Issue 29

A. Caporale et alii, Frattura ed Integrità Strutturale, 29 (2014) 19-27; DOI: 10.3221/IGF-ESIS.29.03 25 characterized by  , 0 v m f have values of  max greater than the uni-axial compressive strength  c . The failure curves reflect the uni-axial behavior observed in Fig. 1: for a given direction       T 1 2 ˆ ˆ 0 n ,  max decreases with increasing , v eq f and , v m f . -0,12 -0,10 -0,08 -0,06 -0,04 -0,02 0,00 -0,12 -0,10 -0,08 -0,06 -0,04 -0,02 0,00  e 2  (GPa)  e  (GPa)    = 0.8, f v,eq = 30, f v,m = 10, 20    = 0.7, f v,m = 0, f v,eq = 30, 40, 50    = 0.8, f v,m = 0, f v,eq = 30, 40, 50 f v,eq , f v,m Figure 3 : Failure curves in bi-axial compression. -1,50 -1,00 -0,50 0,00 -1,50 -1,00 -0,50 0,00  e    c  e    c    = 0.8, f v,eq = 30, f v,m = 10, 20    = 0.7, f v,m = 0, f v,eq = 30, 40, 50    = 0.8, f v,m = 0, f v,eq = 30, 40, 50 f v,m Figure 4 : Dimensionless failure curves in bi-axial compression. The generic curve of Fig. 3 is obtained by connecting the points           1 2 max 1 2 ˆ ˆ , , 0 , , 0 e e ; this curve intersects the coordinate axes at the points     , 0,0 c and     0, , 0 c , where  c is the uni-axial compressive strength of concrete and is used to determine the dimensionless curve       1 2 max ˆ ˆ , , 0 c . In Fig. 4, the eight curves of Figure 3 are plotted in the dimensionless form: these curves depend on the parameter , v m f . In fact, the curves characterized by  , 0 v m f are the same whatever the parameter  is, whereas the remaining curves vary with , v m f : the area bounded by the dimensionless failure curve decreases with increasing , v m f . Fig. 4 shows that the adopted values of , v m f should be small as large values of , v m f provide a bi-axial compressive strength max 2 2  less than the uni-axial compressive strength when the average stress   2 2 , 2 2 , 0   is prescribed on concrete, in contrast with the experimental failure curve of concrete.