Three-dimensional Green’s Functions For Transversely Isotropic Poroelastic Materials

Fundamental solutions or Green’s functions play an important role in bothapplied and theoretical studies on the physics of solids．By using the principle ofsuperposition, they can be used to solve the engineering problems under arbitraryloads. They are foundations of a lot of further works including numerical calculationand theoretical analysis. They are essential in the boundary element method as well asthe study of cracks，defects and inclusions.Because of its high specific strength and low cost, poroelastic materials havebeen widely used in engineering. Concerning the studies of Green’s functions forporoelastic materials, many references did not consider liquid coupling effect andthermal coupling effect． Because adding liquid coupling and thermal couplingequations breaks the fine properties of the pristine equations．However，there is oftenliquid coupling and thermal coupling effect in the practical environment．In thiscontext, the three dimensional Green’s functions are presented respectively forinfinite, semi-infinite and two-phase transversely isotropic poroelastic materials witha steady point liquid source or point heat source acting．Firstly, the steady general solution of poroelastic materials is described．Forinfinite, semi-infinite and two-phase transversely isotropic poroelastic materials witha point liquid source or point heat source acting, Green’s functions can be obtained byconstructing some new harmonic functions with undetermined constants. Theconstants of the functions can be obtained by using the compact general solution andthe corresponding equilibrium, boundary and continuity conditions．Finally, numerical results of corresponding coupled fields are given graphicallyby contours，including the pore fluid pressure increment, temperature increment andstress. Meanwhile the contours are analyzed, and some valuable engineeringconclusions are obtained．...