Advertisement

Journal of Central South University

, Volume 26, Issue 1, pp 241–255 | Cite as

Pseudo-static analysis of cantilever retaining walls using upper bound limit analysis approach

  • Asadollah Ranjbar Karkanaki
  • Navid GanjianEmail author
  • Farajollah Askari
Article
  • 7 Downloads

Abstract

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.

Key words

retaining wall upper bound pseudo-static analysis safety factor multi-objective optimization 

采用上限分析方法对悬臂式挡土墙进行伪静力分析

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。

关键词

挡土墙 上限 伪静态的分析 安全系数 多目标优化 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference

  1. [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.Google Scholar
  2. [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.Google Scholar
  3. [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.Google Scholar
  4. [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.Google Scholar
  5. [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.Google Scholar
  6. [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.Google Scholar
  7. [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.Google Scholar
  8. [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.Google Scholar
  9. [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.Google Scholar
  10. [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.Google Scholar
  11. [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.Google Scholar
  12. [12]
    POWRIE W. Limit equilibrium analysis of embedded retaining walls [J]. Geotechnique, 1996, 46(4): 709–723.Google Scholar
  13. [13]
    DIAKOUMI M, POWRIE W. Mobilisable strength design for flexible embedded retaining walls [J]. Geotechnique, 2013, 63(2): 95–106.Google Scholar
  14. [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.Google Scholar
  15. [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.Google Scholar
  16. [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.Google Scholar
  17. [17]
    DI SANTOLO A S, EVANGELISTA A. Dynamic active earth pressure on cantilever retaining walls [J]. Computers and Geotechnics, 2011, 38(8): 1041–1051.Google Scholar
  18. [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.Google Scholar
  19. [19]
    CHENG Y. Seismic lateral earth pressure coefficients for c–f soils by slip line method [J]. Computers and Geotechnics, 2003, 30(8): 661–670.MathSciNetGoogle Scholar
  20. [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.Google Scholar
  21. [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.Google Scholar
  22. [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.Google Scholar
  23. [23]
    ISKANDER M, CHEN ZC, OMIDVAR M, GUZMAN I. Rankine pseudo–static earth pressure for c–ø soils [J]. Mechanics Research Communications, 2013, 51: 51–55.Google Scholar
  24. [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.Google Scholar
  25. [25]
    MONONOBE N. Consideration into earthquake vibrations and vibration theories [J]. Journal of the Japan Society of Civil Engineers, 1924, 10(5): 1063–1094.Google Scholar
  26. [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.Google Scholar
  27. [27]
    MONONOBE N, MATSUO H, EDITORS. On the determination of earth pressures during earthquakes [C]// Proceedings, World Engineering Congress. Tokyo, Japan, 1929: 176.Google Scholar
  28. [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.Google Scholar
  29. [29]
    CHEN W F, LIU X. Limit analysis in soil mechanics [M]. Amsterdam: Elsevier, 2012.Google Scholar
  30. [30]
    COULOMB C. Essay on maximums and minimums of rules to some static problems relating to architecture [DB]. 1973.Google Scholar
  31. [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.Google Scholar
  32. [32]
    FINN W. Applications of plasticity in soil mechanics [J]. Journal of Soil Mechanics & Foundations Division, 1967, 93(5): 101–120.Google Scholar
  33. [33]
    JAMES R, BRANSBY P L. Experimental and theoretical investigations of a passive earth pressure problem [J]. Geotechnique, 1970, 20(1): 17–37.Google Scholar
  34. [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.Google Scholar
  35. [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.Google Scholar
  36. [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.Google Scholar
  37. [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.Google Scholar
  38. [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.Google Scholar
  39. [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.Google Scholar
  40. [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.Google Scholar
  41. [41]
    MORGENSTERN N, PRICE V E. The analysis of the stability of general slip surfaces [J]. Geotechnique, 1965, 15(1): 79–93.Google Scholar
  42. [42]
    BISHOP A W. The use of the slip circle in the stability analysis of slopes [J]. Geotechnique, 1955, 5(1): 7–17.Google Scholar
  43. [43]
    SHUKLA S K, GUPTA S K, SIVAKUGAN N. Active earth pressure on retaining wall for c–ø soil backfill under seismic loading condition [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2009, 135(5): 690–696.Google Scholar
  44. [44]
    AASHTO L. LRFD bridge design specifications. Washington, DC: American Association of State Highway and Transportation Officials. 1998.Google Scholar
  45. [45]
    INSTITUTE A C. Building code requirements for structural concrete (ACI 318–05) and commentary (ACI 318R–05) [S]. American Concrete Inst, 2004.Google Scholar
  46. [46]
    HOUSNER, G W. Strong ground motion [C]// WIEGEL R L. Earthquake Engineering. New York: Prentice–Hall, NY, 1974: 75–91.Google Scholar

Copyright information

© Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Asadollah Ranjbar Karkanaki
    • 1
  • Navid Ganjian
    • 1
    Email author
  • Farajollah Askari
    • 2
  1. 1.Department of Civil Engineering, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Iran International Earthquake Engineering InstituteTehranIran

Personalised recommendations