22-Agric-A2 Soil Physics and Mechanics · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 04-Agric-A2 Soil Physics & Mechanics, National Exams May 2014 — a three-hour open-book examination; any non-communicating calculator is permitted. The cover page states that five (5) questions constitute a complete exam paper and that only the first five as they appear in the answer book are marked, that each question is of equal value, and that some questions require a written answer whose clarity and organization matter for marks. All seven printed questions are worked here, because the set is a study resource rather than a timed attempt; on exam day a candidate submits only the first five, in order.
Reference texts. B.M. Das, Principles of Geotechnical Engineering, 9th ed. (weight-volume relationships, permeability, effective stress, shear strength, particle-size classification, flow to wells); R.F. Craig, Craig's Soil Mechanics, 9th ed. (effective stress, seepage, shear strength).
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.
| Characteristic | Value |
|---|---|
| Sample volume, V | 1200 cm³ |
| Mass, smaller of the two printed values | 2.005 kg |
| Mass, larger of the two printed values | 2.915 kg |
| Particle (grain) density, Gs | 2.63 g/cm³ |
Find. Void ratio and porosity (a); wet and dry density (b); degree of saturation (c); and whether the resulting numbers are consistent for a sandy loam (d).
The source table labels the smaller mass (2.005 kg) "Original Mass" and the larger (2.915 kg) "Mass after drying" — but oven-drying only removes water, so the post-drying mass can never exceed the original mass. The only physically consistent reading is that the two labels are reversed: Ms (dry) = 2.005 kg and Mt (original, wet) = 2.915 kg. This solution proceeds on that basis; part (d) shows that even the corrected pairing is not fully self-consistent, which is the intended teaching point of that sub-part.
Approach. Get the solids volume from the dry mass and Gs, then the void volume by difference from the total sample volume; void ratio and porosity follow directly, wet/dry density from the two masses over the same total volume, and degree of saturation from the water volume implied by the mass difference.
d) Are these values appropriate for a sandy loam? Partly. The void ratio (0.574) and porosity (36.5%), and the wet/dry densities, all fall squarely within the normal range for a sandy loam (e typically 0.4–0.7, n roughly 30–45%), so the corrected mass assignment in the Verify callout above is at least internally plausible for this soil type. The degree of saturation, however, computes to about 208% — physically impossible, since a sample cannot hold more water than the volume of its own voids ($S \le 100\%$ always). This signals that the data set still contains an error beyond the simple label swap already corrected: most likely a further error in one of the two masses, the particle density, or the sample volume. Practically, a candidate would flag the void ratio, porosity and densities as usable design values (they are self-consistent and typical) while noting that the saturation figure cannot be trusted and the sample should be re-weighed or re-measured before any water-content-dependent design decision is made.
| Quantity | Value |
|---|---|
| Void ratio, e | 0.574 |
| Porosity, n | 36.5% |
| Wet (bulk) density | 2.429 g/cm³ (2429 kg/m³) |
| Dry density | 1.671 g/cm³ (1671 kg/m³) |
| Degree of saturation, S | ≈208% — physically impossible; data flagged |
