ETL 1110-2-536
31 Dec 94
APPENDIX B: ELEMENT SIZE
B-1. Parametric Study
for a 6-hr time interval doubled the size of the model.
A 48-in. step height nearly matched production rates
for daily concrete placements, however, did not fit the
criteria established in ABAQUS. Therefore, this
the program for transient heat transfer analysis
study focused on a 48-in. element size to determine
requires a relationship between the minimum time
its reliability in reporting temperature data.
step and the element size. The equation to establish
this relationship is given as:
c. One-dimensional heat flow. This study is a
simple one-dimensional heat flow problem, using
(B-1)
∆ t > (ρc/6k)∆ l 2 or < l
(6k∆t/ρc)
material properties for Zintel Canyon Dam. Two
models were generated, one with a 24-in. element
size in either direction and the other with a 48-in.
where:
element size in either direction. Depicted in Fig-
∆t = time step
ure B-1 are the two finite element meshes, and boun-
dary conditions used for the study. One exterior row
ρ
of boundary nodes were held at a constant 50 deg
= density
while the ambient surface conditions along the oppo-
site face was a fixed 90 deg. The thermal models
c
= specific heat
calculated nodal temperatures in 0.25 day increments
for a period of 10 days. Corresponding nodal tem-
k
= thermal conductivity
peratures were compared from both models to deter-
∆l = element dimension
mine accuracy, and if stable heat gain was being
generated. Figure B-2 contains plots of nodal tem-
peratures for both the 24- and 48-in. meshes for
b. Adiabatic heat gain. Adiabatic heat gain in
various times. The only inconsistency was at time t
concrete begins within the first 12 hr after placement
= 0.5 days, for the 48-in. mesh, where a slight incon-
and can continue rapidly until a maximum is attained.
sistency in the heat gain exists. This can be seen in
Therefore, when performing incremental time depen-
Figure B-2.1. Figures B-2a through B-2d, indicate
dent stress analysis for concrete, it is important to
nearly identical heat gain, when comparing nodal
keep the time steps sufficiently small during the early
temperatures at the same time steps of the two
stages of the analysis. Input of the appropriate prop-
models. Because this amount of inconsistency was at
erties for Zintel Canyon Dam into Equation B-1
small, and only occurred at one time step, it was
yields a maximum length of element, using a 6-hr
considered negligible and would not effect the out-
time interval, of 27 in. Analysis for a 12-hr time
come of the study. Therefore, we decided to use a
interval yields a 38-in. element. A 12-hr time inter-
time step of 6 hr (0.25 days) and a maximum element
val is not a good choice for calculating early heat
size in any direction of 48 in.
gain in the concrete, while placing a 27-in. restriction
B-1
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