Vielfache Bruchstrukturen bei einfachen Beanspruchungen — Rechnerische Untersuchungen mit Hilfe der Finite-Element-Methode

Zusammenfassung Die Finite-Element-Methode ist ein neues, auf die Benutzung von Großrechenanlagen ausgerichtetes Rechenverfahren, das sich mit Erfolg bei der Lösung von Spannungs-Verformungs-Problemen anwenden läßt. Diese Methode erwies sich bei technischen Problemen allen anderen Rechenverfahren gegenüber als überlegen und hat in den letzten Jahren in nahezu allen Sparten des Ingenieurwesens, die Felsmechanik eingeschlossen, Eingang gefunden. Seitdem einige Finite-Element-Versionen (z. B.Malina, 1969) elastoplastisches Stoffverhalten und Spannungsumlagerungen beim lokalen Bruchvorgang erfassen können, eignet sich diese Methode auch zur Simulation bestimmter tektonischer Vorgänge.Rechnerisch untersucht wird eine Scheibe der Dicke 1 (ebener Verformungszustand), in der ein kurzer Anriß vorgegeben ist. Ab einer gewissen Beanspruchung pflanzt sich der Anriß durch die Anlage von Neubrüchen fort. Es entsteht eine Scherzone, die durch ein vielfältiges Bruchflächengefüge gekennzeichnet ist. Die entstehenden Bruchflächenmuster hängen auf empfindliche Weise von den Neigungsunterschieden der im Mohrschen Diagramm definierten Grenzkurven für das unzerbrochene Material bzw. für die Diskontinuitäten ab. Die Kohäsion bleibt ohne Einfluß auf das Bruchflächengefüge.Die Rechnung entwickelt zwei Generationen von Scherflächen, ohne daß die von außen auf den Probekörper einwirkende Belastung in Größe und Richtung geändert worden wäre. Nach der Anlage von primären Scherflächenpaaren kommt es zur Entwicklung sekundärer Scherflächenpaare. Primäre und sekundäre Scherflächenpaare haben voneinander abweichende Stellungen. Sie bilden zusammen komplexe Scherkörper, die je nach Materialeigenschaften als Scherlinsen oder als Pseudo-Mohrsche Scherflächenkörper ausgebildet sind. Nach dem Entlasten bleiben im untersuchten Körper beträchtliche Restspannungen zurück, die zur Umkehr der Relativbewegungen entlang bestehender Gleitflächen und zur Anlage von neuen Zugrissen führen.Die in der Rechnung gewonnenen Ergebnisse ermöglichen ein vertieftes Verständnis vieler tektonischer und geotechnischer Erscheinungen (z. B. syn- und antithetische Brüche, Störungen zweiter Ordnung, Scherlinsen, Fiederklüfte, Restspannungen, oberflächenparallele Klüfte, verschiedene Striemungsrichtungen auf einer Harnischfläche, ac-Klüfte, Bruchstrukturen im Dreiaxialversuch). Die Rechnung zeigt, daß vielfache Bruchstrukturen nicht immer durch mehrphasige, unterschiedlich gerichtete Beanspruchungen verursacht sein müssen. Es ist denkbar, daß sie auch bei einfachen Beanspruchungen entstehen können.

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The finite-element-method is a new calculation method, which using big computers can successfully be applied to stress-strain problems. In solving technical problems this method has proved to be better than all other present calculation methods and has been successfully applied in nearly all branches of engineering science, including rock mechanics. Since some finite-element-versions (e.g.Malina, 1969) are able to regard elastoplastic material properties and stress rearrangements due to local fracture this method is also suitable for simulating certain tectonic processes.A plate of unit thickness (plane strain) is considered, in which a small crack already exists. At a certain state of stress, the crack propagates by creating new rupture surfaces. A shear zone develops, which is characterized by a complex fracture fabric. The developing patterns of shear and sliding surfaces change sensitively with the inclination of theMohr envelopes for the unfractured material and the discontinuities resp. Cohesion has no influence on the fracture fabric.The computation gives two generations of shear surfaces, without any change in the magnitude and direction of the external load. After the formation of primary pairs of shear surfaces secondary pairs develop. Primary and secondary shear surfaces differ in their orientation. Together they form complex shear bodies, which, depending on material properties, are shear lenses or quasi-Mohr-shear bodies. With the release of the external load, residual stresses are stored within the plate. These stresses cause a reversal in the sense of sliding movement and development of new fractures.The results of computation allow a better understanding of many tectonic and geotechnical phenomena (e. g. synthetic and antithetic fractures, second order faults, shear lenses, feather joints, residual stresses, surface-parallel joints, different striae orientations on slickensided surfaces, ac-joints, fracture patterns in triaxial compression tests). The computations show that multiple fracture patterns are not necessarily caused by poly-phase, multiaxial loading. It seems possible that these patterns can also develop under simple load conditions.

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Résumé La méthode des éléments finis permet de résoudre avec beaucoup de succès les problèmes de contraintes et de déformations à l'aide d'ordinateurs de grande capacité. Cette méthode s'est révélée supérieure à tous les autres procédés de calcul pour résoudre les problèmes techniques et elle est appliquée depuis quelques années à presque toutes les branches des sciences de l'Ingénieur, y compris la mécanique des roches. Depuis que quelques versions de calcul des éléments finis (par exempleMalina, 1969) peuvent prendre en considération le comportement élasto-plastique des matériaux et les redistributions des contraintes dues à des ruptures locales, cette méthode convient aussi à la simulation des phénomènes tectoniques.Un disque d'épaisseur unitaire (déformations planes), dans lequel existe une courte fissure est soumis au calcul. A partir d'une certaine sollicitation, la fissure se prolonge par de nouvelles ruptures. Ainsi se forme une zone de cisaillement qui est caractérisée par une structure multiple des surfaces de rupture. Le dessin ainsi formé par ces surfaces de rupture dépend sensiblement des différences d'inclinaison des courbes limites telles qu'elles sont définies dans le diagramme deMohr, soit pour le matériau intact, soit pour les discontinuités. La »cohésion« n'a aucune influence sur la structure de ces surfaces de rupture.Le calcul développe deux générations de surfaces de rupture, sans que l'intensité et la direction de la charge extérieure affectant l'échantillon ne soient modifiées. Après le développement des couples de surfaces de rupture primaires, se forment des couples de surfaces de rupture secondaires dont les directions sont différentes des premières. Elles forment ensemble des corps de cisaillement complexe, qui, selon les propriétés du matériau, s'expriment sous la forme soit de lentilles de cisaillement, soit de corps » pseudo-Mohr « de surfaces de cisaillement. Après suppression de la charge, il persiste dans le modèle des contraintes résiduelles importantes qui entraînent des mouvements de retrait le long des surfaces de glissement existantes et de nouvelles fissures dues aux efforts de traction.Les résultats obtenus par le calcul permettent de mieux comprendre de nombreux phénomènes tectoniques et géotechniques (tels que les fractures synthétiques et antithétiques, les failles de deuxième ordre, les lentilles de cisaillement, les fissures réticulées, les contraintes résiduelles, les fissures parallèles à la surface, les diverses directions des stries de glissement sur les miroirs de faille, les fissures de type ac, les structures de fracture dan l'essai triaxial). Le calcul montre que les multiples structures de fracture ne sont pas toujours dues à des efforts multiphasés de directions différentes. On peut penser qu'elles se forment également sous des états de contraintes simples.

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Diese Arbeit ist im SFB 77 - Felsmechanik« -, Karlsruhe, entstanden. Der Autor dankt für vielfache Hilfe und Anregungen, insbesondere den Herren Dr. H.Malina und cand. geol. B.Hoffers.     

Simulation of SH- and P-SV-wave propagation in fault zones

Seismic fault-zone (FZ) trapped waves provide a potentially high-resolution means for investigating FZ and earthquake properties. Seismic waves emitted within and travelling along low-velocity FZ layers may propagate many kilometres within the low-velocity structure associated with the fault. Waveform observation of FZ trapped waves can be modelled in terms of FZ layer velocities, thicknesses and attenuation coefficients. This can greatly improve the resolution of imaged FZ structure and microearthquake locations. At present, broad-band theoretical seismograms are restricted to plane-parallel layers of uniform properties. However, it is not clear how realistic these models are compared with actual fault structures which could, for example, flare outwards near the surface, have irregular boundaries, interior heterogeneities, etc. To address these interpretational uncertainties, we perform finite-difference simulations for irregular FZ geometries and non-uniform material properties within the layers. The accuracy of the numerical solutions are verified by comparison with the analytical solution of Ben-Zion & Aki (1990) for plane-parallel structures. Our main findings are: (1) FZs can widen at the ctustal surface only slightly modifying the trapped waves; (2) velocity variations with depth destroy trapped wave propagation at all wavelengths; (3) FZ trapped waves can be obscured by the presence of a low-velocity surface layer; (4) models with short-scale random structures suggest that trapped waves average out irregular FZ geometries, and hence can be effectively modelled by average-property plane-layered media for the observed range of wavelengths.     

Nifte: The near infrared faint-object telescope experiment

The high sensitivity of large format InSb arrays can be used to obtain deep images of the sky at 3–5 m. In this spectral range cool or highly redshifted objects (e.g. brown dwarfs and protogalaxies) which are not visible at shorter wavelengths may be observed. Sensitivity at these wavelengths in ground-based observations is severely limited by the thermal flux from the telescope and from the earth's atmosphere. The Near Infrared Faint-Object Telescope Experiment (NIFTE), a 50 cm cooled rocket-borne telescope combined with large format, high performance InSb arrays, can reach a limiting flux < 1 Jy (1) over a large field-of-view in a single flight. In comparison, ISO will require days of observation to reach a sensitivity more than one order of magnitude worse over a similar area of the sky. The deep 3–5 m images obtained by the rocket-borne telescope will assist in determining the nature of faint red objects detected by ground-based telescopes at 2 m, and by ISO at wavelengths longer than 5 m.     

Structural Properties and Deformation Patterns of Evolving Strike-slip Faults: Numerical Simulations Incorporating Damage Rheology

We present results on evolving geometrical and material properties of large strike-slip fault zones and associated deformation fields, using 3-D numerical simulations in a rheologically-layered model with a seismogenic upper crust governed by a continuum brittle damage framework over a viscoelastic substrate. The damage healing parameters we employ are constrained using results of test models and geophysical observations of healing along active faults. The model simulations exhibit several results that are likely to have general applicability. The fault zones form initially as complex segmented structures and evolve overall with continuing deformation toward contiguous, simpler structures. Along relatively-straight mature segments, the models produce flower structures with depth consisting of a broad damage zone in the top few kilometers of the crust and highly localized damage at depth. The flower structures form during an early evolutionary stage of the fault system (before a total offset of about 0.05 to 0.1 km has accumulated), and persist as continued deformation localizes further along narrow slip zones. The tectonic strain at seismogenic depths is concentrated along the highly damaged cores of the main fault zones, although at shallow depths a small portion of the strain is accommodated over a broader region. This broader domain corresponds to shallow damage (or compliant) zones which have been identified in several seismic and geodetic studies of active faults. The models produce releasing stepovers between fault zone segments that are locations of ongoing interseismic deformation. Material within the fault stepovers remains damaged during the entire earthquake cycle (with significantly reduced rigidity and shear-wave velocity) to depths of 10 to 15 km. These persistent damage zones should be detectable by geophysical imaging studies and could have important implications for earthquake dynamics and seismic hazard.     

Millimetre/submillimetre-wave emission-line searches for high-redshift galaxies

The redshifted spectral line radiation emitted from both atomic fine-structure and molecular rotational transitions in the interstellar medium (ISM) of high-redshift galaxies can be detected in the centimetre, millimetre and submillimetre wavebands. Here we predict the counts of galaxies detectable in an array of molecular and atomic lines. This calculation requires a reasonable knowledge of both the surface density of these galaxies on the sky, and the physical conditions in their ISM. The surface density is constrained using the results of submillimetre-wave continuum surveys. Follow-up OVRO Millimeter Array observations of two of the galaxies detected in the dust continuum have provided direct measurements of CO rotational line emission at redshifts of 2.56 and 2.81. Based on these direct high-redshift observations and on models of the ISM that are constrained by observations of low-redshift ultraluminous infrared galaxies, we predict the surface density of line-emitting galaxies as a function of line flux density and observing frequency. We incorporate the sensitivities and mapping speeds of existing and future millimetre/submillimetre-wave telescopes and spectrographs, and so assess the prospects for blank-field surveys to detect this line emission from gas-rich high-redshift galaxies.