Issue 10

B. Chiaia et alii, Frattura ed Integrità Strutturale, 10 (2009) 29-37; DOI: 10.3221/IGF-ESIS.10.04 31 assumed to be 1/10 of compression strength ( f ct = 0.1 f c ). The inelastic displacement w of the specimen, and the consequent sliding s of the blocks along the sliding surface, are the parameters governing the average post-peak compressive strain  c of the specimen (Fig. 3). Referring to the specimen depicted in Fig. 3a, post peak strains can be defined by the following equation [8] : H w E H w c c c el c c           1 , (1) where,  c1 = strain at compressive strength f c ;  c = stress decrement after the peak; H = height of the specimen (see Fig. 1b). Figure 3 : The post-peak response of quasi-brittle materials in compression. According to test measurements [8, 9], the post-peak slope of  c -  c increases in longer specimens (Fig.3b), due to the w / H ratio involved in the evaluation of  c [Eq.(1)]. The stress decrement  c can be defined as:     wF f f c c c c       1   (2) where, F ( w ) = non-dimensional function which relates the inelastic displacement w and the relative stress  c / f c during softening (Fig.3c) ; f c = compressive strength (assumed to be positive). Substituting Eq.(2) int o Eq.(1) , it is possible to obtain a new equation for  c :     H w E wF f c c c c      1 1   for  c >  c1 (3) Eq.(3), adopted for the post-peak stage of a generic cement-based material in compression, is based on the definition of F ( w ), which has to be considered as a material property [8-9]. In all cement-based composites, this function should be evaluated experimentally on cylindrical specimens, as performed by Jansen and Shah [9] for plain concrete (Fig.3c). Fig.4a shows the F ( w ) relationships proposed by Fantilli et al. [10]. It consists of two parabolas and a constant branch:   1 2 wb wa f wF c       a b w    2 0 for (4a)   4 4 4 1 2 2 2 2                       w b a w b a a b f wF c  a b w a b     2 for (4b)   0   c f wF  a b w  for (4c)