Question 1 of 9: Short-term versus long-term factors of safety for slopes

Question 1: Short-term versus long-term factors of safety for slopes (7 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

The factor of safety demanded of a slope is not a property of the soil; it is a measure of how much confidence the designer has in the strength that was put into the analysis and in the loading that the slope will actually see. A short-term (undrained, total-stress) analysis is carried out with the undrained shear strength c_u, whereas a long-term (drained, effective-stress) analysis is carried out with c′ and φ′. Everything that makes the first of those two quantities less trustworthy than the second is a reason to insist on a larger margin against failure in the short term.

The undrained strength is the more uncertain parameter. The value of c_u that a laboratory or field test returns depends on the test itself: an unconsolidated-undrained triaxial test on a tube sample, a field vane, a cone factor applied to q_c, and an unconfined compression test on the same clay routinely disagree by thirty per cent or more. Sample disturbance almost always lowers the measured strength, while the field vane usually raises it, so Bjerrum's empirical correction factor μ has to be applied on the basis of plasticity index alone. The undrained strength is also strongly anisotropic and strongly rate-dependent: the strength mobilised on the horizontal part of a deep-seated slip surface can be half the value measured in a vertical-sample compression test, and strength measured at laboratory strain rates over-predicts strength at the rate a real embankment loads a foundation. Effective-stress parameters behave far better. For most soils φ′ is a robust, repeatable number that is essentially insensitive to sampling disturbance, is closely tied to grading and density, and can be bracketed within two or three degrees from experience alone.

A total-stress analysis cannot be checked in the field. An effective-stress analysis makes an explicit statement about pore water pressure that piezometers can confirm or refute during and after construction; if the observed pressures are worse than assumed, the design can be revised before failure. An undrained analysis contains no pore-pressure statement at all. It assumes that no drainage occurs during loading, which is a modelling idealisation rather than a measurement, and in a silty or fissured clay, or where sand lenses or vertical drains are present, partial drainage during construction can move the true condition a long way from either bound.

The short-term condition is the one that is loaded least predictably. End-of-construction is when the rate of fill placement, the weight of plant working on the crest, temporary stockpiles, trench excavations at the toe and construction traffic are at their least controlled, and it is also when the geometry may briefly be steeper than the design section. Long-term loading, by contrast, is a settled and well-defined condition.

Undrained failure gives no warning and is the more damaging event. A saturated clay loaded undrained to failure is essentially brittle: displacements are small until collapse, so the observational method has little to work with. Drained failures in the same material develop slowly through creep and visible tension cracking, giving time to unload the crest or install drainage. In addition, sensitive Canadian clays — the Champlain Sea clays of the St. Lawrence lowlands are the classic case — lose most of their strength on remoulding, so a short-term failure can retrogress far beyond the initial slip. Because a construction-period failure also puts workers and plant directly at risk, its consequence class is higher than that of a long-term movement in a completed and monitored structure.

Where each condition governs. For an embankment or a footing placed on soft saturated clay, the end-of-construction case is the critical one: the applied stress is at a maximum while the foundation has not yet gained strength through consolidation, and the factor of safety increases with time. For a cut slope or an excavation in stiff clay the reverse holds: pore pressures are initially negative and swell towards equilibrium over years, so the factor of safety decreases with time and the long-term case governs. The short-term analysis of a fill is therefore both the governing case and the case built on the weaker data, which is precisely why it attracts the larger factor of safety.