# Discrete element simulation of concrete failure

## Table of contents

### Project data

Titel | TitleSimulation des Betonbruchverhaltens mit diskreten Elementen | Simulation of concrete failure with discrete elements Förderer | FundingInstitute of Concrete Structures, TU Dresden Zeitraum | Periodsince 11.2017 Leiter | Project managerProf. Dr.-Ing. Dr.-Ing. E.h. Manfred Curbach Bearbeiter | ContributorDr.-Ing. Birgit Beckmann |

### Report in the annual report 2019

2D SIMULATION OF CONCRETE FRACTURE WITH DEM

Using numerical simulation based on the Discrete Element Method (DEM), concrete fracture and concrete failure phenomena are investigated in this project.

While single elements resulting from the discretisation of the concrete specimen are only a calculation tool in continuum-based simulations, the single elements represent actually separate concrete particles being able to move kinematically independently in discrete methods or particles-based methods such as DEM. Furthermore, in continuum-based methods, steady fields are an implicit presupposition and, therefore, no gaps and no gaping joints may exist. In contrast, in the DEM, adjacent particles can also move apart from each other and do not need to be permanently connected to their neighbours. This basic approach allows the simulation of actual cracks. A crack that arises during the simulation is discrete, and a crack means an absence of concrete material, i. e. a gap or defect in the concrete. This property of the DEM, that cracks are discrete per se and can be simulated directly, is an essential reason for the choice of this simulation method. A further reason is the inherently contained complexity. Using a great number of particles, that differ only slightly due to random particle generation, but that are principally equal to each other, the complexity and the statistic character arise just due to the interaction of the particles. It means, that two simulations with exactly equal simulation parameters and only with two slightly varying particle ensembles lead to similar, but slightly different results. This mirrors the observations of real laboratory experiments. The same here – no two concrete specimens can have the exact same positions of aggregate, and the fracture patterns of two specimens show statistical deviation at the end of the experiment.

To get the statistical character out of the interaction of “great” many particles, the number of particles does not need not to be that big. Even a number of 2,200 particles is enough to achieve statistically varying results of two different ensembles, i. e. of two test specimen representations of the same concrete charge. The crack patterns of two ensembles with 2,240 particles, that differ only in the particle position due to random particle generation, but have exactly the same simulation parameters beside that, are similar, but slightly differ in the particular crack position – just like in real laboratory experiments, too.

### Report in the annual report 2018

DISCRET ELEMENT SIMULATION OF CONCRETE FAILURE

Concrete fracture phenomena are investigated in this project, specially focusing on the investigation of their statistically varying character. In order to study the matter of failure mechanisms, crack propagation and damage evolution, a two-dimensional numerical simulation based on the Discrete Element Method (DEM) is used for the analysis of concrete behaviour under compression load. Crack patterns, crack initiation and damage evolution are analysed. The cracks are discrete just as in real laboratory experiments. The cracks arise due to the interaction of the concrete particle elements and without the predefinition of any crack zones or crack elements.

This simulation employs a combination of essential elements such as a contact approach including an overlap area, detection of new particle contacts during the simulation instead of neighbouring lists and particles with arbitrarily polygonal shape and, furthermore, the inclusion of statistically varying properties. While the comparison of simulation results to the experimental results was addressed in detail in previous works, the focus of this year’s research is laid on the presentation and description of theoretical background including statistical aspects. Two statistical approaches are used in the simulation. First, randomly varying particle geometries and particle positions are generated due to a random factor used during particle generation. Second, a Weibull-distribution for maximum elongation of the (optional) cohesion linkages is used. The statistic approach is rather elementary instead of elaborate; and there are no macroscopic mechanical effects added to the model. Based on this, there are the complexity of the particle ensemble and the interaction of many simple particles letting macroscopic effects such as cracks and crack patterns emerge.

Using statistical variations of geometrical and material properties, it is shown that even an elementary statistical approach leads to the evolution of statistically varying crack patterns. It shows that the DEM is a suitable approach to study failure and fracture processes.