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24-Bld-A6 Geotechnical Materials and Analysis · Undated paper

Question 7 of 7

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07-BLD-A6 Geotechnical Materials and Analysis, National Examinations (printed exam date May 2019). 3 hours, closed book, 100 marks. Section A (Q1–Q3) is compulsory (40 marks); Section B directs "answer any three of Q4–Q7" (60 marks), but for completeness this solution answers all four.

Reference texts: B.M. Das, Principles of Geotechnical Engineering, 9th ed.; B.M. Das, Principles of Foundation Engineering, 9th ed.

Question 7 (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.

QuantitySymbolValue
Applied surface surcharge$\Delta\sigma$200 kN/m²
Sand layer 1 (dry, above WT)$H_1$, $\gamma_{dry}$2 m, 14.6 kN/m³
Sand layer 2 (saturated, below WT)$H_2$, $\gamma_{sat}$2 m, 17.3 kN/m³
Clay layer (settling layer)$H_3$, $\gamma_{sat}$4 m, 19.3 kN/m³
Liquid limit / $G_s$ / void ratio (clay)$LL$, $G_s$, $e_0$50%, 2.7, 0.9

Find. The primary consolidation settlement $S_c$ of the normally consolidated clay layer.

Δσ = 200 kN/m² Sand ($\gamma_{dry}$=14.6) Groundwater table Sand ($\gamma_{sat}$=17.3) Clay ($\gamma_{sat}$=19.3) e₀ = 0.9, LL = 50% mid-clay Sand $H_1$=2m $H_2$=2m $H_3$=4m
Figure 4 (reproduced): dry sand (2 m) over saturated sand (2 m, water table at the sand–sand interface) over the settling clay layer (4 m) over a sand base. The dashed line marks the clay's mid-height, where $\sigma_0'$ is evaluated.

Approach. Compute the pre-existing effective overburden stress $\sigma_0'$ at the clay's mid-height, take $\Delta\sigma=200$ kN/m² as applied uniformly at that depth (a wide surface surcharge), estimate the compression index from the liquid limit (Skempton's correlation for a normally consolidated clay), and apply the standard settlement formula.

  1. Depth to clay mid-height. $z_{mid}=H_1+H_2+\dfrac{H_3}{2}=2+2+2=6\text{ m}$.
  2. Total stress at mid-height. $\sigma_0=\gamma_{dry}H_1+\gamma_{sat,sand}H_2+\gamma_{sat,clay}\dfrac{H_3}{2}=14.6(2)+17.3(2)+19.3(2)=29.2+34.6+38.6=102.4\text{ kN/m}^2$.
  3. Pore pressure at mid-height. The water table sits at the $H_1/H_2$ interface (2 m depth), so the point is $2+2=4$ m below the water table: $u_0=\gamma_w(4)=9.81\times4=39.2\text{ kN/m}^2$.
  4. Effective overburden stress. $\sigma_0'=\sigma_0-u_0=102.4-39.2=\boxed{63.2\text{ kN/m}^2}$.
  5. Compression index (Skempton, normally consolidated clay). $C_c=0.009(LL-10)=0.009(50-10)=\boxed{0.36}$.
  6. Primary settlement. $S_c=\dfrac{C_c}{1+e_0}H_3\log_{10}\!\left(\dfrac{\sigma_0'+\Delta\sigma}{\sigma_0'}\right)=\dfrac{0.36}{1.9}(4.0)\log_{10}\!\left(\dfrac{63.2+200}{63.2}\right)=0.7579\times\log_{10}(4.166)=0.7579\times0.6198=\boxed{0.470\text{ m}}$.
QuantityResult
Effective overburden at clay mid-height, $\sigma_0'$63.2 kN/m²
Compression index, $C_c$0.36
Primary settlement, $S_c$0.470 m (470 mm)
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