Reliability Analysis of Gully Wall Slope Stability and Gully Bed Erosion of Ekhaguere Gully in Benin City, Nigeria

Abstract

Reliability analysis presents a logical way to quantitatively
estimate the factor of safety (FoS) of geotechnical structures from
a probabilistic viewpoint. However, due to the extensive
computational requirements and poor efficiency of reliability
analysis, its application in estimating the FoS of gully wall slopes
is often hindered. In this study, slope stability reliability analysis
was carried out for the Ekhaguere gully in Benin City, Edo State.
In doing so, ten thousand (10,000) random numbers were
generated for the different soil properties based on the probability
distribution parameters to obtain 10,000 random samples of slope
stability results of FoS for the gully walls (left and right walls of
the gully). Knowing the mean value and the coefficient of variation,
it was possible to define their standard deviations and shapes of
the probability density functions. The probability density functions
(pdf) of three different probability distributions (Normal,
Lognormal and Weibull distributions) were fitted to the histogram
of the FoS values of the gully wall. The pdf describes the relative
likelihood that the variables will have a certain value within the
range of potential values. The results of the reliability analysis
showed that the gully wall slope stability reliability index value of
0.84 is less than the target reliability index value of 3.8
recommended in BS EN 1990, suggesting that the gully slope is
unsafe. Reliability analysis for the gully bed erosion showed that
the probability of getting moderate to severe annual rate of soil
loss is very low and that the likely soil erosion rate will be in the
region of very low to the lower bound of moderate soil loss (0 – 7
tonnes/hectare/year). The results suggest that the predicted
erosion rates for the gully are unsatisfactory.