16-Civ-B3 Geotechnical Design · December 2016

Question 3 of 9: Earth pressure and the relative movement of the retaining structure

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. Professional Engineers Ontario / Engineers Canada National Examinations, December 2016 — 98-Civ-B3 Geotechnical Design. Three hours, OPEN BOOK, any non-communicating calculator. Section A carries five discussion questions of 7 marks each (answer any four); Section B carries four design questions of 24 marks each (answer any three); the examinable total is 4 × 7 + 3 × 24 = 100 marks. All nine questions are worked below, because the set is a study resource rather than a timed attempt.

Reference texts (98-Civ-B3 / 16-Civ-B3 Geotechnical Design).

B. M. Das, Principles of Foundation Engineering, 9th ed. — subsurface exploration (Ch. 2), bearing capacity of shallow foundations (Ch. 3), settlement of shallow foundations including Schmertmann's strain-influence method (Ch. 5), retaining walls (Ch. 8), pile foundations (Ch. 11), drilled shafts (Ch. 12).
B. M. Das, Principles of Geotechnical Engineering, 9th ed. — shear strength (Ch. 12), lateral earth pressure (Ch. 13), slope stability (Ch. 15).
Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed. — the governing Canadian practice document for site investigation, in-situ testing, bearing resistance, deep foundations and earth-retaining structures.
R. F. Craig, Craig's Soil Mechanics, 9th ed. — effective stress, undrained versus drained behaviour, earth pressure, and the total-stress circular-arc slope analysis.
M. J. Tomlinson & J. Woodward, Pile Design and Construction Practice, 6th ed. — shaft adhesion in clay and under-reamed (belled) bored piles.
P. K. Robertson & K. L. Cabal, Guide to Cone Penetration Testing, 6th ed. — CPT interpretation and CPT-versus-SPT selection.

Sources of design charts and assumed values (page-1 Note 6). Note 6 requires the candidate to identify the source of every design chart and of every value assumed where the paper supplies none. They are named at the point of use and collected here:

Adhesion factor α = 0.55 for a drilled shaft in clay (Q6) — O'Neill and Reese (1999), reproduced in Das, Principles of Foundation Engineering, 9th ed., Section 12.9; the exclusion of the top 1.5 m and of one shaft diameter above the bell comes from the same source.
Bearing-capacity factor N_c^* = 9 (Q6) — Skempton (1951), as tabulated in Das, Section 11.11.
Overburden correction C_N = √(p_a/σ'_o) (Q7) — Liao and Whitman (1986), Das Principles of Geotechnical Engineering, Section 17.6.
SPT-to-friction-angle correlation (Q7) — Peck, Hanson and Thornburn (1974) as fitted by Wolff (1989); cross-checked against Kulhawy and Mayne (1990). Both are tabulated in Das, Principles of Foundation Engineering, 9th ed., Section 2.9.
Bearing-capacity factors and shape/depth factors (Q7) — Vesic (1973) and De Beer (1970), Das Sections 3.6 and 3.7.
Strain-influence diagram and the C₁, C₂ factors (Q7) — Schmertmann, Hartman and Brown (1978), Das Section 5.6; the modulus correlation E_s = 500(N₆₀ + 15) kPa is Bowles (1996), reproduced in the same section.
Rankine active coefficient for an inclined backfill (Q9) — Das, Principles of Geotechnical Engineering, 9th ed., Eq. (13.35); the base friction and adhesion reductions k₁ = k₂ = 2/3 are Das Section 8.4.
Unit weight of the submerged backfill (Q9) — assumed equal to the printed moist unit weight, 18 kN/m³, in the absence of a saturated value; the consequence of that assumption is bounded in the Q9 callout.

Section A

Question 3: Earth pressure and the relative movement of the retaining structure (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 statement means that lateral earth pressure is not a property of the soil alone. It is a boundary condition whose value is fixed by how much the wall has moved relative to the ground it retains, and by the direction of that movement. The same backfill, at the same density and the same depth, can push on a wall with less than half — or more than five times — the horizontal stress it exerts on a wall held rigidly in place. Which of those values applies is decided by the structure, not by the soil.

Figure 3.1 — Mobilised earth-pressure coefficient against wall movement. The active state is reached at a movement of roughly 0.001H in dense sand; the passive state needs one to two orders of magnitude more, and the at-rest value applies only while the wall does not move at all.

Consider an element of soil at depth z behind a smooth vertical wall. If the wall does not move, the soil is in the same one-dimensional condition it was in before the wall existed, and the horizontal effective stress is the at-rest value $\sigma'_h = K_0 \sigma'_v$, with $K_0 \approx 1 - \sin\phi'$ for a normally consolidated soil. Now let the wall translate or rotate away from the backfill. The soil behind it extends laterally, so σ'_h falls while σ'_v stays put; the Mohr circle grows until it touches the failure envelope, at which point the soil is shearing and no further reduction is possible. That limiting minimum is the active state, $K_a = \tan^2(45^\circ - \phi'/2)$ for a level backfill and a smooth wall. If instead the wall is pushed into the soil, σ'_h rises until the circle touches the envelope from the other side, giving the passive maximum $K_p = \tan^2(45^\circ + \phi'/2)$.

The movements required are strikingly different, and that asymmetry is the practically important part of the statement. In a dense sand the active state is fully mobilised by a rotation about the base of roughly 0.001H — about 7 mm on a 7 m wall, which any ordinary gravity or cantilever wall accommodates simply by deflecting and settling during backfilling. The passive state needs something of the order of 0.02H to 0.05H, that is 150 to 350 mm on the same wall. In a soft clay both figures are several times larger again. Consequently a designer may count on the full active pressure almost for free, but must never count on the full passive resistance unless the movement needed to develop it is itself acceptable — which is why passive resistance in front of a wall toe is routinely reduced by a factor of two or simply neglected.

Practical example of active pressure being generated. Take the cantilever retaining wall of Question 9. It is cast against a trimmed face, the forms are struck, and the granular backfill is then placed and compacted in lifts behind the stem. Each lift adds vertical stress to the fill already in place and adds lateral thrust to the stem. The stem — a 6.1 m cantilever — deflects outwards at its top by a few millimetres, and the whole wall rotates very slightly about the front edge of its base as the foundation soil beneath the heel compresses more than that beneath the toe. That combined movement is more than enough to satisfy the roughly 7 mm needed for the wedge of soil behind the wall to reach its limiting extension. A wedge bounded by the plane rising at 45° + φ'/2 from the heel slips downwards and outwards by a millimetre or two; its self weight is partly carried by shear on that plane; and the horizontal stress on the wall settles at the active value. If the same wall were braced at its top against a structure — the classic case being a basement wall propped by the ground-floor slab — that movement could not occur and the design pressure would have to be the at-rest value, roughly 50 per cent higher, which is exactly what the codes require for propped basement walls.

Two practical riders follow. Over-compaction of the backfill locks in horizontal stresses well above active and can leave a stiff wall carrying close to at-rest pressures; this is why light plant is specified within a metre or so of a wall. And in a braced excavation the struts are installed progressively, so no single strut level ever experiences the free movement that a cantilever wall does; the earth pressures are redistributed by arching, and are designed for with empirical apparent-pressure envelopes rather than with a triangular active distribution.

Topic. Mobilisation of at-rest, active and passive earth pressure as a function of wall displacement.

Key relations. $\sigma'_h = K \sigma'_v$ with $K_0 = 1 - \sin\phi'$ (normally consolidated), $K_a = \tan^2\left(45^\circ - \phi'/2\right)$, $K_p = \tan^2\left(45^\circ + \phi'/2\right)$; the Rankine failure planes rise at $45^\circ + \phi'/2$ (active) and $45^\circ - \phi'/2$ (passive) from the horizontal.

Why this works. The soil element behind the wall starts on a Mohr circle that does not touch the failure envelope. Movement of the wall changes the horizontal stress while leaving the vertical stress essentially unchanged, so the circle grows in one direction or the other until it becomes tangent to the envelope. Once it is tangent the soil is failing and the stress cannot change further, which is what makes K_a and K_p limiting values rather than arbitrary ones.

Common pitfall. Assuming active and passive develop at the same displacement, and therefore taking full passive resistance in front of a wall toe in the same calculation that assumes full active behind it. The two states are compatible only if the wall is allowed to move far enough for the passive side, which is usually unacceptable in service.

Source. Das, Principles of Geotechnical Engineering, 9th ed., Sections 13.1 to 13.5 (at-rest, Rankine active and passive, and the wall-movement requirements); CFEM, 4th ed., Ch. 26 (earth pressures on retaining structures).

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