J. Inst. Eng. India Ser. A (February–April 2012) 93(1):87–93 DOI 10.1007/s40030-012-0002-y

ARTICLES OF PROFESSIONAL INTEREST

A Methodology to Assess the Degradation in the Structural Response of the Deck of a Reinforced Concrete Road Bridge due to Corrosion of Reinforcing Steel Soumendra Banerjee • Amlan K. Sengupta

Received: 28 October 2010 / Accepted: 12 January 2012 / Published online: 12 April 2012  The Institution of Engineers (India) 2012

Abstract The present paper provides a methodology to analyse the effect of corrosion on the strength and stiffness of the slab-and-girder deck of a road bridge. A linear finite element model of a typical medium span deck of an existing bridge was developed as per the as-built drawings. The vehicular loadings were as per the recommendations of the Indian Roads Congress specifications and the design rating of the bridge. Based on the phenomenon of corrosion, a timedependent reduction in the area of flexural reinforcement near the soffits of the girders, was considered in the model. The effects of flexural cracking, creep and spalling of concrete were incorporated in the model with non-prismatic section properties and their stage-wise variations. From the analyses of a girder section and the computational model, it was observed that due to corrosion, the allowable moment capacity of a girder falls below the demand under dead load plus the rated live load, within the target service life of the bridge. However, the effect of corrosion on the stiffness of the deck is not substantial to be accurately measured by a conventional sensor. It is recommended that the procedure adopted in the paper can be used by the practicing professionals for numerically assessing longer span decks, to have a’priori estimates of the quantities that can be measured in a field test. Keywords Bridge deck  Corrosion of reinforcing bars  Numerical assessment  Reinforced concrete  Structural response

Introduction Many reinforced concrete (RC) transportation structures constructed in the last three to four decades have shown signs of distress. Corrosion of reinforcing bars (rebar) is one of the principal causes of distress in RC bridges, especially in the coastal and industrial areas. The corrosion and simultaneous loading reduce the service life of a bridge. Hence, understanding the influence of corrosion of rebar on the response of a bridge deck to the applied loads, is important for the prediction of service life of a new bridge or the residual life of an existing bridge. Traditionally, a one-time evaluation of load capacity of the deck has been the criteria of rating of a bridge. In the past decade, a continuous evaluation of the overall condition has been emphasized, which is termed as the structural health monitoring of a bridge. For either of the type of evaluation, a numerical assessment helps in refining the objectives of evaluation, the selection and location of instruments for data collection, and corroborating the measured data. In this paper, a methodology for numerical assessment of the degradation of the deck of a typical RC road bridge on a national highway in a coastal region, is presented. The assessment investigates the time-variant longitudinal structural response of the slab-on-girder deck due to the corrosion of rebar.

Research Significance S. Banerjee, Non-member Corps of Engineers, Indian Army, Chandigarh, India A. K. Sengupta (&), Non-member Department of Civil Engineering, Indian Institute of Technology Madras, Chennai 600036, India e-mail: [email protected]

The numerical simulation of the load against deflection behaviour of a bridge deck considering corrosion of rebar, is difficult because of the non-linear effects of cracking, creep and spalling of concrete. In the present study, a conventional linear elastic analysis of a bridge deck was extended to consider these effects in a stage-wise manner.

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The results provide a’priori estimates of variation of the quantities that can be measured to assess the response of a deck subjected to corrosion of rebar. The method of analysis is suitable for practicing professionals to make decisions on instrumentation in structural health monitoring of similar bridges.

Literature Review The corrosion of rebar is modelled in two stages (IRC: SP:60-2002 [1]). •

•

Initiation time (t0): This is the time required for chloride ions (Cl-) or the carbon dioxide (CO2) to diffuse and depassivate the oxide layer around the rebar. Propagation time (tp): This is the time required to show initial distress due to cracking of concrete at the level of the rebar and parallel to them. Subsequently, there is delamination and spalling of the concrete cover.

Table 1 Basic data of bridge deck Attributes

Information

Type

Simply supported RC girderand- slab deck, cast integrally

Span

17.5 m (between the centre-lines of the bearings)

Total width

13.75 m (carriage way for one direction of traffic ? footpath)

Width of carriage way

11.0 m (three lanes)

Footpath

1.5 m (on one side)

Number of longitudinal girders

4

Number of cross girders

2, at the ends

Wearing course

2 kN/m2

End supports

Pot-cum-PTFE bearings

Grade of concrete

M 30

Grade of steel

Fe 415

IRC: SP:60-2002 provides guidelines to estimate t0 and tp, based on models of diffusion of the agents of corrosion, and rate of corrosion of the diameter of a bar, respectively. The following review covers some studies of the effect of corrosion of the primary flexural reinforcement on the strength and serviceability of bridge decks. Cady and Weyers [2] presented a methodology to estimate the time for rehabilitation of a bridge deck subjected to corrosion due to de-icing salts. Weyers [3] estimated the service life of a bridge deck based on the initiation time and the time to crack the concrete. Enright and Frangopol [4] developed a reliability based approach for the prediction of service life of a bridge deck. Palsson and Mirza [5] highlighted that the reduction in the load carrying capacity of a deck subjected to corrosion of rebar, is not only due to the reduced crosssection of the bars, but also due to the loss of bond and ductility of the bars. The reduction in the structural reliability of a bridge deck due to the corrosion of unbonded prestressing strands was numerically demonstrated by Pillai et al. [6].

Analysis of a Bridge Deck Computational Model The basic data of the selected bridge deck from the as-built design drawings is given in Table 1. A cross-section of the bridge deck is shown in Fig. 1a. The sectional and reinforcement details of a girder are shown in Fig. 1b. All the girders were identical. A three dimensional computational model of the deck was developed using SAP 2000, which

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Fig. 1 Cross-sectional details of the bridge deck. a Cross-section of the bridge deck. b Sectional and reinforcement details at mid-span of a girder

can capture the transverse variation of response among the girders. The slab was modelled using thin shell elements. A girder was modelled using a frame element. The reinforcing bars were not modelled explicitly. They were considered through the moment of inertia of the transformed

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section. Based on discretising the section of a girder into layers, the moment of inertia about the centroid of the transformed section (It), can be expressed as follows. X X It ¼ ðIci jCG þ Aci y2ci Þ þ mAsj y2sj ð1Þ i

j

where, Aci is the area of a concrete layer, Asj is the area of a rebar layer, IcijCG is the moment of inertia of a concrete layer about its centroid, M is the modular ratio, yci is the distance of the centroid of a concrete layer from the centroid of the section, ysj is the distance of a rebar layer from the centroid of the section. Shear deformation of a girder was found to be negligible by comparing with an analogous model, where the girders were also modelled using thin shell elements. Since the analysis was limited to service level loads, the assigned constitutive model of concrete was linear elastic. However, the effects of flexural cracking, creep and spalling of concrete were simulated in a stage-wise analysis. This is explained subsequently. First, as a preliminary analysis, the deck was subjected to dead load (DL) alone. The self weights of the girders and the deck were considered in the model. The superimposed dead load due to wearing course was assigned separately as a uniformly distributed load. The weights of parapets and the footpath slab were considered to be negligible. It was observed that the tensile stress at the soffit of each girder at the mid-span exceeded the flexural tensile strength. Hence, for subsequent analysis, an effective moment of inertia (Ieff) was assigned to the central portion of a girder, where the moment demand exceeded the cracking moment. This portion is referred to as the flexurally cracked zone. The cracking moment for a flexurally uncracked section is given by the following equation. Mcr ¼ f cr

were assigned with It. Since the supports were not truly discontinuous due to slight overhangs of a girder, the assignment of non-prismatic section properties (as opposed to a prismatic section with Ieff throughout) leads to better simulation of the flexural stiffness of the girder.

It ymax

ð2Þ

where, fcr is the modulus of rupture of concrete, 0.7 Hfck, fck being the characteristic compressive strength of concrete, ymax is the distance of centroid from the soffit. The value of Ieff was calculated as a weighted average of the moments of inertia of the uncracked (It) and cracked (Icr) transformed sections, as per the recommendation of ACI 318-08 [7]. The weighting factors are functions of the ratio of Mcr and the moment at mid-span, M. "  3  3 # Mcr Mcr Ieff ¼ It þ 1  ð3Þ Icr M M The value of Icr was calculated using Eq. (1) neglecting the concrete below the revised centroid. The remaining two portions of a girder near the supports, where considered to be flexurally uncracked and

Live Loads The following cases of live loads (LL) were considered. Service Live Load The analysis was based on the design LL rating of the carriage way. The LL on footpath was neglected. As per the recommendation of IRC: 6-2000 [8], two live load combinations were considered. (i)

Simultaneous loading of one Class AA tracked vehicle and one Class A vehicle (Fig. 2): To get the maximum moment in a girder from the transverse placement of the vehicles, the Class AA vehicle was placed 1.2 m from the right edge and the Class A vehicle was located centrally over Girder B. These placements satisfied the provisions of minimum edge clearance and minimum inter-vehicle spacing. In the longitudinal direction, the Class AA vehicle was placed centrally in the span. For the Class A vehicle, only one trailer could be placed in the span. The vehicle was placed such that the highest axle load and the resultant of the axle loads were symmetric about the mid-span. (ii) Simultaneous loading of three Class A vehicles: For transverse placement, two vehicles were placed centrally on Girders B and C, and the third vehicle was placed as close as possible to Girder D, satisfying the minimum edge clearance. The longitudinal placement was similar to that mentioned earlier. The higher moment in a girder from the analyses of the two combinations was considered.

Fig. 2 Computational model showing definition of lanes

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The simulation of a field load test provides estimates of measurable quantities, such as deflection, strains, natural frequencies and spectral response, before undertaking the test. Hence, representative static and dynamic tests were simulated as follows. Static Load For a static load test, three 40 T bogie loads were used. For transverse placement, the three vehicles were placed centrally over Girders B, C and D. The criterion of minimum edge clearance was ignored. The vehicles were placed centrally in the longitudinal direction. Dynamic Load For a dynamic load test, a vertical sinusoidal force of amplitude 100 kN at frequencies ranging from 3 to 12 Hz (using a swept sine forcing function at an increment of 0.1 Hz) was defined to simulate a shaker. The load was applied centrally on Girder B. Modelling of Corrosion Under severe exposure conditions, the Cl- induced corrosion was observed to be more critical than CO2 induced corrosion. Hence, only the results of Cl- induced corrosion are presented. The corrosion of bars was considered only in the girders, since these bars are the tension reinforcement for the flexure in the longitudinal direction. Also, due to the proximity of the soffit of the girders to the sea water and close spacing of the longitudinal bars in the girders, corrosion is generally higher in the girders as compared to the deck slab. Due to same exposure conditions, the corrosion in all the four girders was considered to be identical. The girders have three layers of bottom longitudinal bars. Considering the diffusion of Cl- from the soffit to be critical, initial corrosion was expected to set in the lowest row of bars uniformly along the span. For the present study, the equilibrium chloride concentration (C0) at the soffit of a girder was considered to be a high value of 12 kg/m3 (0.5% by weight of dry concrete, based on the observations of Cheung et al. [9]), which built up over a period of 5 years after the bridge was opened for service [3]. The diffusion constant (Dc) was considered to be 40 mm2/year, based on the water-to-cement ratio of 0.42. The threshold value of chloride concentration at the surface of the bars for initiation of corrosion was considered to be 0.83 kg/m3 [10]. The initiation time (t0) beyond the build-up of C0 was found to be 20 years (25 years after the bridge was opened for service). For the propagation time (tp), the rate of corrosion of the diameter of the bars was taken as 73 lm/year, for the critical combination

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of the basic rate of corrosion and the temperature coefficient, as per IRC: SP:60-2002. The propagation time tp was calculated to be 2 years beyond the initiation time (27 years after bridge was opened for service), for the provided effective cover of 40 mm and diameter of bars equal to 32 mm. The reduction in the area of a bar in the lowest row was calculated based on the rate of corrosion, considering uniform corrosion along the circumference. Since the initiation time for corrosion of the second row of bars from the soffit was 75 years, it was not considered in the present study. The reduction in the area of the lowest row of bars was modelled by reducing the moment of inertia of the transformed sections of a girder, for each of the flexurally cracked (Ieff) and uncracked (It) zones of the span of the deck. With the change in area of the lowest row of bars, the centroid of the section shifted up and the values of Ieff and It reduced. After spalling of the cover, the layer of concrete below the bottom row of bars was neglected. For the flexurally uncracked zone, the moment of inertia calculated using Eq. (1) reduced from It and is denoted as Isp. For the flexurally cracked zone, the spalling reduced both Mcr and Ieff, calculated using Eqs. (2) and (3), respectively. Stage-Wise Analysis A stage-wise analysis was undertaken to study the timevariant response of the bridge deck, by simulating the spatial and temporal variations of the section properties of each girder. As mentioned before, the cracking of concrete under flexure was considered by assigning an effective moment of inertia (Ieff) to the central portion of a girder. The two adjacent portions were assigned the moment of inertia of an uncracked transformed section (It). The creep of concrete was considered by reducing the modulus of concrete to a long term effective value as recommended in IS 456: 2000 [11]. Although creep is a continuous phenomenon, its lump-sum effect was considered after the end of 5 years. A linear variation of response was considered between 0 to 5 years as an approximation. The details of the stages are as follows. •

•

Stage 0 (t = 0, at the onset of service, Fig. 3a): Model A0 was analysed for DL only. The value of It was calculated using Eq. (1), with ‘m’ based on the short term modulus of concrete. For the cracked portion of a girder, Ieff was calculated using Eq. (3), based on the moment (M) due to DL alone. Stage I (5 \ t B 25 years, before the initiation of corrosion, Fig. 3b): Model A1 was analysed for the service LL and DL. The effect of creep was considered in the DL analysis only, by reducing the modulus of concrete to a long term effective value as recommended

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shown for t = 30 years. The model was updated at t = 50, 75 and 100 years. The target life of the bridge was selected to be 100 years.

Results The results from the numerical analysis are presented in terms of the flexural strength, stiffness and dynamic properties. Flexural Strength

Fig. 3 Spatial and stage-wise variation of moment of inertia for the elevation of a girder (all dimensions are in metres). a Stage 0. b Stage I (with creep). c Stage II (with creep and corrosion, t ? 27 years). d Stage III (with creep, corrosion and spalling, t = 30 years)

Figure 4 shows the variation of the allowable moment of a girder with the age of the bridge. The allowable moment at a certain instant was computed analytically based on the corresponding area of rebar at the bottom, using the working stress method of IRC: 21-2000. Any degradation of concrete or bond was not considered in the evaluation of the allowable moment. The moment demand in each girder was evaluated using the computational model. It was found to be highest for Girder D, with values of 1747 kN-m and 1448 kN-m for the dead and service live loads, respectively. The results are presented for Girder D only. At about 60 years, the allowable moment falls below the total moment demand of 3195 kN-m. Thus, the deficiency in strength is reflected before the target service life. However, since the allowable moment is well above the moment demand due to dead load alone, the bridge can be operational under a reduced live load rating. Flexural Stiffness

•

•

in IS 456:2000. For selecting the creep coefficient, it was considered that the bridge was put to service after one year of casting of the deck. The value of It was calculated with a long term value of m = 10, as per the recommendation of IRC: 21-2000 [12]. The cracked zone of the span had Ieff based on moment (M) due to DL ? LL. Stage II (25 \ t \ 27 years, before the initiation of spalling, Fig. 3c): Model A2 was analysed considering corrosion in rebar. The reduction in area of rebar reduced both It and Ieff. Since Mcr also reduced, the length of the flexurally cracked zone increased. Figure 3c is shown for t approaching the end of tp (27 years). Stage III (t [ 27 years, after the spalling of the cover, Fig. 3d): Model A3 was analysed with corrosion in rebar and spalling of concrete cover. The spalling of cover reduced the moment of inertia of the flexurally uncracked zone from It to Isp. The length of flexurally cracked zone further increased due to the reduction of Mcr. Also, the value of Ieff further reduced. Figure 3d is

Figure 5a presents the variation of mid-span deflection of Girder D with time, for service loads. It can be observed that the major contribution in the total deflection is due to dead load. At the beginning of Stage I there is a substantial increase in deflection mainly due to creep and flexural

Fig. 4 Allowable moment in a girder versus age of bridge (the moment demand is for Girder D)

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Fig. 6 Mid-span response of Girder D versus time of inspection, for test vehicle

Fig. 5 Mid-span response of Girder D versus age of bridge, for service loads. a Deflection. b Strain in the soffit

cracking of concrete. At the end of Stage II, the spalling of concrete increases the deflection. In Stage III, there is a gradual increase in deflection due to further corrosion of rebar. The maximum values of smeared strain at the soffit of the mid-span of Girder D were obtained from the corresponding values of bending moment (Fig. 5b). Static Load Test The mid-span deflection due to the test vehicles is shown in Fig. 6. The change in deflection due to corrosion is small (&0.02 mm). The measurements will have noise and the effect of temperature. Hence, the selected test vehicle loading is not adequate to monitor the effect of corrosion. ‘ Heavier vehicle is required to create a deflection of 1500 as per the load rating recommendation of IRC: SP:37-2010 [13], where ‘ is the span. Dynamic Load Test First, a free vibration analysis was carried out to observe the first natural frequency of the deck. In Fig. 7a, the variation of the frequency with respect to time is shown. The frequency shifts substantially due to the effect of creep. However, the change in frequency due to corrosion

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Fig. 7 Variation of dynamic properties of the deck with time. a Natural frequency. b Spectral deflection

is small to be detected. Thus, from a measured natural frequency, the corresponding reduction in area of rebar cannot be precisely estimated. A forced vibration analysis was carried at 0, 5 and 50 years, using the dynamic load mentioned earlier. The

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spectral deflection response was recorded in terms of the maximum deflection under steady state for each frequency run. The shift in the peak (resonance corresponding to the natural frequency) shows reduction in stiffness of the deck (Fig. 7b). As observed in Fig. 7a, the shift in the frequency is substantial due to creep, but small due to corrosion.

Conclusions and Recommendations The following conclusions were drawn from the present study. •

•

•

In the initial 5 years, there was a significant increase in the deflection due to creep and flexural cracking. After the corrosion had set in, the increase in deflection was gradual. Similarly, there was a significant shift in the natural frequency of the deck only in the initial 5 years. The corrosion cannot be monitored by measuring deflection or natural frequency alone, as the deck is stiff as compared to the span. A visual inspection and field tests to monitor the conditions of the materials are necessary. Due to corrosion, the allowable moment falls below the demand because of service loads, within the target life of the bridge. Hence, the load rating of the bridge has to be reduced accordingly.

Of course, the strength and stiffness will further reduce with the deterioration of the concrete, which was not considered in the present study.

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References 1. IRC: SP:60-2002, An Approach Document for Assessment of Remaining Life of Concrete Bridges. Indian Roads Congress 2. P.D. Cady, R.E. Weyers, Deterioration rates of concrete bridge decks. J. Transp. Eng. Am. Soc. Civ. Eng. 110(1), 34–44 (1984) 3. R.E. Weyers, Service life model for concrete structures in chloride-laden environments. Mater. J. Am. Concr. Inst. 95(4), 445–453 (1998) 4. M.P. Enright, D.M. Frangopol, Service-life prediction of deteriorating concrete bridges. J. Struct. Eng. Am. Soc. Civ. Eng. 124(3), 309–317 (1998) 5. R. Palsson, M.S. Mirza, Mechanical response of corroded steel reinforcement of abandoned concrete bridge. Struct. J. Am. Concr. Inst. 99(2), 157–162 (2002) 6. R.G. Pillai, M.D. Hueste, P. Gardoni, D. Trejo, K.F. Reinschmidt, Time-variant service reliability of post-tensioned, segmental, concrete bridges exposed to corrosive environments. Eng. Struct. 32, 2596–2605 (2010) 7. ACI 318-08, Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute, USA 8. IRC: 6-2000, Standard Specifications and Code of Practice for Road Bridges, Section II Loads and Stresses. Indian Roads Congress 9. M.M.S. Cheung, J. Zhao, Y.B. Chan, Service life prediction of RC bridge structures exposed to chloride environments. J. Bridge Eng. Am. Soc. Civ. Eng., 14(3), 164–178 (2009) 10. D.M. Frangopol, K.Y. Lin, A.C. Estes, Reliability of reinforced concrete girders under corrosion attack. J. Bridge Eng. Am. Soc. Civ. Eng. 123(3), 286–297 (1997) 11. IS: 456-2000, Indian Standard Code of Practice for Plain and Reinforced Concrete. Bureau of Indian Standards 12. IRC: 21-2000, Standard Specifications and Code of Practice for Road Bridges, Section III Cement Concrete (Plain and Reinforced), Indian Roads Congress 13. IRC: SP:37-2010 (draft), Guide Lines for Evaluation of Load Carrying Capacity of Bridges. Indian Roads Congress

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