22-Agric-A2 Soil Physics and Mechanics · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 04-Agric-A2 Soil Physics & Mechanics, National Exams December 2015 — 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, seepage, effective stress, compaction, shear strength); R.F. Craig, Craig's Soil Mechanics, 9th ed. (effective stress, seepage and flow nets, shear strength); G.O. Schwab et al., Soil and Water Conservation Engineering, 5th ed. (infiltration, erosion estimation, drainage).
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) Total stress vs. effective stress. Total stress, σ, is the full weight of everything above a point in the soil — solids, water and any surface load — divided by the plan area, $\sigma = \gamma z$ (plus surcharge). Pore water pressure, u, carries part of that load hydrostatically but cannot transmit shear, since water has no frictional resistance. Terzaghi's principle isolates the portion of the total stress actually carried through grain-to-grain contacts, the effective stress $\sigma' = \sigma - u$. This distinction matters for shear strength because the Mohr–Coulomb failure criterion, $\tau_f = c' + \sigma'\tan\phi'$, is written in terms of effective, not total, normal stress: it is the grain-to-grain contact force that mobilises interparticle friction and locks the soil skeleton together, while pore water, carrying load without resisting shear, can only reduce available strength (by raising u and lowering σ′) never add to it. A rapid rise in pore pressure — from a flood, an undrained load, or an earthquake — can drop σ′ toward zero and trigger a strength collapse (e.g. quicksand conditions or a liquefaction failure) even though the total stress, and hence the total weight being carried, has not changed at all.
b) USCS classification of a gravel-pit material for a road bed. The Unified Soil Classification System first splits a soil by grain size (coarse- vs. fine-grained, at the #200/0.075 mm sieve), then, for a coarse-grained soil, by gradation and by the character of any fines present. A full road-bed classification therefore needs: (i) a sieve (gradation) analysis down through the #200 sieve, to fix the percent gravel, sand and fines and, for the coarse fraction, the coefficient of uniformity $C_u = D_{60}/D_{10}$ and coefficient of curvature $C_c = D_{30}^2/(D_{10}D_{60})$ that separate well- from poorly-graded gravel (GW/GP) or sand (SW/SP); (ii) if more than about 5% passes the #200 sieve, Atterberg limits (liquid limit and plastic limit) on the fines, to plot the plasticity index against the A-line and classify the fines as silt (ML/MH) or clay (CL/CH), which in turn decides whether the coarse soil carries a dual symbol (GW-GM, GC, etc.); (iii) a specific gravity test, needed to convert the sieve data into the weight-volume relationships used later in the road design; and (iv), for a road-bed use specifically, a Proctor compaction test and a California Bearing Ratio (CBR) test, which are not part of the USCS symbol itself but are exactly the tests a road engineer needs once the material is classified, to set the target compaction density and confirm the subgrade support value. The gradation and plasticity tests are run because they are the only two soil properties USCS actually uses to assign a symbol; the CBR/Proctor pair is run because classification alone does not certify that the material will perform structurally as a road bed.
c) Determining Ksat and static water levels for a dewatering design. The static water level (or levels, if more than one aquifer is present) is obtained from a network of observation wells or piezometers installed around and within the proposed excavation footprint, drilled to different depths to distinguish a shallow unconfined water table from any deeper confined/perched aquifer; water levels are logged over time (ideally through a wet and a dry season) to capture seasonal fluctuation, since a dewatering system sized on a single dry-season reading can be badly under-designed. The saturated hydraulic conductivity of the in-situ material is best obtained from a field pumping (aquifer) test: a well is pumped at a controlled, known rate and the resulting drawdown is measured in the pumping well and in the surrounding observation wells, then fit to the Thiem (steady-state) or Theis (transient) unconfined/confined well equations to back-calculate K — this is preferred over a lab permeameter test on a small sample because it integrates the true in-situ heterogeneity (macro-pores, layering, fissures) that a small disturbed or "undisturbed" core cannot capture. Where a full pumping test is not practical, slug tests in individual piezometers or borehole packer tests give a faster, lower-cost (if less representative) estimate of local K that can still guide a preliminary dewatering design.
d) Estimating annual erosion losses after forest clearing. The standard engineering estimate is the Universal Soil Loss Equation (USLE) (or its revised form, RUSLE), $A = R \cdot K \cdot LS \cdot C \cdot P$, giving average annual soil loss per unit area. Each factor needs its own input data: rainfall erosivity, R, from local rainfall-intensity records (or regional R-factor maps); soil erodibility, K, from the soil's texture, organic-matter content, structure and permeability (available from a soil survey or measured directly); the topographic factor, LS, from field slope length and steepness (surveyed or taken off a DEM); the cover- management factor, C, which is the single factor most affected by the land-use change described — a forest floor's near-continuous litter/canopy cover gives C close to 0.001–0.01, while a newly cleared, cultivated field can push C toward 0.2–0.5 depending on crop and tillage, so C must be re-derived for the intended cropping system and rotation, not carried over from the forested condition; and the support-practice factor, P, reflecting whether contouring, strip-cropping or terracing will be used. Because tile drainage lowers the water table and can also change the site's effective infiltration and runoff response, the erosion estimate should be re-checked once the drainage design is fixed, not computed only for the pre-drainage condition.
