Modelling of Thermal Effects due to Solar Radiation on Concrete ...

<strong>Modelling</strong> <strong>of</strong> <strong>Thermal</strong> <strong>Effects</strong> <strong>due</strong> <strong>to</strong> <strong>Solar</strong> <strong>Radiation</strong>on Concrete PavementsAruna Karunarathne,University <strong>of</strong> Moratuwa, Sri Lankaarunak@uom.lkWasantha Mampearachchi,University <strong>of</strong> Moratuwa, Sri Lankawasanthak@civil.mrt.ac.lkAnura Nanayakkara,University <strong>of</strong> Moratuwa, Sri Lankasman@civil.mrt.ac.lkAbstractRate <strong>of</strong> heat flux from solar radiation, thermal properties <strong>of</strong> concrete and heat loss fromconcrete <strong>due</strong> <strong>to</strong> convection parameters <strong>of</strong> surroundings influence the temperature variation <strong>of</strong> anexposed concrete slab. This paper describes a method <strong>to</strong> simulate the temperature variation andcorresponding deformation <strong>of</strong> a concrete slab using 3D finite element model (FEM) approach.The pavement is idealized as a thin isotropic plate resting on a Winkler-type elastic foundation.Since two-dimensional plate elements are limited <strong>to</strong> linear temperature distribution through thethickness, eight (8) nodes brick element in ANSYS-12 was used for the FEM analysis <strong>to</strong> obtaintemperature variations throughout the surface and the thickness. An experimental investigationwas carried out <strong>to</strong> obtain the temperature variation <strong>of</strong> a concrete slab under solar radiation.Daily temperature variation across the depth <strong>of</strong> the slab and the solar heat flux on the slab weremoni<strong>to</strong>red using thermocouples, solar meter and IR filter. FEM results were verified using bythe experimental investigation.Keywords: <strong>Solar</strong> radiation, concrete pavements, FEM, ANSYS

1. IntroductionVariation <strong>of</strong> the temperature pr<strong>of</strong>ile across a slab is well known and major cause <strong>of</strong> differentialthermal stresses and differential deformation <strong>of</strong> concrete structures. <strong>Thermal</strong> stresses and dryingshrinkage stresses are the most important types <strong>of</strong> stresses developed in exposed slab. Thesestresses are very severe in rigid pavements in tropical countries. Deformation <strong>of</strong> slabs andpavements can lead <strong>to</strong> structural failures, drop in load transfer efficiency, etc. Thereforedetermination <strong>of</strong> ultimate deformation <strong>due</strong> <strong>to</strong> both solar radiation and drying shrinkage isessential for determination <strong>of</strong> joint spacing for concrete slab <strong>to</strong> provide a good load transfer.2. Background2.1 Review <strong>of</strong> literature <strong>of</strong> thermal behaviour <strong>of</strong> concreteTom Burnham and Amir Koubaa in (2001) have measured temperature inside a concrete slab <strong>to</strong>provide new approach for the coefficient <strong>of</strong> thermal expansion and drying shrinkage. Mirambell(1990) studied temperature and stress distribution in plain concrete pavements under thermaland mechanical loads. A three-dimensional (3-D) model, employing 10 layers across the depth<strong>of</strong> the pavement, was used <strong>to</strong> introduce the effects <strong>of</strong> nonlinear temperature distributions.Choubane and Tia (1992) presented an interesting technique for treating the nonlinearity <strong>of</strong> thetemperature gradient. The temperature distribution across the depth <strong>of</strong> the pavement wasdivided in<strong>to</strong> three components: (1) A component that causes axial displacement; (2) acomponent that causes the bending; and (3) the nonlinear component. Furthermore, they deriveda quadratic equation <strong>to</strong> represent the nonlinear temperature distribution throughout the depth <strong>of</strong>the pavement. Harik et al. (1994) developed a linear temperature distribution that is equivalent<strong>to</strong> the nonlinear one in the sense that it yields the same axial force and moment. Ernest,Barenberg, Chetna Rao and Mark Snyder (2001) found the temperature variation across a slabfrom early age <strong>to</strong> long term condition.2.2 Concept <strong>of</strong> the temperature variation in exposed concrete slabPavements slabs have large <strong>to</strong>p surface area than the surrounding area. <strong>Solar</strong> heat flux directlydrops on the surface and heat up the body. Heat dissipation occurs by the convection processthrough the surrounding surfaces and part <strong>of</strong> the heat transfer <strong>to</strong> the ground through the bot<strong>to</strong>msurface. Figure 1 shows the concept <strong>of</strong> this phenomenon.a)b)c)Figure 1: Concept <strong>of</strong> the thermal behavior <strong>of</strong> exposed slaba) A typical ambient temperature variation <strong>of</strong> a day b) A typical <strong>Solar</strong> heat flux variation in the day timec) Temperature variation in the slab

There are many parameters govern the heat dissipation process. Most sensitive fac<strong>to</strong>rs should beclearly identified and quantified <strong>to</strong> develop an effective model. Transient analysis in ANSYScan simulate the non-linear properties <strong>of</strong> the models. Heat flux from solar radiation and heatdissipation through convection process <strong>due</strong> <strong>to</strong> ambient temperature vary with the timethroughout the day. Input heat flux from the solar radiation should be measured <strong>to</strong> incorporatewith the FEM.3. Research significanceThe research provides a procedure <strong>to</strong> obtain temperature distribution in a concrete slab whichexposed <strong>to</strong> solar radiation. Using the appropriate thermal properties <strong>of</strong> concrete, the deformation<strong>of</strong> the slab <strong>due</strong> <strong>to</strong> solar radiation values at the particular locations can be obtained from FEM forvaries thicknesses. It is important in designing joints and load transfer at non-dowelled joints inrigid pavements. Amount <strong>of</strong> curling and warping <strong>of</strong> pavements can also be obtained using theFEM for varies lengths. The FEM approach is very helpful for proper designing <strong>of</strong> rigidpavements with less faulting, cracking and other distresses.4. Experimental investigation4.1 Construction <strong>of</strong> pro<strong>to</strong>type field slabA concrete slab <strong>of</strong> 1 m x1 m with 150 mm thick was cast using grade 25 concrete on compactedsoil (in-situ CBR <strong>of</strong> 25) in open ground <strong>to</strong> obtain uninterrupted solar radiation throughout thedaytime. Orientation <strong>of</strong> the sides <strong>of</strong> the slab was in N-E and S-W directions. Thermocoupleswere fixed <strong>to</strong> formwork and maintained at the center <strong>of</strong> the slab using non-elastic andthermoplastic wires.4.2 Data acquisitionA data logger was used <strong>to</strong> record the temperature measurement at 5 minutes intervals for aperiod <strong>of</strong> 4 weeks. Ambient temperature was also measured near the slab <strong>to</strong>p surface. <strong>Solar</strong>radiation was measured at <strong>to</strong>p <strong>of</strong> the slab and at the other faces using a solar meter with an IRfilter in order <strong>to</strong> obtain solar ration <strong>due</strong> <strong>to</strong> infra-red component.XXBCBCYYx-x viewAAFigure 2: Thermocouple arrangement inside the slabY-Y view

4.3 Experimental results and discussionA solar meter measures the <strong>to</strong>tal solar radiation falls on the ground. Al-Dallal and Zeinin (1986)measured the solar radiation drop on ground surface in Bahrain and divided the <strong>to</strong>tal values in<strong>to</strong>major components in radiation as visible and infrared. Their result shows a sinusoidal variationwith a peak <strong>of</strong> 950 W/m 2 . Figure 3 shows the average daily variation <strong>of</strong> solar radiationmeasurement with and without IR filter. It can be seen that the <strong>to</strong>tal flux take a sinusoidalvariation with a peak value <strong>of</strong> 900 W/m 2 . The measurement with the IR filter gives the heat fluxvariation which is the component required in thermal analysis <strong>of</strong> the slab.Figure 3: Daily solar heat flux on concrete slab surfacesFigure 4 shows the daily ambient temperature variation in air near the concrete slab.Figure 4: Daily ambient temperature variation4.4 Temperature variation cross the depth <strong>of</strong> the slabFig 5 shows the temperature variation 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 <strong>to</strong>p surface while the bot<strong>to</strong>m surface was at slightly higher temperature.. Highesttemperatures <strong>of</strong> <strong>to</strong>p and bot<strong>to</strong>m surfaces have a time lag <strong>of</strong> around 2 hours for the 150 mm thickslab. The time lag governs by the thermal conductivity <strong>of</strong> the concrete.

Figure 6 shows the variations <strong>of</strong> the temperature pr<strong>of</strong>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 variation across the thicknessFigure 6: Temperature pr<strong>of</strong>ile variation across the thicknessAccording <strong>to</strong> the solar radiation measurements, the <strong>to</strong>p surface <strong>of</strong> the slab will have both heatflux input and convection output during the day time (i.e. 06.00 and 17.00 hours). In the nighttime all the surfaces dissipate the accumulated energy by convection. This can be clearly seenfrom Figure 6 where the temperature gradient across the depth <strong>of</strong> the slab changes from positive<strong>to</strong> negative with the time.

5. Finite element model simulation8 nodes brick element (Solid 5) was used <strong>to</strong> simulate both thermal and structural properties <strong>of</strong>concrete slab. Coupled-field analysis in ANSYS is essential <strong>to</strong> carry out both thermal andstructural analysis <strong>to</strong>gether. Input heat flux and the convection heat loss <strong>to</strong> the surrounding werethe boundary conditions given as time functions. Fully transient analysis was carried out for 24hour period.<strong>Solar</strong> radiation (Heat flux) and the ambient temperature variation were given according <strong>to</strong> themeasured values shown in Figure 5 and 6. Concrete and soil properties used for the FEM aregiven in Table 1.Table 1: Material properties used for FEMStructural<strong>Thermal</strong>Property (SI units) Concrete SoilYoung's Modulus2.30E+10 1.20E+08Poison's ratio 0.2 0.25Density 2400 1600<strong>Thermal</strong> conductivity 2.5 0.3Specific heat 700 850Coefficient <strong>of</strong> thermal expansion 1.00E-05Figure 7 shows the three dimensional model developed using ANSYS. It consist 150 mm thickconcrete slab rest on 0.5 m thick soil base.Figure 7: FE model in ANSYS (150 mm thick concrete layer on 0.5 m thick soil)

5.1 Verification <strong>of</strong> model5.1.1 Nodal temperature variationANSYS FEM gives the temperature values in every location at any time. Temperature pr<strong>of</strong>ileacross the thickness <strong>of</strong> the slab has obtained for the whole day. Figure 8 shows the temperaturevalues obtained from the 3D model.Figure 8: Temperature con<strong>to</strong>urs in FEMIt shows the temperature con<strong>to</strong>urs at the time <strong>of</strong> maximum temperature observed on the <strong>to</strong>psurface.Figure 9 shows the daily temperature variation across the slab obtained from the FEM. Thistemperature variation is similar <strong>to</strong> the measured temperature variation shown in Figure 5.Figure 9: Daily temperature variation across the thickness

Top surface has a higher temperature at during the day time and the bot<strong>to</strong>m surface was at ahigher than the <strong>to</strong>p surface during the night time. Time lag between the highest temperatures <strong>of</strong><strong>to</strong>p and bot<strong>to</strong>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 comparison <strong>of</strong> the experimental results and model prediction <strong>of</strong>the temperature variation <strong>of</strong> the concrete slab.Figure 10: Temperature pr<strong>of</strong>ile variation across the thickness- FEMFigure 11: Temperature pr<strong>of</strong>ile variation across the thickness - FEM and actual

Point location from bot<strong>to</strong>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 <strong>of</strong> 0.979 with R 2 <strong>of</strong> 0.971.47Temperature at <strong>to</strong>p surface-Actual (0C)45434139373533312927y = xy = 0.979xR² = 0.97127 29 31 33 35 37 39 41 43 45 47Temperature at <strong>to</strong>p surface-FEM ( C) 0Figure 12: Results accuracy (FEM and actual)Figure 13 shows the temperature pr<strong>of</strong>ile across the slab obtained from the analysis which issimilar <strong>to</strong> the test results shown in Figure 8. It proves the non-linear temperature pr<strong>of</strong>ile acrossthe slab.1501251007550ActualFEM25036 38Temperature(0C)40 42 44 46 48Figure 13: Temperature pr<strong>of</strong>iat 14.00 hours (FEM and actual slab)

6. ConclusionsDaily temperature variation inside a ground concrete slab is directly proportional <strong>to</strong> the ambienttemperature variation. However, the temperature inside the slab is always higher than thesurrounding temperature. During the day time, <strong>to</strong>p surface <strong>of</strong> the concrete slab absorbs solarheat flux and it tends <strong>to</strong> accumulate heat energy inside the slab depending on its thermalproperties. During the night time, the concrete slab begins <strong>to</strong> dissipate energy. The energydissipation <strong>of</strong> the heated concrete slab is governed by convection parameters such as convectionheat transfer coefficient and ambient temperature. According <strong>to</strong> those values, the slab cannotdissipate the whole energy before sun rises the next day. Therefore, temperature inside theconcrete slab has a higher value than the ambient at any time.When the <strong>to</strong>p surface <strong>of</strong> the concrete slab exposed <strong>to</strong> the solar heat flux, the <strong>to</strong>p center point <strong>of</strong>the slab feels the maximum temperature in day time and the bot<strong>to</strong>m center point has themaximum value in night time. These values are governed by the thermal properties <strong>of</strong> concreteother than the input heat flux.The actual slab has a highest temperature <strong>of</strong> 46 0 C at 14.00 hours and a minimum <strong>of</strong> 28 0 C at6.00 hours. Therefore, slab feels about 18 0 C differences in a daily cycle. This difference intemperature can leads <strong>to</strong> the upward and downward curling <strong>of</strong> the slab. During the day time the<strong>to</strong>p surface has the higher temperature values than bot<strong>to</strong>m surface. It has a maximum difference<strong>of</strong> 9 0 C. So there may be an upward curling at the day time. The bot<strong>to</strong>m surface has the highertemperature values at the night time and a maximum difference <strong>of</strong> 2 0 C with bot<strong>to</strong>m surface.That difference leads <strong>to</strong> a downward curling at the night time.FEM verified <strong>to</strong> the data collected in Sri Lanka. Therefore, the verified model can be used <strong>to</strong>obtain the temperatures at any point <strong>of</strong> the concrete pavement slab in a country having tropicalclimate. FEM requires solar radiation and ambient temperature variation throughout the day <strong>to</strong>predict the temperatures at required point <strong>of</strong> a concrete pavement.The verified FEM predicts the temperature induced stresses in rigid pavements. <strong>Thermal</strong>deformations also can be obtained by the FEM and the results can be effectively used <strong>to</strong> designthe joints in concrete pavements. Designing <strong>of</strong> rigid pavement joints neglecting the effects <strong>of</strong>thermal variations can lead <strong>to</strong> faulting, cracking and other distresses. Therefore, this FEM isuseful <strong>to</strong> minimize the damages for the concrete roads at design stage.ReferencesTom Burnham and Amir Koubaa (2001), “a new approach <strong>to</strong> estimate the in-situ thermalcoefficient and drying shrinkage for jointed concrete pavements”, 7th International Conferenceon Concrete Pavements – Orlando, Florida, USA – September 9-13, 2001I. E. Harik, P. Jianping, z H. Southgate and D. Allen, (1994) “Temperature <strong>Effects</strong> on RigidPavements”, Journal <strong>of</strong> Tranportation Engineering, Vol. 120, No. 1, January/February, 1994.

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