniguchi E,Whitman R V,Marr W A.Prediction of earthquake induced deformation of earth dams[J].Soils and Foundations,1983,23(4):126~132.
[14]于洪志,何广讷,杨斌.软土震陷特性的试验研究[J].大连理工大学学报,1996,36(1):76~82.YU Hongzhi,HE Guangna,YANG Bin.Experimental investigation of soil seismic deformation property[J].Journal of Dalian University ofTechnology,1996.36(1):76~82.(in Chinese)
[15]Al-Karni A A.Shear strength reduction due to excess pore water pressure[A].Proceedings of Fourth International Conference on RecentAdvance in Geotechnical Earthquake Engineering and Soil Dynamics and Symposium in Honor of Professor Liam Finn[C].St,Louis:University of Missouri-Rolla,2001.paper No.9~12.
[16]Matsui T,Bahr M A,Abe N.Estimation of shear characteristics degradation and stress-strain relationship of saturated clays after cyclicloadin[J].Soils and Foundations,1992,32(I):161~172.
[17]Yasuhara K,Hyde A F L.Method for estimating postcyclic secant modulus of clays[J].Journal of Geotechnical and GeoenvironmentalEngineering,ASCE,1997,123(3):204~211.
[18]Yasuhara K,Murakami S,Song B W,et al.Postcyclic degradation of strength and stiffness for low plasticity silt[J].Journal ofGeotechnical and Geoenvironmental Engineering,ASCE,2003,129(8):756~769.
[2]汪闻韶,金崇磐,王克成.土石坝的抗震计算和模型实验及原型观测[J].水利学报,1987,(12):1~15.WANG Wenshao,JIN Chongpan,WANG Kecheng.Aseismatic calculation,model and prototype experiments and field monitoring of earth-rock dams[J].Journal of Hydraulic Engineering,1987,(12):1~15.(in Chinese)
[3]迟世春,林皋,孔宪京.堆石料残余体应变对计算面板堆石坝永久变形的影响[J].水力发电学报,1998,(1):59~67.CHI Shichun,LIN Gao,KONG Xianjing.Influence of residual volumetric strain of rockfill material on calculated permanent deformation ofconcrete faced rockfill dams[J].Journal of Hydroelectric Engineering,1998,(1):59~67.(in Chinese)
[4]王玲玲,何蕴龙,费文平.水牛家心墙堆石坝地震永久变形及液化分析[J].岩土力学,2004,25(1):165~168.WANG Lingling,HE Yunlong,FEI Wenping.Analysis of earthquake induced liquetaction and permanent deformation of Shuiniujia centralcore rock-fill dam[J].Rock and Soil Mechanics,2004,25(1):165~168.(in Chinese)
[5]赵剑明,常亚屏,陈宁.高心墙堆石坝地震变形与稳定分析[J].岩土力学,2004,25(增2):423~428.ZHAO Jianming,CHANG Yaping,CHEN Ning.Study on earthquake-induced permanent deformation and dynamic stability of high corerockfill dam[J].Rock and Soil Mechanics.2004,25(Supp.2):423~428.(in Chinese)
[6]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.ZHANG Kexu,LI Mingzai,CHANG Xiangqian.Analysis of earthquake induced permanent deformations for earth dams[J].EarthquakeEngineering and Engineering Vibration,1989,9(1):91~100.(in Chinese)
[7]Kuwano J,Ishihara K,Haya H,et al.Analysis on permanent deformation of embankments caused by earthquakes[J].Soils andFoundations,1991,31(3):97~110.
[8]何广讷,杨斌.计算软土震陷的综合应变势法[A].栾茂田编.土动力学理论与实践[C].大连:大连理工大学出版社,1998,215~218.HE Guangne,YANG Bin.Comprehensive strain potential method for calculation of soft soil seismic deformation[A].LUAN Maotian,ed.,Soil Dynamics-from Theory to Practice[C].Dalian:Dalian University of Technology Press,1998,215~218.(in Chinese)
[9]钱家欢,曾力真,洪振舜.小浪底土坝地震后永久变形预估[J].水利水电科技进展,1993,13(4):70~72.QIAN Jiahuan,ZENG Lizhen,HONG Zhenshun.Prediction of earthquake-induced permanent deformation of Xiaolangdi soil dam[J].Advances in Science and Technology of Water Resources,1993,13(4):70~72.(in Chinese)
[10]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.LIU Hanlong,LU Zhaozhen,QIAN Jiahuan.Earthquake-induced permanent deformation of earth-rock dams[J].Journal of Hehai University(Natural Sciences),1996,24(1):91~96.(in Chinese)
[11]Seff N,Seed H B,Makdisi F I,et al.Earthquake induced deformations of earth dams[R].In:Report No.EERC 76-4,EarthquakeEngineering Research Centre,University of California,Berkeley,1976.
[12]沈珠江.一个计算砂土液化变形的等价粘弹性模式[A].中国土木工程学会第四届土力学及基础工程学术会议论文选集[C].北京:中国建筑工业出版社,1986,199~207.SHEN Zhujiang.An equivalent visco-elastic model for liquefaction deformation calculation of sand[A].Proceedings of the Fourth SoilMechanics and Foundation Engineering Conference of China Civil Engineering Society[C].Beijing:China Architecture and Building Press,1986,199~207.(in Chinese)
[13]Taniguchi E,Whitman R V,Marr W A.Prediction of earthquake induced deformation of earth dams[J].Soils and Foundations,1983,23(4):126~132.
[14]于洪志,何广讷,杨斌.软土震陷特性的试验研究[J].大连理工大学学报,1996,36(1):76~82.YU Hongzhi,HE Guangna,YANG Bin.Experimental investigation of soil seismic deformation property[J].Journal of Dalian University ofTechnology,1996.36(1):76~82.(in Chinese)
[15]Al-Karni A A.Shear strength reduction due to excess pore water pressure[A].Proceedings of Fourth International Conference on RecentAdvance in Geotechnical Earthquake Engineering and Soil Dynamics and Symposium in Honor of Professor Liam Finn[C].St,Louis:University of Missouri-Rolla,2001.paper No.9~12.
[16]Matsui T,Bahr M A,Abe N.Estimation of shear characteristics degradation and stress-strain relationship of saturated clays after cyclicloadin[J].Soils and Foundations,1992,32(I):161~172.
[17]Yasuhara K,Hyde A F L.Method for estimating postcyclic secant modulus of clays[J].Journal of Geotechnical and GeoenvironmentalEngineering,ASCE,1997,123(3):204~211.
[18]Yasuhara K,Murakami S,Song B W,et al.Postcyclic degradation of strength and stiffness for low plasticity silt[J].Journal ofGeotechnical and Geoenvironmental Engineering,ASCE,2003,129(8):756~769.
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