ETL 1110-2-344
31 Dec 93
APPENDIX C: ANALYSES WITH NO UPLIFT
1. Introduction
monolith and the foundation, it was required only to
reposition the pair of nodes on the monolith/
In an effort to simplify the comparison between the
foundation interface. The results of these analyses
are summarized in Table C-1. The variations of KI
traditional method of analysis and the finite
and KII over the range of crack lengths are shown in
element/fracture mechanics based analysis, a series
of analyses was performed for monolith 7E in
Figure C-1.
which the uplift pressure at the base of the monolith
was not considered (the culvert was considered in
(2) The final crack length computed using the
this case). Neglecting the uplift pressure greatly
traditional method of analysis was 9.55 ft. The
simplifies both the modeling of the structure and the
value of 8.58 ft computed using finite element
computation of the stress intensity factors. The
analysis and fracture mechanics is only 10.2% less
master and slave nodes required to model that
than 9.55 ft. When uplift was considered, the dis-
portion where the uplift pressure was applied as
crepancy between the final crack lengths was 43.7%
pore pressures (initial stresses) were not present in
(see Appendix A), which is over four times the
the mesh used for these analyses. Otherwise the
10.2% predicted for this case. The improved agree-
mesh was identical to the one shown in Figure A-4
ment in the predicted final crack lengths may be an
of Appendix A. The material properties and the
indication that the crack length of 8.58 ft is not
remaining applied loads for this investigation were
long enough to be strongly influenced by the cul-
not changed from those used for the analyses
vert. Even though the culvert is relatively large in
described in Appendix A in which uplift was
relation to the monolith, the influence that it would
considered.
have on the stresses and displacements at the base
of the monolith is greatest near the culvert and
decreases as the distance from the culvert increases.
2. Analysis and Results
Based on the observed results, the discrepancy
between the two methods of analysis would be even
a. Estimation of crack length.
less if both the culvert and the uplift were not
considered.
(1) A series of three analyses, each with a
b. Normal stress profiles.
different specified crack length, was performed to
compute an initial estimate of the final crack length.
(1) The normal stress profile along the base of
The prescribed crack lengths for these analyses
the monolith with a crack length of 8.58 ft and no
ranged from 6.0 ft to 9.0 ft in 1.5-ft increments.
uplift is shown in Figure C-2. In order to contrast
No analyses were performed for crack lengths grea-
ter than 9.0 ft because the value of KI was negative
the difference between the traditional and proposed
for a crack length of 9.0 ft and KI was positive for
methods of analysis, the normal stress profile from
all prior analyses. The final crack length of 8.58 ft
the traditional method of analysis is also included in
was found by re-meshing and comparing KI to KIc
Figure C-2. In comparing Figure C-2 (no uplift
as described in paragraph 3d(1) of Appendix A.
case) with Figure A-11 of Appendix A (full uplift
However, since initial stresses were not prescribed
case) the effect of the uplift on the normal stress
for elements adjacent to the interface between the
profile is minor considering the overall shape of the
Table C-1
Summary of Finite Element Analyses With No Uplift
KI
KII
∆Hcrest
a
CMOD
ksi .
√in
ksi√ .
in
ft
in.
in.
6.00
0.411
0.536
0.00800
-0.0762
7.50
0.188
0.536
0.00843
-0.0777
8.58
0.000
0.547
0.00842
-0.0781
9.00
-0.132
0.578
0.00835
-0.0781
C-1
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