Probabilistic Safety Evaluation of a Concrete arch dam Based on Finite Element Modeling and A Reliability <i>L-R</i> Approach

Abstract

The safety assessment of the Pacoima arch dam is investigated in this paper. A Load – Resistance (L-R) method was used to ensure that the dam is safe or if it is at risk of failure. The “probabilistic design system” ANSYS finite element software was used to calculate the probability of failure. The Monte Carlo (MC) method with 50,000 iterations utilized for simulation and the Latin Hypercube method were used for Sampling. Input random variables with normal distribution and coefficient of variation of 15% due to uncertainties were considered and the six random variables used are the concrete modulus of elasticity, Poisson’s ratio of concrete, concrete mass, up-stream normal water level of the reservoir, and the allowable tensile and compressive strength of the concrete. Linear elastic behavior was assumed for the constitutive law of concrete material and if the stress exceeds the allowable stress of the concrete this is considered as a failure limit state. The maximum and minimum principal stresses were considered as the output parameter. Dam body safety was investigated only under self-weight and upstream hydrostatic pressure at the normal water level. The probability of failure of the dam body system was determined as <i>β</i><i>system</i>=3.98, the safety index as p<sub>f</sub><sup>system</sup> =3.42×10<sup>−15</sup> and the dam is at risk of failure. The first and third principal stresses in the dam body were also S1<sup>max</sup>=2.03MPa and S3<sup>min</sup>=4.6MPa, respectively for the worst case of MC simulation.