EFFECTS OF GFRP REINFORCING REBARS ON SHRINKAGE AND THERMAL STRESSES IN CONCRETE

Transcription

1 EFFECTS OF GFRP REINFORCING REBARS ON SHRINKAGE AND THERMAL STRESSES IN CONCRETE Roge H. L. Chen 1 and Jeong-Hoon Choi 2 ABSTRACT The use of Glass Fibe Reinfoced Polyme (GFRP) ebas instead of conventional steel ebas as the einfocement in Continuously Reinfoced Concete Pavement (CRCP) gives solutions to the poblems caused by coosion of einfocement. Howeve, it is necessay to know what effect this eplacement has on the development of concete cacks, which is inevitable in CRCP. Concete shinkage and tempeatue vaiations ae known to be the pincipal factos fo ealy-age cack fomation in CRCP. By employing an analytical model, this study pesents the shinkage and themal stess distibutions in concete due to the estaint povided by GFRP ebas in compaison with that povided by steel ebas. It eveals the advantages of using GFRP ebas as einfocement in CRCP in tems of intenal tensile stess eduction in concete. Numeical calculation of the concete stess distibution in a GFRP einfoced CRCP section subjected to themal change is also pesented. Keywods: GFRP ebas, CRCP, cacks, concete shinkage, themal stess INTRODUCTION Othe than the advantage of eliminating steel coosion, themal and stiffness compatibility between GFRP and concete may also offe possible advantages when GFRP ebas ae used in einfoced concete pavements. Taditional CRCP einfoced by steel ebas has been applied fo a few decades (AASHTO, 1986), and the CRCP behavio has been epoted (Won et al., 1991; Kim et al., 21). Howeve, up to this point, thee is no pecedent fo the use of GFRP as einfocement in CRCP, and little elated wok has been done. It is theefoe necessay to study the mechanical behavio of CRCP einfoced with GFRP ebas. The effects of the GFRP einfocing ebas on shinkage and themal stesses in CRCP wee investigated at the onset of this study, and will be discussed in this pape. The esults of this study will eventually contibute to the development of the design of CRCP with GFRP einfocement. Shinkage and themal stesses in concete have been known to be pincipal factos fo the incipient cacking in concete pavements o bidge decks. Undestanding the development of these stesses is essential to popely contolling cacking, which may ultimately detemine the pefomance and longevity of the concete stuctue. In the case of a feely suppoted concete slab subjected to shinkage o tempeatue vaiation, the concete stesses ae poduced because 1 Pof., Dept. of Civ. and Envi. Engg., West Viginia Univ., Mogantown, WV hchen@wvu.edu 2 Gad. Res. Asst., Dept. of Civ. and Envi. Engg., West Viginia Univ., Mogantown, WV. jchoi@wvu.edu

2 of the estaints povided by the einfocements. While concete shinkage causes tensile stesses in concete (Zhang et al., 2), the tempeatue vaiation can cause eithe tensile o compessive stesses in concete. The themal stesses ae depending on whethe the tempeatues dop o ise and the elationship between the coefficients of themal expansion (CTE) of the concete and the einfocement used. The CTE of concete vaies with diffeent coase aggegate types, and the CTE of the GFRP depends on the composite mateials used. In this pape, analytical esults ae pesented to descibe the effect of GFRP einfocing ebas on shinkage and themal stesses in concete slabs. ANALYTICAL MODEL To appoximate the developments of shinkage and themal stesses in a concete slab, a epesentative concete pismatic model containing a longitudinal einfocing eba at its cente with width (o einfocing space in CRCP) B, height (o thickness in CRCP) H, length L, and eba diamete 2 is consideed. Then, as a matte of analytical convenience, the model is modified into an equivalent cylindical one with the coesponding equivalent diamete 2R, whee R = HB /π, accompanied by the same length and eba diamete as those fo the pismatic model. The schematic details of the models ae shown in Fig. 1. Adopting the shea-lag theoy (Cox, 1952), thee ae seveal assumptions made fo this analysis: 1) the concete and einfocement exhibit elastic behavio, 2) the bond between concete and einfocement is pefect at an infinitely thin inteface, 3) the stiffness of the concete and the einfocement in the adial (-) diection ae the same, 4) the stain in the concete, ε c at a distance R fom the x-axis is equivalent to the estaint-fee concete stain due to the shinkage o tempeatue vaiation, and 5) the tempeatue distibution in the concete and einfocement ae unifom in the adial diection. The effect of concete adial shinkage on the concete stess development in the longitudinal diection is neglected. Also, effects fom the CTE discepancies between the concete and the einfocement in the adial diection ae neglected. When the concete is subjected to a stain, ε c in the longitudinal (x-) diection, the ate of tansfe of load fom concete to einfocement can be assumed as dp/dx = C o (u-v), whee P is the load of the einfocement, and C o is a constant. v and u ae the axial displacements at = R and =, espectively. It is also known fom foce equilibium that dp/dx = 2π τ. Integating the shea stain along the adial diection one gets (u-v) = dp/dx ln(r/ )/(2π G c ), whee G c is the shea modulus of concete. Hence, 2π Gc Co = (1) ln( R / ) Also, dv/dx = ε c and du/dx = ε. Theefoe, 2 d P = C o ( ε ε c ) (2) 2 dx The estaint-fee concete axial stain, ε c, in the above equation can be substituted with eithe shinkage stain at any time t (in days) ε c,s (t) o themal stain ε c,t which ae given by t ε c, s ( t ) = ( ε c, s ) ult and ε c, t = Tαc (3a) 35 + t whee (ε c,s ) ult = ultimate shinkage stain fo dying at 4% RH; T = tempeatue vaiation; and α c = CTE of concete. ε c,s (t) is an empiical equation (Mindess and Young, 1981) fo moist cued concete. The einfocement axial stain due to concete shinkage, ε,s o due to tempeatue 2

3 vaiation, ε,t ae shown as: P ε, s = and A E P ε, t = T α + (3b) A E whee A = einfocement coss-sectional aea, E = Young s modulus of einfocement, and α = CTE of einfocement. Substituting Eq. (3) into Eq. (2) gives the govening diffeential equation fo P, and then, by solving the diffeential equation with bounday conditions that P = at x = and x = L, the einfocement foce, P(x), can be obtained. The axial foce equilibium with the aveage axial concete stess, (σ c ) avg must also be satisfied at any x location: P ( σ ) A =, whee A c is the + c avg c concete coss-sectional aea. Hence, the aveage axial concete stess can be given as follows: L cosh β x t 2 ( σ = c) avg ρe ( ε c, s) ult t L cosh β 2 (Concete Shinkage) (4a) and L cosh β x ( ) 2 ( σ = c) avg ρe T αc α 1 L cosh β 2 (Tempeatue Vaiation) (4b) whee ρ = einfocing atio (A /A c ), and 2Gc / E β = (5) 2 ln( R / ) The negative sign in font of Eq.(4b) indicates compessive axial stesses in concete. The maximum axial stess in concete can be simply found at x = L/2. MATERIAL PARAMETERS In the shinkage stess analysis, Young s modulus of concete, E c, as well as concete shinkage stain, ε c,s (t), ae employed as a time-dependent popeties, and theefoe, the elapsed time, t (days) is the only vaiable. The time-dependent Young s modulus of concete can be evaluated by (Mosley and Bungey, 199) Ec ( t) = E c, 28[ ln( t) ] fo t 28 (6a) Ec ( t) = 119. Ec, 28 fo t > 28 (6b) whee E c,28 = Young s modulus of concete at 28 days. In the themal stess analysis, the concete stesses at 28 days ae estimated fo diffeent tempeatue vaiations; a value of E c,28 is employed hee. Table 1 lists a set of model paametes and mateial popeties used in this study. RESULTS AND DISCUSSION In Fig. 1, the maximum aveage tensile stesses in the concete due to the concete shinkage ae estimated ove a peiod of time. The stesses with eithe steel o GFRP einfocements ae shown in this figue, and they ae compaed with each othe. In the compaison, # 5 ebas with a adius of.3125 in. (ρ =.519) ae employed fo the model length of L = 6 in. Fom the 3

4 figue, it can be seen that the maximum concete stess level ceated by GFRP eba is about onefifth of that by steel eba. This atio is about the same as that of the longitudinal GFRP eba s elastic modulus to steel eba s elastic modulus. TABLE 1. Model Paametes and Mateial Popeties Used in Analysis Paamete and Popeties Value Width, B, (in.) 6 Height, H, (in.) 1 Length, L, (in. ) 6 Ultimate Concete Shinkage Stain, (ε c,s ) ult, (µε) 8 Elastic Modulus of Concete at 28 days, E c,28, (Msi) 4.8 (1), and 5 (2) Poisson s Ratio of Concete, ν c.2 Young s Modulus of Steel Reba (Msi) 29 Longitudinal Young s Modulus of GFRP Reba (Msi) 5.8 CTE of Concete, α c, (µε/ o F) 5.7 (1) and 8. (2) CTE of Steel Reba, α,s, (µε/ o F) 6.6 CTE of GFRP Reba, α,g, (µε/ o F) 5.2 (note: (1) ganite aggegate and (2) siliceous ive gavel coase aggegate used).12 Max. Avg. Tensile Stess (ksi ) x B R Repesentative Pism L L z x y H Time (days ) Steel Fig. 1. Max. Avg. Tensile Stess in Concete vs. Time (ρ =.519 and L = 6 in.) Diffeent sizes of GFRP ebas, #3 though #6 (ρ =.184 though.739), ae also studied in Fig. 2, showing that the maximum concete stess inceases with an incease in the einfocing atio. GFRP ebas with a lowe Young s modulus povide the concete with less estaint than GFRP 4

5 steel ebas do while the concete shinks. The maximum concete stesses fo diffeent values of L ae examined in Fig. 3. The stesses incease with inceases in length, L. Fo the set of paametes (Table 1) used, the maximum concete stess inceasingly conveges to ρe ε c,s (t) when L appoaches, and ρe ε c,s (t) is attained as L eaches about 12 in Max. Avg. Tensile Stess (ksi ) ρ =.739 (#6) ρ =.519 (#5) ρ =.334 (#4).5 ρ =.184 (#3) Time (days ) Fig. 2. Max. Avg. Tensile Stess in Concete vs. Time (L = 6 in. and diffeent GFRP einfocing atios, ρ).25 L = 12 in. ρ E ε c,s (t).2 Max. Avg. Tensile Stess (ksi ) L = 6 in. L = 3 in Time (days ) Fig. 3. Max. Avg. Tensile Stess in Concete vs. Time (ρ =.519 GFRP and diffeent slab lengths, L) 5

6 The discepancy in CTE between concete and einfocement causes the themal stesses in both concete and einfocement. Figs. 4 and 5 show the plots of the maximum aveage axial stess in concete vesus tempeatue change fo two diffeent concete CTEs Max. Avg. Axial Stess (ksi ) α c = 5.7 µε / o F α,s = 6.6 µε / o F α,g = 5.2 µε / o F T ( o F ) Steel GFRP Fig. 4. Max. Avg. Axial Stess in Concete vs. Tempeatue Change (ρ =.519 and L = 6 in.) Max. Avg. Axial Stess (ksi ) α c = 8. µε / o F α,s = 6.6 µε / o F α,g = 5.2 µε / o F T ( o F ) Steel GFRP steel(fem) GFRP(FEM) Fig. 5. Max. Avg. Axial Stess in Concete vs. Tempeatue Change (ρ =.519 and L = 6 in.) 6

7 .5.45 Axial Stess (ksi ) T at top of slab = -5 o F T at bottom of slab = -3 o F (Tempeatue changes linealy fom top to bottom.) α c = 8. µε / o F α,s = 6.6 µε / o F α,g = 5.2 µε / o F steel Fig. 6. Axial Stess in Concete vs. Longitudinal Location by FEM (ρ =.519 and L = 6 in.) The CTE of ganite aggegate concete is lowe than that of steel eba and highe than that of GFRP eba (Table 1). As shown in Fig. 4, this CTE of concete causes tensile concete stess when using steel eba and compessive concete stess when using GFRP eba as tempeatue inceases; in the figue, the positive value epesents the tensile stess, and the negative value the compessive stess. The siliceous ive gavel aggegate concete has a CTE highe than the CTEs of both steel and GFRP ebas, and tempeatue inceases lead to compessive stess development in the concete fo both cases, as shown in Fig. 5. These compessive and tensile states ae evesed as tempeatue deceases. As can be seen in both Figs. 4 and 5, the absolute values of themal concete stesses fom GFRP eba ae less than those fom steel eba, mainly because of GFRP eba s lowe elastic modulus. In addition, both the magnitude and diection of the stess caused by tempeatue vaiation can be contolled by using diffeent combinations of concete and einfocement CTEs. A finite element model (FEM) has also been ceated to compae the esults with those fom the themal analytical model by using the FE analysis pogam, ABAQUS. The concete slab is modeled as fou-node, 2-D elements unde plane stess conditions, and the einfocement is modeled as beam elements with cicula coss-sections. The thickness of the concete 2-D plane stess elements is the width, B, of the concete pismatic model. All the mateial popeties ae assumed to be the same as those used in the themal analytical model (Table 1). The compaison (Fig. 5) shows that the FE esults have a good ageement with the analytical esults. As can be seen in the figues, the tensile stess levels in concete caused by both concete shinkage and tempeatue vaiation ae below the tensile stength of nomal concete. Howeve, othe estaining foces act on a given concete slab, such as fiction fom the subbase unde CRCPs, estaints fom the gides undeneath bidge decks, o estaints fom einfocement ties to neighboing slabs in CRCPs. When these estaints ae consideed, the oveall esulting tensile stess level in the concete will incease, most likely causing cacks in the concete slab. Fig. 6 shows the FEM esults of themal tensile stesses at the top of a einfoced concete pavement x (in. ) GFRP 7

8 along the longitudinal (x-) diection, consideing the afoementioned estaining foces. The fiction fom the subbase is modeled by using hoizontal sping elements with a sping stiffness of 1,35 lb/in., and the einfocement at its ends is constained in longitudinal and otational diections. Fo both cases, using the steel and using the GFRP einfocement, the maximum tensile stess caused by tempeatue vaiation inceases afte consideing the estaints. The maximum tensile stesses in concete einfoced with steel ebas exceed the tensile stength of nomal concete, while that fo the GFRP einfoced concete still stays below the concete tensile stength. The concete pavement einfoced with steel ebas will cack at its middle in this case. It is noted that in the above numeical examples, bond between concete and einfocement is assumed to be pefect. When bond slip is consideed, a smalle concete tensile stess can be expected. Futhemoe, because of the low modulus of elasticity in the GFRP ebas, lage cack spacings followed by wide cack widths in the GFRP einfoced concete pavement can be expected. If it is necessay to shoten the cack spacing o naow the cack width, such as in a CRCP case, a lage amount of GFRP einfocement is needed. SUMMARY In this pape, the concete stess poduced in a GFRP einfoced concete slab due to concete shinkage o tempeatue vaiation is calculated. The analytical solution indicates that the lowe Young s modulus of GFRP ebas esults in the stess eduction in concete. The themal stess in concete can be eithe tensile o compessive, depending on tempeatue vaiation and the CTEs of the concete and einfocement used. Lowe tensile stesses developed in GFRP einfoced concete can also cause the cack spacing to be lage and cack width to be wide in a continuously einfoced concete pavement, when compaed with the CRCP einfoced with the same amount of taditional steel ebas. ACKNOWLEDGMENTS The authos acknowledge the suppot fom USDOT/FHWA (DTFH61-99-X-78). REFERENCES AASHTO (1986), Guide fo Design of Pavement Stuctues, Ameican Association of State Highway and Tanspotation Officials. Cox, M. A. (1952), The Elasticity and Stength of Pape and Othe Fibous Mateials, Bitish Jounal of Applied Physics, 3, Kim, S. M., M. C. Won, and B. F. McCullough (21), CRCP-9 Compute Pogam Use s Guide, Reseach Repot , Cente fo Tanspotation Reseach, The Univesity of Texas at Austin. Mindess, S. and J. F. Young (1981), Concete, Pentice Hall. Mosley, W. H. and J. H. Bungey (199), Reinfoced Concete Design, Macmillan Education Ltd.. Won, M., K. Hankins, and B. F. McCullough (1991), Mechanistic Analysis of Continuously Reinfoced Concete Pavements Consideing Mateial Chaacteistics, Vaiability, and Fatigue, Reseach Repot , Cente fo Tanspotation Reseach, The Univesity of Texas at Austin. Zhang, J., V. C. Li, and C. Wu (2), Influence of Reinfocing Bas on Shinkage Stesses in Concete Slabs, ASCE Jounal of Engineeing Mechanics, 126(12),