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2.4. LimitationsSome components of the physical model verified in this studyare reduced to a certain scale and therefore, does not relate toprototype footing-slope systems faced in the field. In addition, sinceprototype geogrids were used as reinforcements in the laboratorymodels, other components of the footing-slope system, especiallythe soil, may not treat the same behavior as in the prototype. Itmust, therefore, be noticed that such a violation of similituderequirements might provide some effects on the experimentalresults both in qualitative and quantitative aspects.Furthermore, this research has not studied the effect of changesof some variables like tensile stiffness and strength of reinforce-ments on the bearing capacity of the soil.3. Finite element analysis3.1. Conditions analyzedA series of two-dimensional finite element analyses (FEA) ona prototype footing-slope system was performed in order to assessthe laboratory model tests results and find out the deformationstrends within the soil body. The analysis was performed using thefinite element program Plaxis software package (professionalversion 8, Bringkgreve and Vermeer, 1998). Plaxis enables usershandling a broad range of geotechnical problems such as deepexcavations, tunnels, and earth structures such as retaining wallsand slopes. Prototype slopes were supposed to rest on a yieldingfoundation and to extend laterally to a distance of 1.5 times theslope height (H) from the toe of the slope. In general, the initialconditions comprise the initial groundwater conditions, the initialgeometry configuration and the initial effective stress state. Thesand layer in this study was dry, so there was no need to enterground water condition. The analysis does, however, require thegeneration of initial effective stresses by means of K0-procedure.The geometry of the prototype footing-slope systemwas supposedto be the same as the laboratory model (the footing widthB ¼ 100 mm and thickness; slope height ¼ 500 mm). The samegradient of model test slopes, 3(H):2(V), and the material of steelplate for footing, geogrid, grid-anchor and sand were used in theprototype study. The software enables the automatic generation ofsix or 15 node triangle plane strain elements for the soil. 3.2. Finite element modelingA variety of soil models are built in the computer code chosenfor this study. However it was decided to use the non-linear Mohr–Coulomb criteria to model the sand for its simplicity, practicalimportance and the availability of the parameters needed. Theeffect of soil model in predicting the soil behavior has not beendealtwith in this research. The interaction between the geogrid andsoil was modeled at both sides by means of interface elements,which enabled for the specification of a decreased wall frictioncompared to the friction of the soil. The parameters used fornumerical analysis are depicted in Table 4.The geometry of a typical finite element model verified for theanalysis is shown in Fig. 7. The left vertical line of themodel in Fig. 7was constrained horizontally, and the bottom horizontal boundarywas constrained in both the horizontal and vertical directions.The soil parameters assigned for the top and bottom sand layerswere assumed to maintain the same in all the finite elementanalyses for the unreinforced system. For the reinforced case,a reinforcement layer was assigned at the required depth withsuitable strength reduction factors between the contact surfacesand stiffness of the reinforcement entered as additional parame-ters, which were introduced in interface section. Having examined different finite element meshes, a refinedmeshwas introduced to decrease the effect ofmesh dependency onthe finite element modeling of cases including changes in thenumber, type, and the location of geogrid layers. By using theabilities built in the computer code, in the finite element modeling,since the slope surface is not horizontal, the initial stress conditionof the slope was founded first by applying the gravity force due tosoil weight in steps with the geogrid reinforcements in place. Aprescribed footing load was then applied in increments (loadcontrol method) accompanied by iterative analysis up to failure.The modeled boundary conditions showed that the verticalboundary is free vertically and constrained horizontally while thebottomhorizontal boundary is fully fixed. The software enables theautomatic generation of six node triangle plane strain elements forthe soil, and three node tensile elements for the footing and thegeogrid. The analyzed prototype slope geometry, generated mesh,and the boundary conditions are shown in Fig. 7. The anchors weremodeled with fixed end anchors. Fixed-end anchors are springsthat are used to model a tying of a single point. A fixed-end anchoris visualized as a rotated T (—|). The length of the plotted T is arbi-trary and does not have any particular physical meaning.4. Results and discussionA total of 43 model tests were conducted on model plane strainfooting over sand slope. An additional numerical study on theinfluence of reinforcing the sand slope on the response of a proto-type footing was conducted using the finite element model. TheBCR of the footing on the reinforced sand is represented using a non-dimensional factor, called BCR factor.
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