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Contact mechanics of a dilatant region located at a compressed elastic interface. (English) Zbl 1423.74679
Summary: Interfaces possess complex mechanical responses that are governed by several factors including the type of material, the local topography of the interacting surfaces, the stress state and the mode of deformation. This paper examines the mechanics of a mated smooth interface that is subjected to a normal stress and where the contact is perturbed by a circular patch that can experience dilatancy under shear. The analysis of the static stress drop occurring during shear at the interface is examined using a contact mechanics approach that accounts for the separation at the pre-compressed geological interface induced by the development of dilatancy of the patch during relative shear. This paper presents an elementary model of the mechanics that takes into consideration the normal stress evolution during dilatant shearing of the interface. The problem is of particular interest to the modelling of local phenomena that can occur at material interfaces and geological faults that are subjected to steady movement.

MSC:
74M15 Contact in solid mechanics
86A60 Geological problems
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[1] Aleynikov, S. M., Spatial contact problems in geotechnics: boundary element method, (2011), Springer-Verlag Berlin
[2] Aliabadi, M.; Brebbia, C. A., Computational methods in contact mechanics, (1993), Computational Mech Publ Southampton · Zbl 0790.73004
[3] Allman, B. P.; Shearer, P. M., Global variations of stress drop for moderate to large earthquakes, Journal of Geophysical Research, Vol. 114, B01310, (2009)
[4] Anoosheshpoor, A.; Brune, J. N., Quasi-static slip-rate shielding and creeping zones as an explanation for small repeating earthquakes at parkfield, Bulletin of the Seismological Society of America, Vol. 91, 401-403, (2001)
[5] Archard, J. F., Contact and rubbing of flat surfaces, Journal of Applied Physics, Vol. 24, 981-988, (1953)
[6] Bandis, S. C.; Lumsden, A. C.; Barton, N. R., Experimental studies of scale effects on the shear behaviour of joints, International Journal of Rock Mechanics and Mining Sciences, Vol. 18, 1-21, (1981)
[7] Barber, J. R., Contact mechanics, (2018), Springer-Verlag Berlin · Zbl 1400.74001
[8] Barton, N. R., Shear strength criteria for rock, rock joints, rockfill and rock masses: problems and some solutions, Journal of Rock Mechanics and Geotechnical Engineering, Vol. 5, 249-261, (2013)
[9] Barton, N. R.; Choubey, V., The shear strength of rock joints in theory and practice, Rock Mech, Vol. 10, 1-54, (1977)
[10] Barton, N. R.; Stephansson, O. (Eds.), rock joints, (Proceedings of the International Symposium on Rock Joints, (1990), AA Balkema, Rotterdam Loen, Norway)
[11] Beeler, N. M.; Lockner, D. A.; Hickman, S. H., A simple stick-slip and creep-slip model for repeating earthquakes and implication for microearthquakes at parkfield, Bulletin of the Seismological Society of America, Vol. 91, 1797-1804, (2001)
[12] (Ben-Zion, Y.; Sammis, C., Mechanics, structure and evolution of fault zones, (2010), Birkhauser Geoscience Vienna)
[13] Bilek, S. L.; Lay, T., Rigidity variations with depth along interpolate megathrust faults in subduction zones, Nature, Vol. 400, 443-446, (1999)
[14] Borucki, L. J., Mathematical modelling of Polish-rate decay in chemical-mechanical polishing, Journal of Engineerng Mathematics, Vol. 43, 105-114, (2002) · Zbl 1008.74526
[15] Borucki, L. J.; Witelski, T.; Please, C.; Kramer, P.; Schwendeman, D., A theory for pad conditioning for chemo-mechanical polishing, Journal of Engineerng Mathematics, Vol. 50, 1-24, (2004) · Zbl 1073.74027
[16] Boussinesq, J., Application des potentiels a L’etude de l’equilibre et due mouvement des solides elastique, (1885), Gauthier Villars Paris · JFM 17.0952.01
[17] Bowden, F. P.; Tabor, D., Friction and lubrication of solids, (1986), Clarendon Press Oxford · Zbl 0987.74002
[18] Brace, W. F.; Martin, R. J., The test law for effective stress for crystalline rocks of low porosity, International Journal of Rock Mechanics and Mining Science, Vol. 5, 415-436, (1968)
[19] Broberg, B. K., Cracks and fracture, (1999), Academic Press San Diego
[20] Brune, J. N., Tectonic stress and the spectra of seismic shear waves from earthquakes, Journal of Geophysical Research, Vol. 75, 4997-5009, (1970)
[21] Brune, J. N., Correction to “tectonic stress and the spectra of seismic shear waves from earthquakes”, Journal of Geophysical Research, Vol. 76, 5002, (1971)
[22] Chen, W.-F., Limit analysis and soil plasticity, developments in geotechnical engineering, Vol. 7, (1975), Elsevier Amsterdam
[23] Chen, T.; Lapusta, N., Scaling of small repeating earthquakes explained by interaction of seismic and aseismic slip in a rate and state fault model, Journal of Geophysical Research, Vol. 114, (2009)
[24] Chen, Y.; Sammis, C. G., Asperity models for earthquakes, Bulletin of the Seismological Society of America, Vol. 94, 1792-1802, (2003)
[25] Cherepanov, G. P., Mechanics of brittle fracture, (1979), McGraw-Hill New York, (Translation edited by R. De Wit, A.C. Cooley and A.L. Peabody) · Zbl 0442.73100
[26] Christian, J. T.; Baecher, G. P., D.W. Taylor and the foundations of modern soil mechanics, Journal of Geotechnical and Geoenvironmental Engineering, Vol. 141, (2015)
[27] Ciavarella, M., On the effect of wear on asperity height distributions, and the corresponding effect in the mechanical response, Tribology International, Vol. 101, 164-167, (2016)
[28] Cocco, M.; Rice, J. R., Pore pressure and poroelasticity effects in Coulomb stress analysis of earthquake interactions, Journal of Geophysical Research, Vol. 107, (2002), (B2)
[29] Cooke, J. C., Some further triple integral equation solutions, (Proceedings of the Edinburgh Mathematical Society, Vol. 13, (1963)), 303-316 · Zbl 0117.32301
[30] (Curnier, A., Contact mechanics international symposium, (1992), Laboratoire Mecanique Appliquee EPFL, Lausanne)
[31] Davis, R. O.; Selvadurai, A. P.S., Elasticity and geomechanics, (1996), Cambridge University Press Cambridge
[32] Davis, R. O.; Selvadurai, A. P.S., Plasticity and geomechanics, (2003), Cambridge University Press Cambridge
[33] de Pater, A. D.; Kalker, J. J., The mechanics of contact between deformable bodies, (Proc IUTAM Symposium, Ensched, (1975), Delft University Press The Netherlands) · Zbl 0308.00012
[34] (Desai, C. S.; Christian, J. T., Numerical Methods in Geotechnical Engineering, (1975), McGraw-Hill New York) · Zbl 0411.00012
[35] Desai, C. S.; Ma, Y., Modelling of joints and interfaces using the disturbed-state concept, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 16, 623-653, (1992) · Zbl 0766.73054
[36] Desai, C. S.; Siriwardane, H. J., Constitutive laws for engineering materials: with emphasis on geologic materials, (1984), Prentice-Hall Englewood Cliffs, NJ · Zbl 0543.73004
[37] Drucker, D. C.; Prager, W., Soil mechanics and plastic analysis or limit design, Quarterly of Applied Mathematics, Vol. 10, 157-165, (1952) · Zbl 0047.43202
[38] Duvaut, G.; Lions, J. L., Inequalities in mechanics and physics. A series of comprehensive studies in mathematics, (1976), Springer-Verlag Heidelberg · Zbl 0331.35002
[39] Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion and related problems, (Proceedings of the Royal Society, Series A, Vol. 241, (1957)), 376-396 · Zbl 0079.39606
[40] Fichera, G., Boundary value problems of elasticity with unilateral constraints, (Truesdell, C., Handbuch der Physik, Mechanics of Solids II, (1972), Springer-Verlag Berlin), 391-424, vol. VIa/2
[41] Frank, F. C., On dilatancy in relation to seismic sources, Reviews in Geophysics and Space Physics, Vol. 3, 485-503, (1965)
[42] Galin, L. A., Contact problems in the theory of elasticity, (1961), North Carolina State College Raleigh NC, (Translated from Russian by H. Moss)
[43] Gens, A., (Selvadurai, A. P.S.; Boulon, M. J., Mechanics of geomaterial interfaces, (1995), Elsevier New York), 395-420
[44] Gladwell, G. M.L., Contact problems in the classical theory of elasticity, (1980), Sijthoff and Nordhoff, Alphen aan den Rijn The Netherlands · Zbl 0431.73094
[45] Gladwell, G. M.L., On contact problems for a medium with rigid flat inclusions of arbitrary shape, International Journal of Solids and Structures, Vol. 32, 383-389, (1995) · Zbl 0865.73052
[46] Gladwell, G. M.L.; Hara, T., The contact problem for a rigid obstacle pressed between two dissimilar halfspaces, Quarterly Journal of Mechanics and Applied Mathematics, Vol. 34, 251-263, (1981) · Zbl 0462.73093
[47] Goldberg, R.; Siman-Tov, S.; Emmanuel, S., Weathering resistance of carbonate fault mirrors promotes rupture localization, Geophysical Research Letters, Vol. 43, 3105-3111, (2016)
[48] Goodman, R. E.; Dubois, J., Duplication of dilatancy in analysis of jointed rocks, Journal of the Soil Mechanics and Foundations Division, Proceedings of the ASCE, Vol. 98, 399-422, (1972)
[49] Gudehus, G., Finite elements in geomechanics, (1977), John Wiley London
[50] Hanks, T. C., Earthquake stress drops, ambient tectonic stresses and stresses that drive plate motions, Pure and Applied Geophysics, Vol. 115, 441-458, (1977)
[51] Harding, J. W.; Sneddon, I., The elastic stresses produced by the indentation of the plane of a semi-infinite elastic solid by a rigid punch, Proceedings of the Cambridge Philosophical Society, Vol. 41, 16-26, (1945) · Zbl 0060.42001
[52] Hisano, M., Friction at the atomic level-atomistic approaches in tribology, (2018), Wiley-VCH Weinheim, Germany
[53] Hong, T.; Marone, C., Effects of normal stress perturbations on the frictional properties of simulated faults, Geochemistry, Geophysics, Geosystems, Vol. 6, 1-19, (2005), Q03012
[54] Imanishi, K.; Ellsworth, W. L.; Prejean, S. G., Earthquake source parameters determined by the SAFOD pilot hole seismic array, Geophysical Research Letters, Vol. 31, (2004)
[55] Jaeger, J. C., Friction of rocks and stability of rock slopes, Geotechnique, Vol. 21, 97-134, (1971)
[56] Jaeger, J. C.; Cook, N. G.W.; Zimmermann, R. W., Fundamentals of rock mechanics, (2007), Blackwell Publishing London
[57] Johnson, K. L., Contact mechanics, (1985), Cambridge University Press Cambridge · Zbl 0599.73108
[58] Johnson, L. R.; Nadeau, R. M., Asperity model of an earthquake: static problem, Bulletin of the Seismological Society of America, Vol. 92, 672-686, (2002)
[59] Kachanov, M. K.; Sevostianov, I., Micromechanics of materials with applications, (2018), Springer-Verlag Berlin
[60] Kanwal, R. P., Linear integral equations: theory and technique, (1971), Academic Press New York · Zbl 0219.45001
[61] Kassir, M. K.; Sih, G. C., Three-dimensional crack problems: A new selection of crack problems in three-dimensional elasticity, (1975), Noordhoff International Publishing Leyden · Zbl 0312.73112
[62] Kato, A.; Igarashi, T.; Obara, K., Detection of a hidden boso slow slip event immediately after the 2011 mw 9 tohoku-oki earthquake, Japan, Geophysical Research Letters, Vol. 41, 5868-5874, (2014)
[63] Kikuchi, N.; Oden, J. T., Contact problems in elasticity. A study of variational inequalities and finite element methods, (1972), Studies in Applied and Numerical Mathematics, SIAM Philadephia, PA · Zbl 0685.73002
[64] Kitajima, H.; Saffer, D. M., Elevated pore pressure and anomalously low stress in regions of low frequency earthquakes along the nankai trough, Geophysical Research Letters, Vol. 39, L23301, (2012)
[65] Klarbring, A.; Mikelić, A.; Shillor, M., The rigid punch problem with friction, International Journal of Engineering Science, Vol. 29, 751-768, (1991) · Zbl 0749.73072
[66] Kodaira, S.; Likada, T.; Kato, A.; Park, J.-O.; Iwasaki, T.; Kaneda, Y., High pore fluid pressure may cause silent slip in the nankai trough, Science, Vol. 304, 1295-1298, (2004)
[67] Laursen, T. A., Computational contact and impact mechanics, (2003), Springer-Verlag Berlin
[68] Linker, M. F.; Dieterich, J. H., Effects of variable normal stress on rock friction: observations and constitutive equations, Journal of Geophysical Research (Solid Earth), Vol. 97, 4923-4940, (1992)
[69] Love, A. E.H., A treatise on the mathematical theory of elasticity, (1928), Clarendon Press Oxford
[70] Luo, Y.; Ampuero, J.-P., Stability of faults with heterogeneous friction properties and effective normal stress, Tectonophysics, Vol. 733, 257-272, (2018)
[71] Lur’e, A. I., Some three-dimensional problems of the theory of elasticity, Wiley-Interscience, New York, (1964) · Zbl 0122.19003
[72] Marone, C., Laboratory derived friction laws and their application to seismic faulting, Annual Reviews- Earth and Planetary Science, Vol. 26, 643-696, (1998)
[73] Michalowski, R.; Mroz, Z., Associated and non-associated sliding rules in contact friction problems, Archives of Mechanics, Vol. 30, 259-276, (1978) · Zbl 0397.73088
[74] Michalowski, R. L.; Zang, W.; Nadukuru, S. S., Maturing of contacts and ageing of silica sand, Géotechnique, Vol. 68, 132-145, (2018)
[75] Mogi, K., On the pressure dependence of strength of rocks and the Coulomb fracture criterion, Tectonophysics, Vol. 21, 273-285, (1974)
[76] Morris, J. P., Review of rock joint models, (2003), Lawrence Livermore laboratory Report Livermore, CA
[77] Nadeau, R. M.; Johnson, L. R., Seismological studies at parkfield IV. moment release rates and estimates of source parameters for small repeating earthquakes, Bulletin of the Seismological Society of America, Vol. 88, 790-814, (1998)
[78] Nadeau, R. M.; McEvilly, T. V., Fault slip rates at depth from recurrence intervals of repeating micro-earthquakes, Science, Vol. 285, 718-721, (1999)
[79] Nguyen, T. S.; Selvadurai, A. P.S., A model for coupled mechanical and hydraulic behavior of a rock joint, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 22, 29-48, (1998) · Zbl 0947.74035
[80] Nur, A., Dilatancy, pore fluids and premonitory variations of t_{s}/t_{p} travel times, Bulletin of the Seismological Society of America, Vol. 62, 1217-1222, (1972)
[81] Olssen, R.; Barton, N., An improved model for hydromechanical coupling during shearing of joints, International Journal of Rock Mechanics and Mining Sciences, Vol. 38, 317-329, (2001)
[82] Panagiotopoulos, P. D., Inequality problems in mechanics and applications. convex and nonconvex energy functions, (1989), Birkhauser-Verlag Basel
[83] Pellet, F. L.; Selvadurai, A. P.S., Rock damage mechanics, chapter 3 in rock mechanics and engineering, 65-107, (2016), CRC Press Boca Raton, FL, (X.-T. Feng, Ed.)
[84] Persson, B. J.N., Sliding friction: physical principles and applications, (2000), Springer-Verlag Berlin · Zbl 0966.74001
[85] Pietruszczak, S., Fundamentals of plasticity in geomechanics, Vol. Fl, (2010), CRC Press Boca Raton · Zbl 1219.74002
[86] Plesha, M. E., Constitutive models for rock discontinuities with dilatancy and surface degradation, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 11, 345-362, (1987) · Zbl 0612.73108
[87] Plesha, M. E.; Belytschko, T., A constitutive operator splitting method for non-linear transient analysis, International Journal for Numerical Methods in Engineering, Vol. 21, 1729-1745, (1985)
[88] Plesha, M. E.; Ballarini, R.; Parulekar, A., Constitutive model and finite element procedure for dilatant contact problems, Journal of the Engineering Mechanics Division Proc ASCE, Vol. 115, 2649-2668, (1989)
[89] Prasseyto, S. H.; Guttierrez, M.; Barton, N., Nonlinear shear behavior of rock joints using a linearized implementation of the barton-bandis model, Journal of Rock Mechanics and Geotechnical Engineering, Vol. 9, 671-682, (2017)
[90] (Raous, M.; Jean, M.; Moreau, J. J., Contact mechanics, (1995), Plenum Press New York)
[91] Rice, J. R., On the stability of dilatant hardening for saturated rock masses, Journal of Geophysical Research, Vol. 80, 1531-1536, (1975)
[92] Rice, J. R.; Cocco, M., Seismic fault rheology and earthquake dynamics, (Holvus, N.; Hirth, G.; Handy, M. R., Tectonic faults: Agents of change on a dynamic earth, (2007), MIT Press MA), 99-137
[93] Rice, J. R.; Ruina, A. L., Stability of steady frictional slipping, Journal of Applied Mechanics, Vol. 50, 343-349, (1983) · Zbl 0554.73095
[94] Rice, J. R.; Rudnicki, J. W.; Platt, J. D., Stability and localization of rapid shear in fluid-saturated gouge: 1. linearized stability analysis, Journal of Geophysical Research (Solid Earth), Vol. 119, 4311-4333, (2014)
[95] Rossmanith, H.-P., (Proceedings of the First International Conference on Damage and Failure of Interface, (1997), DFI-Vienna, AA Balkema Rotterdam)
[96] Rudnicki, J. W.; Chen, C.-H., Stabilization of rapid frictional slip on a weakening fault by dilatant hardening, Journal of Geophysical Research, Vol. 93, 4745-4757, (1988)
[97] Ruina, A. L., Slip instability and state variable friction laws, Journal of Geophysical Research, Vol. 88, 10359-10370, (1983)
[98] Sammis, C. G.; Rice, J. R., Repeating earthquakes as low-stress-drop events at a border between locked and creeping fault patches, Bulletin of the Seismological Society of America, Vol. 91, 532-537, (2001)
[99] Sammis, C. G.; Nadeau, R.; Johnson, L. R., How strong is an asperity, Journal of Geophysical Research (Solid Earth), Vol. 104, 10609-10619, (1999)
[100] Scholz, C., Earthquakes and friction laws, Nature, Vol. 391, 37-42, (1998)
[101] Scholz, C. H., The mechanics of earthquakes and faulting, (2002), Cambridge University Press Cambridge
[102] Scuderi, M. M.; Colletini, C., The role of fluid pressure in induced vs. triggered seismicity: insights from rock deformation experiments on carbonates, Scientific Reports, Vol. 6, 24852, (2016)
[103] Scuderi, M.; Collettini, C.; Marone, C., Frictional stability and earthquake triggering during fluid pressure stimulation of an experimental fault, Earth and Planetary Science Letters, Vol. 477, 84-96, (2017)
[104] Segall, P.; Lu, S., Injection-induced seismicity: poroelastic and earthquake nucleation effects, Journal of Geophysical Research (Solid Earth), Vol. 120, 5082-5103, (2015)
[105] Selvadurai, A. P.S., Elastic analysis of soil-foundation interaction, developments in geotechnical engineering, Vol. 17, (1979), Elsevier Scientific Publishing Co The Netherlands
[106] Selvadurai, A. P.S., Asymmetric displacements of a rigid disc inclusion embedded in a transversely isotropic elastic medium of infinite extent, International Journal of Engineering Science, Vol. 18, 979-986, (1980) · Zbl 0428.73010
[107] Selvadurai, A. P.S., On an integral equation governing an internally indented penny-shaped crack, Mechanics Research Communications, Vol. 12, 347-351, (1985)
[108] Selvadurai, A. P.S., Matrix crack extension at a frictionally constrained fiber, Journal of Engineering Materials and Technology, Trans. ASME, Vol. 116, 398-402, (1994)
[109] Selvadurai, A. P.S., Separation at a pre-fractured bi-material geological interface, Mechanics Research Communications, Vol. 21, 83-88, (1994) · Zbl 0795.73064
[110] Selvadurai, A. P.S., Boundary element modelling of geomaterial interfaces, (Selvadurai, A. P.S.; Boulon, M. J., Mechanics of geomaterial interfaces, (1995), Elsevier New York), 395-420
[111] Selvadurai, A. P.S., In-plane loading of a rigid disc inclusion embedded in a crack, International Journal of Solids and Structures, Vol. 36, 1701-1714, (1999) · Zbl 0928.74016
[112] Selvadurai, A. P.S., Fracture evolution during indentation of a brittle elastic solid, Mechanics of Cohesive-Frictional Materials, Vol. 5, 325-339, (2000)
[113] Selvadurai, A. P.S., Indentation of a pre-compressed penny-shaped crack, International Journal of Engineering Science, Vol. 38, 2095-2111, (2000)
[114] Selvadurai, A. P.S., Partial differential equations in mechanics, The biharmonic equation, Poisson’s equation, Vol. 2, (2000), Springer-Verlag Berlin · Zbl 0967.35001
[115] Selvadurai, A. P.S., On an invariance principle for unilateral contact at a bi-material elastic interface, International Journal of Engineering Science, Vol. 41, 721-739, (2003) · Zbl 1211.74192
[116] Selvadurai, A. P.S., Deflections of a rubber membrane, Journal of the Mechanics and Physics of Solids, Vol. 54, 1093-1119, (2006) · Zbl 1120.74595
[117] Selvadurai, A. P.S., Bridged defects in continuously and discretely reinforced solids, Journal of Engineering Mathematics, Vol. 95, 359-380, (2015) · Zbl 1360.74131
[118] Selvadurai, A. P.S., Indentation of a spherical cavity in an elastic body by a rigid spherical inclusion: influence of non-classical interface conditions, Continuum Mechanics and Thermodynamics, Vol. 28, 617-632, (2016) · Zbl 1348.74258
[119] Selvadurai, A. P.S., (Atluri, S. N., Contact mechanics in the engineering sciences. Material characterization, micromechanical processes and modelling geosciences, (2010), Tech Science Press GA), 395-420
[120] (Selvadurai, A. P.S.; Boulon, M. J., Mechanics of Geomaterial Interfaces, Studies in Applied Mechanics, Vol. 42, (1995), Elsevier Amsterdam)
[121] Selvadurai, A. P.S.; Katebi, A., An adhesive contact problem for an incompressible non-homogeneous elastic halfspace, Acta Mechanica, Vol. 226, 249-265, (2015) · Zbl 1323.74058
[122] Selvadurai, A. P.S.; Nguyen, T. S., Mechanics and fluid transport in a degradable discontinuity, Engineering Geology, Vol. 53, 243-249, (1999)
[123] Selvadurai, A. P.S.; Singh, B. M., On the expansion of a penny-shaped crack by a rigid disc inclusion, International Journal of Fracture, Vol. 25, 69-77, (1984)
[124] Selvadurai, A. P.S.; Singh, B. M., The annular crack problem for an isotropic elastic solid, Quarterly Journal of Mechanics and Applied Mathematics, Vol. 38, 233-243, (1985) · Zbl 0559.73090
[125] Selvadurai, A. P.S.; Suvorov, A. P., Thermo-poroelasticity and geomechanics, (2016), Cambridge University Press Cambridge
[126] Selvadurai, A. P.S.; Voyiadjis, G. Z., Mechanics of interfaces, (Studies in applied mechanics, Vol. 11, (1986), Elsevier Amsterdam) · Zbl 0662.73074
[127] Selvadurai, A. P.S.; Yu, Q., Mechanics of a discontinuity in a geomaterial, Computers and Geotechnics, Vol. 32, 92-106, (2005)
[128] Selvadurai, A. P.S.; Yu, Q., On the indentation of a polymeric membrane, Proceedings of the Royal Society, Ser A, Vol. 462, 189-209, (2006) · Zbl 1149.74373
[129] Selvadurai, A. P.S.; Suvorov, A. P.; Selvadurai, P. A., Thermo-hydro-mechanical processes in fractured rock formations during glacial advance, Geoscientific Model Development, Vol. 8, 2167-2185, (2015)
[130] Selvadurai, P. A.; Glaser, S. D., Laboratory developed contact models controlling instability on frictional faults, Journal of Geophysical Research (Solid Earth), Vol. 120, 4208-4236, (2015)
[131] Selvadurai, P. A.; Glaser, S. D., Asperity generation and its relationship to seismicity on a planar fault: a laboratory simulation, Geophysical Journal International, Vol. 208, 1009-1025, (2017)
[132] Selvadurai, P. A., Edwards, B. E., Tormann, T., Wiemer, S., & Glaser, S. D. (2018). Characteristics of seismicity on worn faults-source dimensions of frictional precursory seismicity controlled by fault roughness (in preparation).
[133] Sibson, R. H., Fault-valve behaviour and the hydrostatic-lithostatic fluid pressure interface, Earth Science Reviews, Vol. 32, 141-144, (1992)
[134] Siman-Tov, S.; Aharanov, E.; Boneh, Y.; Reches, Z., Fault mirrors along carbonate faults: formation and destruction during shear experiments, Earth and Planetary Science Letters, Vol. 430, 367-376, (2015)
[135] Sneddon, I. N., Mixed boundary value problems in potential theory, (1966), Publishing Co North-Holland, Amsterdam · Zbl 0139.28801
[136] Taylor, D. W., Fundamentals of soil mechanics, (1948), John Wiley New York
[137] Tranter, C. J., Some triple integral equations, Glasgow Mathematical Journal, Vol. 4, 200-203, (1960) · Zbl 0103.07903
[138] Turrin, S.; Hanss, M.; Selvadurai, A. P.S., An approach to uncertainty analysis of rockfall simulation, Computer Modeling in Engineering and Sciences, Vol. 1350, 1-22, (2009) · Zbl 1231.74305
[139] Ufliand, Ia. S., Survey of applications of integral transforms in the theory of elasticity, 65-1556, (1965), North Carolina State College Raleigh, NC, (Engl. Trans. Edited by IN Sneddon) Tech. Rep
[140] Villaggio, P., A unilateral contact problem in elasticity, Journal of Elasticity, Vol. 10, 113-119, (1980) · Zbl 0425.73097
[141] Wan, R.; Nicot, F.; Darve, F., Failure in geomaterials: A contemporary treatise, (2017), Elsevier Inc Amsterdam
[142] Williams, W. E., Integral equation formulation of some three-part boundary value problems, Proceedings of the Edinburgh Mathematical Society, Vol. 13, 317-323, (1963) · Zbl 0115.31702
[143] Willner, K., Kontinuums- und kontaktmechanik. synthetische und analytische darstellung, (2003), Springer-Verlag Berlin
[144] Wriggers, P.; Laursen, T. A., Computational contact mechanics, (2007), Springer-Verlag Berlin
[145] Zang, A.; Stephansson, O., Stress field of the Earth’s crust, (2010), Springer-Verlag Berlin
[146] Zienkiewicz, O. C.; Best, B.; Dullage, C.; Stagg, K. G., Analysis of nonlinear problems in rock mechanics with particular reference to jointed rock systems, (Proceedings 2nd Congress of the International Society for Rock Mechanics, Beograd, Vol. 2, (1970)), 501-509
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.