Time-Dependent Response of an Axially Loaded Elastic Bar in a Multilayered Poroelastic Medium
Publication: Journal of Engineering Mechanics
Volume 133, Issue 5
Abstract
This paper considers load transfer from an axially loaded long elastic bar into a multilayered poroelastic half-space. The problem is analyzed by decomposing the bar-half-space system into an extended half-space governed by Biot’s theory of poroelasticity and a one-dimensional fictitious bar. The interaction problem is formulated in the Laplace transform domain. Vertical displacement of the bar is approximated by an exponential series with a set of arbitrary functions. The arbitrary functions are determined by using a variational method. The vertical displacement influence function of a multilayered half-space subjected to a buried uniform vertical patch load is required in the variational formulation. The required influence function is obtained by employing a previously developed exact stiffness matrix method. Time domain solutions are computed by using a numerical Laplace inversion scheme. Selected numerical results are presented to portray the influence of the bar length–radius ratio, layer configuration, poroelastic material parameters, and loading time history on the time dependent response of a bar.
Get full access to this article
View all available purchase options and get full access to this article.
References
Banerjee, P. K., and Davies, T. G. (1977). “Analysis of pile groups embedded in Gibson soil.” Proc., 9th Int. Conf. Soil Mech. and Found. Engng., 381–386.
Biot, M. A. (1941). “General theory of three-dimensional consolidation.” J. Appl. Phys., 12, 155–164.
Cheng, A. H. D. (1998). “Poroelasticity: Maurice A. Biot memorial issue.” Int. J. Solids Struct., 35, 4513–5032.
Chin, J. T., Chow, Y. K., and Poulos, H. G. (1990). “Numerical analysis of axially loaded vertical piles and pile groups.” Comput. Geotech., 9(4), 273–290.
Chow, Y. K. (1987). “Axial and lateral response of pile groups embedded in nonhomogeneous soils.” Int. J. Numer. Analyt. Meth. Geomech., 11, 621–638.
Detournay, E., and Cheng, A. H. D. (1993). Comprehensive rock engineering: Principles, practice and projects, Vol. 2, Chapter 5: Fundamentals of Poroelasticity, Pergamon, New York.
Guo, W. D., and Randolph, M. F. (1997). “Vertically loaded single piles in nonhomogeneous media.” Int. J. Numer. Analyt. Meth. Geomech., 21(2), 507–532.
Mindlin, R. D. (1936). “Force at a point in the interior of a semi-infinite solid.” Physics (N.Y.), 7, 195–202.
Muki, R., and Sternberg, E. (1969). “On the diffusion of an axial load from an infinite cylindrical bar embedded in an elastic medium.” Int. J. Solids Struct., 5, 587–605.
Muki, R., and Sternberg, E. (1970). “Elastostatic load transfer to a half-space from a partially embedded axially loaded rod.” Int. J. Solids Struct., 6, 69–90.
Niumpradit, B., and Karasudhi, P. (1981). “Load transfer from an elastic bar to a saturated porous elastic soil.” Int. J. Numer. Analyt. Meth. Geomech., 5, 115–138.
Pak, R. Y. S., and Saphores, J.-D. M. (1991). “On the response of a partially embedded rod to axial load.” J. Appl. Mech., 58, 599–602.
Piessens, R. (1975). “Bibliography on numerical inversion of the Laplace transform and applications.” J. Comput. Appl. Math., 1, 115–126.
Poulos, H. G., and Davis, E. H. (1968). “The settlement behaviour of single, axially loaded, incompressible piles and piers.” Geotechnique, 18, 351–371.
Poulos, H. G. (1979). “Settlement of single piles in nonhomogeneous soil.” J. Geotech. Engrg. Div., 105(5), 627–641.
Poulos, H. G., and Davis, E. H. (1980). Pile foundation analysis and design, Wiley, New York.
Rajapakse, R. K. N. D. (1988). “Dynamics of piles: A critical evaluation of continuum solution models.” Proc., CSCE Annual Conf., Vol. 3, 216–236.
Rajapakse, R. K. N. D. (1990). “Response of an axially loaded elastic pile in a Gibson soil.” Geotechnique, 40(2), 237–249.
Randolph, M. F., and Wroth, C. P. (1978). “Analysis of deformation of vertically loaded piles.” J. Geotech. Engrg. Div., 104(12), 1465–1488.
Rice, J. R., and Cleary, M. P. (1976). “Some basic stress diffusion solutions for fluid saturated elastic porous media with compressible constituents.” Rev. Geophys. Space Phys., 14, 227–241.
Sandhu, R. S., and Wilson, E. L. (1969). “Finite element analysis of seepage in elastic media.” J. Engrg. Mech. Div., 95(3), 641–652.
Schapery, R. A. (1962). “Approximate methods of transform inversion for viscoelastic stress analysis.” Proc., 4th U.S. Nat. Congress on Appl. Mech., 2, 1075–1085.
Selvadurai, A. P. S., and Rajapakse, R. K. N. D. (1990). “Axial stiffness of anchoring rod embedded in elastic media.” Can. J. Civ. Eng., 17, 321–328.
Senjuntichai, T., Mani, S., and Rajapakse, R. K. N. D. (2006). “Vertical vibration of an embedded rigid foundation in a poroelastic soil.” Soil Dyn. Earthquake Eng., 26, 626–636.
Senjuntichai, T., and Rajapakse, R. K. N. D. (1995). “Exact stiffness method for quasi-statics of multilayered poroelastic medium.” Int. J. Solids Struct., 32, 1535–1553.
Skempton, A. W. (1954). “The pore pressure coefficients A and B.” Geotechnique, 4, 143–147.
Sneddon, I. N. (1951). Fourier transforms, McGraw-Hill, New York.
Stehfest, H. (1970). “Numerical inversion of Laplace transforms.” Commun. ACM, 13, 105–124.
Terzaghi, K. (1923). “Die berechnung der durchassigkeitsziffer des tones aus dem verlauf der hydrodynamischen spannungsercheinungen.” Sitzungsber. Akad. Wiss. Wien, Math.-Naturwiss. Kl., Abt. 2A, 132, 105–124.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 5 • May 2007
Pages: 578 - 587
Copyright
© 2007 ASCE.
History
Received: Feb 28, 2006
Accepted: Oct 23, 2006
Published online: May 1, 2007
Published in print: May 2007
Notes
Note. Associate Editor: Alexander H.-D. Cheng
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.