Multi-phase problem has drown more attention recently because of its wide involvement in geotechnical engineering problems, not only in instant failure problem like slope failure, but also in long-term stability problem like deep geological repository of high-level radioactive waste. Numerous researches, both in laboratory/field tests and numerical simulation/prediction, have been conducted in this field ceaselessly. Yet it is still far away from the state with which we can satisfy. The key problem is that, in most cases, people have to simplify a real geotechnical problem with some assumptions and to pick up one or several factors he thinks the most important and takes them as his concern while other factors are neglected. For instant, constitutive model is always divided into two parts, one for saturated material and another is for unsaturated. Thermal and viscoplastic effects are the other questions needed to be improved. What should be emphasize here is that, the physical states, such as the saturation (Sr) or the temperature (T) are only the states of a geomaterial, people cannot say that a geomaterial will be a different material when the states are different. Unfortunately, in most cases, a constitutive model usually only considers the geomaterial in a specific state, in other words, it can describe the mechanical behavior of the geomaterial in the specific state but cannot fit anymore at other states.

The aim of this paper is to establish a unified numerical method to treat the multi-phase problems related to the thermo-hydraulic-mechanical-air (THMA) behaviors of geomaterials. For this purpose, a thermo-elastoplastic constitutive model for unsaturated/saturated geomaterial is newly proposed to fulfill the demand. Meanwhile, the moisture characteristic curve (MCC) in the infinitesimal frame proposed by Zhang and Ikariya (2011) is extended to finite deformation scheme based on the intrinsic relationship between the state variable (void ratio e) and the hydraulic state variables (saturation Sr and gravimetric water content w).

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