Physical Model Tests

Physical model tests have developed within the field of geomechanics basically because of the difficulties and costs associated with full scale testing in the field. Model tests provide the means of simulating the conditions of an actual slope in a controlled environment, where parameters more easily can be varied and their effect on the stability of the slope studied.

They also provide the opportunity of testing up to, and beyond, the point of failure, something which can be cumbersome in the field. Model tests are perhaps not a true design method since it is not possible to calculate a slope angle directly from the results. For this, several tests with varying slope angles would need to be carried out and the results compared. On the other

hand, physical models have been very successful in that they have dramatically increased the knowledge and understanding of the possible failure modes in rock slopes (Pentz, 1971;

Stacey, 1973), as was described in Section 3.3.4 in this report. Today, numerical methods have to some extent replaced physical model tests as a means of conducting sensitivity studies.

Nevertheless, model tests should not be neglected as tools to investigate the fundamental failure mechanisms in rock masses.

Three different types of model tests can be distinguished. In the first type of tests, a model material is used in a down-scaled slope model. Loading is only by the gravity forces

developed from the self-weight of the model material. However, horizontal loads can also be applied to the boundaries of the model, thus simulating a horizontal virgin stress field. Since only gravitational loading is used, this type of testing requires relatively large model

dimensions and a model material which is substantially weaker than rock. Good examples of such model tests were those conducted by Barton (1971, 1972, 1974). Model materials are often different types of plaster-sand-water mixes. To ensure correct scaling of the material properties, a number of similitude laws must be fulfilled. This is by far the greatest difficulty associated with this testing method, and the results are often very sensitive to the choice of model material. Boundary effects can also come into play, as well as the manner in which joints are simulated in the model material.

In the second group of model tests, larger loads are applied to a model using conventional testing machines in a laboratory. Uniaxial, biaxial or triaxial loading can be applied. In these tests, stronger materials can be used which are more reminiscent of a hard rock, for example, high strength concrete. For most testing machines, there is a restriction on specimen size which can make it difficult to test a realistic slope geometry when including discontinuities.

Moreover, artificial loading by testing machines does not replicate the actual stress state in a pit slope. This severely restricts the applicability of these tests. Nevertheless, very interesting results have been obtained regarding failure mechanisms using these types of model tests, as was discussed in Section 3.3.4 (Ladanyi and Archambault, 1969, 1972, 1980; Einstein et al., 1970).

The third group of model tests is centrifuge testing. Here, increased body forces are applied by rotating the model horizontally in a high speed centrifuge, thus generating centrifugal forces in the sample (Figure 4.9). This is equivalent to increasing the gravity forces acting on the model slope. The centrifugal acceleration constitutes the scale coefficient for the physical dimensions of the model. Provided that high accelerations can be generated, this approach greatly reduces the demand for a weak model material. In soil mechanics, centrifuge testing is frequently carried out using the actual soil and hence, no material property scaling is necessary

(Veder, 1981; Ko, 1988; Schofield, 1988; Ohshima et al., 1991). However, only gravitational forces can be generated in centrifuges, making centrifuge testing less applicable to cases where high horizontal virgin stresses are believed to be of importance. A big advantage of using centrifuge models it that it is relatively easy to verify the correctness of the models by running several tests with different model sizes and different accelerations ("modeling of models").

Scaling relations can thus be validated, as well as size effects (Ko, 1988).

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The possibility of avoiding the use of a model material makes centrifuge testing very appealing also for rock slopes, although only gravitational forces can be simulated. There is, however, a problem associated with centrifuge testing of rock slopes. Since rocks have much higher strengths than soils, high capacity centrifuges are required. Soil testing is normally conducted with accelerations of less than 300 g (g being the gravitational acceleration at ground surface).

For testing rocks up to the point of failure, much higher accelerations are required. Clark (1988) estimated that for medium to hard rocks, an acceleration of at least 1000 g would be required.

There are a only few centrifuges available which can generate these accelerations. Because of the need to include discontinuities in the model, centrifuge testing of rocks also requires somewhat larger model dimensions, compared to soil testing. Larger model dimensions requires a centrifuge which, besides a high acceleration, also can handle a large mass.

Unfortunately, these two objectives are not easily met simultaneously. Among the centrifuges which can generate 1000 g or more, the load capacity for the models is generally in the range of 1 to 50 kg (Clark, 1988). To put this into perspective, assume that a 500 meter high rock slope is to be simulated. With an acceleration of 1000 g, the slope height would be 0.5

meters. Testing a section through the pit including some surrounding rock increases the size to something of the order of 1 m². Even with a very thin model of say 5 cm thickness, the mass of the model would be 135 kg. This is more than most of these high speed centrifuges can handle, and the lateral model size is still quite small if natural discontinuities are to be used. A new extremely powerful centrifuge is being developed and built at the WES

(Waterways Experiment Station) in Vicksburg, Mississippi. This centrifuge will have a radius of 6.5 meters and have the ability to accelerate 2000 kg at 350 g or 8000 kg at 143 g. In spite of the fact that this is stated to be the world's most powerful engineering centrifuge, it still cannot fulfill the requirements for rock testing discussed above.

The material scale effect introduced due to the substantial down-scaling of the model dimensions can be very significant. For coarse-grained soils, the grain size can be relatively large in relation to the model slope size. This effect is even more pronounced for a

discontinuous rock mass. First, it can be difficult to obtain representative samples of jointed rock masses and secondly, there is a problem with the joint properties and their

scale-dependency. As was discussed in Section 3.5, joint shear strengths depend on the roughness of the joint surface. In a small scale sample the size of the joint surface asperities would be greatly overestimated in relation to the size of the model pit slope. Furthermore,

displacements are smaller on a model scale than in full scale situations and since the mobilized joint shear strength depends on the absolute magnitude of displacement along the joint surface, this violates the scaling rules. This phenomenon was verified experimentally by Iglesia et al.

(1991), who concluded that centrifuge testing is less reliable for testing models involving discontinuities.

One way of avoiding the problem with high speed, high capacity centrifuges is to use a model material. This was the approach taken by Stacey (1973), which is an example of one of the few centrifuge tests specifically aimed at investigating rock slope stability (see Section 3.3.4).

On the downside, this approach greatly diminishes the appeal of centrifuge testing since material property scaling using similitude laws becomes necessary. Other problems associated with centrifuge testing are that it is difficult to completely avoid vertical velocities due to vertical shaking of the centrifuge arm, and boundary effects from the model frame cannot be neglected. Miniature instruments may also have to be developed to be able to measure the performance of the model. It is also relatively complicated, although not impossible, to test saturated model samples, and care must be taken to simulate the correct stress path up to failure in the model (Ko, 1988; Schofield, 1988).

Despite these obstacles, it is believed that centrifuge testing of physical scale models can be of some value for further studies of large scale slope stability. One approach is to use centrifuge

testing for the validation of numerical models (Ko, 1988; Iglesia, 1991). It is much easier to compare the results from a numerical analysis of a certain type of slope behavior with model test results than against field observations. Parameter studies can be more easily conducted in centrifuge testing. Moreover, the model slope does not necessarily have to replicate all aspects of the behavior of an actual slope, which permits simplifications of model procedures and reduces the demands on the centrifuges. For this type of testing, the emphasis should be placed on the investigation of new phenomena and fundamental mechanisms of failure.

At this stage it must also be considered whether an even simpler test, such as the loading of a sample in a conventional testing machine, also can provide sufficient data for verification and validation of numerical or analytical design methods. The advantage of using such a test arrangement is that the test facilities are much more common compared to high capacity centrifuges. The test procedure would also be much simpler and less expensive thus

permitting more tests to be conducted. The loading conditions in such a test are obviously not exactly similar to those in an actual open pit slope. The issue as to whether the correct failure mechanisms can be reproduced must first be clarified before conducting such tests.