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Circular footings resting on geotextile-reinforced sand bed
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Geotextiles and Geomembranes 25 (2007) 377–384 www.elsevier.com/locate/geotexmem
Technical note
Circular footings resting on geotextile-reinforced sand bed P.K. Basudhar, Santanu Saha, Kousik Deb Department of Civil Engineering, IIT Kanpur, Kanpur 208016, India Received 25 May 2006; received in revised form 20 September 2006; accepted 20 September 2006 Available online 3 April 2007
Abstract The note pertains to an experimental study made on circular footings resting on semi-infinite layer of sand reinforced with geotextiles. Using the concept of homogenization of such soils, both analytical and numerical analyses have also been conducted to predict the loadsettlement behavior and compared with experimental observations. The study highlights the effect of the footing size, number of reinforcing layers, reinforcement placement pattern and bond length and the relative density of the soil on the load-settlement characteristics of the footings. r 2007 Elsevier Ltd. All rights reserved. Keywords: Circular footings; Equivalent secant modulus (Eq); FLAC; Geotextile; Homogenization
1. Introduction Behavior of foundations on reinforced sand beds is one of the most interesting topics in geotechnical engineering. Considerable experimental research has been reported to study the behavior of footing resting on geosyntheticreinforced bed (Binquet and Lee, 1975; Andrawes et al., 1983; Guido et al., 1985; Sakti and Das, 1987; Love et al., 1987; Das, 1989, Khing et al., 1994; Manjunath and Dewaikar, 1994; Adams and Collin, 1997; Das et al., 1998a, b; Lee et al., 1999; Dash et al., 2001a, b; Patra et al., 2005, 2006; Bera et al., 2005; Ghosh et al., 2005). From the studies reported in the literature it has been observed that in comparison to the study of the bearing capacity of the strip and square footings on reinforced soil, very limited attention has been paid to that of isolated circular footings. Even the studies on circular footings mostly pertain to the area wherein the underlying soil is reinforced with geogrids or geocells (Dash et al., 2003a, b; Boushehrian and Hataf, 2003; Sitharam and Sireesh, 2004). However, not much work has been conducted to study the behavior of circular footings resting on sand beds reinforced with geotextiles. Thus, there is a necessity to
conduct such studies to develop a theoretical model to predict such behavior that is consistent with experimental observations. Therefore, such a study has been undertaken and reported here. 2. Details of experimental studies The necessary details of the materials used, experimental set-up, tests conducted and the experimental procedures have been presented as follows. 2.1. Materials Dry Ganga sand with coefficient of uniformity 2.53, specific gravity 2.68, maximum void ratio 1.25, minimum void ratio 0.57 and average particle size 0.17 mm was used in the experimental study as founding material. Woven Geotextile (with 0.48 mm thickness, bursting strength 2000 kN/m2 at failure strain of 18% and secant modulus of elasticity 18,000 kN/m2 at 5% elongation) was used for reinforcing the soil. 2.2. Load-settlement tests
Corresponding author. Tel.:+91 512 259 7029; fax:+91 512 259 7395.
E-mail addresses: [email protected] (P.K. Basudhar), [email protected] (K. Deb). 0266-1144/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.geotexmem.2006.09.003
The model tests were carried out in a square tank (0.44 m 0.44 m 0.21 m). Three model circular footings
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of 30, 45 and 60 mm diameter were used. The tank was filled up by Ganga sand at the selected relative density of 45%. To keep the relative density of the sand bed at 45%, the height of free fall and rate of pouring of the sand was chosen to be 100 mm and 3.0 min per 1.0 kg of sand, respectively. The depth of the soil strata was 3.5 times the diameter of the largest footing. The tank width being 7–8 times the footing size, the boundary effects is minimal. Thus, it simulated the semi-infinite condition of the soil medium. The strain-controlled hydraulic type loadingmachine was used for the loading. The rate of strain was chosen to be 0.5 mm/min. A 1000 N capacity proving ring with a least count of 2.31 N was used to record the amount of load applied. The settlement of the footing was measured by using a dial gauge of least counts 0.25 mm. The loading was continued up to the failure of the soil. Tests were done for all the three footings resting on the sand bed with and without reinforcement varying the number of layer of reinforcements from 1 to 3. Their placement has been shown in Fig. 1. Tests were initially conducted for reinforcements of equal lengths, their value being 3.5 times the width of the footing. Subsequently, the reinforcements were placed along the depth in both circular (conical) and rectangular patterns. The length of each reinforcement layer was varied to study the effect of the grip (bond) length. Even for the maximum size of reinforcement (0.21 m diameter) a clear distance of 0.115 m from either end of the wall of the container was maintained. Thus, the edge effect was likely to be marginal. For the 60 mm diameter circular footing, radial horizontal strain corresponding to different stress levels was measured at different points of the reinforcements. For the recording of strains at particular stress level, manually operated system consisting of a manually operated hydraulic jack for lifting the tank was used to replace the strain-controlled machine-operated loading system. It should be noted that each of the loading arrangements was operated separately depending on the need. Most of the studies were conducted keeping the relative density of the sand at 45%. The effect of relative density
0.25D
D
Circular Footing
D 2D 0.21 m 3.5D
0.44 m Fig. 1. Reinforcement arrangement pattern (not in scale).
variation was studied for 45 mm diameter circular footing. In each case, three number of reinforcement layers were considered. In the first case, the sand below the third layer was poured at 45% relative density. Then the third layer of reinforcement was placed. Sand was placed in layers and geotextiles were placed in between. Each sand layer above each reinforcement layer was rolled for a fixed number of times with a solid iron cylinder of 0.40 m length and 50 mm diameter. Then the load-settlement tests were done. For determining the relative density achieved, the following procedure was adopted. Sand was poured up to a certain height at 45% relative density and it was rolled 25 times. Weight and volume of that sand was measured and the resulting relative density achieved was found to be about 73%. Similarly, the resulting relative density for 40 times rolling was estimated to be about 84%. The interaction between the cohesionless soil and geotextiles at different relative densities can be expressed as a factor o (Dembicki and Jermolowicz, 1991) defined as: o ¼ tan c/ tan f, where f is the angle of shearing resistance of soil (can be determined by direct shear test), and c is the friction angle at the soil–geotextile interface for a particular relative density. For determining the friction coefficient between soil and geotextile frictional test (Dembicki and Jermolowicz, 1991) was done in a conventional direct shear test apparatus. In upper box, the soil was placed at the desired relative density. At the top of the lower box, the geotextile was placed by gluing it on the perplex sheet and the tests were conducted at a rate of testing 0.25 mm/min. For example, at 45% relative density the angle of frictional resistance of the dry sand and frictional coefficient between sand and geotextile was found to be 351 and 27.51, respectively. 2.3. Radial horizontal strain measurement To obtain the magnitude of radial horizontal strain of the geotextile placed at different depths, strain gauges (type SM35-10T, gauge length 10 mm, 350 O and 2.1 gauge factor, package tolerance 70.5 O, Transen manufacturers, Bangalore) were used. Strain measurement was made with the help of digital strain indicator (D-3500, 10 channels, portable, battery powered precision instrument, Instrument Division Measurement Company, USA). The surface of the geotextiles was cleaned with degreasing chemicals and subsequently the strain gauges were glued on the cleaned surface at the designated locations. Some pressure was applied on the glued strain gauges so that proper bonding between the strain gauge and the surface is attained. Dummy gauges were used for temperature compensations. Before making any measurement on the strain gauges, it was checked that these are not damaged. The model tests were conducted by using 60 mm diameter circular footing. On each 0.21 m circular geotextile sheet, four strain gauges were attached. They were attached at a distance of 21, 42, 63, and 84 mm from the center of the
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42 mm
84 mm
126 mm
168 mm
210 mm
Geotextile
Strain Gauge
Fig. 2. Strain gauge attachment pattern (not in scale) (footing size ¼ 60 mm).
18 Relative Density = 45%
Unreinforced Soil One Layer Two Layers Three Layers
10 8
Relative Density = 73%
15 Vertical Stress x 104 (N/m2)
Vertical Stress x 104 (N/m2)
12
6 4
Relative Density = 84% 12 9 6 3
2
0
0 0
5
10 Settlement (mm)
15
0
20
5
15 10 Settlement (mm)
20
25
Fig. 4. Stress-settlement curves for different relative densities.
Fig. 3. Stress-settlement curves for 30 mm diameter circular footing.
reinforcement (as shown in Fig. 2). All strain-measuring readings were taken following strictly the steps laid down in the instruction manual. 3. Experiment results 3.1. Load-settlement tests Typical load-settlement plots for 30 mm footing size with and without reinforcements have been shown in Fig. 3. The effect of varying relative density after rolling process was studied and the load-settlement plots have been presented in Fig. 4. 3.2. Radial horizontal strain measurement During the load-settlement tests with 60 mm diameter circular footing, the final radial horizontal strain values at different points on the geotextile layers placed within the
Horizontal Strain (micro-strain x 1000)
7 6
One Layer
5
Two Layers Three Layers
4 3 2 1 0 0
0.5 1 Distance from Centre of Loading (in terms of D)
1.5
Fig. 5. Induced horizontal strain variation at 0.25D placement depth.
sand stratum were measured as presented in Figs. 5 and 6. At different points, the strains were recorded at varying vertical stress levels as shown in Fig. 7.
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4.2. Improvement in the modulus of elasticity
Horizontal Strain (micro-strain x 1000)
4 Placement Depth = 2D
Assuming the whole soil medium to be homogeneous, the equivalent secant modulus (Eq) values have been computed as
Placement Depth = D
3
Placement Depth = 0.25D
s Eq ¼ ,
2
1
0 0
0.5 1 Distance from Centre of Loading (in terms of D)
1.5
Fig. 6. Induced horizontal strain variation at different placement depths.
Horizontal Strain (micro-strain x 1000)
7 Radial Distance = 0.35D 6
Radial Distance = 0.7D Radial Distance = 1.05D
5
Radial Distance = 1.4D 4 3
where e ¼ DL/L, s is the average applied stress, e is the average strain, DL is the settlement of the footing observed and L is the depth of the sand bed ( ¼ 0.21 m). From the experimental stress–strain curves the equivalent secant moduli for all the different sizes of footings and reinforcement conditions have been determined and shown in Fig. 8. The figure depicts that as the number of layer increases, there is a marked improvement of the equivalent secant modulus (Eq). However, as the diameter increases, there is a decrease in the value of Eq for the corresponding reinforcement conditions. The effect of footing size in improving the secant modulus has been represented in Table 1. It is seen that the increase in the value of Eq is more pronounced for smaller size of footings (Fig. 8). In the present study, the secant modulus and the initial tangent modulus are almost identical, as the stresssettlement diagrams are linear almost up to the peak failure stress.
2 200
1 160
0 4
2
Vertical Stress x
6
8
10
Eq (kN/m2)
0
104 (N/m2)
Fig. 7. Stress–horizontal strain plot for single-layer reinforcement at different radial distances.
120 80 Diameter = 60 mm Diameter = 45 mm Diameter = 30 mm
40 0
4. Analyses and discussion
0
In Fig. 3, the stress-settlement diagram corresponding to the unreinforced case signifies local shear failure, whereas the other diagrams for reinforced conditions signify linearly elastic–plastic failure; these curves are similar to the load-settlement diagram for general shear failure case for unreinforced soil. In Fig. 4, it has been observed that for higher relative densities (73% and 84%) there are sharp peak stresses where the failure occurs. Beyond this stress value strain softening has been observed. However, for low-relative density (45%) there is no strain softening.
1
1.5
2
2.5
3
3.5
Number of Reinforcement Layers
In this section, analysis of the test results and their detailed discussions were presented. 4.1. Modes of failure
0.5
Fig. 8. Secant modulus improvement with reinforcement.
Table 1 Size effect on secant modulus improvement Number of layer
0 1 2 3
% decrease in Ed D/D0 1.0
1.5
2.0
0.0 0.0 0.0 0.0
14.3 15.4 27.2 13.1
33.3 35.2 45.7 48.6
Note: D0 ¼ smallest footing size ¼ 30 mm.
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4.3. Analytical prediction of ultimate settlement To compare the experimental values of settlement with analytical predictions, the method proposed by Janbu et al. (1956) as modified by Christian and Carrier (1978) has been used. The average settlement (Se) can be calculated as S e ¼ m0 m1 qn B=E d , where B is the width of the footing (here diameter of the circular footing), qn is the applied footing load, Ed is elastic modulus of the soil, m0 and m1 values depend on the depth of the footing and the thickness between the footing base and hard strata, respectively. The Ed values (same as Eq) have been taken from the stress-settlement results obtained with 30 mm diameter circular footing. This is equivalent to doing a plate load test in situ to determine the Eq values that are subsequently used in predicting the settlement behavior of prototype foundation. This approach of finding Eq had to be adopted as testing of sand samples at a very low-relative density was found to be unsuccessful on a tri-axial setup. The comparison of the results has been presented in Table 2. It can be seen from Table 2 that, there is an excellent agreement between the predicted and observed values for 30 and 45 mm (maximum error less that 12.5%) footing sizes. However, the predictions for the 60 mm footing size have been found to be conservative (maximum error less than 34%) signifying scale effect. 4.4. Numerical prediction of ultimate settlement
381
soil the concept of homogenization was used and the equivalent modulus of elasticity (Eq) was calculated. Like analytical prediction, the Eq values were taken from the stress-settlement results obtained by experiment with 30 mm diameter circular. In the numerical analysis, soil was assumed to be linearly elastic as from the experimental results it has been found that the stress-settlement diagrams are linear almost up to the peak failure stress (Fig. 7). Table 2 shows that the predictions with respect to settlement made by using Janbu’s method are in very close agreement with the values predicted by FLAC analysis as well as the experimentally observed values when the width of the foundation is up to 45 mm (maximum error less than 12.5%). However, when the foundation width is 60 mm the relative error in the predicted values by Janbu’s method is quite significant. This brings out an interesting fact that the prediction of the ultimate settlement by Janbu’s method shows excellent agreement with the settlement values predicted by FLAC and observed by experiments if the model footing size used to determine the Eq value is at least 0.67 times the prototype footing size. However, it is interesting to see that the maximum error between the absolute values of settlement predicted by using the Janbu’s method and FLAC analysis is 34% and 16%, respectively, as compared to the experimental values. Thus, for large size footings the error in predictions is lesser when D/2 Surcharge of Circular Footing
To predict the settlement, a numerical analysis of the problem as stated earlier was also done using fast Lagrangian analysis of continua (FLAC). From consideration of symmetry only half portion of the problem was taken in to account. To minimize the boundary effect, the vertical boundary at the far end, on the right-hand side, was set 0.22 m away (almost seven times of the footing radius) from the center of loading that was assumed to be free in the vertical direction and restricted in horizontal direction. The bottom horizontal boundary was restricted in both the vertical and horizontal directions. The discretization of the medium for modeling is shown in Fig. 9. To use the modulus of elasticity of the reinforced
0.21 m Ganga Sand
0.22 m Fig. 9. The discretization of the medium for numerical modeling using FLAC (not to scale).
Table 2 Comparison of the predicted and the observed settlements Footing size (D in mm)
Settlement (in terms of D) Observed (by experiment)
30 45 60
0.40 0.42 0.44
Predicted (by Janbu’s method, 1956)
Predicted (by FLAC)
1 layer
2 layers
3 layers
1 layer
2 layers
3 layers
0.35 0.44 0.59
0.40 0.38 0.47
0.40 0.44 0.54
0.35 0.44 0.51
0.40 0.38 0.39
0.40 0.45 0.46
Note: Equivalent elastic modulus of the soil has been taken from the stress-settlement results obtained with 30 mm diameter circular plate.
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FLAC is used. Considering several sources of error in conducting experiments, an error of the order of 34% may be considered to be permissible. Thus, use of a simple method amenable to hand computations results in values that are not very much different from a more rigorous and numerically involved solution procedure. Thus, it is concluded that the use of Janbu’s method (1956) can be used with confidence in predicting the settlement response of circular footings resting on reinforced beds using the concept of homogenization.
rectangular in shape. Similarly, Fig. 11 shows that, in general for a fixed percentage increase in settlement, the percentage decrease in material is more for rectangular reinforcement. Thus, it is concluded that the rectangular shape of the reinforcement is preferable as compared to circular shape reinforcement for the overall strength and settlement improvement, as the desired decrease in material is more than 10%. In these figures, the percentage decrease in the material depicts the decrease in grip (bond) length. 4.6. Effect of relative density variation
4.5. Effect of reinforcement placement pattern and grip (bond) length Figs. 10 and 11 show the effects of reinforcement patterns on the improvement of bearing capacity and settlement reduction. Fig. 10 shows that in general for a fixed percentage decrease in bearing capacity, the percentage decrease in material is more when the reinforcement is
4.7. Radial horizontal strain reduction with reinforcement
70 Conical
% Decrease in Material
60
30
From Figs. 5 and 6 it has been found that the radial horizontal strain at any particular point decreases with depth of placement of the reinforcement layer as well as with the increase in the horizontal radial distance from center of loading. In Fig. 6, the small values of strain at 2D (D is the diameter of the footing) depth of placement have revealed that the stresses beyond this depth are not significant. However, as the number of reinforcement layer increases the stiffness of the soil is also increases. Fig. 8 indicates that as the number of reinforcement layer increases the secant modulus value also increases. Thus, due to increase of stiffness use of three layers of reinforcement is effective for reducing the settlement and increasing the bearing capacity of the soil. Though little horizontal strain was measured if the reinforcement layer was placed at a depth of 2D. Fig. 7 shows that the strain values increases with vertical stress applied. The rate of increase of strain values is linear for far-off points, but nonlinear for the nearby points. No effort has been made to theoretically predict the radial horizontal strain values, as the strain calculation based on the concept of homogenization cannot give the strain of the reinforcements. Still the results are presented to find the significant placement depth and also for future modeling of soilreinforcement system.
20
4.8. Reduction of settlement with reinforcement
10
To highlight the beneficial effect of number of reinforcement layers on the settlement reduction, the percentage of settlement reduction compared to the unreinforced condition has been presented in Table 3. It can be observed that with the increase in number of reinforcement layers the settlement decreases with decreasing rate. It is further
Rectangular 50 40 30 20 10 0 60 40 20 % Decrease in Bearing Capacity
0
80
Fig. 10. Effect of reinforcement pattern on strength.
70 Conical
60 % Decrease in Material
The effect of compaction in the reinforcing zone designated by the varying relative density has been presented in Fig. 4. It has been observed that as the relative density increases the bearing capacity also increases, but corresponding to the ultimate bearing capacity, final settlement is more or less the same. The increase of bearing capacities has been found to be 20.8% and 30.6% for the relative densities of 73% and 84%, respectively.
Rectangular 50 40
0 0
50
100 150 % Increase in Settlement
200
Fig. 11. Effect of reinforcement pattern on settlement.
250
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reinforced conditions, the BCR decreases with increase in footing size and later the BCR values become steady.
Table 3 Percentage reduction of settlement Diameter (mm)
Number of layer
30 45 60
5. Conclusions
1 layer
2 layer
3 layer
67.5 60.5 59.1
80.0 70.2 67.0
80.0 76.2 72.7
From the analyses and discussions on the various test results, the following conclusions can be drawn:
Table 4 Percentage increase in BCR Diameter (mm)
Number of layer
30 45 60
1 layer
2 layer
3 layer
181.2 150.0 150.0
387.5 237.5 212.5
456.3 325.0 293.8
8 Unreinforced Soil One Layer Two Layers Three Layers
7 6 BCR
5 4 3 2 1 0 1
1.2
383
1.4
1.6
1.8
2
D / D0 Fig. 12. Size effect on BCR.
observed that for 30 mm footing, the settlement reduction is insignificant if the number of layer is increased from two to three. 4.9. Bearing capacity improvement with reinforcement To have a quantitative estimate of the improvement in the bearing capacity values with respect to the unreinforced one, bearing capacity ratio (BCR) values have been calculated and the corresponding percentage increase in the BCR values have been presented in Table 4. This highlights that there is a substantial increase in the BCR values for each increment in the number of reinforcement layers, even though the settlement improvement is not appreciable (as compared to the BCR improvement) as already discussed. This may be due to the fact that the geotextile do not have bending stiffness and thus cannot appreciably reduce the settlement. The effect of footing size on BCR has been studied and presented in Fig. 12. It has been observed that for
1. The load settlement test conducted for low relative density of the sand bed (45%) revealed that for different number of layers the reinforced sand bed has behaved as a linearly elastic–plastic material. For dense sand, the failure has occurred at a peak stress followed by strain softening phenomenon. 2. The analyses of the observed results showed that modeling of reinforced soil as a complete homogeneous system for predicting the modulus of elasticity are satisfactory. With the increase in the number of layer of reinforcements, there is a marked improvement of the equivalent secant modulus (Eq). As the footing size increases, the Eq value decreases for the corresponding reinforcement conditions. When the footing size double, the maximum percentage decrease in Eq value is of the order of 48%. The increase in the value of Eq is more pronounced for smaller size of footing 3. The theory of elasticity solution proposed by Janbu et al. (1956) are in excellent agreement with the settlement values predicted by using FLAC as well as experimental observations, if the prototype footing size is upto 1.5 times the model footing. There after there is some discrepancy in these values with the error in the predictions differing by 15% (FLAC) to 34% (from the experimental values). 4. For substantial saving in the material the rectangularshaped reinforcement is preferable as compared to the circular reinforcement. 5. The radial horizontal strain measurements indicated that at 2D depth of placement of the reinforcing layer, the strain values become insignificant for three-layered reinforced conditions. 6. With the increase in number of reinforcement layers, the settlement value gradually decreases with decreasing rate. 7. There is a substantial increase in the BCR values for each increment in the number of reinforcement layers; even though the settlement improvement is not appreciable. For three-layer reinforced case, the bearing capacity improvements have been found to be 4.5 times for 30 mm diameter footing and about 3.0 times for 45 and 60 mm diameter footings.
Acknowledgement The authors would like to thank Dr. N. Sivakugan, Head, Civil & Environmental Engineering Department, James Cook University, Townsville, Australia for his kind
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help to use and learn the software FLAC during his stay at IIT Kanpur. References Adams, M.T., Collin, J.G., 1997. Large model spread footing load tests on geosynthetic reinforced soil foundations. Journal of Geotechnical and Geoenvironmental Engineering Division, ASCE 123 (1), 66–72. Andrawes, K.Z., Mcgown, A., Wilson-Fahmy, R.F., 1983. The behavior of a geotextile reinforced sand loaded by a strip footing. In: Eighth European Conference on Soil Mechanics and Foundation Engineering, Helsinki, pp. 329–334. Bera, A.K., Ghosh, A., Ghosh, A., 2005. Regression model for bearing capacity of a square footing on reinforced pond ash. Geotextiles and Geomembranes 23 (2), 261–286. Binquet, J., Lee, K.L., 1975. Bearing capacity tests on reinforced earth slabs. Journal of Geotechnical Engineering Division, ASCE 101 (12), 1241–1255. Boushehrian, J.H., Hataf, N., 2003. Experimental and numerical investigation on the bearing capacity of model circular and ring footings on reinforced sand. Geotextiles and Geomembranes 21, 241–256. Christian, J.T., Carrier, W.D., 1978. Janbu, Bjerrum and Kjaernsli’s chart reinterpreted. Canadian Geotechnical Journal 15. Das, B.M., 1989. Foundation on sand underlain by soft clay with geotextile at sand-clay interface. In: Proceedings of Geosynthetics Conference, San Diego, USA, pp. 203–213. Das, B.M., Khing, K.H., Shin, E.C., 1998a. Stabiliztaion of weak clay with strong sand and geogrid at sand-clay interface. Transportation Research Record 1611, 55–62. Das, B.M., Maji, A., Shin, E.C., 1998b. Foundation on geogrid-reinforced sand-effect of transient loading. Geotextiles and Geomembranes 16, 151–160. Dash, S.K., Krishnaswamy, N.R., Rajagopal, K., 2001a. Bearing capacity of strip footings supported on geocell-reinforced sand. Geotextiles and Geomembranes 19, 235–256. Dash, S.K., Rajagopal, K., Krishnaswamy, N.R., 2001b. Strip footing on geocell reinforced sand beds with additional planar reinforcement. Geotextiles and Geomembranes 19, 529–538. Dash, S.K., Sireesh, S., Sitharam, T.G., 2003a. Model studies on circular footing supported on geocell reinforced sand underlain by soft clay. Geotextiles and Geomembranes 21, 197–219.
Dash, S.K., Sireesh, S., Sitharam, T.G., 2003b. Behaviour of geocellreinforced sand beds under circular footing. Ground Improvement 7 (3), 111–115. Dembicki, E., Jermolowicz, P., 1991. Soil-geotextile interaction. Gotextiles and Geomembranes 10, 249–268. Ghosh, A., Ghosh, A., Bera, A.K., 2005. Bearing capacity of square footing on pond ash reinforced with jute-geotextile. Geotextiles and Geomembranes 23 (2), 144–173. Guido, V.A., Biesiadecki, G.L., Sullivan, M.J., 1985. Bearing capacity of a geotextile-reinforced foundation. In: Proceedings of 11th International Conference on Soil Mechanics and Foundation Engineering, San Francisco, USA, pp. 1777–1780. Janbu, N., Bjerrum, L., Kjaernsli, B., 1956. Veiledning Ved Losing av Fandamenteringsoppgaver. Norwegian Geotechnical Institute Publication No. 16, Oslo. Khing, K.H., Das, B.M., Puri, V.K., Yen, S.C., Cook, E.E., 1994. Foundation on strong sand underlain by weak clay with geogrid at the interface. Geotextiles and Geomembranes 13, 199–206. 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. Canadian Geotechnical Journal 36, 793–806. Love, J.P., Burd, H.J., Milligan, G.W.E., Houlsby, G.T., 1987. Analytical and model studies of reinforcement of a layer of granular fill on a soft clay subgrade. Canadian Geotechnical Journal 24, 611–622. Manjunath, V.R., Dewaikar, D.M., 1994. Model footing tests on geofabric reinforced granular fill overlying soft clay. In: Proceedings of Fifth International Conference on Geotextiles, Geomembranes and Related Products, Singapore, pp. 327–330. Patra, C.R., Das, B.M., Atalar, C., 2005. Bearing capacity of embedded strip foundation on geogrid-reinforced sand. Geotextiles and Geomembranes 23, 454–462. Patra, C.R., Das, B.M., Bhoi, M., Shin, E.C., 2006. Eccentrically loaded strip foundation on geogrid-reinforced sand. Geotextiles and Geomembranes 24 (4), 254–259. Sakti, J.P., Das, B.M., 1987. Model tests for strip foundation on clay reinforced with geotextile layers. Transportation Research Record 1153, 40–45. Sitharam, T.G., Sireesh, S., 2004. Model studies of embedded circular footing on geogrid-reinforced sand beds. Ground Improvement 8 (2), 69–75.
Geotextiles and Geomembranes 25 (2007) 377–384 www.elsevier.com/locate/geotexmem
Technical note
Circular footings resting on geotextile-reinforced sand bed P.K. Basudhar, Santanu Saha, Kousik Deb Department of Civil Engineering, IIT Kanpur, Kanpur 208016, India Received 25 May 2006; received in revised form 20 September 2006; accepted 20 September 2006 Available online 3 April 2007
Abstract The note pertains to an experimental study made on circular footings resting on semi-infinite layer of sand reinforced with geotextiles. Using the concept of homogenization of such soils, both analytical and numerical analyses have also been conducted to predict the loadsettlement behavior and compared with experimental observations. The study highlights the effect of the footing size, number of reinforcing layers, reinforcement placement pattern and bond length and the relative density of the soil on the load-settlement characteristics of the footings. r 2007 Elsevier Ltd. All rights reserved. Keywords: Circular footings; Equivalent secant modulus (Eq); FLAC; Geotextile; Homogenization
1. Introduction Behavior of foundations on reinforced sand beds is one of the most interesting topics in geotechnical engineering. Considerable experimental research has been reported to study the behavior of footing resting on geosyntheticreinforced bed (Binquet and Lee, 1975; Andrawes et al., 1983; Guido et al., 1985; Sakti and Das, 1987; Love et al., 1987; Das, 1989, Khing et al., 1994; Manjunath and Dewaikar, 1994; Adams and Collin, 1997; Das et al., 1998a, b; Lee et al., 1999; Dash et al., 2001a, b; Patra et al., 2005, 2006; Bera et al., 2005; Ghosh et al., 2005). From the studies reported in the literature it has been observed that in comparison to the study of the bearing capacity of the strip and square footings on reinforced soil, very limited attention has been paid to that of isolated circular footings. Even the studies on circular footings mostly pertain to the area wherein the underlying soil is reinforced with geogrids or geocells (Dash et al., 2003a, b; Boushehrian and Hataf, 2003; Sitharam and Sireesh, 2004). However, not much work has been conducted to study the behavior of circular footings resting on sand beds reinforced with geotextiles. Thus, there is a necessity to
conduct such studies to develop a theoretical model to predict such behavior that is consistent with experimental observations. Therefore, such a study has been undertaken and reported here. 2. Details of experimental studies The necessary details of the materials used, experimental set-up, tests conducted and the experimental procedures have been presented as follows. 2.1. Materials Dry Ganga sand with coefficient of uniformity 2.53, specific gravity 2.68, maximum void ratio 1.25, minimum void ratio 0.57 and average particle size 0.17 mm was used in the experimental study as founding material. Woven Geotextile (with 0.48 mm thickness, bursting strength 2000 kN/m2 at failure strain of 18% and secant modulus of elasticity 18,000 kN/m2 at 5% elongation) was used for reinforcing the soil. 2.2. Load-settlement tests
Corresponding author. Tel.:+91 512 259 7029; fax:+91 512 259 7395.
E-mail addresses: [email protected] (P.K. Basudhar), [email protected] (K. Deb). 0266-1144/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.geotexmem.2006.09.003
The model tests were carried out in a square tank (0.44 m 0.44 m 0.21 m). Three model circular footings
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of 30, 45 and 60 mm diameter were used. The tank was filled up by Ganga sand at the selected relative density of 45%. To keep the relative density of the sand bed at 45%, the height of free fall and rate of pouring of the sand was chosen to be 100 mm and 3.0 min per 1.0 kg of sand, respectively. The depth of the soil strata was 3.5 times the diameter of the largest footing. The tank width being 7–8 times the footing size, the boundary effects is minimal. Thus, it simulated the semi-infinite condition of the soil medium. The strain-controlled hydraulic type loadingmachine was used for the loading. The rate of strain was chosen to be 0.5 mm/min. A 1000 N capacity proving ring with a least count of 2.31 N was used to record the amount of load applied. The settlement of the footing was measured by using a dial gauge of least counts 0.25 mm. The loading was continued up to the failure of the soil. Tests were done for all the three footings resting on the sand bed with and without reinforcement varying the number of layer of reinforcements from 1 to 3. Their placement has been shown in Fig. 1. Tests were initially conducted for reinforcements of equal lengths, their value being 3.5 times the width of the footing. Subsequently, the reinforcements were placed along the depth in both circular (conical) and rectangular patterns. The length of each reinforcement layer was varied to study the effect of the grip (bond) length. Even for the maximum size of reinforcement (0.21 m diameter) a clear distance of 0.115 m from either end of the wall of the container was maintained. Thus, the edge effect was likely to be marginal. For the 60 mm diameter circular footing, radial horizontal strain corresponding to different stress levels was measured at different points of the reinforcements. For the recording of strains at particular stress level, manually operated system consisting of a manually operated hydraulic jack for lifting the tank was used to replace the strain-controlled machine-operated loading system. It should be noted that each of the loading arrangements was operated separately depending on the need. Most of the studies were conducted keeping the relative density of the sand at 45%. The effect of relative density
0.25D
D
Circular Footing
D 2D 0.21 m 3.5D
0.44 m Fig. 1. Reinforcement arrangement pattern (not in scale).
variation was studied for 45 mm diameter circular footing. In each case, three number of reinforcement layers were considered. In the first case, the sand below the third layer was poured at 45% relative density. Then the third layer of reinforcement was placed. Sand was placed in layers and geotextiles were placed in between. Each sand layer above each reinforcement layer was rolled for a fixed number of times with a solid iron cylinder of 0.40 m length and 50 mm diameter. Then the load-settlement tests were done. For determining the relative density achieved, the following procedure was adopted. Sand was poured up to a certain height at 45% relative density and it was rolled 25 times. Weight and volume of that sand was measured and the resulting relative density achieved was found to be about 73%. Similarly, the resulting relative density for 40 times rolling was estimated to be about 84%. The interaction between the cohesionless soil and geotextiles at different relative densities can be expressed as a factor o (Dembicki and Jermolowicz, 1991) defined as: o ¼ tan c/ tan f, where f is the angle of shearing resistance of soil (can be determined by direct shear test), and c is the friction angle at the soil–geotextile interface for a particular relative density. For determining the friction coefficient between soil and geotextile frictional test (Dembicki and Jermolowicz, 1991) was done in a conventional direct shear test apparatus. In upper box, the soil was placed at the desired relative density. At the top of the lower box, the geotextile was placed by gluing it on the perplex sheet and the tests were conducted at a rate of testing 0.25 mm/min. For example, at 45% relative density the angle of frictional resistance of the dry sand and frictional coefficient between sand and geotextile was found to be 351 and 27.51, respectively. 2.3. Radial horizontal strain measurement To obtain the magnitude of radial horizontal strain of the geotextile placed at different depths, strain gauges (type SM35-10T, gauge length 10 mm, 350 O and 2.1 gauge factor, package tolerance 70.5 O, Transen manufacturers, Bangalore) were used. Strain measurement was made with the help of digital strain indicator (D-3500, 10 channels, portable, battery powered precision instrument, Instrument Division Measurement Company, USA). The surface of the geotextiles was cleaned with degreasing chemicals and subsequently the strain gauges were glued on the cleaned surface at the designated locations. Some pressure was applied on the glued strain gauges so that proper bonding between the strain gauge and the surface is attained. Dummy gauges were used for temperature compensations. Before making any measurement on the strain gauges, it was checked that these are not damaged. The model tests were conducted by using 60 mm diameter circular footing. On each 0.21 m circular geotextile sheet, four strain gauges were attached. They were attached at a distance of 21, 42, 63, and 84 mm from the center of the
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42 mm
84 mm
126 mm
168 mm
210 mm
Geotextile
Strain Gauge
Fig. 2. Strain gauge attachment pattern (not in scale) (footing size ¼ 60 mm).
18 Relative Density = 45%
Unreinforced Soil One Layer Two Layers Three Layers
10 8
Relative Density = 73%
15 Vertical Stress x 104 (N/m2)
Vertical Stress x 104 (N/m2)
12
6 4
Relative Density = 84% 12 9 6 3
2
0
0 0
5
10 Settlement (mm)
15
0
20
5
15 10 Settlement (mm)
20
25
Fig. 4. Stress-settlement curves for different relative densities.
Fig. 3. Stress-settlement curves for 30 mm diameter circular footing.
reinforcement (as shown in Fig. 2). All strain-measuring readings were taken following strictly the steps laid down in the instruction manual. 3. Experiment results 3.1. Load-settlement tests Typical load-settlement plots for 30 mm footing size with and without reinforcements have been shown in Fig. 3. The effect of varying relative density after rolling process was studied and the load-settlement plots have been presented in Fig. 4. 3.2. Radial horizontal strain measurement During the load-settlement tests with 60 mm diameter circular footing, the final radial horizontal strain values at different points on the geotextile layers placed within the
Horizontal Strain (micro-strain x 1000)
7 6
One Layer
5
Two Layers Three Layers
4 3 2 1 0 0
0.5 1 Distance from Centre of Loading (in terms of D)
1.5
Fig. 5. Induced horizontal strain variation at 0.25D placement depth.
sand stratum were measured as presented in Figs. 5 and 6. At different points, the strains were recorded at varying vertical stress levels as shown in Fig. 7.
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4.2. Improvement in the modulus of elasticity
Horizontal Strain (micro-strain x 1000)
4 Placement Depth = 2D
Assuming the whole soil medium to be homogeneous, the equivalent secant modulus (Eq) values have been computed as
Placement Depth = D
3
Placement Depth = 0.25D
s Eq ¼ ,
2
1
0 0
0.5 1 Distance from Centre of Loading (in terms of D)
1.5
Fig. 6. Induced horizontal strain variation at different placement depths.
Horizontal Strain (micro-strain x 1000)
7 Radial Distance = 0.35D 6
Radial Distance = 0.7D Radial Distance = 1.05D
5
Radial Distance = 1.4D 4 3
where e ¼ DL/L, s is the average applied stress, e is the average strain, DL is the settlement of the footing observed and L is the depth of the sand bed ( ¼ 0.21 m). From the experimental stress–strain curves the equivalent secant moduli for all the different sizes of footings and reinforcement conditions have been determined and shown in Fig. 8. The figure depicts that as the number of layer increases, there is a marked improvement of the equivalent secant modulus (Eq). However, as the diameter increases, there is a decrease in the value of Eq for the corresponding reinforcement conditions. The effect of footing size in improving the secant modulus has been represented in Table 1. It is seen that the increase in the value of Eq is more pronounced for smaller size of footings (Fig. 8). In the present study, the secant modulus and the initial tangent modulus are almost identical, as the stresssettlement diagrams are linear almost up to the peak failure stress.
2 200
1 160
0 4
2
Vertical Stress x
6
8
10
Eq (kN/m2)
0
104 (N/m2)
Fig. 7. Stress–horizontal strain plot for single-layer reinforcement at different radial distances.
120 80 Diameter = 60 mm Diameter = 45 mm Diameter = 30 mm
40 0
4. Analyses and discussion
0
In Fig. 3, the stress-settlement diagram corresponding to the unreinforced case signifies local shear failure, whereas the other diagrams for reinforced conditions signify linearly elastic–plastic failure; these curves are similar to the load-settlement diagram for general shear failure case for unreinforced soil. In Fig. 4, it has been observed that for higher relative densities (73% and 84%) there are sharp peak stresses where the failure occurs. Beyond this stress value strain softening has been observed. However, for low-relative density (45%) there is no strain softening.
1
1.5
2
2.5
3
3.5
Number of Reinforcement Layers
In this section, analysis of the test results and their detailed discussions were presented. 4.1. Modes of failure
0.5
Fig. 8. Secant modulus improvement with reinforcement.
Table 1 Size effect on secant modulus improvement Number of layer
0 1 2 3
% decrease in Ed D/D0 1.0
1.5
2.0
0.0 0.0 0.0 0.0
14.3 15.4 27.2 13.1
33.3 35.2 45.7 48.6
Note: D0 ¼ smallest footing size ¼ 30 mm.
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4.3. Analytical prediction of ultimate settlement To compare the experimental values of settlement with analytical predictions, the method proposed by Janbu et al. (1956) as modified by Christian and Carrier (1978) has been used. The average settlement (Se) can be calculated as S e ¼ m0 m1 qn B=E d , where B is the width of the footing (here diameter of the circular footing), qn is the applied footing load, Ed is elastic modulus of the soil, m0 and m1 values depend on the depth of the footing and the thickness between the footing base and hard strata, respectively. The Ed values (same as Eq) have been taken from the stress-settlement results obtained with 30 mm diameter circular footing. This is equivalent to doing a plate load test in situ to determine the Eq values that are subsequently used in predicting the settlement behavior of prototype foundation. This approach of finding Eq had to be adopted as testing of sand samples at a very low-relative density was found to be unsuccessful on a tri-axial setup. The comparison of the results has been presented in Table 2. It can be seen from Table 2 that, there is an excellent agreement between the predicted and observed values for 30 and 45 mm (maximum error less that 12.5%) footing sizes. However, the predictions for the 60 mm footing size have been found to be conservative (maximum error less than 34%) signifying scale effect. 4.4. Numerical prediction of ultimate settlement
381
soil the concept of homogenization was used and the equivalent modulus of elasticity (Eq) was calculated. Like analytical prediction, the Eq values were taken from the stress-settlement results obtained by experiment with 30 mm diameter circular. In the numerical analysis, soil was assumed to be linearly elastic as from the experimental results it has been found that the stress-settlement diagrams are linear almost up to the peak failure stress (Fig. 7). Table 2 shows that the predictions with respect to settlement made by using Janbu’s method are in very close agreement with the values predicted by FLAC analysis as well as the experimentally observed values when the width of the foundation is up to 45 mm (maximum error less than 12.5%). However, when the foundation width is 60 mm the relative error in the predicted values by Janbu’s method is quite significant. This brings out an interesting fact that the prediction of the ultimate settlement by Janbu’s method shows excellent agreement with the settlement values predicted by FLAC and observed by experiments if the model footing size used to determine the Eq value is at least 0.67 times the prototype footing size. However, it is interesting to see that the maximum error between the absolute values of settlement predicted by using the Janbu’s method and FLAC analysis is 34% and 16%, respectively, as compared to the experimental values. Thus, for large size footings the error in predictions is lesser when D/2 Surcharge of Circular Footing
To predict the settlement, a numerical analysis of the problem as stated earlier was also done using fast Lagrangian analysis of continua (FLAC). From consideration of symmetry only half portion of the problem was taken in to account. To minimize the boundary effect, the vertical boundary at the far end, on the right-hand side, was set 0.22 m away (almost seven times of the footing radius) from the center of loading that was assumed to be free in the vertical direction and restricted in horizontal direction. The bottom horizontal boundary was restricted in both the vertical and horizontal directions. The discretization of the medium for modeling is shown in Fig. 9. To use the modulus of elasticity of the reinforced
0.21 m Ganga Sand
0.22 m Fig. 9. The discretization of the medium for numerical modeling using FLAC (not to scale).
Table 2 Comparison of the predicted and the observed settlements Footing size (D in mm)
Settlement (in terms of D) Observed (by experiment)
30 45 60
0.40 0.42 0.44
Predicted (by Janbu’s method, 1956)
Predicted (by FLAC)
1 layer
2 layers
3 layers
1 layer
2 layers
3 layers
0.35 0.44 0.59
0.40 0.38 0.47
0.40 0.44 0.54
0.35 0.44 0.51
0.40 0.38 0.39
0.40 0.45 0.46
Note: Equivalent elastic modulus of the soil has been taken from the stress-settlement results obtained with 30 mm diameter circular plate.
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FLAC is used. Considering several sources of error in conducting experiments, an error of the order of 34% may be considered to be permissible. Thus, use of a simple method amenable to hand computations results in values that are not very much different from a more rigorous and numerically involved solution procedure. Thus, it is concluded that the use of Janbu’s method (1956) can be used with confidence in predicting the settlement response of circular footings resting on reinforced beds using the concept of homogenization.
rectangular in shape. Similarly, Fig. 11 shows that, in general for a fixed percentage increase in settlement, the percentage decrease in material is more for rectangular reinforcement. Thus, it is concluded that the rectangular shape of the reinforcement is preferable as compared to circular shape reinforcement for the overall strength and settlement improvement, as the desired decrease in material is more than 10%. In these figures, the percentage decrease in the material depicts the decrease in grip (bond) length. 4.6. Effect of relative density variation
4.5. Effect of reinforcement placement pattern and grip (bond) length Figs. 10 and 11 show the effects of reinforcement patterns on the improvement of bearing capacity and settlement reduction. Fig. 10 shows that in general for a fixed percentage decrease in bearing capacity, the percentage decrease in material is more when the reinforcement is
4.7. Radial horizontal strain reduction with reinforcement
70 Conical
% Decrease in Material
60
30
From Figs. 5 and 6 it has been found that the radial horizontal strain at any particular point decreases with depth of placement of the reinforcement layer as well as with the increase in the horizontal radial distance from center of loading. In Fig. 6, the small values of strain at 2D (D is the diameter of the footing) depth of placement have revealed that the stresses beyond this depth are not significant. However, as the number of reinforcement layer increases the stiffness of the soil is also increases. Fig. 8 indicates that as the number of reinforcement layer increases the secant modulus value also increases. Thus, due to increase of stiffness use of three layers of reinforcement is effective for reducing the settlement and increasing the bearing capacity of the soil. Though little horizontal strain was measured if the reinforcement layer was placed at a depth of 2D. Fig. 7 shows that the strain values increases with vertical stress applied. The rate of increase of strain values is linear for far-off points, but nonlinear for the nearby points. No effort has been made to theoretically predict the radial horizontal strain values, as the strain calculation based on the concept of homogenization cannot give the strain of the reinforcements. Still the results are presented to find the significant placement depth and also for future modeling of soilreinforcement system.
20
4.8. Reduction of settlement with reinforcement
10
To highlight the beneficial effect of number of reinforcement layers on the settlement reduction, the percentage of settlement reduction compared to the unreinforced condition has been presented in Table 3. It can be observed that with the increase in number of reinforcement layers the settlement decreases with decreasing rate. It is further
Rectangular 50 40 30 20 10 0 60 40 20 % Decrease in Bearing Capacity
0
80
Fig. 10. Effect of reinforcement pattern on strength.
70 Conical
60 % Decrease in Material
The effect of compaction in the reinforcing zone designated by the varying relative density has been presented in Fig. 4. It has been observed that as the relative density increases the bearing capacity also increases, but corresponding to the ultimate bearing capacity, final settlement is more or less the same. The increase of bearing capacities has been found to be 20.8% and 30.6% for the relative densities of 73% and 84%, respectively.
Rectangular 50 40
0 0
50
100 150 % Increase in Settlement
200
Fig. 11. Effect of reinforcement pattern on settlement.
250
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reinforced conditions, the BCR decreases with increase in footing size and later the BCR values become steady.
Table 3 Percentage reduction of settlement Diameter (mm)
Number of layer
30 45 60
5. Conclusions
1 layer
2 layer
3 layer
67.5 60.5 59.1
80.0 70.2 67.0
80.0 76.2 72.7
From the analyses and discussions on the various test results, the following conclusions can be drawn:
Table 4 Percentage increase in BCR Diameter (mm)
Number of layer
30 45 60
1 layer
2 layer
3 layer
181.2 150.0 150.0
387.5 237.5 212.5
456.3 325.0 293.8
8 Unreinforced Soil One Layer Two Layers Three Layers
7 6 BCR
5 4 3 2 1 0 1
1.2
383
1.4
1.6
1.8
2
D / D0 Fig. 12. Size effect on BCR.
observed that for 30 mm footing, the settlement reduction is insignificant if the number of layer is increased from two to three. 4.9. Bearing capacity improvement with reinforcement To have a quantitative estimate of the improvement in the bearing capacity values with respect to the unreinforced one, bearing capacity ratio (BCR) values have been calculated and the corresponding percentage increase in the BCR values have been presented in Table 4. This highlights that there is a substantial increase in the BCR values for each increment in the number of reinforcement layers, even though the settlement improvement is not appreciable (as compared to the BCR improvement) as already discussed. This may be due to the fact that the geotextile do not have bending stiffness and thus cannot appreciably reduce the settlement. The effect of footing size on BCR has been studied and presented in Fig. 12. It has been observed that for
1. The load settlement test conducted for low relative density of the sand bed (45%) revealed that for different number of layers the reinforced sand bed has behaved as a linearly elastic–plastic material. For dense sand, the failure has occurred at a peak stress followed by strain softening phenomenon. 2. The analyses of the observed results showed that modeling of reinforced soil as a complete homogeneous system for predicting the modulus of elasticity are satisfactory. With the increase in the number of layer of reinforcements, there is a marked improvement of the equivalent secant modulus (Eq). As the footing size increases, the Eq value decreases for the corresponding reinforcement conditions. When the footing size double, the maximum percentage decrease in Eq value is of the order of 48%. The increase in the value of Eq is more pronounced for smaller size of footing 3. The theory of elasticity solution proposed by Janbu et al. (1956) are in excellent agreement with the settlement values predicted by using FLAC as well as experimental observations, if the prototype footing size is upto 1.5 times the model footing. There after there is some discrepancy in these values with the error in the predictions differing by 15% (FLAC) to 34% (from the experimental values). 4. For substantial saving in the material the rectangularshaped reinforcement is preferable as compared to the circular reinforcement. 5. The radial horizontal strain measurements indicated that at 2D depth of placement of the reinforcing layer, the strain values become insignificant for three-layered reinforced conditions. 6. With the increase in number of reinforcement layers, the settlement value gradually decreases with decreasing rate. 7. There is a substantial increase in the BCR values for each increment in the number of reinforcement layers; even though the settlement improvement is not appreciable. For three-layer reinforced case, the bearing capacity improvements have been found to be 4.5 times for 30 mm diameter footing and about 3.0 times for 45 and 60 mm diameter footings.
Acknowledgement The authors would like to thank Dr. N. Sivakugan, Head, Civil & Environmental Engineering Department, James Cook University, Townsville, Australia for his kind
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