Prediction of the ultimate limit state of degradation of concrete structures

Transcription

1 Prediction of the ultimate limit state of degradation of concrete structures John CAIRNS Senior Lecturer Heriot-Watt University Edinburgh EH45 8AP, UK David LAW Research Associate Heriot-Watt University Edinburgh EH45 8AP, UK Employed at Heriot-Watt University since Interests in structural, durability and NDT aspects of reinforced concrete construction as well as strengthening techniques. Convenor fib Task Group Bond Models Research interests include corrosion monitoring using non-destructive electrochemical techniques, durability, electrochemical protection and the life cycle management of reinforced concrete structures. Summary The paper presents a scoping analysis to compare duration of initiation and propagation phases of corrosion related degradation of structural concrete, derived from existing models. The various ways in which corrosion can impair structural capacity are briefly discussed along with relevant limit states. The scoping analysis demonstrates that time to an ultimate limit state of degradation will typically be appreciably greater than that to initiation of corrosion or even to initiation of longitudinal crack formation, although the partial safety factors which would have to be introduced for an assessment against the ultimate limit state would restrict this somewhat. Keywords : Concrete structures; residual life; corrosion; deterioration models. 1 Introduction Figure 1 Tutti s model for deterioration of reinforced concrete Deterioration of structural concrete as a result of reinforcement corrosion is widely considered to be divided into 2 phases, Initiation and Propagation. The model presented by Tuutti [1] is frequently cited as representing the deterioration process, Figure 1. The initiation phase represents the time t 0 for either chlorides or carbonation (or both) to permeate the concrete cover until the threshold level for initiation of corrosion is reached. Active corrosion conditions occur during the propagation phase, which terminates when the end of service life is reached at some (undefined) state. The further into the deterioration process one goes, the more sparse becomes the available models. The great majority of research into service life design and deterioration of structural concrete has dealt with only the initiation phase. A small number of studies have attempted to model the time to longitudinal crack formation. Very few

2 Figure 2 Structure continuing to serve intended function despite active corrosion models are available for the remainder of the propagation phase or for prediction of residual strength as a result of deterioration. Now, although initiation of corrosion represents a useful defining point for the Service Life design of a new structure, it is evident that many structures continue to function, with our without repair, once corrosion has become established, Figure 2. Very few reinforced concrete structures which have collapsed unexpectedly as a result of reinforcement corrosion. Concrete repairs are an expensive business, and should be avoided unless there is a clear benefit. Many structures, particularly in the industrial sector, have a relatively clearly defined useful life. Reliance on an approach which models only the initiation phase could well result in a perceived need for repair on structures which would be capable of fulfilling their useful life without major maintenance. Models which describe structural condition to the point at which a structure can no longer fulfill its function could thus assist informed decisions on the need (or otherwise) for repair. Many models of varying complexity are available for the initiation period, but models for the propagation phase have only been developed more recently and no attempt appears to have been made to relate durations of propagation and initiation phases. The Life-365 program[2], for example, for want of evidence makes the somewhat arbitrary assumption that the propagation period from initiation to repair is fixed at 6 years. It is also of interest to note that while service life models mostly deal with the initiation phase, by contrast condition indicators used in assessment of existing structures generally reflect deterioration only through the propagation phase. This objective of this paper is to deploy such models as are available to evaluate the relative duration of initiation and propagation phases of chloride induced degradation of structural concrete under typical service conditions. The anticipated benefits include an improved perception of the need for concrete repairs and in the definition of condition indicators for tracking of condition. 2 Definition of limit states of degradation A number of limit states have been proposed to define critical points in the deterioration of a structure. Those proposed include initiation of corrosion, initiation of longitudinal cracking, a limiting longitudinal crack width, loss of steel section to a defined level, and loss of structural integrity. It is evident that initiation of corrosion, although representing a crucial change of condition for durability, is of no immediate consequence for structural capacity, and constitutes a limit state of durability only. It is typically reported that corrosion penetrations (i.e. reductions in bar radius) of between 0.01mm and 0.04mm are required to initiate longitudinal cracking. This represents a reduction of less than 2% of cross sectional area for a small diameter bar, and less for larger bars. (For comparison, UK production tolerances on reinforcement are ±6.5% for 8mm and 12mm diameter reinforcement and ±4.5% for sizes 12 and above[3]) Clearly, cracking develops well before loss of bar section becomes structurally significant. Bond strength at initiation of cracking is generally also reported to be similar to or higher than that of the structure as new. Longitudinal cracking will thus precede significant loss of structural capacity, and is also a durability limit state only. A crack width of (typically) 0.3mm is commonly considered to represent

3 a serviceability limit state for structural design. The limit is selected mainly on aesthetic grounds, as narrower cracks are considered to be not readily noticeable. An ultimate limit state is reached when a structure or a part collapses, often with risk of injury. A reasonable margin of safety must therefore be maintained against an ultimate limit state being reached. In the context of corrosion damaged concrete, an ultimate limit state could be reached at collapse of a structure or object, of a component, or, through spalling of cover concrete, of a surface of a component. A section loss (typically of 10% of reinforcement cross section) has on occasion been considered to represent a limiting condition. These considerations lead to the multi-limit state model shown in Figure 3, adapted from that presented by Bamforth [4].The first phase, up to time t 0, is the same as the initiation phase described by Tuutti, and terminates when conditions for a significant rate of corrosion develop at the reinforcing bar. Time t 1 marks initiation of longitudinal cracking, and t 2 time at which a longitudinal crack reaches 0.3mm. The period to an ultimate limit state is represented by time t 3a and t 3b, representing time to spalling and to unacceptable loss of structural capacity. The a and b subscripts are used as it is not evident which limit state will be reached first. Beyond t 3b, a structure could only remain in service through imposition of load limits or provision of Figure 3 Limit states for deterioration additional support. For purposes of analysis here, the limit state of spalling is defined as the time to growth of longitudinal crack width to 2.0mm, based on the studies of Rodriguez et al[5]. Whether spalling needs to be treated as an ultimate limit state may be questioned, and will depend on the location of the structure. It is possible that in some situations where access of personnel beneath a structure is restricted, spalling of cover concrete would not represent a risk of injury. It is also possible to take measures such as fixing catch nets to prevent injury from spalled concrete. Falling concrete is, however, clearly unacceptable on a public structure such as a highway overbridge. The limit state of structural stability cannot be defined by a single measured parameter. Structural failure can occur due to loss of flexural, shear, axial (or rarely torsional) capacity [6]. Each of these could arise from loss of reinforcement cross section, concrete cross section, or of bond between the two. Tentative models for residual structural capacity have been proposed and could be incorporated into a full procedure. However, for simplicity here, the ultimate limit state of structural capacity has been taken as a 10% reduction in the cross sectional area of main reinforcement. This limit has been cited in various reports of investigation of deteriorating structures. Flexural strength may be taken as proportional to residual area of reinforcement. It is worth explaining that, although a 10% reduction in strength might seem to be high, there are good reasons for it to be feasible. Firstly, it is accepted that conventional partial safety factors may be reduced in assessment in view of the better quality of information on an as built structure when compared to the design stage[7]. Secondly, in detailing of reinforcement the area provided is invariably rounded up from the calculated requirement: bar cross sections increase in increments of approximately 50%. Finally, if assessment is based on minimum residual cross sectional area, the usable strength of the bar would tend to be underestimated.

4 3 Deterioration models The models used in this scoping investigation have been developed for chloride attack The initiation period is modelled using Fick s Second Law of diffusion, Equation 1 C x = C s ( 1 erf [x/(2.(d ca.t) 0.5 )] (1) where : C x : Chloride concentration at depth x C s : Chloride concentration at surface erf : error function t : time The apparent chloride diffusion coefficient is taken as a function of time, Equation 2. D ca = D ca(tm) (t/t m ) n (2) where D ca(tm) is the apparent chloride diffusion coefficient at time t m, and n is an empirical coefficient, taken here as for Portland cement concretes following the recommendations of Bamforth and Pocock[8]. Measurements reported by Bamforth and Pocock show that there is a relationship between chloride content, C x, and corrosion rate CR. Within the constraints of their investigation corrosion rate appeared to be independent of cover depth, and is represented by Equation 3. CR = a. e b.cx (3) Bamforth assumed corrosion rate to be negligible for CR<1.2microns/year, and found the best-fit line to the data indicated a threshold value of 0.46% Cl - by weight of cement. Following the suggestion of Andrade et al for cyclic wetting/drying conditions, and setting an upper limit to corrosion rate at a Cl - concentration of 3.0%, the relationships given in Equations 4 have been used. Cl %, CR= % Cl - 3.0%, CR= e Cx microns/year (4) 3.0% Cl - CR = 60 microns/year The models developed within CONTECVET [9] are used to estimate time to cracking and crack width. Corrosion penetration to crack initiation p cr is given by Equation 5. The growth of crack width w cr with continuing corrosion is given by Equation 6. Models for crack width and for residual strength capacity remain largely empirical at present. p cr = ( c/d b 22.6f ct,sp )/1000 (5) w cr = β(p(t) p cr ) 0 (6) where c minimum concrete cover d b bar diameter f ct,sp tensile splitting strength of concrete, taken here from CEB-FIP Model Code 90 p(t) mean corrosion penetration at time t β - an empirical coefficient, taken as 12.5 for bottom cast bars and 10 for top cast bars The residual cross section of the reinforcing bar A res is determined by Equation 7, assuming uniform corrosion. A res = π(d 2p(t)) 2 /4 (7)

5 Analyses have been based on an assumption that concrete strength is inversely proportional to water/cement ratio, and that apparent diffusion coefficient D ca(tm) at an age of 20 years is given by Equation 8, derived from results presented by Bamforth and Pocock. D ca(tm) = 0.74 x x e (5.wc) (8) where wc is the water/cement ratio. 4 Results Results give the time to initiation of corrosion at the threshold value t 0, corrosion, time to onset of longitudinal cracking t 1, time until longitudinal crack width reaches 2.0mm t 3a and time to 10% section loss, t 3b. All results are quoted in years. With so many factors that can influence the process, obvious that a very broad brush approach will have to be taken. Representative values have been used throughout with no attempt made to introduce all the potential influencing factors. It has, admittedly without a great deal of evidence, been assumed that environmental factors will exercise a similar influence on both initiation and propagation phases, and hence as the exercise is concerned with obtaining only relative values for the three phases, that such factors may conveniently be neglected. A base case has been defined from which all parameters have been varied. The base case assumes a bar diameter of 16mm, minimum cover of 30mm, concrete of Grade 35 with w/c ratio of 0.55 and an apparent diffusion coefficient D ca of 1.1 x (At tm = 20 years). A surface chloride level of 0.36% by weight of concrete has been used, representing a typical value for a Portland cement concrete, according to suggestions of Bamforth and Pocock,. For simplicity, this value is assumed to be reached at time 0. Chloride content by weight of cement is taken to be 6.7 times chloride content by weight of concrete, and top cast bars assumed. Figure 4(a) and 4(b) present two comparisons, one for varying minimum cover and another for varying bar diameter. Overall time to reach the limit state of 10% average section loss increases appreciably with cover (increasing length of initiation phase and of propagation phase) and with bar Time (Years) Time (Years) Fig 4(a) Minimum concrete cover (mm) Minimum concrete cover (mm) Fig. 4(b) Figure 4 Comparisons of duration of various phases in useful life

6 diameter (increasing length of propagation phase). Figure 4 shows the initiation phase may typically account for as little as 10% of the useful life of a structure, as determined on the basis of the structure reaching an ultimate limit state. The model has also been used to study the effects of surface chloride concentration (from 0.3% to 0.8% by weight of concrete) and of water/cement ratio (from 0.76 to 0.32). While surface chloride exerts a strong influence on rate of degradation, the share of the lifespan occupied by each stage in the deterioration process is not affected to the same degree. Time to initiation of corrosion remains a fairly constant proportion of time to longitudinal cracking and of time to spalling (30% and 10% respectively), although the duration of each varies by a factor of 4 over the range of surface chloride contents investigated. Reductions in water/cement ratio (and hence also in diffusion coefficient) are predicted to have a strong positive effect on the initiation period, but a modest negative influence on time to crack initiation due to the more brittle nature and lower porosity of high strength concretes. Although the initiation period may be increased by an order of magnitude by use of a higher grade concrete, time to other limit states are reached may only increase by a factor of between Conclusions This brief study thus suggests the propagation phase will provide a significant portion of the useful lifetime of the structure. Clearly the empirical nature of the constituent models and the sweeping simplifications made in arriving at the results outlined can, at this stage, provide no guarantees of the accuracy of the outcomes. However, for certain classes of structure, particularly industrial structures where operational circumstances dictate a clearly definable period of service and zero residual value, improved models for the entire lifespan of a structure might enable appreciable cost savings through the avoidance of unnecessary repair costs. At the very least, results presented here provide justification for more attention to be paid to the development of corrosion rate and residual strength models for the propagation phase of the deterioration of reinforced concrete. References 1. Tuutti K. (1982) Corrosion of steel in concrete. Swedish Cement & Concrete Inst. Report Fo4. 2. Thomas M D A and Bentz E C. (2000) Life-365 computer program for predicting the service life and life-cycle costs of reinforced concrete exposed to chlorides. /support/pageetools 3. BSI (1988) BS4449 :1988 Carbon steel bars for the reinforcement of concrete. British Standards Institution. London. 13 pp. 4. Bamforth P. (1997) Probabilistic performance based durability design of concrete structures. Management of Concrete Structures for long term serviceability. Ed. Byars & McNulty. Telford, London. pp Rodriguez J, Ortega L M, Casal J & Diez J M. (1996) Assessing structural conditions of concrete structures with corroded reinforcement. 4th Int.Congress on Concrete in Service Mankind, Dundee, UK. 6. Cairns J, Du Y & Law D W. Structural assessment of corrosion damaged bridges. Proc Conf on Structural Faults and Repair, London, Engineering Technics Press, Edinburgh. 7. Institution of Structural Engineers. Appraisal of existing structures, 2 nd Edition. IStructE, London, Bamforth P & Pocock D. Design for durability of reinforced concrete exposed to chlorides. Workshop on structures with service life of 100 years - or more, Bahrain, Nov CONTECVET (2001) A validated Users Manual for assessing the residual service life of concrete structures. Rodriguez et al. Available on CD from British Cement Association, Crowthorne, Berkshire.