Abstract
A new mathematical model of poro-thermoelasticity has been constructed in the context of a new consideration of heat conduction with fractional order. One-dimensional application for a poroelastic half-space saturated with fluid is considered. The surface of the half-space is assumed to be traction-free, permeable, and subjected to heating. The Laplace transform technique is used to solve the problem. The inversion of the Laplace transform will be obtained numerically and the numerical values of the temperature, stresses, strains, and displacements will be illustrated graphically for the solid and the liquid.
Highlights
A new mathematical model of poro-thermoelasticity has been constructed in the context of a new consideration of heat conduction with fractional order
The concept of a poroelastic material was introduced by Biot (1955) in order to describe the mechanical behavior of water-saturated soil
The field of poro-thermoelasticity has a wide range of applications especially in studying the effect of using waste materials on disintegration of asphalt concrete mixture (ACM)
Summary
The concept of a poroelastic material was introduced by Biot (1955) in order to describe the mechanical behavior of water-saturated soil. The field of poro-thermoelasticity has a wide range of applications especially in studying the effect of using waste materials on disintegration of asphalt concrete mixture (ACM). Coupled thermal and poromechanical processes play an important role in a number of problems of interest in geomechanics such as stability of boreholes and hydraulic fracturing in geothermal reservoirs or high temperature petroleum-bearing formations This is due to that fact that when rocks are heated/cooled, the bulk solid as well as the pore fluid tends to undergo expansion/contraction. There is strong scientific and industrial interest in developing new mechanical models of liquid saturated rocks such as poro-viscoelasticity with damage mechanics that can include the effects of fluid phase pressurization and transport Porous materials make their appearance in a wide variety of settings, natural, and artificial, and in diverse technological applications. The inversion of the Laplace transform will be obtained numerically and the numerical values of the temperature, displacement, and stress will be illustrated graphically
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