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18-Geol-A4 Structural Geology · December 2013

Question 5 of 5: Choice Question – Stereonet Reading or Deformation Sketching

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

EGBC National Exam — Geological Engineering, 04-Geol-A4 Structural Geology, 2013-Dec. Open book; any non-communicating calculator permitted; 3 hours. The paper is printed as five lettered mega-questions (A–E): Question A instructs "answer 15 of these 20" T/F items, Question B "any and only 8 of the following" (14 term pairs), Question C "any and only 5 of the following" (9 essay topics), Question D "ONE and ONLY ONE of D-I or D-II," and Question E "ONE and ONLY ONE of E-I or E-II."

Check: page 1's NOTES state "FOUR questions constitute a complete exam paper," yet the paper prints FIVE lettered mega-questions (A–E). Read together with "choices in each main question," this is taken to mean a complete SELECTED paper is A + B + C + (D-I or D-II) + (E-I or E-II) — i.e. every lettered question is compulsory, with the internal choice living inside D and E (and inside A/B/C's own "answer N of M" sub-instructions) — not that one of A/B/C/D/E may be skipped outright.

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); Marshak & Mitra, Basic Methods of Structural Geology (stereonets, block diagrams); Hoek, Practical Rock Engineering; Bieniawski, Engineering Rock Mass Classifications (RQD/RMR, rock mass strength).

Question E: Choice Question – Stereonet Reading or Deformation Sketching (ONE and ONLY ONE of E-I or E-II – 10 total; both solved here)

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.

Check: the printed stereoplot gives only approximate cluster positions (quadrants and rough locations), and the question itself only asks for APPROXIMATE/ESTIMATED values. The bedding/lineation attitudes below are therefore representative readings consistent with the cluster positions (limb 1 pole ≈320/50, limb 2 pole ≈140/35, lineation ≈108/19), not exact plotted values — the METHOD (girdle/pi-diagram construction) is the graded content.

E-I – Stereonet reading: fold axis, profile plane, axial plane

E-I Lower-hemisphere stereonet: bedding (B), lineation (L), fold elementsNESWBLF (050/08)profile plane trace (140/82)axial plane trace (050/78)Bedding poles (B), two limbsLineation (L)Fold axis β (~050/08)Profile plane (~140/82)Axial plane (~050/78)
E-I. Two bedding-pole clusters (B, solid, limb 1 ≈320/50 and limb 2 ≈140/35) share a common strike (≈050–230), so their girdle's pole — the fold axis β (blue) — trends approximately 050° and plunges gently (≈8°) NE. The profile plane (green, dashed) is perpendicular to the fold axis; the axial plane (purple, dashed) bisects the interlimb angle. The lineation cluster (L, red, ≈108/19) plots close to, but not exactly on, the fold-axis great circle — consistent with a gently oblique intersection/mineral lineation rather than being exactly axis-parallel.
  1. (a) Fold axis. Both bedding-pole clusters (representing the two limbs) share essentially the same strike (≈050°/230°), so the great circle (girdle) that best fits both clusters has a strike of ≈050° and near-vertical dip; its POLE — the fold axis β — therefore trends approximately 050°, plunging gently (≈8°) to the NE.
  2. (b) Profile plane. The profile plane is by definition perpendicular to the hinge line, so its strike is rotated 90° from the fold axis trend: strike ≈140°. Because the fold axis plunges only gently, the profile plane must dip steeply to remain perpendicular to it: dip ≈82°. Strike/dip ≈ 140°/82°.
  3. (c) Axial plane. The axial plane must contain the fold axis (strike ≈050°, matching the fold-axis trend) and bisects the angle between the two limb dips (≈40°NW on limb 1, ≈55°SE on limb 2): strike/dip ≈ 050°/78° (steep, slightly asymmetric toward the shallower-dipping limb).
  4. (d) Apparent dip on a 180°-striking cliff. The profile plane strikes 140°, dips 82°; the cliff strikes 180° (due N–S), a difference of $\Delta=180-140=40^\circ$: $$\tan(\text{apparent dip}) = \tan(82^\circ)\cos(40^\circ) = 7.115\times0.766 = 5.45 \;\Rightarrow\; \text{apparent dip} = \boxed{79.6^\circ}$$
  5. (e) Fold description (three standard terms). With a gently NE-plunging hinge (≈8°), a steep axial surface (≈78°), and an interlimb angle of roughly $180^\circ-40^\circ-55^\circ\approx85^\circ$ (open range, 70–120°), the fold is best described as an upright, gently (NE-)plunging, open fold.

E-II – Simple-shear deformation of a square, circle, and four reference lines

BEFOREcabdAFTER (γ=1, 45° dextral)bdcaaxis of min. finite stretch
E-II. BEFORE: square + inscribed circle with reference lines a (competent, initially −45°), b (competent, horizontal, parallel to the shear plane), c (competent, initially +45°), and d (ductile-host material, initially vertical). AFTER 45° (γ=1) dextral simple shear: the square becomes a parallelogram, the circle becomes the finite strain ellipse (long axis rotated to ≈31.7° from the shear plane, on the extensional/dextral-consistent side), line b (shear-parallel) is unrotated and unchanged in length, line d (originally perpendicular to shear) rotates toward the shear plane and lengthens, line c (initially at the incremental-stretching orientation) rotates and lengthens further, and line a (initially at the incremental-shortening orientation) rotates and shortens, ending up nearest the ellipse's short axis.
  1. (a)/(b) — deformed geometry. For plane-strain simple shear with shear strain $\gamma=\tan\psi=\tan45^\circ=1$ about a horizontal shear plane, dextral sense (top block translates +x relative to bottom): the square becomes a parallelogram (top edge shifted right by $\gamma\times\text{height}$, side length preserved) and the inscribed circle becomes the finite strain ellipse with axial ratio $R_s=\left(\sqrt{1+\gamma^2/4}+\gamma/2\right)^2\approx2.62$, long axis rotated to $\theta'=\tfrac12\tan^{-1}(2/\gamma)=31.7^\circ$ from the shear plane (upper-right leaning, the extensional quadrant for dextral shear). Line b (parallel to the shear plane) is a "no-rotation" material line: it translates but does not rotate or change length. Line d (originally vertical, perpendicular to shear) rotates by the full shear angle $\psi=45^\circ$ toward the shear direction and lengthens substantially (it now runs corner-to-corner of the parallelogram). Being competent dykes, lines a, b, and c stay straight and simply rotate/stretch rigidly (no internal folding); line d, sharing the host's ductile rheology, deforms homogeneously WITH the host — consistent with the question's own assumption.
  2. (c) — axis of minimum finite stretch. The short axis of the finite strain ellipse (perpendicular to the long axis found above) lies at $\theta'+90^\circ\approx122^\circ$ from the shear plane — the orange dashed line in the AFTER panel. This is the direction of LEAST elongation (though still >1 in this constant-area, non-plane-perpendicular sense for simple shear); it lies closest, among the four reference lines, to originally-competent line a (initially at −45°, the incremental-shortening orientation), which is correspondingly the line that visibly shortens most in the AFTER sketch — though the exact ellipse short axis and line a's rotated orientation are not identical, since only two specific material-line orientations (line b, and one other, not among a/c/d here) have exactly zero finite elongation in simple shear.
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