THE STRESS-DILATANCY RELATION FOR STATIC EQUILIBRIUM OF AN ASSEMBLY OF PARTICLES IN CONTACT

THE EQUILIBRIUM OF A MASS OF INDIVIDUAL PARTICLES SUBJECT TO A UNIFORM DEVIATORIC STRESS SYSTEM IS STUDIED. THE DILATANCY AND STRENGTH OF AN ASSEMBLY OF INDIVIDUAL PARTICLES IN CONTACT WHEN SUBJECTED TO A DEVIATORIC STRESS SYSTEM IS FOUND TO DEPEND ON THE ANGLE OF FRICTION BETWEEN THE PARTICLE SURFACES, ON THE GEOMETRICAL ANGLE OF PACKING, AND ON THE DEGREE OF ENERGY LOST DURING REMOULDING. A THEORETICAL AND EXPERIMENTAL STUDY OF IDEAL ASSEMBLIES OF RODS AND UNIFORM SPHERES ESTABLISHES EXPRESSIONS FOR THE RELATION BETWEEN THE RATE OF DILATANCY AND THE MAXIMUM STRESS RATIO FOR ANY IDEAL PACKING. THE MATHEMATICAL SOLUTION IS EXTENDED TO THE CASE OF A RANDOM ASSEMBLY OF IRREGULAR PARTICLES BY INVESTIGATING THE CONDITIONS UNDER WHICH THE MASS DILATES SUCH THAT THE RATE OF INTERNAL WORK ABSORBED IN FRICTIONAL HEAT IS A MINIMUM. THE MOHR-COULOMB CRITERION OF FAILURE, WHICH IS STRICTLY APPLICABLE TO A CONTINUUM, IS SHOWN NOT TO HAVE GENERAL APPLICATION TO A DISCONTINUOUS ASSEMBLY OF PARTICLES. EXPERIMENTS ON RANDOM MASSES OF STEEL, GLASS, AND QUARTZ IN WHICH ALL THE PHYSICAL PROPERTIES ARE MEASURED INDEPENDENTLY, SHOW THAT THE MINIMUM ENERGY CRITERION IS CLOSELY OBEYED BY HIGHLY DILATANT DENSE OVERCONSOLIDATED AND RELOADED ASSEMBLIES THROUGHOUT DEFORMATION TO FAILURE. FOR THE SPECIAL CASE OF NO VOLUME CHANGE, THE PLANES OF REPETITION OF PATTERN AND RESULTING FORCES ARE IDENTICAL AND THE SOLUTION AGREES THEN WITH THAT BASED ON THE MOHR-COULOMB THEORY. THE WELL-KNOWN SLIP PLANE IN DRAINED DISCONTINUOUS ASSEMBLIES IS PROVED TO BE THE RESULT OF FAILURE AND HAS NOTHING TO DO WITH THE PEAK STRENGTH. THE THEORY IS APPLIED TO CLAYS WITH THE CONCLUSION THAT THE STATEMENT OF SHEAR STRENGTH IN TERMS OF PARAMETERS OF THE GIVEN EQUATION MAY BE APPLIED TO THE ANALYSIS OF THE STABILITY OF SOIL STRUCTURES BY INTEGRATING THE EQUILIBRIUM OF A SERIES OF ELEMENTS OR SLICES OF THE EARTH MASS.

  • Supplemental Notes:
    • Series A: MATH & PHYSICAL SCIENCES, VOL 269, PP 500-527, 23
  • Corporate Authors:

    Royal Society of London Proceedings /UK

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  • Authors:
    • ROWE, P W
  • Publication Date: 0

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Filing Info

  • Accession Number: 00229160
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Aug 15 2004 2:12AM