## 1 Introduction
Therefore, they simulate SFRC as a two-phase material, consisting of a concrete matrix phase and the steel fibers phase. The concrete matrix is simulated using a smeared crack model and solid finite elements, while steel fibers are modeled as embedded elements that can transfer stresses between crack planes of the concrete matrix. A random distribution of fibers inside a structural element is simulated and then inserted into the concrete matrix. Such a model can quantify the variance in SFRC's behavior, using various realizations of potential fiber distributions that lead to different structural behavior that can then be statistically analyzed. [PERSON] et al. [8] presented a similar numerical model for SFRC composed of three main elements: concrete, concrete-fiber interface, and discrete fibers. The spatial distribution of steel fibers is randomly generated, accounting for the wall effect and meshed independently of concrete. The two are later coupled using a coupling technique for non-aligned meshes. As meso- and micro-scale models are not easily applicable on a structural level, [PERSON] and [PERSON] [14] proposed a multilevel modeling framework for SFRC structures. The first level simulates the pullout of a single fiber from the concrete matrix to obtain the pullout force-deformation relation, the second level models the crack bridging effect of a group of fibers using the previously obtained pullout model and the third level represents the structural model that considers the appearance and propagation of cracks and fiber crack-bridging effect using the crack-bridging response obtained from level two. Using such a model, the effect of various design parameters on the structural response of SFRC structures can be investigated starting from the single fiber level. To summarize, analytical models usually incorporate the uncertainty related to fiber distribution and orientation into several coefficients used to deterministically calculate the tensile and residual tensile strength of SFRC, while more advanced, but computationally more expensive, numerical models explicitly consider this uncertainty using Monte Carlo sampling, to generate an instance of a potential fiber mesh of a structural element. While the randomness related to fiber distribution and orientation might be the dominant source of uncertainty, it is not the only one. Conventional reinforced concrete (i.e., without steel fibers) also has a degree of uncertainty related to its structural behavior as a consequence of the inevitable variance in its material and geometric properties [15]. To the best of the authors' knowledge, none of the currently available studies provide a comparison on the relative contribution of these uncertainties to the uncertainty in the structural behavior of an SFRC element. This study compares the uncertainties introduced due to steel fibers with the uncertainties inherent in conventional bar reinforced concrete, at different stages of the beam's flexural behavior. The variance of flexural behavior of SFRC beams is examined by conducting a variance-based sensitivity analysis. To that end, a fiber finite element model capable of simulating the flexural behavior of SFRC beams is presented, with the goal of balancing model accuracy and computational efficiency. The proposed model is validated using experimental results available in the literature. Then, uncertainties in the selected material properties are quantified as probability distributions, calibrated according to the available experimental data and existing probabilistic models. Finally, polynomial-chaos-based global sensitivity analysis is used to identify how uncertainties in the material properties contribute to the uncertainties observed at different stages of the flexural behavior of SFRC beams.