土石坝坡极限抗震能力的下限有限元法
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摘要
基于极限分析下限定理,假设材料严格服从Mohr–Coulomb屈服准则,同时考虑了堆石料内摩擦角较大以及抗剪强度具有非线性的特性,提出了一个用于求解土石坝坝坡极限抗震能力的有限元计算方法。该方法通过静力平衡条件、应力间断面连续条件、边界条件、屈服条件以及所求极限荷载,形成标准的二次锥规划数学模型,并用内点法进行优化迭代求解,得到土石坝坡极限抗震能力的下限值。对一条形基础地基承载力进行下限极限分析,通过与已有计算结果比较表明所提方法的具有很高的计算精度。运用所提方法对一典型心墙土石坝进行抗震极限分析,其计算结果符合土石坝坡在地震作用下的一般破坏规律,证明此方法具有很高的实用价值。
An FEM based on the lower bound theorem of limit analysis is proposed to study the limit aseismic capability of earth-rock-fill dams.Considering the large internal friction angel and non-linear shear strength parameters of rockfill materials,the proposed method formulates the limit analysis as a second-order cone programming(SOCP) problem with constraints based on the conditions of equilibrium,stress discontinuity,stress boundary and native Mohr-Coulomb yield criterion.The lower bound of the limit aseismic capability is then obtained by means of the interior-point algorithm and the iterative approach.Comparison with the published solutions illustrates the correctness and effectiveness of the proposed method for a smooth strip footing problem.The proposed approach is also applied to the seismic stability analysis of a typical rockfill dam with core wall so that the limit aseismic capability of the dam is obtained.The results proclaim the seismic failure mechanisms of earth-rockfill dams and demonstrate the practical value of the proposed method.
An FEM based on the lower bound theorem of limit analysis is proposed to study the limit aseismic capability of earth-rock-fill dams.Considering the large internal friction angel and non-linear shear strength parameters of rockfill materials,the proposed method formulates the limit analysis as a second-order cone programming(SOCP) problem with constraints based on the conditions of equilibrium,stress discontinuity,stress boundary and native Mohr-Coulomb yield criterion.The lower bound of the limit aseismic capability is then obtained by means of the interior-point algorithm and the iterative approach.Comparison with the published solutions illustrates the correctness and effectiveness of the proposed method for a smooth strip footing problem.The proposed approach is also applied to the seismic stability analysis of a typical rockfill dam with core wall so that the limit aseismic capability of the dam is obtained.The results proclaim the seismic failure mechanisms of earth-rockfill dams and demonstrate the practical value of the proposed method.
引文
[1]赵剑明,刘小生,陈宁,等.高心墙堆石坝的极限抗震能力研究[J].水力发电学报,2009,28(5):97–102.(ZHAO Jian-ming,LIU Xiao-sheng,CHEN Ning.Research on the maximum anti-seismic capability of high earth core rock-fill dam[J].Journal of Hydroelectric Engineering,2009,28(5):97–102.(in Chinese))
[2]李广信.高等土力学[M].北京:清华大学出版社,2004.(LI Guang-xin.Advanced soil mechanics[M].Beijing:Tsinghua University Press,2004.(in Chinese))
[3]SLOAN S W.Lower bound limit analysis using finite elements and linear programming[J].International Journal Analytical Method in Geomechanics,1988,12:61–77.
[4]SLOAN S W.Upper bound limit analysis using finite elements and linear programming[J].International Journal Analytical Method in Geomechanics,1989,13(3):263-282.
[5]SLOAN S W,KLEEMAN P W.Upper bound limit analysis using discontinuous velocity fields[J].Computer Methods Application Mechanics Engineering,1995,127:293–314.
[6]YU H S,SALGADO R,SLOAN S W,et al.Limit analysis versus limit equilibrium for slope stability[J].Journal of Geotechnical and Geoenvironment Engineering,ASCE,1998,124(1):1–11.
[7]INDRARATNA B,WIJEWARDENA L S S,BALASUBRAMANIAM A S.Large-scale triaxial testing of greywacke rockfill[J].Géotechnique,1993,43(1):37–51.
[8]柏树田,崔亦昊.堆石的力学性质[J].水力发电学报,1997(3):21–30.(BAI Shu-tian,CUI Yi-hao.The mechanical properties of rockfill[J].Journal of Hydroelectric Engineering,1997(3):21–30.(in Chinese))
[9]李泽,王均星.基于非线性规划的岩质边坡有限元塑性极限分析下限法研究[J].岩石力学与工程学报,2007,26(4):747–753.(LI Ze,WANG Jun-xing.Lower bound limit study on plastic limit analysis of rock slope using finite elements based on nonlinear programming[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(4):747–753.(in Chinese))
[10]BELYTSCHKO T,HODGE PG.Plane stress limit analysis by finite elements[J].Journal of the Engineering Mechanics Division(ASCE),1970,96(6):931–944.
[11]OUAIN N,HERSKOVITS J,BORGES LA,et al.An iterative algorithm for limit analysis with nonlinear yield functions[J].International Journal of Solids and Structures,1993,30(10):1397–1417.
[12]CHRISTIANSEN E,ANDERSEN K D.Computation of collapse states with von Mises type yield condition[J].International Journal for Numerical Methods in Engineering,1999,46(8):1185–1202.
[13]LYAMIN AV,SLOAN SW.Upper bound analysis using linear finite elements and non-linear programming[J].International Journal for Numerical and Analytical Methods in Geomechanics,2002,26(2):181–216.
[14]MAKRODIMOPOULOS A,MARTIN C M.Lower boundlimit analysis of cohesive-frictional materials using second-order cone programming[J].International Journal for Numerical Methods in Engineering,2006,66(4):604–634.
[15]DL5073—2000水工建筑物抗震设计规范[S].北京:中国电力出版社,2000.(DL5073—2000Specifications for seismic design of hydraulic structures[S].Beijing:China Electric Power Press,2000.(in Chinese))
[16]TüTüNCüR H,TOH K C,TODD M J.Solving semidefinite-quadratic-linear Programs Using SDPT3[J].Mathematical Programming,2003,95(2):189–217.
[17]DUNCAN J M,BYRNE P M,WONG K S.Strength,stress-strain and bulk modulus parameters for finite element-analysis of stress and movements in soil masses.Report No.VCB/GT/78-02[R].Berkeley:University of California,1978.
[18]DRESCHER A,DETOURNAY E.Limit load in translational failure mechanics for associative and non-associativematerials[J].Geotechnique,1993,43(3):443–456.
[19]MICHALOWSKI R L,SHI L.Bearing capacity of footing over two-layer foundation soils[J].Journal of Geotechnical Engineering,ASCE,1995,121(5):421–428.
[20]唐洪祥,邵龙潭.地震动力作用下有限元土石坝边坡稳定性分析[J].岩石力学与工程学报,2004,23(8):1318–1324.(TANG Hong-xiang,SHAO Long-tan.Finite element analysis on slope stability of earth-rock dam under earthquake[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(8):1318–1324.(in Chinese))
[21]李国英,沈婷,赵魁芝.高心墙堆石坝地震动力特性及抗震极限分析[J].水利水运工程学报,2010(1):1–8.(LI Guo-ying,SHEN Ting,ZHAO Kui-zhi.Seismic dynamic behavior and limit seismic analysis on high earth core rock-fill dams[J].Hydro-science and Engineering,2010(1):1–8.(in Chinese))
[2]李广信.高等土力学[M].北京:清华大学出版社,2004.(LI Guang-xin.Advanced soil mechanics[M].Beijing:Tsinghua University Press,2004.(in Chinese))
[3]SLOAN S W.Lower bound limit analysis using finite elements and linear programming[J].International Journal Analytical Method in Geomechanics,1988,12:61–77.
[4]SLOAN S W.Upper bound limit analysis using finite elements and linear programming[J].International Journal Analytical Method in Geomechanics,1989,13(3):263-282.
[5]SLOAN S W,KLEEMAN P W.Upper bound limit analysis using discontinuous velocity fields[J].Computer Methods Application Mechanics Engineering,1995,127:293–314.
[6]YU H S,SALGADO R,SLOAN S W,et al.Limit analysis versus limit equilibrium for slope stability[J].Journal of Geotechnical and Geoenvironment Engineering,ASCE,1998,124(1):1–11.
[7]INDRARATNA B,WIJEWARDENA L S S,BALASUBRAMANIAM A S.Large-scale triaxial testing of greywacke rockfill[J].Géotechnique,1993,43(1):37–51.
[8]柏树田,崔亦昊.堆石的力学性质[J].水力发电学报,1997(3):21–30.(BAI Shu-tian,CUI Yi-hao.The mechanical properties of rockfill[J].Journal of Hydroelectric Engineering,1997(3):21–30.(in Chinese))
[9]李泽,王均星.基于非线性规划的岩质边坡有限元塑性极限分析下限法研究[J].岩石力学与工程学报,2007,26(4):747–753.(LI Ze,WANG Jun-xing.Lower bound limit study on plastic limit analysis of rock slope using finite elements based on nonlinear programming[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(4):747–753.(in Chinese))
[10]BELYTSCHKO T,HODGE PG.Plane stress limit analysis by finite elements[J].Journal of the Engineering Mechanics Division(ASCE),1970,96(6):931–944.
[11]OUAIN N,HERSKOVITS J,BORGES LA,et al.An iterative algorithm for limit analysis with nonlinear yield functions[J].International Journal of Solids and Structures,1993,30(10):1397–1417.
[12]CHRISTIANSEN E,ANDERSEN K D.Computation of collapse states with von Mises type yield condition[J].International Journal for Numerical Methods in Engineering,1999,46(8):1185–1202.
[13]LYAMIN AV,SLOAN SW.Upper bound analysis using linear finite elements and non-linear programming[J].International Journal for Numerical and Analytical Methods in Geomechanics,2002,26(2):181–216.
[14]MAKRODIMOPOULOS A,MARTIN C M.Lower boundlimit analysis of cohesive-frictional materials using second-order cone programming[J].International Journal for Numerical Methods in Engineering,2006,66(4):604–634.
[15]DL5073—2000水工建筑物抗震设计规范[S].北京:中国电力出版社,2000.(DL5073—2000Specifications for seismic design of hydraulic structures[S].Beijing:China Electric Power Press,2000.(in Chinese))
[16]TüTüNCüR H,TOH K C,TODD M J.Solving semidefinite-quadratic-linear Programs Using SDPT3[J].Mathematical Programming,2003,95(2):189–217.
[17]DUNCAN J M,BYRNE P M,WONG K S.Strength,stress-strain and bulk modulus parameters for finite element-analysis of stress and movements in soil masses.Report No.VCB/GT/78-02[R].Berkeley:University of California,1978.
[18]DRESCHER A,DETOURNAY E.Limit load in translational failure mechanics for associative and non-associativematerials[J].Geotechnique,1993,43(3):443–456.
[19]MICHALOWSKI R L,SHI L.Bearing capacity of footing over two-layer foundation soils[J].Journal of Geotechnical Engineering,ASCE,1995,121(5):421–428.
[20]唐洪祥,邵龙潭.地震动力作用下有限元土石坝边坡稳定性分析[J].岩石力学与工程学报,2004,23(8):1318–1324.(TANG Hong-xiang,SHAO Long-tan.Finite element analysis on slope stability of earth-rock dam under earthquake[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(8):1318–1324.(in Chinese))
[21]李国英,沈婷,赵魁芝.高心墙堆石坝地震动力特性及抗震极限分析[J].水利水运工程学报,2010(1):1–8.(LI Guo-ying,SHEN Ting,ZHAO Kui-zhi.Seismic dynamic behavior and limit seismic analysis on high earth core rock-fill dams[J].Hydro-science and Engineering,2010(1):1–8.(in Chinese))
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