Mindlin’s problem for an incompressible elastic half-space with an exponential variation in the linear elastic shear modulus

Abbiss, 1979, A comparison of the stiffness of the chalk at Mundford from a seismic survey and a large scale tank test, Geotechnique, 29, 461, 10.1680/geot.1979.29.4.461 Aleynikov, 2011, Spatial contact problems in geomechanics Atkinson, 1975, Anisotropic elastic deformations in laboratory tests on undisturbed London Clay, Geotechnique, 25, 357, 10.1680/geot.1975.25.2.357 Burland, J.B., & Lord, J.A. (1969). The Load-Deformation Behaviour of the Middle Chalk at Mundford, Norfolk: A Comparison Between Full-Scale Performance and In-Situ Laboratory Measurements. Building Research Station CP 6/70. Burland, 1977, A study of ground movement and progressive failure caused by a deep excavation in Oxford Clay, Geotechnique, 27, 557, 10.1680/geot.1977.27.4.557 Butler, 1974 Cooke, R.W., & Price, G. (1973). Strains and displacements around friction piles. In Proceedings of 8th international conference on soil mechanics and foundation engineering, 2, Moscow (pp. 52–60). Costa Filch, 1980, A computer model for the analysis of ground movements in London Clay, Geotechnique, 30, 336, 10.1680/geot.1980.30.3.336 Cripps, 1981, The engineering properties of mudrocks, Quality Journal of Engineering Geology, London, 14, 325, 10.1144/GSL.QJEG.1981.014.04.10 Cripps, 1986, Engineering characteristics of British over-consolidated clays and mudrocks I. Tertiary deposits, Engineering Geology, 22, 349, 10.1016/0013-7952(86)90004-9 Eason, 1955, On certain integrals of Lipschitz–Hankel type involving products of Bessel functions, Philosophical Transactions of the Royal Society of London – Series A: Mathematical and Physical Sciences, 247, 529, 10.1098/rsta.1955.0005 Gibson, 1967, Some results concerning displacements and stresses in a non-homogeneous elastic half-space, Geotechnique, 17, 58, 10.1680/geot.1967.17.1.58 Gladwell, 1980 Hetényi, 1946 Hobbs, N.B. (1974). Factors affecting the prediction of settlement on rock with particular reference to chalk and Trias. In BGS conference on settlement of structures, Cambridge (pp. 579–560). Hooper, 1966, Some numerical results concerning the shear strength of London Clay, Geotechnique, 16, 282, 10.1680/geot.1966.16.4.282 Katebi, 2010, Axisymmetric interaction of a rigid disc with a transversely isotropic half-space, International Journal for Numerical and Analytical Methods in Geomechanics, 34, 1211, 10.1002/nag.854 Klein, 1956, Calculation of Non-homogeneous Distribution of Deformation and Other Mechanical Properties of Soils for Estimating Construction of Compressible Bases, Gos. Idz. Lit. Stroit, i Arckh.Sb., 14 Korenev, 1975, A die resting on an elastic half-space, the modulus of elasticity of which is an exponential function of depth, Doklady Akademii Nauk SSSR, 112 Marsland, A. (1973). Laboratory and in-situ measurements of the deformation moduli of London Clay, Current Paper 24/73, Building Research Establishment, (p. 12). Mindlin, 1936, Force at a point in the interior of a semi-infinite solid, Physics, 7, 195, 10.1063/1.1745385 Mossakowskii, 1958, pressure of a circular punch on an elastic half-space whose modulus of elasticity is an exponential function, Prikladnaya Matematika i Mekhanika, 22, 168 Oliveira, 2012, Boundary element formulation of axisymmetric problems for an elastic half-space, Engineering Analysis with Boundary Elements, 36, 1478, 10.1016/j.enganabound.2012.03.015 1959 Popov, 1959, Bending on an unbounded plate supported by an elastic half-space with a modulus of elasticity varying with depth, Journal of Applied Mathematics and Mechanics, 23, 1566, 10.1016/0021-8928(59)90012-7 Popov, 1973, Axisymmetric contact problem for an elastic inhomogeneous half-space in the presence of cohesion, PMM, 37, 1109 Rajapakse, 1990, A vertical load in the interior of a non-homogeneous incompressible elastic half-space, The Quarterly Journal of Mechanics and Applied Mathematics, 43, 10.1093/qjmam/43.1.1 Rajapakse, 1991, Response of circular footings and anchor plates in non-homogeneous elastic soils, International Journal for Numerical and Analytical Methods in Geomechanics, 15, 457, 10.1002/nag.1610150702 Rakov, 1961, Contact problems of the theory of elasticity for a half-space whose modulus is a power function of depth, Dop. Akad. Nauk Ukr RSR., 3, 286 Rostovtsev, 1961, An integral equation encountered in the problem of a rigid foundation bearing on non-homogeneous soil, Journal of Applied Mathematics and Mechanics, 25, 238, 10.1016/0021-8928(61)90115-0 Rostovtsev, 1964, On the theory of elasticity of a non-homogeneous medium, Journal of Applied Mathematics and Mechanics, 28, 601, 10.1016/0021-8928(64)90060-7 Selvadurai, 1979, Elastic analysis of soil-foundation interaction, Vol. 17 Selvadurai, 1980, Asymmetric displacements of a rigid disc inclusion embedded in a transversely isotropic medium of infinite extent, International Journal of Engineering Science, 18, 979, 10.1016/0020-7225(80)90070-1 Selvadurai, 1993, The axial loading of a rigid circular anchor plate embedded in an elastic halfspace, International Journal for Numerical and Analytical Methods in Geomechanics, 17, 343, 10.1002/nag.1610170505 Selvadurai, 1994, Analytical methods for embedded flat anchor problems in geomechanics, Vol. 1, 305 Selvadurai, 1994, On the problem of a detached anchor plate embedded in a crack, International Journal of Solids and Structures, 31, 279, 10.1016/0020-7683(94)90121-X Selvadurai, 1996, The settlement of a rigid circular foundation resting on a half-space exhibiting a near surface elastic non-homogeneity, International Journal for Numerical and Analytical Methods in Geomechanics, 20, 351, 10.1002/(SICI)1096-9853(199605)20:5<351::AID-NAG830>3.0.CO;2-L Selvadurai, A.P.S. (2000a). On the mathematical modelling of certain fundamental elastostatic contact problems in geomechanics. In Zaman, M., Gioda, G., & Booker, J.R. (Eds.), Modelling in Geomechanics, Chapter 13 (pp. 301–328). Selvadurai, 2000, Partial differential equations in mechanics, Vol. 2 Selvadurai, 2000, On the displacements of an elastic halfspace containing a rigid inhomogeneity, International Journal of Geomechanics, 1, 149, 10.1061/(ASCE)1532-3641(2001)1:2(149) Selvadurai, 2000, Boussinesq’s problem for an elastic halfspace reinforced with a rigid disk inclusion, Mathematics and Mechanics of Solids, 5, 483, 10.1177/108128650000500406 Selvadurai, 2007, The analytical method in geomechanics, Applied Mechanics Reviews, 60, 87, 10.1115/1.2730845 Selvadurai, 1997, A disc inclusion at a non-homogeneous elastic interface, Mechanics Research Communications, 24, 473, 10.1016/S0093-6413(97)00053-0 Selvadurai, 1998, Axisymmetric mixed boundary value problems for an elastic half-space with a periodic non-homogeneity, International Journal of Solids Structures, 35, 1813, 10.1016/S0020-7683(97)00160-1 Selvadurai, 1985, On the load transfer from a rigid cylindrical inclusion into an elastic half space, International Journal of Solids and Structures, 21, 1213, 10.1016/0020-7683(85)90005-8 Selvadurai, 1991, The in-plane loading of a rigid disk inclusion embedded in an elastic halfspace, Journal of Applied Mechanics, 58, 362, 10.1115/1.2897194 Selvadurai, 1986, A Reissner–Sagoci problem for a non-homogeneous elastic solid, Journal of Elasticity, 16, 383, 10.1007/BF00041763 Simons, N.E., & Som, N.N. (1969). The influence of lateral stresses on the stress deformation characteristics of London Clay, In Proceedings of 7th international conference on soil mechanics and foundation engineering, 1, Mexico, (pp. 369–377). Simpson, 1979, A computer model for the behaviour of London Clay, Geotechnique, 29, 149, 10.1680/geot.1979.29.2.149 Skempton, A.W., & Henkel, D.J. (1957). Tests on London Clay from deep borings at Paddington, Victoria and the South Bank. In Proceedings of 4th international conference on soil mechanics and foundation engineering, London, Vol. 1 (pp. 100–106). Sneddon, 1951 Spencer, 1998, Some generalized anti-plane strain problems for an inhomogeneous elastic halfspace, Journal of Engineering Mathematics, 34, 403, 10.1023/A:1004396817942 Ward, 1965, Properties of the London Clay at the Ashford Common Shaft, Geotechnique, 15, 324, 10.1680/geot.1965.15.4.321 Winkler, 1867 Yue, 1995, On the mechanics of a rigid disc inclusion embedded in a fluid saturate poroelastic medium, International Journal of Engineering Science, 33, 633, 10.1016/0020-7225(95)00031-R