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Rock Mechanics and Rock Engineering
https://doi.org/10.1007/s00603-018-1523-0
ORIGINAL PAPER
Mechanical Behavior and Damage Constitutive Model of Granite
Under Coupling of Temperature and Dynamic Loading
Z. L. Wang
1
· H. Shi
1
· J. G. Wang
2
Received: 8 September 2017 / Accepted: 28 May 2018
© Springer-Verlag GmbH Austria, part of Springer Nature 2018
Abstract
Dynamic compression tests of Huashan granite were conducted using an improved split–Hopkinson pressure bar. The effects
of the treatment temperature and strain rate on the mechanical behaviors (for example, the stress–strain curve, dynamic
strength, elastic modulus, energy absorption, and failure mode) of the granite samples were explored. In addition, a statisti-
cal damage constitutive model for the rock was developed based on a Weibull distribution, and the influencing factors of
the model parameters were analyzed. The results show that the enhancement effect of the strain rate on dynamic compres-
sive strength under high temperatures still exists. However, the strain rate has no significant effect on the elastic modulus.
The influences of the treatment temperature on the dynamic strength and elastic modulus are complex. There is a positive
linear correlation between the energy absorbed by the sample and the incident energy. As the strain rate or incident energy
increases, the failure modes of heat-treated samples change from axial splitting to pulverization. Under the same dynamic
loading, an increase in the temperature can exacerbate the fragmentation degree of the sample. The proposed statistical dam-
age constitutive model can accurately describe the effects of the treatment temperature and strain rate on the stress–strain
responses of rock, and its parameters have definite physical meanings. Thus, the model is a very good tool for the analysis
of thermo-mechanical coupling problems involved in deep rock mass engineering.
Keywords Granite · Temperature · Strain rate · Coupling · Mechanical behavior · Damage constitutive model
List of Symbols
ε Strain
̇
Strain rate
ε
0
Scale parameter
𝜀
i
Strain signal of incident wave
𝜀
r
Strain signal of reflected wave
𝜀
t
Strain signal of transmitted wave
η(T) Viscous coefficient at temperature T
σ Stress
σ
*
Effective stress
τ Completely destroyed moment of sample
A Cross-sectional area of pressure bar
c Wave velocity of pressure bar
D
I
Heat-induced damage
D
s
Load-induced damage
DIF Dynamic increase factor
E Elastic modulus of sample
E
0
Elastic modulus of undamaged sample
E
I
Elastic modulus of sample after heat treatment
E
b
Elastic modulus of pressure bar
E
V
Energy absorbed per unit volume of sample
f
s
Static compressive strength
f
d
Dynamic compressive strength
F Strength of microunit
F
0
Mean strength of microunit
m Shape parameter
n Number of failed microunits
N Number of total microunits
P(F) Probability density function of Weibull
distribution
R
2
Coefficient of determination
T Treatment temperature
V
s
Volume of sample
W
I
Incident energy
In Incident wave
Re Reflected wave
* Z. L. Wang
cvewzL@hfut.edu.cn
1
School of Civil and Hydraulic Engineering, Hefei University
of Technology, Hefei 230009, Anhui, China
2
School of Mechanics and Civil Engineering, China
University of Mining and Technology, Xuzhou 221116,
Jiangsu, China
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