Rock Mechanics and Rock Engineering

, Volume 52, Issue 12, pp 4889–4905 | Cite as

Stability Analysis of Rock Structure in Large Slopes and Open-Pit Mine: Numerical and Experimental Fault Modeling

  • Babak Azarfar
  • Seyedsaeid Ahmadvand
  • Javad Sattarvand
  • Behrooz AbbasiEmail author
Original Paper


Deep open-pit mines and large rock slopes expose many diverse rock lithologies and geological structures (e.g., faults, bedding planes) that may reduce the integrity of slopes. Numerical modeling is a powerful tool for simulating these structures; however, there are few guidelines and methods for calibrating/validating and implementing faults in a numerical model. This paper presents a novel laboratory method to calibrate numerical models and highlights the challenges in simulating faults. One of the main issues in reliable modeling of faulted rock structure is the scarcity of experimental analyses in the laboratory under the controlled conditions. Moreover, a comprehensive evaluation of the effect of using the conventional fault modeling methods on the stability of rock structures is required, as well as a benchmarking between theoretical and experimental results. This research combines theory and experiment, to fill the existing gaps, using numerical simulation and laboratory measurements. Using FLAC3D software, the sensitivity and comparative analyses are carried out for the numerical simulations to investigate the stability of rock slopes on large and small scales (overall open-pit slope and bench slope), and the fault zones. The weak zone (WZ), ubiquitous-joint (UJ), and interface (IF) techniques are the widely used methods in the modeling to capture fault slip mechanisms. The factor of safety (FOS) of the slope is monitored upon variation of the design parameters, such as fault and rock mass mechanical properties, fault types, and modeling framework (e.g., mesh density, convergence ratio). In addition, parameters such as shear displacement and shear stress are investigated to deduce the failure mechanism of the studied models. Finally, laboratory tests were performed to calibrate the modeling results and approximate the agreement between theoretical and experimental results. The results of sensitivity analysis showed that choosing an adequately low convergence ratio is critical for estimating FOS. However, beyond a certain convergence ratio, below 10−7, this change is negligible (less than 5%). The results of mesh density sensitivity analysis indicate that the FOS values are insensitive to the mesh density in the WZ method (less than 5% change in FOS), the IF method shows the median sensitivity (5–12% change in FOS), and the UJ method is the most sensitive (FOS values improves by ~ 31%). Comparison between laboratory test and numerical modeling (FOSlab = 1.71, FOSWZ = 1.51, FOSIF = 1.62, and FOSUJ = 1.76) indicates a good agreement between the UJ and IF methods and the laboratory model (~ 3–5% discrepancy). It needs to be mentioned that these analyses/tests are not to favor one method over the other, but rather to emphasize the pros and cons of each within the assumptions of this study.


Slope stability Factor of safety Sensitivity analysis Fault modeling methods Numerical modeling Fault structure laboratory test 

List of Symbols

\(F_{\text{n}}^{(t + \Delta t)}\)

Normal force at each implicit time step \((t + \Delta t)\) (N)

\(F_{\text{si}}^{(t + \Delta t)}\)

Shear force at each implicit time step (t + ∆t) (N)

\(\Delta u_{\text{si}}\)

Incremental relative shear displacement (m)


Area associated with the interface element (m2)


Normal stiffness (Pa m−1)


Shear stiffness (Pa m−1)


Dilation angle (°)


Friction angle (°)


Cohesion (Pa)


Pore pressure (Pa)


Incremental shear stress vector due to interface stress initialization (Pa)


Absolute normal penetration of the interface node into the target face (m)


Angle of discontinuity (°)


Joint friction angle (°)


Joint cohesion (Pa)


Normal stress (Pa)


Shear stress (Pa)


Maximum principal stress (Pa)


Minimum principal stress (Pa)


Initial cohesion (Pa)


Initial internal friction angle (°)


Updated cohesion (Pa)


Updated internal friction angle (°)

\(\left| {F_{\text{s}} } \right|_{\text{o}}\)

Magnitude of shear force (N)


Incremental normal stress added due to interface stress initialization (Pa)


Tensile strength (Pa)



This work was funded by the University of Nevada, Reno (PG11522). Authors thank Dr. Jaak Daemen Dr. Pierre Mousset-Jones and Dr. Loren Lorig (Itasca International Company) for peer-reviewing the paper. Also, authors would like to thank journal’s editor and reviewers.


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Copyright information

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

Authors and Affiliations

  • Babak Azarfar
    • 1
  • Seyedsaeid Ahmadvand
    • 1
  • Javad Sattarvand
    • 1
  • Behrooz Abbasi
    • 1
    Email author
  1. 1.Department of Mining and Metallurgical EngineeringUniversity of Nevada, RenoRenoUSA

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