Anisotropy Characteristics of Stress Relaxation in Coal: An Improved Fractional Derivative Constitutive Model

A nonlinear fractional-order damage model of stress relaxation of net-like red soil

“…Numerous studies 16 , 59 – 62 have shown that the evolution of rheological damage can be assumed as a negative exponential function when considering only the effect of the time of load action. Therefore, a negative exponential form of the damage variable is also used here to characterize the relaxation damage.…”

“…The element rheology models (such as the generalized Kelvin model, Burgers model, and Nishihara model) with a capability to account for the elastic-viscoplastic behavior were verified by some researchers 13 – 15 . However, those conventional element models sometimes have difficulties precisely describing the nonlinear characteristics of soil stress relaxation because the parameters of the viscous element cannot change with time at all 16 . So the fractional derivative model was recently employed to construct a time-dependent constitutive model 17 – 22 , and some beneficial progress has been made.…”

“…Meanwhile, some long-term stress relaxation experiments were performed on the rock 15 , 16 , 19 , 34 , clay 35 , and sand 36 , 37 through improved laboratory equipment. Considerable attention also had been directed to effects of the loading mode 35 , the loading rate 38 – 41 , the dynamic loading 42 , the water content 43 , the axial strain level 8 , and the confining pressure 44 – 46 on the time-dependent behavior of saturated soils.…”

Loading rates dependency of strength anisotropy in coal: Based on the three‐dimensional reconstruction modeling technology

“…9,10 Thus, unraveling the influences of loading rates on the strength of coal is significant for the roadway support, 11 dynamic disaster preventing, 12 and the geo-stress measurement. 13 The loading rate has a significant effect on the mechanical responses of coal and rock and has been broadly investigated in the past few decades. [14][15][16][17][18][19][20] In general, loading/strain rates variation affects the initiation, propagation, and nucleation of micro-cracks, 21,22 interferes with the primary fracture formation, 23 and even alters the constitutive model of coal and rock.…”

“…Coal mining is a time and structural dependent engineering activity, where loading rates and strength anisotropy correlate with various failures in coal mass 9,10 . Thus, unraveling the influences of loading rates on the strength of coal is significant for the roadway support, 11 dynamic disaster preventing, 12 and the geo‐stress measurement 13 …”