Environmental Engineering Reference
In-Depth Information
E
C
A
ROCK
JOINTS
F
D
B
0
WEAK LAYER
Figure 11.4.
Limit equilibrium analysis of a rock slope sliding on a weak layer.
because if one inserts a reasonable joint strength (say c
40°), the program
assumes this applies to the rock and assumes slice slide forces will apply, equivalent to say
a wedge of “rock” with c
0,
40° which will also drive the instability. This is difficult
to overcome in computer programs other than modelling the vertical part of the failure
surface (e.g. EF) as a crack. It is also possible this type of problem will lead to convergence
problems in the non-circular analysis. It is better to analyse such cases using a wedge
analysis (either by hand or a computer wedge analysis).
Other problems which arise are (Duncan 1992):
0,
-
Failure of the person performing the analysis to understand soil mechanics well enough
to know how to define the water pressures, unit weights and shear strengths appropri-
ate for the analysis;
-
Failure of the person performing the analysis to understand the computer program well
enough to define these quantities correctly in the input;
-
Failure of the person performing the analysis and the person reviewing the results to
check the results and properly evaluate their reasonableness.
11.2.3
Three dimensional analysis
The status of three-dimensional analysis is summarised in Duncan (1992), Morgenstern
(1995) and Fell et al. (2000). The Bishop's Simplified, Janbu and Spencer's Methods have
been extended into three dimensions (Hungr et al., 1989, Lam and Fredlund, 1993).
However, none of the available algorithms can account for the internal stresses existing in
a non-rotational and laterally asymmetric problem (Hungr, 1994). A true “rigorous
method” that would satisfy all the available equilibrium conditions has not yet been for-
mulated. As suggested by Hungr (1994), a rigorous three-dimensional method would
require the definition of five spatially distributed inter-column force functions. The solu-
tion for the Factor of Safety and five inter-column force inclination (“i”) coefficients
would require six nested levels of iteration. While modern computers could easily handle
the numerical computation, the correct selection of the inter-column force functions and
possible convergence difficulties pose a daunting research problem.
As summarized by Fell et al. (2000) the use of “rules of thumb” such as a 10% increase
to compensate for the neglect of 3D effects, as suggested in some textbooks, is not advis-
able, because although, as proven by Cavounidis (1987), the Factor of Safety of the criti-
cal 3D sliding surface always exceeds the critical 2D factor, the ratio between the two can
vary within a range of 1.0 to as high as 1.4 (Morgenstern, 1992; Hungr et al., 1989).
Potential problems lie in situations where the stability analysis is used to estimate the
strength of certain materials through back analysis. Neglecting a strong 3D effect in the
back-analysis could result in a serious overestimation of the back-calculated strength.
However provided that the geometry of the failure surface remains the same for the back-
analysis, and the “forward analysis”, this is not a major practical problem.
