PSI - Issue 78

Francesco Martini et al. / Procedia Structural Integrity 78 (2026) 2022–2029

2026

different combinations of silo typologies and service conditions are neatly reported (i.e., sorted values) to derive a unique relationship. The obtained relationships with the values of the coefficients for fitting data are reported in the legend of Figures 2 and 3.

and H/D

Relation between

s

12

data

2

s =-0.025+4.5/(H/D)

10

8

6

s

4

2

0

0

1

2

3

4

5

6

H/D

Figure 2. Definition of the coefficient α s at the variation of silo geometry. Relation between and h /D

mat

mat

20

data

/D) 3

=0.1/(h

mat

mat

15

10

mat

5

0

0

1

2

3

4

5

6

h

/D

mat

Figure 3. Definition of the coefficient α mat at the variation of silo geometry and service conditions.

3. Definition of horizontal and vertical static and seismic pressures After calibrating the coefficients to modify stiffness in the simplified model, the near-complete definition of the proposed modelling approach was achieved by defining the values of horizontal and vertical static and seismic pressures. On the static side, the Janssen’s theory (Janssen, 1985) and the related prescriptions in the Eurocode 8 (2006) were used to derive both horizontal, defined as P h , and vertical, defined as P v , static pressures provided by the content on the silos wall. It is worth specifying that the values of P v is derived by the values of P h through the coefficient of friction. Due to the nature of the simplified model, the entire profile for P h and P v cannot be defined, while both pressure typologies can be estimated only in the points in which the masses are located. This means that the pressure values in the simplified models were obtained through an analytical procedure, starting by the corresponding ones (i.e., at the same height) in the detailed models by Khalil et al. (2024). With this logic, the horizontal pressures of the simplified model were defined as P h 1 , P h 2 , P h 3 , while the vertical pressures of the simplified model were defined as P v 1 , P v 2 , P v 3 . It is worth observing that for the three partial heights of the simplified model, i.e., H 1 , H 2 , and H 3 , the