RESPONSE OF A SOIL HALF-SPACE MODEL TO A DYNAMIC SURFACE LOAD

A PHYSICALLY CONSISTENT MATHEMATICAL MODEL FOR THE STUDY OF ELASTIC SOLIDS IS PROPOSED. BASED ON THIS MODEL THE EQUATIONS OF MOTION FOR A POINT IN THE SOLID ARE DERIVED, AND THEIR VALIDITY IS PROVED BY TRANSFORMING THEM TO THE WELL-KNOWN NAVIER'S EQUATION BY MEANS OF AN INVERSE FINITE DIFFERENCE OPERATOR. THE PHYSICAL CONSISTENCY OF THE MODEL PERMITS THE DERIVATION OF THE EQUATIONS OF MOTION, GIVES THE PHYSICAL INTERPRETATION OF EACH STEP IN MATHEMATICAL DERIVATION AND PERMITS THE CONSTRUCTION OF A PHYSICAL REPRESENTATION OF THIS MODEL TO PERFORM EXPERIMENTAL STUDIES. THE METHOD OF SOLUTION PROPOSED FOR THE EQUATIONS OF MOTION SELECTED FOR THIS PROBLEM WAS TO FIND THE DISPLACEMENTS AT ANY TIME OF ALL POINTS OF A SEMI-INFINITE ELASTIC SOLID DUE TO A CONCENTRATED VERTICAL SURFACE STEP LOAD. A PHYSICAL REPRESENTATION OF THE MATHEMATICAL MODEL CONSISTING OF THOUSANDS OF CUBES AND SPRINGS WAS BUILT AND FOUND TO BEHAVE AS THEORETICALLY PREDICTED. THE LOADING SYSTEM DEVELOPED PERMITS THE APPLICATION OF STEP LOADS WITH ANY INCLINATION AT ANY POINT OF THE SURFACE OR SIDES OF THE MODEL. THE PHOTO-INTERCEPTIVE DISPLACEMENT TRANSDUCERS WERE DEVELOPED TO MEASURE DISPLACEMENTS. FOUR SPECIFICALLY DESIGNED INTERCEPTIVE PLATES WERE USED TO AUTOMATICALLY COMPENSATE FOR THE EFFECT OF THE ROTATIONS. THE INSTRUMENT WAS DESIGNED TO BE PLACED AT ANY POINT IN THE SURFACE OR INTERIOR OF THE 3-DIMENSIONAL MODEL. DISPLACEMENT MEASUREMENTS SHOW A HIGH DEGREE OF REPRODUCIBILITY AND ARE VERY CONSISTENT. THE STUDIES OF THE WAVE ARRIVALS, SHAPES AND AMPLITUDES FROM THE EXPERIMENTAL AND THEORETICAL DISPLACEMENT-TIME CURVES, SHOW THAT THE EXPERIMENTAL MODEL BEHAVES AS THEORETICALLY PREDICTED. /AUTHOR/

  • Supplemental Notes:
    • Res Series NO 13, 385 PP, FIGS, TABS, REFS, 5 APP
  • Corporate Authors:

    Princeton University

    Soil Physics Laboratory
    Princeton, NJ  USA 
  • Authors:
    • Simpser, B D
  • Publication Date: 1968-4

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Filing Info

  • Accession Number: 00235389
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Nov 12 1994 12:00AM