Question 2 of 5: Term Pairs

Question B — Term Pairs (4 marks each: 20 marks)

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.

(1) Stress vs. Strain. Stress is the internal FORCE PER UNIT AREA (a tensor quantity, units of pressure) that a body transmits in response to applied loads — it exists in a rock even if the rock never actually changes shape (e.g. an elastic, unstrained rock under lithostatic load still supports stress). Strain is the resulting geometric CHANGE IN SHAPE, SIZE OR POSITION of the body (a dimensionless ratio of a length, angle or volume change to its original value) that stress may or may not produce, depending on the material's rheology. In short: stress is the cause (a force field), strain is one possible effect (a shape change).

(2) Traction vs. Stress Tensor. Traction is the stress VECTOR resolved on ONE specific plane through a point — a force per unit area with a magnitude and direction tied to that single surface. The stress tensor is the complete, plane-independent description of stress AT A POINT: the full set of 6 independent components (3 normal + 3 shear) from which the traction on ANY arbitrarily-oriented plane through that point can be computed via Cauchy's relation \(t_i=\sigma_{ij}n_j\). A traction is one projection of the tensor; the tensor is the complete field.

(3) Fold Axis vs. Fold Hinge. The fold HINGE is the physical line of maximum curvature on ONE particular folded surface (e.g. one bedding contact) — every folded surface has its own hinge line, and a non-cylindrical fold's hinge line is curved. The fold AXIS is an abstract, single straight-line direction that, when translated parallel to itself, can generate the ENTIRE folded surface; it exists only for cylindrical (or near-cylindrical) folds, is parallel to (but not identical to) the hinge line of a cylindrical fold, and unlike the hinge is not tied to any one bedding surface.

(4) Fault Slip vs. Fault Separation. Slip is the TRUE, three-dimensional relative displacement vector between two points that were coincident before faulting, measured on the fault surface itself — it is a single, unique vector for a given fault movement. Separation is the APPARENT offset of a specific marker (a bed, vein, or other planar feature) measured in a particular direction or on a particular exposure (e.g. "strike separation," "dip separation") — it depends on the orientation of the marker relative to the fault and to the slip vector, so the same true slip can produce very different, even opposite-sense, separations on differently-oriented markers (this is exactly the mechanism tested in Question A, item 1).

(5) Coaxial vs. Non-coaxial Strain. In coaxial (pure shear) strain, the orientations of the principal strain axes remain FIXED in the rock throughout the deformation history — the same material lines stay parallel to the principal axes at every increment, and there is no net rotation of these lines relative to the external reference frame. In non-coaxial (simple shear) strain, the principal axes of successive strain increments ROTATE progressively relative to both the external frame and to any fixed material line, so the material lines that end up parallel to the FINITE principal strain axes were not parallel to the incremental principal axes throughout, and were not mutually perpendicular before straining.