Issue 45

C. Huang et alii, Frattura ed Integrità Strutturale, 45 (2018) 108-120; DOI: 10.3221/IGF-ESIS.45.09 111 1 ( ) Bt t Ae  = (4) During the loading stage, equations of the creep, the creep rate and the creep acceleration can be expressed as: 0 1 2 1 1 1 ( ) ( ) Bt t e e t AB    − − − − = + +   (5) 0 2 ( ) ( ) 0 Bt t e e t A     − − = +  (6) 2 0 2 2 ( ) ( ) 0 t Bt e Be t A      − −  = − +  (7) where  1 (t) is the viscosity of external viscous component of modified model; A and B are the viscosity parameters of viscous elastic element 4, as shown in Fig.3. From Eqn. (4) and (5), it can be found that with the loading time increasing, the viscosity of element 4 increases and the permanent strain decreases. When the loading time tends to infinity, the strain increment tends to zero. The equations can be used to characterizes the consolidation effect of FRAC [4], which is similar to the deformation characteristics of stable creep stage. However, Eqn. (4) and Eqn. (5) still cannot describe the deformation characteristics of the accelerated creep stage of FRAC. From Eqn. (6) and Eqn. (7), the demarcation point of stable creep and accelerated creep do not present in the curve of creep deformation and time of FRAC, so the model cannot be used to describe the rheological time characteristics of viscoelastic material. Figure 3 : Modified Burgers model. Figure 4 : Five units and eight parameters model In order to effectively describe the deformation feature of the whole creep process of FRAC and construct the rheological time parameters of viscoelastic material, a viscoelastic model with five units and eight parameters by adding a viscous component 5 is adopted based on Burgers model, as shown in Fig. 4. In this model, the viscosity of element 5 increases with time firstly and then decreases, that is: 0 3 2 ( ) t at bt c   = − + (8) where,  0 is the initial viscosity of element 5; α, b and c are the viscosity parameters of element 5, moreover, α > 0, b > 0, c > 0, and. b 2 -4  c  0 The creep equation of the model with five units and eight parameters can be expressed as For the loading stage,