Shukla et al., International Journal of Advanced Engineering Research and Studies
E-ISSN2249–8974
Proceedings of BITCON-2015 Innovations For National Development
National Conference on : Innovations In Civil Engineering
Research Paper
IN PLACE STRENGTH OF CEMENT MORTAR/CONCRETE
USING MATURITY AND ACTIVATION ENERGY
Maneesh K. Shukla1, Dr. S.P. Mishra2
Address for Correspondence
1
M.E. Scholar (Structural Engineering), 2Professor, Dept. Of Civil Engg., Bhilai Institute of Technology,
Durg, CG, India
ABSTRACT
Using maturity is a technique to account for the combined effects of time and temperature on the strength development of
concrete. The method provides a relatively simple approach for making reliable estimates of in-place strength during
construction. Experimental measured data are used to assess the rate constant of a mix. Activation energy is used to
calculate age conversion factor which varies with curing temperature. The purpose of this paper is to review of the basic
concepts underlying the method and to explain how the method is applied.
KEY WORDS: Maturity, rate constant, apparent energy, equivalent age.
1. INTRODUCTION
It is apparent that in scaling the economy of a project
it is important to scale it also in construction time. It
is natural to get formwork removed once the cast
member gets enough strength to take on immediate
load from ongoing construction. Hence to avoid
premature removal of formwork, maturity period (for
enough strength) of concrete member may be used as
yard stick.
The method based on maturity relies on the measured
temperature history of the concrete to estimate
strength development during the curing period, when
moisture is available for cement hydration. The
temperature history is used to calculate a quantity
called the maturity index. For eachconcrete mixture,
the relationship between strength (or other property
of interest) and the maturity index is established
beforehand. The strength relationship and the
measured in-place maturity index are used to
estimate the in-place strength.
Consider one of incidents which emphasis the need
and importance of present study
Portions of a multi-story apartment building, under
construction in Fairfax County, suffered a
progressive collapse. Fourteen workers were killed
and 34 were injured in the accident. The National
Bureau of Standards (NBS) was requested by the
Occupational Safety and Health Administration
(OSHA) to assist in determining the technical cause
of the collapse. The NBS report concluded that the
most probable cause of the failure was premature
removal of formwork that resulted in punching shear
stresses that exceeded the capacity of the relatively
young concrete [Carino et al.]
1.1 Maturity Concept
Figure 1: Schematic of temperature history and
temperature-time factor computed according to Eq.
(3).
The maturity concept was created with the intention
to estimate the development of the properties of the
concrete relating them with the historical temperature
during the curing process, in maturity functions that
involve time and temperature (Salvador Filho, 2001).
In the civil construction, the use of the maturity
Int. J. Adv. Engg. Res. Studies/IV/II/Jan.-March,2015/79-82
method is used to determine the approached time in
concrete to reach "in loco" a desired compressive
strength, analyzing the description of temperature to
which occurs the cure and in samples analyzed in
laboratory with controlled temperatures. The use of
the thermal cure in the concrete is sufficiently used to
reduce the curing time of the parts, that exists the
necessity of high rotation of the forms.
The increase of the curing temperature of concrete
speeds up the chemical reactions of hydration of the
cement, conferring larger initial strength and
reducing the time of removal of formworks.
However, second Pinto (2000) any property
mechanics or physics of the concrete that is related
with the hydration degree could be reached by the
maturity method, and not summarizing then to the
process to estimate the compressive strength. Saul
(1951), cited by Peres et al. (2003) it introduced the
maturity concept, relating it with the called
compressive strength law of the profit of resistance
with maturity:
"One same mixture of concrete with one exactly maturity
factor - measured as function of temperature and time has, approximately, the same resistance any that is the
combination of temperature and time to reach the maturity
factor".
Carino (1991) cited by Pinto (2000) considered a
relation of the maturity with the relative degree of
development of the compressive strength, modifying
the law of Saul (1951):
"One same mixture of concrete to one exactly
maturity degree (measured as function of
temperature and time) has, approximately, the same
relative resistance any that is the combination of
temperature and time to reach the maturity degree".
Nurse (1949) cited by Salvador Filho (2001)
suggested that the simple product time x resistance
would be capable to have access the cure effect the
steam in the profit of compressive strength. The
function of Nurse-Saul assumes the following form,
much spread out due to its simplicity, as it shows
equation (3)
1.2 Activation Energy Concept
In accordance with Peres et al. (2003) for the
application of the maturity method are necessary the
knowledge of a parameter of thermal sensitivity of
the mixture, that will be evaluating the dependence of
the speed of the reaction of cement hydration with
the temperature called Apparent Activation Energy
(Ea). According to Atkins (1998) cited by Carvalho
(2002), the activation energy results of idea that the
molecules must possess a minimum amount of
Shukla et al., International Journal of Advanced Engineering Research and Studies
kinetic energy to react. This energy is that necessary
one to transform the reagents and products. In the
exothermical reactions (case of the cement hydration)
the reagents are in a state of bigger energy than the
products. Thus being, the activation energy is the
difference between the energy necessary to activate
the reaction and the level of energy of the reagents.
In a same temperature, reactions that very demand a
high value of activation energy are saidslow
reactions, to the step that low values of activation
energy are indicating of reactions thatoccur quickly.
Bigger values of Ea indicate a necessity of bigger
energy to initiate the reaction, thus implying that this
reaction will be more vulnerable to the influence of
the temperature Carvalho (2002).
Qualitatively the theory da collision explains well the
four factors that influence the speed das reactions
(Plane and Sienko, 1977), cited by Peres et al.
(2003):
 The speed of the chemical reaction depends
on the nature of the chemical reagents
because the activation energy is different of a
reaction for another one;
 The speed of the reaction depends on the
concentration of the reagents, because the
number of collisions increases when the
concentration is increased;
 The speed of the reaction depends on the
temperature, because an increase of the
temperature makes molecules to be moved
more fast, increasing the frequency of the
collisions;
 The speed of the reaction depends on the
presence of catalysers, in way with that the
collisions if become more effective.
Arrhenius observed that the rate constant, k, of many
reactions increased with temperature according to
what has since been called the Arrhenius equation, as
follows:
E-ISSN2249–8974
agerelationship to each set of strength-age data.The
following hyperbolic equation for strength gain
underisothermal curing may be used to generate
strength-age relationship yielding appropriate rate
constant. [Carino, 1984; Knudsen, 1980]
=
(
)
(
……..(1)
)
where
S = strength at age t,
Su = limiting strength,
k = rate constant, 1/day, and
t0 = age at start of strength development.
Thus for given sets of curing temperature, sets of rate
constants may be obtained
Then as stated earlier the Arrhenius equation
provides relationship between rate constant and
activation energy.
=
……..(2)
Using known valuesof T and corresponding value of
k the best fitted curve is obtained from the above
relation to represent the variation of the rate constant
with the temperature.From the curve the activation
energy is calculated.
3.0 DETERMINATION OF MATURITY &
EQUIVALENT AGE
Maturity Index is calculated by following
relationshipNurse-Saul maturity [McIntosh, 1949;
Nurse, 1949; Saul, 1951] function:
= ∑ ( − )∆
………(3)
where
M = maturity index, °C-hours (or °C-days), (also
called as temperature- time factor)
T = average concrete temperature, °C, during the
time interval Δt,
T0 = datum temperature (usually taken to be -10 °C),
t = elapsed time (hours or days), and
= time interval (hours or days).
Figure3: Showing maturity calibration curve
(Courtesy Nelson 2003).
Figure 2: Showing variation of logarithm of rate
constant Vs inverse of temperature
=
A = constant or factor of frequency
According to Pinto (2000) the frequency factor is
used to quantify the probability of that thecollisions
occur in directions favourable to the beginning of the
chemical reaction, with locatedatoms of such form to
make possible new linkings. In if treating to reactions
cement hydration,the use of the term apparent
activation energy becomes more satisfactory, since
they areheterogeneous processes with diverse
reactions that occur simultaneously.
2.0 DETERMINATION OF ACTIVATION
ENERGY
In order to calculate activation energy, rate constant
is required to be calculated through laboratory test
data. The value of the rate constant at each
temperature is determined by fitting a strengthInt. J. Adv. Engg. Res. Studies/IV/II/Jan.-March,2015/79-82
However it was realized that this linear
approximation in above equation might not be valid
when curing temperatures vary over a wide range. As
such concept of equivalent age was formulated based
on the Arrhenius equation [Brown and LeMay, 1988]
to describe the effect oftemperature on the rate of a
chemical reaction.
=∑
∆
………(4)
Where
Term
is known as age conversion factor γ
te= the equivalent age at the reference temperature,
E = apparent activation energy, J/mol,
R = universal gas constant, 8.314 J/mol-K,
T = average absolute temperature of the concrete
during interval Δt, Kelvin, and
Tr= absolute reference temperature, Kelvin.
Shukla et al., International Journal of Advanced Engineering Research and Studies
Figure 4: Showing variation of age conversion factor
with change in concrete temperature for given
activation energy
The introduction of this function overcame one of
the main limitations of the Nurse-Saul function
because it allowed for a non-linear relationship
between the initial rate of strength development and
curing temperature. This temperature dependence is
described by the value of the apparent activation
energy, E.
4. APPLICACTIONS
4.1 Strength-maturity Relationship
To develop the strength-maturity relationship,
cylindrical concrete specimens are prepared using the
mixture proportions and constituents of the
concreteto be used in construction. These specimens
are prepared according to the usual procedures
formaking and curing test specimens in the
laboratory.
After the cylinders are moulded, temperature sensors
are embedded at the centers of at least two cylinders.
The sensors are connected to instruments that
automatically compute maturity orto temperature
recording devices.
The specimens are cured in a water bath or in a moist
curing room. At ages of 1, 3, 7, 14, and28 days,
compression tests are performed on at least two
specimens. At the time of testing, theaverage
maturity value for the instrumented specimens is
recorded. If maturity instruments areused, the
average of the displayed values is recorded. If
temperature recorders are used, thematurity is
evaluated according to Eq. (3) or Eq. (4). A recording
time interval of one-half houror less should be used
for the first 48 hours, and longer time intervals are
permitted for theremainder of the curing period.
A plot is made of the average compressive strength
as a function of the average maturity index. A best-fit
smooth curve is drawn through the data, or regression
analysis may be used todetermine the best-fit curve
for an appropriate strength-maturity relationship. The
resulting curvewould be used to estimate the in-place
strength of that concrete mixture.
Figure 5: Comparison of strength-maturity
relationships; the logarithmic function, Eq. (5), does not
fit the data as well as the linear hyperbolic function,
Eq. (1).
Int. J. Adv. Engg. Res. Studies/IV/II/Jan.-March,2015/79-82
E-ISSN2249–8974
One of the popular strength-maturity relationships is
the following logarithmic equation proposed by
Plowman (1956):
S
a
b log (M)
………(5)
where
a = strength for maturity index M =1,
b = slope of line, and
M = maturity index
Equation (5) is popular because of its simplicity; it
plots as a straight line when a log scale is used for the
maturity index axis, but it has its limitations. It does
not provide a good representation of the relationship
between strength and maturity index for low or high
values ofthe maturity index. It predicts that strength
keeps on increasing with maturity index, that is,
thereis no limiting strength. In fact the slope of the
line, b, represents the strength increase for everytenfold increase in maturity index. Figure 6 illustrates
that it may not be the most appropriateequation to use
for the strength-maturity relationship. In this case,
strength versus equivalent agedata are fitted with Eq.
(5) and the linear hyperbolic equation given by Eq.
(1). It is clear thatEq. (5) does not represent the
relationship between strength and maturity index
over the rangeof values from about 0.4 d to 28 d
shown in the Fig. 5.
3.2 Estimating In-place Strength
The procedure for estimating the in-place strength
requiresmeasuring the in-place maturity. As soon as
it is practicable after concrete placement, temperature
sensors are placed in the fresh concrete. The sensors
should be installed at locations in the structure that
are critical in terms of exposure conditions and
structural requirements. The importance of this step
cannot be over emphasized when the strength
estimates are being used for timing the start of
critical construction operations.
The sensors are connected to maturity instruments or
temperature recording devices that are activated as
soon as is practicable after concrete placement. When
a strength estimate is desired, the maturity index
from the maturity instrument is read or the maturity
index is evaluated from the temperature record.
Using the maturity values and the previously
established
strength
maturity
relationship,
compressive strengths at the locations of the sensors
are estimated.
4.0 CONCLUSION
This paper provides an introduction to the maturity
method for estimating in-place strengthdevelopment
of cement mortar /concrete during construction.
Proper application of this relatively simple procedure
can result in savings by allowing construction
operations to be performed safely at the earliest
possible time. To assure safety, however, the user
needs to understand the inherent approximations and
limitations of the method. Inferences may be drawn
as follows.
 The maturity function is related to the
temperature sensitivity of initial strength
development and there is no single maturity
function that is applicable to all concrete
mixtures. The applicable maturity function
for a given concrete can be obtained by
measuring the variation of the rate constant
with the curing temperature.
 The linear hyperbolic function, is
recommended for analysing strength-age
Shukla et al., International Journal of Advanced Engineering Research and Studies
data to obtain the rate constants at different
curing temperatures.
 Arrhenius equation can be used to represent
the variation of the rate constant with curing
temperature. The temperature sensitivity
factor governs the rate at which the rate
constant increases with temperature and is
analogous to the “activation energy” in the
equation.
 The maturity method is more reliable in
estimating relative strength development
rather than absolute strength.
 Critical construction operations should not
be initiated on the basis of maturity index
values and the strength-maturity relationship
without further verification that the in-place
concrete has the expected strength potential.
REFERENCES















ACI Committee 228. 1995. In-Place Methods to
Estimate Concrete Strength. ACI 228.1R(1995),
American Concrete Institute, Farmington Hills,
MI.
ASTM C 1074. 1998. Practice for Estimating
Concrete Strength by the Maturity Method.
2000ASTM Standards Vol. 04.02, ASTM, West
Conshohocken, PA
Brown, T.L. and LeMay, H.E. 1988. Chemistry:
The Central Science. 4th Ed., Prentice Hall,
Englewood Cliffs, NJ, pp. 494-498.
Byfors, J., 1980. Plain Concrete at Early Ages.
Swedish Cement and Concrete Research
Institute Report 3:80, 464 p.
Carino, N.J., Woodward, K.A., Leyendecker,
E.V., and Fattal, S.G. 1983. A Review of the
Skyline Plaza Collapse. Concrete International,
Vol. 5, No. 7, July, pp 35-42.
Carino, N.J., Knab, L.I., and Clifton, J.R. 1992.
Applicability of the Maturity Method to HighPerformance Concrete. NISTIR-4819, Nat. Inst.
of Stands.and Tech. (US), May, 64 p. Available
from NTIS, Springfield, VA, 22161, PB93157451/AS
Carino, N.J. and Tank, R.C. 1992. Maturity
Functions for Concrete Made with Various
Cements and
Admixtures,” ACI Materials
Journal, Vol. 89, No. 2, March-April, pp. 188196.
Carino, N.J., 1984, “The Maturity Method:
Theory and Application,” Journal of Cement,
Concrete, and Aggregates (ASTM), Vol. 6, No.
2, Winter, pp. 61-73.
Freiesleben Hansen, P. and Pedersen, J. 1985.
Curing of Concrete Structures. CEB Information
Bulletin 166,May, 42 p.
Freiesleben Hansen, P. and Pedersen J.
1977.Maturity Computer for Controlled Curing
and Hardening of Concrete. Nordisk Betong, 1,
pp. 19-34.
Geiker, M. 1983. Studies of Portland Cement
Hydration by Measurements of Chemical
Shrinkage and Systematic Evaluation of
Hydration Curves by Means of the Dispersion
Model. PhD Dissertation, Technical University
of Denmark, 259 p.
Klieger, P. 1956.Effects of Mixing and Curing
Temperatures on Concrete Strength. Journalof
the American Concrete, Vol. 54, No. 12, June,
pp. 1063-1082.
Knudsen, T. 1980.On Particle Size Distribution
in Cement Hydration. Proceedings, 7th
International Congress on the Chemistry of
Cement (Paris, 1980), Editions Septima, Paris,
Vol. II, I-170-175.
Malhotra, V.M. 1971. Maturity Concept and the
Estimation of Concrete Strength. Information
Circular IC 277, Department of Energy Mines
Resources (Canada), Nov., 43 p.
Myers, J. J. 2000.The Use of the Maturity
Method as a Quality Control Tool for High
Performance
Concrete
Bridge
Decks.
Int. J. Adv. Engg. Res. Studies/IV/II/Jan.-March,2015/79-82
E-ISSN2249–8974
Proceedings PCI/FHWA/FIB International
Symposium on High Performance Concrete, L.
S. Johal, Ed., Precast/Prestressed Institute,
Chicago, pp.316-330.

Nurse, R. W. 1949.Steam Curing of Concrete.
Magazine of Concrete Research, Vol. l, No. 2,
1949, pp. 79-88.

Pinto, R. C. A. and Hover, K. C.
1999.Application of Maturity Approach to
Setting Times. ACI Materials Journal, Vol. 96,
No. 6, pp. 686-691.

Plowman, J. M. 1956.Maturity and the Strength
of Concrete. Magazine of Concrete Research,
Vol. 8, No. 22, March, pp. 13-22.

Saul, A. G. A. 1951.Principles Underlying the
Steam Curing of Concrete at Atmospheric
Pressure. Magazine of Concrete Research, Vol.
2, No. 6, March, pp. 127-140.

Tank, R.C. and Carino, N.J. 1991.Rate Constant
Functions for Strength Development of
Concrete. ACI Materials Journal, Vol. 88, No.
1, Jan-Feb, pp. 74-83.
Note: This Paper/Article is scrutinised and reviewed by Scientific
Committee, BITCON-2015, BIT, Durg, CG, India