Three-dimensional bearing capacity analysis of clays under partially drained condition

Iranian Journal of Science & Technology, Transaction B: Engineering, Vol. 34, No. B4, pp …-… Printed in The Islamic Republic of Iran, 2010 1 © Shiraz University 2

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THREE DIMENSIONAL BEARING CAPACITY ANALYSIS OF GRANULAR 7 SOILS, REINFORCED WITH INNOVATIVE GRID-ANCHOR SYSTEM* 8

9 10

M. MOSALLANEZHAD1, N. HATAF2** AND A. GHAHRAMANI2 11 12 1Dept. of Civil Eng., Yasouj University, Yasouj, I. R. of Iran, formerly Ph.D. student at Dept. of Civil Eng., 13

Shiraz University 14 2, 3 Dept. of Civil Eng., Shiraz University, Shiraz, I. R. of Iran 15

Email: [email protected] 16 17

Abstract– Reinforcing soils with biaxial geogrids have been shown to be an effective method for 18 improving the ultimate bearing capacity of granular soils. The pull-out resistance of reinforcing 19 elements is one of the most significant factors in increasing bearing capacity. In this research a 20 new reinforcing element that includes attaching elements (anchors) to ordinary geogrid for 21 increasing the pull-out resistance of reinforcements is introduced. Reinforcement therefore consists 22 of a geogrid and anchors with cubic elements attached to it, named (by the authors) Grid-Anchor. 23 Three-dimensional numerical study was performed to investigate the bearing capacity of square 24 footing on sand reinforced with this system. The effect of depth of the first reinforcement layer, 25 the vertical spacing, the number and width of reinforcement layers, the angle of anchors, the 26 stiffness of reinforcement and anchors and the distance that anchors are effective were 27 investigated. Three-dimensional finite element analysis by "PLAXIS 3D Tunnel" software, 28 indicated that when a single layer of reinforcement is used there is an optimum reinforcement 29 embedment depth for which the bearing capacity is greatest (u=0.5B). There also appeared to be an 30 optimum vertical spacing of reinforcing layers for multi-layer reinforced sand (h=0.25B). The 31 bearing capacity was also found to increase with increasing the number of reinforcement layers, if 32 the reinforcement was placed within a range of effective depth (d=1.25B). In addition, analysis 33 indicated that increasing reinforcement and anchor stiffness beyond a threshold value does not 34 result in further increase in the bearing capacity (1kN for anchors and 100 kN/m for geogrid). 35 Results show that the Grid-Anchor system of reinforcing can increase the bearing capacity 2.74 36 times greater than that for ordinary geogrid and 4.43 times greater than for non-reinforced sand. 37

38 Keywords– Geosynthetics, numerical analysis, finite element, bearing capacity, square footing, reinforced sand, 39 pull-out resistance, grid-anchor, BCR 40 41

1. INTRODUCTION 42 43

The use of geosynthetics in civil engineering projects is growing rapidly. One of these applications is the 44 construction of a reinforced soil foundation to increase the bearing capacity of shallow spread footings. 45 More recently, results of several numerical studies, laboratory and large scale tests to determine the 46 ultimate bearing capacity of square shallow foundations supported by sand reinforced with layers of 47 geogrid have been published in the literature [1-11]. 48

In this paper a new reinforcement element to improve the bearing capacity of soils (patented in I.R. of 49 Iran) has been introduced and numerically studied. The main idea behind the new system is adding 50 anchors to ordinary geogrids, and it has been named Grid-Anchor (it is not a trade name yet). Figure 1 51 shows a schematic arrangement of the system. In this figure a foundation of width B that is supported by 52 ∗Received by the editors November 3, 2007; Accepted March 3, 2010. ∗∗Corresponding author

M. Mosallanezhad et al.

Iranian Journal of Science & Technology, Volume 34, Number B4 August 2010

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the soil reinforced with Grid-Anchor is shown; the anchors are made from 10×10×10 mm cubic elements 53 mounted on elastic strips that are attached with specific angles to the grids. This dimension can be used 54 both in the laboratory or in the field. Both anchors and grids are made from high density polyethylene 55 (HDPE). There are "N" layers of Grid-Anchor, each having width "b", Fig. 1. The top layer of the Grid-56 Anchor is located at a depth "u" below the bottom of the foundation. The distance between consecutive 57 Grid-Anchor layers is equal to "h" and the total depth of reinforcement is equal to "d= u+(N-1)h ". The 58 effective width of anchoring with an angle of "α " is "c". 59

61 63 65

67 69

71 73 75 77 79 81 83 85 87 89 91 92

Fig. 1. Schematic model and photos of the square foundation on Grid-Anchor reinforced soil 93 94 The increase in the ultimate bearing capacity can be expressed in a non-dimensional form called bearing 95 capacity ratio (BCR), defined as: 96

BCR=qu(R) /qu (1) 97 98 where qu = ultimate bearing capacity of un-reinforced soil and qu(R) = ultimate bearing capacity of 99 reinforced soil. 100

It has been shown in the past that, for given values of b/B, h/B and u/B, there is a critical 101 reinforcement depth ratio, d/B=(d/B)cr, at which the bearing capacity ratio practically reaches a maximum 102 value [3,4]. 103

Similarly for given values of d/B, h/B and u/B there is a critical non-dimensional reinforcement width 104 ratio, b/B=(b/B)cr , at which the magnitude of BCR also reaches a maximum value. Most of the published 105 studies on this topic have been directed towards evaluation of (b/B)cr, (d/B)cr, and the variation of BCR 106 with u/B and h/B ( for given values of h/B and u/B ). 107

α

c

b

Grid-Anchors

c

B

Geogrid

BOX: 1X1 m FOOTING: 20X20 cm

Three dimensional bearing capacity analysis of granular…

August 2010 Iranian Journal of Science & Technology, Volume 34, Number B4

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In this paper the results of some 3D numerical finite element analysis on the proposed Grid–Anchor 108 using "PLAXIS 3D Tunnel" software [12], have been presented. 109 Square footing was selected to minimize the dimensional effects (L/B). 110 111

2. BEHAVIOR OF SURFACE SQUARE FOUNDATION ON REINFORCED SOIL 112 113 Akinmusuru and Akinbolade [1], Guido et al. [2], Yetimoglu et al. [3], Omar et al. [4], Ismail and 114 Raymond [5], Hataf and Baziar [6], Chung and Cascante [7], Binesh et al. [8], Esmaili and Hataf [9] and 115 Mosallanezhad et al. [10] have performed several experimental comprehensive tests on pilot scale and 116 Adams and Collin [11] have performed such investigation on full scale square footing on Reinforced soil. 117 Different materials, such as geotextiles and geogrids were used for reinforcement. In almost all of these 118 researches the depth of the first layer of reinforcement (u), the vertical distance between the layers (h), and 119 the number of reinforcement layers (N) have been changed and the effects of those changes on the bearing 120 capacity of soil have been investigated. 121

In all the cited studies, the BCR was found to be greater than unity for reinforced soil, if the 122 reinforcement is placed within the effective depth (this ratio variety is between 1.5 in Omar et al. [4] and 123 2.5 in Yetimoglu et al’s. [3] research). 124

Akinmusuru and Akinbolade [1], conducted their tests on square footing (width=100 mm) and used 125 woven strips as reinforcing elements. They found that for the ratio u/B between 0.5 and 1.0, the increase in 126 BCR was considerable. The optimum value of N was found to be 3. 127

Guido et al. [2] used square footing (width=310 mm) and geotextile for reinforcing their tests. They 128 found that the optimum value of N was also 3 and the optimum value for the width of reinforcement (b) 129 was equal to 2.5 B, where u/B=0.5. 130

Yetimoglu et al. [3] found that the critical value of u/B, b/B and h/B were equal to 0.25, 4.5 and 0.2 131 respectively. 132

Omar et al. [4] used Geogrid for Reinforcement and found that the critical value of u/B, b/B and d/B 133 were equal to 1.0, 4.5 and 1.4, respectively. They also found that BCR was between 2.5 and 4.0. 134

Ismail and Raymond [5] used the finite element method (FEM) to determine the load–displacement 135 responses of strip footings on reinforced layered soils. They reported an optimum ratio u/B = 0.31 in the 136 two layer deposit; the reinforcement was more beneficial to the uniform soil deposit than to the two-layer 137 deposit 138

Adams and Collin [11] reported the critical u/B ratio equal to 0.48. They obtained the critical range 139 for h/B from 0.25 to 1.5 for N=3. 140

Hataf and Baziar [6] used square footing (width=140 mm) and strips from waste tire materials for 141 reinforcement. They found the average critical values of h/B and u/B equal to 0.46 and 0.315, 142 respectively. 143

Chung and Cascante [7] presented results of laboratory testing and numerical simulations on the 144 effect of reinforcement on the low-strain stiffness and bearing capacity of shallow square footing on dry 145 sand. Laboratory tests showed an increase of 100% to 300% not only in bearing capacity, but also in low-146 strain stiffness. Numerical simulations demonstrated that if reinforcements are placed up to a depth of one 147 footing width (B) below the foundation, better re-distribution of the load to deeper layers was achieved. 148 Numerical simulations and experimental results clearly identify a critical zone between 0.3B and 0.5B, 149 where maximum benefits not only on the bearing capacity but also on the low-strain stiffness of the 150 foundation were obtained. 151



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Mosallanezhad et al. [10] used square footing to investigate the bearing capacity of square footing 152 (width=200mm) on soil reinforced with Grid-Anchor and attempted to verify this system with the ordinary 153 system of reinforcing with geogrid. Test results indicated that the use of Grid-Anchor reinforced sand 154 foundations may increase the ultimate bearing capacity of shallow square footing by a factor of 3.0 rather 155 than un-reinforced sand, and 1.8 rather than ordinary geogrid reinforced sand. 156

As outlined above, a number of parametric studies have been reported for soil reinforced with 157 traditionally used products for reinforcing. In the present investigation the capability of Grid–Anchor 158 system as a reinforcing element to increase BCR for square footing is numerically valuated, presented and 159 compared with that for ordinary geogrid. 160 161

3. NUMERICAL ANALYSIS 162 163 The finite element program "PLAXIS 3D Tunnel" (version 2.0) was used to model the square footing on 164 reinforced sand. The "PLAXIS 3D Tunnel" program is a geotechnical finite element package specifically 165 intended for three-dimensional analysis of deformation and stability of tunnels, but can generally be used 166 to analyze any geotechnical engineering project. 167

The simple graphical input procedure enables a quick generation of complex finite element models, 168 and the enhanced output facilities provide a detailed presentation of the computational results. The 169 calculation itself is fully automated and based on robust numerical procedures. 170

The Mohr–Coulomb model was used for soil and 15-node wedge elements were used for analysis. 171 Reinforcement layers and anchors were modeled using the option already built into the program. They are 172 simulated in "PLAXIS" by the use of special only tension elements with no bending stiffness. When 15-173 node soil elements are employed then each reinforcement element is defined by 8-Nodes with three 174 degrees of freedom in each node (Ux, Uy, Uz). 175

The only property in a geogrid dataset is the elastic axial stiffness, EA, entered in units of force per 176 unit width. Geogrid elements in PLAXIS only sustain tension. A fixed-end anchor is a one–node elastic 177 spring element with a constant spring stiffness that is used to model the tying of a single point. They must 178 always be connected to existing geometry lines such as reinforcement, modeled linearly in software. The 179 major anchor property is the axial stiffness, EA; entered in the unit of force. Other parameters used in the 180 analysis are tabulated in Table 1. 181 182

Table 1. Parameters used in the Analysis 183 184

Parameter Value Angle of Internal Friction 40o Cohesion (kPa) 1 Modulus of Elasticity (kPa) 12000 Poisson’s ratio 0.3 Unit Weight (kN/m3) 18.6 Soil Type Sand Soil Model Mohr–Coulomb Axial Stiffness of Reinforcement (kN/m) 28 Axial Stiffness of Anchors (kN) 0.18 Dimension of Footing (mm) 200×200 Length of anchors (mm) 50 Model box (m) 1×1×1

185 The 3D and sectional 2D finite element mesh used for analyses is shown in Fig. 2 and Fig. 3, respectively. 186



5

187 188

Fig. 2. 3D finite element mesh generation for 5 layer reinforcement 189 with 5472 elements (average element size=13 mm) 190

191 192

193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210

211 212

Fig. 3. Undeformed and deformed mesh at section plane across 213 the footing center for 5 layer 214

215 A 200×200 mm footing was selected (EI=8500 kNm2/m, EA=5×106 kN/m, thickness=100 mm) for 216 modeling rigid foundation. 217

For avoiding boundary effects, a model box 1×1×1 m was selected. The model depth was taken 1 m, 218 that is greater than 4B=0.8 m (Prisco et al. [13]) and the width of the model was taken 1 m, i.e. 5B. As in 219 practice in the field, the ends of the geogrid layers are free in x, y and z directions at boundaries. Figure 4 220 shows that the displacement has not reached the boundaries in the analysis. 221

The horizontal part of stress vs. settlement diagram implies that qu has been reached. To see the mesh 222 refining effect, we refined mesh by trial and found that more refinement had no effect on the results. 223 224 225 226



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227 228 229 230

231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258

259 260 261 262

263 264 265

Fig. 4. Selected boundaries and displacement under footing for 3 layer 266 267

4. VERIFICATION OF EFFECTIVENESS OF GRID-ANCHOR SYSTEM 268 269 To verify the effectiveness of Grid–Anchor system in improving the bearing capacity of soils, the behavior 270 of footings on non-reinforced sand, sand reinforced with ordinary geogrid and sand reinforced with Grid-271 Anchor under the same conditions (soil properties, N, b/B, h/B, u/B, anchor and reinforcement stiffness) 272 were investigated. Figure 5 shows the comparison between these three statuses. The effectiveness of using 273 Grid-Anchor system as reinforcement elements in increasing the bearing capacity of footings is evident. 274 As can be seen, the value of BCR is almost three times greater than that for ordinary geogrid in this case. 275

1

1.5

2

2.5

3

3.5

4

4.5

5

Non Rein. Only Geogrid Grid-Anchor

BCR

276 Fig. 5. Variation of BCR with selected reinforcing system 277

(N=5, u/B=0.25, b/B=5, h/B=0.25) 278

Shading of total displacement 3D deformed mesh



7

1.4

1.6

1.8

2

2.2

2.4

2.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

u/B

BC

R

5. PARAMETRIC STUDIES 279 280 In order to determine the effect of different factors on the bearing capacity of sand reinforced with the 281 introduced system, analysis has been performed and the results are presented as follows. 282 283 a) Effect of depth to the first reinforcement layer (u) 284 285

The depth ratio is defined herein as the ratio between u and B (i.e. u/B). Figure 6 shows the typical 286 relationship between BCR and the depth ratio for single–layer reinforced sand, while Fig. 7 shows it for 287 multi-layer reinforcement. As can be seen in single–layer reinforcement there was an optimum value of 288 depth ratio at which the BCR was the highest; this optimum value is around 0.5B. The analysis for the 289 multi-layer reinforced sand indicated that the largest BCR values occurred at a depth ratio of around 290 0.25B. 291

This is in agreement with the numerical studies which indicated that the effect of depth ratio on the 292 BCR in single–layer reinforced sands was different from that in multi layer reinforced sands [14, 2, 3, 11]. 293 295 297 299 301 303 305 307 309 311 313

315 317 319 321 323 325 327

Fig. 6. Variation of BCR with depth ratio in single layer reinforced sand (b/B)= 5 328

1.5

2

2.5

3

3.5

4

4.5

5

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

u/B

BCR

329 Fig. 7. Variation of BCR with depth in multi-layer reinforced sand 330

(N= 5, h/B =0.25, b/B=5 ) 331 332 b) Effect of number of reinforcement layers (N) 333 334

Numerical analysis indicated that the BCR value changes more drastically with the number of 335 reinforcement layers, N, than the other parameters. 336



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The BCR increased with increasing the number of reinforcement layers within a depth of 1.5B and the 337 rate of increase in BCR was less significant beyond this depth; in other words, placing geogrid 338 reinforcement beyond a depth of 1.5B would not significantly increase the bearing capacity. 339

Figure 8 shows a typical variation of BCR with the number of reinforcement layers. For the results 340 shown, the vertical spacing (h) was kept constant. Several researchers have also observed that increasing 341 the number of reinforcement layers beyond a certain value would not increase the BCR significantly ([1, 342 3, 4, 15]). 343

1

1.5

2

2.5

3

3.5

4

4.5

5

0 1 2 3 4 5 6 7

Number of Reinforcement Layers

BCR

344 Fig. 8. Variation of BCR with number of reinforcement 345

layers (u/B=0.25, h/B=0.25, b/B=5.0 ) 346 347 c) effect of vertical spacing of reinforcement (h) 348 349

Numerical studies have indicated that there was an optimum value for the vertical spacing of 350 horizontally placed reinforcement layers. The analysis showed that the optimum vertical spacing was 351 0.25B for three-layer reinforced sand. Figure 9 shows a typical variation of BCR with the normalized 352 vertical spacing of three-layer reinforced sand. 353

354

1.5

1.7

1.9

2.1

2.3

2.5

2.7

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

h/B

BCR

355 Fig. 9. Typical variation of BCR with vertical spacing of 356

reinforcement layers (N=3, u/B=0.25, b/B=5) 357 358 Similar to these findings, Singh [16] indicated that optimum vertical spacing of reinforcement layers for 359 square footing on geogrid reinforced sands varied between 0.15B and 0.25B. On the other hand, Omar et 360 al. [4], Hataf and Baziar [6] and Yetimoglu et al. [3] found this optimum value as 0.33, 0.46 and 0.2 361 respectively. 362 363



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d) Effect of reinforcement width (b) 364 365

Numerical studies have shown that the BCR is generally increased with increasing reinforcement 366 width (b). The bearing capacity ratios obtained from these analyses have been plotted with b/B in Fig. 10. 367 It can be seen from this figure that the BCR attains a maximum, at a (b/B)cr of 4.75 for 5 layers and about 368 3 for 3 layers reinforcement. 369

2

2.5

3

3.5

4

4.5

5

2.5 3 3.5 4 4.5 5

b/B

BC

R

N=5N=3

370 Fig. 10. Variation of BCR with reinforcement width (u/B=0.25, h/B=0.25) 371

372 Hence, the investigation on these two specified numbers of layers show that the optimum normalized 373 reinforced width (b/B)cr increases with the increasing number of reinforcement layer (N). 374

Similarly, Omar et al. [4], based on their study of square footing on geogid-reinforced sand, indicated 375 that the BCR increased with reinforcement width up to an effective value (b/B)cr and remained practically 376 constant thereafter. They reported that the effective b/B ratio was around 4.5 for square foundations. 377

Several researchers have also indicated that increasing reinforcement width beyond a certain value 378 would not increase the BCR significantly. Guido et al. [15] and Singh [16] advocated that the optimum 379 ratio of b/B was approximately 2 for square footing. Fragaszy and Lawton [17] reported that as reinforcing 380 size increased from 3 to 7 times the footing width, the BCR increased rapidly. 381 382 e) Effect of reinforcement stiffness 383 384

In the analysis, reinforcement stiffness, "EA" varied from 10 kN/m to 10000 kN/m. Typical variation 385 of BCR with the reinforcement stiffness for one layer reinforcing is shown in Fig. 11. 386

It is seen that increasing reinforcement stiffness beyond an axial stiffness of approximately 100 kN/m 387 would not result in a significant increase in BCR for single layer reinforcement. This is because of the fact 388 that before the axial stiffness of reinforcement is fully mobilized, geogrid is pulled out and the soil body 389 will slide over the reinforcement. 390

1

1.5

2

2.5

3

3.5

10 100 1000 10000

Stiffness of Reinforcement (KN/m)

BC

R

391 Fig. 11. Variation of BCR with reinforcement stiffness (N=1, u/B=0.25, b/B=5) 392

393



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f) Effect of anchors stiffness 394 395

The fixed-end anchor which is a one-node elastic spring element with a constant spring stiffness tied 396 to a single point was used to model the anchorage system. The major anchor property is the axial stiffness, 397 "EA". The anchor stiffness was tested and found to be 0.25 kN at most. In the analysis, the axial stiffness 398 of the anchors varied from 0.05 kN to 10 kN. 399

Figure 12 shows a typical variation of BCR with the anchor stiffness for single layer reinforcement. 400

1

1.5

2

2.5

3

3.5

4

0 1 2 3 4 5 6 7 8 9 10

Stiffness of Anchors (KN)

BC

R

401 Fig. 12. Variation of BCR with anchor stiffness (N=1, u/B=0.25, b/B=5, 402

h/B=0.25, geogrid Stiffness =28 kN/m) 403 404 Again it can be seen that increasing anchor stiffness beyond a certain value (1kN) would not increase the 405 BCR significantly. This happens because the soil body may collapse before the stiffness of anchors is fully 406 mobilized. 407 408 g) Effect of angle of anchors (α) 409 410

Figure 13 shows a typical variation of BCR with the angle that the anchors make horizontal for three 411 layers reinforcement. The analysis showed that the BCR generally increased with increasing the angle of 412 anchors to approximately 45 degrees. After this angle, BCR begins to decrease with increasing the angle 413 of anchors to 90 degrees; in this case (i.e. α =900) BCR is close to the status of soil being reinforced with 414 ordinary geogrid. 415

1.4

1.6

1.8

2

2.2

2.4

2.6

0 15 45 75 90Horizontal Angle of Anchors (Degree)

BCR

416 Fig. 13. Variation of BCR with angle of anchors 417

(N=3, u/B=0.25, b/B=5, h/B=0.25) 418 419 h) Effect of anchorage width (c) 420 421

The enhanced output facilities of the software provided a detailed presentation of the computational 422 results such as: with clicking on each anchor after calculating the procedure, user can observe the forces 423



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mobilized in them. It has been observed that the anchors at the maximum distance of “0.75B” from the 424 center of the foundation have not been mobilized. As shown in Fig. 14, mobilized forces in anchors that 425 stand entirely beneath the foundation are approximately equal; from the edge of footing to 0.5B from the 426 footing center, the forces in the anchors decrease dramatically beyond that distance. 427

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Center 0.125B 0.25B 0.375B 0.5B 0.625B 0.75B B 1.5B

Distance from centerline

Mob

ilize

d fo

rce

(kN

)

428 Fig. 14. Typical variation of mobilized force in anchors with distance 429

from center in 2nd layer (N=5, u/B=0.25, b/B=5, h/B=0.25) 430 431

6. SUMMARY AND CONCLUSIONS 432 433 A 3 dimensional finite–element study was conducted to investigate the bearing capacity of square footing 434 on Grid-Anchor reinforced sand. The use of innovative Grid-Anchor as reinforcement element to improve 435 bearing capacity of soils compared to using ordinary geogrid was investigated and it is shown that a 436 significant increase in bearing capacity is obtained. The effect of the depth to the first layer of 437 reinforcement, vertical spacing of the reinforcement layer, number of reinforcement layer, size of 438 reinforcement sheet, stiffness of reinforcement and anchors and finally, the angle of anchors on bearing 439 capacity were also investigated. The study brings the following conclusions for Grid-Anchor system: 440 441

1. Grid-Anchor system of reinforcing can increase the bearing capacity 2.74 times greater than that 442 for ordinary geogrid and 4.43 times greater than for non-reinforced sand. 443

2. The value of BCR for square footing could be increased significantly by incorporating Grid-444 Anchor reinforcement at an optimum distance below the foundation base (i.e. d=1.25B). 445

3. The BCR for Grid-Anchor system increases significantly with reinforcement layer number 446 within a certain effective zone. In this study the optimum number of reinforcement layer were 447 found as N=5. 448

4. For multi-layer reinforced sand there is an optimum vertical spacing of reinforcement layer. The 449 optimum spacing for the reinforced sand investigated is 0.25B. 450

5. For multi-layer reinforced sand, the highest BCR occured at an embedment depth of the first 451 reinforcement layer approximately 0.25B, which was different from single-layer reinforcement 452 with u=0.5B. The maximum depth of placement of the first layer of reinforcement should also 453 be less than about 1.5B to take advantage of reinforcement. 454

6. Maximum width of reinforcement layers required for mobilization of maximum BCR is about 455 4.7B. 456

7. Effective angle of anchors was found to be about 45o. 457 8. Effective width of anchorage system was determined to be about 1.5B. 458 9. Increasing the stiffness of reinforcement and anchors beyond a certain value would only result in 459



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a small increase in BCR. For the conditions investigated, these values for one layer reinforcing 460 were 100 kN/m for geogrid and 1 kN for anchors. 461

462 Since the influence of limiting conditions such as footing size, scale effects, density of soil, etc. on BCR 463 have not been investigated, to establish a more accurate design criteria for Grid-Anchor reinforcing 464 system, further studies are in progress by the authors. 465

466 NOMENCLATURES 467

468 469 470 471 472 473 474 475 476 477 478 479

REFERENCES 480 481 1. Akinmusuru and Akinbolade, (1981). Stability of loaded footing on reinforced soil. Journal of Geotechincal 482

Engineering, Vol. 107, No. GT6, pp. 819-827. 483 2. Guido, V. A., Biesiadecki, G. L. & Sullivan, M. J. (1985). Bearing capacity of a geotextile reinforced 484

foundation. Proc. 11th Int. Conf. Soil Mech. And Found. Eng., San Francisco, Calif., pp. 1777-1780. 485 3. Yetimoglu, T., WU, S.T.H. & Saglamer, A. (1994). Bearing capacity of rectangular footing on geogrid –486

reinforced sand. Journal of Geotechnical Engineering, Vol. 120, No.12, pp. 2083 –2099. 487 4. Omar, M. T, Das, B. M, Puri, V. K. & Yen, S. C. (1993). Ultimate bearing capacity of shallow foundations on 488

sand with geogrid reinforcement. Canadian Geotechnical Journal, Vol. 30, pp. 545 –549. 489 5. Ismail, I. & Raymond, G. P. (1995). Geosynthetic reinforcement of granular layered soils. Int. Proceedings of 490

geosynthetics, pp. 317–330. 491 6. Hataf, N. & Baziar, A. (2000). Use of tire shreds for bearing capacity improvement of shallow footing on sand. 492

Proc. Of the 3rd Int. Conf. On Ground Improvement Techniques, Singapore, pp. 189-194. 493 7. Chung, W. & Cascante, G. (2006). Experimental and numerical study of soil-reinforcement effects on the low-494

strain stiffness and bearing capacity of shallow foundations. Journal of Geotechnical and Geological 495 Engineering, Original Paper. 496

8. Binesh, M., Hataf, N. & Ghahramani, A. (2007). Elastic analysis of reinforced soils using point interpolation 497 method. Iranian Journal of Science & Technology, Transaction B: Engineering, Vol. 31, pp. 577-581. 498

9. Esmaili, D. & Hataf, N. (2008). Experimental and numerical investigation of ultimate load capacity of shell 499 foundations on reinforced and unreinforced sand. Iranian Journal of Science & Technology, Transaction B: 500 Engineering, Vol. 32, pp. 491-500. 501

10. Mosallanezhad, M., Hataf, N. & Ghahramani, A. (2008). Experimental Study of Bearing Capacity of Granular 502 Soils, Reinforced with Innovative Grid-Anchor System. Journal of Geotechnical and Geological Engineering, 503 Vol. 26, No. 3, pp. 299-312. 504

11. Adams, M. T. & Collin, J. G. (1997). Large model spread footing load tests on geosynthetic reinforced soil 505 foundations. Journal of Geotechnical and Geoenvironmental Engineering, Vol. 123, No.1, pp. 66-72. 506

BCR Bearing capacity ratio

uq Ultimate bearing capacity of un-reinforced soil

)(Ruq Ultimate bearing capacity of reinforced soil

B Footing width N Number of reinforcement layers c Anchorage width b Reinforcement width u Depth of first layer of reinforcement below footing base d Total reinforced depth α Angle of anchors with horizontal EA Axial stiffness of reinforcement EI Bending stiffness of footing Ux, Uy, Uz Three degree of freedom in each node of reinforcement



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12. Brinkgreve, R. B. J. & Vermeer, P. A. (2005). PLAXIS 3D tunnel ver.2 manuals, A. A. Balkema Publisher. 507 13. Prisco, CDi., Montanelli, F., Remoldi, P., Sinisi, G. & Villa, E. (1998). Shallow foundation on granular soils 508

reinforced by means of geosynthetics. 2nd Int. Conf. on Ground Improvement Techniques, Singapore, pp. 407–509 413. 510

14. Boushehrian, J. H. & Hataf, N. (2003). Experimental and numerical investigation of the bearing capacity of 511 model circular and ring footing on reinforced sand. Geotextile and Geomembranes, Vol. 21, pp. 241 –256. 512

15. Guido, V. A., Chang, D. K. & Sweeney, M. A. (1986). Comparison of geogrid and geotextile reinforced earth 513 slabs. Canadian Geotechnical Journal, Vol. 23, pp. 435 –440. 514

16. Singh, H. R. (1988). Bearing capacity of reinforced soil beds. Ph.D. Thesis, Indian Institute of Science, 515 Bangalore. 516

17. Fragaszy, R. J. & Lawton, E. (1984). Bearing capacity of reinforced sand subgrade. Journal of Geotechnical 517 Engineering Division, ASCE, Vol. 110, No. GT10, pp. 1500 –1507. 518

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Three-dimensional bearing capacity analysis of clays under partially drained condition

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