Question 3 of 9: Design with undrained shear strength, and how it is measured

Question 3: Design with undrained shear strength, and how it is measured (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.

When undrained parameters are the right choice. An undrained, total-stress design is appropriate whenever a saturated fine-grained soil of low permeability is loaded so quickly that no significant drainage occurs during the loading, so that the change in volume is zero and the change in strength during the event is nil. The design condition is then the moment the load arrives, and the analysis is carried out with φ_u = 0 and τ_f = c_u.

A practical example. Consider a steel storage tank, 30 m in diameter, founded on a granular pad over 12 m of soft normally consolidated marine clay in the Fraser River delta, and hydrostatically tested by filling it with water in a few days. The clay has a coefficient of consolidation of the order of 2 m²/year, so with double drainage the time for even fifty per cent consolidation is measured in years while the load is applied in days. Bearing capacity is therefore checked as q_u = 5.14 c_u (1 + 0.2B/L)(1 + 0.2D_f/B) with the undrained strength profile from the site investigation, and the hydrotest is staged so that the clay gains strength through consolidation between increments. The same reasoning covers an embankment raised rapidly on soft clay, a footing on clay checked at end of construction, the short-term stability of a temporary excavation in clay, the capacity of a driven pile at end of driving, and the response of any clay foundation to a seismic or wave load.

Laboratory determination. The unconsolidated–undrained triaxial test (UU, or "quick" test) is the standard: a saturated specimen is confined at a cell pressure representing the field total stress and sheared with drainage closed, giving c_u = q_f/2 with the failure envelope horizontal. Its strength is that the confining stress and, if a pore-pressure transducer is used, the pore pressure at failure can be controlled and observed; its limitation is that the result is only as good as the sample, and tube sampling of a soft or sensitive clay destroys part of the structure and lowers the measured strength. The unconfined compression test is the cheapest version, with c_u = q_u/2; it is quick and needs no cell, but it applies zero confinement, so it under-estimates the strength of a fissured clay badly and cannot be run on a specimen that will not stand alone. Consolidated–undrained triaxial tests with pore-pressure measurement (CU) are the most informative: consolidating the specimen back to the in-situ effective stress before shearing largely undoes the disturbance, and the same test yields c′ and φ′ for the long-term analysis; the cost is time and a skilled operator. The direct simple shear device gives the strength on a horizontal plane, which is the relevant one for the central portion of a deep-seated slip surface and is typically well below the triaxial compression value; laboratory vanes, torvanes and pocket penetrometers are useful only for logging and preliminary strength profiling.

Field determination. The field vane shear test is the primary in-situ method in soft to firm clays: a four-bladed vane is pushed below the borehole base and rotated, and the peak torque gives c_u directly while continued rotation gives the remoulded strength and hence the sensitivity. It is inexpensive, tests a volume of undisturbed ground, and provides a continuous profile, but it shears mainly on a vertical cylindrical surface, is rate-dependent, and over-estimates the strength mobilised in a field failure — hence Bjerrum's correction factor μ, which falls from about 1.0 at low plasticity to roughly 0.6 at a plasticity index near 100. It is also unreliable in fissured, silty or varved deposits. The piezocone gives a continuous profile through c_u = (q_t − σ_v)/N_kt with N_kt commonly between 12 and 20; it is fast and repeatable, but N_kt must be calibrated against vane or triaxial data on the site, so the CPT is best regarded as an interpolator between reference tests rather than an independent measurement. The pressuremeter gives strength and modulus from a cavity-expansion curve on ground disturbed only by the borehole wall, which suits stiff and fissured clays, but it is slow, expensive and sensitive to borehole preparation. The flat dilatometer is quick and gives a useful strength and stress-history profile through empirical correlation. SPT-based correlations for c_u exist but are too crude for design and should be used only to detect gross inconsistency.

Bringing them together. No single test gives the operative strength. Good practice, and CFEM's advice, is to build a design profile from several sources — vane profiles corrected for plasticity, UU or CU triaxial tests on the best samples, and a continuous CPT calibrated against them — and to select a design line that is deliberately on the low side of the scatter, because it is the uncertainty in that line, and not the arithmetic of the stability calculation, that governs the factor of safety chosen in Question 1.