Proyección de los competidores

For two-dimensional analysis of accretionary wedges or thrust belts, that assume arc-normal convergence, models predict that wedge geometry is a function o f the boundary stresses and the bulk rheology o f the wedge (Chappie, 1978; Davis et al., 1983; Dahlen, 1984; Dahlen et al., 1984). Current mechanical analyses o f fold-and- thrust belts and accretionary wedges are based on the critical wedge theory o f Davis et al. (Davis et al., 1983), which assumes time-independent Coulomb (brittle) behaviour o f deforming rocks in the upper lithosphere. A Coulomb wedge is assumed to be capable of deforming internally by fracture and frictional sliding on surfaces with a wide variety of orientations distributed throughout it. The eastern Betic Cordillera can be considered to behave as a Coulomb material for modelling purposes in that it derives considerable

internal strength from the large volume of limestone, and has weak boundary conditions specifically from the basal detachment in Triassic gypsiferous marls.

This model (Figure 3.1) applies to a homogenous wedge o f deformable non- cohesive Coulomb material under compression by a push from the hinterland, and sliding along a rigid base, in which the ratio of pore fluid pressure to the vertical normal stress, A, and the coefficient of internal friction, fi, are constant throughout the wedge. Both o f these assumptions are unlikely in real Coulomb wedges, where A is likely to vary unpredictably through the wedge and y, is dependent on rock type. Another assumption of this model is that the vertical normal traction, q^, at any point within the wedge is defined solely by the lithostatic and hydrostatic overburden.

The general Coulomb criterion for shear traction r a t failure is o f the form:

\r\ = So + f Ko „ - Pf ) ,

where a„ is the normal traction; So is the cohesion; and p /is the pore fluid pressure. The taper of a wedge is the sum o f angles a and f t where a is the local angle o f topographic relief and is the local dip angle o f the rigid base.

Davis et al. (1983) considered cohesion relatively unimportant because at depths of a few kilometres this term becomes insignificant when compared to the pressure- dependent term o f the equation. Fracture experiments on small samples of shales and sandstones have produced values for cohesion in the range o f 5 to 20 MPa, several times less than the cohesion o f granites and other stronger rocks. Davis et al. (1983) considered that because these values for cohesion are derived from small pristine rock samples the cohesion values they produce are likely to be too high, because o f the decrease in rock strength caused by the introduction o f flaws in larger samples. Cohesion has the greatest influence on taper near the toe o f the wedge where it can add significantly to the total strength o f the wedge, and produce a narrower critical taper than the corresponding cohesionless taper. Davis et al. (1983) ignored the effects of cohesion on the toe shape and employed a non-cohesive failure law o f the form:

k h i w c j ; , where a„' is the effective stress a„' = a „ - pf.

The overall mechanics o f fold-and-thrust belts and accretionary wedges along compressive margins has been likened to that o f a wedge o f soil or snow in front of a moving bulldozer (Chappie, 1978; Davis et al., 1983; Dahlen, 1984; Dahlen et al.,

C hap ter 3 - Mechanics

1984), in which the material within the wedge deforms until a critical taper is reached, before sliding stably and growing through accretion o f new material at the toe. A subcritical wedge, with a taper below the critical angle, will deform internally when pushed to thicken the wedge, until the critical angle is attained. Conversely, a wedge that exceeds the critical taper (i.e. becomes supercritical) is likely to extend internally until the critical angle is reached. The critical angle o f taper, 6= a + p, corresponds to an internal state of stress on the verge o f Coulomb failure everywhere (Dahlen, 1984), and is given (Davis et al., 1983) by:

(l-pJp) + (l-AK ’

where A and At are the fluid pressure ratios within the wedge and at the base, equal to A

= - P f / azzCOSjS; is the coefficient o f friction on the base o f the wedge; a is the surface

slope and p is the basal slope of the accretionary wedge in radians; p and p ^ are the average density o f the wedge and the density o f water respectively; and is a dimensionless quantity such that:

dz

A = 2 //-' r "

Jo ,csc0sec2i//(z)-l

where H is the thickness of the wedge parallel to the z-axis (see Figure 3.1); ^ is the angle o f internal friction; and ^ is the angle between Oj and the x axis within the wedge.

Ultimately, critical taper theory relates the basal shear traction o f a wedge to the sum of a function of rheology and a function of the geometry o f the wedge of the form:

= ( p- p J g H a + (1 - X)KpgHd

The first term is the influence o f gravity on the surface slope o f the wedge. It is the same force responsible for causing a glacier to flow in the direction of its surface slope and independently o f the orientation of the basal slope (Davis et al., 1983). The second term is dependent on the taper o f the wedge, and is a measure o f the horizontal compressive forces acting from the rear of the wedge. It is independent o f x.

In the above equations it is clear that the taper is controlled by the coefficient of basal friction and the strength of the rocks composing the wedge, such that a higher basal friction will increase taper and a higher rock strength will decrease taper.

Sandbox models carried out by Davis et al. (1983) verified this by altering basal friction and material strength.

Davis et al. (1983; Dahlen et al., 1984; Dahlen, 1984) applied simplified versions of the above formulae to the actively deforming Taiwan mountain belt on the western edge of the Philippine Sea plate. Known values o f a and were taken from surface and seismic reflection profiles, A from formation tests and sonic log measurements during petroleum exploration, in which they adopted a constant fluid pressure ratio A = A&, and was adopted fi'om Byerlee (1978), in which |t| = 0.85o;,* is used to describe frictional sliding in normal silicate rocks and is translated into 0.85 on the basal decollement where it is logical to assume that pure frictional sliding is taking place (Davis et al., 1983). By calculating the coefficient of internal friction, jU = tan 0, they found that jU = 1.03 and proved the validity of the relationship jU > jU*. The values for (x and fit were used to calculate A for other active wedges around the world by Davis et al. (Davis et al., 1983), in order to successfully test the Coulomb wedge theory.

Fixing jU = jW* and varying A such that A> A& also fitted the taper to observations from Taiwan, emphasising the fact that the essential requirement is that the interior o f the wedge be slightly stronger than the base, for whatever reason. Decreasing basal friction through elevating A^ has the effect o f making a critical wedge supercritical. The reverse is true o f decreased kb such that the wedge will tend to increase its surface slope (Dahlen, 1984).

Increases in jU over ^b within the wedge are to be expected in real life. The basal decollement, for example, is a through-going fracture aligned to permit efficient sliding of the above material under compression. Within the wedge all fractures are unlikely to be aligned as favourably to permit frictional sliding, and locked geological structures are likely to occur and need to be fi*actured to allow further deformation (Davis et al.,

1983; Dahlen et al., 1984).

In summary, the key strength parameters necessary to describe a critical Coulomb wedge are A and A* (Davis et al., 1983; Dahlen et al., 1984; Dahlen, 1984). Coulomb theory is expected to break down below the brittle-plastic transition in the crust, where temperature increases should cause a marked decrease in basal resistance to sliding. This decrease in jXb would cause the wedge taper to decrease, and is observed in both the Himalayas and the Andes (Davis et al., 1983). In the Betic

C h ap ter 3 - Mechanics

External Zones, with a very weak basal layer o f Triassic salt, and strong contrast between the internal strength o f the wedge and the basal layer, a low taper is to be expected.

In the External Zones it is possible to determine p with some confidence, but the upper surface o f the wedge has been subject to erosion so that the slope is not straightforward, making determining 6 problematic. The weak detachment on Triassic salt is unlikely to have a typical value for jUb as used above by others (Davis et al., 1983; Dahlen et al., 1984; Dahlen, 1984), and jU > jU* is likely to apply. Since the wedge is no longer active, actual measurements for A may not reflect conditions during deformation.