NivaarExam PrepOfficial exam papers ↗

24-Bld-A6 Geotechnical Materials and Analysis · December 2018

Question 3 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 Examinations, December 2018. 3 hours, closed book, 100 marks. Section A (Q1–Q3) is compulsory; Section B directs "answer any three of Q4–Q7," 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 3 (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.

Ground level S = 0.6 w = 30% w = 40% (saturated, S=1 — check) ▽ water table element, z=5m 2 m 3 m
Figure 2 (reproduced): uniform sand deposit, partially saturated above 2 m (S=0.6, w=30%) and saturated below (w=40%); effective stress sought at the element 5 m below ground level.

Given. $G_s=2.7$; layer 1 (0–2 m): $S=0.6$, $w=30\%$; layer 2 (2–5 m): $w=40\%$. The water table sits at the 2 m boundary (Check: below it the soil is taken as fully saturated, $S=1$, since no separate $S$ is stated there).

Find. Effective stress $\sigma'$ at 5 m depth.

Approach. Get each layer's void ratio from $e=wG_s/S$, then its unit weight from $\gamma=(Se+G_s)\gamma_w/(1+e)$; sum $\gamma\cdot H$ down to 5 m for total stress, subtract hydrostatic pore pressure measured from the water table.

  1. Layer 1 (partially saturated). $e_1=w_1G_s/S_1=0.30(2.7)/0.6=1.35$. $\gamma_1=\dfrac{(S_1e_1+G_s)\gamma_w}{1+e_1}=\dfrac{(0.6\times1.35+2.7)\times9.81}{2.35}=14.65\text{ kN/m}^3$.
  2. Layer 2 (saturated). $e_2=w_2G_s/S_2=0.40(2.7)/1.0=1.08$. $\gamma_2=\dfrac{(1.08+2.7)\times9.81}{2.08}=17.83\text{ kN/m}^3$.
  3. Total stress at 5 m. $\sigma=\gamma_1(2)+\gamma_2(3)=14.65(2)+17.83(3)=82.78\text{ kPa}$.
  4. Pore pressure. Measured from the water table at 2 m: $u=\gamma_w(5-2)=9.81(3)=29.43\text{ kPa}$.
  5. Effective stress. $\sigma'=\sigma-u=82.78-29.43=\boxed{53.4\text{ kPa}}$.
Final Results — Question 3
QuantityValue
$e_1$ / $\gamma_1$1.35 / 14.65 kN/m³
$e_2$ / $\gamma_2$1.08 / 17.83 kN/m³
$\sigma$ at 5 m82.78 kPa
$u$ at 5 m29.43 kPa
$\sigma'$ at 5 m53.4 kPa