Microsoft Word - ETASR_V11_N1_pp6806-6809 Engineering, Technology & Applied Science Research Vol. 11, No. 1, 2021, 6806-6809 6806 www.etasr.com Pathan et al.: A Theoretical Framework for Service Life Prediction of Reinforced Concrete Structures … A Theoretical Framework for Service Life Prediction of Reinforced Concrete Structures in Chloride Environment using Load Factors Amjad Ali Pathan Department of Civil Engineering Mehran University of Engineering and Technology, Jamshoro, Pakistan amjad.Pathan@faculty.muet.edu.pk Ghous Bux Khaskheli Department of Civil Engineering Isra University Hyderabad, Pakistan ghous.bux@isra.edu.pk Abdul Sami Qureshi Department of Civil Engineering Mehran University of Engineering and Technology, Pakistan sami.qureshi@faculty.muet.edu.pk Abstract-Service life modeling of reinforced concrete structures in a chloride environment is mainly performed without considering the loading effects. Different loading effects can produce different service life results. This study presents a theoretical framework for the modeling of the service life of reinforced concrete structures in a chloride environment using loading factors, showing that, depending on the loading nature (either compression or tension), different diffusion results could be obtained. This paper also highlights various approaches to service life modeling, such as the deterministic, probabilistic, and semi-probabilistic, which consider different ways to estimate the service life of reinforced concrete structures in chloride environments. The importance of various distributions for the input parameters in the chloride ingress modeling was examined. The proposed framework includes a procedure to estimate the probability of concrete failure in chloride environments. Keywords-concrete durability; service life design; service life framework; chloride ingress I. INTRODUCTION Service life modeling, in terms of durability, is performed to estimate the service life and performance of reinforced concrete structures. A structure's performance is defined as its capacity to meet the target service time for its intended performance. Service life modeling estimates the residual life and is needed to apply any repair and maintenance strategies. Several studies have been conducted for modeling the estimation of service life [1-6], presenting various frameworks. In [7], a framework for the degradation of concrete was presented, highlighting the importance of the deterministic, probabilistic, and semi-probabilistic approaches, and the importance of cover thickness, concrete strength, cement type, and water to cement ratio. A detailed study for the chloride ingress parameters was conducted in [6], providing a procedure of using input parameters for the service life modeling of chloride ion ingress. In [8], the service life of concrete was quantified by a reliability index, utilizing the probabilistic method to consider the distribution laws of input parameters. Authors in [9] reported that the initiation period starts with the exposure of structure and ends with the de-passivation of reinforcement. In [2], a probabilistic model was presented and validated with data collected from two projects. The results showed that the chloride ingress process involved great uncertainties and randomness in material input parameters and structure's geometry. The proposed model was validated through a parametric analysis, finding the influences of diffusion co-efficient Do, surface chloride concentration Cs, age factor m, cover depth X, and chloride threshold CTH. Authors in [10] reported that the degrading state of an aging concrete structure could be updated for reliability purposes. Authors in [11] reported that the level of reliability for service life design was generally unclear, proposing that the criteria should be based on long-term experience. In [12], the factors influencing the chloride transport mechanism such as diffusion coefficient, surface chloride ion concentration, and drying and wetting regimes were analyzed, while the results showed that diffusion coefficient, drying, and wetting influenced the maximum transmission depth. In [4], the deterministic approach to analyze service life was reported to fail due to uncertainties on input parameters, while a probabilistic model was proposed and developed. Probabilistic methods including uncertainty parameters for input parameters were presented in [3], considering the sensitivity of the corrosion probability to different parameters and a durable design concrete cover as the most important parameter. A probabilistic model including uncertainties arising from the loadbearing capacity of reinforced concrete structures was proposed in [5]. Durability extension and service life predictions were reported to be important in [1], as corrosion has many consequences such as cracking and spalling of concrete, as well as losses of bond strength in cross- sectional areas of steel. In [6], an in-depth study was presented on the use of the concrete diffusion coefficient. The durability properties of fuel ash concrete and metakaolin concrete were studied in [13] and [14] respectively. This study aims to develop a framework for the chloride diffusion in concrete, considering the loading effect using semi-probabilistic and probabilistic analysis. Corresponding author: Amjad Ali Pathan Engineering, Technology & Applied Science Research Vol. 11, No. 1, 2021, 6806-6809 6807 www.etasr.com Pathan et al.: A Theoretical Framework for Service Life Prediction of Reinforced Concrete Structures … II. CHLORIDE INGRESS MODELING The estimation of chloride content in concrete requires a deep study of the input parameters for service life modeling. The following equation was used in [5] for the probabilistic analysis: ���, �� = � 1 − erf � � �√�� �� (1) The chloride diffusion coefficient D for an aging factor m is given by: ���� = �� � �� � � � (2) A. Service Life Modeling Service life modeling is essential to apply repair and maintenance strategies for existing and enhancing the durability of new structures. Service life modeling can be performed in three different ways: deterministic, probabilistic, or semi-probabilistic. Table I shows a comparison of these three approaches in terms of complexity and Table II summarizes the three approaches. TABLE I. SERVICE LIFE MODELING APPROACHES Approach Obtained results Procedures Deterministic Over-estimated Simple Probabilistic Balanced-estimated Complex Semi-probabilistic Under-estimated Semi-complex TABLE II. SERVICE LIFE MODELING APPROACHES SUMMARIZATION Approach Values C(X,T) CTH Deterministic Mean (µ) Mean (µ) Probabilistic Mean (µ) and standard deviation (σ) Mean (µ) and standard deviation (σ) Semi- probabilistic Mean (µ) and standard deviation (σ) Mean (µ) B. Deterministic In this approach, the values of variables are considered deterministic, and the approach can be conducted as a discrete or continuous overtime study. The deterministic approach considers average values, such as µ, taken as input parameters, and the calculation procedure is simple. The disadvantage of this approach consists of not considering the variation and scatter of input parameters. C. Probabilistic In this approach, the input parameters are defined using distributions. The selection of the distribution depends on available data, previous conducted studies, and designer's experience. This approach uses load and resistance concepts in general. The input parameters for load are taken as C(X,T) as defined in (1) and (2). CTH input values are obtained from the average and standard deviation of available data or previous studies. Τhis procedure gives acceptable results, despite its complexity. The designer's experience in selecting input parameters plays an important role, as an incorrect selection could result in over or under-estimated results. D. Semi-probabilistic In the semi-probabilistic approach, the input parameters for C(X,T) are defined using distributions, while CTH values are considered as a deterministic uniform value without any variation or scatter in resistance. III. LOADING FACTORS Real concrete members perform differently under different loading conditions in experimental tests. Load causes strain in the members, as shown in Table III. A column under loading conditions causes negative strain increasing tortuosity, while a beam under tense causes positive strain lowering tortuosity. In general, parapet walls do not experience any loading and their tortuosity levels are normal. Table IV shows an example of various members’ nature in a bridge structure. A bridge deck experiences both compressive and tensile forces, a column remains under tensile forces, a pier remains under compressive forces, and a deck beam remains under both compressive and tensile forces. TABLE III. MEMBERS UNDER LOAD AND NATURE OF STRAINS Concrete members Strain levels Example Tortuosity level (�) Compression members Negative Columns Higher Tension members Positive Beams Lower Normal members Neutral Parapet walls Normal TABLE IV. EXAMPLES FOR COMPRESSION AND TENSILE MEMBERS IN A BRIDGE Structure Compression members Tension members Comments Bridge deck ✓ ✓ Varies due to the stress level along the deck Bridge columns ✓ Loading causes compressive strain Bridge piers ✓ Loading causes compressive strain Bridge deck beams ✓ ✓ Varies due to the stress level along the length A. Compression Members Service life modeling for compression members, such as the columns in a bridge, may differ from normal concrete under no loading. Members under compression generally develop shrinkage stress, increasing concrete's compactness by filling micro-pores. In such cases, a reduction in diffusion can be observed. So instead of assuming DO as a constant value, a reduced DO can be used. The revised values for DO are shown in Table V. TABLE V. LOADING FACTORS Compression members Tension members Revise DO for compressive strain, so: �� �� !� = �� − 1.1 �� for loading value 0.4 times the limit state value �� �� !� = �� − 1.2 �� for loading value of 0.5 times the limit state value Revise DO for tensile strain, so: �� �� !� = �� + 1.2 �� for loading value 0.4 times the limit state value �� �� !� = �� + 1.4 �� for loading value 0.5 times the limit state value Engineering, Technology & Applied Science Research Vol. 11, No. 1, 2021, 6806-6809 6808 www.etasr.com Pathan et al.: A Theoretical Framework for Service Life Prediction of Reinforced Concrete Structures … B. Tension Members Tension members in a structure are subjected to stresses that cause strains, defined by: & = '.( (3) where ( is stress, E is the modulus of elasticity, and & is the strain. This strain is a measure of expansion in concrete members, producing micro-cracks that accelerate the diffusion process within the concrete body. C. Normal Members In normal members, DΟ with aging factors could be considered as normal. So, a revised diffusion coefficient (D) is needed for service life modeling. IV. DURABILITY PARAMETERS AND THEIR PROBABILITY DISTRIBUTIONS Probabilistic and semi-probabilistic analyses require a probability distribution, which is obtained from large data. The analysis is performed after deciding on the shape of the curve to be developed from large data. This also depends on designer's experience. Table VI shows various distributions used in several studies, and in the present study. TABLE VI. PARAMETERS AND LOAD Parameter Reference [2] [4] [9] [11] Present study Do Log normal Log normal Normal Log normal Normal Co Log normal Log normal Deterministic Log Normal Normal Cs Log normal ---- ---- ---- Normal M Beta ---- Normal ---- Normal Α Normal ---- ---- ---- Normal X Normal Normal ---- Log normal Normal CTH Normal ---- Deterministic Log normal Normal C(X,T) ---- Uniform Beta ---- Normal V. SERVICE LIFE MODELING FRAMEWORK DESIGN Service life modeling can be performed utilizing various simple or complex approaches, as can be seen in Figure 1. Analysis can be performed based on the design level. For instance, a deterministic approach may be followed during the design of a new structure, as it produces a quick result. Later, a semi-probabilistic analysis could be performed. A probabilistic analysis could be performed when detailed information for service life and maintenance is needed, requiring large datasets and experience. VI. UNDERSTANDING THE PROBABILITY OF FAILURE The probability of failure is a common region between both Probability Density Functions (PDFs) of C(X, T) and CΤΗ, as seen in Figure 2. This is based on the concept of load and resistance, as a failure occurs when the load value exceeds resistance. Figure 2 shows the resistance of concrete in terms of its chloride uptake capacity, which is a theoretical chloride content CTH. The load is described by chloride content on depth X over time T written as C(X, T). So, a failure occurs when C(X, T) overlaps the region of CΤΗ. Fig. 1. Flow chart of service life modeling. Fig. 2. Domains of failure and success. VII. DURABILITY PERFORMANCE AND COST EFFECT Concrete's durability performance is directly related to cost- effectiveness, as more durable concrete structures reduce service life cost. Similarly, concrete's poor performance results in earlier demolition of structures raising the overall cost. Enhanced service life can be achieved for new and existing structures by applying a repair strategy before major failures. The design framework includes all necessary parameters for service life modeling. The load effect has a major contribution to the analysis, as concrete performs differently depending on loads' nature. Based on the loads' nature (i.e. compression (columns) and tension (beams)), different results can be obtained. Table VII shows various levels of durability designs and their effect on cost. Durability performance is enhanced by the use of high strength concrete with cementitious materials having chloride binding properties and aggregates with low porosity. Sustainability involves economic considerations, as extending service reduces the total cost of construction and maintenance. Engineering, Technology & Applied Science Research Vol. 11, No. 1, 2021, 6806-6809 6809 www.etasr.com Pathan et al.: A Theoretical Framework for Service Life Prediction of Reinforced Concrete Structures … TABLE VII. ENHANCING DURABILITY PERFORMANCE Criteria Enhancing durability Effect on initial cost Service life cost Resistance Using conventional materials, Ordinary Portland Cement (OPC), and aggregates Low Low Capacity Cementitious additives such as fly ash, slag, silica, and metakaolin are are added to the concrete More More Performance High-performance materials are used in concrete such as OPC with fly ash and silica fume High High Service life- corrosion initiation Corrosion inhibitors are used High High Service life- corrosion propagation Cathode protection measures are applied High High Service life- corrosion cracking Additional measures are applied, such as sealing of cracks and protection of anode and cathode High High Sustainability High strength concrete with low porosity aggregate is used Very high Very high VIII. CONCLUSION This study highlighted the importance of the deterministic, probabilistic, and semi-probabilistic approaches for service life modeling, which give different levels of analysis. The probabilistic analysis is more complex, as it involves a lot of computational stages. A theoretical framework for service life modeling was presented considering the loading factors, while the loading effect on chloride ingress was ignored. Theoretically, it was shown that coefficient D can be applied based on the loads' nature corrections in diffusion. Moreover, it was shown that the diffusion process in concrete is not as straightforward as using (2), but using time steps the chloride content inside the concrete volume increases raising tortuosity and reducing chloride's ingress. Previous studies proposed various distributions for the input parameters of service life modeling. Concrete's performance level can be enhanced by using various high-performance materials, such as OPC with fly ash and silica fume, for sustainable concrete with aggregates with low porosity. This study's results can be concluded as: • Better performance of concrete structures reduces their service life costs. The service life can be estimated based on the level of analysis. • Service life can be estimated based on deterministic, semi- probabilistic, or probabilistic modeling. Probability distributions have been proposed for various parameters. • Chloride diffusion in concrete is a time-dependent process. • Structural loads affect the chloride diffusion in concrete, and different loadings on structural members can produce different results. For instance, the same concrete will perform differently under different load conditions. Beams are generally assumed under both compressive and tensile forces, while columns are assumed under compressive forces. Based on the nature of the loads, the diffusion coefficient may be revised for compression and tension members. • Durability performance could be enhanced from resistance to sustainability. This affects the initial cost of construction and service life, as shown in Table VII. REFERENCES [1] A. Tarighat, "Stochastic modeling and calibration of chloride content profile in concrete based on limited available data," International Journal of Civil Engineering, vol. 10, no. 4, pp. 309–316, Dec. 2012. [2] A. Duan, J.-G. Dai, and W.-L. Jin, "Probabilistic Approach for Durability Design of Concrete Structures in Marine Environments," Journal of Materials in Civil Engineering, vol. 27, no. 2, Feb. 2015, Art. no. A4014007, https://doi.org/10.1061/(ASCE)MT.1943-5533.0001023. [3] B. Saassouh and Z. Lounis, "Probabilistic modeling of chloride-induced corrosion in concrete structures using first- and second-order reliability methods," Cement and Concrete Composites, vol. 34, no. 9, pp. 1082– 1093, Oct. 2012, https://doi.org/10.1016/j.cemconcomp.2012.05.001. [4] C. G. Nogueira and E. D. Leonel, "Probabilistic models applied to safety assessment of reinforced concrete structures subjected to chloride ingress," Engineering Failure Analysis, vol. 31, pp. 76–89, Jul. 2013, https://doi.org/10.1016/j.engfailanal.2013.01.023. [5] D. L. Allaix, V. I. Carbone, and G. Mancini, "Modelling uncertainties for the loadbearing capacity of corroded simply supported RC beams," Structural Concrete, vol. 16, no. 3, pp. 333–341, 2015, https://doi.org/ 10.1002/suco.201500016. [6] M. Shafikhani and S. E. Chidiac, "Quantification of concrete chloride diffusion coefficient – A critical review," Cement and Concrete Composites, vol. 99, pp. 225–250, May 2019, https://doi.org/10.1016/ j.cemconcomp.2019.03.011. [7] E. Possan, D. C. C. Dal Molin, and J. J. O. Andrade, "A conceptual framework for service life prediction of reinforced concrete structures," Journal of Building Pathology and Rehabilitation, vol. 3, no. 1, Jan. 2018, Art. no. 2, https://doi.org/10.1007/s41024-018-0031-7. [8] F. Deby, M. Carcasses, and A. Sellier, "Toward a probabilistic design of reinforced concrete durability: application to a marine environment," Materials and Structures, vol. 42, no. 10, Dec. 2008, Art. no. 1379, https://doi.org/10.1617/s11527-008-9457-8. [9] M. Beck et al., "Deterioration model and input parameters for reinforcement corrosion," Structural Concrete, vol. 13, no. 3, pp. 145– 155, 2012, https://doi.org/10.1002/suco.201200004. [10] R. Schneider et al., "Assessing and updating the reliability of concrete bridges subjected to spatial deterioration – principles and software implementation," Structural Concrete, vol. 16, no. 3, pp. 356–365, 2015, https://doi.org/10.1002/suco.201500014. [11] S. Helland, "Design for service life: implementation of fib Model Code 2010 rules in the operational code ISO 16204," Structural Concrete, vol. 14, no. 1, pp. 10–18, 2013, https://doi.org/10.1002/suco.201200021. [12] X. Gang, L. Yun-pan, S. Yi-biao, and X. Ke, "Chloride ion transport mechanism in concrete due to wetting and drying cycles," Structural Concrete, vol. 16, no. 2, pp. 289–296, 2015, https://doi.org/ 10.1002/suco.201400035. [13] O. M. Ofuyatan, F. A. Olutoge, and O. A. Olowofoyeku, "Durability Properties of Palm Oil Fuel Ash Self Compacting Concrete," Engineering, Technology & Applied Science Research, vol. 5, no. 1, pp. 753–756, 2015. [14] A. Saand, M. A. Keerio, and D. K. Bangwar, "Effect of Soorh Metakaolin on Concrete Compressive Strength and Durability," Engineering, Technology & Applied Science Research, vol. 7, no. 6, pp. 2210–2214, Dec. 2017, https://doi.org/10.48084/etasr.1494.