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Time-Dependent Propagation of 3-D Cracks in Rocks Under Hydromechanical Coupling

  • Jie Mei
  • Lei YangEmail author
  • Xiangchao Sheng
  • Guangxiao Song
  • Weimin Yang
  • Bo Zhang
Original Paper
  • 128 Downloads

Abstract

Crack propagation and rock failure under hydromechanical coupling have typical time-dependent characteristics, and the subcritical crack propagation is one of the most important causes of rock instability. Rheological tests based on mortar specimens containing single internal 3-D cracks and the corresponding numerical simulations are carried out to investigate the time-dependent characteristics of the crack propagation, the failure mode of rocks, and the effects of water pressure and crack dip angle. The mortar specimen exhibits a tensile-shear failure mode under the hydromechanical coupling as observed in rheological tests, and a macro-fracture penetrates the upper and lower ends of the specimen. The propagation rate of the crack decreases first and then increases. The crack propagation can be divided into three stages according to the relationship between the propagation rate and fracture parameters. The water pressure significantly reduces the time required for rock failure due to its promoting effect on the crack propagation rate, which has negative effects on the long-term stability of rocks. Cracks with a dip angle of 45° are more likely to cause rock failure under hydromechanical coupling, while cracks with larger dip angles exhibit a better long-term stability.

Keywords

Hydromechanical coupling Subcritical crack Stress intensity factor Water pressure Dip angle 

List of Symbols

a

Half-length of crack long-axis

b

Half-length of crack short-axis

liA

Crack initial length

lcB

Crack critical length

n

Stress corrosion index

pw

Water pressure

v

Crack propagation rate of the crack front

vi

Propagation rate of the point i

vm

Propagation rate of the point corresponding to the median propagation length

A, A′

Endpoints of crack long-axis

B, B′

Endpoints of crack short-axis

C

Crack propagation constant

D

Diameter of the specimen

ERR

Energy release rate

H

Height of the specimen

Kc

Mixed-mode fracture toughness

Ke

Equivalent stress intensity factor

KI, II, III

Stress intensity factor for Mode I, II, and III fracture

KI,II,IIIr

The components of the tensile, slip, and tear stresses related to the resolved Mode I, II, and III stress intensity factors

Kth

Threshold value for subcritical propagation

M, N

Measuring points along the wing crack front

SIF

Stress intensity factor

T

Crack propagation time

α

Crack dip angle

β

Crack deflection angle

β

Crack kink angle

γI, II, III

Weight coefficients corresponding to Mode I, II, and III stress intensity factors

ηI, II, III

Weight coefficients corresponding to the components of tensile, slip, and tear stresses

θ

Position angle of the crack front

σi

Crack initiation stress

li

Crack propagation length at point i

lm

The specified median propagation length

t

Time required for each crack propagation step

Notes

Acknowledgements

This research work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51509146, 51879148 and 51879151).

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Jie Mei
    • 1
  • Lei Yang
    • 1
    Email author
  • Xiangchao Sheng
    • 1
  • Guangxiao Song
    • 1
  • Weimin Yang
    • 1
  • Bo Zhang
    • 2
  1. 1.Geotechnical and Structural Engineering Research Center, Shandong UniversityJinanChina
  2. 2.School of Civil EngineeringShandong UniversityJinanChina

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