PSI - Issue 48

Youcef Cheikhaoui et al. / Procedia Structural Integrity 48 (2023) 81–87 Cheikhaoui et al/ Structural Integrity Procedia 00 (2023) 000 – 000

86 6

collapse. The curve in figure 6 clearly shows the decrease of the probability of failure with the increase of the W/H ratio. From this, it can be pronounced that the probability of survival as a function of increasing the W⁄H shape ratio.

0 0.2 0.4 0.6 0.8 1

R² = 0,9829

probability of failure

0

1

2

3

4

W/H ratio

Fig. 6. The variation of the probability of failure as a function of the W/H ratio

Thus, a parametric study was performed according to our case study such that the dispersion parameter m=2.36, the specimen strength δ0=103.6 MPa, The load to be applied S=3 MPa. The calculation results are presented in curves 7 and 8

Fig. 7. a. The evolution of the survival probability with increasing shape ratio w/h for different volumes under an applied load σp=3 (M pa). b. The evolution of the probability of survival as a function of the increase of the shape ratio w/h for different loads to be applied for a pillar of volume= 50 m3. According to the calculations presented in the curves of figure 7a, we notice that there is a critical value of the W/H ratio for each volume of the pillar where the survival probability stabilizes at one for a small volume; however, it stabilizes quickly with a small W/H ratio. As an example, we have:  For v=18 m3 no evolution beyond W/H=1  For v=100 m3 no evolution beyond W/H=1.5 For more precision, we present in figure 7b, the variation of the survival probability as a function of the increase of the shape ratio w/h for different loads to be applied for a pillar of volume= 50 m3. It should also be noted that the load is another factor that must be taken into consideration in the choice of pillar design. The same findings were raised for loads. The probability of survival stabilizes at 1 for a small load, however

it stabilizes quickly with a small W/H ratio, thus:  For S=3 MPa no evolution beyond W/H=1.5  For S=49 MPa no evolution beyond W/H=2.5