31 Dec 93
curves. In all plots showing normal stress profiles
The line of action for the resultant force from the
(Figures A-11 of Appendix A, B-2 of Appendix B,
finite element analysis was 11.79 ft to the right of
and C-2), the normal stress near the crack tip is a
the toe as opposed to 11.82 ft from the traditional
relatively small negative value instead of zero.
These errors in the normal stress are a consequence
c. Shear stress profiles. The shear stress pro-
of the nodal strain projection technique, which is
very sensitive to the level of mesh refinement
file along the base of the monolith for a crack
length of 8.58 ft is shown in Figure C-3. In com-
around sharp corners and notches. However, the
paring Figure C-3 with Figure A-12 of Appendix A
normal stresses on the crack surface at a short dis-
the effect of the uplift on the shear stress profile is
tance away from the crack tip are zero in all cases.
minor in terms of the overall shape of the curves, as
This demonstrates that the effect of the crack tip on
was the case with the normal stresses. However,
the nodal stresses is indeed local and that the small
the shear stress profile in Figure C-3 does show a
error in the normal stress at the crack tip should not
slight increase between the right side of the culvert
be a cause for concern.
and the crack tip before going to zero on the crack
surface. It could be argued that this demonstrates
(2) The resultant force in the vertical direction
that the effect of the culvert on stresses (and dis-
and the line of action for the resultant force were
placements) at the base of the monolith may be
computed for the finite element solution and the
traditional analysis technique. Since uplift was not
limited to certain cases. The resultant force in the
considered, the actual estimated final crack lengths
horizontal direction was computed for the finite
for the two methods of analysis were used in these
element solution and the traditional analysis tech-
nique. The resultant force from the finite element
equivalent force systems regardless of crack length).
analysis was 250.62 kips as opposed to 249.78 kips
The calculated resultant force from the finite ele-
from the traditional analysis technique.
ment analysis was 519.41 kips as opposed to
515.90 kips from the traditional analysis technique.
Figure C-3. Shear stress profile at the base of monolith for a = 8.58 ft: no uplift