Modelo sistémico

tests

During the 1970s and 1980s, a series of large scale, in situ block tests were performed by Pratt and co-workers in the USA, in order to evaluate test methods and instrumentation suitable for nuclear waste disposal projects which were being planned at that time. The block tests were designed to give large-scale properties (1 to 3 metres scale) under controlled loading condi-tions (using flatjacks), and some were at elevated tem-peratures (using borehole heaters).

The effects of stress application on velocity and per-meability in jointed granite were first investigated on a large scale by Pratt et al., 1977, who used a flat-jack loaded block measuring 3  3  3 m, which con-tained three sub-parallel, vertical joints. The rock was an anisotropic, but quite massive granite, and the site was in Wyoming, USA. The authors investigated vel-ocity changes as a function of applied stress (0 to 9 MPa) applied either parallel or perpendicular to the jointing (so-called E-W or N-S velocities, respectively).

Results for different measurement lengths, including 0.15 m long laboratory samples, are shown in Figure 9.6.

The lab samples, which may have experienced micro-cracking on release by drilling, show the strongest V_p response to stress increase. Although the 3 m cubed block was released on all four vertical sides, the ‘contact’ with

‘virgin’ rock stresses along its intact base may presumably be the reason for less response of V_pto stress along these in situ measurement lengths of 1.0 and 2.85 metres. The block also remained nearly saturated, compared to the lab sample ‘0.15 m, D’ (D  dry, S  saturated).

More details of the in situ response of rock mass velocity to increasing stress are given in Figure 9.6c.

Increased wetting of the surface of the block caused the small (0.1 km/s) increases in velocity seen between the pairs of curves 4 and 9, 1 and 8 respectively. The authors finally presented a composite plot (fully coupled behav-iour) of joint displacement (mm), flow rate along joint J₁ (cm³/s) and velocity, each as a function of stress.

Figure 9.6d shows that increased closure of the joint after about 2 to 3 MPa normal loading, caused a plateau on the permeability-stress curve, and a sharp reduction in the sensitivity of V_pto further stress increase, espe-cially beyond 5 MPa loading. This is consistent with stress-V_p data reviewed in Chapter 5, and broadly in line with the non-linear effect of depth on velocity shown in Figures 5.36, 9.4 and 9.5.

Another in situ block test, this time in jointed sand-stone in Colorado, USA was reported by Swolfs et al., 1981. The block was 2 m³in volume and contained a near-vertical joint. The joint was calcite filled, and appeared to be about 1.5 mm wide at the surface. The P-wave velocity of the surrounding jointed rock of about 1.5 km/s appeared to be independent of joint fre-quency and orientation. This is surprising in view of the presumably drained state of the test site (Figure 9.7a). However, ‘moist’ laboratory samples had about the same value of V_p.

In situ stresses of about 1 MPa were relieved by line drilling of three sides of the block. The long side of 2.3 metres and 1.2 m depth was parallel to the joint. This resulted in V_pand V_schanging from 1.5 and 0.8 km/s to 0.9 and 0.5 km/s respectively. Calculated values of E_dynamicthereby changed from 3.3 to 1.2 GPa, assum-ing a rock density of 1.97 gm/cm³, because the sand-stone has a high porosity of 25%. The uniaxial strength was about 11 MPa, and static Young’s modulus was 2.3 GPa, based on laboratory samples. The block was loaded uniaxially (normal to the joint) and biaxially, using multiple flatjacks in each of the three slots.

The effect on P-wave and S-wave velocities is shown in Figures 9.7c and d. Pre-excavation velocities (shaded lines) were reached at about 1 MPa. This is exactly the stress acting when undisturbed velocities were measured.

An anomalous increase in joint deformation was also recorded above this same stress level of about 1 MPa.

The authors also applied shear stresses to the joint by activating the flatjacks at the end of the block, while holding a constant normal stress across the joint (0.7 or 1.4 MPa). Since the block was attached at its base, joint shearing was limited (even at the top surface of the block) to about 0.7 mm, which represents pre-peak strength. Dilation was negligible (10 m), and is per-haps the reason why V_pand V_sslightly increased during application of shear stress to 3.0 MPa, probably mostly in response to the simultaneous application of normal stress of 0.7 or 1.4 MPa (Figure 9.7a). If significant dilation had occurred during increased shearing, a reduced velocity would presumably have resulted. The small velocity response to moderate stress change seems to be a feature of relatively unjointed, porous rock.

The authors also performed a permeability test using injection in a central hole that intersected the joint.

They calculated a permeability of 3.7  10^7m/s.

There are several interesting coincidental values of the reported tests that we can compare with the Q_c-V_p -M-L model (Figure 9.4). If we follow the ambient

P-wave velocity of 1.5 km/s at the ambient stress of about 1 MPa (equivalent to about 20–25 metres of overbur-den) in the lower left-hand corner of the Q-V_p-M-L chart, we find a Q_cvalue of about 0.4 at 25% porosity.

Independent of this, the 1/Q_cmodel for Lugeon estima-tion suggests a back-calculated Qc-value of 0.27. This is very close to the velocity-based estimate. The low uni-axial strength of 11 MPa means that the Q-value can be estimated as about (0.4 or 0.27) 100/11  3.6 or 2.5.

These are close on a six-order of magnitude Q-scale.

The estimation of deformation modulus (M) can be based directly on V_paccording to Figure 9.4. Thus we see that 2 GPa is estimated, which is close to the labora-tory value of 2.3 GPa, and to the E_dynamic estimates of 1.2 GPa (unloaded) and 3.3 GPa (undisturbed, loaded to approximately 1 MPa). In this case this deformation modulus estimate is based on V_p (Figure 9.4, right-hand column of M values derived from):

(9.3) and this gives a more accurate estimate of 2.1 GPa when V_p1.5 km/s. The relevant modulus value is also obtained using the direct equation between M and Q:

(9.4) which again gives an estimated 2.1 GPa, when using Q
 0.01. We refer to Q
as ‘Q-prime’ since it has not been corrected for porosity. The real Q_cvalue needs the porosity correction, and final correction for the ratio _c/100, to reach the assumed rock mass quality Q, which we estimated from both velocity measurement and independent Lugeon testing as ranging from about 2.7 to 3.6.

Further checks on rock mass quality can be made the direct way by using the authors’ descriptions of the jointing; three sets, spaced at 0.6, 0.9 and 0.3 metres, with the most prominent set filled with about 3 mm of calcite. Via the volumetric joint count of Palmström, 1983, we can calculate J_v6.1, and RQD
95%.

M
10Q^1/3_c M
10^{(Vp 0.5 )/3}

Figure 9.7 a,b) Loaded block test in (drained) unit of in situ sand-stone containing a vertical joint, loaded on three sides by flat-jacks. c,d) V_p– and V_s– stress trends for uniax-ial and biaxuniax-ial loading, compared with pre-slot veloci-ties – shaded. e) Effect of joint shearing on V_pat two different normal stress levels. Swolfs et al., 1981.

The independently estimated Q-value is therefore approximately as follows:

All of the above estimates are very close, considering the logarithmic (six orders of magnitude) Q-value rock quality scale. We have thus demonstrated that Q, V_p, M and L are inter-related, and that we may be able to include the Lugeon value in this inter-relation, if care is taken to eliminate irrelevant non-deforming, channel flow cases. The implication is that depth or stress level, also an axis in Figure 9.4, also plays an important role in these mutual inter-relationships.

Using an analogue material for heavily jointed rock, namely coal, one can also see how there is great potential sensitivity between velocity, stress level and permeability,

which will also be present in jointed rock masses at large scale, when in situ effective stress states are altered by large scale pumping or injection experiments.

Three bituminous coals having large differences in hardness and degree of jointing (cleats, etc.) showed almost equally great sensitivity to applied stress level, despite their five order of magnitude range of perme-abilities (0.1 to 100 millidarcys). Somerton et al., 1975, applied mean stresses over the range 1 to 14 MPa and noted between two and three orders of magnitude reduction in permeability (Figure 9.8).

Simultaneous monitoring of ultrasonic velocity showed increases of velocity of about 0.3 to 0.6 km/s (from 1.8 km/s when stress-free) for each order of mag-nitude reduction in permeability. This is shown in Figure 9.9a together with the V_p-stress behaviour of one of the coals in Figure 9.9b. Both these figures indicate greatest changes in V_p and permeability at the lowest

Q RQD

Figure 9.8 Permeability – stress coupling for three bituminous coals, due to the detailed cleating or jointing: an extreme ana-logue for jointed rock masses. Somerton et al., 1975.

Figure 9.9 a) Permeability-V_pcoupling for two of the bituminous, cleated coals. b) Velocity-mean stress coupling for one of the cleated coals. Somerton et al., 1975.

stress levels (and lowest velocities), just as found in rock masses, due to improved acoustic coupling across joints.