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:

simple one-dimensional heat flow problem, using

(B-1)

∆ *t *> (ρ*c*/6*k*)∆ *l * 2 or < *l*

(6*k*∆*t*/ρ*c*)

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

= specific heat

calculated nodal temperatures in 0.25 day increments

for a period of 10 days. Corresponding nodal tem-

= 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

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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