18-Geol-A4 Structural Geology · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2019 — 18-Geol-A4 Structural Geology. Three-hour, closed-book exam; a Casio or Sharp approved calculator, protractor, drawing compass and ruler are permitted. All questions (A–D) constitute the complete 100-mark paper.
Reference texts: Davis, Reynolds & Kluth, Structural Geology of Rocks and Regions, 3rd ed. — stress/strain tensors, Mohr-Coulomb failure, Anderson's theory of faulting, shear-zone kinematics; Fossen, Structural Geology, 2nd ed. — fold classification, shear-sense indicators, crystal-plastic deformation mechanisms; Marshak & Mitra, Basic Methods of Structural Geology — three-point strike/dip problems and structure-contour construction.
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.
| # | Statement | Ans. | Why |
|---|---|---|---|
| A1 | Traction = state of stress at a point | F | Traction is the stress vector on one specific plane; the full state of stress at a point requires the stress tensor (all planes), not a single traction. |
| A2 | Mode I cracks form ⊥ $\sigma_1$ | F | Mode I (opening) cracks propagate perpendicular to $\sigma_3$ and parallel to $\sigma_1$ — the opposite of the statement. |
| A3 | Layer thickness controls fold wavelength | T | Biot–Ramberg buckling theory: dominant wavelength $\propto$ thickness $\times$ (viscosity ratio)$^{1/3}$; thickness is the first-order control. |
| A4 | Flexural flow → only Class 1B folds | T | Flexural-slip/flow folding preserves orthogonal layer thickness, i.e. produces parallel (Class 1B, Ramsay) folds. |
| A5 | Coaxial strain has no shear | F | Coaxial (pure shear) means the principal strain axes do not rotate relative to the external frame; shear strain along non-principal directions is still present. |
| A6 | Nonrigid deformation = dilation and/or distortion | T | By definition, anything that is not pure rigid-body translation/rotation is a change in size (dilation) and/or shape (distortion). |
| A7 | Mode II displacement ⊥ fracture front | T | Mode II (sliding) fractures displace parallel to the fracture plane and perpendicular to the crack front (in-plane shear). |
| A8 | Axial surface trace = max-curvature locus | T | The axial surface, by definition, is the surface joining the hinge lines (points of maximum curvature) of successive folded layers. |
| A9 | Principal strain axes were $\perp$ before strain | T | The principal axes of the strain ellipsoid are the eigenvectors of $F^{T}F$; this pair (in 2-D) always exists and is mutually perpendicular both before and after any finite homogeneous strain. |
| A10 | Differential stress drives distortion | T | $\sigma_1-\sigma_3$ is the deviatoric (non-hydrostatic) stress; the hydrostatic/mean stress produces only dilation, the deviatoric part drives shape change. |
| A11 | Ideal plastic: strain $\propto$ stress | F | An ideally plastic material strains at constant stress once yield is reached (flat stress–strain curve); linear stress–strain is elastic (Hookean) behaviour. |
| A12 | Griffith's Law = frictional sliding | F | Griffith's criterion describes tensile-stress concentration at pre-existing microcrack tips causing new fracture; frictional sliding on an existing plane is the Coulomb/Amontons law. |
| A13 | Nabarro–Herring = intracrystalline point-defect migration | T | Nabarro–Herring creep is vacancy diffusion through the grain interior (lattice/volume diffusion), distinct from Coble creep (grain-boundary diffusion). |
| A14 | Bedding intersects axial cleavage only once | F | A bedding surface threading through a train of folds is crossed by the axial-planar cleavage once per hinge — more than once for a multi-hinge fold train. |
| A15 | Bedding/cleavage intersection lineation gives the axial surface orientation | F | The intersection lineation is parallel to the fold axis (a line) — it does not by itself fix the axial surface's dip/strike (a plane). |
| A16 | Edge dislocation $\parallel$ Burgers vector | F | An edge dislocation line is perpendicular to its Burgers vector; a screw dislocation line is parallel to its Burgers vector. |
| A17 | Reclined fold: hinge plunges $\perp$ axial-surface strike | T | By Fleuty's classification, a reclined fold's hinge line plunges directly down the dip of its axial surface, i.e. perpendicular to that surface's strike. |
| A18 | Stress tensor fully defined by 6 components | T | The stress tensor is symmetric ($\sigma_{ij}=\sigma_{ji}$): 3 normal + 3 shear = 6 independent components. |
| A19 | Sheath fold is cylindrical | F | Sheath folds are strongly non-cylindrical (hinge line curves through up to 180°, forming a tube/sheath) — the opposite of cylindrical, though high shear strain is correctly implicated. |
| A20 | Poisson's ratio = $\sigma/\varepsilon$ same direction | F | That description is Young's Modulus. Poisson's ratio is the ratio of transverse strain to axial strain (both strains, perpendicular directions). |
| # | Blank | Answer |
|---|---|---|
| A21 | Two mechanisms of buckle folding | Buckling (layer-parallel shortening amplifying an initial irregularity) and bending (a force applied transverse/oblique to layering). |
| A22 | Apparent relative displacement of a fault | Separation (as distinct from true slip). |
| A23 | Diffusion along grain boundaries | Coble creep (grain-boundary diffusion creep). |
| A24 | Equal-inclination points on a folded layer's surfaces | Dip isogons (Ramsay's Class 1/2/3 fold classification). |
| A25 | Fault melt that freezes to glass | Pseudotachylyte. |
| A26 | $\phi_f$ in frictional sliding | The angle of sliding friction: $\mu_s=\tan\phi_f$ in the Coulomb/Amontons frictional-sliding criterion $\tau=\mu_s\sigma_n$. |
| A27 | Coulomb Law of Failure | $\tau = C_0 + \sigma_n\tan\phi$ (shear stress at failure = cohesion + normal stress $\times$ tan of the internal friction angle). |
| A28 | Two types of point defects | Vacancies and interstitials. |
