Rock Fractures in Geological Processes Agust Gudmundsson Index More Information

Home , Cataclasite, Exfoliation joint, Horst (geology), Slickenside, Strike and dip

Cambridge University Press 978-0-521-86392-6 - Rock Fractures in Geological Processes Agust Gudmundsson Index More information

Index

absolute tension 14 breccias accuracy 20, 21 density of 54 Anderson’s theory of faulting 36 Young’s modulus of 99, 178 angle of internal friction 194, 195 brittle angle of repose 194 deformation 16, 41, 51 anisotropic material 90 failure 19, 190–223 anisotropic rocks 18 failure and strength 190–193 holes in 176 fault zone 214 aperture (of fractures) 18, 21, 31 fracture 1, 10 of hydrofractures 270, 272 brittle-ductile transition 140–144, 213–223, 566 of tension fractures 239, 263, 265, 270 strain and 141 aperture variation 266–269 bulk modulus 96, 105 numerical models of 395 apparent dip 14 carbonates 101 arrest of fractures 64, 176, 177, 179–180, 289, 335, cataclasite 142 382–388, 447–450 cataclastic flow 143 aspect (length/thickness) ratios of mineral veins 537 cavity aspect ratio definition of 153 of cavities 173 stresses around 167–172 of dykes 336 censoring 345 of veins 400, 516 chemical bonds 101 atom 100 circular hole 162–167, 172–181 atomic view of elasticity 100–106 coefficient of internal friction 194 attitude of fractures 14, 16 cohesion 194 axes, principal 35 cohesionless material 194 axial collapse caldera 529 compression 43 columnar joints 7, 127, 261, 324, 327 extension 43 compliance 13 component of stress 8 stress 43 composite materials 289, 294, 384 tension 43 compressive force 31 compressive regime bar, elastic 13 Griffith criterion and 212 basin, stress in 43, 112 compressive strength 11 bedding plane 15 from the stress-strain curve 192 biaxial compressive stress 8 compression 45 as positive 8 compressive field 216 cone sheets 338–339, 535 tension 43 confining pressure 135, 142, 204, 298, 567 body forces 30 conglomerate 37 bond energy, of atoms 105 conjugate faults 197, 222, 361 boundary conditions constitutive equation 10 geometric 17 contact, between layers 15 loading 17 continuum mechanics 29 breakout 164 controlling dimension, of a fracture 257 570

571 Index

convergent plate boundaries 43, 45, 236, 244 dip 14 Cook-Gordon debonding (delamination) 159, 384 dip-slip fault 15 core, fault 299–302, 439–455 low-angle 354 Coulomb normal 354 criterion 19, 36, 45, 195–203 reverse 354 envelope of failure 195 thrust 354 line of failure 196 overthrust 354 material 193–195 discontinuity 14 crack 2, 14 dislocation 144 displacement modes of 260–265 dislocation geometries of 255–260 edge 144 Griffith (Griffith crack) 205–212, 222, 326, 416 screw 144 mathematical model of 401 displacement 66–71 mode I 260–265 definition of 63 mode II 260–265 field 66 mode III 260–265 of a fault 15, 16, 255–276 models of 255–276 vector 66–71 resistance 211 distortion 40 crack-extension force 288 divergent plate boundaries 14, 69, 81, 236, 246 creep 10, 513 driving crystal plasticity 143–144 pressure 239, 525–529 crystal slip line 8 shear stress 192 cubic law 470–476 stress 237 curtailment 345 ductile behaviour 10, 11 damage zone, fault 299–302, 439–455 deformation 1, 20, 141, 143–145 darcy (a unit) 469 failure 190 Darcy’s law 466–470, 482, 484, 503 fracture 10 deflection of fracture 291–294, 382–388, strain 141 447–450 ductility, of rock 140 deformation 8, 76 Dundurs parameters 387 brittle 16, 41, 51 dyke 4, 7, 49, 66–69, 335–338 ductile 1, 20, 141, 143–145 sandstone 513 elastic 10, 134, 141, 294 dynamic (absolute) viscosity 21, 468, 471 heterogeneous 76 dynamic moduli (elastic constants) 19 homogeneous 76 inhomogeneous 76 earthquakes 16, 18, 133, 192, 513 plastic 10, 140, 214 Earth’s crust, stresses in 8 rigid-body rotation 64 Earth’s free surface 174 rigid-body translation 64 edge dislocation 144 surface 169, 400–404 effective stress 201, 203 degree of connectivity between pores 469 elastic 10 deviatoric stress 40–41 behaviour 10 distortion and 40 constants 95–109 deviatoric stress reduction, brittle deformation constants, atomic view of 100–106 and 41 constants, ranges of values of 97, 98 dextral strike-slip faults 15, 197, 243, 275, 281 deformation 10, 134, 141, 294 differential stress 126, 243 inclusion 154 diffusion 143, 144 linear (linear elastic behaviour) 10 diffusional flow 143 mismatch 384–388 dilatancy, microcracking and 134 moduli 19, 95, 99, 561–563 dilatation 78 non-linear (non-linear elastic behaviour) 90, dilation 78 91, 99 distortion and 71 resilience 120 mean stress and 40 electric forces 101 dimensions, of a quantity 21 electron 100

572 Index

element 100 nucleation, minimum depth of 427 elevation head 471 oblique slip 15, 367–368 elliptical hole 156–161 relay ramps of 357, 430 fracture modelled as 160 reverse 7, 15 elongation 72, 77 right-lateral 15, 243, 361 empirical failure criteria 203–205 rocks 156, 214, 300, 442 en echelon fractures 362, 419–429 sinistral 15, 16 energy of a strained body 91, 118–120 slickensides 15, 367–368 energy release rate 211–212, 222, 289, 296–309, slip, evolution of 450–455 384–388, 447–449 soft linked 359 engineering methods for stress measurement 18 strike-slip 15 engineering strain 72 throw 15, 16 envelope, Mohr’s 203–204 trace 362 equilibrium, lithostatic 110–111, 167, 170 transfer 361, 359 evolution of fault slip 450–455 fault zones 20, 141, 142, 156, 213–223, 300–302 excess pressure 45, 526 ground-water flow and 496 in a reservoir 239 versus faults, definition 354–355 excess pressure gradient 527, 536, 542 local stresses and 441–447 exfoliation 187 faults and fault zones 354–355 exfoliation fractures (joints) 329 faults, Anderson’s theory of 244, 236 extension 8, 11, 72, 73 faults, classification of 36 axial 43 fibers, mineral 333 uniaxial 100 field measurements of fractures 342–346 extension fractures 14, 233–243, 319–346, 373–405, field, of lines of forces 158 525–540 fissure 357 in relation to stress 235 fissure swarm 66–69, 71, 84, 357 types of 235 fixed-grip (constant) displacement 210 extensional strain 79 flat jack, stress measurements using 18 flats 358 flexural rigidity 348 failure flow channelling 473 brittle 19, 190–223 flow criterion, plastic 19 ductile 10 flow shear 19, 190–223, 417–419 of magma 538, 545–546 strength and 190–193 of oil 469–484, 525–540 failure criteria 19, 20 straight 472 combined criterion 213–214 ductile 143 criterion for solids 19 radial 472 fatigue 11 fluid pressure fault aperture and 507–508 as distinct from a fault zone 358 total 167, 168, 201 core 299–302, 439–455 fluid transport damage zone 299–302, 439–455 in the fault core 510–512 dextral 15, 197, 243, 275, 281 in the fault damage zone 508–510 dip-slip 15 orthogonal fracture sets and 475–476 displacement 15, 16, 255–276 single fracture set and 473–475 footwall of 15, 16, 354 fluid-driven fracture, as a type of an extension growth of 430–438 fracture 235 hanging wall of 15, 16 fluid-filled reservoirs 47 hard linked 359 focal mechanisms, stresses from 18 heave of 15, 16 force 6 initiation 416–429 intensity of 6 left-lateral 15, 16, 243 forces listric 358 between atoms, attractive 101 local stresses of 441–447 between atoms, repulsive 101 normal 15 Fourier series, overpressure modelled by 391

573 Index

fracture granular aperture of 18, 21, 31 flow 143 arrest (fracture arrest) 64, 66–69, 176, 177, 179, material 193–195 180, 289, 335, 382–388 media, Darcy’s law and 468 controlling dimension of 257 gravity, as body force 31, 49 definition of 1–2, 14 Griffith deflection 291–294, 382–388, 447–450 cracks 205–212, 222, 326, 416 frequency 344 criterion for rocks 19, 212–213, 419 hydraulic (hydraulic fracture) 137, 163, 181, 530, theory 205–212 533 ground-water flow 498–507 intensity 344 growth of faults 430–438 mechanics (fracture mechanics) 291–297 mechanics (fracture mechanics), Griffith theory and hard-linked fault 359 206 head permeability 477–486, 496–517, 525–540 elevation 471 plane 14 hydraulic 472 pressure 191 pressure 471 shear (shear fracture) 14 total 472 spacing 344 Heim’s rule 46 strike and dip dimension of 257 heterogeneous tension (tension fracture) 14 deformation 76 tip stresses of 390–404 material 90 toughness (fracture toughness) 212, 288–310, 289 rock 18 trace length of 343 strain 76 tunnel shaped 259 Hoek-Brown criterion 204 volumetric flow rate in 525–529 hole fractures circular 162–167, 172–181 basic types of 233–237 definition of 153 displacement modes of 260–265 elliptical 156–161 en echelon 362, 419–429 in anisotropic rock 176–180 field measurements of 342–346 homogeneous frequency of 344 deformation 76 geometric models of 255–260 material 90 hook-shaped 358, 359, 361 rock 18 hybrid 15 strain 76 mixed-mode 15, 255–265, 306, 324, 358, 384, 386, Hooke’s law 11–13 447 atomic view of 104 propagation of 118, 211, 288–310, 377–388, basic assumptions of 89 447–450 one-dimensional 89–92 spacing of 344 principal strains in terms of principal free surface 17, 48, 92 stresses 93 definition of 47, 51, 110, 121 principal stresses in terms of friction principal strains 94 angle of internal 194, 195 three-dimensional 92–95 coefficient of internal 194 hook-shaped fractures 358, 359, 361 law of 194 horizontal stress 7, 64, 111–113 horst 365 general compression (triaxial compression) 45 hyaloclastite 54, 321, 337 general stress 46 hybrid fractures 15 geometric models of fractures 255–260 hydraulic geostatic stress 110 conductivity 468 gouge, in fault zones 142, 214, 497, 519 fractures 137, 163, 181, 530, 533 graben 30 fracturing, stresses from 18 grain size 15, 143 gradient 468 effects of increase in 143 head 472

574 Index

hydrofracture oblique 417 aperture of 266–272 orthogonal 329, 490 arrest of 64, 176, 177, 179, 180, 289, 335, 382–388, 447–450 kinematic 81 as a type of an extension fracture 235 deflection of 291–294, 382–388, 447–450 laboratory measurements of rock properties 19, 20, inclined 535 108, 121, 178, 237 overpressure (driving pressure) of 525–529 Lame’s constant 95, 97, 98 propagation of 239, 377–382 physical meaning of 96 vertical 534 laminar flow, definition of 468 hydrofractures 14, 163, 239–243, 270–272, 319, law of friction (between bodies in contact) 194 377–405, 525–540 layered rocks 290, 310, 348, 390, 395–400, 478 man made (artificial) 137, 163, 181, 530, 533 layering, mechanical 390–400, 446, 477–478 hydrostatic pressure 40 left-lateral fault 15, 243, 361 hydrostatic linear elastic 10 pressure in fluids 42 linear stress-strain relation for rock (material) 90 stress 40, 42 lines of force 47, 158 listric faults 15, 358 igneous intrusions 298, 402 lithostatic incipient shear failure 197 equilibrium 110–111, 167, 170 pressure 167, 182, 239, 526 inclined sheets 3, 154, 179, 251, 336, 338–339, 535 stress 46, 110, 113–114 inclusion, elastic 154 load 9, 17 incompressible constant (uniform load) 210 material 100 loading 9, 132–133 rock 98 loading conditions of rocks, types of 138 incremental strain 79, 80 local sheets 3, 154, 179, 251, 336, 338–339, 535 inelastic 10, 90 local stresses in fault zones 441–447 infill material, in a fracture 344 logarithmic strain 72 inhomogeneous deformation 76 initiation of faults 416–429 marker in-situ (site or field) 12 horizon 15 strength 191 layer 15, 16 tensile strength, highest values 321 material tensile strength, measurements of 191 behaviour 98, 220 instantaneously strained rock (material) 90 equations 10 intensity of fractures 344 toughness 119, 211, 222, 288–310 interface 15 mathematical crack model 401 interior crack 257 maximum principal stress 35 intermediate principal stress 35 mean stress 40 internal friction deviatoric stress and 40 angle of 194, 195 measuring strain 77–81 coefficient of 194 mechanical behaviour of a rock 9 isobars 47 mechanical layers 390–400, 446, 477–478 isostatics 47 microcracks 14, 133–139, 301 isotopes 101 mineral fibres 333 isotropic (hydrostatic) compression 46 mineral veins 5, 332–335, 536–539 isotropic minimum depth of normal-fault nucleation 427 rock 18 minimum principal stress 35 material 90 mismatch, elastic 384–388 strain field 78 mixed-mode fractures 15, 255–265, 306, 324, 358, stress 42 384, 386, 447 mode I crack 260–265 joint, definition 15 mode II crack 260–265 joints 323–332 mode III crack 260–265 as exfoliation fractures 329 Modified Griffith criterion, fault initiation and 419 columnar 7, 127, 261, 324, 327 moduli, elastic 19, 95, 99, 561–563

575 Index

modulus plane strain 117 of elasticity (Young’s modulus) 95 plane stress 116 of rigidity 96 two-dimensional stress and 36 Mogi model (in volcanology) 70 plastic 10 Mohr’s deformation 10, 140, 214 circles 38–41 material, rigid and 194 criterion 203 zone 194 criterion, definition of 19 plate tectonics 66 envelope 203–204 plug 325 stress circle 38 Poisson’s effect 111, 117 molecule 101 Poisson’s number 97 Poisson’s ratio 18, 92, 95–100 natural strain 72 for fluids 99 equation for 79 Poisson’s relation 97 neck 325 polyaxial stress 42 necking, plastic 10 pore-fluid pressure 142, 201–203, 444 neutron 100 porosity 469 nominal stress 157 effects of increase in 142 non-linear elastic 90–91, 99 potential energy non-linear stress-strain relation for rock (material) 90 Darcy’s law and 468 normal faults 10, 15, 16, 30, 37, 71, 234, 236, 238, of a body 210 244, 354–359 of atoms 105 dykes and 263 power-law size distribution 473, 507 growth of 430–437 precision 20 initiation of 421–429 prefixes 21, 558 normal strain 9, 72 pressure normal stress 6, 7, 33 head 471 components of 80 overburden 110 notch, definition of 153 pore-fluid 142, 201–203, 444 nucleus, atomic 100 primary bonds 101 principal axes, stress 35 oblique joints 417 principal planes of stress 35 oblique-slip faults 15, 367–368 principal stresses 35–36 ocean ridges 80 process zone of a fracture 299–302 octahedral shear stress 235 propagation of fractures 118, 211, 288–310, 377–388, offset, fracture linkage and 358, 361 447–450 one-dimensional Hooke’s law 11 proton 100 orthogonal joints 329, 490 pseudodyke 247–248 outcrop scale 14 pull-apart 362–364 overburden pressure 110 pure shear 78, 44 overcoring 18 push-up 365–366, 363 overlap, fracture linkage and 358 overlapping spreading centres 368 overpressure 239, 388–399 quadratic elongation 78 overthrust 354 quark 100

palaeostresses 18 radial part-through crack 256 flow 472 penny-shaped crack 257 stress 166–169 perfectly elastic material 103 radius of curvature 160 perfectly plastic material 216 ramps 358 permeability 469, 477–482, 512–515 and flats 358 anisotropy of 482 regional dykes 315 changes with crustal depth 481 relative tension 14 coefficient of 469 relay ramps 357, 430 effects of fractures on 480 reopening pressure 191 intrinsic 469 residual strength 135

576 Index

resilience, elastic 120 simple shear 46 reverse faults 7, 15 sinistral faults 15 ridge-push 69 slickenside 15, 367–368 Riedel shears 367 slip of faults 450–455 rift zones 45, 48, 49, 66–68, 83–86, 155, 155–183, slip plane (yield plane, failure plane) 194 374–377, 416–437 soft rock 13 right-lateral fault 15, 243, 361 soft-linked fault 359 rigid-body softness 13 rotation 64 spherical stress 40 translation 64 stable static equilibrium, of a rock body 197 rigidity, modulus of 96 state of stress 18 rigid-plastic failure mode 194 at a point 7, 33, 34, 50 rock failure 19, 28, 190–223 static moduli 19 rock fracture, basic definition of 1 stiff, rock 12 rock properties 18, 561–567 stiffness 11, 12, 13 rock strength 15, 367, 564 straight flow 472 basic definition of 190 strain 8–9, 63–81, 89–121 rock as a geometric concept 71 incompressible 98 at a point 75 effective elastic constants of 106 deviatoric 78 non-linear behaviour of 99 elongation as a type of 72, 77 rollover anticline 358 energy (strain energy) 91, 118–120 rough walls, fluid flow and 473 engineering 72 rounding, rules of 21 engineering and nominal 72 rupture 2 finite 72 hardening 141 heterogeneous 76 sag pond 364 homogeneous 76 Saint-Venant’s principle 66 incremental 79, 80 sandstone dyke 513 infinitesimal 72, 90 scalar, definition 7, 28 logarithmic 72 scientific notation 21 measurements 77–81 secant modulus 136 natural 72 secondary bonds 101 normal 9 sedimentary basins 112, 114, 126, 245, 270, 328, 367, plane 117 424, 425, 426, 428, 511, 512, 527, 539 quadratic elongation as a type of 78 seismic measurements of elastic moduli 19 rate 80 seismogenic layer 16, 133, 142, 192, 214, 274 shear 9, 73 semi-trace length 345 softening 140, 141 shear spherical 78 failure, incipient 197 stretch as a type of 77 fracture 14 tensor 75 modulus 96 total 72 strain 9, 73 units of 72 strength 11, 192, 194 volume change as a type of 78 stress 7, 33, 37 strain-rate, effects of increase in 142 zone 20, 141, 142, 214, 355 streamline flow, definition of 468 shear-stress component 33 streamlines, as analogy with stress concentration shear-stress concentration 159 159 sheets, inclined 3, 154, 179, 251, 336, 338–339, 535 strength SI units 20, 557 compressive 11 sign convention for stress and strain 8 in-situ (site or field) 191 significant figures 20 of rock 15, 367, 564 silicates 101 shear 11, 192, 194 sills 292, 293, 323, 336, 340–341, 348–349, 380, tensile 14, 11, 137, 564 383–388, 525–543 tensile in-situ 565

577 Index

stress 6–8, 28–51 two-dimensional 36, 42, 196, 214 at a point 7, 33, 34, 50 units of 6 axial 43 vector 20, 29, 31–34 barrier 382, 530, 531 vector, definition 32 component 33 vertical 53, 110 compressive 8 stress-field homogenisation 378 concentration factor 160 stress-strain concentration, cavities and 167–172 curve 91, 96, 104, 133–140, 289 concentration, circular holes and 162–167, relations 89–120 172–181 stretch, strain measure 77 concentration, definition and examples 47, stria 367 153–181 striations 15, 564 concentration, holes close to the surface and strike 11, 14 172–175 strike and dip dimensions, of a fracture 257 concentration, holes in anisotropic rocks and strike-slip faults 15 176–180 structural geology, basic definitions from 13–16 contours 47 surface energy 210 deviatoric 40–41 surface force 30–31 difference, crustal strength and 192 surface forces, on surfaces of two types 31 drop 192 surface, free 17, 48, 92 effective 201, 203 symbols, used in more than one meaning 4 ellipse 42 tangent modulus 136 ellipsoid 42 target unit, hydraulic fracture and 530 field 46–49 tectonic stress 112 field, heterogeneous 48 temperature, effects of increase of 143 field, homogeneous 48 tensile field, homogenisation of 378 cut-off 198 horizontal 7, 64, 111–113 force 31 hydrostatic 40, 42 fractures, induced at holes 164 intensity factor 212, 289, 297, 302–305 regime, Griffith criterion and 212 isotropic 42 strength 11, 14, 137, 564 mean (mean stress) 40 strength, definition of 191 measurements of 18, 162–167 strength, field measurements of 191 nominal 157 strength, highest in-situ values 321 on an arbitrary plane 28, 36–38 strength, in-situ (field) 565 plane 116 stress 6–8, 28–51 polyaxial 42 stress, as negative 8 principal axes of 35 tension fracture 14, 237–239, 265–270, 320–322 radial 166–169 as a type of an extension fracture 235 raiser 153 development of 373–377 shadow 207 tensor shear 7, 33, 37 definition 29, 34–35 sign convention of 8 rank one 29 sphere 42 rank two 29 spherical 40 rank zero 29 states 42–46 tensor field tectonic 112 three-dimensional stress 41, 42 tensile (absolute) 43 through crack 255 tensile (biaxial) 45 throw, on a fault 15, 16 tensile (isotropic) 46 thrust 15 tensile (uniaxial) 43 thrust fault 15 tensile 35, 134 tip line 265, 266 tensor 29, 33, 34–35 tip stresses of fractures 390–404 trajectories 47–49, 158 total head 472 trajectories, free surface and 48 total pressure, in a reservoir 240 triaxial 42 tough material 10

578 Index

toughness 10, 288–310 viscoelastic 10 of rock 298–299, 565–566 viscosity, dynamic (absolute) 21, 468, 471 fracture (fracture toughness) 212, 288–310, 289 viscous (streamline) flow 468 material (material toughness) 119, 211, 222, volcano 3, 183, 251, 256, 293, 529, 547, 550 288–310 volumetric flow rate 242, 467, 470–476, 525–529 trace length, of a fracture 343 von Mises criterion 20, 216–221 traction 7, 29 traction vector 7 Weibull’s weakest-link theory 137 trajectories, stress 47–49, 158 wing fractures (cracks) 501 transcurrent (wrench) faults 359 work, done on a body 295 transfer faults 361, 359 transform faults 2, 67, 261, 361–363, 366, 432, 440 yield Tresca criterion 20, 195, 214–216, 217 criterion 19 triaxial stress 42 strength 19, 135 trimming 345 stress 135, 135 true dip 201 stress, in uniaxial tension or compression 215 true strain 72 stress, plastic deformation and 10 truncation 345 Young’s modulus 11, 12, 13, 18, 95–96, 99, 104, 106, tunnel-shaped fracture 259 108 two-dimensional stress 36, 42, 214, 196 as a measure of interatomic forces 104 common range of values for rocks 99 underlap 358, 361 dynamic 108 uniaxial effective 109 compression 43, 44 for a linear-elastic material 99 strain 114 for fluids 99 stress (tension) 43 for an in-situ rock mass 108 unstable crack propagation, condition for 211 force-separation curve and 105 upscaling 107 reduction factor of 109 secant modulus 136 vector, definition of 7, 29 static 108 vertical stress 53, 110 tangent modulus 136 view north (south, east, or west), definition of 5 values for rocks 561–562