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Behaviour of model footing resting on sand bed reinforced with multi-directional reinforcing elements
Geotextiles and Geomembranes 44 (2016) 568e578
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Behaviour of model footing resting on sand bed reinforced with multidirectional reinforcing elements M. Harikumar*, N. Sankar, S. Chandrakaran Department of Civil Engineering, National Institute of Technology, Calicut, Kerala, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 September 2015 Received in revised form 28 March 2016 Accepted 29 March 2016
Laboratory plate load tests are conducted on a model footing resting on sand bed reinforced with plastic multi-directional reinforcements. The bearing capacity, settlement and heave are evaluated and the effect of depth to first layer, spacing between reinforcements in a layer, number of layers and spacing between layers are investigated. The bearing capacity at 25 mm settlement improved by almost 1.3 times for a single layer of reinforcement, placed at an optimum depth of 0.5B. An increase in number of layers beyond four resulted in a reduction in improvement of bearing capacity. Four layers of reinforcement, spaced vertically apart at 0.5B resulted in a maximum increase of 185% in the bearing capacity. For the same area, the multi-directional reinforcing elements provide additional confinement to the soil mass due to the three dimensional projections, compared to the conventional geosynthetic reinforcements such as geogrids. Even while comparing the economic aspects, the multi-directional elements prove to be a viable alternative to the conventional planar geosynthetics. An artificial neural network based model has also been developed, which would aid the engineers to effectively predict the ultimate bearing capacity and settlements of the model footing, resting on reinforced sand, before these reinforcing elements are actually applied in the field. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Geosynthetics Bearing capacity Settlements Plate load test Multi-directional reinforcements Heave
1. Introduction The concept of mechanically stabilized earth has been widely used in various geotechnical applications such construction of embankments, pavements, bridge abutments, soft ground improvement and so on. Addition of reinforcements to soil have been performed by either incorporating continuous reinforcement inclusions such as sheet, bar or strip within a soil mass in a welldefined pattern, or by randomly mixing discrete fibres with a soil fill. The effect of the conventional geosynthetic reinforcements on soil has been extensively investigated.(Fleming et al., 2006; Iizuka et al., 2004; Katarzyna, 2006; Latha and Murthy, 2006; Park and Tan, 2005; Patra et al., 2005; Varuso et al., 2005; Yetimoglu et al., 2005; Abu-Farsakh et al., 2015 and Davarifard and Tafreshi, 2015). Planar geosynthetic reinforcement layers substantially improved the strength and deformation characteristics of cohesionless soils (Chandrasekaran et al., 1989; Haeri
* Corresponding author. E-mail address: [email protected] (M. Harikumar). http://dx.doi.org/10.1016/j.geotexmem.2016.03.008 0266-1144/© 2016 Elsevier Ltd. All rights reserved.
et al., 2000 and Venkatappa Rao et al., 2005; Tafreshi and Dawson, 2010a; Tafreshi and Dawson, 2010b). Randomly oriented discrete geosynthetic fibres improved the strength, stiffness and reduced the post peak loss of shear in sands (Gray and Ohashi, 1983; Gray and AI-Refeai, 1986; Al-Refeai, 1991; Ranjan et al., 1994; Kaniraj and Gayathri, 2003; Yetimoglu and Salbas, 2003 and Park and Tan, 2005). Geogrid layers incorporated in soil fills improved the bearing capacity and reduced soil settlements (Alamshahi and Hataf, 2009; Mosallanezhad et al., 2008; Ghazavi and Mirzaeifar, 2010; El Sawwaf and Nazir, 2010; El Sawwaf and Nazir, 2012; Shin and Das, 2000; Sitharam and Sireesh, 2012 and Zidan, 2012). The concept of three dimensional reinforcement was first introduced by Lawton et al. (1993), through laboratory investigations on sand reinforced with geo-jacks. Placing geo-jacks on top of geogrids substantially improved the performance of the soil bed. The combination of geogrid and geojacks performed better than the combination of geogrid and gravel. Zhang et al. (2008) investigated the use of three dimensional reinforcements in the form of rings with varying heights of vertical elements. In these investigations, the three dimensional elements were found to possess the inherent advantages of two dimensional
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reinforcements, along with the additional passive resistances introduced by the three dimensional components. In this paper, results from laboratory plate load tests conducted on square footing resting on sand bed reinforced with single and multiple layers of multi-directional reinforcements are presented, in order to determine the feasibility of using multi-directional reinforcements to improve the bearing capacity of soil and to investigate the significance of parameters such as volume ratio of reinforcements, depth to first layer, spacing between reinforcements in a layer, spacing between layers and number of layers. An empirical model using artificial neural network modelling is also described, using which a field engineer can predict the improvement in strength parameters of reinforced soil, before the reinforcing elements are actually applied in the field.
2. Test materials Fig. 1. Particle size distribution of sand used for the study.
2.1. Sand Locally available clean river sand obtained from the premises of NIT Calicut, Kerala, India was oven dried and was used for the present study. The engineering and index properties of sand used for the study are listed in Table 1. Under the USCS classification, sand is classified as poorly graded. The grain size distribution is described in Fig. 1.
2.2. Multi-directional reinforcements Reinforcing elements were manufactured from injection moulding of Acrylonitrile Butadiene Styrene (ABS) plastic granules. ABS is derived from acrylonitrile, butadiene, and styrene. Acrylonitrile is a synthetic monomer produced from propylene and ammonia; butadiene is a petroleum hydrocarbon obtained from the C4 fraction of steam cracking; styrene monomer is made by dehydrogenation of ethyl benzene, which is a hydrocarbon. ABS combines the strength and rigidity of acrylonitrile and styrene polymers with the toughness of polybutadiene rubber. ABS has superior properties in terms of hardness, gloss, toughness, and electrical insulation. The reinforcements consisted of four legs or protrusions in a single plane (xey) and two protrusions in plane perpendicular to this plane (z), with an average length of 30 mm and a diameter of 5 mm were used for the study, as shown in Fig. 2. The engineering properties of the reinforcing elements are explained in Table 2.
3. Test setup The test setup for laboratory plate load test consists of the following:
Table 1 Properties of sand used for the study. Soil Parameters
Value
USCS classification Minimum Density, kN/m3 Maximum Density, kN/m3 D10 D30 D60 Uniformity Coefficient, Cu Coefficient of curvature, Cc Angle of shearing resistance, 4
SP 12.75 15.7 0.25 0.38 0.5 2.0 1.15 37.4
a. Test tank of size 750 mm 750 mm 750 mm, made of mild steel sheets 1.5 mm thick and stiffened by horizontal and vertical bracings with mild steel angle sections on all faces. b. MS plate 150 mm 150 mm 25 mm c. Hydraulic jack, 50 kN capacity, with a ram diameter of 63 mm. d. Dial gauges, 30 mm travel with 0.01 mm sensitivity The test tank was fabricated keeping in mind the size of the model footing to be tested. As per Indian standards [IS:1888e1982], the width of the test tank should be five times the width of the model footing, to minimize scale effect. The sides and bottom of the tank were fabricated from 1.5 mm thick mild steel sheets. The sheets were screwed on to angle sections at the corners of the box structure. The box was stiffened by horizontal and vertical bracings to avoid yielding of the tank while being loaded, as shown in Fig. 3. The base of the plate was roughened by gluing on a thin layer of sand to it. A hand operated hydraulic jack of 50 kN capacity, abutting against a reaction frame was used to apply the required load to the system. 3.1. Preparation of test bed Sand was poured into the tank using raining technique. In order to achieve a desired relative density, the corresponding height of fall required was determined, by performing trials with varying heights of fall. The densities were determined, in each trial by using steel containers of known volume. From the values of maximum and minimum dry densities, the relative density was calculated, in each trial. A curve was plotted between the height of fall and relative density, from which the height of fall required for filling sand at any given relative density could be obtained. For all tests, the relative density was maintained at 65%, consistent with the previous experimental investigations using multi-directional inclusions performed by the same authors (Harikumar et al., 2015). The sand bed prepared in the test tank at different levels is shown in Fig. 4. 4. Reinforcement configuration The effect of parameters such as volume ratio of reinforcements, depth to first layer, intra and inter-layer between layers and number of layers are investigated in the test. Previous investigations conducted by Lee et al. (1999), Sitharam and Sireesh (2004), Bera et al. (2005) and Latha and Somwanshi (2009) on conventional
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Fig. 2. Multi-directional reinforcements.
Table 2 Properties of multi-directional reinforcements. Material
ABS plastic
Density Melting point Volume Mean length Mean diameter
0.997 g/cc 104 C 2914.4 mm3 30 mm 5 mm
where B is the width of the model footing. Considering a 2:1 distribution of a vertical load on the surface, the maximum width over which the load is distributed, even at a depth of 2B is 4B. Hence, in this investigation, the width of a reinforcement layer was fixed at 4B. The depth to the first layer of reinforcement is designated as u, the spacing between layers, as d and the spacing between multidirectional elements in a single layer, as s. B represents the plate width and b represents the width of the reinforcing elements. Ground displacements, both settlements and heave are represented by d. Initially, the multi-directional reinforcements were arranged in a single layer, with s/b ¼ 0. Since the width of reinforcement layers is confined to 4B, this configuration corresponds to a volume ratio of 0.3%. All reinforcement parameters are expressed in the form of dimensionless factors such as u/B, d/B, s/b and d/B. Fig. 5 explains the nomenclature used for the study. b ¼ width of reinforcing element B ¼ width of plate u ¼ depth to first layer d ¼ spacing between layers s ¼ spacing between reinforcing elements in a single layer N ¼ number of layers.
5. Test procedure Fig. 3. Horizontal and vertical stiffening of the model test tank.
geosynthetics indicate that an increase in the width of a reinforcement layer beyond 4B, had no substantial effect on the bearing capacity of soil. Additionally, the maximum depth of influence of a vertical load is governed by the depth of pressure bulb, equal to 2B,
Fig. 4. Preparation of test bed.
The inner faces of the test tank was made smooth to reduce the boundary effects. The height of fall required, corresponding to a relative density of 65% was calculated as discussed in the previous section. Sand was filled in layers of 50 mm thickness. The weight of sand required for each lift was predetermined and while filling, it was ensured that the calculated quantity was completely filled for each lift. The sand surface was levelled and the multi-directional inclusions were placed at the required depth. In order to ensure
Fig. 5. Arrangement of reinforcement layers.
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shown in Fig. 7b. Heave was measured on the left and right sides of the plate at a distance of 1B from the plate edge, by means of two dial gauges. 6. Testing program
Fig. 6. Test setup.
that the centers of the reinforcement layer, reaction frame and the tank coincide, a temporary formwork was fabricated, with inner dimensions of 600 mm 600 mm. The centre of this formwork was matched with the centre of the tank and the reaction frame. The reinforcements were then placed inside the formwork, which was later removed. At the top of sand layers, the plate was placed at the centre of the tank. The ram of the hydraulic jack was placed on top of the plate, the top of which abutted against the reaction frame. Two dial gauges were placed at diametrically opposite ends of the plate, in order to measure the settlement. The load applied was indirectly calculated from the pressure gauge attached to the hydraulic jack. The load was applied in small increments of 0.6 kN. As per IS:1888e1982, each increment of load was maintained until the rate of settlement, under this load appreciably reduced to a value of 0.02 mm/min. Along similar guidelines, the loading was continued until a settlement of 25 mm was attained. The test setup is described in Fig. 6. Reinforcements are placed inside formwork fabricated, as shown in Fig. 7a. The formwork is later removed and the next layer of sand placed over the reinforcing elements, as
The testing program commenced with the test on unreinforced sand bed. The tests on reinforced sand bed was categorized into three phases. Phase I involved the determination of optimum depth to the first layer of reinforcement. These tests were conducted using a single layer of reinforcement, with varying u/B. Once the optimum depth was fixed, Phase II was employed, which consisted of determining an optimum spacing between reinforcing elements, at the optimum depth. The reinforcements were placed in a single layer, at the optimum depth, at three different spacing of s/b ¼ 0, 1 and 1.5. Finally, Phase III involved determining the optimum number of layers of reinforcing elements. In this phase, the depth of first layer of reinforcements was kept at the optimum value, while the number of layers was varied from one to four, keeping the final layer of reinforcement at a depth of 2B, in all cases. Placing reinforcements beyond a depth of 2B was considered ineffective, as it was ineffective in improving the bearing capacity substantially (Latha and Somwanshi, 2009). The phases used for the test and the corresponding values of various parameters are shown in Table 3. 7. Results and discussion 7.1. Depth to first layer Typical pressure vs. settlement curves for the model footing on unreinforced and reinforced sand bed is shown Fig. 8. The tests correspond to Phase I, in which the multi-directional reinforcements are laid out in a mat-pattern, with an overall length and width of 4B (600 mm). The reinforcing elements were placed, close to each other, such that the spacing between them, s/b ¼ 0. This corresponds to a volume ratio of 0.3%.Each test was performed twice and the average of the settlement values was taken into consideration, to account for accuracy. It can be seen that placement of a single layer of reinforcement, too close to the surface (u/B ¼ 0.1), does not
Fig. 7. a) Temporary formwork arrangement and b) Placing reinforcing elements and filling with sand.
Table 3 Phases of tests used for the study. Phase
Variables
Values
Study on
I II III
u/B s/b N, d/B
0.1, 0.3, 0.5, 0.7 0, 0.5, 1 N ¼ 1, 2, 3, 4 and d/B ¼ 0, 1.5, 0.75, 0.5
Depth to first layer Spacing between reinforcing elements No of layers, spacing between layers
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M. Harikumar et al. / Geotextiles and Geomembranes 44 (2016) 568e578 Table 4 Test parameters for varying depth to first layer of reinforcement. Test parameter
BCR SRR Heave ratio
Fig. 8. Applied pressure vs. settlement for varying depth to first reinforcement layer.
improve the settlement response significantly. As the depth to first layer increases beyond 0.1B, the response improved considerably. This is because, at shallow depths of placement, the magnitude of mobilized frictional resistance at the sand-reinforcement interface is relatively less, due to the smaller overburden pressure. Placing the first reinforcement layer at a depth greater than 0.7B, had an adverse effect on bearing capacity and settlement values, since the settlements began to increase, although the values were better, compared to the settlement in unreinforced soil. This behaviour is due to increased thickness of sand layer over the reinforcements, resulting in higher settlement. The corresponding impact of depth of reinforcement on surface heave is shown in Fig. 9. Surface heave reduces with increasing depth of placement of reinforcement upto u/B ¼ 0.5, and thereafter decreases. The improvements in bearing capacity and settlement behaviour are quantified using three factors viz. bearing capacity ratio (BCR), Settlement reduction ratio (SRR) and Heave ratio (dx100/B). BCR is calculated as the ratio between the ultimate bearing capacity of reinforced sand to that of unreinforced sand. The ultimate bearing capacity in all cases, in the study is calculated, corresponding to a settlement of 25 mm.
SRR ¼
BCR, SRR and heave ratio at varying depth to first layer of reinforcement 0.1
0.3
0.5
0.7
1.03 0.06 2.38
1.25 0.59 1.99
1.3 0.72 2.17
1.24 0.67 2.58
su is the settlement of unreinforced sand bed at a given pressure and sr represents settlement of reinforced sand bed at the same pressure. Heave ratio is defined as the ratio between the maximum heave, observed at a distance of 1B from the edge of the plate for unreinforced sand bed to the maximum heave observed in reinforced sand bed. Table 4 shows the BCR and SRR for varying depth to first layer of reinforcement. Fig. 10 shows the variation in BCR corresponding to 25 mm settlement. For a single layer of reinforcement, the bearing capacity improved 1.3 times, corresponding at a depth of placement, 0.5B. Settlement reduction factor was calculated for various depths to first layer of reinforcement, as shown in Fig. 11. A maximum reduction of 0.72 was obtained corresponding to u/ B ¼ 0.5 with zero spacing between reinforcing elements. The variation of heave ratio with depth of first reinforcement layer is
su sr su
where,
Fig. 9. Applied pressure vs. surface heave for varying depth to first reinforcement layer.
Fig. 10. BCR corresponding to 25 mm settlement vs. depth to first layer of reinforcement.
Fig. 11. SRR vs depth to first layer of reinforcement.
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Fig. 12. Heave ratio vs. depth to first layer of reinforcement.
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Fig. 15. BCR at 25 mm settlement vs. Intra-layer spacing, s/B.
7.2. Spacing between reinforcing elements
Fig. 13. Ground displacement profile for varying u/B.
shown in Fig. 12. Similar to the trends observed, the maximum reduction in heave corresponds to a depth of 0.5B. It is worth noting that, the improvement in bearing capacities is only marginal due to the presence of a single layer of reinforcing inclusions alone. The actual mechanism of earth reinforcement by these inclusions can be considered to be a combination of a localized confining effect imparted to the sand bed between the reinforcing element layers and the frictional resistance between the 3D protrusions on the surface of the inclusions and sand. The general ground displacement profile in terms of settlement and heave with variation in depth of first reinforcement layer is described in Fig. 13.
The optimum depth of placement of the first layer of reinforcement was determined as 0.5B. The tests performed in Phase I, involved placing the reinforcing elements placed close to one another (s/b ¼ 0; b being the width of the reinforcing element). The next phase involved the determination of optimum spacing between the reinforcing elements. Two different configurations of reinforcement arrangement, viz. s/b ¼ 0.5 and s/b ¼ 1 were tested. The schematic of the different configurations are shown in Fig. 14. The variation of BCR, SRR and heave ratio corresponding to varying reinforcement spacing are described in Fig. 15, Fig. 16 and Fig. 17 respectively. As expected, placing the reinforcing elements close to one another, with zero spacing between them, accounts for maximum improvement in the strength parameters, on account of increased volume ratio of reinforcement, leading to an increased surface area of contact between inclusions and the sand bed. However, it is to be noted that the reduction in strength improvement, when the reinforcements are arranged at a spacing of s/ b ¼ 0.5 and s/b ¼ 1 is only marginal, as shown in Table 5. Considering the practical difficulties in placing the reinforcing elements one by one, at zero spacing between them in field applications, and the economic aspects of the project, the placement of reinforcements at a spacing of s/b ¼ 1, proves to be feasible. Thus, considering a balance between the strength improvement and the overall economic benefits, an intra-layer spacing of s/b ¼ 1 is adopted for the study. 7.3. Number of layers and spacing between layers In all tests conducted in this phase, the depth to first reinforcement layer is fixed at 0.5B. The number of reinforcement layers
Fig. 14. Schematic of reinforcement layout for: a) s ¼ 0b b) s ¼ 0.5b and c) s ¼ 1b
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M. Harikumar et al. / Geotextiles and Geomembranes 44 (2016) 568e578 Table 6 Reinforcement configuration.
Fig. 16. SRR vs. Inter layer spacing, s/b.
Fig. 17. Heave ratio for varying Intra layer spacing, s/b.
is varied from one to four, the final layer being kept at a depth of 2B. Between the layers at depths of 0.5B and 2B, the reinforcement layers were placed at equal spacing between them. The thickness of the reinforcing elements was around 0.2B. Hence, it was not possible to place the reinforcements at spacing less than 0.5B, due to practical difficulties in ensuring the correct placement of reinforcing elements and compaction of the sand above. Placing a layer above 0.5B depth was not considered in this phase, as the optimum depth for a single reinforcement layer was obtained as 0.5B. The configurations followed in Phase III are described in Table 6. The response of the model footing resting on sand bed with different number of reinforcing layers is shown in Fig. 18. The bearing capacity increased with an increase in number of reinforcing layers, coupled with a decrease in settlements. This is due to the ability of reinforcements to spread the superimposed load to larger depths, where the confining and overburden pressures are higher. However, the effect of an additional layer reduced with an
No. of layers
Depth to first layer (u/B)
Inter-layer spacing (d/B)
1 2 3 4
0.5 0.5 0.5 0.5
0 1.5 0.75 0.5
increase in the number of layers. Fig. 19 and Fig. 20 show the improvement in BCR and SRR with number of layers of reinforcement, respectively. It can be seen that as the number of layers increased from 2 to 3, a steep increase of about 45% was observed in BCR and SRR, whereas this improvement reduced to about 14% and 3% for BCR and SRR respectively, when the number of layers increased beyond 3. Similarly, the reduction in heave observed was about 10% when the number of layers increased from 2 to 3, and only 0.6% when the number of layers increased from 3 to 4, as shown in Fig. 21. Table 7 shows the bearing capacity ratios for the experimental phases, calculated for different settlement-footing width ratios. It can be seen that there is a considerable improvement in bearing capacities, even at lower s/B ratios of 5%, unlike the conventional geogrid reinforcements, which require a minimum initial strain, to effectively mobilize the frictional resistance at the sandreinforcement interface, thereby improving the bearing capacity. for reinforced earth applications. Since the tests are conducted on laboratory scale models, the effect of confinement and scaling play a significant role. Extensive large scale field studies are currently being conducted by the authors to determine the exact behaviour of multi-directional reinforcements. A comparison of the improvements in bearing capacities imparted by conventional geogrid reinforcements and the multidirectional elements developed in this study, under similar test conditions and soil properties is provided in Table 8. It can be seen that the multi-directional reinforcements perform on par with the conventional geosynthetic reinforcing systems. Additionally, for a given aerial coverage, the cost of manufacturing these elements is about 50% less, compared to the conventional reinforcements. However, the method is slightly labour-intensive as laying the reinforcing elements requires trained personnel. 7.4. Artificial neural network (ANN) modelling The formulation of a 3D finite element model for the present problem is quite challenging, since it involves modelling the individual 3D reinforcing elements, which is extremely difficult. Also,
Table 5 Test parameters for varying intra-layer spacing of reinforcements and u/B ¼ 0.5 Test parameter
BCR SRR Heave ratio
BCR, SRR and heave ratio at varying intra layer spacing (s/b) and u/B ¼ 0.5 0
0.5
1
1.297 0.72 2.17
1.27 0.68 3.92
1.24 0.55 3.97
Fig. 18. Applied pressure vs. settlement for varying number of layers.
M. Harikumar et al. / Geotextiles and Geomembranes 44 (2016) 568e578
Fig. 19. BCR vs. number of layers of reinforcement.
since the relationship between the experimental input and output parameters is quite complex, a more rational approach would be to create an empirical model, which can effectively predict the behaviour of the reinforced soil mass, under different conditions of tests. This can be achieved vide artificial neural networks. Neural network models were formulated using MATLAB, in order to predict the ultimate bearing capacity and settlement of a model square footing resting on a sand bed reinforced with multi-directional inclusions. The network was trained using gradient descent with momentum and adaptive learning rate backpropagation technique. The impact of test parameters such as, the depth to first layer of reinforcement, spacing between reinforcing elements in a layer, number of layers and spacing between layers have been analysed. Two ANN models were constructed: each consisting of 4 nodes in the input layer, 10 nodes in the hidden layer and a single node in the output layer. The configuration of the model is shown in Fig. 22.
7.5. Depth to first layer of reinforcement From the experimental results, it is known that the ultimate bearing capacity of the sand bed improved with the depth of placement of reinforcing layer, upto 0.5B and then decreased on further increasing the depth. Similarly, the maximum settlement undergone by the plate decreased with increasing depth of reinforcement layer upto about 0.5B, and then increased. The ANN model predicts the trend in variation of these parameters reasonably well, as shown in Fig. 23a and Fig. 23b.
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Fig. 21. Heave ratio vs. number of layers of reinforcement.
7.6. Intra-layer spacing Arranging the reinforcing inclusions, at a spacing of s/b ¼ 0 resulted in a maximum improvement in the strength parameters. However, an increase in the intra-layer spacing, resulted in only a marginal variation in strength. The ANN model predicts this negligible variation in ultimate bearing capacity and maximum settlements, with increase in intra-layer spacing, almost exactly, as shown in Fig. 24a and Fig. 24b respectively. 7.7. Number of layers of reinforcing inclusions The ultimate bearing capacity increased with number of reinforcing layers. However, the rate of improvement reduced with increase in number of layers. Maximum improvements were
Table 7 BCR for different configurations under different s/B ratios. s/B, % u/B variable 0.1 0.3 0.5 0.7 s/b variable 0 1 N variable 2 3 4 5
5
10
15
20
30
1.07 1.4 1.55 1.52
1.03 1.31 1.39 1.36
1.03 1.27 1.31 1.26
1.03 1.24 1.26 1.21
1.02 1.19 1.24 1.17
1.55 1.39
1.39 1.26
1.31 1.24
1.26 e
1.24 e
1.48 1.83 1.96 1.99
1.27 1.63 1.76 1.77
1.26 1.49 1.69 1.86
e e e e
e e e e
Table 8 Comparison of improvement in bearing capacities from various studies.
Fig. 20. SRR vs number of layers of reinforcement.
Study
Geogrid aperture size (mm)
Phanikumar et al. (2009) Latha and Somwanshi (2009) Abu-Farsakh et al. (2015) Present study
6 30 25 30
6 30 25 30
Percentage improvement in ultimate bearing capacity with no of layers. 1
2
3
12 e e 29
18.5 60 42 92
29 92 47 71
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8. Conclusions
Depth to first layer
Ultimate bearing capacity
Intra-layer spacing Hidden layer No. of layers
Settlement
Inter-layer spacing Fig. 22. ANN hierarchy for plate load tests.
observed when the number of layers increased from two to three. Similarly, the maximum reduction in peak settlements were observed when the number of layers increased from two to three. The variation in the strength parameters, both measured and predicted is described in Fig. 25a and Fig. 25b. Overall, the ANN models predicted the ultimate bearing capacity and settlements, very close to the measured values, as seen in the aggregation of points near to the 450 line in Fig. 26a and Fig. 26b. The correlation coefficients for the bearing capacity model and settlement model are 0.97 and 0.93 respectively. The models were also effective in describing the general trend in the variation of the test parameters. Although the neural network model is developed based on the laboratory tests, the results show that if similar models are developed based on actual field tests, excellent results could be obtained.
Based on the results from experimental investigations on the behaviour of a model footing resting on sand bed reinforced with plastic multi-directional reinforcements, the following conclusions can be drawn: a. An appreciable increase in bearing capacity was observed as the depth to the first layer of reinforcement increased beyond 0.1B. The optimum depth of placement of the first layer was 0.5B. Placing reinforcements beyond 0.5B depth, in a single layer, resulted in a reduction in increase of bearing capacity. The bearing capacity increased by 1.3 times and the settlements reduced by almost 72%. b. Within a single layer of reinforcement, the maximum improvement in BCR was obtained corresponding to zero spacing between the inclusions. However, there was only a marginal decrease in BCR with an increase in intra-layer spacing. Hence, considering a balance between the strength improvement and economical aspects, an optimum spacing of 1b was adopted. BCR increased with increase in number of reinforcement layers. As the number of layers increased from 2 to 3, a steep increase of about 45% was observed in BCR, whereas this improvement reduced to about 14% when the number of layers increased beyond 3. SRR showed similar trends, the improvements being 43% and 3% respectively. A similar trend was observed, even for Heave ratio. c. Owing to the size of the reinforcing elements and the practical difficulties in laying and compacting sand layers between the
Fig. 23. BCR and maximum settlement vs. depth to first layer of reinforcement.
Fig. 24. Ultimate bearing capacity and maximum settlement vs. Intra-layer spacing, s/b.
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Fig. 25. Ultimate bearing capacity vs. Number of reinforcement layers, N.
Fig. 26. Measured vs. Predicted ultimate bearing capacity and maximum settlement.
reinforcing elements, a minimum spacing of 0.2B was required to be maintained between the reinforcement layers. Hence, considering these factors, the optimum layer spacing was maintained as 0.5B. d. The ANN model effectively predicted the ultimate bearing capacity and maximum settlements from the laboratory model footing tests. The model was used to investigate the effect of depth to first reinforcement layer, intra and inter layer spacing and the number of reinforcement layers. The response of the sand fractions to changes in these parameters, under varied test conditions were recorded effectively by the neural network models. The ultimate bearing capacity and the settlements, were also predicted close to the measured values with correlation coefficients of 0.97 and 0.93 respectively. References Abu-Farsakh, M.Y., Akond, I., Chen, Q., 2015. Evaluating the performance of geosynthetic-reinforced unpaved roads using plate load tests. Int. J. Pavement Eng. http://dx.doi.org/10.1080/10298436.2015.1031131. Al-Refeai, T., 1991. Behavior of granular soils reinforced with discrete randomly oriented inclusions. Geotext. Geomembr. 10, 319e333. Alamshahi, S., Hataf, N., 2009. Bearing capacity of strip footings on sand slopes reinforced with geogrid and grid-anchor. Geotext. Geomembr. 27 (3), 217e226. Bera, A.K., Ghosh, A., Ghosh, A., 2005. Regression model for bearing capacity of a square footing on reinforced pond ash. Geotext. Geomembr. 23 (3), 261e285. Chandrasekaran, B., Broms, B.B., Wong, K.S., 1989. Strength of fabric reinforced sand under axisymmetric loading. Geotext. Geomembr. 8 (4), 293e310. Davarifard, S., Tafreshi, S.N.M., 2015. Plate load tests of multi-layered geocell reinforced bed considering embedment depth of footing. Procedia Earth Planet. Sci. 15, 105e110. El Sawwaf, M., Nazir, A.K., 2010. Behavior of repeatedly loaded rectangular footings resting on reinforced sand. Alexandria Eng. J. 49 (4), 349e356.
El Sawwaf, M., Nazir, A.K., 2012. Cyclic settlement behavior of strip footings resting on reinforced layered sand slope. J. Adv. Res. 3 (4), 315e324. Fleming, I.R., Sharma, J.S., Jogi, M.B., 2006. Shear strength of geomembraneesoil interface under unsaturated conditions. Geotext. Geomembr. 24 (5), 274e284. Ghazavi, M., Mirzaeifar, H., 2010. Bearing capacity of multi-edge shallow foundations on geogrid-reinforced sand. In: 2nd International Symposium on Environmental Engineering, 600, pp. 1e9. Gray, D.H., AI-Refeai, T., 1986. Behavior of fabric-versus fiber-reinforced sand. J. Geotech. Eng. ASCE 112 (8), 804e820. Gray, D.H., Ohashi, H., 1983. Mechanics of fiber reinforcement in sand. J. Geotechnical Eng. 109 (3), 335e353. Haeri, S.M., Nourzad, R., Oskrouch, A.M., 2000. Effect of geotextile reinforcement on the mechanical behavior of sands. Geotext. Geomembr. 18 (6), 385e402. Harikumar, M., Sankar, N., Chandrakaran, S., 2015. Response of sand reinforced with multi-oriented plastic hexa-pods. J. Soil Mech. Found. Eng. 52 (4). Iizuka, A., Kawai, K., Kim, E.R., Hirata, M., 2004. Modeling of the confining effect due to the geosynthetic wrapping of compacted soil specimens. Geotext. Geomembr. 23 (5), 329e358. Kaniraj, S.R., Gayathri, V., 2003. Geotechnical behavior of fly ash mixed with randomly oriented fiber inclusions. Geotext. Geomembr. 21, 123e149. Katarzyna, Z.A., 2006. Shear strength parameters of compacted fly asheHDPE geomembrane interfaces. Geotext. Geomembr. 24 (2), 91e102. Latha, M.G., Murthy, V.S., 2006. Investigations on sand reinforced with different geosynthetics. Geotechnical Test. J. 29 (6), 474e481. Latha, G.M., Somwanshi, A., 2009. Bearing capacity of square footings on geosynthetic reinforced sand. Geotext. Geomembr. 27, 281e294. Lawton, E.C., Khire, M.V., Fox, N.S., 1993. Reinforcement of soils by multioriented geosynthetic inclusions. J. Geotechnical Eng. 119 (2). Lee, K.M., Manjunath, V.R., Dewaikar, D.M., 1999. Numerical and model studies of strip footing supported by a reinforced granular fill-soft soil system. Can. Geotechnical J. 36, 793e806. Mosallanezhad, M., Hataf, N., Ghahramani, A., 2008. Experimental study of bearing capacity of granular soils reinforced with innovative grid-anchor system. J. Geotechnical Geol. Eng. 26 (3), 299e312. Park, T., Tan, S.A., 2005. Enhanced performance of reinforced soil walls by the inclusion of short fiber. Geotext. Geomembr. 23 (4), 348e361. Patra, C.R., Das, B.M., Atalar, C., 2005. Bearing capacity of embedded strip foundation on geogrid-reinforced sand. Geotext. Geomembr. 23 (5), 454e462.
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Phanikumar, B.R., Prasad, R., Singh, A., 2009. Compressive load response of geogridreinforced fine, medium and coarse sands. Geotext. Geomembr. 27 (3), 183e186. Ranjan, Gopal, Vasan, R.M., Charan, H.D., 1994. Behavior of plastic fiber-reinforced sand. Geotext. Geomembr. 13, 555e565. Shin, E.C., Das, B.M., 2000. Experimental study of bearing capacity of a strip foundation on geogrid-reinforced sand. Geosynth. Int. 7 (No. 1), 59e71. Sitharam, T.G., Sireesh, S., 2004. Model studies of embedded circular footing on geogrid-reinforced sand beds. J. Ground Improv. 8 (2), 69e75. Sitharam, T.G., Sireesh, S., 2012. Behavior of embedded footings supported on geogrid cell reinforced foundation beds. Geotechnical Test. J. 28 (5), 1e12. Tafreshi, S.N.M., 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 (1), 72e84. Tafreshi, S.N.M., Dawson, A.R., 2010. Behaviour of footings on reinforced sand subjected to repeated loading e comparing use of 3D and planar geotextile. Geotext. Geomembr. 28 (5), 434e447.
Varuso, R.J., Grieshaber, J.B., Nataraj, M.S., 2005. Geosynthetic reinforced levee test section on soft normally consolidated clays. Geotext. Geomembr. 23 (4), 362e383. Venkatappa Rao, G., Dutta, R.K., Ujwala, D., 2005. Strength characteristics of sand reinforced with coir fibers and coir geotextiles. Electron. J. Geotechnical Eng. 1e13. Paper 0602. Yetimoglu, T., Salbas, O., 2003. A study on shear strength of sands reinforced with randomly distributed discrete fibers. Geotext. Geomembr. 21 (2), 103e110. Yetimoglu, T., Inanir, M., Inanir, O.E., 2005. A study on bearing capacity of randomly distributed fiber-reinforced sand fills overlying soft clay. Geotext. Geomembr. 23 (2), 174e183. Zhang, M.X., Zhou, H., Javadi, A.A., Wang, Z.W., 2008. Experimental and theoretical investigation of strength of soil reinforced with multi-layer horizontal vertical orthogonal elements. Geotext. Geomembr. 26, 1e13. Zidan, A.F., 2012. Numerical study of behavior of circular footing on geogridreinforced sand under static and dynamic loading. Geotechnical Geol. Eng. 30 (2), 499e510.
Contents lists available at ScienceDirect
Geotextiles and Geomembranes journal homepage: www.elsevier.com/locate/geotexmem
Behaviour of model footing resting on sand bed reinforced with multidirectional reinforcing elements M. Harikumar*, N. Sankar, S. Chandrakaran Department of Civil Engineering, National Institute of Technology, Calicut, Kerala, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 September 2015 Received in revised form 28 March 2016 Accepted 29 March 2016
Laboratory plate load tests are conducted on a model footing resting on sand bed reinforced with plastic multi-directional reinforcements. The bearing capacity, settlement and heave are evaluated and the effect of depth to first layer, spacing between reinforcements in a layer, number of layers and spacing between layers are investigated. The bearing capacity at 25 mm settlement improved by almost 1.3 times for a single layer of reinforcement, placed at an optimum depth of 0.5B. An increase in number of layers beyond four resulted in a reduction in improvement of bearing capacity. Four layers of reinforcement, spaced vertically apart at 0.5B resulted in a maximum increase of 185% in the bearing capacity. For the same area, the multi-directional reinforcing elements provide additional confinement to the soil mass due to the three dimensional projections, compared to the conventional geosynthetic reinforcements such as geogrids. Even while comparing the economic aspects, the multi-directional elements prove to be a viable alternative to the conventional planar geosynthetics. An artificial neural network based model has also been developed, which would aid the engineers to effectively predict the ultimate bearing capacity and settlements of the model footing, resting on reinforced sand, before these reinforcing elements are actually applied in the field. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Geosynthetics Bearing capacity Settlements Plate load test Multi-directional reinforcements Heave
1. Introduction The concept of mechanically stabilized earth has been widely used in various geotechnical applications such construction of embankments, pavements, bridge abutments, soft ground improvement and so on. Addition of reinforcements to soil have been performed by either incorporating continuous reinforcement inclusions such as sheet, bar or strip within a soil mass in a welldefined pattern, or by randomly mixing discrete fibres with a soil fill. The effect of the conventional geosynthetic reinforcements on soil has been extensively investigated.(Fleming et al., 2006; Iizuka et al., 2004; Katarzyna, 2006; Latha and Murthy, 2006; Park and Tan, 2005; Patra et al., 2005; Varuso et al., 2005; Yetimoglu et al., 2005; Abu-Farsakh et al., 2015 and Davarifard and Tafreshi, 2015). Planar geosynthetic reinforcement layers substantially improved the strength and deformation characteristics of cohesionless soils (Chandrasekaran et al., 1989; Haeri
* Corresponding author. E-mail address: [email protected] (M. Harikumar). http://dx.doi.org/10.1016/j.geotexmem.2016.03.008 0266-1144/© 2016 Elsevier Ltd. All rights reserved.
et al., 2000 and Venkatappa Rao et al., 2005; Tafreshi and Dawson, 2010a; Tafreshi and Dawson, 2010b). Randomly oriented discrete geosynthetic fibres improved the strength, stiffness and reduced the post peak loss of shear in sands (Gray and Ohashi, 1983; Gray and AI-Refeai, 1986; Al-Refeai, 1991; Ranjan et al., 1994; Kaniraj and Gayathri, 2003; Yetimoglu and Salbas, 2003 and Park and Tan, 2005). Geogrid layers incorporated in soil fills improved the bearing capacity and reduced soil settlements (Alamshahi and Hataf, 2009; Mosallanezhad et al., 2008; Ghazavi and Mirzaeifar, 2010; El Sawwaf and Nazir, 2010; El Sawwaf and Nazir, 2012; Shin and Das, 2000; Sitharam and Sireesh, 2012 and Zidan, 2012). The concept of three dimensional reinforcement was first introduced by Lawton et al. (1993), through laboratory investigations on sand reinforced with geo-jacks. Placing geo-jacks on top of geogrids substantially improved the performance of the soil bed. The combination of geogrid and geojacks performed better than the combination of geogrid and gravel. Zhang et al. (2008) investigated the use of three dimensional reinforcements in the form of rings with varying heights of vertical elements. In these investigations, the three dimensional elements were found to possess the inherent advantages of two dimensional
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reinforcements, along with the additional passive resistances introduced by the three dimensional components. In this paper, results from laboratory plate load tests conducted on square footing resting on sand bed reinforced with single and multiple layers of multi-directional reinforcements are presented, in order to determine the feasibility of using multi-directional reinforcements to improve the bearing capacity of soil and to investigate the significance of parameters such as volume ratio of reinforcements, depth to first layer, spacing between reinforcements in a layer, spacing between layers and number of layers. An empirical model using artificial neural network modelling is also described, using which a field engineer can predict the improvement in strength parameters of reinforced soil, before the reinforcing elements are actually applied in the field.
2. Test materials Fig. 1. Particle size distribution of sand used for the study.
2.1. Sand Locally available clean river sand obtained from the premises of NIT Calicut, Kerala, India was oven dried and was used for the present study. The engineering and index properties of sand used for the study are listed in Table 1. Under the USCS classification, sand is classified as poorly graded. The grain size distribution is described in Fig. 1.
2.2. Multi-directional reinforcements Reinforcing elements were manufactured from injection moulding of Acrylonitrile Butadiene Styrene (ABS) plastic granules. ABS is derived from acrylonitrile, butadiene, and styrene. Acrylonitrile is a synthetic monomer produced from propylene and ammonia; butadiene is a petroleum hydrocarbon obtained from the C4 fraction of steam cracking; styrene monomer is made by dehydrogenation of ethyl benzene, which is a hydrocarbon. ABS combines the strength and rigidity of acrylonitrile and styrene polymers with the toughness of polybutadiene rubber. ABS has superior properties in terms of hardness, gloss, toughness, and electrical insulation. The reinforcements consisted of four legs or protrusions in a single plane (xey) and two protrusions in plane perpendicular to this plane (z), with an average length of 30 mm and a diameter of 5 mm were used for the study, as shown in Fig. 2. The engineering properties of the reinforcing elements are explained in Table 2.
3. Test setup The test setup for laboratory plate load test consists of the following:
Table 1 Properties of sand used for the study. Soil Parameters
Value
USCS classification Minimum Density, kN/m3 Maximum Density, kN/m3 D10 D30 D60 Uniformity Coefficient, Cu Coefficient of curvature, Cc Angle of shearing resistance, 4
SP 12.75 15.7 0.25 0.38 0.5 2.0 1.15 37.4
a. Test tank of size 750 mm 750 mm 750 mm, made of mild steel sheets 1.5 mm thick and stiffened by horizontal and vertical bracings with mild steel angle sections on all faces. b. MS plate 150 mm 150 mm 25 mm c. Hydraulic jack, 50 kN capacity, with a ram diameter of 63 mm. d. Dial gauges, 30 mm travel with 0.01 mm sensitivity The test tank was fabricated keeping in mind the size of the model footing to be tested. As per Indian standards [IS:1888e1982], the width of the test tank should be five times the width of the model footing, to minimize scale effect. The sides and bottom of the tank were fabricated from 1.5 mm thick mild steel sheets. The sheets were screwed on to angle sections at the corners of the box structure. The box was stiffened by horizontal and vertical bracings to avoid yielding of the tank while being loaded, as shown in Fig. 3. The base of the plate was roughened by gluing on a thin layer of sand to it. A hand operated hydraulic jack of 50 kN capacity, abutting against a reaction frame was used to apply the required load to the system. 3.1. Preparation of test bed Sand was poured into the tank using raining technique. In order to achieve a desired relative density, the corresponding height of fall required was determined, by performing trials with varying heights of fall. The densities were determined, in each trial by using steel containers of known volume. From the values of maximum and minimum dry densities, the relative density was calculated, in each trial. A curve was plotted between the height of fall and relative density, from which the height of fall required for filling sand at any given relative density could be obtained. For all tests, the relative density was maintained at 65%, consistent with the previous experimental investigations using multi-directional inclusions performed by the same authors (Harikumar et al., 2015). The sand bed prepared in the test tank at different levels is shown in Fig. 4. 4. Reinforcement configuration The effect of parameters such as volume ratio of reinforcements, depth to first layer, intra and inter-layer between layers and number of layers are investigated in the test. Previous investigations conducted by Lee et al. (1999), Sitharam and Sireesh (2004), Bera et al. (2005) and Latha and Somwanshi (2009) on conventional
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Fig. 2. Multi-directional reinforcements.
Table 2 Properties of multi-directional reinforcements. Material
ABS plastic
Density Melting point Volume Mean length Mean diameter
0.997 g/cc 104 C 2914.4 mm3 30 mm 5 mm
where B is the width of the model footing. Considering a 2:1 distribution of a vertical load on the surface, the maximum width over which the load is distributed, even at a depth of 2B is 4B. Hence, in this investigation, the width of a reinforcement layer was fixed at 4B. The depth to the first layer of reinforcement is designated as u, the spacing between layers, as d and the spacing between multidirectional elements in a single layer, as s. B represents the plate width and b represents the width of the reinforcing elements. Ground displacements, both settlements and heave are represented by d. Initially, the multi-directional reinforcements were arranged in a single layer, with s/b ¼ 0. Since the width of reinforcement layers is confined to 4B, this configuration corresponds to a volume ratio of 0.3%. All reinforcement parameters are expressed in the form of dimensionless factors such as u/B, d/B, s/b and d/B. Fig. 5 explains the nomenclature used for the study. b ¼ width of reinforcing element B ¼ width of plate u ¼ depth to first layer d ¼ spacing between layers s ¼ spacing between reinforcing elements in a single layer N ¼ number of layers.
5. Test procedure Fig. 3. Horizontal and vertical stiffening of the model test tank.
geosynthetics indicate that an increase in the width of a reinforcement layer beyond 4B, had no substantial effect on the bearing capacity of soil. Additionally, the maximum depth of influence of a vertical load is governed by the depth of pressure bulb, equal to 2B,
Fig. 4. Preparation of test bed.
The inner faces of the test tank was made smooth to reduce the boundary effects. The height of fall required, corresponding to a relative density of 65% was calculated as discussed in the previous section. Sand was filled in layers of 50 mm thickness. The weight of sand required for each lift was predetermined and while filling, it was ensured that the calculated quantity was completely filled for each lift. The sand surface was levelled and the multi-directional inclusions were placed at the required depth. In order to ensure
Fig. 5. Arrangement of reinforcement layers.
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shown in Fig. 7b. Heave was measured on the left and right sides of the plate at a distance of 1B from the plate edge, by means of two dial gauges. 6. Testing program
Fig. 6. Test setup.
that the centers of the reinforcement layer, reaction frame and the tank coincide, a temporary formwork was fabricated, with inner dimensions of 600 mm 600 mm. The centre of this formwork was matched with the centre of the tank and the reaction frame. The reinforcements were then placed inside the formwork, which was later removed. At the top of sand layers, the plate was placed at the centre of the tank. The ram of the hydraulic jack was placed on top of the plate, the top of which abutted against the reaction frame. Two dial gauges were placed at diametrically opposite ends of the plate, in order to measure the settlement. The load applied was indirectly calculated from the pressure gauge attached to the hydraulic jack. The load was applied in small increments of 0.6 kN. As per IS:1888e1982, each increment of load was maintained until the rate of settlement, under this load appreciably reduced to a value of 0.02 mm/min. Along similar guidelines, the loading was continued until a settlement of 25 mm was attained. The test setup is described in Fig. 6. Reinforcements are placed inside formwork fabricated, as shown in Fig. 7a. The formwork is later removed and the next layer of sand placed over the reinforcing elements, as
The testing program commenced with the test on unreinforced sand bed. The tests on reinforced sand bed was categorized into three phases. Phase I involved the determination of optimum depth to the first layer of reinforcement. These tests were conducted using a single layer of reinforcement, with varying u/B. Once the optimum depth was fixed, Phase II was employed, which consisted of determining an optimum spacing between reinforcing elements, at the optimum depth. The reinforcements were placed in a single layer, at the optimum depth, at three different spacing of s/b ¼ 0, 1 and 1.5. Finally, Phase III involved determining the optimum number of layers of reinforcing elements. In this phase, the depth of first layer of reinforcements was kept at the optimum value, while the number of layers was varied from one to four, keeping the final layer of reinforcement at a depth of 2B, in all cases. Placing reinforcements beyond a depth of 2B was considered ineffective, as it was ineffective in improving the bearing capacity substantially (Latha and Somwanshi, 2009). The phases used for the test and the corresponding values of various parameters are shown in Table 3. 7. Results and discussion 7.1. Depth to first layer Typical pressure vs. settlement curves for the model footing on unreinforced and reinforced sand bed is shown Fig. 8. The tests correspond to Phase I, in which the multi-directional reinforcements are laid out in a mat-pattern, with an overall length and width of 4B (600 mm). The reinforcing elements were placed, close to each other, such that the spacing between them, s/b ¼ 0. This corresponds to a volume ratio of 0.3%.Each test was performed twice and the average of the settlement values was taken into consideration, to account for accuracy. It can be seen that placement of a single layer of reinforcement, too close to the surface (u/B ¼ 0.1), does not
Fig. 7. a) Temporary formwork arrangement and b) Placing reinforcing elements and filling with sand.
Table 3 Phases of tests used for the study. Phase
Variables
Values
Study on
I II III
u/B s/b N, d/B
0.1, 0.3, 0.5, 0.7 0, 0.5, 1 N ¼ 1, 2, 3, 4 and d/B ¼ 0, 1.5, 0.75, 0.5
Depth to first layer Spacing between reinforcing elements No of layers, spacing between layers
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M. Harikumar et al. / Geotextiles and Geomembranes 44 (2016) 568e578 Table 4 Test parameters for varying depth to first layer of reinforcement. Test parameter
BCR SRR Heave ratio
Fig. 8. Applied pressure vs. settlement for varying depth to first reinforcement layer.
improve the settlement response significantly. As the depth to first layer increases beyond 0.1B, the response improved considerably. This is because, at shallow depths of placement, the magnitude of mobilized frictional resistance at the sand-reinforcement interface is relatively less, due to the smaller overburden pressure. Placing the first reinforcement layer at a depth greater than 0.7B, had an adverse effect on bearing capacity and settlement values, since the settlements began to increase, although the values were better, compared to the settlement in unreinforced soil. This behaviour is due to increased thickness of sand layer over the reinforcements, resulting in higher settlement. The corresponding impact of depth of reinforcement on surface heave is shown in Fig. 9. Surface heave reduces with increasing depth of placement of reinforcement upto u/B ¼ 0.5, and thereafter decreases. The improvements in bearing capacity and settlement behaviour are quantified using three factors viz. bearing capacity ratio (BCR), Settlement reduction ratio (SRR) and Heave ratio (dx100/B). BCR is calculated as the ratio between the ultimate bearing capacity of reinforced sand to that of unreinforced sand. The ultimate bearing capacity in all cases, in the study is calculated, corresponding to a settlement of 25 mm.
SRR ¼
BCR, SRR and heave ratio at varying depth to first layer of reinforcement 0.1
0.3
0.5
0.7
1.03 0.06 2.38
1.25 0.59 1.99
1.3 0.72 2.17
1.24 0.67 2.58
su is the settlement of unreinforced sand bed at a given pressure and sr represents settlement of reinforced sand bed at the same pressure. Heave ratio is defined as the ratio between the maximum heave, observed at a distance of 1B from the edge of the plate for unreinforced sand bed to the maximum heave observed in reinforced sand bed. Table 4 shows the BCR and SRR for varying depth to first layer of reinforcement. Fig. 10 shows the variation in BCR corresponding to 25 mm settlement. For a single layer of reinforcement, the bearing capacity improved 1.3 times, corresponding at a depth of placement, 0.5B. Settlement reduction factor was calculated for various depths to first layer of reinforcement, as shown in Fig. 11. A maximum reduction of 0.72 was obtained corresponding to u/ B ¼ 0.5 with zero spacing between reinforcing elements. The variation of heave ratio with depth of first reinforcement layer is
su sr su
where,
Fig. 9. Applied pressure vs. surface heave for varying depth to first reinforcement layer.
Fig. 10. BCR corresponding to 25 mm settlement vs. depth to first layer of reinforcement.
Fig. 11. SRR vs depth to first layer of reinforcement.
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Fig. 12. Heave ratio vs. depth to first layer of reinforcement.
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Fig. 15. BCR at 25 mm settlement vs. Intra-layer spacing, s/B.
7.2. Spacing between reinforcing elements
Fig. 13. Ground displacement profile for varying u/B.
shown in Fig. 12. Similar to the trends observed, the maximum reduction in heave corresponds to a depth of 0.5B. It is worth noting that, the improvement in bearing capacities is only marginal due to the presence of a single layer of reinforcing inclusions alone. The actual mechanism of earth reinforcement by these inclusions can be considered to be a combination of a localized confining effect imparted to the sand bed between the reinforcing element layers and the frictional resistance between the 3D protrusions on the surface of the inclusions and sand. The general ground displacement profile in terms of settlement and heave with variation in depth of first reinforcement layer is described in Fig. 13.
The optimum depth of placement of the first layer of reinforcement was determined as 0.5B. The tests performed in Phase I, involved placing the reinforcing elements placed close to one another (s/b ¼ 0; b being the width of the reinforcing element). The next phase involved the determination of optimum spacing between the reinforcing elements. Two different configurations of reinforcement arrangement, viz. s/b ¼ 0.5 and s/b ¼ 1 were tested. The schematic of the different configurations are shown in Fig. 14. The variation of BCR, SRR and heave ratio corresponding to varying reinforcement spacing are described in Fig. 15, Fig. 16 and Fig. 17 respectively. As expected, placing the reinforcing elements close to one another, with zero spacing between them, accounts for maximum improvement in the strength parameters, on account of increased volume ratio of reinforcement, leading to an increased surface area of contact between inclusions and the sand bed. However, it is to be noted that the reduction in strength improvement, when the reinforcements are arranged at a spacing of s/ b ¼ 0.5 and s/b ¼ 1 is only marginal, as shown in Table 5. Considering the practical difficulties in placing the reinforcing elements one by one, at zero spacing between them in field applications, and the economic aspects of the project, the placement of reinforcements at a spacing of s/b ¼ 1, proves to be feasible. Thus, considering a balance between the strength improvement and the overall economic benefits, an intra-layer spacing of s/b ¼ 1 is adopted for the study. 7.3. Number of layers and spacing between layers In all tests conducted in this phase, the depth to first reinforcement layer is fixed at 0.5B. The number of reinforcement layers
Fig. 14. Schematic of reinforcement layout for: a) s ¼ 0b b) s ¼ 0.5b and c) s ¼ 1b
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M. Harikumar et al. / Geotextiles and Geomembranes 44 (2016) 568e578 Table 6 Reinforcement configuration.
Fig. 16. SRR vs. Inter layer spacing, s/b.
Fig. 17. Heave ratio for varying Intra layer spacing, s/b.
is varied from one to four, the final layer being kept at a depth of 2B. Between the layers at depths of 0.5B and 2B, the reinforcement layers were placed at equal spacing between them. The thickness of the reinforcing elements was around 0.2B. Hence, it was not possible to place the reinforcements at spacing less than 0.5B, due to practical difficulties in ensuring the correct placement of reinforcing elements and compaction of the sand above. Placing a layer above 0.5B depth was not considered in this phase, as the optimum depth for a single reinforcement layer was obtained as 0.5B. The configurations followed in Phase III are described in Table 6. The response of the model footing resting on sand bed with different number of reinforcing layers is shown in Fig. 18. The bearing capacity increased with an increase in number of reinforcing layers, coupled with a decrease in settlements. This is due to the ability of reinforcements to spread the superimposed load to larger depths, where the confining and overburden pressures are higher. However, the effect of an additional layer reduced with an
No. of layers
Depth to first layer (u/B)
Inter-layer spacing (d/B)
1 2 3 4
0.5 0.5 0.5 0.5
0 1.5 0.75 0.5
increase in the number of layers. Fig. 19 and Fig. 20 show the improvement in BCR and SRR with number of layers of reinforcement, respectively. It can be seen that as the number of layers increased from 2 to 3, a steep increase of about 45% was observed in BCR and SRR, whereas this improvement reduced to about 14% and 3% for BCR and SRR respectively, when the number of layers increased beyond 3. Similarly, the reduction in heave observed was about 10% when the number of layers increased from 2 to 3, and only 0.6% when the number of layers increased from 3 to 4, as shown in Fig. 21. Table 7 shows the bearing capacity ratios for the experimental phases, calculated for different settlement-footing width ratios. It can be seen that there is a considerable improvement in bearing capacities, even at lower s/B ratios of 5%, unlike the conventional geogrid reinforcements, which require a minimum initial strain, to effectively mobilize the frictional resistance at the sandreinforcement interface, thereby improving the bearing capacity. for reinforced earth applications. Since the tests are conducted on laboratory scale models, the effect of confinement and scaling play a significant role. Extensive large scale field studies are currently being conducted by the authors to determine the exact behaviour of multi-directional reinforcements. A comparison of the improvements in bearing capacities imparted by conventional geogrid reinforcements and the multidirectional elements developed in this study, under similar test conditions and soil properties is provided in Table 8. It can be seen that the multi-directional reinforcements perform on par with the conventional geosynthetic reinforcing systems. Additionally, for a given aerial coverage, the cost of manufacturing these elements is about 50% less, compared to the conventional reinforcements. However, the method is slightly labour-intensive as laying the reinforcing elements requires trained personnel. 7.4. Artificial neural network (ANN) modelling The formulation of a 3D finite element model for the present problem is quite challenging, since it involves modelling the individual 3D reinforcing elements, which is extremely difficult. Also,
Table 5 Test parameters for varying intra-layer spacing of reinforcements and u/B ¼ 0.5 Test parameter
BCR SRR Heave ratio
BCR, SRR and heave ratio at varying intra layer spacing (s/b) and u/B ¼ 0.5 0
0.5
1
1.297 0.72 2.17
1.27 0.68 3.92
1.24 0.55 3.97
Fig. 18. Applied pressure vs. settlement for varying number of layers.
M. Harikumar et al. / Geotextiles and Geomembranes 44 (2016) 568e578
Fig. 19. BCR vs. number of layers of reinforcement.
since the relationship between the experimental input and output parameters is quite complex, a more rational approach would be to create an empirical model, which can effectively predict the behaviour of the reinforced soil mass, under different conditions of tests. This can be achieved vide artificial neural networks. Neural network models were formulated using MATLAB, in order to predict the ultimate bearing capacity and settlement of a model square footing resting on a sand bed reinforced with multi-directional inclusions. The network was trained using gradient descent with momentum and adaptive learning rate backpropagation technique. The impact of test parameters such as, the depth to first layer of reinforcement, spacing between reinforcing elements in a layer, number of layers and spacing between layers have been analysed. Two ANN models were constructed: each consisting of 4 nodes in the input layer, 10 nodes in the hidden layer and a single node in the output layer. The configuration of the model is shown in Fig. 22.
7.5. Depth to first layer of reinforcement From the experimental results, it is known that the ultimate bearing capacity of the sand bed improved with the depth of placement of reinforcing layer, upto 0.5B and then decreased on further increasing the depth. Similarly, the maximum settlement undergone by the plate decreased with increasing depth of reinforcement layer upto about 0.5B, and then increased. The ANN model predicts the trend in variation of these parameters reasonably well, as shown in Fig. 23a and Fig. 23b.
575
Fig. 21. Heave ratio vs. number of layers of reinforcement.
7.6. Intra-layer spacing Arranging the reinforcing inclusions, at a spacing of s/b ¼ 0 resulted in a maximum improvement in the strength parameters. However, an increase in the intra-layer spacing, resulted in only a marginal variation in strength. The ANN model predicts this negligible variation in ultimate bearing capacity and maximum settlements, with increase in intra-layer spacing, almost exactly, as shown in Fig. 24a and Fig. 24b respectively. 7.7. Number of layers of reinforcing inclusions The ultimate bearing capacity increased with number of reinforcing layers. However, the rate of improvement reduced with increase in number of layers. Maximum improvements were
Table 7 BCR for different configurations under different s/B ratios. s/B, % u/B variable 0.1 0.3 0.5 0.7 s/b variable 0 1 N variable 2 3 4 5
5
10
15
20
30
1.07 1.4 1.55 1.52
1.03 1.31 1.39 1.36
1.03 1.27 1.31 1.26
1.03 1.24 1.26 1.21
1.02 1.19 1.24 1.17
1.55 1.39
1.39 1.26
1.31 1.24
1.26 e
1.24 e
1.48 1.83 1.96 1.99
1.27 1.63 1.76 1.77
1.26 1.49 1.69 1.86
e e e e
e e e e
Table 8 Comparison of improvement in bearing capacities from various studies.
Fig. 20. SRR vs number of layers of reinforcement.
Study
Geogrid aperture size (mm)
Phanikumar et al. (2009) Latha and Somwanshi (2009) Abu-Farsakh et al. (2015) Present study
6 30 25 30
6 30 25 30
Percentage improvement in ultimate bearing capacity with no of layers. 1
2
3
12 e e 29
18.5 60 42 92
29 92 47 71
576
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8. Conclusions
Depth to first layer
Ultimate bearing capacity
Intra-layer spacing Hidden layer No. of layers
Settlement
Inter-layer spacing Fig. 22. ANN hierarchy for plate load tests.
observed when the number of layers increased from two to three. Similarly, the maximum reduction in peak settlements were observed when the number of layers increased from two to three. The variation in the strength parameters, both measured and predicted is described in Fig. 25a and Fig. 25b. Overall, the ANN models predicted the ultimate bearing capacity and settlements, very close to the measured values, as seen in the aggregation of points near to the 450 line in Fig. 26a and Fig. 26b. The correlation coefficients for the bearing capacity model and settlement model are 0.97 and 0.93 respectively. The models were also effective in describing the general trend in the variation of the test parameters. Although the neural network model is developed based on the laboratory tests, the results show that if similar models are developed based on actual field tests, excellent results could be obtained.
Based on the results from experimental investigations on the behaviour of a model footing resting on sand bed reinforced with plastic multi-directional reinforcements, the following conclusions can be drawn: a. An appreciable increase in bearing capacity was observed as the depth to the first layer of reinforcement increased beyond 0.1B. The optimum depth of placement of the first layer was 0.5B. Placing reinforcements beyond 0.5B depth, in a single layer, resulted in a reduction in increase of bearing capacity. The bearing capacity increased by 1.3 times and the settlements reduced by almost 72%. b. Within a single layer of reinforcement, the maximum improvement in BCR was obtained corresponding to zero spacing between the inclusions. However, there was only a marginal decrease in BCR with an increase in intra-layer spacing. Hence, considering a balance between the strength improvement and economical aspects, an optimum spacing of 1b was adopted. BCR increased with increase in number of reinforcement layers. As the number of layers increased from 2 to 3, a steep increase of about 45% was observed in BCR, whereas this improvement reduced to about 14% when the number of layers increased beyond 3. SRR showed similar trends, the improvements being 43% and 3% respectively. A similar trend was observed, even for Heave ratio. c. Owing to the size of the reinforcing elements and the practical difficulties in laying and compacting sand layers between the
Fig. 23. BCR and maximum settlement vs. depth to first layer of reinforcement.
Fig. 24. Ultimate bearing capacity and maximum settlement vs. Intra-layer spacing, s/b.
M. Harikumar et al. / Geotextiles and Geomembranes 44 (2016) 568e578
577
Fig. 25. Ultimate bearing capacity vs. Number of reinforcement layers, N.
Fig. 26. Measured vs. Predicted ultimate bearing capacity and maximum settlement.
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