Strength and Deformation of the Earth's Lithosphere

Active Tectonics is essentially about deformation of Earth's outermost layers at a variety of spatial and temporal scales. In this chapter, we explore the basic principles of deformation of different rock types at a wide range of environmental conditions. Much of our knowledge of rock deformation is based qualitatively on observations by structural geologists. However, for quantitative strength estimates and deformation parameters we draw particularly on rock mechanics experiments, and observations by seismologists and geodesists.

Strength and deformation mechanisms vary in particular as a function of:

Composition - with less effect on frictional strength estimates and large effects on crystal plastic strength. We are particularly interested in the rheology of major constituents in crustal rocks, feldspar and quartz in continental crust, and olivine in mantle rocks.

Confining pressure - in particular for brittle deformation mechanisms. Confining pressure in the Earth increases approximately by 26 MPa/km in the crust and by 35 MPa/km in the mantle. The effective pressure Pe = Pl - Pp is less well known, with estimates spanning the full range between hydrostatic and lithostatic pore pressures.

Temperature - in particular for crystal plastic (dislocation creep etc.) deformation mechanisms. The geothermal gradient lies between 15-35 °C/km, with the lower values being representative for stable cratons, and the higher values with thinned crust or otherwise elevated gradients.

Strain rate - mostly for crystal plastic deformation mechanisms

Fluid content - Water may weaken a rock through the effective pressure effect at brittle conditions and through hydrolytic weakening and diffusive processes aiding ductile flow.

A number of deformation mechanisms may act under given conditions, however, overall rocks will deform by the weakest mechanism (weakest link) available at those conditions. That is, if we can define the distribution of rock types, pressure, temperature, water content, and strain rate in the lithosphere as a function of depth, we can determine a strength profile through the crust.


Deformation regimes in the Earth's crust

The following broad domains can be defined, with considerable debate still existing about even the most fundamental issues:

Brittle upper crust: Deformation occurs by frictional faulting (on new or pre-existing faults) and by cataclastic flow (distributed stable micro-fracturing). Byerlee's friction law (empirically derived from experimental determination of "maximum shear stress" on a wide range of rock types) is based on the concept of Coulomb's friction law for pre-existing fault surfaces and predicts a linear increase of rock strength with depth following the following relationship:

t = S + s* m, where t is the shear stress at failure of a pre-existing fracture, s is the effective normal stress, and m is the coefficient of friction. Byerlee determined m to be 0.85 and S = 0 at confining pressures up to 2000 bars (200 MPa), and m= 0.6 and S= 800 bars at greater confining pressures. The strength increase with depth differs between extensional, strike-slip, and compressional situations due to the different orientation of fractures and normal stresses on them (Anderson's fault model). Apparently the frictional strength is rather independent of mineralogy, strain rate, and temperature, however, each of these parameters may have some effect.

Semi-brittle regime: Broad region within which both brittle cataclasis and crystal plastic deformation mechanisms occur. Least well understood from experiments and strength estimates vary widely in this region.

Ductile lower crust and asthenosphere: Depending on rock type, strain rate and fluid content high-temperature ductile flow by dislocation creep and other crystal plastic mechanisms dominates and causes rock strength to diminish rapidly with increasing depth. The effect of stress on steady state strain rate follows a power law rheology. Experimentally observed constitutive flow laws of the form

(e.g. Sibson 1983) predict that deformation rate (and thus fabric development) is a function of the differential stress, (s1 - s3) raised to a power n. The brittle-ductile transition can thus be considered to be the depth beyond which the activation of crystal-plastic dislocation creep, dynamic recrystallization, and/or diffusive mass transfer of one or more mineral constituents allows the rock to flow macroscopically. Below the transition a material will fail predominantly by brittle fracture if its strength is exceeded.

Commonly, however, strength envelopes are modified (strength estimates reduced in particular near in the semi-brittle regime) to account for parameters not considered in the definition of the deformation laws.


Further Reading

Carter, N.L., and M.C. Tsenn, Flow properties of continental lithosphere, Tectonophysics, 136, 27-63, 1987.

Hansen, F.D., and N.L. Carter, Creep of selected crustal rocks at 1000 MPa, EOS Trans. Am. Geophys. Un., 63, 437, 1982.

Kirby, S.H., Tectonic stresses in the lithosphere: Constraints provided by the experimental deformation of rocks, J.Geophys.Res., 85, 6353-6363, 1980.

Kirby, S.H., Rheology of the lithosphere, Rev. Geophys. Space Phys., 21 (6), 1458-1487, 1983.

Kirby, S.H., Rock mechanics observations pertinent to the rheology of the continental lithosphere and the localization of strain along shear zones, Tectonophysics, 119 (1-27), 1985.

Ross, J.V., and P.D. Lewis, Brittle-ductile transition. Semi-brittle behavior., Tectonophysics, 167, 75-79, 1989.

Sibson, R.H., Continental fault structure and the shallow earthquake source, J. geol. Soc. London, 140, 741-767, 1983.


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