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16-Civ-B3 Geotechnical Design · December 2013

Question 4 of 9: Why long-term slope stability is checked with a smaller margin

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. National Examinations, December 2013 — 98-Civ-B3 Geotechnical Design. Three hours, open book, any non-communicating calculator. Section A holds five 7-mark discussion questions (answer any four); Section B holds four 24-mark design questions (answer any three), so the examinable total is 4 × 7 + 3 × 24 = 100 marks. Every one of the nine questions is answered here, because the set is a study resource rather than a sitting.

Reference texts. B. M. Das, Principles of Foundation Engineering (9th ed.) and Principles of Geotechnical Engineering (9th ed.); Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM, 4th ed.) — the governing Canadian reference for foundation practice; R. F. Craig, Craig's Soil Mechanics (9th ed.); D. P. Coduto, Foundation Design: Principles and Practices (3rd ed.).

Sources of design charts and assumed values (paper Note 6). The paper requires every chart and assumed value to be identified. Bearing-capacity factors are Terzaghi’s (Das, Foundation Engineering, Table 3.1, with Nγ after Kumbhojkar 1993); the pile end-bearing factor Nq* is read from Meyerhof’s chart (Das Fig. 11.14) and cross-checked against Janbu’s closed-form expression; the adhesion factor α is Das Table 11.5 (Terzaghi, Peck & Mesri); the strain-influence distribution is Schmertmann, Hartman & Brown (1978). Assumed values — specific gravity of solids Gs = 2.65 for the Question 8 backfill, base friction δ = ⅔φ′ and base adhesion ca = ⅔c′ (CFEM §24), and a driving-parameter value K = 1.4K0 for a high-displacement driven pile (Das §11.11) — are flagged where they are used.
Check — Question 6 text and figure disagree. The printed text of Question 6 states a 1 m × 1 m square footing with γ = 20 kN/m³ and φ = 36°, while Figure 3 is drawn for a 2.5 m footing with γ = 18 kN/m³ and φ′ = 38°. The question text governs (it is the instruction to the candidate); the figure is used only for the embedment Df = 1.5 m and for the CPT modulus profile, which the text does not restate. The alternative reading is noted at the end of the answer.

Question 4: Why long-term slope stability is checked with a smaller margin (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.

A factor of safety is a margin against uncertainty, not a fixed number, so it should be set by how well the governing condition is known. Three things make the long-term condition better known than the short-term one, and each justifies a smaller margin.

The parameters are more reliable. Long-term stability is an effective-stress problem governed by $c^{\prime}$ and $\phi^{\prime}$, which are genuine soil properties: they are reproducible between specimens and between laboratories, they do not depend on sampling disturbance to nearly the degree that $c_u$ does, and they do not change with the rate at which the test is run. The undrained strength that governs the end-of-construction case is not a property at all but a response, dependent on the consolidation state, the stress path and the sampling history, and in a compacted fill it is also dependent on placement water content. A parameter known to 5 % deserves a smaller factor than one known to 30 %.

The loading condition is stable and observable. By the time the dam has been in service for years the pore pressures have reached a steady seepage regime that can be drawn as a flow net, measured with piezometers and checked against the phreatic surface. The end-of-construction pore pressures, by contrast, depend on the rate of placement, the compaction water content and the drainage path, and they can only be estimated. A condition that can be monitored and corrected needs less built-in conservatism than one that must be guessed once.

The consequence of the short-term case is different. The critical short-term states — end of construction for the upstream and downstream faces, and rapid drawdown for the upstream slope — are transient, and a failure during them happens while the reservoir is empty or falling and while the contractor is on site. A long-term failure occurs under full reservoir with the dam in service. In practice this cuts the other way for consequence, which is why the numbers do not fall very far: typical Canadian and international dam practice takes about FS ≥ 1.5 for long-term steady seepage, 1.3 for end of construction and 1.1–1.2 for rapid drawdown — the long-term figure is the largest of the three in absolute terms, but it is the one applied to the best-known parameters, and the transient cases are permitted lower values precisely because they are short-lived. Where the question’s wording bites is in comparing a long-term effective-stress analysis with a short-term total-stress analysis of the same slope: the drained analysis is allowed the smaller margin because its inputs are the more trustworthy.

Parameters and properties required. The effective-stress shear-strength parameters $c^{\prime}$ and $\phi^{\prime}$ for the core, the outer zones and the foundation; the residual parameters $c^{\prime}_r \approx 0$ and $\phi^{\prime}_r$ where a pre-existing slip surface, a fissured clay or a bedding plane may control; the bulk and saturated unit weights $\gamma$ and $\gamma_{sat}$; the pore-pressure regime, expressed either as a phreatic surface with a flow net or as a pore-pressure ratio $r_u = u/\gamma z$; the coefficient of permeability $k$ (and its anisotropy $k_h/k_v$) for the seepage analysis; the coefficient of consolidation $c_v$ if the transition from the undrained to the drained state has to be timed; and the index properties (Atterberg limits, clay fraction, activity) that indicate swelling, dispersivity and the likely drop from peak to residual strength.

Tests recommended. For the strength parameters, consolidated-drained (CD) triaxial tests on saturated specimens are the direct measurement, but in a clay of low permeability they are very slow, so the practical choice is consolidated-undrained triaxial tests with pore-pressure measurement (CU-bar), which give the same effective-stress envelope in a fraction of the time; run them at three confining pressures bracketing the in-situ stress, on specimens compacted to the specified placement density and water content. Add slow drained direct shear or, better, ring-shear tests to obtain the residual angle where a pre-existing shear surface or a stiff fissured clay is present. For the pore-pressure regime, run falling-head or constant-head permeability tests in the oedometer/triaxial cell and in-situ packer or field pumping tests in the foundation, and install vibrating-wire piezometers in the core, the filters and the foundation for construction and operational monitoring. Run oedometer tests for cv and compressibility, and standard classification tests (Atterberg limits, grading, hydrometer, standard Proctor compaction) on every borrow source. Where the outer zone is granular, in-situ density and CPT profiling complete the set.