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Sampler clearances and area ratio (68 mm)

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.

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).

Formulae (D1D_1 = inside dia. of cutting edge, D2D_2 = inside dia. of tube, D3D_3 = outside dia. of cutting edge, D4D_4 = outside dia. of tube):

Ci=D2−D1D1×100,Co=D3−D4D4×100,Ar=D32−D12D12×100C_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: D1=68D_1 = 68 mm, D2=70D_2 = 70 mm, D3=74D_3 = 74 mm, D4=72D_4 = 72 mm.

Ci=70−6868×100=2.94%Co=74−7272×100=2.78%Ar=742−682682×100=8524624×100=18.43%\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 Ar≤10%A_r \le 10\%, Ci=0.5C_i = 0.5-3%3\%, Co=0C_o = 0-2%2\%.

  • Ci=2.94%C_i = 2.94\% is within 0.5-3%.
  • Co=2.78%C_o = 2.78\% exceeds 2%.
  • Ar=18.43%A_r = 18.43\% is much more than 10%.

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

✓ Answer checked by Claude Sonnet 5.5

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