Abstract
In the paper is considered the case of plane strain of the skeleton of a consolidating halfspace loaded by a tangential force at the surface. The considerations are based on the linear theory of flow of a liquid through porous, deformable media, as formulated by M. A. Biot. As a result of the solution of the linear consolidation theory, the formula is derived which determines the setting of the surface of a consolidation halfspace as a function of time. The solution is compared with the solution of an analogous boundary value problem of elasticity.The solution derived corresponds to a unit load and constitutes a Green function; thus it may be used to the construction of solutions in the cases of arbitrary, also time-dependent, loading of the surface.
References
M. A. BIOT, General solutions of the equations of elasticity and consolidation of a porous material, J. Appl. Phys., 23, 91-96, 1956.
M. A. BIOT, D. G. WILLIS, The elastic coefficients of the theory of consolidation, J. Appl. Phys., 24, 594-601, 1957.
W. DERSKI, A method of solving of the system equations of consolidation theory, Bull. Acad. Polon. Sci., serie Sci. Techn., 12, 10, 1964.
W. DERSKI, I. KISIEL, O warunkach początkowych w zagadnieniach teorii konsolidacji, Arch. Hydr., 16, 1, 31-37, 1969.
G. DOETSCH, Praktyka przekształcenia Laplace'a, PWN, 1964.
W. NOWACKI, Teoria sprężystości, PWN, 1970.
W. I. SMIRNOW, Matematyka wyższa, PWN, 2, 1960.
M. A. BIOT, D. G. WILLIS, The elastic coefficients of the theory of consolidation, J. Appl. Phys., 24, 594-601, 1957.
W. DERSKI, A method of solving of the system equations of consolidation theory, Bull. Acad. Polon. Sci., serie Sci. Techn., 12, 10, 1964.
W. DERSKI, I. KISIEL, O warunkach początkowych w zagadnieniach teorii konsolidacji, Arch. Hydr., 16, 1, 31-37, 1969.
G. DOETSCH, Praktyka przekształcenia Laplace'a, PWN, 1964.
W. NOWACKI, Teoria sprężystości, PWN, 1970.
W. I. SMIRNOW, Matematyka wyższa, PWN, 2, 1960.
