Bearing capacity of circular footing on geocell–sand mattress overlying clay bed with void

Geotextiles and Geomembranes 27 (2009) 89–98

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Bearing capacity of circular footing on geocell–sand mattress overlying clay bed with void S. Sireesh a, T.G. Sitharam b, Sujit Kumar Dash c, * a

Department of Civil and Environmental Engineering, University of Texas at Arlington, Arlington, TX 76019, USA Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India c Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 May 2008 Received in revised form 31 August 2008 Accepted 23 September 2008 Available online 11 November 2008

The potential benefits of providing geocell reinforced sand mattress over clay subgrade with void have been investigated through a series of laboratory scale model tests. The parameters varied in the test programme include, thickness of unreinforced sand layer above clay bed, width and height of geocell mattress, relative density of the sand fill in the geocells, and influence of an additional layer of planar geogrid placed at the base of the geocell mattress. The test results indicate that substantial improvement in performance can be obtained with the provision of geocell mattress, of adequate size, over the clay subgrade with void. In order to have beneficial effect, the geocell mattress must spread beyond the void at least a distance equal to the diameter of the void. The influence of the void over the performance of the footing reduces for height of geocell mattress greater than 1.8 times the diameter of the footing. Better improvement in performance is obtained for geocells filled with dense soil. Ó 2008 Elsevier Ltd. All rights reserved.

Keywords: Model test Bearing capacity Circular footing Geocell reinforcement Layered soil Underground void

1. Introduction The presence of underground void can cause serious engineering problem leading to instability of the foundation, incurring, severe damage to the super structure. If the void is located just below the footing at shallow depth, the consequence can be very costly and dangerous. Wang and Badie (1985) have reported that voids occur under structures at greater frequency in areas having soluble rock formations such as limestone and dolomite and also in areas having active mining operations. Besides, voids can be caused due to tension cracks in unsaturated cohesive soils; differential settlement of municipal soil waste; settlement of localized lens of compressible soil; thawing of subsurface ice lenses; settlement of poorly compacted trench backfill; collapse of underground cavities such as natural caves, tunnels, mine workings, pipes and tanks (Giroud et al., 1990). Several studies have been reported on the performance of footing above void (Baus and Wang, 1983; Badie and Wang, 1984; Wang and Badie, 1985; Wang and Hsieh, 1987; Azam et al., 1991). From these studies it has been observed that upon loading, the supporting soil below the footing collapses in the form of a wedge

* Corresponding author. Tel.: þ91 361 258 2417; fax: þ91 361 258 2440. E-mail address: [email protected] (S.K. Dash). 0266-1144/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.geotexmem.2008.09.005

into the void underlying. When void is found in the foundation soil, the potential remedial measures the designer may consider are to fill the void with competent material through grouting, use piles to bypass the void and transmit the load to a competent layer underneath or to place the foundation at a suitable depth as per stability analysis that the void lies below the critical depth thereby does not influence the performance of the proposed foundation. Among these, the last alternative is relatively easy and less expensive. However, in many cases the available cover soil above the void may be of less thickness than the critical one. In such situations, an additional layer of competent soil could be provided on the ground; over this the foundation should be placed. This fill soil when reinforced adequately would further enhance the performance of the footing. Das and Khing (1994) have carried out laboratory model load tests on strip footing, supported by a dense sand layer underlain by soft clay bed, with a continuous rectangular void located below the centerline of the foundation, with a layer of planar geogrid at the sand-clay interface. It has been observed that, with the provision of geogrid reinforcement, the magnitude of the ultimate bearing capacity increases substantially. Blivet et al. (2002) through fullscale tests have observed that planar geosynthetic reinforcement can effectively limit the risk of serious accidents due to localized sinkholes under highway and railway embankments. Ast and Haberland (2002) and Leitner et al. (2002) have reported successful

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use of high tensile geogrids together with cement-stabilised soil block under traffic load of high speed trains to over-bridge underlying sinkholes. Giroud et al. (1990), Wang et al. (1996), Briancon and Villard (2008) have presented analytical methods for design of planar geosynthetics reinforced soil system overlying void. Recently, through load tests, Dash et al. (2001, 2003b), Sitharam et al. (2005), Yoon et al. (2008), Zhou and Wen (2008) have observed that soil reinforcement in the form of interconnected cells, called geocells, gives rise to substantial increase in load carrying capacity and reduction in settlement of the footing. Bathurst and Karpurapu (1993), Rajagopal et al. (1999), Madhavi Latha and Murthy (2007) and Wesseloo et al. (2008) have studied the stress–strain behavior of soil reinforced with single and multiple geocells. The geocell reinforcement owing to its threedimensional configuration arrests the lateral spreading of the infill soil and creates a relatively stiffened mat that redistributes the footing pressure over wider area, on the underlying poor soil, thereby giving rise to enhanced load carrying capacity. Through load tests on reinforced sand foundations, Dash et al. (2004) have observed that the geocell system is a superior form of reinforcement over the planar one. For tests with planar reinforcement, failure occurred at a settlement around 15% of footing width, when the footing pressure was around 4 times the ultimate capacity of the unreinforced case. In comparison, the response with geocell reinforcement did not show a clear failure even at a large settlement equal to about 45% of the footing width, with a load as high as 8 times the ultimate bearing capacity of the unreinforced soil. The reinforcing action in case of planar reinforcement is primarily due to restraining of strain in soil, through mobilisation of frictional resistance at soil reinforcement interface. While, in case of geocell it is through overall confinement. Therefore in case of planar reinforcement the degree of mobilisation of strength of reinforcement is limited to the shear strength of interface while in case of geocell it is much higher. Madhavi Latha and Murthy (2007) through triaxial compression tests too have observed that geocell is a superior form of reinforcement than the planar one. The present study reports the results of a series of laboratory model tests carried out on a circular footing supported by geocell reinforced sand beds overlying clay bed with a continuous circular void. Voids formed due to settlement in trench backfill can be simulated as infinitely long void (Giroud et al., 1990). Tisserand (1983) has reported a case of geomembrane failure due to void resulting from trench backfill settlement. When size of the void is very large, compared to the tire contact area in case of highways or rail contact area in case of railways, the void can be considered as a long continuous void. Bonaparte and Berg (1987) have reported that a funnel-shaped sinkhole under Vera Cruz Road in Upper Saucon Township, Leigh County, Pennsylvania was covered with a 1.2 m thick by 35 m long planar geogrid-reinforced soil mattress. Test results with continuous void, could be used with approximation, for voids of finite size, particularly when they occur in greater frequency that their spacing is relatively small. Such situation may occur in areas having limestone and dolomite formations and also in areas that have a history of active mining operations.

(Cc) of 1.05, effective particle size (D10) of 360 mm and specific gravity of 2.63. The soil is classified as poorly graded sand with letter symbol SP according to the USCS. The maximum and minimum void ratios of the sand are found to be 0.66 and 0.48, respectively. The dry densities of the same at relative densities of 48%, 59% and 70% are 16.4 kN/m3, 16.6 kN/m3 and 16.8 kN/m3, respectively. The peak angle of shearing resistance (4) of the dry sand at 48%, 59% and 70% relative densities (ID) as determined from triaxial compression tests are found to be 37, 39 and 41, respectively. The geocells were formed using a biaxial geogrid made of oriented polymers. The geogrid is having square shape aperture opening of size 0.035  0.035 m. The properties of the geogrid obtained from standard multi-rib tension test as per ASTM: D 6637 (2001) are listed in Table 1. 2.2. Test setup The model tests were conducted in a test bed-loading frame assembly in the laboratory. The model footing was made of a rigid steel plate of 0.15 m diameter (D) and 0.03 m thickness. The soil beds were prepared in a test tank with inside dimensions of 0.9 m  0.9 m  0.9 m (length  width  height). A circular window of 0.095 m diameter was made on the test tank sidewall along the centerline, at a height of 0.11 m (i.e. 0.73D) from the base of the tank. This circular window was used for creating the void in the clay subgrade. The void was located at a constant distance (t ¼ 0.75D, Fig. 3), from the surface of the clay layer. On the clay bed, a sand layer was placed and the model footing was placed on the sand layer. The base of the model footing was roughened by cementing a thin layer of sand to it with epoxy glue. The footing was loaded with a hydraulic jack supported against the reaction frame. The test setup is depicted in Fig. 1. Baus and Wang (1983) have observed that with the void in the foundation bed the footing undergoes punching failure, with the soil mass underneath collapsing into the void that the shear planes are confined to the soil mass just below the footing. In the experiments under the present study, the footing was observed to have undergone punching failure. In pilot tests, the pressure on the walls of the test tank was measured using earth pressure cells. No pressure change was recorded till the end of the tests. Besides, the deformation (heave/settlement) on the fill surface, measured at a distance of 1D away from the edge of the footing shows that even with geocell mattress of relatively large height and width (i.e. h ¼ 3.6D, b ¼ 4.9D) the fill surface has undergone settlement at places away from the loading plate indicating that the geocell mattress has sunk down and hence has got pulled away from the tank boundary. These observations indicate that the tank used in the present investigation is large enough and is not likely to interfere with the failure zones and hence the experimental results. 2.3. Preparation of clay beds The clayey soil was first pulverised and then mixed with predetermined amount of water. In order to achieve moisture

2. Laboratory model tests 2.1. Materials used

Table 1 Properties of geogrid and joint used for making geocells.

A natural silty clay soil was used to prepare the clay subgrade for this study, which had 60% fines fraction smaller than 75 mm sieve size. The liquid limit, plastic limit and specific gravity of the soil were found to be 40%, 17% and 2.66, respectively. As per the Unified Soil Classification System (USCS) the soil can be classified as clay with low plasticity (CL). The sand used in this investigation was dry. It has a coefficient of uniformity (Cu) of 2.22, coefficient of curvature

Property

Ultimate tensile strength Failure strain Initial modulus Secant modulus at 5% strain Secant modulus at 10% strain

Value Geogrid

Joint

20 kN/m 18% 183 kN/m 160 kN/m 143.4 kN/m

7.5 kN/m 28% 40 kN/m 42 kN/m 29 kN/m

S. Sireesh et al. / Geotextiles and Geomembranes 27 (2009) 89–98

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pertaining to soil samples collected from different locations in the test bed, was found to be within 1.5%. Using the measured value of water content and bulk density the degree of saturation (Sr) of the soil is back calculated. The average degree of saturation is found to be in the order of 100%. The preparation of clay subgrade was temporarily ceased at the bottom level of the circular window and the surface was levelled using a scoop. A lubricated hollow PVC (Poly Vinyl Chloride) pipe was inserted through the circular window across the test tank along its width. The soil around the PVC pipe was also compacted in 0.025 m lifts. The PVC pipe was held in position, in the desired alignment, on the clay surface such that it should not get out of alignment during compaction of clay around it. In each lift, the clay–soil was first hand packed adjacent to the pipe and the wooden board was placed over the clay surface, flushed with the pipe, followed by compaction done by the drop hammer. This procedure was continued till the summit of the pipe was reached. After this, formation of clay bed was continued till the desired height, following the usual procedure. 2.4. Preparation of reinforced sand beds

Fig. 1. Test setup.

equilibrium, the moist soil was kept in airtight containers for about a week. To prepare the test bed, the moist soil was placed in the test box and compacted in 0.025 m thick layers till the desired height was reached. For each layer the required amount of soil to produce a desired bulk density was weighted out and placed in the test box making use of a metal scoop. The soil was then gently levelled out and compacted to proper depth by placing a wooden board on the surface and hitting the board with a drop hammer, using depth marking on the sides of the box as guide. Through a series of trials, the amount of soil, water content of soil, height of fall and number of blows of the drop hammer required to achieve the desired density for each lift were determined a priori. The compaction energy was about 299 kJ/m3. By carefully controlling the water content and compaction, a fairly uniform test condition was achieved throughout the test programme. In order to verify the uniformity of the test bed undisturbed samples were collected from different locations in the test bed to determine the in situ unit weight, moisture content and vane shear strength of the clay soil. For each vane shear test, undisturbed soil sample was collected from the test bed through a cylindrical container, by pressing the container through its open end into the soil bed. For passage of air, to avoid air locking, the container base had a hole of about 1 mm diameter. The container with soil was mounted in the vane shear apparatus. The shear vane was gently lowered into the soil and the test was carried out. Table 2 presents the average values of different properties of the compacted moist clay and their ranges measured in the test bed. The coefficient of variability of these test data,

The geocell mattress was formed on top of the compacted clay bed. The geocell layer, which is a continuous cellular structure, was prepared by cutting the biaxial geogrids to required length and height from full rolls and placing them in transverse and diagonal directions with bodkin joints at the connections (Fig. 2). The bodkin joint is formed by pulling the ribs of the diagonal geogrid up through the transverse geogrid and slipping a dowel through the loop created (Bush et al., 1990; Simac, 1990). The dowels used for making geocell joints in the present study were plastic strips of 0.008 m width and 0.003 m thickness cut from commercially available plastic sheets made of low-density polymer. The joint strength of the geocells was determined through wide width tensile test (ASTM: D 6637-01), with geogrid specimens having a horizontal bodkin joint at mid length. The results are given in Table 1. Usually two different patterns, diamond and chevron (Fig. 2), are used to form geocells. However, all the geocell mattresses in the present investigation were prepared in chevron pattern only, as it gives better performance improvement in comparison to the diamond pattern (Dash et al., 2001). Typical dimensions of the geocell structure used in the present study are shown in Fig. 2. After formation, the geocell cage was kept on the clay surface in the desired alignment. Then the geocell pockets were filled with sand using sand raining technique. More details on the construction of geocells can be found in Bush et al. (1990). The height of fall to achieve the desired relative density was determined, a priori, by performing a series of trials with different heights of fall. The relative densities achieved were monitored by

Transverse member

Diagonal member Pocket opening

0.1 m

Table 2 Properties of clay bed. Property

Range

Average value

Moisture content Bulk unit weight (gb) Vane shear strength (cu)

24.3–25.2% 19.9–20.2 kN/m3 9.0–10.5 kPa

24.9% 20.0 kN/m3 10 kPa

Diamond pattern Bodkin joint

0.14 m b Chevron pattern

Fig. 2. Plan view showing different patterns of formation of geocells.

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collecting samples in small cans of known volume placed at different locations in the test tank. The difference in densities measured at various locations was found to be less than 1%. The density of the soil placed within the geocell mattress was also monitored by collecting soil samples from this layer as explained earlier. The reduction in soil density in this layer due to the presence of geocell mattress was found to be less than 1%, which is negligible. This is because the geocells, being made of geogrids having percent open area of more than 80%, do not affect much the free flow of sand during rain leading to this marginal reduction in placement density. 2.5. Test procedure Upon filling the tank up to the desired height, the fill surface was levelled and the footing was placed on a predetermined alignment, such that the loads, from the loading jack, would be transferred concentrically to the footing. A recess was made into the footing plate at its centre to accommodate a ball bearing through which vertical loads were applied to the footing. Before loading the model footing, the PVC pipe was carefully withdrawn through the sidewall window, to create a void in the clay subgrade. It should be noted that the void was continuous throughout the test tank along the centerline of the footing. During removal of the pipe the deformations on the footing were recorded using dial gauges (Dg1 and Dg2; see Fig. 3). In all the test beds, the subsidence due to the weight of footing and other accessories was found to be negligible (i.e. less than 0.5% of footing diameter, in case of reinforced soil beds and less than 1% of the footing diameter, in case of unreinforced soil beds). The footing was pushed into the soil at a rate of nearly 0.002 m per minute. This relatively fast rate of loading would produce undrained response in the saturated clay bed, which is one of the worst field conditions expected, because in this case the angle of friction of soil is zero. Such phenomenon is common in case of railways and highways, where the loading is transient in nature. The load transferred to the footing was measured through a pre-calibrated proving ring placed between the ball bearing and the loading jack. Footing settlements were measured through two dial gauges (Dg1 and Dg2; see Fig. 3) placed on either side of the centre line of the footing. The footing settlement reported here is the average value of the readings taken at the two different points. 2.6. Test variables The geometry of the test configuration considered in this study is shown in Fig. 3. The geocell mattress in all the tests was of square shape. The pocket size (dc) of the geocells is taken as the diameter of an equivalent circular area of the geocell pocket opening. A typical geocell pocket opening is shown through the hatched area in Fig. 2.

Dg1

Dg2 Footing

D

u

Six different series of tests (i.e. A through F) were carried out by varying different parameters such as thickness of unreinforced sand layer (H), width (b) and height (h) of geocell layer, density of sand (ID); the details of which are given in Table 3. The pocket size of the geocells (dc) was kept constant throughout the test programme. Results from laboratory load tests on circular footing supported on geocell reinforced sand beds by the authors indicate that the performance improvement increases when the placement depth of geocell mattress (u) was increased from 0 to 0.05D and then continues to decrease with further increase in placement depth (Sitharam and Sireesh, 2005). The small cushion of sand (thickness, 0.05D) above the geocell layer protects the geocell wall from direct contact with the footing and hence prevents early local buckling of the same, giving rise to an increased performance. Therefore, in the present study, geocell mattress was placed at u/ D ¼ 0.05 in all the tests. The void was located at constant distance (0.73D), from the base of the test tank, throughout the test programme. It should be mentioned here that the findings of Baus and Wang (1983) indicate that the bearing capacity is not significantly affected by the position of the void with respect to the bedrock surface, as long as the distance between the footing and the top of the void remains constant and the top of the void is above the bedrock surface. Das and Khing (1994), from a series of experiments, have observed that the bearing capacity ratio, that quantifies the increase in bearing capacity due to geogrid reinforcement at the interface of sand layer overlying clay bed with void, increases with t/B (‘t’ is thickness of clay cover over the void, ‘B’ is width of footing) to a maximum value at t/B z 0.75 and then decreases to a constant value at greater depth. From this observation it could be said that in the range of t/ B ¼ 0.75, the reinforcement plays a major role. In view of this, in the present study, t/D of 0.75 was adopted throughout the test programme. The diameter of the void was also kept constant (i.e. dv ¼ 0.6D) in all the tests. Under series A, tests were conducted on unreinforced soil beds with different thickness of the overlying sand layer (H), at 70% relative density. In series B, tests were conduced on unreinforced soil beds with different densities (ID) of the overlying sand layer. In order to have a direct comparison of the results for the unreinforced and reinforced cases, the thickness of the overlying sand layers in these test series was kept equal to the height of the corresponding geocell mattresses as tested in other test series. Tests in series C, D and E were carried out with geocell reinforcement. The objective of these three series of tests (i.e. C, D and E) is to find out the influence of the width, and height of the geocell layer and density of the infill sand on the overall performance of the footing, respectively. Tests in series F were carried out with geocell reinforcement along with a planar geogrid layer at its base in order to understand the influence of the additional basal geogrid layer on the performance of the system. The planar reinforcement was left free in the soil, without being connected to the geocell layer. 3. Results and discussions

Sand Geocell layer

h

Base geogrid

b

t Clay

H

dv

Void

0.73D Fig. 3. Geometry of the reinforced sand bed overlying soft clay bed with void.

The bearing pressure–settlement responses observed from different series of tests are presented in Figs. 4–8. The typical close match between the results from repeat tests of identical cases (i.e. trial 1 and trial 2) illustrated in Fig. 6 indicates the uniformity achieved in the test conditions. From Fig. 4, that presents the pressure–settlement responses of the footing for different thickness of sand layer (H) overlying the clay bed with void (test series A), it could be observed that both stiffness (i.e. slope of the pressure–settlement response) and bearing capacity of the foundation bed increase, with increase in the thickness of the sand layer. With increase in thickness of the soil

S. Sireesh et al. / Geotextiles and Geomembranes 27 (2009) 89–98 Table 3 Details of laboratory model tests.

bearing pressure (kPa) 0 Details of test parameters

A

Unreinforced

B

Unreinforced

C

Geocell alone

Constant: ID ¼ 70%, cu ¼ 10 kPa, t/D ¼ 0.75, dv/D ¼ 0.6 Variable: H/D ¼ 0.0, 0.65, 1.25, 1.85, 2.45, 3.05, 3.65 Constant: cu ¼ 10 kPa, H/D ¼ 2.45, t/D ¼ 0.75, dv/D ¼ 0.6 Variable: ID ¼ 48%, 59%, 70% Constant: ID ¼ 70%, cu ¼ 10 kPa, dc/D ¼ 0.8, h/D ¼ 2.4, u/D ¼ 0.05, t/D ¼ 0.75, dv/D ¼ 0.6 Variable: b/D ¼ 1.3, 1.9, 2.5, 3.1, 3.7, 4.3, 4.9, 5.5 Constant: ID ¼ 70%, cu ¼ 10 kPa, dc/D ¼ 0.8, b/D ¼ 4.9, u/D ¼ 0.05, t/D ¼ 0.75, dv/D ¼ 0.6 Variable: h/D ¼ 0.6, 1.2, 1.8, 2.4, 3.0, 3.6 Constant: cu ¼ 10 kPa, dc/D ¼ 0.8, h/D ¼ 2.4, b/D ¼ 4.9, u/D ¼ 0.05, t/D ¼ 0.75, dv/D ¼ 0.6 Variable: ID ¼ 48%, 59%, 70% Constant: ID ¼ 70%, cu ¼ 10 kPa, dc/D ¼ 0.8, b/D ¼ 4.9, u/D ¼ 0.05, t/D ¼ 0.75, dv/D ¼ 0.6 Variable: h/D ¼ 0.6, 1.2, 1.8, 2.4, 3.0, 3.6

E

Geocell alone

F

Geocell with base geogrid layer

200

300

400

500

10

footing settlement, s/D (%)

Type of reinforcement

Geocell alone

100

0

Test series

D

93

20 h/D = 2.4, u/D = 0.05 Unreinforced b/D = 1.3 b/D = 1.9

30

b/D = 2.5 b/D = 3.1 b/D = 3.7 b/D = 4.3

40

b/D = 4.9 b/D = 5.5 Unreinforced Geocell reinforced

50 Fig. 5. Bearing pressure versus footing settlement responses showing influence of width of geocell mattress – test series C.

layer over the void, the influence of the footing load on the void is minimised. Besides, the arching induced shearing resistance of soil (Terzaghi, 1943) increases, with increase in thickness of the soil layer over the void, leading to increased bearing capacity. The improvement in bearing capacity of the foundation bed, due to the provision of sand layer over clay, is quantified using a nondimensional improvement factor, IFs. This is defined as the ratio of footing pressure (qs) with sand layer overlying clay bed to the footing pressure (qo) with clay bed alone, both considered at equal footing settlement. Table 4 presents the values of the bearing capacity improvement factor (IFs) at different footing settlements for different thickness of the sand layer (H/D). It may be observed

that more than 11-fold increase in bearing capacity (IFs > 11) could be obtained with provision of sand layer of thickness 3.65D over the clay bed with void. Figs. 5–7 depict the pressure–settlement responses obtained from different series of tests with geocell reinforcement in the sand layer overlying the clay bed with void (test series C, D and E). It could be observed that while the unreinforced foundation beds have undergone a clear cut failure, with the provision of geocell reinforcement of adequate size (i.e. b/D  1.9, h/D  1.8), the bearing pressure continues to increase till settlement is as high as 40% of

bearing pressure (kPa) 0

100

200

300

bearing pressure (kPa) 400

500

0

0

400

500

600

700

800

900

1000 1100

h/D = 0.6 h/D = 1.2

H/D = 0.65

10

H/D = 1.25 H/D = 1.85 H/D = 2.45 H/D = 3.05 H/D = 3.65

30

h/D = 1.8 (trial 2) h/D = 3.0 h/D = 3.6

20

Unreinforced Geocell reinforced

30

40

40

50

50

Fig. 4. Bearing pressure versus footing settlement responses showing influence of thickness of unreinforced sand bed – test series A.

h/D = 1.8 (trial 1) h/D = 2.4

footing settlement, s/D (%)

footing settlement, s/D (%)

300

b/D = 4.9, u/D = 0.05

H/D = 0.0

20

200

0 Unreinforced

10

100

Fig. 6. Bearing pressure versus footing settlement responses showing influence of height of geocell mattress – test series A and D.

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bearing pressure (kPa) 0

100

200

300

400

500

0 b/D = 4.9, h/D = 2.4 u/D = 0.05 ID = 48 % ID= 59 %

10

ID= 70 %

footing settlement, s/D (%)

Unreinforced Geocell reinforced

20

30

40

50 Fig. 7. Bearing pressure versus footing settlement responses showing influence of relative density of infill soil in geocells – test series B and E.

the footing width. The void was constantly observed throughout the test. In the region below the footing, the void started closing in, at a settlement ratio (s/D) of around 10–15%, which is reflected in terms of change in slope in the pressure–settlement responses of the footing. The void continued to reduce in volume with increased loading and at relatively higher settlement (s/D ¼ 25–30%), got completely closed, in the region under the footing. With further loading it continued to close in, in the adjacent region, out side the footing boundary. The increased stiffness of pressure–settlement responses indicates the reduction in settlement of the footing due to the provision

bearing pressure (kPa) 0 0

200

400

600

800

1000

1200

b/D=4.9, u/D=0.05 h/D = 0.6 h/D = 1.2 h/D = 1.8

10

h/D = 2.4

footing settlement, s/D (%)

h/D = 3.0 h/D = 3.6 Geocell alone

20

Geocell + Base geogrid

30

40

50 Fig. 8. Bearing pressure versus footing settlement responses showing influence of base geogrid layer – test series D and F.

of geocell reinforcement. Besides, the footing settlement was almost uniform (i.e. equal readings in dial gauges, Dg1 and Dg2) till large settlement. From this observation it could be said that for relatively flexible structures such as liquid storage tank, earth embankment, low cost unpaved road, etc., supported on geocell reinforced sand beds overlying void, an increase in the permissible settlement in the design is not likely to cause inconvenience. The improvement in bearing capacity due to the provision of geocell reinforcement is quantified using a non-dimensional factor IFc, defined as the ratio of footing pressure with geocell reinforcement (qc) at a given settlement to the corresponding pressure on unreinforced soil (qs) at the same settlement. The variation of improvement factor IFc with footing settlement for different test cases are presented in Table 5. It may be observed that with provision of geocell reinforcement in the overlying sand layer of thickness 3.6D, the bearing capacity can further be improved by about 2.7 times (IFc ¼ 2.73; test series D, h/D ¼ 3.6), compared to the case with sand layer alone. The soil mass between the footing and void which otherwise yields and collapses into the void, in wedge form, under footing penetration (Badie and Wang, 1984) is now encapsulated by the geocells. The relatively rigid geocell walls intercept the rupture planes in the soil, thereby, the geocell–soil behave as a composite material that inhibits development of failure wedge in the soil mass (Dash et al., 2007). Hence the geocell mattress effectively bridges the void and transmits footing pressure into adjacent regions, thus reducing the influence of the load on the void, which leads to increased performance improvement. From Fig. 8 (test series D and F), it could be observed that the base geogrid layer further improves the bearing capacity and stiffness of the foundation bed. The bearing capacity improvement due to the basal geogrid layer is quantified using the non-dimensional factor IFg, defined as the ratio of footing pressure with geocell and planar reinforcement (qcg) at a given settlement to the footing pressure with geocell reinforcement alone (qc) at the same settlement. The variation of the bearing capacity improvement factor (IFg) with footing settlement for different heights of geocell (h/D) is shown in Table 6. For geocell layer of height (h) 3.6D, with the provision of additional layer of planar geogrid at its base, the bearing capacity could further be improved by a factor of about 1.26 (IFg ¼ 1.26). From the data presented in Tables 5 and 6, it could be summarized that, with the provision of geocell reinforcement and basal geogrid, in the sand layer of thickness (H) 3.65D, a 3.4 fold improvement in performance (i.e. IFc  IFg ¼ 2.73  1.26 ¼ 3.44) could be obtained. When coupled with the improvement due to the sand layer (IFs ¼ 11.81, Table 4), the overall load carrying capacity of the footing increases by about 40 times (i.e. 3.44  11.81 ¼ 40.6), compared to the case with clay bed alone. 3.1. Influence of width of geocell layer The influence of the width of the geocell layer (b), on the performance of the footing, is depicted in Fig. 5 and Table 5 (test series C). It could be observed that for geocell mattress of plan area almost equal to that of the footing (b/D ¼ 1.3) the performance improvement is practically negligible (IFc of the order of 1.00). It should be pointed out that, based on their study on circular footing on geocell reinforced sand overlying soft clay without void, the authors have observed that, with geocell mattress of width (b) ¼ 1.2D and height around half of the present one (i.e. h/ D ¼ 1.26), almost two fold increase in bearing capacity and visible reduction in settlement could be obtained (Dash et al., 2003b). Similarly Dash et al. (2001) have reported that in the case of strip footing on geocell reinforced homogeneous sand bed, with geocell width equal to the width of the footing and height 2.75 times the footing width, 4-fold increase in bearing capacity is obtained. In all these tests the properties of soil (c and 4) were close to that in the

S. Sireesh et al. / Geotextiles and Geomembranes 27 (2009) 89–98

95

Table 4 Summary of results in terms of bearing capacity improvement factor (IFs) from test series A. Test series

Variable parameter

A

H/D 0.65 1.25 1.85 2.45 3.05 3.65

Bearing capacity improvement factor (IFs) (s/D) 1%

(s/D) 3%

(s/D) 5%

(s/D) 10%

(s/D) 15%

(s/D) 20%

(s/D) 30%

(s/D) 40%

1.70 1.75 2.79 3.20 3.17 4.61

1.80 2.26 2.91 3.74 4.40 6.01

1.68 2.38 3.25 4.42 5.42 7.44

1.62 2.51 3.87 6.09 7.40 10.04

1.62 2.49 3.79 6.24 7.99 11.44

1.62 2.38 3.62 6.02 8.06 11.94

– 2.26 3.44 5.81 7.83 11.63

– – 3.44 5.81 7.93 11.81

present case. The reason for such high performance, in no void case, could be attributed to the end bearing resistance mobilised by the relatively rigid geocell mattress that transmits the footing pressure to deeper zone. Whereas, in the present case, with void, the geocell mattress just gets punched into the void that the end bearing resistance is almost zero, leading to practically negligible performance improvement. The little performance improvement noticed is due to the mobilisation of skin friction along the outer periphery of the geocell mattress, as in the case of a pile. It is of interest to note that with geocell mattress of width close to twice the diameter of footing (b/D ¼ 1.9), more than 60% increase in bearing capacity (IFc ¼ 1.63) and visible reduction in settlement is obtained. In this case the geocell being spread beyond the void over a distance of 0.65D, in both sides, which is more than the diameter of the void (dv ¼ 0.6D), effectively bridges the void and transmits the footing pressure to the surrounding soil leading to increased performance. Hence it could be said that in order to have beneficial effect, the geocell mattress must spread beyond the void at least a distance equal to the diameter of the void. The performance improvement is found to increase with increase in width of the geocell mattress. Dash et al. (2003a) and Dash et al. (2007) through model tests on geocell reinforced sand beds, instrumented with earth pressure cells, have observed that the geocell mattress redistributes the footing pressure over a wider area onto the subgrade soil. With increase in plan area of geocell mattress due to increase in width, it effectively bridges the void and transmits the footing pressure away from the void to the adjacent stable soil mass, which does not yield. Besides, with increased plan area the geocell mattress redistributes the footing pressure over

wider area in the stable soil mass, leading to increased performance. Further increase in performance improvement, with increase in b/D beyond 4.9, is marginal. Given the limited rigidity of the geocell mattress owing to constant height and pocket size, with the limit reaching, the footing pressure does not get transmitted to further wider area thereby negligible increase in performance improvement. 3.2. Influence of height of geocell layer The influence of the height of the geocell layer on the bearing pressure–settlement response of the footing is shown in Fig. 6. It could be observed that the load carrying capacity of the footing increases with increase in height of geocell layer (h/D). For h/ D  1.2, pressure–settlement responses are almost vertical beyond footing settlement(s) of around 10% of footing diameter, indicating that the geocell mattress along with the footing has punched into the void. Dash et al. (2007) through instrumented model tests have observed that the geocell mattress behaves as a flexural member i.e. subgrade supported beam under strip loading, and for higher height of the mattress deep beam behavior becomes predominant. Due to relatively smaller height (h/D  1.2) the geocell layer behaves as a flexible member, thereby gets pulled into the void under footing penetration, hence, fails to effectively transmit the footing pressure to the surrounding stable soil mass, leading to marginal performance improvement. However, for higher height of geocell mattress (h/D  1.8) the bearing pressure continues to increase till footing settlement as high as 50% (s/D ¼ 50%). With increase in the height (h), the moment of inertia and hence bending

Table 5 Summary of results in terms of bearing capacity improvement factor (IFc) from test series C–E. Test series

Variable parameter

(s/D) 1%

(s/D) 3%

(s/D) 5%

(s/D) 10%

(s/D) 15%

(s/D) 20%

(s/D) 30%

(s/D) 40%

C

b/D 1.3 1.9 2.5 3.1 3.7 4.3 4.9 5.5

1.00 1.00 1.11 1.11 1.13 1.13 1.13 1.39

1.00 1.21 1.24 1.38 1.43 1.43 1.49 1.49

1.00 1.30 1.32 1.43 1.48 1.53 1.66 1.73

1.03 1.30 1.32 1.55 1.56 1.60 1.74 1.72

1.04 1.43 1.49 1.59 1.71 1.78 1.94 1.94

1.04 1.53 1.66 1.72 1.85 1.94 2.13 2.14

1.04 1.59 1.78 1.99 2.13 2.23 2.40 2.44

1.00 1.63 1.84 2.25 2.40 2.55 2.76 2.81

h/D 0.6 1.2 1.8 2.4 3.0 3.6

1.31 1.36 1.40 1.13 1.07 1.00

1.46 1.47 1.50 1.49 1.43 1.10

1.66 1.66 1.69 1.66 1.48 1.22

1.98 2.06 2.00 1.74 1.59 1.47

2.03 2.06 2.18 1.94 1.81 1.72

2.05 2.14 2.35 2.13 1.99 1.98

2.11 2.32 2.59 2.40 2.36 2.39

– – 2.85 2.76 2.71 2.73

ID (%) 48 59 70

1.45 1.01 1.13

1.55 1.39 1.49

1.62 1.53 1.66

1.90 1.73 1.74

1.93 1.84 1.94

2.14 2.04 2.13

2.49 2.39 2.40

2.83 2.64 2.76

D

E

Bearing capacity improvement factor (IFc)

96

S. Sireesh et al. / Geotextiles and Geomembranes 27 (2009) 89–98

Table 6 Summary of results in terms of bearing capacity improvement factor (IFg) from test series F. Test series

Variable parameter

F

h/D 0.6 1.2 1.8 2.4 3.0 3.6

Bearing capacity improvement factor (IFg) (s/D) 1%

(s/D) 3%

(s/D) 5%

(s/D) 10%

(s/D) 15%

(s/D) 20%

(s/D) 30%

(s/D) 40%

1.10 1.00 1.00 1.00 1.00 1.00

1.15 1.20 1.25 1.09 1.00 1.00

1.25 1.25 1.30 1.11 1.02 1.01

1.30 1.32 1.32 1.21 1.13 1.06

1.40 1.38 1.39 1.25 1.21 1.08

1.56 1.40 1.43 1.26 1.26 1.09

1.84 1.43 1.46 1.33 1.31 1.13

– – 1.51 1.42 1.35 1.26

and shear rigidity of the geocell mattress increases that it effectively bridges the void and transmits the footing pressure to the adjacent soil mass. Besides, the geocell mattress derives anchorage from both sides of the loaded area through tensile strength of the geocell walls and mobilisation of frictional and soil passive resistance at geocell–soil interfaces. The anchorage resistance increases with increase in depth of geocell mattress. These two factors contribute to the overall improvement in performance of the foundation system. From Table 5 (test series D), it could be observed that the improvement factor (IFc), that indicates the percentage increase in bearing capacity due to geocell reinforcement, increases with increase in the height of the geocell mattress till h/D of 1.8 beyond which it continues to decrease. In the lower height (h) range, where the geocell mattress is prone to punching, the geocell–soil structure breaks, hence, it is the geocell cage that plays major role in sustaining the footing loading. With increase in height (h), the geocell layer shares higher proportion of surcharge load, leading to increase in the value of IFc. At relatively higher height range (h/ D > 1.8), when the geocell mattress is strong enough against punching, it is the geocell–soil composite that sustains the footing loading. With increased thickness of the sand layer, the arching induced resistance of soil mobilised on the rupture plane increases, thereby, the sand layer itself shares higher proportion of the surcharge loading; hence relatively lower percentage of load is transferred to the geocell reinforcement. As a result, higher proportion of geocell strength remains immobilised leading to apparent reduction in performance improvement. From this observation it could be said that the critical height of geocell mattress beyond which the influence of void over the performance of footing reduces is about 1.8 times the diameter of the footing. 3.3. Influence of relative density of sand fill Fig. 7 illustrates the bearing pressure settlement responses of the footing for loose (relative density 48%), medium dense (relative density 59%) and dense (relative density 70%) states of the overlying sand layer, both with and without geocell reinforcement. The bearing capacity improvement factor (IFc) at different settlement levels of the footing for different relative densities of the fill soil is shown in Table 5 (test series E). From Table 5, it could be observed that in lower settlement range (i.e. s/D  5%), the improvement factor (IFc) is slightly higher in case of loose (ID ¼ 48%) and dense (ID ¼ 70%) soil, compared to the case with medium dense (ID ¼ 59%) soil. It should be mentioned here that it is the percentage increase in improvement due to the geocell reinforcement with respect to the unreinforced soil (i.e. IFc) that is higher for loose soil, not the total bearing capacity which increases with increase in relative density of fill soil as shown in Fig. 7. Contrary to this Dash et al. (2001) have observed that in case of strip footing on geocell reinforced homogeneous sand bed the bearing capacity improvement factor is least in case of loose soil and increases with increase in relative density of the soil.

The disagreement is attributed to the difference in geometry of the two problems. With homogeneous sand bed the geocell layer behaves as a subgrade supported footing and when the soil is loose it just settles in the same manner as a footing on loose soil with much of its strength remaining immobilised. Whereas, in the present case, there being a void in the subgrade, the geocell mattress acts as a beam supported at ends and loaded in central portion. When fill soil is loose, the shear strength of the soil being low, the geocell reinforcement shares relatively higher proportion of footing load and transmits to the soil around the void giving rise to higher improvement factor (IFc). Indeed for the case with loose soil (ID ¼ 48%), at relatively higher settlement of footing, the geocell reinforcement which was originally covered with a soil cushion of 0.05D thickness was lifted up at end, thereby was visible on the fill surface, at both the ends along its width. This observation establishes that the geocell reinforcement cage behaves as a centrally loaded beam that it deflects upwards at its both ends. When the fill soil is dense it dilates, due to footing penetration, giving rise to volumetric expansion. The geocells through threedimensional confinement arrest this volume expansion that mobilises higher benefit from the reinforcement leading to higher value of improvement factor (IFc). However, at higher settlement, the improvement factor (IFc) is almost same for all relative densities. With increased settlement the soil undergoes shearing, that the reinforcement shares substantial part of the footing loading, therefore, the IFc calculated is independent of soil density. Though in the case of loose soil the improvement factor (IFc) apparently looks higher, but the overall bearing capacity is higher in case of dense soil (Fig. 7). It is therefore profitable to have a dense fill in the geocells. In field, to have dense fill in geocells, it is suggested that light rolling compaction with some amount of overfilling (i.e. about 150 mm, Bush et al., 1990), should be adopted. With repeated passage of rolling and filling, a dense and compact geocell structure can be achieved. 3.4. Influence of base geogrid layer The bearing pressure versus settlement responses of the footing for different heights of geocell mattress (h/D) with and without a layer of geogrid at its base (test series D and F) are presented in Fig. 8. It is observed that further increase in bearing capacity and stiffness of the foundation bed could be achieved with the provision of an additional layer of planar geogrid at the base of the geocell mattress. Due to footing penetration, the sand in the geocell directly below the footing tends to move down. At higher settlement of the footing, this sand overcomes the frictional resistance on geocell wall and punches down into the subgrade. Ultimately the void collapses leading to high local settlement in the region under the footing. The base geogrid layer inhibits the downward movement of this soil mass through bearing over its ribs. As a result, the geocell soil system remains coherent that enables it to transmit the footing pressure more effectively to the surrounding soil around the void. Besides, the base geogrid restrains the deflection of the geocell mattress through mobilisation of its stiffness by membrane action and anchorage from

S. Sireesh et al. / Geotextiles and Geomembranes 27 (2009) 89–98

soil. Thus, the increase in stiffness and bearing capacity of the foundation bed due to the base geogrid layer is attributed to the stiffening (reduction of settlement) of the geocell mattress in the region under the footing and effective redistribution of footing pressure over the surrounding soil around the void. The increase in the load carrying capacity of the footing due to the base geogrid layer quantified through the improvement factor (IFg) is presented in Table 6. It is of interest to note that, for geocell layer of height (h) equal to 0.6D, a layer of planar geogrid at its base could bring a further improvement in bearing capacity of around 80% that of the case with geocell alone (IFg ¼ 1.84). The influence of the base geogrid layer reduces with increase in height of geocell layer (h/D). With increase in height, the geocell mattress becomes relatively stiffer thereby deflects less under the footing loading. This in turn reduces the deformation in the base geogrid layer leading to mobilisation of lower strength thereby giving rise to reduced performance improvement. From Fig. 8 it could be observed that relatively thinner geocell mattress with a layer of geogrid at its base can perform at par with geocell mattress of higher thickness. Hence, the base geogrid can be used as an effective means for reducing the required thickness of the geocell construction.

4. Scale effect Dimensional analysis has been used by Fakher and Jones (1996) to study the influence of various parameters on the performance of reinforced soil foundation beds. In the present case the important parameters in the geocell reinforced model can be assumed to be: D, dv, t, u, dc, h, b, s, Sr, G, g, cu, 4, qc, qs; where Sr is the stiffness of the reinforcement, G is the shear modulus of soil and g is the unit weight of soil. The other symbols have already been defined. The function (f) that governs the system can be written as

f ðD; dv ; t; u; dc ; h; b; s; Sr ; G; g; cu ; f; qc ; qs Þ ¼ 0

(1)

The fifteen parameters in Eq. (1) are having two fundamental dimensions (i.e. length and force). As per the theory of Langhaar (1951) this system can be studied by any complete set of thirteen (i.e. 15  2) independent parameters (i.e. p1, p2, p3,.p13; Buckingham, 1914). Hence Eq. (1) can be reduced to the following form

       dv t u dc h h b ; ; ; ; ; ; ; gðp1 ; p2 ; p3 ;.p13 Þ ¼ g D D D dc D D D          s S g G cu qc r  ; ; ; ; f ¼ 0 ð2Þ ; Dg qs D Dg G2 

For a prototype footing (p) with diameter N times higher than the model (m)

Dp ¼ N Dm

(3)

For similarity to be satisfied all the p terms should be same both for the prototype and the model.

ðp10 Þp ¼ ðp10 Þm

Gp Gm ¼ Dp gp Dm gm

(4)

In the case of soils in the model and prototype to be of same density, Eq. (4) reduces to

Gp Dp ¼ ¼ N Gm Dm

97

(5)

ðp9 Þp ¼ ðp9 Þm

Srp gp G2p

¼

Srm gm G2m

G2p Srp ¼ 2 ¼ N2 Srm Gm

(6)

Hence, for the findings of the present study to be applicable in practice, the strength of the reinforcement in the prototype reinforced soil foundation bed should be of N2 times the strength of the reinforcement used in the model test, where N is the model scale. In the present model tests the strength and stiffness of the geocell joint is much lower compared to that of the geocell wall material (i.e. geogrid). Therefore, the performance improvement due to geocell reinforcement will be proportionate to the strength and stiffness of the geocell joints rather than the geogrid used to make geocells. Hence, for the results from the present study to be applicable in practice, the prototype geocell (both joint and geogrid) should have a minimum strength and stiffness of N2 times the strength and stiffness of the geocell joint in the present model tests. For example, for applications in highways where the diameter of the tire contact area is about 0.3 m (i.e. N ¼ 2), the geocells should have a minimum ultimate strength of 30 kN/m (i.e. 7.5 kN/m  4) and initial stiffness of 160 kN/m (i.e. 40 kN/m  4). Large-scale tests carried out by Milligan et al. (1986) and Adams and Collin (1997) indicate that the general mechanisms and behavior observed in the model tests are reproduced at large scale. Therefore, qualitatively, this study provides insight into the basic mechanism that establishes the bearing pressure versus settlement responses of the geocell reinforced sand bed overlying soft clay subgrade with continuous void. These results will be helpful in conducting large-scale model tests and simulating through numerical models.

5. Conclusions A series of model load tests have been conducted to evaluate the potential benefits of providing geocell reinforced sand mattress over clay bed with a continuous circular void. The test results clearly demonstrate that geocell mattress can substantially increase the bearing capacity and reduce settlement of the clay subgrade with void. With the relatively rigid geocell walls intercepting the rupture planes in the soil, the geocell-encapsulated soil behaves as a composite material that inhibits development of soil-failure wedge above void, thereby bridges over it and transmits the footing pressure into adjacent regions of stable soil mass, leading to increased performance improvement. The geocell mattress of relatively smaller width just gets punched into the void that the end bearing resistance is almost zero, leading to practically negligible performance improvement. In order to have beneficial effect, the geocell mattress must spread beyond the void at least a distance equal to the diameter of the void. The performance improvement increases, with increase in width of the geocell layer till b/D equal to 4.9, beyond which, further improvement is marginal. With increase in the height of the geocell layer, its moment of inertia and hence bending and shear rigidity of the geocell mattress increases that it effectively bridges the void and transmits the footing pressure to the adjacent soil mass leading to improved performance. There is

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a critical height of geocell mattress beyond which the influence of void over the performance of the footing reduces. The overall bearing capacity of the foundation bed increases with increase in density of the fill soil. It is therefore profitable to have a dense fill in the geocells. Further increase in bearing capacity and stiffness of the foundation bed could be achieved with the provision of an additional layer of planar geogrid at the base of the geocell mattress. The base geogrid layer restrains the deflection of the geocell mattress through mobilisation of its stiffness by membrane action and anchorage from soil, leading to stiffening of the geocell mattress in the region under the footing, giving rise to improved performance. The influence of the base geogrid layer becomes marginal at larger height of geocell layer. With increase in height, the geocell mattress becomes relatively stiffer, thereby, deflects less under the footing loading. This in turn reduces the deformation in the base geogrid layer leading to mobilisation of lower strength, hence, reduced performance improvement. The quantification of the performance improvement indicates that with the provision of geocell reinforcement and basal geogrid, in the granular soil layer (i.e. dense sand of 3.65D thickness) overlying soft subgrade with void, a 3.4-fold improvement in performance (i.e. IFc  IFg ¼ 2.73  1.26 ¼ 3.44) could be obtained. When coupled with the improvement due to the sand layer (IFs ¼ 11.81), the overall load carrying capacity of the footing increases by about 40 times (i.e. 3.44  11.81 ¼ 40.6), compared to the case of clay subgrade with void alone.

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