Experimental investigation of the long-term creep behavior of extremely soft coal rocks and novel nonlinear creep mathematical model with a nonstationary viscous coefficient

Severe rheological failure of extremely soft rocks poses a significant threat to the safety and long-term stability of roadways. Herein, four long-term triaxial creep tests were conducted under low confinements and deviatoric stresses. The results show that greater deviatoric stress leads to more obvious creep deformation, while the confining pressure can delay the occurrence of accelerated creep and restrain the creep rate and lateral deformation. The total axial strain reached 4.03% under 0.6-MPa confinement, and the creep strain of the extremely soft coal rock was much larger than that of hard rocks. Additionally, two important features distinguish extremely soft coal rocks from common rocks, namely, the creep rate did not converge in the steady-state creep stage under each applied stress level and a “gradual” squeezing deformation instability occurred in the accelerated creep stage. Furthermore, the steady-state creep rate increased exponentially with an increase in deviatoric stress and decreased following a power function with confining pressure. Then, a modified Burgers model with a nonstationary viscous coefficient was proposed to reflect the dual and nonlinear influence of confining pressure on steady-state creep rate. Moreover, several principles and suggestions for the long-term stability control of extremely soft rock roadway are discussed. Finally, a novel nonlinear creep constitutive model was established by connecting a nonlinear viscoplastic element considering both creep time and applied stress with the modified Burgers model in series. The findings are essential for creep behavior prediction and stability control in extremely soft rock engineering.