11.2 Semi-empirical Approach
157
If we were to add the effects of monitoring and maintenance (unfortunately almost
non-existent here) by using an ETA the final probability range would not change much
from the one obtained with Method 1, in this particular case.
11.2 Semi-empirical Approach
In order to work within the effort limits normally consented for this type of risk
assessment, especially if swift prioritization is the goal, we will now examine if
a relatively recent set of empirical relations between FoS and p f can be used. The
approach was originally described in (Silva et al. 2008) (we call this the Silva-LambeMarr (SLM) method, after the authors), and later modified in (Altarejos-García et al.
2015).
As with all empirical and simplified approaches caution must be exerted before
using these relations for tailings dams, in particular because neither publication makes
either explicit mention of construction mode (downstream, centre-line, upstream) or
provides a specific discussion of seismic loading, static and/or dynamic liquefaction.
In our practice, we have modified and re-calibrated these approaches specifically for
tailings dams.
The empirical relationships link the FoS (stability) defined by the geotechnical
engineers in charge of a project, using classical stability methods, to the annual
probability of failure.
11.2.1 Category of a Structure
In order to link FoS to p f , the first step is to define the “category” of the structure
under examination. This is done by examining sequentially the aspects of the design
(D1, investigation; D2, testing; D3, analyses and documentation) and construction
(CO) as well as operations and monitoring (OM). We will see these aspects appear
in Table 11.4.
The methodology considers four categories ranging from I (best) to IV (poor, i.e.,
non-engineered) and experience has shown (over a rather large array of cases studied
by the authors) that structures with high failure consequences are generally designed
built and operated in such a way that they fall into category I. Of course, if a structure
has received little or no engineering it will fall in category IV.
Figure 11.1 shows the relationship between FoS and the annual probability for
the four categories.
If we consider, for example, a relative common practice choice of FoS = 1.3, we
pull from Fig. 11.1 the values of the probability of failure displayed in Table 11.3
for the four categories.
The values shown in Table 11.3 mean that, based on the assumed common practice
FoS = 1.3 and the historical values described earlier (the bench-marking range), the
157
If we were to add the effects of monitoring and maintenance (unfortunately almost
non-existent here) by using an ETA the final probability range would not change much
from the one obtained with Method 1, in this particular case.
11.2 Semi-empirical Approach
In order to work within the effort limits normally consented for this type of risk
assessment, especially if swift prioritization is the goal, we will now examine if
a relatively recent set of empirical relations between FoS and p f can be used. The
approach was originally described in (Silva et al. 2008) (we call this the Silva-LambeMarr (SLM) method, after the authors), and later modified in (Altarejos-García et al.
2015).
As with all empirical and simplified approaches caution must be exerted before
using these relations for tailings dams, in particular because neither publication makes
either explicit mention of construction mode (downstream, centre-line, upstream) or
provides a specific discussion of seismic loading, static and/or dynamic liquefaction.
In our practice, we have modified and re-calibrated these approaches specifically for
tailings dams.
The empirical relationships link the FoS (stability) defined by the geotechnical
engineers in charge of a project, using classical stability methods, to the annual
probability of failure.
11.2.1 Category of a Structure
In order to link FoS to p f , the first step is to define the “category” of the structure
under examination. This is done by examining sequentially the aspects of the design
(D1, investigation; D2, testing; D3, analyses and documentation) and construction
(CO) as well as operations and monitoring (OM). We will see these aspects appear
in Table 11.4.
The methodology considers four categories ranging from I (best) to IV (poor, i.e.,
non-engineered) and experience has shown (over a rather large array of cases studied
by the authors) that structures with high failure consequences are generally designed
built and operated in such a way that they fall into category I. Of course, if a structure
has received little or no engineering it will fall in category IV.
Figure 11.1 shows the relationship between FoS and the annual probability for
the four categories.
If we consider, for example, a relative common practice choice of FoS = 1.3, we
pull from Fig. 11.1 the values of the probability of failure displayed in Table 11.3
for the four categories.
The values shown in Table 11.3 mean that, based on the assumed common practice
FoS = 1.3 and the historical values described earlier (the bench-marking range), the