Abstract
The paper describes numerical meso-scale results of a size effect on strength, brittleness and fracture in brittle materials like concrete. The discrete element method (DEM) was used to simulate the size effect during quasi-static splitting tension with the experimental-based meso-structure. The two-dimensional (2D) calculations were carried out on concrete cylindrical specimens with two diameters wherein two different failure modes occurred (quasi-brittle and very brittle with the snap-back instability). Concrete was modelled as a random heterogeneous 4-phase material composed of aggregate particles, cement matrix, interfacial transitional zones and macro-voids, based on x-ray micro-CT-images of the real concrete meso-structure. Attention was paid to the effect of the different specimen diameter on both the strength, brittleness and fracture pattern. Each internal energy component was analyzed in the fracture process zone and beyond it, and compared for the different post-peak behaviour of concrete. The evolutions of the number of broken contacts, coordination number, crack displacements and normal contact forces were also shown. Of specific interest was the fracture initiation and formation of two different failure modes. Next, the 2D DEM results of a size effect for 4 different specimen diameters were directly compared with corresponding experiments from the research literature. The experimental size effect was realistically reproduced in numerical calculations, i.e. the concrete strength and ductility decreased with increasing concrete specimen diameter. The calculated decreasing strength approached an asymptote with increasing cylindrical specimen diameter within the considered specimen size range.
Highlights
The size effect is a fundamental phenomenon in brittle materials like concrete
For the normalized vertical top displacement v/D = 0.35% corresponding to the peak load for D = 0.05 m, the normalized elastic internal energy was equal to Een = 96%, normalized plastic dissipation was Dnp ≈ 0.0%, normalized energy of removed contacts was equal to Ernc = 0.5%, normalized kinetic energy was equal to Ekn ≈ 0% and normalized
In the case of D = 0.15 m, for the normalized vertical top displacement v/D = 0.30% corresponding to the peak load, the normalized elastic internal energy was equal to Een = 73%, normalized plastic dissipation was Dnp ≈ 0.0%, normalized energy of removed contacts was equal to Ernc = 2%, normalized kinetic energy was equal to Ekn ≈ 0% and normalized numerical damping was equal to Dnn = 25% with respect to the total normalized energy (Fig. 7)
Summary
The size effect is a fundamental phenomenon in brittle materials like concrete. It denotes that both the: (1) nominal structural strength (corresponding to the maximal load value reached in the loading process) and (2) material ductility (ratio between the energy consumed during the loading process before and after the load–deflection peak) always. The current paper numerically analyzes a quasi-static size effect in concrete at the meso-level in splitting tension tests during two different failure mechanisms: (1) quasibrittle and (2) very brittle with a snap-back instability. The advantage of the discrete meso-scale approach is that it is able to directly simulate a heterogeneous meso-structure of materials It may be used for a detailed study of mechanisms of the initiation, growth and propagation of both microcracks and discrete macro-cracks that greatly control the macroscopic concrete behaviour [14,15,16,17]. The most advisable testing conditions for an effective and robust characterization of the splitting tensile strength of concrete were discussed in [44]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
