Issue 29

A. Caporale et alii, Frattura ed Integrità Strutturale, 29 (2014) 19-27; DOI: 10.3221/IGF-ESIS.29.03

have values of  max

greater than the uni-axial compressive strength  c



. The failure curves

f

characterized by

0

, v m





T

  1 2 ˆ ˆ 0

,  max



decreases with increasing

reflect the uni-axial behavior observed in Fig. 1: for a given direction

n



, v m f .

and

f

, v eq

0,00 -0,12 -0,10 -0,08 -0,06 -0,04 -0,02 0,00

   = 0.7, f v,m = 0, f v,eq

-0,02

= 30, 40, 50

-0,04

-0,06

   = 0.8, f v,m = 0, f v,eq

 e 2  (GPa)

f v,eq

, f v,m

= 30, 40, 50

-0,08

   = 0.8, f v,eq = 30, f v,m = 10, 20

-0,10

-0,12

(GPa)

 e 

Figure 3 : Failure curves in bi-axial compression.

-1,50

-1,00

-0,50

0,00

0,00

   = 0.7, f v,m = 0, f v,eq

= 30, 40, 50

f v,m

-0,50

 e    c

   = 0.8, f v,m = 0, f v,eq

= 30, 40, 50

-1,00

   = 0.8, f v,eq = 30, f v,m = 10, 20

-1,50

 e 

  c

Figure 4 : Dimensionless failure curves in bi-axial compression.





The generic curve of Fig. 3 is obtained by connecting the points 



  ˆ ˆ



  ,



; this curve intersects the

, 0

, , 0

e

1 2 e

max 1

2

coordinate axes at the points 



and 

   0, , 0 c ˆ ˆ , , 0   

, where  c

  , 0,0 c

is the uni-axial compressive strength of concrete and c . In Fig. 4, the eight curves of Figure 3 are plotted in the

is used to determine the dimensionless curve 





1

2

max



f . In fact, the curves characterized by

are the same

dimensionless form: these curves depend on the parameter , v m whatever the parameter  is, whereas the remaining curves vary with , v m

f

0

, v m

f : the area bounded by the dimensionless failure

, v m f . Fig. 4 shows that the adopted values of

f

f

should be small as large values of

curve decreases with increasing

, v m

, v m



provide a bi-axial compressive strength

less than the uni-axial compressive strength when the average stress

2 2

max

  2 2 , 2 2 , 0 



is prescribed on concrete, in contrast with the experimental failure curve of concrete.

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