ACI STRUCTURAL JOURNAL TECHNICAL PAPER

ACI STRUCTURAL JOURNAL

TECHNICAL PAPER

Title no. 104-S72

Behavior of Corroded Bar Anchorages by S. P. Tastani and S. J. Pantazopoulou An analytical model is developed to describe the mechanics of corrosion-induced bond strength degradation and its implications on development capacity of bar anchorages. The model is a frictional construct whereby bond strength is estimated from the coefficient of friction and the normal confining pressure along the anchorage. Both variables are evaluated considering the relevant design parameters (cover, shrinkage, and transverse reinforcement) and the effects of iron depletion. The model is used to interpret the behavior of corroded anchorages as documented in published experiments. To supplement model calibration with data representative of long anchorages, two series of flexural specimens designed to fail in anchorage after yielding are tested after being conditioned in accelerated corrosion to a predefined damage level in the anchorage zones. The effects of corrosion on bond strength are also considered in CFRP-patch repaired anchorages. The model correlates the experimental evidence obtained from the various alternative test arrangements and successfully reproduces the magnitude and parametric sensitivity of corrosion-induced bond degradation. Keywords: anchorage; assessment; bond; corrosion; cover; cracking; FRP jacket; modeling.

INTRODUCTION Corrosion of steel reinforcement has a detrimental influence on stiffness, ductility, and deformation capacity of exposed reinforced concrete (RC) members and it may significantly compromise their dependable strength.1 For this reason, corrosion is a critical parameter in assessment of residual strength and service-life of old RC construction. In quantifying the residual strength and deformation capacity of an affected structural member, three primary effects need be considered: 1) reduction in bar diameter (bar section loss) owing to iron depletion; 2) embrittlement of steel and the ensuing loss of dependable deformation capacity; and 3) the manifold implications on bond and the development capacity of the reinforcement, which include: • An effective reduction of the coefficient of friction on the bar surface, as the gradually increasing rust layer promotes separation and facilitates slippage between bar and concrete2; • Interruption of the chemical adhesion of concrete on the bar surface by the interpolated rust layer. This is particularly evident after the bar is stressed, therefore contracting laterally due to Poisson’s effect. Confining pressure due to drying shrinkage of concrete may be enhanced by a small amount of rust deposited on the bar. Therefore, for low corrosion level, a slight increase of bond may be seen before bond failure,3,4 a phenomenon that is more pronounced for smooth bars5; • Reduction in rib height of ribbed bars, thereby loosening mechanical interlock with concrete; and • Cracking or even spalling of the cover, owing to the expansive tendency of iron upon oxidation. Cover damage corrupts bond along the bar, thereby reducing or even eliminating the so-called beam action mechanism of 756

behavior6 and weakening the flexural stiffness and moment resistance of the member. Once bond along the shear span is degraded, reliance on the arching action to transfer the loads to the supports increases. This has several implications for safety, as development of the yield force of the reinforcement (the tie of the arch) depends greatly on the anchorage details of the bar near the support (usually a cut-off point for flexural reinforcement). The effect of corrosion on bond mechanics is the subject of the present investigation. To evaluate the influence of rust accumulation on bond strength, analytical modeling and correlation with experimental testing have been pursued. The proposed model refers to the basic frictional construct that underlies the ACI 3187 guidelines and accounts for the influences of corrosion penetration and rust buildup on the coefficient of friction and the normal pressure acting on the bar. The predictive capability of the model is evaluated through comparison with published test results from the literature. Reported bond strengths vary substantially between different investigations. The large range of values is interpreted with reference to the different test setups and the influence these have on the mechanics of bond. To analytically reproduce this variability, it is necessary to properly represent the actual state of stress generated by the support and loading conditions in the concrete cover and along the anchorage in the analysis.8 For model calibration with data concerning longer anchorages that are more representative of the field, two series of RC specimens, cantilever beams, and simply supported slabs are included in the experimental part of the present study. Before mechanical load testing, specimens are subjected to accelerated electrochemical corrosion up to a predefined level of mass loss. Parameters of the experimental study are the post-corrosion residual bond strength and deformation capacity defined as functions of corrosion mass loss. The efficacy of a repair scheme that included replacement of the spalled concrete cover with a cement-based grout and subsequent jacketing with carbon fiber-reinforced polymer (CFRP) wraps in the anchorage zones is assessed by reloading the specimens after repair. RESEARCH SIGNIFICANCE Quantifying the dependable bond strength of corroded reinforcement is an essential step in the assessment of affected RC structures exposed to aggressive environments. The primary contribution of the paper in this direction is formulation and calibration of a simple analytical model for bond strength of corroded reinforcement. The model is based ACI Structural Journal, V. 104, No. 6, November-December 2007. MS No. S-2006-344 received August 21, 2006, and reviewed under Institute publication policies. Copyright © 2007, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published in the SeptemberOctober 2008 ACI Structural Journal if the discussion is received by May 1, 2008.

ACI Structural Journal/November-December 2007

S. P. Tastani is a Research Engineer and an Adjunct Lecturer in the Department of Architecture at Demokritus University (DUTh), Thrace, Greece. She received her Civil Engineering Diploma, MSc, and PhD from DUTh. Her research interests include bond of reinforcement (steel and FRP bars), reinforcement corrosion, and use of FRPs in seismic repair/upgrading of reinforced concrete structures. S. J. Pantazopoulou, FACI, is a Professor in the Department of Civil Engineering at Demokritus University. She received her PhD and MSc in structural engineering from the University of California at Berkeley, Berkeley, CA, and an Engineering Diploma from the National Technical University of Athens, Athens, Greece. She is a member of ACI Committees 341, Earthquake-Resistant Concrete Bridges; 374, Performance-Based Seismic Design of Concrete Buildings; 408, Bond and Development of Reinforcement; and Joint ACI-ASCE Committees 352, Joints and Connections in Monolithic Concrete Structures, and 445, Shear and Torsion. Her research interests include the mechanics of reinforced concrete and earthquake design of reinforced concrete structures.

on the frictional concept for interface action and maintains the format of the code expressions for bond and development capacity while accounting for the primary variables known to affect behavior of corroded anchorages. The paper includes experimental corroboration and calibration of the primary behavioral aspects of the model. Due to its simplicity and familiar format, the model can be easily implemented within a practical framework of assessment where the residual strength, deformation capacity, and failure hierarchy of individual structural members need to be estimated from basic principles. CORROSION-BOND INTERACTION AND BASIS OF ANALYTICAL PROCEDURE Corrosion products have several times the volume of the parent metal (two to six times as large9). Oxides are deposited on the bar surface generating bursting pressure on the perimeter of the hole occupied by the bar, similar to the radial component of bond in an uncorroded ribbed stressed bar. As in the case of bond, pressure owing to rust build-up is resisted by hoop tension in the cover. Bursting pressures owing to either bond or rust build-up compete for the same strength reserve, namely the splitting capacity of the concrete surrounding the bar. In the absence of transverse reinforcement, the tensile strength of concrete sets an upper threshold in the magnitude of attainable expansive pressure, marked by progressive cracking of the cover. The process of crack penetration through the cover concrete has been modeled numerically.10 It was shown that the resistance curve of the ring of the concrete surrounding the bar, given in terms of pressure versus the radial displacement of interior boundary, is a characteristic property that depends primarily on the external-to-internal-ring-diameter ratio and the tensile strength of concrete (Fig. 1). In this context, any displacement of the interior boundary owing to rust accumulation exhausts part of the available cover resistance. Thus, in corroded bar anchorages, only the residual part of the resistance curve is available for the bond mechanism. As corrosion progresses, a fraction of the rust is deposited in the layer of concrete around the bar filling the pores and the cover cracks, whereas any soluble corrosion products may migrate away from the interface layer staining the exposed surface.9,10 Radial cracks initiate in the interior boundary of the cover and propagate outwards with rust build-up.11 Radial pressures that are sustained by hoop stresses in the exterior uncracked part of the cover act to confine the rust layer that is trapped between the bar and the concrete cover. This confining action effectively compacts the rust layer. Compacted rust has mechanical behavior similar to that of cohesionless granular materials.2 Upon through splitting of the cover, hoop stresses and radial ACI Structural Journal/November-December 2007

confining pressure are released. Beyond that point, further ingress of the aggressive agents necessary to sustain corrosion, such as oxygen, vapor, and chlorides, is greatly facilitated, leading to widening of cracks and eventual spalling of the cover concrete. The simplest model representing the stress transfer between steel and concrete is the so-called frictional concept. This model also forms the basis of the ACI 3187 requirements for bond and anchorage. Bond strength fb, quantified herein as an average shear stress acting on the lateral surface of the bar is, apart from initial adhesion fadh, proportional to the normal confining pressure mobilized on the bar over the anchorage. From free body equilibrium of a diametric slice (Fig. 2(a)) of the bar of length Lb, the resultant lateral shear force on the bar surface F equals 0.5πDb fbLb. The normal force N acting on the diametric plane of the bar equals σnDbLb, where the normal confining pressure σn comprises contributions from the hoop stresses of the concrete cover σc, the reaction of stirrups as they cross the splitting plane σst (calculated as the average normal compressive stress in reaction to the stirrup tensile forces), and any transverse compressive stress field σconf existing in the anchorage zone. Considering that F = μN + 0.5πDb fadhLb, where μ is the coefficient of friction, it follows that 2μ 2μ f b = ------σ n + f adh = ------ ( σ c + σ st + σ conf ) + f adh π π

(1a)

The common expression for the familiar frictional equation in design codes7 has the form fb = βσn + fadh

(1b)

Thus, the values of the term β taken from the international literature correspond to the product 2μ/π. Generally, μ

Fig. 1—Response of concrete cover under radial displacement imposed by corrosion.

Fig. 2—(a) Schematic depiction of frictional model; and (b) modeling stirrup pressure along spacing s. 757

decays with slip or crack opening. Stirrups produce a passive confining pressure over the anchorage, but unless they have a rather small diameter, they rarely reach yielding. Note that in unconfined anchorages, slip is approximately twice the radial displacement12 of the internal bar boundary imposed by the displacing ribs. Thus, upon attainment of bond strength at a nominal slip value of 0.1 mm (0.0039 in.), the corresponding radial displacement is 0.05 mm (0.002 in.). (This result was obtained from local bond tests13 with an embedded length Lb = 5Db, cover c = 1.5Db and bar diameter Db = 19 mm [0.748 in.].) The corresponding hoop strain equals the radial displacement divided by the radius to the point considered; thus, at the internal and external boundaries (free surface) the strain is 0.05 mm/9.5 mm = 0.0053 and 0.05 mm/38 mm = 0.0013. In the presence of confining pressure, radial displacement is greatly restrained. For pressures in the order of 0.25fc′ , cover splitting is entirely suppressed and failure occurs by pullout.13 Recently, a new technique for upgrading inadequate anchorages/splices by externally bonding FRP sheets (EB-FRP) orthogonal to the direction of reinforcement has been developed (FRP patch repairs). The technique has been shown to perform well, successfully enhancing anchorage strength and controlling bond degradation beyond attainment of strength, both for common and for corroded anchorages.14 In detailing this repair method, the effective transverse strain εf,eff on the nearest surface of the cover is used to evaluate the sheet stress. For the example considered, εf,eff = 0.0013 > εcr, that is, the cover is split through. This value may be considered as the effective strain of EB-FRP jacket restraining the anchorage when a moderately high level of frictional resistance may be relied upon (μ ≈ 0.7 – 1).7 Due to the kinematic relationship between slip, splitting crack width, and friction, higher values for εf,eff would correspond to lower μ values. Using the format of the code expression7 (in metric units) the average bond strength is calculated from Eq. (1a) as follows

Equation (2) refers to anchorages that usually fail by splitting where the confining contribution of stirrups is limited due to sparse spacing. For this, it is necessary to impose an upper limit of σc + σst ≤ 0.25fc′ .13 Although this is a crude representation of the local stress concentrations around the ribs that engage in concrete, in a general sense, the simple frictional model properly identifies the significance of many important design parameters for bond, and may be easily adapted to the conditions of a corroding reinforcing bar.

t f E f ε f, eff Ast f st, y c ⇒ f b = 0.29 ------ f c′ + 0.19 --------------+ 1.15 -----------------Db Db Nb s Db Nb

PROPOSED ANALYTICAL MODEL The simplest method to introduce the effect of corrosion on the bond capacity fb is to apply a reduction coefficient λ(X) on Eq. (2) with an increasing level of corrosion such as fbcor = λ(X)fb; X is the percent loss of bar radius (referred to as depth of corrosion penetration). A number of models are listed in the literature to represent this trend3,15-17 obtained by fitting experimental bond data. In all cases, bond decays with increasing X; however, the validity of the models is limited when tested with experimental measurements that have not been used in their initial derivation. The discrepancy between models is mostly owing to the great variety of specimen form and test setup used by the individual investigators. Note that bond is usually measured indirectly, that is, it is reduced from the global response of the specimen and testing hardware behaving as a complete structure. Unaccounted for friction between specimen and test hardware, as well as the presence of diagonal compression stress fields in the vicinity of the anchorage are known to superficially enhance the bond capacity.18 Auyeung et al.3 and Hussein et al.4 collected data from direct tension pullout tests (that is, most adverse bond conditions [Fig. 3(a)]). Cabrera16 used conventional pullout tests (very favorable bond conditions [Fig. 3(c)]). Rodriguez et al.15 examined short beam-end tests, and Stanish et al.17 tested simply supported slabs (bond is favored by the pressure at the support in the anchorage region [Fig. 3(b)]). A common drawback in all available empirical models is that a single variable, namely λ(X) is used to account for different sources of bond degradation, that is, the reduced capacity of the cracked cover and the attenuation of the frictional properties of the bar-concrete interface due to corrosion. An alternative approach consistent with the original frictional bond model (Eq. (1a)) is proposed herein, where degradation of all relevant mechanisms is explicitly addressed

where contributions from concrete cover, stirrups, and EB-FRP jackets have been considered. In Eq. (2), the implicit values for the parameters are μ = 0.9 (that is, in Eq. (1b), β ≈ 0.6), and ft′ = 0.5 f c ′ ; c is the concrete cover; Nb is the number of bars restrained by the stirrup legs included in Ast (Ast is the crosssectional area of stirrups crossing the splitting plane); and tf and Ef are the EB-FRP jacket thickness and modulus of elasticity, respectively. The coefficient α averages stirrupinduced confining pressures over the spacing s; note that confining pressure exerted on the bar by a single stirrup layer is maximum at the stirrup location and decays with transverse distance (Fig. 2(b)). Whereas the core of the cross section may be effectively confined over the entire stirrup spacing, most of the bar length is outside the stirrup influence (dashed line). Herein, a parabolic distribution is assumed for the confining pressure over the bar. This corresponds to a uniform effective confining pressure acting on the longitudinal bar over the entire spacing of successive stirrups s approximately equal to 1/3 of the peak value (hence, α = 0.33 in Eq. (2)).

Fig. 3—Test setups used in bond testing. Concrete is: (a) in direct tension; and (b) and (c) in compression.

2μf ′ A st α fst, y 2tf E f ε f, eff⎞ - + -----------------------f b = 2μ ------ × ( σ c + σ st + σ f ) = -----------t- ⎛ c + -------------------πD b ⎝ f t ′N b s f t ′N b ⎠ π

758

(2)

ACI Structural Journal/November-December 2007

res 2 2 = --- μ ( X )σ n + f adh ( X ) = --- μ ( X ) π π [ σ c ( X ) + σ shr ( X ) + σ st ( X ) + σ conf ] + f adh ( X ) cor

fb

(3)

In the proposed model, the coefficient of friction μ as well as the various terms in Eq. (3) that represent normal pressures on the bar surface are functions of corrosion intensity measured by X. The term σshr is the shrinkage stress that is modeled for simplicity as a compressive radial stress. The component of bond attributed to initial adhesion fadh degrades rapidly with either slip or corrosion. For smooth bars, it may represent a sizeable fraction of the total resistance, but for ribbed bars, it is considered insignificant and is only included in Eq. (3) for completeness. Terms entering Eq. (3) are defined in the following sections with regard to the principal design variables as well as with reference to X using simplified mechanistic constructs and physical argument. Calculating crack front in cover Rcr due to rust build-up Radial cracks run through part of the cover of corroded bars, owing to accumulation of the expansive rust products. An important parameter controlling the normal stress components in Eq. (3) is the residual uncracked cover thickness, which can be relied upon to support bond action. The radius of the crack front Rcr is related to the radial displacement ur,o of the internal boundary of the cover ring (around the bar hole) imposed by rust build-up. The variable ur,o is calculated from the depth of corrosion penetration X, and the volumetric ratio of rust to parent iron αrs. For the definition of the associated boundary-value problem, the following considerations are made. Strain-displacement relationships for cover ring—In axisymmetric problems of continuum mechanics, the straindisplacement relations are expressed in polar coordinates: εr = dur /dr and εθ = ur /r where ur is the radial displacement and r is the radius from the line of axisymmetry (Fig. 4(a)). If smeared strain definitions are adopted, these relations hold for the state of strain in the cracked cover concrete. For a known displacement of the interior boundary of the cover ring, the radius of the crack front may be evaluated from these relations by setting the hoop strain equal to the cracking strain of concrete, that is, εθ = εcr = ft′/Ec and hence, Rcr = ur,cr /εcr . The exact variation of the radial displacement from the value ur,o at the internal boundary Rb, to ur,cr at the crack front Rcr , is generally unknown and may only be obtained from a complete solution of the associated nonlinear boundary-value problem.10 Herein, it is assumed that the radial displacement decays from the peak ur,o value according to u r = u r, o – ε r ( r – R b ) ; R b ≤ r ≤ R cr

max

res

– ( σn – σn ) ⁄ Ec

ACI Structural Journal/November-December 2007

2

2

u r, o = ( 1 – α rs )R b ( 2X – X ) ⁄ ( R b + R cr )

(6)

For a given X, the radius of the crack front Rcr is evaluated by substituting Eq. (6) into Eq. (4); setting the radial displacement ur,cr = εcrRcr, it may be shown 2 2 ε cr + 4 ( ε cr + ε r ) ( 1 – α rs ) ⎛ 2X – X ⎞ + ε r – ε cr ⎝ ⎠ R cr = R b -------------------------------------------------------------------------------------------------------------------------------2 ( ε cr + ε r )

(7)

An initial estimate for the depth of corrosion penetration Xcrit associated with cracking is obtained from Eq. (6) by setting ur,o = εcrRb and Rcr = Rb: thus, Xcrit = 1 – [1 – 2εcr / (1 – αrs)]0.5. Second-order translation of internal boundary due to compaction of accumulated rust un,o—The real increase in the radial displacement of the internal concrete boundary un,o not only depends on the rust volume stored in the pores and in the space within cracks, but it is also affected by the degree of compaction experienced by the rust layer as a result of the normal pressure generated by the several mechanisms described previously. Rust behaves as a cohesionless granular material. Its stress-strain law has the form shown in Fig. 4(c) (unloading of rust due to degradation of the σnres is determined by the tangent slope at σn). A pertinent mathematical model of this behavior has been formulated by Lundgren2 where the relationship between the actual radial displacement un,o, the rust strain εcor (radial compaction of the rust layer), and the radial displacement due to free (uncompacted) rust deposition ur,o is as follows (Fig. 4(a))

(4)

where εr is the radial compressive strain resulting from the residual radial stress σnres that acts on the internal boundary (thus, for simplicity, εr is taken constant in the cracked part of the ring). As corrosion proceeds, the radial stress attenuates from its peak value (which represents the stress capacity of the ring σn) following an inelastic path with a slope equal to the initial concrete elastic modulus Ec (Fig. 4(b)). The radial strain is then εr = εr

Hoop strains, being tensile and attaining their peak value at the internal boundary, result in gradual propagation of radial cracks outwards through the cover. Thus, the uniaxial concrete compression stress-strain law suffices to relate the radial strain εrmax at the internal boundary with the corresponding stress σn (for example, Hognestad’s parabola) considering that Poisson effects are diminished after cracking. Translation of internal boundary due to rust accumulation ur,o—The volume of rust ΔVr is related to the volume of depleted metal ΔVs and to the depth of corrosion penetration X (X = ΔDb/Db) through ΔVr = αrs × ΔVs. The volume ratio αrs is usually taken as 2, but higher values are possible if the rust is fully hydrated.10 Assuming uniform corrosion on the bar surface (as opposed to pitting), deposition of the rust volume ΔVr around the bar surface and in the radial cracks of the cover requires a radial displacement of the internal concrete boundary by

(5)

Fig. 4—(a) Thick-walled cylinder model of cover and corrosion indexes; (b) stress-strain law of concrete cover under radial compression and unloading path when radial pressure is reduced; and (c) stress-strain response of rust. 759

u n, o = u r, o – ε cor ( X × R b + u r, o )

(8)

An initial estimate of ur,o was obtained from Eq. (6) for X = Xcrit. Up to this value, the ring capacity σn acting on the intact concrete cover is calculated using the basic mechanics of the ring model as detailed in the following sections. Pressure σn acts both on the cover and on the rust layer as the latter builds up around the bar. Using the constitutive model of compacted rust (Fig. 4(c)), the rust compaction strain εcor is evaluated from σn. The actual (corrected) radial displacement of the internal boundary un,o is then estimated from Eq. (8). From this revised value of the internal boundary translation, all relevant parameters of the problem are recalculated (for example, the crack front Rcr from Eq. (4) after setting ur,cr = εcrRcr and εr = εrmax and the residual normal pressure on the bar). In a stepwise calculation algorithm given in each step, the displacement of the internal boundary un,o and the radial strain εr for a depth of corrosion penetration X, an increment (i) in penetration by ΔX will lead to calculation of the new u n, o as follows (i)

(i)

(i)

(i)

(i – 1)

u n, o = u r, o – ε cor [ ΔX × R b + ( u r, o – u n, o ) ]

(9)

Equation (9) actually estimates the accumulated radial displacement considering the additional compaction of the new rust layer associated with ΔX. If the σnres(i) is less than the achieved maximum value σn, then unloading both cracked concrete and rust is assumed (along the unloading paths shown in Fig. 4(b) and (c), respectively). Capacity of cover ring σc The concrete cover contribution σc in Eq. (3) is the normal pressure on the interior boundary of the hole occupied by the bar that would be required to split the cover (Fig. 1 and 4(a)). Assuming either fully elastic or fully plastic behavior for the ring,19 its capacity to radial pressure is calculated as σc = ζ ft′(c/Db) (ζ = 1, 2, respectively). If radial cracks due to corrosion have propagated to the crack front Rcr , then the residual capacity of the cracked ring is estimated accordingly as ( C c – R cr ) σ c ( X ) = σ c ----------------------- + A ( ε θ, o ); c

(10)

R cr

1 A ( ε θ, o ) = -----Db

∫ σc ( εθ, o )dr

Rb

The first term of Eq. (10) denotes the remaining pressure capacity supported by the uncracked part of the cover ring. Quantity A(εθ,o) is the residual pressure resistance supported by the cracked part of the ring. Its magnitude depends on the post-fracture characteristics of the stress-strain law of concrete in tension that defines its fracture energy.10 This term is calculated when hoop strains at the internal boundary εθ,o = un,o/Rb exceed the cracking strain εcr. Effect of drying shrinkage σshr Drying shrinkage is accounted for as an isotropic (volume) contraction with a magnitude that depends on the conditions and duration of exposure. Accounting for that contraction as a uniform prestrain, the rust volume required to split the 760

cover is effectively increased, whereas shrinkage enables increased bond resistance for small amounts of rust deposition. In the thick-walled cylinder analogy, shrinkage generates compressive stresses in the radial direction σshr as the embedded bar restrains the length change of concrete, acting as a rigid inclusion. In design codes, shrinkage is interpreted as an isotropic contraction by εshr; based on CEB-MC 1990,20 εshr = –0.0003 ≈ –3εcr for humid atmospheric conditions. Thus, the radial stress σshr is taken equal to the modulus of elasticity of concrete times the isotropic strain εshr: σshr = Ec × εshr = –3ft′. Consistent with the assumption of isotropy of shrinkage, a compressive strain equal to εshr is also resolved in the hoop direction. This strain being compressive delays the onset of tensile hoop stresses due to corrosion penetration up to an internal radial displacement lim lim equal to u n, o = εshrRb ( u n, o is the necessary quantity for complete elimination of hoop compressive strains in the cover). After hoop strain exceeds the cracking limit, that is, (un,o/Rb) – εshr ≥ εcr , initiation of cover cracking is inevitable. Beyond that stage, as radial cracks propagate through the cover thickness, shrinkage stress is assumed to reduce proportionately with cover resistance, that is, σshr(X) = –3ft′(Cc – Rcr)/c. The depth of corrosion penetration Xshr that would cause a lim radial displacement of the internal boundary by u n, o may be calculated from the model considering that no radial cracking lim may occur up to that point (that is, u n, o /Rb = εshr). Based on 3,4,15,16 analysis of several case studies, it was found that Xshr ≈ 0.001; this quantity is insensitive to cover thickness and concrete quality. The concrete contribution σconc to bond strength composed of the tensile strength of concrete cover σc(X) and the shrinkage-generated pressure σshr(X) is a lower bound value because it is based on the assumption of symmetric conditions around the ring (central bar in the cover ring): σconc(X) = σc(X) + σshr(X). In actual circumstances, the ring radius is defined by the smallest cover thickness to the free surface of the member. Depending on the actual geometry of the cover (whether the bar is centrally or eccentrically placed in the cross section), the estimated crack propagation represents cracking in the thinner part of the cover only, whereas a large fraction of the thicker part of the cover may remain uncracked. Thus, the normal pressure in the inside boundary of the ring, calculated from the force resultant of hoop stresses along an assumed diametric plane, would be more favorable in an unsymmetric condition where part of the actual cover would exceed the minimum dimension used in the ring model (Fig. 5(a)). To account for this increase in the estimated ring capacity, a geometric factor B ≤ 1 is introduced in the terms representing the cover ring contribution; the factor B accounts for the area ratio of thin to thick cover areas (Fig. 5(a)). The resulting enhanced concrete contribution term is estimated from total

σ conc ( X ) = σ conc ( X ) + B × Δ σ conc

(11)

= ( 1 – B ) × ( σ c ( X ) + σ shr ( X ) ) + B × ( σ c + σ shr ) In Eq. (11), the term Δσconc is the local pressure increase (over the σconc value, which is the minimum value assuming a uniform cover equal to the minimum thickness as shown in Fig. 5(a)) in the thicker part of the bar cover, that is, B × Δσconc = B(σc + σshr – σc(X) – σshr(X)). ACI Structural Journal/November-December 2007

Bursting pressure attained by stirrups σst Stirrups are the first to be affected by corrosion owing to their proximity to the exposed surface, whereas the section loss is more dramatic for the transverse reinforcement as it is usually fabricated from small-diameter bars. Thus, the confining force is lowered by the apparent reduction of the cross-sectional area of the stirrups, estimated as Astcor = Ast(1 – X)2. The depth of corrosion penetration X in the stirrup reinforcement is not necessarily the same as that occurring in the main bars. The interior boundary hoop strain (εθ,ο = un,o/Rb) also represents the initial strain experienced by the hoops or stirrups confining the primary reinforcement, as stirrups are usually in contact with the longitudinal bars. With reference to Eq. (3), where the stirrup stress is denoted by σst(X), stirrups may be considered as being prestressed due to the rust product accumulation up to a stress of Es(un,o/Rb). Therefore, the available radial confining pressure exerted by the corroded transverse reinforcement when bond action is mobilized along the anchorage length is21 cor

cor

A st αf st, y -; σ st ( X ) = ---------------------Db Nb s

(12)

⎧ ( f – E s u n, o ⁄ R b ) ; u n, o ⁄ R b ≤ ε st, y cor f st, y = ⎨ st, y ; u n, o ⁄ R b > ε st, y ⎩o Effect of transverse compressive stress field in anchorage σconf The bond capacity of the anchorage may be superficially enhanced by unaccounted for friction between specimen and test hardware and by the presence of compression stress trajectories that intersect the anchorage (for example, near supports). Such sources of strength need to be considered particularly in correlating with experimental results, as they may effectively enhance the normal stress σn over the anchorage and delay crack propagation. In the case of an inclined compressive stress field, the normal pressure σconf confining the anchorage is estimated from the stress resultant perpendicular to the bar axis, assuming a uniform distribution over the anchorage (Fig. 3(b) and (c)). This stress is transferred from the internal boundary to the crack front as σconf × Rb /Rcr. From the established solution of a hollow thick-walled cylinder subjected to a uniform imploding pressure σconfRb/Rcr on the inner boundary19 with ri = Rcr, the calculated compressive hoop stress is σθ|r = Rcr = σconfRb(Cc2 + Rcr2)/ [Rcr × (Cc2 – Rcr2)]. The associated hoop strain εθ,conf|r = Rcr is also compressive and is obtained by dividing the hoop stress with the initial modulus of concrete Ec. This strain delays crack propagation thereby enhancing the anchorage strength. Its effect can be seen in Eq. (7), if εcr is replaced by εcr – |εθ,conf |r = Rcr |. Modeling adhesion fadh(X) The adhesion component of bond is the shear capacity of the interfacial layer (in the order of 1 MPa [0.145 ksi]), which disintegrates for small values of slip (that is, in excess of 0.02 mm [0.0008 in.]), as the chemical links between concrete and steel break down. Corrosion destroys chemical adhesion. As corrosion products accumulate between the two materials, chemical bonding is eliminated, even for very ACI Structural Journal/November-December 2007

small amounts of interpolated rust. In the proposed model, it is assumed that fadh(Xshr) = 0. Modeling coefficient of friction μ The coefficient of friction μ is taken to be a decaying function with increasing corrosion intensity, reduced from an ideal initial reference value μmax that is representative of the type of bar under consideration (either ribbed or smooth) μ = g ( X ) × μ max

(13)

The function g(X) is qualitatively described based on experimental observation (Fig. 5(b)). Even in uncorroded concrete, the coefficient of friction of a ribbed bar is considered max to degrade from its peak value μ r with increasing slip. In the case of corrosion, rust products accumulating around the bar prevent direct contact between concrete and reinforcement. Being rather cohesionless and longitudinally unconfined, rust offers adverse conditions for friction; as the thickness of the rust layer increases, longitudinal sliding is facilitated further, and the coefficient of friction is drastically reduced. A lower bound of frictional resistance is that of a smooth res corroded bar μ sm ; a ribbed bar is bound to degrade to that level upon complete depletion of the ribs (that is, when the depth of corrosion penetration equals the rib height hr). res Thus, μr|Xu = hr/Rb = μ sm . Values for the various terms defined previously have been quantified indirectly through max res tests published in literature2,7: μ r ≈ 0.7 – 1, μ sm ≈ 0.1 – 0.2. For intermediate levels of rib depletion, linear interpolation is used for the coefficient of friction as illustrated in Fig. 5(b). The initial increase of friction coefficient with corrosion penetration is owing to the effect of drying shrinkage that would have to be overcome before the cover may develop hoop tension. Based on the available experimental data,3,4,16 this effect may be accounted for by increasing the value of μ through a multiplier in the range of 1 to 1.2 up to a critical depth of penetration Xshr (Fig. 5(b)). EXPERIMENTAL PROGRAM The international experimental database on bond of corroded anchorages comprises mostly short anchorage specimens. To supplement model development with data from longer anchorage lengths, two groups of RC specimens were tested in the present study, that is, beam-end specimens (B-group) and slab-strips (S-group). The B-group comprised six prismatic specimens 850 mm (33.46 in.) long, having a 250 mm (9.84 in.) square cross section (Fig. 6(a)). The concrete had an average compressive strength of 21 MPa (3.04 ksi) at 28 days (at the time of testing, it had increased to 28 MPa [4.06 ksi]). Two steel bars with a diameter of Db = 14 mm (0.55 in.) and specified yield strength of fy = 500 MPa

Fig. 5—(a) Definition of B; and (b) variation of µ with X. 761

(72.5 ksi) were cast in each specimen. The bars were placed in the axis of symmetry of the beam cross section, with a clear cover of c = 20 mm (0.79 in.). The required anchorage length was estimated as Lb = fyDb/(4fb) = 415 mm (16.34 in.) (≈30Db, where the nominal bond strength was taken as per EC-222 as fb = 2.25 ft′). The remaining 415 mm (16.34 in.) of the total embeddment length was provided with a bond breaker. To preclude premature shear failure, auxiliary longitudinal and transverse reinforcement was used (four bars of Db = 10 mm [0.39 in.] placed at the corners); only vertical stirrup links with a diameter of 5 mm (0.20 in.) were provided to avoid any confining influence by closed stirrups in the end regions of the test bars. The specimens were loaded as a cantilever beam with one bar pulled out. The test bar was gripped externally using a tendon anchorage wedge that was bearing under the seating plate; the latter was adjusted on the loading frame. To preclude lateral sliding and out-of-plane rotation, two pin supports were fixed on the frame (one on each section side [Fig. 6(a)]). Tip displacement Δtip was obtained as the sum of deflection owing to flexural curvature and deflection owing to bar pullout from the fixed support Δsp (Fig. A1 in the Appendix*). These values were obtained from horizontal and vertical DTs placed at the top of the specimen and near the support region, respectively (Fig. 6(a)). The S-group consisted of four one-way slab-strips with a cross-sectional height, width, and total length of 150 mm (5.91 in.), 330 mm (12.99 in.), and 1200 mm (47.24 in.), respectively (Fig. 6(b)). Concrete compressive strength was 32 MPa (4.64 ksi) at 28 days (at the time of first testing, the strength had increased to 40 MPa [5.80 ksi]). A single layer of two Db = 14 mm (0.55 in.) steel bars with fy = 500 MPa (72.5 ksi) was used as longitudinal reinforcement with a clear cover of c = 30 mm (1.18 in.). Specimens were tested under four-point loading. Reinforcement was covered with a bond breaker in the central region of constant bending moment (400 mm [15.75 in.]) so as to control the bond demand over the bar development length. The available anchorage was 360 mm (14.17 in.) (that is, ≈26Db) and occurred in the shear span; the bar was terminated 40 mm (1.57 in.) beyond the support. In the specimen identification code (Table A1 in the Appendix), the first character marks the specimen type (Bor S-group), the second is the specimen number in the group, while the last two characters refer to the conditioning (c for corroded specimens and R for repairs with FRP jackets).

that is, to achieve complete hydration of rust, a 3-day cycle of wetting/drying was used during conditioning (1/2 day of wetting up to the middepth of the bars followed by 2-1/2 days of drying, where the water level was lowered well under the specimen’s bottom face). Both bars in the S-group were subjected to electrochemical corrosion. In one specimen of the B-series, both longitudinal bars were connected to the power supply (B5cR and B6cR in the Table A1 in the Appendix); this specimen was placed sideways in the corrosion basin so as to achieve simultaneous corrosion of both bars. In all other specimens of the B-group, only one of the two cast bars was corroded. The mass of iron consumed over the time period was estimated by the total amount of current that flowed through the electrochemical corrosion cell using Faraday’s Law. Values for the measured accumulated current Icorr and the estimated depth of corrosion penetration X are given for all specimens in Table A1 (in the Appendix). The duration of corrosion conditioning was similar for the two groups of specimens, but the different concrete strengths and cover-to-bar-diameter ratios (c/Db) produced different degrees of damage with regards to mass loss and cracking. For the B-group (c/Db = 1.43), cracks 2 mm (0.08 in.) wide spread throughout the concrete cover and anchorage length; in some cases, the network of cracks extended through the height of the section (Fig. A2(a) in the Appendix). By the end of the conditioning period of the S-group with c/Db = 2.14, visible longitudinal cracks 0.5 to 1 mm (0.02 to 0.04 in.) wide had developed directly over the bars in the anchorage zones only. Apparently, the bond breakers that were placed in the middle noncorrosive zone (Fig. A2(b) in the Appendix) inhibited the flow of oxygen starving the corrosion mechanism, effectively protecting the bar against rusting in that zone. Mechanical load testing Both groups of specimens were designed to fail in the anchorage after flexural yielding. The test setup and instrumentation are illustrated in Fig. 6. Load was applied monotonically in load increments (up to yielding) of 1 kN (0.11 kips) with continuous monitoring of deformations; displacement control was used beyond yielding. Beam-end specimens The B-group was tested up to various levels of lateral load with critical thresholds being: 1) yielding of longitudinal

Corrosion conditioning of specimens Both groups of specimens were connected to an electrochemical corrosion cell for a period of 2-1/2 to 3 months so as to generate accelerated rust production in the laboratory. One specimen of each group was left uncorroded to be used as a control (B0 and S0 [Table A1 in the Appendix]). Specimens were immersed in a water solution containing 3% per weight NaCl with bars acting as the anode of the circuit. A steel mesh was used as a cathode, placed at the bottom of the corrosion basin. Bars and steel mesh were connected in parallel to the power supply with the salt solution completing the circuit; a power of 6 Volts was impressed at the circuit ends. The electrical current was monitored at 12-hour intervals. To promote accumulation of expansive corrosion products, *

The Appendix is available at www.concrete.org in PDF format as an addendum to the published paper. You may request a hard copy from ACI headquarters for a fee equal to the cost of reproduction plus handling at the time of the request.

762

Fig. 6—Dimensions (in mm) and test setup of specimens tested: (a) beam-end (B-group); and (b) slab (S-group). (Note: 1 mm = 0.0394 in.) ACI Structural Journal/November-December 2007

reinforcement; and 2) the extent of mechanical damage in the anchorage zone at cover spalling; the aim was the reuse of specimens for testing various repairing techniques. Figure A1 (in the Appendix) plots the load-displacement curves obtained during the first loading stage before repair, that is, the c series marked by circles and triangles with no connecting lines (also included in the same figure are the results after the repair, as mentioned in the following). The term cR in the specimen label marks experimental curves obtained from the post-repair loading tests. Loading of Specimen B1c (X = 10.9%) was stopped at 15 kN (3.37 kips) before yielding of the corroded bar, with limited cracking (the yield load of the control Specimen B0 was estimated both analytically and experimentally as 21 kN [4.72 kips]). Testing of Specimens B2c and B3c (X = 6.8 and 9.6%) was stopped just near visible yielding (at approximately 17 kN [3.82 kips]). Nevertheless, a substantial level of damage, including spalling of the cover, was only seen in Specimen B2c. Specimen B4c with a similar degree of corrosion as Specimens B3c and B1c failed abruptly, developing only 25% of the strength of Specimen B0; the embedded bar yielded and subsequently fractured near the support region in the specimen block (it sustained a low yield load due to local bar section loss) without widening of the existing longitudinal cracks or formation of any new cracks associated with bond action. For Specimens B5c and B6c with a low degree of corrosion penetration (X = 2.96 and 3.7%), testing was terminated at higher load (up to 83% of the failure load of Specimen B0). At that stage, transverse cracks had developed in the lower half of the anchorage length whereas the main longitudinal crack owing to corrosion had widened (excessive damage in the case of Specimen B5c). In most specimens, corrosion impaired the flexural stiffness of the members as a result of partial breakdown of bond. Due to lack of bond, it is not possible to mobilize tension stiffening of concrete and crack widths become excessive; in that case, pullout due to slip may govern the total lateral deformation.14 Exceptions to the experimental trends are the responses of Specimen B5c and B6c that also had the lowest degree of corrosion; also, Specimen B3c had a very similar stiffness to Specimen B0 with lower yield point. Comprehensive results of the preloading stage for the B-group are also given in Table A1 (in the Appendix). Average bond stress fb was obtained assuming uniform distribution along the anchorage length and was evaluated from statics of the cantilever’s critical section using the measured peak load P. Slab-strip specimens Bond was measured indirectly in the S-group (the developed bar force was obtained from the statics of the constant moment region) and it was affected by the arching of the compression strut near the support. From the three corroded elements of this group (in all cases X ≈ 4%), Specimen S3c and the control Specimen S0 were loaded to failure. Peak loads were of similar magnitude (121 and 126.5 kN [27.2 and 28.4 kips], respectively), but the mode of failure was different. A large flexural crack opened in the constant moment region of Specimen S0, extending deep in the compression zone where it curved and became almost horizontal as the load increased (Fig. A3(a) in the Appendix). (Note that the single crack is owing to fact that the bar was unbonded in that region.) Near failure, the crack was approximately 3 mm (0.12 in.) wide. A flexure-shear ACI Structural Journal/November-December 2007

crack also opened in the shear span near the point of loading; eventually failure was controlled by this crack that also branched towards the support (the photo in Fig. A3(a) in the Appendix was taken after load removal). Specimen S3c failed abruptly in the anchorage zone due to corrosion precracking with part of the concrete cover exploding away (Fig. A3(b) in the Appendix). Specimens S1c and S2c were loaded up to 65% of the measured strength of Specimen S3 so that they could be reused after repair (Fig. A3(c) in the Appendix). Peak load and the resulting bond stresses are listed in Table A1 (in the Appendix). The influence of specimen type and particularly the confining action of the supports over the bar is assessed by comparison of the test results of the uncorroded specimens of the two series (the uncorroded Specimens B0 and S0 reached average bond capacities of 5.61 MPa (0.81 ksi) and 7.07 MPa (1.03 ksi), respectively (Table A1 in the Appendix), that is, a 20% difference in strength. This difference persisted systematically in comparisons of similarly corroded specimens of the two groups as well (owing to the different specimen forms). Influence of repair on anchorage capacity After the first loading phase, all damaged specimens were repaired in the anchorage zones by CFRP patches externally bonded over the anchorage length and transversely to the longitudinal axis of the members. In all cases, the FRP jacket was anchored laterally along the height of the cross section forming a U-shape (no mechanical anchorage was used). The intent in this repair alternative was to mobilize passive confining of the anchorage zone with consequently favorable influence on bond resistance. Nominal mechanical properties of the jacket materials were as follows. For the CFRP tensile strength: 3500 MPa (508 ksi), strain at failure 1.5%, and sheet thickness of 0.13 mm (0.0051 in.); and for the resin modulus of elasticity: 3800 MPa (552 ksi) and shear strength of 30 MPa (4.35 ksi). Repair was done as follows: in cases of excessive cover damage (Specimens B2cR and B5cR), before application of the CFRP jacket, the concrete fragments and the rust were removed and replaced by a low strength mortar (watercement ratio of 0.7). For all other members with controlled cracking, CFRP plies were just glued to the free surface without any particular preparation (that is, the corners were not chamfered and cracks were not sealed) except for careful cleaning. During repair, the S-type specimens were turned upside down with respect to their testing position, so that cracks were closed having a favorable effect on the anticipated effectiveness of the jacket. The repaired specimens were reloaded monotonically to failure. The contribution of CFRP jacketing on bond resistance in the case of the S-group was clearly favorable. Stiffness increased up to 20% of the initial value of the corroded specimens due to crack closure upon repair, whereas the mode of failure was ductile (in Fig. A3(c) in the Appendix, label R in the plot corresponds to the post-repair response). Measured bond strength fb = 6.7 MPa (0.97 ksi) was reduced by only 5% from the value of the control Specimen S0 (Table A1 in the Appendix). In the B-group, corrosion damage and preloading effects on bond resistance and on the stiffness of load-displacement response were almost nonrecoverable (post-repair response curves are plotted in Fig. A1 (in the Appendix) by the series of symbols with connecting lines). By combining cover replacement with CFRP patching (Specimens B2cR and 763

B5cR), it is possible to develop the available flexural strength (attained at the prerepair loading). Failure for all specimens was marked by excessive slip of reinforcement owing to the preloading effects on the anchorage, the unrecoverable loss in rib height, and the fact that the rust layer was not removed before casting the new cover. Using CFRP patching alone was not as effective as in the case of the S-group, particularly in cases that had sustained a high level of preloading: Specimens B3cR and B6cR could not sustain more than 63% of the preload threshold and failed in a similar manner as Specimen B2cR. Specimens B1cR, which had the lowest degree of mechanical damage (only few narrow cracks near the support due to the low level of prerepair loading, whereas the anchorage had experienced the least damage from bar slip) and was repaired by CFRP layers without cover replacement demonstrated the most favorable performance. Its ultimate load reached 80% of the Specimen B0 strength, with pronounced yielding before failure and unaffected initial stiffness. Measured bond strength fb was lower in most cases (except for Specimen B1cR) than

the bond stress value attained during the first loading cycle (Table A1 in the Appendix). VERIFICATION OF ANALYTICAL MODEL For a given depth of initial corrosion penetration, the residual bond strength may be calculated from Eq. (3), with the proposed values for the frictional coefficient and the calculated values of the normal stress components. In the following paragraphs, the performance of the analytical model is explored through correlation with reported measurements from relevant tests published in the literature3,4,15-17 as well as with the results of the experimental program conducted in the framework of the present study. In total, five different series of tests were considered for model verification. Typical characteristics of the specimens and relevant references are as follows: 1. Short embedment length, concentric bar arrangement, and tension pullout test setup3,4 (Fig. 3(a)); 2. Short embedment length, eccentric bar arrangement, and beam tests15 (Fig. 3(b));

Fig. 7—Model correlation. Data from: (a) conventional pullout tests; (b) direct tension; (c) beam-end ((a), (b), and (c) concern short anchorages); (d) slab strips; and (e) data from current test program ((d) and (e) concern long anchorages). 764

ACI Structural Journal/November-December 2007

3. Short embedment length, concentric bar arrangement, and pullout tests16 (Fig. 3(c)); 4. Long embedment length, eccentric bar arrangement, and slab-strip tests (data from present experimental program, as well as from Stanish et al.17) (Fig. 3(b)); and 5. Long embedment length, eccentric bar arrangement, beam-end tests (data from present experimental study [Fig. 3(b)]), and consideration of patch-FRP repairs. Figures 7(a), (b), and (c) present the behavior of the model when applied to Specimen Series 1 through 3.3,4,15,16 A common characteristic of these cases is the short embedded length of the test bar (4 – 7Db). Stress conditions in the surrounding concrete vary depending on the test setup and support hardware. Overall, the model is in good agreement with the experimental data or with the empirical equations included in Fig. 7 that summarize subgroups of test results. In the case of conventional pullout tests16 of Fig. 7(a), the model is in good agreement with the experimental data in the low range of X values, whereas it becomes rather conservative for higher levels of corrosion penetration. The influence of the reacting confining pressure σconf owing to the test setup (Fig. 3(b) and (c)) was considered in the correlation as specified by Eq. (3). Datapoints circled with the dashed line concern a special concrete mixture containing fly ash. The model best reproduces the data of the direct tension pullout test3,4 as illustrated in Fig. 7(b). In this type of test, longitudinal concrete stresses are tensile in the vicinity of the anchorage, thus they are more consistent with the stress-state surrounding the anchorage in the tension zone of an actual beam. For the beam-end test series15 (Fig. 7(c)) with and without stirrups, the model produces a lower bound trend (according to Rodriguez et al.,15 stirrups were uncorroded). Parameter B was set equal to 0.75 taking into account the eccentric bar arrangement. In the case of long anchorages (Fig. 7(d) and (e)), the model correlates well with the values of bond strength (in the present study, bond strength was measured upon failure of repaired specimens in the second test phase [Fig. 7(e)]). In the correlation, contribution of the FRP jacket (from Eq. (2)) and influence of the inclined compression field due to support reaction were accounted for through Eq. (3) by means of the reacting normal pressure σconf + σf (in the case of data17 of Fig. 7(d): σf = 0). For Specimen Series 4, Parameter B was taken as 0.75 (side-to-bottom-cover ratio ≈ 2). In the B-series of specimens (Series 5, Fig. 7(e)), the composite material did not mobilize sufficient restraining pressure σf, as this would require significant hoop strains at the external boundary. Herein, replacement of corrosioncracked cover as a repair option was analytically modeled by using an intact cover. Thus, only the coefficient of friction μ was reduced as a function of X to account for corrosioninduced deterioration of the bar surface (herein, σconf = 0 because the inclined compression field affected the tail-end of the unbonded bar). In modeling the S-specimens without cover replacement (Fig. 7(e), black line), the combination of confining pressures in the anchorage zones exerted from the support and from the FRP jacket acted favorably to sustain bond strength up to severe values of X, preventing widening of the existing cover cracks (B = 0.75) in the analysis. In all cases, the model consistently reproduced the experimental trends and the varying degree of influence of corrosion on bond strength owing to the stress-state of the concrete in the anchorage zone and the boundary conditions provided by the test setup. ACI Structural Journal/November-December 2007

CONCLUSIONS Two series of RC specimens (slabs and beam-end specimens) were conditioned under accelerated corrosion and subsequently tested under mechanical load so as to investigate bond performance of corroded bar anchorages. Some of the damaged anchorage zones were repaired with partial cover replacement. All specimens were wrapped with a CFRP patch and retested to failure. Test results showed that corrosion affects the mechanics of bond and can result in explosive spalling failure at the anchorage. The efficiency of CFRP patching was controlled by several parameters such as the extent of corrosion damage, the extent of cover damage due to preload, the state of stress in the vicinity of the anchorage, and by whether the damaged cover was replaced before jacketing. To interpret the test results, a mechanical model was developed from first principles based on the frictional concept, whereby bond strength was estimated from the coefficient of friction and the normal confining pressure along the anchorage. Both variables were evaluated considering the relevant design parameters (cover, shrinkage, and transverse reinforcement) and the effects of iron depletion (bar diameter loss). The model’s ability to accurately predict deterioration of bond strength with progressive corrosion penetration was established through extensive correlation with data from several published studies as well as with the data of the present experimental investigation. In all cases, the model consistently reproduced the experimental trends and the varying degree of influence of corrosion on bond strength owing to the stress-state of the concrete in the anchorage zone and the boundary conditions provided by the test setup. ACKNOWLEDGMENTS This research was conducted in the Laboratories of Demokritus University, Greece. Funding was provided by GSRT (Hellenic General Secretary for Research and Technology) through the PENED 2001 program. The composite materials (SikaWrap 230C and Sikadur 330) were donated by SIKA Hellas.

NOTATION

Ast/stcor = cross sectional area of transverse reinforcement, reduced value due to corrosion B = factor that accounts for area ratio of thin to thick cover areas = clear concrete cover thickness and cover measured from bar center c/Cc Db/Rb = bar diameter and radius = modulus of elasticity for concrete, steel, and FRP Ec/s/f = adhesion fadh cor = bond strength and reduced value due to corrosion fb /b = compressive/tensile strength of concrete fc′/ft′ fst,y/fy = yield stress of transverse and longitudinal reinforcement Icorr = total current that flowed through electrochemical cell during corrosion = anchorage length Lb = number of tension longitudinal bars enclosed by stirrups Nb = radius of crack front Rcr r = radius from line of axisymmetry s = stirrup spacing = FRP jacket thickness tf = radial displacement at crack front ur,cr ur,o/n,o = radial displacement, value also affected by rust compaction of internal boundary X = depth of corrosion penetration = volumetric ratio of rust to parent iron αrs Δtip/sp = total displacement and displacement owing to bar pullout at top of B specimens ΔVr = volume of rust products = volume of steel loss ΔVs = radial compressive strain of rust εcor = cracking strain of concrete εcr = effective strain of the externally-bonded FRP sheet εf,eff = shrinkage strain εshr = yield strain of stirrups εst,y = radial compressive strain of concrete εr

765

εθ εθconf μr /sm σc σconf /f

= = = = =

σn/nres

=

σshr σst ζ

= = =

hoop tensile strain of concrete hoop compressive strain due to confining pressure σconf friction coefficient: for ribbed bar, for smooth bar maximum normal pressure for cover splitting confining pressure by transverse compressive stress field, by FRP jacket maximum normal pressure due to frictional bond mechanism and residual value shrinkage stress confining pressure due to stirrups factor that considers concrete ring response (1 for fully elastic and 2 for fully plastic)

REFERENCES 1. Li, C. Q., and Zheng, J. J., “Propagation of Reinforcement Corrosion in Concrete and its Effects on Structural Deterioration,” Magazine of Concrete Research, V. 57, No. 5, 2005, pp. 261-271. 2. Lundgren, K., “A Model for the Bond Between Corroded Reinforcement and Concrete,” Proceedings from Bond in Concrete—from Research to Standards, Budapest, Hungry, 2002, pp. 35-42. 3. Auyeung, Y.; Balaguru, P.; and Chung, L., “Bond Behavior of Corroded Reinforcement Bars,” ACI Materials Journal, V. 97, No. 2, Mar.-Apr. 2000, pp. 214-220. 4. Hussein, N.; Yang, Y.; Kawai, K.; and Sato, R., “Time Dependent Bond Behaviour of Corroded Bars,” Proceedings from Bond in Concrete— from Research to Standards, Budapest, Hungry, 2002, pp. 166-173. 5. Cairns, J.; Du, Y.; and Johnston, M., “Residual Bond Capacity of Corroded Plain Surface Reinforcement,” Proceedings from Bond in Concrete— from Research to Standards, Budapest, Hungry, 2002, pp. 129-136. 6. MacGregor, J., Reinforced Concrete: Mechanics and Design, Prentice-Hill Inc., 1997, 939 pp. 7. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (318R-02),” American Concrete Institute, Farmington Hills, MI, 2002, 443 pp. 8. Tastani, S., and Pantazopoulou, S., “Experimental Evaluation of the Direct Tension-Pullout Bond Test,” Proceedings from Bond in Concrete— from Research to Standards, Budapest, Hungary, 2002, pp. 268-276. 9. Martin-Perez, B., “Service Life Modelling of R.C. Highway Structures Exposed to Chlorides,” PhD thesis, Department of Civil Engineering, University of Toronto, Toronto, ON, Canada, 1998, 164 pp.

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10. Pantazopoulou, S., and Papoulia, K., “Modelling of Cover-Cracking Due to Reinforcement Corrosion in R.C. Structures,” Journal of Engineering Mechanics, ASCE, V. 127, No. 4, 2001, pp. 342-351. 11. Li, C. Q., “Reliability Based Service Life Prediction of Corrosion Affected Concrete Structures,” Journal of Structural Engineering, ASCE, V. 130, No. 10, 2004, pp. 1570-1577. 12. Lura, P.; Plizzari, G.; and Riva, P., “3D Finite-Element Modelling of Splitting Crack Propagation,” Magazine of Concrete Research, V. 54, No. 6, 2002, pp. 481-493. 13. Malvar, J., “Bond of Reinforcement under Controlled Confinement,” ACI Materials Journal, V. 89, No. 6, Nov.-Dec. 1992, pp. 593-601. 14. Harajli, M. H., “Bond Strengthening of Steel Bars Using External FRP Confinement: Implications on the Static and Cyclic Response of R/C Members,” Proceedings of the 7th International Symposium on FiberReinforced Polymer Reinforcement for Concrete Structures, SP-230, C. Shield, J. Busel, S. Walkup, and D. Gremel, eds., American Concrete Institute, Farmington Hills, MI, 2005, pp. 579-596. 15. Rodriguez, J.; Ortega, L.; Casal, J.; and Diez, J., “Assessing Structural Conditions of Concrete Structures with Corroded Reinforcement,” Proceedings from Concrete in the Service of Mankind: Concrete Repair, Rehabilitation and Protection, R. K. Dhir and M. R. Jones, eds., E&FN Spon, 1996, pp. 65-78. 16. Cabrera, J. G., “Deterioration of Concrete Due to Reinforcement Steel Corrosion,” Elsevier Cement and Concrete Composites, V. 8, 1996, pp. 47-59. 17. Stanish, K.; Hooton, R.; and Pantazopoulou, S., “Corrosion Effects on Bond Strength in Reinforced Concrete,” ACI Structural Journal, V. 96, No. 6, Nov.-Dec. 1999, pp. 915-921. 18. CEB Task Group 2.5, “Bond of Reinforcement in Concrete,” FIB Bulletin 10, International Federation for Concrete, Lausanne, Switzerland, 2000, 427 pp. 19. Tepfers, R., “Cracking of Concrete Cover Along Anchored Deformed Reinforcing Bars,” Magazine of Concrete Research, V. 31, No. 106, 1979, pp. 3-12. 20. CEB-FIP Model Code 1990, “Design Code,” Comité Euro-International du Béton, Thomas Telford Publications, London, UK, 1993, 437 pp. 21. Tastani, S., and Pantazopoulou, S., “Recovery of Seismic Resistance in Corrosion-Damaged R.C. through FRP Jacketing,” International Journal of Materials and Product Technology, V. 23, No. 3/4, 2005, pp. 389-415. 22. Eurocode 2, “Design of Concrete Structures (EC-2),” European Committee for Standardization, Brussels, Belgium, 2002, 227 pp.

ACI Structural Journal/November-December 2007

APPENDIX a)

highlighted cracks

b)

non-corrosive zone (bond breaker) Fig. A1 - Cracking pattern at the bottom face of corroded specimens: a) Beam-end and b) Slab.

1

: Δtip Load (kN)

30

30

30

25

25

25

20

20

B0

c 15

cR

10

B0

20

c cR

15

5 B1: X =10.9 (%)

0

30 0

0 10 20 30 40 50 60 70 80 30 0

B2: X =6.8 (%)

B0

20

15

B0

cR

5 B3: X =9.6 (%)

0 10 20 30 40 50 60 70 80 30 0 c

25

25

25

c

10

10

5

Load (kN)

: Δsp

10 20 30 40 50 60 70 80

c B0

B0

20

20

15

15

B6: X=3.7 (%)

15 B4: X =10.2 (%)

10

10

10 cR

5

c

0 0

5

5

0 10 20 30 40 50 60 70 80 0 displ. (mm)

B5: X=2.96 (%)

0 10 20 30 40 50 60 70 80 0 displ. (mm)

cR

10 20 30 40 50 60 70 80 displ. (mm)

Fig. A2 - Experimental load – displacement curves (B-group). Circles mark total cantilever tip displacement; Triangles mark cantilever tip displacement due to slip of the bar at the support. c labels pre-repair corroded response (series without connecting lines), R labels post-repair response (series with connecting lines) [1 kN = 0.225 kip ; 1 2 mm = 0.0394 in.].

150

a) Load(kN)

highlighted flexural crack

b)

c)

S3c

120 90

S1c

60

S2c S1cR

30

S2cR S0

0 0

3

6

9

12

15

18

Deflection (mm)

Fig. A3 - Failure of the a) control (S0) and b) corroded (S3c) specimen. c) Performance of repaired slabs upon reloading [1 kN = 0.225 kip ; 1 mm = 0.0394 in.].

3

21

Slab tests (S – group)

Beam- end specimens (B – group)

Table A1: Comprehensive results of the experimental program. Spec. ID

Corrosion§

Preloading stage

Icorr (Α) / X (%)

B0

Deflection*

P(kN)/ fb(MPa)

Reloading stage P (kN) / fb (MPa)

∆y / ∆ult(mm)

0/0

27.83 f / 5.61

27.83 f / 5.61

29.74 / 104.5

B1cR

12.1 / 10.9

14.85 / 3.19

22.26 / 4.48

23.58 / 54.35

B2cR

7.73 / 6.81

16.34 / 3.28

15.18 / 3.05

33.54 / 33.54

B3cR

10.71 / 9.58

17.11 / 3.44

9.87 / 1.98

21.92 / 21.92

B4c

11.35 / 10.18

6.98f / 1.40

6.98f / 1.40

23.30 / 23.30

B5cR

3.42 / 2.96

23.27 / 4.69

22.26 / 4.48

37.61 / 39.63

B6cR

4.27 / 3.71

20.78 / 4.18

13.16 / 2.64

29.81 / 29.81

S0

0/0

126.47f / 7.07

126.47f / 7.07

7.5 / 9.5

S1cR

12.49 / 4.60

78.57 / 4.37

119.57 / 6.69

5.71 / 10.82

S2cR

9.88 / 3.61

76.79 / 4.27

120.0 / 6.71

5.28 / 9.08

S3cR

10.99 / 4.03

121.36 f / 6.79

121.36 f / 6.79

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Note: 1 MPa = 0.145 ksi; 1 mm = 0.0394 in. fb is an average measure of bond stress. For values obtained prior to anchorage failure (as in the cases of preload) the actual bond stress distribution is not uniform. § : Duration of corrosion process: 75 and 85 days for the B and the S group respectively. Mass loss ∆Ms was defined from the Faraday’s law and corrosion penetration X from ∆Ms=X(2-X)Ms. f : Failure load. * : For the B-group are given values from the tip displ. whereas for the S-group the middle deflection at the corresponding loading of the 5th col.

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