Evolution of ultrasonic velocity and dynamic elastic moduli with shear strain in granular layers

Granular Matter

Volumn 15, Issue 5, 2013, Pages 499-515

  Knuth, Matthew W ^a   Tobin, Harold J ^a   Marone, Chris ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Friction; Shear strain; Ultrasonic properties; Wave speed

Indexed keywords

CONSTITUTIVE PROPERTIES; DYNAMIC ELASTIC MODULI; FRICTIONAL STRENGTH; IN-LABORATORY EXPERIMENTS; STRAIN LOCALIZATIONS; ULTRASONIC PROPERTIES; ULTRASONIC WAVE VELOCITY; WAVE SPEED;

ACOUSTIC WAVE VELOCITY; ACOUSTIC WAVE VELOCITY MEASUREMENT; ELASTICITY; FRICTION; MIXTURES; QUARTZ; SEISMIC WAVES; SHEAR STRAIN; STRUCTURAL GEOLOGY; ULTRASONIC APPLICATIONS; ULTRASONIC WAVES; ULTRASONICS; WAVE PROPAGATION;

LOADING;

EID: 84885422121     PISSN: 14345021     EISSN: 14347636     Source Type: Journal    
DOI: 10.1007/s10035-013-0420-1     Document Type: Article

References (112)

1. AnhDan, L.; Koseki, J.; Sato, T.: Comparison of Young's moduli of dense sand and gravel measured by dynamic and static methods. Geotech. Test. J. 25(4) (2002). doi: 10.1520/GTJ11290J
2. Anthony, J.; Marone, C.: Influence of particle characteristics on granular friction. J. Geophys. Res. 110 (2005). doi: 10.1029/2004JB003399
3. Bachrach, R.; Avseth, P.: Rock physics modeling of unconsolidated sands: accounting for nonuniform contacts and heterogeneous stress fields in the effective media approximation with applications to hydrocarbon exploration. Geophysics 73(6) (2008). doi: 10.1190/1.2985821
4. Bachrach, R.; Dvorkin, J.; Nur, A.M.: Seismic velocities and Poisson's ratio of shallow unconsolidated sands. Geophysics 65(2) (2000). doi: 10.1190/1.1444751
5. Behringer, R.P.; Daniels, K.E.; Majmudar, T.S.; Sperl, M.: Fluctuations, correlations and transitions in granular materials: statistical mechanics for a non-conventional system. Philos. Trans. R. Soc. A 366 (2008). doi: 10.1098/rsta.2007.2106
6. Berryman, J.G.: Long-wavelength propagation in composite elastic media II. Ellipsoidal inclusions. J. Acoust. Soc. Am. 68, 1820-1831 (1980)
7. Berryman, J.G.; Pride, S.R.; Wang, H.F.: A differential scheme for elastic properties of rocks with dry or saturated cracks. Geophys. J. Int. 151, 597-611 (2002)
8. Bocquet, L.; Losert, W.; Schalk, D.; Lubensky, T.C.; Gollub, J.P.: Granular shear flow dynamics and forces: experiment and continuum theory. Phys. Rev. E 65 (2001). doi: 10.1103/PhysRevE.65.011307
9. Boitnott, G.N.; Biegel, R.L.; Scholz, C.H.; Yosioka, N.; Wang, W.: Micromechanics of rock friction, 2: quantitative modeling of initial friction with contact theory. J. Geophys. Res. 97, 8965-8978 (1992)
10. Boudjema, M.; Santos, I.B.; McCall, K.R.; Guyer, R.A.; Boitnott, G.N.: Linear and nonlinear modulus surfaces in stress space, from stress-strain measurements on Berea sandstone. Nonlinear Proc. Geophys. 10, 589-597 (2003)
11. Bourbié, T.; Coussy, O.; Zinszner, B.: Acoustics of Porous Media. Gulf Pub. Co, Editions Technip) (1987)
12. Bradbury, K.K.; Barton, D.C.; Solum, J.G.; Draper, S.D.; Evans, J.P.: Mineralogic and textural analyses of drill cuttings from the San Andreas fault observatory at depth (SAFOD) boreholes: initial interpretations of fault zone composition and constraints on geologic models. Geosphere 3 (2007). doi: 10.1130/GES00076.1
13. Blum, T.E.; Snieder, R.; van Wijk, K.; Willis, M.E.: Theory and laboratory experiments of elastic wave scattering by dry planar fractures. J. Geophys. Res. 116, B08218 (2011). doi: 10.1029/2011JB008295
14. Brignoli, E.G.M.; Gotti, M.; Stokoe, II, K.H.: Measurement of shear waves in laboratory specimens by means of piezoelectric transducers. ATSM Geotech. Test. J. 19(4) (1996). doi: 10.1520/GTJ10716J
15. Brunet, T.; Jia, X.; Johnson, P.A.: Transitional nonlinear elastic behaviour in dense granular media. Geophys. Res. Lett. 35, L19308 (2008). doi: 10.1029/2008GL035264
16. Buckingham, M.J.: Theory of acoustic attenuation, dispersion, and pulse propagation in unconsolidated granular materials including marine sediments. J. Acoust. Soc. Am. 102(5) (1997). doi: 10.1121/1.420313
17. Byerlee, J.: Friction of rocks. Pure Appl. Geophys. 116(4-5) (1978). doi: 10.1007/BF00876528
18. Cadoret, T.; Marion, D.; Zinszner, B.: Influence of frequency and fluid distribution on elastic wave velocities in partially saturated limestones. J. Geophys. Res. 100(B6) (1995). doi: 10.1029/95JB00757
19. Carpenter, B.M.; Marone, C.; Saffer, D.M.: Frictional strength of the san andreas fault from laboratory measurements of SAFOD drill samples. Nat. Geosci. (2011). doi: 10.1038/ngeo1089
20. Carpenter, B.M.; Saffer, D.M.; Marone, C.: Frictional properties and sliding stability of the San Andreas fault from deep drill core. Geology 40, 759-762 (2012). doi: 10.1130/G33007
21. Cascante, G.; Santamarina, J.C.: Interparticle contact behavior and wave propagation. J. Geotech. Geoenviron. Eng. 122, 831-839 (1996)
22. Chester, F.M.; Evans, J.P.; Biegel, R.K.: Internal structure and weakening mechanisms of the San Andreas fault. J. Geophys. Res. 98(B1) (1993). doi: 10.1029/92JB01866
23. Chupin, O.; Rechenmacher, A.L.; Abedi, S.: Finite strain analysis of non-uniform deformations in shear bands in Sand. Int. J. Numer. Anal. Methods Geomech. 36, 1651-1666 (2010). doi: 10.1002/nag.1071
24. Daniels, K.E.; Hayman, N.W.: Force chains in seismogenic faults visualized with photoelastic granular shear experiments. J. Geophys. Res. 113, B11411 (2008). doi: 10.1029/2008JB005781
25. David, E.C.; Zimmerman, R.W.: Pore structure model for elastic wave velocities in fluid-saturated sandstones. J. Geophys. Res. 117, B07210 (2012). doi: 10.1029/2012JB009195
26. Dieterich, J.H.: Modeling of rock friction 1. Experimental results and constitutive equations. J. Geophys. Res. 84(B5) (1979). doi: 10.1029/JB084iB05p02161
27. Dieterich, J.H.: Constitutive properties of faults with simulated gouge. In: Carter, N.L.; Friedman, M.; Logan, J.M.; Stearns, D.W. (eds.) Mechanical Behavior of Crustal Rocks. AGU Monograph, vol. 24, pp. 103-120. Washington DC, AGU (1981)
28. Dvorkin, J.; Nur, A.: Dynamic poroelasticity: a unified model with the squirt and the Biot mechanisms. Geophysics 58(4) (1993). doi: 10.1190/1.1443435
29. Estep, J.; Dufek, J.: Substrate effects from force chain dynamics in dense granular flows. J. Geophys. Res. 117, F01028 (2012). doi: 10.1029/2011JF002125
30. Fortin, J.; Schubnel, A.; Guéguen, Y.: Elastic wave velocities and permeability evolution during compaction of Bleurswiller sandstone. Int. J. Rock Mech. Min. 42 (2005). doi: 10.1016/j.ijrmms.2005.05.002
31. Fortin, J.; Guéguen, Y.; Schubnel, A.: Effects of pore collapse and grain crushing on ultrasonic velocities. J. Geophys. Res. 112(B0827) (2007). doi: 10.1029/2005JB004005
32. Frye, K.M.; Marone, C.: Effect of humidity on granular friction at room temperature. J. Geophys. Res. 107(B11) (2002). doi: 10.1029/2001JB000654
33. Gassmann, F.: Elastic waves through a packing of spheres. Geophysics 16 (1951). doi: 10.1190/1.1437718
34. Goddard, J.D.: Nonlinear elasticity and pressure-dependent wave speeds in granular media. Proc. R. Soc. Lond. A Mat. 430(1878) (1990). doi: 10.1098/rspa.1990.0083
35. Goren, L.; Aharonov, E.; Sparks, D.; Toussaint, R.: The mechanical coupling of fluid-filled granular material under shear. Pure Appl. Geophys. 168, 2289-2323 (2011). doi: 10.1007/s00024-011-0320-4
36. Haines, S.H.; van der Pluijm, B.A.; Ikari, M.; Saffer, D.; Marone, C.: Clay fabrics in natural and artificial fault gouge. J. Geophys. Res. 114(B5), B05406 (2009). doi: 10.1029/2008JB005866
37. Han, D.; Batzle, M.: Velocities of deepwater reservoir sands. Leading Edge 25 (2006). doi: 10.1190/1.2193222
38. Hertz, H.: Über die Berührung fester elasticher Körper. Journal für die reine und angewandte Mathematik 92, 156-171 (1881)
39. Hobiger, M.; Wegler, U.; Shiomi, K.; Nakahara, H.: Coseismic and postseismic elastic wave velocity variations caused by the 2008 Iwate-Miyagi Nairiku earthquake. Jpn. J. Geophys. Res. 117, B09313 (2012). doi: 10.1029/2012JB009402
40. Hong, T.; Marone, C.: Effects of normal stress perturbations on the frictional properties of simulated faults. Geochem. Geophys. Geosyst. 6(3) (2005). doi: 10.1029/2004GC000821
41. Howell, D.W.; Behringer, R.P.; Veje, C.T.: Fluctuations in granular media. Chaos 9(3) (1999). doi: 10.1063/1.166430
42. Ikari, M.J.; Saffer, D.M.; Marone, C.: Effect of hydration state on the frictional properties of montmorillonite-based fault gouge. J. Geophys. Res. 112(B06423) (2007). doi: 10.1029/2006JB004748
43. Ikari, M.; Saffer, D.M.; Marone, C.: Frictional and hydrologic properties of clay-rich fault gouge. J. Geophys. Res. 114, B05409 (2009). doi: 10.1029/2008JB006089
44. Jia, X.: Ultrasound propagation in disordered granular media. Mat. Res. Soc. Symp. Proc. 627 (2000).
45. Jia, X.; Caroli, C.; Velicky, B.: Ultrasound propagation in externally stressed granular media. Phys. Rev. Lett. 82(9) (1999). doi: 10.1103/PhysRevLett.82.1863
46. Kaproth, B.M.; Cashman, S.M.; Marone, C.: Deformation band formation and strength evolution in unlithified sand: the role of grain breakage. J. Geophys. Res. 115, B12103 (2010). doi: 10.1029/2010JB007406
47. Karner, S.L.; Marone, C.: Frictional restrengthening in simulated fault gouge: effect of shear load perturbations. J. Geophys. Res. 106, 19319-19337 (2001)
48. Khidas, Y.; Jia, X.: Anisotropic nonlinear elasticity in a spherical-bead pack: influence of the fabric anisotropy. Phys. Rev. E 81, 021303 (2010)
49. Khidas, Y.; Jia, X.: Probing the shear-band formation in granular media with sound waves. Phys. Rev. E 85, 051302 (2012)
50. King, M.S.: Wave velocities in rocks as a function of changes in overburden pressure and pore fluid saturants. Geophysics 31(1) (1966). doi: 10.1190/1.1439763
51. Knight, R.; Dvorkin, J.; Nur, A.: Acoustic signatures of partial saturation. Geophysics 63(1) (1998). doi: 10.1190/1.1444305
52. Knopoff, L.: Q. Rev. Geophys. 2(4), 625-660 (1964). doi: 10.1029/RG002i004p00625
53. Knuth, M.; Marone, C.: Friction of sheared granular layers: the role of particle dimensionality, surface roughness, and material properties. Geochem. Geophys. Geosyst. 8, Q03012 (2007). doi: 10.1029/2006GC001327
54. Lay, T.; Ammon, C.J.; Hutko, A.R.; Kanamori, H.: Effects of kinematic constraints on teleseismic finite-source rupture inversions: Great Peruvian Earthquakes of 23 June 2001 and 15 August 2007. Bull. Seismol. Soc. Am. 100(3) (2010). doi: 10.1785/0120090274
55. Lee, J.Y.; Francisca, F.M.; Santamarina, J.C.; Ruppel, C.: Parametric study of the physical properties of hydrate-bearing sand, silt, and clay sediments: 2. Small-strain mechanical properties. J. Geophys. Res. 115, B11105 (2010). doi: 10.1029/2009JB006670
56. Linker, M.F.; Dieterich, J.H.: Effects of variable normal stress on rock friction: observations and constitutive equations. J. Geophys. Res. 97(B4) (1992). doi: 10.1029/92JB00017
57. Liu, C.-h.; Nagel, S.R.: Sound in sand. Phys. Rev. Lett. 68(15) (1992). doi: 10.1103/PhysRevLett.68.2301
58. Maeda, N.: A method for reading and checking phase times in autoprocessing system of seismic wave data. Jishin (J. Seismol. Soc. Jpn.) 38, 365-379 (1985)
59. Mainprice, D.; Page, Y.L.; Rodgers, J.; Jouanna, P.: Ab initio elastic properties of talc from 0 to 12 GPa: interpretation of seismic velocities at mantle pressures and prediction of auxetic behaviour at low pressure. Earth Planet Sci. Lett. 274 (2008). doi: 10.1016/j.epsl.2008.07.047
60. Mair, K.; Marone, C.: Friction of simulated fault gouge for a wide range of velocities and normal stresses. J. Geophys. Res. 104, 28899-28914 (1999)
61. Mair, K.; Frye, K.M.; Marone, C.: Influence of grain characteristics on the friction of granular fault zones. J. Geophys. Res. 107(B10):2219 (2002)
62. Majmudar, T.S.; Behringer, R.P.: Contact force measurements and stress-induced anisotropy in granular materials. Nature 435 (2005). doi: 10.1038/nature03805
63. Makse, H.A.; Gland, N.; Johnson, D.L.; Schwartz, L.: Granular packings: nonlinear elasticity, sound propagation, and collective relaxation dynamics. Phys. Rev. E 70(6), 061302 (2004). doi: 10.1103/PhysRevE.70.061302
64. Manjunath, M.; Awasthi, A.P.; Geubelle, P.H.: Wave propagation in random granular chains. Phys. Rev. E 85, 031308 (2012)
65. Marone, C.: Laboratory-derived friction laws and their application to seismic faulting. Annu. Rev. Earth Planet Sci. 26, 643-696 (1998). doi: 10.1146/annurev.earth.26.1.643
66. Marone, C.; Carpenter, B.M.; Schiffer, P.: Transition from rolling to jamming in thin granular layers. Phys. Rev. Lett. 101, 248001 (2008). doi: 10.1103/PhysRevLett.101.248001
67. Mavko, G.: Velocity and attenuation in partially molten rocks. J. Geophys. Res. 85, 5173-5189 (1980)
68. Mavko, G.; Nur, A.: Wave attenuation in partially saturated rocks. Geophysics 44, 161-178 (1979)
69. Mavko, G.; Mukerji, T.; Dvorkin, J.: The Rock Physics Handbook. Cambridge University Press, New York (1998)
70. Mindlin, R.D.: Mechanics of Granular Media. Columbia University Press, New York (1954)
71. Molyneux, J.B.; Schmitt, D.R.: First-break timing: Arrival onset times by direct correlation. Geophysics 64(5) (1999). doi: 10.1190/1.1444653
72. Mühlhaus, H.; Oka, F.: Dispersion and wave propagation in discrete and continuous models for granular materials. Int. J. Solids Struct. 33, 2841-2858 (1996). doi: 10.1016/0020-7683(95)00178-6
73. Papargyri-Beskou, S.; Mylonakis, G.: Wave dispersion studies in granular media by analytical and analytical-numerical methods. Soil Dyn. Earthq. Eng. 29 (2009). doi: 10.1016/j.soildyn.2008.10.003
74. Peraldi, R.; Clement, A.: Digital processing of refraction data study of first arrivals. Geophys. Prospect. 20(3) (2006). doi: 10.1111/j.1365-2478.1972. TB00653
75. Pittman, E.: Effect of fault-related granulation on porosity and permeability of quartzstones, Simpson Group (Ordovician) Oklahoma. Am. Assoc. Pet. Geol. Bull. 65(11), 2381-2387 (1981)
76. Prasad, M.; Meissner, R.: Attenuation mechanisms in sands: laboratory versus theoretical (Biot) data. Geophysics 57(5) (1992). doi: 10.1190/1.1443284
77. Radjai, F.; Wolf, D.E.; Jean, M.; Moreau, J.-J.: Bimodal character of stress transmission in granular packings. Phys. Rev. Lett. 80(1) (1998). doi: 10.1103/PhysRevLett.80.61
78. Rathbun, A.P.; Marone, C.: Effect of strain localization on frictional behavior of sheared granular materials. J. Geophys. Res. 115, B01204 (2010). doi: 10.1029/2009JB006466
79. Rawling, G.C.; Goodwin, L.B.: Cataclasis and particulate flow in faulted, poorly lithified sediments. J. Struct. Geol. 25 (2003). doi: 10.1016/S0191-8141(02)00041-X
80. Rechenmacher, A.L.: Grain-scale processes governing shear band initiation and evolution in sands. J. Mech. Phys. Solids 54, 22-45 (2006)
81. Rechenmacher, A.; Abedi, S.; Chupin, O.: Evolution of force chains in shear bands in sand. Geotechnique 60, 343-351 (2010)
82. Rose, J.L.: Ultrasonic Waves in Solid Media. Cambridge University Press, New York (1999)
83. Santamarina, J.C.; Cascante, G.: Stress anisotropy and wave propagation: a micromechanical view. Can. Geotech. J. 33, 770-782 (1996)
84. Savage, J.C.: Attenuation of elastic waves in granular mediums. J. Geophys. Res. 70, 3935-3942 (1965)
85. Schenker, I.; Filser, F.T.; Hütter, M.; Gauckler, L.J.: The influence of the degree of heterogeneity on the elastic properties of random sphere packings. Granul. Matter 14, 333-340 (2012). doi: 10.1007/s10035-012- 0316-5
86. Scholz, C.H.: Earthquakes and friction laws. Nature 391 (1998). doi: 10.1038/34097
87. Scott, D.R.; Marone, C.; Sammis, C.G.: The apparent friction of granular fault gouge in sheared layers. J. Geophys. Res. 99(B4) (1994). doi: 10.1029/93JB03361
88. Segall, P.; Rice, J.R.: Dilatancy, compaction, and slip instability of a fluid-infiltrated fault. J. Geophys. Res. 100(B11) (1995). doi: 10.1029/95JB02403
89. Sibson, R.H.: Fault rocks and fault mechanics. J. Geol. Soc. Lond. 133 (1997). doi: 10.1144/gsjgs.133.3.0191
90. Sleep, N.H.: Microscopic elasticity and rate and state friction evolution laws. Geochem. Geophys. Geosyst. 13, Q12002 (2012). doi: 10.1029/2012GC004393
91. Stoll, R.D.: Velocity dispersion in water-saturated granular sediment. J. Acoust. Soc. Am. 111(2) (2002). doi: 10.1121/1.1432981
92. Terzaghi, K.: The shearing resistance of saturate soils. In: Proceedings of the 1st International Conference on Soil Mechanism, vol. 1, pp. 54-56 (1936)
93. Tordesillas, A.: Force chain buckling, unjamming transitions and shear banding in dense granular assemblies. Philos. Mag. 87(32) (2007). doi: 10.1080/14786430701594848
94. Tordesillas, A.; Muthuswamy, M.: On the modeling of confined buckling of force chains. J. Mech. Phys. Solids 57 (2009). doi: 10.1016/j.jmps.2009.01.005
95. van der Elst, N.J.; Brodsky, E.E.; Le Bas, P.-Y.; Johnson, P.A.: Auto-acoustic compaction in steady shear flows: experimental evidence for suppression of shear dilatancy by internal acoustic vibration. J. Geophys. Res. 117, B09314 (2012). doi: 10.1029/2011JB008897
96. Vermilye, J.M.; Scholz, C.H.: The process zone: a microstructural view of fault growth. J. Geophys. Res. 103(B6) (1998). doi: 10.1029/98JB00957
97. Vernik, L.; Nur, A.: Ultrasonic velocity and anisotropy of hydrocarbon source rocks. Geophysics 57(5) (1992). doi: 10.1190/1.1443286
98. Vilchinska, N.A.: Force chains in granular media and ultrasound impulse propagation in sand specimen under load. Tech. Acoust. 20, 213-217 (2007)
99. Vlahinić, I.; Jennings, H.M.; Thomas, J.J.: A constitutive model for drying of a partially saturated porous material. Mech. Mater. 41 (2009). doi: 10.1016/j.mechmat.2008.10.011
100. Voltolini, M.; Wenk, H.-R.; Mondol, M.H.; Bjørlykke, K.; Jahren, J.: Anisotropy of experimentally compressed kaolinite-illite-quartz mixtures. Geophysics 74(1) (2009). doi: 10.1190/1.3002557
101. Wang, H.: Quasi-static poroelastic parameters in rock and their geophysical applications. Pure Appl. Geophys. 141 (1993). doi: 10.1007/BF00998332
102. Wang, Y.-H.; Santamarina, J.C.: Attenuation in sand: an exploratory study on the small-strain behavior and the influence of moisture condensation. Granul. Matter 9(6), 365-376 (2007)
103. Winkler, K.; Nur, A.; Gladwin, M.: Friction and seismic attenuation in rocks. Nature 227, 528-531 (1979)
104. Winkler, K.W.; Nur, A.: Seismic attenuation: effects of pore fluids and frictional sliding. Geophysics 47, 1-15 (1982)
105. Wolf, H.; König, D.; Triantafyllidis, T.: Experimental investigation of shear band patterns in granular material. J. Struct. Geol. 25 (2003). doi: 10.1016/S0191-8141(02)00163-3
106. Zhang, H.; Thurber, C.; Rowe, C.: Automatic P -wave arrival detection and picking with multiscale wavelet analysis for single-component recordings. Bull. Seismol. Soc. Am. 93(5) (2003). doi: 10.1785/0120020241
107. Zheng, B.; Elsworth, D.: Evolution of permeability in heterogeneous granular aggregates during chemical compaction: ranular mechanics models. J. Geophys. Res. 117, B03206 (2012). doi: 10.1029/2011JB008573
108. Zienkiewicz, O.C.; Chan, A.H.C.; Pastor, M.; Paul, D.K.; Shiomi, T.: Static and dynamic behavior of soils: a rational approach to quantitative solutions. I. Fully saturated problems. Proc. R. Soc. Lond. A Mat. 429(1877) (1990). doi: 10.1098/rspa.1990.0061
109. Zimmer, M.A.: Seismic velocities in unconsolidated sands: measurements of pressure, sorting, and compaction effects. Ph.D. dissertation, Stanford University (2003)
110. Zimmer, M.; Prasad, M.; Mavko, G.: Pressure and porosity influences on ratio in unconsolidated sands. Leading Edge 21(2) (2002). doi: 10.1190/1.1452609
111. Zimmer, M.A.; Prasad, M.; Mavko, G.; Nur, A.: Seismic velocities of unconsolidated sands: part 1 - pressure trends from 0.1 to 20 MPa 72(1) (2007a). doi: 10.1190/1.2399459
112. Zimmer, M.A.; Prasad, M.; Mavko, G.; Nur, A.: Seismic velocities of unconsolidated sands: part 2 - influence of sorting- and compaction-induced porosity variation. Geophysics 72(1) (2007). doi: 10.1190/1.2364849