SN-Approach to Optimize Fatigue Performance of SFRC

The paper presents a theoretical method to optimize the tensile fatigue performance of steel fibre reinforced concrete. The approach bases on new SN curves and mathematical optimization techniques. The new SN curves take into account stress level and stress ratio as well as governing fibre parameters like fibre type, dosage, orientation and bond behaviour to the concrete’s matrix. Effects of these interacting parameters are captured by a dimensionless ductility index contrasting pre- and post-cracking load bearing capacities. The ductility index relies on the envelope concept and thus establishes equivalence of stress level and crack width dependent fibre effects at static and cyclic loadings. The SN approach is validated by experimental data taken from the literature. Results are in good accordance on average and underline the beneficial effect of steel fibres on the tensile fatigue performance of normal strength concrete. Based on the derivations mathematical optimization techniques are used to theoretically optimize fibre length, shape and crack-width dependent pullout behaviour with respect to fatigue lifetime. In detail, a scalar-valued objective function exemplarily derived from the SN-curves is minimized. In the convex optimization task the Karush-Kuhn-Tucker conditions are both, necessary and sufficient conditions to fulfill minimum requirement. The system of equations is numerically solved with Newton-Raphson Approach and Line Search Algorithm. In doing so the experimental observation of beneficial effects of enhanced fracture energy, fibre length and bond behaviour on numbers of cycles to failure can be theoretically proven.