---
title: "Sampler clearances and area ratio (68 mm)"
subject: "Foundation Engineering"
chapter: 2
key: "semester_5/foundation_engineering:sampler-clearance-68-70"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/sampler-clearance-68-70
site: BCT Engineering
---

# Sampler clearances and area ratio (68 mm)

Foundation Engineering · Chapter 2: Soil Exploration

- Asked in: 2082 Bhadra, 4 marks
- Video: [soil sampler | Area Ratio | Recovery Ratio | Inside clearance | outside clearance | Foundation](https://www.youtube.com/watch?v=oreHo3XXhkU) — Sudip Dhakal
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/sampler-clearance-68-70
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-2

## Question

A soil sampler is used to extract a soil sample. The sampler has an inner diameter of 68 mm at the cutting edge and 70 mm at the sampling tube, while the outer diameter is 74 mm at the cutting edge and 72 mm at the sampling tube. Calculate the inside clearance, outside clearance and area ratio. Based on the calculated values, classify the type of soil sample obtained (disturbed or undisturbed).

## Short answer

Inside clearance Ci=2.94%, outside clearance Co=2.78%, area ratio Ar=18.43%. Ar exceeds 10% and Co exceeds 2%, so the sample is disturbed.

## Answer

**Formulae** ($D_1$ = inside dia. of cutting edge, $D_2$ = inside dia. of tube, $D_3$ = outside dia. of cutting edge, $D_4$ = outside dia. of tube):
$$
C_i = \frac{D_2-D_1}{D_1}\times100,\quad C_o = \frac{D_3-D_4}{D_4}\times100,\quad A_r = \frac{D_3^2-D_1^2}{D_1^2}\times100
$$
Given: $D_1 = 68$ mm, $D_2 = 70$ mm, $D_3 = 74$ mm, $D_4 = 72$ mm.

$$
\begin{aligned} C_i &= \frac{70-68}{68}\times100 = 2.94\% \\ C_o &= \frac{74-72}{72}\times100 = 2.78\% \\ A_r &= \frac{74^2-68^2}{68^2}\times100 = \frac{852}{4624}\times100 = 18.43\% \end{aligned}
$$

**Classification:** limits for an undisturbed sample are $A_r \le 10\%$, $C_i = 0.5$-$3\%$, $C_o = 0$-$2\%$.
- $C_i = 2.94\%$ is within 0.5-3%.
- $C_o = 2.78\%$ exceeds 2%.
- $A_r = 18.43\%$ is much more than 10%.

**Answer:** $C_i = 2.94\%$, $C_o = 2.78\%$, $A_r = 18.43\%$. Because the area ratio and outside clearance are too large, the sample is **disturbed**.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Inside clearance with D1 = 68 and D2 = 70 mm is
   A. 2.94%
   B. 2.78%
   C. 18.43%
   D. 5.88%
   Answer: A. (70 - 68)/68 x 100 = 2.94%. (Key point: Inside clearance)

2. Outside clearance with D3 = 74 and D4 = 72 mm is
   A. 2.94%
   B. 2.70%
   C. 5.56%
   D. 2.78%
   Answer: D. (74 - 72)/72 x 100 = 2.78%. (Key point: Outside clearance)

3. The area ratio is
   A. 10.0%
   B. 2.94%
   C. 8.8%
   D. 18.43%
   Answer: D. (74^2 - 68^2)/68^2 = 852/4624. (Key point: Area ratio)

4. The sample is classed as
   A. undisturbed, since all limits are met
   B. undisturbed, since inside clearance is OK
   C. disturbed, since area ratio and outside clearance exceed limits
   D. cannot be classed
   Answer: C. Ar > 10% and Co > 2%. (Key point: Classification)

## Related in Foundation Engineering

- [Sampler clearances and area ratio (69 mm)](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asampler-clearance-69-73) — Foundation Engineering, chapter 2, asked 2×
- [Sampler clearances and area ratio (59 mm)](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asampler-clearance-59-63) — Foundation Engineering, chapter 2, asked 2×
- [Area ratio of sampler, radius 30 mm](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asampler-area-ratio-radius) — Foundation Engineering, chapter 2