Abstract
This paper examines the interaction between two rigid circular indentors on a poroelastic half-space. The resulting mixed boundary value problem, when formulated in the Laplace transform domain, yields an infinite set of Fredholm integral equations. These integral equations are then solved for some special cases. Numerical results for the case of a single indentor show a good agreement with those obtained by using Heinrich and Desoyer's assumption. For the case in which the radius of one indentor reduces to zero (interaction between a rigid indentor and an externally placed load), the resulting equations are solved by a semi-inverse method to give analytical solutions for the resultant force and moment required to maintain the indentor with no normal displacement. When the indentor is subjected to an axial load but allowed to undergo an additional settlement and tilt, numerical results are presented to demonstrate the manner in which Poisson's ratio and the drainage boundary conditions influence the consolidation of the half-space. Numerical results are also given to illustrate the interaction between two identical indentors when ratio of the radius to the spatial distance between them is small.
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References
K. Terzaghi,Erdbaumechanik auf bodenphysikalischer Grundlage, Franz Deuticke, Leipzig (1925).
M.A. Biot, General theory of three-dimensional consolidation,J. of Appl. Physics 12, 155–164 (1941).
M.A. Biot, General solution of the equations of elasticity and consolidation for a porous material,J. of Appl. Mech. 23, 91–95 (1956).
J. McNamee and R.E. Gibson, Displacement functions and linear transforms applied to diffusion through porous elastic media,Quart. J. Mech. Appl. Math. 13, 98–111 (1960).
J. McNamee and R.E. Gibson, Plane strain and axially symmetric problems of consolidation of a semi-infinite clay stratum,Quart. J. Mech. Appl. Math. 13, 210–227 (1960).
R.L. Schiffman and A.A. Fungaroli, Consolidation due to tangential loads,Proceedings of the 6th International Conference on Soil Mech. and Foundation Engng., Vol.2 188–192, Montreal, Canada (1965).
L.K. Agbezuge and H. Deresiewicz, On the indentation of a consolidating half-space,Israel J. Tech. 12, 322–338 (1974).
C. Chiarella and J.R. Booker, The time-settlement behaviour of a rigid die resting on a deep clay layer,Q. J. Mech. Appl. Math. 28, 317–328(1975).
J. Gaszynski and G. Szefer, Axisymmetric problem of the indentor for the consolidating semi-space with mixed boundary permeability conditions,Arch. Mechaniki Stosowanej 30, 17–26 (1978).
A.P.S. Selvadurai and Z.Q. Yue, On the indentation of a poroelastic layer,Int. J. Num. Anal. Meth. Geomech. 18, 161–175 (1994).
Z.Q. Yue and A.P.S. Selvadurai, On the asymmetric indentation of a consolidating poroelastic half-space,Appl. Math. Modelling 18, 170–185 (1994).
Z.Q. Yue and A.P.S. Selvadurai, On the mechanics of a rigid disc inclusion embedded in a saturated poroelastic medium,Int. J. Engng. Sci. 33, 1633–1662 (1995).
J.R. Rice and M.P. Cleary, Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents,Rev. Geophys. Space Phys. 14, 227–241 (1976).
A.P.S. Selvadurai (ed.),Mechanics of Poroelastic Media, Kluwer Acad. Publ., The Netherlands, (1996).
R. Muki, Asymmetric problems of the theory of elasticity for a semi-infinite solid and a thick plate,Progress in Solid Mechanics Vol. 1 (eds: I.N. Sneddon and R. Hill), North-Holland Publ. Co, Amsterdam (1961), 401–439.
Q. Lan, G.A.C. Graham and A.P.S. Selvadurai, Certain two-punch problems for an elastic layer,Int. J. Solids & Structures.
G. Heinrich and K. Desoyer, Theorie dreidimensionaler Setzungsvorgange in Tonschichten,Ing.-Arch. 30, 225–253 (1961).
I.N. Sneddon, On Muki's solution of the equations of linear elasticity,Int. J. Engng. Sci. 30, 1237–1246 (1992).
I.N. Sneddon,The Use of Integral Transforms, McGraw-Hill Co, (1972).
G. N. Watson,Theory of Bessel Functions, p. 361, 2nd ed., Cambridge University Press (1952).
K.S. Crump, Numerical inversion of Laplace transform using a Fourier series approximation,J. Assoc. Comp. Machin. 10, 311–327 (1976).
A.P.S. Selvadurai, On the displacement induced in a rigid circular punch on an elastic halfspace due to an external force,Mechanics Research Communications 7, 351–358, (1980).
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Lan, Q., Selvadurai, A.P.S. Interacting indentors on a poroelastic half-space. Z. angew. Math. Phys. 47, 695–716 (1996). https://doi.org/10.1007/BF00915270
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DOI: https://doi.org/10.1007/BF00915270