SUBSURFACE DRAINAGE INVESTIGATION 1945-1946: REPORT ON THEORETICAL ANALYSIS OF DRAINAGE OF BASE COURSES

THE PRESENT STATUS OF THE THEORY OF TWO AND THREE DIMENSIONAL MOTION OF GROUNDWATER WITH A FREE SURFACE IS REVIEWED AND THE POSSIBILITIES INVESTIGATED OF APPLYING MODERN INSTRUMENTS OF CALCULATION TO THE DETERMINATION OF THE SHAPE OF THE FREE SURFACE, THE EXTENT OF THE SURFACE OF SEEPAGE AND OTHER PERTINENT DATA IN GRAVITY FLOW SYSTEMS. A COMPREHENSIVE REVIEW IS PRESENTED OF EXISTING LITERATURE. THE RATES OF DRAINAGE OF BASE COURSES ARE CALCULATED BY ASSUMING APPROXIMATE GEOMETRICAL SHAPES FOR THE FREE SURFACE DURING THE PROCESS OF DRAINAGE. THE VARIOUS RATES OF DRAINAGE OBTAINED ARE COMPARED WITH EACH OTHER AND WITH EXPERIMENTAL TESTS CONDUCTED AT THE SOIL LABORATORY. A SURVEY OF THE MATHEMATICAL ANALYSIS OF THE GRAVITY FLOW OF LIQUIDS THROUGH POROUS MEDIUM SHOWS THAT WHILE IT IS EASY TO FORMULATE THE ANALYSIS AS A POTENTIAL PROBLEM STARTING WITH THE FUNDAMENTAL LAW OF DARCY, NEVERTHELESS THE SOLUTION OF THE EQUATION INVOLVED PRESENTS PRACTICALLY INSURMOUNTABLE MATHEMATICAL DIFFICULTIES. THE DIFFICULTIES ARE INTRODUCED BY THE PRESENCE OF THE FREE SURFACE WHOSE FORM IS NOT KNOWN A PRIORI AND CAN ONLY BE DETERMINED BY THE USE OF THE DOUBLE BOUNDARY CONDITION THAT DEFINES IT. EVEN THE CASE OF THE 2-DIMENSIONAL PROBLEM OF A DAM WITH VERTICAL FACES SOLVED BY HAMEL USING THE METHOD OF HODOGRAPHS AND THE METHOD OF CONJUGATE FUNCTIONS PRESENTS DIFFICULTIES IN NUMBERICAL CALCULATIONS. THE THREE-DIMENSIONAL PROBLEM OF THE SEEPAGE INTO A WELL PRESENTS THE SAME DIFFICULTIES BUT SINCE CONJUGATE FUNCTIONS DO NOT APPLY TO THREE-DIMENSIONAL PROBLEMS IT IS NOT POSSIBLE TO APPLY A METHOD SIMILAR TO HAMEL'S TO THIS PROBLEM. THE ASSUMPTION OF SHELL FLOW TO THIS PROBLEM LEADS TO A NONLINEAR DIFFERENTIAL EQUATION FOR THE SHAPE OF THE FREE SURFACE THAT MAY BE STUDIED NUMERICALLY OR BY THE USE OF A DIFFERENTIAL ANALYZER. WITHIN THE SHELF FLOW ASSUMPTION, THE WELL PROBLEM MAY BE FORMULATED AS AN INTEGRAL EQUATION OF CONSIDERABLE COMPLEXITY THAT MAY PERHAPS BE SOLVED BY SOME CONVERGENT METHOD OF SUCCESSIVE APPROXIMATIONS.

  • Supplemental Notes:
    • 57 Pp, 19 FIG, 9 REF
  • Corporate Authors:

    U.S. Army Corps of Engineers

    ,    
  • Authors:
    • Pipes, L A
  • Publication Date: 1946-3

Subject/Index Terms

Filing Info

  • Accession Number: 00234475
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Dec 9 1994 12:00AM