Abstract
Geotechnical engineers have long used the lumped factor of safety approach in design of retaining walls. In recent years, uncertainty inherent in soil properties has caught more attentions from researchers, thus reliability analyses are used widely. In short, combining the probabilistic and deterministic analysis is common practice nowadays and failure probability calculated by risk analysis is a kind of complement of safety factor. In this paper, reliability analysis of a deep excavation is presented using two probabilistic methods called Point Estimate Method (PEM) and Monte Carlo Simulation (MCS) method. Horizontal displacement of the excavated wall, as well as safety of factor, are adopted as a basis for assessing the performance stability of the system. The paper explains why probabilistic analysis with numerical methods is challenging, and how PEM and MCS can be used to calculate the statistical moments of output variables and to estimate probability of failure. The results are presented and compared in terms of statistical moments, probability of occurrence and most likely values at every stage of construction.
Highlights
Due to the deposition nature of soil masses, their properties can vary significantly from place to place, even over short distances
Point Estimate Method (PEM) There are two main distinguishable approaches for the Point Estimate Method: first, the original approach proposed by Rosenblueth [31] and its modified method given by his followers (e.g. [8, 16, 18, 21]) that attempted to save computational cost by reducing the number of prefixed sampling points
The Monte Carlo Simulation (MCS) results in Finite Difference (FD) analysis presented an unstable condition in trials up to n = 400, which indicates that much more simulations are required in complex types of analysis; PEM, despite differences mentioned earlier, can be preferable to MCS in predicting pf values in serviceability reliability analysis of deep excavations with much less computational effort needed
Summary
Due to the deposition nature of soil masses, their properties can vary significantly from place to place, even over short distances. Even when soil properties can be readily determined, inaccuracies in measurement and differences between laboratory and field-scale behavior introduce significant error. The engineering of excavations in soil involves large uncertainties and predictions based on single evaluations have practically zero probability of ever being realized, and design decisions based on them are open to question. [6, 25]) They solved these problems by deterministic calculation using safety factors and adopting conservative assumptions in the process of engineering planning and design. In this way, an engineering system can be over-designed
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