ALBERT

Notes: Abstract A theory of deep earthquakes, termed the inclusion collapse theory, is proposed in this paper. In the inclusion theory of crustal (or shallow) earthquakes, faults were shown to terminate within an inclusion zone. This zone represents a region within the brittle portion of the lithospheric plate that contains open cracks (voids) of varying sizes that, to a first order approximation, are uniformly distributed throughout the inclusion zone. When the lithospheric plate containing these faults and their associated inclusions is subducted into the mantle, the stress normal to the fault planes must increase. A depth is eventually reached where slippage along the fault planes is no longer possible. Earthquakes are postulated to occur at a specified depth within the mantle as a result of processes leading to collapse of these voids. When the long-term modulus of the plate is much greater than the long-term modulus of the mantle, large pressures are shown to develop within the plate during periods of active subduction. These pressures are shown to be sufficient to initiate partial collapse of voids of similar geometry throughout the inclusion zone. The inclusion collapse theory and the concentration of pressure within the plate lead to four results. (1) Earthquakes that are produced by a void collapse mechanism will not occur below a subduction depth calculated to be between 350 and 1000 km (2) The physical process most likely responsible for producing void collapse is the formation of shear, melt zones whose thicknesses are on the order of 1 to 10 cm in the immediate vicinity of the voids. This mechanism, is shown to produce a ‘precursor’ time on the order of a few hundred seconds during which there is a release of shear strain prior to the earthquake. (3) The maximum energy released by void collapse is independent of the source depth. (4) The number of earthquakes produced by this process will decrease hyperbolically with source depth. Source depth, in the context used in this article, refers to the depth in the mantle to the inclusion zone where voids of similar geometry are undergoing partial collapse. The maximum source depth refers to the depth where all voids have closed.

Notes: Abstract The scale invariant inclusion theory of failure is applied to the problem of aftershock sequences. In the inclusion theory, a macrocrack, or void of low aspect ratio, the length of which depends upon the magnitude of the impending mainshock, forms within the inclusion zone of the impending earthquake. The fault zone that precedes the inclusion zone represents that part of the macrocrack that has closed. It is shown that bifurcation (branching) of the macrocrack and its associated fault must occur within the focal region of the inclusion during the growth phase of the earthquake. The bifurcation process produces extensive faulting of the material that comprises the focal region. A prediction of the inclusion theory is that each fault within the focal region will terminate within a zone of concentrated dilatancy that may or may not be in an unstable state. When the zone is unstable, an aftershock will occur. It is shown that these inclusion zones will, on the average, occur near the boundaries of the focal region. Failure of these unstable zones leads to additional failures within the interior portions of the focal region. These failures represent ‘lock point’ failures along the fault(s) and will, in general, exhibit few or no additional aftershocks. The bifurcation model of aftershock sequences leads to five results: (1) The aftershock sequence will exhibit an inverse hyperbolic time decay law when the stresses that are applied at distances far removed from the hypocenter remain constant during the sequence and when there isno interaction between the brittle lithosphere (where aftershocks occur) and the underlying asthenosphere. (2) The mean magnitude of any group of aftershocks within the sequence will be approximately constant in time. (3) The aftershocks will, in general, have focal mechanisms identical to that of the mainshock. (4) Large seismic events that occur throughout the aftershock zone will be independent of one another when the aftershocks are sufficiently far apart (∼two-three ‘fault’ lengths) and when the applied tectonic stresses remain constant during the sequence. (5) The bifurcation model predicts that theb-value of the aftershock sequence will be 1.0 when both the Utsu relationship between aftershock area and mainshock magnitude and the Gutenburg Richter frequency-magnitude relationship are satisfied.

Notes: Summary The density of a subducting plate is shown to become greater than the density of the adjacent mantle rock at a subduction depth on the order of 60 km. The density increase results from high pressures generated within the plate during its motion into mantle rock whose long-term strength is much less than the long-term strength of the plate. This positive density contrast between the plate and mantle is in addition to any positive density contrast that may result from the plate not being in thermal equilibrium with the adjacent mantle rock. The effect of this pressure induced density contrast on the overall down-dip stress distribution in the plate is shown to be insignificant on earthquake formation except, possibly, near the upper, near-surface portions of the plate. Implications of this result in terms of the inclusion collapse theory of deep earthquakes are discussed.

Notes: Summary The scale independent inclusion theory of rock failure developed in Part I is applied to the problem of crustal earthquakes and, in particular, to the problem of premonitory phenomena reported to precede such earthquakes. Several well-known premonitory effects such as anomalous variation in the ratio of longitudinal (V p ) and shear (V s ) seismic velocities,V p /V s , tilt, regional and local crustal movements and stress axis rotation, to mention a few, are shown to be a natural consequence of the physical processes leading to failure in dry rock. The effects of fluids on failure in the focal region of a potential earthquake are considered in terms of the scale independent inclusion theory.

Notes: Abstract Anomalous seismicity changes (increase followed by a decrease) were recorded prior to three moderate rock bursts in the Star mine, Burke, Idaho. In each case, based upon the anomalous seismicity behavior, miners were evacuated or were prohibited from entering active mine stopes that were located in the immediate vicinity of the seismicity buildup prior to the bursts. Analyses of pre- and post-seismic activity are interpreted in terms of, and shown to be consistent with, the inclusion theory of failure. Implications of these observational results for the problem of rock bursts and earthquake prediction are discussed.

Notes: Summary A scale independent failure theory governing the initiation and subsequent growth of the shear fault in rock is presented in this article. Four distinct phases of behavior in this theory are shown to precede fault growth in rock. 1)Dilatant Phase: Cracks form in the rock in response to the applied stresses. This phase begins at a maximum principal stress whose magnitude is usually well below the ultimate strength of the rock. 2)Inclusion Phase: Clusters of cracks develop in the rock at a point in time when the rock is within a few per cent of its ultimate strength. The clusters behave physically as low modulus elastic inclusions embedded within a host material of higher modulus. As a result of this ‘elastic’ contrast, there is a rotation of the principal stress axes and a decrease in the magnitude of the principal stress difference in the focal region of the inclusion; that is, the region into which the inclusion will grow at failure. 3)Closure Phase: In this phase, there is closure of cracks in the focal region in response to the decrease in the magnitude of the principal stress difference due to the formation of the inclusion. As a result of crack closure in the focal region, the stress concentration in the focal region increases and becomes a maximum once all cracks which opened during the dilatant phase are closed. At this time, the transverse tensile stress in the interior of the inclusion also reaches a maximum. Macrocrack growth within the inclusion begins. 4)Growth Phase: Fault growth commences during this phase. Reopening of previously closed cracks occurs due to the increase in the principal stress difference in the focal region resulting from macrocrack growth within the inclusion. New cracks form and rapid growth of the macrocrack (in its own plane) occurs once the length of the mecrocrack exceeds a critical value. The fault represents the portion of the macrocrack which has closed.

Notes: Abstract The scale invariant inclusion theory of failure is applied to the general problem of precursors that precede failure. A precursor is defined to be an effect produced within a physical system which indicates that the process leading to failure of the system has begun. Precursors are grouped into three classes.Class I precursors refer to long-term indicators of impending failure. These may includev p/vs, long-term tilt, and crustal uplift anomalies observed to precede some major shallow earthquakes by afew years. Class II precursors refer to short-term indicators of failure and include: S-bend tilt, electromagnetic radiation, radon emanations, and seismicity changes that have been reported to precede major earthquakes by afew hours. Class III precursors refer tovery short-termphenomena such as long-period (strain) waves,rapid changes in surface ground tilts, and seismicity increase in the hypocentral region that are predicted by the inclusion theory to precede major shallow earthquakes by afew seconds. The physical processes that occur within the inclusion zone of an impending failure that indirectly produce the class II precursors are used with the scale invariant properties of failure to show that their time duration is a direct measure of the average length of the cracks that comprise the inclusion zone. This result is used to derive the precursor time-‘fault’ length relationship that has been observed to hold for class I precursors of shallow earthquakes, mine failures, and laboratory size failures of rock. The physical model proposed for producing class I, class II, and indirectly, the class III precursors leads to six results when both the Utsu relationship between aftershock area and earthquake magnitude and the Gutenberg-Richter energy-magnitude relationship are satisfied. (1) The seismic efficiency factor for failures satisfying the constraints of the inclusion theory is approximately 0.40%. (2) The energy radiated by aftershocks will be at least 1.0% of the energy radiated bythe mainshock. (3) An upper limiting magnitude of any aftershock in the aftershock sequence isM−1.6, whereM is the mainshock magnitude. (4) The time durations of all three precursor classes are shown to be shortened (or lengthened) by a factor inversely proportional to the rate of increase (or decrease) of the far-field stresses during the time duration of the precursor. Changes in far-field stresses, such as might occur to tidal effects, are shown to be of particular importance in initiating class II precursors, and it is shown that tidal stresses provide a mechanism for triggering large earthquakes (M≥6.0) in regions that are at the point of incipient failure. Thus, class II precursors may give the appearance of being independent of magnitude for large earthquakes. (5) When fluids are present in the focal volume of the mainshock, the predicted magnitude, calculated by class I precursors, will always be larger than the observed magnitude. (6) Seismic events that produce the inclusion zone of the impending mainshock will not be followed by aftershocks. These events are predicted to be characterized by anomalously long rupture lengths. The inclusion theory is shown to provide a physical basis for criteria required to predict failure. The implications of the inclusion theory to the problem of earthquake prediction are discussed. The theory is applied to existing earthquake-prone regions.

Notes: Summary An Experimental Determination of the True Uniaxial Stress-Strain Behavior of Brittle Rock Results are presented of an experimental study of the behavior of six rock types deformed under uniaxial compression into their respective post-failure regions. Based on the observation that a rock sample in a post-failure state can be considered to be composed of broken and unbroken rock and assuming that the reduction in load-bearing capability of rock in the post-failure region is due to a reduction of the effective cross-sectional area of the specimen resulting from the growth of large cracks within the rock sample, we show that there is a maximum true stress that the unfractured solid rock can sustain without inelastic deformation. This stress is constant and is defined to be the true failure strength of the rock. The value of this stress is calculated by dividing the force on the rock sample at any point along the post-failure curve by the true load-bearing cross-sectional area of the rock sample at that point. Theoretical and experimental techniques are developed which allow an estimate of the true load-bearing area of the rock sample at any point along the post-failure curve of the sample. For the rock types used in the study, which were deformed to preselected positions along their respective post-failure curves and with the assumption that the fractured rock carried none of the applied load, the two techniques of measuring the effective load-bearing area give results which are equivalent.

Notes: Summary Laboratory and In Situ Mechanical Behavior Studies of Fractured Oil Shale Pillars Preliminary results are reported of a cooperative research agreement between the U. S. Bureau of Mines and the Colony Development Operation of the Atlantic Richfield Corporation. The overall objective of this program is to correlate laboratory and in situ behavior of fractured oil shale pillars and to use this information to develop design criteria for underground room-and-pillar mining of oil shale. In situ stress measurements in the Colony mine have been made in pillars of oil shale containing joints of which the planes of weakness are oriented at low angles (〈45°) to the pillar axis. Four findings of importance have resulted from these measurements. 1) Some pillars are in a post-failure condition, that is, an increase in deformation in the pillars results in a decrease in the load the pillars can sustain; 2) Pillar failure begins when the maximum and minimum stresses within the pillar become approximately 5,000 psi and 800 psi, respectively; 3) In situ measurements suggest that the stresses carried by the “solid” portion of a pillar become constant when the fractured pillar is in a post-failure condition; 4) Severely fractured pillars in a post-failure condition can be stabilized, that is, further fracturing can be prevented, by the addition of small radical confinement such as provided by rock bolting normal to the major joint pattern in the pillar. The latter three observations are predicted from laboratory studies on model pillars of oil shale containing joints oriented with respect to the applied stress field as its in situ counterpart. The application of these results and problems associated with applying them to design room-and-pillar mining in oil shale is discussed.

Notes: Summary The Effect of Normal Stiffness on the Shear Resistance of Rock This paper presents the theory and design of a shear machine whose normal stiffness could be varied by four orders of magnitude. Experimental techniques, testing procedures, and special equipment designed by the Bureau of Mines for determining the effect of normal stiffness on the shear stress-normal displacement behavior of intact and prepared joint surfaces of both hard (granite) and soft (sandstone) rock under constant shear displacement rate are described. Experimental results are presented which show that the effect of increasing the normal stiffness on either intact rock or fractured surfaces is to provide increased normal confinement. Increased normal confinement results in an increased shear strength for rock. Engineering significance of this result is discussed.