Abstract: The uniaxial experiments of western cemented slime sandstone were conducted.Based on the stress-strain variation at pressure consolidation and the damage stage in the constitutive curve，the volumetric strain in the pressure consolidation stage and the acoustic emission in the loading process were considered as the parameters to describe the pressure consolidation and damage characteristic.The Logistic function and exponential function were used to fit the curve of volumetric strain and accumulative acoustic emission respectively to obtain the pressure consolidation and damage function.Take a consideration of the elastic deformation characteristic of the sample，the Logistic and exponential function were combined in a liner to make regression analysis on the stress-strain curve obtained by the uniaxial compression tests of loading control and displacement control (including the before-peak and the whole process).Then，the well-fitting constitutive equation of sandstone under uniaxial compression was established and the meaning of parameters in the pressure consolidation function and damage function were analyzed.

Key words: Uniaxial compression, Acoustic emission, Pressure consolidation, Damage, Constitutive function