Environmental Engineering Reference
In-Depth Information
- Duncan (1992, 1996a). State of the Art: Limit Equilibrium and Finite Element
Analysis of Slopes. Duncan lists over 100 references of case studies;
- Duncan (1994). The role of advanced constitutive relations in practical applications;
-Vaughan (1994). Assumption, Prediction and Reality in geotechnical engineering.
(b)
Examples of strain softening
:
-Progressive failure and other deformation analyses; Potts et al. (1990, 1997), Muir-
Wood et al. (1995), Dounias et al. (1988, 1996), Kovacevic et al. (1997). Duncan
(1996a) lists some of the uncertainties in numerical modelling of dams;
- Degree of compaction of the embankment materials - the actual may be different to
that specified;
- Compaction water content - actual may be different to the specified;
- No test data - e.g. it is not practicable to test rockfill zones;
- Construction sequence and time;
- Simplified approximation of stress-strain behaviour - all constitutive relations are
approximation of real behaviour;
- Reliability of field measurements.
He concludes:
“comparisons of the results of finite-element analyses with field measure-
ments have shown that there is a tendency for calculated deformations to be larger than
measured deformations. The reasons for this difference include: (1) soils in the field tend to
be stiffer than soils at the same density and water content in the lab because of aging effects;
(2) average field densities are higher than the specified minimum dry density, which is often
used for preparing lab triaxial test specimens; (3) samples of inplace materials suffer distur-
bance during sampling, and are less stiff as a result; (4) many field conditions approximate
plane strain, whereas triaxial tests are almost always used to evaluate stress-strain behaviour
and strength; and (5) two-dimensional finite-element analyses over-estimate deformations of
dams constructed in V-shaped valleys with steep valley walls.
By the time of this writing there has been about 30 years of experience with using the
finite-element method to estimate stresses and deformations in slopes and embankments.
This experience has shown the considerable potential of the method for use in engineer-
ing practice and it has pointed up clearly the sources of uncertainty in the results of these
analyses. These are related primarily to difficulties involved in being able to predict the
actual densities and water contents of soils in the field and with being able to anticipate
the sequence of operations that will be followed during construction. With due allowance
for the uncertainties, finite-element analyses afford a powerful method of analysis that is
applicable to a wide variety of engineering problems.”
Duncan (1996a) concluded (as had Vaughan, 1994, who discusses several cases), that
there is much to be gained from the analyses in the understanding of mechanisms, if not
the absolute stresses and deformations.
The authors' experience in this area is limited to that of “user” rather than “doer” of
the analyses. From this it is clear that it is difficult to model the deformation of dams with
any degree of precision. The ability to numerically model generally is greater than the
ability to provide accurate material properties.
There are however often more basic reasons for poor modelling, including not “con-
structing” (or numerically “building”) the slope in steps correctly, assuming drained con-
ditions will apply when in fact undrained behaviour is actually present and not paying
enough attention to the stiffness of the layers (or in particular relative stiffnesses), so the
stress distributions and deformations are poorly modelled.
Few model pore pressures accurately or allow for cracking, softened zones around
cracks, crack water pressures or in many cases, strain weakening. Given that these factors
often control the stresses and deformations in slopes, it is not surprising the modelling is
not good.
