Rock Mechanics and Rock Engineering

, Volume 52, Issue 2, pp 351–372 | Cite as

Lugeon Tests at Partial Saturation: Experimental and Empirical Contributions

  • Brendon R. Jones
  • J. Louis Van Rooy
  • Matthys A. DippenaarEmail author
Original Paper


Implications of improved understanding of variably saturated flow are numerous, especially given the complexity, heterogeneity, and anisotropy of the intermediate fractured vadose zone. One such an implication is the quantification of water movement for engineering purposes, as flow-through unsaturated discontinuities cannot be quantified through commonly applied saturated approaches. This paper presents an experimental study using geotechnical centrifuge modelling to investigate flow behaviour during Lugeon tests, through the fundamental concept of a smooth, clean, open fracture, at partial saturation. The study comprised flow visualisation experiments conducted on transparent replicas of horizontal and inclined fractures, with water injected under a consecutive series of ascending and descending pressures. Findings from the research proved that preferential flow occupied the minority of cross-sectional area despite the hydraulic pressure. Furthermore, the observed behaviour of these preferential pathways indicated non-linear flow. Deviation from linearity occurred at small fluxes and is likely as a result of inertial effects due to fluid bending at the inlet source into the fracture. To assess these non-linear results, the Forchheimer relationship was used to predict the flow rate at the imposed hydraulic heads. As the width of the fracture could not be used as input into the equation, due to the lack of saturation across its width, the width of the flow path was used instead. This resulted in the predicted results comparing well with the measured flow rates, and indicates that the Forchheimer relationship can potentially be used to describe unsaturated flow in discrete, open fractures.


Forchheimer equation Reynolds number Water pressure test Geotechnical centrifuge Flow mechanism Unsaturated Packer 

List of Symbols


Volumetric flow rate (L3/T)


Pressure gradient (M/L/T2)


Fracture width (L)


Linear Forchheimer coefficient (M/L5/T)


Non-linear Forchheimer coefficient (M/L8)


Hydraulic aperture of idealised parallel smooth fracture (L)


Dynamic viscosity of fluid (M/L/T)


Intrinsic permeability defined as e2/12 (L2)


Fluid density (M/L3)


Cross-sectional area (equal to ew) (L2)


Non-Darcy flow coefficient or Forchheimer coefficient (/L)


Reynolds number (–)


Bulk velocity (L/T)


Forchheimer number (–)


Lugeon number (L2/T/M)


Length of the Lugeon-test segment (L)


Effective pressure in the Lugeon-test segment (M)


Hydraulic pressure


Transmissivity (L2/T)


Change in head (L)


Radius of influence during the Lugeon test (L)


Borehole radius (L)



Gratitude is extended to the South African Water Resource Commission ( for their financial support by projects K5/2326, together with the National Research Foundation (NRF). The authors, furthermore, acknowledge the journal, its editors, and reviewers

Compliance with Ethical Standards

Conflict of interest

The authors declare no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Engineering Geology and Hydrogeology, Department of GeologyUniversity of PretoriaPretoriaSouth Africa
  2. 2.GaGE ConsultingJohannesburgSouth Africa

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