To model the behavior of precast segmental tunnel linings under thrust jack loading, cylindrical concrete columns, subjected to concentrated loads, are investigated. Specifically, uniaxial compressive tests have been performed on specimens made with self-compacting concrete and reinforced with two different amounts of steel fibers (0, 30 kg/m3, respectively). In addition, to measure concrete properties, three point bending tests have been carried out in accordance with code rules. As a result, not only the fracture toughness of concrete in compression is improved, but also the ultimate and the maximum splitting loads are remarkably increased by the presence of long fibers. Accordingly, a new formulation of the classical Leonhardt’s approach is eventually proposed. Finally, based on the results of the present research, it seems reasonable to replace reinforced concrete with SFRSCC in structures subjected to high concentrated loads.