The compression behavior of steel-fiber reinforced concrete (SFRC) has been addressed exhaustively in recent decades thereby highlighting a variety of differences with regard to the effect that the addition of fiber has on it. In this paper, a detailed study of the subject is developed for which a database has been created, which includes 197 tests performed on cylindrical concrete specimens with dimensions of 150 × 300 mm ${}^2$ (diameter × height). By means of the response surface methodology, we disclose the relationship that exists between the geometric parameters of the fiber (length, diameter, and aspect ratio), their amount (fraction in volume), and some matrix parameters (compression resistance and maximum size of coarse aggregate) with the different compression responses of the SFRC, which are strength, elastic modulus, critical deformation under maximum load, and the volumetric deformation work in the pre- and post-peak branch. Linear polynomial models are chosen to adjust each response with the defined factors, and said variables are studied in a dimensional and non-dimensional format. From the results obtained, it is verified how the inclusion of steel-fibers produces notable improvements in ductility and the energy absorption capacity of the concrete when significantly increasing the works of volumetric deformation in the pre- and post-peak branch with respect to the matrix without fibers. In addition, a new model is analyzed, which describes the stress–strain curve of the compression behavior of the SFRC based on the increase of ductility and energy absorption. This model is characterized by a softening branch subsequent to the peak load determined by means of the residual compressive strength, a parameter that corresponds to the value of the compressive stress associated with a strain equal to three times that of the peak of the curve, which is significantly dependent on the aspect ratio and fiber content.

We present a new focus for the Krieger–Dougherty equation from a probabilistic point of view. This equation allows the calculation of dynamic viscosity in suspensions of various types, like cement paste and self-compacting mortar/concrete. The physical meaning of the parameters that intervene in the equation (maximum packing fraction of particles and intrinsic viscosity), together with the random nature associated with these systems, make the application of the Bayesian analysis desirable. This analysis permits the transformation of parametric-deterministic models into parametric-probabilistic models, which improves and enriches their results. The initial limitations of the Bayesian methods, due to their complexity, have been overcome by numerical methods (Markov Chain Monte Carlo and Gibbs Sampling) and the development of specific software (OpenBUGS). Here we use it to compute the probability density functions that intervene in the Krieger–Dougherty equation applied to the calculation of viscosity in several cement pastes, self-compacting mortars, and self-compacting concretes. The dynamic viscosity calculations made with the Bayesian distributions are significantly better than those made with the theoretical values.