GALERKIN APPROACH TO UNSATURATED FLOW IN SOILS.

AN ITERATIVE GALERKIN-TYPE FINITE ELEMENT METHOD IS EMPLOYED TO SOLVE THE QUASILINEAR EQUATIONS OF NON-STEADY WATER FLOW IN UNSATURATED AND PARTLY-SATURATED POROUS MEDIA.THE PARAMETERS IN THESE EQUATIONS AS WELL AS THE BOUNDARY CONDITIONS ALONG SEEPAGE FACES ARE HIGHLY NONLINEAR FUNCTIONS OF THE DEPENDENT VARIABLE.OWING TO THIS STRONG NONLINEARITY, PAST ATTEMPT TO SOLVE SUCH PROBLEMS WITH FINITE DIFFERENCE METHODS WERE NEVER COMPLETELY SUCCESSFUL.THE FINITE ELEMENT METHOD APPEARS TO BE COMPUTATIONALLY MORE EFFICIENT THAN THE CONVENTIONAL FINITE DIFFERENCE APPROACH IN OVERCOMING DIFFICULTIES ARISING FROM THE NONLINEAR NATURE OF THE PROBLEM.EXPERIENCE WITH THE FINITE ELEMENT ALGORITHM SHOWS THAT CONVERGENCE IS OFTEN NEAR QUADRATIC.THIS ALGORITHM IS CAPABLE OF HANDLING FLOW IN NONUNIFORM SOILS HAVING COMPLEX BOUNDARIES, ARBITRARY ANISOTROPY, AND AN UNLIMITED NUMBER OF SEEPAGE FACES.FLOW TO A FULLY OR PARTIALLY PENETRATING WELL OF A FINITE DIAMETER TAKING INTO ACCOUNT WELL STORAGE AS WELL AS PUMP CHARACTERISTICS, CAN ALSO BE TREATED.THE RESULTS INDICATE THAT THE CLASSICAL CONCEPT OF A 'FREE SURFACE' IS UNSUITABLE FOR MOST PROBLEMS INVOLVING TRANSIENT SEEPAGE THROUGH POROUS MEDIA.(A).