Abstract
Determination of the physical properties of shale is receiving more attention as the numbers of shale gas exploration projects are initiated, and as hydraulic fracturing becomes an integral exploitation method. In particular, anisotropy caused by the bedding structure of shale needs specific attention. In this paper, an anisotropic mineral brittleness-based model (AMBBM) is proposed that makes use of the discrete element method (DEM) to study shale properties, such as anisotropy of non-penetrating bedding planes and separating brittle and non-brittle minerals. Micro-parameters of the AMBBM are calibrated using uniaxial compressive strength tests and by studying the parameter gradient of smooth joints (SJ), such that the strength of SJ mainly affects the failure load in Brazilian tests (FLBT). It is found that the ratio of cohesion to tensile strength of SJ mainly affects the number of cracks formed, which further leads to different failure modes. Normal stiffness and shear stiffness of SJ exerts different effects on FLBT and stiffness in the model. However, the percentage of cracks of various minerals is less affected. The degree of anisotropy is affected by the angle range of parallel bond replaced by bedding plane. Based on the results, a new validation method for AMBBM is proposed, given that the numerical results show good agreement with experimental results, such as FLBT, splitting modulus, and failure mode. The model can thus be used to study seepage properties of shale gas exploitation and hydraulic fracturing by DEM.
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Abbreviations
- P, σ t :
-
Vertical ultimate loading and failure load in Brazilian test (FLBT)
- D, t :
-
Diameter and thickness of specimen
- θ :
-
Anisotropic angle
- E :
-
Elasticity modulus for transverse isotropy in a plane
- E′:
-
Elasticity modulus for plane perpendicular to isotropy
- G′:
-
Shear modulus for plane perpendicular to isotropy
- ν :
-
Poisson’s ratio for transverse isotropy in a plane
- ν′:
-
Poisson’s ratio for plane perpendicular to isotropy
- AR:
-
Anisotropy ratio
- σ i :
-
FLBT under θ = i (i = 0°–90°)
- C n , n :
-
Categories of contact type and mineral components
- σ n , τ :
-
Normal and shear stress of PB
- E n , E shear :
-
Normal and shear stiffness of PB
- u n , u shear :
-
Normal and shear displacement of PB
- σ max, τ max :
-
Uniaxial compressive strength (UCS) and shear strength of PB
- c, ϕ :
-
Cohesive strength and friction angle of PB
- σ T r , c r , ϕ r :
-
Residual tensile strength, cohesive strength, and friction angle of PB
- Δu s :
-
Incremental shear displacement of PB
- A, R :
-
The area and radius of the SJ particle
- \(\bar{\lambda }\) :
-
Radius multiplier (usually be chosen as 1.0)
- \({\mathbf{F}}\), F n :
-
Force vectors and normal force of SJ
- \({\hat{\mathbf{n}}}_{j}\) :
-
Normal unit force of SJ
- \({\mathbf{F}}_{{\mathbf{s}}}\), \({\mathbf{U}}\) :
-
Shear force vectors and displacement vectors of SJ
- U n , \({\mathbf{U}}_{{\mathbf{s}}}\) :
-
Normal relative displacement and shear relative displacement vectors of SJ
- \(F_{s}^{*}\) :
-
Greatest possible magnitude of shear force
- μ j , φ s :
-
Coefficient of friction and friction angle of SJ
- \({\mathbf{F}}_{{\mathbf{s}}}^{{\prime }}\) :
-
An updated value of shear force
- \(sj\_{k}_{n}\), \(sj\_{k}_{s}\) :
-
Normal and shear stiffness of SJ
- Δ :
-
An increment in updated value of SJ
- φ j :
-
Angle of dilation
- \(\bar{\sigma }_{s}\), τ s , \(\bar{c}_{s}\) :
-
Tensile, shear, and cohesion strength of SJ
- f i :
-
Mineral composition coefficient
- \(\bar{\sigma }_{\text{ave}}\), \(\bar{c}_{\text{ave}}\) :
-
Average tensile strength and cohesion of MBBM
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Acknowledgements
Financial support for this work was provided by the Fundamental Research Funds for the Central Universities (Grant No: 2015XKZD04), a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). The financial support provided by China Scholarship Council (CSC, Grant No: 201606420013) was also gratefully acknowledged.
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Chong, Z., Li, X., Hou, P. et al. Numerical Investigation of Bedding Plane Parameters of Transversely Isotropic Shale. Rock Mech Rock Eng 50, 1183–1204 (2017). https://doi.org/10.1007/s00603-016-1159-x
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DOI: https://doi.org/10.1007/s00603-016-1159-x