r - The Hong Kong Polytechnic University

The 5th Cross-strait Conference on Structural and Geotechnical Engineering (SGE-5)
Hong Kong, China, 13-15 July 2011
IMPACT OF SPATIAL VARIABILITY ON SOIL SHEAR STRENGTH
J. Ching 1 , K. K. Phoon 2 and Y. G. Hu 3
1
Associate Professor, Dept of Civil Engineering, National Taiwan University, Taipei, Taiwan.
Email: jyching@gmail.com. Phone: 886-2-33664328. Fax: 886-2-23631558.
2
Professor, Dept of Civil Engineering, National University of Singapore, Singapore.
3
Ph.D. Student, Dept of Civil Engineering, National Taiwan University, Taipei, Taiwan.
ABSTRACT
The purpose of this study is to understand the mechanism of the effective shear strength for a soil mass in the
presence of spatial variability. Random field finite elements are used to simulate the effective shear strength and
the spatially averaging for the shear strength. Based on the simulation results, Vanmarcke’s theory is consistent
with the spatially averaging for the shear strength. However, the effective shear strength is found to be close to
the average shear strength along the actual slip curve, rather than the spatial averaging over the entire soil mass.
KEYWORDS
random field finite elements, Vanmarcke’s theory, soil shear strength, spatial variability.
INTRODUCTION
Soil properties in the field generally exhibit spatial variability. This is true even if the soil mass is nominally
homogeneous, because small scale heterogeneity are always present due to natural geologic processes that create
and continuously modify the soil in-situ. One important property is the shear strength of the soil. For most
foundation engineering problems, resistances provided by soil mass are the “overall” shear strengths, which are
typically related to spatial averaging over a certain region. Spatial variability is usually modeled by a
homogeneous (or stationary) random field that can be characterized succinctly in a second-moment sense by a
mean value at a point, a variance at a point, and a scale of fluctuation. Vanmarcke (1977) showed that the
averaged property of a random field over a region has a mean value identical to the point mean, while the
variance is less than the point variance.
Vanmarcke’s definition of a spatial average is purely based on an integral of the random field over a given
prescribed volume. The rationale is that the effective shear strength of a soil mass for a particular problem is
governed by the spatial average along a slip curve and this spatial average is more relevant than the value at a
point. There appears to be an implicit assumption that the spatial average defined along a prescribed slip curve is
comparable to the spatial average defined along a critical slip curve that depends on mechanics (equilibrium,
compatibility, and constitutive relations) and boundary conditions. By definition, the critical slip curve is the
curve producing the lowest factor of safety among all possible curves. In principle, it is clear that this critical
curve is fundamentally different from an arbitrary trial slip curve that is prescribed rather than emerging as an
outcome of a finite element or similar analysis. However, it is unclear at this stage if this fundamental difference
would produce effective strengths that are significantly different from simple Vanmarcke-type spatial average
strengths.
The objective of this study is to elucidate this query. There are limited studies in the literature that explore this
query systematically. The outcome of this study is of practical significance, because it is computationally
intensive to identify the critical slip curve and its associated effective strength. In contrast, the second-moment
statistics of a Vanmarcke-type spatial average are available in closed-form.
The above comparison is conducted through random field finite element analyses. A rectangular domain is
divided into finite elements with shear strengths specified by realizations of a random field. The effective shear
strength of the domain is determined by conducting plane-strain compression until failure. Discrepancies
between the effective shear strength and the spatial average will be discussed. As to be expected, these
discrepancies are mostly related to mechanical principles.
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