Bulletin of Engineering Geology and the Environment

, Volume 78, Issue 8, pp 6249–6265 | Cite as

Stability analysis of a group of underground anhydrite caverns used for crude oil storage considering rock tensile properties

  • Bin ZhangEmail author
  • Hanxun Wang
  • Lei Wang
  • Nengxiong Xu
Original Paper


Tensile deformation and damage play an essential role in rock engineering problems. This paper presents a framework for evaluating the stability of a group of anhydrite caverns combining both experimental and numerical methods. In this study, the tensile Young’s modulus and Poisson’s ratio of anhydrite are determined based on the Brazilian disc splitting test. The tests show that the tensile Young’s modulus of anhydrite is less than the compressive Young’s modulus, with a ratio of approximately 0.58–0.91. The tensile Poisson’s ratio is greater than the compressive Poisson’s ratio, with a ratio of approximately 2.47–3.20. Based on the differences between the mechanical parameters (Young’s modulus, Poisson’s ratio) of anhydrite in the tensile and compressive states, a user-defined constitutive model is developed with the Hoek-Brown failure criterion, which describes the tensile and compressive behaviour at a laboratory scale. Finally, a large-scale three-dimensional (3D) anhydrite cavern group located in Anhui Province, China, which was formed by mining activity over the past 10 years, is used as a case study to illustrate the proposed framework. The model for the anhydrite cavern group is established in FLAC3D5.0, and the stability of the anhydrite cavern group used for underground oil storage is then analysed with this model. The simulation results indicate that after the exploitation is completed, there are few plastic zones and tensile elements in the surrounding rock near the cavern group. The maximum value of cavern roof settlement is approximately 5.54 mm. The maximum cavern bottom upheaval is approximately 6.11 mm, and the maximum ground subsidence is approximately 3.0 mm. The results indicate that the Anhui Hengtai anhydrite cavern group possesses good stability potential as an underground oil storage space.


Underground anhydrite caverns Rock tensile properties Underground oil storage Cavern stability 


σx, σy, σz, σxy, σxz, σyz

are normal stress and shear stress in respective directions in a 3D Cartesian coordinate system (MPa);

σ1, σ2, σ3

are the maximum, intermediate and minimum principal stresses, respectively (MPa);

εx, εx, εx, γxy, γxz, γyz

are normal strain and shear strain in respective directions;


is the applied load during the Brazilian disc splitting test (kN);

Gxy, Gxz, Gyz

are shear modulus in respective directions (GPa);


is the compressive Young’s modulus (GPa);


is the tensile Poisson’s ratio (GPa);


is the compressive Poisson’s ratio;


is the tensile Poisson’s ratio;


is the Young’s modulus in the x direction. When normal stress is used, Ex = Ec; otherwise, Ex = Et (GPa);


is the Young’s modulus in the y direction. When normal stress is used, Ey = Ec; otherwise, Ey = Et (GPa);


is the Young’s modulus in the z direction. When the normal stress is pressed, Ez = Ec; otherwise, Ez = Et (GPa);


is the lateral deformation in the y and z directions that is caused by the normal stress in the x direction. When the normal stress is subjected to compressive stress in the x direction, μx = μc; otherwise, μx = μt;


is the lateral deformation in the x and z directions that is caused by the normal stress in the y direction. When the normal stress is subjected to compressive stress in the y direction, μy = μc; otherwise, μy = μt;


is the lateral deformation in the x and y directions that is caused by the normal stress in the z direction. When the normal stress is subjected to compressive stress in the z direction, μz = μc; otherwise, μz = μt;

k1, k2

are the slope of the stress–strain curves in the x and y directions, respectively, in the Brazilian disc splitting test (103/m2);


is the uniaxial compressive strength (UCS; MPa);

\( {\sigma}_3^{cv} \)

is the user-prescribed level of confining stress (MPa);


is the Young’s modulus of an anhydrite rock mass (GPa);


is the tensile strength of an anhydrite rock mass (MPa);

D, mi, mb, s, a

are the Hoek-Brown failure criterion parameters;

\( \Delta {e}_1^p,\Delta {e}_3^p \)

are the plastic strain increment in two directions;


is the plastic factor in the plastic flow rule;

γrf, γaf, γcv

are the plastic factors in the radial flow rule, constant-volume flow rule and composite flow rule, respectively.



This work is funded by the National Natural Science Foundation of China (Nos. 41572301, 40902086 and 61427802) and the Fundamental Research Funds for the Central Universities of China (No. 2-65-2015-071, 2-65-2018-108). Additionally, the authors would like to acknowledge the anonymous reviewers for their valuable comments and suggestions, which significantly improved the quality of this paper.


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Copyright information

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

Authors and Affiliations

  • Bin Zhang
    • 1
    • 2
    Email author
  • Hanxun Wang
    • 1
    • 2
  • Lei Wang
    • 3
  • Nengxiong Xu
    • 1
    • 2
  1. 1.School of Engineering and TechnologyChina University of Geosciences (Beijing)BeijingChina
  2. 2.Key Laboratory of Deep Geodrilling TechnologyMinistry of Land and ResourcesBeijingChina
  3. 3.School of Engineering and Applied SciencesUniversity of the District of ColumbiaWashingtonUSA

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