Low-porosity Crystalline Rocks Research Articles

Machine learning approach to predicting the macro-mechanical properties of rock from the meso-mechanical parameters

The determination of fundamental rock mechanical properties, uniaxial compression strength (UCS) and elastic modulus (E), constitutes a pivotal facet of rock engineering design. However, deriving these properties directly from standard laboratory tests on rock core samples can be challenging, especially when dealing with deep high-stress rock formations and weak fractured strata. Thus, it is crucial to establish a cost-effective and practical approach for predicting the macro-mechanical properties of rocks in situ. In this study, a machine learning approach was proposed to predict UCS and E by upscaling meso-mechanical parameters at particle scale in low-porosity crystalline rocks. To expand the correlation database of rock meso-macro mechanical properties, the meso-mechanical parameters, including the fracture toughness, tensile strength of the rock crystal interface, and the elastic modulus of rock crystal, were accurately measured, using a newly designed mechanical apparatus and a nanoindentation device. The grain-based models implemented in the combined finite discrete element method (FDEM-GBM) were developed based on these experimental results, and their reliability was validated though standard tests. Subsequently, a database, including 225 groups of data, was established using the numerical method. Five machine learning algorithms were applied to develop prediction models for UCS and E through data training in the database. Excellent performance improvement was achieved through the application of the grid-search method. The results indicate the optimized kernel ridge regression (KRR) and gaussian process regression (GPR) models demonstrated excellent performance with relative average errors of 4.9% and 1.1% in predicting UCS and E, respectively. Finally, the predicted values of UCS and E were compared with the experimental results, validating the feasibility of the optimized KRR and GPR models.

The competition between fracture nucleation, propagation, and coalescence in dry and water-saturated crystalline rock

Abstract. The continuum of behavior that emerges during fracture network development in crystalline rock may be categorized into three end-member modes: fracture nucleation, isolated fracture propagation, and fracture coalescence. These different modes of fracture growth produce fracture networks with distinctive geometric attributes, such as clustering and connectivity, that exert important controls on permeability and the extent of fluid–rock interactions. To track how these modes of fracture development vary in dominance throughout loading toward failure and thus how the geometric attributes of fracture networks may vary under these conditions, we perform in situ X-ray tomography triaxial compression experiments on low-porosity crystalline rock (monzonite) under upper-crustal stress conditions. To examine the influence of pore fluid on the varying dominance of the three modes of growth, we perform two experiments under nominally dry conditions and one under water-saturated conditions with 5 MPa of pore fluid pressure. We impose a confining pressure of 20–35 MPa and then increase the differential stress in steps until the rock fails macroscopically. After each stress step of 1–5 MPa we acquire a three-dimensional (3D) X-ray adsorption coefficient field from which we extract the 3D fracture network. We develop a novel method of tracking individual fractures between subsequent tomographic scans that identifies whether fractures grow from the coalescence and linkage of several fractures or from the propagation of a single fracture. Throughout loading in all of the experiments, the volume of preexisting fractures is larger than that of nucleating fractures, indicating that the growth of preexisting fractures dominates the nucleation of new fractures. Throughout loading until close to macroscopic failure in all of the experiments, the volume of coalescing fractures is smaller than the volume of propagating fractures, indicating that fracture propagation dominates coalescence. Immediately preceding failure, however, the volume of coalescing fractures is at least double the volume of propagating fractures in the experiments performed at nominally dry conditions. In the water-saturated sample, in contrast, although the volume of coalescing fractures increases during the stage preceding failure, the volume of propagating fractures remains dominant. The influence of stress corrosion cracking associated with hydration reactions at fracture tips and/or dilatant hardening may explain the observed difference in fracture development under dry and water-saturated conditions.

Relating strain localization and Kaiser effect to yield surface evolution in brittle rocks

SUMMARY The yield surfaces of rocks keep evolving beyond the initial yield stress owing to the damage accumulation and porosity change during brittle deformation. Using a poroelastic damage rheology model, we demonstrate that the measure of coupling between the yield surface change and accumulated damage is correlated with strain localization and the Kaiser effect. Constant or minor yield surface change is associated with strong strain localization, as seen in low-porosity crystalline rocks. In contrast, strong coupling between damage growth and the yield surface leads to distributed deformation, as seen in high-porosity rocks. Assuming that during brittle deformation damage occurs primarily in the form of microcracks, we propose that the measured acoustic emission (AE) in rock samples correlates with the damage accumulation. This allows quantifying the Kaiser effect under cyclic loading by matching between the onset of AE and the onset of damage growth. The ratio of the stress at the onset of AE to the peak stress of the previous loading cycle, or Felicity Ratio (FR), is calculated for different model parameters. The results of the simulation show that FR gradually decreases in the case of weak coupling between yield surface and damage growth. For a strong damage-related coupling promoting significant yield surface change, the FR remains close to one and decreases only towards the failure. The model predicts that a steep decrease in FR is associated with a transition between distributed and localized modes of failure. By linking the evolving yield surface to strain localization patterns and the Kaiser effect, the poroelastic damage rheology model provides a new quantitative tool to study failure modes of brittle rocks.

Folded fabric tunes rock deformation and failure mode in the upper crust

The micro-mechanisms of brittle failure affect the bulk mechanical behaviour and permeability of crustal rocks. In low-porosity crystalline rocks, these mechanisms are related to mineralogy and fabric anisotropy, while confining pressure, temperature and strain rates regulate the transition from brittle to ductile behaviour. However, the effects of folded anisotropic fabrics, widespread in orogenic settings, on the mechanical behaviour of crustal rocks are largely unknown. Here we explore the deformation and failure behaviour of a representative folded gneiss, by combining the results of triaxial deformation experiments carried out while monitoring microseismicity with microstructural and damage proxies analyses. We show that folded crystalline rocks in upper crustal conditions exhibit dramatic strength heterogeneity and contrasting failure modes at identical confining pressure and room temperature, depending on the geometrical relationships between stress and two different anisotropies associated to the folded rock fabric. These anisotropies modulate the competition among quartz- and mica-dominated microscopic damage processes, resulting in transitional brittle to semi-brittle modes under P and T much lower than expected. This has significant implications on scales relevant to seismicity, energy resources, engineering applications and geohazards.

Fractal density modeling of crustal heterogeneity from the KTB deep hole

AbstractFractal or multifractal concepts have significantly enlightened our understanding of crustal heterogeneity. Much attention has focused on 1/f scaling natures of physicochemical heterogeneity of Earth crust from fractal increment perspective. In this study, fractal density model from fractal clustering point of view is used to characterize the scaling behaviors of heterogeneous sources recorded at German Continental Deep Drilling Program (KTB) main hole, and of special contribution is the local and global multifractal analysis revisited by using Haar wavelet transform (HWT). Fractal density modeling of mass accumulation generalizes the unit of rock density from integer (e.g., g/cm3) to real numbers (e.g., g/cmα), so that crustal heterogeneities with respect to source accumulation are quantified by singularity strength of fractal density in α‐dimensional space. From that perspective, we found that the bulk densities of metamorphic rocks exhibit fractal properties but have a weak multifractality, decreasing with the depth. The multiscaling natures of chemical logs also have been evidenced, and the observed distinct fractal laws for mineral contents are related to their different geochemical behaviors within complex lithological context. Accordingly, scaling distributions of mineral contents have been recognized as a main contributor to the multifractal natures of heterogeneous density for low‐porosity crystalline rocks. This finally allows us to use de Wijs cascade process to explain the mechanism of fractal density. In practice, the proposed local singularity analysis based on HWT is suggested as an attractive high‐pass filtering to amplify weak signatures of well logs as well as to delineate microlithological changes.

Factors Affecting Crack Initiation in Low Porosity Crystalline Rocks

Crack initiation in uniaxial compressive loading of rocks occurs well before the peak strength is reached. The factors that may influence the onset of cracking and possible initiating mechanisms were explored using a discrete element numerical approach. The numerical approach was based on grain-based model that utilized the Voronoi tessellation scheme to represent low porosity crystalline rocks such as granite. The effect of grain size distribution (sorting coefficient ranging from 1.5 to 1.03), grain size (average grain size ranging from 0.75 to 2.25 mm), and the heterogeneities of different mineral grains (quartz, K-feldspar, plagioclase) on the onset of cracking were examined. The modelling revealed that crack initiation appears to be a tensile mechanism in low porosity rocks, and that shear cracking along grain boundaries is only a prominent mechanism near the peak strength. It was also shown that the heterogeneity introduced by the grain size distribution had the most significant effect on peak strength and crack initiation stress. The peak strength ranges from 140 to 208 MPa as the grain size distribution varies from heterogeneous to uniform, respectively. However, the ratio of crack initiation to peak stress showed only minor variation, as the heterogeneity decreases. The other factors investigated had only minor effects on crack initiation and peak strength, and crack initiation ratio.

Crack initiation stress in low porosity crystalline and sedimentary rocks

The stress–strain data from 376 laboratory tests carried out on samples of igneous, sedimentary and metamorphic rocks were analyzed to establish the onset of microcracking in compression, referred to as the Crack Initiation (CI) stress. A statistical approach was used to find the geological parameters influencing crack initiation stress. Among various rock properties such as grain size and mineralogy, the proportion of the hardest constituent mineral were found to correlate with CI stress. Foliation induced anisotropy was found to affect the peak strength but its effect on CI stress was less pronounced. The CI stress to peak stress ratio ranged from 0.42 to 0.47 regardless of the material properties in uniaxial compression whereas this ratio ranged from 0.50 to 0.54 when confined. The crack initiation parameters for the Hoek–Brown spalling criterion for igneous rocks can be expressed in terms of the CI stress ratio and the tensile strength. A comparison of tensile strength from the Brazilian and Direct tension tests showed that the Direct tensile strength was approximately 0.77 of the Brazilian tensile strength.

Evaluation of Methods for Determining Crack Initiation in Compression Tests on Low-Porosity Rocks

Laboratory testing of rocks is traditionally carried out to determine the peak strength using the ISRM Suggested Methods or other suitable standards. However, it is well known that in low-porosity crystalline rocks there are at least three distinct stages of compressive loading that can be readily identified if the stress–strain response is monitored during the loading process: (1) crack initiation, (2) unstable crack growth, i.e., crack coalescence and (3) peak strength. Crack initiation is noted as the first stage of stress-induced damage in low-porosity rocks, yet the suggested guidelines of the ISRM for compression tests make no mention of crack initiation. In addition, recent research suggests that crack initiation can be used as an estimate for the in situ spalling strength, commonly observed around underground excavations in massive to moderately jointed brittle rocks. Various methods have been proposed for identifying crack initiation in laboratory tests. These methods are evaluated using ten samples of Aspo Diorite and the results are compared with a simplified method, lateral strain response. Statistically, all methods give acceptable crack-initiation values. It is proposed that the ISRM Suggested Methods be revised to include procedures suitable for establishing the crack-initiation stress.

Origin and orientation of microporosity in eclogites of different microstructure studied by ultrasound and microfabric analysis

This work contributes to the experimental investigations of the origin and 3-D orientation of micropores in low porosity crystalline rocks. The origin and spatial orientation of microporosity in two eclogites with different microstructures were studied by 1) quantitative and qualitative microstructural analysis of grains and grain boundaries, 2) measurement of lattice preferred orientation using the SEM-EBSD method and 3) experimental measurement of velocity of elastic P-waves in spherical samples in 132 directions under confining pressures up to 400 MPa. Results show good correlation between the elastic properties and the orientation of grain boundaries and cleavage planes in clinopyroxene. The magnitude and anisotropy of velocity change with pressure shows that microporosity in the fine-grained sample is relatively large and strongly preferentially oriented, whereas it is significantly lower and less preferentially oriented in the coarse-grained sample. Seeing that the lattice preferred orientation of clinopyroxene is similar in both samples we can deduce from velocity changes that the grain size of the rock forming minerals controls the amount of microporosity. Also, the orientation of microporosity depends mostly on preferred orientation of grain boundaries and somewhat less on the orientation of cleavage planes. Grain boundaries are therefore the most important contributors to the bulk microporosity in the studied rocks.

Elastic properties of granulite facies rocks of Mahabalipuram, Tamil Nadu, India

Compressional and shear wave velocities and attenuation measurements have been carried out in some of the borehole samples of acidic, basic and intermediate granulites of Mahabalipuram, Tamil Nadu, India. The results have been obtained at ambient conditions using ‘time-of-flight’ pulse transmission technique at 1.0 MHz frequency. The results show linear relationships between velocity and density, and velocity and attenuation properties of the rocks. The acidic granulites show lower velocities and higher attenuation than the intermediate and basic granulites. The average values of the Poisson’s ratio of acidic, intermediate and basic granulites have been found to be 0.210, 0.241 and 0.279 respectively. The variations in velocities and attenuation in these low porosity crystalline rocks are found to be strongly influenced by their mineral composition. The laboratory velocity data (extrapolated to high pressure) of the present study and the published field velocity data from deep seismic sounding studies indicate that these granulite facies rocks may belong to mid-crustal depths only.

The Study of Radionuclide Retardation in Fractured Rock by Means of In Situ Resin Impregnation

ABSTRACTTraditional in situ tracer tests estimate contaminant retardation by analysis of the degree and form of tracer breakthrough after transport through the rock. Unfortunately, this approach does not allow direct examination of in situ retardation mechanisms and, in the case of strongly retarded radionuclides, is highly impractical as tracer breakthrough may take months to decades. An alternative method to study retardation is therefore required in such a case and Nagra and PNC have recently employed one such variant to study radionuclide transport in fractured crystalline rock. Here, direct, detailed, examination of in situ radionuclide retardation following tracer injection is carried out by immobilising and recovering the intact fracture and associated rock matrix [1,2].The material can then be studied in the laboratory by standard surface analytical and radiochemical methods and the degree and form of radionuclide uptake can be readily assessed.As part of this work, Nagra and PNC have invested significant effort over the last four years in developing appropriate means of immobilising water-conducting fractures and undisturbed low porosity crystalline rock matrix in a manner which minimises physico-chemical disturbance[3]. After examining a range of options, it was decided to employ in situ resin impregnation as the immobilisation medium as this produced the best results with respect to minimising physico-chemical disturbance of the system while at the same time ensuring impregnation of very fine water saturated pore space. In addition, the polymerised resins improve the rigidity and strength of the rock such that the water saturated structures (pores, fractures or fault gouges) survive the subsequent overcoring and sub-sampling.Two experiments will be discussed: the first has been recently completed in Nagra's underground laboratory in the central Swiss Alps (the Grimsel Test Site, or GTS) and the second is currently ongoing at PNC's Kamaishi In Situ Test Site (KTS) in north-east Japan.In the GTS, retardation of radionuclides is being studied in the Radionuclide Retardation Project (RRP) and two resins have been formulated for different aspects of the study. An epoxy resin has been injected into a complex water-conducting shear zone in a granodiorite following the injection of a cocktail of strongly retarding radionuclides (including 60Co, 237Np, 234. 235U, 99Tc, 152Eu, 113Sn and 75Se [1,2]). To negate the hydrophobic nature of the epoxy resin, a trick has been imported from soil science where isopropanol is first injected to replace the water and only then is the epoxy resin injected. Laboratory tests showed that neither the isopropanol nor the resin should disturb the in situ radionuclide distribution, a result which has since been verified in the field. In parallel with this work, the low porosity (<1%) granodiorite rock matrix behind the shear zone is being examined by means of an in situ injection of an acrylic resin. The very low viscosity of the specially developed acrylic resin allows impregnation (and subsequent visualisation) of the connected microporosity of the matrix, so allowing detailed in situ examination of the depth of available matrix behind the shear zone.These methods have been further refined in the KTS and are currently being applied to several different types of water conducting features. The form and type of connected porosity in the associated granodioritic rock matrix is also being examined in detail [4]. As with the GTS work, the results of the in situ experiments will be compared with laboratory data on retardation and matrix diffusion to assess the transferability of the large volume of laboratory data to the field.The development of the various resins will be discussed along with the applicability of these specially developed resins to other rock types. Finally, the results of the recently concluded GTS tests and the ongoing KTS tests will be presented.

Fault scaling and 1/f noise scaling of seismic velocity fluctuations in the upper crystalline crust

Sonic logs are detailed measurements of the in situ seismic velocity along borehole walls. Power spectra of sonic logs typically decay approximately as the reciprocal of spatial frequency f , regardless of the chemical composition, geologic age, and tectonic history of the probed lithologies. Data sequences of this type are fractal or scale-invariant. The origins of this uniform 1/ f scaling of seismic structure are not clear, particularly in low-porosity crystalline rocks, but faults, fractures, and cracks are considered to be important. Fault structures also follow fractal scaling laws and have significant effects on seismic velocity. This paper presents a quantitative model that evaluates the role played by faults in determining the scaling laws of seismic velocity fluctuations. The model is based on current knowledge of the structure and scaling properties of brittle faults and of associated regions of microcracking. By approximating the relationship between crack density and velocity variation as linear, this model yields a Brownian power spectrum (∝1/ f 2 ) for velocity perturbations across a single fault zone in a medium of otherwise constant velocity. The power spectrum of velocity fluctuations induced by a population of faults is then obtained by superposing the corresponding Brownian power spectra weighted according to the observed frequency-size scaling relationship of brittle faults. The results of this study indicate that the uniform 1/ f scaling of velocity fluctuations in crystalline rocks seems to be linked to the correspondingly uniform scaling properties of fault structures.

Infiltration effects in the tensile rupture of thin walled cylinders of glass and granite: Implications for the hydraulic fracturing breakdown equation

To study the effects of fluid infiltration on fracture initiation in low porosity rock, hollow cylinders of Westerly granite and glass were brought to rupture by pressurization of the internal cavity in a manner analogous to a hydraulic fracturing field test. The samples were subject to hydrostatic confining pressures as high as 60 MPa. The dependence of the internal rupture pressures of the glass tubes on confining pressure were found to be consistent with linear elastic theory which includes a pre-existing inner wall flaw. The granite hollow cylinders were internally pressurized at rates of approx. 2.0, 0.6 and 0.05 MPa/sec (referred to hereafter as fast, normal and slow). For a given pressurization rate fracture, initiation pressures as a function of confining pressure were extremely well fit by a line with slope of unity and pressurization rate dependent intercepts from 10.9, 14.7 and 17.5 MPa for the slow, normal and fast tests, respectively. Observed failure levels for the slow tests are in good agreement with predictions based on experimentally-derived strength and elastic moduli bounds for a saturated porous media. However, failure pressures in the fast tests are too high; that is, the difference between the fast and slow tests is larger than can be rationalized by the theoretical predictions. One possible explanation is that the pore pressures cannot be recharged during the short time of the fast tests. This is also implied by the results of similar tests in which fluid infiltration into the rock is not allowed during inner cavity pressurization. Reduced pore pressures are a possible result of the highly non-linear elastic behaviour (including dilatancy hardening) in the granite due to its low aperture microcrack porosity. The evidence we have found for diminished pore pressure effects on fracture initiation provides support for the empirically-determined hydraulic fracturing breakdown equation in low porosity crystalline rock that omits pore pressure.

Diminished pore pressure in low-porosity crystalline rock under tensional failure: apparent strengthening by dilatancy : Schmitt, D R; Zoback, M D J Geophys ResV97, NB1, Jan 1991, P273–288

Diminished pore pressure in low-porosity crystalline rock under tensional failure: apparent strengthening by dilatancy : Schmitt, D R; Zoback, M D J Geophys ResV97, NB1, Jan 1991, P273–288

On the thermal conductivity of low-porosity crystalline rocks : Scharli, U; Rybach, L TectonophysicsV103, N1–4, 20 March 1984, P307–313

On the thermal conductivity of low-porosity crystalline rocks : Scharli, U; Rybach, L TectonophysicsV103, N1–4, 20 March 1984, P307–313

On the thermal conductivity of low-porosity crystalline rocks

Measurements by a Quick Thermal Conductivity Meter on dry and water-saturated granitic samples at room temperature are reported. For a porosity of 0.8% the difference between dry and water-saturated conductivities amounts to 30%. The measured conductivities are in good agreement with values calculated for a pore configuration model based on interconnected crack-type pores. Rapid thermal conductivity measurements on dry and water-saturated samples have a considerable potential as a method to determine porosity in low-porosity crystalline rocks.

The effect of fluid flow on the magnetic field in low porosity crystalline rock

Changes in the local geomagnetic field have been observed and documented in several seismically active areas prior to, during, and following earthquakes. Mizutani and Ishido (1975) proposed that groundwater may diffuse through a hypocentral region and that the fluid flow can produce an electric potential by means of electrokinetic phenomena. The resulting current flow, in turn, will generate a magnetic field.Fluid flow tests conducted on samples of Westerly granite demonstrated that the diffusion of an electrolytic fluid causes a measurable magnetic field change. At high fluid flow rates, a magnetic field change was observed that was in agreement with theoretically predicted and numerically calculated values. In addition, the sign of the magnetic field changes as the fluid flow direction through the sample was reversed. Moreover, the tests showed that the magnitude of the magnetic field change is dependent upon (1) the porosity of the rock; (2) the pore wall surface area; (3) the permeability of the rock; and (4) zeta potential of the fluid‐pore wall system.

The effects of saturant salinity and pressure on the electrical resistivity of Hawaiian basalts

Summary. AC electrical resistivity of several Hawaiian basalts, saturated with four solutions of varying salinity, is investigated in the hydrostatic pressure range of 0.1 MPa to 0.5 GPa (5 kbar), with pore pressure of nearly 0.1 MPa. At 0.1 MPa, the Archie's empirical relationship holds well for basalts ranging in porosity from < 1 to 30 per cent, and saturated with high salinity solution. Resistivity of saturated basalts increases with pressure. As compared to the data for the low-porosity crystalline rocks reports by Brace & Orange, the resistivity of porous basalts (2-13 per cent porosity) increases less rapidly. The empirical relationship (d log p/dP) - 1 .O GPa-' found for the crystalline rocks also holds for basalts.

Effect of pressure and saturating fluid on the thermal conductivity of compact rock

Regional differences in heat flow of about 15% are often considered to be significant. However, it is shown here that the observed thermal conductivity for dry rock samples may differ by more than 15% from the conductivity that the rocks had in place—saturated and under hydrostatic pressure. Error in the apparent conductivity arises because cracks, which are present in most rocks, form effective barriers to the flow of heat when rocks are dry but have a negligible effect when the rock is saturated or when the cracks are closed by stress. Several formulas are presented for estimating the possible error for low-porosity crystalline rocks. The theoretical expressions show reasonable agreement with measurements made on dry and saturated samples of a granite under axial compressive stress, up to 930 bars.