07-Str-B1 · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Examinations — May 2015 — 07-Str-B1 Geotechnical Design. Three-hour, OPEN-BOOK exam; any non-communicating calculator permitted (the candidate must record its make and model). Format: Section A carries five discussion questions of 7 marks each, of which any FOUR are to be answered; Section B carries four design problems of 24 marks each, of which any THREE are to be answered — a marked total of 100. The paper instructs candidates to state any interpretive assumptions, to identify the source of every design chart and assumed value, and to exercise sound engineering judgment where data are absent. All nine printed questions are worked below, because the set is intended as a study resource.
Reference texts: Das, B.M., Principles of Foundation Engineering (9th ed., Cengage) — general bearing-capacity equation, pile and pile-group capacity, consolidation settlement of footings, retaining walls; Das, B.M., Principles of Geotechnical Engineering (9th ed., Cengage) — lateral earth pressure, effective stress, consolidation theory; Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM, 4th ed., 2006) — Canadian practice for site investigation, SPT/CPT interpretation, pile design and tolerable settlement; Craig, R.F. / Knappett, J.A., Craig's Soil Mechanics (8th ed., CRC Press) — shear strength and earth-pressure theory; Duncan, J.M., Wright, S.G. & Brandon, T.L., Soil Strength and Slope Stability (2nd ed., Wiley) — fully softened and residual strengths for fissured and expansive clays; Fredlund, D.G., Rahardjo, H. & Fredlund, M.D., Unsaturated Soil Mechanics in Engineering Practice (Wiley) — swelling soils and matric suction.
Note — Figure 2 is printed over a coarse halftone. The soil-property annotations inside the photograph-style Figure 2 (Question 8) are printed over a coarse dot screen. The values used below are read from the printed figure and are: upper sand $\gamma = 15\ \text{kN/m}^3$ over 1.5 m, lower sand $\gamma_{sat} = 18\ \text{kN/m}^3$ over 1.5 m, normally consolidated clay 2.5 m thick with $w = 35\%$ and $LL = 48$, over sand; groundwater table at the underside of the footing.
Assumptions declared once, applied throughout. $\gamma_w = 9.81\ \text{kN/m}^3$; reinforced concrete $\gamma_c = 24\ \text{kN/m}^3$; specific gravity of soil solids $G_s = 2.70$ where a void ratio must be back-figured from water content; loads are vertical and concentric unless stated. Every assumption that changes a numerical answer is repeated in the question where it is used.
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 reaction that develops on a boundary in response to the strain imposed on the soil behind it. The statement therefore says that lateral pressure is a displacement-controlled quantity, and the whole of classical earth-pressure theory is built on that idea.
The at-rest condition. If a wall does not move at all, the soil remains in the one-dimensional condition in which it was deposited, and the horizontal effective stress is $\sigma'_h = K_0 \sigma'_v$ with $K_0 \approx 1 - \sin\phi'$ for a normally consolidated soil. For $\phi' = 30^\circ$ this gives $K_0 = 0.50$. Overconsolidated soils carry a locked-in $K_0$ that can exceed 1.0.
The active condition. If the wall yields away from the soil, the soil expands laterally, the horizontal stress falls, the Mohr circle grows until it touches the failure envelope, and the pressure reaches the minimum value the soil can sustain: $K_a = \tan^2(45^\circ - \phi'/2) = 0.333$ for $\phi' = 30^\circ$. Only a very small outward movement is needed — roughly $0.001H$ for dense sand and $0.004H$ for loose sand, and $0.01H$ to $0.02H$ for clays.
The passive condition. If the wall is pushed into the soil, the soil is compressed laterally, the horizontal stress rises until failure is again reached, and the pressure attains the maximum the soil can supply: $K_p = \tan^2(45^\circ + \phi'/2) = 3.00$ for $\phi' = 30^\circ$. The movement required is an order of magnitude larger — of the order of $0.01H$ to $0.05H$ in sand and up to $0.1H$ in clay — because the soil must be compressed rather than allowed to relax. Between the extremes the pressure varies continuously, so a rigid, propped or tied structure that is prevented from moving attracts something close to at-rest pressure, which is 50 % greater than active for the sand above.
An example of passive pressure being generated. Consider an anchored sheet-pile quay wall. The retained soil pushes the wall outward, the wall rotates about a point near the tie rod, and the buried toe of the sheet pile is driven forward, into the soil in front of it. That forward movement of the embedded length compresses the soil ahead of the toe, mobilising passive resistance, and it is that passive block — together with the tie-rod force — that holds the wall. The free-earth-support design method is precisely a statement that the passive resistance below dredge level, reduced by a factor of safety of about 1.5 to 2 on $K_p$, must balance the active thrust above it. Two further everyday examples are the toe of a gravity retaining wall, whose forward sliding is resisted by passive pressure on the buried face of the base slab, and a deadman anchor block, which resists the tie rod purely by the passive wedge that develops in front of it.
The design lesson is that passive resistance should be relied on cautiously: because it needs large movement, and because that movement may be unacceptable to the structure or may be removed by future excavation in front of the wall, it is usual either to neglect it entirely (as is done in Question 9 below) or to apply a large factor of safety to it.
