18-Geol-A4 Structural Geology · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams, Geological Engineering, 04-Geol-A4 Structural Geology, 2017-May. 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 9” essay topics (30 marks), Question C “any and only 4 of 5” items (24 marks), Question D a single compulsory 13-mark Mohr–Coulomb fault-stress problem, and Question E a single compulsory 13-mark stereonet pi-diagram problem.
Reference texts: Davis & Reynolds, Structural Geology of Rocks and Regions, 3rd ed. (fold and fault mechanics, stress and strain, Mohr circle analysis); Fossen, Structural Geology, 2nd ed. (rheology, shear zones, fold classification, finite strain, stereographic pi-diagrams); Marshak & Mitra, Basic Methods of Structural Geology (stereonets, block diagrams, pi-diagram construction); Sylvester (1988) “Strike-slip faults,” GSA Bulletin (Riedel-shear and restraining/releasing-bend geometry, cited via Davis & Reynolds Ch.9).
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.
Both structures are arrays of imbricate thrust faults that splay from a single sole/floor thrust, and both accommodate horizontal shortening by stacking thrust slices, but they differ in whether the individual thrusts merge into a common roof thrust. An imbricate fan is a set of parallel (or sub-parallel) thrust faults that all root into the same floor thrust (sole thrust) at depth but splay upward and do not reconnect — each fault carries its own hanging-wall slice up to (or near) the surface/erosion level, so the slices form a fan-shaped array of overlapping horses that are exposed individually at the topographic/erosional surface. A thrust duplex has the same floor thrust at its base, but the individual thrust slices (horses) are bounded above by a second, throughgoing roof thrust that caps the whole structure — the horses are stacked between the floor and roof thrusts and are not necessarily exposed individually at the surface. The key difference is therefore the presence of a bounding roof thrust: a duplex is a “closed” box of horses between floor and roof thrusts, while an imbricate fan is an “open” splay with no roof thrust, each slice cutting up-section to the surface.
All four variables are plotted as differential stress (σ1−σ3) vs. axial strain, each as a family of curves for “low” vs. “high” value of the variable, holding the others fixed:
In a ductile shear zone the mylonitic foliation (S) is the shear-zone-parallel planar fabric (sub-parallel to the shear-zone boundary at high strain), 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) will show symmetric, non-diagnostic fabrics, which is a common field/lab error.
Parallel (Class 1B) folds maintain constant true (orthogonal) layer thickness around the fold — the dip isogons (lines joining points of equal dip on adjacent surfaces) are perpendicular to bedding and converge toward the concave (core) side, radius of curvature decreases inward, and folding dies out with depth/height (cannot be extended indefinitely without a detachment) unless accommodated by flexural slip between layers. They are typical of folding of strong, well-layered competent sequences at shallow structural levels (e.g. thin- to thick-bedded carbonate/sandstone sequences in a fold-and-thrust belt, formed by flexural-slip/flexural-flow buckling). Similar (Class 2) folds instead preserve constant layer thickness measured parallel to the axial surface (true thickness varies, thinning on the limbs and thickening in the hinge), the dip isogons are parallel to the axial surface (neither converging nor diverging), and the fold shape is geometrically self-similar at every structural level (can, in principle, continue indefinitely with depth). Similar folds are typical of weaker, more ductile rocks (e.g. shale, slate, schist) deformed at deeper structural levels / higher metamorphic grade, where passive flow/homogeneous flattening dominates over flexural slip.
True net slip is the actual 3-D displacement vector of a point on the fault surface between its offset positions in the hanging wall and footwall, and it cannot be measured directly from a single 2-D exposure; it requires (i) a piercing point — a linear or point feature (e.g. an intersection of two markers, a dyke/vein margin, a fold hinge, a stratigraphic contact intersection) that is offset by the fault and whose position can be located precisely on both sides of the fault; (ii) the orientation of the fault plane (strike and dip), since net slip is measured within that plane; and (iii) the 3-D coordinates (or bearing/plunge and distance) of the piercing point on each side, from which the net-slip vector’s trend, plunge and magnitude can be computed as the vector connecting the two piercing-point positions, resolved into the fault plane. Without a genuine piercing point, only an apparent (strike or dip) separation can be measured, not the true net slip.
Dislocation creep is a crystal-plastic deformation mechanism operating at elevated temperature and moderate-to-low strain rate, in which permanent strain accumulates through the nucleation and glide (and thermally-activated climb) of line defects (dislocations) through the crystal lattice, rather than through brittle fracture or diffusive mass transfer. A dislocation is a line defect marking the boundary of a slipped region of the lattice; under differential stress it glides along specific crystallographic slip planes/directions (the crystal’s slip systems), each glide event displacing the lattice by one Burgers vector. Where glide alone is insufficient to relieve local strain incompatibilities (e.g. dislocations pile up at grain boundaries or obstacles), thermally-activated climb allows a dislocation to move out of its glide plane by diffusion of vacancies to/from the dislocation core, bypassing the obstacle. The combined glide-plus-climb process (dislocation creep) produces intracrystalline strain, crystallographic preferred orientation (lattice-preferred orientation fabrics), and dynamic recrystallisation (sub-grain rotation and grain-boundary migration) as dislocation densities build up and are annealed — the microstructural hallmark of mylonitic rocks.
Coaxial strain (pure shear) is a deformation history in which the orientations of the incremental and finite principal strain axes remain fixed (parallel) with respect to an external reference frame throughout progressive deformation — there is no bulk rotation of material lines relative to the principal strain axes beyond that produced by the strain itself. Non-coaxial strain (simple shear) is a deformation history in which the principal strain axes progressively rotate relative to the external frame as strain accumulates, and material lines (other than the principal axes) undergo a component of rigid-body rotation in addition to stretching. Examples of structures formed by coaxial strain: symmetric boudinage of a competent layer under layer-parallel or layer-normal stretching, and symmetric (upright, non-vergent) buckle folds formed by pure-shear layer-parallel shortening. Examples formed by non-coaxial strain: asymmetric (sheared) boudins with rotated, shingled fragments, and rotated (σ/δ) porphyroclasts with asymmetric tails in a ductile shear zone.
The plotted Mohr circle represents the full range of normal and shear stress resolved on planes of every orientation for a given (σ1,σ3) state; because the whole circle lies below the linear Coulomb failure envelope τ=C+σntanφ, no plane in the rock is stressed to failure — this is a stable state of stress. Effective stress is the stress actually transmitted through the mineral grain framework once pore fluid pressure is subtracted from the total stress (σ′=σ−Pp, Terzaghi’s principle); because pore pressure acts equally (isotropically) on all planes, raising Pp reduces both σ1 and σ3 by the same amount, which translates the Mohr circle to the left along the σn axis without changing its radius (i.e. without changing the differential stress or the shear stress on any plane). A stable, sub-critical stress state can therefore be driven to failure purely by increasing pore pressure, with no change whatsoever in the applied total (tectonic) stresses — the mechanism exploited quantitatively in Question D below.