Investigation of microstructural phenomena at aggregate level in concretes using DEM

This paper presents numerical analyses of concrete beams under three-point bending. The discrete element methods (DEM) was used to calculate fracture at the aggregate level. Concrete was described as a four-phase material, which was composed of aggregate, cement matrix, interfacial transitional zones (ITZs) and macro-voids. The beam micro-structure was directly taken from our experiments using x-ray micro-tomography. 3D simulations were carried out with real aggregate modelled as sphere clusters. Numerical results were compared with laboratory outcomes. The special attention was laid on the fracture propagation and some micro-structural phenomena at the aggregate level.


Introduction
The fracture process is a fundamental phenomenon in quasi-brittle materials like concrete.It is very complex since it consists of main cracks with various branches, secondary cracks and micro-cracks.During fracture, micro-cracks first arise in a hardening region on the stress-strain curve which change gradually during material softening into dominant distinct macroscopic cracks up to damage.The fracture process strongly depends upon a heterogeneous structure of materials over many different length scales, changing e.g. in concrete from the few nanometres (hydrated cement) to the millimetres (aggregate particles).In order to properly describe fracture, material micro-structure has to be taken into account since its effect on the global results is pronounced.At the meso-scale, concrete may be considered as a composite material wherein four important phases may be separated: cement matrix, aggregate, interfacial transition zones ITZs between the aggregate and cement matrix and macro-voids.
The main objective of this study is to investigate a complex fracture process in concrete beams under bending at the aggregate level under 3D conditions using the discrete element method (DEM) with angularlyshaped aggregate particles.Discrete models (if they are enough consistent) might progressively replace experimental tests to study the influence of concrete meso-structure (aggregates size, aggregate shape, aggregate roughness, aggregate/mortar volume, macro porosity, etc.) on the concrete behaviour.The disadvantages of DEM are: enormous computational cost and a difficult calibration procedure with respect to geometric and mechanical properties of ITZs.In the calculations, the concrete micro-structure was assumed based on 3D images by means of x-ray microtomography using the micro-tomograph Skyscan 117, which represents a new generation in high-resolution desktop x-ray micro-tomography systems [1].The paper is a continuation of our research outcomes presented in [1], [2] which concerned the crack propagation in concrete beams under 2D conditions only.
Figure 1 shows the 3D μCT image of the cracked cuboidal specimen (80×50×40 mm 3 ), cut out from the beam mid-part after one test [1].The main crack was strongly curved mainly due to presence of aggregate particles.Its shape changed along the specimen depth in spite of the fact that 2D boundary value problem (plane stress) was considered.The discrete macro-crack mainly propagated through ITZs (which were the weakest phase in concrete) and sometimes through macro-voids.It might very rarely propagate through a single weak aggregate particle.The effect of macro-voids on the crack shape was small.The discrete crack was created by bridging the interfacial micro-cracks.It possessed many small branches.ITZs around aggregate particles were characterized by a very non-uniform porous structure and presence of separated small sand particles.They appeared mainly aggregate particles but sometimes they were also visible around larger cement matrix particles.The width of ITZs changed between 30 and 50 lm.The width was independent of the aggregate diameter.

Conclusions
The 3D calculation results for four-phase concrete at the aggregate level using the discrete element model showed satisfactory agreement with experimental observations.They evidently showed that DEM was able to realistically capture the beam strength and fracture in concrete beams at the macro-level under condition that the real aggregate shape and location were mapped.DEM realistically followed a fracture process including the occurrence of micro-and macro-cracks during their onset, formation and propagation (including phenomena of crack bridging, crossing, branching and closing).In addition, it allowed for investigating different interesting micro-structural events occurring at the aggregate level (e.g.force chains, contact breakage, particles rotations).
The experimental discrete macro-crack above the notch was strongly curved and depended on the concrete micro-structure.It was created by bridging the interfacial micro-cracks.It mainly propagated through the weakest contact zones (ITZs) between the cement matrix and aggregate.The width of ITZs varied between 30 and 50 Pm.Their porosity was strongly uniform.The crack rarely propagated through weak aggregate particles.Some small crack branches were also visible.The crack shape was different with the beam depth.Single microcracks also occurred far beyond the macro-crack.
It was found that the mechanical properties of ITZs which were cracks' attractors had a pronounced influence on the crack strength and macro-cracking.The weaker strength of ITZs and their higher number increased the beam ductility (due to a longer crack propagation way).
The external load was transmitted via a network of normal contact forces which formed force chains of a different intensity.The compressive normal contact forces (connected to the tangential contact forces) also developed along the macro-crack due to aggregate interlocking.

Fig. 1 .
Fig. 1.Images of cracked cuboidal specimens cut out from beam obtained by means of 3D μCT: a) general view and b) image with separated phase (blue colour -aggregate, green colour -cement matrix, red colour -crack and air void) [1].

Fig. 2 .
Fig. 2. Front face of concrete beam with meso-region of 50×80×40 mm 2 close to notch (dark grey corresponds to aggregate and light grey is related to cement matrix).

Fig. 5 .
Fig. 5. Calculated cracked region (empty space) above notch from 3D DEM for CMOD=0.1 mm (blue colour corresponds to crack width larger than 0.2 mm, green colour to crack width 0.05-0.2mm and red colour to crack width smaller than 0.05 mm)