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  • 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 © IAEME: www.iaeme.com/ijciet.asp Journal Impact Factor (2013): 5.3277 (Calculated by GISI) www.jifactor.com 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 1
  • 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 2
  • 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 3
  • 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 4
  • 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. 5
  • 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 6
  • 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 7
  • 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) 8
  • 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 ) 9
  • 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 10
  • 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. 2. Elements of X-ray diffraction (Second edition) by B.D.Cullity, department of metallurgical engg. and material science, university of Notre Dame. Hand book of analytical techniques in concrete science and technology. Principles, technique and applications by V.S.Ramachandran and James.J.Beaudoin. Institute for research in construction. National research council Canada Ottawa, Ontario, Canada. 11
  • 12. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 5, Issue 1, January (2014), © IAEME 3. Svinning,K, Bremseth,S.K and Justnes, H.x-Ray diffraction studies on variations in microstructures in Portland clinker correlated to variations in production conditions in the Kiln, Proc.18th international cement micros. page 382-403(1996). 4. Abbas S. Al-Ameeri, K.A.Al- Hussain and M.S Essa, “Constructing a Mathematical Models to Predict Compressive Strength of Concrete from Non-Destructive Testing”, International Journal of Civil Engineering & Technology (IJCIET), Volume 4, Issue 4, 2013, pp. 1 - 20, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316. 5. Current applications of X-ray diffraction residual stress measurement by Paul.S.Prevey, Lambda research in ASM international ,materials park, OH,1996, pp 103-110. 6. Comparative study of residual stress measurement methods on CVD diamond films by J.G.Kim and Jin Yu. Advanced institute of science and technology, department of materials science and engg. P.O.Box 305-701, Kusung-Dong 373-1, Taejon, Korea. 7. Dr. K.V.Ramana Reddy, “Non- Destructive Evaluation of In-Situ Strength of High Strength Concrete Structures”, International Journal of Civil Engineering & Technology (IJCIET), Volume 4, Issue 4, 2013, pp. 21 - 28, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316. 8. X-ray diffraction study of the single crystal elastic modulii of Fe up to 30GPa by Sebastein Merkel, Jinflu Shu, Philippe Gillet in journal of geophysical research published on 13 May 2005. 9. Adil M. Abdullatif and Tareq S. Al-Attar, “Structural Behavior of Reed: Evaluation of Tensile Strength, Elasticity and Stress-Strain Relationships”, International Journal of Advanced Research in Engineering & Technology (IJARET), Volume 4, Issue 1, 2013, pp. 105 - 113, ISSN Print: 0976-6480, ISSN Online: 0976-6499. 10. M.E Hilley, Ed. residual stress measurement by X-ray diffraction, SAE J784a, society of automotive engineers, Warrendak, PA, 1971, p.21-24. 11. Atomistic calculation of size effects on elastic coefficients in nanometer sized tungsten layers and wires by P.Villain, P.Beauchamp, K.F.Badwai, P.Goudeau, P.O.Renaut in January-2004. 12

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