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As El Sawwaf, 2005 mentioned this can be explained as follows; at shallow depthsunder the footing, both the vertical and horizontal soil displace-ments are greater. Maximum benefits could be obtained when soilreinforcement are placed at these depths where mobilized lateralresistances for soil lateral displacements are maximum. When thedepth of geogrid layer increases, both lateral and vertical soildisplacements in the zone between the footing and the geogridlayer increase and hence the bearing capacity decreases.Fig. 10b states a typical response of q Uy for several values ofu/B.4.2. Effect of number of geogrid layersA series of tests were conducted in order to study the effect ofvariation of the number of geogrid layers on the footing-slopebehavior. A typical response of q Uy shown in Fig. 11a indicatesthe effect of the number of geogrid layers on slope behavior. Inthese series, geogrid length and the distance of footing from slopeedge were kept constant but the number of geogrid layers wasvaried for six cases, three cases for geogrid layout and three casesfor grid-anchor. Typical responses of BCR determined from themodel tests against N for a footing located at the slope crest isshown in Fig. 11b. The figures clearly show that the common trendsof FEA shown in Fig. 11b agree appropriately well with those of themodel slope. For the same settlement, the figure indicates that theinclusion of geogrid layers provided an increase in the load bearingcapacity of the model footing. Also, for the same footing load, thesettlement ratio decreased considerably with increasing thenumber of geogrid layers, but this behavior continued until N ¼ 2.For N ¼ 3 there is no increase in BCR or even a reduction in BCR isseen.As it can be seen from Fig. 11b, although, the BCR obtained fromthe FEA seems to be smaller than that for the model slope, thecommon trends of the manner in which BCR differs withthe number of geogrid are in good agreement with those from themodel tests. The BCR increases with the increase of N for the twoseries. However, the rate of increase in BCR decreases with theincreasing number of geogrid layers until N ¼ 2 afterwhich the rateof load improvement becomes much less or even causes a decreasein BCR, similar behavior has been seen in El Sawwaf, 2005 and Leeand Manjunath (2000) works. For practical reasons, no tests werecarried out using more than three geogrid layers due to the limiteddepth of the sand fill. However, the figure indicates that for thecertain sand slope and reinforcement conditions, there are a criticalnumber of reinforcement layers after which the improvement inbearing capacity not only is not considerable but also has anopposite effect. This is consistent with previous studies of strip orsquare plate over entirely dry sand (Omar et al., 1993; Das et al.,1994; Yoo, 2001; El Sawwaf, 2005; Lee and Manjunath, 2000)which demonstrated that there are a critical number of geogridlayers after which the BCR becomes constant.According to El Sawwaf (2005) and Lee and Manjunath (2000),this increase in footing ultimate load can be related to reinforce-ment mechanism which formed from the passive earth resistance,engaging in front of the transverse members, and adhesionbetween the longitudinal/transverse geogrid members and thesand. The mobilized passive earth resistance of soil column limitedin the geogrid apertures along with the engaging limit thespreading of slope and horizontal deformations of sand particles.The mobilized tension in the reinforcement allows the geogrid toresist the formed horizontal shear stresses built up in the soil massinside the loaded area and transfer them to beside stable layers ofsoils leading to a broader and deeper failure zone. Therefore, sandgeogrid interaction not only results in increasing the bearingcapacity due to developed longer failure surface but also results inbroadening the contact area between sand and rigid bottomsurfaceof test box.4.3. Effect of vertical spacing of the geogridSix series of studies were carried out on both model andprototype footing located at the slope crest of sand slope with all parameters kept constant but vertical spacing between layers wasdiffered. Two and three geogrid and grid-anchor layers were testedwith vertical spacing values of h/B ¼ 0.5, 0.75, and 1.0 were studied.The variation of BCR with normalized layer spacing h/B is shown inFig. 12a. The curves clearly show that there is a critical value of h/Bfor which the maximum benefit of the geogrid reinforcements isobtained. The BCR increases with h/B up to approximatelya maximumvalue of 0.75B after which it decreases. A similar trendwas reported for an entirely sand slope by Yoo (2001) and ElSawwaf (2005) and Lee and Manjunath (2000) showing a criticalvalue of h/B ¼ 0.7. Also in Fig. 12b which indicates responses offooting for different values of h/B.5.
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