APPLICATION OF AN INTEGRODIFFERENTIAL EQUATION TO THE ANALYSIS OF GEOTECHNICAL PROBLEMS

An important class of problems in the field of geotechnical engineerin g may be analyzed with the aid of a simple integro-differential equati on. Behavior of ''rigid'' piles(say concrete piles), ''deformable'' pi les(say gravel piles). pile groups, pile-raft foundations, heavily rei nforced earth, flow within circular silos and down drag on cylindrical structures (for example the crusher unit of a mineral processing comp lex) are the type of situations that can be handled by this type of eq uation. The equation under consideration has the form; partial derivat ive w(r, z)/partial derivative + f(z)integral(0)(z)g(xi)(partial deriv ative(2)w(r, xi)/partial derivative r(2) + 1/r partial derivative w(r, xi)/partial derivative r)d xi + h(r, z) = 0 where w(r, z) is the vert ical displacement of a soil particle expressed as a function of the po lar cylindrical space coordinates (r, z) and the symbols f; g and h re present soil properties and the loading conditions. The merit of the a nalysis is its simplicity (both in concept and in application) and the ease with which it can be expressed in a computer code. In the presen t paper the analysis is applied to investigate the behavior of a singl e rigid pile to bedrock. The emphasis, however, is placed on equation, the numerical techique used in its evaluation and validation of the t echnique, hereafter called the ID technique, against a formal program, CRISP, which uses the FEM.