PSI - Issue 78

Annalisa Franco et al. / Procedia Structural Integrity 78 (2026) 1245–1252 4. Assessment of partial safety factor for material In order to apply Eq. (4) and considering that the 3-p Lognormal distribution resulted the most suitable probability distribution for tensile strengths for most cases (see Table 4), the corresponding characteristic and design values can be expressed as follows: 1251

    

    

  

   

  

   

2 X

2 X

σ

σ

1 2

1



ln 1 

( ) ln 1 p 

sign( γ)











2

2









μ

μ













(6a)

X

μ      

e

X

X

X

k

    

    

  

   

   

   

2 X

2 X

σ

σ

1 2

ln 1 

sign( γ) α β ln 1    





R

2

2









μ

μ













X

μ      

e

(6b)

X

X

d

X

Where μ X is the mean value of the variable X and σ X the relative standard deviation; ϑ is the threshold parameter of the 3-p Lognormal distribution (see Table 3) and γ the skewness; Φ represents the cumulative probability function of the standard normal distribution and Φ -1 (p) is the relative quantile function (for p=5%, Φ -1 (p) = − 1.645); α R is the FORM sensitivity factor; β is the target reliability index. By assuming α R =0,8 (strength related problem) and β =3,8 (Consequences Class CC2, 50 years return period according to EN 1990), the obtained design values are reported in Table 5 and in Table 6, together with the characteristic values and the experimental and theoretical parameters ( μ X , σ X ) needed to obtain them.

Table 5. Statistical description of composite system tensile strength σ u

Value GLASS + LM BASALT + LM STEEL + LM STEEL + CM PBO + LM PBO + CM

μ X σ X μ X σ X X k X d γ m

998

1444

3010

2918

3093

3024

Experimental

94

165

56

106

347

309

999

1444

3010

2918

3093

3024

94

168

60

113

358

322

3-p Lognormal

850 737 1,15

1147 806 1,42

2895 2637 1,10

2704 2261 1,20

2504 2008 1,25

2632 2489 1,06

Table 6. Statistical description of dry fabric tensile strength σ f

Value

GLASS

BASALT

STEEL

PBO 3500

μ X σ X μ X σ X X k X d γ m

1066

1432

3103

Experimental

79

106

58

415

1066

1432

3103

3500

81

108

54

425

3-p Lognormal

948 882 1,08

1262 1134 1,11

3003 2855 1,05

2809 2249 1,25

The value of the material partial factor according to Eq. (4) is also reported in Table 5 for each composite system and in Table 6 for each type of dry fabric. It may be observed that the values of γ m vary between 1,06 and 1,42 for the IMC system and between 1,05 and 1,25 for the dry fabric. It is worth noting that the highest value of the partial factor for the IMC system (1,42) is obtained for the basalt fibres, while the lowest value (1,06) is calculated for PBO with cement-based mortar. As regards the dry fabric, the lowest value (1,05) is obtained for steel, while the highest (1,25) for PBO. The outlined results are only relative to the material partial factors, which do not take into account the uncertainties of the resistance model and of geometric deviations normally included in the partial factor γ Rd . If, for a first approximation, one considers the value of γ Rd used for organic matrix based system with the wet lay-up procedure equal to 1,15 (EN 1992-1-1, 2023), the global partial factor γ M , according to eq. (2), ranges between 1,20 and 1,65.