Numerical analyses of deformability tests in jointed rock — “Joint Perturbation” and “No Tension” Finite Element solutions

SummaryNumerical Analyses of Deformability Tests in Jointed Rock — Joint Perturbation and No Tension Finite Element Solutions Sound design of structures in or upon rock requires a thorough knowledge of the rock mass deformability. Field test data interpretation has generally relied upon analytical or Finite Element linear elastic solutions. However, when testing in jointed rock, these can no longer be readily used since the medium cannot resist the tension induced upon loading. Accordingly, other solutions are required. If the discontinuities of the rock mass can all be mapped and their surface properties determined, the Finite Element model will use a Joint Perturbation solution where the joint elements have variable stiffnesses to account for movements along the fractures. If the discontinuities cannot be satisfactorily mapped, a global approach is provided by a No Tension analysis of the stress transfer type. The two techniques are compared in the case of bore hole jack deformability tests and found to agree remarkably well, indicating an appreciable difference from results of linear elasticity.

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ZusammenfassungNumerische Analyse von Verformungsversuchen in geklüfteten Fels — Lösungen mittels Kluft-Perturbation und No Tension Analysis auf Grund der Methode der Finiten Elemente Der Entwurf von Bauwerken in oder auf Fels erfordert eine genaue Kenntnis des Formänderungsverhaltens der Felsmasse. Im allgemeinen basiert die Interpretation der Ergebnisse von Feldversuchen auf den Lösungen des zugehörigen Randwertproblems der linearen Elastostatik mittels klassischer analytischer Methoden oder der Methode der Finiten Elemente. Wenn die Versuche aber in geklüftetem Fels durchgeführt werden, müssen die theoretischen Methoden modifiziert werden, da das Medium keine Zugspannungen aufnehmen kann. Zwei Fälle können unterschieden werden. Erstens: die Kluftflächen der Felsmasse können geometrisch erfaßt und ihre Oberflächeneigenschaften können bestimmt werden; in diesem Falle kann die Finite-Elemente-Lösung eine Kluft-Perturbations-Methode verwenden, in welcher spezielle Kluft-Elemente verschiedener Steifigkeiten normal und tangential zu den Kluftflächen die Bewegungen entlang derselben bestimmen. Zweitens: die Diskontinuitäten der Felsmasse können nicht hinreichend beschrieben werden; für diesen Fall ist vorgekehrt durch die Finite-Element-Analyse vom Typ der Spannungsumlagerung unter Ausschaltung der Zugspannungen (No Tension Analysis), um das globale Verhalten der geklüfteten Felsmasse zu erfassen. Die Lösungen dieser beiden Methoden wurden für den Fall der Bohrloch-Verformungs-Tests verglichen; der Vergleich zeigt ausgezeichnete Übereinstimmung, im Gegensatz zu den Lösungen als lineares Elastizitätsproblem.

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RésuméLa méthode des Eléments Finis appliquée aux résultats d'essais de vérins cylindriques dans les roches fissurées — solutions dites Joint Pertubé et Sans Traction La construction de structures sur ou dans des roches nécessite une connaissance approfendie de la déformabilité du massif rocheux. L'analyse des résultats d'essais en place se fait généralement à l'aide de solutions analytiques ou par Eléments Finis, qui supposent une élasticité linéaire du milieu. De fait, dans les roches fissurées, ces solutions sont inadéquates puisque le milieu ne peut résister aux sollicitations de traction. Il s'agit donc d'utiliser d'autres méthodes d'analyse. Lors qu'il est possible de déterminer la géométrie et les propriétés de toutes les discontinuités, l'on pourra utiliser une solution par Eléments Finis, dite Joint Perturbé dans laquelle la rigidité de surface du joint (ou fissure) peut varier lorsque des movements prennent place au niveau du joint. Si cela est impossible, il faudra utiliser une approche globale dite Sans Traction qui redistribue les contraintes de traction et les dissipe. On compare ces deux types de solutions dans le cas des essais de vérins cylindriques unidirectionnels. Leurs résultats sont identiques et ont nettement différents de ceux obtenus avec une solution élastique linéaire.

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Research supported by the National Aeronautics and Space Administration — Contract NAS 8-21432.

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With 8 Figures     

THE IMPACT-FLOOD CONNECTION: DOES IT EXIST?*

In a recent article in Terra Nova, Kristan-Tollmann and Tollmann (1994) suggested that the Biblical Flood can be explained by seven fragments of a comet that impacted the ocean at seven locations on Earth at 03.00h (C.E.T.) on 23 September, 9545 yr BP. We demonstrate that all the ‘geological proofs’ that allegedly support their conclusions are not supported by the available data on impact cratering. Their hypothesis is based on insufficient and ambiguous data, selective citation, and incomplete comprehension of previous research.     

Supercritical gas sorption on moist coals

The effect of moisture on the CO₂ and CH₄ sorption capacity of three bituminous coals from Australia and China was investigated at 55 °C and at pressures up to 20 MPa. A gravimetric apparatus was used to measure the gas adsorption isotherms of coal with moisture contents ranging from 0 to about 8%. A modified Dubinin–Radushkevich (DR) adsorption model was found to fit the experimental data under all conditions. Moisture adsorption isotherms of these coals were measured at 21 °C. The Guggenheim–Anderson–de Boer (GAB) model was capable of accurately representing the moisture isotherms over the full range of relative pressures.Moist coal had a significantly lower maximum sorption capacity for both CO₂ and CH₄ than dry coal. However, the extent to which the capacity was reduced was dependent upon the rank of the coal. Higher rank coals were less affected by the presence of moisture than low rank coals. All coals exhibited a certain moisture content beyond which further moisture did not affect the sorption capacity. This limiting moisture content was dependent on the rank of the coal and the sorbate gas and, for these coals, corresponded approximately to the equilibrium moisture content that would be attained by exposing the coal to about 40–80% relative humidity. The experimental results indicate that the loss of sorption capacity by the coal in the presence of water can be simply explained by volumetric displacement of the CO₂ and CH₄ by the water. Below the limiting moisture content, the CO₂ sorption capacity reduced by about 7.3 kg t^− 1 for each 1% increase in moisture. For CH₄, sorption capacity was reduced by about 1.8 kg t^− 1 for each 1% increase in moisture.The heat of sorption calculated from the DR model decreased slightly on addition of moisture. One explanation is that water is preferentially attracted to high energy adsorption sites (that have high energy by virtue of their electrostatic nature), expelling CO₂ and CH₄ molecules.