Modelling of Thermal Effects due to Solar Radiation on Concrete ...
Modelling of Thermal Effects due to Solar Radiation on Concrete ...
Modelling of Thermal Effects due to Solar Radiation on Concrete ...
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<str<strong>on</strong>g>Modelling</str<strong>on</strong>g> <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>Thermal</str<strong>on</strong>g> <str<strong>on</strong>g>Effects</str<strong>on</strong>g> <str<strong>on</strong>g>due</str<strong>on</strong>g> <str<strong>on</strong>g>to</str<strong>on</strong>g> <str<strong>on</strong>g>Solar</str<strong>on</strong>g> <str<strong>on</strong>g>Radiati<strong>on</strong></str<strong>on</strong>g><strong>on</strong> C<strong>on</strong>crete PavementsAruna Karunarathne,University <str<strong>on</strong>g>of</str<strong>on</strong>g> Moratuwa, Sri Lankaarunak@uom.lkWasantha Mampearachchi,University <str<strong>on</strong>g>of</str<strong>on</strong>g> Moratuwa, Sri Lankawasanthak@civil.mrt.ac.lkAnura Nanayakkara,University <str<strong>on</strong>g>of</str<strong>on</strong>g> Moratuwa, Sri Lankasman@civil.mrt.ac.lkAbstractRate <str<strong>on</strong>g>of</str<strong>on</strong>g> heat flux from solar radiati<strong>on</strong>, thermal properties <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>crete and heat loss fromc<strong>on</strong>crete <str<strong>on</strong>g>due</str<strong>on</strong>g> <str<strong>on</strong>g>to</str<strong>on</strong>g> c<strong>on</strong>vecti<strong>on</strong> parameters <str<strong>on</strong>g>of</str<strong>on</strong>g> surroundings influence the temperature variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> anexposed c<strong>on</strong>crete slab. This paper describes a method <str<strong>on</strong>g>to</str<strong>on</strong>g> simulate the temperature variati<strong>on</strong> andcorresp<strong>on</strong>ding deformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>crete slab using 3D finite element model (FEM) approach.The pavement is idealized as a thin isotropic plate resting <strong>on</strong> a Winkler-type elastic foundati<strong>on</strong>.Since two-dimensi<strong>on</strong>al plate elements are limited <str<strong>on</strong>g>to</str<strong>on</strong>g> linear temperature distributi<strong>on</strong> through thethickness, eight (8) nodes brick element in ANSYS-12 was used for the FEM analysis <str<strong>on</strong>g>to</str<strong>on</strong>g> obtaintemperature variati<strong>on</strong>s throughout the surface and the thickness. An experimental investigati<strong>on</strong>was carried out <str<strong>on</strong>g>to</str<strong>on</strong>g> obtain the temperature variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>crete slab under solar radiati<strong>on</strong>.Daily temperature variati<strong>on</strong> across the depth <str<strong>on</strong>g>of</str<strong>on</strong>g> the slab and the solar heat flux <strong>on</strong> the slab werem<strong>on</strong>i<str<strong>on</strong>g>to</str<strong>on</strong>g>red using thermocouples, solar meter and IR filter. FEM results were verified using bythe experimental investigati<strong>on</strong>.Keywords: <str<strong>on</strong>g>Solar</str<strong>on</strong>g> radiati<strong>on</strong>, c<strong>on</strong>crete pavements, FEM, ANSYS
1. Introducti<strong>on</strong>Variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> the temperature pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile across a slab is well known and major cause <str<strong>on</strong>g>of</str<strong>on</strong>g> differentialthermal stresses and differential deformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>crete structures. <str<strong>on</strong>g>Thermal</str<strong>on</strong>g> stresses and dryingshrinkage stresses are the most important types <str<strong>on</strong>g>of</str<strong>on</strong>g> stresses developed in exposed slab. Thesestresses are very severe in rigid pavements in tropical countries. Deformati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> slabs andpavements can lead <str<strong>on</strong>g>to</str<strong>on</strong>g> structural failures, drop in load transfer efficiency, etc. Thereforedeterminati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> ultimate deformati<strong>on</strong> <str<strong>on</strong>g>due</str<strong>on</strong>g> <str<strong>on</strong>g>to</str<strong>on</strong>g> both solar radiati<strong>on</strong> and drying shrinkage isessential for determinati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> joint spacing for c<strong>on</strong>crete slab <str<strong>on</strong>g>to</str<strong>on</strong>g> provide a good load transfer.2. Background2.1 Review <str<strong>on</strong>g>of</str<strong>on</strong>g> literature <str<strong>on</strong>g>of</str<strong>on</strong>g> thermal behaviour <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>creteTom Burnham and Amir Koubaa in (2001) have measured temperature inside a c<strong>on</strong>crete slab <str<strong>on</strong>g>to</str<strong>on</strong>g>provide new approach for the coefficient <str<strong>on</strong>g>of</str<strong>on</strong>g> thermal expansi<strong>on</strong> and drying shrinkage. Mirambell(1990) studied temperature and stress distributi<strong>on</strong> in plain c<strong>on</strong>crete pavements under thermaland mechanical loads. A three-dimensi<strong>on</strong>al (3-D) model, employing 10 layers across the depth<str<strong>on</strong>g>of</str<strong>on</strong>g> the pavement, was used <str<strong>on</strong>g>to</str<strong>on</strong>g> introduce the effects <str<strong>on</strong>g>of</str<strong>on</strong>g> n<strong>on</strong>linear temperature distributi<strong>on</strong>s.Choubane and Tia (1992) presented an interesting technique for treating the n<strong>on</strong>linearity <str<strong>on</strong>g>of</str<strong>on</strong>g> thetemperature gradient. The temperature distributi<strong>on</strong> across the depth <str<strong>on</strong>g>of</str<strong>on</strong>g> the pavement wasdivided in<str<strong>on</strong>g>to</str<strong>on</strong>g> three comp<strong>on</strong>ents: (1) A comp<strong>on</strong>ent that causes axial displacement; (2) acomp<strong>on</strong>ent that causes the bending; and (3) the n<strong>on</strong>linear comp<strong>on</strong>ent. Furthermore, they deriveda quadratic equati<strong>on</strong> <str<strong>on</strong>g>to</str<strong>on</strong>g> represent the n<strong>on</strong>linear temperature distributi<strong>on</strong> throughout the depth <str<strong>on</strong>g>of</str<strong>on</strong>g>the pavement. Harik et al. (1994) developed a linear temperature distributi<strong>on</strong> that is equivalent<str<strong>on</strong>g>to</str<strong>on</strong>g> the n<strong>on</strong>linear <strong>on</strong>e in the sense that it yields the same axial force and moment. Ernest,Barenberg, Chetna Rao and Mark Snyder (2001) found the temperature variati<strong>on</strong> across a slabfrom early age <str<strong>on</strong>g>to</str<strong>on</strong>g> l<strong>on</strong>g term c<strong>on</strong>diti<strong>on</strong>.2.2 C<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> the temperature variati<strong>on</strong> in exposed c<strong>on</strong>crete slabPavements slabs have large <str<strong>on</strong>g>to</str<strong>on</strong>g>p surface area than the surrounding area. <str<strong>on</strong>g>Solar</str<strong>on</strong>g> heat flux directlydrops <strong>on</strong> the surface and heat up the body. Heat dissipati<strong>on</strong> occurs by the c<strong>on</strong>vecti<strong>on</strong> processthrough the surrounding surfaces and part <str<strong>on</strong>g>of</str<strong>on</strong>g> the heat transfer <str<strong>on</strong>g>to</str<strong>on</strong>g> the ground through the bot<str<strong>on</strong>g>to</str<strong>on</strong>g>msurface. Figure 1 shows the c<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> this phenomen<strong>on</strong>.a)b)c)Figure 1: C<strong>on</strong>cept <str<strong>on</strong>g>of</str<strong>on</strong>g> the thermal behavior <str<strong>on</strong>g>of</str<strong>on</strong>g> exposed slaba) A typical ambient temperature variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> a day b) A typical <str<strong>on</strong>g>Solar</str<strong>on</strong>g> heat flux variati<strong>on</strong> in the day timec) Temperature variati<strong>on</strong> in the slab
There are many parameters govern the heat dissipati<strong>on</strong> process. Most sensitive fac<str<strong>on</strong>g>to</str<strong>on</strong>g>rs should beclearly identified and quantified <str<strong>on</strong>g>to</str<strong>on</strong>g> develop an effective model. Transient analysis in ANSYScan simulate the n<strong>on</strong>-linear properties <str<strong>on</strong>g>of</str<strong>on</strong>g> the models. Heat flux from solar radiati<strong>on</strong> and heatdissipati<strong>on</strong> through c<strong>on</strong>vecti<strong>on</strong> process <str<strong>on</strong>g>due</str<strong>on</strong>g> <str<strong>on</strong>g>to</str<strong>on</strong>g> ambient temperature vary with the timethroughout the day. Input heat flux from the solar radiati<strong>on</strong> should be measured <str<strong>on</strong>g>to</str<strong>on</strong>g> incorporatewith the FEM.3. Research significanceThe research provides a procedure <str<strong>on</strong>g>to</str<strong>on</strong>g> obtain temperature distributi<strong>on</strong> in a c<strong>on</strong>crete slab whichexposed <str<strong>on</strong>g>to</str<strong>on</strong>g> solar radiati<strong>on</strong>. Using the appropriate thermal properties <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>crete, the deformati<strong>on</strong><str<strong>on</strong>g>of</str<strong>on</strong>g> the slab <str<strong>on</strong>g>due</str<strong>on</strong>g> <str<strong>on</strong>g>to</str<strong>on</strong>g> solar radiati<strong>on</strong> values at the particular locati<strong>on</strong>s can be obtained from FEM forvaries thicknesses. It is important in designing joints and load transfer at n<strong>on</strong>-dowelled joints inrigid pavements. Amount <str<strong>on</strong>g>of</str<strong>on</strong>g> curling and warping <str<strong>on</strong>g>of</str<strong>on</strong>g> pavements can also be obtained using theFEM for varies lengths. The FEM approach is very helpful for proper designing <str<strong>on</strong>g>of</str<strong>on</strong>g> rigidpavements with less faulting, cracking and other distresses.4. Experimental investigati<strong>on</strong>4.1 C<strong>on</strong>structi<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> pro<str<strong>on</strong>g>to</str<strong>on</strong>g>type field slabA c<strong>on</strong>crete slab <str<strong>on</strong>g>of</str<strong>on</strong>g> 1 m x1 m with 150 mm thick was cast using grade 25 c<strong>on</strong>crete <strong>on</strong> compactedsoil (in-situ CBR <str<strong>on</strong>g>of</str<strong>on</strong>g> 25) in open ground <str<strong>on</strong>g>to</str<strong>on</strong>g> obtain uninterrupted solar radiati<strong>on</strong> throughout thedaytime. Orientati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> the sides <str<strong>on</strong>g>of</str<strong>on</strong>g> the slab was in N-E and S-W directi<strong>on</strong>s. Thermocoupleswere fixed <str<strong>on</strong>g>to</str<strong>on</strong>g> formwork and maintained at the center <str<strong>on</strong>g>of</str<strong>on</strong>g> the slab using n<strong>on</strong>-elastic andthermoplastic wires.4.2 Data acquisiti<strong>on</strong>A data logger was used <str<strong>on</strong>g>to</str<strong>on</strong>g> record the temperature measurement at 5 minutes intervals for aperiod <str<strong>on</strong>g>of</str<strong>on</strong>g> 4 weeks. Ambient temperature was also measured near the slab <str<strong>on</strong>g>to</str<strong>on</strong>g>p surface. <str<strong>on</strong>g>Solar</str<strong>on</strong>g>radiati<strong>on</strong> was measured at <str<strong>on</strong>g>to</str<strong>on</strong>g>p <str<strong>on</strong>g>of</str<strong>on</strong>g> the slab and at the other faces using a solar meter with an IRfilter in order <str<strong>on</strong>g>to</str<strong>on</strong>g> obtain solar rati<strong>on</strong> <str<strong>on</strong>g>due</str<strong>on</strong>g> <str<strong>on</strong>g>to</str<strong>on</strong>g> infra-red comp<strong>on</strong>ent.XXBCBCYYx-x viewAAFigure 2: Thermocouple arrangement inside the slabY-Y view
4.3 Experimental results and discussi<strong>on</strong>A solar meter measures the <str<strong>on</strong>g>to</str<strong>on</strong>g>tal solar radiati<strong>on</strong> falls <strong>on</strong> the ground. Al-Dallal and Zeinin (1986)measured the solar radiati<strong>on</strong> drop <strong>on</strong> ground surface in Bahrain and divided the <str<strong>on</strong>g>to</str<strong>on</strong>g>tal values in<str<strong>on</strong>g>to</str<strong>on</strong>g>major comp<strong>on</strong>ents in radiati<strong>on</strong> as visible and infrared. Their result shows a sinusoidal variati<strong>on</strong>with a peak <str<strong>on</strong>g>of</str<strong>on</strong>g> 950 W/m 2 . Figure 3 shows the average daily variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> solar radiati<strong>on</strong>measurement with and without IR filter. It can be seen that the <str<strong>on</strong>g>to</str<strong>on</strong>g>tal flux take a sinusoidalvariati<strong>on</strong> with a peak value <str<strong>on</strong>g>of</str<strong>on</strong>g> 900 W/m 2 . The measurement with the IR filter gives the heat fluxvariati<strong>on</strong> which is the comp<strong>on</strong>ent required in thermal analysis <str<strong>on</strong>g>of</str<strong>on</strong>g> the slab.Figure 3: Daily solar heat flux <strong>on</strong> c<strong>on</strong>crete slab surfacesFigure 4 shows the daily ambient temperature variati<strong>on</strong> in air near the c<strong>on</strong>crete slab.Figure 4: Daily ambient temperature variati<strong>on</strong>4.4 Temperature variati<strong>on</strong> cross the depth <str<strong>on</strong>g>of</str<strong>on</strong>g> the slabFig 5 shows the temperature variati<strong>on</strong> across the slab thickness for 24 hour period. Top surfacehas the highest temperature at the day time. In the evening the lowest temperature was recordedat the <str<strong>on</strong>g>to</str<strong>on</strong>g>p surface while the bot<str<strong>on</strong>g>to</str<strong>on</strong>g>m surface was at slightly higher temperature.. Highesttemperatures <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>to</str<strong>on</strong>g>p and bot<str<strong>on</strong>g>to</str<strong>on</strong>g>m surfaces have a time lag <str<strong>on</strong>g>of</str<strong>on</strong>g> around 2 hours for the 150 mm thickslab. The time lag governs by the thermal c<strong>on</strong>ductivity <str<strong>on</strong>g>of</str<strong>on</strong>g> the c<strong>on</strong>crete.
Figure 6 shows the variati<strong>on</strong>s <str<strong>on</strong>g>of</str<strong>on</strong>g> the temperature pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile during a 24 hour period. It explains thatthere are positive gradients at the day time and negative gradients at the night time.Figure 5: Diurnal temperature variati<strong>on</strong> across the thicknessFigure 6: Temperature pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile variati<strong>on</strong> across the thicknessAccording <str<strong>on</strong>g>to</str<strong>on</strong>g> the solar radiati<strong>on</strong> measurements, the <str<strong>on</strong>g>to</str<strong>on</strong>g>p surface <str<strong>on</strong>g>of</str<strong>on</strong>g> the slab will have both heatflux input and c<strong>on</strong>vecti<strong>on</strong> output during the day time (i.e. 06.00 and 17.00 hours). In the nighttime all the surfaces dissipate the accumulated energy by c<strong>on</strong>vecti<strong>on</strong>. This can be clearly seenfrom Figure 6 where the temperature gradient across the depth <str<strong>on</strong>g>of</str<strong>on</strong>g> the slab changes from positive<str<strong>on</strong>g>to</str<strong>on</strong>g> negative with the time.
5. Finite element model simulati<strong>on</strong>8 nodes brick element (Solid 5) was used <str<strong>on</strong>g>to</str<strong>on</strong>g> simulate both thermal and structural properties <str<strong>on</strong>g>of</str<strong>on</strong>g>c<strong>on</strong>crete slab. Coupled-field analysis in ANSYS is essential <str<strong>on</strong>g>to</str<strong>on</strong>g> carry out both thermal andstructural analysis <str<strong>on</strong>g>to</str<strong>on</strong>g>gether. Input heat flux and the c<strong>on</strong>vecti<strong>on</strong> heat loss <str<strong>on</strong>g>to</str<strong>on</strong>g> the surrounding werethe boundary c<strong>on</strong>diti<strong>on</strong>s given as time functi<strong>on</strong>s. Fully transient analysis was carried out for 24hour period.<str<strong>on</strong>g>Solar</str<strong>on</strong>g> radiati<strong>on</strong> (Heat flux) and the ambient temperature variati<strong>on</strong> were given according <str<strong>on</strong>g>to</str<strong>on</strong>g> themeasured values shown in Figure 5 and 6. C<strong>on</strong>crete and soil properties used for the FEM aregiven in Table 1.Table 1: Material properties used for FEMStructural<str<strong>on</strong>g>Thermal</str<strong>on</strong>g>Property (SI units) C<strong>on</strong>crete SoilYoung's Modulus2.30E+10 1.20E+08Pois<strong>on</strong>'s ratio 0.2 0.25Density 2400 1600<str<strong>on</strong>g>Thermal</str<strong>on</strong>g> c<strong>on</strong>ductivity 2.5 0.3Specific heat 700 850Coefficient <str<strong>on</strong>g>of</str<strong>on</strong>g> thermal expansi<strong>on</strong> 1.00E-05Figure 7 shows the three dimensi<strong>on</strong>al model developed using ANSYS. It c<strong>on</strong>sist 150 mm thickc<strong>on</strong>crete slab rest <strong>on</strong> 0.5 m thick soil base.Figure 7: FE model in ANSYS (150 mm thick c<strong>on</strong>crete layer <strong>on</strong> 0.5 m thick soil)
5.1 Verificati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> model5.1.1 Nodal temperature variati<strong>on</strong>ANSYS FEM gives the temperature values in every locati<strong>on</strong> at any time. Temperature pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ileacross the thickness <str<strong>on</strong>g>of</str<strong>on</strong>g> the slab has obtained for the whole day. Figure 8 shows the temperaturevalues obtained from the 3D model.Figure 8: Temperature c<strong>on</strong><str<strong>on</strong>g>to</str<strong>on</strong>g>urs in FEMIt shows the temperature c<strong>on</strong><str<strong>on</strong>g>to</str<strong>on</strong>g>urs at the time <str<strong>on</strong>g>of</str<strong>on</strong>g> maximum temperature observed <strong>on</strong> the <str<strong>on</strong>g>to</str<strong>on</strong>g>psurface.Figure 9 shows the daily temperature variati<strong>on</strong> across the slab obtained from the FEM. Thistemperature variati<strong>on</strong> is similar <str<strong>on</strong>g>to</str<strong>on</strong>g> the measured temperature variati<strong>on</strong> shown in Figure 5.Figure 9: Daily temperature variati<strong>on</strong> across the thickness
Top surface has a higher temperature at during the day time and the bot<str<strong>on</strong>g>to</str<strong>on</strong>g>m surface was at ahigher than the <str<strong>on</strong>g>to</str<strong>on</strong>g>p surface during the night time. Time lag between the highest temperatures <str<strong>on</strong>g>of</str<strong>on</strong>g><str<strong>on</strong>g>to</str<strong>on</strong>g>p and bot<str<strong>on</strong>g>to</str<strong>on</strong>g>m surfaces during day time obtained from the FEM analysis is around two hourswhich agrees with actual test results shown in Figure 5.Figure 10, 11, 12 and 13 show a comparis<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> the experimental results and model predicti<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g>the temperature variati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> the c<strong>on</strong>crete slab.Figure 10: Temperature pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile variati<strong>on</strong> across the thickness- FEMFigure 11: Temperature pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile variati<strong>on</strong> across the thickness - FEM and actual
Point locati<strong>on</strong> from bot<str<strong>on</strong>g>to</str<strong>on</strong>g>m(mm)Figure 12 shows that FEM results and actual test results are approximately similar. The best fitline for FEM and actual results has a gradient <str<strong>on</strong>g>of</str<strong>on</strong>g> 0.979 with R 2 <str<strong>on</strong>g>of</str<strong>on</strong>g> 0.971.47Temperature at <str<strong>on</strong>g>to</str<strong>on</strong>g>p surface-Actual (0C)45434139373533312927y = xy = 0.979xR² = 0.97127 29 31 33 35 37 39 41 43 45 47Temperature at <str<strong>on</strong>g>to</str<strong>on</strong>g>p surface-FEM ( C) 0Figure 12: Results accuracy (FEM and actual)Figure 13 shows the temperature pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile across the slab obtained from the analysis which issimilar <str<strong>on</strong>g>to</str<strong>on</strong>g> the test results shown in Figure 8. It proves the n<strong>on</strong>-linear temperature pr<str<strong>on</strong>g>of</str<strong>on</strong>g>ile acrossthe slab.1501251007550ActualFEM25036 38Temperature(0C)40 42 44 46 48Figure 13: Temperature pr<str<strong>on</strong>g>of</str<strong>on</strong>g>iat 14.00 hours (FEM and actual slab)
6. C<strong>on</strong>clusi<strong>on</strong>sDaily temperature variati<strong>on</strong> inside a ground c<strong>on</strong>crete slab is directly proporti<strong>on</strong>al <str<strong>on</strong>g>to</str<strong>on</strong>g> the ambienttemperature variati<strong>on</strong>. However, the temperature inside the slab is always higher than thesurrounding temperature. During the day time, <str<strong>on</strong>g>to</str<strong>on</strong>g>p surface <str<strong>on</strong>g>of</str<strong>on</strong>g> the c<strong>on</strong>crete slab absorbs solarheat flux and it tends <str<strong>on</strong>g>to</str<strong>on</strong>g> accumulate heat energy inside the slab depending <strong>on</strong> its thermalproperties. During the night time, the c<strong>on</strong>crete slab begins <str<strong>on</strong>g>to</str<strong>on</strong>g> dissipate energy. The energydissipati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> the heated c<strong>on</strong>crete slab is governed by c<strong>on</strong>vecti<strong>on</strong> parameters such as c<strong>on</strong>vecti<strong>on</strong>heat transfer coefficient and ambient temperature. According <str<strong>on</strong>g>to</str<strong>on</strong>g> those values, the slab cannotdissipate the whole energy before sun rises the next day. Therefore, temperature inside thec<strong>on</strong>crete slab has a higher value than the ambient at any time.When the <str<strong>on</strong>g>to</str<strong>on</strong>g>p surface <str<strong>on</strong>g>of</str<strong>on</strong>g> the c<strong>on</strong>crete slab exposed <str<strong>on</strong>g>to</str<strong>on</strong>g> the solar heat flux, the <str<strong>on</strong>g>to</str<strong>on</strong>g>p center point <str<strong>on</strong>g>of</str<strong>on</strong>g>the slab feels the maximum temperature in day time and the bot<str<strong>on</strong>g>to</str<strong>on</strong>g>m center point has themaximum value in night time. These values are governed by the thermal properties <str<strong>on</strong>g>of</str<strong>on</strong>g> c<strong>on</strong>creteother than the input heat flux.The actual slab has a highest temperature <str<strong>on</strong>g>of</str<strong>on</strong>g> 46 0 C at 14.00 hours and a minimum <str<strong>on</strong>g>of</str<strong>on</strong>g> 28 0 C at6.00 hours. Therefore, slab feels about 18 0 C differences in a daily cycle. This difference intemperature can leads <str<strong>on</strong>g>to</str<strong>on</strong>g> the upward and downward curling <str<strong>on</strong>g>of</str<strong>on</strong>g> the slab. During the day time the<str<strong>on</strong>g>to</str<strong>on</strong>g>p surface has the higher temperature values than bot<str<strong>on</strong>g>to</str<strong>on</strong>g>m surface. It has a maximum difference<str<strong>on</strong>g>of</str<strong>on</strong>g> 9 0 C. So there may be an upward curling at the day time. The bot<str<strong>on</strong>g>to</str<strong>on</strong>g>m surface has the highertemperature values at the night time and a maximum difference <str<strong>on</strong>g>of</str<strong>on</strong>g> 2 0 C with bot<str<strong>on</strong>g>to</str<strong>on</strong>g>m surface.That difference leads <str<strong>on</strong>g>to</str<strong>on</strong>g> a downward curling at the night time.FEM verified <str<strong>on</strong>g>to</str<strong>on</strong>g> the data collected in Sri Lanka. Therefore, the verified model can be used <str<strong>on</strong>g>to</str<strong>on</strong>g>obtain the temperatures at any point <str<strong>on</strong>g>of</str<strong>on</strong>g> the c<strong>on</strong>crete pavement slab in a country having tropicalclimate. FEM requires solar radiati<strong>on</strong> and ambient temperature variati<strong>on</strong> throughout the day <str<strong>on</strong>g>to</str<strong>on</strong>g>predict the temperatures at required point <str<strong>on</strong>g>of</str<strong>on</strong>g> a c<strong>on</strong>crete pavement.The verified FEM predicts the temperature induced stresses in rigid pavements. <str<strong>on</strong>g>Thermal</str<strong>on</strong>g>deformati<strong>on</strong>s also can be obtained by the FEM and the results can be effectively used <str<strong>on</strong>g>to</str<strong>on</strong>g> designthe joints in c<strong>on</strong>crete pavements. Designing <str<strong>on</strong>g>of</str<strong>on</strong>g> rigid pavement joints neglecting the effects <str<strong>on</strong>g>of</str<strong>on</strong>g>thermal variati<strong>on</strong>s can lead <str<strong>on</strong>g>to</str<strong>on</strong>g> faulting, cracking and other distresses. Therefore, this FEM isuseful <str<strong>on</strong>g>to</str<strong>on</strong>g> minimize the damages for the c<strong>on</strong>crete roads at design stage.ReferencesTom Burnham and Amir Koubaa (2001), “a new approach <str<strong>on</strong>g>to</str<strong>on</strong>g> estimate the in-situ thermalcoefficient and drying shrinkage for jointed c<strong>on</strong>crete pavements”, 7th Internati<strong>on</strong>al C<strong>on</strong>ference<strong>on</strong> C<strong>on</strong>crete Pavements – Orlando, Florida, USA – September 9-13, 2001I. E. Harik, P. Jianping, z H. Southgate and D. Allen, (1994) “Temperature <str<strong>on</strong>g>Effects</str<strong>on</strong>g> <strong>on</strong> RigidPavements”, Journal <str<strong>on</strong>g>of</str<strong>on</strong>g> Tranportati<strong>on</strong> Engineering, Vol. 120, No. 1, January/February, 1994.
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