PERFORMANCE-BASED DESIGN APPROACHES FOR DURABILITY DESIGN OF REINFORCED CONCRETE STRUCTURES

Transcription

1 PERFORMANCE-BASED DESIGN APPROACHES FOR DURABILITY DESIGN OF REINFORCED CONCRETE STRUCTURES Rachel N. Muigai (1), Mark G. Alexander (1), Pilate Moyo (1) and Mike B. Otieno (1) (1) CSIRG, Department of Civil Engineering, University of Cape Town, South African Abstract Durability design of reinforced concrete structures has become a pervasive concern worldwide. It is concerned with ensuring the ability of the concrete to resist the penetration of aggressive agents during its intended service life. This largely involves the use of material and construction specifications that control the quality and thickness of the cover layer protecting the reinforcement. It is now evident that structures designed for durability have inherent safety together with economical and environmental advantages. The service life of such structures is prolonged bringing about a reduction in maintenance and repair costs. The environmental load associated with such a structure is also reduced thus enhancing the structure s sustainability. Over time, durability design specifications have shifted from a prescriptive format to a performance-based format. Guidelines on performance-based service life design approaches of concrete structures are given in various codes and design standards. The FIB Model Code (Service Life Design) gives four approaches for service life design as: full probabilistic approach, partial factor design approach, deemed-to-satisfy approach, and avoidance of deterioration approach. Two of these approaches are exemplified in this paper with the aim of creating an understanding of the different solutions the designer has to performance-based durability design. 1. INTRODUCTION The International Standards Organization defines durability as the capability of a structure to perform its intended function over a specified period of time under the influence of agents anticipated in service [1]. The influencing agents include live loading and environmental loading. The durability of concrete structures depends on interactions with the service environment, in which penetration of deleterious substances is highly significant. The ingress of various ions, liquids and gases from the environment is responsible for the deterioration of reinforced concrete (RC) directly or indirectly. For instance, the ingress of chlorides or carbon dioxide depassivates the steel in RC, and in the presence of oxygen and water, steel may corrode [2]. Designing for durability simply means ensuring that the concrete is able to resist the 289

2 penetration of aggressive agents during its intended service life. It largely involves controlling the quality and thickness of the cover layer protecting the reinforcement [3]. This is because the cover layer is most susceptible to poor construction practices (such as poor curing and inadequate compaction) which in turn increases the penetration of aggressive agents from the environment. Thus, durability design requires [4]: (a) knowledge of material transport mechanisms and (b) test methods that reflect and measure the ingress of deleterious agents from the service environment into concrete and (c) structural design and detailing to provide sufficient cover to reinforcement and (d) quality control practices that should be implemented during construction. Conventional structural design codes specify prescriptive requirements with the intention of obtaining concrete durability. The design codes impose requirements on material constituents and proportions, construction practices as well as structural details on the basis of the exposure environment, desired service life and intended exposure conditions on the structure. For example, BS (8110-1:1997) [5] and SANS (2005) [6] give the limiting values of the concrete cover to be provided to all reinforcement, 28-day compressive strength and cement content in order to achieve a durable concrete for a range of water-cement ratios and exposure conditions. This approach to design is termed prescriptive and has a role to play in durability design, but it cannot fulfil the need in all instances. Firstly, the approach does not provide a means to verify or control the presumed concrete quality which is measured by the ability of the concrete to prevent ingress of aggressive agents using durability tests. Secondly, the prescriptive approach does not adequately define the material limit state of the design, that is, the question of whether corrosion will initiate. Also it does not address whether the structure will have to be repaired at the end of its specified service life. Lastly, the prescriptive approach considers concrete strength as the main indicator of durability [7], postulating that a stronger concrete is more durable [8]. However, this is not always the case, especially when high-strength concrete (HSC) is used for resistance against freezing and thawing action and certain forms of chemical attack. In such cases, use of HSC has been shown to lead to the development of shrinkage cracks, making the structure vulnerable to deterioration [9]. For these and other reasons performance-based durability design approaches have been put forward by current design codes of practice that aid in preventing the pre-mature failure of concrete structures in their service environments. The FIB Model Code (Service Life Design) [10] gives four approaches for service life design: the full probabilistic approach, partial factor design approach, deemed to satisfy approach, and avoidance of deterioration approach. The deemed to satisfy approach and full probabilistic approach approaches shall be exemplified in this paper. 2. PERFORMANCE-BASED DESIGN Performance-based design for durability of concrete structures includes the measurement of relevant concrete properties in the design stage in order to assess the potential resistance of the material against deterioration. In South Africa, the durability index approach has been developed to improve the quality of reinforced concrete construction. The approach integrates service life design (SLD) models, with appropriate durability index tests to give performance specifications for structures in a given environment. 290

3 For a marine environment, measurements of the ingress of chloride ions from the sea water into concrete are taken using the chloride conductivity test (CCT), shown in Figure 1. Figure 1: Chloride conductivity test [11] The CCT is a steady state accelerated test that measures the resistance of a 30 mm thick concrete disc (Ø 68 mm) to chloride conduction under the action of an applied voltage across the specimen. A conductivity value for the given concrete is then calculated using Equation 1. i t σ = V A (1) whereσ is the chloride conductivity ( cm ma,t is the specimen thickness ( ) ms ), i is the measured current ( ) cm. 2 cm and A is the cross-sectional area ( ) There exists a correlation between the chloride conductivity value and the diffusion coefficient parameter in Fickian model (Equation 2). x C (x,t) = CS 1 erf (2) (1 m) 2 Dit where, C x,t is the chloride concentration at distance x ( mm ) from the exposed surface at a certain time t; C s is the surface chloride concentration (% Cl - by mass of cement); D i is the chloride diffusion coefficient (m 2 /s) at 28-days, m is a coefficient representing the reduction in chloride diffusion with time due to chloride binding, and erf is the error function. Equation 2 is derived from Fick s second law of diffusion and allows for the durability performance of a structure to be predicted based on considerations of environmental conditions, cover thickness and concrete quality. The Fickian model relies heavily on the chloride conductivity test output characterizing the material quality. This is because of a 291

4 relationship that has been established, by Mackechnie [16], between the 28-day chloride. The study [16] carried out conductivity value ( ) D 2 years σ and the 2 year diffusion coefficient ( ) laboratory-based experimental correlations between 28-day conductivity index values and chloride diffusion coefficients. The specimens covered a range of binder types (100% Portland cement and combinations of PC with supplementary cementitious materials that included Fly ash and Blast Furnace Slag), water/ binder ratios and curing regimes. From the correlations, the study [16] set out a nomogram, in which the two year diffusion coefficient ( ) years D 2 is determined from the 28-day chloride conductivity value and vice versa. Thus, the durability index approach can be used to craft performance-based specifications, based on the service life model (Equation 2) that utilises the chloride conductivity index in its formulation. 3. PERFORMANCE-BASED DESIGN APPROACHES 3.1 Practical Example Two performance-based approaches, i.e. the deemed-to-satisfy and the probabilistic approach, are exemplified for a concrete pier to be cast in-situ in an extreme splash and tidal marine environment using a cement blend of Portland cement and ground granulated blast furnace slag - GGBS: OPC (50:50). GGBS has been selected as it has been found to be beneficial in the marine environment in that it is able to bind chlorides with time and resist the ingress of chlorides [13]. The design task is to specify the required material resistance against chloride penetration in terms of a chloride conductivity value and/or corresponding diffusion coefficient given the parameters in Table 1. The mean and coefficient of variation (COV) for the surface chloride content were determined from the statistical quantification of data from chloride profiling tests carried out on marine structures in the Western Cape (South Africa). South African data on cover depths for both bridge and building structures were used to derive the statistical quantities for the cover depth. The statistical values for C crit were adopted from literature and apply to Portland cement concrete. This is because there is lack of reliable statistically quantified C crit values in literature for blast furnace slag. Table 1: Input parameters for reliability analysis of a RC pier Reference Parameter Units Mean COV # Distribution [14] Concrete cover, x mm Normal [15] Critical chloride content, C crit % Normal This study Surface chloride content, C s % Gamma Design service life, t years Deterministic [16] Reduction factor, m Deterministic COV # = Coefficient of variation; C crit # = This value relates to OPC binder, but is here adopted for other binder types, since reliable data are not yet available 292

5 3.2 The Deemed-to-Satisfy Approach The deemed-to-satisfy approach comprises of a set of rules for dimensioning, materials selection and execution procedures that ensure that the concrete structure remains serviceable during its design service life [7]. This approach, as put forth in the FIB Model Code (Service Life Design) [10], differs from the prescriptive one given by EN [17] and SANS (2005) [6] in that it is based on (i) a statistical evaluation of data acquired from both laboratory and field assessments (ii) calibrated results from practical experience, as opposed to solely from practical experience. The approach as used in the South African context prescribes limiting durability index values for various exposure environments (similar to those in EN206-1 [17]). The limiting values (such as those presented in Table 2) are derived from correlations between laboratory test results and in-service performance of a structure. From Table 2 it can be noted that the limiting chloride conductivity index varies from one binder-type to another for the same exposure environment. This is mainly due to the sensitivity of the chloride conductivity to changes in chloride binding characteristics of different binders and the degree of hydration in the long term [22]. Finding the solution to the example using the deemed-to-satisfy approach involves specifying limits of chloride conductivity index. Thus, for the example, the maximum 28-day chloride conductivity value given in Table 2 is 1.05 ms/cm. In practical terms this implies a GGBS: OPC (50:50) concrete of w/b approximately 0.4 that is moist cured for at least 7 days [23]. Table 2: Maximum Chloride Conductivity Values ( ms/cm ) for Different Classes and Binder Types: Deemed to Satisfy Approach Monumental Structures (Cover = 50 mm) [7] EN 206 class (modified for SA conditions) 70:30 CEM I: Fly Ash 50:50 CEM I: GGBS 50:50 CEM I: GGCS 90:10 CEM I: CSF XS XS2a XS2b, XS3a XS3b These are the maximum values that should not be exceeded in the as-built structure (tested on samples removed at 28 days). 2 FA= Fly Ash; GGBS = Ground granulated blast furnace slag; GGCS = Ground granulated corex slag; CSF = Condensed silica fume 3.3 The Probabilistic Approach The probabilistic approach allows for the assessment of uncertainties caused by inherent random variabilities in concrete properties, insufficient data and lack of knowledge on durability parameters. Probabilistic methods can either be full-probabilistic or semiprobabilistic (partial factor method) and involve the use of reliability-based design and the limit state methodology. The limit-states method (LSM) for design was developed by ISO 2394 (1998) [18] and consequently adopted by various design standards and codes such as the ISO (2008) 293

6 [19] and FIB Model Code (Service Life Design) [10]. Although ISO 2394 includes durability in its principles, the LSM has not been developed for failures due to material deterioration to the extent that it has for failures due to gravity, wind, snow and earthquake loads [19]. The LSM incorporates the use of service life prediction model (Equation 2) that describes the deterioration mechanisms in concrete up to the initiation limit state. The variables in the model are stochastic in nature making it necessary to use a reliability-based design methodology (RBD) for analysing the mathematical model at a given limit state. To carry out a reliability analysis of Equation 2, the parameters in the model are characterised further as either action effect, S () t or as an initiation limit, S lim (ISO 13823, 2008) [19]. Corrosion initiation is said to occur at any time, t, when the condition given by Equation 3 occurs [19]. S > S () t lim (3) Slim is taken to be the critical chloride concentration and () t S is represented by Equation 2. The parameters in the functions S () t and S lim are statistically quantified using data obtained from in-situ and laboratory tests to give their respective distribution types, mean values and coefficient of variation (COV). The statistical information of each of the parameters in Table 1 is then exploited to provide improved uncertainty estimates in the output, which is usually stated in terms of the probability that the condition represented by the LSF occurs. The probability of this occurring during the design service life of the structure is termed the probability of failure ( ) f P [19]. A MATLAB based subroutine developed for this study was applied in carrying out Monte Carlo simulation (MCS) on the respective stochastic quantities of the parameters in Table 1. The simulated values of the parameters in Table 1 were then substituted into Equation 4 and a range of diffusion coefficients and corresponding probabilities of failure ( ) f P calculated Ccrit 1 i = erf 1 ( 1 m x C ) (4) S t D The results of the MCS analysis were represented in the form of a cumulative density function (CDF) as shown in Figure 2. The probability of failure obtained from the analysis was verified for acceptance by comparing it to an acceptable (target) probability of failure, P target such that [20 and 21]: P f { S lim S < 0 } < Pt arg et = P (5) ( ) ( t ) For a target failure probability of 0.067, a diffusion coefficient value of 44.5 mm 2 /year was obtained, which is the limiting value that should be specified in the design. Based on the aforementioned relationship between the 28-day chloride conductivity value and D 2 (See Section 2), the diffusion coefficient D 28 value of 44.5 mm 2-12 /year ( m 2 /s) corresponds to a chloride conductivity value of 0.9 ms/cm. days years 294

7 Figure 2: CDF of probability of failure for diffusion coefficient values 3.4 Probabilistic Approach vs. Deemed-to-Satisfy Approach It can be observed that the design chloride conductivity value obtained from the probabilistic approach is lower than that specified by the deemed-to-satisfy approach of 1.05 ms/cm for the same parameter values (Table 2). This shows that the use of the deemedto-satisfy approach would result in a large underestimation of the required concrete quality, which can result in under designing a RC structure for durability, eventually leading to premature failure of a structure. Using the probabilistic approach, the designer is also able to account for the inherent uncertainty in the service life prediction model. Notwithstanding, the full probabilistic approach has its inherent problems, the first of which is the interpretation of the acceptable (target) probability of failure, P target. The second drawback of the probabilistic approach arises from the fact that the method relies on characterising each parameter in terms of mean, standard deviation and statistical distribution. This is a problem due to the fact that the amount of data available for most of the parameters in the LSF was limited. Thirdly, the probabilistic method relies heavily on numerical methods for analysis. It requires the use of statistical software packages that incorporate numerical methods such as Monte Carlo simulation for analysis. 4. CONCLUSIONS The paper outlines two performance-based design approaches to service life design that have been put forward by current design codes of practice to aid in preventing the pre-mature failure of RC structures in their service environments. These are the full probabilistic approach and deemed-to-satisfy approach, in the FIB Model Code (Service Life Design). REFERENCES [1] ISO (2008), Buildings and Constructed Assets Service life planning -Part 8: Reference service life and service life estimation [2] Basheer, L., Kropp, J., Cleland, D.J., (2001), Assessment of the Reliability of Concrete from its Permeation Properties: A Review, Construction and Building Materials, 15(2001), pp

8 [3] Alexander, M.G., Stanish, K., (2001), Durability design and specification of reinforced concrete structures using a multi-factor approach, Conference Proceedings in Honor of Sidney Mindess. [4] Tikalsky, P.J., David Pustka, D., Marek, P., (2005), Statistical Variations in Chloride Diffusion in Concrete Bridges, American Concrete Institute Structural Journal, May-June 2005 pp [5] BS :1997, (1997), Structural use of concrete- Code of practice for design and construction. [6] SANS (2005) South African National Standard: The Structural use of Concrete, Part 2: Materials and Execution Work, 3 rd Edition, pp. 66. [7] Alexander, M. G., Ballim, Y. and Stanish, K., (2007), A Framework for Use of Durability Indexes in Performance-based Design and Specifications for Reinforced Concrete Structures, Materials and Structures Journal, DOI /s [8] Kwan and Wong Henry H.C., Albert, K.H., (2006):, Durability of Reinforced Concrete Structures, Theory vs. Practice, Department of Civil Engineering, The University of Hong Kong, Hong Kong. [9] Mehta, P. K., (2006), High-Performance, High-Volume Fly Ash Concrete for Sustainable Development, University of California, Berkeley, USA. [10] FIB Model Code for Service Life Design (2006) fib Bulletin 34, EPFL Lausanne, 116 pp. [11] Alexander, M.G., Mackechnie, J.R. and Ballim, Y. (1999) Guide to the use of durability indexes for achieving durability in concrete structures. Research Monograph No 2, Department of Civil Engineering, University of Cape Town, 35 pp. [12] Streicher, P. E, (1997), The Development of a Rapid Chloride Test for Concrete and its use in Engineering Practice, PhD Thesis, University of Cape Town. [13] Mackechnie, J.R. and Alexander, M.G. (1997), A rational design approach for durable marine concrete structures, Journal of The South African Institution of Civil Engineering, 39(1), First Quarter 1997, pp [14] Ronne, P.D., (2005), Variation in Cover to Reinforcement: Local and International Trends, Concrete Beton, 111. [15] Duracrete, (2000), Statistical Quantification of the Variables in the Limit State Functions, The European Union - Brite EuRam III, Project BE /R9, Probabilistic Performance-based Durability Design of Concrete Structures. [16] Mackechnie, J.R., (1996) Prediction of Reinforced Concrete Durability in the Marine Environment, University of Cape Town, PhD Thesis. [17] EN 206-1: Concrete Part 1: Specification, performance, production and conformity. [18] ISO 2394 (1998) General Principles on Reliability for Structures for Durability, pp. 73 [19] ISO (2008) General Principles on the Design of Structures for Durability, ISO TC98/SC2, Final Draft. [20] Li, C. Q., (1997), Deterioration of concrete building structures, Building Research and Information, 25(4), pp [21] Sarja, A., Vesikari, E., (1996), Durability design of concrete structures, 1 st Edition, London Spon Press [22] Gardner, T. (2006) Chloride transport through concrete and implications for rapid chloride testing. MSc (Eng) Thesis, University of Cape Town. [23] Alexander M. G., Streicher P. E. and Mackechnie J. R. (1999) Rapid chloride conductivity testing of concrete, Monograph No. 3, Dept. of Civil Eng. UCT 296