Question 3 of 9: When to design on undrained strength, and how to measure it

Question 3: When to design on undrained strength, and how to measure it (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 govern. The choice between undrained and drained parameters is not a choice about the soil; it is a choice about the relative speed of loading and drainage. An undrained (total-stress, φ_u = 0) analysis is appropriate whenever the load is applied faster than the excess pore pressure it generates can dissipate, so that the water content of the soil beneath the foundation is unchanged at the moment of interest. In practice that means four conditions have to hold together: the soil is fine-grained and saturated, so its permeability is low and its drainage path long; the loading is rapid relative to the coefficient of consolidation; the design case being checked is the end-of-construction condition; and the soil is normally or lightly over-consolidated, so that consolidation will increase its strength and the short term is therefore the critical term.

Concrete situations in which those conditions are met include a footing, raft or embankment built quickly on a soft to firm saturated clay or clayey silt; the bearing capacity of a footing on clay at the end of construction; the capacity of a driven pile at the end of driving, where the α-method uses c_u directly; the stability of a temporary excavation, cut or trench in clay, which is Question 1 of this paper; a staged embankment where each stage must be checked against the strength available before the next is placed; and any rapidly applied transient load such as an earthquake or a sudden drawdown. The undrained case is also the right one for a short-term check on a clay whose long-term parameters are known but whose drainage is obstructed — a footing bearing on clay confined between two impermeable layers, for example.

The converse is worth stating explicitly, because an examiner is looking for the judgement rather than the list. Undrained parameters must not be used for the permanent condition of a foundation on clay when the long-term drained case is more critical: this is the situation for excavations and cuts, where pore pressures rise towards equilibrium after unloading and the strength falls with time; for heavily over-consolidated clays and clay shales, where softening and progressive failure drive the operational strength towards a residual value; for a foundation on a stiff fissured clay, where mass behaviour is controlled by the fissures rather than by an intact-sample c_u; and for all sands and gravels, whose permeability is high enough that they drain essentially as fast as they are loaded. In routine Canadian practice on a soft clay site, both cases are checked and the governing one adopted — CFEM treats the two as complementary rather than alternative.

Laboratory determination. The reference test is the unconsolidated–undrained (UU) triaxial test on an undisturbed sample, run at a cell pressure representing the in-situ total stress and sheared with drainage closed; for a saturated specimen the deviator stress at failure is independent of cell pressure, the Mohr envelope is horizontal and c_u = q_f/2. The unconfined compression test is the same measurement without a cell pressure and gives c_u = q_u/2; it is quick and cheap but only valid for a clay strong enough to stand as a free cylinder. A consolidated–undrained (CU) triaxial with pore pressure measurement is the most informative test, because it yields c_u for the consolidation state imposed and the effective-stress parameters cʹ and φʹ needed for the long-term check, which is why it is the standard test for a staged construction design. The direct simple shear test better represents the horizontal-plane shearing under the centre of an embankment and avoids the triaxialʹs anisotropy bias. For rapid profiling, a laboratory vane, torvane or pocket penetrometer is used on the ends of tube samples, and the fall-cone gives c_u of remoulded material and hence the sensitivity.

The dominant source of error in all of these is sample disturbance. A thin-walled Shelby tube in a soft clay may lose 20 to 30 per cent of the in-situ strength, and stress relief on a stiff clay works the other way, so good practice pairs the laboratory values with an in-situ test rather than trusting either alone. In a sensitive Canadian marine clay — a Champlain Sea or Leda clay — disturbance can be catastrophic, and piston samplers with a large diameter are specified for that reason.

Field determination. The field vane shear test (ASTM D2573) is the classical in-situ measurement in soft to firm clay: a four-bladed vane is pushed to depth and rotated, and c_u follows from the torque at failure and the vane geometry. Because the test shears mostly on vertical planes and does so quickly, the measured value must be corrected for plasticity using Bjerrumʹs factor μ, which falls from about 1.0 at low plasticity index to roughly 0.6 at PI = 60 — omitting that correction on a high-plasticity clay overestimates the design strength by up to 40 per cent. Rotating the vane through ten turns and re-testing gives the remoulded strength and hence the sensitivity, which is the key index for Canadian sensitive clays.

The piezocone (CPTu) is now the workhorse, because it gives a continuous profile rather than a point value: c_u = (q_t − σ_v0)/N_kt, with the cone factor N_kt typically 10 to 20 and best calibrated against vane or triaxial results on the same site. Its pore-pressure channel also identifies thin drainage layers that no sampling programme would find. The flat dilatometer (DMT) and the pressuremeter (PMT) both give c_u together with a stiffness, the pressuremeter being particularly useful in stiff clay and weak rock where a vane cannot be pushed. A plate load test or a full-scale load test measures the mass response directly and is the final arbiter on an important project. SPT correlations of the form c_u ≈ 6N kPa exist but are crude, and in clay the SPT should be regarded as an indicator of consistency and a means of recovering a sample, not as a strength test — a point this subjectʹs papers make repeatedly.

Recommendation. A defensible programme on a clay site uses CPTu soundings to define the stratigraphy and a continuous strength profile, field vane tests at intervals to calibrate N_kt and measure sensitivity, and high-quality piston samples for UU and CU triaxial tests plus oedometer tests at the levels that govern. That combination gives an undrained profile for the short-term check, effective-stress parameters for the long-term check, and the c_v needed to decide which of the two actually governs.