Environmental Engineering Reference
In-Depth Information
3.3.2. Models for Response Variables
The resulting special cubic model for compressive strength, fit by least
squares, is
Compressive Strength (Kg/cm
2
)
= 175.53 ×
x
1
+ 39.66 ×
x
2
+ 31.26 ×
x
3
-
145.43 ×
x
1
×
x
2
-318.60 ×
x
1
×
x
3
- 69.05 ×
x
2
×
x
3
+919.09 ×
x
1
×
x
2
×
x
3
Where,
x
1
= Jarosite
x
2
= Clay
x
3
= CCRs
Models for other Responses
Using the same procedure described for compressive strength, the
following models were fit to water absorption, brick shrinkage, density and
leachate concentration of lead and cadmium
Water absorption (%)
= 10.50×
x
1
+ 18.55 ×
x
2
+ 17.99×
x
3
+ 12.25×
x
1
×
x
2
- 0.88×
x
1
×
x
3
+ 0.089×
x
2
×
x
3
Shrinkage (%)
= 55.37×
x
1
+ 36.18 ×
x
2
+ 12.40×
x
3
- 138.38×
x
1
×
x
2
-
45.36×
x
1
×
x
3
- 60.47 ×
x
2
×
x
3
+362.12 ×
x
1
×
x
2
×
x
3
Density (g/cc)
= 2.10 ×
x
1
+ 1.75×
x
2
+ 1.39×
x
3
- 0.75×
x
1
×
x
2
- 0.58×
x
1
×
x
3
3 + 0.20 ×
x
2
×
x
3
Lead leaching (ppm)
=60.65402 ×
x
1
-144.73432 ×
x
2
-122.59932 ×
x
3
+209.84920×
x
1
×
x
2
+144.65092×
x
1
×
x
3
+431.61193 ×
x
2
×
x
3
-
442.18468 ×
x
1
×
x
2
×
x
3
-385.58903 ×
x
1
×
x
2
× (
x
1
-
x
2
)-300.57591 ×
x
1
×
x
3
× (
x
1
-
x
3
)
Cadmium leaching (ppm)
=+0.16829 ×
x
1
+8.25804 ×
x
2
+8.25740 ×
x
3
-
15.59891×
x
1
×
x
2
- 13.92064 ×
x
1
×
x
3
-30.43336 ×
x
2
×
x
3
+32.96373
×
x
1
×
x
2
×
x
3
+13.45757 ×
x
1
×
x
2
× (
x
1
-
x
2
) +10.42656 ×
x
1
×
x
3
× (
x
1
-
x
3
)
Quadratic models were adequate for responses water absorption and
density. For compressive strength and shrinkage the fitted model includes
special cubic terms that were found to be significant.
Graphical Interpretation of the Response Variables
Validated model results are interpreted graphically using response trace
plots and contour plots and 3 D graph. Figures. 11, 14, 17, 20, 23 and 26
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