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.
The observation is captured in design practice by the adhesion factor $\alpha$ in the total-stress ($\alpha$) method, where the unit shaft resistance is written $f_s = \alpha\, c_u$. Field and load-test evidence places $\alpha$ near unity in soft normally consolidated clays and between about 0.3 and 0.5 in stiff, heavily overconsolidated clays. Das tabulates $\alpha = 1.00$ for $c_u/p_a \le 0.1$ falling to $\alpha \approx 0.30$ at $c_u/p_a = 2.8$ (with $p_a = 100$ kPa). The reasons are physical, not empirical fudging, and they divide into what happens during installation and what happens afterwards.
Installation effects. Driving a displacement pile into soft clay completely remoulds a thin annulus of soil and generates large positive excess pore pressures — often approaching the total overburden pressure. The clay is destructured, so its immediate strength is low, but the excess pore pressure then dissipates radially and the annulus reconsolidates against the pile shaft under an increased effective stress. This is the well-documented phenomenon of set-up, and it restores the shaft strength to roughly the intact undrained strength, sometimes above it. In stiff clay the opposite sequence occurs. The soil is dilatant in shear, so installation generates negative excess pore pressures; as these dissipate, water migrates toward the shaft from the surrounding mass, the clay adjacent to the pile softens and swells, and the long-term shaft strength is lower than the strength that was measured on an undisturbed specimen before construction. A driven pile in stiff clay also opens a gap near the ground surface and shears a polished, remoulded skin against the shaft, in which the mobilised strength tends toward the remoulded or even the residual value rather than the peak.
Mass strength versus specimen strength. Stiff overconsolidated clays are almost always fissured. An undrained triaxial or unconfined test is performed on an intact 38–75 mm specimen selected, in practice, from between the fissures, so the laboratory $c_u$ substantially overstates the strength of the clay mass along a metres-long shaft that must cross many fissures. Soft clays are not fissured in this way, and the specimen strength is a fair estimate of the mass strength.
Progressive failure and brittleness. Stiff clay is brittle: it reaches a peak at small strain and then strain-softens. As a pile is loaded the shaft resistance is not mobilised uniformly — the upper shaft reaches and passes its peak while the lower shaft is still on the rising branch — so the average adhesion at the ultimate load is well below the peak $c_u$. Soft clay is ductile and can mobilise its strength almost simultaneously over the full shaft length, so the averaging penalty is small.
Practical consequence. For the stiff-clay case a total-stress design should be checked against an effective-stress ($\beta$) calculation, and both should be calibrated against a static load test, which is why CFEM recommends load testing wherever shaft resistance in overconsolidated clay dominates capacity.
