Numerical investigation on the stability of deforming fractured rocks using discrete fracture networks: a case study of underground excavation

  • Luyu Wang
  • Weizhong ChenEmail author
  • Xuyan Tan
  • Xianjun Tan
  • Jianping Yang
  • Diansen Yang
  • Xi Zhang
Original Paper


The stability of a fractured rock mass around a subsurface opening is critical to tunnel excavation. The traditional underground excavation analysis is based on a continuum description of randomly distributed discrete pre-existing fractures. In contrast to this, we have developed an improved hybrid finite element method (FEM) to investigate the stability of fractured rocks around an excavation by incorporating the outputs into the FEM codes. The proposed model consists of a discrete fracture network (DFN) model and cohesive zone model (CZM). The DFN model automatically generates a fracture network with a given fracture opening distribution and provides grid generation strategy to the FEM. The CZM captures material failure and intersection and surface contacts through the fracture element with different constitutive laws. As a case study, a DFN model was formulated for the underground excavation at Jinping Hydropower Station, in light of the input requirements of our model, and its deformation analysis was performed. The comparison analysis of rock deformation was made for excavation in both intact rock mass and fractured rock mass under the same boundary conditions. The numerical results show that two different modes of rock failure exist in these two rock masses and that intense deformation at the fractures intersected by the tunnel is responsible for fractured rock mass instability. The proposed approach was verified using data from field investigations. A larger displacement can be produced if the rock mass is weakened by a key block. A sensitivity analysis was carried out to investigate the effects of different model parameters on deformation variations. This study provides an insightful understanding of the deformation of fractured rock mass during tunnel excavation.


Fractured rocks Discrete fractures Underground excavation Stability analysis Hybrid finite element method 


Latin symbols


Fracture width


Length of a fracture


KII Stress intensity factor of pure tensile and shear mode


Elastic modulus tensor of fracture elements


Thickness of fracture elements


Damage factor of fracture elements


Stiffness for the spring in the Bandis–Barton law


Depth of the tunnel


Displacement in the horizontal direction


Displacement in the vertical direction


Center point coordinates of a fracture


Initial endpoint coordinates of a fracture


Translational endpoint coordinates of a fracture


Coordinates on the sides of a fracture domain

Greek symbols


Fracture geometric parameter


Probability density function of a fracture geometric parameter


Standard variance of a fracture geometric parameter


Expectation of a fracture geometric parameter


Horizontal stress factor


Unit weight of rock


Dip of a fracture


Traction-separation law


Dissipated energy of material failure


traction on fracture surface


separation on fracture surface

\( {\sigma}_i^0 \)

peak traction of fracture elements.

\( {\delta}_i^0 \)

Critical separation at which traction reaches its peak

\( {\delta}_i^f \)

Critical separation at which traction becomes zero


Effective displacement of fracture surface


Maximum deformation in the Bandis–Barton law



The authors gratefully acknowledge the support of the Chinese Fundamental Research (973) Program through the Grant No. 2015CB057906.


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Copyright information

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

Authors and Affiliations

  1. 1.State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics Chinese Academy of SciencesWuhanChina
  2. 2.University of Chinese Academy of ScienceBeijingChina
  3. 3.Research Center of Geotechnical and Structural EngineeringShandong UniversityJinanChina
  4. 4.CSIRO EnergyClaytonAustralia

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