Predicting a mathematical models of some mechanical properties of concrete from non destructive testing

Civil and Environmental Research
ISSN 2224-5790 (Paper) ISSN 2225-0514 (Online)
Vol.3, No.10, 2013

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Predicting a Mathematical Models of Some Mechanical
Properties of Concrete from Non-Destructive Testing
Abbas S. Al-Ameeri 1* Karrar.AL- Hussain 2 Madi Essa1
1.Civil, Engineering/ University of Babylon, Babylon City, Iraq
2.Civil, Engineering/University of Babylon, Al-Najaf City , Iraq
* E-mail of the corresponding author: abb68abb21@yahoo.com
Abstract
Nondestructive tests NDT are considered as a one of the methods of evaluation and quality control of concrete.
The fundamental aim of the present study is constructing a mathematical models to predict some mechanical
properties of concrete from Nondestructive testing, in addition the study of (NSC and HSC) properties (density,
compressive strength ,modulus of elasticity and modulus of rupture ) of concrete grade (20-100) MPa) by using
NDT methods namely; Schmidt Hammer test (RN )and Ultrasonic Pulse Velocity test ( UPV) with destructive
test methods at different four ages (7, 28, 56 and 90) days. This study used ready mixes (1:2:4 and 1:1.5:3) and
design mixes (C40, C50, C60, C70, C80, C90 and C100), in order to find the relationship between these properties. of
concrete with (RN and UPV), and compressive strength of concrete-combined NDT(RN and UPV) relationship,
for all mixes (as freelance and as group). The results of compressive strength for both types of concrete NSC and
HSC exhibit an increase with the increase of bulk density and time of curing. Also, the results show a good
correlation between compressive strength and (RN) and the relationship between the two is not affected by
maximum aggregate size (MAS). Also, a good correlation between compressive strength and Ultrasonic Pulse
Velocity (UPV) and The value of UPV in HSC increased 8% from 28 days to 90 days. Also, the results indicated
that the percentages of increase in relationship between static modulus of elasticity and compressive strength for
28 days to 90 days are 15% at low strength, 5.6% at high strength and the relationship between static modulus of
elasticity and rebound number for 28 days to 90 days is3.3%.The results indicate that the percentage of increase
in direct method to surfacing method of UPV for (7, 28, 56 and 90) days is (7%, 5%, 4% and 3.5%) respectively,
due to the higher the continuity of hydration of cement. Also, the pulse velocity of concrete is decreased by
increasing the cement paste, especially for concrete with high w/c.
Keywords— Nondestructive tests, Schmidt hammer test(RN), Ultrasonic pulse velocity test ( UPV) , Density ,
Compressive strength, modulus of elasticity , modulus of rupture.
1. Introduction
The concrete is a composite material that consists essentially of a binding medium within which are embedded
particles or fragments of aggregate. In hydraulic cement concrete the binder is formed from a mixture of
hydraulic cement and water[1],Concrete composites of (Cement ,Aggregates , Water and Admixtures ).
ormal strength concrete NSC is defined by American Concrete Institute (ACI committee 211.1 -02) [2] as
“concrete that has a specified average compressive strength of 40 MPa or less at 28 days” but should be not less
than 17 Mpa (ACI committee 318M-05) [3] and the high strength concrete HSC is defined by American
Concrete Institute (ACI committee 363R-97) [4] as “concrete that has a specified average compressive strength
of 41MPa or more at 28 days. The Mix proportions for HSC are influenced by many factors, including specified
performance properties, locally available materials, local experience, personal preferences and cost [5].
HSC mix proportioning is a more critical process than the design of normal strength concrete mixtures (ACI
Committee 363R-97) [4]. When developing mixture proportions for HSC, three fundamental factors must be
considered in order to produce a mix design satisfying its intended property requirements (mechanical properties
of the aggregates; mechanical properties of the paste and Bond strength at the paste-aggregate interfacial
transition zone) [6], [7] .
For many years in concrete practice, the most widely used test for concrete has been the compression test of
the standard specimens (cube or cylinder) . It is often necessary to test concrete structures after the concrete has
hardened to determine whether the structure is suitable for its designed use. Ideally such testing should be done
without damaging the concrete [8] . The tests available for testing concrete range from the completely nondestructive, where there is no damage to the concrete, through those where the concrete surface is slightly
damaged, to partially destructive tests, such as core tests and pullout and pull off tests, where the surface has to
be repaired after the testing. The range of properties that can be assessed using Non-destructive tests and
partially destructive tests. Nondestructive test define as the test which either do not alter the concrete or result in
superficial local damage [9], [8] .
Non-destructive testing can be applied to both old and new structures. For new structures, the principal
applications are likely to be for quality control or the resolution of doubts about the quality of materials or

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construction. The testing of existing structures is usually related to an assessment of structural integrity or
adequacy [10] .
In addition, in-situ NDT was introduced to supply the engineer with information on one or more of the
following properties of the structural material: in-situ strength properties, durability, density, moisture content,
elastic properties, extent of visible cracks, thickness of structural members having one face exposed, position of
the steel reinforcement and concrete cover over the reinforcement. Most emphasis has been placed on the
determination of in-situ strength and durability [11] .
Non-destructive tests and partially destructive tests is quite large and includes such fundamental parameters as
density, elastic modulus and strength as well as surface hardness and surface absorption, and reinforcement
location, size and distance from the surface. In some cases it is also possible to check the quality of workmanship
and structural integrity by the ability to detect voids, cracking and delaminating [10]one of types of Nondestructive test methods is Schmidt hammer test, In 1940S ERNst Schmidt, a Swiss engineer, developed a
device for testing concrete based upon the rebound principle, This device consists of the following main
components outer body, plunger, hammer, and spring. To perform the test, the plunger retracts against a spring
when pressed against the concrete surface and this spring is automatically released when fully tensioned, causing
the hummer mass to impact against the concrete through the plunger. The rebounding hammer moves the slide
indicator, which records the rebound distance. The rebound distance is measured on a scale numbered from (10
to 100) and is recorded as the rebound number indicated on the scale [12], [13] .
There are Factors influencing of the rebound test results, mix characteristics (cement type, cement content
and coarse aggregate type) and member characteristic (mass, compaction, surface type, age, surface carbonation,
moisture condition and stress state and temperature). The strength-rebound number relationship is depended on
many factors that are influence on test results which may empirically affect the relationship between
compressive strength and rebound number. Practically, it is agreed that there is no unique relationship between
concrete strength and rebound number. Many investigations have been done to obtain a relationship between
rebound number and compressive strength, locally (Raouf and Samurai-99) [14] obtained an experimental
relationship to estimate concrete compressive strength using rebound number
f cu=0.74 RN 1.12
……… (1-1)
Where: fcu: Concrete compressive strength in MPa. (cube) , RN: rebound number.
(Hussam -08) [11] obtained a mathematical relationship between concrete compressive strength (fcu:) and
rebound number (RN), as follows:
……… (1-2)
f cu=- 65.33+2.38 RN
Where: fcu: Concrete compressive strength in Mpa. (cube), RN: Rebound number.
Another method of Nondestructive test is ultrasonic pulse velocity test( UPV).The UPV method is a stress
wave propagation method that involves measuring the travel time, over a known path length, of ultrasonic pulse
waves. The pulses are introduced into the concrete by a piezoelectric transducer and a similar transducer acts as
receiver to monitor the surface vibration caused by the arrival of the pulse. A timing circuit(t) is used to measure
the time it takes for the pulse to travel from the transmitting to the receiving transducers during the materials
path (L). The pulse velocity (V) is given by dividing path length (L) over transit time (t)
V=L / T
……… (1-3)
The presence of low density or cracked concrete increases the travel time which results in a lower pulse velocity.
The factors affecting on strength-pulse velocity relationship water/cement ratio (w/c), aggregate size, grading,
type, and content ,the concrete age, moisture condition, compaction ,curing temperature, path length, level of
stress [13] .
In estimation, the strength of in-situ the concrete strength from pulse velocity measurements, an empirical
relationship must be established on test specimens in the laboratory. In practice, it is generally agreed that there
is no unique relationship between concrete strength and UPV. There exist factors which may affect one
parameter only leading to existence of different relationships.
Locally (Raouf and Samurai-99)[14] obtained an experimental relationship to estimate concrete compressive
strength using rebound number.
fcu= 2.8 e 0.58V
……… (1-4)
Where: fcu: Concrete compressive strength in Mpa. (cube) , V: UPV in (km/sec)
(Hussam-08)[11] obtained a mathematical relationship between concrete compressive strength (fcu) in Mpa and
ultrasonic pulse velocity UPV, as follows:
fcu= 0.086 e 1.58V
………
(1-5)
Where: fcu in (Mpa) and V: UPV in (km/sec).
In many time used combined nondestructive test methods to estimate concrete strength. By combining
results from more than one NDT test, a multivariable correlation can be established to estimate strength.
Combined methods are reported to increase the reliability of the estimated strength. The underlying concept is

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that if the two methods are influenced in different ways by the same factor, their combined use results in a
canceling effect that improves the accuracy of the estimated strength. For example, an increase in moisture
content increases pulse velocity but decreases the rebound number. Locally (Raouf and Samurai -99)[14]
obtained an experimental relationship to estimate concrete compressive strength using combined rebound
number and ultrasonic pulse velocity at different ages (28, 60 and 90) days and by using statistical analysis
methods, the following relation was obtained:
fcu =0.93RN 0.63 e 0.31V
………..(1-6)
Where: fcu : in MPa , RN: Rebound number, V : UPV in (km/sec).
(Hussam -08)[11] obtained an experimental relationship to estimate compressive strength of concrete using
combined rebound number and ultrasonic pulse velocity. By method of multiple linear regression analysis using
(statistica-6.0) computer program, the following relation was obtained:
fcu =0.0031RN 1.65 V 2.075 ………..(1-7)
Where: fcu in (MPa), RN: Rebound number , V: UPV in (km/sec).
2. Experimental Works
This paragraph includes detailed information about description of material and mixes, mixing procedure,
casting and curing and testing are carried out on sample to achieve the aim of this study.
2.1. Materials
NSC and HSC are obtained by selecting suitable materials, good quality control and proportioning. The
material must be conforming to (ACIcommittee211.1-2002)[2]and (ACI committee 363R, 1997)[4] requirements.
2.1.1.Cement
Ordinary Portland cement (OPC) (Type I) was used in this study. The cement was produced by United
Cement Company “UCC”, commercially known as “Tasluja” produced in Al-Sulaymaniyah City. The physical
properties and chemical analysis of this cement were conformed with the
(I.Q.S. No.5 -84)
requirements [15] .
2.1.2 .Fine Aggregate (F.A)
Natural siliceous sand brought from (Al-Ukhaider) region was used in this study. the results showed that the
grading and sulfate content conformed to the (I.Q.S. No.45 -84 Zone2) [16].
2.1.3. Coarse Aggregate (C.A)
Coarse aggregate used in this study was cleaned, cubical, and 100% crushed gravel from (Al-Niba’ee)
region with two maximum size are used (14 , 20) mm. The grading of the aggregate with size (14mm) , (20mm)
and another properties were conformed to the (I.Q.S. No.45-84) [16] .
2.1.4. Silica fume (SF)
Silica fume used in this study was Turkey production , The physical properties and chemical composition of
SF were conformed to the chemical and physical requirements of (ASTM C1240 - 03) [17] .
2.1.5. Superplasticizer (SP)
To produce HSC with silica fume a high range water reducer was used. It was based on polycarboxylic ether
and had the trade mark “Glenium 51”. It was complied with (IQS No.1431-89)[18] and (ASTM C494-05)[19]
type F,
2.1.6. Water
Tap water was used for both mixing and curing of concrete in this work.
2.2. Concrete mixes
In order to achieve the scopes of this study, the work is divided into fifteen sets of concrete mixes, divided
into two sets (ready mixes and design mixes). Mix design for normal strength concrete was made using MAS
(20) mm using (ACI committee 211.1-02)[2] method , the details of the two mix groups are shown in Table 1.

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Table 1 Proportion of first set of mixtures
Mix
symbol

The mix proportion by Vol.

The mix proportion by weight

w/c

Slump (mm)

A1

1:2:4

(1:2.5:4.63)

0.60

5

A2

1:2:4

(1:2.5:4.63)

0.576

10

A3

1:2:4

(1:2.5:4.63)

0.55

15

A4

1:2:4

(1:2.5:4.63)

0.525

20

B1

1:1.5:3

(1:1.91:3.5)

0.45

5

B2

1:1.5:3

(1:1.91:3.5)

0.427

10

B3

1:1.5:3

(1:1.91:3.5)

0.40

15

B4

1:1.5:3

(1:1.91:3.5)

0.375

20

C40

1:0.97:1.8

(1:1.17:2.2)

0.42

75-100

C50

1:0.88:1.68

(1:1.1:2.02)

0.38

75-100

Mix design for high strength concrete was depended on replacement SF (15) % by weight of cement were
used, and using (ACI committee 211.4R)[20] and (ACI committee 211.1R)[21] to choose air content reduced by
one percent by (Holland -05)method [22] .
The initial dosages of superplasticizer depending on slump test result [23] . The MAS of coarse aggregate was
used (14mm), the Table 2 shows the proportion of mixes of high strength concrete .
Table 2 Proportion of second set of mixtures
Mix
Symb
ol
C60
C70
C80
C90
C100

The mix proportion by
weight

Cement
kg/m3

SF
kg/m3

HRWR % wt of
Cementitious

w/(c+p)

Slump (mm)

1:1.07:2.03
1:1.04:1.97
1:0.96:1.82
1:1.24:2.13
1:1.28:2.20

527
543
585
468
442

------70
78

0.08
0.29
0.55
1.9
2.4

0.36
0.33
0.3
0.24
0.22

75-100
75-100
75-100
75-100
75-100

2.3. Casting and curing of test specimens
The molds used were cleaned, assembled and oiled. The concrete was cast in molds in three layers; each layer
compacted by using vibrating Table for adequate time to remove any entrapped air. In the second day the
specimens were demolded and put in water for curing at temperature (24+ 3) ◦C until the day of testing .
2.4 Testing fresh and harden concrete
2.4.1. Slump test
This test is used to determine the workability of concrete mixture according to (I.Q.S. No.354 -90) [24] by
using standard slump cone.
2.4.2. Schmidt hammer test
This test has been done according to (I.Q.S. No.325 -93)[25] on cubic specimens of (150 , 100) mm for NSC
and HSC respectively, edges which have been fixed by applying 7 MPa in a compression machine to avoid any
movement during this test
2.4.3.Ultrasonic pulse velocity test
This test has been done according to (I.Q.S. No.300 -91)[26] on cubic specimens of (150,100) mm for NSC
and HSC respectively, using transducers with frequency 54 kHz,
2.4.4.Compressive Strength
Standard cubes (150) mm for NSC and (100) mm for HSC are used according to (I.Q.S. No.284 -91)[27]. The
machine which used in the tests was one of the electronic type of 2000 kN capacity with (15 N/mm2/minute)
applied load rate.

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Density-kg/m3

3. Results and discussion
Both tests of Schmidt hammer rebound number and Ultrasonic pulse velocity are carried out simultaneously
mmer
on the same cubes of (150 and 100) mm for NSC and HSC respectively. All tests are carried out at (7, 28, 56 and
90) days.
3.1. The relationship between density and (RN and UP
UPV)
The density considered the measurement to describe the properties of concrete, increasing the density of
concrete produce increasing in the surface hardness of concrete, as the result caused increasing in value of
rebound number, and decrease the time of transference ultrasonic wave through the concrete, and consequently
he
increase in velocity of ultrasonic wave produce high strength of concrete, because decreasing the pores due to
using crushed aggregate, high content of cement and SF. The relationship between density and (rebound number
relationship
and Ultrasonic Pulse Velocity) is presented in Figure1,2 respectively for all mixes as group the strength from
(20-100) MPa.
2500
28-day
90-day
2450
2400
2350
D = 162.41ln(RN) + 1796.5
R² = 0.9861
9861
2300
D = 172.72ln(RN) + 1747
R² = 0.9939
2250
15

25

35

45

55
Rebound number

65

75

Figure 1 Relationship between Density and RN at (28
(28-90) days
2500
28-day
90-day

Density-kg/m3

2450
2400
2350

D = 134.98V + 1814.8
V
R² = 0.9287
9287

2300

D = 159.45V + 1680.1
V
R² = 0.8751
8751
2250
3.25

3.65
65

4.05

4.45

4.85

5.25

Ultrasonic pulse velocity-km/sec
Figure 2 Relations
Relationship between Density and (UPV) at (28-90) days
3.2. The Relationship between Compressive Strength and RN
The results show that the relationship between compressive strength and rebound number is different from mix
to other because the difference in properties of the mixes and (w/c) ratio. Also, the results show large similarity
properties
behavior of the mix (A1, A2, A3 and A4) and (B1, B2, B3 and B4) because it is ready mix and normal strength
and just difference is the changing in (w/c) ratio, and show similarity behavior of the mix (C40, C50 and C60),
similarity

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Compressive strength-MPa

and show similarity behavior of the mix(C70, C80, C90 and C100), as shown in Figure3.
110
100
90
80
70
60
50
40
30
20
10
0

1:1.91:3.5
fcu = 2.8789RN - 47.03

1:2.
.5:4.63

fcu = 3.6298RN - 83.197
fcu = 3.3032RN - 82.797
fcu = 2
2.7833RN - 74.533
15

25

35

45

55

65

75

Rebound number
Figure. 3 Relationship between Compressive strength RN at all ages for the mixes(1:2:4, 1:1.5:3, (C40, C50,
strength-RN
C60) and (C70, C80, C90, C100) at all ages.

Compressive Strength-MPa

The Figure 3 shows that the value of RN is affect by mix proportion of concrete, and increasing it because the
increasing coarse aggregate and concrete homogeneity, and this properties caused increasing hardness of
concrete. The Figure 4 shows the relationship between compressive strength of concrete and RN for the all
crete.
mixes at all ages.
After using statistical analyses by (SPSS.19) program, it could be found that the linear expressions are giving
higher coefficient of correlation than other expressions, the expression obtained from Figure 4 for (NSC and
HSC) at (28 and 90) days as follows , it was similar patteRN to those obtained by (Ayden & ect -10)[28]
100
28-day
90
90-day
80
70
60
50

fcu= 1.5896 N - 10.66
5896R
R² = 0.9732

40
30

fcu= 1.5676 N - 18.537
5676R
R² = 0.9644

20
10
0
10

20

30

40

50

60
Rebound number

70

Figure 4 The relationship between Compressive strength
strength-RN at (7, 28, 56, 90) day for all mixes
fcu=1.5676 RN –18.537
……... (3 -1)
at [28days ,R2=0.964]
fcu=1.5896 RN –10.66
……... (3
(3-2)
at[90days ,R2=0.973]
Where: fcu: Concrete compressive strength (cubic) in MPa,
RN: Rebound number. , R: Coefficient of
:
correlation.
3.3. Relationship between Compressive Strength and UPV
The pulse velocity is not related directly to compressive strength but it is agreed that as the concrete

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compressive strength increases, the pulse velocity increases
essive
increases[29]. Also, the results show large similarity behavior
of the mix (A1, A2, A3 and A4) and (B1, B2, B3 and B4) because it is ready mixed and normal strength and just
difference is with changing in (w/c) ratio, and show similarity behavior of the mix (C40, C50 and C60), and show
)
similarity behavior of the mix(C70, C80, C90 and C100), as shown in Figure5,the results show that the relationship
between compressive strength and UPV is large similarity behavior of the all mixes are increasing the UPV by
behavior
the increasing compressive strength of concrete and This increment is not linear and could be presented as
exponential relationship, this result is similar to result from (Ramazan, & etc -04) [30] .
From the Figure5 below which shows that the value of UPV is affect by optimum selection of mix proportion
e
for concrete, and increasing it because the increasing cement content and concrete homogeneity, and this
properties caused decreasing porosity of concrete
concrete.
115
105
95
85
75
65
55
45
35
25
15
5

1:1.91:3.5
1:2
2.5:4.63

2.5

3

3.5

4

4.5

5

5.5

Ultrasonic Pulse Velocity-km/sec
Figure. 5 the relationship between Compressive strength (UPV) for the all mixes (1:2:4, 1:1.5:3, (C40, C50, C60)
strength-(UPV)
and (C70, C80, C90, C100) at all ages.
The Figure 6 shows the relationship between compressive strength UPV for all mixes as group, for (2 , 90)
strength-UPV
(28
days.
The expressions which represent the relationship between compressive strength and UPV from Figure 6 for
(NSC and HSC) at (28 , 90) days.
fcu=0.5993 e 0.9981V
……….(3-3)
fcu=0.4736 e 1.10351V ……….(3-4)
4)
Where:
fcu in (MPa) and V:UPV in (km/sec).

at [28days ,R2=0.9755]
at [90days ,R2=0.9753]

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100
90

28-day

80

90-day

70
60
50
40
30

fcu = 0.4736 1.1035V
4736e

20
fcu= 0.5993 0.9981V
5993e

10
0
3

3.3

3.6

3.9

4.2

4.5

4.8
4

5.1



Figure 6 the relationship between Compressive strength (UPV) at all ages for the mixes (1:2:4, 1:1.5:3, (C40, C50,
strength-(UPV)
C60) and (C70, C80, C90, C100) at all ages.
3.4. Combined Non-destructive Tests
destructive
It is advantageous to use more than one method of NDT at a time, especially when a variation in properties of
concrete affects the test results in opposite directions. Such as the case with the presence of moisture in concrete:
case
an increase in the moisture content increases the UPV, but decreases the rebound number recorded by the
rebound hammer [31], [32] .
The using combination of test results of UPV and RN to estimate compressive strength of concrete. By method
strength
of multiple linear regression analysis using (SPSS.19) computer program to obtained mathematical expression,
graph it by (axcel.2010), it becomes easy to obtain an expression which represents the relation between UPV and
rebound number versus compressive strength.
und
The Figures 7, 8, 9 and 10 show for all mixes as the group at (28 and 90) days, the results are similar to the
results obtained from (Raouf and Samurai
Samurai-99[14] and Qasrawi-2000[33] ). The expressions can be expresse as
2000[33]
expressed
follows:
fcu=0.42 RN 0.63 e 0.58V
……….(3-5)
……….(3
at [28days , R2= 0.9929]
0.45 0.85V
fcu=0.25 RN
e
……….(3-6)
……….(3
at [90-days, R2= 0.9954]
Where:
fcu in (MPa), and V:UPV in (k
:UPV (km/sec).
120
110
100
90
80
70
60
50
40
30
20
10
0

UPV in km/sec

0

10

20

30

40

50

60

70

Rebound number
Figure 7 Curves for comp. strength of concrete and combined UPV and RN at 28 days

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Observed data MPa

Predicted vs. Observed values – 28 day
fcu = 0.42* R0.63 * exp(0.58*V)


Figure 8 Comparison of predicted comp. strength with measured comp. strength of concrete at age 28 days
130
120
110
100
90
80
70
60
50
40
30
20
10
0

UPV in km/sec

0

10

20

30

40

50

60

70

Rebound number
Figure 9 Curves for comp. strength of concrete and combined UPV and RN at 90 days
combined

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Observed Values MPa

Predicted vs. Observed values – 90 day
fcu= 0.25* R0.45 * exp (0.85*V)

Figure 10 Comparison of predicted comp. strength with measured comp. strength of concrete at age 90 days
Figures 11 and 12 show for all mixes as the group and for all ages, the results are similar to the results obtained
from (Raouf and Samurai-99)[14]. The expressions can be expressed, as follows:
at[All ages R2 = 0.9729]

fcu=0.44 RN 0.65 e 0.55V ……….(3-7)
Where:

fcu in (MPa) and V:UPV in (km/sec).


120
UPV in km/sec

100
80
60
40
20
0
0

10

20

30

50
60
70
Rebound number
Figure 11 Curves for comp. strength of concrete and combined UPV and RN at (all ages )
concrete

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Observed values MPa

Predicted vs. Observed values – at all age
fcu = 0.44* R 0.65 * exp (0.55*V)

Figure 12 Comparison of predicted comp. strength with measured comp. strength of concrete at all ages

Modulus of Elastisity-GPa

3.5. The relationship between Static Modulus of Elasticity &(Compressive Strength, RN & UPV)
The modulus of elasticity of concrete is one of the most important mechanical properties of concrete. It is
closely related to the properties of cement paste, the stiffness and volume of selected aggregate. The modulus of
elasticity of concrete increased for high contents of aggregate of high rigidity; whereas it decreases with the
contents
increase in hardened cement paste content and increasing porosity. The specimens were tested first by UPV
before being tested for static elastic modulus.
Figure 13 shows that the increasing of compressive strength leads to increasing in the modulus of elasticity.
easing
The result is similar to the result obtained from (Hussam
(Hussam-08)[11].
Figure 14 shows that the relationship between the modulus of elasticity and RN. This relation is similar to the
relation of modulus of elasticity with compressive strength [13]. The increasing in compressive strength of
concrete produces increasing in the modulus of elasticity and this property gives the increasing in value of RN
and UPV. Figure 15 shows the relationship between the modulus of elasticity and UPV. This relation is a linear
ationship
regression model .
60
55

28-day
day
90-day
day

50
45
40
35

Ec = 23.156
156ln(fcu) - 52.242
30
Ec = 24.16
16ln(fcu) - 55.691

25
20
15
15

25

35

45

55

65

75

85

95

105

compressive strength MPa
Figure 13 Relationship between compressive strength and static modulus of elasticity
The results indicate that the percentage of increase in static modulus of elasticity for 28 days to 90 days
static
was 15% at low strength to 5.6% at high strength due to the continuity of hydration of concrete.

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60
28-day

55

90-day
50
45
40
35
Ec= 30.913ln(RN) - 75.684
ln(RN)

30

Ec = 31.217ln(RN) - 75.522
ln(RN)

25
20
15

25

35

45

55

65

75

Rebound nember
Figure 14 Relationship between Rebound number and modulus of elasticity
The relationship in Figure 15 indicates that the percentage of increase in relationship between Ec and RN for
28 days to 90days is 3.3% due to the continuity of hydration of concrete.

60
28-day
90-day

50
40
30

Ec = 24.238 (V) - 64
64.038
R² = 0.9881

20

Ec = 29.267 (V) - 90.
.933
R² = 0.9493

10
0
3.25

3.75
3

4.25

4.75

5.25

km/sec
Figure 15 Relationship between (UPV) and modulus of elasticity
The relationship in Figure 15 indicates that the percentage of increase in relationship between Ec and UPV
re
for 28 days to 90 days are 42% at low strength to 6.3% at high strength due to the continuity of hydration of
concrete and SF.
3.6. The relationship between Modulus of Rupture &(Compressive strength, RN and UPV)
Rupture
Results indicate that the two types of concretes NSC and HSC exhibited continuous increase in modulus of
rupture with an increase of curing age. However, the rate of modulus of rupture gain of concretes at early ages is
higher than those at later ages. It is well accepted that as the concrete compressive strength increases, the
well-accepted
modulus of rupture also increases but at a decreasing rate as shown in Figure 16.The relationship between
modulus of rapture and RN is similar to those obtained for compressive strength, except that the scatter of the
results is greater. These results are similar to the results obtained from (Malhotra &Carino -04) )[13]. as shown
in Figure 17. It is also well-accepted with the increase of UPV, the compressive strength increases and as a
accepted
increase
result the modulus of rapture but decreases with time lapse as shown in Figure 18.

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Modulus of Rupture -MPa

10
9

28-day

8

90-day

7
6
fr = 4.743ln(fcu) - 12.945
R² = 0.7991
7991

5
4
3

fr = 4.6755ln(fcu) - 12.878
R² = 0.8088
8088

2
1
0
0

20

40

60
80
100
Compressive Strength-MPa
MPa
Figure 16 Relationships between modulus of rupture and compressive strength
The relationship in Figure 16 shows that the results indicate the percentage of increase in the relationship
that
between fr and fcu for 28 days to 90 days is 3.6% due to the continuity of hydration of concrete.
10

Modulus of Rupture-MPa

9

28-day

8

90-day

7
6
5

fr= 6.9274ln(RN) - 20.14
ln(RN)
R² = 0.9173
9173

4
3

fr= 7.0597ln(RN) - 20.45
ln(RN)
R² = 0.9114
9114

2
1
0
0

20

40

60
80
Rebound number

Figure 17 Relationship between Rebound number and modulus of rupture
The Figure 17 shows the results which indicate that the percentage of increase in the relationship between
igure
fr and RN for 28 days to 90 days is 3.64% due to the continuity of hydration of concrete.

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5
28-day

4.75

90-day

4.5
4.25
4
3.75

v = 0.6705ln(fr) + 3.3944
ln(fr)
R² = 0.7645
7645

3.5

v = 0.8062ln(fr) + 2.9113
ln(fr)
R² = 0.8158
8158

3.25
3
0

1.5

3

4.5

6

7.5
9
Modulus of rupture
rupture-MPa

10.5

Compressive Strength -MPa

Figure 18 Relationship between (UPV) and modulus of rapture
The relationship in Figure 18 indicates that the percentage of increase in relationship between fr and UPV for 28
he
days to 90 days are 7.3% at low strength to 4.4% at high strength due to the continuity of hydration of concrete.
3.7. Relationship between direct (D) and surfacing (S) test of UPV
Indirect transmission should be used when only one face of the concrete is accessible, when the depth of a
surface crack is to be determined or when the quality of the surface concrete relative to the overall qual is of
quality
interest. Furthermore, this arrangement gives pulse velocity measurements which are usually influenced by the
concrete near the surface. This region is often of different composition from that of the concrete within the body
of a unit and the test results may be unrepresentative of that concrete. The indirect velocity is invariably lower
t
than the direct velocity on the same concrete element. This difference may vary from 5% to 20% depending
largely on the quality of the concrete under test [10], the relationship between direct and surfacing method of
UPV is shown in Figs. 19, 20 and 21.
80
7-direct
70
7-surfacing
60
50
40
30
20
10
0
2.5

3

3.5

4

4.5

km/sec
Figure 19 Relationship between direct and surfacing method of UPV at 7 days all mixes

91

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100
90

28-direct

80

28-surfacing

70
60
50
40
30
20
10
0
3

3.2

3.
.4

3.6

3.8

4
4.2
4.4
4.
.6
4.8
km/sec

Figure 20 Relationship between direct and surfacing method of UPV at 28 day all mixes
100

90

90-direct

80

90-surfacing

70
60
50
40
30
20
10
0
3.25

3.75

4.25

4.75

5.25

km/sec
Figure 21 Relationship between direct and surfacing method of UPV at 90 day all mixes
The Figures above show that the waves velocity of surfacing method less than the waves velocity of direct
method by (7, 5 and 3.5)% at (7, 28and 90) days respectively because the porosity of concrete that is near the
days
surface more than the porosity of deep concrete [10] [34] .
3.8. Effect the properties of concrete and the age on Non
Non-destructive tests
Since cement content, aggregate content and w/c ratio, may affect the readings obtained from RN and UPV,
any attempts to compare or estimate concrete strength will be valid only if they are all standardized for the
concrete under test and for the calibration specimens. These influences have different magnitudes. Figures 22
different
and 23 show the increase of the cement content results in the increase of cement paste and decrease of the
porosity. This property affected UPV greater than RN as the final results increase the value of RN and UPV [35].

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4.8
4.6
4.4
4.2
4
3.8
7-day
day
28-day
day
56-day
day
90-day
day

3.6
3.4
3.2
3
200

250

300

350

400

450

500
550
600
650
Cement content -kg/m3
kg/m
Figure 22 Relationship between UPV and cement content

Rebound Number

Figures 24 and 25 show that the increase of coarse aggregate content in concrete results in an increase the
density of concrete and in turn result in an increase in value of the UPV and RN.
55
50
45
40
35
30
7-day
7
28-day
28
56-day
56
90-day
90

25
20
15
200

300

400

500

600
700
Cement Content -kg/m3
Figure 23 Rela
Relationship between RN and cement content
In the Figures above, the increase of cement content increases the value of UPV without exceeding (500
kg/m3) because side effects, such as shrinkage increase ,porosity increase, need high water content and
consequently less strength of concrete. The RN increases with increase of the cement content but with less rate
when high content of cement is available.

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4.8
4.6
4.4
4.2

7-day
28-day
56-day
90-day

4
3.8
3.6
3.4
3.2
3
1000

1050

1100

1150

1200

1250
1300
1350
Coarse aggregate content
Figure 24 Relationship between UPV and aggregate content

Rebound Number

45
40
35

7-day
28-day
56-day
90-day

30
25
20
15
1000

1200
1250
1300
1350
Coarse aggregate content
content-kg/m3
Figure 25 Relationship between RN and aggregate content
In the Figures 24 and 25 above, it can be observed that the increase of coarse aggregate content produces
increase in the value of UPV and RN, and the rate of increasing seems at last ages because the difference value
of UPV and RN minimizes at last ages. The use of high content of coarse aggregate and crushed give the merger
N
between aggregate and the paste consequently gives high density of concrete which in turn produces an increase
of the UPV and RN value.
riation
Water/Cement ratio variation in concrete mixes has often been used to establish the relationship of (compressive
strength of concrete and ultrasonic pulse velocity) with w/c ratio, especially when checking the quality of
concrete at a particular age. The presence of water voids due to changes in the w/c ratio in fully compacted
voids
concrete, leads to a similar decrease in both strength and pulse velocity [36]. Figures 26 and 27 show the
relationship between (compressive strength and UPV) with w/c ratio.
1050

1100

1150

94

compressive strength -MPa

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7-day
28-day
56-day
90-day

100
80
60
40
20
0
0.1

0.2

0.3

0.4

0.5

0.6
0.7
W/C ratio

Figure 26 Relationship between compressive strength and w/c ratio
between


5.5
7-day
28-day
56-day
90-day

5

4.5

4

3.5

3
0.1

0.2

0.3

0.4

0.6
6
0.7
w/c %
Figure 27 Relationship between UPV and w/c ratio
Figures above exhibits that the increasing w/c ratio decreases compressive strength and UPV because
of the access in porosity of concrete and consequently decreases the compressive strength and give low UPV
decreases
[35]
4. Conclusion
Concretes with compressive strengths in excess of 60 N/mm2 are more easily achieved with SF.
High early compressive strength (in excess of 25 N/mm2 at 24 hours) can be achieved.
Linear expressions are obtained to represent the relationship between density and UPV for (28 and 90) days
ssions
respectively, as follows:
.........(4-1)
.........(4
[28-day, R2 = 0.9287]
D = 134.98(V)+1814.8
D = 159.45(V)+1680.1
.........(4-2)
.........(4
[90-day, R2 = 0.8751]
The results show a good correlation between compressive strength and rebound number and the relationship
between the two is not affected by maximum aggregate size (MAS)
Linear expressions are obtained to represent the relationship between compressive strength and RN for all
represent
mixes as group for (28 and 90) days respectively, as follows:
fcu = 1.5676 RN - 18.537 .........(4
.........(4-3)
[28-day, R2 = 0.964]
fcu = 1.5896 RN - 10.66
.........(4-4)
.........(
[90-day, R2 = 0.973]
The value of UPV in HSC increased 8% from (28 to 90) days because of using SF.
Exponential expressions are obtained to represent the relationship between compressive strength and UPV

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for 28 and 90days respectively, as follows:
fcu = 0.5993 e 0.9981 V
.........(4-5)
[28-day, R2 = 0.9755]
fcu = 0.4736 e 1.1035 V
.........(4-6)
[90-day, R2 = 0.9753]
The results indicate that the percentage of increase in direct method to surfacing method of UPV for (7, 28,
56 and 90) days are (7%, 5%, 4% and 3.5%) respectively, due to the higher the continuity of hydration of
cement.
The combined use of UPV and rebound number improves the accuracy of the process of estimation of
concrete compressive strength of (HSC).
The results show that the relation between UPV and RN versus compressive strength, can be expressed for
all the mix as a case freelance for all ages, as follows:
fcu = 0.37 RN 0.75 e 0.5V .........(4-7)
[all ages, R2 = 0.9908]
for (1:2:4)
fcu = 0.172 RN 0.7 e 0.75V .........(4-8)
[all ages, R2 = 0.994]
for (1:1.5:3)
fcu = 0.15 RN 0.47 e 0.95V .........(4-9)
[all ages, R2 = 0.8416] for (C40, C50 and C60)
fcu = 0.18 RN 1.33 e 0.17V ........(4-10)
[all ages, R2 = 0.962] for (C70, C80, C90 and C100)
The results show that the relation between UPV and rebound number versus compressive strength, can be
expressed for all the mix as group, for (28 and 90) days, as follows:
fcu = 0.42 RN 0.63 e 0.58V
.........(4-11)
[28-days, R2 = 0.9929]
fcu = 0.25 RN 0.45 e 0.85V
.........(4-12)
[90-days, R2 = 0.9954]
The results show that the relation between UPV and rebound number versus compressive strength, can be
expressed for all the mix as group, for all ages, as follows:
.........(4-13)
[all ages, R2 = 0.9729]
fcu = 0.44 RN 0.65 e 0.55V
The pulse velocity of concrete is decreased by increasing the cement paste, especially for concrete with high
w/c ratio.
The increasing of cement content gives increasing in value of UPV but not exceeded (500 kg/m3).
Rebound number can't be affected by changing MAS of coarse aggregate.
The increasing of coarse aggregate content produces increasing the value of RN and UPV.
References
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