Dv. Griffiths et Ga. Fenton, 3-DIMENSIONAL SEEPAGE THROUGH SPATIALLY RANDOM SOIL, Journal geotechnical and geoenvironmental engineering, 123(2), 1997, pp. 153-160
This paper brings together random field generation and finite-element
techniques to model steady seepage through a three-dimensional (3D) so
il domain in which the permeability is randomly distributed in space.
The analyses focus on the classical problem of steady seepage beneath
a single sheet pile wall embedded in a finite layer of soil. The analy
ses treat the soil permeability as a spatially random property with sp
ecified mean, variance, and spatial correlation length. The influence
of the spatial correlation or ''scale of fluctuation'' is given specia
l consideration, since this aspect is not always included in probabili
stic geotechnical analysis. The value of permeability assigned to each
element comes from a lognormally distributed random field derived fro
m local averages of a normally distributed random field. The local ave
raging allows the dement dimensions to be rationally accounted for on
a statistical basis. The influence of three-dimensionality is given pa
rticular emphasis and contrasted with results that are obtained using
an idealized two-dimensional model. For the computationally intensive
3D finite-element analyses, strategies are described for optimizing th
e efficiency of-the code in relation to memory and central processing
unit requirements. Monte Carlo simulations are performed to establish
statistics relating to quantities of interest to designers such as the
flow rate. The potential value of this approach is emphasized by pres
enting the results in the context of reliability-based design.