ISRM Suggested Method for the Lugeon Test

Appendix

Estimation of the equivalent isotropic coefficient of permeability (hydraulic conductivity K) and estimation of the transmissivity (T).

1.1 General Considerations

Available equations and techniques to estimate the permeability/hydraulic conductivity coefficient (K) based on Lugeon test results, in general, are based on Darcy’s law and consideration of a laminar flow regimen. The use of the diagrams shown in Table 6 allows evaluation of the flow regime from the test results. The recommended practice is the use of the lowest stage of pressures when the objective is the evaluation of the rock mass permeability. The higher stages of pressure are used when the objective is to estimate grouting absorption. Diagrams obtained from the test are used to select the best linear relationships and the average values are to be used in the formulae.

Due to the specific difficulties related to the application of the flow laws valid for rock fractures (Louis 1967; Rissler 1978; Quadros 1982), the equivalent isotropic hydraulic conductivity coefficient K is used in the current practice to interpret results of Lugeon test. If the characteristics and number of the discontinuities in the test section are known, some of the main features contributing to the flow might be deduced.

1.2 Estimation of the Equivalent Isotropic Permeability or Hydraulic Conductivity Coefficient (K) and Estimation of the Transmissivity (T) Based on the Lugeon Test Results

• (a) Method proposed by Franciss (1970)

The method proposed by Franciss is based on Babouchkine (1965) for the analysis of flow in wells where the test section is at a certain distance from the water table (which is the general practice). According to the author, the equivalent hydraulic conductivity coefficient can be estimated using the following equation valid for laminar flow (refer Table 6):

$$K = \frac{Q}{2 \pi H L}\ln \left[ {\frac{0.66L}{D/2}} \right] .$$

(5)

• (b) Use of Thiem’s equation to estimate the transmissivity T (Thiem 1906)

The transmissivity T can be related to the permeability/hydraulic conductivity (K) in the test interval through the expression $K = \frac{T}{L}$ and the use of a radial flow model, where L is assumed to have the following two meanings:

• (i) L is equal to the length of the test section. In this case, a general porous media approach is used to interpret the test results. This hypothesis considers that the rock matrix is pervious.

• (ii) L = e, where e is the equivalent aperture of the joint (or joints) appearing in the test interval. In this case, a radial flow model is used to evaluate the transmissivity around the test section and the rock matrix is assumed to be impervious.

According to Thiem (1906),

$$T = \frac{{Q{\text{ln }}\left[ {\frac{R}{r}} \right]}}{2 \pi P}.$$

(6)

In Thiem’s equation (Eq. 6), the radius of influence R is affected by many factors, and among them:

• The hydraulic conductivity of the test section which is deeply dependent on the hydraulic conductivities of the rock joints;

• the interconnectivity of the joints;

• the hydraulic boundaries;

• the pressures applied during the test.

As this parameter occurs within a natural logarithmic function, one can use an approximation. For example, for a borehole in HQ diameter (95.3 mm, r = 0.0477 m) considering R values of 1, 5, 10 and 100 m, the value of Ln (R/r) would be, respectively, 3.04 m, 4.61 m, 5.3 m and 7.65 m. Hence, the value of R attributed to Eq. 5 will have only a small effect on the estimated value for the transmissivity, T, using Eq. 6 and the Lugeon test results.

• (c) Practical rule proposed by Nonveiller (1989)

A simple relationship between 1 LU and K is proposed by Nonveiller (1989), for a test interval of 5-m length, where r is the radius of the borehole

$$\begin{aligned} K & = 1.5 \times 10^{ - 5} \,{\text{LU}}\,\left( {\text{in cm/s}} \right),\,{\text{ when}}\, \, r = 4.6\,{\text{cm,}} \\ K & = 1.3 \times 10^{ - 5} \,{\text{LU}}\,\left( {\text{in cm/s}} \right),\,{\text{ when}}\, \, r = 7.6\,{\text{cm}}. \\ \end{aligned}$$

As this relation considers only the length of the test interval, its use should be restricted for rough estimates.

• (d) Representation of a jointed rock mass as a cubic network of conducting joints, following Snow (1968) and Barton et al. (1985) (Fig. 4).

Note that the e versus S curves for specific Lugeon values are derived from the given equation which assumes that flow is possible through two of the three sets, or through lesser fractions of all three assumed sets as the gradient rotates around the cube. The next step is to convert e to E (mechanical/physical aperture) using the joint roughness coefficient JRC, then test that E > 4 d₉₅ of the cement particles and choose grout type and injection pressure accordingly.

The hydraulic aperture can be estimated using the following formula:

$$e \, \approx \, (L \, \times \, 6 \times \, S \, \times \, 10^{ - 8} )^{1/3}$$

(7)

In this equation, the hydraulic aperture (e) and the mean fracture spacing (S) are in mm. Each of the above apply to a given structural domain, to the whole borehole, or to a specific rock type (Barton 2004).