The nemesis of success is failure.
Of course, consequences of failures can vary significantly from case to case. Not all slope “failures” are catastrophic. Some constitute unsatisfactory performances or minor irritations.
Slope Hazard Characterization
Factor of Safety (FoS) and Probability of Failure (PoF) are commonly used to characterize the hazard of a slope. FoS and PoF describe the state of equilibrium of a potential volume (on a slope cross-section) between the topographic surface and a potential sliding surface with respect to sliding.
Common methods to evaluate FoS and PoF use the Limit Equilibrium Method (LEM) and do not support the type of risk-based decision-making currently required in the transportation and mining industries (Adams 2015).
A FoS of 1.0 describes the point of meta-stable equilibrium, when resistance equates loadings. At that point, PoF is 50%, like a coin toss.
A slope failure is much more complex than how it is modeled by the LEM. In practice, failure does not occur simultaneously along a single discrete basal surface, but rather local failures progressively develop into a larger slope failure (Oboni & Bourdeau 1983).
Factor of Safety
Lithology, water table position and geomechanical parameters of the materials within the slope generally dictate the shape and volume of the sliding masses. None of the drivers has precise, certain values; even after numerous and successful investigations and lab testing, there will be ranges of values.
Thus, it is common practice for engineers to select prudent parameters and calculate the FoS. If the engineer includes a seismic acceleration in the disturbing forces, then the analysis becomes pseudostatic. If the analysis is under drained conditions, the analysis used is effective stress analysis (ESA); if the analysis is done under undrained conditions, it is known as undrained strength analysis (USA).
FoS is generally a single value. Engineers sometimes express FoS as a range to explicitly indicate a certain level of uncertainty. Another way of addressing those inevitable uncertainties is to conduct sensitivity analyses. During these studies, the engineer varies each significant parameter systematically over its maximum credible range to determine its influence on FoS.
Probability of Failure
Various approaches can be used to evaluate the PoF. Significant parameters are stochastic variables. We can define them either by their first and second moment (average and variance), possibly their bounds and, in some cases, their third statistical moment (skewness). If data quality and quantity is high, one can estimate the distribution of each parameter.
Once one describes all the significant selected parameters as above, the calculation of PoF can proceed, generally by determining the parameters of the distribution of FoS and then assuming PoF=p(FoS<=1). Although this assumption is not formally correct, it is generally valid.
Various approaches are available to determine the parameters of the distribution of FoS, as follows:
- Direct evaluation (only feasible for simple slopes, e.g. triangular, planar failures)
- Point estimates methods (e.g. Rosenblueth point estimates 1975), which can accommodate all common cases with good understanding of mean and coefficient of variation of the parameters, perhaps with their bound values
- Monte Carlo simulation (requires assuming distributions for all parameters)
- Other sophisticated probabilistic approaches (such as Oboni & Bourdeau 1983)
Discussion
Based on the definitions above, FoS and PoF express the proneness of a potential volume (on a slope cross-section) between the topographic surface and a potential sliding surface with respect to failing as a monolith. Thus, they constitute a hazard quantification. However, the first is deterministic and the second probabilistic. Both approaches are geomechanical and use force and strength parameters. They deliver non-annualized values, as they are geomechanical only.
Adams (2015) noted that a major problem of evaluating PoF using LEM is indeed the lack of time dependency. In the absence of time-dependent input variables, PoF does not have a timescale. The PoF of a slope is likely related to the rate of stress redistribution, the rate of material strength degradation (e.g. via weathering and rock mass relaxation), and the temporal probabilities of triggering events, such as rainfall or earthquakes.
Furthermore, these approaches have no provision for evaluating the impact of a multitude of important parameters such as human factors, monitoring and maintenance of the slope, potential for exceptional meteorological conditions, etc.
New Approaches
In recent years, more sophisticated approaches offering a blend between the geomechanics approach and semi-empirical evaluations of the quality of the slope have emerged. They are now used and proven (Silva et al. 2008). They fill in the missing time dependency by estimating the number of potential accidents over a certain time, e.g. next n years, life of the structure. Of course, these approaches require regular updates as conditions and parameters change over time.
ORE2_Slopes™ is a subset of the universal proprietary Optimum Risk Estimates (ORE) platform specific to manmade slopes (including pits), analogous to ORE2_Dams™ and ORE2_Dykes™. The platform was created by Oboni Riskope Associates Inc. in 2014. This specific approach is applicable anywhere and uses symptoms or diagnostic points in the history of the manmade slope from inception to the day of the evaluation. The diagnostic points are summarized below. For each point, the specific methodology allows a pre-determined set of answers. We then combine them mathematically to deliver an estimate of the PoF, including uncertainties. Explicit consideration of uncertainties is indeed a fundamental step towards reasonable, transparent and ethical risk assessments (Oboni 2017, Oboni F ISBN-10: 3030194469 2019).
Diagnostic Points in Slope Risk Assessment Analyses
Below is a list of diagnostic points we use in manmade slopes−specific approach:
- Physical aspects of the slope and its equipment
- Construction (supervision, berms, erosion, divergence from plans, etc.)
- Geotechnical investigations and testing
- Prior analyses and documentation of the project
- Various stability, deformation, erosion, liquefaction aspects as applicable:
- stability analyses (ESA, USA, pseudostatic, PoF)
- instability symptoms
- settlements (actual and analyses)
- liquefaction and internal erosion
- Operations, monitoring, maintenance and repairs
Based on the list above, one can easily update evaluations with generally available or observable data (e.g. on site, monitoring and satellite). Any missing data are explicitly outlined in the evaluations.
As one can understand from this summary, the link between extant client’s databases and archives, possible satellite observation and ORE2_Slopes becomes seamless. In addition, this could lead to extensive automation if clients owning multiple slopes are so inclined.
