采用上限分析方法对悬臂式挡土墙进行伪静力分析（英文）
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摘要
鉴于悬臂式挡土墙在建设和开发项目中的广泛应用,合理考虑地震荷载的优化设计和分析是一个典型的工程问题。本文提出了一种利用上限法进行挡土墙拟静力分析的新算法。该算法可用于基于该机理墙体内外稳定性设计和校核。该算法的主要特点之一是能够有效地利用多目标优化,同时确定失效楔块的临界条件、作用在墙体上的最小安全系数和最大受力,以及墙体的最小重量。由所提出的失效机制所得到的结果表明,在使用上限极限分析方法时,作用力的最大化应同时考虑通过墙根后部平面方向的优化。本文还应用该算法确定了地震加速度系数的临界方向。地震加速度系数的临界方向定义为作用在墙体上的最大力方向,以保证墙体稳定的安全系数最小。本研究结果与基于极限平衡法和有限元分析的类似研究结果一致,通过遗传算法优化确定了关键失效机制。
Given the extensive utilization of cantilever retaining walls in construction and development projects, their optimal design and analysis with proper attention to seismic loads is a typical engineering problem. This research presents a new algorithm for pseudo-static analysis of retaining walls employing upper bound method. The algorithm can be utilized to design and check the external and internal stability of the wall based on the proposed mechanism. One of the main features of this algorithm is its ability to determine the critical condition of failure wedges, the minimum safety factor and maximum force acting on the wall, as well as the minimum weight of the wall, simultaneously, by effectively using the multi-objective optimization. The results obtained by the proposed failure mechanisms show that, while using the upper bound limit analysis approach, the active force should be maximized concurrent with optimizing the direction of the plane passing through the back of the heel. The present study also applies the proposed algorithm to determine the critical direction of the earthquake acceleration coefficient. The critical direction of earthquake acceleration coefficient is defined as the direction that maximizes the active force exerted on the wall and minimizes the safety factor for wall stability. The results obtained in this study are in good agreement with those of similar studies carried out based on the limit equilibrium method and finite element analysis. The critical failure mechanisms were determined via optimization with genetic algorithm.
Given the extensive utilization of cantilever retaining walls in construction and development projects, their optimal design and analysis with proper attention to seismic loads is a typical engineering problem. This research presents a new algorithm for pseudo-static analysis of retaining walls employing upper bound method. The algorithm can be utilized to design and check the external and internal stability of the wall based on the proposed mechanism. One of the main features of this algorithm is its ability to determine the critical condition of failure wedges, the minimum safety factor and maximum force acting on the wall, as well as the minimum weight of the wall, simultaneously, by effectively using the multi-objective optimization. The results obtained by the proposed failure mechanisms show that, while using the upper bound limit analysis approach, the active force should be maximized concurrent with optimizing the direction of the plane passing through the back of the heel. The present study also applies the proposed algorithm to determine the critical direction of the earthquake acceleration coefficient. The critical direction of earthquake acceleration coefficient is defined as the direction that maximizes the active force exerted on the wall and minimizes the safety factor for wall stability. The results obtained in this study are in good agreement with those of similar studies carried out based on the limit equilibrium method and finite element analysis. The critical failure mechanisms were determined via optimization with genetic algorithm.
引文
[1]YEPES V,ALCALA J,PEREA C,GONZALEZ-VIDOSA F.A parametric study of optimum earth-retaining walls by simulated annealing[J].Engineering Structures,2008,30(3):821-830.
[2]CERANIC B,FRYER C,BAINES R.An application of simulated annealing to the optimum design of reinforced concrete retaining structures[J].Computers&Structures,2001,79(17):1569-1581.
[3]SHEIKHOLESLAMI R,KHALILI B G,SADOLLAH A,KIM J H.Optimization of reinforced concrete retaining walls via hybrid firefly algorithm with upper bound strategy[J].KSCE Journal of Civil Engineering,2016,20(6):2428-2438.
[4]NAMA S,SAHA A K,GHOSH S.Parameters optimization of geotechnical problem using different optimization algorithm[J].Geotechnical and Geological Engineering.2015,33(5):1235-1253.
[5]ZENG X,STEEDMAN R S.Rotating block method for seismic displacement of gravity walls[J].Journal of Geotechnical and Geoenvironmental Engineering,2000,126(8):709-717.
[6]CHOUDHURY D,AHMAD S M.Stability of waterfront retaining wall subjected to pseudo-static earthquake forces[J].Ocean Engineering,2007,34(14):1947-1954.
[7]AHMAD S M,CHOUDHURY D.Seismic rotational stability of waterfront retaining wall using pseudodynamic method[J].International Journal of Geomechanics,2010,10(1):45-52.
[8]BASHA B M,BABU G L.Seismic rotational displacements of gravity walls by pseudodynamic method with curved rupture surface[J].International Journal of Geomechanics,2009,10(3):93-105.
[9]BASHA B M,BABU G L.Optimum design of bridge abutments under seismic conditions:Reliability-based approach[J].Journal of Bridge Engineering,2010,15(2):183-195.
[10]SIDDHARTHAN R,ARA S,NORRIS G M.Simple rigid plastic model for seismic tilting of rigid walls[J].Journal of Structural Engineering,1992,118(2):469-487.
[11]NOURI H,FAKHER A,JONES C.Development of horizontal slice method for seismic stability analysis of reinforced slopes and walls[J].Geotextiles and Geomembranes,2006,24(3):175-187.
[12]POWRIE W.Limit equilibrium analysis of embedded retaining walls[J].Geotechnique,1996,46(4):709-723.
[13]DIAKOUMI M,POWRIE W.Mobilisable strength design for flexible embedded retaining walls[J].Geotechnique,2013,63(2):95-106.
[14]AL A L,SITAR N.Seismic earth pressures on cantilever retaining structures[J].Journal of Geotechnical and Geoenvironmental Engineering,2010,136(10):1324-1333.
[15]AULBACH B,ZIEGLER M,SCHüTTRUMPF H.Design aid for the verification of resistance to failure by hydraulic heave[J].Procedia Engineering,2013,57:113-119.
[16]LI Xin-po,YONG Wu,HE Si-ming.Seismic stability analysis of gravity retaining walls[J].Soil Dynamics and Earthquake Engineering,2010,30(10):875-878.
[17]DI SANTOLO A S,EVANGELISTA A.Dynamic active earth pressure on cantilever retaining walls[J].Computers and Geotechnics,2011,38(8):1041-1051.
[18]KLOUKINAS P,DI SANTOLO A S,PENNA A,DIETZ M,EVANGELISTA A,SIMONELLI A L.Investigation of seismic response of cantilever retaining walls:Limit analysis vs shaking table testing[J].Soil Dynamics and Earthquake Engineering,2015,77:432-445.
[19]CHENG Y.Seismic lateral earth pressure coefficients for c-φsoils by slip line method[J].Computers and Geotechnics,2003,30(8):661-670.
[20]YANG X L.Upper bound limit analysis of active earth pressure with different fracture surface and nonlinear yield criterion[J].Theoretical and Applied Fracture Mechanics,2007,47(1):46-56.
[21]EVANGELISTA A,DI SANTOLO A S,SIMONELLI A L.Evaluation of pseudostatic active earth pressure coefficient of cantilever retaining walls[J].Soil Dynamics and Earthquake Engineering,2010,30(11):1119-1128.
[22]ZHANG J M,SONG F,LI D J.Effects of strain localization on seismic active earth pressures[J].Journal of Geotechnical and Geoenvironmental Engineering,2009,136(7):999-1003.
[23]ISKANDER M,CHEN ZC,OMIDVAR M,GUZMAN I.Rankine pseudo-static earth pressure for c-?soils[J].Mechanics Research Communications,2013,51:51-55.
[24]SHAMSABADI A,XU S Y,TACIROGLU E.A generalized log-spiral-Rankine limit equilibrium model for seismic earth pressure analysis[J].Soil Dynamics and Earthquake Engineering,2013,49:197-209.
[25]MONONOBE N.Consideration into earthquake vibrations and vibration theories[J].Journal of the Japan Society of Civil Engineers,1924,10(5):1063-1094.
[26]OKABE S.General theory of earthquake pressure and seismic stability of retaining wall and dams[J].J Japanese Soc of Civil Engng.1924,10(6):1277-1323.
[27]MONONOBE N,MATSUO H,EDITORS.On the determination of earth pressures during earthquakes[C]//Proceedings,World Engineering Congress.Tokyo,Japan,1929:176.
[28]HILL R.A theory of the yielding and plastic flow of anisotropic metals[C]//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences.The Royal Society,1948:281-297.
[29]CHEN W F,LIU X.Limit analysis in soil mechanics[M].Amsterdam:Elsevier,2012.
[30]COULOMB C.Essay on maximums and minimums of rules to some static problems relating to architecture[DB].1973.
[31]RANKINE WM.On the mathematical theory of the stability of earth-work and masonry[J].Proceedings of the Royal Society of London,1857,8(1):60-61.
[32]FINN W.Applications of plasticity in soil mechanics[J].Journal of Soil Mechanics&Foundations Division,1967,93(5):101-120.
[33]JAMES R,BRANSBY P L.Experimental and theoretical investigations of a passive earth pressure problem[J].Geotechnique,1970,20(1):17-37.
[34]CHEN W,ROSENFARB J.Limit analysis solutions of earth pressure problems[J].Journal of the Japanese Society of Soil Mechanics and Foundation Engineering,1973,13(4):45-60.
[35]RICHARS R,HUANG C,FISHMAN K L.Seismic earth pressure on retaining structures[J].Journal of Geotechnical and Geoenvironmental Engineering,1999,125(9):771-778.
[36]SHERIF M A,FANG Y S.Dynamic earth pressures on walls rotating about the top[J].Journal of the Japanese Society of Soil Mechanics and Foundation Engineering,1984,24(4):109-117.
[37]CALTABIANO S,CASCONE E,MAUGERI M.Static and seismic limit equilibrium analysis of sliding retaining walls under different surcharge conditions[J].Soil Dynamics and Earthquake Engineering,2012,37:38-55.
[38]LI X,SU L,WU Y,HE S.Seismic stability of gravity retaining walls under combined horizontal and vertical accelerations[J].Geotechnical and Geological Engineering,2015,33(1):161-166.
[39]CHANG M,CHEN W F.Lateral earth pressures on rigid retaining walls subjected to earthquake forces[M].School of Civil Engineering,Purdue University,1981.
[40]KARKANAKI A R,GANJIAN N,ASKARI F.Stability analysis and design of cantilever retaining walls with regard to possible failure mechanisms:An upper bound limit analysis approach[J].Geotechnical and Geological Engineering.2017,35(3):1079-1092.
[41]MORGENSTERN N,PRICE V E.The analysis of the stability of general slip surfaces[J].Geotechnique,1965,15(1):79-93.
[42]BISHOP A W.The use of the slip circle in the stability analysis of slopes[J].Geotechnique,1955,5(1):7-17.
[43]SHUKLA S K,GUPTA S K,SIVAKUGAN N.Active earth pressure on retaining wall for c-?soil backfill under seismic loading condition[J].Journal of Geotechnical and Geoenvironmental Engineering,2009,135(5):690-696.
[44]AASHTO L.LRFD bridge design specifications.Washington,DC:American Association of State Highway and Transportation Officials.1998.
[45]INSTITUTE A C.Building code requirements for structural concrete(ACI 318-05)and commentary(ACI 318R-05)[S].American Concrete Inst,2004.
[46]HOUSNER,G W.Strong ground motion[C]//WIEGEL R L.Earthquake Engineering.New York:Prentice-Hall,NY,1974:75-91.
[2]CERANIC B,FRYER C,BAINES R.An application of simulated annealing to the optimum design of reinforced concrete retaining structures[J].Computers&Structures,2001,79(17):1569-1581.
[3]SHEIKHOLESLAMI R,KHALILI B G,SADOLLAH A,KIM J H.Optimization of reinforced concrete retaining walls via hybrid firefly algorithm with upper bound strategy[J].KSCE Journal of Civil Engineering,2016,20(6):2428-2438.
[4]NAMA S,SAHA A K,GHOSH S.Parameters optimization of geotechnical problem using different optimization algorithm[J].Geotechnical and Geological Engineering.2015,33(5):1235-1253.
[5]ZENG X,STEEDMAN R S.Rotating block method for seismic displacement of gravity walls[J].Journal of Geotechnical and Geoenvironmental Engineering,2000,126(8):709-717.
[6]CHOUDHURY D,AHMAD S M.Stability of waterfront retaining wall subjected to pseudo-static earthquake forces[J].Ocean Engineering,2007,34(14):1947-1954.
[7]AHMAD S M,CHOUDHURY D.Seismic rotational stability of waterfront retaining wall using pseudodynamic method[J].International Journal of Geomechanics,2010,10(1):45-52.
[8]BASHA B M,BABU G L.Seismic rotational displacements of gravity walls by pseudodynamic method with curved rupture surface[J].International Journal of Geomechanics,2009,10(3):93-105.
[9]BASHA B M,BABU G L.Optimum design of bridge abutments under seismic conditions:Reliability-based approach[J].Journal of Bridge Engineering,2010,15(2):183-195.
[10]SIDDHARTHAN R,ARA S,NORRIS G M.Simple rigid plastic model for seismic tilting of rigid walls[J].Journal of Structural Engineering,1992,118(2):469-487.
[11]NOURI H,FAKHER A,JONES C.Development of horizontal slice method for seismic stability analysis of reinforced slopes and walls[J].Geotextiles and Geomembranes,2006,24(3):175-187.
[12]POWRIE W.Limit equilibrium analysis of embedded retaining walls[J].Geotechnique,1996,46(4):709-723.
[13]DIAKOUMI M,POWRIE W.Mobilisable strength design for flexible embedded retaining walls[J].Geotechnique,2013,63(2):95-106.
[14]AL A L,SITAR N.Seismic earth pressures on cantilever retaining structures[J].Journal of Geotechnical and Geoenvironmental Engineering,2010,136(10):1324-1333.
[15]AULBACH B,ZIEGLER M,SCHüTTRUMPF H.Design aid for the verification of resistance to failure by hydraulic heave[J].Procedia Engineering,2013,57:113-119.
[16]LI Xin-po,YONG Wu,HE Si-ming.Seismic stability analysis of gravity retaining walls[J].Soil Dynamics and Earthquake Engineering,2010,30(10):875-878.
[17]DI SANTOLO A S,EVANGELISTA A.Dynamic active earth pressure on cantilever retaining walls[J].Computers and Geotechnics,2011,38(8):1041-1051.
[18]KLOUKINAS P,DI SANTOLO A S,PENNA A,DIETZ M,EVANGELISTA A,SIMONELLI A L.Investigation of seismic response of cantilever retaining walls:Limit analysis vs shaking table testing[J].Soil Dynamics and Earthquake Engineering,2015,77:432-445.
[19]CHENG Y.Seismic lateral earth pressure coefficients for c-φsoils by slip line method[J].Computers and Geotechnics,2003,30(8):661-670.
[20]YANG X L.Upper bound limit analysis of active earth pressure with different fracture surface and nonlinear yield criterion[J].Theoretical and Applied Fracture Mechanics,2007,47(1):46-56.
[21]EVANGELISTA A,DI SANTOLO A S,SIMONELLI A L.Evaluation of pseudostatic active earth pressure coefficient of cantilever retaining walls[J].Soil Dynamics and Earthquake Engineering,2010,30(11):1119-1128.
[22]ZHANG J M,SONG F,LI D J.Effects of strain localization on seismic active earth pressures[J].Journal of Geotechnical and Geoenvironmental Engineering,2009,136(7):999-1003.
[23]ISKANDER M,CHEN ZC,OMIDVAR M,GUZMAN I.Rankine pseudo-static earth pressure for c-?soils[J].Mechanics Research Communications,2013,51:51-55.
[24]SHAMSABADI A,XU S Y,TACIROGLU E.A generalized log-spiral-Rankine limit equilibrium model for seismic earth pressure analysis[J].Soil Dynamics and Earthquake Engineering,2013,49:197-209.
[25]MONONOBE N.Consideration into earthquake vibrations and vibration theories[J].Journal of the Japan Society of Civil Engineers,1924,10(5):1063-1094.
[26]OKABE S.General theory of earthquake pressure and seismic stability of retaining wall and dams[J].J Japanese Soc of Civil Engng.1924,10(6):1277-1323.
[27]MONONOBE N,MATSUO H,EDITORS.On the determination of earth pressures during earthquakes[C]//Proceedings,World Engineering Congress.Tokyo,Japan,1929:176.
[28]HILL R.A theory of the yielding and plastic flow of anisotropic metals[C]//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences.The Royal Society,1948:281-297.
[29]CHEN W F,LIU X.Limit analysis in soil mechanics[M].Amsterdam:Elsevier,2012.
[30]COULOMB C.Essay on maximums and minimums of rules to some static problems relating to architecture[DB].1973.
[31]RANKINE WM.On the mathematical theory of the stability of earth-work and masonry[J].Proceedings of the Royal Society of London,1857,8(1):60-61.
[32]FINN W.Applications of plasticity in soil mechanics[J].Journal of Soil Mechanics&Foundations Division,1967,93(5):101-120.
[33]JAMES R,BRANSBY P L.Experimental and theoretical investigations of a passive earth pressure problem[J].Geotechnique,1970,20(1):17-37.
[34]CHEN W,ROSENFARB J.Limit analysis solutions of earth pressure problems[J].Journal of the Japanese Society of Soil Mechanics and Foundation Engineering,1973,13(4):45-60.
[35]RICHARS R,HUANG C,FISHMAN K L.Seismic earth pressure on retaining structures[J].Journal of Geotechnical and Geoenvironmental Engineering,1999,125(9):771-778.
[36]SHERIF M A,FANG Y S.Dynamic earth pressures on walls rotating about the top[J].Journal of the Japanese Society of Soil Mechanics and Foundation Engineering,1984,24(4):109-117.
[37]CALTABIANO S,CASCONE E,MAUGERI M.Static and seismic limit equilibrium analysis of sliding retaining walls under different surcharge conditions[J].Soil Dynamics and Earthquake Engineering,2012,37:38-55.
[38]LI X,SU L,WU Y,HE S.Seismic stability of gravity retaining walls under combined horizontal and vertical accelerations[J].Geotechnical and Geological Engineering,2015,33(1):161-166.
[39]CHANG M,CHEN W F.Lateral earth pressures on rigid retaining walls subjected to earthquake forces[M].School of Civil Engineering,Purdue University,1981.
[40]KARKANAKI A R,GANJIAN N,ASKARI F.Stability analysis and design of cantilever retaining walls with regard to possible failure mechanisms:An upper bound limit analysis approach[J].Geotechnical and Geological Engineering.2017,35(3):1079-1092.
[41]MORGENSTERN N,PRICE V E.The analysis of the stability of general slip surfaces[J].Geotechnique,1965,15(1):79-93.
[42]BISHOP A W.The use of the slip circle in the stability analysis of slopes[J].Geotechnique,1955,5(1):7-17.
[43]SHUKLA S K,GUPTA S K,SIVAKUGAN N.Active earth pressure on retaining wall for c-?soil backfill under seismic loading condition[J].Journal of Geotechnical and Geoenvironmental Engineering,2009,135(5):690-696.
[44]AASHTO L.LRFD bridge design specifications.Washington,DC:American Association of State Highway and Transportation Officials.1998.
[45]INSTITUTE A C.Building code requirements for structural concrete(ACI 318-05)and commentary(ACI 318R-05)[S].American Concrete Inst,2004.
[46]HOUSNER,G W.Strong ground motion[C]//WIEGEL R L.Earthquake Engineering.New York:Prentice-Hall,NY,1974:75-91.