Illustrate the common brittle-ductile shear zone structures. Using the stress ellipsoid, deduce the mechanism of faults.

Brittle-Ductile Shear Zone Structures

Brittle-ductile shear zones exhibit a mix of deformation features. The dominance of brittle or ductile behavior depends on factors like temperature, pressure, fluid presence, and rock type. Common structures include:

• Brittle Structures: These are indicative of deformation under low temperatures and pressures.
  • Faults: Fractures along which there has been movement. Types include normal, reverse, and strike-slip faults.
  • Fractures: Fractures without significant displacement.
  • Joints: Fractures where movement has occurred, but not along the entire fracture surface.
  • Breccia: Angular rock fragments cemented together, formed by brittle fracturing.
• Ductile Structures: These form under high temperatures and pressures.
  • Folds: Bends in rock layers due to compressive stress. Types include anticlines and synclines.
  • Foliation: Parallel alignment of platy minerals, creating a layered texture.
  • Lineation: Parallel alignment of elongate minerals or structural features.
  • Mylonites: Fine-grained, highly deformed rocks formed by intense ductile shearing.
• Mixed Structures: Often observed in brittle-ductile shear zones.
  • S-C Fabrics: Characteristic of shear zones, with 'S' representing shear bands and 'C' representing more ductile shear foliation.
  • Riedel Shears: Synthetic and antithetic shear fractures forming at acute angles to the main fault.
  • Drag Folds: Folds formed due to frictional drag along a fault plane.

Stress Ellipsoid and Fault Mechanisms

The stress ellipsoid is a geometric representation of the state of stress at a point within the Earth’s crust. It’s defined by three principal stresses: σ₁ (maximum compressive stress), σ₂ (intermediate stress), and σ₃ (minimum compressive stress). The orientation and magnitude of these stresses control the type of fault that forms.

Mohr-Coulomb Failure Theory

Faulting occurs when the shear stress on a plane exceeds the shear strength of the rock. The Mohr-Coulomb failure criterion defines this relationship. It states that failure occurs when:

τ = C + μσ_n

Where:

• τ = Shear stress
• C = Cohesion
• μ = Coefficient of internal friction
• σ_n = Normal stress

Fault Types and Stress Ellipsoid

The relationship between the stress ellipsoid and fault type can be summarized as follows:

• Normal Faults: σ₁ is vertical, and σ₃ is horizontal. Extension dominates. The hanging wall moves down relative to the footwall.
• Reverse Faults (including Thrust Faults): σ₁ is vertical, and σ₃ is horizontal. Compression dominates. The hanging wall moves up relative to the footwall. Thrust faults have a low angle of dip (<30°).
• Strike-Slip Faults: σ₁ and σ₃ are horizontal. Shear stress dominates. Movement is horizontal and parallel to the strike of the fault. Right-lateral faults have movement to the right when facing the fault, and left-lateral faults have movement to the left.

Diagrammatic Representation: (A diagram showing the stress ellipsoid with σ₁, σ₂, and σ₃, and how different fault planes relate to it would be included here in an exam setting. It would show the orientation of the maximum and minimum principal stresses relative to the fault plane.)

The angle between the fault plane and the σ₁ axis (angle of internal friction) is critical. A steeper angle indicates a more brittle failure, while a shallower angle suggests more ductile behavior. The presence of fluids can reduce the effective normal stress, promoting faulting at lower stress levels.

Fault Type	Stress Regime	σ1 Orientation	σ3 Orientation
Normal	Extension	Vertical	Horizontal
Reverse/Thrust	Compression	Vertical	Horizontal
Strike-Slip	Shear	Horizontal	Horizontal