16-Civ-A4 Geotechnical Materials and Analysis · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper: National Examinations — May 2014 · 98-Civ-A4 Geotechnical Materials and Analysis · 3 hours, closed book · 100 marks · answer all six questions. A formula sheet plus m–n influence and Newmark charts are supplied at the back of the paper.
Reference texts. B. M. Das, Principles of Geotechnical Engineering (9th ed.); R. F. Craig / Knappett & Craig, Craig’s Soil Mechanics (8th ed.); Holtz, Kovacs & Sheahan, An Introduction to Geotechnical Engineering; M. Budhu, Soil Mechanics and Foundations. Canadian practice: Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM, 4th ed.). Unit weight of water taken as $\gamma_w = 9.81\ \text{kN/m}^3$ throughout.
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.
This is a conceptual question; the answer is given as prose with an accompanying Mohr diagram.
The vertical effective stress $\sigma_v'$ in the soil behind a wall is fixed by the overburden. The horizontal effective stress $\sigma_h'$ depends on how the wall moves, and is written as $\sigma_h' = K\,\sigma_v'$ where the earth-pressure coefficient $K$ takes three limiting values.
At-rest ($K_0$). If the wall does not move, the soil undergoes no lateral strain and stays in its original (elastic) state. For a normally consolidated soil Jaky’s relation gives $K_0 = 1 - \sin\phi'$ (typically $0.4$–$0.5$), so $\sigma_h' \lt \sigma_v'$. On the Mohr diagram the circle spans $\sigma_h'$ to $\sigma_v'$ and lies entirely below the failure envelope — the soil is not failing.
Active ($K_a$). If the wall yields away from the backfill, the soil expands laterally, $\sigma_h'$ decreases while $\sigma_v'$ (the major principal stress) is unchanged. $\sigma_h'$ falls until the soil fails, at $\sigma_h' = K_a\,\sigma_v'$ with $K_a = \tan^2\!\left(45^\circ - \phi'/2\right)$. The Mohr circle grows to the left until it is tangent to the failure envelope; this is the minimum lateral pressure the soil can sustain.
Passive ($K_p$). If the wall is pushed into the soil, $\sigma_h'$ increases and eventually exceeds $\sigma_v'$, so the horizontal stress becomes the major principal stress. Failure occurs at $\sigma_h' = K_p\,\sigma_v'$ with $K_p = \tan^2\!\left(45^\circ + \phi'/2\right) = 1/K_a$. The Mohr circle now grows to the right of $\sigma_v'$ until it is again tangent to the envelope; this is the maximum (limiting) lateral resistance the soil can develop.
