Deformability tests

ISRM (1975) divide deformability tests into two types; static and dynamic. Static deformability tests involve the incremental application of a known load over a given area of the rock mass while recording measurements of the deformational response of the rock mass after each increment of load is applied. Dynamic deformability tests measure the propagation velocity of sound waves through a known volume of the rock mass. ISRM

(1975) describes some in-situ static and dynamic tests used in determining rock mass deformability. Most structures on rock usually have a bearing area vastly greater than the average discontinuity spacing of the rock foundation. Therefore the deformation of the rock mass beneath the structure consists of deformations of both the intact rock and along and across the discontinuities.

The aim of deformability tests is to estimate the deformation modulus, E. The results of a deformability test are typically analysed using elastic theory. The use of elastic theory to evaluate these parameters is justified by the fact that the stress strain curve is close to linear and the creep properties are secondary (Lama and Vutukuri, 1978b).

The term “deformation modulus” is used instead of “elastic modulus” or “Young’s modulus” because jointed rock masses do not behave elastically (ISRM, 1975). Therefore the deformation modulus is defined as the ratio of stress to strain during loading of a rock mass including elastic and inelastic behaviour, whereas the elastic modulus is the ratio of stress to strain below a proportional limit.

The different methods of estimating the deformation modulus do not necessarily give similar estimates of the deformation modulus. Generally, Estatic < Eearthquake < Eseismic <

Eintact rock (Wylie, 1999).

Eintact rock clearly offers the greatest estimate of deformation modulus because there is no

significant deformation across discontinuity planes which are a major factor in lower deformation moduli in rock masses. Eearthquake is the modulus of the rock mass shaking at

1-10 Hz.

Eseismic is greater than Estatic because the seismic pulse is applied over a very short time

interval and more significantly, it is a very low stress pulse such that the measured response is entirely elastic (Hendron, 1968). The more gradual application of load in Estatic tests comprises both elastic and plastic deformation.

2.3.2.3.1.1 Static methods of deformability testing: The Plate bearing test.

Lama and Vutukuri (1978b) divide static tests into three types:

1. Plate bearing tests

2. Pressure tunnel tests

3. Borehole tests.

The plate bearing test is the simplest and most common of these three tests and as such is reviewed here. As its name suggests, the pressure tunnel test is applied to the surface of tunnel. No records of pressure tunnel tests have been found on closely jointed rock masses in New Zealand, and are therefore not considered in this thesis. Similarly borehole tests have only been developed with the last 20 years and no information has been found with respect to tests within closely jointed rock masses. Accordingly, the pate bearing test will only be considered here.

2.3.2.3.1.1.1 Description

The plate bearing test involves applying a normal load over a prepared flat surface through a flexible or rigid plate and measuring the resulting deformations at various points either on the plate or surrounding it. These deflection measurements can then be entered into an expression derived from the Boussinesq solution (Timoshenko and Goodier, 1951) for the deflection beneath a point load on an elastic half space to back- calculate the deformation modulus, E or the Poisson’s ratio, ν.

The expression derived from the Boussinesq solution is dependent upon the shape of the plate and the measurement point at which the deflection is measured. A variety of expressions for various combinations of plate shapes, measurement points and layered foundations have been collated in Poulos and Davis (1974). Solutions for the deformation modulus are dependent on whether the plate is rigid or flexible.

Figure 2.13: Giroud (1968) influence factors for elastic deformation beneath rectangle (reproduced from Poulos and Davis, 1974).

The most common plate shape is that of a square or rectangle. The solution for this shape for vertical displacement at the surface of a flexible plate is given by Giroud (1968) as follows

(

)

_pbI E δν 2 1− = (2.3)

where δ = surface deformation. p = uniform load on the plate.

b = length of the shorter side of the plate.

I is the influence factor (dimensionless) which is a function of α and the point of measurement as shown in Figure 2.13.

It is assumed in this method that the plate is flexible, the load is uniformly distributed across the plate and that the foundation is homogeneous and isotropic. Because this is clearly not the case for all rock masses, some errors may result. While errors will not be that significant for rigid plates, if the rock layer in contact with the rigid plate is allowed to displace laterally, the resulting parabolic loading will give extreme conditions.

The solution for a rigid plate is given by Whitman and Richart (1967) (as reported in Poulos and Davis, 1974)) as follows;

(

)

BL P E z δβ ν2 1− =

where P = total vertical load

B, L = loading dimensions

βz = factor dependent on L and B as shown in Figure 2.14.

Figure 2.14: Whitman and Richart (1968) influence factor for elastic deformation beneath rigid rectangle (reproduced from Poulos and Davis, 1974).

Ideally, several loading plates of various sizes should be used to extrapolate the deformation modulus at the scale of interest. However due to economic considerations and the difficulty of applying suitably high uniform pressures, the loaded area is

generally less than 1m2 (Stagg, 1968). Tests are usually carried out in excavations so that the rock mass is undisturbed.

2.3.2.3.1.1.2 Interpretation of results

Figure 2.15 represents the typical results expected from a plate bearing test. The deformation modulus (Ed) is equal to the total deformation after load (P1/Dt1) and the

elastic modulus (Ee) is equal to (P/D1). The initial modulus, E0 is represented by the

gradient of line C.

Not all pressure displacement curves are similar to Figure 2.15. Figure 2.16 shows the four types of pressure displacement curves.

Curve a is the most common type whereby increasing pressure on the loading plate steadily compacts the joints within the rock mass. This curve would be typical of highly fractured rocks with high intact strengths. Dvorak & Peter (1961) stated that rock masses that exhibit this behaviour would have super-linear compressibility.

Figure 2.16: Typical types of pressure displacement curves. (Lama and Vutukuri, 1978b).

Curve b is the result of crushing of weak material beneath the loading pad. This in turn attracts more load onto the weaker material thus accelerating the vertical deformations measured on the loading pad with increasing load. Ultimately a bearing failure of the material may occur. These rock masses that exhibit sub-linear compressibility (Dvorak & Peter, 1961).

Curve c results from stress causing localised failures within the rock mass. As the weaker material is crushed, load is transferred onto stiffer material until the stress reaches a level at which local failure of the stiff material occurs until load is transferred onto stiffer material and so on.

Curve d is the result of application of load onto unweathered and undisturbed rock masses previously subjected to high stresses such as in deep excavations.

Each curve in Figure 2.16 also shows a certain amount of hysteresis on unloading resulting from resistance due to friction along joints and plastic deformations following relaxation after removal of load. Lama and Vutukuri (1978b) state that hysteresis is more

prominent in more weathered and fractured rock masses (curve b) and therefore the ratio of the deformation modulus at loading and unloading can be considered to be a function of the jointing and weathering within a rock mass.

Figure 2.17: Stress displacement curve showing blast damage (Lama and Vutukuri, 1978b).

Lama and Vutukuri (1978b) list four difficulties when estimating modulus values from plate loading tests.

1. Care should be taken when plate loading in trenches as the conditions beneath the plate may not satisfy the assumption of a semi-infinite elastic half space. The flat surface around the loaded area should be at least equal to the loaded area.

2. Initial deformation of the ground surface is influenced by the condition of the material layers closest to the loading plate. Figure 2.17 shows initially large deflections with load as the blast damaged section of the rock mass is loaded. At higher levels of stress the

elastic moduli for each unload-reload cycle appear to be more consistent as the undamaged material further from the loading plate is stressed.

The rock layers further from the plate may be less stiff than the closest layers as shown in Figure 2.18. Ultimately only the material within two diameters of the plate significantly affects the deformation at the surface. Therefore if the plate is increased in size more information can be obtained about the lower layers at the expense of higher and thinner layers. Also as the applied stress upon the rock mass increases, the effect of any anisotropy on the modulus value will decrease due to the greater confining stresses.

Figure 2.18: Stress displacement curve showing previous relaxation of rock. (Lama and Vutukuri, 1978b).

3. In closely jointed or altered rock and for small loading plates subject to sustained or cyclic loading, high shear stresses can develop beneath the loading plate, which serve to lower the back-calculated value for the modulus.

4. Joint orientations can affect the distribution of stress beneath the loaded plate. Similar behaviour can be found in inhomogeneous materials where one layer is much stiffer than another. This can cause excess stress to be attracted onto the stiffer rock and cause higher deformation than expected in that strata and less in the other. In this case, an appreciation of scale is needed and care should be taken when selecting modulus values.

2.3.2.3.1.2 Dynamic methods of deformability testing

Dynamic methods determine the deformation moduli by measuring the speed of propagation of both longitudinal and transverse sound waves reflected from within the rock mass. The sound wave is generated by hitting the ground with a hammer or discharging an explosive source and received through a geophone placed at a known distance from the application point of the disturbance.

The elastic modulus of an isotropic elastic material is calculated from the following expressions (Stagg, 1968);

For longitudinal waves, and

(

)(

)

(

νν)

υ

ρ

α

− − + = 1 2 1 1 2 E (2.4)

For transverse waves

(

υ

)

ρ

β +

=2 2 1

E (2.5)

where α = longitudinal wave velocity

ρ = rock mass density.

For closely jointed rock masses in-situ seismic velocities will tend to be low because of attenuation through the discontinuity network. Seismic velocities will be slightly greater if the rock mass is saturated.

Dynamic tests are cheap and rapid and can affect a significant proportion of the rock mass of interest, but do not often appear to correlate well to moduli derived from static tests. Stagg (1968) suggests two reasons that may account for this. Firstly, while static deformability tests are affected by fissures within the rock mass, dynamic tests will not be as affected, especially if these are filled with water, and secondly, seismic velocities are more affected by elastic strains and not plastic strains, whereas a static test is affected by both.

In document Rock mass strength and deformability of unweathered closely jointed New Zealand greywacke (Page 57-67)