18-Geol-A4 Structural Geology · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams, Geological Engineering, 04-Geol-A4 Structural Geology, 2017-Dec. Open book; any non-communicating calculator permitted; 3 hours; 100 marks. The paper is printed as five lettered mega-questions (A–E): Question A “answer all” 20 T/F items (20 marks), Question B “any and only 5 of 10” essay topics (30 marks), Question C “any and only 4 of 7” items (24 marks), Question D a single compulsory 12-mark Mohr–Coulomb hydrofracture/fault-reactivation problem, and Question E a single compulsory 14-mark stereonet π-diagram problem.
Reference texts: Davis & Reynolds, Structural Geology of Rocks and Regions, 3rd ed. (fold and fault mechanics, stress and strain, Mohr–Coulomb analysis, fault-valve behaviour); Fossen, Structural Geology, 2nd ed. (rheology, shear zones, fold classification, finite strain, stereographic π-diagrams); Marshak & Mitra, Basic Methods of Structural Geology (stereonets, block diagrams, joint/vein mechanics).
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.
In progressive simple shear the instantaneous stretching axes (ISA) stay fixed at 45° to the shear plane, but the finite strain ellipse's long axis rotates progressively toward the shear plane as shear strain γ accumulates. A rigid planar marker (vein or dyke) crossing the shear zone at a fixed material angle therefore experiences a changing strain field as deformation proceeds: early on, if the marker lies in the instantaneous shortening field (between the flattening axis and the shear plane), it is compressed and buckles/folds; as γ grows, the rotating strain ellipse sweeps its extensional field across the marker's orientation, and the same vein — now rotated closer to the shear plane — enters the extension field and is stretched, thinning and breaking into boudins. The vein therefore commonly preserves BOTH histories along its length: an early-formed, tightly folded (ptygmatic) segment overprinted by later boudinage as progressive rotation carried it from the shortening into the stretching field — a widely used shear-sense indicator in its own right.
A plumose (or "plume") structure is the feather-like ornamentation left on a Mode I (extension) joint surface as the crack tip propagates. Fracture initiates at a flaw (the origin) where the surface is smoothest (the mirror zone); as propagation accelerates the surface roughens into a mist zone and then a coarser hackle zone, whose ridges diverge outward from the origin like the barbs of a feather or the tributaries of a river traced upstream. Because the plume barbs always fan out AWAY from the origin and converge back toward it, the plumose pattern is a direct, physical record of local propagation direction — tracing the barbs upstream to their point of convergence locates the fracture's initiation point.
Both structures are arrays of imbricate thrust faults that splay from a single sole/floor thrust and accommodate horizontal shortening by stacking thrust slices (horses), but they differ in whether the individual thrusts merge into a common roof thrust. An imbricate fan is a set of parallel thrust faults that all root into the same floor thrust at depth but splay upward and do not reconnect — each fault carries its own hanging-wall slice up to the surface/erosion level, so the slices form a fan-shaped array exposed individually at surface. A thrust duplex has the same floor thrust at its base, but the horses are capped above by a second, throughgoing roof thrust — the horses are boxed between floor and roof and are not individually exposed at surface. In both geometries, in-sequence (piggyback) propagation is foreland-directed: each successive thrust breaks out in the footwall of (i.e. structurally beneath and in front of) the previous one, so propagation is toward the foreland and each younger fault is structurally lower than, and out ahead of, the last.
Strain hardening (work hardening) is the increase in the stress required to continue plastic deformation as strain accumulates beyond yield — on a stress–strain curve the post-yield segment continues to rise (rather than flattening at a constant flow stress), because dislocations multiply and tangle with increasing strain, progressively impeding further dislocation glide and raising the flow stress needed to keep deforming. A practical example is repeatedly bending a metal paperclip or wire back and forth: each successive bend requires more force than the last, the material stiffens locally at the bend, and it eventually fails by fatigue/embrittlement rather than continuing to flow — the geological analogue is a quartz mylonite deforming faster than dynamic recrystallization can remove the accumulating dislocations, so the rock locally hardens even while deforming plastically.
All four variables are plotted as differential stress (σ1−σ3) vs. axial strain, each as a family of curves for a "low" vs. "high" value of the variable, holding the others fixed:
a) Brittle (upper) crust: frictional/Coulomb behaviour dominates (Byerlee's law), so the controlling extrinsic variables are confining/effective normal stress (which sets frictional strength, and therefore scales strongly with depth) and pore fluid pressure (which reduces effective stress and can trigger failure at a given depth without any change in total stress — directly relevant to Question D). Temperature has only a secondary effect in this regime.
b) Ductile (lower) crust: thermally-activated creep dominates, so the controlling extrinsic variables are temperature (exponential control on creep rate via an Arrhenius-type flow law) and strain rate (power-law stress dependence of creep strength) — both directly set the flow stress in dislocation-creep/diffusion-creep regimes, while confining pressure and pore pressure become comparatively unimportant once the rock is flowing rather than fracturing.
In a ductile shear zone the mylonitic foliation (S) is the shear-zone-parallel planar fabric, and the stretching lineation is contained within that foliation plane, parallel to the transport/slip direction (the X-axis of the local strain ellipsoid). Because all of the classic shear-sense indicators (S–C fabric, rotated porphyroclast asymmetry, mica-fish obliquity) are only unambiguous when viewed on the section that contains the transport direction and is perpendicular to the foliation, the correct plane of observation is the one perpendicular to the mylonitic foliation and parallel to the stretching lineation (the "XZ" section of the strain ellipsoid). Cutting a thin section or outcrop face on any other orientation (e.g. perpendicular to the lineation) shows symmetric, non-diagnostic fabrics — a common field/lab error.
Active (buckle) folding is driven by layer-parallel shortening of a competent layer with a viscosity contrast against its weaker matrix; the fold's wavelength is intrinsically selected by the Biot–Ramberg relation (dominant wavelength ∝ layer thickness × (viscosity ratio)1/3, see Question C7). It is typical of fold-and-thrust belts and foreland regions where competent layers (limestone, sandstone, veins) are shortened. Passive folding occurs where the layering has little or no viscosity contrast with its surroundings (or is too thin/weak to buckle independently); the layers are simply transposed/dragged along with the flow of the surrounding material, so fold geometry is imposed externally (by pre-existing irregularities or the bulk strain field) rather than selected by an intrinsic instability. It is typical of high-strain ductile shear zones and mylonite zones, where sheath folds and highly attenuated similar-style folds form by passive amplification of small initial perturbations in the transposed layering.
Mechanical: (1) fluids reduce the effective normal stress via Terzaghi's principle (σ′=σ−Pp), lowering the differential stress needed to trigger brittle failure — the hydrofracturing and fault-reactivation mechanism solved quantitatively in Question D; (2) fluids lubricate grain boundaries and fault surfaces, reducing frictional resistance to slip.
Chemical: (1) pressure solution — stress-driven dissolution at grain contacts, diffusive transport, and reprecipitation in low-stress sites — enables ductile-like volume loss/shape change at temperatures far below those needed for crystal-plastic flow (classic in cleavage development); (2) hydrolytic weakening, where dissolved water in the crystal lattice (e.g. of quartz) facilitates dislocation climb and reduces crystal-plastic flow strength; (3) fluid-driven mineral reactions/metasomatism (e.g. serpentinization) can change a rock's bulk rheology outright, often dramatically weakening it.
Strain partitioning is the heterogeneous distribution of a bulk deformation into spatially and/or kinematically distinct domains, where different components of the total strain (or different strain styles) are accommodated by different structures or zones rather than every domain experiencing the same combined deformation. Applied to shear zones: bulk oblique (transpressional) plate-boundary deformation is commonly partitioned into discrete strike-slip fault zones that accommodate the non-coaxial (simple shear) component, separated by fold-and-thrust belts that accommodate the coaxial (pure-shear shortening) component — rather than every structure everywhere showing uniform oblique-slip. This partitioning explains why many orogens show parallel strike-slip faults developed alongside, but structurally separate from, thrust belts.
