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Influence of relative density of soil on performance of fiber-reinforced soil foundations
Geotextiles and Geomembranes xxx (2017) 1e9
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Technical note
Influence of relative density of soil on performance of fiber-reinforced soil foundations Vaibhav Sharma*, Arvind Kumar Department of Civil Engineering, Dr. B R Ambedkar National Institute of Technology, Jalandhar 144011, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 October 2016 Received in revised form 6 June 2017 Accepted 9 June 2017 Available online xxx
An experimental study has been carried out for studying the influence of combinations of relative densities of two layered soil system. The model tests have been performed for the case of circular and ring footings resting on randomly distributed fiber reinforced sand (RDFS) layer overlying unreinforced sand bed. The influence of relative density on, different type of footings i.e. circular and ring (ri/ro ¼ 0.3, 0.4, 0.5, 0.6) footings; percentages of fiber in RDFS layer i.e. 0.5%, 0.75%, 1.00%, and 1.25%; and thickness of RDFS layer i.e. 0.5B, 0.75B, and 1.00B have been studied. Results have indicated that relative density, of both the RDFS layer as well as the bottom unreinforced sand layer, significantly influences the ultimate bearing capacity as well as the settlement. Improvement in terms of bearing capacity ratio (BCR) is more when top RDFS layer is compacted at 70% relative density with bottom unreinforced sand having 30% relative density. Moreover, in terms of settlement reduction, maximum improvement is observed when both the layers were compacted at 70% relative density. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Geosynthetics Relative density Ring footing Model tests Fibers Bearing capacity Settlement
1. Introduction Improving the engineering behavior of soil has been a major concern for geotechnical engineers ever since the introduction of ground improvement techniques. There are many ways to improve the engineering properties of soil like, incorporation of reinforcements into the soil (say: geosynthetics; metal strips; discrete fibers which can further be randomly distributed or aligned in the direction of planes of weak zone of soil), replacing the weak soil with strong soil up to significant depth, and/or densifying the weak soil up to significant depth or in other words increasing the relative density of soil. Ring shear tests were carried out on sand both for unreinforced and fiber reinforced under large shear strains. It was observed that denser samples behaved more efficiently in increasing and maintaining the ultimate shear strains (Consoli et al., 2007). Plate load tests were conducted on unreinforced and fiber reinforced sand at low, medium and dense relative density of sand, respectively. It was found out that the effect of fiber inclusion was more pronounced for higher relative densities. Moreover, higher relative density suppresses the
* Corresponding author. E-mail addresses: [email protected] (V. Sharma), agnihotriak@ nitj.ac.in (A. Kumar).
dilation which results in increase in effective stress and hence increases the strength and stiffness of the soil (Consoli et al., 2009). The influence of relative density of soil on the improvement in performance of geocell reinforcement by using model plate load tests was studied. It was concluded that for effective utilization of geocell reinforcement; the soil should be compacted to higher density (Dash, 2010). Many researchers in the past have improved the soil properties by the introduction of reinforcement elements in the soil strata. Out of the reinforcement elements, randomly distributed discrete inclusions have been the main attraction of researchers in the past few years. A very major advantage of fibers as reinforcement elements among the other types of reinforcements is that; there are no weak zones left in the soil strata as in the case of other types of reinforcements. Researchers (Al-Refeai, 1991; Freitag, 1986; Gray and Al-Refeai, 1986; Gray and Ohashi, 1983; Maher and Ho, 1993) started the initial testing on fiber-reinforced soil. The pressure-settlement and stress-strain behavior of fiber reinforced soil was compared by conducting model plate-load tests and triaxial tests, respectively. Both the pressure-settlement and stress-strain behavior was improved by the introduction of randomly distributed fibers in soil (Consoli et al., 2003). Numerical as well as experimental study was carried out to understand the influence of randomly distributed fiber inclusions in sand through
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Please cite this article in press as: Sharma, V., Kumar, A., Influence of relative density of soil on performance of fiber-reinforced soil foundations, Geotextiles and Geomembranes (2017), http://dx.doi.org/10.1016/j.geotexmem.2017.06.004
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V. Sharma, A. Kumar / Geotextiles and Geomembranes xxx (2017) 1e9
triaxial tests. Inclusion of fibers in the soil makes the stress concentrations more diffuse and restricts the formation of shear bands (Babu et al., 2008). Split tensile and unconfined compression tests were carried out to estimate the Mohr-Coulomb failure envelope of unreinforced and fiber reinforced artificially cemented sands (Consoli et al., 2013). In the recent past more studied were carried out on different types of geosynthetic inclusions to study their effect on geotechnical properties of soil (Ajayi et al., 2017; Chen et al., 2015; Choo et al., 2017; Consoli et al., 2017; Festugato et al., 2017; Harikumar et al., 2016; Huang, 2017; Khachan and Bhatia, 2016; Kumar and Gupta, 2016; Madhusudhan et al., 2017; Miranda Pino and Baudet, 2015; Sharma and Kumar, 2017). Researchers have studied the effect of ground improvement technique by conducting model as well as field plate load tests by using different types of reinforcements. Metal strips, bars, planar, 3-D (geocell) and fiber reinforcements are the major types of reinforcement elements, which are very useful in improving the bearing capacity of soil. Different shapes of footings have been considered in the past, but ring footings which are very useful for tall towers, silos, and chimney, etc. Have not gained much attention. Researchers (Egorov, 1965; Fisher, 1957) started working on studying the behavior of ring footings. Later field plate load tests were conducted on dense calcareous sand (Al-Sanad et al., 1993; Ismael, 1996) and concluded that circular and ring plates have same average pressure settlement curves. Other researchers (Hataf and Razavi, 2003; Laman and Yildiz, 2003; Naderi and Hataf, 2014; Ohri et al., 1997; Sawwaf and Nazir, 2012) conducted laboratory model tests on ring footings and reported that the optimum value (on the basis of ultimate bearing capacity) of radius ratio (ri/ro), for ring footing lies in the range of 0.2e0.4, where ri and ro are the internal and external radius of ring footing under consideration. Majority of the work, related to model tests on footings, has been carried out by considering a uniform relative density of soil (reinforced with geogrid/planar reinforcement) under the footing up to larger depths. Very limited efforts have been made in the past to study the behavior of model footings when placed as, (a) strong soil overlying weak soil or, (b) weak soil overlying strong soil (Brown and Meyerhof, 1971; Hanna and Meyerhof, 1979; Kumar et al., 2013; Kumar and Walia, 2006; Meyerhof, 1974; Michalowski and Shi, 1995). Moreover, no study has been carried out on ring footings resting on randomly distributed fiber reinforced sand. Considering these gaps in the literature, an effort has been made to study the behavior of ring and circular footings resting on randomly distributed fiber-reinforced sand. Moreover, three combinations of fiber-reinforced sand overlying unreinforced sand have been considered and they are; (a) top fiber-reinforced sand compacted at 50% RD, overlying sand compacted at 30% RD, (b) top fiber-reinforced sand compacted at70% RD and underlying sand compacted at 30% RD. and, (c) top fiber-reinforced sand compacted at70% RD and underlying sand compacted at 70% RD. Hence the aim of this paper is to study the effect of RD of sand, i.e., loose (30%), medium (50%) and dense (70%), on. Footing type i.e. circular, and ring footing with radius ratio (ri/ro) of 0.3, 0.4, 0.5, and 0.6; Different percentages of randomly distributed fibers, i.e. 0.5%, 0.75%, 1.00%, and 1.25% by dry weight of sand; Different thicknesses (h1) of fiber-reinforced sand layer, i.e., 0.5B, 0.75B, and 1.0B, where B is the outer diameter for ring, or, diameter for circular footing. Moreover a numerical example has been solved, for the better understanding of the readers by clearly highlighting the influence of relative density, fiber percentage, and thickness of RDFS layer.
2. Test material Sand used in the model testing was obtained from Nasrala, Punjab, India. According to Unified Soil Classification System, the sand was classified as poorly graded, SP. Specific gravity (Gs) of sand was found out to be 2.65. The maximum and minimum dry unit weights of sand were found out to be 16.8 kN/m3 and 13.6 kN/m3, respectively, and the corresponding values of minimum and maximum void ratios were 0.56 and 0.93, respectively. The effective size (D10), mean size (D50), coefficient of curvature (Cc) and coefficient of uniformity (Cu) for the sand were 0.150 mm, 0.290 mm, 0.97 and 2.21, respectively. Fibers used as a reinforcing element for sand in the model testing were macro-synthetic and non-corrosive fibers as shown in Fig. 2. For the effective anchoring of the fibers into the sand matrix they have an engineered contoured profile which enhances its performance. Physical and chemical properties of fibers are presented in Table 1. 2.1. Experimental setup and test program Total 190 model plate load tests were carried out as shown in Table 2. A testing-cum-loading frame assembly was used for conducting model tests. The soil bed was prepared in a testing tank with inside dimensions of 1.5 m long, 1.5 m wide and 1 m deep. The model footings were made from mild steel, and were corrected to the desired size, thickness (25 mm) and shape (ring and circular). One circular footing and four ring footings were used in this study. Diameter for circular footing was 0.3 m and, the ratio of inner radius to outer radius of ring footings (ri/ro) of 0.3, 0.4, 0.5, and 0.6, were used in the study by keeping the outer diameter of ring to be constant i.e. 0.3 m. The footing was loaded until the failure (large uniform settlement corresponding to very small increment in load) or fully extended manually operated hydraulic jack. Two 0.01 mm sensitivity dial gauges were placed on either and opposite side of the footing to calculate settlement for every equal increment of load. It was not possible to place hydraulic jack directly on ring footings because it will slip through the opening of the ring footings. So, in order to avoid this, first a loading platform was placed on ring footing followed by the hydraulic jack. Then loading of ring footing was possible. Test setup and detail of loading platform is shown in Fig. 1. 2.2. Preparation of bed and test procedure Bed consists of two layers of sand as shown in Fig. 1. First, bottom unreinforced sand layer is filled, by using sand raining technique, at a known and desired density followed by leveling after reaching desired height. Second, top randomly distributed fiber reinforced sand (RDFS) layer was filled. For laying top RDFS layer, first dry weight of fibers and sand was calculated using equation (1), and (2). This means that fibers were added as a replacement of sand.
WRDFS ¼ V gRDFS
(1)
WRDFS ¼ Ws þ Wf ¼ ps WRDFS þ pf WRDFS
(2)
where, WRDFS, Ws, and Wf is dry weight of, RDFS layer, sand and, fibers, respectively; gRDFS is dry unit weight of RDFS layer; V is the total volume of RDFS layer to be placed; ps and pf are the percentages of sand and fibers in RDFS layer, respectively. For the preparation of RDFS layer, sand and fibers were hand
Please cite this article in press as: Sharma, V., Kumar, A., Influence of relative density of soil on performance of fiber-reinforced soil foundations, Geotextiles and Geomembranes (2017), http://dx.doi.org/10.1016/j.geotexmem.2017.06.004
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3
Table 1 Chemical and physical properties of fibers. Fiber length Type Absorption Specific gravity (Gf) Electrical conductivity Tensile strength (N/mm2) Diameter (mm)
45 mm Macro Nil 0.91 Low 400 0.95
Acid and salt resistance Ignition point Melt point Thermal conductivity Alkali resistance Elastic modulus (N/mm2) Shape
High >550 c (1022 F) 164 c (328 F) Low Alkali proof 7000 Continuously deformed
Table 2 Test plan. Series
Condition
h1/B
*RD1 (%)
*RD2 (%)
Fiber content (%)
Footing type (ri/ro)
Number of tests
I II III IV V
Sand only Sand only RDFS RDFS RDFS
0 0 0.5, 0.75, 1.0 0.5, 0.75, 1.0 0.5, 0.75, 1.0
30 70 50 70 70
30 70 30 30 70
0 0 0.5, 0.75, 1.0, 1.25 0.5, 0.75, 1.0, 1.25 0.5, 0.75, 1.0, 1.25
0, 0, 0, 0, 0,
5 5 60 60 60
Total tests
0.3, 0.3, 0.3, 0.3, 0.3,
0.4, 0.4, 0.4, 0.4, 0.4,
0.5, 0.5, 0.5, 0.5, 0.5,
0.6 0.6 0.6 0.6 0.6
190
NOTE: * For details refer Fig. 1.
Fig. 1. Testing setup and assembly.
mixed. The RDFS layer was filled in equal shifts of 100 mm and compacted. Fibers were mixed randomly in each layer manually in order to achieve homogeneity of the sand-fiber mix. Tank's inner walls were marked so as to ensure the thickness of layers. Random distribution of fibers and obtaining a homogeneous fiber-sand mix is difficult to achieve because there are chances of segregation, which is due to the different specific gravities of both, fiber and sand. So, to minimize this problem, dry fibers (calculated as explained before) were soaked in water before adding to sand for mixing. This was done in order to make them wet, which in turn coats fiber with thin layer of water. They were then transferred to
sieves so that the excess water gets removed and then transferred to the sand for mixing. Each layer of RDFS was compacted using a wooden rammer so that the layer achieves desired thickness. After filling of RDFS layer, it was leveled. Footing was centered carefully, so that the loading should be concentric. Then loading platform was placed over the footing (in case of ring footing), centered, and followed by the placing of hydraulic jack over it as shown in Fig. 1. Two sensitive dial gauges were placed on either and opposite side of the footing to measure the settlement. Then equal load increment was applied through manually operated hydraulic jack.
Please cite this article in press as: Sharma, V., Kumar, A., Influence of relative density of soil on performance of fiber-reinforced soil foundations, Geotextiles and Geomembranes (2017), http://dx.doi.org/10.1016/j.geotexmem.2017.06.004
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V. Sharma, A. Kumar / Geotextiles and Geomembranes xxx (2017) 1e9
equations (3) and (4), and are as follows: 3.1. Effect of relative density on different types of footing
Fig. 2. Fibers used.
3. Results and discussions The influence of relative density in the performance of RDFS layer overlying unreinforced sand bed was studied by using two non-dimensional factors as: 1. Improvement in ultimate bearing capacity (BCR: bearing capacity ratio), which compares the bearing capacity of circular footing resting on unreinforced sand to that of bearing capacity of given footing resting on RDFS layer overlying sand. It is defined in Equation (3). 2. Improvement in settlement (SR: settlement reduction), which compares the settlement, of circular footing resting on unreinforced sand with settlement of given footing resting on RDFS layer overlying sand, corresponding to the ultimate bearing capacity obtained. It is defined in Equation (4).
BCR ¼
SR ¼
Figs. 3 and 4 show the pressure settlement curves for different, combinations of relative densities of top and bottom layers, and types of footings, respectively. From Fig. 3, it can be inferred that the ultimate bearing capacity increases as the top layer of sand, mixed with randomly distributed fibers, gets compacted to higher relative density. When RD1 is 50% and RD2 is 30%, the ultimate bearing capacity of circular, and ring footing (ri/ro ¼ 0.40) is 500 and 568 kN/m2, respectively. When RD1 is compacted to a higher relative density of 70% and keeping the RD2 constant at 30%, the ultimate bearing capacity of circular, and ring (ri/ro ¼ 0.40) footing is increased to 528 and 605 kN/m2, respectively. Fig. 6 shows that as radius ratio (ri/ro) increases from 0 to 0.4, ultimate bearing capacity increases, and then on increasing radius ratio beyond 0.4, ultimate bearing capacity decreases. When radius ratio is 0, 0.3, 0.4, 0.5, and 0.6, the corresponding ultimate bearing capacity values were 555, 600, 655, 540, and 505 kN/m2, respectively. Similarly, the settlement values were 17.5, 15, 10.5, 16.5, and 16.5 mm, respectively. Fig. 5 shows the variation of BCR, and SR, with radius ratio for different combinations of relative densities of top and bottom layers of sand, respectively. It can be inferred from Fig. 5, that there exists an optimum value of ri/ro ¼ 0.4, both in the terms of BCR and SR at all combinations of relative densities of top and bottom layers of sand, where performance is maximum. From Fig. 5, it can be inferred that as the radius ratio is increased, the BCR first increases upto radius ratio of 0.4, and on further increasing this value, the BCR value starts decreasing. Experimental study on ring footings resting on geogrid reinforced sand was carried out and found out that for radius ratio of 0.4, optimum behavior of ring footing was observed. This behavior of ring footing is due to the interference effect of ring footing's internal diameter (Sawwaf and Nazir, 2012). Whenever a footing (placed over soil) is loaded three zones gets
UBC of given footing resting over RDFS layer overlying unreinforced sand at their respective relative densities UBC of circular footing resting over unreinforced sand at relative density same as that of the bottom layer
Settlement of given footing resting over RDFS layer overlying unreinforced sand at their respective relative densities Settlement of circular footing resting over unreinforced sand at relative density same as that of the bottom layer
From Fig. 1 as shown in test setup, it can be seen that there are two layers of sand. Top layer is of RDFS with relative density as RD1, and bottom unreinforced layer with relative density as RD2. So there are different series of tests that have been considered for the study and can be referred from Table 2. For calculating the value of BCR and SR for series III and IV, the RD of denominator term in equations (3) and (4) is 30%, and for series V, it has been taken as 70%. In this paper, UBC was obtained by using tangent intersection method. In this method initial linear portion of pressure settlement curve is extended and final linear portion is extended backward, so that both extended lines intersect at a point. Pressure corresponding to this intersection point is taken as ultimate bearing capacity. Effect of relative density on different types of footings, percentage of fibers and thickness of fiber reinforced sand layer has been studied using the improvement factors as explained in
(3)
(4)
developed under it. These are zone I (remains in elastic equilibrium and moves with the footing), zone II (radial shear zone, which pushes the zone III), and zone III (rankine's passive zone) (Terzaghi, 1943). As the footing advances in downward direction, zone II pushes zone III outwards. As this case is similar to the interference effect of closely spaced footings, zone III from both the interfering footings gets intersected, which further causes the arching of the soil in zone III, and helps in improving bearing pressure. This effect is found to be limited up to radius ratio of 0.4; thereafter on further increasing the radius ratio, no arching of soil takes place. Fig. 5 shows that as the top layer of RDFS is compacted at 50% relative density and bottom layer at 30% relative density, then BCR value is 5, and 5.68, for circular and ring (ri/ro ¼ 0.40) footing, respectively. And when the top RDFS layer is compacted at even higher relative density of 70% by keeping the bottom layer compacted at 30% relative density, the BCR value has increased to 5.28,
Please cite this article in press as: Sharma, V., Kumar, A., Influence of relative density of soil on performance of fiber-reinforced soil foundations, Geotextiles and Geomembranes (2017), http://dx.doi.org/10.1016/j.geotexmem.2017.06.004
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0
100
200
Pressure (kN/m2) 300 400 500
600
1% fiber; h1/B = 1.0
20
40
40
60
RD1 = 50%; RD2 = 30%
80
RD1 = 70%; RD2 = 30%
100
RD1 = 70%; RD2 = 70%
140
100
200
Pressure (kN/m2) 300 400 500
Settlement (mm)
600
700
800
RD1 = 70%, RD2 = 70% 1% fiber; h1/B = 1.0
20 40 60
120 140
100
ri/ro = 0.4
0
100
80
120
Fig. 3. Pressure settlement curve for different combinations of relative densities.
80
60
ri/ro = 0
140
0
ri/ro = 0 ri/ro = 0.3 ri/ro = 0.4 ri/ro = 0.5 ri/ro = 0.6 Fig. 4. Pressure settlement curve for different types of footings.
0.9
7 1% fiber; h1/B = 1.0
0.8
6
0.7
5
100
200
Pressure (kN/m2) 300 400 500
0
20
120
600
700
800
RD1 = 70%, RD2 = 70% h1/B = 1.0
0% fiber 0.50% fiber 0.75% fiber 1.00% fiber 1.25% fiber ri/ro = 0 ri/ro = 0.4 Fig. 6. Pressure settlement curve for different percentages of fibers.
term in denominator for series III and IV in Table 2. On the other hand, if the ultimate bearing capacity is compared instead of BCR for the same case it will be more and increasing with the increase in relative density. The ultimate bearing capacity increases from 518 to 555 kN/m2, and 608e655 kN/m2, for circular and ring footing (ri/ ro ¼ 0.4), respectively for the case when relative density of both layers is increased from 50% to 70%. Fig. 5 shows that as the top RDFS layer is compacted at relative density of 50% and bottom layer at 30% relative density, the SR value is 0.53 for ring footing (ri/ro ¼ 0.40). And when the top RDFS layer is compacted at higher relative density of 70%, by compacting the bottom layer at 30%, the SR value decreases to 0.43, for ring footing (ri/ro ¼ 0.4). Similarly, when both the top RDFS and lower unreinforced sand layers were compacted to same relative density i.e. 50%, then SR value is 0.26 for ring footing (ri/ro ¼ 0.40). Moreover, increasing the relative density of both the layers to 70%, the SR value decreases to 0.23, for ring footing (ri/ro ¼ 0.4). Maximum improvement in terms of SR has been observed when the relative densities of both the top RDFS layer as well as lower unreinforced sand layer were compacted at same and higher relative density (70%).
0.6
4
0.5
3
0.4
SR
BCR
0
800
Settlement (mm)
Settlement (mm)
0
700
5
0.3
2 1
RD1 = 50%; RD2 = 30%
RD1 = 70%; RD2 = 30%
0.2
RD1 = 70%; RD2 = 70%
BCR
0.1
SR
0 0
0.1
0 0.2
0.3
ri/ro
0.4
0.5
0.6
0.7
Fig. 5. Variation of BCR and SR with ri/ro.
and 6.05, for circular and ring (ri/ro ¼ 0.40) footing, respectively. Similarly, when both the top RDFS and bottom unreinforced sand layers were compacted to same relative density of 50%, then BCR value is 2.78, and 3.27, for circular and ring (ri/ro ¼ 0.40) footing, respectively. Furthermore, increasing these relative densities to 70%, the BCR value decreases to 2.47, and 2.91, for circular and ring footing (ri/ro ¼ 0.4), respectively. This shows that more improvement is observed when the bottom sand layer has lesser relative density as that of the top RDFS layer, rather than having same relative density as that of the top RDFS layer. The lesser and decreasing values of BCR is because of the fact that, the value of denominator in equation (3) is more as compared to the value of
3.2. Effect of relative density on fiber content Fig. 6 shows the pressure settlement curves for different percentages of fibers. From Fig. 7, it can be inferred that as the percentage of fibers in sand is increased, there is an increase in ultimate bearing capacity. It also shows that the pressure settlement curves for ring footings (ri/ro ¼ 0.4) are above the circular footing for same conditions. When percentage of fiber is increased from 0 to 1.25%, the ultimate bearing capacity gets increased from 225 to 575 kN/m2, and 275e670 kN/m2, for circular and ring footings (ri/ro ¼ 0.4), respectively. Similarly settlement has decreased from 45 to 15 mm, and 40 to 9 mm, for circular and ring footing (ri/ro ¼ 0.4), respectively. Fig. 7 shows the variation of BCR, and SR, with different percentages of fibers for different combinations of relative densities of top RDFS and bottom sand layer, respectively. From Fig. 7, it can be seen that as the percentage of fibers is increased from 0.50 to 1.25%, BCR value increases both for circular as well as for ring footings (ri/ ro ¼ 0.40). For RD1 ¼ 50%; RD2 ¼ 30%; when percentage of fibers is increased from 0.5 to 1.25%, the BCR value for circular and ring footing (ri/ro ¼ 0.40) gets increased from 4.18 to 5.25, and 5.15 to 6.00, respectively. Similarly for RD1 ¼ 70%; RD2 ¼ 30%; the BCR value was found out to be increased from, 4.43 to5.48, and 5.40 to 6.35, respectively; For RD1 ¼ 70%; RD2 ¼ 70%, the BCR value increases from 2.04 to 2.56, and 2.58 to 2.98, respectively. Moreover,
Please cite this article in press as: Sharma, V., Kumar, A., Influence of relative density of soil on performance of fiber-reinforced soil foundations, Geotextiles and Geomembranes (2017), http://dx.doi.org/10.1016/j.geotexmem.2017.06.004
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1
6.8
0
5.8
2.8
0.8 -0.2 0.25
RD1 = 50%; RD2 = 30% RD1 = 70%; RD2 = 30% RD1 = 70%; RD2 = 70% ri/ro = 0 ri/ro = 0.4 0.5
0.2
Note: 1. BCR values are shown by line joining empty markers. 0 2. SR values are shown by line joining filled markers. -0.2 0.75 1 1.25 1.5 Fiber content (%)
600
700
800
RD1 = 70%, RD2 = 70% 1% fiber
40 Settlement (mm)
SR
BCR
3.8
1.8
Pressure (kN/m2) 300 400 500
20
0.6 0.4
200
0
0.8
4.8
100
60 80 100
h1/B = 0.5 h1/B = 0.75
120
h1/B = 1.0
140
ri/ro = 0
160
Fig. 7. Variation of BCR and SR with fiber content, for h1/B ¼ 1.0.
h1/B = 0
ri/ro = 0.4
Fig. 8. Pressure settlement curve for different thicknesses of RDFS layers.
3.3. Effect of relative density on thicknesses of RDFS layer Fig. 8 shows the pressure settlement curves for different thicknesses of top RDFS layers for circular and ring footing (ri/ro ¼ 0.40). It can be inferred from Fig. 8 that as the value of h1/B increases, the ultimate bearing capacity for both the circular and ring footing increases. When h1/B increases from 0 to 1.00, the ultimate bearing capacity of circular, and ring footing increases from 225 to 555 kN/ m2, and 275e655 kN/m2, respectively. Fig. 9 shows the variation of BCR with h1/B, for circular and ring footing, for all combinations of relative densities of top RDFS and bottom sand layer. From Fig. 9, it can be inferred that as the thickness of top RDFS layer increases, the corresponding BCR value increases. Improvement in terms of BCR is more when top RDFS and bottom sand layer has different relative densities, instead of having
7
0.8
6
0.7 0.6
5
0.5
4
0.4 3 2 1
SR
BCR
ring footing (ri/ro ¼ 0.4) was found out to be performing better than the circular footing at all combinations of relative densities of top RDFS and bottom sand layer. Furthermore, when RD1 ¼ 50% and RD2 ¼ 30%, 1.25% fiber content and h1/B ¼ 1.00; the BCR value is 5.25, and 6.00 for circular, and ring (ri/ro ¼ 0.4) footing, respectively. And when RD1 is compacted at higher relative density of 70% and RD2 ¼ 30%, 1% fiber content and h1/B ¼ 1.00; the BCR value has increased to 5.28, and 6.05, for circular, and ring (ri/ro ¼ 0.4) footing, respectively. This means that compacting the top RDFS layer to higher density, keeping its thickness constant; the consumption of fibers can be reduced to 1.00% from 1.25%. From Fig. 7, it can be inferred that as the percentage of fibers increased from 0.50 to 1.25%, there is an improvement in terms of settlement reduction, both for circular as well as ring footing (ri/ ro ¼ 0.40), for all the combinations of relative densities of top RDFS and bottom sand layer. For RD1 ¼ 50%; RD2 ¼ 30%; when percentage of fibers is increased from 0.5 to 1.25%, the SR value for circular and ring footing (ri/ro ¼ 0.40) gets decreased from 0.85 to 0.68, and 0.73 to 0.46, respectively. Similarly for RD1 ¼ 70%; RD2 ¼ 30%; the SR value decreases from, 0.69 to 0.41, and 0.60 to 0.36, respectively; For RD1 ¼ 70%; RD2 ¼ 70%, the SR value decreases from 0.49 to 0.33, and 0.44 to 0.22, respectively. Furthermore, improvement in terms of settlement was found to be maximum, when both the top RDFS and bottom sand layers were compacted to 70% relative density. Moreover, when RD1 ¼ 50% and RD2 ¼ 30%, 1.25% fiber content and h1/B ¼ 1.00; the SR value is 0.68, and 0.46 for circular, and ring (ri/ro ¼ 0.4) footing, respectively. And when RD1 is compacted at higher relative density of 70% and RD2 ¼ 30%, 1% fiber content and h1/B ¼ 1.00; the SR value has improved to 0.54, and 0.43, for circular, and ring (ri/ro ¼ 0.4) footing, respectively.
0.3 RD1 = 50%; RD2 = 30% RD1 = 70%; RD2 = 30% RD1 = 70%; RD2 = 70% ri/ro = 0 ri/ro = 0.4
Note: 1. BCR values are shown by line joiningempty markers. 2. SR values are shown by line joining filled markers.
0 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 h1/B
0.2 0.1 0
1
1.05 1.1
Fig. 9. Variation of BCR and SR with h1/B at 1% fiber content.
same relative densities. For RD1 ¼ 50%; RD2 ¼ 30%; when the thickness of RDFS layer is increased from 0.5B to 1.0B (where B is the diameter of circular and outer diameter of ring footing), the BCR value for circular and ring footing (ri/ro ¼ 0.40) gets increased from 3.98 to 5.00, and 4.80 to 5.68, respectively. Similarly for RD1 ¼ 70%; RD2 ¼ 30%; the BCR value was found out to be increased from, 4.35 to 5.28, and 5.19 to 6.05, respectively For RD1 ¼ 70%; RD2 ¼ 70%, the BCR value increases from 2.22 to 2.47, and 2.60 to 2.91, respectively. Moreover when RD1 ¼ 50% and RD2 ¼ 30%, 1.00% fiber content and h1/B ¼ 1.00; the BCR value is 5, and 5.68 for circular, and ring (ri/ro ¼ 0.4) footing, respectively. And when RD1 is compacted at higher relative density of 70% and RD2 ¼ 30%, 1% fiber content and h1/B ¼ 0.75; the BCR value is 4.7, and 5.00, for circular, and ring (ri/ ro ¼ 0.4) footing, respectively. This means that compacting the top RDFS layer to higher density, keeping the fiber content constant; the majority of improvement has been obtained when thickness of RDFS layer is lesser that 1.00B. Fig. 9 shows the variation of SR with h1/B, for circular and ring footing for all the combinations of relative densities of top RDFS and bottom sand layer. From Fig. 9, it can be found out that as the thickness of top RDFS layer increases, the corresponding SR value increases. For RD1 ¼ 50%; RD2 ¼ 30%; when the thickness of RDFS layer is increased from 0.5B to 1.0B (where B is the diameter of circular and outer diameter of ring footing), the SR value for circular, and ring footing (ri/ro ¼ 0.40) gets decreased from 0.75 to 0.73, and 0.60 to 0.53, respectively. Similarly for RD1 ¼ 70%; RD2 ¼ 30%; the BCR value was found out to be decreasing from, 0.68 to 0.54, and 0.48 to 0.43, respectively; For RD1 ¼ 70%; RD2 ¼ 70%, the BCR value decreasing from 0.51 to 0.39, and 0.38 to 0.23,
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respectively. Maximum improvement in terms of settlement was found out, when both the top RDFS and bottom sand layer was compacted to 70% relative density. Moreover when RD1 ¼ 50% and RD2 ¼ 30%, 1.00% fiber content and h1/B ¼ 1.00; the SR value is 0.73, and 0.53 for circular, and ring (ri/ro ¼ 0.4) footing, respectively. And when sand with RD1 is compacted at higher relative density of 70% and RD2 ¼ 30%, 1% fiber content and h1/B ¼ 0.75; the SR value has improved to 0.56, and 0.46, for circular, and ring (ri/ro ¼ 0.4) footing, respectively.
favg ¼ tan1
7
fðtan f1 Þ h1 g þ ðtan f2 Þ h2 h1 þ h2
(5)
cavg ¼
ðc1 h1 Þ þ ðc2 h2 Þ h1 þ h1
(6)
gavg ¼
ðg1 h1 Þ þ ðg2 h2 Þ h1 þ h1
(7)
Table 3 shows the values of angle of internal friction, cohesion, and soil unit weight used in this problem.
4. Numerical problem Statement:
Shear criterion:
Fig. 10 shows the data obtained from a plate load tests conducted on a circular footing, of 0.3 m diameter, when placed on the surface. Determine the allowable load on a 3 m diameter circular foundation, if the permissible settlement of foundation is 20 mm and factor of safety against shear failure is 3. Five tests were carried out on different combinations with top layer (reinforced/unreinforced) of thickness 1B at relative density RD1 and bottom sand layer at relative density RD2. In reinforced layer, the fiber percentage is 1%.
For shear failure criterion, the equations used to calculate the ultimate, and safe bearing capacity (Terzaghi, 1943) are shown in Eqns. (8) and (9), respectively.
qu ¼ 1:2cavg Nc þ qNq þ 0:3gavg BNg qns ¼
(8)
qu F
(9)
where, Nc, Nq, and Ng are the bearing capacity factors (Terzaghi, 1943), and F is the factor of safety against shear failure (taken as 3 in this example).
Solution: Settlement criterion: As it is the case of two layered soil, in which top layer is reinforced with randomly distributed fibers and the bottom layer is unreinforced. So, the average value of angle of internal friction, soil cohesion, and soil unit weight is considered using Eqns. (5)e(7), (Bowles, 1997).
0
100
200
Pressure (kN/m2) 300 400
500
600
0 For RDFS h1/B = 1; fiber = 1%
20
Settlement (mm)
40
80 100 120 140 160
3 2 2 Bp Bf þ 30 5 Sp ¼ 4 Bf Bp þ 30
(10)
After calculating safe bearing capacity from both the criterions, lower of the two is reported as the safe bearing capacity, and multiplying this value with the area of the actual foundation, allowable load is calculated. Table 4 shows the results of the numerical problem. It clearly shows the significance of relative density on the ultimate bearing capacity of RDFS sand layer overlying unreinforced sand layer.
RD1 = 50%; RD2 = 30% RD1 = 70%; RD2 = 30% 30% RD (Unreinforced) RD1 = 50%; RD2 = 30% (Unreinforced) RD1 = 70%; RD2 = 30% (Unreinforced)
60
For settlement criterion, Eqn. (10) (Terzaghi and Peck, 1948), is used to calculate the settlement of test plate from the corresponding pressure settlement curve, after knowing the dimensions of actual foundation. After calculating the settlement of test plate, corresponding bearing capacity is noted down from the pressure settlement curve and designated (extrapolated) as safe bearing capacity of actual foundation.
5. Conclusions
Fig. 10. Pressure settlement curves.
An experimental study has been under taken to study the
Table 3 Parameters used in the numerical problem. Cohesion (kN/m2)
Combination of RD (%) RD1
RD2
f1
f2
c1
c2
g1
g2
RDFS
50 70 30 50 70
30 30 30 30 30
34 38 29 32 36.5
29 29 29 29 29
10 16 0 0 0
0 0 0 0 0
15.1 15.7 14.4 15.1 15.7
14.4 14.4 14.4 14.1 15.4
Unreinforced
Angle of internal friction (degree)
Soil unit weight (kN/m2)
Condition
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V. Sharma, A. Kumar / Geotextiles and Geomembranes xxx (2017) 1e9
Table 4 Results of numerical problem. S. No.
1 2 3
RD1
30 50 70
RD2
30 30 30
Safe bearing capacity ¼ qns (kN/m2)
Qallowable (kN)
Shear criterion
Settlement criterion
RDFS
Sand only
RDFS
Sand only
RDFS
Sand only
e 191.34 297.5
76.46 93.1 122.81
e 215 255
40 70 91
e 1352.5 1802.5
282.74 494.8 643.24
ultimate bearing capacity and settlement behavior, of circular and ring footings resting on RDFS layer overlying unreinforced sand layer, with different combinations of relative densities of top RDFS, and bottom unreinforced sand layers. The following conclusions can be drawn from the results discussed. Increasing the relative density of sand results in increase in the ultimate bearing capacity as well as there is improvement in settlement reduction. Maximum improvement in terms of BCR was observed when top RDFS and bottom sand layers were compacted to different relative densities instead of having same relative density i.e. RD1 ¼ 70% and RD2 ¼ 30%. Maximum improvement, in terms of BCR and SR, was observed when, ri/ro ¼ 0.40 for all combinations of relative densities of top RDFS and bottom unreinforced sand layer. When RD1 ¼ 70% and RD2 ¼ 30%; h1/B ¼ 1.00, and 1.25% fiber; BCR value, of circular, and ring footing (ri/ro ¼ 0.40), is 5.48, and 6.35, respectively. Similarly, when RD1 ¼ 70% and RD2 ¼ 30%; h1/B ¼ 1.00, and 1.25% fiber; SR value, of circular, and ring footing (ri/ro ¼ 0.40), is 0.33, and 0.20, respectively. On increasing the percentage of fibers in RDFS layer, both BCR and SR values have improved. When RD1 ¼ 70% and RD2 ¼ 30%; h1/B ¼ 1.00, and fiber prcentage is increased from 0.5 to 1.25%; BCR value, of ring footing (ri/ro ¼ 0.40), gets improved from 5.40 to 6.35. When RD1 ¼ 70% and RD2 ¼ 30%; h1/B ¼ 1.00, and fiber percentage is increased from 0.5 to 1.25%; SR value, of ring footing (ri/ro ¼ 0.40), gets improved from 0.44 to 0.20. Compacting the top RDFS layer to higher relative density (70%) compared to lesser relative density (50%) by keeping the lower layer compacted at 30% relative density and the thickness of RDFS constant (1.00B); consumption of fibers can be reduced to 1% from 1.25%. Increasing the thickness of RDFS layer significantly increases the improvement both in terms of BCR and SR, for all combinations of relative densities of top RDFS layer and bottom sand layer. When RD1 ¼ 70% and RD2 ¼ 30%; 1% fiber, and h1/B increased from 0.50 to 1.00; BCR value, for ring footing (ri/ro ¼ 0.40), gets improved from 5.19 to 6.05. When RD1 ¼ 70% and RD2 ¼ 70%; 1% fiber, and h1/B increased from 0.50 to 1.00; SR value gets improved from 0.38 to 0.23. Notation The following symbols are used in this paper: B Bp, Bf Cc Cu c1, c2 D10
width of footing width of plate, and foundation, respectively; and coefficient of curvature coefficient of uniformity cohesion of top RDFS, and bottom unreinforced sand layer, respectively effective size of sand
D50 Gs, Gf h1, h2
mean size of sand specific gravities of sand, and fibers respectively thickness of top RDFS, and bottom unreinforced sand layer, respectively pf percentage of fiber in randomly distributed fiber reinforced sand layer ps percentage of sand in randomly distributed fiber reinforced sand layer Qallowable allowable load on the foundation qu, qns ultimate, and safe bearing capacity of sand with different combinations of relative densities RD1, RD2 relative density of top RDFS, and bottom unreinforced sand layer, respectively ri, ro internal, and external radius of ring footing, respectively ri/ro ¼ n radius ratio Sp, Sf settlement of plate, and foundation, respectively Wf dry weight of fiber WRDFS weight of randomly distributed fiber reinforced sand layer Ws dry weight of sand g1, g2 dry unit weight of top RDFS, and bottom unreinforced sand layer gRDFS dry unit weight of randomly distributed fiber reinforced sand layer f1, f2 angle of internal friction of top RDFS, and bottom unreinforced sand layer, respectively References Ajayi, O., Pen, L.L., Zervos, A., Powrie, W., 2017. Scaling relationships for strip fibre e reinforced aggregates. Can. Geotech. J. 54 (5), 710e719. Al-Refeai, T., 1991. Behavior of granular soils reinforced with discrete randomly oriented inclusions. Geotext. Geomembranes 10 (4), 319e333. Al-Sanad, H.A., Ismael, N.F., Brenner, R.P., 1993. Settlement of circular and ring plates in very dense calcareous sands. J. Geotech. Eng 119 (4), 622e638. Babu, G.L.S., Vasudevan, A.K., Haldar, S., 2008. Numerical simulation of fiberreinforced sand behavior. Geotext. Geomembranes 26 (2), 181e188. Bowles, J.E., 1997. Foundation Analysis and Design, fifth ed. McGraw-HillX, New York. Brown, J.D., Meyerhof, G.G., 1971. Experimental study of bearing capacity in layered clays., in: Proc., Int. Soil Mechanics and Foundation Engineering Conf. Mexico. Chen, M., Shen, S.L., Arulrajah, A., Wu, H.N., Hou, D.W., Xu, Y.S., 2015. Laboratory evaluation on the effectiveness of polypropylene fibers on the strength of fiberreinforced and cement-stabilized Shanghai soft clay. Geotext. Geomembranes 43 (6), 515e523. Choo, H., Yoon, B., Lee, W., Lee, C., 2017. Evaluation of compressibility and small strain stiffness characteristics of sand reinforced with discrete synthetic fibers. Geotext. Geomembranes (Accepted for publication). Consoli, N.C., Casagrande, M.D.T., Coop, M.R., 2007. Performance of a fibreotechnique 57 (9), 751e756. reinforced sand at large shear strains. Ge , A., 2003. Plate load test on Consoli, N.C., Casagrande, M.D.T., Prietto, P.D.M., Thome fiber-reinforced soil. J. Geotech. Geoenvironmental Eng 129 (10), 951e955. , A., Dalla Rosa, F., Fahey, M., 2009. Effect of Consoli, N.C., Casagrande, M.D.T., Thome otechnique relative density on plate loading tests on fibre-reinforced sand. Ge 59 (5), 471e476. Consoli, N.C., Consoli, B.S., Festugato, L., 2013. A practical methodology for the determination of failure envelopes of fiber-reinforced cemented sands. Geotext. Geomembranes 41, 50e54. Consoli, N.C., Nierwinski, H.P., Peccin da Silva, A., Sosnoski, J., 2017. Durability and strength of fiber-reinforced compacted gold tailings-cement blends. Geotext. Geomembranes 45 (2), 98e102. Dash, S.K., 2010. Influence of relative density of soil on performance of geocellreinforced sand foundations. J. Mater. Civ. Eng. 22 (5), 533e538. Egorov, K.E., 1965. Calculation of bed for foundation with ring footing, in: Sixth International Conference on Soil Mechanics and Foundation Engineering. pp. 41e45. Festugato, L., Menger, E., Benezra, F., Kipper, E.A., Consoli, N.C., 2017. Fibre-reinforced cemented soils compressive and tensile strength assessment as a function of filament length. Geotext. Geomembranes 45 (1), 77e82. Fisher, K., 1957. Zur Berechnung der setzung von fundamenten in der form einer reisformigen ringflache. Der Bauing. 35 (5), 172e174. Freitag, D.R., 1986. Soil randomly reinforced with fibers. J. Geotech. Eng. 112 (8), 823e826. Gray, D.H., Al-Refeai, T., 1986. Behavior of fabric- versus fiber-reinforced sand. J. Geoteh. Eng. 112 (8), 804e820. Gray, D.H., Ohashi, H., 1983. Mechanics of fiber reinforcement in sand. J. Geotech.
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V. Sharma, A. Kumar / Geotextiles and Geomembranes xxx (2017) 1e9 Eng. 109 (3), 335e353. Hanna, A.M., Meyerhof, G.G., 1979. Ultimate bearing capacity of foundations on a three-layer soil, with special reference to layered sand. Can. Geotech. J. 16 (2), 412e414. Harikumar, M., Sankar, N., Chandrakaran, S., 2016. Behaviour of model footing resting on sand bed reinforced with multi-directional reinforcing elements. Geotext. Geomembranes 44 (4), 568e578. Hataf, N., Razavi, M.R., 2003. Behavior of ring footing on sand. Iran. J. Sci. Technol. Trans. B 27, 47e56. Huang, C.C., 2017. Model tests on the bearing capacity of reinforced saturated sand ground. Geosynth. Int. 24 (2), 114e124. Ismael, N.F., 1996. Loading tests on circular and ring plates in very dense cemented sands. J. Geotech. Eng 122 (4), 281e287. Khachan, M.M., Bhatia, S.K., 2016. Influence of fibers on the shear strength and dewatering performance of geotextile tubes. Geosynth. Int. 23 (5), 317e330. Kumar, A., Gupta, D., 2016. Behavior of cement-stabilized fiber-reinforced pond ash, rice husk ash-soil mixtures. Geotext. Geomembranes 44 (3), 466e474. Kumar, A., Ohri, M.L., Bansal, R.K., 2013. Pressure settlement characteristics of strip footings on reinforced layered soil. Int. J. Civ. Structual Eng 4 (2), 136e146. Kumar, A., Walia, B.S., 2006. Bearing capacity of square footings on reinforced layered soil. Geotech. Geol. Eng 24 (4), 1001e1008. Laman, M., Yildiz, A., 2003. Model studies of ring foundations on geogrid-reinforced sand. Geosynth. Int. 10 (5), 142e152. Madhusudhan, B.N., Baudet, B.A., Ferreira, P.M.V., Sammonds, P., 2017. Performance of fiber reinforcement in completely decomposed granite. J. Geotech.
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Geoenvironmental Eng 143 (8), 1e11. Maher, M.H., Ho, Y.C., 1993. Behavior of fiber-reinforced cemented sand under static and cyclic loads. Geotech. Test. J. 16 (3), 330e338. Meyerhof, G.G., 1974. Ultimate bearing capacity of footings on sand layer overlying clay. Can. Geotech. J. 11 (2), 223e229. Michalowski, R.L., Shi, L., 1995. Bearing capacity of footings over two-layer foundation soils. J. Geotech. Eng 121 (5), 421e428. Miranda Pino, L.F., Baudet, B.A., 2015. The effect of the particle size distribution on the mechanics of fibre-reinforced sands under one-dimensional compression. Geotext. Geomembranes 43 (3), 250e258. Naderi, E., Hataf, N., 2014. Model testing and numerical investigation of interference effect of closely spaced ring and circular footings on reinforced sand. Geotext. Geomembranes 42 (3), 191e200. Ohri, M.L., Purhit, D.G.M., Dubey, M.L., 1997. Behavior of ring footings on dune sand overlaying dense sand, in: International Conference of Civil Engineers. Tehran, Iran. Sawwaf, M. El, Nazir, A., 2012. Behavior of eccentrically loaded small-scale ring footings resting on reinforced layered soil. J. Geotech. Geoenvironmental Eng. 138 (3), 376e384. Sharma, V., Kumar, A., 2017. Strength and bearing capacity of ring footings resting on fibre-reinforced sand. Int. J. Geosynth. Gr. Eng 3 (9), 1e17. Terzaghi, K., 1943. Theoretical Soil Mechanics. Wiley. Terzaghi, K., Peck, R.B., 1948. Soil Mechanics in Engineering Practice, first ed. John Wiley and Sons, New York.
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Technical note
Influence of relative density of soil on performance of fiber-reinforced soil foundations Vaibhav Sharma*, Arvind Kumar Department of Civil Engineering, Dr. B R Ambedkar National Institute of Technology, Jalandhar 144011, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 October 2016 Received in revised form 6 June 2017 Accepted 9 June 2017 Available online xxx
An experimental study has been carried out for studying the influence of combinations of relative densities of two layered soil system. The model tests have been performed for the case of circular and ring footings resting on randomly distributed fiber reinforced sand (RDFS) layer overlying unreinforced sand bed. The influence of relative density on, different type of footings i.e. circular and ring (ri/ro ¼ 0.3, 0.4, 0.5, 0.6) footings; percentages of fiber in RDFS layer i.e. 0.5%, 0.75%, 1.00%, and 1.25%; and thickness of RDFS layer i.e. 0.5B, 0.75B, and 1.00B have been studied. Results have indicated that relative density, of both the RDFS layer as well as the bottom unreinforced sand layer, significantly influences the ultimate bearing capacity as well as the settlement. Improvement in terms of bearing capacity ratio (BCR) is more when top RDFS layer is compacted at 70% relative density with bottom unreinforced sand having 30% relative density. Moreover, in terms of settlement reduction, maximum improvement is observed when both the layers were compacted at 70% relative density. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Geosynthetics Relative density Ring footing Model tests Fibers Bearing capacity Settlement
1. Introduction Improving the engineering behavior of soil has been a major concern for geotechnical engineers ever since the introduction of ground improvement techniques. There are many ways to improve the engineering properties of soil like, incorporation of reinforcements into the soil (say: geosynthetics; metal strips; discrete fibers which can further be randomly distributed or aligned in the direction of planes of weak zone of soil), replacing the weak soil with strong soil up to significant depth, and/or densifying the weak soil up to significant depth or in other words increasing the relative density of soil. Ring shear tests were carried out on sand both for unreinforced and fiber reinforced under large shear strains. It was observed that denser samples behaved more efficiently in increasing and maintaining the ultimate shear strains (Consoli et al., 2007). Plate load tests were conducted on unreinforced and fiber reinforced sand at low, medium and dense relative density of sand, respectively. It was found out that the effect of fiber inclusion was more pronounced for higher relative densities. Moreover, higher relative density suppresses the
* Corresponding author. E-mail addresses: [email protected] (V. Sharma), agnihotriak@ nitj.ac.in (A. Kumar).
dilation which results in increase in effective stress and hence increases the strength and stiffness of the soil (Consoli et al., 2009). The influence of relative density of soil on the improvement in performance of geocell reinforcement by using model plate load tests was studied. It was concluded that for effective utilization of geocell reinforcement; the soil should be compacted to higher density (Dash, 2010). Many researchers in the past have improved the soil properties by the introduction of reinforcement elements in the soil strata. Out of the reinforcement elements, randomly distributed discrete inclusions have been the main attraction of researchers in the past few years. A very major advantage of fibers as reinforcement elements among the other types of reinforcements is that; there are no weak zones left in the soil strata as in the case of other types of reinforcements. Researchers (Al-Refeai, 1991; Freitag, 1986; Gray and Al-Refeai, 1986; Gray and Ohashi, 1983; Maher and Ho, 1993) started the initial testing on fiber-reinforced soil. The pressure-settlement and stress-strain behavior of fiber reinforced soil was compared by conducting model plate-load tests and triaxial tests, respectively. Both the pressure-settlement and stress-strain behavior was improved by the introduction of randomly distributed fibers in soil (Consoli et al., 2003). Numerical as well as experimental study was carried out to understand the influence of randomly distributed fiber inclusions in sand through
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triaxial tests. Inclusion of fibers in the soil makes the stress concentrations more diffuse and restricts the formation of shear bands (Babu et al., 2008). Split tensile and unconfined compression tests were carried out to estimate the Mohr-Coulomb failure envelope of unreinforced and fiber reinforced artificially cemented sands (Consoli et al., 2013). In the recent past more studied were carried out on different types of geosynthetic inclusions to study their effect on geotechnical properties of soil (Ajayi et al., 2017; Chen et al., 2015; Choo et al., 2017; Consoli et al., 2017; Festugato et al., 2017; Harikumar et al., 2016; Huang, 2017; Khachan and Bhatia, 2016; Kumar and Gupta, 2016; Madhusudhan et al., 2017; Miranda Pino and Baudet, 2015; Sharma and Kumar, 2017). Researchers have studied the effect of ground improvement technique by conducting model as well as field plate load tests by using different types of reinforcements. Metal strips, bars, planar, 3-D (geocell) and fiber reinforcements are the major types of reinforcement elements, which are very useful in improving the bearing capacity of soil. Different shapes of footings have been considered in the past, but ring footings which are very useful for tall towers, silos, and chimney, etc. Have not gained much attention. Researchers (Egorov, 1965; Fisher, 1957) started working on studying the behavior of ring footings. Later field plate load tests were conducted on dense calcareous sand (Al-Sanad et al., 1993; Ismael, 1996) and concluded that circular and ring plates have same average pressure settlement curves. Other researchers (Hataf and Razavi, 2003; Laman and Yildiz, 2003; Naderi and Hataf, 2014; Ohri et al., 1997; Sawwaf and Nazir, 2012) conducted laboratory model tests on ring footings and reported that the optimum value (on the basis of ultimate bearing capacity) of radius ratio (ri/ro), for ring footing lies in the range of 0.2e0.4, where ri and ro are the internal and external radius of ring footing under consideration. Majority of the work, related to model tests on footings, has been carried out by considering a uniform relative density of soil (reinforced with geogrid/planar reinforcement) under the footing up to larger depths. Very limited efforts have been made in the past to study the behavior of model footings when placed as, (a) strong soil overlying weak soil or, (b) weak soil overlying strong soil (Brown and Meyerhof, 1971; Hanna and Meyerhof, 1979; Kumar et al., 2013; Kumar and Walia, 2006; Meyerhof, 1974; Michalowski and Shi, 1995). Moreover, no study has been carried out on ring footings resting on randomly distributed fiber reinforced sand. Considering these gaps in the literature, an effort has been made to study the behavior of ring and circular footings resting on randomly distributed fiber-reinforced sand. Moreover, three combinations of fiber-reinforced sand overlying unreinforced sand have been considered and they are; (a) top fiber-reinforced sand compacted at 50% RD, overlying sand compacted at 30% RD, (b) top fiber-reinforced sand compacted at70% RD and underlying sand compacted at 30% RD. and, (c) top fiber-reinforced sand compacted at70% RD and underlying sand compacted at 70% RD. Hence the aim of this paper is to study the effect of RD of sand, i.e., loose (30%), medium (50%) and dense (70%), on. Footing type i.e. circular, and ring footing with radius ratio (ri/ro) of 0.3, 0.4, 0.5, and 0.6; Different percentages of randomly distributed fibers, i.e. 0.5%, 0.75%, 1.00%, and 1.25% by dry weight of sand; Different thicknesses (h1) of fiber-reinforced sand layer, i.e., 0.5B, 0.75B, and 1.0B, where B is the outer diameter for ring, or, diameter for circular footing. Moreover a numerical example has been solved, for the better understanding of the readers by clearly highlighting the influence of relative density, fiber percentage, and thickness of RDFS layer.
2. Test material Sand used in the model testing was obtained from Nasrala, Punjab, India. According to Unified Soil Classification System, the sand was classified as poorly graded, SP. Specific gravity (Gs) of sand was found out to be 2.65. The maximum and minimum dry unit weights of sand were found out to be 16.8 kN/m3 and 13.6 kN/m3, respectively, and the corresponding values of minimum and maximum void ratios were 0.56 and 0.93, respectively. The effective size (D10), mean size (D50), coefficient of curvature (Cc) and coefficient of uniformity (Cu) for the sand were 0.150 mm, 0.290 mm, 0.97 and 2.21, respectively. Fibers used as a reinforcing element for sand in the model testing were macro-synthetic and non-corrosive fibers as shown in Fig. 2. For the effective anchoring of the fibers into the sand matrix they have an engineered contoured profile which enhances its performance. Physical and chemical properties of fibers are presented in Table 1. 2.1. Experimental setup and test program Total 190 model plate load tests were carried out as shown in Table 2. A testing-cum-loading frame assembly was used for conducting model tests. The soil bed was prepared in a testing tank with inside dimensions of 1.5 m long, 1.5 m wide and 1 m deep. The model footings were made from mild steel, and were corrected to the desired size, thickness (25 mm) and shape (ring and circular). One circular footing and four ring footings were used in this study. Diameter for circular footing was 0.3 m and, the ratio of inner radius to outer radius of ring footings (ri/ro) of 0.3, 0.4, 0.5, and 0.6, were used in the study by keeping the outer diameter of ring to be constant i.e. 0.3 m. The footing was loaded until the failure (large uniform settlement corresponding to very small increment in load) or fully extended manually operated hydraulic jack. Two 0.01 mm sensitivity dial gauges were placed on either and opposite side of the footing to calculate settlement for every equal increment of load. It was not possible to place hydraulic jack directly on ring footings because it will slip through the opening of the ring footings. So, in order to avoid this, first a loading platform was placed on ring footing followed by the hydraulic jack. Then loading of ring footing was possible. Test setup and detail of loading platform is shown in Fig. 1. 2.2. Preparation of bed and test procedure Bed consists of two layers of sand as shown in Fig. 1. First, bottom unreinforced sand layer is filled, by using sand raining technique, at a known and desired density followed by leveling after reaching desired height. Second, top randomly distributed fiber reinforced sand (RDFS) layer was filled. For laying top RDFS layer, first dry weight of fibers and sand was calculated using equation (1), and (2). This means that fibers were added as a replacement of sand.
WRDFS ¼ V gRDFS
(1)
WRDFS ¼ Ws þ Wf ¼ ps WRDFS þ pf WRDFS
(2)
where, WRDFS, Ws, and Wf is dry weight of, RDFS layer, sand and, fibers, respectively; gRDFS is dry unit weight of RDFS layer; V is the total volume of RDFS layer to be placed; ps and pf are the percentages of sand and fibers in RDFS layer, respectively. For the preparation of RDFS layer, sand and fibers were hand
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V. Sharma, A. Kumar / Geotextiles and Geomembranes xxx (2017) 1e9
3
Table 1 Chemical and physical properties of fibers. Fiber length Type Absorption Specific gravity (Gf) Electrical conductivity Tensile strength (N/mm2) Diameter (mm)
45 mm Macro Nil 0.91 Low 400 0.95
Acid and salt resistance Ignition point Melt point Thermal conductivity Alkali resistance Elastic modulus (N/mm2) Shape
High >550 c (1022 F) 164 c (328 F) Low Alkali proof 7000 Continuously deformed
Table 2 Test plan. Series
Condition
h1/B
*RD1 (%)
*RD2 (%)
Fiber content (%)
Footing type (ri/ro)
Number of tests
I II III IV V
Sand only Sand only RDFS RDFS RDFS
0 0 0.5, 0.75, 1.0 0.5, 0.75, 1.0 0.5, 0.75, 1.0
30 70 50 70 70
30 70 30 30 70
0 0 0.5, 0.75, 1.0, 1.25 0.5, 0.75, 1.0, 1.25 0.5, 0.75, 1.0, 1.25
0, 0, 0, 0, 0,
5 5 60 60 60
Total tests
0.3, 0.3, 0.3, 0.3, 0.3,
0.4, 0.4, 0.4, 0.4, 0.4,
0.5, 0.5, 0.5, 0.5, 0.5,
0.6 0.6 0.6 0.6 0.6
190
NOTE: * For details refer Fig. 1.
Fig. 1. Testing setup and assembly.
mixed. The RDFS layer was filled in equal shifts of 100 mm and compacted. Fibers were mixed randomly in each layer manually in order to achieve homogeneity of the sand-fiber mix. Tank's inner walls were marked so as to ensure the thickness of layers. Random distribution of fibers and obtaining a homogeneous fiber-sand mix is difficult to achieve because there are chances of segregation, which is due to the different specific gravities of both, fiber and sand. So, to minimize this problem, dry fibers (calculated as explained before) were soaked in water before adding to sand for mixing. This was done in order to make them wet, which in turn coats fiber with thin layer of water. They were then transferred to
sieves so that the excess water gets removed and then transferred to the sand for mixing. Each layer of RDFS was compacted using a wooden rammer so that the layer achieves desired thickness. After filling of RDFS layer, it was leveled. Footing was centered carefully, so that the loading should be concentric. Then loading platform was placed over the footing (in case of ring footing), centered, and followed by the placing of hydraulic jack over it as shown in Fig. 1. Two sensitive dial gauges were placed on either and opposite side of the footing to measure the settlement. Then equal load increment was applied through manually operated hydraulic jack.
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equations (3) and (4), and are as follows: 3.1. Effect of relative density on different types of footing
Fig. 2. Fibers used.
3. Results and discussions The influence of relative density in the performance of RDFS layer overlying unreinforced sand bed was studied by using two non-dimensional factors as: 1. Improvement in ultimate bearing capacity (BCR: bearing capacity ratio), which compares the bearing capacity of circular footing resting on unreinforced sand to that of bearing capacity of given footing resting on RDFS layer overlying sand. It is defined in Equation (3). 2. Improvement in settlement (SR: settlement reduction), which compares the settlement, of circular footing resting on unreinforced sand with settlement of given footing resting on RDFS layer overlying sand, corresponding to the ultimate bearing capacity obtained. It is defined in Equation (4).
BCR ¼
SR ¼
Figs. 3 and 4 show the pressure settlement curves for different, combinations of relative densities of top and bottom layers, and types of footings, respectively. From Fig. 3, it can be inferred that the ultimate bearing capacity increases as the top layer of sand, mixed with randomly distributed fibers, gets compacted to higher relative density. When RD1 is 50% and RD2 is 30%, the ultimate bearing capacity of circular, and ring footing (ri/ro ¼ 0.40) is 500 and 568 kN/m2, respectively. When RD1 is compacted to a higher relative density of 70% and keeping the RD2 constant at 30%, the ultimate bearing capacity of circular, and ring (ri/ro ¼ 0.40) footing is increased to 528 and 605 kN/m2, respectively. Fig. 6 shows that as radius ratio (ri/ro) increases from 0 to 0.4, ultimate bearing capacity increases, and then on increasing radius ratio beyond 0.4, ultimate bearing capacity decreases. When radius ratio is 0, 0.3, 0.4, 0.5, and 0.6, the corresponding ultimate bearing capacity values were 555, 600, 655, 540, and 505 kN/m2, respectively. Similarly, the settlement values were 17.5, 15, 10.5, 16.5, and 16.5 mm, respectively. Fig. 5 shows the variation of BCR, and SR, with radius ratio for different combinations of relative densities of top and bottom layers of sand, respectively. It can be inferred from Fig. 5, that there exists an optimum value of ri/ro ¼ 0.4, both in the terms of BCR and SR at all combinations of relative densities of top and bottom layers of sand, where performance is maximum. From Fig. 5, it can be inferred that as the radius ratio is increased, the BCR first increases upto radius ratio of 0.4, and on further increasing this value, the BCR value starts decreasing. Experimental study on ring footings resting on geogrid reinforced sand was carried out and found out that for radius ratio of 0.4, optimum behavior of ring footing was observed. This behavior of ring footing is due to the interference effect of ring footing's internal diameter (Sawwaf and Nazir, 2012). Whenever a footing (placed over soil) is loaded three zones gets
UBC of given footing resting over RDFS layer overlying unreinforced sand at their respective relative densities UBC of circular footing resting over unreinforced sand at relative density same as that of the bottom layer
Settlement of given footing resting over RDFS layer overlying unreinforced sand at their respective relative densities Settlement of circular footing resting over unreinforced sand at relative density same as that of the bottom layer
From Fig. 1 as shown in test setup, it can be seen that there are two layers of sand. Top layer is of RDFS with relative density as RD1, and bottom unreinforced layer with relative density as RD2. So there are different series of tests that have been considered for the study and can be referred from Table 2. For calculating the value of BCR and SR for series III and IV, the RD of denominator term in equations (3) and (4) is 30%, and for series V, it has been taken as 70%. In this paper, UBC was obtained by using tangent intersection method. In this method initial linear portion of pressure settlement curve is extended and final linear portion is extended backward, so that both extended lines intersect at a point. Pressure corresponding to this intersection point is taken as ultimate bearing capacity. Effect of relative density on different types of footings, percentage of fibers and thickness of fiber reinforced sand layer has been studied using the improvement factors as explained in
(3)
(4)
developed under it. These are zone I (remains in elastic equilibrium and moves with the footing), zone II (radial shear zone, which pushes the zone III), and zone III (rankine's passive zone) (Terzaghi, 1943). As the footing advances in downward direction, zone II pushes zone III outwards. As this case is similar to the interference effect of closely spaced footings, zone III from both the interfering footings gets intersected, which further causes the arching of the soil in zone III, and helps in improving bearing pressure. This effect is found to be limited up to radius ratio of 0.4; thereafter on further increasing the radius ratio, no arching of soil takes place. Fig. 5 shows that as the top layer of RDFS is compacted at 50% relative density and bottom layer at 30% relative density, then BCR value is 5, and 5.68, for circular and ring (ri/ro ¼ 0.40) footing, respectively. And when the top RDFS layer is compacted at even higher relative density of 70% by keeping the bottom layer compacted at 30% relative density, the BCR value has increased to 5.28,
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0
100
200
Pressure (kN/m2) 300 400 500
600
1% fiber; h1/B = 1.0
20
40
40
60
RD1 = 50%; RD2 = 30%
80
RD1 = 70%; RD2 = 30%
100
RD1 = 70%; RD2 = 70%
140
100
200
Pressure (kN/m2) 300 400 500
Settlement (mm)
600
700
800
RD1 = 70%, RD2 = 70% 1% fiber; h1/B = 1.0
20 40 60
120 140
100
ri/ro = 0.4
0
100
80
120
Fig. 3. Pressure settlement curve for different combinations of relative densities.
80
60
ri/ro = 0
140
0
ri/ro = 0 ri/ro = 0.3 ri/ro = 0.4 ri/ro = 0.5 ri/ro = 0.6 Fig. 4. Pressure settlement curve for different types of footings.
0.9
7 1% fiber; h1/B = 1.0
0.8
6
0.7
5
100
200
Pressure (kN/m2) 300 400 500
0
20
120
600
700
800
RD1 = 70%, RD2 = 70% h1/B = 1.0
0% fiber 0.50% fiber 0.75% fiber 1.00% fiber 1.25% fiber ri/ro = 0 ri/ro = 0.4 Fig. 6. Pressure settlement curve for different percentages of fibers.
term in denominator for series III and IV in Table 2. On the other hand, if the ultimate bearing capacity is compared instead of BCR for the same case it will be more and increasing with the increase in relative density. The ultimate bearing capacity increases from 518 to 555 kN/m2, and 608e655 kN/m2, for circular and ring footing (ri/ ro ¼ 0.4), respectively for the case when relative density of both layers is increased from 50% to 70%. Fig. 5 shows that as the top RDFS layer is compacted at relative density of 50% and bottom layer at 30% relative density, the SR value is 0.53 for ring footing (ri/ro ¼ 0.40). And when the top RDFS layer is compacted at higher relative density of 70%, by compacting the bottom layer at 30%, the SR value decreases to 0.43, for ring footing (ri/ro ¼ 0.4). Similarly, when both the top RDFS and lower unreinforced sand layers were compacted to same relative density i.e. 50%, then SR value is 0.26 for ring footing (ri/ro ¼ 0.40). Moreover, increasing the relative density of both the layers to 70%, the SR value decreases to 0.23, for ring footing (ri/ro ¼ 0.4). Maximum improvement in terms of SR has been observed when the relative densities of both the top RDFS layer as well as lower unreinforced sand layer were compacted at same and higher relative density (70%).
0.6
4
0.5
3
0.4
SR
BCR
0
800
Settlement (mm)
Settlement (mm)
0
700
5
0.3
2 1
RD1 = 50%; RD2 = 30%
RD1 = 70%; RD2 = 30%
0.2
RD1 = 70%; RD2 = 70%
BCR
0.1
SR
0 0
0.1
0 0.2
0.3
ri/ro
0.4
0.5
0.6
0.7
Fig. 5. Variation of BCR and SR with ri/ro.
and 6.05, for circular and ring (ri/ro ¼ 0.40) footing, respectively. Similarly, when both the top RDFS and bottom unreinforced sand layers were compacted to same relative density of 50%, then BCR value is 2.78, and 3.27, for circular and ring (ri/ro ¼ 0.40) footing, respectively. Furthermore, increasing these relative densities to 70%, the BCR value decreases to 2.47, and 2.91, for circular and ring footing (ri/ro ¼ 0.4), respectively. This shows that more improvement is observed when the bottom sand layer has lesser relative density as that of the top RDFS layer, rather than having same relative density as that of the top RDFS layer. The lesser and decreasing values of BCR is because of the fact that, the value of denominator in equation (3) is more as compared to the value of
3.2. Effect of relative density on fiber content Fig. 6 shows the pressure settlement curves for different percentages of fibers. From Fig. 7, it can be inferred that as the percentage of fibers in sand is increased, there is an increase in ultimate bearing capacity. It also shows that the pressure settlement curves for ring footings (ri/ro ¼ 0.4) are above the circular footing for same conditions. When percentage of fiber is increased from 0 to 1.25%, the ultimate bearing capacity gets increased from 225 to 575 kN/m2, and 275e670 kN/m2, for circular and ring footings (ri/ro ¼ 0.4), respectively. Similarly settlement has decreased from 45 to 15 mm, and 40 to 9 mm, for circular and ring footing (ri/ro ¼ 0.4), respectively. Fig. 7 shows the variation of BCR, and SR, with different percentages of fibers for different combinations of relative densities of top RDFS and bottom sand layer, respectively. From Fig. 7, it can be seen that as the percentage of fibers is increased from 0.50 to 1.25%, BCR value increases both for circular as well as for ring footings (ri/ ro ¼ 0.40). For RD1 ¼ 50%; RD2 ¼ 30%; when percentage of fibers is increased from 0.5 to 1.25%, the BCR value for circular and ring footing (ri/ro ¼ 0.40) gets increased from 4.18 to 5.25, and 5.15 to 6.00, respectively. Similarly for RD1 ¼ 70%; RD2 ¼ 30%; the BCR value was found out to be increased from, 4.43 to5.48, and 5.40 to 6.35, respectively; For RD1 ¼ 70%; RD2 ¼ 70%, the BCR value increases from 2.04 to 2.56, and 2.58 to 2.98, respectively. Moreover,
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1
6.8
0
5.8
2.8
0.8 -0.2 0.25
RD1 = 50%; RD2 = 30% RD1 = 70%; RD2 = 30% RD1 = 70%; RD2 = 70% ri/ro = 0 ri/ro = 0.4 0.5
0.2
Note: 1. BCR values are shown by line joining empty markers. 0 2. SR values are shown by line joining filled markers. -0.2 0.75 1 1.25 1.5 Fiber content (%)
600
700
800
RD1 = 70%, RD2 = 70% 1% fiber
40 Settlement (mm)
SR
BCR
3.8
1.8
Pressure (kN/m2) 300 400 500
20
0.6 0.4
200
0
0.8
4.8
100
60 80 100
h1/B = 0.5 h1/B = 0.75
120
h1/B = 1.0
140
ri/ro = 0
160
Fig. 7. Variation of BCR and SR with fiber content, for h1/B ¼ 1.0.
h1/B = 0
ri/ro = 0.4
Fig. 8. Pressure settlement curve for different thicknesses of RDFS layers.
3.3. Effect of relative density on thicknesses of RDFS layer Fig. 8 shows the pressure settlement curves for different thicknesses of top RDFS layers for circular and ring footing (ri/ro ¼ 0.40). It can be inferred from Fig. 8 that as the value of h1/B increases, the ultimate bearing capacity for both the circular and ring footing increases. When h1/B increases from 0 to 1.00, the ultimate bearing capacity of circular, and ring footing increases from 225 to 555 kN/ m2, and 275e655 kN/m2, respectively. Fig. 9 shows the variation of BCR with h1/B, for circular and ring footing, for all combinations of relative densities of top RDFS and bottom sand layer. From Fig. 9, it can be inferred that as the thickness of top RDFS layer increases, the corresponding BCR value increases. Improvement in terms of BCR is more when top RDFS and bottom sand layer has different relative densities, instead of having
7
0.8
6
0.7 0.6
5
0.5
4
0.4 3 2 1
SR
BCR
ring footing (ri/ro ¼ 0.4) was found out to be performing better than the circular footing at all combinations of relative densities of top RDFS and bottom sand layer. Furthermore, when RD1 ¼ 50% and RD2 ¼ 30%, 1.25% fiber content and h1/B ¼ 1.00; the BCR value is 5.25, and 6.00 for circular, and ring (ri/ro ¼ 0.4) footing, respectively. And when RD1 is compacted at higher relative density of 70% and RD2 ¼ 30%, 1% fiber content and h1/B ¼ 1.00; the BCR value has increased to 5.28, and 6.05, for circular, and ring (ri/ro ¼ 0.4) footing, respectively. This means that compacting the top RDFS layer to higher density, keeping its thickness constant; the consumption of fibers can be reduced to 1.00% from 1.25%. From Fig. 7, it can be inferred that as the percentage of fibers increased from 0.50 to 1.25%, there is an improvement in terms of settlement reduction, both for circular as well as ring footing (ri/ ro ¼ 0.40), for all the combinations of relative densities of top RDFS and bottom sand layer. For RD1 ¼ 50%; RD2 ¼ 30%; when percentage of fibers is increased from 0.5 to 1.25%, the SR value for circular and ring footing (ri/ro ¼ 0.40) gets decreased from 0.85 to 0.68, and 0.73 to 0.46, respectively. Similarly for RD1 ¼ 70%; RD2 ¼ 30%; the SR value decreases from, 0.69 to 0.41, and 0.60 to 0.36, respectively; For RD1 ¼ 70%; RD2 ¼ 70%, the SR value decreases from 0.49 to 0.33, and 0.44 to 0.22, respectively. Furthermore, improvement in terms of settlement was found to be maximum, when both the top RDFS and bottom sand layers were compacted to 70% relative density. Moreover, when RD1 ¼ 50% and RD2 ¼ 30%, 1.25% fiber content and h1/B ¼ 1.00; the SR value is 0.68, and 0.46 for circular, and ring (ri/ro ¼ 0.4) footing, respectively. And when RD1 is compacted at higher relative density of 70% and RD2 ¼ 30%, 1% fiber content and h1/B ¼ 1.00; the SR value has improved to 0.54, and 0.43, for circular, and ring (ri/ro ¼ 0.4) footing, respectively.
0.3 RD1 = 50%; RD2 = 30% RD1 = 70%; RD2 = 30% RD1 = 70%; RD2 = 70% ri/ro = 0 ri/ro = 0.4
Note: 1. BCR values are shown by line joiningempty markers. 2. SR values are shown by line joining filled markers.
0 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 h1/B
0.2 0.1 0
1
1.05 1.1
Fig. 9. Variation of BCR and SR with h1/B at 1% fiber content.
same relative densities. For RD1 ¼ 50%; RD2 ¼ 30%; when the thickness of RDFS layer is increased from 0.5B to 1.0B (where B is the diameter of circular and outer diameter of ring footing), the BCR value for circular and ring footing (ri/ro ¼ 0.40) gets increased from 3.98 to 5.00, and 4.80 to 5.68, respectively. Similarly for RD1 ¼ 70%; RD2 ¼ 30%; the BCR value was found out to be increased from, 4.35 to 5.28, and 5.19 to 6.05, respectively For RD1 ¼ 70%; RD2 ¼ 70%, the BCR value increases from 2.22 to 2.47, and 2.60 to 2.91, respectively. Moreover when RD1 ¼ 50% and RD2 ¼ 30%, 1.00% fiber content and h1/B ¼ 1.00; the BCR value is 5, and 5.68 for circular, and ring (ri/ro ¼ 0.4) footing, respectively. And when RD1 is compacted at higher relative density of 70% and RD2 ¼ 30%, 1% fiber content and h1/B ¼ 0.75; the BCR value is 4.7, and 5.00, for circular, and ring (ri/ ro ¼ 0.4) footing, respectively. This means that compacting the top RDFS layer to higher density, keeping the fiber content constant; the majority of improvement has been obtained when thickness of RDFS layer is lesser that 1.00B. Fig. 9 shows the variation of SR with h1/B, for circular and ring footing for all the combinations of relative densities of top RDFS and bottom sand layer. From Fig. 9, it can be found out that as the thickness of top RDFS layer increases, the corresponding SR value increases. For RD1 ¼ 50%; RD2 ¼ 30%; when the thickness of RDFS layer is increased from 0.5B to 1.0B (where B is the diameter of circular and outer diameter of ring footing), the SR value for circular, and ring footing (ri/ro ¼ 0.40) gets decreased from 0.75 to 0.73, and 0.60 to 0.53, respectively. Similarly for RD1 ¼ 70%; RD2 ¼ 30%; the BCR value was found out to be decreasing from, 0.68 to 0.54, and 0.48 to 0.43, respectively; For RD1 ¼ 70%; RD2 ¼ 70%, the BCR value decreasing from 0.51 to 0.39, and 0.38 to 0.23,
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V. Sharma, A. Kumar / Geotextiles and Geomembranes xxx (2017) 1e9
respectively. Maximum improvement in terms of settlement was found out, when both the top RDFS and bottom sand layer was compacted to 70% relative density. Moreover when RD1 ¼ 50% and RD2 ¼ 30%, 1.00% fiber content and h1/B ¼ 1.00; the SR value is 0.73, and 0.53 for circular, and ring (ri/ro ¼ 0.4) footing, respectively. And when sand with RD1 is compacted at higher relative density of 70% and RD2 ¼ 30%, 1% fiber content and h1/B ¼ 0.75; the SR value has improved to 0.56, and 0.46, for circular, and ring (ri/ro ¼ 0.4) footing, respectively.
favg ¼ tan1
7
fðtan f1 Þ h1 g þ ðtan f2 Þ h2 h1 þ h2
(5)
cavg ¼
ðc1 h1 Þ þ ðc2 h2 Þ h1 þ h1
(6)
gavg ¼
ðg1 h1 Þ þ ðg2 h2 Þ h1 þ h1
(7)
Table 3 shows the values of angle of internal friction, cohesion, and soil unit weight used in this problem.
4. Numerical problem Statement:
Shear criterion:
Fig. 10 shows the data obtained from a plate load tests conducted on a circular footing, of 0.3 m diameter, when placed on the surface. Determine the allowable load on a 3 m diameter circular foundation, if the permissible settlement of foundation is 20 mm and factor of safety against shear failure is 3. Five tests were carried out on different combinations with top layer (reinforced/unreinforced) of thickness 1B at relative density RD1 and bottom sand layer at relative density RD2. In reinforced layer, the fiber percentage is 1%.
For shear failure criterion, the equations used to calculate the ultimate, and safe bearing capacity (Terzaghi, 1943) are shown in Eqns. (8) and (9), respectively.
qu ¼ 1:2cavg Nc þ qNq þ 0:3gavg BNg qns ¼
(8)
qu F
(9)
where, Nc, Nq, and Ng are the bearing capacity factors (Terzaghi, 1943), and F is the factor of safety against shear failure (taken as 3 in this example).
Solution: Settlement criterion: As it is the case of two layered soil, in which top layer is reinforced with randomly distributed fibers and the bottom layer is unreinforced. So, the average value of angle of internal friction, soil cohesion, and soil unit weight is considered using Eqns. (5)e(7), (Bowles, 1997).
0
100
200
Pressure (kN/m2) 300 400
500
600
0 For RDFS h1/B = 1; fiber = 1%
20
Settlement (mm)
40
80 100 120 140 160
3 2 2 Bp Bf þ 30 5 Sp ¼ 4 Bf Bp þ 30
(10)
After calculating safe bearing capacity from both the criterions, lower of the two is reported as the safe bearing capacity, and multiplying this value with the area of the actual foundation, allowable load is calculated. Table 4 shows the results of the numerical problem. It clearly shows the significance of relative density on the ultimate bearing capacity of RDFS sand layer overlying unreinforced sand layer.
RD1 = 50%; RD2 = 30% RD1 = 70%; RD2 = 30% 30% RD (Unreinforced) RD1 = 50%; RD2 = 30% (Unreinforced) RD1 = 70%; RD2 = 30% (Unreinforced)
60
For settlement criterion, Eqn. (10) (Terzaghi and Peck, 1948), is used to calculate the settlement of test plate from the corresponding pressure settlement curve, after knowing the dimensions of actual foundation. After calculating the settlement of test plate, corresponding bearing capacity is noted down from the pressure settlement curve and designated (extrapolated) as safe bearing capacity of actual foundation.
5. Conclusions
Fig. 10. Pressure settlement curves.
An experimental study has been under taken to study the
Table 3 Parameters used in the numerical problem. Cohesion (kN/m2)
Combination of RD (%) RD1
RD2
f1
f2
c1
c2
g1
g2
RDFS
50 70 30 50 70
30 30 30 30 30
34 38 29 32 36.5
29 29 29 29 29
10 16 0 0 0
0 0 0 0 0
15.1 15.7 14.4 15.1 15.7
14.4 14.4 14.4 14.1 15.4
Unreinforced
Angle of internal friction (degree)
Soil unit weight (kN/m2)
Condition
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V. Sharma, A. Kumar / Geotextiles and Geomembranes xxx (2017) 1e9
Table 4 Results of numerical problem. S. No.
1 2 3
RD1
30 50 70
RD2
30 30 30
Safe bearing capacity ¼ qns (kN/m2)
Qallowable (kN)
Shear criterion
Settlement criterion
RDFS
Sand only
RDFS
Sand only
RDFS
Sand only
e 191.34 297.5
76.46 93.1 122.81
e 215 255
40 70 91
e 1352.5 1802.5
282.74 494.8 643.24
ultimate bearing capacity and settlement behavior, of circular and ring footings resting on RDFS layer overlying unreinforced sand layer, with different combinations of relative densities of top RDFS, and bottom unreinforced sand layers. The following conclusions can be drawn from the results discussed. Increasing the relative density of sand results in increase in the ultimate bearing capacity as well as there is improvement in settlement reduction. Maximum improvement in terms of BCR was observed when top RDFS and bottom sand layers were compacted to different relative densities instead of having same relative density i.e. RD1 ¼ 70% and RD2 ¼ 30%. Maximum improvement, in terms of BCR and SR, was observed when, ri/ro ¼ 0.40 for all combinations of relative densities of top RDFS and bottom unreinforced sand layer. When RD1 ¼ 70% and RD2 ¼ 30%; h1/B ¼ 1.00, and 1.25% fiber; BCR value, of circular, and ring footing (ri/ro ¼ 0.40), is 5.48, and 6.35, respectively. Similarly, when RD1 ¼ 70% and RD2 ¼ 30%; h1/B ¼ 1.00, and 1.25% fiber; SR value, of circular, and ring footing (ri/ro ¼ 0.40), is 0.33, and 0.20, respectively. On increasing the percentage of fibers in RDFS layer, both BCR and SR values have improved. When RD1 ¼ 70% and RD2 ¼ 30%; h1/B ¼ 1.00, and fiber prcentage is increased from 0.5 to 1.25%; BCR value, of ring footing (ri/ro ¼ 0.40), gets improved from 5.40 to 6.35. When RD1 ¼ 70% and RD2 ¼ 30%; h1/B ¼ 1.00, and fiber percentage is increased from 0.5 to 1.25%; SR value, of ring footing (ri/ro ¼ 0.40), gets improved from 0.44 to 0.20. Compacting the top RDFS layer to higher relative density (70%) compared to lesser relative density (50%) by keeping the lower layer compacted at 30% relative density and the thickness of RDFS constant (1.00B); consumption of fibers can be reduced to 1% from 1.25%. Increasing the thickness of RDFS layer significantly increases the improvement both in terms of BCR and SR, for all combinations of relative densities of top RDFS layer and bottom sand layer. When RD1 ¼ 70% and RD2 ¼ 30%; 1% fiber, and h1/B increased from 0.50 to 1.00; BCR value, for ring footing (ri/ro ¼ 0.40), gets improved from 5.19 to 6.05. When RD1 ¼ 70% and RD2 ¼ 70%; 1% fiber, and h1/B increased from 0.50 to 1.00; SR value gets improved from 0.38 to 0.23. Notation The following symbols are used in this paper: B Bp, Bf Cc Cu c1, c2 D10
width of footing width of plate, and foundation, respectively; and coefficient of curvature coefficient of uniformity cohesion of top RDFS, and bottom unreinforced sand layer, respectively effective size of sand
D50 Gs, Gf h1, h2
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Please cite this article in press as: Sharma, V., Kumar, A., Influence of relative density of soil on performance of fiber-reinforced soil foundations, Geotextiles and Geomembranes (2017), http://dx.doi.org/10.1016/j.geotexmem.2017.06.004