Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2023 / Paper 1 / 2

The offset layered sequence indicates reverse slip on the west-dipping fault: its western hanging wall moved up relative to the eastern footwall. With the fault strike perpendicular to the east–west image plane, an Andersonian faulting regime has ${\sigma }_1$ horizontal east–west, ${\sigma }_2$ horizontal north–south, and ${\sigma }_3$ vertical. Draw opposing compression arrows east–west and a smaller opposing pair vertically; the intermediate pair points into and out of the page.

For example, in east, north, up coordinates, a compression-positive effective stress tensor consistent with a $30^{\circ }$ reverse fault and zero cohesion isThese magnitudes illustrate one possible stress tensor, rather than a measurement from the photograph. With $\mu =1/\sqrt{3}$, the ${\sigma }_1$–${\sigma }_3$ Mohr circle is tangent to the Mohr-Coulomb failure criterion at a plane $30^{\circ }$ from horizontal. The original failure-mechanics figure above sketches these principal stress directions.

Interpret the vertical, apparently unoffset fractures as opening geological joints. Their normals are east–west, so the least principal stress ${\sigma }_3$ must be east–west and sufficiently tensile in effective stress. The other two principal stresses lie within the vertical north–south geological joint plane; their ordering cannot be recovered from this fracture orientation alone.

One example, with compression positive and coordinates east, north, up, isHere ${\sigma }_1$ is vertical, ${\sigma }_2$ north–south, and ${\sigma }_3=-3\mathrm{MPa}$ east–west. The geological joint opens east–west when its tensile strength is $3\mathrm{MPa}$. An isotropic pore pressure can make the east–west effective stress tensile even while the total normal stress remains compressive. Draw opening arrows pointing away from the vertical fracture, rather than sliding arrows along it.

Use compression-positive effective stress normal to the plane ${\sigma }_n^{\prime }$ on the horizontal axis and shear stress $\tau$ on the vertical axis. For any chosen pair of principal stresses, Mohr's circle has centre $C=({\sigma }_1^{\prime }+{\sigma }_3^{\prime })/2$ and radius $R=({\sigma }_1^{\prime }-{\sigma }_3^{\prime })/2$.

For the reverse fault example, $C=60\mathrm{MPa}$ and $R=30\mathrm{MPa}$. Draw the two Mohr-Coulomb failure criterion lines $\tau =\pm {\sigma }_n^{\prime }/\sqrt{3}$. The tangencies areThese are shear failure points with nonzero shear stress. The two smaller three-dimensional Mohr circles use $({\sigma }_1^{\prime },{\sigma }_2^{\prime })$ and $({\sigma }_2^{\prime },{\sigma }_3^{\prime })$; they lie inside the outer circle and do not touch the envelope in this example.

For the opening geological joints, use the tensile failure criterion ${\sigma }_n^{\prime }=-T_0$. The example gives $C=3.5\mathrm{MPa}$, $R=6.5\mathrm{MPa}$ and $T_0=3\mathrm{MPa}$. The circle first touches this vertical cutoff at $({\sigma }_n^{\prime },\tau )=(-3,0)\mathrm{MPa}$. Thus the geological joints form on planes normal to ${\sigma }_3$ and have zero resolved shear stress. A complete brittle envelope can combine this tensile cutoff with compressive Mohr-Coulomb failure criterion, using sufficient cohesion that shear failure does not occur first. The failure-mechanics figure displays these two distinct constructions.

The reverse fault requires strong east–west compression; the vertical opening geological joints require the least principal stress in the effective stress tensor east–west. They need not have formed at the same time or under the same local stress field. Compression can form the reverse fault during burial and crustal shortening; subsequent tectonic exhumation, unloading, relaxation, cooling or another tectonic episode can rotate the principal stress ordering and permit opening geological joints.

Furthermore, local stress near faults, layer interfaces and topography can differ from the regional stress. A high pore pressure shifts every Mohr circle left by $p$, helping tensile failure, but isotropic pore pressure alone cannot exchange the east–west and vertical principal stress ordering. Determine relative timing using cross-cutting relations, offsets of geological joints, and any generations of fracture-filling minerals. Spatial coexistence is therefore evidence of a deformation history, rather than a requirement that the two failure diagrams describe one simultaneous homogeneous stress state.

Within a shallow fault zone undergoing brittle fracture, repeated sliding crushes and grinds grains. Expect fault gouge, potentially rich in fine clay minerals, and coarser angular fault breccia; a cohesive, cemented crushed rock is a cataclasite. Slickensides or displaced grains can record the sliding direction.

An opening geological joint need not contain any fault rock: it may be an open crack. If fluids circulated, it can contain a mineral vein, for example calcite or quartz, grown from the fracture walls. Thus comminuted fault rock supports shear, while open space or a crack-filling mineral vein supports opening. Mineral filling is conditional on fluid chemistry and timing; its precise composition cannot be inferred from the photograph.