(2) Mechanical properties.

at or near the anticipated project maximum placement

temperature. If experience does not allow for

(a) Modulus of elasticity. The modulus of elas-

reasonably accurate estimation of the maximum plac-

ticity is defined as the ratio of normal stress to corre-

ing temperature, tests should be conducted at a lower

sponding strain below the proportional limit. For

and upper temperature to bracket the temperature rise.

practical purposes, only the deformation which occurs

Typical values for adiabatic temperature rise for mass

concrete range from 20 to 35 F at 5 days to 30 to

during loading is considered to contribute to the strain

45 F at 28 days. A curve of temperature rise versus

in calculating the modulus of elasticity. Subsequent

time will be input into the ABAQUS program

increases in strain due to sustained loading are

through the user subroutine DFLUX or HETVAL as

referred to as creep. The modulus of elasticity is a

function of the degree of hydration and therefore is

discussed in paragraph A-5*a*(2).

time dependent. It is also temperature dependent;

however, the effect within the range of temperatures

(b) Specific heat. Specific heat is the amount of

involved in a NISA is negligible and therefore is not

heat required per unit mass to cause a unit rise of

modeled in ABAQUS. The modulus of elasticity is

temperature. Specific heat is also referred to as heat

determined according to CRD-C 19 (USAEWES

capacity. It is affected by temperature changes, but

1949e). To adequately model the time dependency of

for the range of temperatures expected in a NISA, it

the modulus of elasticity, tests should be conducted at

should be assumed to be constant. The specific heat

ages of 1, 3, 7, 14, 28, 56, and 90 days, as well as

is determined according to CRD-C 124 (USAEWES

the design age. Typical values for the modulus for

1949b). The test should be conducted at an age of at

mass concrete are about 1 106 psi at 1 day and

least 7 but not more than 28 days. Typical values for

about 5 106 psi at 90 days. A curve of modulus

specific heat of mass concrete range from 0.18 to

versus time will be input into ABAQUS through the

0.28 Btu/lb-F.

UMAT subroutine.

(c) Thermal diffusivity. Thermal diffusivity is a

(b) Poisson's Ratio. Poisson's Ratio is defined

measure of the rate at which temperature change can

as the ratio of the lateral to the longitudinal strain

occur in a material. It is determined according to

resulting from a uniformly distributed axial stress. It

CRD-C 36 (USAEWES 1949c) for conventional

is determined according to CRD-C 19. Typical val-

concrete and CRD-C 37 (USAEWES 1949d) for mass

ues for Poisson's Ratio for mass concrete range from

concrete. The test should be conducted at an age of

0.15 to 0.20. The value input into ABAQUS should

at least 7 but not more than 28 days. Typical values

be based on test data at ages greater than 7 days and

for thermal diffusivity of mass concrete range from

0.03 to 0.06 ft2/hr. The value of thermal diffusivity

on engineering judgement.

is not input into ABAQUS but is used to calculate the

(c) Creep. Creep is defined as time-dependent

thermal conductivity of the concrete.

deformation due to sustained load. Creep results in a

progressive increase in strain under a state of constant

(d) Thermal conductivity. Thermal conductivity

stress. Creep is closely related to the modulus of

is defined as the quantity of heat flowing through a

elasticity and compressive strength of the concrete

unit thickness over a unit area of the material sub-

and is thus a function of the age of the concrete at

jected to a unit temperature difference between the

loading. Creep is determined according to CRD-C 54

two faces. This parameter is most sensitive to the

(USAEWES 1949g). For purposes of a NISA, at

proportion of cement paste, free water, and aggregate.

least three ages of loading should be conducted:

It is calculated from the thermal diffusivity and

1 day, 3 days, and 14 days. Typical values for creep

specific heat according to CRD-C 44 (USAEWES

of mass concrete are about 1 10-6 microns/psi at a

1949f). Thermal conductivity of mass concrete is not

test age of 60 days for a specimen loaded at 1 day

significantly affected by changes in temperature over

age and about 0.2 10-6 microns/psi at a test age of

typical ambient temperature ranges. Typical values

60 days for a specimen loaded at 14 days age. A

for thermal conductivity of mass concrete range from

curve of creep which is a function of the modulus

1 to 2 Btu/ft-hr-F.

A-12

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