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Prediction of Portland C ement Strength Using Statistical
Methods
To cite this Article: , 'Prediction of Portland C ement Strength Using Statistical
Methods', Materials and Manufacturing Processes, 22:3, 333 - 336
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Materials and Manufacturing Processes, 22: 333–336, 2007
Copyright © Taylor & Francis Group, LLC
ISSN: 1042-6914 print/1532-2475 online
DOI: 10.1080/10426910701190352
Prediction of Portland Cement Strength Using Statistical Methods
P. E. García-Casillas1 , C. A. Martinez1 , H. Camacho Montes1 , and A. García-Luna2
1
Instituto de Ingeniería y Tecnología, Universidad Autónoma de Cd. Juárez, Juárez Chih, México
2
Departamento de Investigación y Desarrollo, Cd. Chihuaha Chih, México
The Portland cement strength is the most important mechanical property that should be tested for quality control. Because 28 days represents
a very long period for the cement industry, a faster determination of the cement strength represents a favorable research objective of the recent
research in the cement industry. In the present work, a mathematical model for the prediction of cement strength is developed based on a standard
specifications for Portland cement: chemical-mineralogical synthesis of the cement (%C3 S, %C2 S, %C3 A, %C4 AF), fineness by air permeability
apparatus, lime saturation factor (LSF), particle size distribution, position parameter, and uniform factor. The strength values predicted were
validated with consistently high accuracy, based on a linear regression of selected physical and chemical characteristics routinely obtained in the
cement laboratory. The maximum errors were 4.54%, 2.66%, and 4.86% at 3, 7, and 28 days, respectively. The proposed model provides the
opportunity to predict the compressive strength in a very short time and this will save cost and make a competitive advantage in the Portland
Cement production market.
Keywords Alite; ASTMC109; Belite; Cement industry; Chemical-mineralogical synthesis; Clinker; Compressive strength; Dicalcium silicate;
Mathematical model; Portland cement; Quantitative X-ray diffraction analyses; Statistical methods; Tetracalcium aluminoferrite; Tricalcium
aluminate; Tricalcium silicate.
1. Introduction
Vital interest to the cement chemistry are the factors that
affect the cement’s strength performance in concrete. In
general, these include:
1)
2)
3)
4)
5)
6)
Generally, it is known in the cement industry which
cement characteristics (such as C3S and Blaine fineness)
affect the strength, but may not know how these
characteristics change with cement type or manufacturer.
A value can be assigned to the Compositional changes in
the chemistry of cement. If a quantitative choice can be
made of the most economic set of characteristics required to
make a change in strength performance, more cost effective
cements can be produced. The advantages in competitive
market situation are obvious and may well favor one process
over another.
Accordingly to current state of the art literature physical
and chemical data about cement has been produced in a
massive amount, but the chemistry must wait until the
mortar cube strengths are obtained in period of 28 days in
accordance with ASTM C109(1).
Changes in phase chemistry;
Changes in clinker burning condition;
Changes in clinker cooling condition;
Cement fineness and particle size distribution;
Alkali levels and weather alkali salts are water soluble;
Skill of laboratory personnel.
Although this list is not complete, many of the factors
are considered in the tests made in the modern cement plant
laboratory under ASTM C114 to meet the requirements of
ASTM C150. The methods for establishing the test values
can vary widely, phase chemistry can be calculated from
an oxide analysis, or measured directly by quantitative
X-ray diffraction analyses. The results are often somewhat
different, raising the question of which method yields the
most accurate response. There are two methods for the faster
determination of cement strength: the accelerated strength
test methods [1] and the use of suitable mathematical
models [2–5]. A fundamental question is how to predict the
strength performance of these cementations systems based
on data from the cement manufacturing process. Answering
this question is the objective of the investigation reported
here in.
2. Experimental
A lineal regression model was chosen to explain the
fundamental relationship between strength performances
and cement characteristics. The cement used was ordinary
Portland cement, having a 28-day compressive strength of
40 MPa. The data used for the development of the strength
model and the standard test method are given in Tables 1 and
2, respectively, which present the chemical-mineralogical
data and the data concerning the fineness of the cement,
respectively.
3. Result and discussion
The following series of variables have been tested in order
to certify their effect on the cement strength:
Received January 16, 2006; Accepted September 11, 2006
Address correspondence to P. E. García Casillas, Instituto de Ingeniería
y Tecnología, Universidad Autónoma de Cd. Juárez, Ave. del Charro #
610, C.P. 32250, Cd. Juárez Chih., México; E-mail: pegarcia@uacj.mx
and perlaelviagarcia@yahoo.com
A) Chemical-mineralogical variables: Percentage content
of C3 S, C2 S, C3 A, C4 AF, Na2 O, SO3 fCaO, values of
C3 A/C4 AF, C3 S/C2 S, lime saturation factor (LSF) (%),
alumina ratio;
333
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334
P. E. GARCÍA-CASILLAS ET AL.
Table 1.—Variables of the 10 samples of Portland cement.
Sample
1
2
3
4
5
6
7
8
9
10
C3 S/C2 S
C3 A/C4 AF
LSF (%)
Sb (cm2 /g)
Pp µm
P80 µm
<3 µm
3–32 µm
3–16 µm
16–24 µm
7.96
7.51
6.35
6.00
6.23
5.93
6.35
5.95
6.56
7.22
0.77
0.75
0.79
0.79
0.79
0.76
0.76
0.79
0.79
0.75
111.9
112.3
113.7
114.4
113.9
114.4
113.7
114.5
113.3
112.6
4060
4075
4296
4186
4163
4163
4058
4097
4128
4098
15.44
15.57
15.57
15.59
15.78
15.52
15.65
15.94
15.99
15.54
24.69
25.62
24.99
25.50
25.83
25.24
25.50
25.87
25.79
26.12
28.28
27.21
28.65
28.42
28.20
27.60
28.21
29.05
29.16
27.06
59.80
59.02
58.80
58.63
57.84
59.36
58.45
56.95
56.76
58.87
38.41
38.09
37.24
37.61
37.02
38.19
37.43
36.62
36.61
37.30
12.45
12.81
12.87
12.12
12.65
12.70
12.56
12.19
12.21
13.10
B) Particle size distribution variables: Specific surface Sb
position parameter Pp 80% passing size P80 , uniformity
factor n;
C) Size fractions variables: Percentage content in <3 µm,
3–32 µm, 31 µm, 3–16 µm, and 16–24 µm.
The selection of the variables that contribute to the
prediction of the cement strength is based on stepwise
regression analysis. In Fig. 1, the variables that are inserted
in mathematical models by this statistical procedure are
illustrated. It must be noticed that, in case of strongly
correlated parameters, the effect of each one on the
development of cement strength cannot be drawn from this
figure.
The stepwise regression analysis of the data presented in
Table 1 leads to Eq. (1):
!A! = !B! · !C!
(1)
Figure 1.—Selected variables by stepwise regression analysis for the
prediction of cement strength (dark blocks are variables that contribute to the
cement strength).
where
!
!
! Strength at 3 days !S3 " !
!
!
!A! = !! Strength at 7 days !S7 " !!
! Strength at 28 days !S28 " !
!
!
! C3S/C2S !
!
!
! C3A/C4AF !
!
!
!
! LSF!%"
!
!
! Sb !cm2 /g" !
!
!
!
!
!C! = ! Pp !µm"
!
!
! P80 !µm"
!
!
!
! <3 µm
!
!
! 3–32 µm !
!
!
! 3–16 µm !
! 16–24 µm !
Variable
Tricalcium silicate (C3S)
Dicalcium silicate (C2S)
Tricalcium aluminate (C3A)
Tetracalcium alulminoferrite (C4AF)
LSF(%)
Sb (cm2 /g)
<3 µ# 3–32 µ# 3–16 µ# 16–24 µm
!
!
! 0$00 0$00 0$00 X4 0$00 X6 0$00 X8 X9 X10 !
!
!
!B! = !! Y1 0$00 Y3 0$00 Y5 Y6 Y7 0$00 0$00 0$00 !!
!Z
Z2 Z3 0$00 Z5 Z6 Z7 Z8 0$00 Z10 !
1
Eq. (1) result in:
S3 = 0$0826Sb − 127P80 + 30$377!%3 − 32 µm"
−49$91!%3 − 16 µm" + 27$509!%16 − 24 µm"
CS
S7 = 0$3 3 − 9$04LSF + 123$04pp − 32$59P80
C2 S
−6$85!% < 3 µm"
Table 2.—Test method for Portland cement.
Test method
Description
ASTM-C150
Standard specification for Portland cement
ASTM-C114
ASTM-C204
Laser diffraction
Standard test methods for chemical analysis of hydraulic cement
Standard test method for fineness of hydraulic cement by air permeability apparatus
Distribution particle size
(2)
(3)
335
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PREDICTION OF PORTLAND CEMENT STRENGTH
Figure 2.—Predicted vs. measured strength of Portland cement.
S28 = −164!2
CA
C3 S
+ 1054!7 3 − 132!9LSF + 444!3pp
C2 S
C4 AF
+ 67!87P80 + 1!69 "% < 3 µm#
+ 128!07"%3 − 32 µm# − 34!68"%16 − 24 µm#! (4)
The measured and predicted strength values are presented
in Fig. 2. The average difference between measured and
predicted strength are 4.53%, 3.65%, and 4.86% or more
specifically, 11.69, 12.28, and 19.87 k/cm2 for the models
2, 3, and 4, respectively.
In order to investigate the fitting quality of the multiple
regression models 2, 3, and 4 in the data set, the statistic
Figure 3.—Compressive cement strength vs. predicted cement strength at 3,
7, and 28 days.
multiple coefficient of determination R2 (R square) was
determined. The R2 is 0.9989, 0.9975, and 0.9979 for the
models 2, 3, and 4, respectively. This R2 values mean
that 99.8% of the derivation squares sum in the measured
strength values about their mean is attributable to the leastsquares prediction equations indicating which that S3 model
best fit the data.
In Fig. 3, the values of cement strength after 3, 7,
and 28 days vs. predicted values are presented. Therefore
the simulation of the strength development is very
satisfactory.
From the relations 2, 3, and 4, it is obvious that the
fineness of the cement is the significant factor for the
strength after 3 days. More specifically, the particle fractions
(3, 3–16, and 16–24 µm have a positive effect on the strength
while the fraction 24–32 µm has a negative one. In addition,
the increase of the specific surface and P80 of the cement
leads to higher strength values.
The cement strength after 7 days is affected by the ratios
C3S/C2S and the LSF value as well as by the characteristics
of the particle size distribution Pp and P80 . The fraction
with size less than 3 µm lowers the strength value as it was
expected.
The 28 day strength is affected by the LSF value
and the ratios C3S/C2S and C3A/C4AF. Besides it is
observed that the fraction 16–24 µm has a positive effect
while the fractions 3, 3–16 and 24–32 µm have a negative
one.
It must be noticed that it is not possible to extract
conclusions concerning the individual contribution of the
C3S/C2S, C3A/C4AF, and LSF values on the strength as
these variables are strongly correlated.
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336
The models described by Eqs. (2)–(4) have been tested
for the prediction of the strength of cements produced by the
Mexican companies and the results were very satisfactory.
4. Conclusion
The following conclusions can be drawn from the present
study:
1. A mathematical model for the prediction of the 3, 7, and
28 day compressive strength of the cement is developed
based on stepwise regression analysis;
2. The proposed model predicts the cement strength with
a satisfactory accuracy. At early ages the strength is
affected mainly by the fineness parameters;
3. At later ages, the chemical-mineralogical synthesis of the
cement influences the strength growth;
4. The 28 days strength is strongly affected by the
distribution of the cement particles in the size fractions
<3 µm, 3–16 µm, 16–24 µm, and 24–32 µm. Specifically
the 16–24 µm fraction is the only one which has a positive
effect on the strength development.
P. E. GARCÍA-CASILLAS ET AL.
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