What is back-analysis of a failed slope?
Back-analysis of a failed slope inverts the usual stability calculation: instead of assuming soil strengths and computing a factor of safety, back-analysis takes the observed failure geometry, fixes the factor of safety at one at the instant of movement, and solves for the strength that must have been mobilized. When a slope has already failed, the interesting question is not whether the slope was stable.
Slope back-analysis is the most direct evidence available about what the ground actually did at full scale. Slope back-analysis is also a model assembled substantially from inference, and it should be read with that in mind.
Why can’t a conventional forward stability analysis settle what happened on a slope that has already failed?
A conventional forward stability analysis cannot settle what happened on a slope that has already failed: applied after the failure, it usually returns a factor of safety comfortably above one, because its inputs describe intact soil and assumed water conditions rather than the conditions that actually existed on the failure surface at the moment it moved. A conventional stability analysis takes laboratory strengths and design groundwater conditions and reports a factor of safety.
Slope back-analysis reverses which quantity is unknown. In a back-analysis, the failure itself becomes the datum, and the model is calibrated until it reproduces an event that is already known to have occurred.
How is the failure surface located for a slope back-analysis?
The failure surface for a slope back-analysis is defined at its ends by visible features and inferred between them, and locating it is most of the work, because the back-analysis is only as good as the geometry fitted to it. The head scarp and tension cracks define the upslope limit of the failure surface, the toe bulge defines the downslope limit, and comparison of pre- and post-failure topography from LiDAR or photogrammetry gives the displaced mass its shape and its volume.
Between those endpoints the failure surface is inferred. Borings advanced through the slide mass into stable ground below identify the shear zone by disturbed or slickensided material, and inclinometers grouted across the shear zone register the depth at which displacement concentrates. Where slope movement is ongoing, an inclinometer is the single most persuasive line of evidence available.
Why does slope back-analysis set the factor of safety at one?
Slope back-analysis sets the factor of safety at one because, at the instant a slope failed, driving and resisting forces were in balance by definition. Setting the factor of safety to one and solving for strength converts that observation into a number, and that number reflects the field-scale behavior of the entire failure surface, including fabric, fissures and variability too large to reproduce in a laboratory specimen.
That field-scale view is the genuine advantage of slope back-analysis. A hand-sized laboratory specimen samples a few cubic centimeters of a deposit; the slide sampled the whole failure surface at once, under the actual drainage and loading conditions of the day it moved, and produced an unambiguous result.
Can a slope back-analysis recover both soil strength and pore-water pressure?
No — a slope back-analysis cannot recover both the shear strength along the failure surface and the pore-water pressure acting on it, because the equation carries both as unknowns that matter and one has to be fixed before the other can be solved for. The choice of which to fix is not a technicality.
This is where piezometric data earns its cost in a slope back-analysis. If pore pressures at the depth of the failure surface were measured near the time of movement, strength can be back-calculated with real confidence. If pore pressures were not measured, the analyst assumes a groundwater condition, and every back-calculated strength inherits that assumption.
How do limit equilibrium methods model a failed slope in a back-analysis?
Limit equilibrium methods, the standard tools for slope back-analysis, divide the sliding mass into vertical slices and enforce equilibrium, and they differ mainly in how they treat the forces between slices and which equilibrium conditions they satisfy. Limit equilibrium methods that satisfy both force and moment equilibrium are generally preferred where the geometry is not simple.
Most slope back-analyses are two-dimensional, run on a section chosen as representative. Real slides have width, and because a two-dimensional model ignores the end resistance, back-calculated strength from a plane-strain section tends to be conservative — lower than reality — by an amount that depends on the slide’s proportions.
How should a back-calculated slope strength be compared with laboratory test results?
A back-calculated strength from a slope back-analysis is compared with laboratory results by checking it against measured values that together bracket what the material can plausibly offer: direct shear results under ASTM D3080, triaxial results under ASTM D4767, and residual strengths from large-displacement testing. A back-calculated strength is a hypothesis until it is compared against those measured values.
Agreement between the back-calculated strength and residual laboratory strength is a meaningful finding, consistent with movement along a pre-existing surface. A back-calculated strength well below anything the laboratory can produce signals that the back-analysis model is wrong somewhere, most often in the assumed water condition.
What are the limits of slope back-analysis?
The honest limits of slope back-analysis are that it is non-unique and that it returns an average. Different combinations of strength, pore pressure and failure surface geometry can reproduce the same slope failure equally well, and back-analysis cannot distinguish among them on its own without independent measurements.
Slope back-analysis also returns an average: a single mobilized strength is assigned to a failure surface that may cross several materials. The back-analysis result cannot capture progressive failure, in which strength is exceeded at one point and the failure surface propagates rather than mobilizing everywhere at once.
What does a defensible slope back-analysis look like?
A defensible slope back-analysis states its assumed geometry, its assumed piezometric surface and the method used, then presents a sensitivity study showing how the back-calculated strength shifts across the plausible range of each assumption.
Where the back-calculated strength holds steady across that range, it is strong evidence. Where a modest change in assumed groundwater swings the answer across the range of plausible materials, the slope back-analysis has identified what was never measured rather than what the soil was, and the report should say so.
This article on slope back-analysis is general technical orientation, not a failure analysis, an engineering opinion, or advice on any specific matter. Determining the cause of a particular incident requires hands-on examination by a credentialed expert.