*Article* **Material Analysis of Steel Fibre Reinforced High-Strength Concrete in Terms of Flexural Behaviour. Experimental and Numerical Investigation**

#### **Czesław Bywalski \*, Maciej Ka ´zmierowski, Mieczysław Kami ´nski and Michał Drzazga**

Faculty of Civil Engineering, Wroclaw University of Science and Technology, Wybrze ˙ze Wyspia ´nskiego 27, 50-370 Wrocław, Poland; maciej.kazmierowski@pwr.edu.pl (M.K.); mieczyslaw.kaminski@pwr.edu.pl (M.K.); michal.drzazga@pwr.edu.pl (M.D.)

**\*** Correspondence: czeslaw.bywalski@pwr.edu.pl; Tel.: +48-71-320-3397

Received: 13 February 2020; Accepted: 30 March 2020; Published: 1 April 2020

**Abstract:** The paper presents the results of tests for flexural tensile strength (fct,fl) and fracture energy (Gf) in a three-point bending test of prismatic beams with notches, which were made of steel fibre reinforced high-strength concrete (SFRHSC). The registration of the conventional force–displacement (F–δ) relationship and unconventional force-crack tip opening displacement (CTOD) relationship was made. On the basis of the obtained test results, estimations of parameters fct,fl and Gf in the function of fibre reinforcement ratio were carried out. The obtained results were applied to building and validating a numerical model with the use of the finite element method (FEM). A non-linear concrete damaged plasticity model CDP was used for the description of the concrete. The obtained FEM results were compared with the experimental ones that were based on the assumed criteria. The usefulness of the flexural tensile strength and fracture energy parameters for defining the linear form of weakening of the SFRHSC material under tension, was confirmed. Own equations for estimating the flexural tensile strength and fracture energy of SFRHSC, as well as for approximating deflections (δ) of SFRHSC beams as the function of crack tip opening displacement (CTOD) instead of crack mouth opening displacement (CMOD), were proposed.

**Keywords:** high-strength concrete; steel fibres; flexural tensile strength; fracture energy; numerical analysis
