True or false — is the undrained friction angle zero for both soils?: 16-Civ-B3 Geotechnical Design, Undated paper, Q3

Question 3: True or false — is the undrained friction angle zero for both soils? (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.

Answer: FALSE, as a general statement. The result $\phi_u=0$ is not a property of clay; it is a property of a fully saturated soil tested undrained. Neither an expansive clay nor a glacial till can be assumed fully saturated in the state in which it is normally sampled and tested, so neither can be assumed to give a horizontal undrained envelope.

Unconsolidated-undrained triaxial tests at three cell pressures. Saturated (left): every circle has the same diameter and the envelope is horizontal. Partly saturated (right): the air voids compress, the effective stress rises with cell pressure, and the envelope curves upward.

Why $\phi_u=0$ holds when the soil is saturated. In an unconsolidated-undrained test the drainage line is shut from the outset, so no water leaves or enters. Skempton’s pore-pressure equation for an isotropic increment is $\Delta u = B\,\Delta\sigma_3$, and for a fully saturated soil $B=1$ because water is effectively incompressible relative to the skeleton. Raising the cell pressure therefore raises the pore pressure by exactly the same amount, and the effective confining stress is unchanged:

$$\begin{aligned}\sigma_3'&=\sigma_3-u \quad\Rightarrow\quad \Delta\sigma_3' \\ &=\Delta\sigma_3-B\,\Delta\sigma_3 \\ &=0 \quad (B \\ &=1).\end{aligned}$$

Every specimen therefore fails at the same deviator stress, all the total-stress Mohr circles have the same diameter, and the envelope tangent to them is the horizontal line

$$\boxed{\tau_f=c_u=\tfrac{1}{2}(\sigma_1-\sigma_3)_f,\qquad \phi_u=0 }$$

which is the familiar $\phi=0$ result. Note what it is not: it is not a statement that the soil has no friction. The effective-stress friction angle $\phi'$ of both these soils is perfectly ordinary; $\phi_u=0$ merely records that in a saturated undrained test the cell pressure never reaches the skeleton.

Soil A, expansive clay. Expansive clays are the classic counter-example, because their engineering problem is that they sit above the water table in a partly saturated, desiccated state and change volume with moisture. For a partly saturated specimen $B \lt 1$ — often well below 0.5 at low degrees of saturation — so part of each cell-pressure increment goes into compressing and dissolving the air voids and into the matric suction, and the effective stress rises. Successive Mohr circles then grow with cell pressure, and the envelope curves upward with an apparent $\phi_u$ of typically 5 to 15 degrees over the usual range. The envelope only flattens once the cell pressure has been raised far enough to drive the specimen to full saturation. Sampling and trimming a desiccated expansive clay also releases suction and lets the specimen swell, which changes $c_u$ before the test starts.

Soil B, glacial till. A till is a dense, heavily overconsolidated, well-graded mixture running from clay to cobbles. Three separate effects break the $\phi_u=0$ idealisation. It is commonly unsaturated above the water table, so the argument above applies. Its coarse fraction means the specimen is not truly undrained at the standard strain rate: local drainage and pore-pressure redistribution occur within the specimen during shear, so the measured strength rises with cell pressure. And a 50 or 100 mm specimen of a soil containing gravel is not representative, so the scatter between the three circles is often larger than the trend one is trying to read. In practice a UU envelope on till is reported with a small but non-zero $\phi_u$.

Correct form of the statement. It becomes true if it is qualified: for fully saturated specimens of both soils, unconsolidated undrained triaxial tests give $\phi_u=0$ and a strength that is independent of cell pressure. Without that qualification it is false, and the practical consequence is real: a design that takes $c_u$ from a UU test on a partly saturated sample has taken a suction-enhanced strength that will be lost the first time the soil wets up.

Topic. The $\phi_u=0$ concept and the conditions under which it is valid.

Key relations. $\Delta u=B[\Delta\sigma_3+A(\Delta\sigma_1-\Delta\sigma_3)]$; $B=1$ for $S_r=100\%$ and $B \lt 1$ otherwise; $\sigma'=\sigma-u$; $c_u=\tfrac{1}{2}(\sigma_1-\sigma_3)_f$.

Why this works. In a saturated undrained test the whole of an all-round total stress increment is carried by the pore water, so the effective stress state at failure, and hence the strength, is fixed by the water content the specimen arrived with, not by the cell pressure the operator chose.

Common pitfall. Reading $\phi_u=0$ as a soil property and applying it to any clay. It is a test condition, and it fails for unsaturated, fissured, or coarse-grained soils, and for any soil allowed to consolidate under the cell pressure before shear.

Source. Das, Principles of Geotechnical Engineering, 9th ed., ch. 12 (shear strength); Craig’s Soil Mechanics, 8th ed., ch. 5; CFEM 4th ed., ch. 3.

Question 3 of 9: True or false — is the undrained friction angle zero for both soils?

Question 3: True or false — is the undrained friction angle zero for both soils? (7 marks)