Ideal Fracture Displacement Modes

Rock deformation experiments of rocks loaded to failure under triaxial compression demonstrate symmetrical orientation of fractures with respect to the three effective principal stresses: σ₁’ > σ₂’ > σ₃’ where compressive stress is positive. The type of fracture that will develop is dependent upon the value of minimum effective principal stress (σ₃’), the difference between the maximum and minimum effective principal stresses (σ₁’- σ₃’), and the tensile strength of the rock.

There are three ideal displacement modes of fractures based on the angle with respect to σ₁’: mode I, mode II, and mode III.

 

Mode I displacement is referred to as opening or tensile mode and is purely extensional. These fractures develop at an orientation perpendicular to σ₃’ and within the σ₁’ stress plane.

 

Mode II displacement is referred to as forward shear mode, where the fracture surfaces slide over one another in a direction perpendicular to the fracture tip.

 

Mode III displacement is referred to as transverse shear mode, where the fracture surfaces move relative to one another in a direction parallel to with the fracture tip. Both mode II and III fracture planes are oriented parallel to σ₂’ and at an angle less than 45° to σ₁’.

Source: Agust Gudmundsson (2011) Rock Fractures in Geological Processes

Trishear Fault-Propagation Folding

Fault-propagation folds are produced by deformation that takes place just in front of the propagating fault. The fault tip propagates upsection, and the fold develops above the ramp with uniform fold angles.

 Figure: A) Kink-band model, B) Fold above thrust fault,

C) Fold above reverse fault, D) Fold above normal fault.

(Erslev 1991)

 

Fault-propagation fold hinges tighten and converge downward, forming a triangular zone of deformation that is concentrated on the tip of the propagating fault. This downward convergence of deformation is modeled as triangular shear zones. This lends the name to trishear fault-propagation folds.

Figure: Models of homogeneous and heterogeneous

fault-propagation trishear folds. A) Thrust faults,

B) Reverse faults, C) Normal faults. (Erslev 1991)

Understanding the geometry of fault-propagation folding is useful in creating balanced models of fold and thrust belts. Fault-propagation trishear folds are common in the Laramide structures of the Bighorn Basin in Wyoming.

All information from: Eric A. Erslev (1991) Trishear fault-propagation folding

Rigid Body Deformation & Shear Strain

Deformation is a change in form or shape. Rock masses can be translated or rotated as rigid units during deformation, without any internal change in shape. Fault blocks moving during deformation with no internal distortion.

A displacement field shows the change in position points before and after deformation in a group of displacement vectors. The displacement field does not, however, show how the particles moved during deformation history, but links the undeformed and deformed states. Particle paths show the motion of those points during deformation.

Rotation indicates rigid rotation of the entire deformed rock body. It involves uniform rotation of the rock volume relative to an external coordinate system. Large-scale rotations occur in thrust nappes or tectonic plates, usually around vertical axes. Fault blocks may rotate around horizontal axes in extensional settings.

Translation is where every particle in the rock body moves in the same direction, over the same distance. Displacement fields consist of parallel vectors of equal length. Translation of nappes can occur over 10s or 100s km.

Shear strain describes the strain due to rotation about an axis. It is deformation which involves change in internal shape.

Simple shear is a special type of constant-volume plane strain deformation. No stretching or shortening of lines or movement in the third direction of particles occurs. It is non-coaxial deformation, meaning that lines parallel to the principal strain axes have rotated away from their initial positions.

Subsimple shear is a spectrum of planar deformations between pure shear and simple shear. Internal rotation is less than for simple shear.

Pure shear is a perfect coaxial deformation. Particles parallel to the principal axes do not rotate from their initial positions. Pure shear is a plane strain with no volume change associated.

Rigid body deformation (rotation & translation),

and shear strain (simple, subsimple, & pure shear).

From Haakon Fossen's Structural Geology (2010).

ImageJ - Thin Section Porosity

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