16-Civ-B3 Geotechnical Design · December 2014

Question 3 of 10: Earth pressure and relative wall movement; how passive pressure is generated

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 2014 — 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 five design questions of 24 marks each (answer any three); the examinable total is 4 × 7 + 3 × 24 = 100 marks. All ten 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. — bearing capacity (Ch. 3), stress increase in a soil mass (Ch. 6), retaining walls (Ch. 8), pile foundations (Ch. 11).
B. M. Das, Principles of Geotechnical Engineering, 9th ed. — lateral earth pressure (Ch. 13), shear strength (Ch. 12), slope stability (Ch. 15), subsurface exploration (Ch. 17).
Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed. — the governing Canadian practice document for site investigation, bearing resistance, deep foundations and earth-retaining structures.
R. F. Craig, Craig's Soil Mechanics, 8th ed. — earth pressure theory and slope stability.
D. P. Coduto, Foundation Design: Principles and Practices, 2nd ed. — in-situ testing and SPT correlations.
J. E. Bowles, Foundation Analysis and Design, 5th ed. — bearing capacity factors and retaining-wall stability tables.

Sources of charts and assumed values (page-1 Note 6). Note 6 of this paper requires the candidate to identify the source of every design chart and every assumed value. Each chart reading and each assumption below is therefore named where it is used, and the values assumed in the absence of data are collected here:

Q6 — adhesion factor α from Das, Principles of Foundation Engineering, Table 11.6 (Terzaghi, Peck & Mesri form, α against $c_u/p_a$); $\lambda$ from Vijayvergiya & Focht (1972) as tabulated by Das, Table 11.7.
Q7 — overburden correction $C_N$ from Liao & Whitman (1986); $\phi'$ from Wolff (1989) and from Hatanaka & Uchida (1996), both reproduced in Das, Ch. 2; settlement-controlled bearing pressure from Meyerhof (1965) as given by Das, Ch. 5, used only as a serviceability check because the question forbids direct correlations of bearing capacity to penetration index. Table I prints the blow counts as field values $N_f$; with no hammer data they are converted as $N_{60} = N_f$, i.e. a safety hammer at the reference 60 per cent energy ratio with borehole, sampler and rod-length factors of 1 (Das, Ch. 2, hammer-efficiency and correction-factor tables).
Q8 — embankment influence factor from Osterberg (1957), reproduced as Das Fig. 6.24; the closed form of that chart is used so the reading carries no chart-scaling error.
Q9 — Meyerhof general bearing-capacity equation with the shape factors of De Beer (1970) and the depth factors of Hansen (1970), as set out in Das, Ch. 3.
Q10 — Coulomb active earth-pressure coefficient, Das Eq. 13.31; unit weight of the mass-concrete wall assumed $\gamma_c = 24\ \text{kN/m}^3$ (CFEM 4th ed., normal-density concrete), the only value the figure does not supply.

Question 3: Earth pressure and relative wall movement; how passive pressure is generated (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.

Earth pressure is not a property of the soil alone; it is the boundary stress that happens to be compatible with the strain the wall permits. Until the wall moves, the soil behind it is in the state it was placed in, and the horizontal stress is the at-rest value $\sigma'_h = K_0 \sigma'_v$, with $K_0 \approx 1 - \sin\phi'$ for a normally consolidated soil. The Mohr circle for that state does not touch the failure envelope: the soil is nowhere near failure and the wall is carrying more load than either limiting theory would predict.

Figure 3.1 — Earth-pressure coefficient against wall displacement. The active state is reached after a very small outward movement; the passive state needs roughly an order of magnitude more movement, and the pressure it can deliver is about fifteen times larger.

Once the wall yields away from the backfill, the soil element behind it is allowed to expand laterally. The vertical stress is unchanged, so the horizontal stress falls, the Mohr circle grows, and when it touches the failure envelope the soil has reached the active state, $K_a = \tan^2(45^\circ - \phi'/2)$. The movement needed is remarkably small — roughly 0.001 of the wall height in a dense sand and 0.004 in a loose sand, rising to about 0.02 in a soft clay. Almost any real wall that is not propped will deliver that much, which is why the active case is the normal design assumption for a free-standing retaining wall.

If instead the wall is pushed into the backfill, the soil is compressed laterally, the horizontal stress rises above $\sigma'_v$, and the limiting passive state $K_p = \tan^2(45^\circ + \phi'/2)$ is reached. For $\phi' = 36^\circ$ the three coefficients are $K_a = 0.26$, $K_0 = 0.41$ and $K_p = 3.85$: a factor of about fifteen between the two limits, for a soil whose strength has not changed at all. The passive state, however, requires a much larger strain, of the order of 0.02 to 0.05 of the wall height, because the soil must be compressed rather than allowed to relax.

Example — how passive pressure is generated. Consider an anchored sheet-pile wall retaining a 7 m dredged cut, tied back at the top to a deadman anchor block. The active thrust on the retained side pushes the sheeting outward; the tie rod holds the top, so the sheeting rotates about the anchor and its embedded toe swings forward into the soil in front of the wall. That forward movement of the toe is what generates the passive resistance below dredge level, and free-earth-support design is simply the statement that moments about the anchor of the active thrust and of the passive resistance balance. The same mechanism appears at the deadman: as the tie rod pulls the block towards the water, the soil on the far face of the block is compressed and develops passive resistance, which is the anchor's entire holding capacity. Other everyday examples are the toe of a cantilever retaining wall bearing forward against the soil in front of it, and the abutment of an integral bridge, where thermal expansion of the deck in summer drives the abutment several millimetres into the backfill and cycles the pressure up towards $K_p$ year after year.

The practical consequence is that passive resistance must never be taken at full value. Because the deformation required is large — typically far larger than a structure can tolerate — CFEM and normal practice apply a factor of the order of 1.5 to 2 to the computed passive resistance, or mobilise only the fraction of $K_p$ consistent with the allowable movement, and disregard the passive contribution of any soil that could be excavated, scoured or allowed to loosen in the future.

Topic: the dependence of lateral earth pressure on wall movement; active, at-rest and passive limiting states.

Key relations: $K_0 \approx 1 - \sin\phi'$ (normally consolidated); $K_a = \tan^2\!\left(45^\circ - \dfrac{\phi'}{2}\right)$; $K_p = \tan^2\!\left(45^\circ + \dfrac{\phi'}{2}\right)$; hence $K_p / K_a = \tan^4\!\left(45^\circ + \dfrac{\phi'}{2}\right)$.

Why this works: both limiting coefficients come from the same Mohr circle touching the same failure envelope; only the direction in which the horizontal stress is driven differs. The at-rest state sits between them because the circle has not yet been expanded to touch the envelope, and the coefficient therefore depends on the stress history, not on failure.

Common pitfall: designing a propped or tied wall for active pressure when the prop prevents the movement that active pressure requires. A stiff, restrained wall — a basement wall cast against its own excavation, a bridge abutment on piles — must be designed for at least $K_0$, and for an over-consolidated or compacted backfill for more than that.

Source: B. M. Das, Principles of Geotechnical Engineering, 9th ed., Ch. 13 (Lateral earth pressure — at-rest, Rankine active and passive); CFEM 4th ed., Ch. 26 (Earth pressures against rigid walls); R. F. Craig, Craig's Soil Mechanics, 8th ed., Ch. 6.

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