1 some basic theory, and the importance of rock type
2.4 Weathering and moisture content
Effects of weathering on the physical and seismic prop-erties of four rock types from a dam site (quartz diorite) and from three quarries (andesite, basalt and dacite) were reported by Saito, 1981. This very comprehensive study, involving hundreds of samples with different weathering grades and porosities, gives a very useful picture of some key trends between strength, hardness, porosity, degree of water saturation and P-wave veloc-ity. These behavioural trends are fundamental to an understanding of the in situ behaviour, where the addi-tion of joints to the cracks and pores tested here, adds another layer of complexity.
Saito, 1981, collected numerous block samples of the different rocks and weathering grades and cast these in regular shaped concrete blocks, before coring cylindrical samples for his tests. Schmidt (N-hammer) tests were made on these larger blocks. Figure 2.16a illustrates and describes the typical weathered zones (1 to 5), and an idea of the ranges of compression strengths (dry sam-ples) and porosities are given in Figure 2.16b and 2.16c. The very different porosities of the three volcanic rocks compared to the crystalline quartz diorite are well reflected in the clear separation of the Vpvalues shown in Figure 2.16c.
The extended Vprange of 1 km/s to almost 6 km/s was the result of the huge range of porosities (57% to 1%). When only uniaxial strength and velocity were plotted (Figure 2.16d) the fundamental differences in porosity were not seen due to the relatively high strength of the three volcanic rock types. Figure 2.16e shows how Saito’s Schmidt (N) hammer rebound data related to Vpin a quite linear manner, not showing the same ‘plateau’ effect seen with Vpversus c. This is an encouraging aspect of this ultra-simple test method, which was adopted for registering the compressive strength of (fresh or weathered) rock-joint walls (JCS) in the shear strength criterion of Barton and Choubey, 1977.
Figure 2.15 Vp- cdata for Tertiary mudstones and sandstones from Japan. Aydan et al., 1992 and Sato et al., 1995.
(a)
(b)
(d) (e)
(c)
Figure 2.16 (a to e) Effects of weathering at four sites in Japan cause huge ranges of porosity, strength and P-wave velocity. Saito, 1981.
The significant differences of behaviour caused by porosity reappear when degree of water saturation and its effect on Vpare shown side-by-side in Figure 2.17a and 2.17b. The higher porosities corresponding to higher weathering grades show very strong (even 200–300%) increases in Vp from initial low values, as saturation exceeds about 85%. Much less sensitivity to saturation (just a weak linear effect) was seen for the fresher, low porosity, high Vpsamples, where Vpincreased from just 5 km/s to 5.5 km/s with saturation, in the case of a low porosity sample.
The Vp/Vsratios that Saito derived from many hun-dreds of data are shown in Figure 2.17c. These particular data are for dry samples. Vp/Vsratios are seen to reduce from about 2.0 at low velocity to about 1.6 at high vel-ocity, broadly following the trends discussed in Chapter 1.
An example of the effect of saturation is given a sim-ple theoretical basis by Grainger et al., 1973. Their eval-uation of chalk foundation qualities at the proposed site for a proton accelerator facility in Norfolk, England revealed one anomalous result, when low quality chalk (grade V), which was normally sampled above the water
(a) (b)
(c)
Figure 2.17 Top: a), b) effect of water saturation on Vp. Bottom: c) Dry Vs/Vptrend over a wide range of Vp. Saito, 1981.
where Vfl velocity in fluid, Vsdvelocity in solid, and
ratio of the path length in the fluid to the total path length (i.e. the ‘porosity’) The authors assumed Vsd2.3 km/s for the intact chalk fragments, and first assumed dry conditions with VflVair0.33 km/s, when substituting the meas-ured value for grade V 0.7 km/s in equation 2.1, to give 0.29. Returning to the assumed saturated conditions, using the calculated ‘porosity’ of 0.29 and VflVwater1.44 km/s, the authors calculated a P-wave velocity for the saturated chalk of 1.97 km/s, close to that measured by the shallow refraction seismic.
An interesting variant of the above time average equation is illustrated for the case of jointed rock, by the manner in which joints are assumed to change the seis-mic velocity. McDowell, 1993, presented the classic equation of Wyllie et al., in the form:
(2.2) where L is the path length
n is the number of joints
w is the average width of the joints
In practice the velocity through dry jointed rock is lower than given by the above, even when the velocity through air (Vp330 m/s) is taken into account. This is because an air-filled joint will tend to act as an acoustic barrier, except round its ends or across points of con-tact. The actual travel distance has increased, but (L) has not been corrected in the above equation.
In the case of water-filled (Vp1.44 km/s) or clay-filled joints, the formula is likely to be more correct, due to the improved coupling across the joint walls. The saturated condition was successfully modelled by the matrix version of the time average equation, in the above
the degree of saturation on Vpin the absence of pres-sure (Figure 2.17a,b). In fact, the combined effect of degree of saturation and stress level have significant influ-ence in rock engineering projects due to the common
‘environmental changes’ that are introduced when we excavate a tunnel, slope or foundation, causing changes of stress (especially unloading) and changes in the pore pressures and drainage routes in the so-called ‘excav-ation disturbed zone’ (EDZ), which will be reviewed in detail in Chapter 7.
The excavation process (blasting, boring, ripping, etc.) causes stress redistribution and the release of radial stresses. Monitoring of Vpin such zones sometimes shows areas of increase, but more usually significant reduc-tions in velocity, especially when the rock mass is signifi-cantly jointed or damaged by the high tangential stresses, and by the excavation process itself, particularly if by less careful versions of drilling-and-blasting.
It is usually assumed that the release of radial stress and the formation of new fractures by blast gasses are the two chief causes of velocity (and modulus) reductions in the EDZ. However, the results of tests on the effect of saturation in weathered and micro-cracked materials (Saito, 1981 and Kelsall et al., 1986) seen in Figures 2.7 and 2.17, obviously suggest a third mechanism of vel-ocity reduction, namely drying out. The presence or absence of stress and the dry or saturated state create the largest ‘environmental’ changes to Vpbesides weathering state (n%, , c).
Nur and Simmons, 1969, classic experiment with repeated measurements of Vpon a sample of Chelmsford granite (n 1%) showed a reduction of Vp from 5.4 km/s (when the sample was saturated) to a value of about 3.9 km/s after four days at room temperature, while drying out. The rapid change in the first 5 hours, even though the rock is of low porosity, is seen in Figure 2.18.
Nur and Simmons, 1969, data also show very strong sensitivity to confining stress, especially in the case of dry samples, which would mean that an unloaded tun-nel wall ( r0) in a dried-out rock mass would tend to show significantly lower velocities than if still saturated.
L
If velocity reductions appear to exceed what one would expect in relation to reasonable modulus reductions in an EDZ (from Chapter 7), then drying out seems to be a distinct possibility. The tabulations below, that also belong with high stress data from Part II, show the potential strength of such effects, in comparing dry and saturated samples. (Data extracted from Nur and Simmons tabulations, and rounded).
The very fine grain size in the Solenhofen limestone (0.01 mm) compared to the millimetre-size, or several millimetre-size grains of the other rocks, and its complete lack of crack porosity is the reason for the almost com-plete lack of pressure sensitivity for this rock. Micro-cracks are presumably the chief cause of the above sensitivities to pressure and degree of saturation in the case of the
crystalline rocks (upper half of Table 2.2). A large-scale parallel would be the effect of ‘environment’ (stress and degree of saturation) on jointed rock which we will see in other data sets in later chapters, in particular the data connected with EDZ experiments (Chapter 7).
To conclude this section on the combined effects of mois-ture and pressure, some data sets will be ‘borrowed’ from future topics in this book, namely the higher pressure world of Part II, relevant to petroleum reservoirs and earthquake related tectonophysics.
An idea of the eventual non-linear nature of Vp-stress data, is given in some early King, 1966, experiments with hydrostatic loading of sandstones, shown in Figure 2.19 with classic psi and ft/sec units. The water-saturated and dry states show classic ‘knee’ shapes, and velocities that begin to converge at high stress, due to closure of microcracks. The improved coupling with water, still gives the highest velocity in the saturated state. The maximum pressures in King’s experiments were about 35 MPa.
The strong effect of extreme confining pressure, espe-cially when these pressures go far beyond the uniaxial strength of the rocks, is typically illustrated by classic
‘knee’ shaped Vp– 3curves. Figure 2.20 shows a variety of behaviours from high pressure laboratory test results on dry samples, given by Wepfer and Christensen, 1991.
A compressible shale (3.0 to 5.7 km/s) and a porous sandstone (2.2 to 4.0 km/s) show strongest effects of con-fining pressure, while low porosity sandstone, dolomite and limestone show only 200 to 300 m/s increases. The authors refer to velocity hysteresis; the effect of pressure in closing cracks in the stress range 0–200 MPa (0–2 kb) is
Figure 2.18 Slow air-drying of a saturated sample of granite reduces Vpby 1.5 km/s. Nur and Simmons, 1969.
Table 2.2 Confining pressure and dry/saturation effects on the Vp (km/s) of some hard rocks (Nur and Simmons, 1969).
Confining Pressure (MPa)
Vp km/s Rock type Porosity 0 5 10 20 40
dry Casco granite 0.7% 3.3 4.2 5.1 5.7 6.0
saturated 5.3 5.8 6.0 6.1 6.3
dry Westerly granite 0.9% 3.8 4.5 5.0 5.3 5.6
saturated 5.5 5.6 5.7 5.8 5.9
dry Troy granite 0.2% 4.5 5.7 5.9 6.2 6.3
saturated 5.7 6.2 6.2 6.3 6.4
dry Webatuck dolomite 0.7% 5.0 5.9 6.4 6.7 6.9
saturated 6.4 6.6 6.7 6.8 6.9
dry Solenhofen limestone 4.7% 5.6 5.6 5.6 5.6 5.6
saturated 5.6 5.6 5.6 5.7 5.7
dry Bedford limestone 12.3% 2.6 2.8 3.0 3.4 3.8
saturated 4.5 4.6 4.7 4.8 4.8
permafrost, and monitoring of the ground-freezing method, for tunnelling though unstable water bearing areas under environmentally-sensitive areas such as city streets, could each benefit from seismic monitoring to determine the progression or regression of the ice front.
Data given by Timur, 1968, show velocity increases upon freezing that vary from about 20 to 50% for many saturated porous rocks, as compared to their P-wave velocities at room temperature. In general, the largest increases are for the most porous rocks. A shale showed only 8% increase. Dry rock samples are hardly affected by cooling below 0°C.
The enormously contrasted temperature-velocity graphs for the dry and saturated states, for the first few
Figure 2.20 High pressure effects on Vp(500 to 1000 MPa) for a variety of rock types. Wepfer and Christensen, 1991.
Figure 2.19 Effect of dry and water-saturated states on Vp -versus-stress, for a sandstone, King, 1966. (Note: an inter-mediate curve for kerogen, lying just below the water-saturated curve, has been removed since not relevant to Part I).
degrees below 0°C, is nicely demonstrated in Figure 2.21. This contrast is due to the different rates of freez-ing in pore volumes that have different area/volume ratios. Surprisingly perhaps, the author explains that the smallest pores actually freeze later due to less favourable area/ volume ratios. In the ‘macro-discontinuity’ world
of jointed rock, one would expect that the smaller, finer tips of cracks and joints would freeze first, due to the more stationary conditions, making ‘ice-wedging’
such an effective mechanism of weathering in moun-tainous terrain, and in more northerly and southerly climates.
(a)
(b)
Figure 2.21 Contrasting effects of low temperature on Vpfor Berea sandstone in the dry and wet state, with 131.3 MPa in each case.
Timur, 1968.
3
In this chapter the ‘simple’ approach to anisotropy caused by micro-cracks or jointing will be taken, considering principally P-wave, azimuthal anisotropy, and anisotropy caused by stress difference. Besides micro-cracks that may be aligned due to tectonic history or due to existing or applied stress anisotropy, there will be fundamental rea-sons for velocity anisotropy in foliated, schistose, layered or inter-bedded rocks with unequal layer stiffness. When jointing and faulting are included, with the special effects of stress anisotropy on these larger scale features, the potential causes of velocity anisotropy will be numerous.
Although velocity anisotropy complicates interpretation, at the same time it also provides important information for a rock engineering project, and of course for a frac-tured petroleum reservoir, if correctly interpreted. It will be seen that the classic alignment of a dominant joint set with the maximum horizontal stress direction is often a cause of a double-anisotropy effect. Both the near-surface and high stress treatment of P-wave anisotropy, as intro-duced in this chapter, will be supplemented in Chapter 14, by studies at considerably greater depth, principally in fractured reservoirs. In Chapter 15 the anisotropy information found in shear waves will finally be the focus of attention, as a lot more information is contained in waves that polarize in parallel (fast qS1), and (slow qS2) perpendicular directions relative to the discontinuities.
These shear wave components show dispersive, frequency dependent levels of anisotropy, caused, in principle, by the dimensions, density and stiffnesses of the fracturing and jointing. There are also those who attribute the shear-wave anisotropy at depth mostly to micro-cracks.
3.1 An introduction to velocity