Probabilistic models for the erosion rate in embankments and reliability analysis of earth dams

Abstract Probabilistic models for the concentrated leak erosion of earthen water retaining structures are presented. The models predict the values of the critical shear stress, the coefficient of erosion and the pipe radius enlargement, starting from other measurable soil properties and the geometrical dimensions of the embankment. The models account for both the non-cohesive and cohesive contributions to the erosion behavior. A Bayesian approach is used for the treatment of the unknown parameters. An importance sampling simulation is adopted to calibrate the models and estimate the posterior distribution of the unknown model parameters using laboratory and in situ experimental data. The new proposed probabilistic model for the pipe radius is then used to develop fragility curves that capture the pipe enlargement as a function of time for a given earth dam.

[1]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[2]  Zhenlin Yang,et al.  A Modified Family of Power Transformations , 2006 .

[3]  Stéphane Bonelli,et al.  Investigating concentrated leak erosion behaviour of cohesive soils by performing hole erosion tests , 2012 .

[4]  R. Müller,et al.  Formulas for Bed-Load transport , 1948 .

[5]  Henrik O. Madsen,et al.  Structural Reliability Methods , 1996 .

[6]  Alfredo Ang H.-S.,et al.  Probability concepts in engineering planning and design, vol i : basic principles , 1979 .

[7]  Michael Collins,et al.  The influence of clay on the threshold of movement of fine sandy beds , 1997 .

[8]  G. J. Hanson,et al.  APPARATUS, TEST PROCEDURES, AND ANALYTICAL METHODS TO MEASURE SOIL ERODIBILITY IN SITU , 2004 .

[9]  Robin Fell,et al.  Laboratory Tests on the Rate of Piping Erosion of Soils in Embankment Dams , 2004 .

[10]  A. Kiureghian,et al.  Multivariate distribution models with prescribed marginals and covariances , 1986 .

[11]  Anders Rønnquist,et al.  Global Buckling Reliability Analysis of Slender Network Arch Bridges: An Application of Monte Carlo-Based Estimation by Optimized Fitting , 2017 .

[12]  Gregory J. Hanson,et al.  Erodibility of cohesive streambeds in the loess area of the midwestern USA , 2001 .

[13]  R. Fell,et al.  The statistics of embankment dam failures and accidents , 2000 .

[14]  Robin Fell,et al.  Investigation of Rate of Erosion of Soils in Embankment Dams , 2004 .

[15]  Stéphane Bonelli,et al.  The scaling law in the hole erosion test with a constant pressure drop , 2008 .

[16]  G. J. Hanson,et al.  SURFACE ERODIBILITY OF EARTHEN CHANNELS AT HIGH STRESSES PART II - DEVELOPING AN IN SITU TESTING DEVICE , 1990 .

[17]  S. Bonelli,et al.  Piping flow erosion in water retaining structures: inferring erosion rates from hole erosion tests and quantifying the failure time , 2010 .

[18]  Stéphane Bonelli,et al.  Concentrated Leak Erosion , 2013 .

[19]  Robin Fell,et al.  State of The Art on the Likelihood of Internal Erosion of Dams and Levees by Means of Testing , 2013 .

[20]  Armen Der Kiureghian,et al.  PROBABILISTIC SEISMIC DEMAND MODELS AND FRAGILITY ESTIMATES FOR RC BRIDGES , 2003 .

[21]  Armen Der Kiureghian,et al.  Probabilistic Capacity Models and Fragility Estimates for Reinforced Concrete Columns based on Experimental Observations , 2002 .

[22]  Paolo Gardoni,et al.  Probabilistic capacity models and fragility estimates for RC columns retrofitted with FRP composites , 2014 .

[23]  M. V. Ledden,et al.  Sand-mud segregation in estuaries and tidal basins , 2003 .

[24]  R. P. Beasley,et al.  The tractive force theory applied to stability of open channels in cohesive soils , 1959 .

[25]  F. Richards.  A Method of Maximum‐Likelihood Estimation , 1961 .

[26]  Kevin S. Richards,et al.  Critical appraisal of piping phenomena in earth dams , 2007 .

[27]  Gregory J. Hanson,et al.  DEVELOPMENT OF A JET INDEX TO CHARACTERIZE EROSION RESISTANCE OF SOILS IN EARTHEN SPILLWAYS , 1991 .

[28]  Paolo Gardoni,et al.  Probabilistic Models for Erosion Parameters and Reliability Analysis of Earth Dams and Levees , 2016 .