Question 3 of 7: Weight-Volume Relationships from a Pushed Copper-Pipe Field Sample

Question 3: Weight-Volume Relationships from a Pushed Copper-Pipe Field Sample (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.

Approach. Take the pipe volume as the total sample volume, get the solids volume from the dry mass and the assumed G_s, then work through the standard weight-volume relationships.

1. Total sample volume. The pipe is a cylinder, D = 2 cm, L = 10 cm: $$V = \frac{\pi}{4}D^2 L = \frac{\pi}{4}(2)^2(10) = \boxed{31.42\ \text{cm}^3}$$
2. Volume of solids, void ratio, and porosity. With $\rho_w = 1\ \text{g/cm}^3$, $$V_s = \frac{M_s}{G_s\rho_w} = \frac{45.8}{2.65} = 17.28\ \text{cm}^3, \qquad V_v = V - V_s = 31.42 - 17.28 = 14.13\ \text{cm}^3$$ $$e = \frac{V_v}{V_s} = \frac{14.13}{17.28} = \boxed{0.818}, \qquad n = \frac{V_v}{V} = \frac{14.13}{31.42} = \boxed{45.0\%}$$
3. Bulk and dry densities. $$\rho = \frac{M_t}{V} = \frac{49.2}{31.42} = \boxed{1.566\ \text{g/cm}^3}\ (15.36\ \text{kN/m}^3), \qquad \rho_d = \frac{M_s}{V} = \frac{45.8}{31.42} = \boxed{1.458\ \text{g/cm}^3}\ (14.30\ \text{kN/m}^3)$$
4. Degree of saturation. Water mass $M_w = M_t - M_s = 3.4\ \text{g}$, so $V_w = 3.4\ \text{cm}^3$ and $$S = \frac{V_w}{V_v}\times 100 = \frac{3.4}{14.13}\times 100 = \boxed{24.1\%}$$

d) Are these values appropriate for a fine-grained soil? A void ratio of 0.82 and porosity of 45% sit comfortably within the typical range for a fine-grained (silt/clay) soil (roughly e = 0.5–1.5 for clays, somewhat lower for silts), so the pore structure looks physically reasonable. The degree of saturation, however, is unusually low — only 24% — for a sample described as "undisturbed" and taken from below the ground surface, where fine-grained soils are very often close to fully saturated unless the site sits well above the water table or in an arid climate. This mismatch is the strongest indicator in the data set that something happened to the sample between collection and weighing (see part e), rather than that the in-situ soil is genuinely that dry.

e) Improving the sampling, testing and analysis approach. A rigid copper pipe pushed by hand compresses and disturbs the soil fabric (unlike a proper thin-wall Shelby tube, whose sharpened cutting edge minimises remoulding), so the measured density may not represent the true in-situ state. The low degree of saturation strongly suggests moisture was lost by evaporation during transport/storage before weighing; sealing both ends immediately with wax or a cap, and weighing the sample as soon as possible after extraction, would remove that source of error. A larger-diameter sample would reduce the relative disturbance from the pipe wall and give a more representative average; measuring G_s directly with a pycnometer, rather than assuming a "typical" value, removes one more assumption from the calculation; and taking several replicate samples at the same location would let the engineer report a mean and a scatter rather than a single, possibly unrepresentative, number.