Keywords: uni-axial compression test, FEM, Mohr-Coulomb criterion, discrete element method.

Concrete is one kind of composite whose mechanical behaviour is quite complicated. Compressive strength and tensile strength are the essential material failure parameters. In certain research cases such as seismic analyses, shear strength may also be taken into account. These parameters are determined experimentally, compression strength by compression tests, tensile strength by tensile tests or three-point-bending tests, for example. Since in general the tensile strength of concrete is much less than its compression strength, concrete is assumed to only have strength in compression. Structures are often designed based on its compression strength only. Once the pressure in concrete reaches such compression limit, the material is treated as if it has failed.

By observing the compression laboratory test of a cubic specimen, the most severe compression area in material (the inner central area), does not match the damage pattern (side wedge peeling). Such a compression failure might just be a frictional slip in a certain plane where the maximum friction resistance is controlled by the Mohr-Coulomb criterion. In order to see how this procedure works for concrete, two numerical tools, the traditional finite element method (FEM) and the discrete element method (DEM), are employed to analyse a concrete cube subject to uni-axial compression. Two numerical results as well as the laboratory test result will be compared with each other in the present study.

Based on the FEM result, high compressive vertical stress occurs along eight edges and at the center of the model. The laboratory test shows that the crack initiates from the edges, propagates into specimen, and causes surface chips to peel off. The vertical stress distribution does not match with the observation of the laboratory test. The statement: "Concrete fails if the material reaches its compressive strength" may not be fully applicable. A similar situation also applies to the distribution of von-Mises stress as well. High von-Mises stress occurs along eight edges and at the center of the model. The failure mechanism cannot be explained solely by the compressive stress or the von-Mises stress. The Mohr-Coulomb failure criterion, therefore, becomes a candidate for reasoning about such failure phenomenon.

The numerical procedure is as follows:

1. Fill the container with elements (cylinders in this study).
2. Adjust the radius of elements so that the specified cavity ratio can be satisfied.
3. Check unbalanced elements and give a period of time for natural relaxation and condensation.
4. Initialize bonding strength.
5. Remove sidewalls of the container so that four vertical faces of the specimen become traction free.
6. Give another period of time for natural relaxation.
7. The top and bottom walls of the container move slowly toward each other at a constant speed until the specimen fails.

Using the DEM, a concrete cube, in the present analysis, consists of a lot of two-dimensional particles. The contacts between particles are handled by using the equivalent springs. By carefully choosing the appropriate values of the internal parameters, the simulated fracture profile is in fair agreement with the laboratory test result. On the other hand, the internal parameters can be determined by comparing the Young's modulus, the overall compressive strength, and the fracture profile of the the numerical model to those of the lab test specimen. A set of the parameters are found to be able to describe the cube specimen behaviour fairly well. Of course, there are many parameters that may affect the result and there could be some other set of the parameters that can fit the behaviour better. This matter is worth further research.

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