Page:4SIGHT manual- a computer program for modelling degradation of underground low level waste concrete vaults (IA 4sightmanualcomp5612snyd).pdf/45

where the capital letters $X$, $T$, and $P$ refer, respectively, to the dimensionless distance, time, and pressure. The quantity $D_{o}$ is the chloride diffusivity of the concrete, and $k_{o}$ is the permeability. $L$ is simply any characteristic length. Using these definitions, the advection-diffusion equation (2) becomes

The equation will be simplified further later using material properties related to porosity.

7.5Atkinson-Hearne Model

As yet, a dependable mechanistic model does not exist for sulfate attack. Therefore, to incorporate sulfate attack, the depth of sulfate degradation is calculated using the Atkinson and Hearne [5] model:

	$E$		Youngs modulus
	$C_{o}$		External sulfate concentration
	$C_{E}$		Concentration of sulfate as ettringite
	$D$		Sulfate diffusion coefficient
	$\alpha$		Roughness factor
	$\gamma$		Fracture surface energy
	${?}$		Poisson ratio

Since the Atkinson-Hearne model gives the location of the sulfate front, 4SIGHT presumes that all of the concrete behind the sulfate front has been completely disintegrated, giving it the properties of the surrounding soil. Since the transport coefficients of soil are much larger than concrete, the external boundary conditions are advanced to the sulfate front, creating a moving boundary condition.

The Youngs modulus, roughness factor, fracture surface energy, and Poisson ratio must be determined from experimental measurements. The quantity $C_{E}$ can be either calculated from the cement composition, or more accurately from experiment. To experimentally determine $C_{E}$, the sulfate reacted per unit mass hydrated cement is plotted against the logarithm of time. This data is fit to the equation [5]

where $m$ is the moles of sulfate reacted in the cement, $m_{o}$ is the free parameter of the regression, $t$ is time, $c$ is the concentration of sulfate in liquid, $t_{r}$ is the characteristic time for reaction, and $c_{k}$ is the concentration in kinetic experiments. The maximum value of $m$

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