Issue 53

Y.D. Shou et alii, Frattura ed Integrità Strutturale, 53 (2020) 434-445; DOI: 10.3221/IGF-ESIS.53.34 440 C OMPARISON OF ELASTOPLASTIC DAMAGE COUPLED MODEL OF COAL AND ROCK WITH EXPERIMENTAL RESULTS Determination of damage evolution characteristics of coal and rock he elastoplastic coupling model is established in section 3.2. According to Eqn. (4), the elastic stiffness matrix of isotropic damaged materials is expressed by shear modulus and bulk modulus. Moreover, the elastic modulus and Poisson's ratio vary with the damage variable d . Based on Eqn. (4), the effect of damage on elastic mechanical properties can be determined accurately. For the moderate damage condition, the degradation of elastic mechanical properties [26-28] can be expressed as ( ) ( ) 0 1 k d k d  = − ， ( ) ( ) 0 1 d d    = − (9) where 0 k and 0  are respectively the bulk modulus and shear modulus of undamaged materials,  and  are the two parameters of coal-rock to present the effect of damage on the elastic mechanical properties of coal-rock. According to the damage criterion, the thermal forces related to the damage variable d Y can be linearized as 0 d d Y Y md = + (10) where 0 d Y is the initial energy release threshold, m is a parameter to control the damage evolution rate. Determination of expression of plastic properties of coal and rock The yield equation of coal and rock includes some main characteristics, such as pressure sensitivity, unconnected plastic flow, asymmetric response under pressure and tension loading, plastic hardening and so on. The three-dimensional nonlinear strength criterion proposed by Zhou et al. [29] is introduced to determine yield surface of coal-rock, which is expressed as follows: 2 1 3 2 3 ( ) - - ( ) p c c F n m        = + + (11) where n and m are the strength parameters, c  denotes uniaxial compressive strength of rocks, 1 2 3 , ,    are the major, intermediate and minor principal stresses, respectively. When the damage variable is considered, the nonlinear strength criterion Eqn. (11) is rewritten in another form ( ) ( ) 2 1 2 ( , , ) 2 3 cos 3 1 3 cos 3 2 sin 0 3 p p c c F d J trd I m n J m m n           =       − − + + − + − =           (12) where the stress angle is equal to 3 1 2 1 2 2 ( ) arctan 3( )          − + =   +   , 30 30 o o   −   , 1 I is the first invariant of stress, 2 J is the second invariant of deviator stress, c  is an uniaxial compressive strength of an intact rock material, m and n are strength parameters of rocks. The cumulative inverse strain can be determined as 2 : 3 p p p e e  = (13) where 1 3 p p p e tr    = − T