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

Question 3 of 5: Effective Shear-Strength Parameters and A f from CU Triaxial Tests

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 (Nd = 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), Cc and the preconsolidation break in Q4’s Figure 4(a), and the OCR–Af 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 3: Effective Shear-Strength Parameters and Af from CU Triaxial Tests (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.

Given. Three CU triaxial tests on saturated clay with $u_o=0$:

Specimenσ3 (kPa)σ1−σ3 (kPa)uf (kPa)
A15010382
B300202169
C450305252

Find. The effective-stress parameters $c'$ and $\phi'$, Skempton’s pore-pressure parameter $A_f$ at failure, and whether the clay is normally or over-consolidated.

Approach. Convert each test to effective principal stresses, plot the failure states as stress points $\big(p',\,q\big)$ (per the formula sheet), fit the modified failure line $K_f$, and recover $c',\phi'$ from its slope and intercept. Compute $A_f=\Delta u/\Delta(\sigma_1-\sigma_3)$ and classify with Figure 3.

q = ((σ1′−σ3′)/2) kPap′ = (σ1′+σ3′)/2 kPaKf line: tan α′=0.437φ′≈26°, c′≈0
Modified failure envelope (Kf line) through the three stress points; it passes essentially through the origin.
  1. Effective principal stresses. With $\sigma_1=\sigma_3+(\sigma_1-\sigma_3)$ and $\sigma'=\sigma-u$: $$\text{A: }\sigma_3'=68,\ \sigma_1'=171;\quad \text{B: }131,\ 333;\quad \text{C: }198,\ 503\ \text{kPa}.$$
  2. Stress points. $p'=\tfrac12(\sigma_1'+\sigma_3')$, $q=\tfrac12(\sigma_1'-\sigma_3')=\tfrac12(\sigma_1-\sigma_3)$: $$\text{A }(119.5,\ 51.5);\quad \text{B }(232,\ 101);\quad \text{C }(350.5,\ 152.5)\ \text{kPa}.$$
  3. Fit the $K_f$ line. Least-squares through the three points gives slope $\tan\alpha' = 0.437$ and intercept $a' \approx 0$: $$q = a' + p'\tan\alpha', \qquad \tan\alpha'=0.437,\ a'\approx 0.$$
  4. Effective parameters. $$\phi' = \sin^{-1}(\tan\alpha')=\sin^{-1}(0.437)=25.9^{\circ}\approx 26^{\circ},$$ $$c' = \frac{a'}{\cos\phi'}\approx 0.$$ $$\boxed{c' \approx 0,\qquad \phi' \approx 26^{\circ}}$$
  5. Skempton’s $A_f$. Since $u_o=0$, the failure pore pressure is entirely shear-induced, so $A_f = \Delta u/\Delta(\sigma_1-\sigma_3)=u_f/(\sigma_1-\sigma_3)$: $$\text{A: }82/103=0.80;\ \text{B: }169/202=0.84;\ \text{C: }252/305=0.83 \Rightarrow \boxed{A_f \approx 0.82}.$$
  6. Classification. The envelope passes through the origin ($c'\approx0$) and $A_f\approx0.8$ is large and positive (contractive, positive excess pore pressure). Entering Figure 3 with $A_f\approx0.8$ gives $\mathrm{OCR}\approx1$. All three indicators agree: the clay is normally consolidated.
ParameterResult
Effective cohesion, c′≈ 0 kPa
Effective friction angle, φ′≈ 26°
Skempton’s Af≈ 0.82
OCR / state≈ 1 → normally consolidated