ETL 1110-2-365
31 Aug 94
monolith is, the closer a typical strip near the center
volume change. These volume changes may be due
of the monolith will approach the plane-strain
to heat generation and subsequent cooling, autogenous
condition. If substantial out-of-plane loadings exist,
shrinkage, creep/stress relaxation, or other mecha-
then behavior due to these loads should be thor-
nisms. Restraint limits the changes in dimensions
oughly investigated through the use of 2-D strips
and causes corresponding tensile, compressive, tor-
taken in the out-of-plane direction or by performing a
sional, or flexural stresses in concrete. Of primary
3-D analysis.
concern in mass concrete structures is restraint which
causes tensile stresses and corresponding tensile
(3) Constitutive relations. A NISA includes con-
strains. Restraint may be either external or internal.
stantly changing material properties which means that
External restraint is caused by bond or frictional
from one time increment to the next the properties of
forces between the concrete and the foundation or
the material are different. The properties include
underlying and adjacent lifts. The degree of external
nonlinear behavior such as creep. This precludes the
restraint depends upon the relative stiffness and
use of superposition. The change in strain from one
strength of the newly placed concrete and the
step to the next is used in the calculation of the new
restraining material and upon the geometry of the
stress state as well as updating the constitutive matrix
section. Abrupt dimensional changes or openings in
which is used in computing the displacements in the
a monolith such as wall offsets, culvert valve shafts,
following time increment. This differs from a con-
gallery entrances and offsets, reentrant corners, etc.,
ventional linear elastic analysis where the constitutive
have caused external restraints that have resulted in
matrix remains constant throughout the analysis.
cracking in existing structures. Internal restraint is
caused by temperature gradients within the concrete.
(4) Drying shrinkage. Because most NISA's use
The warmer concrete in the interior of the mass pro-
moderately large element sizes and because in a
vides restraint as the concrete in the periphery of the
NISA shrinkage can be treated only at the FE integra-
mass cools at a different rate due to heat transfer to
tion points, the effects of drying shrinkage near the
its surroundings. The degree of internal restraint
surface of the structure are neglected. However,
depends upon the total quantity of heat generated, the
drying shrinkage is typically insignificant for these
severity of the thermal gradient, the thermal and
types of structures when compared to autogenous
mechanical properties of the concrete, and thermal
shrinkage.
boundary conditions.
(5) Reinforcing. Since excluding reinforcing
(2) Material parameters. A number of material
from an analysis provides conservative results, initial
parameters can affect cracking related to restrained
analyses can be performed without the effects of
volume change. They include: (a) heat generation of
reinforcement. The effects of reinforcing on resulting
the concrete; (b) mechanical properties of the con-
structural behavior are small if no cracking occurs,
crete including compressive and tensile strength,
but if cracking does develop, modeling of the rein-
tensile strain capacity, modulus of elasticity, linear
forcement can be very beneficial for control of the
coefficient of thermal expansion, and creep/stress
cracking.
relaxation; (c) autogenous shrinkage of the concrete;
and (d) thermal properties of the concrete including
(6) Crack model. The cracking model used in a
specific heat and thermal conductivity. These con-
NISA is a smeared crack approach. This approach
crete properties are governed by the selection of
will predict the general extent of cracking occurring
materials used to make the concrete, including
but does not directly predict the exact length of
cementitious materials (portland cement type, ground
cracks or the crack mouth opening displacements. A
granulated iron blast furnace slag, and pozzolans such
discussion of the smeared crack model and how it is
as fly ash), aggregates, chemical admixtures, etc., and
implemented in the analysis is given in para-
by the proportions of these materials in the concrete
mixture. Many of these properties are also depen-
graph A-5e(4) and in Annex 2 of Appendix A.
dent upon the maturity of the concrete and are thus
time and temperature dependent. Optimization of the
f. Parameters affecting cracking in mass
selection of concrete mixture materials and propor-
concrete.
tions should be a part of a properly conducted con-
crete materials study. Due consideration should be
(1) Restraint of volume change. Cracking in
given to the performance and economy of the
mass concrete is primarily caused by restraint of
A-8
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