Temperature Effects on the

Strength-Maturity Relation of

Mortar

Nicholas J. Carino

Structures and Materials Division

Center for Building Technology

National Engineering Laboratory

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

March 1981

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IQQ DEPARTMENT OF COMMERCE

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81-2244

1981
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APR 1 5 1981

NBSIR 81-2244 ^ '

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• TEMPERATURE EFFECTS ON THE . 6< STRENGTH-MATURITY RELATION OF a j. ?

MORTAR }

c. a

Nicholas J. Carino

Structures and Materials Division

Center for Building Technology

National Engineering Laboratory

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

March 1981

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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TEMPERATURE EFFECTS ON THE STRENGTH-MATURITY

RELATION OF MORTAR

Nicholas J. Carino

ABSTRACT

A study was performed to gain a fundamental understanding of the traditional

maturity method used to predict the in-place strength of concrete. Research

was undertaken to answer two questions; 1) What are the quantitative

effects of curing temperature on the compressive strength-maturity relation

of concrete? 2) Is there an age beyond which temperature no longer affects

the strength-maturity relation of concrete? To simplify testing, mortar cubes

were used as specimens for compressive strength determinations. Penetration

resistance measurements were performed to determine initial and final setting

times. Phase I of the research addressed the first question and involved

preparing and curing specimens at 5 , 12 , 23 , 32 and 43 C. Phase II

addressed the second question and involved curing specimens at 5 and 32 C

for short periods, followed by additional curing at 23 C. It was found that

initial set occurred at approximately the same maturity regardless of the

curing temperature. A three-parameter hyperbolic equation was used to

represent the strength-maturity relation. The parameters, determined by

regression analysis, were found to vary systematically with curing temperature.

Theoretical justification for the hyperbolic equation is presented and a key

assumption in the maturity method is identified. The strength versus age data

were also analyzed and a new concept, effective age, is suggested as a possible

alternative for representing the combined effects of time and temperature on

the compressive strength development of concrete.

Keywords; Concrete; compressive strength; curing temperature; early age;

final set; hydration; initial set; laboratory testing; maturity;

mortar; regression analysis; strength prediction; temperature

effects.

iii
TABLE OF CONTENTS

Page

ABSTRACT iii

LIST OF FIGURES v LIST OF TABLES vii

LIST OF SYMBOLS vlii

1.0 INTRODUCTION 1

1.1 General 1

1.2 Background of the Maturity Concept 2

2.0 EXPERIMENTAL PROCEDURE 10

2.1 Selection of Procedure 10

2.2 Specimen Preparation 10

2.3 Temperature Histories 11

2.4 Penetration Resistance Tests 12

2.5 Compression Tests 13

3.0 RESULTS 14

3.1 Maturity at Time of Setting 14

3.2 Compressive Strength 18

3.2.1 Equation for Strength-Maturity Relation 18

3.2.2 Phase I Results 18

3.2.3 Phase II Results 24

3.3 Uniformity of Batches 24

4.0 ANALYSIS AND DISCUSSION OF RESULTS 39

4.1 Setting Behavior 39

4.2 Temperature Effects on Strength-Maturity Relations 43

4.3 When is "Early Age" 52

5.0 BASIS OF CLASSICAL MATURITY CONCEPT 57

6.0 AN ALTERNATIVE APPROACH FOR COMPUTING MATURITY 66

7.0 SUimRY AND RECOI-IMENDATIONS 72

8.0 REFERENCES 74

APPENDIX A PENETRATION RESISTANCE TEST DATA 77

APPENDIX B COMPRESSIVE STRENGTH TEST DATA 80

iv
LIST OF FIGURES

Figure

1.1 The "crossover effect" due to dissimilar initial

temperatures 5

1.2 The hyperbolic strength-maturity function (a) and linear

transformations (b) and (c) 7

3.1 Penetration resistance versus maturity (phase I,

high w/c) 16

3.2 Penetration resistance versus maturity (phase I, low w/c) 17

3.3 Penetration resistance versus maturity (phase II,

5 C initial temperature) 20

3.4 Penetration resistance versus maturity (phase II,

32°C initial temperature) 21

3.5 Shapes of the probable and assumed

strength-maturity relation 22

3.6 Compressive strength versus maturity (phase I, high w/c) 25

3.7 Compressive strength versus maturity (phase I, low w/c) 26

3.8 Compressive strength versus maturity (phase II,

5 C initial temperature) 28

3.9 Compressive strength versus maturity (phase II,

32°C initial temperature) 29

3.10 Average weight of cubes and 95 percent confidence intervals

(phase I) 30

3.11 Average weight of cubes and 95 percent confidence intervals

(phase II, 5 C initial temperature) 32

3.12 Average weight of cubes and 95 percent confidence intervals

(phase II, 32 C initial temperature) 33

3.13 Individual cube weights (phase I, 5°C) 34

3.14 Individual cube weights (phase I, 12°C) 35

3.15 Individual cube weights (phase I, 23°C) 36

3.16 Individual cube weights (phase I, 32°C) 37

v
Figure Page

3.17 Individual cube weights (phase I, 43°C) 38

4.1 Age at initial set versus cumulative average

temperature (phase I) 40

4.2 Maturity at initial set versus cumulative average

temperature (phase I) 41

4.3 Maturity at initial and final set versus cumulative

average temperature (phase II) 42

4.4 Initial slopes of strength-maturity relations versus

cumulative average temperature (phase I) 45

4.5 Variation of K with cumulative average temperature (phase I) .... 47

m

4.6 Variation of offset maturity, M , with cumulative average

temperature (phase I) 48

4.7 Schematic representation of strength-maturity

relations at early maturities 49

4.8 Variation of limiting compressive strength with temperature

(phase I) 51

4.9 Early age temperature histories of phase II specimens 53

5.1 Comparison of exponential and hyperbolic strength-age

relations (phase I) 59

5.2 Compressive strength versus age (phase I, high w/c) 61

5.3 Compressive strength versus age (phase I, low w/c) 62

5.4 Variation of rate constant, k, with cumulative

average temperature (phase I) 64

6.1 Fit of Arrhenius function to k-temperature data, (phase I) 67

6.2 Variation of offset age, t , with cumulative average

temperature (phase I) 68

6.3 Strength ratio versus effective age (phase I, low w/c) 71
LIST OF TABLES

Table Page

1 Penetration Resistance Data Analysis, Phase I 15

2 Penetration Resistance Data Analysis, Phase II 19

3 Results of Strength-Maturity Data Analysis, Phase I 24

4 Results of Strength-Maturity Data Analysis, Phase II 27

5 Summary of Parameters (Phase I) 44

6 Summary of F-Test of Variances 54

7 Comparison of Exponential and Hyperbolic Strength-Age

Functions 58

vii
LIST OF SYMBOLS

a t ) ^2 > b j c = regression coefficients

d, g, A, B, C, K = regression coefficients

K*, K*, S*, M*

m

= regression coefficients

A

e = effective age

E = activation energy divided by gas constant

F = F-statistic used in testing for differences among

regression curves

k = rate constant in strength-age relations

K

m

= initial slope of strength-maturity curve divided by Su

M = maturity

M.

f s = maturity at final set

M

o = offset maturity, when strength development is assumed

to begin

M

s = maturity at initial set

N,N

o = degrees of freedom associated with sum of squared residuals

R,R

o = sum of squared residuals

R = penetration resistance

Su = limiting compressive strength for curing at temperature T

T = temperature of concrete or mortar

T

o = datum temperature below which no strength gain occurs in

hardened concrete

T

s = standard curing temperature

t = age of concrete or mortar

t e

= equivalent age at the standard curing temperature

= time of final set

viii
LIST OF SYMBOLS (Continued)

t = offset age, when strength development is assumed

to begin

t = time of initial set

s At = period of time

ix

1 . 0 INTRODUCTION

1.1 GENERAL

In the life of a typical reinforced concrete structure, the most critical

period is during construction. During this time, concrete is weak and, if

unanticipated construction loads are applied, catastrophic collapse may

occur. There exists, therefore, a need to provide, and encourage the use of,

methods for estimating the in-place strength of concrete, so that formwork

removal will be safe. The maturity method is one possible procedure for this

application and that is the subject of this report.

Concrete gains strength gradually as a result of chemical reactions (hydration)

between cement and water. For a specific concrete mixture, strength at any

age is related to the degree of hydration. The rate of hydration and, therefore,

strength development of a given concrete mix will be a function of the concrete

temperature during hydration. Thus, strength of concrete depends on its timetemperature history (assuming that sufficient moisture is always present for

hydration). Maturity is a term used to represent quantitatively the cumulative

effects of temperature and time up to any given age; it is computed from the

temperature-time history of the concrete.

It has been postulated that for a given mixture, concrete specimens tested

at equal maturities will have equal strengths, irrespective of their thermal

histories; that is, there exists a unique strength-maturity relation for each

concrete mixture. This hypothesis is referred to as the "maturity concept."

By monitoring the in-place temperature of newly-placed concrete, maturity at

any age can be computed and strength can be estimated.

To apply the maturity method, the strength-maturity relation for the concrete

mixture is developed in the laboratory and used to estimate strength for

various in-place maturity values. However, it has been shown [26]* that the

estimated strengths may be inaccurate if the in-place temperature history at

early ages was significantly different from that of the laboratory specimens

used to develop the calibration curve. The error may be on either the high

or low strength side, depending on the temperature history of field cured

concrete. Thus, the strength-maturity relation of a given concrete is not

unique, but is a function of the temperature history at early ages and,

perhaps, other factors.

In order to enhance the reliability of the maturity method as a tool for

in-place strength predictions of new concrete constructions, it is necessary

to gain a fundamental understanding of the quantitative effects of early age

temperature on the strength-maturity relation. This was the motivation for

the study reported herein.

The study sought to answer two questions:

1) What are the quantitative effects of curing temperature on the

compressive strength-maturity relation of concrete?

* Refers to numbered references at end of report.

1
2) Is there an age beyond which temperature no longer effects the

strength-maturity relation of concrete?

Phase I of this study addressed the first question and Phase II addressed the

second question.

The following section gives a brief history of the development of the maturity

concept

.

1.2 BACKGROUND OF THE MATURITY CONCEPT

Since complete reviews of the maturity concept have been written [1, 2] only a brief history dealing with the most significant developments will be presented.

The roots of the concept are found in a series of papers that deal with

accelerated curing methods for concrete. In 1949, McIntosh [3] reported on experiments to develop procedures for electric curing of concrete. In seeking

a procedure to predict the strength development characteristics for different

temperature-time histories during electric curing, he suggested that the product

of time and temperature above a datum temperature could be used to summarize the

effects of curing history. A datum temperature of -1.1 C (30 F) was suggested,

and the product of time and temperature above the datum was called the "basic

age." However, he found that when strength was plotted as a function of basic

age, there was not a unique relation as expected. McIntosh concluded that

strength development of concrete was governed by more complex factors than a simple product of temperature and time.

Several months after McIntosh’s paper had appeared. Nurse [4] described the

principles of low-pressure steam curing. He suggested that the product of time

and temperature could be used to summarize the effects of different steam curing

cycles. Nurse did not suggest using a datum temperature and his calculations

involved the curing chamber temperatures not the actual concrete temperatures.

Nevertheless, he showed that when the relative strength development was plotted

as a function of (time x temperature), the data for different concretes and

curing cycles fell reasonably close to a single non-linear curve. This was the

first evidence to show that the product of time and temperature could be used

to approximate the combined effects of these two factors on strength development

In 1951, Saul [5] summarized the conclusions drawn from research at the Cement

and Concrete Association in England on the principles o.f steam curing. This

presentation can be regarded as the basis of our current maturity concept. The

term "maturity" was for the first time linked to the product of time and tempera

ture. Saul recognized that once concrete has set it will continue to harden at

temperatures below 0 C, and he suggested that maturity should be reckoned with

respect to the lowest temperature at which hardening is observed. Thus,

maturity should be computed as follows:

M = I (T - T ) At

o

( 1 . 1 )

where M is the maturity, T is the average temperature of the concrete over

the time interval At and T is the datum temperature. Saul recommended a datum temperature of -10.5 C ('13°F). Equation (1.1) is the definition of

maturity currently used in the United States and is the definition used in

this report.

2
Saul stated that, under special conditions, samples of similar concrete will

have approximately equal strengths if they have equal maturities, independent

of the temperature-time history. The special conditions were that the concrete

should not be heated too rapidly during the start of the steam curing cycle.

Saul recognized an important phenomenon which helps to explain why the maturity

concept is intrinsically an approximation. During early ages, temperature has

a greater effect than time on strength development, while at later ages time

is more important. We now understand that this is because hydration is primarily

a thermally-activated reaction which at later ages becomes diffusion controlled

[32]. Thus, the assumption, implied by the maturity concept, that time and

temperature play equal roles in the strength development of concrete can not be

completely valid. Nevertheless, Saul demonstrated that as an approximation,

the maturity concept provided a simple method to account for the effects of

different temperature-time histories on the strength development of concrete.

Saul's maturity function (eq 1.1) can also be used to convert a temperaturetime history to an equivalent age at a standard temperature, as follows:

2CT-T )At

o

(T -T ) (1.2)

s o

where t is the equivalent age at the standard temperature T , and T is the

datum temperature. In application of eq (1.2) only those time intervals in

which the concrete temperature was greater than T^ would be considered.

In 1953, Bergstrom [6] demonstrated that the maturity concept was a useful

approach for accounting for the effects of different normal curing histories.

He analyzed previous data on temperature effects on strength development in

terms of maturity and found that, in most cases, there was little deviation

of the data from a common curve. To calculate maturity, Bergstrom assumed

that the temperatures of the concrete specimens were the same as the ambient

curing temperatures.

Plowman [7] presented a controversial paper on the maturity concept in 1956.

One objective of his work was experimental determination of the datum temperature to be used for calculating maturity. He found it to be -11.7°C (11°F)

Further, he made standard concrete cubes which were cured at temperatures

varying between -11.5 and 18 C after an initial 24 hour curing period at normal

curing temperature (16 to 19 C) . Cubes were tested at regular intervals and

the results were plotted as strength versus the logarithm of maturity. The

data was well grouped about a straight line, so Plowman proposed the following

strength-maturity relation:

S = a + b log M (1.3)

where S is compressive strength, M is maturity, and ^ and ^ are constants which

can be predicted from the water-cement ratio of the concrete and the type of

cement. There was much objection [8] to the proposed relation; the following

major points were raised and they indicate the limitations of Plowman's proposal:

3
1) The relation predicts infinite strength as maturity approaches infinity.

2) The linear relation is not valid at very early maturities, and only

intermediate maturity values result in an approximately linear

relationship between strength and log (maturity)

.

3) The datum temperature may not be constant with increasing maturity.

Thus, it appeared that Plowman's proposal was too simplistic and of limited

applicability. A deficiency in Plowman's procedure was that all specimens were initially cured at a standard temperature for 24 hours before being exposed to

different curing temperatures. Thus, the early age temperature histories of all

specimens were identical.

McIntosh [9] presented the results of a study in which specimens were exposed to

different early age temperatures. For equal maturities, it was shown that those

specimens exposed to low early age temperature were weaker at early maturities

and stronger at later maturities than specimens exposed to a higher early age

temperature. It was concluded that a strength-maturity relation that is based

solely on the product of time and temperature above a datum value can not account

for the "quality of cure" as affected by initial curing temperature. Klieger

[10] also reported that initial curing temperature influenced the shape of the

strength-maturity relation.

The great flurry of activity and' ifiterest in the maturity concept that occurred

in the early to mid 1950 's was followed by a period of inactivity in which only

a few research reports dealt with the topic. In 1962, Alexander and Taplin [11]

reported the results of a study to determine how well concrete and cement paste

obeyed the maturity concept when cured at different temperatures (5 , 21 and

42 C). In agreement with previous results, they found that the curing temperature had systematic effects on the strength-maturity relations of the pastes and

concretes. The nature of the effects are summarized in a schematic fashion in

figure 1.1. In 1968, Verbeck and Helmuth [12] presented a qualitative explanation

of why the "cross-over effect" in figure 1.1 occurs. An increase in initial

temperature will result in more than proportional increases in the initial rate

of hydration and the initial rate of strength development. However, with rapid

hydration, reaction products do not have time to become uniformly distributed

within the pores of the hardening paste, and a "shell" of low permeability

hydration products builds up around the cement grains. The shell impedes

hydration of the unreacted portion of the grains at later ages. Thus, what

appears as a strength reduction at higher maturities due to high temperature,

may be because of the inability of the cement grains to continue hydrating due

to the "shell" of low permeability reaction products.

In the late 1960's, a new interest in the maturity concept appeared. Swenson

[13] reported the first case in which the concept was used in an engineering

application. He used the maturity concept in a collapse investigation to

estimate what the concrete strength might have been at the time of collapse.

In the United States, Hudson and Steele [14, 15] proposed the use of the

maturity concept for predicting the 28-day strength of concrete based upon

tests at early ages. Their results have recently been incorporated in ASTM

C 918-80 Standard Test Method for Developing Early Age Compression Test Values

and Projecting Later Age Strengths.

4
EFFECT

OF

TEMPERATURE

ON

STRENGTH-MATURITV

RELATION

>

hH-

•

ZD

f—

<t

(/) h- UJ Z O HX

5

Figure

1.1

The

"crossover

effect"

due

to

dissimilar

curing

temperature.
An alternative to Plowman's logarithmic strength-maturity relation was presented by Chin [16] in 1971, who suggested that a hyperbolic function be

used as follows:

S

M

CM+A (1.4)

where A and C are constants defining the hyperbolic curve. Chin's equation

overcomes a major drawback of Plowman's relation. According to eq (1.4),

strength approaches a limiting value as maturity approaches infinity.

Examination of eq (1.4) reveals that the limiting strength has the value

1/C. The values of the constants A and C can be obtained from linear

regression analysis of the strength-maturity data; this is made possible

by transforming eq (1.4) into the following form:

^

= CM + A (1.5)

Thus C is the slope and A is the Intercept of the straight line obtained when

M/S is plotted versus M. The Inverse of the slope represents the limiting

strength and the inverse of the intercept represents the initial slope of the

hyperbolic strength-maturity curve. Clifton and Pommersheim [17] recommend

that it is more appropriate to use the following linear form of eq (1.4) to

determine the constants A and C

1

S

( 1 . 6 )

In this case the inverse of strength is plotted against the inverse of maturity

and the intercept of the straight line represents the inverse of the limiting

strength while the slope is the inverse of the initial slope of the hyperbolic

strength-maturity curve. The relationships between the hyperbolic curve and

the linear transformations are illustrated in figure 1.2.

Chin showed that his own data [18] was well represented by eq (1.5) with correlation coefficients varying from 0.939 to 0.999. In the study reported herein,

a modified version of the hyperbolic function represented by eq (1.4) was used

to analyze the data and further discussion of the function is presented in

chapters 3 and 5.

Weaver and Sadgrove [19] used the equivalent age concept in developing a manual for formwork striking times under various temperature conditions. They

suggested that the following expression for equivalent age gave better strength

predictions at early ages than the Saul function eq (1.2):

= 4t

e 1296

(1.7)

6
Figure 1.2 The hyperbolic strength-maturity function (a), and linear

transformations (b) and (c)

.

7
By using eq (1.7), the actual age of the concrete is transformed to an equivalent age of curing at 20°C. In another report [20] , Sadgrove reported

that for later maturities, the Saul function for equivalent age was more

precise than his recommendation.

In the mid 1970' s several reports appeared dealing with application of the

maturity concept under actual field conditions. Bickley [21] reported on using it during slipforming of the C.N. Tower in Canada, Mukherjee [22]

reported on its use for predicting the in-place strength of slabs, and Nisbett

and Maitland [23] used the concept for in-place strength predictions on a canal

bypass project in Ontario.

As a result of its investigations of construction failures, the Center for

Building Technology, National Bureau of Standards (NBS) has become involved in

the application of the maturity concept as a tool for in-place strength determin

ation of concrete at early ages. Research has been conducted to demonstrate

the applicability of the method and at the same time point out the important

deficiencies. Lew and Reichard [24] demonstrated the applicability of using

maturity to predict the development of other mechanical properties of concrete

besides its compressive strength. It was shown that the development of indirect

tensile strength, modulus of elasticity and pullout bond strength of steel bars

could also be related to maturity. These experiments were conducted using

nominal constant curing temperatures of 2 , 12 , and 23 C. The initial mix

temperature was constant for all specimens and specimens were moved into the

different temperature chambers soon after molding had been completed.

In a second study at NBS [25] , the influence of cement type and cement content

were investigated. Based on their test data and previous data published

elsewhere. Lew and Reichard recommended the following model for the strengthmaturity relation:

S = K

1 + Ka [log (M - 30)]^

( 1 . 8 )

where maturity is expressed in °F-days and 30°F-days represents the maturity

below which compressive strength is effectively zero. The constants K, a and b

were obtained from non-linear least squares regression analysis using the

program DATAPLOT developed at NBS. It was demonstrated that the values of the

constants were systematic functions of cement type and water-cement ratio, so that a user could determine an approximate strength-maturity relation for his

concrete mix by choosing the appropriate values of K, a and b from the published

figures

.

In a later study at NBS [26]

,

the applicability of the maturity method under

simulated field conditions was investigated. Three different concrete mixes

were used to fabricate plain concrete slabs containing push-out cylinder molds.

In addition, push-out cylinder molds were filled and stored in a moist curing

room. The slabs were coated with a membrane curing compound, covered with wet

burlap and stored outdoors (during the spring). The object was to determine

whether the strength-maturity relations for the field-cured push-out cylinders

were the same as those for the companion laboratory-cured cylinders.

8
The results of this study were perplexing: for batches 1 and 2, there was

good agreement between the strength-maturity relations of the field-cured and

lab-cured specimens, but for batch 3 there was considerable discrepancy.

Closer examination of the temperature histories of all specimens revealed

that for batch 3 the field-cured cylinders experienced much higher early age

temperatures than the lab-cured ones. On the other hand, for the other batches

the early age temperatures were not as dissimilar for field and lab-cured

specimens. Thus, an important deficiency of the maturity concept was confirmed:

when the initial temperature history of the field-cured concrete is significantly different from that present during the development of the laboratory

calibration curve, the reliability of the strength predictions becomes

questionable.

The aim of a still later study performed at NBS [27] was to determine during

which stage of the early age of concrete did temperature affect the subsequent

strength-maturity relation. Cylindrical specimens (76 x 152 mm high) were

molded at ambient temperature (mix temperature was 30 C) and then moved into

temperature chambers at 43°C and -1°C. At ages of 6, 18, 30 and 48 hours,

groups of the cylinders were moved out of these chambers and allowed to cure

in a 21°C environment until tested for compressive strength. In addition,

another series of specimens was kept continuously in the 21 C chamber. At

ages of 1, 3, 5, 7 and 28 days, strength tests were performed; and, from

recorded temperature data, the strength-maturity relations were constructed.

The results of this study were surprising. For the specimens initially stored

in the 43 C chamber, there were no significant differences among the strengthmaturity relations for the different storage times. Similar conclusions were

drawn, for the specimens stored at -1 C. In addition, there was no significant

difference between the maturity relation of the specimens stored continuously

at 21 C and those stored initially at 43 C. However, there was a difference

between the maturity relations of the 43 C and 21°C treatments compared with

the -1 C treatments; the difference being the "crossover" effect represented in

figure 1.1. From these results it was concluded the critical early age, when

temperature affects the shape of the subsequent strength-maturity relation,

occurred during the first six hours.

In summary, the maturity concept has demonstrated itself as being a useful

approximation to account for the combined effects of time and temperature on the strength development of properly cured concrete (that is, an adequate

supply of moisture is available for hydration). It has been demonstrated [26]

that the reliability of the method is reduced when the early age temperatures

of the in-place concrete are significantly different from those present in the

specimens used for the development of the calibration strength-maturity function.

In order to enhance confidence in using the maturity concept for in-place

strength prediction, a more fundamental and quantitative understanding is

required of the early age temperature effects.

9
2.0 PROCEDURE

2.1 SELECTION OF PROCEDURE

As previously discussed, there were two objectives in the present study:

1) To determine in quantitative terms the effects of temperature on the

strength-maturity relation of concrete.

2) To determine the age of concrete beyond which temperature no longer

affects the strength-maturity relation.

Since it is known that the strength development of concrete is primarily

affected by the strength development of the cement paste, it was decided to

conduct the experiments with mortar specimens rather than concrete. This

would greatly simplify the testing procedure, since 50 mm mortar cubes could

be used instead of the much larger standard cylindrical specimens of concrete.

Also, the cubes would not require special preparations prior to testing, that

is, no capping with sulfur is needed. In addition, the mortar cubes would

require less material to fabricate and less storage space would be required

during curing compared to standard concrete specimens. Since the main effects

of temperature would be on the cement hydration, these effects would manifest

themselves with mortar specimens as well as if concrete were used.

In addition to performing compression tests, it was decided to conduct early

age setting tests using the resistance to penetration method as described in

ASTM test method C 403 [28]. Such tests would furnish information on the

initial stages of strength development which could not be obtained from

compression testing.

The test program was divided into two phases: Phase I addressed the first

objective and Phase II addressed the second objective.

2.2 SPECIMEN PREPARATION

Mortar was produced with Type I portland cement, Ottawa sand (ASTM C 109)

and tap water. For Phase I, the following sand-cement-water mixtures were

used (S:C:W oven-dry weight basis):

1. High w/c (3:1:0.56)

2. Low w/c (2:1:0.43)

For Phase II, only the low water/cement ratio mix was used.

Mortar was mixed in an environmental chamber having 50 percent relative

humidity and at various temperatures as to be discussed. A bench top mortar

mixer was used and the mixing sequence was as follows

1) With a trowel, dry mix the preweighed quantities of sand and cement

in the bowl.

2) Add the preweighed quantity of water and mix for about 10 seconds with

a trowel.

3) Mix at low speed for 30 seconds.

10
4) Cover bowl and let stand for 1-1/2 minutes.

5) Final mix at low speed for 1 minute.

For Phase I, twenty-four (24) cubes having 50 mm (2 in) sides and one 50x50x305

mm (2x2x12 in) prism were molded per batch. For Phase II, 18 cubes and two

prisms were molded per batch. Steel molds were lightly coated with oil, and

grease was used as a water seal between the side molds and the removable

bottom plates. The molds were filled in two layers, tamping each layer with

a rubber tamper. After striking off the mortar, the molds were carefully

submerged in lime-saturated water baths within the environmental chamber.

Immersion was used, rather than covering the top surface of the molded specimens,

to ensure no evaporation occurred after molding. Evaporation would affect

the early setting characteristics.

Due to the large number of specimens and the limited table space in the

chamber, the specimens for Phase I were prepared in the following sequence:

1) Fill prism and two cube molds (three cubes per mold) and submerge.

2) Fill three cube molds and submerge.

3) Fill three cube molds and submerge.

For Phase II the sequence was as follows:

1) Fill the two prism molds and submerge.

2) Fill two cube molds and submerge.

3) Fill two additional cube molds and submerge.

4) Fill the remaining two cube molds and submerge.

The entire operation, from the addition of the water to placement of the last

mold under water took from 30 to 45 minutes to complete. Age was reckoned

from the time water and cement came into contact.

The molds were stripped from the cubes at maturities (as defined by eq 1.1 but

using a datum temperature of -11.7 C (11 F)) varying between 12 and 17 C-days

and were returned to the water baths.

2.3 TEMPERATURE HISTORIES

For the Phase I study, mortar cubes were prepared and maintained within ±1°C

of the following temperatures: 5 , 12°, 23 , 32° and 43°C. All ingredients

and molds were stored in the environmental chamber overnight to bring these to

uniform temperature, and all specimens were prepared in the chamber. After

demolding, the pans which comprised the water baths were stored in refrigerators and ovens to maintain the desired temperatures. The 23 C bath was located

in an air-conditioned room. Ice or warm water was added to the water baths as required to maintain the desired temperatures during the critical early ages.

Temperature histories were recorded for the prism specimen and two cube

specimens per batch. It was felt that storing the specimens under water would

minimize temperature variations among specimens, and so two instrumented cubes

were felt to be sufficient for each batch. Copper-cons tantan thermocouples were

11
embedded at the approximate center of the specimens. For each batch, a thermocouple was embedded in a cube from the first and final series in the

molding sequence.

The Phase I specimens were designated as follows;

I-XX-H

I-XX-L

where XX indicates the curing temperature in degrees Celsius and the letters

H and L denote the high and low water-cement ratio mixes, respectively.

For the Phase II study, prism and cube specimens were prepared and initially

stored at 5°C and 32°C; then at three different stages in the setting process,

they were moved to 23°C water baths located in an air-conditioned room. A

separate batch of mortar was made for each treatment process since the mixer

capacity was insufficient to produce at one time the required mortar for all

the specimens.

The Phase II specimens were designated as follows:

II-5-X

II-32-X

where X is a letter (F, I or H) which was used to identify when the molds were moved from the environmental chamber to the 23 C water baths. The letter F

indicates that the transfer occurred after final set had occured, I indicates

the transfer occurred at initial set, and H signifies that the transfer was made at a time equal to one-half the time needed to reach initial set. These

stages in the setting process are explained in the next section. It took from

30 minutes to 1 hour to bring the temperature of the specimens from 5 or 32°C to 23°C.

2.4 PENETRATION RESISTANCE TESTS

The transformation of concrete from its initial fluid state to a hardened con- dition is a gradual process and is referred to as setting. Since the transition

is gradual there are no well-defined boundaries between hardened and unhardened

concrete. In order to compare the setting characteristics of different concrete

mixtures, arbitrary stages of setting have been adopted. The most widely used

approach for quantifying the degree of setting is by resistance to penetration

of a round flat-faced rod. Resistance to penetration is measured by a springloaded device, and the test must be performed on mortar, wet-sieved from the

concrete so that interference with coarse aggregate particles is avoided. By

convention, the term "initial set" is used to Indicate the degree of setting

corresponding to 3.5 MPa (500 psi) penetration resistance; this is roughly the

stage beyond which vibration can not be used to further consolidate concrete.

The term final set corresponds to a penetration resistance of 27.6 MPa

(4000 psi) and is roughly equivalent to a compressive strength of about 0.7 MPa

(100 psi) [29].

12
In Phase I, a small pocket penetrometer was used which was only capable of

recording a maximum resistance of 4.8 MPa. Penetration resistances were

recorded at five times during the initial ages; the first reading was taken at

a resistance of roughly 1 MPa and the remaining tests were performed at regular

intervals so that the final reading was more than 3.5 MPa. Each test consisted

of two insertions of the penetrometer into the prism specimen. The distance

between centers of insertion was roughly 25 mm. The prisms were removed from

the water baths for penetration testing and returned to the baths after testing.

In Phase II, a penetration device meeting the requirements of ASTM C 403 was

used so that the setting process could be followed up to final set. In this case two prisms were used so that 10 tests could be performed at regular time

intervals; each test consisted of one insertion in each of the two prisms. The

locations for the tests were chosen in a random fashion using a random number

table so that any non-uniformity would not bias the results. A center-tocenter distance of 25 mm was maintained between adjacent penetration test

insertions

.

It must be mentioned that the prisms did not strictly comply with the standard

procedure of ASTM C 403, which requires a minimum mortar depth of 140 mm. However, the prisms were used because less mortar was required than the standard specimen, and there would be less problem with temperature rise due to

heat of hydration. Use of 50 mm deep mortar specimens would probably result

in slightly greater values of penetration resistance than the deeper specimen

due to interference from the bottom of the mold. However, it is unlikely that

this difference would obscure the temperature effects that were being studied.

2.5 COMPRESSION TESTS

Compression tests were performed using a universal hydraulic testing machine

of 267 kN (60 kip) capacity. The cubes were loaded at a convenient rate up

to one-half the expected ultimate load and thereafter loaded at 3.2 kN/minute

(7.2 kip/minute) until ultimate load was reached.

For Phase I, three cubes were tested at each of seven maturity levels, chosen

so that the shape of the strength-maturity curve could be well-defined.

Prior to testing, the cubes were weighed to the nearest 0.001 kg after blotting

with a rag to remove surface water. The weights of the cubes were used as a rough indicator of the homogeneity of the mortar from batch to batch. In

Phase II, three cubes were tested at five maturity levels per batch.

Anticipating that there would be differences between the cubes molded at the

beginning and those molded at the end of the casting sequence, because of

evaporation and sand absorption of the water, the cubes were tested in random

order. The cubes were numbered in sequence as they were cast, and the sequence

for compression testing was based upon selections from a random number table.

As will be seen, this procedure was not entirely successful, and it was modified for Phase II so that one cube was selected from each of the three

stages of the casting sequence for each compression test.

13
3.0 RESULTS

3.1 MATURITY AT TIME OF SETTING

As discussed in section 2.4, the setting behavior for the various temperature

treatments was monitored by measuring penetration resistance of the mortar

prisms. For each penetration test, the age was recorded and the corresponding

maturities were computed according to eq (1.1) from the temperature records

using -11.7°C (11°F) as the datum temperature.

The normal practice for determining the time required to reach initial and

final set is by plotting the test results and drawing a best fit smooth

curve; the curve is then used to interpolate (or extrapolate) the setting time.

In this study, a non-linear, least-squares fit analysis was used to determine

the best line for interpolation and extrapolation. The principal objective

was to determine whether setting times had any correlation with maturity.

Phase I Results:

The complete data showing age, penetration resistance values, and computed

maturities are presented in Appendix A. The usual practice has been to plot

penetration resistance on a log scale versus time, and use a best-fit straight

line for determining the times of initial and final set. In this study,

penetration resistances were plotted against maturity and several equations

were used in the least squares fit analysis to determine which had the best

fit, as measured by the estimated residual standard deviation and the

significance level of the lack-of-fit F-test. The following equations were

studied:

R = ab

M

(power function) (3.1)

log (R) = c + dM (logarithmic function) (3.2)

R a + a^M + a^M (parabolic function) (3.3)

where R represents penetration resistance, M is maturity and the other symbols

represent regression coefficients. It is emphasized that these equations were

not chosen for physical significance, but to give a smooth curve with the best

precision for interpolating the values of maturity at initial set. Regression

analysis was performed with DATAPLOT [31], an interactive non-linear least

squares fit program with plotting capabilities. Overall, it was found that the

parabolic model gave the best fit of the data.

Table 1 summarizes the results of the Phase I data analysis. The column

labelled a represents the significance level of the lack-of-fit F-test;

values of less than 5 percent are usually Indicators that the chosen model

is not the best to use. However, low values of may also result when there are outliers in the data which have small values of replication standard

deviation. So, plots of the data should be used to evaluate whether the

lack of fit is real or due to outliers.

Figures 3.1 and 3.2 present the penetration resistance versus maturity data

along with the best fit parabolas. Inch-pound units are shown since data were

recorded in these units.

14
TABLE

1.

PENETRATION

RESISTANCE

DATA

ANALYSIS,

PHASE I

tH CO <T> vO CO iH in in CM CO 1—1 CO in <!• rN. tH in

00 00 00 \0 »x> vO vO vO

m

CO

CO lO <r I—

CO CM CT\

c4 00 c^ ID CO 00 lO iH

m o cn 1 MT <r <! CO rH fH CM iH iH c^

li iH fH 1—

iH fH iH iH tH o

4Jc m CM iH

m

m o CO o^

Pk 0) • 3 O lO ID CO in iH o CJ^ CJN

m CM

P4 CM CJ> cy> <r fH cr> iH CM

(UCU

CO

Pd

COCU CM ro o

CM <N <r vo o m CM

m

cn fO CM CM cn CM COCM

O /-N CO *H

pL< CO M a

Pd

O CO

CM CM COCM <t 00 CM rH 00

cn tH CM CM CO

O

CM

O

CM

CO

(1) HI1 w Cd cd Ed

•rl 1 1 1 P4 CM CO CM CO

<U

m fH CM CO

CO 1 M 1 M 1 H 1 H 1 M

hd1 hJ1 hJ1 hJ 1 CM CO CM CO (U m T—

CM CO 4J 1 1 1 1 1 o M M H H M !S

CJ o

CO

(U

4-1I co

4-1 •r( IW

M-4O

•H

O

4-1 cd (4

CO

O iH

•H •!-(

CU nj tJ *h>

T3 (U

O 4-1 0)

<U CO

CJ

>-i TO Cl iH

c4 T3 T) C V4

cO c4 O -H H 4J

c4 c4 iH t4 U TO *H c

CO c C2 *H

C4 60 do c 4-1 •H 4J o CO CO cd 4-1 4J •H U4 >-< 4-1 rH l4-( (U CU

CS CCJ

O 4J > > a d •H c Cl •H •T3 rH U o o I—

•H (U :3 o o

CU CO > 4J

01 (U 0) rt o o u U4 1—

S H H

II II II

Q CO

CO Pi (U§

CO

15

isi

to

MPa

divide

by

145

psi/MPa

F-day

to

°C-day

divide

by

1.8 ^
PENETRATION

RESISTANCE

OS.

MATURITY,

HIGH

U/C

16

MATURITY

(°F-DAYS)
PENETRATION

RESISTANCE

OS.

MATURITY,

LOU

U/C

o

OJ

in

ro

LJ)

LO

nj

in

#

in

o

o

(U0) ca SH

lu

cdp

4Jo

c

<u

(In

CNfO

(U

)-l D

&0

•H

fti 9

00

o

CD

<S

'T

O

OJ

Q.UJ liJ U) »-• U) I OUJ

17

MATURITY

(°F-DAYS)
Phase II Results:

Data for the Phase II penetration tests are also presented in Appendix A.

Table 2 presents the results of the regression analysis and the computed

maturities at initial and final set. Figures 3.3 and 3.4 are plots of the

penetration resistance versus maturity data and the best fit parabolic

curves

.

3.2 COMPRESSIVE STRENGTH

3.2.1 Equation for Strength-Maturity Relation

An objective of the study was to determine, in a quantitative manner, the

effects of temperature on the strength-maturity relation of the mortar

specimens. If the strength-maturity relation could be represented by an

equation, determining the effects of temperature on the parameters of the

equation would meet the objective. The probable true shape of the strengthmaturity relation of a given concrete at a given temperature is as shown in

figure 3.5. There are four regions: 1) the plastic state during which

concrete is fluid and incapable of supporting a static load in an unconfined

condition; 2) the setting stage during which concrete transforms from the

plastic to rigid state; 3) a stage of rapid strength gain; and 4) the stage

during which the rate of strength development decreases and strength slowly

approaches a limiting value. The exact shape of the initial portion of the

curve is not well known because of the difficulty in testing concrete at such

early maturities; and from an engineering point of view, it is not important

because of the low strength of the concrete. In this study, the actual

strength-maturity curve was approximated by a hyperbola having the following

formula (see figure 3.5):

(M-M ) o

1 CM-M^) C3.4) o_

B Su

This equation is a modification of that proposed by Chin Ll6j , with a refinement to account for the fact that a finite value of maturity is required before

rapid strength development begins to occur. As written in eq (3.4), the

parameter B is the initial slope of the curve at M , and Su is the limiting

strength as maturity approaches infinity. The parameters B, Su and M were determined by non-linear regression analysis using DATAPLOT. °

In Phase I, the adequacy of eq (3.4) in representing the various strengthmaturity relations was studied. Chapter 5 discusses the basis of the hyperbolic

curve.

18
TABLE

2.

PENETRATION

RESISTANCE

DATA

ANALYSIS,

PHASE

II

CO>> cn v£) \o

cd <T\ o r>. vO SO

73 • • • • • 1 CN C3^ o o0

fH iH iH iH

CO c» CO <y> cy> ON 00

cd 00 CO C3> CO rH • • • • • • 1 so in CM ON rH

f*4 CM Csj CM tH tH Csi

CO

cd T3I CJ o

CO>s

m o CM o Cd o CO CO CM • * • • • 1 VO CNJ CM pH rH rH rH rH rH

CO CTs 00 <!• 00 ON o 00 o^ 00 • • • • • • 00 00 so so r>.

CMO

CO

<u

4-1I [L

M-l

»4-l O 4-> CJ CJ 00 CO 00 O mT o

<u • • • • • • •H CJ

CJ CO so

O CO rH UJ c cd 8 P4 <1- CM so cd o rH

(U •H •H CU > 4-) IW

s-> 0) cd

O 4J XI •iH 0) > CU CO 4J Td (U o 0) V4 X 13 rH CO

cd cd Cd /~s X) X o *lH rH

CO •H iH 00 SO CM so c P4 •H 4J Cd Pi CO <! 00 in so CM cd cd *4-1 •H C

CU rH rH 1—I I—1

rH 4-)

X •iH

C *H

s_x CO C! 8 •H <4H

cd So c 4-1 •iH

U 4J . o CO CO Cd Cd r 'iH 4J rH 14-4

O ' V Cd Cd

O 4J 4-1 CO •H O CO '3- Cs| vO o 3 •iH *H

Pu CO COC3N o C3N *iH

X rH U4 P4 CU rH I—i

rH •H (U 3 3

s.-/ CU CO > 4-> 4-1 CU (U (U Cd Cd

U4 S-i iH e 6

II II II II II

pH

M

w CO pH M w1 1 1 1 CU 1 1 CM CM CM

•H in

m

m CO CO CO ..

P4 1 1 1 1 1 1 (U

0)

M

MMMMM 4J CO M M M H H H oz P w

Crt pi §

pi:^ CO CO

U

oo4J 4J M U

(U CU > > o o H H

19

isi

to

MPa

divide

by

145

psi/MPa

F-day

to

°C-day

divide

by

1.8

°F/
PENETRATION

RESISTANCE

US.

MATURITY

(PHASE

II,

5*^0

20

MATURITY

(oP-DAYS)
PENETRATION

RESISTANCE

US*

MATURITY

(PHASE

II,

32°C) o

n

if) nj

0

01

if)

Q.UIZ: Q: UJ V) i-i O) I- <C Z O UJ

21

QJd

4-* (d

i-i 0)a

to •H

4J

o

CN

fO

(U

CO 5

Pu

C

o

•H

(0 4J

0)c

0)

(Uu

3

00

'H

(X4

I

MATURITY

(op-DAYS)
PROBABLE

AND

ASSUMED

STRENGTH-MATURITY

RELATIONS

a:

Z)

0)l-Q^UJZOI22

Figure

3.5

Shapes

of

the

probable

and

assumed

strength-maturity

relation.
3.2.2

Phase I Results

The complete data of the Phase I compressive strength tests are presented in

Appendix B. The results of the least squares fit analysis are given in table

3. Except for the 12°C low water-cement ratio mix, the lack-of-fit F-test

level of significance is greater than 5 percent, indicating the appropriateness

of the hyperbolic model to represent the data. However, the replication and

residual standard deviations appear to indicate a lack of batch-to-batch

uniformity. This is probably due to the method of selecting the sequence

for testing the mortar cubes. As previously mentioned, a random selection was

used, but it now appears that the cubes should have been selected so that the

tests at each maturity included a cube from the beginning, middle and end of

the batch. The strength results showed that the cubes from the end of the

batch were consistently stronger than those from the beginning. More discussion

of this problem will be presented in a following section.

Figures 3.6 and 3.7 show average compressive strength data as a function of

maturity. Also shown are the hyperbolic curves based on the least-squares

fit analysis.

3.2.3 Phase II Results

The data for the Phase II tests are given in Appendix B, and table 4 summarizes

the values of the parameters from the least-squares fit analysis.

In Phase II, the cubes were selected so that tests at each maturity included a cube randomly selected from the beginning, middle and end of each batch. This

procedure resulted in high values of replication standard deviation, but the

lack-of-fit F-tests indicate that the hyperbolic model is a good representation

of the data.

Figures 3.8 and 3.9 show the average strengths at each maturity and the best

fit curves for the appropriate Phase I data for comparison. In figure 3.8, the

solid curve is for constant curing at 5 C, and the dashed line is for constant

curing at 23 C. In figure 3.9, the solid and dashed curves are for constant

curing at 23 and 32 C, respectively.

3.3 UNIFORMITY OF BATCHES

Since an objective of Phase I was to determine temperature effects on the

strength-maturity relations of two mortar mixes, it was important that the

batches of mortar have the same water content for the various thermal treatments. It was anticipated that the evaporation rate would vary as the mixing

temperature varied from 5 to 43 C. In order to have a general indicator of

batch-to-batch uniformity, the weights of the mortar cubes were recorded

prior to compression testing. If a particular batch had excessive evaporation

during the casting phase, the water-cement ratio of that batch would decrease

and result in an increase in the weight of the cubes.

Figure 3.10 shows the average weight of the mortar cubes and the 95 percent

confidence intervals for the two mortar mixes as a function of the nominal

mixing temperature (Phase I). The results show that there were no significant

differences among the weights of the 5°, 12°, 23° and 32°C mixes, but the 43°C

23
TABLE

3.

RESULTS

OF

STRENGTH-MATURITY

DATA

ANALYSIS,

PHASE I 3 C

0)o

0)a

(Hi

m

Q

CO •H

PLI CO3. § .5 3

CO COcu 3

C/l

•H

COPU

c/3

COa

M

>>

cO '3I O

COcu

CO

0) *H

(U

c/1

r—i o 00 ON o CO CO

m • • CO o o C3N o CM CO m

tH in CO r>. 00

m NO

N

<Ti NO iH 00 o CM 00 CM o

CN CM CM o CJN CM ON 00 00

m

iH CO CO rH <r CO pH pH CO

VO o 00 in CM o CM o pH O ON CO ON o m o ON CJN c^

CM CO iH <1- CO pH pH CM

CO iH iHm 00 CJN <r pH

O • • <r CO ON CM rH NO m CM CM CO

iH

CM rH o CO CJN pH CJN CO CM CM CM tH CO CM CM pH pH

<f CM CM

m C'* CJN o NO 00 00 CN 00 m iH NO pH CJN NO

CM iH CO CM ?H pH

mm o o o o m o o in

iH CM tH 00 in rH o in CO m 00 iH pH ON 00 <1* CO CJN CO CO <r <r o CJN CJN 00 r>. rH

CM 00 CM rH CM pH . pH pH o CO pH CM CO CM CO 00

00

m o CM NO

m CJN pH CO I—1

CM CO CO NO 00

Ed

W CD1 w hj hj 1-J tu 1 hJ 1 1 1 1 CM CO CM CO 1 CM CO CM CO m i-H CM CO in pH CM CO M 1 M M 1 M M M M H H H

Oo (1) •uo

25

rC

4J

CU 3

3- 3 o 4J iH 3

CO 60 3

I—1 3 O 3 •H •H

•rl 4-1 •U 3 M •H 3 O 6 •rl "H 3 •H 0> 4-1 •H 1—1 S 3 3

•3 *H

M-l H-4 14-1 > O o o -3 3

V4 -3 3 3 3 3 O O O 3 tJ

•H •H •H 3 U

4-1 4J 4J 3 3 3 3 3 4J -3

•H •H •H

m 3 > > > 3 3 3 3 3 U

T3 T3 o m

•H t3 TJ T3 +J rH 3 3 3 3 3 3 3 3 O 3

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II II II II II PQ 3 ^ C/3

C/3 CO a/)

C/3 C/3 Pli W

Pi

30

•U 4J 3 J-l 0) 0) > > 3 3 O O O U O O H H f}iI

24

isi

to

MPa

divide

by

145

psi/MPa

F-day

to

°C-day

divide

by

1.8

°F/
COHPRESSIUE

STRENGTH

VS.

MATURITY,

HIGH

U/C

25

Figure

3.6

Compressive

strength

versus

maturity

including

best-fit

hyperbolic

curves

(Phase

I,

high

w/c).
COHPRESSIUE

STRENGTH

US.

MATURITY,

LOU

U/C

26

Figure

3.7

Compressive

strength

versus

maturity

including

best-fit

hyperbolic

curves

(Phase

I,

low

w/c).
TABLE

4.

RESULTS

OF

STRENGTH-MATURITY

DATA

ANALYSIS,

PHASE

II o

cn

cn

C/3

CO

C

0)o

0)a.

•H CM 00 I—o> o

CO CO vO <j\ 00 00

Oh '3' mT

m CM I—

CM

(0cu

to

nJ o vo 00 <r cr> cn

T3 • • • • • • 1 Pn 00 vO 00 CM

nJ 3

CO

PQ

00

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'3- r0000

CO <r

v£> sf

CO

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CM ov

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CMCOvO

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(0 <r cn cn C3V CM 00 & cn cn mT rH iH rH

X!

4-) 003

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m sf |o CM |o 0- P4

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C PI

CO 4-1

V 4J 3 3 a 3 3 3 W '3

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to •H

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td

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Pi 1 1 1 1 1 1 +J 3 H M M M M M O

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HM

M

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II II II II II pq 3 CO CO CO So pc; CO CO P-i W

Pi

27
STRENGTH

VS.

MATURITY

(PHASE

II,

S°C)

I

I- QOiJ Z O IX

28

Figure

3.8

Compressive

strength

versus

maturity

(Phase

II,

5®C

initial

temp.)

compared

with

best-fit

hyperbolic

curves

from

Phase

I.
STRENGTH

US

MATURITY

(PHASE

II,

320C)

O) I- liJ Z O i~ X

29

Figure

3.9

Compressive

strength

versus

maturity

(Phase

II,

32

°C

initial

compared

with

best-fit

hyperbolic

curves

from

Phase

I.
AVERAGE

WEIGHT

OF

CUBES

FOR

EACH

BATCH o

\

o

ca>

in

Q

UJ

a

<t

in

Ui

o

oc

UJ

UIo

Z

UJ « Q ^ IX oc

U. UJ Z K- O zIX X

U)

OJ

1—I

I—

r

ooo

T—I—I—I——I—I—I—

r

ODO

T—I—I—

r

o

i/)

o

'T

<S> cn

cu

<u

(0CO X

Pu

cO>M

(U

4-t c

0)u

3

bC

LO U) o U)

C7) Oi 00 00 r^

(\J 03 03 03 03

i1

1

> Lu a: <r o Lu 3U>-»OXI- C3QC<r SEICO

30

NOMINAL

MIXING

TEMPERATURE

(DEGREES

C)
cubes were slightly heavier. This discrepancy may be due to the inability of

the chamber to maintain a 50 percent relative humidity at this high temperature.

Therefore, it may be concluded that the mortars cured at 43°C were of slightly

lower water-cement ratios than the other batches.

Figures 3.11 and 3.12 show the average cube weights and 95 percent confidence

intervals for the 5° and 32°C initial treatments of Phase II, respectively.

Figure 3.11 also shows the 95 percent confidence interval for the average

weight of series I-5-L. It can be concluded that there were no significant

differences among the weights of the cubes prepared at 5 C in Phases I and II.

Figure 3.12 shows the confidence interval for series I-32-L. It appears that

the Phase II specimens prepared at 32 C were slightly heavier than the

companion Phase I specimens. Heavier weights would probably be associated

with a lower water-cement ratio. No explanations for these differences

could be found.

Another anticipated problem was the degree of within-batch uniformity due

to absorption of water by the sand and evaporation. It was believed that the

specimens from the end of the batch might be different from those at the

beginning. Figures 3.13 through 3.17 show the weights of each cube that was tested in Phase I. The cubes were numbered consecutively in the order they

were cast; cubes numbered 1 through 24 were from the high water-cement ratio

mix and numbers 25 through 48 were from the low ratio mix. For most cases,

the distributions of weights indicate a rise in weight with increasing cube

number. Thus, it appears that for each mix the cubes from the end of the

batch would be of slightly lower water-cement ratio. This difference is

clearly manifested in Appendix B where the weights and strengths of the cubes are tabulated.

31
AVERAGE

CUBE

WEIGHT,

5^

SERIES

d-o-o

I lA

I

oeo

Z>

Qi. Ul

I-z

D-D-d

UJQ

O

X

lA

(A

1—I—I—

1—I—I—

I r T—I—I—

U) «s> LA O


 O) o> 00 00

n OJ OJ CU OJ

3UJH-IOXI- OCZ<EC(A

32

SERIES

Figure

3.11

Average

weight

of

cubes

and

95

percent

confidence

intervals

(Phase

II,

5®C

initial

temperature).
AVERAGE

CUBE

WEIGHT,

32°

SERIES OOD

I OJ

cn

I

QCO

Ll

:>UJ

I-z

— —

UJo

UJA

h-t u.z

o

o

iA

O)

T—I—

1—I—1—t—I—

1—I—I—

o in o U) o o Oi o> 00 00 n cu (U cu cu

3LJHHOXI- V)

33

SERIES

FlpLure

3,12

Average

weight

of

cubes

and

95

percent

confidence

intervals

(Phase

II,

32

*C

initial

temperature).
WEIGHT

OF

CUBES

FOR

5

DEGREES

C

LD

I3UJHHOXI- ock:<ee:u)

34

Figure

3.13

Individual

cube

weights

(Phase

I,

5®C)

,
UEIGHT

OF

CUBES

FOR

12

DEGREES

C

I/)

I

I

•#

•

•

•

A

u/c u/c

#

i •

•

•

•

•

O 3 1-4 o

X -J o •

wi > #

• O

O

O

0

o

< o

o

o

o

<

o

o

o

o

' ' o

o

o

o

> o

(S O) 00 r- n OJ OJ cu

3UJ»-iOXI- ocx<Ez:(A

o

n

cu

o

QL

UJ

e:3

UJ

3

O

35

i

Figure

3.1A

Individual

cube

weights

(Phase

I,

12®C)

.
UEIGHT

OF

CUBES

FOR

83

DEGREES

C

#

#

i •

u/c U/C

•#

#

#

•

#

XO 3

o

X -1

o •

w

#

• •

#

< O

O

O

>

o

o

o

o

0

o

<

J

> o

<

o

0

0

>

o

o

0

1—I—I—I——I—I—I—I——I—I—I—

9

o o> 00 r- n O] OJ (U

3UJHHOXI- oq^<xe:o)

o

in

'T

n

OJ

UJ

(X» e:

UJ

CQ

Z)

o

36

Figure

3.15

Individual

cube

weights

(Phase

I,

23*C)
WEIGHT

OF

CUBES

FOR

33

DEGREES

C

L/>

o O 9

Oi 00 m OJ (U (U

3UJHHOXI- <30^<LEHf»

UJ

ca

LU

13O

37

Figure

3.16

Individual

cube

weights

(Phase

I,

32“C).
UEIGHT

OF

CUBES

FOR

A3

DEGREES

C

o

LD

3LUi^OXt- OQ^ <ES:U)

Figure

3.17

Individual

cube

weights

(Phase

I,

43°C).
4.0 ANALYSIS AND DISCUSSION OF RESULTS

4.1 SETTING BEHAVIOR

Phase I ;

As previously mentioned, the purpose in studying the setting behavior of the

mortars was to determine whether initial and final set were correlated with

maturity. In Phase I, the initial setting times were interpolated from

semilogarithmic plots of penetration resistance versus time from initial

mixing. The computed setting times are plotted in figure 4.1 as a function

of the cumulative average temperature at initial set. It is observed that

there is a consistent relation between time and temperature. As the

cumulative average temperature increases, the age at initial set decreases.

If initial set were to occur at a constant maturity, the following relationship should exist between setting time and temperature:

M

t = ^ s CT - T^)

where t

f

T

= time at initial set

= maturity at initial set

= temperature

= datum temperature

(4.1)

Figure 4.1 shows the best fit curves obtained by fitting eq (4.1) to the data;

M and T were found from the least squares fit. The values of M were

s o o o s 7.4 and o.2 C-days (13.3 and 11.1 F-days) for the high and low water-cement

ratio mixes, respectively; while the values of T were -9.8 and -10.6 C

(14.3 and 12.8 F) , respectively. Thus, the analysis indicates that the

assumption that initial set will occur at a constant maturity is a good one;

also the best fit values of T are not very different from the value suggested

for computing maturity of hardened concrete, that is, -11.7°C (11°F)

.

Figure 4.2 shows the maturities at initial set, computed from the best fit

curves discussed in section 3.1, as a function of cumulative average temperature

at initial set. There is some tendency for a decrease in maturity at initial

set as temperature increases, but the decrease is not very significant over

the wide range of temperatures studied.

The assumption that initial set occurs at a constant value of maturity can be

significant information in designing the placement rates of concrete in

vertical formwork for different temperature conditions.

Phase II :

In Phase II, penetration tests were carried out to determine both initial and

final setting times. The results were given in table 2, and figure 4.3 shows

the maturities at initial and final set versus the cumulative average

temperature at that degree of setting. It should be noted that in Phase II

39
AGE

AT

INITIAL

SET

US.

TEMPERATURE

40

TEMPERATURE
MATURITY

AT

INITIAL

SET

US*

TEMPERATURE

41

TEMPERATURE

Figure

4.2

Maturity

at

initial

set

versus

cumulative

average

temperature

(Phase

I).
flATURITV

AT

SETTING

US.

AUERAGE

TEMPERATURE

42

AUERAGE

TEMPERATURE
the temperature histories of the specimens were all different. It is seen that

despite differences in thermal treatment, the maturities at initial set were

reasonably constant; thus confirming the results of Phase I. However, the

magnitudes of the maturities at initial set were slightly greater than those

obtained in Phase I for the low water-cement ratio mix, no reason for this

discrepancy can be suggested, other than the inherent scatter associated with

this type of testing.

The maturities at final set, on the other hand, do show a significant variation

with cumulative average temperature. The variation is consistent: an increase

in temperature reduces the maturity at final set.

The results of the setting tests offer some insight into the behavior of

cement during early ages of hydration. As mentioned in discussing figure 3.5,

the real strength-maturity curve has an S shape. At low maturities, there is

little activity until the acceleratory phase when setting occurs is reached,

and the concrete transforms into the hardened state. Since maturity at

initial set was practically independent of temperature, it appears that

during the early period the reaction rate increases proportionally with

temperature. However, when the acceleratory stage begins, the reaction rate

no longer appears to be a linear function of temperature. An increase in

temperature produces more than a proportional increase in reaction rate, and

the maturity at final set decreases with temperature.

The fact that final set does not occur at constant maturity is early evidence

that the strength-maturity function of a given concrete will depend on temperature

.

4.2 TEMPERATURE EFFECTS ON STRENGTH-MATURITY RELATIONS

It was assumed in section 3.2.1 that the strength-maturity function of a given concrete should be represented by the hyperbolic function:

(M - M ) o

, (M - M ) (3.4)

o B Su

The offset maturity, M , is adopted as a simplification of the actual early age

setting and hardening Behavior (refer to figure 3.5). The parameters B, Su and

M are all functions of temperature; a goal of this investigation was to determine

i? the parameters varied in a systematic fashion with temperature, so that

appropriate relations could be suggested for applying temperature corrections to

the strength-maturity function. Table 5 lists the best-fit values of these

parameters and the corresponding cumulative average temperatures of specimens

at the time when the first compression tests were performed.

The first parameter to investigate is parameter B, the slope of the curve at

M = M . Figure 4.4 shows the values of B obtained in Phase I as a function of

the cumulative average temperature. The points follow a consistent pattern.

As expected, the values of B are a function of temperature and water-c ment

ratio. It was felt that a more meaningful approach would be to separate these

two effects. Thus, the strength-maturity function was rewritten as follows:

43
TABLE

5.

SUMMARY

OF

PARAMETERS

(PHASE

I)

Ui

73 CO <T» CM tH CO vO CNJ CO 1 CM CO vD o CO <1* m o pE4 O O O o tH o o o o O O O O o o o o o o o

f—

CD CD

O CD o o o (D CD o m o o o o m o o LO

•H iH CM iH 00 in rH o 3 CO CO m 00 1-H rH C3^ 00 CO CJN w cu >d- CO o CTi ON 00 r-~

cO

CAOf

B * Oo H

O

fn

CMCO CM CM oCM

CO

CO

(T> CM CM

(Ti

CX3 to

CM

OCO

CM vO

CO

m o\

>X5 CO00

CO

W PC 33 33 i-J iJ i-J i-I cu W 1 1 1 hJ 1 1 1 1 • • •H 1 CM CO CM CO 1 CM CO CM CO CU M to 1—

CM CO <r to rH CM CO <r 4-) CU 1 1 1 1 1 1 1 1 1 1 O

c/3M

MMMM

M

HMMM z o

CO 00

•H

cn ^

Cl, OJ m no

"H>

/-s /-N •H cu CO vD CM rH o\ lO 00 CO CM o to 73 U 33 33 3 O m CM CO CM CM m CM CO CM CO CO •u rt rH CM CO rH CM CO CU cd cu 'w' Vw^ 73 c3 >-i •H T3 > I •H C_) TOO

cOO

cnto

(-1 }-l 0) cu > >

C!C o o o o o o H H

0) >-i CL, O E M-l (U •U 73

CD

Q) E

00 Cl

CCJ o

Cl lh lO 00 00 CO 1—

o <3> C3^ 4J cd CU u • • 73 > cu

c—im C3> cr. CM

m CO C33 C33 •H 1 cd CL,

m 00

O

m r-. 00

O CO pif r—i CU3 CU cu >

•H

CC3 rH3

CJ

44

at

time

when

first

compression
INITIAL

SLOPE

US.

TEMPERATURE

45

TEHPERATURE

Figure

4.4

Initial

slopes

of

strength-maturity

relations

versus

cumulative

average

temperature

(Phase

I)

.
s (4.2)

CM - M ) Su

o_

1 ^ (M - M ) K

m

where K = B/Su.

m

In this way, the effect of the water-cement ratio on the initial slope could

be separated from the effect due to temperature.

Figure 4.5 shows the values of K versus temperature, and it appears that K

has no significant dependence on strength level. It will, therefore, be

assumed that the data from both mortar mixes can be treated as a single

sample. To express the temperature dependence in mathematical form, two

models were investigated:

K = K* + bT (4.3)

m m

K

m

dT

c exp

where K*, b, c and d are regression parameters,

m

(4.4)

It was found that both functions fitted the data with the same precision, so it is suggested that a linear relation as represented by eq (4.4) provides a suitable approximate method for correcting the initial slope of the strengthmaturity relation when the in-place initial temperature of concrete is

significantly different from that present during development of the calibration

curve.

The next parameter to investigate is the offset maturity parameter, M . Figure

4.6 shows the best-fit values of M obtained in Phase I. As expected, based on the previous discussion of fina? set, the offset maturity is a linear

decreasing function of temperature. Also shown in this figure are the

maturities at final set from Phase II, and it is seen that there is significant

correlation between M and the maturity at final set. Figure 4.7 is a schematic representation of the probable early age strength-maturity curves

at two extreme temperatures, and Illustrates why there is a correlation

between M and the maturity at final set. Because the reaction rate during

the setting process is not a linear function of temperature, an increase in

temperature will lower the maturity at final set, which in turn reduces the

offset maturity. Note also the change in slope B with temperature.

Since the differences between M and maturity at final set appear to be small

and since M can only be found ?rom non-linear regression analysis, it is

suggested tftat the offset maturity can be approximated as the value of maturity

at final set (this quantity could be measured in the laboratory) . Then, it

remains to account for the variation in final set, , as a function of

t s temperature, T. The limited data in figure 4.6 appear to indicate that, over

the investigated temperature range, the following linear approximation would

be adequate:

46
PARAHETR

KM

VERSUS

TEMPERATURE

47

TEMPERATURE

Figure

4.5

^'ariation

ofK

with

cumulative

average

temperature

(Phase

I).
OFFSET

HATURITY

US.

TEMPERATURE

li. O

O

o

® ^ O

'T n oj

^

o

OJ

- ®

o

OJ

O U_ Li- CO UJ E— E <r I- ZD Qs: »-• I- > U. • O<E>0D

o

48

TEPIPERATURE

Figure

4.6

Variation

of

offset

maturity,

with

cumulative

average

temperature

(Phase

I)

,
STRENGTH-PIATURITV

RELATIONS

AT

EARLY

MATURITIES

49

Figure

4.7

Schematic

representation

of

strength-maturity

relations

at

early

maturities.
M = M* - fT (4.5)

o f s

where M* and f are parameters defining a straight line.

Finally, there is the limiting strength, Su. Figure 4.8 shows the variation

in the computed best-fit values of Su as function of cumulative average

temperature. It is evident that there is a consistent relationship between

limiting strength and temperature. However, the results from the high

water-cement ratio mix were more scattered than the results from the low

ratio mix. Analysis of the low water-cement ratio results indicated that a linear relationship between limiting strength and temperature gave almost as good a fit as a more complex exponential fit. Thus, it is suggested that,

over the temperature range studied, the dependence of limiting strength on curing temperature can be adequately represented by a linear function as follows

Su = S* - gT (4.6)

where S* and g are parameters defining a straight line

Substituting equations (4.4), (4.6), and (4.7) into 4.3, the strength-maturity

relation becomes:

[M - M^g(T)] Su(T)

1 (T)^ W -

where M^^(T) = maturity at final set = M* - fT

K (T) = initial rate constant = K* + bT

m

Su(T) = limiting strength = S* - gT

The linear correction factors are adequate for the temperature range of

5 to 43 C, which would include the vast majority of concrete placements

during construction.

Chapter 5 will explain the fundamental assumption implied by the maturity

concept which accounts for why the above temperature correction factors are needed.

50
LIMITING

COHPRESSIUE

STRENGTH

US.

TEMPERATURE

51

TEMPERATURE

Figure

4.8

Variation

of

limiting

compressive

strength

with

curing

temperature

(Phase

I).
4 3 WHEN IS "EARLY AGE"

The purpose of the Phase II experiments was to determine the length of the

early age period during which temperature affected the subsequent strengthmaturity function. To accomplish this, specimens were cured at 5°C and 32 C

for different time periods and then moved to 23 C. In planning the time

periods when the moves were to be performed, it was postulated that a critical

factor would be the degree of setting at the time of movement. Therefore,

three stages of setting were arbitrarily chosen as the "times" when movement

from the extreme temperatures to 23 C would be performed. These stages were

final set, initial set and a time equal to one-half the time to achieve

initial set. Because setting time is affected by temperature, the movement

times for the 5 and 32 C initial curing temperatures were different.

Figure 4.9 shows the temperature-time histories, up to an age of 24 hours,

for the six treatments of Phase II. It can be seen that the procedure of

changing the temperature of the water baths was effective in bringing about

a rapid change in the temperature of the specimens.

The results of the compressive strength tests of Phase II were summarized in

figure 3.8, figure 3.9 and table 4. It is desirable to determine whether

differences existed among the strength-maturity curves of the three treatments

for each initial curing temperature and whether differences existed between

the strength-maturity curves of Phase II specimens and the corresponding

Phase I specimens. To determine whether significant differences existed, the

F-test of variances was used.

In applying the significance test, the sum of the squared residuals of the

best fit curve for the combined data is compared with the total sum of squared

residuals when separate curves are used for each data group. For example, if

the sum of the squared residuals for the regression curve of the combined

data is R with corresponding degrees of freedom N , and if the total squared

residuals for separate regression curves is R with total degrees of freedom

of N, the following F-statistic is calculated:

F

R - R

oR

N

N - N

o (4.8)

The computed value of F is compared with tabulated values of F for (N - N) and

N degrees of freedom at a chosen significance level. If the computed°F-value

is larger than the tabulated value, then it is concluded that, at the chosen

level of significance, differences exist among the separate regression curves.

In this study the significance level was chosen as 0.05, and the average

strengths at each maturity were used in the regression analyses.

The results of the tests of differences among data groups are summarized in

table 6. The left-hand portion of the table gives the residual standard

deviations and degrees of freedom for the individual data groups that were

compared. Bartlett’s test for homogeneity of variance resulted in a chi-square

value of 3.64 which is not significant at the 0.05 level and so we are justified

52
EARLY

AGE

TEMPERATURE

HISTORIES

(PHASE

II)

in

nj

I- UJ co. UJ 3 u o

o

53

Figure

A.9

Early

age

temperature

histories

of

Phase

II

specimens.
TABLE

6.

SUMMARY

OF

F-TEST

OF

VARIANCES

(U>3aCo

•H

COCO

0)u

bO

CU

}-i

M-loco

•rl

CO •H>T3T3

>-i cO T3d

CO 4J

CO

cOd

nd

•H

CO

CUd

II

C/D

pcS

CUo2

54

O.F. =

degrees

of

freedom

associated

with

residual

standard

deviation *

indicates

statistically

significant

value

ofF

at

the 5

percent

significance

level
in comparing these data groups. The right-hand portion of the table gives

the residual standard deviations and degrees of freedom for various combined

data groups; also shown are the computed and tabulated (at the 0.05 significance level) values of the F-statistic. The sum of the squared residuals is

the product of the degrees of freedom and the square of the residual standard

deviation.

The first combined group included all the Phase II treatments. The computed

value of F was greater than the tabulated value (9.35 versus 2.62), so one concluded that the initial temperature treatments at 5 and 32 C altered the

strength-maturity function for subsequent curing at 23 C. This result was

expected.

Next, the three 5°C treatments were grouped, and the F-value (6.53) indicated

that differences existed among the strength-maturity relations for the three

treatments. However, the differences were not as expected. Examination of

figure 3.8 and table 4 reveals that the major difference in this group is the

limiting strength of the series removed from 5 C at Initial set, which is

greater than those of the two other treatments. Based on the explanation of

Verbeck and Helmuth [12], it would be expected that limiting strength should

be an increasing function of time spent at the lower temperature. It is not

clear whether the higher limiting strength of the specimens moved at initial

set is significant or just a rare statistical event. When the data of the H

and F treatments were grouped, the F-value (1.57) was not significant and it can be concluded that the strength-maturity functions were the same for the

two extreme exposure times at 5 C. This suggests the possibility that the

data of the initial set group is anomalous compared with the H and F treatments .

The H and F treatments at 5°C were compared with constant curing at 5° and at

23 C in Phase I. The computed F-values (3.01 and 6.85) indicate that these

treatments resulted in strength-maturity functions similar to constant curing

at 5 but dissimilar to constant curing at 23 C. Examination of figure 3.8,

table 3 and table 4, however, reveals that the initial shapes of the H and F

strength-maturity relations were closer to the 23 C constant temperature

treatment, but the shapes at later maturities were closer to the 5°C constant

temperature treatment. Thus, it may be concluded that the initial exposure at

5 C altered the limiting strength but did not significantly alter the initial

slope of the strength-maturity curves compared with constant curing at 23°C.

For the 32°C initial treatments, the results did not follow the same pattern

as the 5 C treatments. First, there was no significant difference among the

three 32 C treatments as indicated by the very low F-value (0.09) in table 6.

When the 32 C treatments were grouped with the Phase I data, it was found that

the 32 C treatments had the same strength-maturity curves as constant curing

at 23 C. Thus, the conclusion in this case is that Initial curing at 32°C did

not significantly alter the strength-maturity relations compared with constant

curing at 23°C.

The lack of similarity in the effects of the 5°C and 32°C initial exposures on

the resultant strength-maturity relations reveals that the effects of early age

55
temperature are more complicated than had been anticipated when the test program was designed. It appears that the degree of setting is not the critical factor

to use for quantifying which stage should be classified as "early age."

Perhaps an underlying reason for the differences in behavior of the 5° and 32°C

treatments may be the effects of temperature on the growth of calcium

hydroxide crystals. Berger and McGregor have shown that calcium hydroxide

crystal growth rates at 15 C were greater than at 25 and 35°C, and the

growth rates at 25 and 35 C were similar [33].

56
5.0 BASIS OF CLASSICAL MATURITY CONCEPT

It may be argued that the quantity

M = / (T-T )dt

o

C5.1)

has no meaning when trying to describe a physical phenomenon involving chemical

reactions, such as the hydration of cement. It has been suggested* that the

effects of time and temperature on the strength development of concrete can be

predicted based on simple kinetic rate theory. Also, it might be asked why

the hyperbolic function was adopted as the best representation of the strengthmaturity relation. This chapter will attempt to reconcile these points.

First, let us consider the shape of the strength versus time relation of

concrete cured at constant temperature. If one assumes that the rate of

strength development will be a function of the quantity of unreacted cement,

and if the strength of concrete is assumed to be directly related to the

amount of cement hydration that has occurred, the following rate equation may

be proposed:

= k Cl - S/Su) (5.2)

where t = time

S = strength at any time

Su = limiting strength

k = rate constant

Upon integration, we obtain

- In (1 - —) = kt + C (5.3)

where the constant of integration, C, is evaluated by the boundary condition

S = 0 for t = t . The offset time t , which is analogous to M as illustrated

in figure 4.7, is used to account for the fact that strength gain as expressed

by eq (5.2) will not occur until the acceleratory stage is reached. The final

result, assuming that strength gain follows a simple first order reaction law,

is as follows:

S = Su LI - exp(-k(t-t^))] (5.4)

The above exponential function was applied to the average strength-age data of

Phase I and the constants Su, k and t were found for each series (see table 7). o

' '

* E. L. Schaffer, personal communication.

57
TABLE

7.

COMPARISON

OF

EXPONENTIAL

AND

HYPERBOLIC

STRENGTH-AGE

FUNCTIONS

Q •H cn 00 cn CT> cn

O 00 CO

O

cn

n VO

m a\ (7\ o CM iH OV vO rH

rAa 1-^

m rH iH CM CM CM CM vO

iH

m 00 lO vO

m CO 00 <r o n3 vO CM 00 o O CO rH O o

4J T3 • o O1 o CO

O o o o O o <MHWaO

•H o m o o m

m o m

mm 3 n o> o CO VO OV OV CM iH VO

W

w a. o o\ r-* f-H CO

m CM CO CO m CO OV 00 00

CM in CM o cr> tH iH C3V nJ Ov •vj- m CM 00 m m CJV cn

vO CM 00 00 cn C3Vm C3V

O CM CO vO o rH CM CO vO • • Sw/ o O o C3 CD o o CD O O

/-s o •H

O o in o m OV

m MT

C/3 CO OV in 00 VO cnm 00 00 CJv Pi a CM iH iH cn CM

VO CM CO VO 00 OO cn CO j"

m o cd o m CO CM iH O vO CO CM t-H

4-» • • • • • • • • • • s-/ 1—1 o O o O iH o o O O

OM

hJO o in

Om o inm o o m 3 •rl vO CM o LT) m <yv o vO 3 CO 1—1 m 00 I—1

iH vO 'd- CO OV

pLi CO Cu vO CO <! o C3V OV 00

s-/ I—1 H

VO CO C3V rH cyv vO vO CO'

m

00 VO 00 COm C3V vO vO o

vO CM o rH OV CO 00 o rH <r m o rH iH m m o o o o o iH o o d o 1—1 m 00 cn r—1

00 OV <3- CO CM 00 m VO m vO 00 in vO m vO

p" 00 CJV o rH 00 CJV o iH CM CM CM CO CO CM CM CM cn CO

c/3

KW Pd

W

W 1 H CM CO CM

Pim t—1

CM CO

W 1 1 1 1 CO H . M M H

Pd1 Hd i-J Hd

hJ 1 1 1 1 • • CO 1 CM CO CM CO tu m 1—1

CM CO 'CTW 1 1 1 1 1 1 o M M H H H M

58

To

convert

psi

to

MPa

divide

by

145

psi/MPa
COMPARISON

OF

HYPERBOLIC

AND

EXPONENTIAL

STRENGTH

FUNCTIONS

0)l-Q^UJZOI-X QL(/)i-i

59

Figure

5.1

Comparison

of

hyperbolic

and

exponential

best-fit

curves

with

data

from

Phase

I.
Figure 5.1 shows how the exponential function fits the data of two series from

Phase 1. The fit is reasonable, but the exponential curve reaches the limiting

strength too quickly and the predicted values of this strength appear too low.

The conclusion is that the first order rate equation is not the most appropriate

one to use.

In terms of our knowledge of cement hydration, it is understandable why a first

order reaction is inappropriate. As cement grains hydrate, ions must diffuse

from the unreacted cores through hydrated products to the pore spaces where

they precipitate. Thus, as hydration progresses there is a continually

increasing barrier to further hydration (the hydrate layer around the cement

grains). Various models have been proposed [32j to try to explain the phenomena

involved in cement hydration, but they have not been very successful. In

general they are complex and only apply to simple systems in which only one

or two compounds are present.

The rate equation (eq 5.2) can be altered so as to approximate the added

obstacles of hydrate layers. Based on empirical evidence, Bernhardt [30]

suggested that a second order rate equation was more appropriate, as follows:

d(S/Su)

dt (1 - S/Su)^ (5.5)

Upon integration, one obtains

1 - S/Su

= kt + C (5.6)

The constant C can be found using the same boundary condition as above. Thus,

C = 1 - kt

and

S =

(t - t ) Su

o_ (5.7)

Equation 5.7 is a hyperbolic curve with limiting strength Su and an Initial

slope at t = t^ equal to (k • Su)

.

Table 7 shows the values of Su, t and k obtained from regression analysis.

The residual standard deviations ?or the hyperbolic model are significantly

lower than those for the exponential model. Figure 5.1 shows a better fit for

the hyperbolic model in representing a sample of the data. Figures 5.2 and

5.3 show the best fit hyperbolic strength-age curves for each series in

Phase I.

60
STRENGTH

US*

^^GE,HIGH

U/C

RATIO

Figure

5.2

Compressive

strength

versus

age

including

best-fit

hyperbolic

curves

(Phase

I,

high

w/c).
STRENGTH

US*

AGE,

LOU

U/C

RATIO

00

in I- q: uj z: <5 1- X Q.in»-«

62

Figure

5.3

Compressive

strength

versus

age

including

best-fit

hyperbolic

curves

(Phase

I

,

low

w/c)

.
The data support the suggestion that a second order reaction rate (eq 5.5) is

appropriate for the strength development of concrete after final setting has

occurred. If eq (5.7) were to be used to predict strength as function of age

and temperature, the variations of these parameters with temperature must be

known. The variation of Su with temperature has already been discussed in

chapter 4.

Figure 5.4 shows the values of k for the hyperbolic model as a function of

temperature. It appears that k is not strongly influenced by water-cement

ratio and it appears to be a non-linear function of temperature. Assuming,

however, that k.is a linear function of temperature, and that k is equal to zero at the temperature, T , below which no strength gain is observed in

hardened concrete, k could be represented by the following expression;

k = K (T - T ) m o (5.8)

where K is the slope of the line. If eq (5.8) is substituted into eq (5.7),

we obtaTn the following:

or

S =

- t ) o Su

K (T - T )

''' ^^ ^o^

m o

S

(T - T^) (t - t ) Su

o o i + (T - T^) (t - t^)

m

(5.9)

(5.10)

Let us further simplify eq (5.10) by introducing the quantity M to represent

the product of time and temperature above T , and introduce the quantity M to

represent the corresponding product at age

°

(M - M )

1

, K Su Su

m

(5.11)

Equation (5.11) is precisely the hyperbolic strength-maturity function presented

in section 3.2.1 with the term K Su replacing B in eq (3.4). We now see the

fundamental assumption implied by the maturity concept, and why the concept

gives poor results when applied to concretes curing at vastly different temperatures. The assumed linear variation of k with temperature is not adequate to

represent the effects of temperature on strength development; hence, when

samples of a given concrete are cured at two dissimilar temperatures, there will

be two different strength-maturity relations.

63
RATE

CONSTANT

(lO

UERSUS

TEMPERATURE

in

<3 3

»-• o

o

I- r-

»-• •

O

I- I V)UJ o

tt IT I I I

^ "

1 | I 1 r ^

I I > >

^

I I I I

o

n

o

OJ

I

nj

I L/) in 
 LO o

03 r- lO (U

o

o

o

UJ

0^

ID

I-

<£

CL

UJ

CL'

c

UJ

=><Z»J3UJ OLl. ^ ^ \ Q <r >

64

Figure

5.4

Variation

of

rate

constant,

k,

with

curing

temperature

(Phase

I).
As a matter of interest, figure 5.4 shows the best fit straight line obtained

by fitting eq (5.8) and the best fit line obtained by using T = -11.7°C

(11°F) . The best fit value of T is 4.4°C (40°F) , this would°mean that concrete

cured at 4.4°C would not gain strength. Thus, T must be chosen as less than

4.4°C to account for the observed hardening below 4.4 C. We see that for

T = -11.7 C, the predicted value of k will be very different from the true

value and hence, as shown by the results of this study, the strength-maturity

relations will show a significant effect due to curing temperature.

It is now understood why Sadgrove [20] suggested the use of eq (1.7) to

compute equivalent age. The parabolic expression is an attempt to produce a better approximation of the k-temperature curve than Saul’s implied straight

line approximation.

Since the Saul maturity function (eq 1.1) does not appear to be the best

approach for accounting for the combined effects of temperature and time on strength development of concrete, it may be desirable to seek an alternative

approach for computing maturity. This is the subject of the following chapter.

65
6.0 AN ALTERNATIVE APPROACH FOR COMPUTING MATURITY

To explore whether there is an alternative approach for computing maturity,

we begin with the strength-age relation presented in chapter 5;

O ~

(5.7)

r+(t-t) k o

Rearranging terms, this can be rewritten as follows:

k(t-t ) Su

c = 2

^ 1 + k(t-t ) (6.1)

o To incorporate temperature effects, it is necessary to determine the variation

of k and t with curing temperature. Note that Su will also be a function of

temperature, but that dependence has already been discussed (see figure 4.8).

Since hydration is an exothermic reaction, it has been suggested that the rate

constant, k, can be related to temperature according to the Arrhenius equation,

as follows:

k = A exp (-E/Tj^) ( 6 . 2 )

where A = constant

E = the activation energy divided by the gas constant

Tj^ = absolute temperature

Thus, as a first attempt, eq (6 .’,2) was fitted to the values of k versus

absolute temperature (columns 3 and 2 in Table 7) . The results are shown in

figure 6.1; the agreement between the best-fit curve and the values of k is

excellent. In addition, the following power law was also fitted:

k = B exp (CT) (6.3)

where B and C are regression coefficients and T is temperature.

The power law also gave a good fit but not quite as good as the Arrhenius

function; the residual standard deviation for the power law was 0.037, while it was 0.033 for the Arrhenius function. It was, therefore, concluded that the

effect of temperature on k could be better represented by the Arrhenius function.

The relationship between the best fit values of t and temperature (columns 5 and 2 in Table 7) is indicated in figure 6.2. The first observation is that t is essentially independent of the water-cement ratio of the mortar. Also

66
RATE

CONSTANT

(K)

VERSUS

TEMPERATURE

67

ABSOLUTE

TEMPERATURE

(°K)
OFFSET

AGE

US.

TEMPERATURE

o

L/)

UJ

<S>

m o

o

(U

UJ

q: Z)

I-

<L

UJ

Q.

UJ

(U

^ouj o<r>cn

Li) o

68

Figure

6.2

Variation

of

offset

age,

t

,

with

cumulative

average

temperature

compared

with

age

at

final

set.
shown in figure 6.2 are the final set times obtained from Phase II, and it is

seen that, with good approximation, t can be taken as equal to the age at

final set, t_ . There appears to be a well-defined relation between t and

temperature wRich can be represented as follows:

to b a + T

% t fs (6.4)

where a and b are regression coefficients and T is temperature.

Therefore, by substituting into eq (6.1) the temperature dependences

represented by eqs (4.7), (6.2) and (6.4), one obtains a single equation to

represent strength development under isothermal (constant temperature) curing

conditions. Further examination of eq (6.1) suggests an alternative approach

to the Saul maturity function for accounting for the combined effects of

temperature and time on strength development. Let us introduce the quantity

"effective age", Ae, to represent the product of the rate constant, k, and

age beyond t^

Ae = k(t-t ) o (6.5)

Equation (6.1) can be rewritten as follows:

_ Su Ae

^ 1 + Ae ( 6 . 6 )

According to eq (6.6), the curve representing strength versus effective age

would be a hyperbola with an initial slope equal to Su and asymptotic to Su as effective age approaches infinity. Since Su is affected by curing temperature,

for a given concrete mixture, there would be a family of strength-effective

age curves; each curve representing a different curing temperature.

Equation (6.6) can also be written as follows:

S_ = Ae

Su 1 + Ae (6.7)

Equation (6.7) expresses a very significant relationship: relative strength

development is a single-valued function of effective age . To illustrate how

well the strength-data from this study obey eq (6.7), the strengths of the low

water-cement ratio mortars in Phase I were non-dimensionalized by dividing

them by the appropriate values of Su presented in column 4 of Table 7. The

relative strengths are plotted versus effective age in figure 6.3. Effective

age was computed according to eq (6.5) and employing the temperature functions

represented by eqs (6.2) and (6.4). The following were the best-fit values

of the parameters in the above temperature functions (they result in the curves

shown in figures 6.1 and 6.2):

A = 7.96 X 10^ (1/day)

E = 5015 °K

b = 9 °C-days

a = 3°C,

69
Also shovm in figure 6.3 is the hyperbola represented by the right-hand side

of eq (6.7). Note that effective age is a dimensionless quantity. Overall,

the points fall very close to the hyperbolic curve, and it may be concluded

that relative strength development is indeed related to effective age according

to eq (6.7) irrespective of curing temperature.

Thus, the concept of effective age may be an appropriate alternative to the

Saul function to properly account for the combined effects temperature and

time on strength development. To apply this new method requires knowing three

factors:

1) the relation between the basic reaction rate, k, and temperature,

2) the relation between curing temperature and limiting strength, and

3) the relation between temperature and age at initial set.

Future research will be required to understand how these three factors are affected by changes of the constituents of a concrete mix. Also it needs to be

demonstrated how this method would be applied when temperature is not constant.

70
STRENGTH

RATIO

UERSUS

EFFECTIOE

AGE

71

EFFECTIUE

AGE
7.0 SUMMARY AND RECOMMENDATIONS

Phase I of the research was undertaken to gain a quantitative understanding of

the effects of curing temperature on the strength-maturity relation of concrete.

In order to simplify testing, mortar was used in place of concrete since it was believed that portland cement would be the main ingredient affected by temperature. Curing temperatures of 5 , 12 , 23 , 32 and 43 C were used. Compressive

strength tests were performed at regular maturity intervals, and penetration

resistance tests were conducted on fresh mortar to gain an understanding of

temperature effects on setting time.

Concerning the effects of temperature on setting time, it was found that for a given mortar mix initial set occurred at approximately the same maturity (as

computed by the Saul function) . The fact that initial set occurs at approximately

the same maturity may be useful in designing the rate of concrete placement into

vertical formwork (such as walls) under different temperature conditions. In

Phase II, final setting times were also determined and they were found to occur

at decreasing maturity as temperature increased.

In order to determine the quantitative effects of temperature on the strengthmaturity relation, a three-parameter equation was used to approximate actual

strength-maturity curves. The assumed model is a hyperbolic curve defined by

1) an "offset maturity", M , when strength begins to develop, 2) an initial

slope at M , and 3) an asymptotic limiting strength, Su, as maturity increases

to infinity. The variations of these three parameters with curing temperature

were used to quantify the temperature effects. It was found that the limiting

strength decreased in an approximately linear fashion with increasing curing

temperature; the initial slope increased in an approximately linear fashion

with increasing temperature; and the offset maturity varied inversely with

curing temperature. The results of Phase II tests indicated that the offset

maturity was approximately the same as the maturity at final set, and the

latter value would be recommended for use in application of the three-parameter

strength-maturity model. Thus, it was concluded that simple temperature

corrections could be applied to the parameters of the strength-maturity relation,

to enhance the reliability of strength predictions based upon the maturity

concept over a wide temperature range.

The purpose of the Phase II experiments was to determine the extent of the

"early age" beyond which temperature would no longer have significant effects

on the strength-maturity relation. Mortar specimens were initially cured at 5

and 32 C; at predetermined stages of setting, the temperatures of the specimens

were changed to 23 C for subsequent curing and compression testing. Movement

from the extreme temperatures to 23 C were made at 1) time equal to one-half

the time to reach initial set, 2) time of initial set, and 3) time of final

set. Stages of setting were chosen rather than equal time periods at the

extreme temperatures because it was believed that the former factor was more

likely to be decisive in controlling the point beyond which temperature would

no longer affect the strength-maturity relation. The results, however, appeared

to contradict this supposition. For the 5 C initial treatments, the limiting

strengths were greater than the case of constant curing at 23°C and similar to

the value for constant curing at 5 C; the initial slopes, on the other hand,

were similar to the value for constant curing at 23 C. The 32 C initial

72
treatments did not show the same trends; in all cases, the strength-maturity

relations were nearly identical to 23 C constant curing. Thus, it appears

that degree of setting is not the critical factor governing the extent of

"early age."

The systematic variations of the parameters of the strength-maturity model

observed in Phase I caused us to ask whether an alternative approach to the Saul

maturity function could be used to represent the combined effects of time and

temperature on strength development. Hence, a detailed analysis of the strengthage data of Phase I was performed. Kinetic rate theory was used to provide

justification for an hyperbolic strength-age function, and comparison with the

data showed such a model to be superior to a first-order exponential model. It

was also shown that if the rate constant in the strength-age relation was assumed

to be a linear function of temperature, the resulting strength-age function was precisely the hyperbolic strength-maturity relation employed in analysis of the

Phase I data. However, the computed values of the rate constant were found to be

a non-linear function of temperature. Thus, a newly recognized implicit assumption

in the classical maturity method has been identified, and we now understand why

the "cross-over" effect occurs in strength-maturity relations for curing at

dissimilar temperatures.

Analysis of the strength-age data revealed that the rate constant was independent

of the strength level of the mix (that is, water-cement ratio) and that it was related to curing temperature according to the Arhennius equation. By employing

the Arrhenius function, rather than a linear function to represent the variation

of the rate constant with temperature, a single equation was developed to

represent the strength-age relations for different curing temperatures. The

product of time and the rate constant yields a non-dimensional quantity, which

has been named "effective age" and indicates the fraction of limiting strength

that has been attained by that time. A plot of fractional strength data versus

effective age showed that a single hyperbolic curve was a good representation

of the data.

In summary, the research has indicated that there exist rational means by which

a strength-maturity calibration curve may be altered so that its reliability is

maintained over a wide temperature range. Also, it appears that the concept of

"effective age" offers another approach for accounting for time and temperature

effects on strength-development. However, before making recommendations on field application of the suggested procedures, three fundamental questions need

to be addressed: ^

1) Will concrete display the same responses to different curing temperatures

as the mortar specimens used in this research?

2) How are the proposed correction factors or the effective age concept

to be applied under conditions of daily temperature fluctuations?

3) What characteristics of cement chemistry have the greatest effect on

the response to different curing temperatures?

These questions should serve as a guide in planning future research in this

area, and the answers to the questions will provide information to formulate

recommendations for an approach that can be employed to reliably predict

in-place strength of concrete at early ages and under varying thermal histories.

73
8.0 REFERENCES

1. Carino, N. J., The Maturity Concept - It’s Development and Future, NBS

publication, in review, 1980.

2. Malhotra, V. M. , Maturity Concept and the Estimation of Concrete Strength - A Review, Department of Energy, Mines and Resources, Mines Branch, Ottawa,

Information Circular IC-277, 43 pages (1971).

3. McIntosh, J. D., Electrical Curing of Concrete, Magazine of Concrete

Research, No. 1, 21-28 (Jan. 1949).

4. Nurse, R. W. , Steam Curing of Concrete, Magazine of Concrete Research 1^, No. 2, 79-88 (June 1949).

5. Saul, A. G. A., Principles Underlying the Steam Curing of Concrete at

Atmospheric Pressure, Magazine of Concrete Research No. 6, 127-140

(March 1951)

.

6. Bergstrom, S. G. , Curing Temperature, Age and Strength of Concrete, Magazine

of Concrete Research^, No. 14, 61-66 (Dec. 1953).

7. Plowman, J. M. , Maturity and the Strength of Concrete, Magazine of Concrete

Research^, No. 22, 13-22 (March 1956).

8. Discussion of Reference 16, Magazine of Concrete Research No. 24,

169-183 (Nov. 1956).

9. McIntosh, J. D., The Effects of Low-Temperature Curing on the Compressive

Strength of Concrete, R.I.L.E.M. Symposium on Winter Concreting,

(Copenhagen, 1956).

10. Klieger, P., Effect of Mixing and Curing Temperatures on Concrete Strength,

Journal of the American Concrete Institute No. 12, 1063-1082 (June 1958).

11. Alexander, K. M. and Taplin, J. H. , Concrete Strength, Cement Hydration and

the Maturity Rule, Australian Journal of Applied Science 277-284

(1962).

12. Verbeck, G. J. and Helmuth, R. H. , Structure and Physical Properties of

Cement Paste, Proceedings of the Fifth International Symposium on the

Chemistry of Cement, Part III, 1-32 (Tokyo 1968).

13. Swenson, E. G. , Estimation of Strength Gain of Concrete, Engineering Journal

September, 1967.

14. Hudson, S. B. and Steele, G. W. , Prediction of Potential Strength of Concrete

from Early Tests, Highway Research Record, No. 370, Highway Research

Board, 25-35 (1971).

15. Hudson, S. B. and Steele, G. W. , Developments in the Prediction of Potential

Strength of Concrete from Results of Early Tests, Transportation Research

Record, No. 558, Transportation Research Board, 1-12 (1975).

74
16. Chin, F. K. , Relation Between Strength and Maturity of Concrete, Journal

of the American Concrete Institute 68, No. 3, 196-203 C^arch 1971).

17. Poranersheira, J. M. and Clifton, J. R. , Prediction of Strength-Maturity

Relationships for Portland Cement Systems, NBS publication in review, 1980.

18. Chin, F. K. , Strength Tests at Early Ages and at High Setting Temperatures,

Transportation Research Record, No. 558, Transportation Research Board,

69-76 (1975).

19. Weaver, J; and Sadgrove, B. M. , Striking Times of Formwork-Tables of

Curing Periods to Achieve Given Strengths, Construction Industry Research

and Information Association, Report 36, (London, Oct. 1971).

20. Sadgrove, B. M. , Prediction of Strength Development in Concrete Structures,

Transportation Research Record, No. 558, Transportation Research Board,

19-28 (1975).

21. Bickley, J. A., Practical Application of the Maturity Concept to Determine

In-Situ Strength of Concrete, Transportation Research Record, No. 558,

Transportation Research Board, 45-49 (1975).

22. Mukherjee, P. K. , Practical Application of Maturity Concept to Determine

In-Sltu Strength of Concrete, Transportation Research Record, No. 558,

Transportation Research Board, 87-92 (1975).

23. Nisbet, E. G. and Maitland, S. T., Mass Concrete Sections and the Maturity

Concept, Canadian Journal of Civil Engineering, Vol. 3, 1976.

24. Lew, H. S., and Reichard, T. W. , Mechanical Properties of Concrete at

Early Ages, Journal of the American Concrete Institute 7^, No. 10,

533-542 (Oct. 1978).

25. Lew, H. S. and Reichard, T. W. , Prediction of Strength of Concrete from

Maturity, Accelerated Str'ength Testing, SP-56, American Concrete Institute,

229-248 (1978).

26. Carino, N. J. and Lew, H. S., Applicability of the Maturity Concept to

Predict Strength of Field-Cured Concrete, NBS publication in review, 1980.

27. Volz, C. K. , New Developments in the Maturity Concept, M. S. Report, The

University of Texas at Austin, (December 1979).

28. ASTM Annual Book of Standards, Part 14, (1979).

29. Sprouse, J. H. and Peppier, R. B., Setting Time, Chapter 9 in Significance

of Tests and Properties of Concrete and Concrete-Making Materials, ASTM

STP 169B, 105-121 (1978).

30. Bernhardt, C. J. , Hardening of Concrete at Different Temperatures,

R.I.L.E.M. Symposium on Winter Concreting, (Copenhagen, 1956).

75
31. Filliben, J. J., DATAPLOT - An Interactive System for Graphics, Fortran

Function Evaluation and Linear/Non-Linear Fitting, Proceedings of the

Statistical Computing Section of the American Statistical Association,

1978.

32. Pommersheim, J. and Clifton, J. R. , Mathematical Models of Cement

Hydration, Cements Research Progress; Chapter 13, 281-307 (1979).

33. Berger, R. L. and McGregor, J. D., Effect of Temperature and Water-Solid

Ratio on Growth of Calcium Hydroxide Crystals Formed During Hydration of

Tricalcium Silicate; Journal of the American Ceramic Society No. 2,

73-79 (1973).
APPENDIX A

PENETRATION RESISTANCE DATA

PENETRATION READINGS AGE MATURITY

SERIES (psi) (MPa) (hour) (°F-days) (° C-days)

140, 160 0.97, 1.10 7.00 8.33 4.91

240, 240 1.66, 1.66 8.00 10.13 5.63

I-5-H* 270, 280 1.86, 1.93 9.00 11.42 6.34

370, 430 2.55, 2.97 10.33 13.13 7.29

470, 470 3.24, 3.24 11.33 14.42 8.01

180, 180 1.24, 1.24 5.50 9.92 5.21

240, 270 1.66, 1.86 6.58 11.88 6.60

I-12-H 360, 430 2.48, 2.97 7.75 13.92 7.73

470, 500 3.24, 3.45 8.25 14.83 8.24

520, 550 3.59, 3.79 8.50 15.25 8.47

50, 60 0.34, 0.41 3.00 7.79 4.33

230, 210 1.59, 1.45 4.50 11.67 6.48

I-23-H 340, 300 2.34, 2.07 5.00 12.96 7.20

480, 430 3.31, 2.97 5.50 14.21 7.89

620, 590 4.28, 4.07 6.00 15.50 8.61

110, 120 0.76, 0.83 3.00 9.76 5.42

440, 500 3.03, 3.45 4.00 13.00 7.22

I-32-H 520, 500 3.57, 3.45 4.17 13.55 7.53

610, 660 4.21, 4.55 4.33 14.09 7.83

640, 710 4.41, 4.90 4.42 14.36 7.98

180, 180 1.24, 1.24 2.25 9.21 5.12

330, 310 2.28, 2.14 2.58 10.56 5.87

1-4 3-H 390, 370 2.69, 2.55 2.75 11.24 6.24

630, 590 4.34, 4.07 3.00 12.25 6.81

610, 580 4.21, 4.00 3.08 12.59 6.99

180, 150 1.24, 1.03 6.00 7.75 4.31

270, 250 1.86, 1.72 7.00 ; 9.04 5.02

I-5-L 390, 360 2.69, 2.48 8.00 10.33 5.74

420, 470 2.90. 3.24 8.67 11.21 6.23

550, 560 3.79, 3.86 9.33 12.08 6.71

210, 190 1.45, 1.31 4.50 8.13 4.52

310, 300 2.14, 2.07 5.58 10.04 5.58

I-12-L 370, 370 2.55, 2.55 6.25 11.25 6.25

540, 590 3.72, 4.07 7.00 12.58 6.99

620, 660 4.28, 4.55 7.25 13.00 7.22

* See section 2.3 for key to these symbols

77
PENETRATION READINGS AGE MATURITY

SERIES (psi) (MPa) (hour) (°F-day) (°C-day)

60, 40 0.41, 0.28 2.50 6.50 3.61

210, 190 1.45, 1.31 3.50 9.08 5.04

I-23-L 350, 320 2.41, 2.21 4.00 10.38 5.77

570, 470 3.93, 3.24 4.50 11.67 6.48

550, 600 4.48, 4.14 4.75 12.29 6.83

100, 100 0.69, 0.69 2.50 8.08 4.49

310, 270 2.14, 1.86 3.00 9.72 5.40

I-32-L 400, 360 2.76, 2.48 3.25 10.54 5.86

590, 560 4.07, 3.86 3.50 11.35 6.31

6.10, 600 4.20, 4.14 3.58 11.62 6.46

140, 130 0.97, 0.90 1.75 7.13 3.96

230, 240 1.59, 1.66 2.08 8.47 4.71

1-4 3-L 380, 380 2.62, 2.62 2.33 9.49 5.27

590, 570 4.07, 3.93 2.52 10.23 5.68

640, 700 4.41, 4.83 2.63 10.70 5.94

130, 140 0.90, 0.97 8.00 10.18 5.65

230, 200 1.57, 1.38 9.50. 12.06 6.70

330, 360 2.28, 2.48 10.75 13.63 7.57

420, 400 2.90, 2.76 11.75 14.88 8.27

II-5-I 460, 520 3.17, 3.59 12.50 15.83 8.79

800, 840 5.52, 5.79 13.50 17.91 9.95

1600, 1480 11.03, 10.21 14.33 20.05 11.14

1880, 2400 12.97, 16.55 15.00 21.79 12.11

2520, 2680 17.38, 18.48 15.25 22.84 12.69

3960 27.31 16.17 24.79 13.77

124, 128 0.86, 0.88 6.25 7.81 4.34

180, 170 1.24, 1.17 8.00 10.02 5.57

340, 300 2.34, 2.07 9.50 11.92 6.62

II-5-F 340, 380 2.34, 2.62 10.50 13.18 7.32

530, 470 3.66, 3.24 11.50 14.44 8.02

680, 750 4.69, 5.17 12.75 16.00 8.89

960, 940 6.62, 6.48 14.00 17.58 9.77

1760, 1760 12.14, 12.14 16.42 ' 20.61 11.45

2480, 2400 17.10, 16.55 18.00 22.61 12.56

3200, 2920 22.07, 20.14 19.58 24.61 13.67

160, 160 1.10, 1.10 7.00 10.18 5.66

270, 300 1.86, 2.07 7.75 12.12 6.73

410, 530 2.83, 3.66 8.50 14.05 7.81

780, 900 5.38, 6.21 9.25 15.99 8.88

II-5-H 1440, 1320 9.93, 9.10 10.00 17.12 9.96

1960, 1960 13.52, 13.52 10.58 19.42 10.79

2800, 2600 19.31, 17.93 11.00 20.49 11.38

3800, 3520 26.21, 24.28 11.50 21.79 12.11

3440, 3400 23.72, 23.45 11.75 22.44 12.47

3920, 4080 27.03, 28.14 12.00 22.08 12.82

78
SERIES

PENETRATION[ READINGS AGE MATURITY

Cpsl) CMPa) (hours) (°F-days) (°C-days)

125, 160 0.86, 1.10 2.92 9.33 5.18

245, 360 1.69, 2.48 3.33 10.96 6.09

440, 400 3.03, 2.76 3.58 11.77 6.54

560, 580 3.86, 4.00 3.83 12.59 6.99

II-32-I 920, 1140 6.34, 7.86 4.25 13.92 7.73

1520, 1620 10.48, 11.17 4.75 15.35 8.53

2500, 2540 17.24, 17.52 5.33 16.87 9.37

3160, 3280 21.79, 22.62 5.92 18.38 10.21

4920, 4300 33.93, 29.66 6.42 19.72 10.96

4800 33.10 6.67 20.37 11.32

215, 220 1.48, 1.52 3.17 10.42 5.79

365, 365 2.52, 2.52 3.25 11.24 6.24

570, 580 3.93, 4.00 3.72 12.21 6.78

820, 810 5.66, 5.59 4.0 13.24 7.36

1140, 1260 7.86, 8.69 4.25 13.95 7.75

II-32-F 1590, 1400 10.97, 9.66 4.55 14.93 8.29

2640, 2440 18.21, 16.83 4.83 15.86 8.81

3560, 3400 24.55, 23.45 5.08 16.73 9.29

4160, 3880 28.69, 26.76 5.33 17.49 9.72

5240, - 36.14, - 5.62 18.41 10.23

155, 160 1.07, 1.10 3.42 10.50 5.83

270, 250 1.86, 1.72 4.03 12.08 6.71

430, 420 2.97, 2.90 4.50 13.28 7.38

680, 650 4.69, 4.48 4.92 14.35 7.97

890, 900 6.14, 6.21 5.33 15.41 8.56

II-32-H 1120, 1100 7.72, 7.59 5.67 16.26 9.03

1480, 1530 10.21, 10.55 6.17 17.53 9.73

2120, 2520 14.62, 17.38 6.58 18.60 10.33

2860, 3000 19.72, 20.69 6.92 19.46 10.81

3680, 3660 25.38, 25.24 7.42 20.76 11.53

79
APPENDIX B

COMPRESSIVE STRENGTH DATA

CUBE WEIGHT COMPRESSIVE STRENGTH AGE MATURITY

NUMBER (grams) (psi) (MPa) (days) (°F-day) (°C-day)

16 277 105 0.72

23 278 110 0.76

3 278 125 0.86

115 0.79 1.32 40.5 22.5

9 278 960 6.62

10 278 900 6.21

24 281 1000 6.90

955 6.59 3.45 112.6 62.6

11 280 1990 13.72

19 280 2135 14.72

22 281 2075 14.31

2065 14.24 6.98 229.5 127.5

I-5-H

14 279 3000 20.69

1 280 2900 20.00

4 278 2775 19.14

2890 19.93 13.30 435.7 242.1

15 279 3960 27.31

6 281. 4210 29.03

21 281 4340 29.93

4170 28.76 27.04 851.1 472.9

2 282 4875 33.62

18 281 5025 34.66

7 280 4740 32.69

4880 33.66 47.06 1437.8 798.8

12 282 5140 35.24

13 280 5110 35.34

5 280 5125 35.45

5125 35.34 67.14 2033.0 1129.4

9 276 250 1.72

4 276 255 1.76

2 277 260 1.79

255 1.76 1.00 43.8 24.3

22 283 1110 7.66

5 276 785 5.41

18 277 1055 7.28 2.08 92.4 51.3

985 6.79

21 281 2065 14.24

16 276 1960 13.52

14 279 1775 12.24

1935 13.34 4.54 194.3 108.0

80
CUBE WEIGHT COMPRESSIVE STRENGTH AGE MATURITY

SERIES NUMBER (grams) (psi) (MPa) (days) (°F-day) (°C-day)

20 281 3040 20.97

15 278 2525 17.41

10 278 2500 17.24

2690 18.55 9.00 387.2 215.1

13 280 3275 22.59

I-12-H 12 279 3160 21.79

7 . 281 3050 21.03

3160 21.79 19.00 812.9 451.6

23 283 4215 29.07

6 282 3400 23.45

1 280 3150 21.72

3590 24.76 31.96 1374.5 763.6

11 281 3900 26.90

24 282 4525 31.21

19 284 4575 31.55

4335 29.90 45.96 1980.3 1100.2

24 280 285 1.97

11 279 190 1.31

20 282 270 1.86

250 1.72 0.51 32.0 17.8

14 281 820 5.66

19 283 1185 8.17

21 283 1180 8.14

1060 7.31 1.15 73.3 40.7

3 279 1565 10.79

1 278 1525 10.52

I-23-H 16 283 2110 14.55

1735 11.97 2.40 153.7 85.4

8 278 2475 17.07

15 283 2400 16.55

13 281 2340 16.14

2405 16.59 5.04 319.0 177.2

22 283 3560 24.55

7 278 2725 18.79

23 283 3725 25.69

3340 23.03 10.01 632.0 351.1

9 278 3075 21.21

10 280 3250 22.41

6 280 3440 23.72

3255 22.45 21.00 1315.1 730.6

81
CUBE WEIGHT COMPRESSIVE STRENGTH AGE MATURITY

SERIES NUMBER (grams) (psi) (MPa) (days) (°F-day) (°C-day)

2 279 3365 23.21

18 282 4175 28.79

12 280 3165 21.83

3570 24.62 33.96 2114.1 1174.5

7 278 305 2.10

23 278 345 2.38

15 280 330 2.28

325 2.24 0.41 32.3 17.9

6 279 1010 6.97

1 278 1015 7.07

18 277 1065 7.34

1030 7.10 0.82 65.4 36.4

I-32-H 13 279 2025 13.97

2 280 1890 13.03

24 282 2100 14.48

2005 13.83 1.82 144.7 80.4

14 280 2875 19.83

19 280 2850 19.66

21 280 2875 19.83

2865 19.76 4.14 329.9 183.3

5 280 3525 24.31

3 281 3250 22.41

16 281 3375 23.28

3385 23.34 8.97 711.6 395.3

22 282 3990 27.52

9 280 3765 25.97

8 281 3765 25.97

3840 26.48 16.00 1269.0 705.0

10 279 3840 26.48 ’ 17 280 4060 28.00

12 281 3815 26.31

3905 26.93 25.82 2044.3 1135.7

15 283 315 2.17

6 281 275 1.90

21 284 325 2.24

305 2.10 0.26 25.5 14.1

82
CUBE WEIGHT COMPRESSIVE STRENGTH AGE MATURITY

SERIES NUMBER (grams) (psl) (MPa) (days) (°F-day) (°C-day)

9 284 1355 9.34

2 279 1190 8.21

18 283 1270 8.76

1270 8.76 0.60 59.4 33.0

3 280 2315 15.97

16 284 2260 15.59

13 283 2300 15.86

1-4 3-H

2290 15.79 1.42 141.2 78.5

22 288 3190 22.00

1 281 2985 20.59

12 285 3225 22.24

3135 21.62 3.17 313.1 174.0

10 286 3690 25.45

4 282 3360 23.17

23 286 3415 23.55

3490 24.07 5.99 591.5 328.6

20 284 3950 27.24

14 283 3750 25.86

7 284 3835 26.45

3845 26.52 12.99 1282.8 712.7

5 285 3960 27.31

24 285 3900 26.90

11 283 4100 28.28

3990 27.52 20.00 1975.8 1097.7

43 289 375 2.59

30 284 255 1.76

35 287 315 2.17

315 2.17 1.29 40.1 22.3

38 286 2380 16.41

28 286 2250 15.52

32 284 2150 14.83

2260 15.59 3.41 112.2 62.3

33 286 4240 29.24

37 287 4435 30.59

31 285 4050 27.93

4240 29.24 6.94 239.2 132.9

45 292 6590 45.45

39 289 6100 42.07

47 292 6725 46.38

6470 44.62 13.27 445.8 247.7

I-5-L 42 288 8675 59.83

34 288 8075 55.69

27 289 7725 53.28

8160 56.28 27.01 861.2 478.4

83
CUBE WEIGHT COMPRESSIVE STRENGTH AGE MATURITY

SERIES NUMBER (grams) (pst) (MPa) (days) (°F-day) (°C-day)

40 286 9040 62.34

44 292 9810 67.66

25 289 8160 56.28

9005 62.10 47.01 1452.1 806.7

48 291 9740 67.17

26 290 8675 59.83

46 293 9665 66. 66

9360 64.55 67.11 2033.0 1129.4

26 285 640 4.41

42 288 600 4.14

44 289 725 5.00

655 4.52 0.97 42.6 23.7

29 290 1915 13.21

38 288 2135 14.72

39 289 2235 15.55

2100 14.48 2.04 91.3 50.7

I-12-L 40 288 4200 28.97

25 288 3840 26.48

34 289 4060 28.00

4035 27.83 4.51 193.2 107.3

46 292 6575 45.35

43 290 6390 44.07

31 287 5965 41.14

6310 43.52 8.97 386.2 214.5

45 292 7790 53.72

47 291 8190 56.48

35 290 7690 53.03

7890 54.41 18.97 811.7 451.0

33 293 8365 57.69

28 287 8000 55.17

27 287 7313 50.43

7890 54.41 31.93 1373.6 763.1

48 292 9440 65.10

30 293 8800 60.69

36 292 8975 61.90

9070 62.55 45.93 1979.2 1099.6

8A
CUBE WEIGHT COMPRESSIVE STRENGTH AGE MATURITY

SERIES NUMBER (grams) (psi) (MPa) (days) (°F-day) (°C-day)

28 285 430 2.97

31 285 420 2.90

37 288 450 3.10

435 3.00 0.48 29.9 16.6

27 286 1855 12.79

48 292 2140 14.76

35 287 1920 13.24

1970 13.59 1.11 71.1 39.8

I-23-L 26 287 3775 26.03

25 287 3625 25.00

45 290 3700 25.51

3700 25.52 2.36 152.1 84.5

30 288 5875 40.52

46 292 6125 42.24

36 288 5525 38.10

5840 40.28 5.01 317.6 176.4

40 290 7150 49.31

43 292 7200 49.66

38 292 7175 49.48

7175 49.48 9.97 630.4 350.2

32 287 8140 56.14

33 287 8110 55.93

39 292 8600 59.31

8285 57.14 20.99 1314.1 730.1

47 293 8390 57.86

42 291 8850 61.03

34 289 8450 58.28

8565 59.07 33.92 2112.5 1173.6

44 290 715 4.93 ' 26 285 585 4.03

29 286 600 4.14

630 4.34 0.38 29.6 16.4

28 284 1915 13.21

25 285 1900 13.10

39 290 2195 15.14

2000 13.79 0.79 63.0 35.0

I-32-L 31 288 4040 27.86

37 289 3950 27.24

27 286 3775 26.03

3920 27.03 1.79 142.3 79.0

85
CUBE

NUMBER

WEIGHT

(grams)

COMPRESSIVE STRENGTH AGE

(days)

MATURITY

(psl) (MPa) (°F-day) (°C-day)

48 290 5850 40.34

35 291 5875 40.52

41 292 5825 40.17

5850 40.34 4.11 327.5 181.9

45 291 6975 48.10

30 288 6625 45.69

46 295 7365 50.79

6990 48.21 8.94 709.4 394.1

36 290 7465 51.48

40 291 7540 52.00

43 293 7865 54.24

7620 52.55 15.97 1266.5 703.6

38 290 7815 53.90

33 287 7550 52.07

42 292 7750 53.45

7705 53.14 25.79 2041.9 1134.4

27 290 390 2.69

45 294 485 3.34

39 293 475 3.28

450 3.10 0.22 21.3 11.8

40 292 2575 17.76

30 290 2475 17.07

38 294 2590 17.86

2545 17.55 0.56 55.8 31.0

35 292 4540 31.31

44 295 4660 32.14

26 292 4490 30.97

4565 31.48 1.38 137.5 76.4

37 296 6175 42.59

42 292 5775 39.83

28 293 6040 41.66

5995 41.34 3.13 309.4 171.9

33 293 6290 43.38

48 295 6450 44.48

25 292 6410 44.21

6385 44.03 5.95 587.8 326.6

31 292 6950 47.93

29 293 7250 50.00

47 297 8075 55.69

7425 51.21 12.94 1278.7 710.4

46 297 8350 57.59

36 293 7475 51.55

34 296 7950 54.83

7925 54.66 19.96 1971.4 1095.2

86
CUBE WEIGHT COMPRESSIVE STRENGTH AGE MATURITY

SERIES NUMBER (grams) (psi) (MPa) (days) (°F-day) (°C-day)

4 286 540 3.72

8 287 615 4.24

13 289 690 4.76

615 4.24 0.95 42.2 23.4

5 290 3575 24.66

12 289 3990 27.52

18 • 289 4390 30.28

II-5-I

3985 27.48 2.90 164.8 91.6

3 287 6640 45.79

11 290 7450 51.38

17 289 7985 55.07

7360 50.76 8.18 487.4 270.8

6 290 8890 61.31

10 289 9375 64.66

16 288 9825 67.76

9365 64.59 19.87 1205.1 669.5

1 288 9325 64.31

7 288 9665 66.66

13 292 10375 71.55

9790 67.52 34.01 2072.5 1151.4

1 287 370 2.55

8 288 445 3.07

18 286 575 3.97

460 3.17 1.13 42.6 23.6

5 287 3140 21.66

9 289 3560 24.55

17 287 4050 27.93

3585 24.72 3.06 164.3 91.3

II-5-F

4 287 6250 43.10

11 289 6650 45.86

16 288 7950 54.83

6950 47.93 8.36 487.7 270.9

3 292 8190 56.48

10 290 8685 59.90

13 290 9090 62.69

8655 59.69 20.05 1205.6 669.8

6 288 8350 57.57

12 292 9575 66.03

15 289 9950 68.62

9290 64.07 34.18 2073.0 1151.7

87
SERIES

CUBE

NUMBER

WEIGHT

(grams)

COMPRESSIVE STRENGTH AGE

(days)

MATURITY

(psi) (MPa) (°F-day) (°C-day)

3 286 560 3.86

12 287 665 4.59

15 287 885 5.90

695 4.79 0.78 40.7 22.6

1 289 3340 23.03

7 287 3890 26.83

13 288 4475 30.86

3900 26.90 2.70 161.7 89.8

4 289 6150 42.41

8 287 6750 46.55

II-5-H 18 287 7325 50.52

6740 46.48 8.01 485.9 270.0

6 288 7925 54.66

•

11 290 8140 56.14

17 288 8935 61.62

8335 57.48 19.70 1203.8 668.8

5 290 9015 62.17

9 287 9060 62.48

16 289 9825 67.76

9300 64.14 33.84 2071.5 1150.8

6 291 705 4.86

9 289 740 5.10

17 291 840 5.79

760 5.24 0.60 40.8 22.7

3 292 3760 25.93

11 292 3700 25.52

II-32-I 16 292 4090 28.21

3850 26.55 2.35 149.4 83.0

1 291 6550 45.17

10 291 6225 42.93

13 292 6715 46.31

6495 44.79 8.02 498.6 277.0

4 294 8025 55.34

8 290 7850 54.14

15 294 8125 56.03

8000 55.17 20.05 1235.6 686 .

5 293 8515 58.72

7 291 8400 57.93

18 292 8525 58.79

8480 58.48 31.34 1929.7 1072.1

88
CUBE WEIGHT COMPRESSIVE STRENGTH AGE MATURITY

SERIES NUMBER (grams) (psi) (MPa) (days) (°F-day) (°C-day)

5 289 730 5.03

11 289 725 5.00

13 291 820 5.66

760 5.24 0.57 39.2 21.8

3 289 3860 26.62

10 289 3575 24.66

18 293 4075 28.10

- 3840 26.48 2.31 148.3 82.4

6 292 6625 45.69

12 291 6590 45.45

17 292 6860 47.31

6690 46.14 7.99 497.3 276.3

II-32-F

1 290 7140 49.24

7 292 7985 55.07

16 293 8135 56.10

7755 53.48 20.01 1234.3 685.7

4 292 8325 57.41

8 293 8590 59.24

15 292 8525 58.79

8480 58.48 31.31 1928.2 1017.2

3 288 615 4.24

11 288 660 4.55

13 292 695 4.79

655 58.48 0.62 40.0 22.2

1 290 3815 26.31

10 290 3690 25.45

18 295 3810 26.28

3770 45.17 2.27 143.8 79.9

II-32-H

4 292 6300 43.45

8 292 6775 46.72

17 295 6575 45.34

6550 45.17 7.95 493.4 274.1

5 292 7725 53.28

12 290 7175 49.48

16 296 8275 57.07

7725 53.28 19.98 1230.5 683.6

6 292 8590 59.24

7 292 8600 59.31

13 295 8415 58.03

8535 58.86 31.27 1930.6 1072.5

8y
,ai

- NBS-114A (REV. 2-ec) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET {See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 81-2244

2. Performing Orgaui. Report No.| 3. Publication Date

March 1981

4. TITLE AND SUBTITLE

Temperature Effects on the Strength-Maturity

Relation of Mortar

5. AUTHOR(S)

Nicholas J. Carino

6. PERFORMING ORGANIZATION (if joint or other than NBS, see instructions)

national bureau of standards

DEPARTMENT OF COMMERCE.

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or iess factual summary of most significant information. If document includes a significant

bibliography or iiterature survey, mention it here) A Study was performed to gain a fundamental understanding of the traditional

maturity method used to predict the in-place strength of concrete. Reserach was undertaken to answer two questions: 1) What are the quantitative effects of curing

temperature on the compressive strength-^naturity relation of concrete? 2) Is there an age beyond which temperature no longer affects the strength-maturity relation of

concrete? To simplify testing, mortar cubes were used as specimens for compressive

strength determinations. Penetration resistance measurements were performed to

determine initial and final setting times. Phase I of the research addressed the

first question and involved preparing and curing specimens at 5°, 12°, 23°, 32° and

43°C. Phase II addressed the second question and involved curing specimens at 5°

and 32°C for short periods, followed by additional curing at 23°C. It was found

that initial set occurred at approximately the same maturity regardless of the

curing temperature. A three-parameter hyperbolic equation was used to represent the

strength-maturity relation. The parameters, determined by regression analysis, were

found to vary systematically with curing temperature. Theoretical justification for

the hyperbolic equation is presented and a key assumption in the maturity method is

identified. The strength versus age data were also analyzed and a new concept,

effective age, is suggested as a possible alternative for representing the combined

effects of time and temperature on the compressive strength development of concrete

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

concrete; compressive strength; curing temperature; early age; final set; hydration;

initial set; laboratory testing; maturity; mortar; regression analysis; strength

prpd^r^^r>n; ^ Pinppratiirp

13. AVAILABILITY

feci U niimited

I I For Official Distribution, Do Not Release to NTIS

I I Order From Superintendent of Documents, U.S, Government Printing Office, Washington, D.C. 20402.

Order From National Technical Information Service (NTIS), Springfield, VA, 22161

14. NO. OF

PRINTED PAGES

98

15. Price

$ 9.50

USCOMM-DC 6043-P80 Ml