System reliability analysis of the external stability of reinforced soil structures

A probabilistic model is formulated in order to assess the reliability of the external stability of reinforced soil structures, in the presence of geotechnical and material uncertainty. Three modes of failure are taken into account (bearing capacity, sliding and excessive eccentricity) and overall stability is modelled as an in-series system. Geomaterial shear strength properties are modelled as beta-distributed random variables and system reliability is computed using a Monte Carlo simulation algorithm that does not require arbitrary assumptions of independence between potential failure modes. Dependency between failure modes is evaluated in terms of coefficients of linear correlation. As an illustration of the developed methodology, a case example is analysed and results are discussed in the context of system reliability analysis. For this example, the results demonstrate that the bearing capacity failure mode is subjected to a higher degree of uncertainty, compared to sliding and excessive eccentricity. The computed system probability of failure indicates that commonly accepted simplifications of complete independence or perfect correlation between the failure modes (expressed through first-order reliability bounds) may not be appropriate, particularly when the reliability bounds are not close to each other. On the other hand, the second-order reliability bounds seem to accurately reflect the computed system probability of failure. Finally, in the present study, the results indicate that ignoring the cross-correlation between the shear strength parameters has an impact on the computed system probability of failure.

[1]  Alfredo H.-S. Ang,et al.  Reliability of Structures and Structural Systems , 1968 .

[2]  J. Christian,et al.  Reliability Applied to Slope Stability Analysis , 1994 .

[3]  Donald E. Myers,et al.  Reliability and Statistics in Geotechnical Engineering , 2005, Technometrics.

[4]  B. Munwar Basha,et al.  Target reliability based design optimization of anchored cantilever sheet pile walls , 2008 .

[5]  Ioannis E. Zevgolis,et al.  Probabilistic analysis of retaining walls , 2010 .

[6]  Kok-Kwang Phoon,et al.  Multiple Resistance Factor Design for Shallow Transmission Line Structure Foundations , 2003 .

[7]  Craig H. Benson,et al.  Method to Estimate the System Probability of Failure of Mechanically Stabilized Earth (MSE) Walls , 2005 .

[8]  Trevor L. L. Orr,et al.  Selection of characteristic values and partial factors in geotechnical designs to Eurocode 7 , 2000 .

[9]  B. Munwar Basha,et al.  Optimum design of cantilever sheet pile walls in sandy soils using inverse reliability approach , 2008 .

[10]  Franco Oboni,et al.  Simplified use of the beta distribution and sensitivity to the bound locations , 1985 .

[11]  O. Ditlevsen.  Narrow Reliability Bounds for Structural Systems , 1979 .

[12]  Victor Elias,et al.  Mechanically Stabilized Earth Walls and Reinforced Soil Slopes Design and Construction Guidelines , 1997 .

[13]  K Close,et al.  AMERICAN ASSOCIATION OF STATE HIGHWAY AND TRANSPORTATION OFFICIALS COMPUTER SYSTEMS INDEX , 1976 .

[14]  B. M. Basha,et al.  Seismic reliability assessment of external stability of reinforced soil walls using pseudo-dynamic method , 2009 .

[15]  Wilson H. Tang,et al.  Probability concepts in engineering planning and design , 1984 .

[16]  Ioannis Zevgolis,et al.  Numerical and probabilistic analysis of reinforced soil structures , 2007 .

[17]  Claudia Cherubini,et al.  Reliability evaluation of shallow foundation bearing capacity on c', Φ' soils , 2000 .

[18]  A. H. S. Ang,et al.  Probability Concepts in Engineering Planning and Design Volume II Decision , 1984 .

[19]  Gordon A. Fenton,et al.  Bearing-capacity prediction of spatially random c ϕ soils , 2003 .

[20]  J. C. Cluley,et al.  Probabilistic Reliability: an Engineering Approach , 1968 .

[21]  Ioannis E. Zevgolis,et al.  Stochastic Modeling of Redundancy in Mechanically Stabilized Earth (MSE) Walls , 2008 .

[22]  Kok-Kwang Phoon,et al.  Evaluation of Geotechnical Property Variability , 1999 .

[23]  G. R. Dodagoudar,et al.  Reliability analysis of reinforced soil walls under static and seismic forces , 2008 .

[24]  Hid N. Grouni,et al.  Reliability based design in civil engineering , 1988 .

[25]  Craig H. Benson,et al.  Reliability-Based Design for External Stability of Mechanically Stabilized Earth Walls , 2005 .

[26]  Robert V. Whitman,et al.  EVALUATING CALCULATED RISK IN GEOTECHNICAL ENGINEERING , 1984 .

[27]  K. Grace,et al.  Probabilistic Reliability: An Engineering Approach , 1968 .

[28]  Peter Lumb,et al.  Safety factors and the probability distribution of soil strength , 1970 .

[29]  Kok-Kwang Phoon,et al.  Engineering Judgment in the Evolution from Deterministic to Reliability-Based Foundation Design , 1996 .

[30]  Ioannis E. Zevgolis,et al.  System Reliability of Cantilever Retaining Walls with Correlated Failure Modes , 2006 .