Issue 51

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

mortars according to experimental results [24, 25]. Conversely, the compressive strength of masonry, 0 m f is generally assessed by means of compressive tests performed on masonry specimens. The mechanical model based on failure criterion allows to assess the confinement curve under a non-uniform stress state 1 2    typically developed in non axisymmetric confined elements. For these elements, two main lateral stresses can be identified 1 ,min l f   and confinement model depends on these parameters. In fact, for finite element modeling where lateral stresses are usually non-uniform, a mechanical model is essential to account for non-uniform stresses and it can be easily implemented. In the following section, the classical failure criterions were used to derive confinement models. Drucker-Prager model The Drucker-Prager model [26] provides the boundaries of the failure surface D P f  as function on the internal stress state, 1  , 2  , 3  and on the strengths of material ( 0 m f and mt f ): 2   ,max l f . The values, ,min l f and ,max l f depend on the confinement system used for the strengthening strategy. The

            1  2 2 3





1 



 

2





      



3

1 2 3 , ,   







(1)

f

f

f

f

D P 

m

m

m

1

2

3

0

0

0

 3 1





3

f . The lateral stresses are the

The entire failure surface can be normalized to the compressive strength of masonry 0 m

same, 1 

  

f

f depends on the strengthening system

assuming an axisymmetric confinement, where the value, l

l

2

used. The equation of the failure surface (1) D P f 

according to Drucker-Prager model can be written in normalized form, D P f 

, as follows:

 









1 



3 

1

2

2

1 

1 3  

1 





2

  

  

 

f

f

2

l

mc  

  





1 

3 

f

,

(2)

2

 3 1



 3 1



D P 

f

f







3

m

m

0

0

Fig. 1 shows the three-dimensional failure surface assuming the value  changing from 0 up to 1 with a step of 0.2.

Figure 1 : Failure surface according to a Drucker-Prager model assuming  changing from 0 until to 1 with a step of 0.2.

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