Estimating mechanical properties of concrete before designing reinforced concrete structures is among the design requirements. Steel fibers have a considerable effect on the mechanical properties of reinforced concrete, particularly its tensile strength. So far, numerous studies have been done to estimate the relationship between tensile strength of steel fiber reinforced concrete (SFRC) and other SFRC characteristics using regression analyses. But, in order to determine appropriate relations according to these methods, we need to estimate the basic structure of relations. Genetic programming (GP) method has solved this problem. In this study, the results of 367 laboratory specimens collected from the literature are used to present some relations to predict the tensile strength of SFRC using GP. The proposed relations are more accurate than the relations which have been presented thus far.

The constitutive relationships presented for concrete modeling are often associated with unknown material constants. These constants are in fact the connectors of mathematical models to experimental results. Experimental determination of these constants is always associated with some difficulties. Their values are usually determined through trial and error procedure, with regard to experimental results. In this study, in order to determine the material constants of an elastic-damage-plastic model proposed for concrete, the results of 44 uniaxial compression and tension experiments collected from literature were used. These constants were determined by investigating the consistency of experimental and modeling results using a genetic algorithm optimization tool for all the samples; then, the precision of resulted constants were investigated by simulating cyclic and biaxial loading experiments. The simulation results were compared to those of the corresponding experimental data. The results observed in comparisons indicated the accuracy of obtained material constants in concrete modeling.

Several researchers have proved that the constitutive models of concrete based on combination of continuum damage and plasticity theories are able to reproduce the major aspects of concrete behavior. A problem of such damage-plasticity models is associated with the material constants which are needed to be determined before using the model. These constants are in fact the connectors of constitutive models to the experimental results. Experimental determination of these constants is always associated with some problems, which restricts the applicability of such models despite their accuracy and capabilities. In the present paper, the values of material constants for a damage-plasticity model determined in part I of this work were used as a database. Genetic programming was employed to discover equations which directly relate the material constants to the concrete primary variables whose values could be simply inferred from the results of uniaxial tension and compressive tests. The simulations of uniaxial tension and compressive tests performed by using the constants extracted from the proposed equations, exhibited a reasonable level of precision.  The validity of suggested equations were also assessed via simulating experiments which were not involved in the procedure of equation discovery. The comparisons revealed the satisfactory accuracy of proposed equations.