It is also the math ematical description of the relative position of two infinitesimal points during the deformation of rocks. When rocks are subjected to small strains at low confining pressure (or mean stress) we find that the stress is proportional to the strain, and the strain is recoverable (i.e. In the lab, if we dont want to run our experiments for hundreds of years, its not feasible to achieve strain rates much below 10-8 strains per second. Geological strain rates are of the order of 10-12 10-15 strains per second. What about the rest of the stress? Stress is a dynamic term whereas strain is purely kinematic.

Real rocks are a bit more complicated than the ideal. Where the pressure is due to overlying rock, not fluid, the term lithostatic stress is sometimes used. \par \pard \widctlpar \par }. If the confining pressure is higher still, or the temperature is raised, a different type of behaviour occurs. Newton's first law of motion states that "Every body persists in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces impressed on it". Even in everyday life, its difficult to measure a force or stress directly. Two points can change by translating together, rotating around each other, or changing in distance relative to one another. 1 Pascal isnt enough to do detectable damage to any kind of rock. \par \pard \fi720\ri-180\widctlpar\tx2160\tx6480\tx8819 \par Structural geology is the study of the geometry, kinematics, and dynamics of rock structures. The very presence of faults and folds in the crust suggests that rocks, seemingly at rest, were once su bject to forces that changed their original state by motion of one point relative to another. The strain rate is proportional to the stress. A study of the motion causing the geometries within rocks is called {\b kinematics}. High gradients occur in a region of magmatic intrusion. {\b Geometric analysis} is the descriptive or qualitative portion of structural geology. Experimental rigs are used to study the types of stress that are necessary to produce different kinds of strain in rocks. However, pressure is still a useful concept. basin \par \pard \fi720\widctlpar\tx2160\tx6480\tx8639 {\b \par }\pard \fi720\widctlpar {\b Dynamics} is the study of the forces which caused the deformations studied during kinematic analysis. It is only because the spring has very precisely known dynamic properties (stress and strain are proportional for the spring) that we can use that strain to infer something about your weight. Structural geology is the study of the deformation of rocks. In an experimental rig the result is a loud bang and the sample disintegrates. The unit of stress is 1 N/m2 or 1 Pa (Pascal). Normal stress, also known as normal traction n is the part of that stress that acts perpendicular to the surface. \par \par Like any physical science, structural geology comes complete with its table of numerical data and symbols for physical properties.

Each 1 m2 of the skin of the submarine experiences the same force, acting perpendicular to that surface. structural Second, its possible to prove that there are always three mutually perpendicular planes that experience no shear stress. All these units can be used to describe pressure. For example, when you stand on a bathroom scale, you are deforming a spring (thats strain!). Finally, the rock composition exerts considerable influence as well. Each surface of a mineral grain within the Earth experiences a different force concentration depending on its orientation. A great deal has been learned from such experiments. You may encounter the atmosphere (atm), and the pound per square inch (psi). A comparable table involves numerical data which depend on circumstances such as geographic location and are, therefore, not strictly physical constants. First, if we represent all the stresses acting on all the surfaces as vectors, drawn as arrows, the tails of those arrows make an ellipse (in 2-D) or an ellipsoid (in 3-D). We call them principal stresses and label them, in order: The directions of the principal stresses are called the stress axes. The normal stresses they experience are the maximum, minimum, and an intermediate value of normal stress. Note: some textbooks define two different quantities: traction is the force per unit area on a single plane, a vector quantity; stress is the total of forces acting on all possible planes that pass through a point in the Earths crust, a tensor quantity. At first sight this is a bewildering mess of forces, all acting in different directions at the same point, but there are some relationships between the various forces that simplify things. Water, air, magmas, and rock salt may show approximately Newtonian behaviour. Hydrostatic stress is the special case where 1 = 2 = 3 and is equivalent to pressure in a fluid. 1 - Introduction\tab \tab \chpgn \par }{\*\pnseclvl1\pnucrm\pnstart1\pnindent720\pnhang{\pntxta . In the Earths crust the result is an earthquake. Hydrostatic stress is the type of stress experienced by a submerged submarine. At temperatures close to their melting point, some rocks show a much simpler type of flow behaviour without a yield stress. In a general way, these three regimes correspond respectively to typical states of stress near the three types of plate boundary: spreading centres, transform faults, and subduction zones. It is the part of the stress that acts within the solid components of a porous rock. For this reason, near the Earths surface, one of the principal stresses is approximately vertical, and the other two are approximately horizontal. Its very important to distinguish dynamic concepts from kinematic ones. In solids, the situation is more complex. As stress and strain are increased, eventually most rocks undergo a catastrophic loss of strength, with the release of stored strain energy. What controls how a given rock will respond to stress? In much of the Earths crust, the state of stress is non-hydrostatic. This idea was first promoted by Scottish geologist William Masson Anderson in 1905, and has become known as the Andersonian theory of stress. What we mean by pressure under those circumstances is mean stress. The effective stress is the true stress minus the fluid pressure. Kinematics, as you learned when taking elementary physics, is a mathematical description of the motion of objects. In an experiment this is called brittle fracture or brittle failure. In ideal plastic behaviour, a sample shows no deformation at all until a certain stress (yield stress) is reached. If that fluid is itself under pressure, it partially supports the mineral grains, and reduces the stresses between the solid parts of the rock, making them behave as if they were located at a shallower depth. }}{\*\pnseclvl4\pnlcltr\pnstart1\pnindent720\pnhang{\pntxta )}}{\*\pnseclvl5 \pndec\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}{\*\pnseclvl6\pnlcltr\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}{\*\pnseclvl7\pnlcrm\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}{\*\pnseclvl8\pnlcltr\pnstart1\pnindent720\pnhang {\pntxtb (}{\pntxta )}}{\*\pnseclvl9\pnlcrm\pnstart1\pnindent720\pnhang{\pntxtb (}{\pntxta )}}\pard\plain \qc\ri-180\widctlpar\tx6480\tx8819 \f8 {\fs36 Structural Geology \par Lecture 1 \par }{\b\fs36 Introduction: \par The parameters of structural geology \par }(constants, conversion factors, etc) \par \par \pard \fi720\widctlpar\tx2160\tx6480\tx8639 Structural geology boils down to a study of Newton's famous laws of motion as they pertain to the deformation of rocks within the earth. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. Pressure is the state of stress in a stationary fluid, like water. Force is measure in Newtons where 1 N is the force necessary to accelerate a mass of 1 kg by 1 m/s2. The Earths surface is approximately a plane of zero shear stress (give or take a few ocean currents and wind storms). {\rtf1\mac \deff8\deflang1033{\fonttbl{\f1\fnil\fcharset2\fprq2 Symbol;}{\f8\fnil\fcharset77\fprq2 Times;}}{\colortbl;\red0\green0\blue0;\red0\green0\blue212;\red2\green171\blue234;\red31\green183\blue20; \red242\green8\blue132;\red221\green8\blue6;\red252\green243\blue5;\red255\green255\blue255;\red0\green0\blue128;\red0\green128\blue128;\red0\green100\blue17;\red128\green0\blue128;\red128\green0\blue0;\red128\green128\blue0;\red128\green128\blue128; \red192\green192\blue192;}{\stylesheet{\widctlpar \f8 \snext0 Normal;}{\*\cs10 \additive Default Paragraph Font;}{\*\cs15 \additive\fs18\dn6 \sbasedon10 Subscript;}{\s16\widctlpar\tqc\tx4320\tqr\tx8640 \f8 \sbasedon0\snext16 header;}{ \s17\widctlpar\tqc\tx4320\tqr\tx8640 \f8 \sbasedon0\snext17 footer;}}{\info{\title Structural Geology}{\author Terry Engelder}{\operator Terry Engelder}{\creatim\yr1998\mo1\dy12\hr17\min40}{\version1}{\edmins0}{\nofpages0}{\nofwords0}{\nofchars0} {\vern49235}}\widowctrl\ftnbj\aenddoc\hyphcaps0\formshade \fet0\sectd \sbknone\linex0\endnhere {\header \pard\plain \s16\widctlpar\tqc\tx4320\tqr\tx8640 \f8 Lect. This is just the difference between the largest and the smallest principal stress: d = 1 3. This is stress. A related concept is the differential stress. Its the most important type of stress for metamorphic petrologists, because high mean stress (high pressure) tends to produce dense minerals like garnet and glaucophane. Shear stress also known as shear traction s is the part that acts parallel to the surface. After an initial phase of elastic deformation, the sample starts to deform in a ductile manner: it flows without breaking. The ellipsoid is called the stress ellipsoid. In the case of structural geology kinematics is the description of the path that r ocks took during deformation. Physics has its table of fundamental and derived physical constants which includes the speed of light ({\i c }= 3 x 10{ \fs18\up6 8} m/sec), Avogadro's number ({\i N}{\i\fs18\dn4 o} = 6.02 x 10{\fs18\up6 23} / mole), and universal gas constant (R = 8.23 joules/(mole)(K\'a1 ). For example, if we observe that layers of slate have undergone a lot more strain than interbedded quartzite layers, we might deduce that the quartzite was more competent. Thereafter, it deforms freely so that however much shortening is imposed by the rig, its impossible to get the stress to go any higher. This gradient can vary from 10\'a1C/km in a glaucophane-schist terrain to 40\'a1 C/km. Anderson distinguished three near-surface tectonic regimes depending on which stress axis was vertical. This type of stress-strain relationship is called elastic. (Engineers often use the opposite convention, which is mathematically more logical, but requires pressure to be a negative quantity, which is less intuitive for most people). }}{\*\pnseclvl3\pndec\pnstart1\pnindent720\pnhang{\pntxta . Because most normal stresses within the Earth act inward, geologists represent compressive normal stress as positive, and use negative numbers for tensile stresses. Real rocks show complicated mixtures of these behaviour types, making these quantities very hard to measure. For every stres s the rocks respond with a finite strain. A study of the forces that cause the motion is called {\b dynamics} .

For each of the above idealized types of behaviour, there is a parameter that measures a rocks strength, or resistance to stress. At this level we refer to both concepts as stress; the sense is almost always clear from the context. In a sense rock structures would not have formed, if rocks had not been subject to a stress. More useful units are: 1 GPa is roughly the pressure at the base of the crust, about 30 km down. The mean stress is the average of the three principal stresses. Viscous behaviour is sometimes also called Newtonian. In porous rock, the pore spaces are typically filled with fluid, often water, but sometimes oil or natural gas. Another table consists of a list of common physical properties w hich are represented by symbols including letters of the Greek alphabet. Although words like stress and strain have very similar meanings in everyday life, their scientific meanings are very different. \par \par \par \pard \qc\widctlpar {\fs28 Table of symbols for the structural geologist} \par \pard \widctlpar\tqc\tx1440\tqc\tx4320\tqc\tx7200 \par \par \tab Symbol\tab Name \tab Units \par \par \tab {\f1 r}\tab density\tab ML{\fs18\up6 -3} \par \par \tab {\f1 s}\tab stress\tab ML{\fs18\up6 -1}T{\fs18\up6 -2 \par } \par {\f1 \tab t}\tab shear stress\tab ML{\fs18\up6 -1}T{\fs18\up6 -2 \par } \par \tab {\f1 s}{\fs18\dn4 n}\tab normal stress\tab ML{\fs18\up6 -1}T{\fs18\up6 -2 \par } \par {\f1 \tab e}\tab strain\tab dimensionless [LL{\fs18\up6 -1}]{\fs18\up6 \par } \par {\f1 \tab }E\tab Young's Modulus\tab ML{\fs18\up6 -1}T{\fs18\up6 -2 \par } \par {\f1 \tab n}\tab Poisson's ratio\tab dimensionless{\fs18\up6 \par } \par {\f1 \tab g}\tab Engineering shear strain\tab dimensionless{\fs18\up6 \par } \par \tab P{\fs18\dn4 p}\tab pore pressure\tab ML{\fs18\up6 -1}T{\fs18\up6 -2 \par } \par \tab {\f1 f}\tab porosity\tab dimensionless \par \par \tab T\tab temperature\tab C\'a1{\fs18\up6 \par \par }\tab q\tab heat flow\tab JL{\fs18\up6 -2}T{\fs18\up6 -1 \par \par }\tab {\f1 k}\tab thermal conductivity\tab JL{\fs18\up6 -1}T{\fs18\up6 -1}C\'a1{\fs18\up6 -1} \par \par {\f1 \tab }z\tab depth\tab L{\fs18\up6 \par } \par \pard \qc\widctlpar {\fs28 \par \par Table of numerical data for the structural geologist} \par \par \pard \widctlpar\tqc\tx1440\tqc\tx4320\tqc\tx7200 \tab \par \tab Symbol\tab Name \tab Magnitude \par \par \tab g\tab average gravity at sea level\tab 9.8 m/sec{\fs18\up6 2 \par \par \tab }{\f1 r}{\fs18\dn4 m}\tab mean density of the mantle\tab 4.5 x 10{\fs18\up6 3} kg/m{\fs18\up6 2 }(4.5 g/cm{\fs18\up6 2}) \par \par \tab {\f1 r}{\fs18\dn4 quartz}\tab density of quartz\tab 2.65 x 10{\fs18\up6 3} kg/m{\fs18\up6 2 }(2.65 g/cm{\fs18\up6 2}) \par \par \pard \qc\widctlpar \par \par {\fs28 \par Table of conventions for the structural geologist} \par \pard \widctlpar\tqc\tx1440\tqc\tx4320\tqc\tx7200 \par \par \pard \widctlpar\tqc\tx2160\tqc\tx6480\tqc\tx7200 \tab Name\tab Convention \tab \par \par \tab Principal stresses\tab {\f1 s}{\fs18\dn4 1} > {\f1 s}{\fs18\dn4 2} > {\f1 s}{\fs18\dn4 3} \par \par \pard \qc\widctlpar\tqc\tx2160\tqc\tx6480\tqc\tx7200 {\ul Stresses in the crust} \par \par \pard \widctlpar\tqc\tx2160\tqc\tx6480\tqc\tx7200 \tab Maximum horizontal stress\tab S{\fs18\dn4 H} \par \pard \qc\widctlpar \tab {\f1 \par }\pard \widctlpar\tqc\tx2160\tqc\tx6480\tqc\tx7200 \tab Minimum horizontal stress\tab S{\fs18\dn4 h} \par \pard \qc\widctlpar \tab {\f1 \par }\pard \widctlpar\tqc\tx2160\tqc\tx6480\tqc\tx7200 \tab Vertical horizontal stress\tab S{\fs18\dn4 v \par }\tab \par {\fs18\dn4 \tab }Compressional normal stress\tab positive \par \par \tab Tensile normal stress\tab negative\tab \par \pard \qc\widctlpar \tab {\f1 \par }{\fs28 \par \par \par \par Table of conversion factors for the structural geologist} \par \pard \widctlpar\tqc\tx1440\tqc\tx4320\tqc\tx7200 \par \par \pard \qc\widctlpar\tqc\tx1440\tqc\tx4320\tqc\tx7200 {\b Stress and pressure} \par \par 1 atm = 14.5 psi = 1 bar = 10{\fs18\up6 6} dynes/cm{\fs18\up6 2} = 10{\fs18\up6 5} N/m{\fs18\up6 2} = 10{\fs18\up6 5} Pascals (Pa) \par \par 1 MPa = 10 bars = 10{\fs18\up6 6} N/m{\fs18\up6 2} \par \par {\ul pressure} applies to a fluid \par \par {\ul stress} applies to a solid \par \pard \widctlpar\tqc\tx1440\tqc\tx4320\tqc\tx7200 \tab \par \par \pard \qc\widctlpar {\fs28 \par \par Table of definitions for the structural geologist} \par \pard \widctlpar\tqc\tx1440\tqc\tx4320\tqc\tx7200 \par \par \pard \widctlpar\tqc\tx2160\tqc\tx6480\tqc\tx7200 \tab Name\tab Definition \tab \par \par \tab A Component of Principal Stress\tab {\f1 s}{\fs18\dn4 ii} or {\f1 s}{\fs18\dn4 i \par \par }\tab Any Component of Stress\tab {\f1 s}{\fs18\dn4 ij} \par \par \tab Differential Stress\tab {\f1 s}{\fs18\dn4 d} = {\f1 s}{\fs18\dn4 1} - {\f1 s}{\fs18\dn4 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0a2873292073686f770a3138383220333537206d6f7665746f0a323234202f54696d65732d526f6d616e2066310a2832292073686f770a3231313320323631206d6f7665746f0a333834202f53796d626f6c2066310a282b292073686f770a3234303420323631206d6f7665746f0a333834202f53796d626f6c2066320a28 73292073686f770a3236353720333537206d6f7665746f0a323234202f54696d65732d526f6d616e2066310a2833292073686f770a3137353020373933206d6f7665746f0a333834206e730a2833292073686f770a2f746869636b2030206465660a2f7468207b20647570207365746c696e657769647468202f746869636b 206578636820646566207d206465660a31362074682038363320343031206d6f7665746f2031393534203020726c696e65746f207374726f6b650a656e640aa000bfa10064006a4d4154480001005e0b0c02000101000a01028473030f01000b0112836d0011000a02863d030e000001028473030f01000b01028831001100 0a02862b028473030f01000b010288320011000a02862b028473030f01000b01028833001100000a01028833000000006f69a0008dff00000000}}}}} \par \par \tab Deviatoric Stress (3 components)\tab {\f1 s}{\fs18\dn4 m} - {\f1 s}{\fs18\dn4 1}, {\f1 s}{\fs18\dn4 m} - {\f1 s}{\fs18\dn4 2}, {\f1 s}{\fs18\dn4 m} - {\f1 s}{\fs18\dn4 3 \par \par }\tab Effective Stress\tab {\f1 s}{\fs18\dn4 i} - P{\fs18\dn4 p} \par \pard \qc\widctlpar {\fs28 \par \par \par Table of equations for the structural geologist} \par \pard \widctlpar\tqc\tx1440\tqc\tx4320\tqc\tx7200 \par \par \pard \qc\widctlpar\tqc\tx1440\tqc\tx4320\tqc\tx7200 {\b Stress and pressure} \par \par P{\fs18\dn4 p} = {\f1 r}{\fs18\dn4 H}{\fs14\dn4 2}{\fs18\dn4 O}gz S{\fs18\dn4 v} = {\f1 r}{\fs18\dn4 rock}gz \par \par if {\f1 r}{\fs18\dn4 rock} = 2.5 x 10{\fs18\up6 3} kg/m{\fs18\up6 3}, g = 9.8 m/sec{\fs18\up6 2}, z = 10{\fs18\up6 3} m, \par \par then S{\fs18\dn4 v} = 2.5 x 10{\fs18\up6 5} kg/m-sec{\fs18\up6 2} = 25 MPa/km \par \pard \widctlpar\tqc\tx1440\tqc\tx4320\tqc\tx7200 \par \pard \fi720\widctlpar\tx2160\tx6480\tx8639 \par \par Finally, the average geothermal gradient ({\up6 dT}/{\dn6 dz}) within the crust of the earth is about 20\'a1C/km where T is temperature and z is depth.