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.
a) Saturated hydraulic conductivity, Ksat. A proportionality constant in Darcy's law, $v = Ki$, describing how easily water moves through a porous medium once every pore is filled with water (the flow-limiting resistance is then set purely by pore geometry, not by partial air-blocking). It has units of velocity (m/s, cm/s, m/day) and is measured directly with a constant- or falling-head permeameter, or estimated from grain size (e.g. the Hazen approximation). Ksat spans roughly ten orders of magnitude across soil types, from ≈10-9 m/s in intact clay to >10-2 m/s in clean gravel, which is why it dominates seepage, drainage and dewatering design.
b) Effective stress, σ′. The portion of the total stress acting on a soil mass that is actually transmitted through grain-to-grain contacts of the soil skeleton, after subtracting the neutral (pore water) pressure: $\sigma' = \sigma - u$ (Terzaghi's principle). It is effective stress — not total stress — that governs soil strength, compressibility and volume change, because pore water carries load without mobilising friction between grains.
c) Soil texture. The relative proportions, by dry mass, of sand-, silt- and clay-sized particles in a soil, read off a texture triangle once the three percentages are known from a sieve/hydrometer analysis. Texture is a fixed mineralogical/particle-size property (distinct from structure, which describes how the particles are arranged) and is the primary control on a soil's drainage, water-holding capacity, and workability for both agricultural and engineering purposes.
d) Loam. A texture class centred on a well-balanced mixture of sand, silt and clay (roughly 40% sand / 40% silt / 20% clay, with tolerance either way), so that the soil combines the drainage and aeration of sand with the water- and nutrient-holding capacity of silt and clay. It is generally regarded as the most agriculturally productive texture class and sits near the middle of the USDA texture triangle.
e) Porosity, n. The fraction of a soil's total volume occupied by voids (air and/or water), $n = V_v/V \times 100\%$. Porosity is a bulk-volume measure of how much pore space is available to store or transmit fluid, and (together with the void ratio, $e = V_v/V_s = n/(1-n)$) is the starting point for almost every other weight-volume calculation.
f) Moisture content, w. The mass of water in a soil sample expressed as a percentage of the dry (solids) mass, $w = M_w/M_s \times 100\%$, determined by weighing a sample before and after oven-drying at 105–110°C to constant mass. Moisture content (dry-basis, the geotechnical convention) is distinct from the wet-basis water fraction sometimes quoted in agronomy, and the two must never be interchanged in a calculation.
g) Mohr's circle. A graphical construction that plots normal stress (horizontal axis) against shear stress (vertical axis) for every plane orientation passing through a stressed point, drawn as a circle of radius $(\sigma_1-\sigma_3)/2$ centred at $(\sigma_1+\sigma_3)/2$ once the two principal stresses are known. It lets an engineer read off the stress on any inclined plane directly, and, superimposed with a Mohr–Coulomb strength envelope, shows at a glance whether — and on which plane — a soil element has failed.
h) Proctor density. The maximum dry density a soil can reach for a specified compactive effort (standard or modified Proctor), obtained from a laboratory compaction test that plots dry density against moisture content to find the peak (the optimum moisture content). It is the reference value against which field compaction is checked (e.g. "95% Proctor"), because dry density alone is meaningless without knowing the moisture content and effort used to achieve it.
i) Phreatic surface. The free (unconfined) water table — the surface within a soil or aquifer at which pore water pressure equals atmospheric pressure ($u = 0$) and below which the soil is saturated. It marks the top boundary of the zone of saturation and, in seepage analysis, is a line of known (atmospheric) pressure head along which a flow net must be constructed.
j) Cohesive soil. A fine-grained soil (clay, or plastic silt) whose shear strength includes a component, cohesion c (or c′ in effective-stress terms), that exists even at zero normal stress, arising from electrochemical bonding and adsorbed water films between platy clay particles rather than from interparticle friction alone. Cohesive soils are plastic, have low permeability, and (unlike cohesionless sand) can stand unsupported in a vertical cut for a time — the practical distinction most often tested against "cohesionless" granular soils.
