Small Scale Experiments to Assess the Bearing Capacity of Footings on the Sloped Surface

Article Small Scale Experiments to Assess the Bearing Capacity of Footings on the Sloped Surface

Mohammad Nurul Islam Department of Civil and Environmental Engineering, University of Pittsburgh, Pittsburgh, PA 15213, USA; [email protected]

Received: 10 October 2020; Accepted: 17 November 2020; Published: 20 November 2020

Abstract: Construction of civil engineering structures on or next to a slope requires special attention to meet the bearing capacity requirements of soils. In this paper, to address such a challenge, we present laboratory-scale model tests to investigate the effect of footing shape on the sloped surface. The model comprised of a well stiffened mild steel box with three sides fixed and one side open. We considered both with and without reinforcement to assess the effectiveness of reinforcement on the sloped surface. Also, we used three types of footing (i.e., square, rectangular, and circular) to measure the footing shape effects. We considered three different slope angles to evaluate the impact of the sloped face corresponding to the applied load and the reinforcement application. We obtained that the maximum load carrying capacity in the square footing was higher than the rectangular and the circular footing for both the reinforced and the unreinforced soil. With the increase of geo-reinforcement in all three footing shapes and three sloped angles, the load carrying capacity increased. We also noticed a limiting condition in geo-reinforcement placement effectiveness. And we found that with the increase of slope, the load bearing capacity decreased. For a steep slope, the geo-reinforcement placement and the footing shape selection is crucial in achieving the external load sustainability, which we addressed herein.

Keywords: bearing capacity; slope angle; geo-reinforcement; footing shape; model tests

1. Introduction In the past, it was common to avoid civil engineering structures construction on a sloped surface due to the design and analysis complexities and associated time-dependent differential settlement. However, for the urbanization expansion and population increase, it is sometimes inevitable to consider the structure construction on or next to the inclined surface [1]. On the other hand, in geological locations where mountains dominate, the bearing capacity of the slope surface requires extra attention to avoid any failure of structure. Among others, bridge footing, towers for transmission and telecommunication, and retaining walls are also founded on sloped surfaces. The footing shape may be different (e.g., rectangular, circular, square, or any combination) considering the requirements of the structure. For the strip footing, Terzaghi [2] first presented the ultimate bearing capacity of soil considering the shear strength properties of soil. Later on, for different footing shapes, among others, Meyerhof [3]; Vesic [4]; de Buhan and Garnier [5]; Cerato and Lutenegger [6]; Gourvenec [7]; and Georgiadis [8] also proposed modification to the Terzaghi proposed method. Construction of a structure on any sloped surface is relatively more challenging compared to a plain surface because of complex load distribution phenomena and subsequent responses. However, ground improvement methods using geo-reinforcement, development, and advancement of engineering technology added value to utilize problematic soil (Duncan et al. [9]). In this regard, it is essential to find out the bearing capacity of foundation on the sloped surface, which is the motivation of the present paper. Also, in the last few decades, a wide range of geo-reinforcement elements have

Eng 2020, 1, 240–248; doi:10.3390/eng1020016 www.mdpi.com/journal/eng Eng 2020, 1, FOR PEER REVIEW 2 Eng 2020, 1 241 been used to improve the bearing capacity of soils. Among others, Koerner [10] presented details design methods using geogrids, geonets, geomembranes, geosynthetic clay liners, geopipe, geofoam, been used to improve the bearing capacity of soils. Among others, Koerner [10] presented details and geocomposites. However, considering cost and effectiveness, availability of reinforcement, and design methods using geogrids, geonets, geomembranes, geosynthetic clay liners, geopipe, geofoam, design perspective, the application of geotextiles is popular over others [11]. Therefore, in our small- and geocomposites. However, considering cost and effectiveness, availability of reinforcement, and scale experiments, we also used geotextiles. design perspective, the application of geotextiles is popular over others [11]. Therefore, in our The bearing capacity of geomaterials at slope depends on many factors and can be summarized small-scale experiments, we also used geotextiles. under five headings. They are the geometry of the sloped surface, loading condition, soil properties, The bearing capacity of geomaterials at slope depends on many factors and can be summarized footing properties, and reinforcement types. The first one also includes the height of slope, the under five headings. They are the geometry of the sloped surface, loading condition, soil properties, normalized edge distance (i.e., the edge distance from slope/the footing width), planes’ weakness, footing properties, and reinforcement types. The first one also includes the height of slope, and slope angle [8]. The loading condition includes vertical load or inclination of the applied load the normalized edge distance (i.e., the edge distance from slope/the footing width), planes’ weakness, [12,13]. The foundation soil properties comprise of soil types, the cohesion, the angle of internal and slope angle [8]. The loading condition includes vertical load or inclination of the applied friction, the modulus of elasticity, the Poisson’s ratio, the permeability, and the relative density [6]. load [12,13]. The foundation soil properties comprise of soil types, the cohesion, the angle of internal Also, footing shape, reinforcement types, properties, and spacing of the geo-reinforcement have a friction,significant the effect modulus on the of bearing elasticity, capacity the Poisson’s of the sl ratio,ope. However, the permeability, there is little and research the relative where density footing [6]. Also,shapes footing are considered shape, reinforcement for a sloped types,surface properties, considering and the spacing reinforced of theand geo-reinforcement the unreinforced soil have for a significantthe identical effect test on conditions the bearing varying capacity slope of the angl slope.e, which However, we therepresent is littleherein research through where laboratory footing shapesexperiments. are considered for a sloped surface considering the reinforced and the unreinforced soil for the identical test conditions varying slope angle, which we present herein through laboratory experiments. 2. Statement of the Problem 2. Statement of the Problem We present the problem statement in Figure 1. The study domain’s height and length are H and H L, respectively.We present theThe problemwidth (W statement) is along inthe Figure perpendicular1. The study direction domain’s of the height paper and (see length also Figure are 1b).and LWe, respectively. consider δ Theas the width slope (W angle.) is along We consider the perpendicular three faces direction are fixed, of and the one paper face (see is alsoopen Figure (see also1b). WeFigure consider 2a) soδ thatas the we slope could angle. investigate We consider the slope three failure faces for are loading. fixed, andWe only one faceconsider is open the (seevertical also Figureload (2Pa)) without so that weeccentricity. could investigate Also, we the assume slope the failure leng forth and loading. the width We only of the consider rectangular the vertical footing load are (P) without eccentricity. Also, we assume the length and the width of the rectangular footing are l l and 𝑤= , respectively; while for the square and the circular footing w = l, dc = w = l, respectively, l and w = 2 , respectively; while for the square and the circular footing w = l, dc = w = l, respectively, where dc represents the diameter of the circle. The ratio (𝜉) of footing’s base and the distance between where d represents the diameter of the circle. The ratio (ξ) of footing’s base and the distance between the edgec of the slope or the boundary opposite to the open face is kept constant. In Figure 1, s is the the edge of the slope or the boundary opposite to the open face is kept constant. In Figure1, s is the spacing of the geotextile and d represents the depth of the geotextile from the base of the footing. spacing of the geotextile and d represents the depth of the geotextile from the base of the footing.

Load P bw= ξ b w b Footing

Clay H c′′,,ϕ γ Geotextile s Geotextile

L W

(a) (b)

Figure 1. Schematic diagram of a shallow footing near slope. (a) Side view and (b) cross-section along theFigure footing. 1. Schematic diagram of a shallow footing near slope. (a) Side view and (b) cross-section along the footing. We assume that the soil mass is homogeneous and obey the Mohr-Coulomb criteria where parametersWe assume are the that eff ectivethe soil cohesion mass is (homogeneouc0) and thes e ffandective obey angle the ofMohr-Coulomb internal friction criteria(ϕ0) .where Also, inparameters Figure1, the are specific the effective weight cohesion is presented 𝑐 as andγ. Thethe effective soil mass angle will sustain of internal the applied friction vertical 𝜑. Also, load in (P ) Figure 1, the specific weight is presented as 𝛾. The soil mass will sustain the applied vertical load (P)

Eng 2020, 1 242 as long as the porous media meets the equilibrium condition and the stress state along the outside of the footing boundary is in the limiting condition (see also Duncan et al. [9]). Also, there are several theories for the failure mechanism of the sloped surface (see also Anderson and Richards [14]). We summarized these theories under two headings: failure mechanism due to the instability and failure mechanism due to the punching [5]. In this regard, Duncan et al. [9]) discussed a total of 13 case studies for slope failures and demonstrated possible reasons for the failure of each case. In this paper, we discuss failures of the sloped surface developed beneath the footing due to the punching and the geomaterials instability. In AppendixA, we present failure resistance mechanisms of reinforced soil. Additionally, assuming c0, ϕ0, γ, ξ, and H are constant (see Figure1), if we equate the average shear stress along the slip surface to obtain the factor of safety, the slope angle is the critical criterion, which we present herein through the experimental results for both the reinforced and unreinforced soil. In the next section, we discuss the properties of soil and geotextiles used for experiments.

3. Properties of Soil and Geotextiles The soil used in our experiment was comprised of clay (12.0%), silt (52.0%), sand (34.0%) and gravel (2.0%). The liquid limit, the plastic limit, and the shrinkage limit of the soil are 52.0%, 26.0%, and 23.0%, respectively. The effective cohesion and the effective angle of internal friction are 5 kPa and 330, respectively. The specific gravity of the soil is 2.61. We performed sieving and the hydrometer test for the grain size distribution of the soil. We determined the Atterberg limit test using a semi-automatic cone penetrometer. We obtained the shear strength parameter using the direct shear test machine. For all laboratory experiments, we followed the American Society for Testing and Materials (ASTM) standards. Additionally, the geotextiles used in the experiments were multifilament woven geotextiles. From laboratory tests, we also obtained the geotextiles’ thickness, weight, the maximum extension, the tensile strength, the California Bearing Ratio (CBR) punching, and the vertical permeability (see also Koerner [10] and Koerner [11]). We present the details of geotextiles properties in Table1.

Table 1. Properties of geotextiles.

Property Unit Values Type - Multiﬁlament Woven Thickness mm 1.90 Weight gm/m2 245.0 Strip Method % 16.75 Maximum Extension Grab Method % 35.43 Strip Method kN/m 7.61 Tensile Strength Grab Method kN/m 28.65 CBR Punching kN 1.89 Vertical Permeability m/sec 1.85 10 6 × − Note: CBR = California Bearing Ratio

4. Experimental Methods We developed a rectangular box made of mild steel for laboratory experiments to assess the bearing capacity of footings on the sloped surface. The dimensions of the box were W = 45.72 cm D = 45.72 cm L = 60.96 cm, where W = width, H = height, and L = length (see also Figure2a). × × The three faces of the box were closed, and one side was open. We used grooves and screw along the length and width of the box so that the developed pressure in the experimental setup would not cause failure. We applied medium viscosity oil in the inner surface of the box to minimize the sidewall eﬀect. Also, we prepared three mild steel footings of equal thickness (i.e., square, rectangular, and circular) to investigate the footing shape eﬀects. Eng 2020, 1 243 Eng 2020, 1, FOR PEER REVIEW 4

AsAs partpart ofof thethe samplesample preparation, we we firs firstt oven-dried oven-dried soil soil samples samples and and sieved. sieved. Then, Then, we wedetermined determined the the grain grain size size distribution distribution and and physical physical properties. properties. Throughout Throughout the testing, wewe keptkeptthe the optimumoptimum moisture moisture content content constant. constant. Also, Also, during during the the tests, tests, we keptwe kept an identical an identical distance distance from thefrom edge the ofedge the slopeof the and slope footing, and footing, the spacing the spacing of the geotextiles, of the geotextiles, and the distanceand the distance from the from footing the base footing to avoid base theirto avoid effects. their We effects. maintained We maintained three slope three angles slope to evaluate angles theto evaluate slope angle the eslopeffects. angle These effects. angles These were 35angles◦, 40◦ ,were and 35°, 45◦. 40°, Additionally, and 45°. Additionally, to keep the uniformity to keep the of uniformity the compaction of the compaction of the soil in of the the mild soil in steel the box,mild we steel compacted box, we the compacted soil layer the by layer.soil layer Then, by we la usedyer. Then, identical we pocketused identical penetrometer pocket reading penetrometer during thereading sample during preparation. the sample We placed preparation. a geotextile We placed at a uniform a geotextile depth, andat a weuniform used similardepth, geotextilesand we used to maintainsimilar geotextiles their properties to maintain constant. their In properties this regard, constant. for geotextile In this placement, regard, for we geotextile followed placement, Koerner [10 we] andfollowed Koerner Koerner [11]. Also, [10] and we Koerner kept the [11]. size andAlso, thickness we kept ofthe the size geotextile and thickness constant of the to geotextile avoid their constant effects (seeto avoid also Islam their eteffects al. [15 (see]). also Islam et al. [15]). WeWe used used the the Universal Universal Testing Testing Machine Machine (UTM) (UTM) with with an an electric electric load load cell cell (see (see Figure Figure2 b)2b) to to apply apply loadload through through the the footings. footings. WeWe applied applied load load at at the the centroid centroid of of the the footing footing to to avoid avoid the the loading loading angle angle eeffectffect and and the the eccentricity eccentricity influence. influence. We alsoWe usedalso aus dataed a logger data tologger measure to measure the settlement. the settlement. We recorded We therecorded load every the load 0.5 mm every deformation 0.5 mm deformation interval until interval the sloped until the surface sloped failed. surface failed.

P Mild Steel Box L Footing

Soil Proving Ring

Geotextile Dial gauge

D D bB d H GeotextileGeotextile

W W

(a)(b)

Figure 2. Schematic diagram of (a) the experimental setup and (b) the loading arrangement. Figure 2. Schematic diagram of (a) the experimental setup and (b) the loading arrangement. 5. Results and Discussions 5. Results and Discussions We considered three types of footing (square, rectangular, and circular) for slope angles 35◦, 40◦, We considered three types of footing (square, rectangular, and circular) for slope angles 35°, 40°, and 45◦ to study the effect of footing shape and the slope angle. We performed these tests on both theand unreinforced 45° to study andthe effect reinforced of footing soil. Also,shape to and evaluate the slope the angle. reinforcement We performed effect, these we considered tests on both single the andunreinforced double layer and geotextiles,reinforced soil. maintaining Also, to evaluate a uniform the distance reinforcement throughout effect, thewe tests.considered From single Figure and3, wedouble observe layer that geotextiles, the load carrying maintaining capacity a uniform in the square distance footing throughout is higher comparedthe tests. From to the Figure circular 3, and we theobserve rectangular that the footing load carrying shape. The capacity square in footing the square develops footing the lowis higher mean compared stress compared to the tocircular the other and twothe shapesrectangular of footings footing and shape. results The in square the high footing operative develops frictional the low angles. mean Therefore, stress compared the load to carryingthe other capacitytwo shapes in the ofsquare footings footing and results is high in for the the high equivalent operative longest frictional dimension angles. in Therefore, the rectangular the load footing carrying and thecapacity equivalent in the diameter square footing of the circularis high for footing. the equivalent This stress longest dependency dimension on the in footing the rectangular shape is relatedfooting toand the the critical equivalent state strength diameter [16 of]. the Also, circular Michalowski footing. This [17] reportedstress dependency that with theon the increase footing of footingshape is aspectrelated ratio, to the the critical bearing state capacity strength factor [16]. also Also, increased Michalowski (see also [17] Salgado reported et al.that [18 with]; Gourvenec the increase [13 ]).of Moreover,footing aspect Cerato ratio, and the Lutenegger bearing capacity [6] presented factor that also the increased bearing capacity(see also inSalgado the square et al. footing [18]; Gourvenec is higher than[13]). the Moreover, circular footing.Cerato and However, Lutenegger in the [6] previous presented study that ofthe the bearing footing capacity shape einffect, the thesquare combined footing influenceis higher ofthan the the slope circular angle footing. and the reinforcementHowever, in the were previous ignored, study which of the we addressedfooting shape in this effect, paper the throughcombined laboratory influence experiments. of the slope angle From and Figure the3 ,reinforcement we also find thatwere with ignored, the increase which we of slopeaddressed angle, in thethis load paper carrying through capacity laboratory decreases, experime whichnts. supportsFrom Figure Georgiadis 3, we also [8]. find that with the increase of slope angle, the load carrying capacity decreases, which supports Georgiadis [8].

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0 Single Layer_450 Single Layer_400 Single Layer_35 35 35 35 Square Square Square 28 Circular 28 Circular 28 Circular Rectangular Rectangular Rectangular 21 21 21

14 14 14

7 7 7

0 0 0 0246810 0246810 0246810 Settlement (mm) Settlement (mm) Settlement (mm) (d)(e) (f) Load (kN)

(g)(h) (i)

FigureFigure 3. 3. EffectEﬀect of of footing footing shape: shape: ( (aa––cc)) unreinforced unreinforced soil, soil, ( (dd––ff)) single single layer layer geotextile geotextile reinforced reinforced soil, soil, andand ( (gg––ii)) double double layer layer geotextile geotextile reinforced reinforced soil. soil.

DuringDuring the the application application of of load load to to the the footing, footing, load load transfers transfers through through particles particles of the of thesoil soil mass. mass. In responseIn response to loads, to loads, particles particles may may break break or ordislocat dislocatee due due to tothe the slip slip action action along along the the sliding sliding plane, plane, resultingresulting in in the the instabilities instabilities of of soil soil grains. grains. We We could could explain explain such such behavior behavior using using the the micromechanics micromechanics ofof particles particles (see (see Islam Islam et et al. al. [19]). [19]). For For the the unreinfo unreinforcedrced soil soil mass, mass, if if the the load load bearing bearing capacity capacity exceeds exceeds thethe limiting limiting criteria, criteria, the the porous porous media media may may fail fail [9]. [9]. However, However, we we could could minimize minimize such such an an instability instability usingusing geotextiles, geotextiles, which which increase increase the the strength strength proper propertiesties of the of porous the porous media media (see Koerner (see Koerner [10]). Also, [10]). geotextilesAlso, geotextiles resist the resist punching the punching failure failure beneath beneath the footing the footing and reduce and reduce the effect the eofﬀ ectcircular of circular or non- or circularnon-circular slip surface slip surface by increasing by increasing the thefactor factor of safety of safety on onthe the sloped sloped surface. surface. On On the the other other hand, hand, mathematically, the area ratio of footings for square, circular, and rectangular in this paper are present as 4𝑙:𝜋𝑙:2𝑙, which also impact in the maximum load bearing capacity due to the surface area.

Eng 2020, 1 245 mathematically, the area ratio of footings for square, circular, and rectangular in this paper are present Eng 2020, 1, FOR PEER REVIEW 6 as 4l2 : πl2 : 2l2, which also impact in the maximum load bearing capacity due to the surface area. InIn Figure Figure 4,4, we we present present the the reinforcement reinforcement effect e ffect for for each each sloped sloped surface surface and and each each footing footing shape. shape. InIn addition, addition, in in Figure Figure 5,5, we pr presentesent the maximum load bearing capacity for each footing. We We observe thatthat with with the the increase increase of of reinforcement, reinforcement, the the maximu maximumm load load bearing bearing capacity capacity also also increases. increases. However, However, thethe maximum maximum load load carrying carrying capacity capacity decreases decreases with with the the rise rise in in the the slope slope angle. angle. We We also also notice notice that that thethe average average maximum maximum load load carrying carrying capacity capacity in in the the square square footing footing for for the the unreinforced unreinforced soil soil and and 35° 35◦ slopeslope surface surface are are 14.11% 14.11% and and 29.48% 29.48% higher higher compared compared to to the the circular circular footing footing and and the the rectangular rectangular footing,footing, respectively. respectively. However, However, th theseese values values for for the the single single layer layer geotextile geotextile are are 32.01% 32.01% and and 71.26%, 71.26%, respectively,respectively, whilewhile for for the the double double layer layer geotextile, geotex identicaltile, identical values arevalues 34.15% are and 34.15% 75.57%, and respectively. 75.57%, respectively.Also, from Figure Also,5 ,from we observe Figure that5, we the observe percentile that values the percentile mentioned values above mentioned decrease with above the decrease increase withof slope the angle.increase Comparing of slope angle. the square Comparing footing the results square for 35footing◦ slope results surface for with 35° identicalslope surface conditions with identicaland the conditions other two footings,and the other we findtwo thatfootings, the changes we find that in the the ultimate changes loadin the carrying ultimate capacity load carrying in the capacitysingle layer in andthe doublesingle layer geotextileand double are 2.14%layer andgeotextile 4.31%. are These 2.14% results and demonstrate 4.31%. These an optimum results demonstrategeotextile placement an optimum layer geotextile for a specific placement soil depositlayer for with a specific the sloped soil deposit surface, with which the sloped is essential surface, in whichfinding is anessential economic in finding ground an improvement economic ground method. improvement method.

(a)(b) (c)

(d)(e) (f)

Figure 4. Cont.

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(g)(h) (i) (g)(h) (i)

Figure 4. Effect of geotextile reinforcement and footing shape: (a–c) for 45°; (d–f) for 40°; and (g–i) for Figure 4. Eﬀect of geotextile reinforcement and footing shape: (a–c) for 45◦;(d–f) for 40◦; and (g–i) for Figure35° sloped 4. Effect surfaces. of geotextile reinforcement and footing shape: (a–c) for 45°; (d–f) for 40°; and (g–i) for 35°35◦ slopedsloped surfaces. surfaces.

FigureFigure 5.5. MaximumMaximum load carrying capacity: ( (aa)) unreinforced unreinforced soil, soil, (b (b) )single single layer layer geotextile, geotextile, and and (c ()c ) double layer geotextile. Figuredouble 5. layer Maximum geotextile. load carrying capacity: (a) unreinforced soil, (b) single layer geotextile, and (c) 6. Conclusionsdouble layer geotextile. 6. Conclusions We presented the sloped surface load carrying capacity comparing the reinforced and the 6. ConclusionsWe presented the sloped surface load carrying capacity comparing the reinforced and the unreinforced soil considering three footing shape and three slope angles. We found that the square unreinforcedWe presented soil considering the sloped three surface footing load shape carrying and threecapacity slope comparing angles. We the found reinforced that the and square the footing provided higher resistance than the circular and the rectangular footing. Also, for all three unreinforcedfooting provided soil considering higher resistance three footingthan the shape circular and and three the slope rectangular angles. footing.We found Also, that for the all square three footing shapes, the load bearing capacity decreased with an increase in the slope angle. In contrast, footingfooting provided shapes, the higher load resistancebearing capacity than the decreased circular withand thean increaserectangular in the footing. slope angle.Also, forIn contrast, all three the resistance in soil increased with the reinforcement application by minimizing the punching failure footingthe resistance shapes, in the soil load increased bearing with capacity the reinforcement decreased with application an increase by minimizing in the slope the angle. punching In contrast, failure and the instability of geomaterial. theand resistance the instability in soil of increased geomaterial. with the reinforcement application by minimizing the punching failure For any specific soil deposit with a sloped surface, it is critical to select the footing shape to achieve and theFor instability any specific of geomaterial. soil deposit with a sloped surface, it is critical to select the footing shape to the maximum benefit to sustain the external loading on the footing. Considering the foundation and achieveFor anythe specificmaximum soil benefitdeposit to with sustain a sloped the extesurface,rnal loadingit is critical on theto select footing. the Consideringfooting shape the to the loading condition, a ground improvement system through the geo-reinforcement application can achievefoundation the andmaximum the loading benefit condition, to sustain a ground the improvementexternal loading system on throughthe footing. the geo-reinforcement Considering the be introduced. However, we also observed limiting criteria from our experimental evidence for a foundationapplication and can the be loadingintroduced. condition, However, a ground we also improvement observed limiting system criteriathrough from the geo-reinforcementour experimental specific slope, the geo-reinforcement, and the footing shape. After the limiting condition, the percentile applicationevidence for can a be specific introduced. slope, However,the geo-reinforcem we also observedent, and limitingthe footing criteria shape. from After our experimentalthe limiting increase in the ultimate bearing capacity for the geotextile is negligible. evidencecondition, for the a percentilespecific slope, increase the in geo-reinforcemthe ultimate bearingent, and capacity the footingfor the geotextileshape. After is negligible. the limiting condition,Funding: This the researchpercentile received increase no external in the ultimate funding. bearing capacity for the geotextile is negligible. Acknowledgments: The author acknowledges the laboratory technician in preparing the experimental setup. Conflicts of Interest: The author declares no conflict of interest.

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Appendix A Appendix A

Appendix A.1. Failure Mechanisms of Reinforced Soil Failure Mechanisms of Reinforced Soil Application of geotextile functions as a reinforcement which provides resistance to the tension by inducingApplication the ofstress geotextile state [20]. functions Also, asgeotexti a reinforcementles support which the planar provides load resistance and the tonormal the tension load. byThereby, inducing geotextiles the stress increase state [ 20the]. stability Also, geotextilesof sloped surface. support In thethis planarregard, load among and others, the normal Shukla load.[20] Thereby,demonstrated geotextiles detailed increase failure the stabilitymechanisms of sloped of rein surface.forced Insoil. this In regard, Figure among 2, we others,present Shukla the basic [20] demonstratedmechanisms of detailed reinforced failure soil. mechanisms of reinforced soil. In Figure2, we present the basic mechanisms of reinforced soil.

Load P Tensile stress Lateral stress

Potential failure surface

Geotextile

δ Reinforced soil

FigureFigure A1. A1.Schematic Schematic failurefailure resistanceresistance mechanismmechanism in reinforced soil.

ReferencesFunding: This research received no external funding.

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