Golden Ratio in the Green’s Functions of Poromechanics and Thermomechanics

Abstract

This paper presents the analytical transient responses of a point fluid sink or a point heat source in the strata. Green’s functions of the elastic displacements and excess pore fluid pressure or temperature increment of strata are derived by using Laplace–Hankel integral transforms. The strata are modelled as a poroelastic or thermoelastic half space in the mathematical modelling. Poroelasticity and thermoelasticity are applied on the formulation of basic governing equations and analogy is drawn between poroelasticity and thermoelasticity. Attention is focused on the golden ratio which appears in the magnitude of maximum ground surface horizontal displacement and corresponding vertical displacement of the half space Green’s functions. The analytical study concludes that golden ratio exists in these phenomena, and the horizontal displacement should be properly considered in the prediction of displacements induced by groundwater withdrawal or buried heat source.