Straininduced weakening

Although differences in the effective elastic thickness and flexural strength of the lithosphere (Section 7.6.4) may explain variations in the length of border faults and the width of rift basins, they have been much less successful at explaining another major source of variability in rifts: the degree of strain localization in faults and shear zones. In some settings normal faulting is widely distributed across large areas where many faults accommodate a relatively small percentage of the total extension (Section 7.3). However, in other areas or at different times, extension may be highly localized on relatively few faults that accommodate a large percentage of the total extension. Two approaches have been used to explain the causes of this variability. The first incorporates the effects of a strain-induced weakening of rocks that occurs during the formation of faults and shear zones. A second approach, discussed in Section 7.6.6, shows how vertical contrasts in the rheology of crustal layers affect the localization and delocalization of strain during extension.

In order for a normal fault to continue to slip as the crust is extended it must remain weaker than the surrounding rock. As discussed in Section 7.6.4, the deflection of the crust by faulting changes the stress field surrounding the fault. Assuming elastic behavior, Forsyth (1992) showed that these changes depend on the dip of the fault, the amount of offset on the fault, and the inherent shear strength or cohesion of the faulted material. He argued that the changes in stresses by normal faulting increase the yield strength of the layer and inhibit continued slip on the fault. For example, slip on high-angle faults create surface topography more efficiently than low-angle faults, so more work is required for large amounts of slip on the former than on the latter. These processes cause an old fault to be replaced with a new one, leading to a delocalization of strain. Buck (1993) showed that if the crust is not elastic but can be described with a finite yield stress (elastic-plastic), then the amount of slip on an individual fault for a given cohesion depends on the thickness of the elastic-plastic layer. In this model the viscosity of the elastic-plastic layer is adjusted so that it adheres to the Mohr-Coulomb criterion for brittle deformation (Section 2.10.2). For a brittle layer thickness of >10 km and a reasonably low value of cohesion a fault may slip only a short distance (a maximum of several kilometers) before a new one replaces it. If the brittle layer is very thin, then the offset magnitude can increase because the increase in yield strength resulting from changes in the stress field due to slip is small.

Although layer thickness and its inherent shear strength play an important role in controlling fault patterns, a key process that causes strain localization and may lead to the formation of very large offset (tens of kilometers) faults is a reduction in the cohesion of the faulted material. During extension, cohesion can be reduced by a number of factors, including increased fluid pressure (Sibson, 1990), the formation of fault gouge, frictional heating (Montesi & Zuber, 2002), mineral transformations (Bos & Spiers, 2002), and decreases in strain rate (Section 2.10). Lavier et al. (2000) used simple two-layer models to show that the formation of a large-offset normal fault depends on two parameters: the thickness of the brittle layer and the rate at which the cohesion of the layer is reduced during faulting (Plate 7.4a,b between pp. 244 and 245). The models include an upper layer of uniform thickness overlying a ductile layer having very little viscosity. In the ductile layer the yield stress is strain-rate- and temperature-dependent following dislocation creep flow laws (Section 2.10.3). In the upper layer brittle deformation is modeled using an elastic-plastic rheology. The results show that where the brittle layer is especially thick (>22 km) extension always leads to multiple normal faults (Plate 7.4c between pp. 244 and 245). In this case the width of the zone of faulting is equivalent to the thickness of the brittle layer. However, for small brittle layer thicknesses (<22 km), the fault pattern depends on how fast cohesion is reduced during deformation (Plate 7.4d,e between pp. 244 and 245). To obtain a single large-offset fault, the rate of weakening must be high enough to overcome the resistance to continued slip on the fault that results from flexural bending.

These studies provide some insight into how layer thickness and the loss of cohesion during faulting control the distribution of strain, its symmetry, and the formation of large-offset faults. However, at the scale of rifts, other processes also impact fault patterns. In ductile shear zones changes in mineral grain size may promote a switch from dislocation creep to grain-size-sensitive diffusion creep (Section 2.10.3), which can reduce the yield strengths of layers in the crust and mantle. In addition, the rate at which a viscous material flows has an important effect on the overall strength of the material. The faster it flows, the larger the stresses that are generated by the flow and the stronger the material becomes. This latter process may counter the effects of cohesion loss during faulting and could result in a net strengthening of the lithosphere by increasing the depth of the brittle-ductile transition (Section 2.10.4). At the scale of the lithosphere, it therefore becomes necessary to examine the interplay among the various weakening mechanisms in both brittle and ductile layers in order to reproduce deformation patterns in rifts.

Huismans & Beaumont (2003, 2007) extended the work of Lavier et al. (2000) by investigating the effects of strain-induced weakening in both brittle (frictional-plastic) and ductile (viscous) regimes on deformation patterns in rifts at the scale of the lithosphere and over time periods of millions of years. This study showed that strain softening in the crust and mantle can produce large-offset shear zones and controls the overall symmetry of the deformation. Figure 7.26a shows a simple three-layer lithosphere where brittle deformation is modeled by using a frictional-plastic rheology that, as in most physical experiments, is adjusted so that it adheres to the Mohr-Coulomb failure criterion. Ductile deformation is modeled using a thermally activated power law rheology. During each experiment, ambient conditions control whether the deformation is fric-tional-plastic (brittle) or viscous (ductile). Viscous flow occurs when the state of stress falls below the frictional-plastic yield point. Variations in the choice of crustal rheology also allow an investigation of cases where the crust is either coupled or decoupled to the mantle lithosphere. Coupled models involve deformation that is totally within the frictional-plastic regime. Decoupled models involve a moderately weak viscous lower crust. Strain-induced weakening is specified by linear changes in the effective angle of internal friction (Section 2.10.2) for frictional-plastic deformation and in the effective viscosity for viscous deformation. The deformation is seeded using a small plastic weak region.

A reference model (Fig. 7.26b,c) shows how a symmetric style of extensional deformation results when strain softening is absent. An early phase of deformation is controlled by two conjugate frictional-plastic shear zones (S1A/B) that are analogous to faults and two forced shear zones in the mantle (T1A/B). During a subsequent phase of deformation, second generation shear zones develop and strain in the mantle occurs as focused pure shear necking beneath the rift axis. Figures 7.26d and e show the results of another model where frictional-plastic (brittle) strain softening occurs and the resulting deformation is asymmetric. An initial stage is very similar to the early stages of the reference model, but at later times strain softening focuses deformation into one of the conjugate faults (S1B). The asymmetry is caused by a positive feedback between increasing strain and the strength reduction that results from a decreased angle of internal friction (Section 2.10.2). Large displacements on the S2A and T1B shear zones cut out a portion ofthe lower crust (LC) at point C (Fig. 7.26, insert) and begin to exhume the lower plate. By 40 Ma, a symmetric necking of the lower lithosphere and continued motion on the asymmetric shear zones results in the vertical transport of point P until mantle lithosphere is exposed. The model shown in Fig.7.26f and g combines both frictional-plastic and viscous weakening mechanisms. The early evolution is similar to that shown in Fig. 7.26d, except that S1B continues into the ductile mantle. The two softening mechanisms combine to make deformation asymmetric at all levels of the lithosphere where displacements are mostly focused onto one shear zone. These models show how a softening of the dominant rheology in either frictional-plastic or viscous layers influences deformation patterns in rifts through a positive feedback between weakening and increased strain.

The effect of strain-dependent weakening on fault asymmetry also is highly sensitive to rift velocity. This sensitivity is illustrated in the models shown in Fig. 7.27. The first model (Fig. 7.27a) is identical to that shown in Fig. 7.26d and e except that the velocity is decreased by a factor of five to 0.6 mm a-1. Reducing the velocity has the effect of maintaining the thickness of the frictional-plastic layer, which results in deformation that is more strongly controlled by the frictional regime than that shown in Fig. 7.26e. The overall geometry matches a lithospheric-scale simple shear model (cf. Fig. 7.21b) in which the lower plate has been progressively uplifted and exhumed beneath a through-going ductile shear zone that remains the single major weakness during rifting. By contrast, a velocity that is increased to 100 mm a-1 (Fig. 7.27b) results in deformation that is more strongly controlled by viscous flow at the base of the frictional layer than that in the model involving slow velocities. However, at high velocities the strain softening does not develop in part because of the high viscous stresses that result from high strain rates. The model shows no strong preference for strain localization on one of the frictional fault zones. The deformation remains symmetrical as the ductile mantle undergoes narrow pure shear necking. These results suggest that increasing or decreasing rift velocities can either promote or inhibit the formation of large asymmetric structures because varying the rate changes the dominant rheology of the deforming layers.

These experiments illustrate the sensitivity of deformation patterns to strain-induced weakening mechanisms during faulting and ductile flow. The results suggest that extension is most likely to be asymmetric in models that include frictional-plastic fault zone weakening mechanisms, a relatively strong lower crust, and slow rifting velocities. However, before attempting to

Crust: Wet quartz Frictional plastic pc = 2800 kg m''

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un coupled Decoupled t quartz

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Mantle Lithosphere and Sublithospheric Mantle Dry Olivine

Frictional plastic y pm = 3300 kg m-3

Isothermal mantle, Temperature = 1330 oC 1

coupled Decoupled

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t quartz

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0 1500 150 Stress (MPa)

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1200 km

x1200"C 400

x1200"C 400

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400 500

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20 40 60 80 100 120

20 40 60 80 100 120

35 km

85 km

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Figure 7.26 (a) Model geometry showing temperature structure of the crust, mantle lithosphere and sublithospheric mantle (images provided by R. Huismans and modified from Huismans & Beaumont, 2003, by permission of the American Geophysical Union. Copyright © 2003 American Geophysical Union). Initial (solid lines) and strain softened (dashed lines) strength envelopes are shown for an imposed horizontal extensional velocity of Vext = 3 mm a~\ with Vb chosen to achieve mass balance. Decoupling between crust and mantle is modeled using a wet quartzite rheology for the lower crust. (b,c) Reference model of extension when strain softening is absent. Models of extension involving (d,e) frictional-plastic (brittle) strain softening and (f,g) both frictional-plastic and viscous weakening mechanisms. Models in (b-g) show a subdivision of the crust and mantle into an upper and lower crust, strong frictional upper mantle lithosphere, ductile lower lithosphere, and ductile sublithospheric mantle. Scaling of quartz viscosity makes the three upper layers frictional-plastic in all models shown. t, time elapsed in millions of years; Ax, amount of horizontal extension. Vertical and horizontal scales are in kilometers. Vext = 3 mm a- for every model.

Figure 7.27 Models of extension involving frictional-plastic (brittle) strain softening at (a) low extensional velocities (Vext = 0.6 mm a~') and (b) high extensional velocities (Vext = 100mm a~'). Models also show rift sensitivity to (c) a weak and (d) a strong middle and lower crust at Vext = 3 mm a- (images provided by R. Huismans and modified from Huismans & Beaumont, 2007, with permission from the Geological Society of London). t, time elapsed in millions of years; Ax amount of horizontal extension. Vertical and horizontal scales are in kilometers.

Figure 7.27 Models of extension involving frictional-plastic (brittle) strain softening at (a) low extensional velocities (Vext = 0.6 mm a~') and (b) high extensional velocities (Vext = 100mm a~'). Models also show rift sensitivity to (c) a weak and (d) a strong middle and lower crust at Vext = 3 mm a- (images provided by R. Huismans and modified from Huismans & Beaumont, 2007, with permission from the Geological Society of London). t, time elapsed in millions of years; Ax amount of horizontal extension. Vertical and horizontal scales are in kilometers.

apply these results to specific natural settings, it is important to realize that the effects of strain-induced weakening can be suppressed by other mechanisms that affect the rheology of the lithosphere. For example, a comparison of two models, one incorporating a weak lower crust (Fig. 7.27c) and the other a strong lower crust (Fig. 7.27d), illustrates how a weak crust can diminish crustal asymmetry. This suppression occurs because conjugate frictional shears that develop during rifting sole out in the weak ductile lower crust where they propagate laterally beneath the rift flanks. As rifting progresses, viscous flow in a weak lower crust results in a nearly symmetric ductile necking of the lower lithosphere. These examples show that the degree of rift asymmetry depends not only on strain softening mechanisms and rifting velocities, but also on the strength of the lower crust.

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