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Terzaghi's and Biot's Poromechanics in Terms of Quaternions
The presence of a moving fluid in porous media modifies their mechanical response. In particular, the deformation of rocks originate from lithostatic compression, pore-fluid pressure and thermal stresses. This paper introduces an original application of the hypercomplex numbers known as Quaternions to model non-isothermal processes in porous rocks. The general thermoporoelastic linear theory is introduced in four dimensions and reformulated as a set of quaternions. The need of the fourth dimension appears naturally because of the pores' presence. It is shown that a minimum set of four independent experimental coefficients are necessary for the coupling of four strain tensors: two for the bulk porous medium, one for the fluid, and one for the total thermal expansion. Once a basic set of parameters are defined, any other coefficient can be deduced algebraically. This formulation could become a new mathematical tool to represent thermoporoelastic phenomena because includes both, the fluid pressure changes and the temperature changes.
Terzaghi's and Biot's Poromechanics in Terms of Quaternions
The presence of a moving fluid in porous media modifies their mechanical response. In particular, the deformation of rocks originate from lithostatic compression, pore-fluid pressure and thermal stresses. This paper introduces an original application of the hypercomplex numbers known as Quaternions to model non-isothermal processes in porous rocks. The general thermoporoelastic linear theory is introduced in four dimensions and reformulated as a set of quaternions. The need of the fourth dimension appears naturally because of the pores' presence. It is shown that a minimum set of four independent experimental coefficients are necessary for the coupling of four strain tensors: two for the bulk porous medium, one for the fluid, and one for the total thermal expansion. Once a basic set of parameters are defined, any other coefficient can be deduced algebraically. This formulation could become a new mathematical tool to represent thermoporoelastic phenomena because includes both, the fluid pressure changes and the temperature changes.
Terzaghi's and Biot's Poromechanics in Terms of Quaternions
Suárez-Arriaga, M. C. (author)
Fifth Biot Conference on Poromechanics ; 2013 ; Vienna, Austria
Poromechanics V ; 1488-1497
2013-06-18
Conference paper
Electronic Resource
English
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