Indentation of a poroelastic solid by a smooth rigid sphere is analyzed within the framework of Biot's theory. The particular cases when the spherical indenter is loaded instantaneously to a fixed depth with the surface of the semi-infinite domain being either fully undrained or in a mixed drainage condition are solved. Constituents of the poroelastic medium are assumed to be slightly compressible. The solution procedure based on the McNamee-Gibson displacement function method is adopted in this work. Problem formulation and the solution procedure are first introduced. Effect of poroelasticity on the contact stress and the transient indentation force response is then discussed. The asymptotic behaviors for the normalized transient force at early and late times are derived. Though derivation of these fully coupled solutions requires the aid of a variety of mathematical techniques, the normalized transient force responses are remarkably simple and show only weak dependence on one derived material constant, which lend itself to convenient use for poroelastic characterization of geomaterials such as rocks in the laboratory.

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