On the theory of consolidation with double porosity. II. (English) Zbl 0601.73109
[For part I see ibid. 20, 1009-1035 (1982; Zbl 0493.76094).]
The theory of consolidation with double porosity is further substantiated by establishing certain general results concerning the mathematical behavior of the relevant partial differential equations. Specifically, by following standard procedures in mechanics, uniqueness and a variational principle are established. Moreover, an indirect method of solution which allows boundary value problems of the theory of consolidation with double porosity to be reduced to the study of elementary boundary value problems of the theory of heat conduction is proposed for a wide class of problems. Analytical solutions to two boundary value problems frequently encountered in practice are also obtained by the proposed method.
The theory of consolidation with double porosity is further substantiated by establishing certain general results concerning the mathematical behavior of the relevant partial differential equations. Specifically, by following standard procedures in mechanics, uniqueness and a variational principle are established. Moreover, an indirect method of solution which allows boundary value problems of the theory of consolidation with double porosity to be reduced to the study of elementary boundary value problems of the theory of heat conduction is proposed for a wide class of problems. Analytical solutions to two boundary value problems frequently encountered in practice are also obtained by the proposed method.
MSC:
| 74L10 | Soil and rock mechanics |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74G30 | Uniqueness of solutions of equilibrium problems in solid mechanics |
| 74H25 | Uniqueness of solutions of dynamical problems in solid mechanics |
Keywords:
column problem; boreholl problem; consolidation; double porosity; variational principle; indirect method of solution; elementary boundary value problems; heat conductionCitations:
Zbl 0493.76094References:
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