Kenneth A. Snyder

“ There is sufficient oxygen present for corrosion. This a conservative approach to corrosion. The concrete vault begins service approximately 100 days after casting. Therefore, the transport properties have reached about 90% of their assymptotic values. The external ion concentration and hydraulic head are constant over the life of the vault. As the sulfate front advances, the concrete in its wake can be treated like soil and the external conditions can be advanced to this point. ”

“ The advantage of the method used by 4SIGHT is the ability to incorporate the synergism of multiple degradation processes. Rather than calculate rates of attack, 4SIGHT uses a single transport equation to propagate ions through the concrete. Keeping the system in chemical equilibrium allows interaction of degradation mechanisms. ”

“ As the porosity of the concrete changes, the transport properties also change. The change in the transport properties will effect the hydraulic pressure distribution in the concrete since the transport properties will not by uniform throughout the concrete. ”

“ When a sufficient concentration of chloride ions reaches the rebar, corrosion begins. The corrosion stage begins at the onset of corrosion and lasts until failure of the of the steel reinforcement, which is typically only a few years hence. Since the initiation stage may last for hundreds of years, the duration of the corrosion stage is insignificant to the total lifetime of the reinforcement. ”

“ 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. ”

“ As the sulfate front proceeds into the concrete, the effective thickness of the concrete decreases. At some point in time the roof has an insufficient thickness to support its load. At this time, structural failure of the roof will occur. ”

“ As the sulfate penetrates the concrete, the concrete fails and the external boundary conditions move into the concrete. Also note that the pressure (P) is zero from 0.75 to 1.00 meters. Since the concrete was cracked, the permeability of the cracked portion of the concrete overwhelmed the uncracked portion, resulting in virtually no pressure drop across the crack. This increases the pressure gradient across the remaining untracked concrete. ”

“ If a salt exists as solid, the constituent ion concentration product equals the solubility product. The sum of the free charges from all available ions equals zero, insuring local charge neutrality. Given the salt , composed of anion and cation , condition 1 above implies that if exists as a solid then
where is the ion solubility product. ”

“ Due to this apparently steady state, an empirical relation between , the chloride diffusivity in , and was developed for cement paste by Atkinson, Nickerson, and Valentine [8] and Walton, Plansky, and Smith [9]
for values of in the range (0.2-0.6) .
for cement paste can also be related to using the universal relation for the formation factor due to hydration, , [10] :
where is the concrete chloride diffusivity, is the free ion diffusivity of chloride ions, and is the Heaviside function. The quantity is a constant for all ions. ”

“ Additionally, chloride ions are present in the soil at a concentration of 0.40 moles per liter (EXTERNAL Cl = 0.40) . and engineering drawings indicate that the reinforcement bars are located 60 centimeters from the top of the roof (REBAR = 0.60) . Thorough soil analysis indicates that sodium ions are also present at a concentration of 2.40 moles per liter (EXTERNAL Na = 2.40) , giving a nearly neutral soil pH.
Internal to the concrete the pH is approximately 13. ”

“ THe relative change in permeability can be calculated using . The Katz-Thompson equation relates permeability to [15] :
(32) where is the diameter of the largest sphere which can pass through the pore space of the sample. Also, given that [16] , the relative change in permeability becomes
(33) The final dimensionless advection-diffusion equation is a combination of eqns. 14, 31, and 33:
(34) There is one such equation for chemical species . ”

“ The interactive mode simply waits for the user to type in the various input parameters at run-time. When executed in batch mode, the user first edits an ASCII file containing the input parameters as if typed during interactive mode. ”

“ As the is leached, the porosity increases. Let the value of porosity after leaching be , and the diffusivity be . Unfortunately, the ratio is not simply because as calcium hydroxide is leached from the paste the ratio does not retrace eqn. 27. Rather, the ratio is greater than , as demonstrated by the NIST microstructural model.
The NIST cement microstructural model [14] was used to determine the relation for upon leaching. Results for a paste are shown in Figure 2. The formation factor decreases with decreasing porosity due to hydration, denoted by circles. ”

“ Eqn. 2, 3, and 11 can be combined to form a system of equations to propagate ions through a porous media. However, the system of equations can be condensed by a transformation into dimensionless variables. ”

“ The authors wish to acknowledge the financial support of the U.S. Nuclear Regulatory Commission (NRC) . Mr. Jacob Philip was the NRC Program Manager and his advice was greatly appreciated. The authors would also like to express their thanks to Dr. ”