Content of PetroWiki is intended for personal use only and to supplement, not replace, engineering judgment. SPE disclaims any and all liability for your use of such content. More information

# Pore fluid effects on rock mechanics

Fluids can alter rock mechanical properties through:

• Fluid pressure
• Chemical reactions with mineral surface
• Lubricating moving surfaces.

The primary fluids encountered are brines and hydrocarbon oils and gases. Drilling, completion, and fracturing fluids can also be present, and their effects are typically studied to prevent formation damage.

This page will concentrate on the role of water and, in particular, how water saturation can influence rock strengths measured in the laboratory or derived from well logs.

## Effective stress

Pore fluid pressures will reduce the effective stress supported by the rock mineral frame. For an elementary volume of rock the effective stress can be defined as the stress, depending on the applied tension σ and pore pressure p, which controls the strain or strength behaviour of soil and rock (or a generic porous body) for whatever pore pressure value or, in other terms, the stress which applied over a dry porous body (i.e. at p = 0) provides the same strain or strength behaviour which is observed at p ≠ 0.[1] This effect has been well known since the publication of Karl Terzaghi (e.g. Terzaghi and Peck[2] and references therein) and has been documented by numerous investigators. The most common form for the effective stress law is

....................(1)

where σe is the effective stress, σa the applied stress on the rock surface, Pp, and the pore pressure. The expression of the effective stress coefficient n (which is not porosity) varies in accordance to the adopted work hypothesis, such as stress-strain or strength behavior of soil or rock, compressibility of grains, high confining stress etc. According to the first formulation proposed by Terzaghi, n = 1. This latter formulation is the most appropriate in order to study the strength/failure behavior of soil and rock.

In analyzing the of stress-strain behavior of rock, n is also called Biot’s poroelastic term and is expressed as:

....................(2)

where Kd is the dry rock bulk modulus and Ko the mineral bulk modulus. Because for shallow rocks the bulk modulus is usually much lower than the mineral modulus, n is often close to unity; nevertheless at depth of some kilometer in the Earth crust it may significantly deviate from this value. Several other formulations have been proposed for the effective stress along the past century. Among these, Terzaghi's one seems particularly appropriate, for its simplicity and as it describes with excellent approximation a wide variety of real cases.[1]

In Rock failure relationships all of the stresses used to describe rock failure were actually effective stresses, calculated according to Terzaghi's formulation (i.e. n = 1). Rock failure can be dramatically affected by pore pressure, as indicated in Fig. 1. An envelope is plotted for a sandstone with porosity of 25%. For applied principal stresses of 225 MPa for σ1, 175 MPa for σ3, and a Pp of 75 MPa, the effective Mohr circle plots well within the field of stability. The pore pressure has been subtracted from both applied stresses to give effective principal stresses of 150 and 100 MPa. If pore pressure is increased, the effective stresses decrease, and the Mohr circle is shifted left until eventually the envelope may be contacted and the rock fails by brittle fracture. On the other hand, if pore pressure decreases, the Mohr circle shifts right, and the rock may contract the Roscoe surface and fail by compaction or grain crushing. In any case, if pore pressures are known, their effects can be accounted for in a straightforward way.

Problems can arise experimentally because of the inability of pore pressure to reach equilibrium. If fluid can flow freely and constant pore pressure is maintained, then an experiment is termed "drained." If deformation is too rapid, permeability low, fluid viscosity high, or boundaries are sealed, then fluid is trapped in the rock, and fluid pressure changes as a function of rock deformation. Brace and Martin[3] showed that strain rates must be very low in crystalline rocks of low permeability to maintain a uniform pore pressure and follow a macroscopically defined effective stress law. For most sandstones, permeability is sufficient to provide drained conditions. Problems usually occur in low-permeability rocks such as siltstone or shales. Considerable effort and time are usually needed to allow constant pore pressure, or merely to maintain pore pressure equilibrium (Steiger and Leung[4]). Tests are made under undrained conditions, but the resulting changes in pore pressure must then be measured or otherwise calculated. These effects are mechanical problems that are often difficult to deal with, but the processes are basically well understood.

## Chemical effects

A more subtle problem involves chemical effects of pore fluids. Water is an active, polar compound, and numerous investigations (Griggs[5] and Kirby[6]) have shown that even small amounts of water or brine can have a substantial influence on rock mechanical properties. Colback and Wiid[7] demonstrated how even changes in the relative humidity or partial pressure of water in the pores can lower rock strength dramatically (Fig. 2). Colback and Wiid[7] and Dunning and Huff[8] saw a direct relationship between the loss in rock strength and the chemical activity of the pore fluid. Meredith and Atkinson,[9] Freeman,[10] and others have shown increased crack velocities and acoustic emissions at constant crack intensity factors when water is introduced. Ujtai et al.[11] saw substantial effects of water on all time-dependent tests for creep strain, fatigue, and slow crack growth.

In general, uniaxial compressive strength is reduced by 20 to 25% in wet rocks. This implies that many laboratory measurements result in rock strengths that are systematically too high.

A strong influence of the chemical activity on rock mechanical properties is supported by other types of measurements. Seismic properties depend upon mineral grain stiffness and the stiffness of grain-to-grain contacts. In completely dry rocks (oven-dried under vacuum), there is almost no seismic attenuation, and rocks are stiff. Even small amounts of water, a few monolayers, can appreciably lower rock stiffness and seismic velocities.

## Bulk lubrication

Common experience leads us to expect many geologic materials, such as soils, to be substantially weaker when wet. This effect is readily observed in chalk and shales. Surface bonding energies and water surface tension result in strong capillary forces that draw and hold water in pore spaces. Water penetrates and separates grains. Grain movement is facilitated by motion in mobile fluid layers. This is a highly scientific way of saying "slippery when wet." Clay minerals in particular are well known for their ability to absorb large quantities of water. Swelling properties of clays and shales are often studied for drilling engineering purposes. Not only do clays have lower friction surfaces when wet, but water absorption and the resulting clay expansion can disaggregate the rock matrix. Loss of strength because of such mechanisms is more important in poorly consolidated or unconsolidated sediments. Dobereiner and DeFreitas[12] and Morgenstern et al.[13] report a 60% reduction in strength for muddy sediments upon saturation. At this point, we have not developed a systematic way of including a lubrication factor except as an implicit part of clay corrections (see Compressive strength of rocks#Effect of clay content or as a measured reduction of the shear or Young’s modulus. We would expect the loss of intergrain friction to reduce the shear modulus significantly.

## Nomenclature

 Kd = dry bulk modulus, GPa or MPa Ko = mineral bulk modulus, GPa or MPa n = effective stress coefficient Pp = pore pressure, MPa σe = effective stress σa = stress on the rock surface

## References

1. Guerriero, V. and Mazzoli, S. 2021. Theory of Effective Stress in Soil and Rock and Implications for Fracturing Processes: A Review. Geosciences, 11 (3), 119, https://doi.org/10.3390/geosciences11030119 .
2. Terzaghi, K. and Peck, R.B. 1948. Soil Mechanics in Engineering Practice. New York: John Wiley & Sons.
3. Brace, W.F. and Martin III, R.J. 1968. A test of the law of effective stress for crystalline rocks of low porosity. Int. J. Rock Mech. Min. Sci. & Geomech. Abstracts 5 (5): 415-426. http://dx.doi.org/10.1016/0148-9062(68)90045-4.
4. Steiger, R.P. and Leung, P.K. 1989. Predictions of wellbore stability in shale formations at great depth. In Rock at Great Depth: Rock Mechanics and Rock Physics at Great Depth—Proceedings of an International Symposium, Pau, 28–31 August 1989, ed. V. Maury and D. Fourmaintraux, Vol. 3, 1209. London: Taylor & Francis.
5. Griggs, D.T. 1967. Hydrologic weakening of quartz and other silicates. Geophys. J. R. Astron. Soc. 14: 19–31.
6. Kirby, S.H. 1984. Introduction and digest to the Special Issue on Chemical Effects of Water on the Deformation and Strengths of Rocks. Journal of Geophysical Research: Solid Earth 89 (B6): 3991-3995. http://dx.doi.org/10.1029/JB089iB06p03991.
7. Colback, P.S.B. and Wiid, B.L. 1965. The Influence of Moisture Content on the Compressive Strength of Rock. Ha Noi, Vietnam: National Mechanical Engineering Research Institute (NARIME).
8. Dunning, J.D. and Huf, W.L. 1983. The effects of aqueous chemical environments on crack and hydraulic fracture propagation and morphologies. Journal of Geophysical Research: Solid Earth 88 (B8): 6491-6499. http://dx.doi.org/10.1029/JB088iB08p06491.
9. Meredith, P.G. and Atkinson, B.K. 1983. Stress corrosion and acoustic emission during tensile crack propagation in Whin Sill dolerite and other basic rocks. Geophys. J. R. Astron. Soc. 75 (1): 1-21. http://dx.doi.org/10.1111/j.1365-246X.1983.tb01911.x.
10. Freiman, S.W. 1984. Effects of chemical environments on slow crack growth in glasses and ceramics. Journal of Geophysical Research: Solid Earth 89 (B6): 4072-4076. http://dx.doi.org/10.1029/JB089iB06p04072.
11. Ujtai et al. 1987. Effects of water on all time-dependent tests for creep strain, fatigue, and slow crack growth.
12. Dobereiner, L. and De Freitas, M.H. 1986. Geotechnical properties of weak sandstones. Geotechnique 36 (1): 79-94. http://dx.doi.org/10.1680/geot.1986.36.1.79.
13. Morgenstern, N.R. and Eigenbrod, K.D. 1974. Classification of Argillaceous Soils and Rocks. Journal of the Geotechnical Engineering Division (ASCE) 100 (10): 1137-1156.