Dilation in granite during servo-controlled triaxial strength tests
Highlights
► A servo-controlled press was prepared to control volumetric strain on triaxial compressive tests. ► A series of unconfined and confined compressive tests were performed on three types of granite rock samples. ► We investigated the stress–strain response particularly focusing dilation. ► The plastic shear-strain and confinement-stress-dependent dilation angle of granite was captured and quantified.
Introduction
Granites, very common in Galicia (NW Spain) as in many other parts of the globe, are typically used as slabs and plaques in construction and civil engineering works and also as aggregate. Underground excavations in granite rock masses for civil engineering and mining applications are also very common, so a better understanding of granite behaviour should contribute to improving design capabilities, construction techniques and safety in the execution of excavations in this type of rock mass.
In the late 1960s and early 1970s, a number of authors [1], [2], [3], [4] were able to study the behaviour of rock failure beyond the peak of the stress–strain curve using a closed loop servo-controlled test machine. In this period also, Crouch [5] improved existing testing capabilities in experimentally determining volumetric strain in the post-failure range of compressive tests. Since then, many other authors (e.g., Medhurst in his doctoral thesis [6] and others [7], [8]) have performed tests in both soft and hard rocks (including coal, limestone, marble, sandstone, quartzite and granite) aimed at obtaining complete stress–strain curves. Although a good knowledge of this curve is of paramount relevance to rock mechanics [9], [10], it is no easy task to estimate it at the scale of the rock mass.
Since avoiding rock mass failure is usually a major rock mechanics goal, knowledge of what happens after failure could seem to be of little or no interest. However, a number of authors [11], [12] have indicated that knowing the post-failure plastic parameters for rock masses is necessary to achieve modelling objectives, understand certain rock behaviour mechanisms and estimate the extent of plastic zones around excavations.
Moreover, the use of numerical modelling has increased substantially in recent years and not only relies on reliable input parameters but also opens up possibilities for more complex and realistic models. Accordingly, now more than ever, it is important to be able to provide realistic representations of the complete stress–strain curve and to correctly characterize rock behaviour in numerical models.
A reasonable parameter for evaluating plastic behaviour is the dilation angle (ψ). However, due to inherent difficulties in obtaining it, dilatancy has seldom been taken into consideration in initial numerical models; and when it was considered, the approach, typically poorly developed and simplistic, generally consisted of an associated flow rule (friction angle made equal to the dilation angle: ϕ=ψ) or a non-associated flow rule (ψ=0). Neither approach is realistic enough [13], [14] and so could result in possible calculation errors.
In an attempt to provide a more correct approach to dilatancy, a number of authors [15], [16], [17], [18], [19], [20], [21], [22] have proposed parameters or models that fit the dilatant behaviour of rocks. The need for real data to compare with modelling results is a common issue in all of these studies and serves as the starting point for our own study. In other words, for samples of three granitic rocks we provide real confined and unconfined stress test data for a press with fully servo-controlled loading.
In recent years, a number of authors have argued that some rocks and rock masses behave in a strain-softening manner [23], which means that, after achieving maximum stress, they can still withstand some load. Strain-softening is founded in the incremental theory of plasticity and has been developed to model plastic deformation processes. One of the main features of strain-softening is that the failure criterion and the plastic potential do not only depend on the stress tensor σij, but also on a plastic parameter generically denoted as η or γp which takes account for the processes and mode of strength transition, in such a way that this plastic parameter is null in the elastic region, and if η>0, the strain softening appears until the residual strength is reached. Thus, the behaviour model is plastic-strain-dependent.
In order to characterize a strain-softening rock or rock mass, the following basic information is needed: (a) Elastic parameters; (b) Peak, evolving and residual failure criteria; and (c) Post-failure deformability parameters.
To completely characterize post-failure behaviour, we need to know not only the evolving and residual failure criteria, but also the parameters that link the post-failure stress-strain relationship and the relationship between strains. A correct description could be achieved, for instance, if we know either (a) the dilation angle and the drop modulus (computed as the mean negative slope of the curve σ1–ε1 after peak strength and in the first 50% of softening) or (b) the dilatancy and the plastic parameter values for which dilatancy and evolving failure criterion are achieved.
Due to the complex nature of this kind of behaviour, standard presses cannot properly compute rock sample strain once peak strength is surpassed. Therefore, a press with servo-controlled loading capable of controlling post-failure processes is necessary to study this second part of stress–strain curves.
Section snippets
Testing equipment
For previous studies our laboratory had set up a servo-control system in a standard 200-tonne press, in such a way that the servo could control the loading rate in terms of stress or strain and perform different types of tests as required, for instance, tests with a number of unloading–reloading cycles (Fig. 1). We obtained quite reproducible post-failure results for unconfined compressive tests in moderately weathered granite [24].
Developed to classify the shape of the complete stress–strain
Tested rocks
An experimental programme was planned to study three granitic rocks locally known as Amarelo País, Blanco Mera and Vilachán, all hard rocks extensively used as building and ornamental materials.
Amarelo País, classified as slightly weathered granite, has a tan colour and is a coarse-grained hard rock (1–3 mm). Blanco Mera is a bright white-coloured granite, also a coarse-grained hard rock (1–6 mm). Vilachán, classified as a micaceous granite, is a pale-coloured, medium-grained hard rock (0.5–1 mm).
Testing
Samples were cut from 40-cm cubes taken from the sawing facilities of a rock supplier. Some 30 specimens measuring 54 mm in diameter (NX size) were cut for each rock type in order to have a reliable number of samples to test.
Unconfined and confined (0–15 MPa) compression strength tests were performed on around 30 samples representing each rock type. Other tests, namely, density, tilt and Brazilian tests, aimed at characterizing the rocks were also performed, always applying the best rock
Classic parameters
The results obtained in Table 3, Table 4, Table 5 were analysed in order to deduce the main geomechanical features of the rocks. First, peak and residual Mohr–Coulomb (M–C) and Hoek–Brown (H–B) failure criteria were fitted to the peak and residual strength values obtained as a result of testing. These fits, together with the original test data, are presented in Fig. 5 and the main results are shown in Table 6, Table 7, Table 8. Residual strength has been generally estimated as the lowest
Conclusions
Within the framework of a study of the post-failure behaviour of rocks and rock masses, an experimental programme based on a press with fully servo-controlled loading was set up in order to test and study post-failure stress–strain behaviour in granite samples. A total of around 90 unconfined and confined compression strength tests with loading–unloading cycles and computation of volumetric strain in confined tests were performed. This ensured for every cycle that the strength attained
Acknowledgements
The authors thank the Spanish Ministry of Science and Technology for financial support under Contract Reference Number BIA2009-09673 associated with the project entitled: ‘Studies of underground excavations in rock masses’, which funded developments in this paper. This project was partially financed by means of ERDF funds of the EU. Ailish M. J. Maher is acknowledged for revising the English in a version of this manuscript.
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