A Novel Fatigue Damage Model of Rock considering Temperature Effects

Table 1

Comparison of damage models.

Author	Damage evolution equations	Damage variable	Initial damage
Xie et al. [24]		Elastic modulus method	0
Wang et al. [25]		Residual strain method	0
Liu et al. [26]		Energy dissipation method	0
Xiao et al. [27]		Residual strain method	D0
Xiao et al. [28]		Residual strain method	D0

D is the fatigue damage variable, D₀ is the fatigue initial damage, n is the cyclic number, is the fatigue life, and are the unloading stiffness and initial elastic modulus in the fatigue loading and unloading process of elastoplastic damaged materials, and and are the total strain and the residual plastic strain after unloading, respectively. n₀ is the hardening index, a₀, b₀, c, and m are the material constants, respectively. f is the frequency; is the amplitude of stress. B and k₀ are the mechanical constants. is an energy release per unit volume with the dimension 1 J/mm³ ; Y is the released damage strain energy during a loading-unloading cycle. is instability proportion factor, is the instability factor, and p is instability velocity factor. a₁ is the linear damage rate, b₁ is the instability proportion factor, and x₀ represents the critical instability center.