Page:4SIGHT manual- a computer program for modelling degradation of underground low level waste concrete vaults (IA 4sightmanualcomp5612snyd).pdf/49

the permeability of the crack, $k_{c}$, and the permeability of the uncracked concrete, $k_{o}$:

$k_{s}={\frac {w}{L+w}}k_{c}+{\frac {L}{L+w}}k_{o}$

(20)

$={\frac {w}{L+2}}{\frac {w^{2}}{12}}+{\frac {L}{L+w}}k_{o}$

(21)

Since $w^{3}/12$ is typically far greater than $Lk_{o}$, the permeability of the slab can be approximated by the permeability due to the crack. Further, if each of the cracks of width $w$ are spaced a distance $a$ apart, the permeability of the slab, $k_{s}$, is

$k_{s}={\frac {w^{3}}{12a}}$

(22)

Joints can be handled in a similar manner as cracks. However, joints will typically be very much wider than cracks. Since joints will presumably extend the entire thickness of the slab, once the joint fails, the flow through the joint would overwhelm the transport of ions through the central portion of the slab. In fact, the transport coefficients would be as great as, or greater than, those of the soil. Therefore, upon failure of the joint, 4SIGHT assumes that the roof fails to impede the flow of water into the vault, the transport properties of the concrete should be approximated by the transport properties of soil, and the calculation ceases.

8Chemical Equilibrium

After each time step, each computational element is brought to chemical equilibrium by satisfying two conditions:

1. If a salt exists as solid, the constituent ion concentration product equals the solubility product.
2. The sum of the free charges from all available ions equals zero, insuring local charge neutrality.

Given the salt $A_{\beta }C_{\alpha }$, composed of anion $A^{\alpha -}$ and cation $C^{\beta +}$, condition 1 above implies that if $A_{\beta }C_{\alpha }$ exists as a solid then

$\left[A^{\alpha -}\right]^{\beta }\left[C^{\beta +}\right]^{\alpha }=K_{sp}$

(23)

where $K_{sp}$ is the ion solubility product. Condition 2 implies that with $m$ anions and $n$ cations present in the pore solution:

$\sum _{i=1}^{m}\alpha A_{i}^{\alpha -}=\sum _{j=1}^{n}\beta C_{j}^{\beta +}$

(24)

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