Keywords: fiber concrete, finite element analysis, mesh generation, nonlinear analysis, numerical simulation, smeared model, creep strain.

Fiber reinforced concrete is effectively used for tunnels and bridges in order to prevent the fall of concrete block due to the spreading of cracks induced by external loads and drying shrinkage of concrete material. The development of fiber reinforced concrete material with better structural quality has been required and newly developed fiber materials are actually used for the reinforcement. Such development requires generally long period for the development and the cost becomes high, since it has been mainly achieved by material and structural experiments.

The authors propose numerical simulation method (i.e., numerical experimental method) of fiber reinforced concrete instead of material and structural experiments. The method is based on the finite element method, and steel fibers are treated. The location and direction of fibers in concrete material are automatically determined by the use of random numbers in order to realize the condition of actual fiber concrete. The finite element model is prepared by using Delaunay triangulation, which is a geometric subdivision, and all fibers decided by random numbers are actually generated by the triangulation process. If necessary, the result the location and direction of fibers are slightly modified in order to avoid the generation of elements with bad geometry, which is effective to obtain good numerical solution. Non-linear behavior of concrete is treated in the analysis of three point bending problem of a beam.

The aim of this survey is to know how the steel and plastic fibers are effective to prevent the falling of concrete blocks after cracking starts. In case of steel fibers we can expect additional strength by the addition of steel fiber, and the numerical results show as we expect; the structure becomes stronger according to the increase of the volume of steel fiber. The addition of such fiber is effective after cracking appears in concrete, since fibers bridge two faces of cracks and prevent the falling of concrete block. The influence of fibers on creep shrinkage of fiber reinforced concrete is also investigated as an application for the model.

The results show that, reinforcing concrete with short steel fibers increases the strength of concrete for carrying force and increase its modulus of elasticity. The mean role of steel fibers is clear after cracking starts. The fibers continue to carry stress beyond matrix cracking, which helps maintain structural cohesiveness in the material and increase the ductility of concrete. However if it is possible to align steel fibers parallel to the principal tensile stress, it will improve the ability of steel fibers to increase the strength of concrete.

The enhanced behavior of steel fiber reinforced concrete over its unreinforced counterparts comes from its improved capacity to absorb energy during fracture. While a plain unreinforced matrix fails in a brittle manner at the occurrence of cracking stresses, the fibers in fiber reinforced concrete continue to carry stress beyond matrix cracking, which helps maintain structural integrity and cohesiveness in the material. The paper shows results which display the effect of fibers after cracks occur.

As an application for the analysis, the fiber influence on creep of fiber reinforced concrete has been presented. The model prediction of the creep strain is compared to the model of Zhang, which is agreeable with the experimental work. The results show a good agreement between models even though it is a little bit higher creep strain with the finite element model in a range of (2% - 3%)

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