PSI - Issue 48

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

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3.2. Determination of the probability of survival of the pillars The equation proposed as an analytical approach to estimate the strength of a pillar such that Rp = σ f the stress to be applied for at least one of the defects is activated (failure), thus: (0.97) = 23.60 ( ⁄ℎ ) 5.15 −0.42 ሺ •ሻ (10) Where: : Pillar volume (m 3 ). ⁄ℎ : Pillar slenderness. : The applied stress (MPa). An example of the results on block 5/1 in a depth of 106.5 meter and a height of the fixed pillars equal 2 meters (see Appendix A).

Fig. 4. The disposition of the pillars located in the 5/1 panel

We note by comparing the results obtained that there is an intense relation of dependence between the probability of failure and the slenderness ratio as well as the extraction rate (Appendix 1). It is clear that there is an inverse relation between the two parameters. For example the pillar n° 20 of width w=1.5m and height h=2 m (slender) with an extraction rate τ =90% with a probability of failure P f =0.99 (failed pillar). On the other hand the pillar n° 29 of width w=3 m and height h=2 m (less slender pillar) with an extraction rate τ =78%, has a probability of failure P f =0.12 (very stable), figure 5.

Fig. 5. Photos of two pillars of different stability in the mine Chaabat el Hamra

We can see that the variation of the probability of failure as a function of the slenderness ratio W/H. As an example, the 29 pillars of block 5-1 presented in figure 4 highlight the phenomenon of confinement linked to the increase of the W/H ratio which reinforces the probability of survival of the pillars so that the least slender pillar is the most likely to