24-Bld-A6 Geotechnical Materials and Analysis · December 2017
Question 6 of 7
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
07-Bld-A6 Geotechnical Materials and Analysis — National Exam, December 2017. Closed book, 3 hours; drawing instruments and either a Casio or Sharp approved calculator required; the formula sheet and influence charts printed at the back of the exam are reproduced/used inline where needed. Section A (Questions 1–3, 40 marks, answer all) and Section B (Questions 4–7, 20 marks each, the paper asks for any three of four) — all seven questions are answered below.
Reference texts: B. M. Das, Principles of Geotechnical Engineering, 9th ed. (phase relations, seepage/flow nets, stress distribution, consolidation, shear strength); R. F. Craig / J. Knappett, Craig's Soil Mechanics, 9th ed. (flow nets, effective-stress strength parameters); Canadian Foundation Engineering Manual (CFEM), 4th ed.
Check — assumptions and source notes for this paper. (1) Question 4's flow net (Nf = 5 flow channels, Nd = 14 equipotential drops, point A read as three drops upstream of the downstream exit, exit-field length ≈ 2 m) is used with a soil total unit weight of 20 kN/m³. (2) Question 5(ii)'s "approximate" method is extended from the formula sheet's centre-of-rectangle formula to a corner point (point A here is not centred on the loaded area) using the standard mirror/quartering superposition trick, valid because the approximate formula is linear in load exactly like the exact one. (3) Question 6's least-squares fit through the three effective-stress points gives an intercept of −0.7 kPa — not distinguishable from zero with only three data points — so c′ is taken as 0, consistent with the expected behaviour of a normally consolidated clay. (4) Question 7's figure shows three distinct layer thicknesses — H1 = 1.5 m (sand above the water table), H2 = 1.5 m (sand below the water table), H3 = 2 m (the clay layer, void ratio e = 0.75) — and all three values are used below.
Given. Three CU triaxial tests with pore-pressure measurement on the same saturated clay:
Table 1 — CU triaxial results at failure
σ3 (kPa)
(σ1−σ3) (kPa)
u (kPa)
150
103
82
300
202
169
450
305
252
Find. Effective shear-strength parameters c′, φ′; the expected (σ1−σ3) at $\sigma_3'=250$ kPa; whether the clay is NC or OC; and whether these parameters govern the dam's long-term stability.
Approach. Convert each test to effective stresses, plot the modified (stress-point) coordinates $p'=\tfrac12(\sigma_1'+\sigma_3')$, $q'=\tfrac12(\sigma_1'-\sigma_3')$ given on the formula sheet, fit the best straight line, and convert its slope/intercept to c′, φ′ via $\phi'=\sin^{-1}(\tan\alpha)$, $c'=a/\cos\phi'$.
Effective stresses and modified coordinates. With $\sigma_3'=\sigma_3-u$, $\sigma_1'=\sigma_3+(\sigma_1-\sigma_3)-u$:
σ3′
σ1′
p′
q′
68
171
119.5
51.5
131
333
232.0
101.0
198
503
350.5
152.5
Fit the modified line. Least-squares through the three (p′, q′) points gives slope $\tan\alpha=0.437$ and intercept $a=-0.7$ kPa (indistinguishable from zero given only three data points), so
$$\phi' = \sin^{-1}(0.437) = \boxed{25.9^{\circ}}, \qquad c' = \frac{a}{\cos\phi'} \approx \boxed{0\ \text{kPa}}.$$
Predicted principal stress difference at $\sigma_3'=250$ kPa. With $K_p=\tan^2(45+\phi'/2)=\tan^2(57.97^{\circ})=2.554$ and $c'\approx0$,
$$\sigma_1' = \sigma_3'K_p+2c'\sqrt{K_p} = 250(2.554) = 638.5\ \text{kPa},$$
$$(\sigma_1-\sigma_3)_{\text{pred}} = \sigma_1'-\sigma_3' = 638.5-250.0 \boxed{\approx\ 388\ \text{kPa}}.$$
(i) Normally or over consolidated? The Skempton pore-pressure ratio $A_f=u/(\sigma_1-\sigma_3)$ is 0.80, 0.84 and 0.83 for the three tests — consistently large and positive. A clay that generates such large positive excess pore pressure under undrained shear is contracting strongly, the signature of a normally consolidated clay; a heavily over-consolidated clay would instead show a much smaller, zero, or negative Af (dilative response). The near-zero effective cohesion intercept from step 2 reinforces this conclusion, since c′ ≈ 0 is exactly what is expected for a normally consolidated clay tested at stresses beyond its (negligible) preconsolidation pressure.
(ii) Suitability for long-term stability.Yes. "Long-term" stability of an earth dam corresponds to the fully drained, steady-state seepage condition, once construction and consolidation excess pore pressures have dissipated — exactly the condition that EFFECTIVE stress parameters describe. Because these c′, φ′ values were obtained by measuring pore pressure directly and converting to effective stress (rather than reporting total-stress parameters), they are the correct strength parameters for a long-term (effective-stress) slope-stability analysis of the dam, provided the fill is placed and consolidates to a similar (normally consolidated, saturated) state as the tested specimens.
