Behavior of Concrete as a Barrier Material for Nuclear Waste Disposal
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BEHAVIOR OF CONCRETE AS A BARRIER MATERIAL FOR NUCLEAR WASTE DISPOSAL R. J. JAMES AND Y. R. RASHID ANATECH Research Corp., P.O. Box 9165, La Jolla, CA
92038
INTRODUCTION A current method for disposal of nuclear waste is the immobilization of the waste in cement-based grout and burial in reinforced concrete vaults. The concrete vault provides the containment barrier to prevent leaching into the environment. During the solidification process the concrete is subjected to high transient temperatures while the vault is being filled. Subsequently, because of heat generation in the waste, the concrete is subjected to elevated temperatures for the duration of the vault life, which invokes considerations of long term stability of the concrete both as a material and as a structural element. Under these conditions of elevated temperatures and long hold times, the effects of creep and cracking in concrete play a significant role in determining the structural and barrier integrity of the containment structure. Cracking in concrete initiates when the local tensile strain reaches about 0.01%. Significant amounts of compressive strain due to creep in thermally loaded, confined structures may lead to split cracking due to the Poisson effect. Moreover. because of the presence of thermal gradients, particularly during the filling process, cracking due to local bending may occur. In addition, and more importantly, for temperatures above 200 OF, the elastic modulus of concrete degrades with time even at constant temperature due to thermally activated damage. Since the stress due to thermal loads is proportional to the modulus, this leads to continual redistribution of load that may cause additional cracking. This paper deals with an analytical modeling of concrete, considering creep, cracking and stiffness degradation, as a means for evaluating long term functional requirements under barrier applications for nuclear waste disposal. The analytical foundation necessary to build a constitutive model capable of simulating the response of concrete at elevated temperature is presented. The three key components of this model are 1) creep, 2) material property degradation, and 3) cracking. CREEP As a starting reference point, consider a material element under a general time-dependent state of stress, strain and temperature. The increment in strain, deij, under the assumptions of small strain. can be expressed as the sum of four components; namely elastic, plastic, free thermal expansion, and creep;
S+
+
+ C ij
The elastic strain increments through Hooke's law as de
e =
are
de[CiJkiok]
-
ij(1) ij
related to the
Cijkldakl + dCijkl
ij incremental
stresses
~kl
(2)
where Cijkl Bijkl
=
= (l-v)
8
Bljkl/E,
(3)
ik j
(4)
6
- VBijkl,
E is Young's modulus, v is Poisson's ratio and 8 is the Kronecker delta. For this work the material is considered isotropic unless internal damage from cracking occurs. Additionally Young's modulus is temperature dependent and may degrade with time under time-invariant elevated temperatures. The d
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