8.3 Stress and strain in the earthquake source region
3 min read•august 9, 2024
Earthquakes occur when stress builds up in rocks until they break. This section explores how stress and strain interact in the source region, setting the stage for .
Understanding stress components, strain types, and fault mechanics is crucial for grasping earthquake processes. We'll look at how these factors combine to trigger seismic events and shape their characteristics.
Stress Components
Stress Tensor and Principal Stresses
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- Stress tensor represents the state of stress at a point in a material
- Consists of nine components describing forces acting on infinitesimal cube faces
- Principal stresses define maximum and minimum normal stresses
- Three principal stresses (σ1, σ2, σ3) act perpendicular to principal planes
- Principal stresses determined by solving characteristic equation of stress tensor
- Eigenvalues of stress tensor correspond to magnitudes of principal stresses
- Eigenvectors indicate directions of principal stresses
Shear and Normal Stress
- acts parallel to surface, causing sliding or deformation
- Normal stress acts perpendicular to surface, causing compression or tension
- Shear stress crucial in fault mechanics and earthquake generation
- Normal stress influences friction and fault strength
- Relationship between shear and normal stress determines fault stability
- Stress state on a plane described by combination of shear and normal stresses
- Stress resolution used to calculate shear and normal stress on arbitrary planes
Strain and Deformation
Elastic Strain and Material Behavior
- Strain measures relative displacement between particles in a material
- involves reversible deformation under applied stress
- Characterized by linear relationship between stress and strain (Hooke's Law)
- Elastic moduli describe material's resistance to deformation (, shear modulus)
- relates lateral strain to axial strain in elastic materials
- Elastic strain energy stored in material during deformation
- Release of elastic strain energy contributes to earthquake generation
Types of Strain and Deformation Mechanisms
- Volumetric strain involves changes in material volume
- Shear strain results in shape change without volume change
- occurs when stress exceeds elastic limit, causing permanent deformation
- characterized by sudden failure and fracturing
- Ductile deformation involves continuous, plastic flow without fracturing
- Strain rate affects material behavior and deformation mechanisms
- Time-dependent strain includes creep and stress relaxation phenomena
Fault Mechanics
Coulomb Failure Criterion and Mohr Circle
- Coulomb failure criterion defines conditions for shear failure on a plane
- Expressed as , where τ is shear stress, C is cohesion, μ is friction coefficient, σn is normal stress
- Mohr circle graphically represents stress state on all possible planes
- Radius of Mohr circle indicates maximum shear stress
- Failure occurs when Mohr circle touches or exceeds failure envelope
- Failure envelope determined by material properties and stress conditions
- Mohr circle analysis used to predict fault orientation and slip direction
Stress Drop and Fault Strength
- Stress drop measures stress release during earthquake rupture
- Calculated as difference between initial and final shear stress on fault
- Typical earthquake stress drops range from 1 to 10 MPa
- Stress drop influences earthquake ground motion and seismic energy release
- Fault strength determined by frictional properties and effective normal stress
- Static fault strength resists initial slip, while dynamic strength controls ongoing slip
- Fault weakening mechanisms (thermal pressurization, lubrication) reduce fault strength during rupture
- Stress accumulation and fault strength evolution control earthquake recurrence intervals
Key Terms to Review (23)
Brittle deformation: Brittle deformation refers to the process where rocks break or fracture when subjected to stress, rather than bending or flowing. This type of deformation occurs under relatively low temperatures and pressures, typical of shallow crustal environments, leading to faults and fractures that can significantly affect the Earth's surface during seismic events.
Charles Francis Richter: Charles Francis Richter was an American seismologist best known for developing the Richter scale, a logarithmic scale used to measure the magnitude of earthquakes. His work fundamentally changed how we quantify seismic events, providing a standardized way to compare their size and impact, influencing the understanding of earthquake characteristics, seismic instrumentation, stress and strain in earthquake regions, and the structure of the Earth's mantle and core.
Compressional stress: Compressional stress is a type of stress that occurs when an object is subjected to forces that push or squeeze it together. In the context of the earthquake source region, this stress plays a critical role in the formation of faults and the accumulation of energy that can eventually lead to seismic events. Understanding compressional stress helps explain how rocks behave under pressure and contributes to our knowledge of earthquake mechanics.
Elastic rebound theory: Elastic rebound theory explains how energy is stored in rocks when they are subjected to stress, leading to deformation until the strength limit is exceeded, resulting in a sudden release of energy that causes an earthquake. This theory illustrates the relationship between tectonic forces, the buildup of strain along faults, and the subsequent rupture that generates seismic waves.
Elastic strain: Elastic strain refers to the temporary deformation of a material when it is subjected to stress, which means it can return to its original shape once the stress is removed. In the context of the earthquake source region, elastic strain is crucial because it accumulates in rocks over time due to tectonic forces, and this stored energy is released during an earthquake, resulting in seismic waves.
Fault slip: Fault slip is the relative movement between two sides of a fault during an earthquake, measured in units of distance. This movement occurs due to the accumulation and release of stress in the Earth's crust, influencing the way strain is built up and released. The concept of fault slip is critical for understanding how seismic events release energy and relate to seismic moment and magnitude as well as the patterns of seismicity along and within tectonic plates.
Fault zone: A fault zone is a region where there is a significant amount of deformation and displacement of Earth's crust due to tectonic forces. This area typically includes multiple faults, which are fractures in the Earth's crust where blocks of rock have moved relative to one another. The stress accumulated in these zones can lead to earthquakes when the energy is released suddenly.
Moment Magnitude Scale: The moment magnitude scale is a logarithmic scale used to measure the total energy released by an earthquake, providing a more accurate representation of its size compared to earlier magnitude scales. This scale relates closely to the seismic moment, which incorporates the area of the fault that slipped, the average amount of slip, and the rigidity of the rocks involved. It is crucial in understanding seismic activity, especially for large earthquakes and those occurring in different geological settings.
Normal faulting: Normal faulting occurs when the Earth's crust is extended, causing one block of rock to move downward relative to another block. This type of faulting is primarily associated with extensional tectonic settings, where tectonic forces stretch the crust, leading to the formation of features like rift valleys and basins. Understanding normal faulting is crucial for analyzing earthquake mechanics, the distribution of stress and strain in the Earth's crust, and the dynamic processes during an earthquake rupture.
Plastic strain: Plastic strain is the permanent deformation that occurs in a material when the applied stress exceeds its yield strength. This type of strain indicates that the material has undergone a change in shape that will not return to its original form once the stress is removed, making it crucial for understanding how rocks behave under stress in the earthquake source region. Recognizing plastic strain helps in predicting how materials will respond during seismic events, influencing the stability of geological formations.
Poisson's Ratio: Poisson's ratio is a measure of the proportional relationship between lateral strain and axial strain when a material is deformed elastically. It helps to understand how materials behave under stress, influencing seismic wave velocities, elasticity, and the response of geological materials during stress events like earthquakes.
Reverse faulting: Reverse faulting occurs when two blocks of the Earth's crust are pushed together, causing one block to be thrust over the other along a fault line. This type of fault is primarily associated with compressional stress, which results in a shortening of the crust and is a key feature in regions experiencing tectonic plate convergence. Reverse faults can lead to significant ground shaking during earthquakes and influence the dynamics of seismic events.
Richard Feynman: Richard Feynman was a renowned American theoretical physicist known for his work in quantum mechanics and particle physics. He played a key role in the development of modern physics, and his contributions extend to various fields, including the principles of measurement and observation that are crucial in understanding seismic phenomena.
Richter Scale: The Richter Scale is a logarithmic scale used to measure the magnitude of seismic events, specifically earthquakes, by quantifying the amplitude of seismic waves recorded on seismographs. This scale helps in comparing the sizes of different earthquakes and provides a standardized way to communicate their intensity.
Rift zone: A rift zone is a tectonic feature characterized by a region where the Earth's crust is being pulled apart, leading to the formation of a series of faults and fissures. These areas often signify where tectonic plates are diverging, creating new crust as magma rises to the surface. Rift zones are crucial in understanding the stress and strain within the earthquake source region, as they are areas of active geological movement that can produce significant seismic activity.
Rock strength: Rock strength refers to the ability of rock materials to withstand applied stress without failing or deforming. This characteristic is essential in understanding how rocks behave under various stress conditions, particularly in regions where tectonic forces are at play, influencing the occurrence and intensity of earthquakes.
Rupture: Rupture refers to the breaking or fracturing of rock along a fault line, which releases accumulated stress and causes an earthquake. This sudden release of energy occurs when the strain on the rock exceeds its strength, resulting in displacement along the fault. Understanding rupture is crucial in grasping how stress and strain build up in the earthquake source region and eventually lead to seismic events.
Seismic wave propagation: Seismic wave propagation refers to the movement of energy through the Earth's layers in the form of seismic waves generated by earthquakes or other seismic sources. Understanding how these waves travel helps in interpreting the Earth's internal structure and the behavior of materials under stress, revealing vital information about elasticity and stress-strain relationships as well as the conditions within earthquake source regions.
Shear Stress: Shear stress is the force per unit area exerted parallel to a material's surface, typically resulting in deformation or change in shape. This concept is crucial in understanding how rocks respond to forces within the Earth's crust, especially in relation to faulting and the mechanics of earthquakes. As tectonic plates move and interact, shear stress can build up until it exceeds the strength of the rocks, leading to sudden slip events and seismic activity.
Strike-slip faulting: Strike-slip faulting is a type of fault where two blocks of the Earth's crust slide past one another horizontally. This lateral movement occurs due to shear stress, which results from tectonic forces acting parallel to the fault plane. Understanding this type of faulting is crucial because it can lead to significant earthquakes and is commonly associated with transform plate boundaries.
Subduction zone: A subduction zone is a geological feature where one tectonic plate is forced beneath another, leading to significant geological activity including earthquakes and volcanic eruptions. These zones are critical for understanding stress and strain in the earthquake source region as they involve complex interactions between converging plates, which can create intense seismic activity and influence earthquake rupture processes and dynamics.
Tensile stress: Tensile stress is a measure of the internal forces that develop in a material when it is subjected to tension, defined as the force applied per unit area. It plays a crucial role in understanding how materials deform under load and is essential for analyzing the behavior of geological materials during deformation processes. The relationship between tensile stress and strain is foundational to the concepts of elasticity, and it becomes particularly significant in the context of earthquake sources where the stress state influences fault mechanics and the generation of seismic waves.
Young's Modulus: Young's Modulus is a measure of the stiffness of a material, defined as the ratio of stress (force per unit area) to strain (deformation) in the linear elastic region of a material. This property is crucial in understanding how materials respond to stress and strain, influencing seismic wave velocities and the behavior of materials in the earthquake source region.