This paper proposes a new formulation of governing equation of three phase medium, consisting of solid skeleton, gas, and water through a generalized fluid vector and validation with leaking test. The proposed generalized fluid vector consists of generalized degrees of freedom in pore pressures; one for gas, other for water, in case of two degrees of freedom. This fluid vector can be further generalized to take into account the multiple degrees of freedom of pore pressures, such as mixtures of oil, water, air, natural gasses, etc. The use of the generalized fluid vector allows the apparently a simpler formulation of the governing equations dealing with three or larger number of phases of materials. The simpler formulation in mathematical terms reduces to and coincides with that of two phase medium and thus has significant advantages when the complexities in pore filling materials are increased. Example analysis of this formation for validation is performed based on a 1D leaking test of a partially saturated soil column. In overall, the computed results are consistent with those of the previous bench marking test and numerical study, and thus confirm the applicability of the proposed formulation of partially saturated soil.
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