The concept of ultimate bearing capacity (UBC) of shallow foundations under varied loads is important for foundation engineers. In the design of foundations, the soil classification, behaviour and UBC are the most essential factors. There are two criteria to select the UBC for shallow foundations, namely the stability against shear failure and the settlement within the safe limit.
A foundation under load will undergo settlement due to the horizontal and vertical movement of soil particles below the foundation. In the case of centric vertical load on the footing, stress distribution will be uniform below the footing and the footing will undergo equal settlement at both edges. On the other hand, if the load is eccentric, the stress distribution below the footing will be non-uniform causing unequal settlement at two edges which will result in the tilt of footing. The tilt will increase with the increasing eccentricity to width ratio (
In soil engineering practice, several techniques for soil improvement have been used to modify the soil behaviour and reduce the foundation settlement. In the past few years, it was found that the value of UBC increases with the use of reinforcing materials such as geotextile, geosynthetics and geogrid. Many types of research have been done on the behaviour of UBC of shallow foundation supported by unreinforced and reinforced sand using a laboratory model (Meyerhof [15], Das et al. [5], Yoo [31], Shin et al. [27, 28], Michalowski [16], Patra et al. [21, 22], El Sawwaf [25], Sitharam and Sireesh [29], Ornek [19]). From these studies, it can be concluded that the reinforced soil improves the UBC and reduces the foundation settlement. Recently, the effects of load eccentricity, inclination and combined effects of both eccentric and inclined loads on the UBC of shallow foundation located over reinforced and unreinforced sand bed have been studied experimentally, analytically and numerically by different investigators (Hjiaj [9], Kumar et al. [11,12], Foye et al. [6], Padmini et al. [20], Loukidis et al. [14], Latha and Somwanshi [13], Nazir and Azzam [17], Sawwaf and Nazir [26], Patra et al. [23], Rabi Narayan Behera [3], Krabbenhoft, et al. [10], Ornek [19], Badakhshan and Noorzad [1, 2], Ganesh et al. [7]). All researchers concluded that the value of UBC rises with increasing the number of geogrid reinforcing layers because the soil-reinforcement contains a series of interlocking cells that can keep the soil within its pockets and making an interlocking action between soil and geogrid. The interlocking action permits the geogrid to bear the horizontal stresses beneath the foundation and transfer them to the adjacent stable layer of the soil, which improves the vertical behaviour of the model foundation.
Several researchers studied the effect on strip footing subjected to centrically inclined loads. Little work is reported in the literature on the problem of strip footings subjected to eccentric-inclined loads. It is seen that to date no study is performed to address the effects of eccentrically inclined loads in both dimensions, i.e. lateral and longitudinal. The purpose of the study is to investigate the behaviour of model rectangular footing placed over multiple layers of the geogrid reinforced sand subjected to eccentric-inclined loads in both dimensions. The non-dimensional parameters called bearing capacity ratio (
Fig. 1 shows the schematic view of the experimental model apparatus used in this study. The test tank is rectangular, having dimensions of 1.24 m × 0.90 m × 0.93 m (L ′ B ′ H). All sides of the test tank were braced using horizontal steel beams. The horizontal steel beams were fitted at mid-depth of the test tank to avoid bulging during the model plate load test.
Rectangular shape model footing was made from a mild steel plate, having dimensions of 0.24 m × 0.18 m × 0.015 m (L ′ B ′ T). Holes were made at the desired centric and eccentric points to accommodate the ball-bearing as shown in Fig. 1(b). The holes represented the eccentric points
In this study, manually operated screw jack loading was used. The ultimate load was calculated with the help of a pre-calibrated proving ring. The displacement of footing was noted with the help of two dial gauges having the least count 0.01 mm arranged on the footing diagonally. The load was transferred to the model footing with the help of ball-bearing. Fig. 2(a) shows the test arrangements of embedded model footing. During testing, three fixed frames were used for axial vertical and inclined loading (α = 0°, 7° and 14°) as shown in Fig. 2(b).
The sand was collected locally from the riverbed of Yamuna River, Yamuna Nagar (India). It was free from roots and organic matters, etc. Physical properties and gradation curves of subjected soil have been tabulated and shown in Table 1 and Fig. 3, respectively.
Properties of Yamuna sand.
Soil type | SP |
Specific gravity, |
2.65 |
Effective particle size, |
0.17 |
Uniformity coefficient, |
3.53 |
Coefficient of curvature, |
0.80 |
Working dry density, |
15.71 |
Maximum dry unit weight, |
17.5 |
Minimum dry unit weight, |
12.9 |
Angle of internal friction, ( |
36 |
Maximum void ratio, |
0.77 |
Minimum void ratio, |
0.50 |
In this study, polypropylene (PP) bi-axial geogrid (Bx20/20) having an ultimate tensile strength of about 7 kN/m2 was used for reinforcing the sand. The geogrid was provided by Maruti Rubplast Private Limited. The geogrid had a square-shaped aperture (0.039 m ′ 0.039 m) and provides an equal ultimate tensile strength in all directions.
The sand was placed in the test tank in a layer of 0.02 m from a fixed height of 0.20 m by rainfall method. To achieve the desired relative density, it was determined a priori by performing a series of trials with different heights of fall. In each trial, the densities were monitored by collecting samples in a small container of known volume placed at a different location in the test tank. In all model tests, the average unit weight and relative density of the sand were kept as 15.71 kN/m3 and 68%, respectively. While doing the experiment the tank was fully emptied before filling sand for the next experiment. So, the case of the densification of sand at the bottom layers can be discarded.
The factors that affect the behaviour of shallow foundation resting on reinforced sand are
Three-hundred and fifteen numbers of experiments were conducted in total to examine the effects of model footing with varied parameters including the number of the geogrid reinforced layers (
A series of model tests were conducted using rectangular footing with embedment ratio (
Various tests were performed to examine the behaviour of model footing with variable parameters such as depth of embedment (
In the present study, a non-dimensional parameter called bearing capacity ratio (
Results of eccentrically loaded (
|
|||||||
---|---|---|---|---|---|---|---|
0 | 0 | 0 | 212 | 2.2 | 1.00 | 1.00 | 1.00 |
0 | 1 | 0 | 240 | 3.8 | 1.13 | 1.73 | 1.00 |
0 | 2 | 0 | 282 | 4.1 | 1.33 | 1.86 | 1.00 |
0 | 3 | 0 | 348 | 4.7 | 1.64 | 2.14 | 1.00 |
0 | 4 | 0 | 368 | 6 | 1.74 | 2.73 | 1.00 |
0 | 0 | 0.05 | 190 | 2.3 | 1.00 | 1.00 | 0.90 |
0 | 1 | 0.05 | 210 | 3.3 | 1.11 | 1.43 | 0.88 |
0 | 2 | 0.05 | 278 | 3.5 | 1.46 | 1.52 | 0.99 |
0 | 3 | 0.05 | 320 | 4.2 | 1.68 | 1.83 | 0.92 |
0 | 4 | 0.05 | 330 | 5 | 1.74 | 2.17 | 0.90 |
0 | 0 | 0.1 | 152 | 2.5 | 1.00 | 1.00 | 0.72 |
0 | 1 | 0.1 | 190 | 2.6 | 1.25 | 1.04 | 0.79 |
0 | 2 | 0.1 | 252 | 2.8 | 1.66 | 1.12 | 0.89 |
0 | 3 | 0.1 | 298 | 4 | 1.96 | 1.60 | 0.86 |
0 | 4 | 0.1 | 308 | 4.5 | 2.03 | 1.80 | 0.84 |
0 | 0 | 0.15 | 138 | 2.2 | 1.02 | 1.00 | 0.65 |
0 | 1 | 0.15 | 171 | 2.3 | 1.27 | 1.05 | 0.71 |
0 | 2 | 0.15 | 240 | 2.5 | 1.78 | 1.14 | 0.85 |
0 | 3 | 0.15 | 255 | 3.8 | 1.89 | 1.73 | 0.73 |
0 | 4 | 0.15 | 290 | 4.2 | 2.15 | 1.91 | 0.79 |
0.5 | 0 | 0 | 330 | 1.4 | 1.00 | 1.00 | 1.00 |
0.5 | 1 | 0 | 370 | 3.8 | 1.12 | 2.71 | 1.00 |
0.5 | 2 | 0 | 400 | 4 | 1.21 | 2.86 | 1.00 |
0.5 | 3 | 0 | 450 | 4.2 | 1.36 | 3.00 | 1.00 |
0.5 | 4 | 0 | 470 | 5 | 1.42 | 3.57 | 1.00 |
0.5 | 0 | 0.05 | 310 | 1.3 | 1.00 | 1.00 | 0.94 |
0.5 | 1 | 0.05 | 360 | 2.8 | 1.16 | 2.15 | 0.97 |
0.5 | 2 | 0.05 | 390 | 3.7 | 1.26 | 2.85 | 0.98 |
0.5 | 3 | 0.05 | 420 | 4 | 1.35 | 3.08 | 0.93 |
0.5 | 4 | 0.05 | 460 | 5 | 1.48 | 3.85 | 0.98 |
0.5 | 0 | 0.1 | 262 | 1.3 | 1.00 | 1.00 | 0.79 |
0.5 | 1 | 0.1 | 322 | 1.5 | 1.23 | 1.15 | 0.87 |
0.5 | 2 | 0.1 | 352 | 2.1 | 1.34 | 1.62 | 0.88 |
0.5 | 3 | 0.1 | 365 | 3 | 1.39 | 2.31 | 0.81 |
0.5 | 4 | 0.1 | 400 | 3.2 | 1.53 | 2.46 | 0.85 |
0.5 | 0 | 0.15 | 250 | 1 | 1.00 | 1.00 | 0.76 |
0.5 | 1 | 0.15 | 302 | 1.5 | 1.21 | 1.50 | 0.82 |
0.5 | 2 | 0.15 | 320 | 2 | 1.28 | 2.00 | 0.80 |
0.5 | 3 | 0.15 | 332 | 2.7 | 1.33 | 2.70 | 0.74 |
0.5 | 4 | 0.15 | 372 | 2.8 | 1.49 | 2.80 | 0.79 |
1 | 0 | 0 | 400 | 3.2 | 1.00 | 1.00 | 1.00 |
1 | 1 | 0 | 460 | 6 | 1.12 | 1.88 | 1.00 |
1 | 2 | 0 | 510 | 7 | 1.24 | 2.19 | 1.00 |
1 | 3 | 0 | 540 | 7.5 | 1.32 | 2.34 | 1.00 |
1 | 4 | 0 | 580 | 8.5 | 1.41 | 2.66 | 1.04 |
1 | 0 | 0.05 | 398 | 3.1 | 1.00 | 1.00 | 0.97 |
1 | 1 | 0.05 | 440 | 5 | 1.11 | 1.61 | 0.96 |
1 | 2 | 0.05 | 480 | 5.2 | 1.21 | 1.68 | 0.94 |
1 | 3 | 0.05 | 500 | 6 | 1.26 | 1.94 | 0.93 |
1 | 4 | 0.05 | 560 | 8 | 1.41 | 2.58 | 0.64 |
1 | 0 | 0.1 | 360 | 2.1 | 1.00 | 1.00 | 0.88 |
1 | 1 | 0.1 | 410 | 2.8 | 1.14 | 1.33 | 0.89 |
1 | 2 | 0.1 | 428 | 4.2 | 1.19 | 2.00 | 0.84 |
1 | 3 | 0.1 | 470 | 4.5 | 1.31 | 2.14 | 0.87 |
1 | 4 | 0.1 | 510 | 6 | 1.42 | 2.86 | 0.91 |
1 | 0 | 0.15 | 310 | 1.5 | 1.00 | 1.00 | 0.76 |
1 | 1 | 0.15 | 380 | 2.5 | 1.23 | 1.67 | 0.83 |
1 | 2 | 0.15 | 400 | 2.8 | 1.29 | 1.87 | 0.78 |
1 | 3 | 0.15 | 420 | 3.5 | 1.35 | 2.33 | 0.78 |
1 | 4 | 0.15 | 480 | 4.5 | 1.55 | 3.00 | 0.86 |
Results of eccentrically loaded (
|
|||||||
---|---|---|---|---|---|---|---|
0 | 0 | 0 | 212 | 2.2 | 1.00 | 1.00 | 1.00 |
0 | 1 | 0 | 240 | 3.8 | 1.13 | 1.73 | 1.00 |
0 | 2 | 0 | 282 | 4.1 | 1.33 | 1.86 | 1.00 |
0 | 3 | 0 | 348 | 4.7 | 1.64 | 2.14 | 1.00 |
0 | 4 | 0 | 368 | 6 | 1.74 | 2.73 | 1.00 |
0 | 0 | 0.05 | 180 | 2.2 | 1.00 | 1.00 | 0.85 |
0 | 1 | 0.05 | 206 | 3.2 | 1.14 | 1.45 | 0.86 |
0 | 2 | 0.05 | 270 | 3.5 | 1.50 | 1.59 | 0.96 |
0 | 3 | 0.05 | 312 | 3.7 | 1.73 | 1.68 | 0.90 |
0 | 4 | 0.05 | 325 | 4.5 | 1.81 | 2.05 | 0.88 |
0 | 0 | 0.1 | 148 | 1.8 | 1.00 | 1.00 | 0.70 |
0 | 1 | 0.1 | 160 | 2 | 1.08 | 1.11 | 0.67 |
0 | 2 | 0.1 | 248 | 3 | 1.68 | 1.67 | 0.88 |
0 | 3 | 0.1 | 270 | 3.2 | 1.82 | 1.78 | 0.78 |
0 | 4 | 0.1 | 305 | 3.8 | 2.06 | 2.11 | 0.83 |
0 | 0 | 0.15 | 132 | 1.2 | 1.00 | 1.00 | 0.00 |
0 | 1 | 0.15 | 140 | 1.5 | 1.06 | 1.25 | 0.58 |
0 | 2 | 0.15 | 232 | 2 | 1.76 | 1.67 | 0.82 |
0 | 3 | 0.15 | 212 | 2.8 | 1.61 | 2.33 | 0.61 |
0 | 4 | 0.15 | 280 | 3.3 | 2.12 | 2.75 | 0.76 |
0.5 | 0 | 0 | 330 | 1.4 | 1.00 | 1.00 | 1.00 |
0.5 | 1 | 0 | 370 | 3.8 | 1.12 | 2.71 | 1.00 |
0.5 | 2 | 0 | 400 | 4 | 1.21 | 2.86 | 1.00 |
0.5 | 3 | 0 | 450 | 4.2 | 1.36 | 3.00 | 1.00 |
0.5 | 4 | 0 | 470 | 5 | 1.42 | 3.57 | 1.00 |
0.5 | 0 | 0.05 | 300 | 1.5 | 1.00 | 1.00 | 0.91 |
0.5 | 1 | 0.05 | 338 | 2.8 | 1.13 | 1.87 | 0.91 |
0.5 | 2 | 0.05 | 380 | 3 | 1.27 | 2.00 | 0.95 |
0.5 | 3 | 0.05 | 400 | 4 | 1.33 | 2.67 | 0.89 |
0.5 | 4 | 0.05 | 450 | 5 | 1.50 | 3.33 | 0.96 |
0.5 | 0 | 0.1 | 258 | 1.3 | 1.00 | 1.00 | 0.78 |
0.5 | 1 | 0.1 | 310 | 2.7 | 1.20 | 2.08 | 0.84 |
0.5 | 2 | 0.1 | 342 | 2.9 | 1.33 | 2.23 | 0.86 |
0.5 | 3 | 0.1 | 358 | 3.5 | 1.39 | 2.69 | 0.80 |
0.5 | 4 | 0.1 | 380 | 3.8 | 1.47 | 2.92 | 0.81 |
0.5 | 0 | 0.15 | 240 | 1 | 1.00 | 1.00 | 0.73 |
0.5 | 1 | 0.15 | 280 | 1.5 | 1.17 | 1.50 | 0.76 |
0.5 | 2 | 0.15 | 300 | 2.4 | 1.25 | 2.40 | 0.75 |
0.5 | 3 | 0.15 | 328 | 2.6 | 1.37 | 2.60 | 0.73 |
0.5 | 4 | 0.15 | 360 | 3 | 1.50 | 3.00 | 0.77 |
1 | 0 | 0 | 400 | 3.2 | 1.00 | 1.00 | 1.00 |
1 | 1 | 0 | 460 | 6 | 1.12 | 1.88 | 1.00 |
1 | 2 | 0 | 510 | 7 | 1.24 | 2.19 | 1.00 |
1 | 3 | 0 | 540 | 7.5 | 1.32 | 2.34 | 1.00 |
1 | 4 | 0 | 580 | 8.5 | 1.41 | 2.66 | 1.04 |
1 | 0 | 0.05 | 390 | 2 | 1.00 | 1.00 | 0.95 |
1 | 1 | 0.05 | 430 | 3 | 1.10 | 1.50 | 0.93 |
1 | 2 | 0.05 | 470 | 4.8 | 1.21 | 2.40 | 0.92 |
1 | 3 | 0.05 | 490 | 5.1 | 1.26 | 2.55 | 0.91 |
1 | 4 | 0.05 | 550 | 6.2 | 1.41 | 3.10 | 0.98 |
1 | 0 | 0.1 | 342 | 1.4 | 1.00 | 1.00 | 0.83 |
1 | 1 | 0.1 | 400 | 2.4 | 1.17 | 1.71 | 0.87 |
1 | 2 | 0.1 | 420 | 3.1 | 1.23 | 2.21 | 0.82 |
1 | 3 | 0.1 | 450 | 3.4 | 1.32 | 2.43 | 0.83 |
1 | 4 | 0.1 | 500 | 6 | 1.46 | 4.29 | 0.89 |
1 | 0 | 0.15 | 302 | 1.1 | 1.00 | 1.00 | 0.74 |
1 | 1 | 0.15 | 362 | 2.4 | 1.20 | 2.18 | 0.79 |
1 | 2 | 0.15 | 385 | 2.8 | 1.27 | 2.55 | 0.75 |
1 | 3 | 0.15 | 400 | 2.9 | 1.32 | 2.64 | 0.74 |
1 | 4 | 0.15 | 460 | 3.5 | 1.52 | 3.18 | 0.82 |
Results of rectangular footing subjected to inclined loading (a°) in unreinforced and reinforced sand conditions.
|
|||||||
---|---|---|---|---|---|---|---|
0 | 0 | 0 | 212 | 2.2 | 1.00 | 1.00 | 1.00 |
0 | 0 | 1 | 240 | 3.8 | 1.13 | 1.73 | 1.00 |
0 | 0 | 2 | 282 | 4.1 | 1.33 | 1.86 | 1.00 |
0 | 0 | 3 | 348 | 4.7 | 1.64 | 2.14 | 1.00 |
0 | 0 | 4 | 368 | 6 | 1.74 | 2.73 | 1.00 |
0 | 7 | 0 | 134 | 2.8 | 1.00 | 1.00 | 0.63 |
0 | 7 | 1 | 222 | 3.4 | 1.66 | 1.21 | 0.93 |
0 | 7 | 2 | 240 | 3.8 | 1.79 | 1.36 | 0.85 |
0 | 7 | 3 | 280 | 4 | 2.09 | 1.43 | 0.80 |
0 | 7 | 4 | 310 | 4.5 | 2.31 | 1.61 | 0.84 |
0 | 14 | 0 | 110 | 1.7 | 1.00 | 1.00 | 0.52 |
0 | 14 | 1 | 154 | 2.4 | 1.40 | 1.41 | 0.64 |
0 | 14 | 2 | 224 | 3 | 2.04 | 1.76 | 0.79 |
0 | 14 | 3 | 268 | 4.1 | 2.44 | 2.41 | 0.77 |
0 | 14 | 4 | 282 | 4.3 | 2.56 | 2.53 | 0.77 |
0.5 | 0 | 0 | 330 | 1.4 | 1.00 | 1.00 | 1.00 |
0.5 | 0 | 1 | 370 | 3.8 | 1.12 | 2.71 | 1.00 |
0.5 | 0 | 2 | 400 | 4 | 1.21 | 2.86 | 1.00 |
0.5 | 0 | 3 | 450 | 4.2 | 1.36 | 3.00 | 1.00 |
0.5 | 0 | 4 | 470 | 5 | 1.42 | 3.57 | 1.00 |
0.5 | 7 | 0 | 270 | 1.7 | 1.00 | 1.00 | 0.82 |
0.5 | 7 | 1 | 300 | 2.5 | 1.11 | 1.47 | 0.81 |
0.5 | 7 | 2 | 350 | 3 | 1.30 | 1.76 | 0.88 |
0.5 | 7 | 3 | 400 | 3.5 | 1.48 | 2.06 | 0.89 |
0.5 | 7 | 4 | 422 | 4 | 1.56 | 2.35 | 0.90 |
0.5 | 14 | 0 | 195 | 1.2 | 1.00 | 1.00 | 0.59 |
0.5 | 14 | 1 | 232 | 1.5 | 1.19 | 1.25 | 0.63 |
0.5 | 14 | 2 | 300 | 2.5 | 1.54 | 2.08 | 0.75 |
0.5 | 14 | 3 | 340 | 2.6 | 1.74 | 2.17 | 0.76 |
0.5 | 14 | 4 | 360 | 4 | 1.85 | 3.33 | 0.77 |
1 | 0 | 0 | 400 | 3.2 | 1.00 | 1.00 | 1.00 |
1 | 0 | 1 | 460 | 6 | 1.12 | 1.88 | 1.00 |
1 | 0 | 2 | 510 | 7 | 1.24 | 2.19 | 1.00 |
1 | 0 | 3 | 540 | 7.5 | 1.32 | 2.34 | 1.00 |
1 | 0 | 4 | 580 | 8.5 | 1.41 | 2.66 | 1.04 |
1 | 7 | 0 | 350 | 3.2 | 1.00 | 1.00 | 0.85 |
1 | 7 | 1 | 385 | 4.1 | 1.10 | 1.28 | 0.84 |
1 | 7 | 2 | 455 | 4.4 | 1.30 | 1.38 | 0.89 |
1 | 7 | 3 | 490 | 6.12 | 1.40 | 1.91 | 0.91 |
1 | 7 | 4 | 520 | 6.98 | 1.49 | 2.18 | 0.93 |
1 | 14 | 0 | 270 | 3 | 1.00 | 1.00 | 0.66 |
1 | 14 | 1 | 322 | 3.2 | 1.19 | 1.07 | 0.70 |
1 | 14 | 2 | 390 | 3.5 | 1.44 | 1.17 | 0.76 |
1 | 14 | 3 | 420 | 3.8 | 1.56 | 1.27 | 0.78 |
1 | 14 | 4 | 430 | 5 | 1.59 | 1.67 | 0.77 |
Results of eccentrically inclined, loaded (α°,
|
||||||||
---|---|---|---|---|---|---|---|---|
0 | 7 | 0 | 0.05 | 112 | 1.7 | 1.00 | 1.00 | 0.53 |
0 | 7 | 1 | 0.05 | 190 | 3.2 | 1.70 | 1.88 | 0.79 |
0 | 7 | 2 | 0.05 | 220 | 3.5 | 1.96 | 2.06 | 0.78 |
0 | 7 | 3 | 0.05 | 242 | 3.8 | 2.16 | 2.24 | 0.70 |
0 | 7 | 4 | 0.05 | 280 | 4.2 | 2.50 | 2.47 | 0.76 |
0 | 7 | 0 | 0.1 | 106 | 1.6 | 1.00 | 1.00 | 0.50 |
0 | 7 | 1 | 0.1 | 170 | 2.4 | 1.60 | 1.50 | 0.71 |
0 | 7 | 2 | 0.1 | 185 | 3 | 1.75 | 1.88 | 0.66 |
0 | 7 | 3 | 0.1 | 225 | 3.4 | 2.12 | 2.13 | 0.65 |
0 | 7 | 4 | 0.1 | 252 | 3.7 | 2.38 | 2.31 | 0.68 |
0 | 7 | 0 | 0.15 | 95 | 1.6 | 1.06 | 1.00 | 0.45 |
0 | 7 | 1 | 0.15 | 155 | 2 | 1.72 | 1.25 | 0.65 |
0 | 7 | 2 | 0.15 | 172 | 2.2 | 1.91 | 1.38 | 0.61 |
0 | 7 | 3 | 0.15 | 202 | 2.5 | 2.24 | 1.56 | 0.58 |
0 | 7 | 4 | 0.15 | 230 | 2.8 | 2.56 | 1.75 | 0.63 |
0 | 14 | 0 | 0.05 | 100 | 1.4 | 1.00 | 1.00 | 0.47 |
0 | 14 | 1 | 0.05 | 135 | 2 | 1.35 | 1.43 | 0.56 |
0 | 14 | 2 | 0.05 | 220 | 2.5 | 2.20 | 1.79 | 0.78 |
0 | 14 | 3 | 0.05 | 232 | 3 | 2.32 | 2.14 | 0.67 |
0 | 14 | 4 | 0.05 | 245 | 3.7 | 2.45 | 2.64 | 0.67 |
0 | 14 | 0 | 0.1 | 84 | 1.3 | 0.95 | 1.00 | 0.40 |
0 | 14 | 1 | 0.1 | 122 | 1.5 | 1.39 | 1.15 | 0.51 |
0 | 14 | 2 | 0.1 | 195 | 2 | 2.22 | 1.54 | 0.69 |
0 | 14 | 3 | 0.1 | 228 | 2.5 | 2.59 | 1.92 | 0.66 |
0 | 14 | 4 | 0.1 | 231 | 2.7 | 2.63 | 2.08 | 0.63 |
0 | 14 | 0 | 0.15 | 76 | 1.2 | 1.00 | 1.00 | 0.36 |
0 | 14 | 1 | 0.15 | 102 | 1.3 | 1.34 | 1.08 | 0.43 |
0 | 14 | 2 | 0.15 | 180 | 1.8 | 2.37 | 1.50 | 0.64 |
0 | 14 | 3 | 0.15 | 200 | 2.1 | 2.63 | 1.75 | 0.57 |
0 | 14 | 4 | 0.15 | 210 | 2.3 | 2.76 | 1.92 | 0.57 |
0.5 | 7 | 0 | 0.05 | 258 | 1.3 | 1.00 | 1.00 | 0.78 |
0.5 | 7 | 1 | 0.05 | 282 | 2 | 1.09 | 1.54 | 0.76 |
0.5 | 7 | 2 | 0.05 | 331 | 2.5 | 1.28 | 1.92 | 0.83 |
0.5 | 7 | 3 | 0.05 | 370 | 2.6 | 1.43 | 2.00 | 0.82 |
0.5 | 7 | 4 | 0.05 | 400 | 3.8 | 1.55 | 2.92 | 0.85 |
0.5 | 7 | 0 | 0.1 | 221 | 1.2 | 1.00 | 1.00 | 0.67 |
0.5 | 7 | 1 | 0.1 | 242 | 1.5 | 1.10 | 1.25 | 0.65 |
0.5 | 7 | 2 | 0.1 | 310 | 2.4 | 1.40 | 2.00 | 0.78 |
0.5 | 7 | 3 | 0.1 | 340 | 2.5 | 1.54 | 2.08 | 0.76 |
0.5 | 7 | 4 | 0.1 | 360 | 2.8 | 1.63 | 2.33 | 0.77 |
0.5 | 7 | 0 | 0.15 | 208 | 0.98 | 1.04 | 1.00 | 0.63 |
0.5 | 7 | 1 | 0.15 | 220 | 1.1 | 1.10 | 1.12 | 0.59 |
0.5 | 7 | 2 | 0.15 | 270 | 1.4 | 1.35 | 1.43 | 0.68 |
0.5 | 7 | 3 | 0.15 | 290 | 1.6 | 1.45 | 1.63 | 0.64 |
0.5 | 7 | 4 | 0.15 | 320 | 2 | 1.60 | 2.04 | 0.68 |
0.5 | 14 | 0 | 0.05 | 188 | 0.98 | 1.00 | 1.00 | 0.57 |
0.5 | 14 | 1 | 0.05 | 225 | 1.1 | 1.20 | 1.12 | 0.61 |
0.5 | 14 | 2 | 0.05 | 285 | 1.8 | 1.52 | 1.84 | 0.71 |
0.5 | 14 | 3 | 0.05 | 300 | 2.3 | 1.60 | 2.35 | 0.67 |
0.5 | 14 | 4 | 0.05 | 320 | 2.8 | 1.70 | 2.86 | 0.68 |
0.5 | 14 | 0 | 0.1 | 178 | 0.9 | 1.00 | 1.00 | 0.54 |
0.5 | 14 | 1 | 0.1 | 200 | 1 | 1.12 | 1.11 | 0.54 |
0.5 | 14 | 2 | 0.1 | 250 | 1.4 | 1.40 | 1.56 | 0.63 |
0.5 | 14 | 3 | 0.1 | 280 | 1.6 | 1.57 | 1.78 | 0.62 |
0.5 | 14 | 4 | 0.1 | 290 | 2.7 | 1.63 | 3.00 | 0.62 |
0.5 | 14 | 0 | 0.15 | 160 | 0.7 | 1.00 | 1.00 | 0.48 |
0.5 | 14 | 1 | 0.15 | 170 | 0.8 | 1.06 | 1.14 | 0.46 |
0.5 | 14 | 2 | 0.15 | 220 | 1.3 | 1.38 | 1.86 | 0.55 |
0.5 | 14 | 3 | 0.15 | 250 | 1.4 | 1.56 | 2.00 | 0.56 |
0.5 | 14 | 4 | 0.15 | 270 | 1.6 | 1.69 | 2.29 | 0.57 |
1 | 7 | 0 | 0.05 | 340 | 1.6 | 1.00 | 1.00 | 0.83 |
1 | 7 | 1 | 0.05 | 360 | 3.2 | 1.06 | 2.00 | 0.78 |
1 | 7 | 2 | 0.05 | 440 | 4 | 1.29 | 2.50 | 0.86 |
1 | 7 | 3 | 0.05 | 460 | 4.62 | 1.35 | 2.89 | 0.85 |
1 | 7 | 4 | 0.05 | 480 | 5 | 1.41 | 3.13 | 0.86 |
1 | 7 | 0 | 0.1 | 300 | 1.6 | 1.00 | 1.00 | 0.73 |
1 | 7 | 1 | 0.1 | 320 | 3 | 1.07 | 1.88 | 0.70 |
1 | 7 | 2 | 0.1 | 390 | 3.2 | 1.30 | 2.00 | 0.76 |
1 | 7 | 3 | 0.1 | 420 | 3.9 | 1.40 | 2.44 | 0.78 |
1 | 7 | 4 | 0.1 | 430 | 4.2 | 1.43 | 2.63 | 0.77 |
1 | 7 | 0 | 0.15 | 270 | 1 | 1.00 | 1.00 | 0.66 |
1 | 7 | 1 | 0.15 | 290 | 2.5 | 1.07 | 2.50 | 0.63 |
1 | 7 | 2 | 0.15 | 340 | 2.8 | 1.26 | 2.80 | 0.67 |
1 | 7 | 3 | 0.15 | 380 | 3.1 | 1.41 | 3.10 | 0.70 |
1 | 7 | 4 | 0.15 | 395 | 3.3 | 1.46 | 3.30 | 0.71 |
1 | 14 | 1 | 0.05 | 290 | 2.8 | 1.12 | 1.12 | 0.63 |
1 | 14 | 2 | 0.05 | 372 | 3 | 1.43 | 1.20 | 0.73 |
1 | 14 | 3 | 0.05 | 390 | 3.4 | 1.50 | 1.36 | 0.72 |
1 | 14 | 4 | 0.05 | 400 | 3.6 | 1.54 | 1.44 | 0.71 |
1 | 14 | 0 | 0.1 | 242 | 1.5 | 1.00 | 1.00 | 0.59 |
1 | 14 | 1 | 0.1 | 270 | 1.8 | 1.12 | 1.20 | 0.59 |
1 | 14 | 2 | 0.1 | 320 | 2 | 1.32 | 1.33 | 0.63 |
1 | 14 | 3 | 0.1 | 360 | 2.5 | 1.49 | 1.67 | 0.67 |
1 | 14 | 4 | 0.1 | 380 | 3 | 1.57 | 2.00 | 0.68 |
1 | 14 | 0 | 0.15 | 198 | 1.2 | 1.00 | 1.00 | 0.48 |
1 | 14 | 1 | 0.15 | 220 | 1.5 | 1.11 | 1.25 | 0.48 |
1 | 14 | 2 | 0.15 | 270 | 1.8 | 1.36 | 1.50 | 0.53 |
1 | 14 | 3 | 0.15 | 320 | 2 | 1.62 | 1.67 | 0.59 |
1 | 14 | 4 | 0.15 | 350 | 2.1 | 1.77 | 1.75 | 0.63 |
In the case of eccentric loading, the UBC value is calculated from the load–settlement curves that are shown in Fig. 6(a). From the graphs, it can be concluded that the embedment depth ratio
The load–settlement curve for inclined loading with an embedment depth is shown in Fig. 6(b). The centric loads were applied with different inclination angles changed from 0° to 14°. The ultimate load decreases as the load inclination angle increases and it is expected that
The load–settlement curve for different eccentric-inclined loading in both dimensions is shown in Fig. 6(c). These results indicate that the value of
Results of eccentrically inclined, loaded (α°,
|
||||||||
---|---|---|---|---|---|---|---|---|
0 | 7 | 0 | 0.05 | 105 | 2.2 | 1.00 | 1.00 | 0.50 |
0 | 7 | 1 | 0.05 | 180 | 3 | 1.71 | 1.36 | 0.75 |
0 | 7 | 2 | 0.05 | 212 | 3.5 | 2.02 | 1.59 | 0.75 |
0 | 7 | 3 | 0.05 | 232 | 4 | 2.21 | 1.82 | 0.67 |
0 | 7 | 4 | 0.05 | 262 | 4.2 | 2.50 | 1.91 | 0.71 |
0 | 7 | 0 | 0.1 | 99 | 1.9 | 1.00 | 1.00 | 0.47 |
0 | 7 | 1 | 0.1 | 165 | 2.2 | 1.67 | 1.16 | 0.69 |
0 | 7 | 2 | 0.1 | 178 | 2.5 | 1.80 | 1.32 | 0.63 |
0 | 7 | 3 | 0.1 | 199 | 3 | 2.01 | 1.58 | 0.57 |
0 | 7 | 4 | 0.1 | 232 | 3.2 | 2.34 | 1.68 | 0.63 |
0 | 7 | 0 | 0.15 | 84 | 1.7 | 1.00 | 1.00 | 0.40 |
0 | 7 | 1 | 0.15 | 152 | 1.9 | 1.81 | 1.12 | 0.63 |
0 | 7 | 2 | 0.15 | 168 | 2.2 | 2.00 | 1.29 | 0.60 |
0 | 7 | 3 | 0.15 | 175 | 2.8 | 2.08 | 1.65 | 0.50 |
0 | 7 | 4 | 0.15 | 220 | 3.2 | 2.62 | 1.88 | 0.60 |
0 | 14 | 0 | 0.05 | 98 | 1.2 | 1.00 | 1.00 | 0.46 |
0 | 14 | 1 | 0.05 | 132 | 1.4 | 1.35 | 1.17 | 0.55 |
0 | 14 | 2 | 0.05 | 210 | 2 | 2.14 | 1.67 | 0.74 |
0 | 14 | 3 | 0.05 | 220 | 2.8 | 2.24 | 2.33 | 0.63 |
0 | 14 | 4 | 0.05 | 242 | 2.9 | 2.47 | 2.42 | 0.66 |
0 | 14 | 0 | 0.1 | 88 | 2 | 0.47 | 1.00 | 0.42 |
0 | 14 | 1 | 0.1 | 120 | 1.2 | 0.64 | 0.60 | 0.50 |
0 | 14 | 2 | 0.1 | 190 | 1.7 | 1.01 | 0.85 | 0.67 |
0 | 14 | 3 | 0.1 | 201 | 2.5 | 1.07 | 1.25 | 0.58 |
0 | 14 | 4 | 0.1 | 222 | 2.6 | 1.18 | 1.30 | 0.60 |
0 | 14 | 0 | 0.15 | 64 | 1 | 1.00 | 1.00 | 0.30 |
0 | 14 | 1 | 0.15 | 100 | 1.2 | 1.56 | 1.20 | 0.42 |
0 | 14 | 2 | 0.15 | 170 | 1.5 | 2.66 | 1.50 | 0.60 |
0 | 14 | 3 | 0.15 | 180 | 2 | 2.81 | 2.00 | 0.52 |
0 | 14 | 4 | 0.15 | 201 | 2.1 | 3.14 | 2.10 | 0.55 |
0.5 | 7 | 0 | 0.05 | 252 | 1.1 | 1.00 | 1.00 | 0.76 |
0.5 | 7 | 1 | 0.05 | 270 | 1.4 | 1.07 | 1.27 | 0.73 |
0.5 | 7 | 2 | 0.05 | 322 | 1.6 | 1.28 | 1.45 | 0.81 |
0.5 | 7 | 3 | 0.05 | 360 | 2.5 | 1.43 | 2.27 | 0.80 |
0.5 | 7 | 4 | 0.05 | 380 | 3 | 1.51 | 2.73 | 0.81 |
0.5 | 7 | 0 | 0.1 | 210 | 1.1 | 1.00 | 1.00 | 0.64 |
0.5 | 7 | 1 | 0.1 | 232 | 1.2 | 1.10 | 1.09 | 0.63 |
0.5 | 7 | 2 | 0.1 | 300 | 1.7 | 1.43 | 1.55 | 0.75 |
0.5 | 7 | 3 | 0.1 | 332 | 2.2 | 1.58 | 2.00 | 0.74 |
0.5 | 7 | 4 | 0.1 | 320 | 3 | 1.52 | 2.73 | 0.68 |
0.5 | 7 | 0 | 0.15 | 200 | 1 | 1.00 | 1.00 | 0.61 |
0.5 | 7 | 1 | 0.15 | 210 | 1.1 | 1.05 | 1.10 | 0.64 |
0.5 | 7 | 2 | 0.15 | 260 | 1.6 | 1.30 | 1.60 | 0.65 |
0.5 | 7 | 3 | 0.15 | 278 | 1.8 | 1.39 | 1.80 | 0.62 |
0.5 | 7 | 4 | 0.15 | 298 | 2 | 1.49 | 2.00 | 0.63 |
0.5 | 14 | 0 | 0.05 | 185 | 1 | 1.00 | 1.00 | 0.56 |
0.5 | 14 | 1 | 0.05 | 215 | 1.1 | 1.16 | 1.10 | 0.58 |
0.5 | 14 | 2 | 0.05 | 282 | 1.5 | 1.52 | 1.50 | 0.71 |
0.5 | 14 | 3 | 0.05 | 290 | 1.8 | 1.57 | 1.80 | 0.64 |
0.5 | 14 | 4 | 0.05 | 310 | 2 | 1.68 | 2.00 | 0.66 |
0.5 | 14 | 0 | 0.1 | 162 | 0.8 | 1.00 | 1.00 | 0.49 |
0.5 | 14 | 1 | 0.1 | 189 | 0.9 | 1.17 | 1.13 | 0.51 |
0.5 | 14 | 2 | 0.1 | 242 | 1.2 | 1.49 | 1.50 | 0.61 |
0.5 | 14 | 3 | 0.1 | 270 | 1.4 | 1.67 | 1.75 | 0.60 |
0.5 | 14 | 4 | 0.1 | 280 | 1.5 | 1.73 | 1.88 | 0.60 |
0.5 | 14 | 0 | 0.15 | 152 | 0.6 | 1.00 | 1.00 | 0.46 |
0.5 | 14 | 1 | 0.15 | 165 | 0.7 | 1.09 | 1.17 | 0.45 |
0.5 | 14 | 2 | 0.15 | 210 | 0.9 | 1.38 | 1.50 | 0.53 |
0.5 | 14 | 3 | 0.15 | 240 | 1.2 | 1.58 | 2.00 | 0.53 |
0.5 | 14 | 4 | 0.15 | 255 | 1.4 | 1.68 | 2.33 | 0.54 |
1 | 7 | 0 | 0.05 | 328 | 1.2 | 1.00 | 1.00 | 0.80 |
1 | 7 | 1 | 0.05 | 344 | 2.5 | 1.05 | 2.08 | 0.75 |
1 | 7 | 2 | 0.05 | 430 | 3 | 1.31 | 2.50 | 0.84 |
1 | 7 | 3 | 0.05 | 450 | 5 | 1.37 | 4.17 | 0.83 |
1 | 7 | 4 | 0.05 | 470 | 6.2 | 1.43 | 5.17 | 0.84 |
1 | 7 | 0 | 0.1 | 290 | 1 | 1.00 | 1.00 | 0.71 |
1 | 7 | 1 | 0.1 | 310 | 2.2 | 1.07 | 2.20 | 0.67 |
1 | 7 | 2 | 0.1 | 380 | 2.5 | 1.31 | 2.50 | 0.75 |
1 | 7 | 3 | 0.1 | 400 | 3.1 | 1.38 | 3.10 | 0.74 |
1 | 7 | 4 | 0.1 | 420 | 3.4 | 1.45 | 3.40 | 0.75 |
1 | 7 | 0 | 0.15 | 260 | 0.9 | 1.00 | 1.00 | 0.63 |
1 | 7 | 1 | 0.15 | 282 | 1.5 | 1.08 | 1.67 | 0.61 |
1 | 14 | 1 | 0.1 | 260 | 1.8 | 1.13 | 1.20 | 0.57 |
1 | 7 | 2 | 0.15 | 320 | 1.8 | 1.23 | 2.00 | 0.63 |
1 | 7 | 3 | 0.15 | 360 | 2.5 | 1.38 | 2.78 | 0.67 |
1 | 7 | 4 | 0.15 | 370 | 2.8 | 1.42 | 3.11 | 0.66 |
1 | 14 | 0 | 0.05 | 255 | 1.7 | 1.00 | 1.00 | 0.62 |
1 | 14 | 1 | 0.05 | 280 | 2.8 | 1.10 | 1.65 | 0.61 |
1 | 14 | 2 | 0.05 | 362 | 3 | 1.42 | 1.76 | 0.71 |
1 | 14 | 3 | 0.05 | 380 | 3.4 | 1.49 | 2.00 | 0.70 |
1 | 14 | 4 | 0.05 | 390 | 4.5 | 1.53 | 2.65 | 0.70 |
1 | 14 | 0 | 0.1 | 230 | 1.5 | 1.00 | 1.00 | 0.56 |
1 | 14 | 2 | 0.1 | 305 | 2 | 1.33 | 1.33 | 0.60 |
1 | 14 | 3 | 0.1 | 350 | 2.5 | 1.52 | 1.67 | 0.65 |
1 | 14 | 4 | 0.1 | 360 | 3.4 | 1.57 | 2.27 | 0.64 |
1 | 14 | 0 | 0.15 | 190 | 1.1 | 1.00 | 1.00 | 0.46 |
1 | 14 | 1 | 0.15 | 210 | 1.4 | 1.11 | 1.27 | 0.46 |
1 | 14 | 2 | 0.15 | 260 | 1.8 | 1.37 | 1.64 | 0.51 |
1 | 14 | 3 | 0.15 | 310 | 2 | 1.63 | 1.82 | 0.57 |
1 | 14 | 4 | 0.15 | 330 | 2.4 | 1.74 | 2.18 | 0.59 |
The load–settlement curve for different embedded model footing with multiple layers of the geogrid reinforcement at centric vertical loading is shown in Fig. 7. From the graphs, it can be seen that the value of UBC of model footing increases with an increase in the depth of embedment and the settlement of the model foundation also increases with the same. These figures also indicate that the value of UBC increases with the increasing numbers of reinforcing layers at any depth of embedment (
These figures also indicate that the value of UBC increases with increasing the numbers of reinforcing layers. With the increase of the number of reinforcing layers in the contact area, the interlocking between sand particles and reinforcing layers are also increasing. Thus, the larger displacement and shear stresses are built up into the soil beneath the model foundation and transferred in reinforcement layers to the larger mass of soil. Therefore, the failure wedge becomes larger and the frictional resistance in failure planes become more [2].
This study aims to investigate the optimum number of geogrid layers to take the maximum benefit of soil reinforcement. The four layers of geogrid were adopted in the present study. The first layer of geogrid (
A series of laboratory tests were conducted to know the behaviour of the UBC of shallow rectangular foundation on unreinforced and multi-layered geogrid reinforced sand, under eccentric and inclined load with an embedment ratio varying from 0 to 1. Only one type of sand at one average relative density of compaction was used for all the tests. The test sand was reinforced with multiple layers of the bi-axial geogrid which varied from 0 to 4. The load eccentricity ( The value of UBC reduces about 33% and 31% with an increase in the load eccentricity 0 to 0.15 in both dimensions. Similarly, the reduction is in the range of 21% and 24% if the footing is placed over geogrid reinforced sand. As the load inclination increases from 0° to 14°, the UBC is decreased by 48%. Similarly, this decrement is in the range of 24% when the footing is placed on reinforced sand. The value of UBC increases by about 75% with an increasing number of layers of geogrid reinforcement ( The value of UBC increases by about 93% with an increasing the depth of embedded footing ( The The optimum layer of reinforcement is