CONSOLIDATION OF SOIL UNDER TIME-DEPENDANT LOADING AND VARYING PERMEABILITY

USE OF THE THEORY OF CONSOLIDATION IN MANY INSTANCES IS FOUND TO BE LESS THAN SATISFACTORY DUE TO THE WORKING CONDITIONS INHERENT IN THE USUAL THEORY. THIS PAPER EXTENDS THE THEORY BY GENERALIZING THE CONDITIONS OF DERIVATION TO INCLUDE VARIATIONS IN THE RATE OF LOADING AND VARIATIONS IN THE COEFFICIENT OF PERMEABILITY DURING THE PROCESS OF CONSOLIDATION. INCLUDING THE TWO ADDITIONAL WORKING CONDITIONS, THE BASIC DIFFERENTIAL EQUATION IS DERIVED IN ITS MOST GENERAL FORM. THE RESULTING DIFFERENTIAL EQUATION IS NON-LINEAR, BUT AN EXPONENTIAL APPROXIMATION IS DEVELOPED TO LINEARIZE IT, THEREBY PERMITTING SOLUTION OF THE CONSOLIDATION BOUNDARY VALUE PROBLEM. THE ONE-DIMENSIONAL CONSOLIDATION PROBLEM IS TREATED IN DETAIL FOR A CLAY-SOIL LAYER SANDWICHED BETWEEN TWO SAND LAYERS. A GENERAL SOLUTION IS PRESENTED FOR CONSTANT PERMEABILITY AND AN ARBITRARY LOADING RATE. SPECIFIC SOLUTIONS ARE PRESENTED FOR THE CONSOLIDATION DURING A LINEAR CONSTRUCTION PERIOD. WITH THESE SOLUTIONS, WORKING CURVES ARE PRESENTED FOR ACTUAL TIME COMPUTATIONS. IN ADDITION, THE THEORY OF VARIABLE PERMEABILITY IS DEVELOPED IN DETAIL IN TERMS OF SPECIFIC SOLUTIONS. THE CONSOLIDATION OF A DOUBLY-DRAINED LAYER OF CLAY-SOIL UNDER THE INFLUENCE OF TWO- AND THREE-DIMENSIONAL LOADING IS PRESENTED. THESE SOLUTIONS ARE DEVELOPED IN GENERAL, AND FOR SPECIFIC LINEAR LOADING FUNCTIONS, CONSIDERING CONSTANT PERMEABILITY. EXTENSIONS TO PROBLEMS OF VARIABLE PERMEABILITY ARE INDICATED. THE THREE-DIMENSIONAL CONSOLIDATION PROBLEM IS ALSO SPECIFICALLY ORIENTED TO THE RADIAL DRAINAGE OF A TRIAXIAL TEST SPECIMEN UNDER A STRESS- CONTROLLED LOADING. SAND-DRAIN PROBLEMS FOR EQUAL-STRAIN CONDITIONS AND RADIAL FLOW ONLY ARE COVERED IN DETAIL. THE EXACT SOLUTION TO CONSOLIDATION UNDER CONSTANT LOAD BUT VARIABLE PERMEABILITY IS PRESENTED IN TERMS OF THE WELL- KNOWN CONSTANT PERMEABILITY SOLUTION, WHICH CONSIDERS A PERFECT DRAIN WITHOUT SMEAR. CONSTANT PERMEABILITY SOLUTIONS ARE PRESENTED FOR THE CASE OF A LINEAR CONSTRUCTION LOADING, IN WHICH THE PRESENCE OF A SMEAR ZONE IS INCLUDED IN THE SOLUTION. THE EXPONENTIAL LINEARIZING APPROXIMATION IS DEVELOPED FOR SITUATIONS OF VARIABLE LOAD AND PERMEABILITY FOR THE CASE OF SAND DRAINS WITHOUT SMEAR. A SET OF WORKING CURVES IS PRESENTED FOR THE DESIGN OF SAND-DRAIN INSTALLATIONS USING THESE THEORIES