Issue 51

G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23

 . The positive solution of the previous

The Eqn. (5) is an algebraic second order equation in the unknown parameter, 3

 for different lateral stress states 1 





equation provides the maximum compressive strength, 3

:

2





1 1

2



1  1  12 12 2 1 2           

1 

(6)

3

2

 points to change the internal lateral stress state 1 2   

represents the confinement curve.

The envelope of the 3

Henky-Von Mises model Henky-Von Mises model [27, 28] was developed for homogeneous materials with compressive strength, 0 m 1   , but it is interesting in order to assess the drawbacks of the other models. This model provides the boundaries of the failure surface by means of the following equation:       2 2 2 2 1 2 3 1 2 3 0 1 2 2 3 1 3 0 0 , , H VM m m m f f f f                     (7) f equal to the tensile strength, mt f (i.e. 1   ). This assumption is certainly not justified for the masonry, where

The Eqn. (7), expressed in normalized form and under an uniform lateral stress state, becomes:

  

  

f

f

2

2

l

1      mc

1 

  

3 

1 

1 3  





(8)

f

,

2

2

3

H VM 

f

f

m

m

0

0

Fig. 3 shows the three-dimensional failure surface model independent on  .

Figure 3 : Failure surface according to a Henky-Von Mises model independent on  .

The solution of the Eqn. (8) for confinement is represented by the positive stress, 3  :

1 

 

1 

(9)

3

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