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.
It will change, and the change can be in either direction. For a strip footing on sand with $c' = 0$ the ultimate bearing capacity reduces to
$$q_u = q\,N_q F_{qd} + \tfrac{1}{2}\,\gamma\, B\, N_\gamma F_{\gamma d}$$so every term depends on a quantity that is not a permanent property of the ground: the surcharge $q$ at founding level, the unit weight $\gamma$ that is mobilised in the failure wedge, and the bearing-capacity factors, which are exponential functions of the friction angle $\phi'$. Anything that alters the water regime, the density, the embedment or the stress level alters the capacity.
The dominant mechanism is the water table. A rise of the groundwater table into the failure zone replaces total unit weight by buoyant unit weight, roughly halving $\gamma$ in the $N_\gamma$ term and reducing the effective surcharge $q$ if the rise reaches above founding level. Because both terms shrink by nearly a factor of two, a seasonal or long-term rise from below the influence zone to founding level can reduce $q_u$ by about 50 %. This is not a hypothetical: irrigation, leaking services, loss of a pumping regime, river-level regulation and climate-driven changes in recharge all raise water tables over the life of a structure. Conversely, permanent dewatering raises capacity.
Changes in density and $\phi'$. Sand ages and creeps under sustained load; measured $\phi'$ and stiffness of freshly placed or freshly densified sand increase measurably over months to years, which raises capacity. Traffic and machine vibration densify loose sand but can also loosen very dense sand toward a critical state. Seismic shaking of a loose, saturated sand generates excess pore pressure and, in the limit, liquefaction, which removes almost all bearing capacity for the duration of the event; this is a live design case in coastal British Columbia. Because $N_q$ and $N_\gamma$ grow exponentially with $\phi'$, even a few degrees matter: at $\phi' = 30^\circ$, $N_q = 18.4$, while at $\phi' = 40^\circ$, $N_q = 64.2$.
Changes in embedment. Scour beside a watercourse, erosion of an unprotected slope, frost heave and thaw, adjacent excavation, service trenching along the footing and even landscaping that removes fill all reduce $D_f$ and therefore the $q N_q$ term, which for a shallow strip footing is usually the larger of the two.
A stress-level effect that is easy to miss. The strength envelope of sand is curved; the secant $\phi'$ mobilised at failure decreases as confining stress increases. A wide, heavily loaded footing therefore operates at a lower effective $\phi'$ than a small plate test on the same sand would suggest, so capacity does not scale linearly with $B$.
Conclusion for design. The capacity is not a constant. Design for the most adverse credible water level over the design life, take $\phi'$ from tests at the correct stress level, protect the embedment against scour and excavation, and remember that on sand the serviceability limit state — settlement — usually governs the allowable pressure long before the ultimate limit state does.
