Density and V P

The strong influence of density on P-wave velocity, and the stabilisation of density below the weathered zone are nicely demonstrated in Figure 2.1 (Ikeda, 1993). The marked fluctuations in velocity at depth were interpreted by the author as due to high shear stresses, which were interpreted from hydraulic fracturing conducted in the same holes. (Presumably the elastic isotropic estimate of _{H max}, based on the ‘3P-Q’ model was several times the magnitude of the measured _{H min}). Note the typical rapid increase in velocities in the 25 to 75 m depth zone, which partly mirror density increases and are partly related to joint closure and less frequent jointing.

In the case of a range of rock types including marl and peridotite, Kujundzíc and Grujíc, 1966 found a linear relation V_p4.75 – 7.3 (r  0.88) for V_p in km/s,

and density  in gm/cm³. Seismic velocities ranged from 2.3 to 6.5 km/s, and densities from 2.1 to 3.0 gm/cm³.

Early Bulgarian experiences with seismic registration of weathering effects are provided by Iliev, 1966. Fresh and weathered monzonite were shown to have the fol-lowing ranges of properties, and linear relationships between V_p–n% and V_p– (gm/cm³). (See Figure 2.2)

V_pkm/s E (GPa) (gm/cm³) n%

Fresh monzonite 5.0 50 2.61 2

Weathered monzonite 1.4 6 2.34 12

The linear V_p–n% and V_p– relationships conceal a non-linear V_p–uniaxial compressive strength trend. When a reduction in V_pdue to _cand due to n% are assumed, the strength of the porosity relationship as above, needs modification. Iliev, 1966, noted that a weathering coef-ficient could usefully be defined as the ratio (V_po–V_pw)/

V_po where sub-scripts (o) and (w) signify fresh and weathered. The coefficient approaches values of 0 and 1 at opposite ends of the weathering scale.

Many of the long span bridges in Japan have been constructed in soft rock such as Tertiary mudstones and sandstones, or weathered Tertiary granites. The long span bridges of the Honshu - Shikoku Bridge system described by Yamamoto et al., 1995, and Ishikawa et al., 1995, had foundation sizes in the 50 to 100 m range but nevertheless had contact pressures as high as 1 to 2 MPa.

For this reason, Japanese authorities devised compre-hensive routines for geological and geotechnical investi-gations. Seismic methods, in situ deformability, strength and classification schemes were used extensively, espe-cially when trying to extrapolate the results of in situ testing at more convenient onshore sites, to the actual undersea locations of the pier foundations.

The data given in Figure 2.3 shows in situ seismic-velocity-based rock classes, porosities, densities and degree of saturation, each intimately linked. This remark-able, and useful diagram covers all the sub-titles of this

Figure 2.1 Influences of weathering, depth of measurement and density on Vp and resistivity. Ikeda, 1993.

The authors used an extended version of the Tanaka and Japan Highways classification (which involved the six classes A, B, C_H, C_M, C_L and D where subscripts mean high, medium and low), and included three

classes at the lowest end of the scale (D_H, D_M, D_L) for rock masses with velocities in the range 1.5 to 2.7 km/s.

Table 2.1 shows the scheme adopted, which cross-cor-relates with deformation modulus, density, porosity and resistivity.

A large collection of laboratory Vp– (gm/cm³), and V_p–n% data is given by Kelsall et al., 1986, for the case of basalts from California and dolerites from S.W. England. Data that fall outside the general trend for the intact rock are ascribed to fissured and persistently microcracked rock, shown by the black data points in Figures 2.4 and 2.5.

The lower seismic velocity of the fissured samples is accentuated by the air-dried state of these samples.

When plotted on a log-linear scale, the uniaxial strength is seen to broadly correlate with the air-dry V_p value. The data set given in Figure 2.6 goes to

Figure 2.2 Effects of weathering on V_pof monzonite are seen in linear V_p-n% and V_p- relationships. Iliev, 1966.

Figure 2.3 Inter-relationships between rock class, Vp, porosity, density and degree of saturation at the Honshu - Shikoku Bridge project in Japan. Ishikawa et al., 1995.

Table 2.1 Extended (low velocity) Japanese classification scheme used at Honshu-Shikoku Bridges, showing cross-correlation of parameters.

Note extreme range of densities due to weathering. Yamamoto et al., 1995.

Rock class V_pr(km/s) Rt ( • m) E_sb(GPa) _c(10³kg/m³) _R(10³kg/m³) n_c(%) n_R(%)

D_L 1.5–1.8 1–4 0.05–0.3 1.7–2.1 1.55–1.75 33–58 50–64

D_M 1.8–2.2 4–7 0.3–0.8 2.1–2.3 1.75–2.0 19–33 37–50

D_H 2.2–2.7 7–12 0.8–1.5 2.3–2.5 2.0–2.15 11–19 27–37

C_L 2.7–3.3 12–20 1.5–3.0 2.5–2.55 2.15–2.3 6–11 20–27

C_M 3.3–4.0 20–50 3.0–6.0 2.55–2.6 2.3–2.4 3.5–6 15–20

C_H 4.0–4.8 50–120 6.0–12.0 2.6–2.65 2.4–2.5 2.0–3.5 11–15

Note: V_pr: P-wave velocity of rock mass; Rt: resistivity of rock mass; E_sb: deformation modulus from pressure meter; _c: density of core; _R: density of rock mass; n_c: porosity of core; n_R: porosity of rock mass.

unusually high levels of strength (500 MPa) and veloc-ity (7.5 km/s); the latter a direct function of the high density (2.9–3.1 gm/cm³) of the dolerites. Note the ratio of V_p (air-dry) to V_p (saturated) given in Figure 2.7. The samples with the pre-existing fissures show greatest contrast in these velocities, due to the positive effect of wave transmission through water filled fissures (or joints).

Before leaving this section on (mostly) V_pand density trends, caused by weathering, it is instructive to also look at extreme V_p values due to exceptionally high dens-ities, both from natural causes and from the influence

of high stresses (1000 MPa or 10 kbars). The velocity of a variety of high density rocks such as dunite and ser-pentinite are shown in Figure 2.8. For densities in the range of 2.5 to 4.5 gm/cc, velocities ranged from 6 to more than 9 km/s at these extremely high pressures (Birch, 1961).

Velocity (and of course density), have been used with success for identifying minerals from host rocks.

Salisbury et al., 2000, used seismic imaging of known ore bodies in central and eastern Canada, together with high pressure laboratory tests, using what they termed a

‘crack closure pressure’ of 200 MPa confining pressure.

They drew various envelopes in velocity-density space, to distinguish commonly occurring sulphide ores, and

Figure 2.4 Effects of dry density on V_p for air-dry samples of dolerites. Note increased density of fissured samples, presumably indicating a subtle change in composition.

Kelsall et al., 1986.

Figure 2.5 Effects of porosity variations on V_pfor air-dry samples of dolerites. Note increased density of the fissured sam-ples, presumably indicating a change in composition.

Kelsall et al., 1986.

typical silicate host rocks. We may select some contrast-ing combinations:

Pyrite: V_p8.0 km/s density  5.0 gm/cm³ (the extreme member) Pyrrhotite: V_p4.7 km/s density  4.6 gm/cm³ Chalcopyrite: V_p5.5 km/s density  4.1 gm/cm³ Serpentinite: V_p5 to density  2.4 to

7 km/s 2.9 gm/cm³

(host rock) At the shallowest depths of the earth’s crust, namely the soil cover, specific depth-density-V_p relationships are also evident. Brandt, 1955, developed a theory for the influence of pressure and porosity (and saturation) on the seismic velocity in porous granular media. His

elasticity-based, Hertz contact theory predicted that V_p should be proportional to the 1/6 power of the effective stress. He then compared (in Figure 2.9) this V_p-depth gradient with test data for soil, clay and gravel meas-ured by Nasu, 1940. The slopes of the test data plotted

Figure 2.6 Vp–_crelation for high strength and weathered rocks.

Kelsall et al., 1986.

Figure 2.7 Air-dry and saturated V_pvalues for intact and fissured samples of dolerite. Kelsall et al., 1986.

Figure 2.8 Extreme Vp-density data for crustal rocks at 1000 MPa confinement. Birch, 1961. (Numbers: next to open cir-cles  mean atomic weights; on diagonal lines  con-stant mean atomic weights (approx.)).

on log (V_p)–log (depth) scales, ranged from 1/2 to 1/7, bracketing his theoretical gradient prediction of 1/6.

In practice this data and the accompanying theory can help to explain the virtual seismic ‘disappearance’ of heavily stressed, faulted gouge at great depth or at large induced stress levels. Such was experienced, for example, ahead of a stuck TBM in an 800 m deep tunnel where cross-hole tomography was designed to investigate a known fault (Contract report, NGI, 1998).