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Effect of footing shape and load eccentricity on behavior of geosynthetic reinforced sand bed
Geotextiles and Geomembranes 45 (2017) 58e67
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Technical note
Effect of footing shape and load eccentricity on behavior of geosynthetic reinforced sand bed Ehsan Badakhshan*, 1, Ali Noorzad Geotechnical Engineering, Faculty of Civil, Water & Environmental Engineering, Shahid Beheshti University, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 May 2015 Received in revised form 22 January 2016 Accepted 30 November 2016
This paper presents the results from a laboratory modeling tests and numerical studies carried out on circular and square footings assuming the same plan area that rests on geosynthetic reinforced sand bed. The effects of the depth of the first and second layers of reinforcement, number of reinforcement layers on bearing capacity of the footings in central and eccentral loadings are investigated. The results indicated that in unreinforced condition, the ultimate bearing capacity is almost equal for both of the footings; but with reinforcing and increasing the number of reinforcement layers the ultimate bearing capacity of circular footing increased in a higher rate compared to square footing in both central and eccentrial loadings. The beneficial effect of a geosynthetic inclusion is largely dependent on the shape of footings. Also, by increasing the number of reinforcement layers, the tilt of circular footing decreased more than square footing. The SR (settlement reduction) of the reinforced condition shows that settlement at ultimate bearing capacity is heavily dependent on load eccentricity and is not significantly different from that for the unreinforced one. Also, close match between the experimental and numerical load-settlement curves and trend lines shown that the modeling approach utilized in this study can be reasonably adapted for reinforced soil applications. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Geosynthetics Circular and square footings Bearing capacity Reinforced sand
1. Introduction For the last four decades in Civil Engineering, application of geosynthetics has been known as a common technique to increase the ultimate bearing capacity of soils and decrease the settlement of footings. Among the range of geosynthetics available in the market, geotextiles are the most preferred type of geosynthetic materials for reinforcing the foundation beds. Many researchers (Hughes and Withers, 1974; Binquet and Lee, 1975a, 1975b; Huang and Tatsuoka, 1988, 1990; Adams and Colin, 1997; Alawaji, 2001; Ghosh et al., 2005; Kumar et al., 2007; Mosallanezhad et al., 2007; Tafreshi and Dawson, 2010; Ghazavi and Afshar, 2013; Pinho-Lopes et al., 2015) reported when reinforcements were placed at an optimum depth below a footing (strip, square, rectangular foundations) the beneficial effect of reinforcement can observed. These studies were focused on the ratio of the first layer of reinforcement from the foundation base, u, the foundation size, B, (u/B); the ratio of the reinforcement width, b, to the foundation
* Corresponding author. E-mail address: [email protected] (E. Badakhshan). 1 http://www.sbu.ac.ir. http://dx.doi.org/10.1016/j.geotexmem.2016.11.007 0266-1144/© 2016 Elsevier Ltd. All rights reserved.
size (b/B); and the ratio of the total reinforced depth, h, to the foundation size (h/B) and critical ratios of them. In the field of soil reinforcing with geosynthetic layers (in sand or clay) for circular foundations in centrally loaded, there has not been a lot of researches as compared to other foundations in the literature. Sitharam and Sireesh (2004) conducted a number of laboratory model tests to determine the bearing capacity of an embedded circular footing supported by sand bed reinforced with multiple layers of geotextiles. The test results demonstrated that the ultimate bearing pressure increased with embedment depth ratio of the foundation. Also, Basudhar et al. (2007) carried out experimental and numerical analyses on behavior of circular footings with different size resting on reinforced sand with geotextile and reported that with increase in number of reinforcement layers, the settlement value gradually decreased. Similarly, Boushehrian and Hataf (2003) found that for the circular footings on reinforced sand the maximum bearing capacity occurs at different values of embedment depth ratio depending on the number of reinforcement layers. For ratios of u/D greater than one reinforcement layers had no significant effect on bearing capacity. They also reported that choosing a rigid reinforcement did not always improve the effect on bearing capacity. Yetimuglu et al., 1994
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conducted laboratory model tests to investigate the bearing capacity of rectangular footings on geotextile reinforced sand. For a single layer of reinforcement, the optimal placement depth was found to be 0.3 times the footing width. Lovisa et al. (2010) studied behavior of pre-stressed geotextile reinforced sand bed supporting a loaded circular footing and found out that effects of the pre-stressed reinforcement configuration were evident for greater footing depths, in comparison with unreinforced and reinforced without pre-stressing. The results of the laboratory model tests for strip and square foundations supported on reinforced sand with geosynthetic layers demonstrated that for the development of maximum bearing capacity, the maximum depth of reinforced zone is about 2B for strip foundation and 1.4B for square foundation, where B is width of footing (Omar et al., 1993). The maximum depth of placement of the first layer of reinforcement should be less than about B to take advantage of reinforcement. In the same vein, Khing et al. (1994) conducted model tests on a strip footing supported by reinforced sand. Results showed that the maximum benefit of reinforcement in increasing the bearing capacity was obtained when the depth ratio of the first reinforcing layer to the foundation width was less than unity. Further, Latha and Somwanshi (2009) concluded that effective depth of the reinforcement zone below a square footing is twice the width of the footing, beyond which the inclusion of reinforcement layers will not result in significant improvement in the bearing capacity of the footing and, within the effective reinforcement zone, the optimum spacing of reinforcing layers is about 0.4 times the width of the footing. Moreover, Mandal and Sah (1992) revealed that the ratio u/B for the most efficiently possible condition of the reinforcement must be selected less than 0.3. Noorzad and Mirmoradi (2010) studied the behavior of cohesive soil reinforced with a geotextile by tri-axial compression tests and found that with increasing relative compaction, the peak strength of the sample and axial strain at failure increases. In another investigation, Mosallanezhad et al. (2007) dealt with the influence of a new generation of reinforcement (named by them as Grid-Anchor) on the increase of the bearing capacity of square foundation. They found that the critical value of u/B, h/B and b/B are equal to 0.25, 0.25 and 4.5, respectively. They also demonstrated that BCR for this system is greater than that of ordinary reinforcement. Up to now, few studies are developed experimentally to identify the critical values of reinforcement layers for reinforcing of the soil under the strip and rectangular foundations, when loading has been applied with eccentricity (Sadoglu et al., 2009; Patra et al., 2006; Ornek, 2014; Turker et al., 2014; Sadoglu, 2015). Sawwaf and Nazir (2012) studied the behavior of eccentrically loaded small scale ring footings resting on sand. They reported that the behavior of an eccentrically loaded ring footing significantly improved with an increase in the depth and relative density of the replaced compacted sand layer. All the above model tests have been carried out in optimum condition, over which the highest efficiency of the reinforcing layers is expected. As it can be easily noted in the previous studies no attention has been paid to the effect of footing shapes and load eccentricities resting on unreinforced and reinforced soil. Hence, the present study has been aimed to investigate the effect of foundation shape with the same plan area (for circular and square footings) in central and eccentral loadings on the bearing capacity, settlement and tilt of footings in unreinforced and reinforced sand bed. 2. Materials To investigate the effect of eccentric loading on a circular footing resting on reinforced sand with geotextile layers, the necessary details of the experimental studies are presented as follows:
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2.1. Sand Oven dried poorly graded medium sand from the west of Iran is used in this study. The particle size distribution is determined using the dry sieving method according to ASTM D 422-90. This sand can be classified as SP in the unified soil classification system (USCS) with coefficient of uniformity 2.89 (Cu), coefficient of curvature 1.05 (Cc) and effective size of 0.27 (D10). The specific gravity of soil particles, maximum and minimum dry densities and maximum and minimum void ratios of the sand are found to be 2.65, 1.64 (g/ cm3), 1.44 (g/cm3), 0.89 and 0.65, respectively. The angle of internal friction of dry sand at a relative density of 60% obtained from the direct shear box (6 cm 6 cm) test is 38 . 2.2. Geosynthetic In order to provide horizontal reinforcement material for the model test, geotextile layers is used with tensile strength of 7.68 kN/m. This type of reinforcement is an extruded polymer sheet made by using high density polyethylene (HDPE). The reason for selecting this type of reinforcement is almost the same peak tensile strength in every direction. The properties of this reinforcement are obtained from manufacture's manual of the product are given in Table 1. 2.3. Model footings Model of the circular and square footings are made of steel plates of 15 mm thickness. The diameter of the circular footing and the width of square footing are selected as 120 mm and 106 mm (both footings had the same plan area equal to 11300 mm2), respectively. The bases of both footings are made rough by gluing a layer of geonet on the bottom surface of them with epoxy glue so as to ensure uniform roughness in all tests. Cone shaped grooves are opened on the footings so that different load eccentricities can be applied. Under the grooves 2-mm thickness are left so that eccentricity cannot change during testing. Fig. 1 shows circular and square foundations and the footing's rough bases that are used in this study. The Kern of footing is defined as the part of footing where the whole footing undergoes compressive pressure when the load is applied in other places except for the center. Loading on the Kern boundary caused the pressure at edge of footing to become zero. For circular foundation, Kern boundary is R/4 and loading inside the Kern boundary, whole footing area is under pressure. In this study, one load eccentricity (on the Kern boundary) is selected for both foundations: R/4 for circular footing and B/6 (in one-way) for square footing. The load eccentricities can be applied on the model footing by small holes whose locations are shown in Fig. 2, where point 1 is repeated for both foundations and points 2 and 3 are loaded for circular and square model footing, respectively. 3. Test apparatus and experimental program Laboratory tests are performed in a square test tank with inside
Table 1 Properties of geotextile. Physical and mechanical property
Value
Polymer type Tensile strength (kN/m) Extension at 1/2 peak load (%) Extension at maximum load (%) Tensile strength at 10% extension (kN/m) Weight (g/m2)
Polyethylene 7.68 3.2 20.2 6.8 730
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Fig. 2. The Kern of circular and square foundations and loaded locations.
Fig. 1. Circular and square footings and rough bases.
dimensions of 0.8 0.8 0.8 m in length, width and height, respectively. Plan size of the tank is 6.5 times the diameter of footing to ensure that the rupture surface is contained within the test tank. An electrically operated hydraulic jack is used for the load application system. The amount of the load applied is measured using a load cell with a capacity of 2500 kg. The displacements are measured by LVDTs (Linear Variable Differential Transducer) and these data are recorded by means of a data logger. The test apparatus is shown in Fig. 3. In all the tests, sand unit weight and compaction relative density are 15.14 kN/m3 and 60%, respectively. To achieve the desired relative density, the sand is placed by sand raining technique. The height of free pouring obtained through several trials in an especial aluminum cup with a certain volume of 130 mL. Based on the minimum and maximum void ratios of the sand, the relation between the height of fall and the corresponding relative density is developed. Afterwards, it is found that the sand should be filled in 50 mm thickness intervals in order to achieve the desired density. The tank filled up until the depth of the sand reached 700 mm, about 6 times the diameter of footing. During the pouring of sand, a cup with a certain volume is placed in the tank and after each test relative density of the sand in the cup is calculated as a sample of the tank soil. The variation of relative density of sand found to be 60% ± 4 in all tests. In the reinforced cases, a square shaped reinforcement layer, 4.5 times the diameter of circular footing (b/D ¼ 4.5) based on previous researches (Sitharam and Sireesh, 2004; Basudhar et al., 2007; Latha and Somwanshi, 2009; Liu, 2015), is placed after leveling the surface of the bed and sand pouring is continued to the next level of reinforcement or footing. In order to find out the effect of number of reinforcement layers on bearing capacity at the first,
optimum depth ratio of reinforcement layers are measured for square and circular footings then number of reinforcement layers increased up to 3. Laboratory tests are conducted with controlling displacement in rate of 1 mm/min. Applying displacement is continued up to the failure of the soil.
4. Finite element procedure A numerical study is implemented to complement the findings of the laboratory study and to understand the reinforcement behavior mechanism further in light of stress and displacement distributions underneath the footings. The finite element analysis is used to model tests of circular and square footings on reinforced sand to verify the laboratory model test results and understand the deformation trend within the reinforcement layers. For both
Fig. 3. Schematic view of the experimental apparatus.
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circular and square footings, all the numerical analyses are carried out in a three-dimensional space. Boundary conditions are chosen such that displacement of the horizontal boundary is restricted in all directions, while vertical boundaries are restricted horizontally and free to move in the vertical direction (smooth rigid). Also the nodes at the base are fixed against displacements in both directions (rough rigid). In order to analyze the actual configuration of the experiments, the dimensions and properties of different components (soil, foundation and reinforcement layers) are chosen such that they represent those used in the actual test. The reinforcement layers are also modeled as a linear elastic material using membrane element as was suggested by Kotake et al. (2001), Hussein and Meguid (2016), Yang et al., 2016, Mosallanezhad et al. (2016) and Abdesssemeda et al. (2015). The thickness of reinforcement layer is assumed 4 mm in all models as actual condition. Secant modulus of elasticity for the reinforcement per unit length which chosen from the manufacturer's manual is about 219 kN/m. Analyses are performed under displacement control. In modeling the yielding of frictional material (sand) in this study, the elastic-perfectly plastic Drucker-Prager constitutive model with a non-associated flow rule is used. The parameters adopted for the analysis are given in Table 2. The parameters (d) and (b) are the cohesion and internal frictional angle used in the Drucker-Prager constitutive model. More details on these parameters can be found in Helwany (2007). The model is divided into four main domains; the top soil (above the reinforcement), the bottom soil (below the reinforcement), foundation and the reinforcement layers. The soil is discretized using 8-node linear brick elements while the reinforcement is modeled with 4-noded rectangular membrane elements which having negligible bending stiffness. The mesh density is a significant metric used to control accuracy. The most fundamental and accurate method for evaluating mesh quality is to refine the mesh until a critical result. In this paper for evaluating the quality of mesh two ways is utilized. One of the ways is to compare numerical results with test data and other way is included mesh refinement (density of the mesh) and interpretations of results discontinuities (i.e. it doesn't change significantly with each refinement). For this particular, four types of mesh global size are adapted as 0.034, 0.024, 0.014 and 0.004. The results indicate as the mesh density increases, the ultimate bearing capacity not changes significantly after 0.034. The analyzed prototype soil geometry, generated mesh, geosynthetic and the footings along with their elements are shown in Fig. 4. The total number of nodes and elements generating the given mesh is about 912803 and 7734, respectively. It is worth to say that a small cohesion value (1 kN/m2) is used in this study to improve the stability of the analyses and avoid any singularity that may arise. The interaction between reinforcement and sand is
Table 2 Material properties used in numerical models. Value Soil
Reinforcement
Friction angle (degree) Density (kN/m3) Modulus of elasticity (MPa) Poisson's ratio Cohesion (kPa) Dilatancy (degree) Secant stiffness (kN/m) Flow rule
39 14.40 40 0.30 1 0 e non-associate 0.63 0.77 e e e
e 0.0073 54.8 0.30 e e 219 e e e 219 0.50 0.005
d (kPa) Tensile stiffness (kN/m)
m Eslip
modeled at both sides by using interface elements. For define interface between the sand (solid elements) and the reinforcement layers (membrane elements) a parametric study is conducted and indicated that using the surface to surface contact model with the traditional node to surface contact formulation is suitable. It should be noted that the behavior of the soil-reinforcement interface is simulated using the Coulomb friction model with two material parameters such as friction coefficient (m) and tolerance parameter (Eslip). 5. Optimum depth of reinforcement layers One of the important parameters in reinforced soil is the depth of embedment of reinforcement layers below the footing. The optimum spacing of reinforcement layers for u and h is studied experimentally in this section. The performance improvement is expressed as a non-dimensional parameter (BCR), which is defined as Equation (1), the ratio of ultimate bearing capacity of reinforced soil to the ultimate bearing capacity of unreinforced soil.
BCR ¼
quðreinforcedÞ quðunreinforcedÞ
(1)
According to previous studies, several findings are reported for u and h in central loading condition. Researchers emphasized that there is critical values for u and h beyond which further increase have not any effect on bearing capacity. Boushehrian and Hataf (2003), Latha and Somwanshi (2009), Mosallanezhad et al. (2007) have shown through the tests on circular and square footings that the optimum depth of the first reinforcement layer and the vertical spacing between reinforcement layers that provide the maximum BCR vary from 0.2 to 0.5 for u/D or u/B and from 0.3 to 0.6 for h/D or h/B, respectively (here u is the depth of first layer of reinforcement and h is the vertical spacing between layers). For centrically and eccentrically loaded footings, eight different depths including u/ D ¼ u/B ¼ 0.25e0.66 below the footing are considered for the first and second layers of reinforcement. The results for embedment depth ratios of the first layer of reinforcement versus the BCR are shown in Fig. 5a. As it is obvious in this figure, the depth ratio of u/ D ¼ u/B ¼ 0.42 gives the highest BCR in central and eccentrical loadings. For the second layer of reinforcement, different depth ratios including h/D ¼ h/B ¼ 0.25e0.66 are considered to determine the optimum value of h/D or h/B by maintaining u/D ¼ u/B ¼ 0.42 as a constant. Results of h/D or h/B changing with the BCR are shown in Fig. 5b for both central and eccentrial loadings. It can be seen from this figure that, for depth ratio of h/D ¼ h/B ¼ 0.42, the maximum BCR has occurred. Thus, the optimum value for u and h in all tests can be taken equal to u/D ¼ h/D ¼ u/B ¼ h/B ¼ 0.42. Consequently, for the multiple reinforcement layers, the embedment depth ratio is chosen based the results of second layer as 0.42. 6. Loadesettlement behavior
Characteristics
b
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Load-settlement curves from the 8 laboratory tests and numerical analyses which were carried out on centrically loaded in both reinforced and unreinforced conditions are shown in Fig. 6a and b for circular and square footings, respectively. Every test is repeated twice to verify the repeatability and consistency of test results and averages of each of the test are drawn. It should be noted that the difference of load-settlement curves were less than 2% and the patterns of load-displacement were the same. As it can be seen in these diagrams, although the numerical results do not fit completely to the experimental results, but the agreement is reasonably well. This discrepancy may be related to the model, soil and foundation parameters chosen and the differences of the
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Fig. 4. The finite element meshes in three-dimensions, a) circular footing, b) square footing, c) geocynthetic and d) soil bed.
boundary conditions in numerical and experimental models (Alamshahi and Hataf, 2009). The ultimate bearing capacity of the foundation is obtained from the curves of load-settlement by the tangent method as suggested by Boushehrian and Hataf (2003), because curves did not have pronounced peaks. In this method, a tangent line is plotted along the start portion of the load-settlement curves and the other tangent line is plotted along the end portion. Then the intersection point of these two lines is considered as the ultimate bearing capacity on load axis (Boushehrian et al., 2011). This figure confirms the significant increase in the bearing capacity of the footing with the number of reinforcement layers. With increasing the number of reinforcement layers the contact area and interlocking between them and sand particles increase. Consequently, larger displacements and shear stresses built up in the soil under the footing and transferred by reinforcement layers to larger mass of soil. Therefore the failure wedge became larger and the frictional resistance on failure planes became greater. The ultimate bearing capacity of both circular and square footings versus increasing the number of reinforcement layers are shown in Fig. 7. It is evident that the circular and square footings with the same plan area have almost equal ultimate bearing capacities in unreinforced condition but in reinforced condition by increasing the number of reinforcement layers the ultimate bearing capacity of circular footing has a larger amount than the square footing. In other words, for circular footings, reinforcement layers have a more effect in comparison with square footings. Based on the numerical results the main reason for the larger increase in ultimate bearing capacity in circular footing in comparison with square footing in the same test condition may be attributed to reinforcement mechanism which limits the spreading and lateral deformations of sand. The circular footing causes a bigger mobilized tension in reinforcement layers that enables the reinforcement to resist the imposed horizontal shear stresses built up in the mass beneath the loaded area by transferring the footing load to deeper layers of soil. Therefore, the failure wedge becomes larger and the frictional resistance on failure planes becomes greater. Variations of measured BCR from model tests and numerical analyses against number of reinforcement layers are also shown in Fig. 7. The BCR increases with increasing N. Although the
Fig. 5. Variation of BCR with a) u/D or u/B and b) h/D or h/B ratio.
BCR obtained from the numerical analyses appears to be lower than that measured from the experimental tests, the general trends of the BCR variation with the number of reinforcement layers agrees fairly well in both finite element models and experimental models. When the reinforcement layers are utilized for soil improvement
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Fig. 7. Ultimate bearing capacity and BCR versus N for circular and square footings. Fig. 6. Load versus settlement for reinforced and unreinforced sand, a) circular footing and b) square footing.
and enhancing the bearing capacity, it is preferable to use circular foundation instead of a square foundation. It can be concluded that the more benefit effect of reinforcement layers in increasing the bearing capacity appears for circular footings rather than square footings that may result in decreasing size and economic design of the footing.
settlement, the improvement index is defined as Equation (2). According to this non-dimensional quantity, which is called SR (settlement reduction), is defined as the ratio of footing settlement in reinforced soil (Su(reinforced)) to the footing settlement in unreinforced soil at the ultimate bearing capacity (Su(unreinforced)). The settlement and SR for each test and numerical analysis on both unreinforced and reinforced conditions are given in Table 3.
SuðreinforcedÞ
7. Displacement fields
SR ¼
Vertical displacements of reinforcement layers embedded in sand are shown in Fig. 8a and b for both circular and square footings, respectively. These figures clearly indicate that when reinforcement layers are used for circular footing, the vertical displacement domain is developed larger in comparison with square footing and reinforcement layer endures a larger stress. Consequently ultimate bearing capacity would be increased. The maximum displacement is found to decrease with the addition of reinforcement layer. For N ¼ 3 (Fig. 8a), the vertical displacement of the upper layer (located closer to the footing) is larger than that of the lower one. As the experimental tests and numerical analysis are under strain control conditions, the developed tensile stresses in the reinforcements increased when three geosynthetic layers are installed under the footing. Similarly, the upper reinforcement layer carrying more tensile stresses compared to the lower layer. It is worth to note that in both circular and square footings, most of the reinforcement deformations and stresses occurred mainly in the area immediately below the footing with small deformation away from the loaded area. Besides, in the present study to determine the efficiency of reinforcement layers on the footing
From this table, it is realized that by increasing the number of reinforcement layers the ultimate bearing capacity occurred at a lower settlement rather than unreinforced condition. Using reinforcement layers caused the footing settlement corresponding to the constant load intensity reduced. From the SR factor it can be concluded that the settlement pertinent to ultimate bearing capacity of circular footing without reinforcement layers is larger than eccentrically loaded circular footing in reinforced condition. Based on the results of this study, the ultimate bearing capacity in square footing occurs in a lower settlement in comparison to circular footings with the same plan area in both unreinforced and reinforced conditions. With increasing the number of reinforcement layers up to three layers the settlement at ultimate bearing capacity and SR decreased for circular and square footings. Based on the centrically experimental and numerical load-settlement curves, the ratio between settlement of footings at ultimate bearing capacity (Su) to the width of square footing or diameter of circular footing, namely, Su/B or Su/D, in the reinforced cases are typically 20% and 30% lower than that in the unreinforced cases, respectively. This means that the value of Su/B or Su/D for the reinforced
SuðunreinforcedÞ
(2)
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Fig. 8. Vertical displacement contours for reinforcement layers; A) Circular footing, B) Square footing.
Table 3 SR for both unreinforced and reinforced sand. Footing
Circular
e
Centric
R/4
Square
Centric
B/6
N
0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
Experimental
Numerical
Su (mm)
SR
Su (mm)
SR
23.06 21.40 16.92 15.68 16.66 13.31 11.38 10.03 20.06 18.40 14.92 13.68 14.42 12.65 10.64 10.02
1.00 0.92 0.73 0.68 1.00 0.80 0.68 0.60 1.00 0.92 0.74 0.69 1.00 0.88 0.74 0.69
18.52 17.31 16.40 14.82 17.54 14.14 12.39 11.88 16.30 15.11 14.42 14.10 15.66 14.07 13.28 12.77
1.00 0.93 0.89 0.80 1.00 0.81 0.71 0.68 1.00 0.94 0.90 0.81 1.00 0.90 0.85 0.82
condition is not significantly different from that for the unreinforced one. In eccentrically loading it is observed that settlements at ultimate bearing capacity are heavily dependent on load eccentricity. For square and circular footings, respectively, the Su/B or Su/ D, in the eccentrically loaded cases are typically 45% and 55% lower than the centrically loaded cases for both unreinforced and reinforced condition. In other words, in eccentrically loaded footing, as the effective area of footing decreased the ultimate bearing capacity achieved at a smaller settlement in comparison with when the load acting on the full area of footing in centrically cases. The SR for circular footing is lower than that in square footing. In unreinforced condition, square footings have bigger ultimate
bearing capacity at lower settlement as compared to circular footings. The results of this research showed that for the footings with the same plan area, using of reinforcement layers are more suitable for circular shape in comparison with square shape in terms of ultimate bearing capacity and settlement level corresponds to the settlement at ultimate bearing capacity footing. Based on the numerical analyses the displacement pattern in the case of unreinforced sand bed for the both square and circular footing shows severe lateral deformation near the ground surface and heaves on the ground surface near the footing, indicating general shear mode of failure. However, for the case of circular footing on the reinforced sand bed, there is considerable reduction in lateral deformation near ground surface and heave of the ground surface adjacent to the footing in comparison with square footing. With increasing the number of reinforcement layers, the lateral flow of the soil adjacent to the circular footing is found to be more arrested in comparison square footing. This finding proved that, in reinforced sand condition, the circular shape brings a higher load carrying capacity in comparison with square shape where the plan area on them is the same.
8. Load eccentricity effects Ultimate bearing capacity of circular and square footings in the case of eccentrical loading which are determined from loadsettlement curves are summarized in Table 4. The results showed that by considering the load eccentricity, the BCR increased for both footings. This increase in BCR for eccentrically loaded footing, in comparison with centrically loaded footing, is previously shown in an experiment by Sadoglu et al. (2009) for strip footing on geotextile reinforced sand. Similar conclusion is also reported by
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Table 4 Results of circular and square footings in both unreinforced and reinforced sand. Footing type
Circular
e
Centric
R/4
Square
Centric
B/6
N
0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
qu (N)
BCR
Tilt (degree)
Test
Numerical
Test
Numerical
Test
Numerical
1318 3192 4415 5523 956 2480 3518 4120 1457 2361 3143 3876 940 1922 2429 3081
1481 3210 4771 5836 1016 2566 3590 4321 1636 2250 2843 3637 970 2398 3020 3819
1.00 2.42 3.35 4.19 1.00 2.59 3.68 4.31 1.00 1.62 2.16 2.66 1.00 2.04 2.58 3.28
1.00 2.17 3.22 3.94 1.00 2.53 3.53 4.25 1.00 1.38 1.74 2.22 1.00 2.47 3.11 3.94
e e e e 7.72 6.39 5.12 4.11 e e e e 6.65 6.44 5.81 5.17
e e e e 6.74 5.84 4.90 4.43 e e e e 6.03 5.91 5.16 4.58
Sawwaf and Nazir (2012) for eccentrically loaded ring footing on reinforced layered soil. It clearly observes that by increasing the number of reinforcement layers from one layer to three layers the BCR increases. Also, this table demonstrates that there is a close agreement between the results of numerical analyses and experimental tests. However, the ultimate bearing capacities in the numerical analyses are some extent greater than that of the laboratory tests. Also, when reinforcement layers are used, ultimate bearing capacity ratio (BCR) increased greatly in circular footing in comparison with square footing in central and eccentrical loadings. In other words, the reinforcement layers have more influence for circular footing than the square footing in the both loadings. The effect of reinforcement layers on the behavior of footings tilt, as an unknown issue, is investigated to recognize the effect of reinforcement layers on the BCR for eccentrically loaded footings. When a footing is subjected to eccentrical loading, footing tilt is inevitable. In this study, in order to calculate the tilt of footing, two LVDTs are used for measuring the settlement of footing in two different places: one LVDT is along the loading rod and the other LVDT is on the footing surface at the certain point that is along the load eccentricity. The tilt of footing is calculated with respect to difference between settlements recorded by two LVDTs. The quantities of footing tilts at ultimate bearing capacity of every test and analysis are measured and are summarized in Table 4. In unreinforced soil condition it is also observed that the tilt of circular footing was larger than square footing. The results of vertical displacement contours obtained from finite element method for the circular and
square footings resting on sand are illustrated in Fig. 9. These data confirm the laboratory model tests results and demonstrate the deformation trends within the soil mass. As it can be observed, the settlement of square footing decreases in comparison with circular footing at eccentrical loading (e ¼ B/6 and e ¼ R/4 for square and circular footings, respectively). In another words, when the loading has eccentricity, circular footing experiences more settlement that causes larger tilt. This behavior may be attributed to the Meyerhof (1953) hypothesis that load eccentricity leads to a decrease in effective area of footing. As it is expected, by increasing the number of reinforcement layers, the tilt of footing decreased for both footings but tilt of circular footing decreases more than square footing in experimentally and numerically models. Also in eccentrical loading, when footings have the same plan area, the reinforcement layers have more influence for circular footing in comparison to square footing. 9. Scale effects The adopted circular and square footings in laboratory and numerical studies were reduced to a certain scale while the used sand, and reinforcement layers were the same in the models and the numerical analyses. Therefore, the response of the experimental and numerical results may not be the same as the behavior of the field tests and scale effects might cause some influence on the results. The current research has limitations of scale effects and can not be directly extrapolated for the field cases. However, the results
Fig. 9. Vertical displacement contours under footing in eccentrically loaded.
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from this study provided important insight into the performance of reinforcement layers for different footing shapes with the same plan area. Based on the Fakher and Jones (1996) analysis about the influence of various parameters on the performance of reinforced soil foundation beds, Sireesh et al. (2009) reported that the important parameters in the reinforced soil models can be attributed to stiffness of the reinforcement (k), plan area of footing (A) and shear modulus of soil (G). For a Larger Scale Model (LSM) with area of N times higher than the models that used in this research (M) as Equation (3), the findings of this paper may be utilized by satisfying Equations (4) and (5).
References
AðLSMÞ ¼N AðMÞ
(3)
GðLSMÞ pffiffiffiffi ¼ N GðMÞ
(4)
kðLSMÞ G2ðLSMÞ
¼
kðMÞ G2ðMÞ
(5)
Consequently based on Equation (6), the reinforcement strength in the larger scale model should be N times the reinforcement strength which used in the model test. 2 kðLSMÞ GðLSMÞ ¼ 2 ¼N kðMÞ GðMÞ
reinforcement forces in comparison with square footings. This phenomenon causes to reinforcement layers more resistance against the imposed horizontal shear stresses built up in the soil mass beneath the loaded area. Also in eccentrical loading, tilt of circular footing was larger than square footing and by reinforcing the tilt of footing decreased for both footings. At the end, the comparison of numerical analysis with experimental results demonstrate that the utilized approach for modeling of reinforcement layers in 3D is suitable for solving geosynthetic-reinforced soil systems.
(6)
For example, for a circular footing with 113000 mm2 plan area (about 10 times the current study), as in this research geosynthetic with ultimate tensile strength 7.68 kN/m is used, the findings of this present study is applicable, when reinforcement strength in the larger scale foundation be 10 times the strength of the reinforcement used in the model test (about 77 kN/m).
10. Conclusion The behavior of centrically and eccentrically loaded circular and square footings with the same plan area supported on unreinforced and reinforced sand are studied based on a series of laboratory tests and numerical analyses. In order to understand the beneficial effects of reinforcement layers on the bearing capacity, tests with different numbers of reinforcement layers (N ¼ 1, 2 and 3) are performed. The following conclusions can be drawn from the present study: In unreinforced condition, the ultimate bearing capacity is almost equal for both of the footings (although ultimate bearing capacity of square footing is slightly more than that in circular footing); but with reinforcing and increasing the number of reinforcement layers the ultimate bearing capacity of circular footing increased in a higher rate compared to square footing. The BCR increases with increasing the number of reinforcement layers for both of the footings (square and circular) but the reinforcement layers have more effect for circular footing in comparison with square footing and the rate of increasing (BCR) for circular footing is higher than square footing. Furthermore, a close compatibility is observed between the experimental and numerical results concerning the trend of behavior. Numerical results demonstrated that the reinforcement layers improved the bearing capacity by transferring the footing load to deeper soil layers and thus reduced the stresses and strains underneath the footing. Ultimate bearing capacity decreased regarding load eccentricity and making use of reinforcement layers causes to circular footings mobilize higher
Abdesssemeda, M., Kenai, S., Bali, A., 2015. Experimental and numerical analysis of the behavior of an airport pavement reinforced by geogrids. Construc. Build. Mat. 94, 547e554. Adams, M., Collin, J., 1997. Large model spread footing load tests on geosynthetic reinforced soil foundations. J. Geotech. Geoenviron. Eng. 123, 66e72. Alamshahi, S., Hataf, N., 2009. Bearing capacity of strip footings on sand slopes reinforced with geogrid and grid-anchor. Geotext. Geomembr. 27, 217e226. Alawaji, H.A., 2001. Settlement and bearing capacity of geogrid-reinforced sand over collapsible soil. Geotext. Geomembr. 19, 75e88. Basudhar, P.K., Saha, S., Deb, K., 2007. Circular footings resting on geotextile- reinforced sand bed. Geotext. Geomembr. 25, 377e384. Binquet, J., Lee, K.L., 1975a. Bearing capacity tests on reinforced earth slabs. J. Geotech. Geoenviron. Eng. 101, 1241e1255. Binquet, J., Lee, K.L., 1975b. Bearing capacity analysis of reinforced earth slabs. J. Geotech. Geoenviron. Eng. 101, 1257e1276. Boushehrian, J., Hataf, N., 2003. Experimental and numerical investigation of the bearing capacity of model circular and ring footing on reinforced sand. Geotext. Geomembr. 21, 241e256. Boushehrian, A.H., Hataf, N., Ghahramani, A., 2011. Modeling of the cyclic behavior of shallow foundations resting on geomesh and grid-anchor reinforced sand. Geotext. Geomembr. 29, 242e248. Fakher, A., Jones, C.J.F.P., 1996. Discussion on ‘‘Bearing capacity of rectangular footings on geogrid reinforced sand’’. By Yetimoglu, T., Wu, J.T.H., Saglamer, A., 1994. J. Geotech. Geoenviron. Eng. 122, 326e327. Ghazavi, M., Afshar, J.N., 2013. Bearing capacity of geosynthetic encased stone columns. Geotext. Geomembr. 38, 26e36. Ghosh, A., Ghosh, A., Kumar, B., 2005. Bearing capacity of square footing on pond ash reinforced with jute-geotextile. Geotext. Geomembr. 23, 144e173. Helwany, S., 2007. Applied Soil Mechanics with ABAQUS Applications. John Wiley & Sons Pub, Hoboken, New Jersey, USA. Huang, C.C., Tatsuoka, F., 1988. Prediction of bearing capacity in level sandy ground reinforced with strip reinforcement. In: Proceedings of International Geotechnical Symposium on Theory and Practice of Earth Reinforcement, Japan, pp. 191e196. Huang, C.C., Tatsuoka, F., 1990. Bearing capacity of reinforced horizontal sandy ground. Geotext. Geomembr. 9, 51e82. Hughes, J.M.O., Withers, N.J., 1974. Reinforcing soft cohesive soil with stone columns. Ground Eng. 7, 42e49. Hussein, M.G., Meguid, M.A., 2016. A three-dimensionalfinite element approach for modeling biaxial geogrid with application to geogrid-reinforced soils. Geotext. Geomembr. 44, 295e307. Khing, K.H., Das, B.M., Puri, V.K., Yen, S.C., Cook, E.E., 1994. Foundation on strong sand underlain by weak clay with geogrid at the interface. Geotext. Geomembr. 13, 199e206. Kotake, N., Tatsuoka, F., Tanaka, T., Siddiquee, M.S.A., Huang, C., 2001. FEM simulation of the bearing capacity of level reinforced sand ground subjected to footing load. Geosynth. Int. 501e549. Kumar, A., Ohri, M.L., Bansal, R.K., 2007. Bearing capacity tests of strip footings on reinforced layered soil. Geotech. Geol. Eng. 25, 139e150. Latha, M., Somwanshi, A., 2009. Effect of reinforcement form on the bearing capacity of square footings on sand. Geotext. Geomembr. 27, 409e422. Liu, H., 2015. Reinforcement load and compression of reinforced soil mass under surcharge loading. J. Geotech. Geoenviron. Eng. 141 (04015017), 1e10. Lovisa, J., Shukla, S.K., Sivakugan, N., 2010. Behavior of prestressed geotextilereinforced sand bed supporting a loaded circular footing. Geotext. Geomembr. 28, 23e32. Mandal, J.N., Sah, H.S., 1992. Bearing capacity tests on geogrid-reinforced clay. Geotext. Geomembr. 11, 327e333. Meyerhof, G.G., 1953. The bearing capacity of foundations under eccentric and inclined loads. In: Proceedings of the Conference on Soil Mechanics and Foundation Engineering. Switzerland, Zurich, pp. 440e453. Mosallanezhad, M., Hataf, N., Ghahramani, A., 2007. Experimental study of bearing capacity of granular soils reinforced with innovative grid-anchor system. J. Geotech. Geoenviron. Eng. 26, 299e312. Mosallanezhad, M., Taghavi, S.H.S., Hataf, N., Alfaro, M.C., 2016. Experimental and numerical studies of the performance of the new reinforcement system under pull-out conditions. Geotext. Geomembr. 44, 70e80. Noorzad, R., Mirmoradi, S.H., 2010. Laboratory evaluation of the behavior of a
E. Badakhshan, A. Noorzad / Geotextiles and Geomembranes 45 (2017) 58e67 geotextile reinforced clay. Geotext. Geomembr. 28, 386e392. Omar, M.T., Das, B.M., Puri, V.K., Yen, S.C., 1993. Ultimate bearing capacity of shallow foundations on sand with geogrid reinforcement. Can. Geotech. J. 30, 545e549. Ornek, M., 2014. Estimation of ultimate loads of eccentric-inclined loaded strip footings rested on sandy soils. Neural. Comput. Appl. 25, 39e54. Patra, C.R., Das, B.M., Bhoi, M., Shin, E.C., 2006. Eccentrically loaded strip foundation on geogrid-reinforced sand. Geotext. Geomembr. 24, 254e259. Pinho-Lopes, M., Paula, A.M., Lopes, M.L., 2015. Pullout response of geogrids after installation. Geosynth. Int. 22, 339e354. Sadoglu, E., 2015. Numerical analysis of centrally and eccentrically loaded strip footing on geotextile-reinforced sand. Geosynth. Int. 22, 225e234. Sadoglu, E., Cure, E., Moroglu, B., Uzuner, B.A., 2009. Ultimate loads for eccentrically loaded model shallow strip footings on geotextile-reinforced sand. Geotext. Geomembr. 27, 176e182. Sawwaf, M., Nazir, A., 2012. Behaviour of eccentrically loaded small scale ring footing resting on reinforced layered soil. J. Geotech. Geoenviron. Eng. 138, 376e384.
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Sireesh, S., Sitharam, T.G., Kumar Dash, S., 2009. Bearing capacity of circular footing on geocell-sand mattress overlying clay bed with void. Geotext. Geomembr. 27, 89e98. Sitharam, T.G., Sireesh, S., 2004. Model studies of embedded circular footing on geogrid-reinforced sand beds. Ground Improv. 8, 69e75. Tafreshi, S.N., Dawson, A.R., 2010. Comparison of bearing capacity of a strip footing on sand with geocell and with planar forms of geotextile reinforcement. Geotext. Geomembr. 28, 72e84. Turker, E., Sadoglu, E., Cure, E., Uzuner, B., 2014. Bearing capacity of eccentrically loaded strip footings close to geotextile-reinforced sand slope. Can. Geotech. J. 51, 884e895. Yang, K., Jonathan, T.H., Rong-Her, C., Yi-Shou, C., 2016. Lateral bearing capacity and failure mode of geosynthetic-reinforced soil barriers subject to lateral loadings. Geotext. Geomembr. 1e14. Yetimuglu, T., Wu, J.T., Saglamar, A., 1994. Bearing capacity of rectangular footings on geogrid- reinforced sand. J. Geotech. Eng. 120, 2083e2099.
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Technical note
Effect of footing shape and load eccentricity on behavior of geosynthetic reinforced sand bed Ehsan Badakhshan*, 1, Ali Noorzad Geotechnical Engineering, Faculty of Civil, Water & Environmental Engineering, Shahid Beheshti University, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 May 2015 Received in revised form 22 January 2016 Accepted 30 November 2016
This paper presents the results from a laboratory modeling tests and numerical studies carried out on circular and square footings assuming the same plan area that rests on geosynthetic reinforced sand bed. The effects of the depth of the first and second layers of reinforcement, number of reinforcement layers on bearing capacity of the footings in central and eccentral loadings are investigated. The results indicated that in unreinforced condition, the ultimate bearing capacity is almost equal for both of the footings; but with reinforcing and increasing the number of reinforcement layers the ultimate bearing capacity of circular footing increased in a higher rate compared to square footing in both central and eccentrial loadings. The beneficial effect of a geosynthetic inclusion is largely dependent on the shape of footings. Also, by increasing the number of reinforcement layers, the tilt of circular footing decreased more than square footing. The SR (settlement reduction) of the reinforced condition shows that settlement at ultimate bearing capacity is heavily dependent on load eccentricity and is not significantly different from that for the unreinforced one. Also, close match between the experimental and numerical load-settlement curves and trend lines shown that the modeling approach utilized in this study can be reasonably adapted for reinforced soil applications. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Geosynthetics Circular and square footings Bearing capacity Reinforced sand
1. Introduction For the last four decades in Civil Engineering, application of geosynthetics has been known as a common technique to increase the ultimate bearing capacity of soils and decrease the settlement of footings. Among the range of geosynthetics available in the market, geotextiles are the most preferred type of geosynthetic materials for reinforcing the foundation beds. Many researchers (Hughes and Withers, 1974; Binquet and Lee, 1975a, 1975b; Huang and Tatsuoka, 1988, 1990; Adams and Colin, 1997; Alawaji, 2001; Ghosh et al., 2005; Kumar et al., 2007; Mosallanezhad et al., 2007; Tafreshi and Dawson, 2010; Ghazavi and Afshar, 2013; Pinho-Lopes et al., 2015) reported when reinforcements were placed at an optimum depth below a footing (strip, square, rectangular foundations) the beneficial effect of reinforcement can observed. These studies were focused on the ratio of the first layer of reinforcement from the foundation base, u, the foundation size, B, (u/B); the ratio of the reinforcement width, b, to the foundation
* Corresponding author. E-mail address: [email protected] (E. Badakhshan). 1 http://www.sbu.ac.ir. http://dx.doi.org/10.1016/j.geotexmem.2016.11.007 0266-1144/© 2016 Elsevier Ltd. All rights reserved.
size (b/B); and the ratio of the total reinforced depth, h, to the foundation size (h/B) and critical ratios of them. In the field of soil reinforcing with geosynthetic layers (in sand or clay) for circular foundations in centrally loaded, there has not been a lot of researches as compared to other foundations in the literature. Sitharam and Sireesh (2004) conducted a number of laboratory model tests to determine the bearing capacity of an embedded circular footing supported by sand bed reinforced with multiple layers of geotextiles. The test results demonstrated that the ultimate bearing pressure increased with embedment depth ratio of the foundation. Also, Basudhar et al. (2007) carried out experimental and numerical analyses on behavior of circular footings with different size resting on reinforced sand with geotextile and reported that with increase in number of reinforcement layers, the settlement value gradually decreased. Similarly, Boushehrian and Hataf (2003) found that for the circular footings on reinforced sand the maximum bearing capacity occurs at different values of embedment depth ratio depending on the number of reinforcement layers. For ratios of u/D greater than one reinforcement layers had no significant effect on bearing capacity. They also reported that choosing a rigid reinforcement did not always improve the effect on bearing capacity. Yetimuglu et al., 1994
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conducted laboratory model tests to investigate the bearing capacity of rectangular footings on geotextile reinforced sand. For a single layer of reinforcement, the optimal placement depth was found to be 0.3 times the footing width. Lovisa et al. (2010) studied behavior of pre-stressed geotextile reinforced sand bed supporting a loaded circular footing and found out that effects of the pre-stressed reinforcement configuration were evident for greater footing depths, in comparison with unreinforced and reinforced without pre-stressing. The results of the laboratory model tests for strip and square foundations supported on reinforced sand with geosynthetic layers demonstrated that for the development of maximum bearing capacity, the maximum depth of reinforced zone is about 2B for strip foundation and 1.4B for square foundation, where B is width of footing (Omar et al., 1993). The maximum depth of placement of the first layer of reinforcement should be less than about B to take advantage of reinforcement. In the same vein, Khing et al. (1994) conducted model tests on a strip footing supported by reinforced sand. Results showed that the maximum benefit of reinforcement in increasing the bearing capacity was obtained when the depth ratio of the first reinforcing layer to the foundation width was less than unity. Further, Latha and Somwanshi (2009) concluded that effective depth of the reinforcement zone below a square footing is twice the width of the footing, beyond which the inclusion of reinforcement layers will not result in significant improvement in the bearing capacity of the footing and, within the effective reinforcement zone, the optimum spacing of reinforcing layers is about 0.4 times the width of the footing. Moreover, Mandal and Sah (1992) revealed that the ratio u/B for the most efficiently possible condition of the reinforcement must be selected less than 0.3. Noorzad and Mirmoradi (2010) studied the behavior of cohesive soil reinforced with a geotextile by tri-axial compression tests and found that with increasing relative compaction, the peak strength of the sample and axial strain at failure increases. In another investigation, Mosallanezhad et al. (2007) dealt with the influence of a new generation of reinforcement (named by them as Grid-Anchor) on the increase of the bearing capacity of square foundation. They found that the critical value of u/B, h/B and b/B are equal to 0.25, 0.25 and 4.5, respectively. They also demonstrated that BCR for this system is greater than that of ordinary reinforcement. Up to now, few studies are developed experimentally to identify the critical values of reinforcement layers for reinforcing of the soil under the strip and rectangular foundations, when loading has been applied with eccentricity (Sadoglu et al., 2009; Patra et al., 2006; Ornek, 2014; Turker et al., 2014; Sadoglu, 2015). Sawwaf and Nazir (2012) studied the behavior of eccentrically loaded small scale ring footings resting on sand. They reported that the behavior of an eccentrically loaded ring footing significantly improved with an increase in the depth and relative density of the replaced compacted sand layer. All the above model tests have been carried out in optimum condition, over which the highest efficiency of the reinforcing layers is expected. As it can be easily noted in the previous studies no attention has been paid to the effect of footing shapes and load eccentricities resting on unreinforced and reinforced soil. Hence, the present study has been aimed to investigate the effect of foundation shape with the same plan area (for circular and square footings) in central and eccentral loadings on the bearing capacity, settlement and tilt of footings in unreinforced and reinforced sand bed. 2. Materials To investigate the effect of eccentric loading on a circular footing resting on reinforced sand with geotextile layers, the necessary details of the experimental studies are presented as follows:
59
2.1. Sand Oven dried poorly graded medium sand from the west of Iran is used in this study. The particle size distribution is determined using the dry sieving method according to ASTM D 422-90. This sand can be classified as SP in the unified soil classification system (USCS) with coefficient of uniformity 2.89 (Cu), coefficient of curvature 1.05 (Cc) and effective size of 0.27 (D10). The specific gravity of soil particles, maximum and minimum dry densities and maximum and minimum void ratios of the sand are found to be 2.65, 1.64 (g/ cm3), 1.44 (g/cm3), 0.89 and 0.65, respectively. The angle of internal friction of dry sand at a relative density of 60% obtained from the direct shear box (6 cm 6 cm) test is 38 . 2.2. Geosynthetic In order to provide horizontal reinforcement material for the model test, geotextile layers is used with tensile strength of 7.68 kN/m. This type of reinforcement is an extruded polymer sheet made by using high density polyethylene (HDPE). The reason for selecting this type of reinforcement is almost the same peak tensile strength in every direction. The properties of this reinforcement are obtained from manufacture's manual of the product are given in Table 1. 2.3. Model footings Model of the circular and square footings are made of steel plates of 15 mm thickness. The diameter of the circular footing and the width of square footing are selected as 120 mm and 106 mm (both footings had the same plan area equal to 11300 mm2), respectively. The bases of both footings are made rough by gluing a layer of geonet on the bottom surface of them with epoxy glue so as to ensure uniform roughness in all tests. Cone shaped grooves are opened on the footings so that different load eccentricities can be applied. Under the grooves 2-mm thickness are left so that eccentricity cannot change during testing. Fig. 1 shows circular and square foundations and the footing's rough bases that are used in this study. The Kern of footing is defined as the part of footing where the whole footing undergoes compressive pressure when the load is applied in other places except for the center. Loading on the Kern boundary caused the pressure at edge of footing to become zero. For circular foundation, Kern boundary is R/4 and loading inside the Kern boundary, whole footing area is under pressure. In this study, one load eccentricity (on the Kern boundary) is selected for both foundations: R/4 for circular footing and B/6 (in one-way) for square footing. The load eccentricities can be applied on the model footing by small holes whose locations are shown in Fig. 2, where point 1 is repeated for both foundations and points 2 and 3 are loaded for circular and square model footing, respectively. 3. Test apparatus and experimental program Laboratory tests are performed in a square test tank with inside
Table 1 Properties of geotextile. Physical and mechanical property
Value
Polymer type Tensile strength (kN/m) Extension at 1/2 peak load (%) Extension at maximum load (%) Tensile strength at 10% extension (kN/m) Weight (g/m2)
Polyethylene 7.68 3.2 20.2 6.8 730
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Fig. 2. The Kern of circular and square foundations and loaded locations.
Fig. 1. Circular and square footings and rough bases.
dimensions of 0.8 0.8 0.8 m in length, width and height, respectively. Plan size of the tank is 6.5 times the diameter of footing to ensure that the rupture surface is contained within the test tank. An electrically operated hydraulic jack is used for the load application system. The amount of the load applied is measured using a load cell with a capacity of 2500 kg. The displacements are measured by LVDTs (Linear Variable Differential Transducer) and these data are recorded by means of a data logger. The test apparatus is shown in Fig. 3. In all the tests, sand unit weight and compaction relative density are 15.14 kN/m3 and 60%, respectively. To achieve the desired relative density, the sand is placed by sand raining technique. The height of free pouring obtained through several trials in an especial aluminum cup with a certain volume of 130 mL. Based on the minimum and maximum void ratios of the sand, the relation between the height of fall and the corresponding relative density is developed. Afterwards, it is found that the sand should be filled in 50 mm thickness intervals in order to achieve the desired density. The tank filled up until the depth of the sand reached 700 mm, about 6 times the diameter of footing. During the pouring of sand, a cup with a certain volume is placed in the tank and after each test relative density of the sand in the cup is calculated as a sample of the tank soil. The variation of relative density of sand found to be 60% ± 4 in all tests. In the reinforced cases, a square shaped reinforcement layer, 4.5 times the diameter of circular footing (b/D ¼ 4.5) based on previous researches (Sitharam and Sireesh, 2004; Basudhar et al., 2007; Latha and Somwanshi, 2009; Liu, 2015), is placed after leveling the surface of the bed and sand pouring is continued to the next level of reinforcement or footing. In order to find out the effect of number of reinforcement layers on bearing capacity at the first,
optimum depth ratio of reinforcement layers are measured for square and circular footings then number of reinforcement layers increased up to 3. Laboratory tests are conducted with controlling displacement in rate of 1 mm/min. Applying displacement is continued up to the failure of the soil.
4. Finite element procedure A numerical study is implemented to complement the findings of the laboratory study and to understand the reinforcement behavior mechanism further in light of stress and displacement distributions underneath the footings. The finite element analysis is used to model tests of circular and square footings on reinforced sand to verify the laboratory model test results and understand the deformation trend within the reinforcement layers. For both
Fig. 3. Schematic view of the experimental apparatus.
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circular and square footings, all the numerical analyses are carried out in a three-dimensional space. Boundary conditions are chosen such that displacement of the horizontal boundary is restricted in all directions, while vertical boundaries are restricted horizontally and free to move in the vertical direction (smooth rigid). Also the nodes at the base are fixed against displacements in both directions (rough rigid). In order to analyze the actual configuration of the experiments, the dimensions and properties of different components (soil, foundation and reinforcement layers) are chosen such that they represent those used in the actual test. The reinforcement layers are also modeled as a linear elastic material using membrane element as was suggested by Kotake et al. (2001), Hussein and Meguid (2016), Yang et al., 2016, Mosallanezhad et al. (2016) and Abdesssemeda et al. (2015). The thickness of reinforcement layer is assumed 4 mm in all models as actual condition. Secant modulus of elasticity for the reinforcement per unit length which chosen from the manufacturer's manual is about 219 kN/m. Analyses are performed under displacement control. In modeling the yielding of frictional material (sand) in this study, the elastic-perfectly plastic Drucker-Prager constitutive model with a non-associated flow rule is used. The parameters adopted for the analysis are given in Table 2. The parameters (d) and (b) are the cohesion and internal frictional angle used in the Drucker-Prager constitutive model. More details on these parameters can be found in Helwany (2007). The model is divided into four main domains; the top soil (above the reinforcement), the bottom soil (below the reinforcement), foundation and the reinforcement layers. The soil is discretized using 8-node linear brick elements while the reinforcement is modeled with 4-noded rectangular membrane elements which having negligible bending stiffness. The mesh density is a significant metric used to control accuracy. The most fundamental and accurate method for evaluating mesh quality is to refine the mesh until a critical result. In this paper for evaluating the quality of mesh two ways is utilized. One of the ways is to compare numerical results with test data and other way is included mesh refinement (density of the mesh) and interpretations of results discontinuities (i.e. it doesn't change significantly with each refinement). For this particular, four types of mesh global size are adapted as 0.034, 0.024, 0.014 and 0.004. The results indicate as the mesh density increases, the ultimate bearing capacity not changes significantly after 0.034. The analyzed prototype soil geometry, generated mesh, geosynthetic and the footings along with their elements are shown in Fig. 4. The total number of nodes and elements generating the given mesh is about 912803 and 7734, respectively. It is worth to say that a small cohesion value (1 kN/m2) is used in this study to improve the stability of the analyses and avoid any singularity that may arise. The interaction between reinforcement and sand is
Table 2 Material properties used in numerical models. Value Soil
Reinforcement
Friction angle (degree) Density (kN/m3) Modulus of elasticity (MPa) Poisson's ratio Cohesion (kPa) Dilatancy (degree) Secant stiffness (kN/m) Flow rule
39 14.40 40 0.30 1 0 e non-associate 0.63 0.77 e e e
e 0.0073 54.8 0.30 e e 219 e e e 219 0.50 0.005
d (kPa) Tensile stiffness (kN/m)
m Eslip
modeled at both sides by using interface elements. For define interface between the sand (solid elements) and the reinforcement layers (membrane elements) a parametric study is conducted and indicated that using the surface to surface contact model with the traditional node to surface contact formulation is suitable. It should be noted that the behavior of the soil-reinforcement interface is simulated using the Coulomb friction model with two material parameters such as friction coefficient (m) and tolerance parameter (Eslip). 5. Optimum depth of reinforcement layers One of the important parameters in reinforced soil is the depth of embedment of reinforcement layers below the footing. The optimum spacing of reinforcement layers for u and h is studied experimentally in this section. The performance improvement is expressed as a non-dimensional parameter (BCR), which is defined as Equation (1), the ratio of ultimate bearing capacity of reinforced soil to the ultimate bearing capacity of unreinforced soil.
BCR ¼
quðreinforcedÞ quðunreinforcedÞ
(1)
According to previous studies, several findings are reported for u and h in central loading condition. Researchers emphasized that there is critical values for u and h beyond which further increase have not any effect on bearing capacity. Boushehrian and Hataf (2003), Latha and Somwanshi (2009), Mosallanezhad et al. (2007) have shown through the tests on circular and square footings that the optimum depth of the first reinforcement layer and the vertical spacing between reinforcement layers that provide the maximum BCR vary from 0.2 to 0.5 for u/D or u/B and from 0.3 to 0.6 for h/D or h/B, respectively (here u is the depth of first layer of reinforcement and h is the vertical spacing between layers). For centrically and eccentrically loaded footings, eight different depths including u/ D ¼ u/B ¼ 0.25e0.66 below the footing are considered for the first and second layers of reinforcement. The results for embedment depth ratios of the first layer of reinforcement versus the BCR are shown in Fig. 5a. As it is obvious in this figure, the depth ratio of u/ D ¼ u/B ¼ 0.42 gives the highest BCR in central and eccentrical loadings. For the second layer of reinforcement, different depth ratios including h/D ¼ h/B ¼ 0.25e0.66 are considered to determine the optimum value of h/D or h/B by maintaining u/D ¼ u/B ¼ 0.42 as a constant. Results of h/D or h/B changing with the BCR are shown in Fig. 5b for both central and eccentrial loadings. It can be seen from this figure that, for depth ratio of h/D ¼ h/B ¼ 0.42, the maximum BCR has occurred. Thus, the optimum value for u and h in all tests can be taken equal to u/D ¼ h/D ¼ u/B ¼ h/B ¼ 0.42. Consequently, for the multiple reinforcement layers, the embedment depth ratio is chosen based the results of second layer as 0.42. 6. Loadesettlement behavior
Characteristics
b
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Load-settlement curves from the 8 laboratory tests and numerical analyses which were carried out on centrically loaded in both reinforced and unreinforced conditions are shown in Fig. 6a and b for circular and square footings, respectively. Every test is repeated twice to verify the repeatability and consistency of test results and averages of each of the test are drawn. It should be noted that the difference of load-settlement curves were less than 2% and the patterns of load-displacement were the same. As it can be seen in these diagrams, although the numerical results do not fit completely to the experimental results, but the agreement is reasonably well. This discrepancy may be related to the model, soil and foundation parameters chosen and the differences of the
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Fig. 4. The finite element meshes in three-dimensions, a) circular footing, b) square footing, c) geocynthetic and d) soil bed.
boundary conditions in numerical and experimental models (Alamshahi and Hataf, 2009). The ultimate bearing capacity of the foundation is obtained from the curves of load-settlement by the tangent method as suggested by Boushehrian and Hataf (2003), because curves did not have pronounced peaks. In this method, a tangent line is plotted along the start portion of the load-settlement curves and the other tangent line is plotted along the end portion. Then the intersection point of these two lines is considered as the ultimate bearing capacity on load axis (Boushehrian et al., 2011). This figure confirms the significant increase in the bearing capacity of the footing with the number of reinforcement layers. With increasing the number of reinforcement layers the contact area and interlocking between them and sand particles increase. Consequently, larger displacements and shear stresses built up in the soil under the footing and transferred by reinforcement layers to larger mass of soil. Therefore the failure wedge became larger and the frictional resistance on failure planes became greater. The ultimate bearing capacity of both circular and square footings versus increasing the number of reinforcement layers are shown in Fig. 7. It is evident that the circular and square footings with the same plan area have almost equal ultimate bearing capacities in unreinforced condition but in reinforced condition by increasing the number of reinforcement layers the ultimate bearing capacity of circular footing has a larger amount than the square footing. In other words, for circular footings, reinforcement layers have a more effect in comparison with square footings. Based on the numerical results the main reason for the larger increase in ultimate bearing capacity in circular footing in comparison with square footing in the same test condition may be attributed to reinforcement mechanism which limits the spreading and lateral deformations of sand. The circular footing causes a bigger mobilized tension in reinforcement layers that enables the reinforcement to resist the imposed horizontal shear stresses built up in the mass beneath the loaded area by transferring the footing load to deeper layers of soil. Therefore, the failure wedge becomes larger and the frictional resistance on failure planes becomes greater. Variations of measured BCR from model tests and numerical analyses against number of reinforcement layers are also shown in Fig. 7. The BCR increases with increasing N. Although the
Fig. 5. Variation of BCR with a) u/D or u/B and b) h/D or h/B ratio.
BCR obtained from the numerical analyses appears to be lower than that measured from the experimental tests, the general trends of the BCR variation with the number of reinforcement layers agrees fairly well in both finite element models and experimental models. When the reinforcement layers are utilized for soil improvement
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63
Fig. 7. Ultimate bearing capacity and BCR versus N for circular and square footings. Fig. 6. Load versus settlement for reinforced and unreinforced sand, a) circular footing and b) square footing.
and enhancing the bearing capacity, it is preferable to use circular foundation instead of a square foundation. It can be concluded that the more benefit effect of reinforcement layers in increasing the bearing capacity appears for circular footings rather than square footings that may result in decreasing size and economic design of the footing.
settlement, the improvement index is defined as Equation (2). According to this non-dimensional quantity, which is called SR (settlement reduction), is defined as the ratio of footing settlement in reinforced soil (Su(reinforced)) to the footing settlement in unreinforced soil at the ultimate bearing capacity (Su(unreinforced)). The settlement and SR for each test and numerical analysis on both unreinforced and reinforced conditions are given in Table 3.
SuðreinforcedÞ
7. Displacement fields
SR ¼
Vertical displacements of reinforcement layers embedded in sand are shown in Fig. 8a and b for both circular and square footings, respectively. These figures clearly indicate that when reinforcement layers are used for circular footing, the vertical displacement domain is developed larger in comparison with square footing and reinforcement layer endures a larger stress. Consequently ultimate bearing capacity would be increased. The maximum displacement is found to decrease with the addition of reinforcement layer. For N ¼ 3 (Fig. 8a), the vertical displacement of the upper layer (located closer to the footing) is larger than that of the lower one. As the experimental tests and numerical analysis are under strain control conditions, the developed tensile stresses in the reinforcements increased when three geosynthetic layers are installed under the footing. Similarly, the upper reinforcement layer carrying more tensile stresses compared to the lower layer. It is worth to note that in both circular and square footings, most of the reinforcement deformations and stresses occurred mainly in the area immediately below the footing with small deformation away from the loaded area. Besides, in the present study to determine the efficiency of reinforcement layers on the footing
From this table, it is realized that by increasing the number of reinforcement layers the ultimate bearing capacity occurred at a lower settlement rather than unreinforced condition. Using reinforcement layers caused the footing settlement corresponding to the constant load intensity reduced. From the SR factor it can be concluded that the settlement pertinent to ultimate bearing capacity of circular footing without reinforcement layers is larger than eccentrically loaded circular footing in reinforced condition. Based on the results of this study, the ultimate bearing capacity in square footing occurs in a lower settlement in comparison to circular footings with the same plan area in both unreinforced and reinforced conditions. With increasing the number of reinforcement layers up to three layers the settlement at ultimate bearing capacity and SR decreased for circular and square footings. Based on the centrically experimental and numerical load-settlement curves, the ratio between settlement of footings at ultimate bearing capacity (Su) to the width of square footing or diameter of circular footing, namely, Su/B or Su/D, in the reinforced cases are typically 20% and 30% lower than that in the unreinforced cases, respectively. This means that the value of Su/B or Su/D for the reinforced
SuðunreinforcedÞ
(2)
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Fig. 8. Vertical displacement contours for reinforcement layers; A) Circular footing, B) Square footing.
Table 3 SR for both unreinforced and reinforced sand. Footing
Circular
e
Centric
R/4
Square
Centric
B/6
N
0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
Experimental
Numerical
Su (mm)
SR
Su (mm)
SR
23.06 21.40 16.92 15.68 16.66 13.31 11.38 10.03 20.06 18.40 14.92 13.68 14.42 12.65 10.64 10.02
1.00 0.92 0.73 0.68 1.00 0.80 0.68 0.60 1.00 0.92 0.74 0.69 1.00 0.88 0.74 0.69
18.52 17.31 16.40 14.82 17.54 14.14 12.39 11.88 16.30 15.11 14.42 14.10 15.66 14.07 13.28 12.77
1.00 0.93 0.89 0.80 1.00 0.81 0.71 0.68 1.00 0.94 0.90 0.81 1.00 0.90 0.85 0.82
condition is not significantly different from that for the unreinforced one. In eccentrically loading it is observed that settlements at ultimate bearing capacity are heavily dependent on load eccentricity. For square and circular footings, respectively, the Su/B or Su/ D, in the eccentrically loaded cases are typically 45% and 55% lower than the centrically loaded cases for both unreinforced and reinforced condition. In other words, in eccentrically loaded footing, as the effective area of footing decreased the ultimate bearing capacity achieved at a smaller settlement in comparison with when the load acting on the full area of footing in centrically cases. The SR for circular footing is lower than that in square footing. In unreinforced condition, square footings have bigger ultimate
bearing capacity at lower settlement as compared to circular footings. The results of this research showed that for the footings with the same plan area, using of reinforcement layers are more suitable for circular shape in comparison with square shape in terms of ultimate bearing capacity and settlement level corresponds to the settlement at ultimate bearing capacity footing. Based on the numerical analyses the displacement pattern in the case of unreinforced sand bed for the both square and circular footing shows severe lateral deformation near the ground surface and heaves on the ground surface near the footing, indicating general shear mode of failure. However, for the case of circular footing on the reinforced sand bed, there is considerable reduction in lateral deformation near ground surface and heave of the ground surface adjacent to the footing in comparison with square footing. With increasing the number of reinforcement layers, the lateral flow of the soil adjacent to the circular footing is found to be more arrested in comparison square footing. This finding proved that, in reinforced sand condition, the circular shape brings a higher load carrying capacity in comparison with square shape where the plan area on them is the same.
8. Load eccentricity effects Ultimate bearing capacity of circular and square footings in the case of eccentrical loading which are determined from loadsettlement curves are summarized in Table 4. The results showed that by considering the load eccentricity, the BCR increased for both footings. This increase in BCR for eccentrically loaded footing, in comparison with centrically loaded footing, is previously shown in an experiment by Sadoglu et al. (2009) for strip footing on geotextile reinforced sand. Similar conclusion is also reported by
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Table 4 Results of circular and square footings in both unreinforced and reinforced sand. Footing type
Circular
e
Centric
R/4
Square
Centric
B/6
N
0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
qu (N)
BCR
Tilt (degree)
Test
Numerical
Test
Numerical
Test
Numerical
1318 3192 4415 5523 956 2480 3518 4120 1457 2361 3143 3876 940 1922 2429 3081
1481 3210 4771 5836 1016 2566 3590 4321 1636 2250 2843 3637 970 2398 3020 3819
1.00 2.42 3.35 4.19 1.00 2.59 3.68 4.31 1.00 1.62 2.16 2.66 1.00 2.04 2.58 3.28
1.00 2.17 3.22 3.94 1.00 2.53 3.53 4.25 1.00 1.38 1.74 2.22 1.00 2.47 3.11 3.94
e e e e 7.72 6.39 5.12 4.11 e e e e 6.65 6.44 5.81 5.17
e e e e 6.74 5.84 4.90 4.43 e e e e 6.03 5.91 5.16 4.58
Sawwaf and Nazir (2012) for eccentrically loaded ring footing on reinforced layered soil. It clearly observes that by increasing the number of reinforcement layers from one layer to three layers the BCR increases. Also, this table demonstrates that there is a close agreement between the results of numerical analyses and experimental tests. However, the ultimate bearing capacities in the numerical analyses are some extent greater than that of the laboratory tests. Also, when reinforcement layers are used, ultimate bearing capacity ratio (BCR) increased greatly in circular footing in comparison with square footing in central and eccentrical loadings. In other words, the reinforcement layers have more influence for circular footing than the square footing in the both loadings. The effect of reinforcement layers on the behavior of footings tilt, as an unknown issue, is investigated to recognize the effect of reinforcement layers on the BCR for eccentrically loaded footings. When a footing is subjected to eccentrical loading, footing tilt is inevitable. In this study, in order to calculate the tilt of footing, two LVDTs are used for measuring the settlement of footing in two different places: one LVDT is along the loading rod and the other LVDT is on the footing surface at the certain point that is along the load eccentricity. The tilt of footing is calculated with respect to difference between settlements recorded by two LVDTs. The quantities of footing tilts at ultimate bearing capacity of every test and analysis are measured and are summarized in Table 4. In unreinforced soil condition it is also observed that the tilt of circular footing was larger than square footing. The results of vertical displacement contours obtained from finite element method for the circular and
square footings resting on sand are illustrated in Fig. 9. These data confirm the laboratory model tests results and demonstrate the deformation trends within the soil mass. As it can be observed, the settlement of square footing decreases in comparison with circular footing at eccentrical loading (e ¼ B/6 and e ¼ R/4 for square and circular footings, respectively). In another words, when the loading has eccentricity, circular footing experiences more settlement that causes larger tilt. This behavior may be attributed to the Meyerhof (1953) hypothesis that load eccentricity leads to a decrease in effective area of footing. As it is expected, by increasing the number of reinforcement layers, the tilt of footing decreased for both footings but tilt of circular footing decreases more than square footing in experimentally and numerically models. Also in eccentrical loading, when footings have the same plan area, the reinforcement layers have more influence for circular footing in comparison to square footing. 9. Scale effects The adopted circular and square footings in laboratory and numerical studies were reduced to a certain scale while the used sand, and reinforcement layers were the same in the models and the numerical analyses. Therefore, the response of the experimental and numerical results may not be the same as the behavior of the field tests and scale effects might cause some influence on the results. The current research has limitations of scale effects and can not be directly extrapolated for the field cases. However, the results
Fig. 9. Vertical displacement contours under footing in eccentrically loaded.
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from this study provided important insight into the performance of reinforcement layers for different footing shapes with the same plan area. Based on the Fakher and Jones (1996) analysis about the influence of various parameters on the performance of reinforced soil foundation beds, Sireesh et al. (2009) reported that the important parameters in the reinforced soil models can be attributed to stiffness of the reinforcement (k), plan area of footing (A) and shear modulus of soil (G). For a Larger Scale Model (LSM) with area of N times higher than the models that used in this research (M) as Equation (3), the findings of this paper may be utilized by satisfying Equations (4) and (5).
References
AðLSMÞ ¼N AðMÞ
(3)
GðLSMÞ pffiffiffiffi ¼ N GðMÞ
(4)
kðLSMÞ G2ðLSMÞ
¼
kðMÞ G2ðMÞ
(5)
Consequently based on Equation (6), the reinforcement strength in the larger scale model should be N times the reinforcement strength which used in the model test. 2 kðLSMÞ GðLSMÞ ¼ 2 ¼N kðMÞ GðMÞ
reinforcement forces in comparison with square footings. This phenomenon causes to reinforcement layers more resistance against the imposed horizontal shear stresses built up in the soil mass beneath the loaded area. Also in eccentrical loading, tilt of circular footing was larger than square footing and by reinforcing the tilt of footing decreased for both footings. At the end, the comparison of numerical analysis with experimental results demonstrate that the utilized approach for modeling of reinforcement layers in 3D is suitable for solving geosynthetic-reinforced soil systems.
(6)
For example, for a circular footing with 113000 mm2 plan area (about 10 times the current study), as in this research geosynthetic with ultimate tensile strength 7.68 kN/m is used, the findings of this present study is applicable, when reinforcement strength in the larger scale foundation be 10 times the strength of the reinforcement used in the model test (about 77 kN/m).
10. Conclusion The behavior of centrically and eccentrically loaded circular and square footings with the same plan area supported on unreinforced and reinforced sand are studied based on a series of laboratory tests and numerical analyses. In order to understand the beneficial effects of reinforcement layers on the bearing capacity, tests with different numbers of reinforcement layers (N ¼ 1, 2 and 3) are performed. The following conclusions can be drawn from the present study: In unreinforced condition, the ultimate bearing capacity is almost equal for both of the footings (although ultimate bearing capacity of square footing is slightly more than that in circular footing); but with reinforcing and increasing the number of reinforcement layers the ultimate bearing capacity of circular footing increased in a higher rate compared to square footing. The BCR increases with increasing the number of reinforcement layers for both of the footings (square and circular) but the reinforcement layers have more effect for circular footing in comparison with square footing and the rate of increasing (BCR) for circular footing is higher than square footing. Furthermore, a close compatibility is observed between the experimental and numerical results concerning the trend of behavior. Numerical results demonstrated that the reinforcement layers improved the bearing capacity by transferring the footing load to deeper soil layers and thus reduced the stresses and strains underneath the footing. Ultimate bearing capacity decreased regarding load eccentricity and making use of reinforcement layers causes to circular footings mobilize higher
Abdesssemeda, M., Kenai, S., Bali, A., 2015. Experimental and numerical analysis of the behavior of an airport pavement reinforced by geogrids. Construc. Build. Mat. 94, 547e554. Adams, M., Collin, J., 1997. Large model spread footing load tests on geosynthetic reinforced soil foundations. J. Geotech. Geoenviron. Eng. 123, 66e72. Alamshahi, S., Hataf, N., 2009. Bearing capacity of strip footings on sand slopes reinforced with geogrid and grid-anchor. Geotext. Geomembr. 27, 217e226. Alawaji, H.A., 2001. Settlement and bearing capacity of geogrid-reinforced sand over collapsible soil. Geotext. Geomembr. 19, 75e88. Basudhar, P.K., Saha, S., Deb, K., 2007. Circular footings resting on geotextile- reinforced sand bed. Geotext. Geomembr. 25, 377e384. Binquet, J., Lee, K.L., 1975a. Bearing capacity tests on reinforced earth slabs. J. Geotech. Geoenviron. Eng. 101, 1241e1255. Binquet, J., Lee, K.L., 1975b. Bearing capacity analysis of reinforced earth slabs. J. Geotech. Geoenviron. Eng. 101, 1257e1276. Boushehrian, J., Hataf, N., 2003. Experimental and numerical investigation of the bearing capacity of model circular and ring footing on reinforced sand. Geotext. Geomembr. 21, 241e256. Boushehrian, A.H., Hataf, N., Ghahramani, A., 2011. Modeling of the cyclic behavior of shallow foundations resting on geomesh and grid-anchor reinforced sand. Geotext. Geomembr. 29, 242e248. Fakher, A., Jones, C.J.F.P., 1996. Discussion on ‘‘Bearing capacity of rectangular footings on geogrid reinforced sand’’. By Yetimoglu, T., Wu, J.T.H., Saglamer, A., 1994. J. Geotech. Geoenviron. Eng. 122, 326e327. Ghazavi, M., Afshar, J.N., 2013. Bearing capacity of geosynthetic encased stone columns. Geotext. Geomembr. 38, 26e36. Ghosh, A., Ghosh, A., Kumar, B., 2005. Bearing capacity of square footing on pond ash reinforced with jute-geotextile. Geotext. Geomembr. 23, 144e173. Helwany, S., 2007. Applied Soil Mechanics with ABAQUS Applications. John Wiley & Sons Pub, Hoboken, New Jersey, USA. Huang, C.C., Tatsuoka, F., 1988. Prediction of bearing capacity in level sandy ground reinforced with strip reinforcement. In: Proceedings of International Geotechnical Symposium on Theory and Practice of Earth Reinforcement, Japan, pp. 191e196. Huang, C.C., Tatsuoka, F., 1990. Bearing capacity of reinforced horizontal sandy ground. Geotext. Geomembr. 9, 51e82. Hughes, J.M.O., Withers, N.J., 1974. Reinforcing soft cohesive soil with stone columns. Ground Eng. 7, 42e49. Hussein, M.G., Meguid, M.A., 2016. A three-dimensionalfinite element approach for modeling biaxial geogrid with application to geogrid-reinforced soils. Geotext. Geomembr. 44, 295e307. Khing, K.H., Das, B.M., Puri, V.K., Yen, S.C., Cook, E.E., 1994. Foundation on strong sand underlain by weak clay with geogrid at the interface. Geotext. Geomembr. 13, 199e206. Kotake, N., Tatsuoka, F., Tanaka, T., Siddiquee, M.S.A., Huang, C., 2001. FEM simulation of the bearing capacity of level reinforced sand ground subjected to footing load. Geosynth. Int. 501e549. Kumar, A., Ohri, M.L., Bansal, R.K., 2007. Bearing capacity tests of strip footings on reinforced layered soil. Geotech. Geol. Eng. 25, 139e150. Latha, M., Somwanshi, A., 2009. Effect of reinforcement form on the bearing capacity of square footings on sand. Geotext. Geomembr. 27, 409e422. Liu, H., 2015. Reinforcement load and compression of reinforced soil mass under surcharge loading. J. Geotech. Geoenviron. Eng. 141 (04015017), 1e10. Lovisa, J., Shukla, S.K., Sivakugan, N., 2010. Behavior of prestressed geotextilereinforced sand bed supporting a loaded circular footing. Geotext. Geomembr. 28, 23e32. Mandal, J.N., Sah, H.S., 1992. Bearing capacity tests on geogrid-reinforced clay. Geotext. Geomembr. 11, 327e333. Meyerhof, G.G., 1953. The bearing capacity of foundations under eccentric and inclined loads. In: Proceedings of the Conference on Soil Mechanics and Foundation Engineering. Switzerland, Zurich, pp. 440e453. Mosallanezhad, M., Hataf, N., Ghahramani, A., 2007. Experimental study of bearing capacity of granular soils reinforced with innovative grid-anchor system. J. Geotech. Geoenviron. Eng. 26, 299e312. Mosallanezhad, M., Taghavi, S.H.S., Hataf, N., Alfaro, M.C., 2016. Experimental and numerical studies of the performance of the new reinforcement system under pull-out conditions. Geotext. Geomembr. 44, 70e80. Noorzad, R., Mirmoradi, S.H., 2010. Laboratory evaluation of the behavior of a
E. Badakhshan, A. Noorzad / Geotextiles and Geomembranes 45 (2017) 58e67 geotextile reinforced clay. Geotext. Geomembr. 28, 386e392. Omar, M.T., Das, B.M., Puri, V.K., Yen, S.C., 1993. Ultimate bearing capacity of shallow foundations on sand with geogrid reinforcement. Can. Geotech. J. 30, 545e549. Ornek, M., 2014. Estimation of ultimate loads of eccentric-inclined loaded strip footings rested on sandy soils. Neural. Comput. Appl. 25, 39e54. Patra, C.R., Das, B.M., Bhoi, M., Shin, E.C., 2006. Eccentrically loaded strip foundation on geogrid-reinforced sand. Geotext. Geomembr. 24, 254e259. Pinho-Lopes, M., Paula, A.M., Lopes, M.L., 2015. Pullout response of geogrids after installation. Geosynth. Int. 22, 339e354. Sadoglu, E., 2015. Numerical analysis of centrally and eccentrically loaded strip footing on geotextile-reinforced sand. Geosynth. Int. 22, 225e234. Sadoglu, E., Cure, E., Moroglu, B., Uzuner, B.A., 2009. Ultimate loads for eccentrically loaded model shallow strip footings on geotextile-reinforced sand. Geotext. Geomembr. 27, 176e182. Sawwaf, M., Nazir, A., 2012. Behaviour of eccentrically loaded small scale ring footing resting on reinforced layered soil. J. Geotech. Geoenviron. Eng. 138, 376e384.
67
Sireesh, S., Sitharam, T.G., Kumar Dash, S., 2009. Bearing capacity of circular footing on geocell-sand mattress overlying clay bed with void. Geotext. Geomembr. 27, 89e98. Sitharam, T.G., Sireesh, S., 2004. Model studies of embedded circular footing on geogrid-reinforced sand beds. Ground Improv. 8, 69e75. Tafreshi, S.N., Dawson, A.R., 2010. Comparison of bearing capacity of a strip footing on sand with geocell and with planar forms of geotextile reinforcement. Geotext. Geomembr. 28, 72e84. Turker, E., Sadoglu, E., Cure, E., Uzuner, B., 2014. Bearing capacity of eccentrically loaded strip footings close to geotextile-reinforced sand slope. Can. Geotech. J. 51, 884e895. Yang, K., Jonathan, T.H., Rong-Her, C., Yi-Shou, C., 2016. Lateral bearing capacity and failure mode of geosynthetic-reinforced soil barriers subject to lateral loadings. Geotext. Geomembr. 1e14. Yetimuglu, T., Wu, J.T., Saglamar, A., 1994. Bearing capacity of rectangular footings on geogrid- reinforced sand. J. Geotech. Eng. 120, 2083e2099.