Double effective stress of porous media (by Li chuanliang)

At present, the concept of effective stress has undergone three periods:

1. Terzaghi's effective stress         

            σ_eff= σ-p

 2. Biot’s effective stress

              σ_eff= σ-αp

 3. Double effective stress

     In 2000, Li chuanliang, a professor of Southwest petroleum university(China), proposed the definition of double effective stress. It means that there are two effective stress in porous media, the Primary Effective Stress and the Structural Effective Stress. The definition is given as follows:

(1)   Primary effective stress     σ_eff= σ-φp ； where φ is porosity;

(2)   Structural effective stressσ_eff= σ-φ_cp ; (φ_c=1-R_c ;  where R_c is cementation level)

   He also thinks in the porous media t there are two types of deformations， the Primary Deformation and the Structural Deformation. The total strain of a porous medium is an algebraic sum of primary strains and structural strains. Primary strain is caused by the deformation inside particles of porous media，while structural strain by the relative displacements between particles. Usually，primary strain is elastic，while structural strain is viscous（including macro- and micro-damage and failure of porous media） Primary effective stress determines the primary strain， while structural effective stress determines the structural strain.But the Li chuanliang’s Double effective stress has not been wildly applied, expercially in the poroelasticity field. I don’t kown why. How do you think about the Double effective stress? Please share your attitude and let us have a talk.