Flexural fatigue analysis of a CFRP form reinforced concrete bridge deck

Composite Structures 93 (2011) 2895–2902

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Flexural fatigue analysis of a CFRP form reinforced concrete bridge deck Lijuan Cheng ⇑ Department of Civil and Environmental Engineering, University of California, Davis, One Shields Avenue, Davis, CA 95616, USA

a r t i c l e

i n f o

Article history: Available online 27 May 2011 Keywords: Bridge deck Fiber reinforced polymer Stay-in-place Form Fatigue

a b s t r a c t Concrete bridge decks reinforced with fiber reinforced polymer (FRP) composite panels have recently been used where the FRP panels also serve as the permanent formwork for concrete. Comparing to their short-term behavior, their long-term performance especially under repeated traffic loads (fatigue) has not yet been widely known. This paper presents a fatigue analysis tool developed for a new steel-free concrete bridge deck reinforced with carbon FRP stay-in-place form. The developed model takes into account the cyclic creep of concrete in compression, the reduction in flexural stiffness due to fatigue tensile cracking and the reduction in modulus of rupture under cyclic loading. Comparisons with experimental data show reasonable agreement where a full-size 2-span deck specimen was subjected to millions of fatigue cycles. The parametric study recommends reducing the amount of FRP reinforcement and concrete strength of the current design, and lower loading rate may introduce more stiffness degradation in the system. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Structural forms made of fiber reinforced polymer (FRP) composites have recently been used for concrete bridge structures due to their light weight, high specific stiffness, ease in installation and good durability properties. They are currently existing in the field in either open forms such as permanent formwork for bridge decks and flooring systems [1–3], or in closed forms such as stay-in-place tubular shells for concrete bridge columns and pylons [4–6]. The use of the structural forms as both primary tensile reinforcement and stay-in-place form cannot only accelerate the construction process, but also enhance the long-term durability [7] and could potentially reduce the life-cycle cost of the structure system. Infrastructures such as bridges often experience heavy daily traffic loads that induce repetitive stress cycles (fatigue) in the materials during the service life of the structure. For example, a typical reinforced concrete (RC) bridge deck may experience up to 700 million stress cycles during a course of a 120 years life span [8], and an overpass on a typical highway with a design life of 40 years can go through a minimum of 5.8 billion loading cycles of varying intensities [9,10]. These repeated loading may lead to internal cracking of a member that degrades its stiffness and load-carrying characteristics. For FRP structural form reinforced concrete systems, FRP composites have been found to improve the cracking behavior of concrete bridge decks [2] and concrete filled FRP tubes under fatigue loading [6]. However, appropriate ⇑ Tel.: +1 530 754 8030; fax: +1 530 752 7872. E-mail address: [email protected] 0263-8223/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2011.05.014

fatigue analysis and design tools for these systems especially concrete bridge decks are still lacking in the open literature [11,12]. The objective of this study was to develop and validate an analytical tool for predicting the flexural fatigue response of a recently developed concrete bridge deck system reinforced with carbon fiber reinforced polymer (CFRP) stay-in-place form [2,13]. This concrete bridge deck is free of steel and the CFRP form has a configuration of a flat laminated CFRP plate stiffened with rectangular stand-ups filled with non-structural foam and interlocking ribs at the interface (as shown in Fig. 1). The static behavior under monotonic loads of this CFRP-concrete deck has already been investigated [13,2], where two series of single-span specimens were tested monotonically for flexural response and the results were compared with the analytical model conducted in the same study. The failure of the static specimens was mainly caused by the combined flexure and shear cracks in concrete (no failure in FRP or interface). To provide the tensile resistance at the intermediate continuity regions (negative bending moment areas), thin layers of carbon/epoxy mesh are used for top tensile reinforcement. The cyclic creep response of concrete in compression, the reduction in flexural stiffness due to fatigue tensile cracking, and the reduction in modulus of rupture under cyclic loading are considered in this model. The validity of the model was conducted through comparisons with existing test data on reinforced concrete beams [14] and a full-scale 2-continuous span deck system subjected to 2.36 millions of fatigue loads [15]. A parametric study was followed using this verified model, where the effect due to CFRP panel thickness, concrete compressive strength, loading rate and load range was investigated.

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Fig. 1. Illustration of a CFRP form reinforced concrete bridge deck unit.

2. Fatigue models When subject to repetitive stresses caused by loads such as fatigue traffic loads, material progressive and irreversible deterioration occurs in a structure. The propagation of fatigue cracks can lead to failure of the concrete structure. The main reasons that the effect of fatigue shall be considered in the design of reinforced concrete structures have been well documented in the first and subsequent reports of the ACI Committee 215 [16]. 2.1. Fatigue of concrete The commonly used models for characterizing the fatigue behavior of concrete include the ones developed by Whaley and Neville [17,18] and Holmen [19]. Whaley and Neville’s model was developed based on a study that evaluated the non-elastic deformation of concrete subjected to fatigue loading where prismatic concrete specimens were fatigued in compression under constant environmental conditions. The main variables considered were the mean concrete stress and stress range, which was then used to develop the expressions for creep strain and concrete modulus. Reasonable fatigue predictions were obtained when the mean stress was kept at or below 45% and the stress range kept at or below 30% of the concrete static strength at the beginning of loading [17]. Holmen’s model was developed with a similar goal of characterizing the fatigue behavior of concrete subjected to fatigue loading in compression, but the tests were conducted on both cylindrical and prismatic specimens [19]. During his study, the concrete mix and age, environmental conditions, sinusoidal loading pattern and frequency were kept constant. The maximum strain in concrete was described as being the sum of two independent components: the endurance-related strain and the time-dependent strain. The total strain was found to increase in three typical stages: Stage I consisted of a rapid increase that occurred up to approximately 10% of the total fatigue life of the specimen; Stage II consisted of a uniform increase that occurred between 10% and approximately 80% of the total fatigue life; and Stage III consisted of a rapid increase till the final failure [19]. During the first and second stages, the endurance component of the strain varied as the cycle ratio changed (the ratio between the current cycle number and the total fatigue life) and was a function of the secant modulus. The time-dependent strain was a function of the stress levels. The primary considerations and design parameters are rather similar in both Whaley’s and Holmen’s models, but Whaley and Neville’s model appears to be much simpler and is thus adopted in the current study for a straight forward implementation. The cyclic creep strain of concrete (ec) consists of the mean strain component and the cyclic strain component. It is defined

as a function of mean stress ratio (rm), stress range (D), number of cycles (N), and time computed in hours (t), as described in Eq. (1) below.

ec ¼ 129rm t1=3 þ 17:8rm DN1=3

ð1Þ

where the mean stress ratio and the stress range are calculated from the maximum (rmax) and minimum (rmin) applied compressive stress in concrete and the nominal compressive strength of concrete (fc0 ), i.e.,

rm ¼ ðrmax þ rmin Þ=ð2fc0 Þ D ¼ ðrmax  rmin Þ=fc0

ð2Þ ð3Þ

Knowing the cyclic creep strain, the cycle dependent secant modulus of elasticity for concrete in compression (EN) after N fatigue cycles can be computed by Eq. (4) where E is the initial modulus of elasticity in concrete.

rmax

EN ¼ rmax þe E

ð4Þ

c

2.2. Fatigue of CFRP structural form Matrix is known to be more susceptible to fatigue than fibers which typically contain fewer defects than matrix and are hence more resistant than matrix itself to crack initiation [20]. FRP composites are commonly made of layers of unidirectional or angled fiber/matrix composite. Any crack that forms in the matrix does not easily propagate across the fiber, resulting in better fatigue resistance in FRP composites in general than other materials such as steel and concrete. In this study, the structural form reinforcement is designed to consist of eight layers of unidirectional carbon fabric and four layers of E-glass chopped strand mat (CSM). Although the fatigue life of FRP composites can be affected by the applied stress range and the rate of loading [21,22], carbon fiber reinforced polymer (CFRP) composites generally exhibit much better fatigue performance than glass fiber reinforced polymer (GFRP) composites [23]. Moreover, as reported in the experiment [15], at the end of the 2 million cycles of fatigue service load, the tensile strain in the CFRP form plate was measured as 0.00012, which is significantly lower than the specified allowable limit (i.e., 0.003), clearly indicating that the FRP plate was not highly loaded and had a significant reserve capacity. Note that the degradation in the E-glass CSM layers is neglected since they contribute little to the strength of the plate. Therefore, the strength and stiffness degradation in the CFRP form reinforcement due to fatigue under the normal environment is insignificant and is assumed to be negligible during the analysis (i.e., fatigue resistant).

L. Cheng / Composite Structures 93 (2011) 2895–2902

3. Fatigue analysis of CFRP form reinforced concrete deck The modular bridge deck system recently developed [2] is constructed from a normal weight concrete slab free of steel rebars but reinforced with a carbon fiber reinforced polymer composite stayin-place form. Fig. 1 illustrates a typical 1.2 m wide unit section of this deck system where the CFRP form is made of a flat panel with foam-filled rectangular stiffeners extruded on the top and sand/resin based shear ribs at the surface. The bottom flat panel consists of eight layers of unidirectional carbon fabric with an areal weight of 305 g/m2 and a unit thickness of 0.38 mm in each layer together with the use epoxy resin. To achieve certain thickness of the panel, four layers of E-glass chopped strand mat are inserted in between the carbon fabric layers in a symmetric lay-up scheme. Each Eglass layer has an areal weight of 458 g/m2 and a unit thickness of 0.92 mm [13]. These chopped strand mats consist of randomly oriented short fibers and generally have very low mechanical property and their contribution to the overall strength of the plate is negligible. The tensile reinforcement provided by the CFRP plate is equivalent in its axial tensile stiffness to two mild steel rebars (20 M with a unit area of 300 mm2 and a modulus of 204 GPa). In order to provide sufficient resistance to the construction load on the form plate (such as the self-weight of concrete), rectangular stiffeners containing primarily unidirectional carbon fabric filled with foam core are adhesively bonded via epoxy resin onto the top surface of the CFRP form. The rectangular stiffeners are 41 mm wide, 105 mm high and spaced 305 mm apart (as shown in Fig. 1). The foam filler has a density of 0.961 kN/m3, a compressive strength of 0.785 MPa and a Young’s modulus of 27.4 MPa. The shear interaction between the concrete slab and form is further enhanced by sand treating the panel surface and installing sandepoxy based shear ribs at the interface (spaced at 152 mm). The shear ribs are made of sand-epoxy paste using press molding and have a trapezoidal shape (i.e., 15 and 10 mm wide at the bottom and top edge, and 10 mm high). The improvement on the concrete-panel interaction due to the presence of sand and shear ribs has been reported elsewhere [2] where a series shear-bond tests on 610 mm wide deck sections were performed. An analytical procedure based on the conventional bending theory is developed in this study where the Whaley and Neville’s concrete fatigue model is adopted. During this procedure, a discrete layered approximation and a typical sectional analysis are involved during each cycle. The concrete-CFRP deck section is divided into a number of discrete rectangular layers or segments with specified thickness (considering different contributions from concrete, CFRP plate, rectangular stiffeners and foam fillers, as shown in Fig. 2). The strain in each layer or segment is assumed to be uniform and equal to the actual strain at the center of the layer. Within each layer or segment, the stresses in concrete, CFRP plate, rectangular stiffeners and foam are different due to the different modulus in each material. The stress is thus not uniform over the layer and the resulting force is the summation of contributions from each component calculated from the product of the stress in the

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material and the area of the corresponding component (if it exists in that segment). The bending moment contribution of that layer is calculated in the similar way where before summation, the resulting force in each component is multiplied by the distance of the center of the component from the section top flange. The resultant axial force and the bending moment are obtained by the summation of all the layers in the section. It is obvious that the precision of this discrete layered approximation will be greatly improved as the number of the layers or segments increases (i.e., the thickness of each layer or segment becomes smaller). The moment–curvature response of the section (slope of the strain distribution profile) during each cycle can be obtained using an iterative process of adjusting the neutral axis position for a given strain distribution to maintain the horizontal force equilibrium of the section. Other main assumptions adopted during this analysis include: (1) linear elastic behavior of the CFRP form which remains unchanged during the fatigue loading cycles; (2) negligible contribution to the tensile strength from concrete; (3) perfect bonding between the concrete and CFRP form (such that the conventional bending theory is applied here. No slippage or debonding was actually observed between the concrete and CFRP form during the experiment [15]; and (4) the final failure of the structure is governed by any of the following three criteria: (a) crushing of concrete in compression (e.g., the maximum compressive strain exceeds the allowable level of 0.003 [24]; (b) rupture of CFRP in tension (e.g., the maximum tensile strain exceeds the allowable level of 0.003 for service limit design [16]; and (c) excessive deflection in the structure under serviceability considerations (e.g., the deflection ratio exceeds the design allowable level of L/800 = 2.92 mm where L is the span length of the system [25]. Besides these three failure criteria, the termination condition for the analysis also includes the exceeding of the practical limit on the total number of fatigue cycles that is set for the fatigue analysis conducted in this study (e.g., 2 million cycles, specified minimum number of cycles for truck loading in AASHTO [25]. For a given number of cycles (N), the cycle dependent effective moment of inertia (Ie,N) provides a transition between the gross and cracked moment of inertia. Per ACI 1999 [24], this effective moment of inertia can be obtained from the following equation.

Ie;N ¼ Icr;N þ

 3 M cr;N ðIg  Icr;N Þ Ma

ð5Þ

where Ig is the gross moment of inertia and Icr,N is the cracked moment of inertia after Nth cycle. Ma is the maximum value of the applied moment and Mcr,N is the cracking moment after Nth cycle computed from the following equation:

Mcr;N ¼

Ig fr;N ðh  yÞ

ð6Þ

where h is the height of the member cross-section and y is the depth of neutral axis. fr,N is the reduced modulus of rupture due to cyclic loading and can be computed from Eq. (7) [17,26]:

Fig. 2. Schematics of section discretization of CFRP form reinforced concrete deck.

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fr;N ¼ fr 1 



log N 10:954

ð7Þ

where fr is the modulus of rupture of concrete and N is the number of fatigue cycles. The deflection of the CFRP-concrete deck after N cycles can then be calculated from Eq. (8) where /(load, span) is a function of the applied load, the span length of the member and the loading and boundary conditions based on the conventional beam theory.

d¼

/ðload; spanÞ EN Ie;N

ð8Þ

The implementation of the step-by-step procedure for the fatigue analysis of such a CFRP-concrete deck system is outlined as follows. (1) Given the geometrical and material information, find the initial static stress distribution corresponding to the applied moments on the deck system. (2) Obtain the mean stress ratio (rm) and the stress range (D) from Eq. (2) and (3). (3) Divide the deck cross-section into a number of small fiber layers. Set the beginning of the fatigue analysis where time t = 0 and cycle N = 1. (4) Calculate the cyclic creep strain of concrete (ec) for each fiber layer along the cross-section after N cycles using Eq. (1). (5) Calculate the secant modulus of elasticity for concrete in compression (EN) after N cycles from Eq. (4). (6) Find the reduced modulus of rupture in concrete (fr,N) using Eq. (7). (7) Adjust the location of the neutral axis (y) till the force equilibrium in the section is reached. Use the cracked moment of inertia (Icr,N) and the cracking moment (Mcr,N) from Eq. (6). (8) For a complete moment–curvature response of the system at the current time (t), repeat Steps 4–8 with a small incremental change of the moment until termination criteria is met (i.e., either the strain in concrete or CFRP exceeds their corresponding allowable levels, or the user-specified total number of cycles is reached). (9) To estimate the deflection under fatigue at the current time (t) after N cycles, substitute the effective moment of inertia (Ie,N) calculated from Eq. (5) into Eq. (8) with an appropriate expression for the specific function /. (10) Check the failure criteria as previously defined. If none of these criteria violates, repeat Steps 4–10 with an increment of time (Dt). Otherwise, terminate the analysis and complete with output results. 4. Model verification 4.1. Model verification using test data from existing literature [14] To illustrate the validity of the fatigue model developed in this study, the experimental data reported by Papakonstantinou in 2000 [14] are first adopted here for model evaluation. In this experimental study, eight reinforced concrete beam specimens strengthened with glass fiber reinforced polymer composite sheets were tested under 3-point fatigue at a frequency of either 2 Hz or 3 Hz with different load ranges. Since the section of the member consists of reinforced concrete and GFRP sheets, the section discretization as previously described for CFRP form reinforced concrete section is modified accordingly. The same flexural fatigue model is applied here. The specimens had a span length of 1220 mm (with a totally length of 1320 mm), a width of 152 mm and a uniform thickness of 152 mm. Four steel rebars (with a diameter of 12.7 mm) were used as the flexural reinforcement (two in

the tension and two in the compression region) and twenty stirrups (with a diameter of 9.5 mm) were placed as the shear reinforcement. The average compressive strength of concrete was reported as 40 MPa, the yield strength of steel was 427 MPa, and the tensile strength of the glass FRP sheet was 1730 MPa. Static tests were conducted during the fatigue loading to measure the deflection and stress level. Further detailed information on specimens and test setup is available in [14]. Among the eight fatigue tests reported in [14], test data on three specimen cases (S-2, S-6 and S-8) representing different fatigue frequency and load range are selected for comparison purpose. Specimen S-2 was tested at 3 Hz and the ratio of the applied load to yield load (Pmax/Py) was 0.58. S-6 was tested at 2 Hz and the ratio of Pmax/Py was 0.81. S-8 was tested at 2 Hz with a ratio of 1.0. Fig. 3 compares the experimental data on the deflection response vs. the number of cycles in specimens S-2, S-6 and S-8 with the analytical results obtained from the fatigue model developed in this study. Since the values of the experimental deflections reported in [14] were normalized by the first value recorded after the beginning of the fatigue test, the analytical results here were also normalized by their corresponding deflection at the very first cycle. It can be seen that reasonable agreement is obtained between the existing test data [14] and the developed fatigue model, where the average difference between the two is less than 1%. 4.2. Model verification using test results on CFRP form reinforced concrete slab A full-size 2-continuous span bridge deck constructed from this CFRP form reinforced concrete slab (as shown in Fig. 4) was tested under flexural fatigue where the specimen was subjected to 2.36 million cycles fatigue loads [15]. This continuous span configuration was selected to represent its typical application in a multiple-span concrete slab-on-girder type of bridge system. Each span had a center-to-center span length of 2.337 m and a uniform slab width of 1.22 m in the specimen. The thickness of the bottom CFRP plate was 6.3 mm with an actual longitudinal modulus of 60.4 GPa measured per ASTM 3039 [27]. The thickness of the concrete slab was 196 mm (common for concrete bridge slabs [25] and its compressive strength reached 46.6 MPa on the day of testing. At the interior support, tensile reinforcement in the form of carbon/epoxy mesh was placed near the top surface of the slab (as shown in Fig. 1) to resist the negative bending moment. Five layers of this fiber mesh made of longitudinal and transverse carbon fiber strands (with a grid size of 25 mm) were bundled together and embedded about 25 mm below the concrete top surface. The tensile strength of each mesh was experimentally obtained as 841.7 MPa from a series of 254 mm long sample strands [2]. The detailed material properties are summarized in Table 1. The specimen was simply supported with a pin (at one exterior support) and two rollers (at the interior and the other exterior supports). To simulate the actual loading effect due to one axle of AASHTO HS-20 truck wheel load [25], two patch loads of 84 kN (fatigue service loads) were placed through two actuators 1.829 m apart on top of the specimen in the traffic direction (including a dynamic allowance factor of 15% accounting for the fatigue limit state). The load range varied between 4.5 kN (Pmin) and 168 kN (Pmax = 1.0Pservice) at a constant loading rate (frequency) of 5 Hz. It should be noted that the maximum load exerted by each actuator during the fatigue test (the first 2 million cycles) is approximately 27% of the average failure load reported for the single-span tests of the half width deck specimens under a monotonic load [13]. At the end of each 250,000 cycles, the fatigue test was paused and a monotonic load was applied to assess the flexural stiffness degradation in the deck. It should be noted that the CFRP form only existed at the bottom of the concrete slab as tensile reinforcement and did not extend to

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1.06

1.06

Specimens S-6 and S-8 Normalized Deflection

Normalized Deflection

Specimen S-2 1.04

1.02

Test (Papakonstantinou 2000)

1.00

Analysis 0.98

0

200000

400000

600000

1.04

1.02

0.98

800000

Test (S-6, Papakonstantinou 2000) Analysis (S-6) Test (S-8, Papakonstantinou 2000) Analysis (S-8)

1.00

0

20000

40000

60000

80000

100000

120000

Number of Cycles

Number of Cycles

Fig. 3. Comparison of normalized deflection vs. number of cycles from reference [14].

Mid-span Deflection (mm)

1 0.9

Test (Ref[15])

0.8

Analysis

0.7 Actuators

0.6 0.5 914

914 Steel plate Elastomeric pad (510x250 mm)

0.4

Steel roller

Steel pin

0.3

Concrete abutment

0.2

Actuator location

250

510

0.1 0

(Unit: mm)

0

200000

400000

600000

800000

1000000 1200000 1400000 1600000 1800000 2000000

Number of Cycles (N) Fig. 4. Comparison of deflection response on CFRP form reinforced concrete slab [15].

Table 1 Material properties. Material

Property

Value

Reference

Concrete slab

Thickness Compressive strength

196 mm 46.6 MPa

AASHTO ASTM C39/39 M

CFRP form reinforcement

Thickness Longitudinal modulus Longitudinal tensile strength

6.3 mm 60.4 GPa 223 MPa

— ASTM D3039 ASTM D3039

Foam filler for stiffeners

Density Compressive strength Young’s modulus

96.1 kg/m3 0.79 MPa 27.4 MPa

Manufacturer’s data Manufacturer’s data Manufacturer’s data

Carbon/epoxy (CFRP) mesh

Tensile strength

841.7 MPa

ASTM D3039

the top of the cross section at the interior support. Therefore, during the analysis, a separate concrete section was created at the interior support (continuity region) which experienced negative bending moments. The moment curvature and fatigue analyses were then performed for both sections along the span length and the middle continuity region. Fig. 4 shows the comparison between the analysis and the experimental response of the maximum midspan deflection in the deck during the first 2 million cycles of

fatigue service load. Good agreement is noted between the analytical predictions and the experimental data through the loading history. These deck deflections under the 2 million cycles of fatigue service load are far below the allowable design level (i.e., L/800 = 2.92 mm), indicating a fairly conservative system in the current design. This was also confirmed by the observations from the test that the strain levels in both concrete and CFRP were even less than 5% of the corresponding allowable limits. It can also be

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sin and the deck span-to-depth ratio remain unchanged. The same pin-roller boundary conditions as applied in the experiment are used in this study (simply supported with a pin at one exterior support and a roller at both the interior and the other exterior support). Noticing the over-conservative design in the current deck system, the number of carbon fiber reinforcement layers in the CFRP form plate (nCFRP) is reduced from eight layers to four layers and six layers, resulting in a reduced form thickness (tCFRP) of 4.4 mm and 5.1 mm, respectively. The symmetric stacking sequence in the laminate is maintained for these cases and the number of chopped strand mat layers is kept the same as before. Among all these cases, the concrete strength, loading rate and load range are the same as the current design case. To study the effect due to concrete compressive strength (fc0 ), a range from 16.5 MPa to 34.5 MPa is selected for the concrete where the CFRP form consists of four layers of carbon fabric. The effect due to different loading rates (f) and load ranges (Pmax/Pservice) is also investigated and the ranges are listed in Table 3, where the deflection (d) is measured at failure or at 2 million cycles, whichever occurs first. It is also normalized by the deflection at the first fatigue cycle (d1) of each individual case. According to the analysis results in Table 3, the normalized deflection under fatigue (deflection damage or stiffness degradation) decreases as the amount of CFRP reinforcement increases. However, this deflection damage increases from 1.45 to 1.95 when the concrete strength is increased from 16.5 MPa to 34.5 MPa. These two parameters seem to affect the fatigue response in the deck more significantly than the loading rate or frequency (f). In all cases considered herein, none of the failure is caused by concrete crushing, CFRP rupture or excessive deflection. The number of cycles shown in Table 3 corresponds to the practical 2-million cycle limit (specified minimum number of cycles for truck loading in AASHTO [25] that is set for the fatigue analysis conducted in this study. It appears that the current deck design could be further optimized by reducing the number of CFRP layers. Fig. 6 illustrates the effect due to different loading rates (frequency f) on the fatigue damage in the deck system. It can be seen that the deflection damage under fatigue loading increases as the loading rate decreases. The fatigue damage is more substantial when the loading rate is below 5 Hz, above which little difference is observed. It is also clear that as the load range (Pmax/Pservice) increases, the deflection

Table 2 Comparison of strains at different fatigue stages. End cycle number

1 500000 1000000 1500000 2000000

Fatigue analysis

Experiment [15]

Concrete

CFRP

Concrete

CFRP

0.000151 0.000169 0.000174 0.000178 0.00018

0.000414 0.000418 0.000419 0.000419 0.00042

0.00080 0.000107 0.000119 0.000131 0.000124

0.000107 0.000119 0.000129 0.000126 0.000129

seen from Fig. 4 that the deflection appears to increase more quickly at the initial stage of the fatigue history and this deflection gain reaches a minimum as the number of fatigue cycles increases (with a steady region noted in the response). Furthermore, both the tensile and compressive strains in the CFRP and concrete are at extremely low levels (as shown in Table 2) throughout the fatigue cycles. At the end of the 2 million cycles, the experimentally measured strain in the concrete and CFRP plate reached only 0.000124 and 0.000129, respectively, significantly lower than their allowable limit (i.e., 0.003 as specified in [15]. The corresponding strain obtained from the fatigue analysis was also only 0.00018 and 0.00042 for concrete and CFRP plate, respectively. These strains all showed a similar slow and steady increasing trend as the number of fatigue cycles increased. The curvature response of the section located at the maximum bending moment region is illustrated in Fig. 5, as compared with the test data calculated from the strain results presented in [15]. Note that a linear strain distribution along the deck section was assumed herein due to the fact that the strain was only measured on the most top (concrete) and bottom (CFRP) surfaces of the deck section during the experiment [15]. It can be seen that the difference between the analytical and experimental curvature response is relatively large, implying the need to further examine the linear strain distribution assumed herein. 5. Parametric study The effect due to the amount of CFRP reinforcement, concrete compressive strength, loading rate (frequency) and load range is studied next using the previously verified analytical model. Other material and geometrical parameters such as the types of fabric/re-

0.01

CL

L/4

0.008

L/2

Mmax

L/4

N ε top

Curvature (1/m)

SG58

φN

0.006

N

ε bot Strain gage locations in the fatigue test SG65

0.004

Test (Ref [15]) Analysis

0.002

0

0

200000

400000

600000

800000

1000000 1200000 1400000 1600000 1800000 2000000

Number of Cycles (N) Fig. 5. Comparison of curvature response on CFRP form reinforced concrete slab [15].

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L. Cheng / Composite Structures 93 (2011) 2895–2902 Table 3 Summary of effect due to different design parameters. Value

Constants

Number of cyclesd (N)

Normalized deflectione (d/d1)

Number of carbon layer [or plate thickness], nCFRP [or tCFRP, mm]

4 [4.4] 6 [5.1] 8 [6.3]b

fc0

= 46.6 MPa f = 5 Hz Pmax/Pservicec=1.0

2 million 2 million 2 million

2.47 2.08 1.83

Compressive strength of concrete, fc0 (MPa)

16.5 24.1 34.5

nCFRP = 4 f = 5 Hz Pmax/Pservice = 1.0

2 million 2 million 2 million

1.45 1.62 1.95

Loading rate (frequency), f (Hz)

0.5 1 5 10 15

nCFRP = 4 fc0 = 16.5 MPa Pmax/Pservice = 1.0

2 2 2 2 2

million million million million million

1.57 1.53 1.45 1.43 1.42

Load range, Pmax/Pservicec

1.0b 1.5 2 2.5 3

nCFRP = 8 fc0 = 46.6 MPa f = 5 Hz

2 2 2 2 2

million million million million million

1.83 1.32 1.21 1.19 1.18

Parameter a

a b c d e

The symmetric stacking sequence with the same number of glass CSM layers is maintained. The current design case. Pservice is the fatigue service load representing one axle of HS-20 truck wheel load of 168 kN (Pmin = 4.5 kN remains unchanged). Number of cycles at failure or at 2 million cycles, whichever occurs first. Deflection d is measured at failure or at 2 million cycles, whichever occurs first. It is normalized by the deflection at the first fatigue cycle (d1) of each individual case.

Normalized Mid-span Deflection ( δ/δ1)

1.6 1.5 1.4 1.3

f = 0.5 Hz f = 1 Hz

1.2

f = 5 Hz 1.1

f = 10 Hz f = 15 Hz

1 0.9

0

200000

400000

600000

800000

1000000 1200000 1400000 1600000 1800000 2000000

Number of Cycles (N) Fig. 6. Deflection damage response under different loading rates.

damage in the system decreases fairly linearly for cases with load range larger than 1.0 according to Table 3. 6. Conclusions Structural forms made of fiber reinforced polymer composites have recently attracted attention as an efficient type of reinforcement for concrete structures. In addition to the light weight and improved durability, their dual-function serving as the stay-inplace permanent formwork for concrete makes them more advantageous when a rapid construction is desired in the field. Comparing to their performance under monotonic static loading, the long-term fatigue behavior under repeated loading is relatively less known to date. Repetitive stresses due to fatigue often introduce progressive and irreversible deterioration in the material, which can cause collapse or catastrophic failure in the structure. The research discussed in this paper presents a suitable model that

is developed based on the existing Whaley and Neville’s concrete fatigue model to analyze and predict the fatigue damage of a steel-free CFRP form reinforced concrete bridge deck system. The specificities of this proposed model include: (a) it applies to concrete slabs reinforced with FRP forms made of a flat laminated CFRP plate stiffened with rectangular stand-ups in the positive bending moment region; (b) the analysis considers the multi-span configuration in the member where the continuity region (i.e., negative bending moment area) is reinforced with CFRP meshes; and (c) the model neglects the fatigue degradation of the CFRP form due to the known satisfactory fatigue resistance in carbon-based FRP composites. Therefore, this model does not necessarily apply to cases where glass FRP stay-in-place form is utilized as the tensile reinforcement. The validity of this model is further verified through comparisons with the experimental data reported in the existing literature followed by a parametric study of the proposed model.

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The main conclusions drawn from the current study include: (1) the flexural stiffness of the deck degrades rather gradually as the number of fatigue cycles increases but no failure in FRP or concrete is found during the 2 million cycles; (2) the deflection damage decreases as the amount of CFRP reinforcement increases and the concrete strength decreases, and these two parameters show to affect the fatigue response more significantly than the loading rate and range; (3) the deflection damage is more substantial under the lower loading rates (frequencies) during the fatigue history when compared with cases under higher loading rates. Future work on this study can be extended to incorporating the interfacial bond behavior between the concrete and CFRP form, different loading protocol and loading pattern, and developing an automated optimal design procedure for the system. Acknowledgements The author would like to thank her current and former students (Kanielle Gordon and Hazim Yilmaz) at the University of California, Davis for their assistance on this paper. References

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