16-Civ-B3 Geotechnical Design · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations, May 2017 — 16-Civ-B3 Geotechnical Design; three hours, open book, any non-communicating calculator. Section A holds five discussion questions worth 7 marks each of which four are marked; Section B holds four design questions worth 24 marks each of which three are marked, so 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 marked script.
Reference texts. B. M. Das, Principles of Foundation Engineering, 7th–9th ed. (Cengage); B. M. Das, Principles of Geotechnical Engineering; R. F. Craig, Craig's Soil Mechanics, 8th ed. (Knappett & Craig); Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed.; J. E. Bowles, Foundation Analysis and Design; ASTM D1586 (SPT) and D5778 (CPT).
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.
Part 1 — the need for correction. The raw field blow count N is not a soil property. It is the number of blows to drive a standard split-spoon sampler 300 mm, and that number depends as much on the equipment and the depth of the test as on the sand itself. Every published correlation — relative density, friction angle, allowable bearing pressure for 25 mm settlement, liquefaction resistance — was calibrated against a corrected value, so applying a correlation to a raw N is a category error that can be wrong by a factor of two. Four corrections matter in practice.
Energy ratio. The theoretical free-fall energy of the 63.5 kg hammer dropping 762 mm is 475 J. The energy actually delivered to the rod string is between about 45 per cent of this for a rope-and-cathead system with a donut hammer and about 80 per cent for an automatic trip hammer. Because blow count is inversely proportional to delivered energy, the same sand gives roughly half the blow count under an efficient hammer. The corrected value is referenced to 60 per cent, N60 = N × (ER/60), and this correction alone can change a design by more than any other.
Overburden pressure. Penetration resistance in a sand rises with confining stress at constant relative density, so a shallow test and a deep test in the same uniform deposit return quite different N values. Correlations with relative density and friction angle require the value normalised to a reference stress of one atmosphere, (N1)60 = CN N60, with the Liao and Whitman form CN = (pa/sigma'v)0.5 capped at about 1.7. Without it a loose shallow sand and a dense deep sand can return the same raw N.
Rod length, borehole diameter and sampler configuration. Below about 10 m the rod string reflects the stress wave efficiently and no correction is needed, but at shallow depths the short rod string returns the wave before penetration is complete and the blow count is inflated, so CR falls to about 0.75 for rods shorter than 4 m. A borehole larger than 115 mm relaxes the surrounding sand and lowers N, giving CB of 1.05 to 1.15. A split-spoon designed for a liner but used without one gives lower friction on the sample and a blow count about 10 to 20 per cent low, corrected by CS.
Fine sands and silty sands below the water table. A dense fine sand or silty sand dilates when sheared rapidly by the sampler, generating negative pore pressure and a temporarily inflated resistance. Terzaghi and Peck's correction, N' = 15 + 0.5(N60 − 15) for N60 greater than 15, removes this artefact. Finally, the whole test must be judged against the material: in gravel a single particle jammed in the shoe destroys the reading, and in soft clay the test has poor resolution.
Part 2 — stability or settlement in dense sand? Settlement governs, and usually by a wide margin. The reason is that the two limit states scale quite differently with the friction angle. Bearing capacity depends on the bearing-capacity factors, which grow exponentially with phi': at phi' = 40 degrees, Nq and Ngamma are of order 64 and 109, so a 3 m wide strip footing at 1.5 m depth in a sand of unit weight 19 kN/m3 has an ultimate bearing capacity of about 5144 kPa and, at a factor of safety of 3, an allowable pressure of about 1715 kPa. Settlement, by contrast, depends on the soil stiffness, which grows only roughly linearly with penetration resistance. Meyerhof's rule for 25 mm of settlement of a footing on sand, qall = 11.98 N60[(3.28B + 1)/(3.28B)]2 kPa with B in metres, gives about 509 kPa for the same footing at N60 = 35. The serviceability pressure is therefore about one third of the pressure the ground could carry, and it is the serviceability pressure that the engineer must use.
Three further reasons reinforce this. Dense sand is stiff but not infinitely so, and settlement occurs essentially immediately as the structure is built, so it is not relieved by construction sequencing as consolidation settlement of a clay partly is. Differential settlement, not total settlement, damages a structure, and in a natural sand deposit the variability of stiffness from footing to footing is large, so a substantial part of the allowable 25 mm is consumed by differential movement. And the consequences differ in kind: a bearing-capacity failure in dense sand would require a load several times the design load, whereas exceeding the settlement criterion merely requires the stiffness to be somewhat lower than assumed. The engineering conclusion is that in dense sand the footing size is chosen from a settlement calculation and the bearing-capacity check is a formality that is satisfied automatically — the reverse of the situation in a soft clay, where the undrained bearing capacity is low and stability governs.
