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A finite element analysis of strain localization for soft rock using a constitutive equation with strain softening

Eine Finite-Element-Analyse der lokalisierten Verformung von weichem Gestein bei einem Stoffgesetz mit Entfestigung

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Summary

It is well known that deformation and/or strain of geological materials localize when they come close to the failure state. In the present: study, we try to analyze the deformation problem using a constitutive relation with strain hardening and strain softening. The constitutive model of a soft rock and overconsolidated clay using an elasto-plastic constitutive theory with memory was originally developed by Adachi and Oka. This type of formulation is shown to be easily applied to analyze the material behavior of strain softening because there is a similarity to that in viscoplasticity. Using the proposed model, the loss of uniqueness of the solution to the initial value problem can be avoided and a special or complicated numerical technique, e.g., an arc length method, does not need to be used. When we use constitutive equations with strain softening in a finite element analysis, there is a problem of strong mesh size dependency of numerical results. To remedy the mesh size dependency, we generalize the Adachi-Oka model based on the concept of non-localization by Bazant. We apply the proposed constitutive model to the behavior of a sedimentary soft rock in the drained triaxial compression test. It is found that mesh size dependency becomes smaller using the non-localization of the constitutive model.

Übersicht

Bekanntlich findet bei geologischen Stoffen in der Nähe des Versagenszustandes eine Lokalisierung der Verformung statt. Die Analyse dieses Problems wird in diesem Beitrag auf der Grundlage eines Stoffansatzes mit Ver- und Entfestigung unternommen. Entwickelt wurde das zugrunde gelegte elastischplastische Stoffmodell mit Gedächtnis von Adachi und Oka für weiches Gestein und übermäßig verdichteten Ton. Wegen der Ähnlichkeit zur Viskoplastizität läßt sich diese Formulierung des Stoffgesetzes leicht auf die Analyse des Verhaltens von entfestigendem Material anwenden, da der Eindeutigkeitsverlust der Lösung des Anfangswertproblems vermieden wird und besondere Rechenverfahren wie etwa die Bogenlängenmethode nicht benötigt werden. Bei der Benutzung von Stoffgesetzen in einer Finite-Element-Rechnung hängen die Ergebnisse stark von der Netzeinteilung ab. Um dies abzustellen, wird das Modell von Adachi und Oka auf der Grundlage von Bazant's Konzept der Nichtlokalisierung verallgemeinert. Anwendungsbeispiel ist das Verhalten von weichem Gestein im drainierten Triaxial-Test. Es zeigt sich, daß mit dem Konzept der Nichtlokalisierung im Stoffmodell der Einfluß der Netzeinteilung geringer wird.

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Authors and Affiliations

  1. School of Transportation Engineering, Kyoto University, 606, Kyoto, Japan

    T. Adachi (Professor Toshihisa Adachi)

  2. Department of Civil Engineering, Gifu University, Yanagido, 501-11, Gifu, Japan

    Kyoto F. Oka (Professor Fusao Oka)

  3. Department of Civil Engineering, Gifu University, Yanagido, 501-11, Gifu, Japan

    A. Yashima Gifu (Associate Professor Atsushi Yashima)

Authors
  1. T. Adachi
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  2. Kyoto F. Oka
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  3. A. Yashima Gifu
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Adachi, T., Oka, K.F. & Gifu, A.Y. A finite element analysis of strain localization for soft rock using a constitutive equation with strain softening. Arch. Appl. Mech. 61, 183–191 (1991). https://doi.org/10.1007/BF00788052

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  • DOI: https://doi.org/10.1007/BF00788052

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