###### Abstract  
Several stress-strain models were used to predict the strengths of steel fiber reinforced concrete, which are distinctive of the material. However, insufficient research has been done on the influence of hybrid fiber combinations (comprising two or more distinct fibers) on the characteristics of concrete. For this reason, the researchers conducted an experimental program to determine the stress-strain relationship of 30 concrete samples reinforced with two distinct fibers (a hybrid of polyvinyl alcohol and steel fibers), with compressive strengths ranging from 40 to 120 MPa. A total of 80% of the experimental results were used to develop a new empirical stress-strain model, which was accomplished through the application of the particle swarm optimization (PSO) technique. It was discovered in this investigation that the new stress-strain model predictions are consistent with the remaining 20% of the experimental stress-strain curves obtained. Case studies of hybrid-fiber-reinforced concrete constructions were investigated in order to better understand the behavior of such elements. The data revealed that the proposed model has the highest absolute relative error (ARE) frequencies (ARE 10%) and the lowest absolute relative error (ARE > 15%) frequencies (ARE > 15%). 202020219 February  
The hybrid steel-polypropylene fibers have been the subject of a lot of research. Because the fibers contribute to the toughness, which lowers brittle failure under static and dynamic stresses, HFRC exhibits an increased reaction. It also improves energy absorption. It is well acknowledged that steel fibers can improve mechanical properties such as compressive and tensile strengths; ductility; impact resistance; toughness; and so on (ACI Committee 544 [11]). However, the effect of the combinations of hybrid fibers (two or more different types of fibers) on the concrete properties is not extensively addressed. Requirements for high-strength fiber reinforced concrete has been increasing significantly over the past few decades due to the need for design members that are small in size, which also decreases the mass of members, to lead to effective seismic-resistant concrete structure [12; 13]. By extending the post-peak region of stress-strain diagrams, which is otherwise nearly nonexistent or steeply sloped in high-strength concrete (HSC), the fibers in FRC improve toughness [13]. This enhancement in structural response can only be considered once the stress-strain curves of the resulting FRC have been studied in detail. Stress-strain diagrams can be used to assess the toughness of FRC. By extending the post-peak region of stress-strain diagrams, which is otherwise nearly nonexistent or steeply sloped in high-strength concrete (HSC), the fibers in FRC improve toughness [13]. This enhancement in structural response can only be considered once the stress-strain curves of the resulting FRC have been studied in detail. Stress-strain diagrams can be used to assess the toughness of FRC. In addition, using the steel fibers for reinforcing the normal strength concrete (NSC) and reactive powder concrete (RPC) had been investigated [14]. Where, the study confirmed that the aggregate interlock, crack surface friction and steel fiber content are the main three factors influenced the shear strength of the NSC, meanwhile, on RPC, only the factors of crack surface friction and steel fibers are affected. The effects of replacing Portland cement with pumice powder and nano-clay were studied [15]. The possibility of making pervious concrete with varied amounts of recycled concrete aggregate (RCA) was made with a combination of new and used materials, including recycled and industrial fibers. The author(s) recommends the usage of pervious concrete containing 50% RCA and 2% steel fiber in the constructions of structures. Other researchers investigated the use of recycled concrete aggregate and pozzolanic additives in fiber-reinforced pervious concrete reinforced with industrial and recycled fibers [16].