Kiyotoshi Sakaguchi

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.

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.

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.

Hydraulic fracturing and permeability enhancement in granite from subcritical/brittle to supercritical/ductile conditions

Hydraulic fracturing experiments were conducted at 200–450 °C by injecting water into cylindrical granite samples containing a borehole at an initial effective confining pressure of 40 MPa. Intensive fracturing was observed at all temperatures, but the fracturing characteristics varied with temperature, perhaps due to differences in the water viscosity. At the lowest considered temperature (200 °C), fewer fractures propagated linearly from the borehole, and the breakdown pressure was twice the confining pressure. However, these characteristics disappeared with increasing temperature; the fracture pattern shifted toward the formation of a greater number of shorter fractures over the entire body of the sample, and the breakdown pressure decreased greatly. Hydraulic fracturing significantly increased the permeability at all temperatures, and this permeability enhancement was likely to form a productive geothermal reservoir even at the highest considered temperature, which exceeded both the brittle–ductile transition temperature of granite and the critical temperature of water.

Stress buildup and drop in inland shallow crust caused by the 2011 Tohoku-oki earthquake events

To examine the change in stress between before and after the Tohoku-oki Mw9.0 earthquake, we performed stress measurements after the earthquake in the Kamaishi mine in Iwate prefecture in northern Japan, located near the northern termination of the mainshock rupture, following previous measurements before the earthquake in the same mine. The results showed that the magnitudes of the three-dimensional principal stresses and the vertical stress drastically increased after the mainshock and, at 1 year after the earthquake, were more than double those before the earthquake. The principal stress magnitudes then decreased with time and returned to almost pre-earthquake levels at about 3 years after the earthquake. These changes can be interpreted in terms of coseismic rupture of the mainshock and the occurrence of aftershocks in the Sanriku-oki low-seismicity region (SLSR), where the Kamaishi mine is located. The drastic increase in stress suggests that the SLSR may act as a barrier to further rupture propagation.

Rock Stress Determination Utilizing Strain Change on Hemispherical Borehole Bottom Surface during Overcoring.

This paper presents a new procedure for rock stress determination, which utilizes the strain change on a hemispherical borehole bottom surface during overcoring, and the limitation of the applicability of the hemispherical-ended borehole technique.The observation equations using the strain coefficients analyzed by FEM at four stages during overcoring is formulated. It is clarified that a more accurate rock stress can be determined by the new procedure, comparing with the conventional one, and shown concretely that the investigation of the measurement quality can be easily carried out, analyzing the residuals between measured and theoretical strains during overcoring. Furthermore, to make clear the limitation of the applicability of the hemispherical-ended borehole technique, the relation between a rock stress state existing prior to boring and drilled direction of borehole for measurement, is analyzed taking notice of the induce stress on a hemispherical borehole bottom surface at two stages during overcoring. It is indicated that the drilled direction of a borehole for measurement may be chosen to minimize the induced stress on the borehole bottom surface during overcoring, when the borehole is drilled in arbitrary direction under a rock stress state existing prior to boring. Then, it is concluded that the investigation of the measurement quality and the calibration test of overcored rock are indispensable to determine rock stress by the hemispherical-ended borehole technique with a high reliability.