Rock Dilation Research Articles

Elastic/viscoplastic constitutive equations for rock

Abstract The experimental data needed for the formulation of a constitutive equation to describe the creep of rocks in uniaxial or triaxial tests are reviewed and the influence of loading rate on dilatancy is pointed out. The assumptions which have to be made in obtaining a constitutive equation from these experimental data are specified. A general constitutive equation is then formulated for rocks, which can describe their elastic and viscoplastic properties for any triaxial compressive stress state. Dilatancy and volumetric compressibility of rocks are defined in mathematical terms and so are the concepts of the compressibility/ dilatancy boundary and that of damage. Various time-dependent effects which can be modelled with such a constitutive equation are illustrated. It is shown, for instance, how the loading rate influences the dilatancy and/or the compressibility as well as the various stress-strain curves and the ultimate failure. The peculiarities of the creep phenomenon as described by the model are discussed. Numerical examples are given for several rocks. Various mining engineering problems have already been solved with such constitutive equations.

THE OBSERVATION OF FAULTING PROCESS IN ROCK BY COMPUTER TOMOGRAPHY

Seismic CT was employed to observe how dilatancy of rock localizes before faulting. The seismic CT can map the spatial distribution of P wave velocities. Since P wave velocity is determined by the extent of dilatancy (density, orientation, and aspect ratio of microcracks), mapping the seismic pofile is useful for observing nondestructively the progressive development of dilatancy. The specimen of Ohshima granite was compressed at a constant deformation rate under uniaxial stress. The reconstructions were made within the plane perpendicular to the loading axis. The maps clearly show the metamorphic changes of dilatancy before faulting; at first the formation of diffuse dilatancy occurred, the localization of dilatancy to a few near-surface areas followed at the next stage, and finally a failure zone appeared intersections of localized dilatant areas.

LOCALIZED DILATANCY IN ROCK OBSERVED BY SEISMIC COMPUTER TOMOGRAPHY

To observe how dilatancy of rock localizes before faulting, we attempted to map the P wave velocity field (seismic profile) of some sliced plane of the specimen by analyzing a number of the first arrival times. This technique, termed seismic CT, is useful to study the process of dilatancy localization, because P wave velocity is influenced by the extent of dilatancy. Here, we present the results of reconstruction made on the specimen of Ohshima granite within the plane parallel to the loading axis. The specimen was once compressed beyond the maximum load carrying capability under uniaxial conditions. The map clearly shows that the shape of the localized dilatancy determines the mode of failure, which occurs by faulting inclined to the specimen axis on conjugate faults.

Creep, dilatancy and compressibility of rocks around pressure shafts and oil wells (In French) : Cristescu, N Rev Fr GeotechN31, 1985, P11–22

Creep, dilatancy and compressibility of rocks around pressure shafts and oil wells (In French) : Cristescu, N Rev Fr GeotechN31, 1985, P11–22

THE PRECURSORY COMPLEXITY AND REGULARITY OF THE TANGSHAN EARTHQUAKE

Based on the re-examined precursory data of the Tangshan earthquake of July 28, 1976, the complexity and regularity shown by the pre-earthquake anomalies as well as the problems brought about to the practical prediction are analyzed. Three main points are discussed: 1) The diversity and three stages of the precursors of the Tangshan earthquake; 2) The synchronism as well as difference in time of the emergence and pattern changes of the precursors; 3) The relative concentration of the intermediate-term anomaly and the scattered distribution of the short-term and imminent anomalies in space. Furthermore, according to the research results achieved in recent years in China, the physical mechanisms of the precursors of the Tangshan earthquake are identified. The rock dilatancy of the focal body, aseismic fault creep, and mass movement are considered as the basic causes of the precursory complexity.

Dilatancy of rocks (In French) : Sirieys, P Rev Fr GeotechN27, 1984, P23–25

Dilatancy of rocks (In French) : Sirieys, P Rev Fr GeotechN27, 1984, P23–25

Discrete memory in rock: A review

Discrete memory is a phenomenon observed in elastic‐plastic materials with a material memory of a restricted type. Instead of the entire stress path, only a discrete set of stress reversal points is memorized. For certain types of stress path, parts of the discrete memory can be completely erased. In a series of experiments in which brittle rock was stressed under triaxial conditions, I have found that rock exhibits discrete memory which is associated with the phenomenon of dilatancy. Dilatancy in rock is characterized by an inelastic increase in volume strain that occurs when the sample is subjected to differential compressive stresses. The microcracking responsible for the inelastic strain produces substantial changes in elastic wave velocities. To very high precision the strains and elastic waves velocities in dilatant rock show discrete memory. Memory of maxima and minima of the stress difference can be developed, with multiple points remembered simultaneously. Discrete memory provides a strong constraint on possible mechanisms of dilatancy and brittle failure. Two models have been proposed for the basic crack mechanism: a shear crack and a tensile crack. Analysis of the shear crack shows that qualitatively it is capable of generating the observed properties but there are important details of discrete memory that are difficult to explain using this model. An analysis of the response of a tensile crack to cyclic loading, together with the introduction of an energy‐dissipating function, shows that a stable population of such cracks can produce discrete memory. The origin of the energy dissipation is not clear.

Constitutive model describing dilatancy and cracking in brittle rocks : Moss, W C; Gupta, Y M J Geophys Res, V87, NB4, 10 April 1982, P2985–2998

Constitutive model describing dilatancy and cracking in brittle rocks : Moss, W C; Gupta, Y M J Geophys Res, V87, NB4, 10 April 1982, P2985–2998

Rock dilatancy in uniaxial tests

Rock Dilatancy in Uniaxial Tests A procedure to find an elastic/viscoplastic constitutive equation able to describe rock dilatancy in uniaxial unconfined creep tests is given starting from experimental data. The influence of the loading rate on the rock dilatancy can also be described with this model. It is shown that a creep of the volume takes place during tests and that this volume creep has the following property: the volume strain is oscillating before ariving at its final stable value. This property is described by the proposed mathematical model using a variable viscosity coefficient which may change sign. According to the model the volume creep takes place during loading only.

Memory, relaxation and microfracturing in dilatant rock : Holcomb, D J J Geophys Res, v86, NB7, 10 July 1981, P6235–6248

Memory, relaxation and microfracturing in dilatant rock : Holcomb, D J J Geophys Res, v86, NB7, 10 July 1981, P6235–6248

A constitutive model describing dilatancy and cracking in brittle rocks

A micromechanical constitutive model, based on the responses of sliding cracks and elliptic cracks, is used to simulate the inelastic deformation of brittle rock. In addition to the usual incremental equations, the model has the following features: (1) activation equations that include the effects of friction and relate the far‐field stresses to sliding and elliptic crack openings and lengths, (2) a stress intensity analysis of the sliding cracks that determines how much the cracks may grow, and (3) expressions for the crack strains that are constructed directly from the amount of crack sliding, opening, growth and the number of sliding and elliptic cracks in a given region. Numerical simulations of uniaxial and triaxial loading experiments on Westerly granite were compared with experimental data to determine the validity of the constitutive model. These comparisons show that most of the uniaxial stress data and the loading portion of the triaxial data can be simulated quantitatively. The unloading portion of the triaxial data cannot be simulated properly, suggesting that a nonfrictional mechanism, not included in our model, may dominate the response in this region.

Stress path, strength and dilatancy of rocks : Chen Yong; Yao Xiaoxin; Geng Naiguang Scientia Sinica, V23, N4, April 1980, P492–501

The following three experiments along various stress paths were carried out to study thestrength and dilatancy of Jinan gabbro and Changping granite: case A, the maximumprincipal stress σ_1 was increased until the rock failed; case B, starting from a given stressstate,σ_1 was kept constant and confining pressure was decreased until the rock failed; caseC,σ_1 was kept constant and confining pressure was increased; and no rupture occurred inthis case. It has been found that both strength and dilatancy are ralated to the stress paths.Under certain conditions,the strength of rock in case B is lower than that in case A. Com-pared with the dilatancy of rock in case A, the rock in case B is in a super-dense state, andin case C in an ultra-dilatant state.

Time-dependent failure of rock under cyclic loading

Abstract A simple model which describes the failure of brittle rock under cyclic compressive loading is presented. It is assumed that the damage incurred by the material during each stress cycle is due to the extension of tensile microcracks and that the specimen will fail when the microcrack damage reaches a critical level. Two mechanisms for crack extension, stress corrosion and cyclic fatigue are assumed to act simultaneously and independently. The rate of crack growth due to stress corrosion was determined from an empirical relationship for the static fatigue of glass. The equation describing the rate of crack growth due to cyclic fatigue was taken to be similar to those derived for structural metals. By combining the crack extension rates due to these two processes, the time to failure for a specimen subjected to a given cyclic loading program was computed. The time to failure was found to depend strongly on the mean differential stress and the magnitude of the stress change during each cycle. At high mean stress and low cycle amplitude, stress corrosion dominates, whereas at low mean stress and high cycle amplitude, cyclic fatigue dominates. The predictions of the model are in good agreement with existing experimental data. Further, the model explains the observed breakdown of discrete memory in dilatant rock under certain stress conditions.

Memory, relaxation, and microfracturing in dilatant rock

When Palisades diabase and Westerly granite are made dilatant by cyclic differential stress not exceeding ≅ 85% of fracture strength, they behave as nonelastic, energy‐absorbing media. However, in some ways, their properties show reversibility more typical of elastic media. The quasi‐elastic behavior is characterized by the property ‘memory’. Memory in dilatant rock is manifested by the closure of material property hysteresis loops when the sample is returned to certain previous differential stress states. Simple examples of memory have been observed before in Westerly granite. The present work confirms the existence of memory for strain and compressional wave velocity in Westerly granite and Palisades diabase at confining pressures between 250 and 1500 bars. Memory of maxima or minima of the stress difference can be developed, with multiple points remembered simultaneously. A theory of memory based on reversible tensile Griffith cracks was developed which predicts a variety of phenomena, many of which have been observed. A property that is not predicted is the healing which occurs when unloading is stopped and the load is held constant. A time‐dependent increase in velocity and decrease in sample volume is observed, consistent with the healing of cracks. Relaxation ceases after approximately 2 min. After relaxation, a further decrease in load produces an initial elastic response followed by a return to the previous nonelastic behavior. Perfect memory is lost when microfracturing occurs as a result of either exceeding the previous absolute maximum stress or extensive cycling. Acoustic emissions are observed for conditions where memory is not perfect and are not observed when memory is perfect. Using travel time data, a new, low value was found for the dependence of dilatancy onset on pressure.

Locked in stresses, creep and dilatancy of rocks, and constitutive equations : Rock Mech, V13, N1, Aug 1980, P5–22

Locked in Stresses, Creep and Dilatancy of Rocks, and Constitutive Equations A micro rheological analysis is presented of the deformation characteristics of rocks based on the multi mineral and polycrystalline structure of igneous metamorphic and some sedimentary rocks; in addition the polygranular structure of sandstone-type rocks is also considered. Due account is taken with the history of rock formation and tectonics. Torsional creep test results on Ichang sandstone are presented and analysed. A new method of testing is introduced whereby the sample is subjected to a step wise loading function and the deformation measured as a function of the time. In this manner the creep as a function of stress and time can be obtained very easily from tests on only one sample. A hypothesis is presented on the origin and formation of “locked in” stresses the release of internal strain energy is studied at the hand of some typical test results. The practical importance of these stress pockets is discussed and it is stressed that creep and “locked in” stresses are fundamental factors in the behaviour of rocks which must be carefully studied in practice. On the basis of experimental results and physical reasoning constitutive equations are set up, which are three dimensional generalisations of the experimental Griggs equation:γ =a +b logt +ct, whereby the material parameters are scalar functions of the stress invariants.

Hypothesis Combining Dilation, Natural Hydraulic Fracturing, and Dolomitization to Explain Petroleum Reservoirs in Monterey Shale, Santa Maria Area, California: ABSTRACT

Fractured reservoirs in the generally siliceous Monterey Shale of the Santa Maria area represent an anomalous lithology and type of fracturing. Some, perhaps all, are not fractured chert but parts of the Monterey embrittled by dolomitization. Reservoir fractures, unlike ubiquitous Monterey fractures, are mostly abundant, disordered, open extension fractures that commonly produce epigenetic, dolomitic breccias. These dolomite-cemented breccias commonly contain open voids, many of which are 15 cm across or larger. Breccias locally have an exploded appearance and contain some matched fragments separated by vein-like or dike-like matrix, which apparently was an injected slurry of water and oil containing fragments of dolomite and dolomitic Monterey Shale. The highly organic Monterey also served as the source rock and probably originated as a rich diatomaceous slope sediment beneath an oxygen-minimum zone. The depositional site was much larger than the Santa Maria area and unconfined to silled basins. Local dolomitization may have been due, at least in part, to rising solutions and injected slurries. The reservoirs are explained by a hypothesis involving repeated episodes of rock dilation followed by natural hydraulic fracturing, all produced by episodic but continued tectonic compression of the region (principal, maximum, effective stress oriented northeastward). Increasing fluid pressures enlarged underpressured dilation microfractures into macrofractures and produced breccias by hydraulic fracturing. Viscous oil expressed from indurated Monterey was pumped into voids as part of overpressured slurries whose fragments were propping agents. Dolomite precipitated from slurries, on pressure release by fracturing, partly healing the fractures. Repetition of these events fractured additional rock, so that the reservoirs grew outward and somewhat upward. End_of_Article - Last_Page 977------------

The reversible Griffith crack: A viable model for dilatancy

Previous work (paper 1) on the mechanism of dilatancy has outlined the deficiencies of the sliding crack model. We have developed a new model, based on reversible Griffith cracks, that is in accord with experimental results to data. These results can be summarized as follows: (1) dilatant rock exhibits volume increases at sufficiently high increasing differential stress, (2) there is substantial hysteresis in physical properties between increasing and decreasing stress, (3) examination of stressed and unstressed samples, using a scanning electron microscope, reveals stress‐induced cracks that are preferentially oriented with the crack plane close to the maximum compressive stress axis, (4) few shear cracks (required by the sliding crack model) are observed, and (5) dilatant rock exhibits ‘memory’ of the maximum differential stress since the last complete unloading. When returned to this stress state, the physical properties return to their previous values but at other stress states there is large hysteresis between loading and unloading. A classical Griffith crack exhibits all of these properties if it is postulated to be reversible. That is, below a critical stress, the crack closes in an unstable mode and healing occurs. This behavior requires close registration of the crack faces.

Locked in stresses, creep and dilatancy of rocks, and constitutive equations

Locked in Stresses, Creep and Dilatancy of Rocks, and Constitutive Equations A micro rheological analysis is presented of the deformation characteristics of rocks based on the multi mineral and polycrystalline structure of igneous metamorphic and some sedimentary rocks; in addition the polygranular structure of sandstone-type rocks is also considered. Due account is taken with the history of rock formation and tectonics. Torsional creep test results on Ichang sandstone are presented and analysed. A new method of testing is introduced whereby the sample is subjected to a step wise loading function and the deformation measured as a function of the time. In this manner the creep as a function of stress and time can be obtained very easily from tests on only one sample. A hypothesis is presented on the origin and formation of “locked in” stresses the release of internal strain energy is studied at the hand of some typical test results. The practical importance of these stress pockets is discussed and it is stressed that creep and “locked in” stresses are fundamental factors in the behaviour of rocks which must be carefully studied in practice. On the basis of experimental results and physical reasoning constitutive equations are set up, which are three dimensional generalisations of the experimental Griggs equation:γ =a +b logt +ct, whereby the material parameters are scalar functions of the stress invariants.

The effect of water on the subcritical crack growth in silicate rocks

We investigated experimentally the effect of water on the velocity of crack propagation in an andesite and a basalt. The relation between the stress intensity factor K I at the crack tip and the crack velocity V was measured using the double torsion method. Experiments were conducted with the rock specimens either water-saturated or air-dry at laboratory humidity. Stress-dependent, slow crack growth was observed in both rocks used. The velocity of crack growth in water-saturated rocks was shown to be 2 ~ 3 orders of magnitude greater than in the room-dry ones. Our experimental results agree well with a general equation for crack velocity developed by Wiederhorn (1969). The present results suggest that stress-corrosion cracking should be an important process for the mechanism of dilatancy, creep and other characteristic behavior in the polycrystalline silicate rocks.

Hypothesis Involving Dilation and Natural Hydraulic Fracturing to Explain Petroleum Reservoirs in Monterey Shale, Santa Maria Area, California: ABSTRACT

Fractured reservoirs in the siliceous Monterey Shale of the Santa Maria area represent anomalous lithology and anomalous type of fracturing. Some, perhaps all, reservoirs are not fractured chert but chert embrittled by dolomitization. Abundant reservoir extension fractures are disordered and open, commonly containing epigenetic dolomite breccias. These fractures are partly dolomite-cemented but contain common open voids, many 15 cm across, some larger. Breccias locally have an exploded appearance and contain matched fragments separated by veins, which apparently were injected as a slurry of water, oil, and fragments of dolomite and dolomitic Monterey Shale. The highly organic Monterey served also as source rock and probably originated as richly diatomaceous slope sediment beneath an oxygen-minimum zone at a depositional site much larger than the Santa Maria area, and not confined to a specific silled basin. Local dolomitization may have been due, at least in part, to rising solutions and injected slurries. These reservoirs are explained by an hypothesis involving repeated episodes of rock dilation followed by natural hydraulic fracturing, all produced by continued episodic tectonic compression of the region (principal, maximum, effective stress oriented northeastward). High fluid pressures enlarged underpressured dilation microfractures into macrofractures and produced breccias by hydraulic fracturing. Viscous oil derived from the Monterey Shale was forced into voids as part of overpressured slurries whose breccia fragments were End_Page 770------------------------------ propping agents. Dolomite precipitated from slurries partly healed the fractures. End_of_Article - Last_Page 771------------