Abstract
To analyze the strain-based non-Darcy permeability properties in crushed rock accompanying mass loss, a self-designed seepage testing system for crushed rock accompanying mass loss is adopted. Based on the collected lost mass and time series of seepage velocity and the pressure gradient, permeability parameters and strain are obtained. Time-dependent characteristics of permeability parameters and strain are divided into three stages. Permeability and strain increase while non-Darcy flow β factor and acceleration coefficient decrease with seepage process lasting. Exponential functions between permeability parameters and strain are established, where strain is the volumetric strain, being in good agreement with conclusions drawn by scholars before. The coefficients of exponential functions are analyzed combining with the lost mass ratio. It shows that a greater mass loss leads to a larger permeability, inducing the greater possibility of water inrush; samples with the lost mass ratio less than 5% have the least water inrush possibility.
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Abbreviations
- a i :
-
The local derivative of seepage velocity when ti = iτ, LT−2
- c a :
-
The acceleration coefficient, -
- c a0 :
-
The initial value of acceleration coefficient, -
- c a i :
-
The predictive value of acceleration coefficient, -
- c ar :
-
The reference value of acceleration coefficient, -
- Ck, Cβ, \( {C}_{c_a} \) :
-
The coefficients of the fitting relationships, -
- d :
-
The inner diameter of the cylinder of permeameter, L
- d i :
-
The diameter of the current mudstone grains, L
- d M :
-
The maximum diameter of mudstone grains, L
- Dk, Dβ, \( {D}_{c_a} \) :
-
The coefficients of the fitting relationships, -
- \( {G}_p^i \) :
-
The pressure gradient of the fluid, L−2MT−2
- H 0 :
-
The initial height of the sample, L
- H c :
-
The current height of the sample, L
- j :
-
The times of collecting the lost mass, -
- k :
-
Permeability, L2
- k 0 :
-
The initial value of permeability, L2
- k i :
-
The predictive value of permeability, L2
- k r :
-
The reference value of permeability, L2
- m li :
-
The lost mass collected every other time, M
- mβ, \( {m}_{c_a} \) :
-
The reference values of power exponents, -
- M :
-
The mass of the sample, M
- M d :
-
The mass of the grains with a diameter less than di, M
- M T :
-
The total mass of all the grains, M
- n :
-
The Talbot power exponent (TPE), -
- nk, nβ, \( {n}_{c_a} \) :
-
The reference values of power exponents corresponding to the porosity reference value, -
- p :
-
Permeate pressure, L−1MT−2
- p(di):
-
The percentage with a diameter less than di, -
- r l :
-
The lost mass ratio, -
- v :
-
Seepage velocity, LT−1
- v i :
-
The seepage velocity when ti = iτ, LT−1
- V :
-
The volume of the sample without initial compression, L3
- V 0 :
-
The volume of the tight sample with the same mass, L3
- V c :
-
The current volume of the sample, L3
- x :
-
The plumb direction coordinate of the sample, -
- β :
-
The non-Darcy flow β factor, L−1
- β 0 :
-
The initial value of non-Darcy flow β factor, L−1
- β i :
-
The predictive value of non-Darcy flow β factor, L−1
- β r :
-
The reference value of non-Darcy flow β factor, L−1
- ΔH :
-
The loading displacement of the sample, L
- ε 1 :
-
The first principal strain, -
- ε 2 :
-
The second principal strain, -
- ε 3 :
-
The third principal strain, -
- ε ci :
-
The current strain of the sample, -
- ε V :
-
The volumetric strain, -
- μ :
-
Kinematic viscosity of the seepage fluid, L−2MT
- ρ :
-
The density of the fluid, L−3M
- ρ p :
-
The density of the sample, L−3M
- ρg ∇ z :
-
The volume force, L−2MT−2
- \( {\sum}_{i=1}^j{m}_{li} \) :
-
The total lost mass, M
- ϕ 0 :
-
The original porosity of the sample, -
- ϕ c :
-
The sample’s current porosity, -
- ϕ ci :
-
The porosity of the sample, -
- ϕ r :
-
The reference value of porosity, -
- \( \frac{\partial p}{\partial x} \) :
-
The pressure gradient of the fluid, L−2MT−2
- ∇z :
-
The unit vector in the direction of gravity action, -
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Acknowledgments
The authors thank the authors of all the references, and also thank the reviewers and editors for their careful reading of this paper and valuable suggestions.
Funding
This work is supported by the National Natural Science Fund of China (11502229), the Natural Science Foundation of Jiangsu Province of China (BK20160433), the Opening Fund of Key Laboratory of Safety and High-efficiency Coal Mining, Ministry of Education (Anhui University of Science and Technology) (JYBSYS2019207), the Program of Outstanding Young Scholars in Yancheng Institute of Technology(2014), the Program of Yellow Sea Elite in Yancheng Institute of Technology (2019), and the Program of Yellow Sea Team in Yancheng Institute of Technology (2019).
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Responsible Editor: Zeynal Abiddin Erguler
Luzhen Wang and Hailing Kong are co-first authors.
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Wang, L., Kong, H., Yin, Y. et al. Strain-based non-Darcy permeability properties in crushed rock accompanying mass loss. Arab J Geosci 13, 406 (2020). https://doi.org/10.1007/s12517-020-05387-7
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DOI: https://doi.org/10.1007/s12517-020-05387-7