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Abstract The constitutive equation is given by means of a constitutive modeling approach based on the theory of mixtures. The volume fraction of each constituent of the saturated mixtures can describe pore structure of coal and connect constituent stress with true stress. Assuming isotropic elastic behavior and that the change of the elastic energy equals the change of surface energy，gas adsorption-induced coal swelling and the volume fraction of each constituent of the saturated mixtures are derived. Consequently，the stress-strain relation under triaxial stresses is derived. By comparing the stress-strain curves of coal containing different gas components，the effect of adsorption on the constitutive relation of gas-filled coal is analyzed. Meanwhile，the theoretical values from the proposed constitutive relation are compared with the experimental results. Results from the constitutive relation agree well with experimental curves. It is shown that the constitutive equations are able to describe the difference in deformation behavior with respect to gas adsorption，which is affected by the difference in gas adsorption and that the stress-strain relation，under the same porosity and pore pressure，even when the skeleton structure of the coal satisfies the Hooke¢s linear elastic constitutive relation.
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Received: 08 May 2008
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