Page:4SIGHT manual- a computer program for modelling degradation of underground low level waste concrete vaults (IA 4sightmanualcomp5612snyd).pdf/47

can be calculated from the initial quantity of C3A in the cement. If this maximum value is labelled $m_{c}$, the value of $t$ for $m=m_{c}$ is the time at which all of the C3A is consumed, $t=t_{\infty }$.

The model proposed by Atkinson and Hearne assumes that reaction is the controlling rate process. Therefore, the time to spalling should be greater than the time required for complete consumption of the C3A. The time to spalling is [5]

where

In the event that $t_{\textit {spall}}<t_{\infty }$, $C_{E}$ must be calculated in a self consistent manner using eqns. 16, 17, and 18. More complete details can be found in [5]. For ordinary portland cements, it is likely that $t_{\textit {spall}}>t_{\infty }$. Therefore, since it is assumed that the quantity of external sulfate is sufficiently great to act as an infinite reservoir (external concentration is constant), $C_{E}$ can be calculated from the C3A content of the cement. Since each mole of ettringite requires one mole of $Al_{2}O_{3}$[6], the molar concentration of $Al_{2}O_{3}$ will be the molar concentration of ettringite. Given a concrete mix have $x_{cem}$ kilograms of cement per cubic meter of concrete, and the cement having a weight fraction of $\phi _{Al_{2}O_{3}}$ of aluminum oxide, the moles of ettringite formed per cubic meter of concrete is

with the $Al_{2}O_{3}$ molar weight of 0.10196 kg per mole.

7.6Effects of Cracks and Joints

Although not a degradation mechanism per se, effects due to the presence of cracks and joints can be incorporated into the models for transport of the ions. Since the roof slab will likely be a supported member such that the bottom of the roof slab will be in tension, it is assumed that cracks will appear on the bottom of the slab and extend upwards to the neutral axis of the slab. In the case of joints, 4SIGHT assumes that the joint extends through the entire depth of the root slab. The joint is filled with a joint compound with a known permeability and service life.

The permeability of a cracked slab is calculated assuming the crack walls are smooth and parallel. Given the square slab with $L$ and depth $D$ having cracks with width $w$ penetrating the full depth $D$ of the slab, the permeability of the slab is a weighted sum of

18