13.4 Numerical Simulation
459
Fig. 13.12 Equation of state
50
75
100
125
150
175
200
225
250
50
100
150
200
250
300
350
p crush =1.32×f c -6.09
R
2 =0.996
Forquin et al. (2008)
Xu et al. (2020)
Unosson et al. (2006)
Williams et al. (2009)
Fitting curve
P
crush (MPa)
Uniaxial compressive strength f c (MPa)
(a)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0
5
10
15
20
25
30
35
0.000
0.005
0.010
0.00
0.05
0.10
0.15
0.20
0.25
0.30
First phase
K= 30
( crush , P crush )
K lock = 23.5
( plock , P lock )
Marsh (1980)
Gebbeken et al. (2006)
Yan et al. (2000)
Riedel et al. (2008)
Grandy (1996a, 1996b)
Gao (2011)
Zhang et al. (2012)
Jiao et al. (2011)
Fitting curve
Pressure (GPa)
Volumetric strain
(b)
Table 13.6 Equation of state parameters
μ crush
P crush (GPa) μ plock P lock (GPa) μ lock
K 1 (GPa) K 2 (GPa) K 3 (GPa)
0.0053 0.159
0.17
5.01
0.078 69
−211
981
(3) Damage evolution parameters
To construct the relationship between the parameters η and λ, this study adopted the
piecewise equation recommended by Yin et al. (2020), which has the form as