Kinematic model in extension

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Table of contents

1 General Introduction 
1.1 Geology of extensional collapses
1.1.1 Natural examples of gravity and tectonic extensional modes
1.1.2 Kinematic model in extension
1.1.3 Analogue modeling
1.2 Mechanics of extensional collapses
1.2.1 Fluid Pressure
1.2.2 The Critical Coulomb Wedge (CCW) theory
1.2.3 Numerical modeling
1.3 Methodology used here : Limit Analysis and Sequential Limit Analysis
1.4 Manuscript content
2 Tectonic and gravity extensional collapses in over-pressured cohesive and frictional wedges2 
2.1 Introduction
2.2 Limit analysis for extension
2.2.1 Prototype and collapse mechanisms
2.2.2 Theorem of effective virtual powers
2.2.3 Maximum strength theorem (MST)
2.3 Gravitational collapse
2.3.1 General stability conditions based on the MST
2.3.2 Comparison with CCW theory
2.3.3 The role of cohesion in a triangular wedge
2.3.4 Experimental validation
2.4 Tectonic extensional collapse
2.4.1 Mechanism (1): decollement fully activated
2.4.2 Mechanism (2): a normal fault rooting at the back-wall
2.4.3 Mechanism (3): a normal fault and a shear plane rooting on the decollement
2.4.4 Comparison with CCW theory for extensional collapse
2.4.5 Experimental validation
2.5 Application to North Chile
2.6 Conclusion
3 Deformation pattern during normal faulting: a sequential limit analysis 
3.1 Introduction
3.2 Sequential Limit Analysis of a Homogenous Wedge under Extension
3.3 Simulation Results and Interpretation by the CCW Theory
3.3.1 Numerical Results for the Case of a Dry Wedge
3.3.2 Internal Deformation Pattern for the Case of a Dry Wedge
3.3.3 Numerical Results for the Case of an Overpressured Wedge
3.4 Roles of Fault Softening and of Sedimentation
3.4.1 Reference Simulations
3.4.2 Fault Softening
3.4.3 Sedimentation and No Fault Softening
3.4.4 Combined Effects of Sedimentation and Fault Softening
3.5 Application to Jeanne d’Arc Basin, Grand Banks, Newfoundland
3.6 Conclusions
4 Reappraisal of gravity instability conditions for offshore wedges: consequences for overpressures in the Niger Delta 
4.1 Introduction
4.2 Gravity instabilities with Limit Analysis
4.2.1 General prototype
4.2.2 Application of Limit Analysis
4.3 Validation for an inclined layer
4.3.1 Comparison with other analytical results
4.3.2 Validation with sandbox experiments in fluid overpressured conditions
4.4 Application to the offshore Niger Delta
4.4.1 Stability conditions
4.4.2 Stability Analysis of Niger Delta
4.5 Concluding discussions
5 Role of fluid overpressures on the shape of normal faults in brittle, upper crust 
5.1 Introduction
5.2 The prototype
5.2.1 The velocity field
5.2.2 The bounding of the tectonic force
5.3 Convergence analysis and validation with slip-line theory
5.3.1 Convergence analysis
5.3.2 Validation with the slip-line theory
5.4 Results of normal faulting
5.4.1 Influence of geometries of the prototype
5.4.2 Influence of fluid-retention depth ZFRD and material cohesion
5.5 Applications to sedimentary upper crust
5.5.1 Faulting in NW Gulf of Mexico
5.5.2 Faulting in offshore Niger Delta
5.6 Concluding discussions
6 Conclusions 
6.1 Limit Analysis
6.1.1 Gravity and tectonic extensional collapses
6.1.2 Gravity instability with a resistive toe
6.1.3 Formation of low-angle and listric normal fault
6.2 Sequential Limit Analysis
6.3 Perspectives
A Appendix for Chapter 2
1 Different fluid pressure parametrizations
2 Exact critical Coulomb wedge theory (ECCW)
B Electronic Supplement to Chapter 2
1 Theorem of virtual powers with acceleration contribution
2 A weak expression of Archimedes theorem
3 Derivation of three upper bounds
C Electronic Supplement to Chapter 3
1 Preliminary
2 The upper bound forces for three mechanisms in Section 3.3
3 Upper bound for a normal fault piercing the cover, Sections 3.4 and 3.5
4 Kinematics of hanging-wall deformation
5 Cross-sections of Jeanne d’Arc Basin, Section 3.5
6 Some results of inverse analysis for Section 3.5
D Appendix for Chapter 4 173
1 General solution of the kinematic approach of LA
1.1 General prototype
1.2 Inclined layer
1.3 Triangular Wedge
E Electronic Supplement to Chapter 4
1 Different fluid pressure parametrizations
2 Analytical collapse length and fault dips for an inclined layer
F Appendix for Chapter 5
1 Geometric relations
2 Velocity relations and Limit Analysis