16-Civ-A4 Geotechnical Materials and Analysis · May 2017

Question 1 of 5: Compaction, Structure, Gradation and Undrained Strength

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

Notes on this paper

Paper format: PEO/EGBC National Examination 16-Civ-A4 — Geotechnical Materials and Analysis, May 2017. Closed book, 3 hours, 100 marks. Answer ALL questions (5 × 20 marks). All required charts and equations were supplied at the back of the paper.

Reference texts: Das, B.M. & Sobhan, K., Principles of Geotechnical Engineering, 9th ed. (Cengage); Holtz, Kovacs & Sheahan, An Introduction to Geotechnical Engineering, 2nd ed.; Knappett & Craig, Craig’s Soil Mechanics, 8th ed.; Budhu, Soil Mechanics and Foundations, 3rd ed.

Check (source figures): Q2’s flow net is a hand-drawn sketch; the counts used (N_d = 10, one drop to B and nine to A) were taken from the printed net and carry the usual ±1-field tolerance. Void ratio (e₀), C_c and the preconsolidation break in Q4’s Figure 4(a), and the OCR–A_f read in Q3’s Figure 3, are read off hand-plotted curves. Conclusions are robust to these reading tolerances; each is flagged where it bites.

Question 1: Compaction, Structure, Gradation and Undrained Strength (4 × 5 = 20 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.

(i) Saturated permeability at points A, B and C

[Figure not reproduced: Figure 1 from the exam: compaction curves with points A, B and C. See the official exam paper or the cited reference text.]

Figure 1 (exam figure): A is on the low-effort curve, dry of optimum (flocculated); B is on the high-effort curve at the same water content as A; C is on the low-effort curve, wet of optimum, at the same dry density as A (dispersed).

Permeability of a compacted fine-grained soil is controlled far more by fabric than by water content alone. Compacting dry of optimum produces a flocculated (edge-to-face, randomly oriented) fabric with large, well-connected inter-aggregate pores — a high permeability path. Compacting wet of optimum re-orients the platelets into a dispersed (parallel, face-to-face) fabric that closes those macro-pores and forces a tortuous flow path — a low permeability. Superimposed on this, a higher dry density (smaller void ratio) always lowers permeability.

Reading Figure 1: the vertical dashed line puts A and B at the same water content on the dry side (A on the low-effort curve, B on the high-effort curve); the horizontal dashed line puts A and C at the same dry density (C on the low-effort curve, wet of optimum).

Highest k — point A. A is dry of optimum with a flocculated, open fabric and has the lowest dry density of the three, so it has the largest, best-connected pores. Lowest k — point C. C has the same dry density as A but lies wet of optimum, so its fabric is dispersed; at equal void ratio a dispersed fabric is much less permeable than a flocculated one (often by one or more orders of magnitude). Point B sits between them: it is still dry of optimum, but the higher effort makes it denser and partly re-orients the particles, so it is less permeable than A. Order: A > B > C. This is the classic Lambe result for compacted clays (Holtz, Kovacs & Sheahan, Ch.5).

(ii) Typical compaction curves for GW and CH

Well-graded gravel (GW): tall, sharp peak at low water content. High-plasticity clay (CH): low, flat peak at high water content.

A well-graded gravel (GW) packs to a high dry density at low water content, producing a tall, sharply-peaked curve; a high-plasticity clay (CH) reaches only a modest density and needs a great deal of water, producing a low, flat curve shifted to the right. Representative standard-Proctor values (SI units):

Soil	Max. dry density, ρ_d,max	(γ_d,max)	Optimum moisture content
GW (well-graded gravel)	≈ 2.0–2.15 Mg/m³	≈ 20–21 kN/m³	≈ 8–11 %
CH (high-plasticity clay)	≈ 1.4–1.5 Mg/m³	≈ 14–15 kN/m³	≈ 22–28 %

(iii) Compression index of GW versus CH

The CH clay has the far higher compression index. Compressibility comes from the re-arrangement and squeezing of the platey clay fabric under load; a high-plasticity clay has a large void ratio and highly compressible structure, whereas a well-graded gravel is a rigid, granular skeleton whose grains barely move. Reasonable values:

GW: C_c ≈ 0.01–0.03 (essentially incompressible; settlement is immediate/elastic, not consolidation).
CH: C_c ≈ 0.4–0.5. Using Skempton’s correlation $C_c = 0.009\,(LL-10)$ with a typical CH liquid limit $LL \approx 60$ gives $C_c = 0.009(60-10)=0.45$.

Test: the one-dimensional consolidation (oedometer) test (ASTM D2435); C_c is the slope of the virgin portion of the $e$–$\log \sigma'$ curve.

(iv) Effective friction angle of Sand A versus Sand B

The coefficient of curvature $C_z = D_{30}^{2}/(D_{10}\,D_{60})$ measures how smoothly a gradation is filled between $D_{10}$ and $D_{60}$; a well-graded sand requires $1 \le C_z \le 3$ (with $C_u \ge 6$). Sand B, with $C_z = 1$, has the lower φ′. Sand A ($C_z = 2$) sits squarely in the well-graded band, so its finer grains fill the voids between coarser ones, giving denser packing, more inter-particle contacts and greater interlock — hence a higher φ′. $C_z = 1$ sits on the lower edge of the band; a uniform, single-sized sand also has $C_z \approx 1$ (with $C_u \approx 1$), so, other things being equal, Sand B is the one closer to a uniform gradation. It packs less densely with less interlock, so Sand B mobilizes the lower effective friction angle. If Sand B also had $C_u \ge 6$ it would still be classed as well graded, and the difference in φ′ would be small.

(v) Undrained friction angle from UU tests

In an unconsolidated–undrained (UU) triaxial test on a fully saturated clay, any increase in cell pressure is carried entirely by the pore water ($B=1$), so the effective stress — and therefore the shear strength — is unchanged. Every Mohr circle at failure has the same diameter and the total-stress envelope is horizontal: φ_u ≈ 0°.

Soil A (expansive clay): saturated and fine-grained ⇒ φ_u ≈ 0°, strength expressed as an undrained cohesion c_u = s_u.
Soil B (glacial till): a dense, well-graded mix of gravel, sand, silt and clay that is often partially saturated. Because $B \lt 1$ and the granular fraction develops real frictional resistance, added cell pressure does raise the strength, so the UU envelope shows a positive φ_u > 0° (typically a few degrees up to ~10–15°).

Topic: Compaction–structure–property links, gradation indices, and the φ_u=0 concept.

Key relations: $C_c = 0.009(LL-10)$; $C_u=D_{60}/D_{10}$, $C_z=D_{30}^{2}/(D_{10}D_{60})$; UU on saturated clay ⇒ $\phi_u=0$ (constant $s_u$).

Why this works: Moulding water content sets the clay fabric (flocculated dry of optimum, dispersed wet of optimum), which governs permeability and, with density, strength and compressibility. Gradation controls packing density and hence φ′. In an undrained test on saturated soil the pore water, not the skeleton, absorbs the cell pressure, so strength is independent of confinement.

Common pitfall: assuming the wet-of-optimum point always has the lowest permeability regardless of density, or reporting φ_u>0 for a saturated clay (it must be ~0). Do not confuse coefficient of curvature C_z with compression index C_c.

Source: Das & Sobhan, Principles of Geotechnical Engineering 9th ed., Ch.6 (compaction), Ch.7 (permeability), Ch.11–12 (consolidation & shear strength); Holtz, Kovacs & Sheahan Ch.5–11.

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