# Review Article Probabilistic Evaluation of Service Life ... concrete, concrete cover, age, and most

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Review Article Probabilistic Evaluation of Service Life for Reinforced Concrete Structures

Sanjeev Kumar Verma,1 Sudhir Singh Bhadauria,2 and Saleem Akhtar1

1 Civil Engineering Department, University Institute of Technology, Rajiv Gandhi Technological University, Airport Road Bhopal, Madhya Pradesh 462036, India

2 S.G.S. Institute of Technology and Science, Indore, Madhya Pradesh 452003, India

Correspondence should be addressed to Sanjeev Kumar Verma; sanjeev.apm@gmail.com

Received 13 December 2013; Accepted 8 January 2014; Published 18 February 2014

Academic Editors: I. Smith and X. Zhou

Copyright ยฉ 2014 Sanjeev Kumar Verma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Degradation of performance and deterioration of different components of reinforced concrete (RC) structures increase with the age of structure. This deterioration of reinforced component depends on several parameters. However, modeling service life of RC structure by considering all the parameters is a difficult job, as most of the parameters are uncertain in nature. Probabilistic models account well for the uncertainties in the parameters responsible for deterioration of RC structures. This paper presents a review of several recent service life models developed using probability based concepts.

1. Introduction

Performance and service life of a RC structure are gov- erned by several parameters such as strength, quality of concrete, concrete cover, age, and most significantly by exposure conditions. According to Li et al. [1] behavior or performance of concrete structures depends on various physical and chemical related phenomena but it is hard to combine various analytical models in order to simulate real degradation process. Hence, because of random nature of the parameters governing the performance of RC structures, probabilistic approach is better to develop reliable service life prediction model. Probabilistic models calibrated with monitored field data can provide more reliable models to predict the probabilities of corrosion. This category includes models based on probability or statistical concepts such as probability function, reliability based models, Monte Carlo simulation, Markov chain methods, and fuzzy logic. In probablistic analysis three steps can be distinguished: (a) definition of failure modes (limit states) and corresponding models, (b) quantification of the statistics of the random variables, and (c) calculation of the desired results as, for instance, failure probabilities [2]. Present paper reviewed several probability based service life models developed by

researchers for evaluating the probability of failure and estimating the residual life of RC structures.

2. Service Life

Service life of a RC structure can be defined as time period during which structure will fulfill the required performance under defined repair and maintenance. Zhang and Ba [3] defined service life as the life before critical chloride con- centration led to reinforcement corrosion. According to Chai et al. [4] period from initial use to depassivation can be considered as service life. Vorechovska et al. [5] consid- ered depassivation of reinforcement due to carbonation or chlorination as the end of service life. Parameswaran et al. [6] considered the time during which the performance of a concrete structure will be kept at a compatible level to fulfill the performance as service life, provided that it is properly maintained. Rostam [7] defined service life as the number of years during which the structure shall perform satisfactorily without unforeseen high costs for maintenance. Martin- Perez and Lounis [8] defined service life as the time until damage accumulation reaches an unacceptable or limit state. According to Abu-Tair et al. [9] end of service life is reached

Hindawi Publishing Corporation Chinese Journal of Engineering Volume 2014, Article ID 648438, 8 pages http://dx.doi.org/10.1155/2014/648438

2 Chinese Journal of Engineering

Ingress of harmful agents starts at this stage

Design and planning Construction Occupied/in use

Propagation of deterioration

Initiation of deterioration

No sign of deterioration

Crack formation Increase in

deterioration rate Failure

Ingress continue

Harmful agents attain threshold limit

Increase in ingress rate

Figure 1: Different levels of service life.

when either failure occurs or major repair is necessary to keep the structure in service. Teply [10] described service life as the period of time after installation during which all the conditions of the structure meet or exceed the performance. Different levels in service life of a RC structure are presented in Figure 1; these levels are design, construction, in use, period without any deterioration, initiation of deterioration, propagation of deterioration, formation of cracks, rapid deterioration, and finally failure of structure.

According to Figure 1, after design and construction when structure is in use before the initiation of deterioration, there is a phase with no sign of deterioration. Ingress of harmful agents will get initiated during the construction level and continuous during no deterioration level. When ingress of theses harmful agents reaches the threshold limit then it initiates deterioration of RC structures; this deterioration fur- ther propagates and reduces the performance of RC structure. Deterioration propagates and finally results in formation of cracks; these cracks allowmore ingress of harmful agents and further increases the deterioration at a faster rate. Finally this increase in deterioration rate reduces the performance and finally causes the failure of structure.

For modeling the performance of RC structures several parameters such as environmental effects, degradationmech- anisms, durability parameters, and properties of ingredients are required to be considered.Defining the failure of structure is most important for modeling the service life. Failure of a concrete structure can be simply explained on the basis of load โ๐ฟโ and capacity โ๐ถ.โ ๐ฟ and ๐ถ are any destructive effect and resistive capacity. If ๐ฟ is the environmental effect, ๐ถ is the capacity to resist the environmental effects. Hence if ๐ฟ is greater than ๐ถ, this condition will represent the failure of structure โ๐นโ:

{๐น} = {๐ถ < ๐ฟ} . (1)

Therefore probability of failure Pf can be defined as

Pf = ๐ {๐ถ < ๐ฟ} . (2)

3. Several Probabilistic Performance Models

Probabilistic models account well for the uncertainties in the parameters responsible for deterioration of RC structures. Hence, several researchers applied probability concepts for developing performance models. Orcesi and Frangopol [11] implemented amodel using the lifetime functions to evaluate a probability of survival of bridge components. The pos- sible outcomes assossiated with nondestructive inspections (NDIs) are incorporated in an event tree model. Use of life time function for each component of the structural system enables to express the probability that the component survives and also provided a practical methodology for determining optimal NDIs for different components of steel bridges. The expression of the survival function (๐) is shown in the following equation:

๐ (๐ก) = 1 โ ๐น (๐ก) = ๐ (๐ > ๐ก) = โซ

โ

๐ก

๐ (๐ข) ๐๐ข, (3)

where ๐ is the lifetime function that represents the probability that structure will not fail before time ๐ก.๐น is the represents the probability that the structure fails before time ๐ก. ๐ is the time to failure. ๐ is the probability density function. Cusson et al. [12] presented the development of probablistic mechanistic modeling approach supported by durability monitoring to obtain improved predictions of service life of concrete bridge decks exposed to chlorides. Factors influencing the service life are (i) surface chloride content ๐ถs, (ii) chloride diffusion coefficient ๐ท, (iii) threshold chloride content ๐ถth, (iv) corro- sion rate and deterioration rate.

Agarwal et al. [13] described an approach based on Weibull distribution to calculate the deterioration rates of typical bridge elements using historical bridge inspection data and compare the results with those, using the tradition- ally used Markov chains approach. This approach has been incorporated into a computer program that generates the deterioration curves for bridge elements, based on historical bridge inspection data and described a 7-scale condition rating used to calculate the deterioration rates for each bridge element. Bridge condition rating scale ranges from 7 to 1, 7 being new and 1 being failed condition. Mitra et al. [14] developedmethod for obtaining condition index of corrosion distressed RC building using concepts of fuzzy logic and integrates visual inspection with in situ investigations for carbonation and chloride content. Visual assessment is a two stage process: (i) visual survey has been conducted to gain information about physical and chemical state and by recording visible signs of deterioration such as cracks, rust stains, and spalling colour; (ii) condition has been assessed by an expect based on the information obtained in first stage. Vorechovska et al. [5] presented the service life assessment utilizing durability limit states specialized for con- crete structures. Both initiation and propagation periods of reinforcement corrosion are considered and a comprehensi

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