4SIGHT Manual: A Computer Program for Modelling Degradation of Underground Low Level Waste Concrete Vaults/Example

by Kenneth A. Snyder and James R. Clifton

5Example

To illustrate the use of 4SIGHT, consider the following fictitious example. The concrete was designed with a 0.40 water:cement ratio (WC=0.40). Experimental diffusivity measurements using Cl– ions gave 5.0 × 10^-12 m2/sec (DIFF=5.0E-12). No permeability measurements are available. The roof slab is 1.0 meter thick (THICKNESS=1.000). Regularly spaced cracks have been observed on the bottom of the slab. The cracks are approximately 100 μm wide, spaced 2 meters apart, and are assumed to extend upwards to the neutral axis which is 25 centimeters from the bottom of the roof slab (CRACK = 0.000100 AT 2.0 DEPTH 0.25). Also, the roof is buried, giving an effective pressure head of 2 meters. (HEAD = 2.0).

Soil analysis indicates the presence of SO^2–₄ at a concentration of 1.0 moles per liter (EXTERNAL SO4 = 1.0). Engineering analysis indicates that if the sulfate degradation penetrates down 20 centimeters from the top surface of the roof then the vault will collapse (DEPTH = 0.20). 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. Therefore, internal potassium and sodium concentrations are approximately 0.1 (INTERNAL K = 0.1) and 0.05 (INTERNAL Na = 0.05) moles per liter, respectively.

To monitor the ingress of the external ions, calcium (OUTPUT Ca) and chloride (OUTPUT Cl) ions will be included in the output of the final state of the system. Also, to monitor leaching, the solid calcium hydroxide content will also be included in the output (OUTPUT Ca OH).

The input file for this example, example.dat is included in the distribution diskette and reiterated here:

DIFF = 5.0E-12 WC = .40 THICKNESS = 1.000 EXTERNAL Na = 2.40 EXTERNAL Cl = 0.400 EXTERNAL SO4 = 1.00 INTERNAL K = 0.1000 INTERNAL Na = 0.500 OUTPUT Ca OUTPUT Cl OUTPUT Ca OH REBAR = .8000 HEAD = 2.0 CRACK = 0.000100 AT 2.0 DEPTH 0.25 DEPTH = .2000 TIME = 100000

To use this input file, simply include example.dat at the DOS command line. To save the results, redirect the output to a file:

C:\4SIGHT\4SIGHT EXAMPLE.DAT >EXAMPLE.OUT

In this example, the output is stored in EXAMPLE.OUT, an ASCII file which can be imported into any spreadsheet program.

NOTE: This calculation required 90 seconds to complete on a personal computer equipped with a 80486 microprocessor operating at 66MHz.

5.1Internal Parameters.

4SIGHT outputs all of the parameters the user has specified ("USER"), along with default and calculated values ("DEFAULT").

"       This is 4SIGHT (Version 1.0)"

"THICKNESS "   1.00000 "(m)      " "USER"
"DIFF      "   5.0e-12 "(m^2/sec)" "USER"
"PERM      "   9.8e-13 "(m/sec)  " "DEFAULT"
"WC        "   0.40000 "         " "USER"
"HEAD      "   2.00000 "(m)      " "USER"
Sulfate Attack Parameters:
"YOUNGS    "   2.0e+10 "(N/m^2)  " "DEFAULT"
"BETA      "   1.8e-06 "         " "DEFAULT"
"CE        "  350.00000 "(Mol/m^3)" "DEFAULT"
"ROUGHNESS "   1.00000 "         " "DEFAULT"
"GAMMA     "  10.00000 "(J/m^2)  " "DEFAULT"
"POISSON   "   0.20000 "         " "DEFAULT"

"DEPTH     "   0.20000 "(m)      " "USER"
"REBAR     "   0.80000 "(m)      " "USER"
"TIME      "    100000 "(day)    " "USER"
"CRACK =  0.00010 AT  2.00000 DEPTH  0.25000"
"Chloride failure (yr)"      1743
"Sulfate failure (yr)"       447

.5.2Initial State

The report of the initial state lets the user verify the EXTERNAL and INTERNAL conditions of the system.

Initial state of system:

" ION " "EXTERNAL" "INTERNAL"
"   H:"  0.00000  0.00000
"  Ca:"  0.00000  0.00035
"  Na:"  2.40000  0.05000
"   K:"  0.00000  0.10000
"  OH:"  0.00000  0.15070
"  Cl:"  0.40000  0.00000
" SO4:"  1.00000  0.00000
"  pH:"  7.00000 13.17810

These results indicate that the pH of the environment is 7, while the pH or the pore solution is initially 13. To change the pH of the environment the user can simply change the concentration of EXTERNAL anions or cations.

5.3Depth vs. Time

As 4SIGHT is calculating ion transport it regularly prints the current status of the degradation. The sulfate and chloride penetration depths as a function of time are given in the columns labelled SO4 and Cl, respectively. L is the remaining thickness of the slab, K is the hydraulic conductivity, D is the diffusivity, Flux is the flux of pore solution out the bottom of the slab, and pH is the pH of the flux.

"Day"   "L"     "K  "   "D    " "SO4"   "Cl"   "Flux"   "pH"
"   "   "m"     "m/s"   "m^2/s" "m  "   "m "   "ml/dy/m2"

0        1.000 1.3e-12 5.0e-12  0.000  0.000  0.027   13.2
10036   0.988 1.3e-12 5.0e-12  0.012  0.101  0.027   13.2
15055   0.988 1.3e-12 5.0e-12  0.018  0.129  0.027   13.2
20023   0.976 1.3e-12 5.0e-12  0.025  0.150  0.028   13.2
25031   0.969 1.3e-12 5.0e-12  0.031  0.173  0.028   13.2
30018   0.963 1.3e-12 5.0e-12  0.037  0.192  0.028   13.2
35011   0.957 1.3e-12 5.0e-12  0.043  0.211  0.028   13.2
40048   0.951 1.3e-12 5.0e-12  0.049  0.229  0.029   13.2
45104   0.945 1.3e-12 5.0e-12  0.055  0.246  0.029   13.2
50017   0.939 1.3e-12 5.0e-12  0.061  0.263  0.029   13.2
55045   0.933 1.3e-12 5.0e-12  0.067  0.280  0.029   13.2
60015   0.927 1.3e-12 5.0e-12  0.074  0.295  0.030   13.2
65003   0.920 1.3e-12 5.0e-12  0.080  0.311  0.030   13.2
70002   0.914 1.3e-12 5.0e-12  0.086  0.327  0.030   13.2
75013   0.908 1.3e-12 5.0e-12  0.092  0.342  0.031   13.2
80069   0.902 1.4e-12 5.0e-12  0.098  0.357  0.031   13.2
85037   0.896 1.4e-12 5.0e-12  0.104  0.372  0.031   13.2
90050   0.890 1.4e-12 5.0e-12  0.104  0.372  0.031   13.2
95069   0.884 1.4e-12 5.0e-12  0.116  0.401  0.031   13.2
100017   0.878 1.4e-12 5.0e-12  0.122  0.416  0.032   13.2

As per the linear model for sulfate attack, the sulfate front increases linearly with time. The chloride depth has a t^1/2 because of the low Peclet number (the ratio of Darcy to ‘diffusive’ flow [2]). At sufficiently high Peclet number (greater permeability or hydraulic head) the chloride depth approaches a linear relationship to time.

5.4Failure Data

After reporting the time dependent behavior, 4SIGHT reports the reason for termination and the status of the sulfate and chloride penetration:

Exceeded TIME limit.

"T"   17.283
"Day"   100017
"SO4 (m)"   0.122
"Cl (m)"   0.416

These failure data indicate that the calculation terminated because it exceeded the time limit. The termination occurred after 100044 days (586 years), at which point the sulfate and chloride penetration were 0.13 and 0.60 meters, respectively.

5.5Final System State

Upon termination of the calculation, the final state of the system for the slab is printed. The L(m) is measured from the top of the slab. Psi is the hydraulic pressure, vD is the Darcy velocity, xi is the inverse of the formation factor, phi is the porosity, fc is the estimated compressive strength using ACl 211.

Final System state:

"L(m)" "Psi" "vD"  "xi"   "phi"  "pH"  "fc" "Ca"   "Cl"   "CaOH"
0.0000 0.392 0.000 0.0024 0.1634  7.000 5052 0.0000 0.4000 0.000
0.0500 0.392 0.000 0.0024 0.1631  7.000 5057 0.0000 0.4000 0.000
0.1000 0.392 0.000 0.0024 0.1658  7.000 5011 0.0000 0.4000 0.000
0.1500 0.374 0.000 0.0024 0.1663 13.277 5003 0.0001 0.3740 31.599
0.2000 0.342 0.031 0.0025 0.1671 13.351 4989 0.0001 0.3253 31.860
0.2500 0.311 0.031 0.0025 0.1672 13.392 4988 0.0001 0.2773 31.886
0.3000 0.279 0.031 0.0025 0.1672 13.405 4987 0.0001 0.2314 31.899
0.3500 0.248 0.031 0.0025 0.1673 13.394 4986 0.0001 0.1889 31.912
0.4000 0.217 0.031 0.0025 0.1673 13.365 4986 0.0001 0.1509 31.918
0.4500 0.186 0.031 0.0025 0.1673 13.326 4986 0.0002 0.1178 31.919
0.5000 0.155 0.031 0.0025 0.1673 13.286 4986 0.0002 0.0899 31.919
0.5500 0.124 0.031 0.0025 0.1673 13.250 4986 0.0002 0.0671 31.919
0.6000 0.093 0.031 0.0025 0.1673 13.220 4986 0.0003 0.0488 31.919
0.6500 0.062 0.031 0.0025 0.1673 13.199 4986 0.0003 0.0348 31.919
0.7000 0.031 0.031 0.0025 0.1673 13.185 4986 0.0003 0.0242 31.919
0.7500 0.000 0.031 0.0025 0.1673 13.176 4986 0.0004 0.0164 31.919
0.8000 0.000 0.031 0.0025 0.1673 13.173 4986 0.0004 0.0110 31.919
0.8500 0.000 0.031 0.0025 0.1673 13.172 4986 0.0004 0.0073 31.919
0.9000 0.000 0.031 0.0025 0.1673 13.172 4986 0.0004 0.0050 31.919
0.9500 0.000 0.031 0.0025 0.1673 13.172 4986 0.0004 0.0039 31.919
1.0000 0.000 0.031 0.0025 0.1673 13.172 4986 0.0004 0.0039 31.919

Note that the external quantities are duplicated to a depth of 0.1 meters. 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.