Cement composition and its relation with compressive strength
A method for designing a cement composition may include: providing a target compressive strength and a target composition density; selecting at least one cementitious material from a plurality of cementitious materials; calculating a required amount of water to produce a cement composition with the target composition density, the cement composition comprising the water and the at least one cementitious material; calculating a compressive strength of the cement composition based at least in part on a model of compressive strength; comparing the calculated compressive strength to the target compressive strength; and preparing the cement composition with the calculated compressive strength.
1. A method for designing a cement composition comprising:
providing a target compressive strength and a target composition density;
selecting at least one cementitious material from a plurality of cementitious materials;
calculating a required amount of water to produce a cement composition with the target composition density, the cement composition comprising the water and the at least one cementitious material;
calculating a compressive strength of the cement composition based at least in part on a model of compressive strength wherein the model of compressive strength includes a component of reactivity index for each cementitious material in the cement composition;
comparing the calculated compressive strength to the target compressive strength; and
preparing the cement composition with the calculated compressive strength.
2. The method of claim 1 further comprising:
adjusting a concentration of the at least one cementitious material in the cement composition after the step of comparing; and
recalculating the compressive strength of the cement composition.
3. The method of claim 2 wherein the step of adjusting comprises at least one of:
i. increasing a concentration of at least one cementitious material with a relatively higher reactivity index as compared to other cementitious materials if the calculated compressive strength is lower than the target compressive strength,
ii. increasing a concentration of at least one cementitious material with a relatively lower specific gravity as compared to other cementitious materials if the calculated compressive strength is lower than the target compressive strength,
iii. increasing a concentration of at least one cementitious material with a relatively lower reactivity index as compared to other cementitious materials if the calculated compressive strength is greater than the target compressive strength, or
iv. increasing a concentration of at least one cementitious material with a relatively higher specific gravity as compared to other cementitious materials if the calculated compressive strength is greater than the target compressive strength.
4. The method of claim 1 wherein the model of compressive strength comprises at least one correlation between compressive strength and concentration of cementitious material.
5. The method of claim 1 wherein the model of compressive strength comprises a model with the form of:
ln
(
CS
)
=
ln
(
A
)
-
1.5
*
ln
(
B
)
*
1
-
ρ
S
ρ
D
ρ
S
ρ
W
-
1
where CS is compressive strength, A and B are constants dependent on concentrations of cementitious materials in the cement composition calculated by a regression model, ρ s is density of the cement composition,
d is density of a dry blend comprising the cementitious materials, and ρ w is a density of water.
6. The method of claim 1 wherein the model of compressive strength comprises a model with the form of:
where:
CS
=
CS
0
(
w
c
eff
)
n
where
:
c
eff
=
c
cement
+
Σ
α
i
c
i
and where c cement is the mass fraction of Portland cement in a dry blend comprising the cementitious materials, α i is a reactivity index of component i in a dry blend comprising the cementitious materials, c i is the mass fraction of cementitious component i in the dry blend, w/c eff is water-to-cement ratio, CS is compressive strength, CS 0 is a compressive strength of a Portland cement composition where a water to cement ratio is 1, and n is a constant.
7. The method of claim 6 wherein the reactivity index is calculated based at least in part on a correlation comprising constants, wherein the correlation has the general form of:
reactivity index=Π f (p i )
where p i is a measurable physicochemical property of the cementitious component.
8. The method of claim 1 wherein the model of compressive strength comprises a model with the form of:
CS=ΣCS i ;
where CS i is a compressive strength contribution of component I in a dry blend comprising the cementitious materials.
9. A system comprising:
a predictive model database comprising at least one model of compressive strength for a plurality of cementitious materials wherein the model of compressive strength includes a component of reactivity index for each cementitious material; and
a computer system configured to:
accept an input of compressive strength and composition density;
query the predictive model database and select a model;
generate a cement composition, based at least in part on the selected model, compressive strength, and composition density; and
display the cement composition to a user.
10. The system of claim 9 wherein the at least one model of compressive strength correlates concentration of cementitious material to compressive strength.
11. The system of claim 9 wherein the at least one model of compressive strength comprises a model with the form of:
ln
(
CS
)
=
ln
(
A
)
-
1.5
*
ln
(
B
)
*
1
-
ρ
S
ρ
D
ρ
S
ρ
W
-
1
where CS is compressive strength, A and B are constants dependent on concentrations of cementitious materials in the cement composition, ρ s is density of the cement composition, ρ d is density of a dry blend comprising the cementitious materials, and ρ w is a density of water.
12. The system of claim 11 wherein A and B are calculated by a regression model.
13. The system of claim 9 wherein the at least one model of compressive strength comprises a model with the form of:
where
CS
=
CS
0
(
w
c
eff
)
n
where
:
c
eff
=
c
cement
+
Σ
α
i
c
i
and where c cement is the mass fraction of Portland cement in a dry blend comprising the cementitious materials, α i is a reactivity index of component i in a dry blend comprising the cementitious materials, c i is the mass fraction of cementitious component i in the dry blend, w/c eff is water-to-cement ratio, CS is compressive strength, CS 0 is a compressive strength of a Portland cement composition where a water to cement ratio is 1, and n is a constant.
14. The system of claim 13 wherein the reactivity index is calculated based at least in part on a correlation comprising constants, wherein the correlation has the general form of:
reactivity index=Π f (p i )
where p i is a measurable physicochemical property of the cementitious component.
15. The system of claim 9 wherein the at least one model of compressive strength model comprises a model with the form of:
CS=ΣCS i
where CS i is a compressive strength contribution of component i in a dry blend comprising the cementitious materials.
16. The system of claim 9 wherein the computer system is further configured to accept an input of a list of cementitious materials and generate a cement composition from the list of cementitious materials.
17. The system of claim 9 further comprising an experimental data database, the experimental data database comprising a plurality of cement compositions, measured compressive strength for the plurality of cement compositions, and corresponding compositional makeup of the plurality of cement compositions, wherein the at least one model of compressive strength comprises model parameter inputs, wherein the computer system is further configured to query the experimental data database and generate the model parameter inputs and wherein the model parameter inputs are generated by a regression analysis.
18. A method for designing a cement composition comprising:
providing one or more model parameters of a multilinear regression model;
providing a reactivity index based on one or more measurements of at least one physicochemical property of each of one or more cementitious components;
calculating an overall chemical reactivity for a combination of the one or more cementitious components based, at least in part, on the reactivity index and the one or more model parameters;
calculating both a density and a specific surface area of the combination using any selected from: a linear summation and a nonlinear summation;
predicting one or more properties of the cement composition based, at least in part, on the overall chemical reactivity, the density, and the specific surface area; and
preparing the cement composition.
19. The method of claim 18 further comprising:
specifying a target property; and
determining a formulation for the cement composition based, at least in part, on the specification of the target property.
20. The method of claim 19 , wherein the target property comprises at least one target property selected from the group consisting of: compressive strength, tensile strength, Young's modulus of elasticity, and any combination thereof.