An Analytical Model for Water Inflow into a Karst Tunnel in Vuggy and Fractured Porous Rock Aquifers
Publication: International Journal of Geomechanics
Volume 22, Issue 12
Abstract
Vugs and fractures are the main channels within porous rock aquifers and play a dominant role in the water inrush of the karst tunnel. In this paper, a mathematical model of the coupled free-fluid seepage-fluid with second-order accuracy was established to analyze the flow field characteristics of vuggy and fractured porous rock aquifers. The Navier–Stokes equation was used to govern the free fluid flow in vugs and fractures, while the Darcy–Brinkman equation was employed to describe the seepage fluid motion in the porous rock matrix. The analytical solutions for the flow velocity and water discharge were derived under the requirement of continuous velocity and shear stress at the interface between free and seepage fluids. These solutions can be successfully reduced to those of the classical Poiseuille’s law, assuming that the rock matrix is impervious to water. The numerical, experimental, and analytical results were compared to validate the present analytical model, and the results of the analytical model showed greater accuracy compared with the classical Poiseuille’s law and cubic law. Furthermore, the water inrush of the Xiangpingshan karst tunnel was selected as a real engineering case. Perforated bricks were used to stack a vuggy and fractured porous physical tunnel model (1:100) with the same hydraulic conductivity as the Xiangpingshan tunnel. The relative errors between current theoretical and physical tests obtained for the water inflow discharges are within 18%. The current model can provide a reference for predicting the water inflow of karst tunnels in vuggy and fractured porous rock aquifers.
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Acknowledgments
The authors wish to thank the National Nature Science Foundation of China (Grant No. 42107172), the Key Research Project of Sichuan Province (Grant Nos. 2022YFN0023 and 2021YFN0126), the Fundamental Research Funds for the Sichuan University (Grant No. 2021SCU12035), and the Geological Investigation Program of China Geological Survey (Grant No. DD20211379-01) for financial support.
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Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 22 • Issue 12 • December 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Feb 18, 2022
Accepted: May 14, 2022
Published online: Sep 23, 2022
Published in print: Dec 1, 2022
Discussion open until: Feb 23, 2023
ASCE Technical Topics:
- Continuum mechanics
- Engineering fundamentals
- Engineering mechanics
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid flow
- Fluid mechanics
- Fracture mechanics
- Geohazards
- Geology
- Geotechnical engineering
- Hydraulic fracturing
- Hydrologic engineering
- Inflow
- Karst
- Model accuracy
- Models (by type)
- River engineering
- Rivers and streams
- Rocks
- Solid mechanics
- Tunnels
- Water and water resources
- Water management
- Water supply
- Water supply systems
- Water tunnels
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