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The normal effective stress for the simplified Bishop and Janbu methods can be calculated using:
(D.45)
where
(D.46)
Negative effective stresses are usually encountered in Eq. D.45 for cases that involve:
(1)
high pore water pressures,
(2)
a combination of thin slices with a low self-weight and a high "c-value",
(3)
steep slice-base angles.
Most of these problems are associated with the indeterminacy of the limit equilibrium analysis and the
failure to adequately satisfy the conditions for complete static equilibrium.
The influence of negative effective stresses for a slice within the last five percent of the total number of
slices near the crest of the failure surface being analyzed are neglected by XSTABL. This criteria has
been established on the basis that the upper portion of a failure mass may pass through a potentially
cracked zone. For such cases, XSTABL "ignores" the strength contribution of these last few slices (i.e.,
sets shear strength to zero), if calculations reveal a negative normal effective stress. An error is not
reported for such cases.
If a negative effective normal stress is calculated and the slice is not within the last five percent of the
total number of slices, XSTABL examines the scenario and attempts to correct the problem if the
negative stresses are due to excessively high pore water pressures. In such cases, the total normal stress is
computed by adding the pore water pressure to the calculated effective stress. If this results in a positive
total stress, it is concluded that the pore water pressures are excessive and the effective stress is set to
zero. This control essentially "reduces" the calculated pore water pressure at the base of the slice, thus
eliminating the negative effective stress that had been computed initially. If such a correction is made for
any potential failure surface during the analysis, an explanatory warning message is written to the output
file.
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