Mechanics of Structural Deformation PDF

# Mechanics of Structural Deformation ## Rocks Strength - Rocks of earth's crust have strength. - Defined as the force (load) per unit area required to deform the rocks permanently - that is break or yield continuously. - Fluids (gas and liquid) have no strength. They yield continuously under the...

# Mechanics of Structural Deformation ## Rocks Strength - Rocks of earth's crust have strength. - Defined as the force (load) per unit area required to deform the rocks permanently - that is break or yield continuously. - Fluids (gas and liquid) have no strength. They yield continuously under the slightest load(stress). ## Factors Affecting Rock Strength - **Temperature:** Increase of temperature tends to decrease rock strength. - Many solid rocks buried deep within the earth's crust have bent and flowed in response to the heat and pressure of the earth's interior. - The same rocks at the surface deform only by breaking. - **Pressure:** The strength of the rocks increases when placed under uniform pressure - confining pressure - a condition that it is familiar at deep levels below the surface. - As a result of confining pressure, increase of temperature with long geological time, rocks may deform at depth in a form that is totally different from their behavior at the surface. ## Rock Strength Types - **Compressional Strength:** Resistance to uniform pressure applied on rocks. - **Tensional Strength:** Resistance to tension on rocks (tensile strength). - **Shear Strength:** Resistance to forces that cause shear in rocks. - Shear may take place along bedding planes, fault and joint planes, or along cleavage directions. ## Stress and Strain - In estimating different types of rock strengths and the effects they impact on rocks, the terms stress and strain are used. - **Stress:** Physical quantity (σ) defined as the external force (p) applied on a unit area (A) of the rock. i.e. σ = p/A in Newton/mm². ## Examples of Rock Strength (in N/mm²) | Rock Type | Compressional | Tensional | Shear | |---|---|---|---| | Granite | 100-250 | 7-25 | 14-50 | | Sandstones | 20-170 | 4-25 | 8-40 | | Limestones & Dolomites | 30-250 | 5-25 | 3-30 | | Shales & Mudstones | 5-100 | 2-10 | 3-30 | ## Stress on Earth's Crust - Rocks of the earth's crust are naturally subject to various stresses: - Compressional - Tensional (where P is perpendicular to A) - Shear (where P is parallel to A) - **Strain** (e) describes the deformation (distortion) resulting in rocks due to the external stresses. - The strain in rocks may be an elastic strain (where ε α σ i.e. linear change). ## Elastic Limit - Up to a limit called the elastic limit (σ_α): - Stress is removed, and a rock returns to its original form, or - With an increase of stress, it may be plastic (ductile), representing a permanent change in the rock. this occurs at the yield point B beyond the elastic limit. - The change up to stress σ_α is an elastic change, and the rock returns to its original form after the removal of stress. - An example of this behavior is observed through the passage of seismic (elastic waves) in crustal rocks. - At the yield point B, the rocks start to behave plastically (ductile), where the main strain becomes permanent. - Beyond B, and under the absence of any confining pressure, the plastic behavior of the rock may be terminated by total failure (rapture) represented by faulting and jointing. ## Elastic Moduli - The elastic properties of rocks are described by elastic moduli or constants which express quantitavly the relation between different types of stresses and strains. - **Young's Modulus (E):** Describes the elastic change (strain) in materials under compression or tension. - E = stress/strain = p/A * ΔL/L where ΔL is the change in length caused by longitudinal stress. - **Bulk Modulus (K):** Is a measure of the stress : strain ratio under uniform (hydrostatic) pressure which produces ΔV change in volume V. - K = p/A ÷ ΔV/V. - **Rigidity (Shear) Modulus (n):** Is a measure of stress : strain ratio under simple tangential stress (shear). The shearing strain occurs without change in volume. - n = pA/A*η where A is ⊥ to P. ## Rock Behavior - Rocks differ in their mechanical properties. Behavior depends on their type (igneous or sedimentary), porosity, matrix cement, and rate of stress application. - At deep levels within the ground, sedimentary strata under confining stress and high temperature behave plastically (become ductile) forming undulations (folds), and under greater stresses of varying directions caused by different earth's tectonic movements may become fractured (rupture) into joints and faults. ## Types of Rock Deformation - **Elastic Deformation:** For example, occurs during the passage of earthquake waves. It cannot be observed because no permanent effect remains. - **Plastic Deformation:** Can be observed in folds and salt domes etc. because of the remaining permanent effect. - **Rapture:** Can be observed in joints & faults in rocks, especially in brittle rocks. # Folds - Undulations of different shapes observed on the sedimentary strata. - A complete fold consists of an arched portion of the strata (anticline) and a depressed trough in the same strata (syncline). ## Parts of Folds - **Crests (Crest line):** Line which joins the highest point of the fold. - **Troughs:** Depressions, alternating with crests. - **Limbs (Flank):** The sloping side from the crest to the trough. - **Axial Plane:** An imaginary plane bisecting the vertical angle between equal slopes on either side. - **Axis of Fold:** Line of intersection of the axial plane and the bedding. It is the direction in which a fold trends. - **Plunge of Fold:** Dip of the fold axis at any points. ## Types of Folds - **Symmetrical Fold:** Vertical axial plane. - **Asymmetrical Fold:** Axial plane inclined and therefore the limb dip at different degrees. - **Overturned Fold:** With increase of axial plane's inclination, the limbs become dipping in the same direction. - **Recumbent Fold:** The axial plane becomes near horizontal. ## Recognition of Folds in the Field - Repetition of outcrops of beds. - Reversal of dip direction from one outcrop to the other. - In anticlines, the oldest beds occupy the axial position while in synclines, the younger beds will occur there. - A plunging fold gives rise to curved outcrops, the apex of which is called Closure with respect to the flat surroundings. # Joints - Cracks or fractures present in the rocks along which no displacement is observed. - Occur in all types of rocks. - May be vertical, inclined, or horizontal. - Their dip and strike are measured in the same way as sedimentary strata. - Their presence in rocks increase and facilitate the passage of fluids in rocks. - A group of joints having the same direction are called joint sets. ## Types of Joints - **Tension Joints:** Formed as a result of tensional forces. These joints are open and have rough and irregular surfaces. - **Shear Joints:** Caused by shearing stresses involved in folding and faulting of rocks. These are regular and tightly closed. They may occur in two intersecting sets at high angles, forming a "conjugate joint system". ## Classification of Joints 1. Mode of Origin: Either tension or shear 2. Attitude: Either strike, dip, or oblique. - **Strike Joints:** Parallel to strike of rocks. - **Dip Joints:** Parallel to dip of rocks. - **Oblique Joints:** Run in a direction between that of dip and strike joints. # Faults - Fractures along which movement of one side relative to the other has taken place. - Movement may vary from a few centimeters to many kilometers, depending on the nature and magnitude of the stresses and the resistance of rocks. ## Elements of a Fault - **Fault plane:** The plane along which the fracture has taken place, or where one block is moved relative to the other. It is usually formed along the line of least resistance - **Hanging Wall:** The block above the fault plane. - **Foot Wall:** The block below the fault plane. - **Dip of Bed:** Max amount and direction of bed indin - **Strike of Bed:** Any straight horizontal line on the bed surface. - **Dip:** Normal to Strike ## Other Fault Terms - **Hade:** The inclination of the fault plane from the vertical. - **Throw:** The vertical displacement between the hanging and foot walls. - **Heave:** The horizontal displacement. ## Types of Faults - **Normal Fault:** The hanging wall has moved down relative to the foot wall. Such faults occur under tensional forces in the earth's crust. - **Reverse Fault:** The hanging wall is moved upwards relative to the foot wall. Such faults are found in areas of compressional forces of the earth's crust. - **Thrust Fault:** A form of reverse fault with much enlarged hade. - **Strike Fault:** Runs parallel to strike of strata; dip faults are those which run parallel to dip direction of strata (called transverse faults). ## Recognizing Faults in the Field - Fault breccia - Repetition or omission of beds (displacement) - Termination of structures # Unconformity - In the field of strata formation, **conformity** refers to the regular and parallel arrangements of strata where the new lies on top of the old in accordance with the law of super position. - Such a group of strata are called **conformable strata** or beds. - **Unconformity** refers to any break in the formation (sedimentation) of the strata. It refers to an old erosion surface that separates younger series of rocks from the older series. - Represents a long period during which the old series was leveled off by erosion before the deposition of the new series. - Used in geologic time dating. ## Types of Unconformity - **Disconformity:** The beds on either side are parallel. - **Angular Unconformity:** The beds on either side are not parallel. ## Recognizing Unconformity in the Field - Marked difference in fossils. - Presence of conglomerate at the base of the new series. - Difference in structure between the two series. - Difference in conditions of deposition. - Often used as an oil trap.