Physica A 391 (2012) 3366–3378 Contents lists available at SciVerse ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa A probabilistic mechanical model for prediction of aggregates’ size distribution effect on concrete compressive strength Karim Miled a,∗ , Oualid Limam a , Karam Sab b a University of Tunis El Manar, Laboratoire de Génie Civil, Ecole Nationale d’Ingénieurs de Tunis, BP 37 le Belvédère 1002, Tunis, Tunisia b Université Paris-Est, Laboratoire Navier (École des Ponts Paris Tech, IFSTTAR, CNRS), École des Ponts Paris Tech, 6 et 8 avenue Blaise Pascal, 77455 Marne-la-Vallée cedex 2, France article info Article history: Received 27 August 2011 Received in revised form 5 January 2012 Available online 6 February 2012 Keywords: Concrete Compressive strength Aggregates’ size distribution Statistical homogenization abstract To predict aggregates’ size distribution effect on the concrete compressive strength, a probabilistic mechanical model is proposed. Within this model, a Voronoi tessellation of a set of non-overlapping and rigid spherical aggregates is used to describe the concrete microstructure. Moreover, aggregates’ diameters are defined as statistical variables and their size distribution function is identified to the experimental sieve curve. Then, an inter-aggregate failure criterion is proposed to describe the compressive-shear crushing of the hardened cement paste when concrete is subjected to uniaxial compression. Using a homogenization approach based on statistical homogenization and on geometrical simplifications, an analytical formula predicting the concrete compressive strength is obtained. This formula highlights the effects of cement paste strength and aggregates’ size distribution and volume fraction on the concrete compressive strength. According to the proposed model, increasing the concrete strength for the same cement paste and the same aggregates’ volume fraction is obtained by decreasing both aggregates’ maximum size and the percentage of coarse aggregates. Finally, the validity of the model has been discussed through a comparison with experimental results (15 concrete compressive strengths ranging between 46 and 106 MPa) taken from literature and showing a good agreement with the model predictions. © 2012 Elsevier B.V. All rights reserved. 1. Introduction At the mesoscopic level, concrete is generally regarded as a two-phase material; either as small aggregates surrounded by a hardened cement paste or as coarse aggregates dispersed in a mortar matrix. The quasi-brittle failure in compression of concrete had been widely studied in literature since its compressive strength is the main characteristic governing its mechanical behavior. At the macroscopic level, a splitting failure mode is generally observed [1,2] whereas at the microscopic level, other phenomena like damage and plasticity are observed [3,4]. This complex failure depends on the cement paste behavior and also on the topology of the granular skeleton (aggregates’ volume fraction, size distribution and shape). Several empirical and phenomenological models were developed to predict the compressive strength of concrete according to its composition [5–9]. All these models admit that the concrete strength depends on the cement paste strength and the granular skeleton characteristics. The cement paste strength had been widely studied and it is commonly admitted today that it depends mainly on the hardened paste porosity. The latter governed by the water to cement volume ratio has a negative effect on the cement paste strength which decreases also with decreasing the cement strength [10]. Since 1892, ∗ Corresponding author. Tel.: +216 71871476; fax: +216 71871476. E-mail address: karim.miled@enit.rnu.tn (K. Miled). 0378-4371/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2012.01.051