Probabilistic stability analysis: how to communicate risk without hiding uncertainty.

The limitations of binary logic in geotechnical stability.

Geotechnical stability communication is still dominated by a binary logic: it either meets or it doesn't. This format simplifies approvals and audits, but is inadequate for risk management in structures operating under continuous variability. Strength and stiffness vary in space and time, hydraulic conditions change with rain, recirculation, and drainage, the executed geometry is rarely identical to the design, and instrumentation measures the system with noise and gaps. When all this reality is compressed into a single Factor of Safety (FS), the report may appear "clean," but the decision becomes fragile. The typical result is one of two equally undesirable extremes: artificial comfort based on optimistic assumptions, or inflated conservatism to compensate for the fear of the unknown, with cost and operational inefficiency.

The role of probabilistic analysis in risk communication.

Probabilistic stability analysis exists to break this trap. It doesn't eliminate determinism, nor does it replace engineering judgment. It makes uncertainty explicit, quantifies reliability, and translates performance into decision-making language. Instead of simply presenting "FS = 1.35," the focus shifts to the system's behavior under defined operational states, the probability of failure (PoF) and the reliability index (β) associated with these states, as well as understanding which variables truly govern risk. The ultimate goal is not to produce sophisticated numbers; it's to allow operations, engineering, and governance to discuss the same problem without masking what is unknown.

Natural variability versus lack of knowledge

The first step in using probability with integrity is to separate natural variability from lack of knowledge. Natural variability, or random uncertainty, is inherent to the rock mass and materials, reflecting geological heterogeneity, variability in tailings properties, and hydraulic responses. Lack of knowledge, or epistemic uncertainty, arises from insufficient data collection campaigns, unrepresentative samples, incomplete hydraulic conceptual models, unverified mechanisms, and limited operational history. Most "surprise events" in geotechnical engineering do not stem from natural variability, but from epistemic gaps treated as mere details. Mature risk communication begins when this difference becomes explicit, because it changes both the interpretation of the results and the recommended actions: variability is managed with limits and controls; lack of knowledge is reduced with evidence.

The four decision-making products of the probabilistic approach.

A well-designed probabilistic approach delivers four decision-making products that the deterministic approach alone hardly provides. The first is a view of reliability by operating condition. Stability is not a constant; it changes non-linearly with water level, suction loss, drainage regimes, deposition rate, condition of newly deposited material, geometric adherence, and rainfall events. What matters for management is understanding how risk shifts when the system transitions between realistic states, for example, operation with efficient drainage, operation with moderate recharge, post-rain conditions with slow dissipation of pore pressures, scenario of partial drainage failure, and geometric envelope outside the predicted range. By conditioning the response to operational states, the probabilistic approach ceases to be an abstract statistic and becomes an instrument for safe operation.

The second decision-making product is the hierarchy of controls, obtained through sensitivity and importance measures analysis. In any complex geotechnical system, a few variables dominate the risk. These could be the position of the water table, the effective permeability of a key layer, the undrained shear strength of a critical horizon, the drained shear strength of the foundation material, or the uncertainty of the executed geometry in specific regions. The managerial value of this step is direct: it guides where to measure, where to test, where to invest in drainage, and where to reinforce operational discipline. It's not about "improving the model," but about efficiently reducing risk by allocating effort to what truly changes decisions.

The third product is the separation between system risk and risk due to lack of knowledge. Two slopes can exhibit the same "design" safety factor (FS) and still have completely different reliabilities. One may be supported by a robust campaign, consistent instrumentation, and a validated hydraulic model, while the other relies on extrapolations and weak assumptions. The probabilistic approach exposes this difference, especially when looking at tails and not just average values. This transparency is vital because, from a governance perspective, what matters is not only the central margin, but the probability of plausible unfavorable combinations occurring within what is known.

The fourth product is the bridge to trigger-driven decision-making. Risk management is not about accepting a number; it's about defining actions proportional to the system's state, with owners and deadlines. Robust communication converts analysis into operational limits and graded responses, linking PoF and β to observable variables such as water level, gradients, displacements, drainage conditions, and geometric adherence. When risk is conditioned by the state, triggers cease to be arbitrary and become logically traceable: if the water level rises above a certain level shifts the reliability tail, the trigger and the operational response are a consequence, not an opinion.

The risks of "probabilistic theater"

This maturity, however, doesn't come from "running Monte Carlo." There's a real risk of "probabilistic theater": sophisticated reports that give a sense of precision without improving decision-making. Four flaws are recurrent. The first is parameterizing with weak statistics and treating distribution as robustness. Well-behaved distributions don't replace representativeness; a few tests on highly variable materials don't, by themselves, justify an elegant normal distribution. If the baseline is limited, this should be reflected as epistemic uncertainty and explored through alternative scenarios and assumption envelopes, not disguised by statistical adjustment. The second flaw is ignoring dependencies. Geotechnical and hydraulic properties are often correlated, and assuming independence artificially reduces variance and "improves" reliability on paper. The third is reporting unconditioned risk, that is, an average that doesn't reflect how the structure operates and fails. The fourth is starting with statistics and not with the conceptual model. Without a coherent mechanism, a well-justified (drained or undrained) regime, evidence-based hydraulic understanding, and a clear discussion of a plausible critical surface, the probabilistic approach produces numbers that appear scientific but have low practical value.

Narrative discipline and good communication practices

Communicating risk without hiding uncertainty requires narrative discipline. The rule is simple: clarity increases when uncertainty is organized, not when it is swept into the footnotes. Internationally standardized communication typically begins with a short and assertive executive summary, structured around three elements: the current state of the system under defined operating conditions, the associated reliability range, and the constraints that most significantly shift the risk. It then explicitly separates uncertainties that can be accepted, as they are inherent variability within a controllable envelope, from those that need to be reduced due to lack of evidence. This separation is uncomfortable for some organizations because it exposes gaps, but it is precisely what protects against illusory decisions. Without it, auditing becomes a hunt for inconsistencies and operations become trial and error.

Another key practice is to use two complementary metrics, without conflict or redundancy. FS remains useful as a quick technical language, especially for communicating breakdown mode and limit equilibrium coherence. PoF and β are useful for comparing reliability between states and for linking risk to internal criteria and corporate risk appetite. The typical mistake is to substitute one for the other or to present probability as the "final number." What underpins the decision is showing how reliability varies with operational conditions and where the transition points are, those "knees" in the curve where small changes in water level, drainage, or geometry produce a large shift in the probability distribution. That's where limits, triggers, and mitigation priorities are born.

From analysis to action: traceability and governance.

The crucial step in any communication is translating analysis into traceable actions. Probabilistic analysis without an action plan is diagnosis without treatment. A robust narrative connects results to three fronts: immediate controls, uncertainty reduction, and model revision. Immediate controls include operational discipline, operational limits and restrictions, intensified inspections, and responses graded by severity. Uncertainty reduction involves instrumentation driven by sensitivities, test campaigns focused on dominant variables, verification of geometric adherence, and validation of the hydraulic model through water balance and readings. Model revision is the natural consequence when data contradict assumptions; it is not a failure, but institutional learning.

The probabilistic approach as a learning cycle

In practice, the most efficient way to incorporate probabilistics into governance is to treat it as a cycle. First, realistic operational states and associated decision criteria are defined. Then, transparent modeling of assumptions is performed, classifying them by level of evidence, for example, assumptions confirmed by data, plausible assumptions with partial support, and unvalidated assumptions that may alter the mechanism or hydraulic regime. Next, probabilistic analysis with quality governance is performed, including dependencies, explicit treatment of the epistemic by scenarios, and sensitivity reporting. Finally, communication occurs in three layers: an executive layer for decision-making, a managerial layer with triggers, limits, and a plan, and a technical layer with methodology, calibration, validation, and traceability. The cycle closes by confronting the model with the field: piezometric readings, deformations, inspections, rainfall events, and observed performance. If the model does not learn, the report becomes outdated, and confidence becomes merely rhetorical.

Transparency as the basis of trust

The most difficult, and most valuable, point is accepting that transparency about uncertainty can generate discomfort. It reduces the feeling of immediate control, but increases real control. In mature organizations, the goal is not to "prove security" by a single number; it is to demonstrate that the system is understood, that critical uncertainties are recognized, that there is an objective plan to reduce them, and that there are clear triggers to protect people and operations while learning. This is the difference between governance on paper and governance in the field: one speaks of compliance, the other speaks of reliability. When probabilistic analysis is used for this purpose, it ceases to be a statistical appendix and becomes a mechanism for decision-making, prioritization, and accountability, exactly where stability needs to be to truly be a secure system.