1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 5, Issue 1, January (2014), pp. 01-12
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IJCIET
©IAEME
STRUCTURAL HEALTH MONITORING OF CONCRETE STRUCTURES
EVALUATING ELASTIC CONSTANTS AND STRESS-STRAIN
PARAMETERS BY X-RAY DIFFRACTION TECHNIQUE
Prof. N. K. DHAPEKAR
(Research Scholar, K.L.University Vijayawada, Andra Pradesh, India.
Assistant Professor, Head of Civil Engineering Department, K.I.T.E Raipur, Chhattisgarh India)
ABSTRACT
This research paper highlights the applicability of X-ray diffraction method to evaluate the
true and effective modulii of concrete ie; Young’s modulus of elasticity, Bulk modulus of elasticity
and modulus of Rigidity at different temperatures along with compressive strength or compressive
stress and strain. The aim of this study is to explore the possibilities of structural health monitoring
of concrete structures in different temperate regions through X-ray diffraction technique as compared
to the normal Non-Destructive methods like Rebound Hammer, Ultrasonic pulse velocity tests or destructive lab methods used in practice today. This paper consolidates the variation in true and effective modulii along with compressive strength and strain at very low temperate regions (upto 5 degree
Celsius), moderate temperate regions (up to 25 degree Celsius) to high temperate regions (upto 50
degree Celsius).
Key-Words: Structural Health Monitoring, Non-Destructive Method, X-Ray Diffraction,
Modulii of Elasticity, Stress, Strain.
1. INTRODUCTION
Normal laboratory tests (Destructive) are employed on concrete cubes or cylinders for
determining modulus of elasticity and compressive strength. For existing concrete structures as a part
of structural health monitoring of concrete structures various non-destructive tests are employed such
as Rebound hammer, Ultrasonic pulse velocity tests etc; This paper focuses on the study of
behaviour of concrete subjected to prolonged loading at different temperatures which has special importance in structural health monitoring of concrete structures as concrete is not truly elastic material
since it possess the ability to creep during and after the application of load. Modulii of concrete and
it’s corresponding compressive strength are required in the design calculations of concrete
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2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
structures. In the field of structural health monitoring of reinforced concrete structures it is extensively used in the form of modular ratio. There is an agreement on the increasing modulii of elasticity
with the increase in compressive strength of concrete. The equations published highlights the true
modulii and effective modulii at different temperatures. These equations predicts the compressive
strength and strain in concrete which are the key parameters for making decisions about it’s life duration. These equations enables to monitor the structural health of concrete structures in cold countries
(upto 5 degree Celsius) to high temperate regions (upto 50 degree Celsius). In this paper 5 grams of
two powder samples of 15cm x 15cm x 15cm cubes in unstressed condition (cube not subjected to
failure load in compressive testing machine) and stressed condition (cube subjected to failure load in
compressive testing machine) are taken and X-ray diffraction is carried out for M-20 grade normal
concrete.
2. X-RAY DIFFRACTION GRAPH AND PEAK LIST
2.1 M.20 Unstressed sample
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3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
2.2 Graphics M.20 unstressed sample
2.3 Peak List
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4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
2.4 Graphics M.20 stressed sample
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5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
3. MIX DESIGN CALCULATIONS (M-20 GRADE)
3.1. Cement
Cement Type/Brand/Make : OPC 43 Grade.IS:8112 Ultratech Cement Limited.
Specific Surface Area of Cement : 287 Kg./m2 as per IS8112:1989.
Standard Consistency : 28.00 as per IS 456:2000.
Initial Setting : 145 .Min-30 Minutes.
Final Setting: 240 . Maximum-600 Minutes.
Compressive strength in MPaa. 3 Days – 38.5 N/mm2 ( 23 min.-IS8112-2013 )
b. 7 Days – 50.5 N/mm2 ( 33 min. – IS8112-2013 )
c. 28 Days – 57.5 N/mm2 (43 min. – 58 Mpa max.)-IS8112-2013.
(CaO-0.70SO3)- 0.80 – 0.66 min- IS8112-1989
(2.8SiO2+1.2Al2O3+0.65Fe2O3)- 0.80 – 1.02 max.-IS8112-1989.
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6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
Chemical Requirements
Insoluble residue(%by mass)-2.53 (3 - min.-IS8112-1989).
Magnesia(% by mass) – 2.20 ( 6.0 – min.-IS8112-1989)
Sulphuric anhydride(% by mass) – 1.85 (3.0-max.-IS8112-1989)
Total loss of ignition(% by mass) – 1.85 (5.0 max.-IS8112-1989)
Total Chloride(% by mass) – 0.01 (0.10 max.-IS8112-1989)
Soundness –
Le-Chat Expansion(mm) – 1.00 (10 max-IS8112-1989)
Auto-Clave Expansion(%) – 0.140 ( 0.80 max.-IS8112-1989)
3.2 Fine and Coarse aggregates
3.2.1. Data on ingredients
OPC/PPC/PSC/RHC/HAC/SRC/LHC – Ultratech OPC-43 Grade (Hirmi Cement Works) –
Sp.Gravity – 3.13 – Mix Design Quantity – 350kg/Cum.
Fine Aggregate-I (Natural Sand) – Source Mahanadi – Sp.Gr. 2.63 – Water absorption 2.55Mix Design 791 Kg/Cu m.
Coarse Aggregate-III(20mm) – Mandir Hasaud/Khapri – Sp.Gr.2.79 – Water Absorption 1.05Mix Design 744Kg/Cu m.
Coarse Aggregate-IV(12.5mm)-Mandir Hausad/Khapri-Mix Design 0Kg/Cu m.
Coarse Aggregate-IV(10mm)-Mandir Hausad/Khapri-Sp.Gr. 2.78-Water Absorption-1.55-Mix
Design 399 Kg/Cum.
Water-Source is Borewell-Sp.Gravity 1.00 –Mix Design 175 Kg/Cu m.
Density of concrete per cubic meter is 2460.2 Kg/m3.
3.2.2 Mix Code
Characteristic strength at 28 days(N/mm2)-20
Standard Deviation(N/mm2)-5.0(As per IS456 2000)
Value of ‘ t ‘ – 1.65 (As per IS456 2000)
Target mean strength at 28 days(N/mm2)-28.25
Workability in terms of slump(mm)-100+/-15
Exposure condition – moderate.
Min.Cementetious content(Kg/Cum)-350.
Max.water cement ratio-0.50
Nominal max.size of aggregates(mm)-20
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7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
3.3 Strength Analysis
No.of Days
473
21.02
8165
468
20.80
469
20.84
8135
543
24.13
8255
549
24.40
8200
542
24.09
8220
28 Days
Compressive Strength
(N/mm2)
8180
7 Days
Load in
KN.
8105
3 Days
Wt.in
grams.
657
29.20
8180
645
28.70
28 days results as on 08.09.2013
4. TRUE MODULII OF ELASTICITY
4.1 Low temperate regions (up to 5 degree Celsius)
β Cos θ = ( K . λ ) / Dwhere
β = FWHM (⁰ 2 Th.) = 0.0836 (Refer 2.3)
2θ = Pos. (⁰ 2 Th.) = 26.5668 (Refer 2.3)
θ = 13.28⁰
λ = 1.54 K-Alpha 2 [A⁰] (Refer 2.1) K = 0.90
D = (K . λ ) / (β Cos θ )
D = (0.90 x 1.54) / ( 0.0836 x Cos 13.28)
D = 17.00 A⁰ = Particle size in A⁰.
For true modulus of elasticity ( E ) ,
β Cosθ =(K λ / D)+{4Sinθ[2CPtµ3]0.5}/E0.5
CP = Enthalpy
t =Temperature in⁰ Kelvin=273+5=278⁰K
µ = Poisson’s ratio = 0.18
0.0836 Cos13.28 = ( 0.90 x 1.54 / 17.0) + {4Sin13.28[2 x 879 x 278 x 0.183]0.5}/ E0.5
0.0813=0.0815+{0.9188[53.387]}/ E0.5
-2 x 10-4 = 49.051 / E0.5
E true = 6.015 x 1010 N/m2 where
E = 2G ( 1+µ ) = 3K (1-2µ )
G = Modulus of rigidity.
K = Bulk modulus of elasticity.
Gtrue = ( 6.015 x 1010 ) / 2 ( 1+ 0.18)
Gtrue = 2.548 x 1010 N/m2
Ktrue = 6.015 x 1010 / 3(1 - 2µ )
Ktrue = 3.132 x 1010 N/m2
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8. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
4.2 Moderate temperate regions (up to 25 degree Celsius)
D = (K . λ) / (β Cos θ )
D = (0.90 x 1.54) / (0.0836 x Cos 13.28)
D = 17.00 A⁰ = Particle size in A⁰.
For true modulus of elasticity,
β Cosθ =(K λ / D)+{4Sinθ[2CPtµ3]0.5}/E0.5
CP = Enthalpy
t =Temperature in⁰ Kelvin=273+25=298⁰K
µ = Poisson’s ratio = 0.18
0.0836 Cos13.28 = (0.90 x 1.54 / 17.0) + {4Sin13.28[2 x 879 x 298 x 0.183]0.5}/ E0.5
0.0813=0.0815+{0.9188[55.274]}/ E0.5
-2 x 10-4 = 50.785 / E0.5
E true = 6.447 x 1010 N/m2 where
E = 2G (1+µ) = 3K (1-2µ )
G = Modulus of rigidity.
K = Bulk modulus of elasticity.
Gtrue = 2.731 x 1010 N/m2
Ktrue = 3.357 x 1010 N/m2
4.3 High temperate regions (up to 50 degree Celsius)
D = (K . λ) / (β Cos θ)
D = (0.90 x 1.54) / (0.0836 x Cos 13.28)
D = 17.00 A⁰ = Particle size in A⁰.
For true modulus of elasticity (E),
β Cosθ =(K λ / D)+{4Sinθ[2CPtµ3]0.5}/E0.5
CP = Enthalpy
t =Temperature in⁰ Kelvin=273+50=323⁰K
µ = Poisson’s ratio = 0.18
0.0836 Cos13.28 = (0.90 x 1.54 / 17.0) + {4Sin13.28[2 x 879 x 323 x 0.183]0.5}/ E0.5
0.0813=0.0815+{0.9188[57.546]}/ E0.5
-2 x 10-4 = 52.873 / E0.5
E true = 6.988 x 1010 N/m2 where
E = 2G ( 1+µ ) = 3K (1-2µ )
G = Modulus of rigidity.
K = Bulk modulus of elasticity.
Gtrue = 2.961 x 1010 N/m2
Ktrue = 3.639 x 1010 N/m2
5. EFFECTIVE MODULII OF ELASTICITY
5.1 Low temperate regions (up to 5 degree Celsius)
β Cos θ = ( K . λ ) / Dwhere
β = FWHM (⁰ 2 Th.) = 0.0669 (Refer 2.4)
2θ = Pos. (⁰ 2 Th.) = 26.7827 (Refer 2.4)
θ = 13.39⁰
λ = 1.54 K-Alpha 2 [A⁰] (Refer 2.4)
K = 0.90 ( )
D = ( K . λ ) / (β Cos θ )
D = ( 0.90 x 1.54 ) / ( 0.0669 x Cos 13.39)
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9. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
D = 21.2 A⁰ = Particle size in A⁰.
For effective modulus of elasticity,
β Cosθ =(K λ / D)+{4Sinθ[2CPtµ3]0.5}/E0.5
CP = Enthalpy
t =Temperature in⁰ Kelvin=273+5=278⁰K
µ = Poisson’s ratio = 0.18
0.0669 Cos13.39 = (0.90 x 1.54 / 21.2) + {4Sin13.39[2 x 879 x 278 x 0.183]0.5}/ E0.5
0.0650=0.0653+{0.9263[53.387]}/E0.5
-3.000 x 10-4 = 49.452 / E0.5
E effective = 2.717 x 1010 N/m2 where
E = 2G ( 1+µ ) = 3K (1-2µ )
G = Modulus of rigidity.
K = Bulk modulus of elasticity.
Geffective = 1.151 x 1010 N/m2
Keffective = 1.415 x 1010 N/m2
5.2 Moderate temperate regions (up to 25 degree Celsius)
D = (K . λ ) / (β Cos θ )
D = (0.90 x 1.54) / (0.0669 x Cos 13.39)
D = 21.20 A⁰ = Particle size in A⁰.
For effective modulus of elasticity,
β Cosθ =(K λ / D)+{4Sinθ[2CPtµ3]0.5}/E0.5
CP = Enthalpy
t =Temperature in⁰ Kelvin=273+25=298⁰K
µ = Poisson’s ratio = 0.18
0.0669 Cos13.39 = ( 0.90 x 1.54 / 21.2) + {4Sin13.39[2 x 879 x 298 x 0.183]0.5}/ E0.5
0.0650=0.0653+{0.9263[55.274]}/E0.5
-3 x 10-4 = 51.200 / E0.5
E effective = 2.912 x 1010 N/m2 where
E = 2G ( 1+µ ) = 3K (1-2µ )
G = Modulus of rigidity.
K = Bulk modulus of elasticity.
Geffective = 1.234 x 1010 N/m2
Keffective = 1.517 x 1010 N/m2
5.3 High temperate regions (up to 50 degree Celsius)
D = (K . λ ) / (β Cos θ )
D = (0.90 x 1.54) / (0.0669 x Cos 13.39)
D = 21.20 A⁰ = Particle size in A⁰.
For true modulus of elasticity (E),
β Cosθ =(K λ / D)+{4Sinθ[2CPtµ3]0.5}/E0.5
CP = Enthalpy
t =Temperature in⁰ Kelvin=273+50=323⁰K
µ = Poisson’s ratio = 0.18
0.0669 Cos13.39 = (0.90 x 1.54 / 21.2) + 4Sin13.39[2 x 879 x 323 x 0.183]0.5}/ E0.5
0.0650=0.0653+{0.9263[57.546]}/E0.5
-3.00 x 10-4 = 53.304 / E0.5
E effective = 3.157 x 1010 N/m2 where
E = 2G ( 1+µ ) = 3K (1-2µ )
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10. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
G = Modulus of rigidity.
K = Bulk modulus of elasticity.
Geffective = 1.337 x 1010 N/m2
Keffective = 1.644 x 1010 N/m2
5.4 M.20 grade concrete
Sr
No.
True modulii of concrete
Temp
E ( N/m2 )
G ( N/m2 )
K ( N/m2 )
1
5⁰ C
6.015 x 1010
2.548 x 1010
3.132 x 1010
2
25⁰ C
6.447 x 1010
2.731 x 1010
3.357 x 1010
3
50⁰ C
6.988 x 1010
2.961 x 1010
3.639 x 1010
Effective modulii of concrete
E ( N/m2 )
G ( N/m2 )
K ( N/m2 )
4
5⁰ C
2.717 x 1010
1.151 x 1010
1.415 x 1010
5
25⁰ C
2.912 x 1010
1.234 x 1010
1.517 x 1010
6
50⁰ C
3.157 x 1010
1.337 x 1010
1.644 x 1010
5.5 Stress calculations
Only particular set of grains contributes to particular hkl reflection.
d = 1.03246 A⁰ @ 2θ = 96.5044⁰
do = 1.03468 A⁰ @ 2θ = 96.2292⁰
Strain = (d – do) / d0
€ = (1.03246- 1.03468) / 1.03468
€ = -2.145 x 10-3
Stress = € x Keff.
Stress= (-2.145 x 10-3) x (1.415 x 1010)
Stress= -30.351 x 106 N/m2
Stress= -30.351 N/mm2
@ 5 degree Celsius
Stress = € x Keff.
Stress=( -2.145 x 10-3 ) x (1.517 x 1010 )
Stress= -30.351 x 106 N/m2
Stress= -32.539 N/mm2
@ 25 degree Celsius
Stress = € x Keff.
Stress=(-2.145 x 10-3) x (1.644 x 1010)
Stress= -35.263 x 106 N/m2
Stress= -35.263 N/mm2
@ 50 degree Celsius
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11. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
Negative sign is only because atomic spacing (d) is less in stressed condition as compared to
do ie; atomic spacing in A⁰ in unstressed condition. These stresses may also be called as compressive
strength after 28 days. So finally compressive strength after 28 days is tabulated below.
Stresses / Compressive strength after 28 days of curing by
X-Ray Diffraction Method
01.
Temperature
5⁰ C
25⁰ C
50⁰ C
02.
Stresses / Compressive Strength
in Mpa. By XRD method.
30.351
32.539
35.263
Stresses / Compressive strength after 28 days of curing by
Compression testing machine in lab
( Refer table 3.3)
01.
Temperature
5⁰ C
25⁰ C
50⁰ C
02.
Stresses / Compressive Strength
in Mpa.
-
28.95
-
(Average
strength.)
5.5 CONCLUSION
True and effective modulii of elasticity can be determined through X-ray diffraction
technique at different temperatures. The observed increase of elastic constants with increase in
temperature reflects strengthening of interatomic bonding. Larger values of true modulii of concrete
composition is due to large elastic energy as compared to effective modulii. Compressive strength
computed by X-ray diffraction technique is matching with the average compressive strength determined by Compressive testing machine (CTM).X-ray diffraction method can be implemented as a
alternative method for determining the compressive strength of concrete.
5.6 ACKNOWLEDGEMENTS
The authors would like to acknowledge the support of Indian Institute of Technology
Bombay for the X ray diffraction report of M.20 grade concrete powder.
5.7 REFERENCES
1.
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Hand book of analytical techniques in concrete science and technology. Principles, technique
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12. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME
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