A study on the time-dependent microfracturing and strength of Oshima granite

Uniaxial compressive loading experiments where axial strain rate or dilatant volumetric strain rate was kept constant were carried out using a servo-controlled hydraulic testing machine. The rock studied was Oshima granite. In order to investigate the effect of the strain rate on the strength, a theory based on the assumption of redistribution of the pre-existing microcracks due to subcritical crack growth was examined. Results expected from the theory were well borne out by the observations. The strength was expressed by power-functions of both axial strain rate and dilatant strain rate. The stress corrosion index of Oshima granite appeared to be 31 ± 3, which agreed well with the values reported previously.When the axial strain rate was held constant, the acoustic emission rate increased exponentially and the b-value, the exponent in the frequency-magnitude relation of the acoustic emissions, decreased with increasing applied stress. When the dilatant volumetric strain rate was kept constant, the acoustic emission rate and the b-value remained constant and independent of the stress increase. Furthermore, when the dilatant strain rate was held constant at a higher value, the b-value was constant at a lower level. As the decrease in the b-value indicates the higher dilatant strain rate, the b-value is one of the most useful key parameters in the fracture predictions.     

Quantification of Aperture and Relations Between Aperture,Normal Stress and Fluid Flow for Natural Single Rock Fractures

Accurate quantification of rock fracture aperture is important in investigating hydro-mechanical properties of rock fractures. Liquefied wood’s metal was used successfully to determine the spatial distribution of aperture with normal stress for natural single rock fractures. A modified 3D box counting method is developed and applied to quantify the spatial variation of rock fracture aperture with normal stress. New functional relations are developed for the following list: (a) Aperture fractal dimension versus effective normal stress; (b) Aperture fractal dimension versus mean aperture; (c) Fluid flow rate per unit hydraulic gradient per unit width versus mean aperture; (d) Fluid flow rate per unit hydraulic gradient per unit width versus aperture fractal dimension. The aperture fractal dimension was found to be a better parameter than mean aperture to correlate to fluid flow rate of natural single rock fractures. A highly refined variogram technique is used to investigate possible existence of aperture anisotropy. It was observed that the scale dependent fractal parameter, K _v, plays a more prominent role than the fractal dimension, D _a1d, on determining the anisotropy pattern of aperture data. A combined factor that represents both D _a1d and K _v, D _a1d × K _v, is suggested to capture the aperture anisotropy.     

A new method of modelling the rock micro-fracturing process in double-torsion experiments using neural networks

Microfracturing of rock is a complicated damage evolution process. Inaccurate prediction of micro-fracturing behaviours suggests a need for the development of a better modelling method. Analysis of acoustic emission (AE) measurements in double-torsion tests indicates that micro-fracturing behaviours during the loading stage have fractal time structures. This fractal behaviour can be described by C(t) ∝ t^D, where D is the correlation exponent, t is the time and C(t) is the correlation integral. Furthermore, by utilizing measured AE data, a new method has been developed to model the AE behaviours of micro-fracturing in rock, in air, and following soaking in water and in a chemical solution of DTAB. The neutral models NN (10,21,2) and NN (10,20,2) were found to describe reasonably well the AE behaviours of micro-fracturing in rock under air and DTAB conditions, and water conditions, respectively. The cumulative AE events and the cumulative AE counts predicted by the neural models agreed well with those measured in experiments. Copyright © 1999 John Wiley & Sons, Ltd.     

New techniques in rock mass classification: application to welded tuffs at the Nevada Yucca Mountain

Summary Many rock mass classification systems exist to assist the engineer in assessing the rock support requirements for underground design. On-going research in this area is directed at attempting to utilize the fractal dimension and the acoustic emission response of the tuffs at the Nevada Yucca Mountain to further aid in rock mass classification. Acoustic emission response is shown to be correlated with the porosity of the sample. Engineering behaviour of the rock varies dramatically with porosity; events and peak amplitude offer a means to distinguish between fracture porosity and pore porosity and consequently the engineering behaviour of the rock. Fractal dimension is used to characterize the roughness of fracture surfaces. Two fractal dimension calculation methods, one based on the semi-variogram for the surface and the other based on the use of dividers, are applied for this purpose. The divider method is shown to resolve deviation from a straight line; the semi-variogram method is shown to identify statistical similarity to various types of noise.Nomenclature D fractal dimension - AE acoustic emission - b b-value determined from log(frequency) against log(amplitude) plots - (h) semi-variogram function - h lag distance for semi-variogram function - H an exponent term related to fractal dimension asD=2 –H     

Extensional aspects of earthquake induced ruptures determined by an analysis of fracture bifurcation

Numerical and experimental investigation of symmetric fracture bifurcation (Kalthoff, 1972), has shown that for forks with small branch angles α<α_c, where α_c is approximately 14°, the propagation of the branches tends to enlarge the angle. For forks with larger branch angles, α>α_c, the propagation of the branches tends to diminish the angle. Forks with the critical angle α_c will propagate in their original direction. Kalthoff theorized that the branch angle changes as a function of K_I/K_II, where K_I and K_II are the stress intensity factors for tensile and shear (sliding) modes, respectively, and K_I is considerably larger than K_II. In this study I test the hypothesis that this fracture mechanic theory applies to the analysis of fault bifurcation in the crust, particularly in cases of rapid fracture.Fractures produced during the 1968 earthquake at the Coyote Creek fault in California are intensively branched and an example of rapid rupture. The angular behaviour of the branching ruptures in eight forks follows Kalthoffs theory unusually well. This implies that fracture at the surface was dominated by the tensile mode. Additional observations that support this implication are: series of prominent ruptures which show openings (of 20–30 mm per rupture), the symmetrical and bilateral forking, the high-intensity and angular shapes of individual branches, the opening of grabens associated with several bifurcations, lack of bifurcation in the southern break of the Coyote Creek fault, and the patterns of en echelon fractures which reflect mixed mode surfacial rupture.Hence, contrary to previous interpretations, according to field evidence and fracture mechanic theory, the fault bifurcation and opening along the Coyote Creek fault are not compatible with local tension caused by the primary shear. Fracture probably occurred by different mechanical modes at depth and at the surface. While faulting may have originated by shear at depth, rupture at the surface was dominated by far-field tension associated with NE-SW extension in South California. The present model predicts the directions of fracture propagation along the fault.     

Relationship Between the Geometric Parameters of Rock Fractures,the Size of Percolation Clusters and REV

Modeling fractured rocks with numerical methods requires some derived parameters, among which the fracture network connectivity and the size of the representative elementary volume (REV) are both of crucial importance. Percolation and REV analyses were made by the RepSim code. The program uses input parameters such as fractal dimension of the fracture midpoints (D _c), length exponent (E) and relative dip (α ^r) data. For percolation analysis, the relative sizes of the largest percolation clusters have been calculated by stochastic realizations of the simulated fracture networks with different parameter triplets. Furthermore, fracture networks can be classified into three major types on the basis of their (E,D _c,α ^r) parameters. For the REV calculations, the porosity of the generated fracture network was calculated. The derived REV size of a fracture network depends essentially on input parameters and shows a decreasing tendency with increasing D and E and vice versa. The method mentioned above was tested on both metamorphic samples of the Pannonian Basin and Variscan granitoid rocks of the Mórágy Complex. Percolation values predicted for the Mórágy granite are highly sensitive to alterations in the input parameters. The amphibolite bodies displayed a modeled fracture network with 80 to 90% of all fractures being interconnected, while the largest achievable percolation cluster size of gneiss is less than 10%. The REV size of the amphibolite is about 20 m as a result of connected fractures filling the whole body, while gneiss has lower porosity and higher REV (approximately 70 m).     

Comparing Reservoir and Outcrop Specimens for Mixed Mode I–II Fracture Toughness of a Limestone Rock Formation at Various Conditions

Summary A fracture toughness study was conducted on a limestone rock formation from a petroleum reservoir in Saudi Arabia, and results were compared with those for outcrop specimens from the same geological formation. The objective was to investigate the possibility of using outcrop specimens to estimate the fracture toughness behavior of reservoir rock at in-situ conditions of temperature and confining pressure. The study was made on reservoir specimens from a depth of about 3.5 km, at both ambient and reservoir conditions. Mixed mode I–II fracture toughness at reservoir conditions of high temperature and confining pressure was studied using straight notched Brazilian disk (SNBD) specimens under diametrical compression. Tests were conducted at ambient conditions, at an effective confining pressure (σ₃) of 28 MPa (4000 psi), and at a temperature of 116^°C. The results showed a substantial increase in fracture toughness under confining pressure. Under σ₃=28 MPa, the pure mode-I fracture toughness (K _IC), increased by a factor of about 3.2, and the pure mode-II fracture toughness (K _IIC) increased by a factor of 4.4, compared to those under ambient conditions. On the other hand, K _IC at 116^°C was only 25% more than that at ambient conditions. These results were compared with recent results for outcrop specimens from the same geological formation. The results reveal that outcrop specimens can be successfully used to predict the fracture behavior of reservoir specimens at in-situ conditions, in spite of some differences at ambient conditions. Additionally, fracture toughness envelopes were obtained for reservoir specimens at ambient and high pressure conditions, in both positive and negative regions. Received September 14, 2000; accepted February 22, 2002 Published online September 2, 2002     

华南早三叠世的古地磁学与大地构造

从华南几个具代表性地点的下三叠统灰岩中,获得了有意义的古地磁学初步结果。这些结果支持华南存在分离板块的设想。根据新近获得的地质与古地磁学证据,推断华南存在4个岩石图板块。它们是扬子(D=232.4°,I=-11.8°,K=28.2,α₉₅=5.5°),湘桂(D=198.0°,I=32.2°,α₉₅=12.9°),华夏(D=88.0°,I=13.0°,K=20.1,α₉₅=9.1°)和海南(上二叠统D=338.2°,I=15.9°,K=10.2,α₉₅=14.3°)板块。4个板块的古地磁极位分散,纬度差明显,并存在碰撞后的局部与区域性的旋转作用,尤其是顺时针旋转。华南早中生代的大地构造可理解为4个来自古特提斯和冈瓦纳的岩石圈碎块与欧亚大陆聚合作用的产物。     

Effect of stress history on CPT and DMT results in sand

In order to investigate the effect of stress history on in-situ test results in granular sediments, a series of CPTs and DMTs are performed on Busan sand prepared in the calibration chamber. K_D is found to be the most sensitive to the stress history among CPT and DMT measurements. E_D and q_c are observed to be similarly affected by the stress history and, therefore, the E_D–q_c relation appears to be almost independent of the stress history. The K_D–D_R relation established without considering the stress history is likely to overestimate the relative density of OC sand. It is shown that the existence of the pre-stress of the granular sediment can be indirectly recognized by an estimation of the relative density larger than 100% when using the K_D–σ_v′–D_R relation suggested for NC sand. Although q_c/σ_v′–K_D/K₀ and E_D/σ_v′–K_D/K₀ relations are heavily influenced by the stress history, q_c/σ_m′–K_D/K₀ and E_D/σ_m′–K_D/K₀ relations are observed to be independent of the stress history. Based on these relations, charts to evaluate the K₀ value from q_c and/or DMT indices are developed for both NC and OC sands. The design chart based on E_D/σ_m′–K_D/K₀ and E_D/σ_v′–K_D/K₀ relations is expected to be practically useful as the usage of this chart requires only DMT indices. The developed design charts are applicable to Busan sand but different sets of equations and charts may be developed for other sands.     

Testing Study of Subcritical Crack Growth Mechanism During Water Rock Interaction

Subcritical crack growth plays an important role in evaluating the long-term stability of structures in rocks. By applying the constant-displacement-relax method, two groups of test specimens that one immersed in groundwater and the other in air were tested to get the parameters of subcritical crack growth in double torsion test. The relations of the stress intensity factor K _I versus the subcritical crack growth velocity V were obtained under the two different environments, and the behavior of subcritical crack growth was also analyzed. The results showed: the relations of lg K _I  ? lg V accorded with linear rules, which is in good agreement with Charles theory; Compared with specimens in nature state, the lg K _I  ? lg V curves of saturated water specimens locate top left comer of those of air specimens. The slope of curve is smaller, and the intercept is bigger, which shows that the water–rock interaction speeds up the subcritical crack growth. And A increases 2.9 × 10¹⁸ folds but n decreases from 85.12 to 40.83 because of the water–rock interaction. Meanwhile, the fracture toughness K _IC also decreases obviously from 2.55 in air to 2.26 in water due to water rock interaction. The testing results provide a basis for time-dependence of rock engineering stability.     

Study on acoustic emission characteristics of sandstone under different fracture modes

To investigate the characteristics of the sandstones under two fracture modes which are tensile fracture and shear fracture, we proposed three-point bending test and a modified shear test. Meanwhile, numerical simulations using particle flow code (PFC) and acoustic emission (AE) analysis are performed to obtain their differences. The AE hits and amplitude analyses prove that no matter which mode, they experience obvious three stages. The AE hit curve and amplitude are lower in the first stage. Then, the curve goes up steadily and the amplitude value becomes relatively large in the second stage. Entering into the third stage, the curve increases quickly to its peak value and a lot of AE signals with higher amplitude are generated. Moreover, AE b-value analysis is also used to make crack magnitude assessment. It was obvious that the distribution of b-value curve can be divided into three stages, which are just corresponding to the division of AE hits and amplitude distributions. The b-values are diverse and fluctuating largely in stage I and then show small fluctuations and have increasing trends in the whole process in stage II whereas finally exhibit sharp down to the minimum points at the stage III. The average b-values for tensile fracture tests are in the range of 0.877–1.09 whereas for shear fracture tests are within the range of 0.815–0.876. Comparing to tensile fracture, when shear fracture occurs in the rock sample, the AE energy releases faster and the proportion of large magnitude cracks is larger. The research results in this article could make more instructive and applied value to in situ non-destructive monitoring of fissure development for engineering rock mass.     

Application of Cracked Triangular Specimen Subjected to Three-Point Bending for Investigating Fracture Behavior of Rock Materials

Numerical and experimental studies were performed on a new fracture test configuration called the edge cracked triangular (ECT) specimen. Using several finite-element analyses, the fracture parameters (i.e., K _I, K _II, and T-stress) were obtained for different combinations of modes I and II. The finite-element results show that the ECT specimen is able to provide pure mode I, pure mode II, and any mixed-mode loading conditions in between. Also, a series of mixed-mode fracture experiments were conducted on Neiriz marble rock using the proposed specimen. Furthermore, the generalized maximum tangential stress (GMTS) criterion was used to predict the experimental results. The GMTS criterion makes use of a three-parameter model (based on K _I, K _II, and T) for describing the crack tip stresses. Due to the significant positive T-stresses that exist in the ECT specimen, typical minimum fracture toughness values were expected to be obtained when the ECT specimen is used. The direction of fracture initiation and the path of fracture growth were also obtained theoretically using the GMTS criterion, and good agreement was observed between the experimental fracture path and theoretical simulations. The fracture study of this specimen reveals that the ECT specimen can be also used in mixed-mode fracture studies of rock materials in addition to the conventional circular or rectangular beam test samples.     

Tensile Fracture Strength of Brisbane Tuff by Static and Cyclic Loading Tests

This research presents the results of laboratory experiments during the investigation of tensile strength–strain characteristics of Brisbane tuff disc specimens under static and diametral cyclic loading. Three different cyclic loading methods were used; namely, sinusoidal cyclic loading, type I and II increasing cyclic loading with various amplitude values. The first method applied the stress amplitude?cycle number (s–n) curve approach to the measurement of the indirect tensile strength (ITS) and fracture toughness (K _IC) values of rocks for the first time in the literature. The type I and II methods investigated the effect of increasing cyclic loading on the ITS and K _IC of rocks. For Brisbane tuff, the reduction in ITS was found to be 30 % under sinusoidal loading, whereas type I and II increasing cyclic loading caused a maximum reduction in ITS of 36 %. The maximum reduction of the static K _IC of 46 % was obtained for the highest amplitude type I cyclic loading tested. For sinusoidal cyclic loading, a maximum reduction of the static K _IC of 30 % was obtained. A continuous irreversible accumulation of damage was observed in dynamic cyclic tests conducted at different amplitudes and mean stress levels. Scanning electron microscope images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both inter-granular fracturing and trans-granular fracturing. The main characteristic was grain breakage under cyclic loading, which probably starts at points of contact between grains and is accompanied by the production of very small fragments, probably due to frictional sliding within the weak matrix.     

The influence of porosity gradients on mixing coefficients in sediments

The surface layer of aquatic sediments is a zone characterized by both porosity gradients and intensive mixing. In the standard approach, porosity gradients are ignored when estimating mixing intensity. Here, model formulations with both constant and varying porosity are contrasted to estimate mixing coefficients D_b from tracer depth profiles. Complementing the well-known exponential solution of the constant-porosity model, we present a general solution to the variable-porosity model in terms of hypergeometric functions. When using these models in a forward way, the tracer activities predicted by the variable-porosity model are higher than those generated by the constant-porosity model. Similarly, when inverse modelling, D_b values estimated by the variable-porosity model are systematically higher than those derived from the constant-porosity model. Still, differences in D_b values remain relatively small. When applying both mixing models to excess ²¹⁰Pb data profiles from slope sediments, a maximal difference of 30% is obtained between D_b values, the average deviation being 16%. A systematic exploration of parameter space predicts a maximal underestimation of 60% when deriving D_b values from the constant-porosity mixing model. Given the uncertainty imposed by other model assumptions underlying the diffusive mixing model, the influence of porosity gradients on D_b values must be classified as rather modest. Hence, the current mixing coefficient database is not biased by the constant porosity approximation.     

Fracture toughness analysis on cracked ring disks of anisotropic rock

Summary  This paper presents a combination of the Boundary Element Method (BEM) and the cracked ring test to determine the mixed-mode (I–II) fracture toughness of anisotropic rocks. The proposed BEM is used to accurately calculate the Stress Intensity Factors (SIFs) of a cracked anisotropic plate. An anisotropic Hualien marble of Taiwan with a distinct foliation was selected to conduct the cracked ring tests. Based on the measurement of the failure load during the test, the mixed-mode (I–II) fracture toughness can be determined. Experimental results show that the radius ratio, inclination and crack angle significantly affect the fracture toughness. The mode-I fracture toughness (K _IC ) is shown to decrease with the increase in hole diameter, whereas the mode-II fracture toughness (K _IIC ) increases with the increase in hole diameter when the crack angle β is equal to 0°. The experimental methods proposed have the advantage that the material is easily prepared, the test procedure is simple, and the cost is low. Correspondence: Chia-Hau Chen, Chao-Shi Chen, Department of Resources Engineering, National Cheng Kung University, 701 Tainan, Taiwan     

A two-phase model for the description of the influence of cracks on the P- and S-wave velocities in dry and saturated rock samples

The premonitory variations of seismic-wave velocities before earthquakes originate from various cracking processes before the fracture. It can be shown that these variations are comparable with wave-velocity variations in porous model samples with defined pore sizes. Furthermore, it is possible to describe analytically the variation of wave velocities as a function of the parameter K₀, which describes the fracturing process, and a material/depth parameter AP. On the basis of the wave velocity vs. pressure curves of rocks, it is possible to determine K₀ and A. Using the material/depth parameter AP sediments in covering strata and eruptive rocks in regions of earthquakes of shallow to medium depth can be descirbed. A relationship between Δυ_D and ΔK₀ can be established. For acid to ultrabasic rocks, a variation of up to 2 km/s indicates a variation of K₀ of 0.1–1.0.Moreover, it is possible to establish a relationship between K₀ and the number as well as the mean length of cracks in the rock. The solutions differ depending on the cracks being closed or open. For closed cracks a wave-velocity minimum of 6% results. For oper cracks the variations of the number and mean length of cracks are taken into account by means of a stochastic process; the resulting variations of K₀ and the wave velocity car adequately explain the variations in seismic-wave velocity. Variations of the pore pressure have an influence on K₀and the wave velocity only under most favourable geologica conditions; generally they are insignificant. Also for S-wavc velocities and for the ratio υ_p/υ_s the wave velocity vs. pressure equations are valid; it is possible to state K₀ and A-values.     

Seismic source characteristics in Kachchh and Saurashtra regions of Western India: b-value and fractal dimension mapping of aftershock sequences

Seismic source characteristics in the Kachchh rift basin and Saurashtra horst tectonic blocks in the stable continental region (SCR) of western peninsular India are studied using the earthquake catalog data for the period 2006–2011 recorded by a 52-station broadband seismic network known as Gujarat State Network (GSNet) running by Institute of Seismological Research (ISR), Gujarat. These data are mainly the aftershock sequences of three mainshocks, the 2001 Bhuj earthquake (M _w 7.7) in the Kachchh rift basin, and the 2007 and 2011 Talala earthquakes (M _w ≥ 5.0) in the Saurashtra horst. Two important seismological parameters, the frequency–magnitude relation (b-value) and the fractal correlation dimension (D _c) of the hypocenters, are estimated. The b-value and the D _c maps indicate a difference in seismic characteristics of these two tectonic regions. The average b-value in Kachchh region is 1.2 ± 0.05 and that in the Saurashtra region 0.7 ± 0.04. The average D _c in Kachchh is 2.64 ± 0.01 and in Saurashtra 2.46 ± 0.01. The hypocenters in Kachchh rift basin cluster at a depth range 20–35 km and that in Saurashtra at 5–10 km. The b-value and D _c cross sections image the seismogenic structures that shed new light on seismotectonics of these two tectonic regions. The mainshock sources at depth are identified as lower b-value or stressed zones at the fault end. Crustal heterogeneities are well reflected in the maps as well as in the cross sections. We also find a positive correlation between b- and D _c-values in both the tectonic regions.

     

In-situ rock stress measurement from rock cores using the acoustic emission method and deformation rate analysis

In this study the possibilities of the acoustic emission (AE) technique and deformation rate analysis (DRA) were investigated to measure in situ rock stress. The rock cores were obtained from three vertically drilled exploratory boreholes from the surface and one borehole drilled from within an underground coal mine. The AE method was found to determine in situ rock stress with reasonable accuracy using AE signatures in repeated loadings of a rock core specimen. Based on the results of in situ stress estimation from the AE method, the time interval, up to seven years, did not strongly influence the previous stress determination using the AE method. Cored rock recollected the in situ stress condition reasonably well (within ±10%), when compared to the results from over coring and hydraulic fracturing technique. Also, there was significant correlation between overburden pressure and estimated vertical stress from the AE method.     

Interpretation of reservoir rock mechanical properties by direct methods

Direct core analysis results of bulk density, porosity permeability, resistivity, transit time, and strength were correlated with logging data from an oil well. The interpretations were made in terms of index values between field and laboratory data obtained for the two reservoir units studied. An engineering classification scheme was suggested. Other rock engineering properties such as sonic velocity and dynamic modulus were calculated as well. An attempt was made to predict the fracture pressure gradient (FPG) of rock formation. This work has revealed the possibility of using the direct measured data to evaluate some of the in situ rock behavior.Notations K _L Liquid Permeability (m.d.) - K _g Gas permeability - a Constant dependent on rock type - poissons ratio - R _c Resistance of brine saturated core (ohm.m) - R _w Resistivity of Brine (Salt water) (ohm.m) - I _s Point Load Index value (Kg/cm²) - g accelaration constant of gravity - _ac Apparant acoustic log porosity - _D Apparent density log porosity - q Shaliness index - p Poisson ratio index - P _o Over burden pressure (Psi)     

Relationships Between Fundamental Seismic Hazard Parameters for the Different Source Regions in Turkey

Turkey has been divided into eight different seismic regions taking into consideration the tectonic environments and epicenters of the earthquakes to examine relationships of the modal values (a/b), the expected maximum magnitudes (M_max) and the maximum intensities (I_max). For this purpose, the earthquakes for the time period 1900–1992 from the Global Hypocenter Data Base CD-ROM prepared by USGS, and for the time period 1993–2001 from the PDE data and IRIS data are used. Concerning the relationships developed between different magnitude scales and between surface wave magnitudes (M_S) and intensity for different source regions in Turkey, we have constructed a uniform catalog of M_S. We have estimated the values of M_max and I_max using the Gumbel III asymptotic distribution. Highest a-values are observed in the Aegean region and the lowest b-values are estimated for the North Anatolian Fault. Maximum values of a/b, M_max and I_max are related to the eastern and western part of the North Anatolian Fault and the Aegean Arc. The lowest values of all parameters are observed near the Mid Anatolian Fault system. Linear relationships have been calculated between a/b, M_max and I_max using orthogonal regression. If one of the three parameters is computed, two other parameters can be calculated empirically using these linear relationships. Hazard maps of M_max and I_max values are produced using these relationships for a grid of equally spaced points at 1°. It is observed that the maps produced empirically may be used as a measure of seismic hazard in Turkey.