Soviet Mining

, Volume 11, Issue 4, pp 323–327

# A mathematical model of the electrical resistivity of a deformed rock

• B. G. Tarasov
• V. V. Ivanov
• V. V. Dyrdin
Rock Mechanics and Rock Pressure

## Conclusions

1. 1.

When (ρ12 = 1, as the moisture content rises, the graph of ρ vs σav rapidly becomes linear; as the moisture content of coal rises, the inclinations, of the lines to the axis of σav decrease.

2. 2.

When ρ12 ≪ 1, the resitivity depends very markedly on the moisture content. The presence of even very small amounts of water in the pores alters the conductivity of a rock by many orders of magnitude in comparison with that of the dry rock. In this case (when the moisture content is WS>0.5–0.6%), we can use Eq. (11), which gives a linear relation between ρ and σav.

3. 3.

For dry rocks the graph of ρ vs σav is nonlinear. A qualitative comparison between the curves in Fig. 2a-b and those obtained experimentally by Petukhov and Dal’nov [1] reveals that the model considered by us for a deformed porous medium gives a fair expression of the main laws accompanying the change in electrical conductivity of rocks during deformation. For the limitations mentioned above, the relation in Eq. (10) can be used to calculate ρ(σav) for any form of the function ɛv = ɛvav), expressing any rheological hypothesis corresponding to a real rock.

## Keywords

Porous Medium Electrical Resistivity Coal Seam Water Saturation Lignite
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Literature Cited

1. 1.
I. M. Petukhov and A. S. Dal’nov, “Investigation of the state of stress in a thick coal seam by the electrometric resistance method,” in: Stress Measurements in the Solid Rock [in Russian], Material from Third Seminar, Novosibirsk (1972).Google Scholar
2. 2.
B. G. Tarasov and V. V. Dyrdin, “On the relation between the geoelectric currents round mine workings and the mechanical state of the solid rock,” Fiz.-Tekh. Probl. Razrabotki Polezn. Iskop., No. 5 (1973).Google Scholar
3. 3.
A. S. Semenov, “The influence of structure on the resistivity of an aggregate,” Material from All-Union Scientific-Research Geological Institute (Geophysics) [in Russian], Symposium 12, Gostekhizdat, Moscow (1948).Google Scholar
4. 4.
V. N. Dakhnova Industrial Geophysics [in Russian], Gostoptekhizdat, Moscow (1947).Google Scholar
5. 5.
V. N. Kobranova, The Physical Properties of Rocks [in Russian], Gostoptekhizdat, Moscow (1962).Google Scholar
6. 6.
S. V. Kuznetsov, “On the problem of deformed porous media (a model of a deformed porous medium),” in: Rheological Aspects of Rock Mechanics [in Russian], Izd-vo AN KazSSR, Alma-Ata (1964).Google Scholar
7. 7.
B. T. Akin’shin and A. A. Filinkov, “Determination of the stress in lignite seams by registration of changes in the natural moisture content of the coal,” in: Measurement of Stresses in the Solid Rock, Material of Third Seminar [in Russian], Novosibirsk (1972).Google Scholar