Summary
When subjected to cyclic shearing, loose dry sand densifies, and undrained saturated sand may liquefy. These phenomena have to be described in terms of the complete loading history. An effective procedure for such a description would be to utilize the concept of “internal state variable.” In this work, relative void ratio (i.e. the difference in void ratio and its minimum value) and pore water pressure are considered as internal variables for densification and liquefaction phenomena, respectively. Incorporating these quantities into a thermodynamic framework and in conjunction with evolutionary equations, a unified theory for densification and liquefaction of a macroscopically homogeneous sample of isotropic cohesionless sand is proposed, and the corresponding stress-strain relation is then developed. The basic observation underlying the theory is that these phenomena involve a rearrangement of grains at microlevel, that requires expenditure of a certain amount of energy which increases as the void ratio approaches its minimum value, and decreases as the excess pore water pressure increases. Based on this energy consideration the evolutionary equations are developed in such a manner that when combined with stress-strain relation, they yield expressions relating stress (or strain) to the number of cycles and other relevant parameters. On the basis of rather rough estimates these relations are then rendered explicit and the results are applied to predict some of the existing experimental data.
Übersicht
Unter dem Einfluß von zyklischen Scherbeanspruchungen wird trockener Sand verdichtet, gesättigter nasser Sand kann verflüssigt werden. Um diese Erscheinungen zu erfassen, muß der gesamte Belastungsverlauf berücksichtigt werden. Man kann dazu die inneren Zustandsvariablen verwenden. Hier werden das relative Füllungsverhältnis und der Porenwasserdruck als innere Variable für Verdichtung und Verflüssigung verwendet. Es wird eine allgemeine Theorie für makroskopisch homogenen, isotropen und kohäsionslosen Sand vorgeschlagen. Daraus werden die Spannungs-Dehnungs-Beziehungen abgeleitet. Der Theorie liegt die Beobachtung zugrunde, daß die genannten Phänomene eine Umorientierung der Sandkörner im Mikrobereich erforderlich machen. Die hierzu notwendige Energie steigt, wenn sich das Füllungsverhältnis seinem größten Wert nähert, und sie sinkt, wenn der Porenwasserdruck ansteigt. Mit Hilfe dieser Energie-Betrachtungen werden die Verdichtungsgleichungen so formuliert, daß sie in Verbindung mit den Spannungs-Dehnungs-Beziehungen Aussagen über Spannung und Dehnung in Abhängigkeit von der Zykluszahl gestatten. Durch rohe Abschätzungen lassen sich explizite Ausdrücke finden, deren Ergebnisse zur Voraussage von experimentellen Daten verwendet werden.
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References
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Dedicated to Professor Hans Ziegler on his seventieth birthday
This work has been supported in part by the Atomic Energy Organization of Iran, and in part by the U.S. Geological Survey under Contract No. 14-08-0001-17770
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Nemat-Nasser, S., Shokooh, A. A framework for prediction of densification and liquefaction of sand in cyclic shearing. Ing. arch 49, 381–392 (1980). https://doi.org/10.1007/BF02426917
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DOI: https://doi.org/10.1007/BF02426917