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The tensioned membrane theory was first developed by I P.Giroud to determine the <br />tensile strength required in a geosynthetic supporting a soil layer over a void. hater <br />Giroud along with Bonparte, Beech and Gross, combined Terzaghi's arching theory with <br />the tension membrane theory and laid the foundation for landfill liner support technology. <br />Essentially, the tension membrane equation enables one to transfer a uniformly distributed <br />normal force into a horizontal reinforcing material that will sag to a given strain limit. <br />The relationship between tension and strain in a liner support design is revealing. As the <br />strain limit is reduced, the required tensile strength increases. As a result, in a strain based <br />design, the factor of safety is applied directly and indirectly to the allowable strain and the <br />required tension respectively. <br />Combining the work performed at the University of Florida with Terzaghi's original work <br />and the experiments conducted by the Army Corps, one can now correlate the shape of <br />the soil arch to the strength of the soil. This is particularly helpful when there is more than <br />one strata of soil within the arching zone. For landfill liner support applications, one has <br />the ability to calculate the dimensions of the arch within the soil liner system above the <br />geogrid and the dimensions of the arch within the waste above the soil liner system. (See <br />Figure 1). <br />Figure 2 provides the relationship between the width of the yielding zone and the height of <br />the soil arch based on the soil strength parameter. Using this figure one can determine the <br />dimensions of the arch within the soil and waste layers. This will enable one to determine <br />the uniform normal pressure over the yielding area at the base of the <br />liner system. Using Giroud's tension membrane equation one can then calculate the <br />required geogrid tension at the allowable strain limit. Finally, one can select the <br />appropriate geogrid. A step by step procedure along with a design example follows. <br />(4) <br />11 <br />