Laboratory Testing and Modeling of Creep Deformation for Sandstone Including Initial Temperature Damage

Abstract

In the exploitation of deep geothermal resources, modeling and predicting deformation of surrounding rock after initial temperature damage is of great significance for preventing instability of underground structure. Hence, in this study, a series of cyclic loading/unloading creep experiments were carried out on sandstone samples including 7 kinds of initial temperature damage. It can be seen that under same stress level, loading, creep, unloading and recovery strain all arrive at the minimum value when damaging temperature is 500 ℃. Then, based on the proportion of the accelerating creep time and macro-creep failure characteristics, a newly creep failure tendency index ${f}_{\mathrm{ci}}$ was presented and it achieves the maximum value at 500 ℃ temperature damage, then 500 ℃ is regarded as a critical temperature status in transformation of creep failure mode, i.e., from tensile failure to shear failure. To describe the total creep deformation of sample including initial temperature damage, based on the given temperature-varying loading deformation modulus, viscosity parameters and relaxation time, by introducing Caputo fractional derivative comparing to relaxation time-dependent function, a fractional viscoelastic-damage creep model considering initial temperature damage was proposed. The validation of the proposed creep model was verified by creep experimental data of sample including initial temperature damage, and the effect of damaging temperature and fractional order on total creep deformation were revealed. Finally, a prediction of creep deformation was performed using the proposed fractional viscoelastic model in infinite time-scale, it is demonstrated that when loading stress exceeds to long-term strength of sample and loading time approaches infinity, creep failure is bound to occur and failure time can be predicted accurately.

Highlights

• 1. Creep failure mechanism, mode and evaluation index of sandstone including different initial temperature damage was revealed and established based on the proportion of the accelerating creep time.

• 2. A fractional time-varying viscoelasticity damage creep model considering initial temperature damage was proposed based on the relaxation time-dependent function.

• 3. Creep failure time and deformation of rock material can be predicted by the proposed viscoelastic creep model under infinite loading time, which is based on mechanical parameters of creep failure stage.