Koji Matsuki

Synthetic rough fractures in rocks

Natural fractures serve a very important function in the transport of fluid through rocks, as well as in the flow of electrical charge and heat. The creation of numerically synthesized fractures can aid the study of the physical processes connected with fractures. Synthetic fracture is the term used to describe fractures that are created numerically in such a way that they share the same mean geometrical characteristics as specific natural fractures measured by profiling, by a process known as tuning. We have modified methods for producing synthetic rough surfaces whose geometric properties are tuned to mimic natural fracture surfaces in rocks in order to create synthetic fractures that are statistically identical to those found in rocks. One important such modification has been the incorporation of a method that allows the surfaces to be matched at long wavelengths and unmatched at short wavelengths, with the degree of matching varying smoothly in between, as it does for real fractures. We have compared numerically synthetic fractures created using the new method with fractures created using an existing technique that uses a mismatch wavelength as a sudden discontinuity between matched and unmatched behavior, as well as data from fractures in real rocks. This comparison has shown that the new technique provides much more realistic numerically synthesized fractures than previous methods. Synthetic fractures created with the new method have been used in normal closure and fluid flow modeling, and the results are reported in a companion paper.

Stress and rock mechanics issues of relevance to HDR/HWR engineered geothermal systems: review of developments during the past 15 years

This paper reports the findings of the Stress and rock mechanics working group of the Academic Review of Hot Dry Rock/Hot Wet Rock (HDR/HWR) Engineered Geothermal Systems convened in Sendai, Japan in 1997. Key developments in the fields of stress and rock mechanics that are relevant to the development of HDR/HWR systems and that have occurred since the last Academic Review in 1982 are described. Rock mechanics is here taken to include basic studies of fluid flow through fractures. Key unresolved issues that are important for HDR/HWR systems are also discussed.

Fluid flow in synthetic rough fractures and application to the Hachimantai geothermal hot dry rock test site

Fracture profiles from the Hachimantai geothermal hot dry rock (HDR) test site in northern Japan have been measured and analyzed to characterise their geometrical properties. These properties have been used to create a population of numerical synthetic fractures that were tuned to imitate all the geometric and statistical properties of the natural fracture (described in a companion paper). Such fractures have been used as input boundary conditions in three types of modeling. (1) Simple elastic normal closure relating the aperture of the fracture to applied normal load. (2) Hagen-Poiseuille calculations of fluid transmissivity in the fracture as a function of normal load, fracture fluid pressure, and temperature. (3) Two-dimensional flow modeling within the rough walled fracture using Reynolds equation. The modeled closure of these fractures provided a realistic relationship between normal and fracture fluid pressure and aperture. When this pressure/aperture relationship was combined with a Hagen-Poiseuille approach to calculating fluid transmissivity in the fracture, we obtained results which, when compared with data from field transmissivity tests at the Hachimantai site, showed that the functional dependence of fluid transmissivity with fracture fluid pressure was well modeled, but overestimated by a factor of about 2. Reynolds equation flow modeling was carried out in the synthetic fracture to ascertain the extent to which the Hagen-Poiseuille law was overestimating the transmissivity due to the rough surfaces affecting the fluid flow in the fracture. When the calculations were corrected for this effect, the overestimation in the fluid transmissivity was reduced considerably.

Time-dependent closure of a fracture with rough surfaces under constant normal stress

Abstract Time-dependent closure of a fracture with rough surfaces subjected to stepwise normal stress was considered theoretically by viscoelastic modeling of rock. A formula for the relationship between constant normal stress and time-dependent closure as a function of time was derived based on the aperture distributions of a fracture and the relaxation modulus YE′(t) of rock. Theoretical consideration showed that the ultimate closure of a fracture under constant normal stress can be estimated from the normal stress–elastic closure curve by using the values of the relaxation modulus at t=0 and ∞, and that the ultimate time-dependent closure is independent of the normal stress if the elastic closure is linear with the logarithm of the normal stress. Experiments and a Monte Carlo simulation on time-dependent closure under constant normal stress were conducted for a hydraulic fracture created in granite in the laboratory to provide the verification of the theory. The results obtained in the experiments showed that the ultimate time-dependent closure of a hydraulic fracture was almost independent of the normal stress when the elastic closure was linear with the logarithm of the normal stress. A Monte Carlo simulation on time-dependent closure of a fracture under constant normal stress showed that time-dependent closure of a fracture for which the elastic closure is linear with the logarithm of the normal stress does not depend on the normal stress because the increase in contact area during time-dependent closure increases with the normal stress.

Specimen size requirements for determining the inherent fracture toughness of rocks according to the ISRM suggested methods

Abstract In order to clarify the specimen size requirements for determining the inherent fracture toughness of rocks according to the Suggested Methods proposed by ISRM, short rod testing has been carried out for eight rocks. The K -resistance curve was evaluated for these rocks as well as for three rocks from a previous study. From the results, the specification of the specimen size requirements in order to determine the inherent fracture toughness of rocks is proposed in terms of the critical crack extension at which the corrected (level II) fracture toughness reaches a constant value.

The in situ stress states associated with core discing estimated by analysis of principal tensile stress

Abstract Core discing occurs due to tensile stress induced by boring within or below a core stub when the minimum principal stress is nearly in the same direction as the core axis. To determine the effects of the core length on the magnitude and direction of tensile principal stress, a finite element analysis was carried out for an HQ core of different lengths for 77 in situ stress conditions. According to the minimum value and the mean inclination relative to the core axis for ‘the maximum semi-axial tensile stresses’, 30 in situ stress conditions were identified as being stress conditions under which core discing is likely to occur, and conditions necessary for in situ stress were proposed. The critical tensile stress, which is the tensile stress that can produce a tensile fracture that propagates throughout a cross-section, was analyzed for these stress conditions and a new criterion for core discing, which can be applied to a core of any length, was proposed. The stress conditions estimated by the criterion were consistent with previous experimental results for a long core and for thin discs. According to the criterion, the relationship between the core length and the in situ stress necessary for core discing was examined. Our analysis showed that the stress field can be divided into three regions and that core discing of short length mostly occurs at great depth. The average relationship between the core length and the disc thickness was determined by assuming that the position of a fracture is given by the mean position of ‘the maximum semi-axial tensile stresses’. Our theoretical estimates reproduced previous experimental results regarding the effects of stress magnitude on the thickness of the disc. Thus, the present proposed criterion can be used to estimate the stress condition for core discing with a given disc thickness.

2. Size effect in the fracture toughness of Ogino tuff

Abstract Splitting tests were conducted using large specimens of Ogino tuff in order to investigate the process of fracture propagation and also to clarify the size effect in fracture toughness of the rock-including specifically the effects of thickness, width and height of specimen as well as that of crack length. Two types of stiff loading apparatus, a wedge type and a screw type, were used for controlling fracture propagation; and fracture toughness during the process of fracture propagation was determined with compliance calibration. From the results on size effects, a standard size of the specimen was proposed to obtain a specimen size-independent fracture toughness value in the splitting test.

Damage in a rock core caused by induced tensile stress and its relation to differential strain curve analysis

Abstract A finite element analysis was carried out to analyze the distribution of tensile stress within and below a long HQ core stub for 77 in situ stress conditions. The maximum tensile stress experienced by the core along the axis during boring under in situ stress was accumulated in an equal-area stereonet for a central part of the cross-section. The maximum tensile stress accumulated for a central area of less than about 60% of the total cross-sectional area was concentrated in a certain direction, which was nearly the same direction as the minimum principal stress for all of the stress conditions, except those in which the minimum principal stress ( σ 3 ) was equal to the intermediate principal stress ( σ 2 ). When σ 2 = σ 3 , the direction of the cumulative maximum tensile stress lay approximately in the plane of σ 2 = σ 3 , which is perpendicular to the maximum principal stress. Based on the assumption that a penny-shaped crack is produced normal to the maximum tensile stress in proportion to the magnitude of such stress, the crack density in the core was analyzed by calculating strain under hydrostatic pressure as in differential strain curve analysis (DSCA). The maximum principal crack density in the central part of the core was much greater than the intermediate and minimum principal crack densities, excluding special cases in which σ 2 = σ 3 . The direction of the maximum crack density was similar to that of the accumulated maximum tensile stress. Thus, the direction of the maximum crack density obtained by DSCA predicts the direction of the minimum principal stress rather than that of the maximum principal stress, if the distribution of pre-existing microcracks before stress relief is isotropic and if additional microcracks are produced only by tensile stress during boring under in situ stress. To verify this, crack parameters were measured by DSCA for two cores of quartz-diorite, which were taken by overcoring when the hemispherical-ended borehole technique was used to measure in situ stress. The directions of the maximum crack parameters measured by DSCA were nearly the same as that of the minimum principal stress for one of the cores. For the other core, for which the magnitudes of the intermediate and minimum principal stresses were close to each other and, accordingly, the direction of the minimum principal stress was uncertain, the direction of the maximum crack density estimated by damage analysis under the assumption that σ 2 = σ 3 coincided with the directions of the maximum crack parameters measured by DSCA.

Shear behaviour of fractured rock as a function of size and shear displacement

This paper presents laboratory results regarding the shear behaviour of an artificial tensile fracture generated in granite. We used a direct shear rig to test fractures of different sizes (from 100 mm to 200 mm) under various shear displacements up to 20 mm and cyclic shear stresses with constant normal stress of 10 MPa. To determine the evolution of surface damage and aperture during shear, cyclic loading was performed at designated shear displacements. These changes in the surfaces topography were measured with a laser profilometer ‘non-contact surface profile measurement system’. In addition, changes were also measured directly by using pressure-sensitive film. The results showed that the standard deviation (SD) of the initial aperture of the sheared fracture significantly increases with both shear displacement and size, which result in an increase in the non-linearity of the closure curve (since the matedness of the fracture surfaces decreases with shear displacement). Therefore, we concluded that shear dilation is not only governed by the surfaces sliding over each other, but is also strongly influenced by the non-linearity of closure with shear displacement. Furthermore, while the shear stiffness of the fracture during the initial stage decreases with fracture size, it increases with fracture size in the residual stage. This can be attributed to the fact that only small asperities with short wavelengths were mainly damaged by shearing. Moreover the result showed that the damaged zones enlarge and localise with shear displacement, and eventually tend to form perpendicular to the shear displacement.

Possibility of Shear Type Fracture in Viscoplastic Material under Confining Pressures

Transition from opening‐mode wing crack growth to shear type fracture has been investigated by conducting triaxial compression tests under confining pressures, using epoxy resin cylindrical specimens. The epoxy resin used exhibited viscoplastic deformation characteristics under confining pressures, which is expected to simulate the nonlinear deformation observed commonly for rocks at great depths and to provide useful insight in understanding of the fracture transition in rocks. Under the range of confining pressures, 10 MPa–30 MPa, an array of opening‐mode wing cracks were initiated from a preexisting inclined penny‐shaped crack, as the axial stress was increased. Only the extension of a wing crack was observed to take place under no confining pressure condition. It was shown that the growth of the wing cracks were suppressed when higher confining pressures were applied and shear type fracture consisting of several wing cracks was induced as the deformation progressed. The experimental observation sugges...