Estimation of Critical Stress in Jointed Concrete Pavement

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1 Available online at ScienceDirect Procedia - Social and Beavioral Scien ce s 04 ( 03 ) 08 7 nd Conference of Transportation Researc Group of India (nd CTRG) Estimation of Critical Stress in Jointed Concrete Pavement Swati Roy Maitra a *, K. S. Reddy b and L. S. Ramacandra c a Scientist,Civil Engineering Department, IIT Karagpur,Karagpur, India b Professor,Civil Engineering Department, IIT Karagpur,Karagpur, India c Professor,Civil Engineering Department, IIT Karagpur,Karagpur, India Abstract Pavements are subjected to repeated traffic loads along wit temperature variation trougout teir service life. In concrete pavement, critical stresses are developed due to te combined effect of weel load and positive temperature differential leading to initiation of cracks. In tis paper, a metodology as been presented for evaluating te critical stress in concrete pavement based on finite element tecnique. A generalized expression for estimating te critical stress as been developed considering various combinations of pavement configurations, axle loads and temperature differential. Tis equation can be effectively utilized to obtain te critical stress in concrete pavement for any combination of axle load and nonlinear positive temperature gradient witout performing a rigorous finite element analysis. Based on te generalized expression, a modif 03 Te Te Autors. Publised Publised by Elsevier by Elsevier Ltd. Open Ltd. access under CC BY-NC-ND license. Selection and and peer-review under under responsibility responsibility of International of International Scientific Scientific Committee. Committee. Keywords: Concrete pavement; critical stress; weel load stress; temperature differential; finite element analysis *Corresponding autor. Tel.: ; address: swati@civil.iitkgp.ernet.in Te Autors. Publised by Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of International Scientific Committee. doi: 0.06/j.sbspro.03..3

2 Swati Roy Maitra et al. / Procedia - Social and Beavioral Sciences 04 ( 03 ) Introduction Pavements are subjected to repeated traffic loads trougout teir service life. In concrete pavements, te repeated application of traffic loads along wit temperature variation may lead to initiation of cracks at te igly stressed locations. Te cracks propagate troug te pavement wic may finally lead to failure of pavements due to fatigue. Due to temperature alone, cracks may also initiate in te newly-constructed pavements. Variation in temperature affects te stresses in concrete slab in two ways. Te daily variation in temperature causes quick canges in termal gradients troug te dept of concrete slab, wile te seasonal variation results into different average temperature in concrete slab. Te concrete slab will tend to curl upward or downward wen it is subjected to an increasing or decreasing temperature variation troug its dept. Due to its self-weigt, te slab is not allowed to curl, resulting in te development of curling stresses in te pavement. In concrete pavement, te combined effect of weel load and temperature gradient is responsible for te development of critical stresses. In te guidelines of Indian Roads Congress (IRC: 58, 00) for te analysis and design of concrete pavements, toug te procedure for calculation of weel load stress is now modified based on analytical approaces, te estimation of curling stress is still empirical in nature. Te IRC approac of computing curling stress follows conservative results. Also te combined effect of weel load stress and curling stress is not simply additive in nature. Te variation of temperature troug te dept of concrete slab is nonlinear in nature, wic as been considered as linear in te Indian design code. Terefore, an attempt as been made in tis study to develop a generalized expression for identifying and estimating te critical stress in te slab subjected to te combined action of weel load and nonlinear temperature differential based on finite element metod. Tis ready-to-use equation can be utilized conveniently by te practicing engineers for te design of concrete pavement. Finally, a te curling stress on concrete pavement.. Metodology In concrete pavement, te critical combination tat gives te maximum tensile stress at te slab bottom is wen axle load at te longitudinal edge of te pavement is combined wit positive temperature gradient (Maitra et al., 009a). In tis paper, a metodology as been presented for evaluating te critical stress in concrete pavement due to te combined action of weel load and positive temperature gradient based on finite element tecnique. A sensitivity analysis as been carried out in tis work using a validated tree-dimensional (3-D) finite element (FE) model for jointed concrete pavement (Maitra, 0). Te 3-D FE model was validated using a structural evaluation data of an in-service concrete pavement on te national igway in India. Te details of te validation procedure are discussed elsewere (Maitra, 0). For te sensitivity analysis, different pavement configuration, axle load and positive temperature gradient ave been considered and are discussed in te following sections... Pavement Configuration A tree-panel concrete pavement system of dimension 4500 mm 3500 mm, separated by transverse joints as been considered. Te plain cement concrete (PCC) slab is supported over foundation, comprised of layers of base and granular subbase (GSB) over prepared (compacted) subgrade. In India, dry lean concrete (DLC) base and wet mix macadam (WMM) subbase are generally used (IRC: 58, 00). Te interface between concrete slab and DLC base is generally constructed as unbonded by providing a 5 micron polytene seet as bond-breaker,

3 0 Swati Roy Maitra et al. / Procedia - Social and Beavioral Sciences 04 ( 03 ) 08 7 wic is te usual practice in India. Transverse joints for te pavement system are considered to be provided wit 3 mm diameter dowel bars 600 mm in lengt and spaced at 300 mm center to center for transferring te applied weel load to te adjacent panels. Te slab panels are considered to be discontinuous beyond te widt of te slab. Fig. sows te scematic of te tree-panel concrete pavement system. Various combinations of ticknesses and material properties for slab and foundation as considered in te sensitivity analysis are given in Table. 5 micron polytene seet 4500 mm 3 mm diameter 300 mm c/c PCC Slab DLC base WMM subbase Subgrade Transverse joint Fig. : Scematic Representation of te Tree-Panel Concrete Pavement Table : Properties of PCC, DLC, GSB & Subgrade Considered for te Sensitivity analysis Parameters Layers PCC DLC GSB Subgrade Tickness ( in mm) 50, 300, 350, , Density ( in kn/m 3 ) Coefficient of termal expansion ( in mm/mm/ C) Elastic Modulus (E in kpa) 5, 30, 35 0, 4, ) Modulus of Subgrade Reaction (k in MPa/mm) , 0.08, 0., 0.5, 0.0

4 Swati Roy Maitra et al. / Procedia - Social and Beavioral Sciences 04 ( 03 ) Details of Axle Load Five different axle loads- 80 kn, 0 kn, 60 kn, 00 kn and 40 kn, were considered for te present analysis. Te loads were selected as representatives of te typical axle load spectrum observed on Indian igways. Te axle loads are placed wit te outer weel tangential to te longitudinal edge of te central panel middle panel. Te figure also gives te details of te geometrical arrangement of te weel loads on te axle. Te stress will be critical below te outer weel near te longitudinal edge of te pavement. Load transfer between te panels was assumed to be only troug te dowel bars placed across te transverse joints and te contribution of aggregate interlocking as been neglected mm 30 mm 800 mm 3500 mm 60 mm 34.4 mm Fig. : Details of Axle Load and Critical Stress Location on te Pavement.3. Temperature Measurement in Laboratory In te laboratory, experiments were performed to observe te variation of temperature witin concrete specimens. Measurement of temperature was done on two concrete cylinders. Concrete cylinders of 50 mm diameter and 300 mm in eigt were cast in te laboratory for tis purpose. Te surface of te cylinder was covered and ot air was blown at one end of te cylinder. Te oter end was covered wit soil. Five termometers were inserted wit equal intervals along te lengt of te cylinder to measure temperatures at different locations. Fig. 3 sows te potograp of te experiment performed in te laboratory for temperature measurement. From te experiment, typical nonlinear variation of temperature was observed witin te concrete specimens. Fig. 4 sows some typical variations obtained from te experiment. Similar variations of temperature troug te

5 Swati Roy Maitra et al. / Procedia - Social and Beavioral Sciences 04 ( 03 ) 08 7 dept of slab were also observed by oter researcers on model concrete pavements (Venkatasubramanian, 964; Balbo and Severi, 00; Beckemeyer et al., 00). Fig. 3: Temperature Measurement in te Laboratory Fig. 4: Typical Variations of Temperature witin Concrete Specimen.4. Temperature Differential Based on te laboratory experiment, a non-linear temperature variation witin te slab dept was considered for te sensitivity analysis. Te temperature difference (T D ) between te top and te bottom surface of te slab was varied from 0 to 30 C. To simplify te analysis, te non-linear temperature variation was approximated by a bilinear variation, as sown in Fig. 5. In te figure, T top, T bottom and T mid are te temperatures at te top fiber, bottom fiber and at te mid-dept of te concrete slab respectively. From te trends of temperature variations presented in Fig. 4, te following relationsip can be considered among T top, T mid and T bottom. T mid T bottom 3 T top T bottom () T top Dept of Slab T mid T bottom Fig. 5: Bilinear Variation of Temperature in te Slab Dry lean concrete (DLC) layer was assumed to ave uniform temperature trougout its dept. Temperature at te bottom fiber of te concrete slab was assigned to te DLC layer.

6 Swati Roy Maitra et al. / Procedia - Social and Beavioral Sciences 04 ( 03 ) Finite Element Modeling of te Pavement Te tree-panel concrete pavement sections were analyzed using a compreensive tree-dimensional finite element model (Maitra, 0). Te model as been developed using te commercial structural analysis software ANSYS. Plain cement concrete (PCC) slab, dry lean concrete (DLC) base and granular subbase (GSB) were modeled as linear, elastic and isotropic materials. Eigt-noded solid brick elements (SOLID45) were used to model tese E ) were used to represent te material caracteristics of eac of tese layers. Te density ( ) of te layers and coefficient of termal expansion ( ) of concrete slab and DLC layer were te oter input parameters used in te analysis. Te subgrade was modeled as Winkler foundation (Westergaard, 96). Winkler model is te idealization of te soil medium as a bed of closely spaced, independent, linear springs. Two-noded linear spring elements (COMBIN4) of ANSYS package were used to model te Winkler foundation. Te effective normal stiffness of te spring element was obtained by multiplying te modulus of subgrade reaction (k) wit te influencing area of tat element. Te interface between concrete slab and DLC base was modeled as eiter bonded or unbonded by using contact elements (CONTA78). Te interface coefficient of friction between PCC slab and DLC base is taken as 0.5 for unbonded interface due to te presence of polytene seet. For bonded interface, te friction between te two layers is very ig and te coefficient of friction is taken as 0. Tese values were selected on te basis of te results of te pus-off tests of concrete slabs on different types of base and subbase wit different interface conditions reported by Maitra et al. (007). Dowel bars along te transverse joints were modeled as 3-D beam elements (BEAM4). Te beam elements representing te dowel bars are connected wit te solid brick elements of concrete slab. One end of te dowel bars are generally covered wit plastic seets (a common practice in India). To represent tis, a series of contact elements (CONTA78) are used to connect te beam elements of dowel bars wit te concrete slab (Maitra et al., 009b). It is assumed tat te dowel bars ave zero looseness around tem. Te properties of te steel dowel bars considered for te analysis are: elastic modulus (E) = ) = 0.3. Te modulus of dowel support (K ) between dowel bars and concrete was taken as 450 MPa/mm for te sensitivity analysis. Fig. 6 sows te finite element model of te tree panel concrete pavement system drawn in ANSYS software. Concrete slab, DLC base and granular subbase are sown as brick elements, wile te Winkler foundation representing subgrade is sown as series of linear springs. Te axle load at te critical location is also sown at te middle slab panel. PCC slab Subgrade GSB DLC Fig. 6: Finite Element Model for te tree-panel Concrete Pavement

7 4 Swati Roy Maitra et al. / Procedia - Social and Beavioral Sciences 04 ( 03 ) Estimation of Critical Stress Concrete pavement, wit various configurations, axle loads and nonlinear temperature differentials were analyzed using te 3-D FE model and te critical stress due to te combined effect of weel load and positive temperature gradient were determined. A regression analysis is carried out using all tese results. Based on te regression analysis, a generalized expression for estimating te critical stress due to te combined action of axle load and nonlinear positive temperature gradient as been developed. Te relationsip was developed as a function of pavement parameters, axle load and temperature differential. Te generalized expression for estimating te critical stress ( cr ) is given as equation. Te critical stress occurs at te bottom of te slab below te outer weel at te longitudinal edge of te pavement (Ref. Fig. 4). In tis work, te pavement combinations effective slab tickness ( e ) was considered to take care of te effect of bonded or unbonded dry lean concrete (DLC) base layer of te pavement (Zollinger et al., 005). r P TD.35 kl A 3. 5 e c c () (R =0.89, F stat = > F critical = 4.93, t stat of (P/ e D / c ) ( k l ) > t critical =.94) were, cr = Critical stress due to weel load and positive temperature gradient in MPa P A = Total axle load in N e = Effective slab tickness wit bonded or unbonded interface condition in mm = Coefficient of termal expansion of concrete in mm/mm/ C T D = Temperature difference between top and bottom fiber of concrete slab in C c = Tickness of concrete slab in mm k = Modulus of subgrade reaction in MPa/mm l E 3 e 4 ( ) k c = Radius of relative stiffness (RRS) in mm (3) E c = Elastic modulus of PCC layer in MPa e = Effective tickness of PCC layer in mm Te expressions for te effective tickness of PCC layers are given by equations (4) to (6) (Ioannides et al., 99). For fully-bonded layers, 3 3 E 3 E x x E E e e b na na (4) were, x na = Neutral axis distance from top of PCC layer in mm

8 Swati Roy Maitra et al. / Procedia - Social and Beavioral Sciences 04 ( 03 ) x na For unbonded layers, E E E E (5) e e u E 3 3 E were, E and E = Elastic moduli of PCC and DLC layers respectively in MPa and = Ticknesses of PCC and DLC layers respectively in mm 3 (6) Equation sows tat te critical stress ( cr ) depends significantly on pavement configuration (expressed in terms of effective tickness and radius of relative stiffness), and te strengt of te supporting soil, along wit te magnitude of axle load and te temperature differential. Tis ready-to-use equation can be conveniently utilized to obtain te critical stress in concrete pavement wit various configurations for any combination of axle load and nonlinear positive temperature gradient witout performing a rigorous finite element analysis. 4. Comparison wit IRC Metod Te critical stress, obtained from te generalized expression (equation ), as been compared wit tat recommended by IRC metod (IRC: 58, 00) for a given pavement system. Te design example given in IRC: 58 (00) as been considered for tis purpose. Salient features of te pavement system are given below. Flexural strengt of concrete = 4.5 MPa Elastic modulus of concrete = 30,000 MPa Coefficient of termal expansion of concrete = mm/mm/ C Effective modulus of subgrade reaction wit DLC base = 0.08 MPa/mm Tickness of slab = 330 mm Axle load = 40 kn (single axle) Temperature differential = C Te weel load stress is estimated using te stress carts given in IRC: 58 (00) based on IITRIGID computer program. Te load stress works out to be.4 MPa. C temperature differential, te curling / temperature stress is estimated as.73 MPa. Ec TDC tc (7) were, tc = Temperature / curling stress

9 6 Swati Roy Maitra et al. / Procedia - Social and Beavioral Sciences 04 ( 03 ) 08 7 C values of te pavement L = Pavement dimension, along wic te temperature stress is to be calculated knowing te L/l Te oter parameters were previously defined. Terefore, te total critical stress ( cr ) is te summation of te load stress and te temperature stress and is equal to 4.4 MPa (= ) as per IRC: 58 (00). Considering te present analysis, te corresponding critical stress ( cr ) for te pavement system given in IRC: 58, 00, as estimated from equation is 3.7 MPa. Tis value is found to be less (about.6%) as compared to tat obtained from te IRC metod. It is tus observed tat IRC: 58 (00) overestimates te critical stress for te combined action of weel load and temperature gradient in a concrete slab. 5. Based on te relationsip developed for estimating te critical stress at te edge of te jointed concrete estimating te temperature stress ( tc ). By comparing te critical stress ( cr ) obtained from te regression analysis (equation ) wit tat obtained by (C m ) as given by equation 8 is proposed. m kl E Te parameters were previously defined. C 7 (8) c e C m ) considering te effective tickness of slab wit te corresponding radius of relative stiffness values for estimating temperature stress for any pavement configuration. 6. Conclusion Tis paper presents a metodology for estimating te critical stress in concrete pavement due to te combined action of weel load and positive temperature gradient using a compreensive tree-dimensional finite element model. A generalized expression as been proposed to evaluate te critical stress in concrete slab. Tis equation can be effectively utilized in te design of concrete pavement to obtain te critical stress for any combination of axle load and nonlinear positive temperature gradient witout performing a rigorous finite element analysis. A comparison wit IRC: 58 (00) metod sows tat te critical stress, particularly te temperature stress is temperature stress coefficient as been suggested, wic can now be used to estimate te curling stress on concrete pavement.

10 Swati Roy Maitra et al. / Procedia - Social and Beavioral Sciences 04 ( 03 ) References ual, ANSYS Inc., Cannonsburg, PA, 00. Transportation Researc Record, 809, TRB, Wasington D.C., -. Beckemeyer, C. A -in Curling in Jointed Plain Concrete Pavement Case Study of Pennsylvania I- Transportation Researc Record, 809, TRB, Wasington D.C., Guidelines for te Te Indian Roads Congress, New Deli. Transportation Researc Record, 370, TRB, Wasington D.C., 0-8. Influence of interface condition on concrete pavement response - an experimental evaluation Proceedings of te International Conference on Advanced Caracterisation of Pavement and Soil Engineering Materials, Atens, Greece, Vol., J. of Transportation Engineering, ASCE, 35(8), J. of Transportation Engineering, ASCE, 35(), Tecnology Karagpur, India. Investigation on Temperature and Friction Stresses in Bonded C Indian Institute of Tecnology, Karagpur, India. nfluence on crete Indian Institute of. P.D. Tesis, Public Roads, 7, Zollinger, C., Zollinger, D. G., Dallas L. and Runway 5L Pavements, Colorado Springs, Colorado, 3, 0 9. Eigt International Conference on Concrete