r - The Hong Kong Polytechnic University

those of the average shear strength along the actual slip curve. The effective shear strength is found to be
typically slightly larger than the average shear strength along the actual slip curve. The difference is believed to
be due to the asperity of the actual slip curve, i.e., the overall shear strength is the composition of the average
shear strength along the slip curve and the dilation effect induced by the asperity.
In the case where Vanmarcke’s theory is taken to estimate the statistical behaviors of the effective shear strength,
the theory generally overestimates the mean value of the overall shear strength but underestimates the variance.
The overestimation of the mean value gets worse when the scale of fluctuation is close to the size of the soil
mass, while the underestimation of the variance gets worse when the scale of fluctuation is small.
REFERENCES
Kennedy, J. and Eberhart, R. (1995). “Particle swarm optimization”, Proceedings of IEEE International
Conference on Neural Networks, Vol IV, 1942–1948.
Pham, H.T.V. and Fredlund, D.G. (2003). “The application of dynamic programming to slope stability analysis”,
Canadian Geotechnical Journal, 40, 830-847.
Fenton, G.A. and Vanmarcke, E.H. (1990). “Simulation of random fields via local average subdivision”, Journal
of Engineering Mechanics, ASCE, 116(8), 1733-1749.
Vanmarcke, E.H. (1977). “Probabilistic modeling of soil profiles”, Journal of Geotechnical Engineering
Division, ASCE ,103(11), 1227-1246.
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