Inhomogeneous Rock Research Articles

Variational principles developed for and applied to porous-elastic solids

A dual variational principle is formulated for a general porous-elastic material in Laplace transform space. The material may be anisotropic and spatially inhomogeneous. As an application of the theory, we consider two problems of a crack in an infinite strip of inhomogeneous rock. In the first we bound the Stress Intensity Factor in both the transform and real time domains. For the second, we place bounds on a function of the poroelastic Stress Intensity Factor and pore pressure gradient coefficient, in transform space. The bounds are compared with an effective medium solution in both cases. We discuss the significance of the method with regard to bounding effective properties in non-static problems. We obtain, in implicit form, bounds on effective permeability for a rigid porous solid in transform space. These suggest the effective property is history dependent. Asymptotic methods are used to obtain large and small time results.

In situ stress heterogeneity and crack density distribution

Stress magnitude distribution often shows a heterogeneous state which is influenced by the inhomogeneity of rocks or formations. A new analytic method is investigated to study the relationship between the stress state and rock material properties. Crack densities, which are obtained from the core materials and log data have been compared with the in situ shear stress variation with depth. The crack densitites change gradually together with the shear stress state. Herein, a model is presented in which stress release from the high shear stress state is accompanied by crack growth, but once these stresses are relieved, crack growth stops.

The relations between mean rock stress and fluid flow in the crust: With reference to vein- and lode-style gold deposits

Fluid movement in the crust at the typical depths of formation of vein- and lode-style gold deposits will be dominated by upward flow. Focussing of upward flow into discrete channelways, as required to form gold deposits, is due to lateral gradients in fluid pressure. Fluid channelways should have lower fluid pressures than surrounding rock, if lateral gradients are induced by variations in permeability. This is, however, at variance with inferences from quartz-vein structures of high relative fluid pressures during the formation of gold deposits. Focussing into zones of low mean rock stress will, in contrast, be associated with high relative fluid pressures in the zone of focussed fluid flow. Variations in mean rock stress are a direct consequence of a regional deviatoric stress acting on an inhomogeneous rock sequence. Analysis of stress fields shows a wide variety of potential sites of low mean stress, dependent on the geometry of rock units, and on patterns of faults, fractures or shear zones. A model of fluid focussing in the crust due to variations in mean stress is thus consistent with the large variety of structural setting of vein- and lode-gold deposits observed in nature. Use of the model, through the technology of ‘stress-mapping’, has the potential to generate viable exploration targets.

Radiowave propagation in a coal seam with inhomogeneous rock walls

An idealized slab model of a horizontal coal seam is adopted. The structure is laterally uniform, but the media within and outside the slab are allowed to be inhomogeneous in the vertical direction. A general mode equation is obtained, and simplifications are made to facilitate computation of the propagation constant of the dominant mode. Using an exponential variation of the rock conductivity, it is shown that the frequency dependence of the attenuation rate is strongest for a conductivity increasing with distance into the rock media.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Local effects on tidal strain measurements at Esashi, Japan

SUMMARY Finite element modelling has been used to make a quantitative investigation of local factors affecting the measurement of tidal strain at the Esashi earth tide station. Factors investigated, with the approximate magnitude of the perturbation produced by each, are topography (12 per cent), regional geology (1 per cent), inhomogeneity of the elastic properties of the granodiorite from which the strainmeter tunnels were excavated (3 per cent), and the cavity effect (2 per cent). Correction for these factors reduces the average discrepancy between the observed strains (observational accuracy ~1 per cent) and those predicted from the solid earth and ocean loading tide from 23 to 8 per cent. After such correction the ratios of observed to modelled amplitudes of the O1 and M2 tides on each strainmeter are in fair agreement, but these ratios differ from strainmeter to strainmeter; they are about 7 per cent too large on the N-S and NE-SW strainmeters and 9 per cent too small on the E-W instrument. These studies illustrate the difficulties involved in relating strains measured in an observatory such as Esashi to those representative of the surrounding region and suggest that, with the level of detail and sophistication used, this relationship cannot be modelled to much better than 10 per cent. Systematic differences between results from the mid-point and free-end strainmeters imply that the effects of small-scale rock inhomogeneities have not been modelled correctly.

Statistical theory of emission processes in loaded structurally inhomogeneous rocks and the problem of predicting dynamic phenomena

Statistical theory of emission processes in loaded structurally inhomogeneous rocks and the problem of predicting dynamic phenomena

Elastoplastic problem for a structurally inhomogeneous rock mass weakened by a circular working

Elastoplastic problem for a structurally inhomogeneous rock mass weakened by a circular working

Identification of geometric characteristics of inhomogeneous rock masses by AIC method: Ohnishi, Y; Higashide, A Proc International Symposium on Engineering in Complex Rock Formations, Beijing, 3–7 November 1986P945–950. Publ Beijing: Science Press, 1986

Identification of geometric characteristics of inhomogeneous rock masses by AIC method: Ohnishi, Y; Higashide, A Proc International Symposium on Engineering in Complex Rock Formations, Beijing, 3–7 November 1986P945–950. Publ Beijing: Science Press, 1986

A geochemical study of the Proterozoic Sandsjön granite, south-western Sweden

Abstract The Sandsjon granite, with a U-Pb zircon age of 1210 Ma, belongs to the younger ensialic granites in the South-western Gneiss Complex of the Baltic Shield. The granite is red to reddish grey, medium- to coarse medium-grained, and foliated. The geochemical characterization is based on 55 new whole-rock analyses. Statistical treatment of the analyses results in a split of the granite massif into two chemically distinguishable groups. These two groups occupy defined areas within the massif but no mappable criteria to recognize the two granite types can be found. The separation into two groups is most evident in the distribution of the immobile elements incl. REE. Also the contents of sericite, myrmekite and perthite together with the accessories zircon and allanite separate the two groups. It is suggested that these differences are due to inhomogeneous source rocks for the Sandsjon granite and that a vestigial source rock palaeocontact can be traced.

A hybrid boundary element—finite element method of stress analysis for bolt-reinforced inhomogeneous ground

A numerical implementation of stress analysis for bolt-reinforced ground is presented by combining the use of boundary and finite elements. The stresses and deformations around underground openings are derived by considering the interactions between rock movement, bolt tension and bending. The rocks are piecewise inhomogeneous and contain planes of weakness. Boundary elements are used to represent the openings and interfaces between strata, while rock bolts which can be fully grouted or partially grouted are represented by finite elements. The reinforcements of bolts are related to the movements of rocks and the displacement discontinuities along the planes of weakness. Furthermore, the effect of the bearing plates is simulated by using additional boundary elements in contact with the surface of the openings. With the use of an indirect formulation method for inhomogeneous solids, all the effects of rock inhomogeneities, unloading along opening surfaces, sliding and/or separations along planes of weakness, bolt reinforcements at axial and transverse directions, and the reactions of bearing plates are incorporated into a mechanical model for the entire domain of interest. Several examples are presented which show that the numerical method developed and adopted in this paper is very efficient in solving the rock bolting problems.

THE VEIN TYPE OF OIL AND GAS TRAP

Recent investigations have led the authors to identify a new type of hydrocarbon trap, the formation of which involves dilatation and hydrothermal reworking. In principle, these can involve any rock type, but in practice, vein-type traps form primarily in inhomogeneous brittle and soluble rock types, and the features may be either primary or acquired during epigenesis. The traps form along seismically stressed zones where these meet favorable rocks and can develop in multiple stages. The presence of the traps is confirmed by findings the authors have obtained during surveys in the Salym and Krasnolena regions of West Siberia. This article discusses the development of a gross fracture porosity by seismic fracturing followed by deposition and later solution of vein minerals and suggests methods of exploration for such fracture zones. 15 references.

Sulfur and lead isotope studies of stratiform Zn-Pb-Ag deposits, Anvil Range, Yukon; basinal brine exhalation and anoxic bottom-water mixing

Five stratiform Zn-Pb-Ag deposits are known in Early Cambrian metapelitic rocks along a curvilinear trend in the Anvil Range, central Yukon. The Anvil Range deposits occur along the southwestern boundary of the Selwyn basin in the stratigraphic transition zone between metapelites of the Mt. Mye unit and calcareous phyllites of the overlying Vangorda unit. The massive sulfides are associated closely with anomalously thick graphitic phyllites, apparently related to a second-order basin. A typical Anvil cycle of mineralization begins with a ribbon-banded graphitic-quartzitic-pyritic unit. This grades upward into sulfide-bearing quartzite, quartzitic massive sulfide, massive sulfide, and finally a baritic massive sulfide horizon. Sericitic alteration envelopes irregularly encompass each deposit and locally are developed best in footwall rocks.Detailed sulfur isotope studies have been carried out on the DY and Grum deposits and on one representative drill hole from the Faro deposit. The delta 34 S values of sulfide minerals generally range from 10 to 22 per mil and are similar in all three deposits. The delta 34 S values of pyrite in unmineralized samples from the district exhibit a wider range, from 6 to 34 per mil, and show distinct upward stratigraphic increase due to a stagnation cycle in the basin.The delta 34 S values of barite samples are strongly dependent on bottom-water conditions and mode of mixing during brine exhalation. They range from 22 to 26 per mil in the Faro deposit to 36 to 42 per mil in the DY deposit. These variations are due to mixing of isotopically light sulfate (18-20ppm) in Ba-bearing ore fluid and isotopically heavy residual sulfate (30-60ppm) in anoxic seawater.Thirty-eight samples of galena from the DY, Grum, Faro, SB, and Swim deposits have been analyzed for lead isotope ratios. In general, the lead isotope ratio data indicate an upper crustal lead source, with the Proterozoic Grit unit which is inferred to underlie the district being the most likely source rock. A small component of mantle leads from mafic igneous rocks or due to source rock inhomogeneity is also indicated.Graphitic host lithologies, lack of stratiform iron oxides, delta 34 S values of sedimentary pyrite, and sulfide sulfur-organic carbon variations in unmineralized cores indicate formation of the Anvil deposits in strongly reduced bottom water related to a previously unknown Early Cambrian anoxic event.

地殻応力測定結果にみられる岩盤の不均質性の影響

Stress relief method has been often adopted to measure the in-situ stress state, and in this method various types of gauge have been used. If different types of gauge are used, different results can be expected. Moreover, stress distribution in an inhomogeneous rock mass is probably not uniform. Although these problems remain, they have not been clearly elucidated with in-situ data. In this study, the results measured in the same site with both hollow inclusion gauges and doorstopper-type 8-element gauges are compared. Consequently, it is shown that both results indicate the same tendency of a horizontally uniaxial compressive stress state. However, there are some differences in the magnitudes of the stresses between the two methods of measurement. Furthermore, upon examining the data obtained in this site in detail and referring to the data of two other sites, the effect of the inhomogeneity in a rock mass is discussed. As a result, it is concluded that the magnitude of in-situ stress in hard intact rock is larger than that in soft weathered rock and the dnfference between them is from 2 to 4MPa.

Studying hydrofractures by high frequency seismic monitoring

Two experiments were carried out in salt and granite to address several questions regarding the utility of seismological techniques for monitoring the propagation of a hydrofracture. More specifically, could techniques developed for earthquake analysis be used to characterize the detectable acoustic emission (AE) activity associated with the hydrofracture process, and could the AE activity be used to define the geometry of the hydrofracture, and characterize its manner of propagation? To answer these and other questions, 3-D arrays of piezoelectric sensors were placed around the immediate hydrofracture zones in a small scale laboratory experiment (300 x 300 x 450 mm triaxially confined salt block) and a shallow, 35 m, field experiment (5 x 5 x 5 m granite mine). Confirmation of the seismic techniques was provided by using dyed fluids for the hydrofracture experiments and later visually inspecting the hydrofracture zones by breaking the salt block apart and mining back the rock in the granite mine. Results of the experiments show that there is abundant detectable discrete seismic activity, and that high frequency seismicity can be very useful for determining the path and geometry of the hydrofracture. Tensile failure “events” can be directly related to the actual path of the hydrofracture, whereas the shear failures are not as closely related to the actual fracture path, but are nevertheless related to the overall dimensions of the hydrofracture. Source sizes of individual events as inferred from the seismic data varied from 5 to 7 mm in the salt block experiment (average grain size = 5 m) to 5 to 10 cm in the granite field experiment. Energy release of the events averaged 10 2 N-m (10) 9 dyne-cm) in the laboratory and 10 3 N-m (10 10 dyne-cm) in the field experiment. All events in the laboratory test were primarily tensile failure in nature as inferred from the waveform radiation patterns; however, in the field experiment, there were shear events as well as “harmonic tremor” type events in addition to the tensile failure. The occurrence rate, spatial, and temporal distribution of the events indicate that the hydrofracture growth pattern, at least for these two cases, is not symmetrical and does not follow the often assumed symmetric paths. The data indicate that the hydrofracture process is a complicated phenomenon and that the “fracture” is actually made up of a network of fractures which forms a zone around a main fracture. The overall direction of the hydrofracture and the surrounding zone is strongly influenced by rock inhomogeneities and anisotropy as well as the stress directions.

FUNDAMENTAL STUDY ON IDENTIFICATION OF ELASTIC CONSTANTS AND GEOMETRY CHARACTERISTICS OF INHOMOGENEOUS ROCK MASSES

Recently attension is being directed toward developing a numerical procedure whose objective is to determine a set of parameters from a set of observed displacements at the field. The procedure, so called “Identification or Inverse” problem, is general and can be applied to any geotechnical problems, in which the system parameters are to be identified. In this paper, the method to identify the elastic constants and geometry characteristics of inhomogeneous rock masses is presented. Elastic parameters are calculated by the optimization process in mathematical programing. Geometry characteristics are determined by Akaike's information criterion (AIC) which estimates the maximum likelihood of the system. Several examples of tunnel problems with loosend area are examined and evaluated by the proposed method.

Fracture systems and fault-block tectonics : Zhang Wenyou; Li Yinhuai; Zhong Jiayou Sci Sin, V24, N12, Dec 1981, P1717–1731

Rocks under stress exceeding their shear shrength, X-shaped conjugated fracture-net willappear, taking the inclpient Luders' bands as their foundation. Owing to non-uniformof stress and inhomogeneity of rock, one branch of fractures develops better than another.Under still further increasing stress, zigzag fractures of tensile nature usually develop byadapting each other alternately to the already formed X-shaped shear surfaces. Thus we maytentatively assume that fracture usually starts with shear fracturing deformation and deve-lops and ends with tensile fracturing deformation. Fracture systems may be tentatively clas-sified into 3 fundamental categories, i.e. X-shaped shear fracture systems, Y-shaped shear-tension fracture systems, and I-shaped tensile fracture systems. Once a fracture system isformed, their activities may be grouped into 5 categories as follows, (i) compression, (ii) ten-sion, (iii) shear (sinistral and dextral), (iv) compression-shear, and (v) tension-shear. Therole that a fracture can play in tectonic deformation is mainly determined by the depth whichit penetrates. Based on this principle, fractures may elassified into 4 major categories andanother one, (i) lithospheric fracture, (ii) crustal fracture, (iii) foundational fracture, (iv)superficial fracture, and (v) interlayer gliding fracture. Fault-blocks eut by various fracturenet-works of different depth into the earth may be also divided into 4 major categories ofdifferent thickness, i.e. lithospheric, crustal, foundational and superficial fault-blocks. Relativemovements between the fault-blocks may play an important role in controlling the formationand deformation of the overlying strata.

Limit state equations for gas saturated homogeneous and inhomogeneous media and rock

Limit state equations for gas saturated homogeneous and inhomogeneous media and rock

Theoretical interaction between noncircular supports in underground workings and an inhomogeneous viscoelastic rock mass

Theoretical interaction between noncircular supports in underground workings and an inhomogeneous viscoelastic rock mass

Experimental-analytical method of determining the abutment pressure at a seam-roof contact in inhomogeneous rock : Maksyutenko, L Y; Alekseev, A D Sov Min Sci, V13, N1, Jan–Feb 1977, P71–73

Experimental-analytical method of determining the abutment pressure at a seam-roof contact in inhomogeneous rock : Maksyutenko, L Y; Alekseev, A D Sov Min Sci, V13, N1, Jan–Feb 1977, P71–73

Finite element analysis of foundation on inhomogeneous rock mass : Ohnishi, Y Mem Fac Engng Kyoto Univ, V39, N3, July 1977, P403–415

Finite element analysis of foundation on inhomogeneous rock mass : Ohnishi, Y Mem Fac Engng Kyoto Univ, V39, N3, July 1977, P403–415