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16-Civ-A4 Geotechnical Materials and Analysis · December 2019

Question 2 of 6: Short-discussion concepts

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

Notes on this paper

Paper format: National Examinations (PEO/Engineers Canada) — 16-Civ-A4 Geotechnical Materials and Analysis, December 2019. Six questions, 100 marks, closed book, 3 hours; all questions are to be answered. A formula sheet, an m–n influence chart and a Newmark chart are provided at the back of the paper.

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

Question 2: Short-discussion concepts (10 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.

[Figure not reproduced: Figure 1 from the exam: Sand A and Sand B grain sketches. See the official exam paper or the cited reference text.]

Figure 1 (cropped from the exam paper) — Sand A is gap graded: a group of large grains and a separate group of much finer grains, with the intermediate sizes missing. Sand B is well graded: a continuous range of sizes from coarse to fine.
  1. Item 1 — Sand A has the higher permeability. Sand A is gap graded (a form of poor grading): it has large grains and a few very fine ones, but none of the intermediate sizes. Without those in-between sizes the voids between the large grains are not filled in step by step, so large, connected pore channels remain and the few fines sit loosely in them. Sand B is well graded: each smaller size fits into the voids left by the next larger size, so it packs to the densest arrangement with the smallest pore throats. Seepage is controlled by the size of those pore throats (Hazen’s $k \approx C\,D_{10}^{2}$ expresses the same idea through the effective size), so Sand A, with its open coarse skeleton, has the higher saturated permeability and Sand B the lower.
  2. Item 2 — Sample D (the OC clay) has the greater peak strength. At the same effective consolidation stress the over-consolidated clay is denser and dilatant; on undrained shear it tends to expand and therefore generates negative excess pore pressure, which raises the effective stress at failure and produces a pronounced peak. The normally consolidated clay is contractive, builds positive pore pressure, and strain-hardens to a lower ultimate strength.
  3. Item 3 — both are approximately the same (iii). For a given sand the effective-stress failure envelope is unique ($c'\approx0$, one $\phi'$) and does not depend on drainage. At the same effective confining stress the CU and CD tests therefore mobilise the same $\phi'$ and hence essentially the same shear strength. (Only the measured undrained peak would differ if the two specimens were at markedly different densities, through the sign of the pore pressure they develop; as “identical samples” they coincide.)
  4. Item 4 — (i) the volume increases. A dense sand sheared drained dilates: the interlocked grains must ride up over one another to fail, so the specimen expands until it reaches the critical (constant-volume) state.
  5. Item 5 — statement (i) is true: total stress equals pore-water pressure. In free water there are no soil grains and hence no grain-to-grain contact, so the effective stress is zero. From $\sigma'=\sigma-u$ with $\sigma'=0$ we get $\sigma=u$: at 1 m depth both the total vertical stress and the pore pressure equal $\gamma_w(1)=9.81\ \text{kPa}$. Statement (ii) would require $\sigma'=u\neq0$, which contradicts $\sigma'=0$.