07-Str-B1 · May 2015

Question 5 of 9: Investigation and Strength Parameters for a Highway Embankment Built of Highly Expansive Soil

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

Notes on this paper

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 5: Investigation and Strength Parameters for a Highway Embankment Built of Highly Expansive Soil (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.

Investigation. The programme has two halves: characterising the foundation deposit and characterising the borrow that will become the embankment. Along the alignment, sink boreholes and test pits at spacings of 100 to 200 m, closer at cut–fill transitions and at any watercourse crossing, and take continuous samples through the active zone — the depth over which seasonal moisture change occurs, typically 2 to 4 m in the Canadian prairies but deeper where desiccation cracks are visible. Block samples or thin-walled tube samples are essential, because the fabric that controls the strength of an expansive clay is its fissure and slickenside network, which an SPT split spoon destroys.

Identification and swell testing come next: Atterberg limits (highly expansive clays commonly have $LL > 60$ and $PI > 35$), grain size with hydrometer, activity $A = PI / (\%_{<2\mu m})$, the plasticity index divided by the clay-size fraction, free-swell index, and — the two tests that actually govern design — the oedometer swell potential under the anticipated overburden and the swell pressure at constant volume. Mineralogy by X-ray diffraction confirms smectite content. Because the strength of an unsaturated expansive clay is dominated by matric suction, measure the in-situ moisture and suction profile with depth and repeat it across a wet and a dry season (filter-paper method, thermal conductivity sensors or tensiometers), and determine the soil–water characteristic curve. Install standpipes and, if a perched table is likely, vibrating-wire piezometers.

Shear strength parameters for the stability analysis. Three distinct strengths are needed, and choosing among them is the heart of the question.

Short-term (end-of-construction) stability — undrained parameters $c_u$, $\phi_u = 0$ from unconsolidated-undrained triaxial tests on undisturbed foundation samples and on samples compacted to the specified placement moisture and density. This case governs while excess pore pressures from placement have not dissipated.
Long-term (drained) stability of the compacted fill — effective-stress parameters from consolidated-drained triaxial tests, or consolidated-undrained tests with pore-pressure measurement, on saturated specimens. For a compacted, fissured, highly plastic clay the correct envelope for a first-time slide is not the peak but the fully softened strength: $c' = 0$ with $\phi'_{fs}$ measured on a normally consolidated, remoulded specimen. Peak strengths measured on intact compacted specimens are lost as the fill wets, swells and softens through seasonal cycles, and using them is the classic cause of delayed slope failures in expansive fills.
Reactivated slides — if the investigation finds pre-existing shear surfaces, slickensides or evidence of ancient landsliding in the foundation, the operating strength is the residual $c'_r \approx 0$, $\phi'_r$ measured in a ring-shear (Bromhead) apparatus. For high-plasticity clays $\phi'_r$ can fall to 8–12°, which is far below any triaxial peak value.

The unsaturated strength envelope $\tau = c' + (\sigma - u_a)\tan\phi' + (u_a - u_w)\tan\phi^b$ explains why a freshly built, dry embankment appears stable: its suction supplies an apparent cohesion. That suction is not a design asset — it vanishes on wetting — so the long-term analysis must be run at zero suction with fully softened parameters and the worst credible pore-pressure regime.

Other design criteria. Flatten the slope (3H:1V or flatter is usual for high-plasticity fills) and consider benching; place the clay slightly wet of optimum at a moderate compactive effort, since compaction dry of optimum at high density maximises swell pressure; moisture-condition the borrow before placement and control it strictly during construction. Treat the outer 1.0 to 1.5 m of the slope as sacrificial: cap it with a non-expansive cover or stabilise it with lime, which reduces plasticity and swell durably. Provide comprehensive drainage — crowned and sealed shoulders, lined ditches, subsurface drains at the fill/foundation contact — because it is water, not load, that destroys these slopes. Add erosion protection and vegetation with a shallow root system; design for the volume change beneath the pavement structure (differential heave causes roughness long before the slope fails), for post-construction settlement of the foundation, for frost penetration, and for the seismic case. Finally, instrument the works with inclinometers and piezometers and monitor them for several seasonal cycles, since the critical condition for an expansive fill typically arrives years after opening.

Topic. Slope stability of embankments constructed from highly expansive (high-plasticity, swelling) clay.

Key relations. Effective-stress strength $\tau_f = c' + \sigma'\tan\phi'$; unsaturated form $\tau_f = c' + (\sigma - u_a)\tan\phi' + (u_a-u_w)\tan\phi^b$; fully softened envelope $c' = 0$, $\phi'_{fs}$; residual envelope $c'_r \approx 0$, $\phi'_r$; swell potential and swell pressure from the oedometer; activity $A = PI/(\%_{<2\mu m})$.

Why this works. An expansive clay loses strength by wetting rather than by loading. Cyclic wetting and drying opens fissures, destroys the cementation and structure that give an intact specimen its peak strength, and drives the mass toward the fully softened condition, which is simply the normally consolidated strength of the remoulded material. Because a first-time slide in such a fill develops progressively along a surface where different points are at different strains, the average mobilised strength cannot exceed the fully softened value; where a slip surface already exists, strains are large enough that only the residual strength remains.

Common pitfall. Designing with peak effective-stress parameters measured on intact, as-compacted specimens, which typically overstates long-term strength by a factor of two or more, and assuming the as-built suction will persist. A second pitfall is compacting the expansive clay to a high dry density well dry of optimum to satisfy a generic earthworks specification, which maximises the swell pressure the structure will later have to accommodate.

Source. Duncan, Wright & Brandon, Soil Strength and Slope Stability, 2nd ed., Ch. 5 (fully softened and residual strengths); Fredlund, Rahardjo & Fredlund, Unsaturated Soil Mechanics in Engineering Practice, Ch. 9 and 14; CFEM 4th ed., §9 (Special Soil Types) and §17 (Slopes).

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