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Rock failure in terms of pulse and ambient stresses

For strong, dry, unweathered, igneous basic rocks the relationship between principal stresses at failure is given, with reasonable accuracy, by the relationship:

where S1 and S3 are the greatest and least principal stresses at failure, S0 is the uniaxial strength of the rock and K is a constant determined by the angle of sliding friction of the rock (a), such that:

For a value of a=37° the value of £=4.0, and the angle which the shear plane makes with the axis of maximum principal stress is 26.75° (Price, 1966).

It can be inferred, therefore, that the development of arcuate thrusts is controlled by three main factors: (1) the material constants of the rock (i.e. the value of S0 and K; (2) the magnitude of the stress pulse; and (3) the orientation and magnitude of the ambient stresses in the lithosphere at a particular time, immediately prior to the arrival of the stress pulse.

The Snowball 500 ton TNT explosion generated several parallel shear planes which dip at a relatively low angle, inward toward GZ. These fracture planes, which cropped out at a maximum distance from GZ of approximately twice the radius of the crater rim, were exposed in deep radial trenches at least as far back as directly beneath the crater rim. From the orientation of the fracture planes and the thrust movements sometimes seen on these planes, there can be little doubt that these fractures originated as thrusts. (In those

Figure 7.36 Schematic representation of stress orientations S1, S2 and S3 at different distances from GZ. LOTh=limit of thrusts and LOVTF=limit of vertical tensile fractures.

trenches which showed normal fault movement on these planes, this inward movement can be explained by a relatively small degree of rebound 'slumping' of the sediments towards the crater.)

Beyond the crater, several radiating vertical tensile fractures developed. As we have seen in Chapter 5, the stress conditions necessary to generate such vertical tensile fractures are significantly different from those required for the generation of thrusts.

For vertical tensile fractures, the least principal stress (S3) must act circumferentially, while for thrusts, it is the intermediate principal stress (S2) that must act circumferentially, while the least principal stress (S3) must be near vertical. The maximum principal stress (Sj) in both these instances acts radially (Figure 7.36). It has been argued in Chapter 6 that, for the necessary stress conditions which can give rise to the location of (LO) and generation of vertical tensile fractures (LOVTF), one must invoke the action of the circumferential extension that is caused by the propagation of the hemispherical, compressive, pressure-pulse induced by the explosion or impact. Once one or more major vertical, radiating, tensile fractures is/are initiated by these circumferential tensile stresses, then, provided they reach down into the asthenosphere, where pressure-release melting takes place, rapid migration of the fluid melt will widen and extend these tensile fractures by the hydraulic fracture mechanism (Price and Cosgrove, 1990).

The development of these vertical fractures will, therefore, give rise to a positive increase in the magnitude of the circumferential stresses, which immediately changes from the least principal stress (S3) to the intermediate principal stress (S2) (LOTh in Figure 7.36). These stress conditions are maintained throughout the brief period that remains of the propagating stress pulse P. It is suggested that it is during this brief period that the pulse stress, superimposed upon the ambient stress field, gives rise to the circumferential thrust planes.

As we are concerned here with the generation of thrusts that can be induced in oceanic lithosphere by such a pressure pulse (Pp), it is now apposite to recall the magnitude of the probable ambient stresses that exist in such rocks, down to a depth of about 30 km. Below this level, except in very old, thick, ocean lithosphere, a thrust, or a number of such fractures that penetrate to a depth of 30 km, will so weaken the lithosphere that the lower, more ductile lithosphere will, sooner or later, yield and, as the result of ductile shear, permit an extension of the lower part of the thrust to cut completely through to the asthenosphere. Because of the weakness of the lower portion of the oceanic lithosphere, the lower zone will behave as a weak plastic material. The upper, brittle thrust fault will gradually degenerate, with depth, into a shear zone which is likely to increase gradually in dip until it reaches an angle of 45°.

As we saw in Chapter 2, the ambient stress in elastic lithosphere is made up of a series of elements. The first of these is the vertical stress (Sz) that is generated by the weight of a 'column' of rock in oceanic lithosphere (Table 7.2a), where the vertical stress is given by Sz =d.g.z (where d is the density of the rock, g is the gravitational constant and z is the depth in the appropriate units). At a depth of 30 km, the vertical stress in oceanic lithosphere will be approximately 9.9 kb. The values of Sz from 0 to 30 km are listed in Table 7.2a, and from 0 to 20 km in Table 7.2b.

Table 7.2a

Z(km)

Sz (kb)

Sh=Sz/(m-1) (kb)

Ambient stress Pulse (20 kb)+ambient

Sx (+6) (kb) Sy (+1.5) (kb) S1 (Sx+20) S2 (Sy+5) (kb) (kb)

S3=Sz (kb)

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