Probabilistic analysis of the active earth pressure on earth retaining walls for c-ϕ soils according to the Mazindrani and Ganjali method

Abstract

The determination of the earth pressure coefficients (K) in geotechnical engineering is one of the most critical procedures in designing earth retaining walls. However, most earth pressure theories are made for either clay or sands, where the c-ϕ soils are the least analysed. In this paper, an analysis of the earth pressure for drained mixed soils based in Mazindrani and Ganjali (J Geotech Geoenviron Eng 123:110–112, 1997) theory was carried out. Earth pressure coefficients are generally used in a deterministic way and can represent designs under an inadmissible risk. Therefore, Reliability-based design arises as an essential tool to deal with soil variability as one of the main aspects of the geotechnical uncertainties. The influence of the soil variability in the active earth pressure for a c-ϕ soil was performed through probabilistic analysis concerning the Ka coefficient of variation (Cv) of both shear strength parameters. The sensitivity analysis shows a Cv in which the cohesion begins to have a more significant correlation with Ka than the friction angle. The results show an increase of the statistical Ka concerning the deterministic value as the soil variability and the soil slope (β) increase. Although the statistical value does not increase significantly, a statistical analysis on gravity walls and sheet pile walls in c-ϕ soils shows a significant probability of failure (pf) increase. The pf obtained through the c-ϕ variability can be considered inadmissible even if the required FS are met.

Reliability analysis and uncertainty quantification of clay and sand slopes stability evaluated by Fellenius and Bishop’s simplified methods

“…Recently, probabilistic analyses have been implemented to assess the probabilistic outcomes, such as the failure probability or reliability index (RI) of the geotechnical problems [3,7,8]. Three methods, including the mean value first-order second-moment method (MVFOSM), the first-order reliability method (FORM), and Monte Carlo simulation (MCS), are commonly applied to assess probabilistic safety levels.…”

“…Three methods, including the mean value first-order second-moment method (MVFOSM), the first-order reliability method (FORM), and Monte Carlo simulation (MCS), are commonly applied to assess probabilistic safety levels. MVFOSM, the simplest method, is the earliest procedure employed to deal with uncertainties [4,8,9]. MVFOSM uses Taylor's series to approximate the first two terms of statistical properties, i.e., the mean and standard deviation, to assess RIs.…”