E. Z. Lajtai

The effect of water on the time-dependent deformation and fracture of a granite

Abstract The effect of water on the deformation, fracture and strength of Lac du Bonnet granite has been investigated through a variety of experimental techniques: standard short-term tests for compressive strength and fracture toughness, and longer-term, time dependent experiments that measure creep, static fatigue and slow crack velocity. When specimens of this granite are tested while in direct contact with water, such conventional measures of the short-term strength as the uniaxial compressive strength and the fracture toughness decrease by about 5% from the levels measured at room temperature and humidity. Because short-term tests require a few minutes to complete, part or all of this decrease in strength may only be due to time-dependent processes. When results of other, longer-term tests are extrapolated to zero elapsed time, the indication is that at very rapid loading rates (instantaneous or dynamic loading condition), the effect of water on strength may be negligible. In all time-dependent tests for creep strain, static fatigue and slow crack velocity, the effect of water is substantial. The creep strain and slow crack velocity increase and the long-term strength decreases when water is introduced into the previously dry testing environment. The size of the change, however, depends on the stress level (applied stress relative to the instantaneous strength). It is small at high stress levels becoming more substantial as the stress level is decreased. For example, at a stress level of 65%, the steady state creep rate of the lateral strain increased by 300% when water was allowed to flood the previously dry environmental chamber.

The effect of strain rate on rock strength

SummaryThe effect of the strain rate on strength has been evaluated for two widely different rock types, a brittle limestone (Tyndallstone) and a ductile salt rock (Lanigan potash rock).Results of static and dynamic fatigue tests on Tyndallstone, a dolomitic limestone, show an increase in strength with increasing strain or stressing rate although the rate effect is very small. Although the static and dynamic fatigue tests are expected to yield the same stress corrosion parameter, no such agreement has been observed.Dynamic fatigue tests of the more ductile salt rock showed a substantial rate effect. The usual strength criteria, that consider the influence of confining pressure alone, are no longer adequate to describe the strength of Lanigan potash. A general strength criterion, that incorporates the effect of both the confining pressure and the strain rate, is proposed.

Criteria for brittle fracture in compression

Abstract Fracture nucleation and propagation in the compressive stress field of the geological and the mining environment is considered with the purpose of formulating an empirical, but general fracture criterion that is in agreement with experimental evidence. Present fracture criteria are inadequate for compressive loading. The boundary stress-based theories ignore the effect of the stress gradient while the critical stress intensity concept of fracture mechanics neglects the normal stress that acts parallel with the direction of fracture propagation. A new, empirical crack resistance (CR) function is defined based on experimental data and then combined with an ‘averaged’ state of stress in front of the cracktip to formulate a ‘crack driver’ (CD) function. The crack driver is analogous to the safety factor, but with values greater than unity representing the fractured state. The crack driver concept is implemented to predict the nucleation and propagation of fracture in a compressive environment. The evolution of the failure process around underground openings is then described, with special reference to the primary, the remote and the slabbing types of fracture of rock mechanics and mining terminology.

Fitting strength criteria to intact rock

SummaryRock strength data covering the full range of possible stress conditions are presented for three rocks: a granite, a limestone and a salt rock. The Hoek and Brown square root parabola and the Johnston criteria are fitted to the strength data coming from around 500 laboratory tests. The fitting procedure is facilitated by a specially built PC code, ROCKER, which is available to anyone on request.The Hoek and Brown criterion is modified through the inclusion of a third parameter to account for the low tensile strength of the salt rock. A new criterion, the Rocker function is formulated to follow strength data closely in the tension-low confining pressure region.

Tensile fracture from circular cavities loaded in compression

When a block of rock containing an equi-dimensional void is loaded in compression, the resulting fracture may form at one of three basic positions: at the tensile stress concentration of the perimeter (primary fracture), at the compressive stress concentration of the perimeter (slabbing fracture), or off the perimeter, remote to the cavity (remote fracture). All three are genetically similar; they form and propagate parallel to the direction of the maximum compressive stress. The location of the fracture with respect to the cavity is controlled by the cavity size and the confining pressure.Although LEFM solutions exist for the primary fracture, the mathematical crack of fracture mechanics is ill-suited to analyze fractures that form in a primarily compressive state of stress (remote and slabbing fractures); the mathematical crack is independent of the compressive stress acting along its plane. A stress-based solution is proposed that incorporates the effect of both the maximum and the minimum principal stress. The major shortcoming of conventional stress-based techniques, the lack of size dependence, is removed by a procedure of stress averaging over a constant distance or area. For the case of the cylindrical cavity, stress averaging along the primary fracture path can be built into a closed-form solution. Averaging stresses over a constant area requires numerical techniques.Physical experiments, involving the compression loading of cylindrical cavities in three rocks: a granite, a limestone and a salt rock provide data for the comparison and the calibration of the theoretical criteria. Stress averaging over a constant area gave the best agreement with the test data.

En echelon crack-arrays in potash salt rock

SummaryThere are two types of fracture patterns in the yield pillars of the potash mines of Saskatchewan. The individual members of both patterns are tensile (extension) fractures that propagate parallel with the maximum principal stress trajectory (perpendicular to the minimum principal stress). The difference between the two patterns lies in the arrangement of the member fractures. In theen echelon tensile crack-array, the macroscopic fracture consists of individual tensile cracks that are slightly offset from each other. They have only a small overlap and the child crack seems to form randomly on either side of its parent. Consequently, the en echelon tensile crack-array inherits the axial orientation of its members. In contrast, the tensile cracks of anen echelon shear crack-array, have a larger overlap and their lateral displacement from each other is biased in one direction. Therefore, the crack-array is no longer axial but inclined 20–25 degrees from the maximum principal stress direction. With increasing stress, the shear crack-array often collapses, forming theenvelope orhourglass structures of the potash mines.

Stress corrosion cracking of Lac du Bonnet granite in tension and compression

Rocks subjected to long-term loading have been known to suffer microcracking. The rate of cracking is sensitive to the type of the applied stress (tensile or compressive), and the magnitude of the stress relative to the instantaneous strength. In addition, crack growth is influenced by the environment (pressure and temperature) including the presence or absence of moisture.For tensile loading, the sensitivity of granite to time-dependent cracking is demonstrated through a fracture mechanics test known as double torsion. The crack velocity versus stress intensity function is established for two environments, room temperature and humidity and room temperature and 100 percent humidity.For compressive loading, time dependent cracking is evaluated from creep tests conducted in uniaxial compression in the same two environments. The rate of cracking is defined by finding the functional relationship between the rate of crack growth, expressed as the rate of crack volume strain, and uniaxial compressive stress.A variety of mathematical functions has been fitted to the obtained data. The traditionally-used power and exponential relationships give good correlation for both crack velocity and crack volume strain rate.The crack volume strain rate versus stress function can be integrated to obtain a lifetime estimate for Lac du Bonnet granite. After 1 000 years of loading in uniaxial compression at room temperature and 100 percent humidity, the strength of this granite could reduce from 225 MPa to 90–100 MPa.

Delayed failure in rock loaded in uniaxial compression

SummaryThe long-term response to sustained compressive loading of two crystalline hard rocks of the Canadian Shield has been investigated. Static fatigue tests conducted on granite and anorthosite have shown that in a humid environment the long-term strengths of these crystalline igneous rocks could be less than 60 percent of their dry instantaneous strengths. Such reduction in strength has implications for the design and construction of deep tunnels, mines and other underground installations. The particular case of a nuclear fuel waste vault located at a depth of one kilometer is considered.Considering a service life of 1,000 years, a vault one kilometer deep in granite could suffer time-dependent spalling in highly stressed regions of the rock where the maximum principal stress exceeds about 130 MPa. Anorthosite has a lower instantaneous strength than granite and it is sensitive to static fatigue as well. A vault in anorthosite would be subject to time-dependent spalling of the perimeter rock in places where the maximum principal stress is above 80 MPa.

Mapping the state of fracture around cavities

The state of stress around cavities is heterogeneous. Consequently, the state of fracture may also vary from point to point. Under compressive loading, cavity may be in one of four possible states: pre-fracture (pre-microfracture initiation), microfracture propagation (initiation to the onset of dilata dilatancy to failure) and post-failure. These four states are separated by the crack initiation stress, the crack damage stress and the failure stress. fracture events with confining pressure is examined with reference to three intact rocks: a brittle granite, a semi-brittle limestone and a ductile sal The maximum principal stress (σ1) at crack initiation, crack damage (onset of dilatancy), yielding and failure are established as a function stress (σ3). For a single intact rock, all four fracture events can be represented using one function (the Rocker function) with a single fac various fracture states. The proposed fracture criteria, based on the experimental data, are combined with the existing state of stress to prepare a fracture map around an elli intact Lac du Bonnet granite. The state of stability is expressed through a newly defined stability factor, the unconfined strength ratio (USR), wh to the traditional safety factor. In contrast to the conventional safety factor in rock mechanics (SFstrength/σ1), which is σ3

Primary fracture propagation from circular cavities loaded in compression

When a brittle elastic material containing a cavity is loaded in uniaxial compression, fractures may form in three basic positions around the cavity; at the tensile stress concentration (primary fracture), at positions inside the material remote from the perimeter of the cavity, and at the compressive stress concentration. Granite blocks containing a circular cavity of radius between 2.5 mm and 50 mm were tested in uniaxial compression to collect data on primary fracture propagation. The laboratory results indicate that primary crack propagation is a stable process at small scales but approaches instability at large scales. A finite width crack model is presented which is able to capture this scale dependent behavior. The model illustrates that both tensile and compressive stresses play an important role in the primary fracture process.