PREDICTION OF CONCRETE CRACK OPENING CAUSED BY REINFORCING BAR CORROSION Concrete cracks caused by bar corrosion

Transcription

1 PREDICTION OF CONCRETE CRACK OPENING CAUSED BY REINFORCING BAR CORROSION Concrete cracks caused by bar corrosion Y. KITSUTAKA Department of Architecture and Building Science, Tokyo Metropolitan University, Tokyo, Japan N. NAKAMURA Concrete Laboratory, Japan Testing Center for Construction Materials, Tokyo, Japan Durability of Building Materials and Components 8. (1999) Edited by M.A. Lacasse and D.J. Vanier. Institute for Research in Construction, Ottawa ON, K1A R6, Canada, pp National Research Council Canada 1999 Abstract The influence of reinforcing bar corrosion on the crack opening width of reinforced concrete surface was investigated. A fracture mechanics based numerical analysis method was developed in order to predict the crack width on the concrete surface due to the expansive force of the corroded reinforcing bar. The corrosion accelerating tests for reinforced concrete model specimens were performed on the various kinds of concrete, and relationships of crack opening and the degree of corrosion were clarified. The crack width obtained from the accelerated test agreed well with the results of s from the numerical analysis by considering the creep effect and the tension softening properties of concrete. Keywords: Crack, corrosion, reinforcing bar, fracture mechanics, tension softening 1 Introduction In order to increase the durability of existing reinforced concrete structures, it is essential to grasp the deterioration phenomena of such structures and select suitable repair methods. Critical deterioration of reinforced concrete structures can be explained as a phenomenon in which "corrosion of reinforcing steel or reaction of aggregate causes cover concrete to be subjected to expansive or tensile action, and the resulting cracking with concomitant acceleration of reinforcement corrosion reduces the strength of reinforcing bars, lowering the structural yield capacity of the member." In other words, it is important in terms of durability for concrete to be sound against expansive and tensile forces inducing corrosion. Also, carbonation and salt damage

2 are regarded as factors (internal deterioration forces) for causing expansive forces of reinforcing bars. It is fundamental to the study of concrete durability to elucidate the process of failure of cover concrete subjected to such deteriorating internal forces and find a method of preventing such failure. Though a number of studies have been conducted regarding reinforcement corrosion, there have been few studies on the changes in the crack width and propagation of a fracture process zone after the onset of cracking on the concrete surface. Analysis by fracture mechanics incorporating the softening properties of concrete is considered particularly effective in analyzing crack propagation of nonlinear materials, such as cementitious materials. In this study, the authors grasp crack opening on the surfaces of various concretes resulting from corrosion-induced expansion of reinforcing steel by electrolytic corrosion s and propose an analysis method based on nonlinear fracture mechanics using cohesion force models. Comparisons are made between analyzed and tested results. A method of estimating the cross-sectional loss of reinforcing bars from the crack opening on the concrete surface is discussed as well. 2 Experimental procedure 2.1 Materials and specimens Five types of mortars/concretes are used: normal strength plain mortar (NPL), normal strength fiber reinforced mortar (NVF), high strength plain mortar (HPL), high strength fiber-reinforced mortar (HVF), and normal concrete (Ncon). Fiberreinforced specimens are included to represent those with particularly high tensile toughness. The mix proportions are given in Table 1. The cement is high flow cement; the fine aggregate is manufactured sand from Hachioji; and the coarse aggregate is crushed quartz from Danto. Silica fume and super plastisizer are used as the mineral and chemical admixture, respectively. The fibers are made of Vinylon with a specific gravity of 1.3, length of 3 mm, and strength of 9 kgf/mm 2. The 28- day compressive strength and tensile strength of the specimens are given in Table 1. Fig. 1-a) shows the geometry of the specimens. Prismatic specimens by by 15 mm in size are used, in which round bars 2 mm in diameter are embedded with specified cover depths by using a processed mold. The cover depths are basically 5, 15, and 3 mm to include the situation where insufficient cover causes durability Table 1: Mix propotion Specimen sign W/B water cement SF sand gravel SP fiber tensile compressive strength strength i % j ( kg/m 3) i i MPa) MPa) Normal plain mortar NPL Normal fiber mortar NVF High plain mortar HPL High fiber mortar HVF Normal concrete Ncon B=SF+cement SF: silica fume SP: super plastisizer

3 problems. Protruding ends of round bars are coated with epoxy resin and a sealing compound to prevent corrosion. The crack width is measured using two π-gages attached to each specimen. Two specimens are used for each set of conditions. 2.2 Apparatus The electrolytic corrosion equipment is shown in Fig. 1-b). A situation in which reinforcing steel corrodes uniformly due to, e.g., internal chlorides is simulated in this study. The bottom of a specimen is immersed in salt water (an NaCl % solution), and a 3V constant voltage is impressed from a DC regulated power source through the bar, the anode, and a copper plate partly immersed in the salt water, the cathode. Specimens were mostly submerged in salt water in past studies, but this causes rust to exude, leading to errors. For this reason, only the bottom of the specimen is immersed in salt water in this study, and the entire surface of the specimen is covered with a cloth wet with salt water. Also, all of the equipment is sealed to prevent evaporation of salt water. The voltage at the resistance in series connection is recorded using a data logger, to determine the current for estimating the amount of corrosion and calculate the integrated current, I m (Ah). As the actual amount of corrosion products is difficult to determine accurately, the weight losses are measured to evaluate the losses by corrosion. This was done by removing rust from the bar after the tests and measuring the changes in weight. These are then converted to weight losses per unit area, which are taken as the corrosion loss, w (mg/cm 2 ). The integrated current and corrosion loss being proportional, their conversion factor, α, is determined by Eq. (1). Table 2 gives the average conversion factors of bars in the specimens. w = α I m (1) cover T Reinforcing bar 2mmƒÓ π - gage crack coating cap specimen ƒ data logger DC regulated power source 3V 15 (mm) NaCl { a) specimen b) apparatus Fig. Fig. 1: 1: Outline of of test test

4 Table 2: Corrosion data of reinforcing bar specimen weight loss ratio corrosion loss integrated current conversion factor r ƒ - cover(mm) w Im (%) (mg/cm 2 ) (Ah) (mg/ah cm 2 ) NPL- T NPL NPL NVF NVF NVF HPL- T HPL HVF Ncon Load (kn) Ncon NPL HPL HVF NVF Cohesive stress (MPa) Normal strength Ncon NPL NVF HPL High strength HVF Load point (mm) a) Load - load point displacement curve Crack opening displacement (mm) b) Tension softening diagram Fig. 2: Analysis of tension softening diagram 2.3 Tension softening properties of materials In addition to compressive strength and Young's modulus, tension softening curves are effective in evaluating the material properties of concretes used for the crack propagation analysis. Three-point bending tests over a span of 4 mm were therefore conducted using a servo-controlled loading tester on notched beams by by 45 mm in size of mortars and concretes under analysis to determine the loadload point displacement curves. These are approximated to tension softening curves by polylinear approximation analysis (Kitsutaka 1997) and then converted to bilinear tension softening curves by least square approximation to facilitate the crack analysis. Fig. 2-a) and 2-b) show the measured load-load point displacement curves and determined tension softening curves, respectively. Though the maximum load and initial bond stress of high strength mortars/concretes are higher than those of normal mortars/concretes, their reductions in the softening zone are greater, showing a tendency towards brittleness. The addition of fibers significantly improved the toughness of both normal and high strength mortars/concretes. Table 3 gives the bilinear parameters for analysis determined by least square approximation. In the

5 table, Ec denotes Young's modulus, ft denotes initial tensile stress, δ 1 and σ 1 denote displacement and stress at the elbow point, respectively, and Wc and σ 2 denote critical crack opening displacement and stress at Wc, respectively (see Fig. 3). Table 3: bilinear parameters sign Ec ft ƒâ1 ƒð1 wc ƒð2 (GPa) (MPa) (mm) (MPa) (mm) (MPa) NPL NVF Ncon HPL HVF Cohesive stress (MPa) σ ft ƒð 2 ƒð 1 1 m 1 ƒâ c Crack opening displacement ƒâ Fig. 3: Bilinear type tension softening curve m m 2 3 Results and discussion The principal cracks occurred along the reinforcing bar upward into cover concrete and downward in the opposite direction of each specimen. The cracks on the surfaces were all within the measurable ranges of π-gages, causing no difficulty in measuring the crack width. In addition to principal cracks, minute cracks developed laterally from the bar, forming a cross of cracks in mortars without fibers. In concretes and fiber-reinforced mortars, minute cracks developed radially from the bar, exhibiting a tendency of dispersing crack-propagating forces. Fig. 4 shows the relationships between the crack mouth opening displacement (CMOD) and the corrosion loss of reinforcement determined by conversion from the integrated current using Eq. (1). The opening displacement for each specimen is the average of two π- gage measurements. The crack width tends to increase as the corrosion loss increases in all cases. High strength mortar/concrete specimens (H) tend to lead to a higher rate of crack width gains after the crack onset than normal strength specimens (N). This may be because cracks propagate in a brittle manner in high strength mortar/concrete after the crack onset, due to its dense microstructure. In normal strength mortar/concrete, the stress is relaxed by minute cracks and plastic deformation around the bar due to its weak microstructure. Though no marked difference is observed in the rate of crack propagation between mortars/concretes with and without fibers after crack onset, fibers delay the crack onset, exhibiting their reinforcing effect. The addition of fibers particularly delays cracking of high strength specimens (HVF-15). In regard to the relationship between the cover depth and the corrosion loss required for cracking, the larger the cover depth, the larger the corrosion loss required for cracking. Cover depth strongly affects the crack onset time.

6 weight loss i j NPL-5 weight loss i j NVF assumed cracking point 5.13 (mg/cm 2 ) (mg/cm 2 ).1.4 Crack width.3 (mm) NPL (mg/cm 2 ) NPL (mg/cm 2 ) NVF NVF (mg/cm 2 ) HPL-5 HVF (mg/cm 2 ) (mg/cm 2 ) HPL Ncon (mg/cm 2 ) (mg/cm 2 ) 12.(mg/cm 2 ) corrosion loss of reinforcing 2 ) Fig. 4: Relation between crack width and corrosion loss of reinforcing bar.2.1

7 4 Analysis method Crack opening in Mode I (deformation under tension) induced by reinforcement corrosion is modeled by cohesive force model. As shown in Fig. 5-a) and 5-b), the process is modeled in two phases, i.e., before and after surface crack opening. The stress generated at each node along the crack is assumed to be either the cohesive force, σ, or the extending force, P, equivalent to the expansive force of reinforcement, in consideration of the nonlinear elastic deformation of concrete. Formulation is then made using Eqs. (2) and (3) on the basis of the principle of superposition so that the sum of the stress intensity factors at the tip of the fictitious crack resulting from the stress at each node can be balanced with the crack opening displacement at each node calculated from the stress intensity factor. The stress intensity factor for specimens of a simple shape can be readily referred to in handbooks (Tada et al. 1985) and other sources. K(a) = K p (a) + K r (a) : δ(a, x) = δ p (a, x) + δ r (a, x) (2, 3) where K(a) = stress intensity factor at the crack tip when the crack length is a, K p (a) and K r (a) = stress intensity factors at the crack tip due to equivalent expansive force of reinforcement and cohesive force, respectively. δ(a, x) = crack opening displacement at x, δ p (a, x) and δ r (a, x) = crack opening displacements at x due to equivalent expansive force of reinforcement and cohesive force, respectively. The equivalent expansive force of reinforcement is modeled as Eq. (4) by assuming a constant expansive pressure on the bar surface and extracting only the intensity component in the crack opening direction. T, D, and I(x) denote the cover depth, bar T D T D reinforcing bar reinforcing bar P P process zone process zone ƒð( a, x ) P (a,x) crack length a P (a,x) ƒâ( a, x ) ƒð ƒâ( a, x) a CMOD crack width x c ƒð( a, c) K(a ) a) before cracking b) after cracking Fig. 5: Modeling of crack propagation by reinfrcing bar corrosion

8 diameter, and component function, respectively. P(a, x) = P (a)i(x), I(x) = 1 1 2(x T) D 2, (T x T + D) (4) The relationship between the cohesive stress (negative values) and the crack opening displacement is expressed using a tension softening curve, which is a material characteristic. A bilinear curve is applied in this study (see Fig. 3). σ(a, x) = m(δ, x) δ + n(δ, x), δ = δ(a, x) (5) The cohesive force at the bar position is assumed to be nil. The crack opening displacements can be expressed by the integral equation of stress intensity factors according to Castigliano's theorem. By eliminating P(a) and rearranging the equations Eqs. (2) and (3), integral equation (6) is obtained. H (a,x,c) is a weight function and independent of the acting force. δ(a, x) = 1 E σ(a,c)h(a, x, c) dc a (6) The distribution of crack opening displacement at a given fictitious crack length of a can be determined by solving nonlinear simultaneous equations obtained by substituting constitutional equations (5) into Eq. (6) and discretizing the equations. The cohesive stress distribution and expansive force can also be determined. Nonlinear simultaneous equations are solved by iteration of the solution until the inclination of constitutional functions of all nodes coincide to determine the optimum solution (Kitsutaka 1997). 5 Analysis results Fig. 4 shows the analysis results of various corrosion test conditions using bilinear parameters of each specimen given in Table 2. The corrosion loss was calculated from the analysis results of reinforcement expansion (crack opening displacement of cohesive force models). As for rust data, Young's modulus and volumetric expansion of rust were assumed to be 25 MPa and 2.5, respectively, referring to the literature (Sumimoto et al. 1989). An analysis taking account of creep displacement of mortar/concrete surrounding reinforcement was also conducted. In this case, the crack opening displacement at which the expansive pressure on the reinforcement is the same was calculated taking account of the creep coefficient. The creep coefficient was assumed to be 1. and.5 according to compressive strength for N series (approximately 5 MPa) and H series (approximately MPa), respectively.

9 1. 2MPa Concrete ƒó=1.5 2MPa Concrete ƒó=1.5.8 D=6mm D=mm.6.4 cover (mm) ƒó= MPa Concrete 1. 5MPa Concrete ƒó=1. 5MPa Concrete D=2mm.8 Crack width (mm).6.4 D=6mm cover (mm) D=mm ƒó=1. ƒó=1..2 5MPa Concrete D=2mm 1. MPa Concrete ƒó=.5.8 D=6mm cover (mm) ƒó=.5 ƒó=.5.2 MPa Concrete MPa Concrete D=mm D=2mm 1. MPa Concrete +fiber ƒó=.5.8 cover (mm) ƒó=.5 ƒó=.5.2 MPa Concrete +fiber MPa Concrete +fiber D=mm D=2mm Fig. 6: Relationship between crack width and cross-sectional loss of reinforcement

10 Fig. 4 reveals that the analysis results taking account of creep generally exhibit good agreement. This may be because the plastic deformation around reinforcement due to expansive pressure can be expressed by creep coefficients. Also, the results agree better for the high strength series than the normal strength series. This may be partly because high strength specimens tend to lead to a single brittle crack, which agrees well with the cohesive force model assuming a single crack, whereas normal strength specimens lead to cracks dispersed around reinforcement. Fig. 6 shows the relationship between the crack width and the percentage of cross-sectional loss based on this analysis. The diagrams exhibit the relationships for the following conditions: three compressive strengths, 2, 5, and MPa, for which the creep coefficient, f, is assumed to be 1.5, 1., and.5, respectively, three bar diameters, 6,, and 2 mm, and five cover depths,, 2, 3, 4, and 5 mm. Using these diagrams, an approximate percentage of a cross-sectional loss can be estimated from the crack width on the surface for each concrete strength, internal bar diameter, and cover depth. The percentage of cross-sectional loss of reinforcement increases as the crack width increases. When the crack widths are the same, a larger cover depth or larger bar diameter indicates a lower percentage of cross-sectional loss. 6 Conclusions 1) The relationship between the crack width on concrete surfaces and the corrosion loss of reinforcement was grasped through electrolytic corrosion s on specimens in which a reinforcing bar was embedded using normal and high strength mortar/concrete with or without fiber reinforcement. 2) A method of analyzing the relationship between crack width and corrosion loss of reinforcement based on fracture mechanics was presented. The integration of creep deformation around reinforcing bars led to relatively good agreement with results. 3) The authors proposed diagrams for estimating the cross-sectional losses of internal reinforcing bars from the surface crack width. 4) The addition of fibers improved the crack resistance of specimen. 7 References Kitsutaka, Y. (1997) Fracture parameters by polylinear tension-softening analysis, J. Engrg. Mech., ASCE, 123(5), pp Tada, H., Paris, P. C., and Irwin, G. R. (1985) The Stress Analysis of Cracks Handbook, 2nd Ed., Paris Productions Inc., St. Louis, Mo. Tsunomoto, M., Kajikawa, Y. and Kawamura, M. (1989) Elasto-plastic analysis of expansive behaviour due to corrosion of reinforcement, Proc. Japan Soc. Civil. Engrg., 42 pp