A probabilistic multiparameter framework for the modeling of fatigue crack growth in concrete K. Bhalerao a , W. Shen b , A.B.O. Soboyejo a , W.O. Soboyejo b, * a Department of Food, Agricultural and Biological Engineering, The Ohio State University, Columbus, OH 43210, USA b Department of Mechanical and Aerospace Engineering, The Princeton Materials Institute, Princeton University, P.O. Box CN 5263, Princeton, NJ 08544-5263, USA Abstract This paper presents a probabilistic multiparameter framework for the modeling of fatigue crack growth in three grades of concrete. The framework relies on the use of ranked fatigue crack growth rate data (with speciﬁed occurrence probability levels) in the formulation of multiparameter fatigue crack growth expressions. These relate ranked fatigue crack growth rates to crack driving force parameters such as the stress intensity factor range, maximum stress intensity factor, stress ratio and occurrence probability level. A probabilistic framework is then presented for the estimation of material reliability or failure probability due to fatigue crack growth. The probabilistic model is then validated for the available data. Ó 2002 Published by Elsevier Science Ltd. Keywords: Probabilistic; Multiparameter; Modeling; Fatigue; Crack growth; Concrete 1. Introduction The development of an extensive global network of infrastructure has been achieved largely by the use of concrete [1]. This has stimulated the growth of a trillion- dollar industry that supplies much of the infrastructure materials for pavements, buildings, and oil wells [1]. However, in all these applications, sub-critical crack growth may occur at stress levels that are well below the critical conditions required for failure under monotonic loading [2]. Such sub-critical crack growth is generally associated with cyclic loading due to freeze–thaw cycles [3], mechanical loading by traﬃc, and wind loading on structures. These cyclic loads can give rise to fatigue crack growth processes [2,4] that may be exacerbated by the additional eﬀects of the environment [5]. The analysis of fatigue crack growth in concrete is complicated by the heterogeneous nature of concrete. Depending on the local combinations of sand, cement andaggregate,thismaygiverisetosigniﬁcantvariations in fatigue crack growth rates within any given mix of concrete. This suggests that a statistical/probabilistic framework is needed for the modeling of crack growth in concrete. Furthermore, a wide range of parameters may inﬂuence fatigue crack growth rates in concrete. These include mechanical parameters such as: the stress intensity factor range, stress ratio and the maximum stress intensity factor. Fatigue crack growth rates may also be inﬂuenced by environmental parameters such as relative humidity and temperature, which are not con- sidered in this paper. This paper presents a multiparameter framework for the probabilistic fracture mechanics modeling of fatigue crack growth in concrete. The approach is demonstrated for three concrete mixes with strengths of 30, 35 and 40 MPa. The ‘‘scatter’’ in the fatigue crack growth rate data is shown to be well characterized by log-normal statistical distribution. Fatigue crack growth rates at speciﬁc probability levels are also shown to be well de- scribed by multiparameter fracture mechanics expres- sions that relate the measured fatigue crack growth rates to the stress intensity factor range, stress ratio, maxi- mum stress intensity factor and occurrence probability. The fracture mechanics expressions are then used as inputs into a probabilistic framework for the estimation of crack growth rates associated with speciﬁed proba- bility levels. Finally, the implications of the results are * Corresponding author. Tel.: +1-609-258-5609; fax: +1-609-258- 5877. E-mail address: soboyejo@princeton.edu (W.O. Soboyejo). 0958-9465/02/$ - see front matter Ó 2002 Published by Elsevier Science Ltd. doi:10.1016/S0958-9465(02)00074-4 Cement & Concrete Composites 25 (2003) 607–615 www.elsevier.com/locate/cemconcomp