Rock Mechanics and Rock Engineering

, Volume 52, Issue 3, pp 673–689 | Cite as

Deformation and Damage Failure Behavior of Mudstone Specimens Under Single-Stage and Multi-stage Triaxial Compression

  • Sheng-Qi YangEmail author
  • Wen-Ling Tian
  • Hong-Wen Jing
  • Yan-Hua Huang
  • Xu-Xu Yang
  • Bo Meng
Original Paper


In tunnel engineering, due to the effect of excavation disturbance, the surrounding rock mass can produce an excavation damage zone with different damage extents. Therefore, knowledge of rock deformation and damage behavior is especially significant for the design of deep tunnel support. However to date, a few experiments and numerical simulations have been conducted to investigate the deformation and mechanical failure behavior of damaged rocks. Therefore, in this research, multi-stage triaxial compression test was used to investigate the mechanical behavior of mudstone specimens with different damage extents by experiment and two-dimensional particle flow code. First, a group of micro-parameters was calibrated by single-stage triaxial compression experiments of mudstone, and the numerical results agree very well with the experimental results. Then, multi-stage triaxial compression experiment and discrete element modeling of mudstone specimens were carried out. The more axial strain the specimens sustained, the less strength they had (because the degree of damage increased). A damage variable was defined by the ratio of the area of micro-cracks to the total area of the specimen. As the post-stress reducing ratio increases, the damage variable increases rapidly until the post-stress reducing ratio reaches 0.4; then, it remains constant. The force field were analyzed to reveal the damage evolution mechanism in the mudstone specimens under multi-stage triaxial compression.


Mudstone Multi-stage triaxial compression Strength reduction PFC2D Damage evolution 

List of Symbols


Excavation damage zone


Scanning electronic microscopy


Uniaxial compressive strength


Acoustic emission


Computer tomography


Particle flow code


X-ray diffraction








Micro-crack area


Total area


Young’s modulus of the particle

\({\bar {E}_{\text{c}}}\)

Young’s modulus of the parallel bond


Ratio of normal-to-shear stiffness of the particle

\({\bar {k}_{\text{n}}}{\text{/}}{\bar {k}_{\text{s}}}\)

Ratio of normal-to-shear stiffness of the parallel bond


Confining pressure


Axial deviatoric stress


Maximum principal stress


Ratio of the difference between σdP and σdU


The peak strength obtained by the axial deviatoric stress–strain curves


The deviatoric stress unloading at the point


Axial strain


Radial strain


Maximum supporting capacity


Internal friction angle

\({D_\lambda }\)

Damage variable


Particle friction coefficient


Parallel-bond normal strength


Parallel-bond shear strength



This research was supported by the National Natural Science Foundation of China (51734009) and the Fundamental Research Funds for the Central Universities (2015XKZD05). We also would like to express our sincere gratitude to the editor and three anonymous reviewers for their valuable comments, which have greatly improved this paper.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil EngineeringChina University of Mining and TechnologyXuzhouChina
  2. 2.Shandong Provincial Key Laboratory of Civil Engineering Disaster Prevention and MitigationShandong University of Science and TechnologyQingdaoChina

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