Issue 10

B. Chiaia et alii, Frattura ed Integrità Strutturale, 10 (2009) 29-37; DOI: 10.3221/IGF-ESIS.10.04 32 The parabolas are both defined by the same coefficients a , b and have the same extreme point at w = -0.5 b / a , whereas w = - b / a (i.e. twice the value at extreme point) is considered the maximum inelastic displacement corresponding to F ( w ) higher than zero. Figure 4 : The stress-inelastic displacement relationship proposed by Fantilli et al. [10]. In the case of the plain concrete specimens, the values a = 0.320 mm -2 and b = -1.12 mm -1 were obtained by means of the least square approximation of several tests [10]. As observed in Fig.4b, the curves defined b y Eqs.(4) fall within the range of the data experimentally measured by Jansen and Shah [9]. In the case of multi-axial compression, stress-inelastic displacement relationships, which should reproduce the confined post-peak stage, cannot be found in the existing literature. As is well known, two types of confinement, namely passive and active, can be produced. In compressed columns, passive confinements provided by transversal reinforcement (i.e., stirrups, tubes, strips, spirals, etc.), are only activated by concrete displacements. Thus, to define quantitatively this contribution, it is necessary to know the stress-transversal displacement relationship of concrete. Active confinement is due to external stresses  3 applied by multi-axial compression tests on cubes in two or three directions, or by triaxial tests on cylinders (see the book by van Mier [8] f or a review). Only a single campaign of triaxial tests, performed by Jamet et al. [11] on micro-concrete, is reported in the current literature. In that case, the applied confinement was relatively high (  3 >3 MPa), if compared to those produced by stirrups in ordinary RC columns. In accordance with Eurocode 2 [4], in columns under concentric compression, transverse reinforcement can develop about  3 = 1MPa [12]. Consequently, with the aim of analyzing the equivalent confing pressures produced by a new Fiber-reinforced Self-consolidating concrete (called Sismabeton), the comparison between the results of new triaxial tests on NC, SC and Sismabeton cylinders under uniaxial compression are reported. E XPERIMENTAL PROGRAM he post-peak behaviour of cement-based composites under multi-axial compression has been investigated at the Department of Structural and Geotechnical Engineering of Politecnico di Torino (Italy) by means of triaxial tests on concrete cylinders (Fig.5a). The experimental equipment, named HTPA (High Pressure Triaxial Apparatus) and described by Chiaia et al. [13], is generally used to test cylindrical specimens made of soft rocks. Each triaxial test consists of two stages. A specimen is initially loaded with a hydrostatic pressure σ 3 ( Fig.5b ), then deviatoric loads P are applied along the longitudinal direction with a velocity of 0.037 mm per minute ( Fig.5c) . During the second stage of loading, the confining pressure  3 = const . is applied to the lateral surface, whereas the longitudinal nominal stress  c becomes: 2 3 4 D P c      (5) where, P = applied deviatoric load; D = diameter of the cross-section. Through a couple of LVDT, local longitudinal displacements, and therefore nominal longitudinal strains  c , are also measured (Fig. 5a) . Two confining pressures, namely σ 3 = 0 MPa and σ 3 = 1 MPa (reached in 10 minutes), are applied to the specimens. During the application of hydrostatic loads (Fig.5b) , stress increments are electronically recorded every 10 seconds. T