07-Str-A3 · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. Engineers Canada / PEO National Examinations, May 2016 — 07-Str-A3 Geotechnical Materials and Analysis. Closed book, three hours, 100 marks, one approved Casio or Sharp calculator, drawing instruments required. All six questions are compulsory and are weighted 20 / 10 / 10 / 20 / 20 / 20. The paper carries its own appendix (pages 8–11): a formula sheet, the rectangular-loading m–n influence chart and a Newmark influence chart whose influence value is printed on the formula sheet as $\sigma_z = 0.005\,N q$, i.e. $I_N = 0.005$ over 200 elements. Values quoted below are taken from those sheets.
Reference texts.
Check — three readings of the printed paper, carried as stated.
(1) Question 1 is headed “(4 x 5 = 20 marks)” but prints five lettered parts (i)–(v). All five are answered and the header total of 20 marks is kept as printed; the mismatch is a printing slip in the source, not a missing part.
(2) Figure 1 (part (ii)) prints no dimension for the depth of the permeable stratum. The dam base is dimensioned $L = 15$ m and the section is drawn to a single horizontal scale, so the stratum has been scaled off the drawing at $T \approx 5.6$ m ($T/L = 0.37$). The answer to (ii) does not depend on that number — it is read from the printed flow net — but the independent numerical check below does, and the sensitivity is stated where it is used.
(3) In Figure 4 the stem of Question 5(b) says point $A$ is at the “back of the piling”, while the dot is drawn on the upstream (headwater) face of the sheet pile, 1 m below ground. The drawn face is answered, and the value on the downstream face at the same elevation is reported alongside it.
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.
Peat is not simply a very soft clay, and the answer has to start from why. Its solid phase is fibrous plant matter with a specific gravity of only about 1.4–1.7 rather than 2.65; its natural water content is commonly 200–1500 %; its void ratio can be 5 to 15 against 0.6–1.5 for an inorganic clay; and its compression index $C_c$ is measured in units, not in hundredths. The practical consequence is that the settlement is very large, that a large share of it is creep rather than consolidation, and that it continues for the design life of the structure rather than stopping at the end of primary consolidation. An analysis that computes only $C_c$ and Terzaghi time factors will underestimate the long-term movement badly.
Field work. The investigation is aimed first at the geometry of the deposit, because peat thickness varies sharply over short distances and the settlement is proportional to it. Continuous probing or dynamic cone soundings on a close grid map the base of the peat; test pits and a peat sampler — a Macaulay or Russian side-cut sampler, which recovers fibrous material that a thin-walled tube would shred — give the profile and undisturbed material for the laboratory. A piezocone (CPTu) with pore-pressure dissipation tests gives a continuous stratigraphic log and an in-situ $c_h$; the field vane is used with caution because the fibres reinforce the failure surface and inflate the reading. Piezometers and settlement plates are installed at the outset, and on any project of size a trial embankment or test fill is built and monitored: for peat this is the single most reliable predictor there is, and back-analysis of the observed settlement is worth more than any laboratory extrapolation.
Laboratory index tests. The classification tests establish that the material really is peat and how decomposed it is: organic content by loss on ignition (ASTM D2974) — above 75 % organic the material is classified as peat under ASTM D4427; fibre content and the von Post degree of humification H1 to H10; natural water content; specific gravity of solids; bulk density; and pH and ash content, which matter for the durability of any buried concrete or steel.
The controlling test: one-dimensional consolidation. An oedometer test — incremental loading, or constant rate of strain — is run on undisturbed specimens through the stress range the structure will impose. Two features distinguish a peat oedometer test from a routine one. Each load increment must be held long enough (a week or more, not the standard 24 hours) for the secondary branch to be established as a straight line on the $\log t$ plot, because that branch is the answer. And the results are best expressed as strains rather than void ratios, since $e_0$ is so large that the conventional forms become clumsy.
| Parameter | Symbol | Where it comes from | Typical value in peat |
|---|---|---|---|
| Initial void ratio | $e_0$ | phase relations from $w$, $G_s$, $\gamma$ | 5–15 |
| Preconsolidation pressure | $\sigma_p'$ | Casagrande construction on the $e$–$\log\sigma'$ plot | small; often only a desiccation crust |
| Compression index / ratio | $C_c$, $C_{c\varepsilon}=C_c/(1+e_0)$ | slope of the virgin line | $C_c$ 2–10; $C_{c\varepsilon}$ 0.3–0.6 |
| Recompression index | $C_r$ | unload–reload loop | $\approx 0.1\,C_c$ |
| Coefficient of consolidation | $c_v$ | $\sqrt{t}$ or $\log t$ fitting of each increment | high initially, falls by an order of magnitude |
| Secondary compression index | $C_\alpha$, $C_{\alpha\varepsilon}$ | slope of the straight branch after $t_p$ | $C_{\alpha\varepsilon}$ 0.02–0.08 |
| Creep ratio | $C_\alpha/C_c$ | from the two above | 0.04–0.06 — the highest of any soil |
How the analysis proceeds. The total settlement is assembled from three parts, computed in order.
Immediate settlement $s_i$ is the undrained distortion under the load, estimated from elasticity with an undrained modulus back-figured from the trial fill or from $E_u \approx 100$–$300\,s_u$. It is usually a small part of the total in peat and is often absorbed into the construction tolerance.
Primary consolidation $s_c$ follows from the oedometer parameters applied layer by layer, using the recompression branch while the stress stays below $\sigma_p'$ and the virgin branch above it:
$$s_c = \sum_j H_j\left[C_{r\varepsilon}\log\frac{\sigma_p'}{\sigma_{0}'} + C_{c\varepsilon}\log\frac{\sigma_{0}'+\Delta\sigma'}{\sigma_p'}\right]_j ,$$with the vertical stress increment $\Delta\sigma'$ at the middle of each sub-layer taken from an elastic distribution of the kind computed in Question 4. Its rate comes from $T_v = c_v t/H_{dr}^2$, but the answer must record that $c_v$ is not constant in peat — it falls sharply as the void ratio collapses — so a staged calculation with an updated $c_v$ is more defensible than a single time factor. In practice primary consolidation in peat is fast, weeks to a few months, because the layers are thin and the initial permeability is high.
Secondary compression $s_s$ is the part that decides the design, and it is computed from the straight branch of the $\log t$ plot:
$$s_s = C_{\alpha\varepsilon}\,H\,\log_{10}\!\left(\frac{t}{t_p}\right).$$For a 3 m peat layer with $C_{\alpha\varepsilon} = 0.05$, primary complete after one year and a 30-year design life,
$$s_s = (0.05)(3000\ \text{mm})\log_{10}\!\frac{30}{1} = (0.05)(3000)(1.4771),$$ $$\boxed{s_s \approx 222\ \text{mm of creep alone, after primary consolidation has finished}}$$which is why the analysis cannot stop at $s_c$.
The estimate is then compared against what the structure can tolerate, and if it cannot, the report moves to mitigation rather than to a more refined calculation. The options, roughly in order of increasing cost, are: preloading with a temporary surcharge, which pushes the peat past the design stress so that the structure sees only the flatter recompression branch and much of the creep is spent in advance; staged construction with monitoring, since bearing failure of the fill, not settlement, often governs the rate at which load can be applied; lightweight fill (EPS geofoam, expanded shale, wood chips) to reduce the load itself; excavation and replacement, which is usually economic where the peat is less than about 3–4 m thick; or piles or a piled raft carried to a competent stratum, with the slab structurally suspended and a void beneath it, accepting that negative skin friction from the settling peat must be added to the pile load. Whichever is chosen, an observational approach with settlement plates and piezometers is written into the specification, because the back-analysis is more trustworthy than the prediction.
