318
On the other hand, it can be noted that, given its ROC curve plot, this curve has an AUC
equivalent to 0.91, which means that our model has a diagnostic power of 91%. This implies
that there is a 91% probability the model will correctly classify a pillar as damaged, compared
to a random guess referred to that same pillar. Given the above, this model has a quality in its
classification ability typified as “good”.
The most significant variables in the model, in terms of the average information gain over
the modelled output, are those referred to the mechanic response of the rock mass in which
pillars are emplaced to shear stresses and strains and seismic-nature variables, being the mining process explained as a joint effect whose convergence, given the resulting limit-state values, is a necessary and sufficient condition for collapses to occur.
Finally, it can be noted that the optimal value which discriminates the “damaged” and
“undamaged” instances in the model is equivalent to a 34% cut-off probability, which defines
a 95% sensitivity and specificity indexes. In order to use multiples of 10 and thus easily partitioning the PVI’s interval from 0% to 100%, a threshold discrimination value of 30% was
selected. This way, the model has a 96% sensibility and 94% specificity over the training set.
6.2 PVI Plot over training, validation and application sets
The results for the plotting of the PVI over the training, validation and application sets, are
sequentially shown in Fig. 6.
6.3 Results discussion
a. About the model’s structure:
Given the threshold discrimination value of 30% cut-off probability, the diagnostic precision
indicators are the ones observed in Table 4.
These values are near state-of-the-art at the scale of experimental models and reflect high
robustness both from the phenomenon understanding perspective and the associated experimental design.
In terms of each productive sector that conforms the training case, we have:
i. In Esmeralda, the pillars labeled as vulnerable by the PVI correspond to 39% of the total,
with an average PVI of 78%. Of the remaining pillars, 61% have been classified as undamaged, having an average PVI value of 4%.
ii. In RENO-Dacita, the pillars labeled as vulnerable by the PVI are 13% of the total, with an
average PVI of 75%. The remaining pillars were classified as undamaged, with an average
PVI value of 11%.
Regarding the above, the obtained values suggest that a segmentation in terms of obtained
PVI values considering the 30% cutoff probability stablished in section 6.1 as well as the average PVI values of the collapsed pillars (see Table 5).
b. About the PVI plot over the production sectors:
Given the results shown in Fig. 6, for the validation set, the following remarks can be
acquainted in terms of the pillars labeled as “damaged” by the PVI:
− Diablo Regimiento is a production sector with practically no vulnerable pillars, and it is
reasonable to assume the only pillar labeled as vulnerable contained in it as a model outlier, thus being these results an excellent reflection of the present operating conditions of
Diablo Regimiento, since this sector actually has the best geomechanical behavior in El
Teniente Mine.
− The southern zone of Esmeralda presents three areas that can be labeled as vulnerable,
located in the northern, east and central sections of this production sector. Since South
Esmeralda is an area which is operated via two separated caving fronts, splitting this sector
in two sections called Bloque 1 and Bloque 2 (both separated by a rib pillar denoted locally
as “Pilar Interbloques” (P.I.)) it is natural to assume the area labeled as vulnerable over
the P.I. (the central one) is associated with unfavorable convex geometries of the induced
On the other hand, it can be noted that, given its ROC curve plot, this curve has an AUC
equivalent to 0.91, which means that our model has a diagnostic power of 91%. This implies
that there is a 91% probability the model will correctly classify a pillar as damaged, compared
to a random guess referred to that same pillar. Given the above, this model has a quality in its
classification ability typified as “good”.
The most significant variables in the model, in terms of the average information gain over
the modelled output, are those referred to the mechanic response of the rock mass in which
pillars are emplaced to shear stresses and strains and seismic-nature variables, being the mining process explained as a joint effect whose convergence, given the resulting limit-state values, is a necessary and sufficient condition for collapses to occur.
Finally, it can be noted that the optimal value which discriminates the “damaged” and
“undamaged” instances in the model is equivalent to a 34% cut-off probability, which defines
a 95% sensitivity and specificity indexes. In order to use multiples of 10 and thus easily partitioning the PVI’s interval from 0% to 100%, a threshold discrimination value of 30% was
selected. This way, the model has a 96% sensibility and 94% specificity over the training set.
6.2 PVI Plot over training, validation and application sets
The results for the plotting of the PVI over the training, validation and application sets, are
sequentially shown in Fig. 6.
6.3 Results discussion
a. About the model’s structure:
Given the threshold discrimination value of 30% cut-off probability, the diagnostic precision
indicators are the ones observed in Table 4.
These values are near state-of-the-art at the scale of experimental models and reflect high
robustness both from the phenomenon understanding perspective and the associated experimental design.
In terms of each productive sector that conforms the training case, we have:
i. In Esmeralda, the pillars labeled as vulnerable by the PVI correspond to 39% of the total,
with an average PVI of 78%. Of the remaining pillars, 61% have been classified as undamaged, having an average PVI value of 4%.
ii. In RENO-Dacita, the pillars labeled as vulnerable by the PVI are 13% of the total, with an
average PVI of 75%. The remaining pillars were classified as undamaged, with an average
PVI value of 11%.
Regarding the above, the obtained values suggest that a segmentation in terms of obtained
PVI values considering the 30% cutoff probability stablished in section 6.1 as well as the average PVI values of the collapsed pillars (see Table 5).
b. About the PVI plot over the production sectors:
Given the results shown in Fig. 6, for the validation set, the following remarks can be
acquainted in terms of the pillars labeled as “damaged” by the PVI:
− Diablo Regimiento is a production sector with practically no vulnerable pillars, and it is
reasonable to assume the only pillar labeled as vulnerable contained in it as a model outlier, thus being these results an excellent reflection of the present operating conditions of
Diablo Regimiento, since this sector actually has the best geomechanical behavior in El
Teniente Mine.
− The southern zone of Esmeralda presents three areas that can be labeled as vulnerable,
located in the northern, east and central sections of this production sector. Since South
Esmeralda is an area which is operated via two separated caving fronts, splitting this sector
in two sections called Bloque 1 and Bloque 2 (both separated by a rib pillar denoted locally
as “Pilar Interbloques” (P.I.)) it is natural to assume the area labeled as vulnerable over
the P.I. (the central one) is associated with unfavorable convex geometries of the induced