ABSTRACT
Experimental investigations on model pile groups of configuration (2x1, 3x1, 2x2, 3x2) along with a single pile subjected to uplift loads were conducted in dry dense sand. The embedment length to diameter ratios of L/d=12 and 38, center to center spacing of piles in the groups 3d, 4.5d and 6d and two surface characteristics were used. The loaddisplacement response, ultimate resistance and the variation of group efficiency with the spacing and number of piles in a group have been studied. The efficiency of a pile group increases with an increase in the spacing. For rough groups it decreases with increase in length of piles. A simplified method has been proposed to predict the ultimate uplift capacity of a pile group. The method takes into consideration of the embedment length to diameter ratio, spacing of piles in a group, its configuration, soilpile friction angle and soil properties. A comparison of the predicted values of the ultimate resistance by the simplified analysis with the writers’ experimental values, and, also with those reported by others, showed reasonably good agreement.
Keywords: Pile groups, Axial uplift loads, ultimate uplift capacity, foundations, sandy soil
INTRODUCTION
Structures like transmission towers, jetty structures, mooring systems for surface and submerged platforms; bridge abutments are constructed on pile foundations, which have to resist uplift loads. Generally the limiting friction approach along with the equilibrium conditions is used to evaluate the uplift resistance of piles and piles groups. The uplift capacity theories are based on the formation of the failure surface around the pile or the group under the action of uplift loads. The review is restricted to piles or pile groups embedded mostly in cohesionless soil. Several investigations on the behaviour of single piles under uplift loads are reported by Alawneh et al (1999), Chattopadhyay and Pise (1986), Chaudhuri and Symons (1983), Das (1983), Das and Seeley (1975), Downs & Chieurzzi (1966), Ireland (1957), Ismael (1989), Ismael & Klym(1979), Kulhawy (1984), Levacher and Sieffert (1984), Rao and Venkatesh (1985), Ruffier and Mahler (1989), Sowa (1970), Vesic (1970).However, a limited number of studies on the ultimate uplift capacity of pile groups embedded in sand are available( Chattopadhyay (1994), Das et al (1976), Mukherjee (1997), Patra and Pise (1999), Siddamal (1989)).
Meyerhof and Adams (1968) proposed a general theory of uplift resistance for a strip footing in soil based on the observations and test data of others (Adams and Hayes (1967) Balla (1961), Parr and Vanner (1962), Turner (1962), and Wisman (1966)). The theory has been developed for a strip footing with the assumption that soil mass having approximately truncated pyramidal shape is lifted up. For shallow footing depths the failure surface reaches the ground surface. They have taken the pile or footing friction angle, d, as approximately 2/3 of the angle of shearing resistance. The derived theory was modified to take into account the effect of group action of square and rectangular arrangement of piles and circular footings. They considered the smaller value of the sum of the uplift capacity of individual footings or of the equivalent pier foundation consisting of the footings and enclosed soil mass as the uplift capacity of a group. It always results into the efficiency of a group to be £1. Das et al. (1976) concluded from the pullout tests on model pile groups in sand that the efficiency of a group increases with increase in spacing between the piles. The efficiency decreases with increase in number of piles in a group. However, investigations by Das et al (1976) showed that the observed group efficiency is >1 at a certain spacing of piles in some groups. Madhav (1987) studied theoretically the interaction between two identical piles in tension. He has modeled the soil as homogeneous, linear elastic medium and used boundary integral technique. The reduction in individual capacity due to the existence of another pile is quantified and it is found to depend on the spacing and length to diameter ratio of piles and type of variation with depth of pile soil interface strength. Typical values of group efficiencies for 3^{2}, 5^{2}, 7^{2} and 9^{2} are reported. Comparison of the predictions with the available model tests and fullscale test results showed good correlation. Siddamal (1989) carried out experimental investigation on typical model pile groups 1x 1, 2 x 1, 2 x 2, subjected to uplift loading in sand. He observed that the group efficiency decreased with an increase in the size of a group. They were in the range of 0.73 to 1.00 for 2 x 1 and 0.51 to 0.75 for 2 x 2 pile groups. Chattopadhyay (1994) conducted uplift tests on groups of 2, 3, and 4 number of model piles for various spacing and length of embedment in dry sand and compacted clay. He reported that group efficiency varies with embedment length, number of piles in a group and spacing of piles in a group and the observed group efficiency is > 1 at a certain spacing of piles in some groups. Mukherjee (1997) found out failure surfaces around pile groups under vertical uplift load both experimentally and by using Finite Element Technique. Using the observed failure surface profile he calculated the uplift capacity by limit equilibrium method. Patra and Pise (1999) conducted uplift tests subjected to pulling loads on 2x1, 2 x 2 model pile groups. The variation of group efficiency with the spacing has been reported.
It is noticed from the review of the literature that there are several variables like group size, shape, spacing, embedment length to diameter ratio of piles, soil type and its density and soilpile friction angle which affect the efficiency, ultimate resistance and behaviour of pile groups. Field test results could yield the most rational approach for understanding the group behaviour. However, the high cost measured both in time and money of obtaining high quality data from fullscale field tests and considering the large number of variables involved as described above led to determine if accurate data could be obtained by conducting model tests in controlled soil condition in the laboratory. In the absence of resources and scope of prototype, smallscale laboratory tests can substantiate the effect of the above variables. The results obtained could also be utilized for checking the validity of the analysis and enriching the profession with data where limited information is available. Simplified analysis, involving different variables in the soilpile group interaction, and based on the experimental results, would be helpful for predicting the ultimate resistance of pile groups.
SCOPE OF THE STUDY
In this paper Laboratory model tests on group of piles have been carried out in dense sand under axial uplift loads to study the loaddisplacement response, ultimate resistance and efficiency varying the parameters like shape, size, spacing and embedment length of piles in groups, soilpile friction angle. Simplified analysis, which considers the above parameters, is proposed to predict the uplift resistance of pile groups. The experimental values of the ultimate resistance observed in the present investigation along with the published experimental results of other researchers (Das et al (1976), Siddamal (1989), Chattopadhyay (1994)) have been compared with the predictions made by the proposed method.
EXPERIMENTAL SET UP AND TESTING PROGRAMME
Figure 1 shows the elevation of the experimental set up.
Figure 1. The Elevation of Experimental Assembly
Foundation
Uniform dry Ennore sand was used as foundation medium in a model tank of size .914m by .762m, .914m deep. The specific gravity and uniformity coefficient of the sand are 2.64 and 1.6 respectively. The unit weight of the sand during testing was 16.4 kN/m^{3} (relative density=80%). The corresponding angle of shearing resistance f = 37^{o}.
Piles and Pile Caps
Aluminium alloy tubes of 19 mm outer diameter, 0.81mm wall thickness were used as model piles. For increasing the wall friction of pile, fine Ennore sand was pasted around the pile by adhesive. The lengths to diameter ratios of piles were 12 and 38. The soilpile friction angle d between smooth and rough surfaces of piles and sand was evaluated from the direct shear test results. They were 20^{o} (referred as smooth) and 31^{o} (referred as rough) for the test condition of sand used. Pile groups having rough piles are referred as rough pile groups and those with smooth piles as smooth pile groups.
Aluminium plates of 40 mm width, 30 mm depth and variable lengths were used as pile caps for single, 2 x 1, 3 x 1, 2 x 2, 3 x 2 pile groups. Holes were made in the pile caps so that the piles could be put in vertical position at the required spacing of 3, 4.5 and 6 times the diameter of piles.
Model Tests
Pile groups of configuration (2 x 1, 3 x 1, 2 x 2, 3 x 2) having embedment ratios 12 and 38, center to center spacing between the piles as 3d, 4.5d and 6d were tested. Along with the group of piles a single pile was also tested.
Experimental Procedure
After placing the piles with the pile cap in the model tank, sand was poured in the tank through a slot hopper keeping height of fall 450 mm and continuously moving the hopper horizontally manually (rainfall technique). Uplift load was applied to the pile cap through a double pulley arrangement with flexible wire attached to the pile cap (Figure 1). The other end was attached to the loading pan. Subsequently the loads were applied by dead weight over the loading pan starting from the smallest with gradual increase in stages. Dial gauge readings corresponding to axial displacements were recorded. The density of sand was checked by a dynamic penetrometer which was specially fabricated for this purpose. The numbers of blows were recorded at different locations in the tank using the penetrometer. They were same for equal penetration, confirming the uniformity of sand density.
TEST RESULTS
LoadDisplacement Diagrams
Typical results of the uplift load versus axial displacement of pile group (3 x 2) are shown in Figure 2. The load displacement curves are nonlinear and become roughly parallel to the displacement axis. Axial failure is considered when the piles move out of the soil. At a particular value of the displacement, the axial pull increases with increase in soilpile friction angle, f, and spacing of piles in the groups. The effect of soilpile friction angle, d, is quite significant on the loadaxial displacement response of a group.
Figure 2. Uplift Load versus Axial Displacement ( 3 x 2 Pile group, L/d=38)
Ultimate Uplift Capacity
Ultimate resistance for different cases has been estimated from the pullaxial displacement diagrams. It is taken corresponding to the point wherein the pullaxial displacement curve exhibits a peak value of the uplift load or maintains continuous increase in displacement with no further increase in the load. The net ultimate resistance of pile groups was found out by subtracting the weight of piles and pile cap.
The variation of net ultimate resistance per pile with the spacing is shown in Figures 3(a) and (b). The ultimate resistance occurred at a pile head displacement of about 0.5 to 2.5% of pile diameter for smooth pile groups and at 1 to 5% of pile diameter for rough pile groups. It increases linearly with an increase in spacing for all the groups. Rough pile groups offer significantly more resistance than smooth ones.
For L/d=12 and smooth pile groups (Figure 3(a)), the ultimate resistance per pile is less than that of a single pile capacity. However, for rough pile groups it is more than that of a single pile capacity for 3 x 1, 2 x 2 pile groups at spacing 6d.
Figure 3 (a). Ultimate Uplift Capacity per Pile versus Spacing(L/d=12)
For L/d=38 and smooth pile groups (Figure 3(b)) the ultimate resistance per pile is more than that of single pile value at spacing 4.5d and 6d.
Figure 3 (b). Ultimate Uplift Capacity per Pile versus Spacing (L/d=38)
For L/d=38, 2x1 and rough pile groups, the ultimate resistance per pile is more than that of a single pile value at spacing 4.5d and 6d.
For all rough pile groups (L/d=38), the ultimate resistance per pile decreases with an increase in number of piles in a group and also with the change in its configuration (line to a square and to a rectangular group). Similar behaviour was also reported by Meyerhof and Adams (1968).
Group Efficiency
The uplift capacity of a pile group is generally studied by group efficiency 'h'. It is expressed as
(0) 
where Qug = ultimate uplift capacity of pile group
Qu = ultimate uplift capacity of single pile
n1 = number of rows in a pile group
n2 = number of columns in a pile group
Efficiencies of the pile groups are shown in Figures 4 (a) and (b) for L/d=12 and L/d=38 respectively. Generally, the efficiency increases with an increase in spacing.
For pile groups with L/d=12 it is about 65 to 80 % for 2 x 1, 80 to 120% for 3 x 1, 50 to 100% for 2 x 2, and 50 to 85 % for 3 x 2 groups. The efficiency for rough pile groups is about 10 to 30 % more than the smooth groups.
Figure 4 (a). Efficiency versus Pile Spacing (L/d=12)
Figure 4 (b). Efficiency versus Pile Spacing (L/d=38)
For pile groups having L/d=38 the efficiency is about 80 to 180 % for 2x1, 65 to 135 % for 3x1, 75 to 120 % for 2x2 and 60 to 150% for 3x2 pile groups. Lower and higher values are associated with 3d and 6d spacing respectively. Higher efficiencies are observed for smooth pile groups and lower for rough groups. The efficiency for smooth pile groups is about 20 to 40 % more than the rough groups. Partial slip was observed for single smooth pile while loading. However, smooth pile group behaved like a pier. The increase in ultimate resistance of a smooth pile group is responsible for the increase in the group efficiency of smooth groups. For rough pile groups the efficiency decreases with increase in number of piles in a group and with change in its configuration (line to a square and to a rectangular group). Similar trend has been reported for rough pile groups by Meyerhof and Adams (1968) and Das et al (1976). For all rough pile groups (L/d=12 and L/d38), the efficiencies decrease with increase in pile length.
ANALYSIS OF RESULTS
A simplified method has been developed in this section to analyze the observed results. The proposed method is based on the reported analysis of Meyerhof and Adams (1968) for the group of footings and shafts.
Single Pile Capacity
The single pile capacity has been evaluated here as suggested by Chattopadhyay and Pise (1986). They have derived an expression for the gross and net ultimate uplift resistance of a single pile. They considered the variables like the angle of shearing resistance (f), soilpile friction angle (d) and l = L/d ratio in the analysis.
The net uplift capacity of a single pile is expressed as (Chattopadhyay and Pise (1986)),
(1) 
where A_{1} = net uplift coefficient factor as given by Chattopadhyay and Pise (1986)
g = unit weight of the soil
d = diameter of the pile
The values of the net uplift capacity factors A_{1} for different slenderness ratios, l, and soilpile friction angle, g, as given by Chattopadhayay and Pise (1986) are reproduced through Figures App. III(a) to III(e).
Pile Group Capacity
It is approximately assumed here that under the action of uplift force, the pile group capacity is contributed by three parts (Figure 5). These are (i) the central portion including the piles and the enclosed soil mass (ii) half the edge portions and (iii) the weight of the soil enclosed in the central portion. As an illustration, for 2 x 1 pile groups (shown in Figure 5), lnoq is the central portion and lmn and opq are the edge portions.
Uplift Resistance Offered by the Central Portion
The central portion it is considered as pier in the simplified analysis. The uplift resistance of the central portion is approximately expressed (Meyerhof and Adams (1968)) as
(2) 
where
Q_{uc} = uplift resistance offered by the central portion
a = center to center distance of the piles along the length
b = center to center distance of the piles along the width
g = unit weight of the soil
k = vertical component of earth pressure coefficient governing
the uplift resistance generated along the central portion of the pile group.
f = angle of shearing resistance of soil
d = soilpile friction angle of the pile
L = embedment length of the pile
From the experimental observations, it has been found that the soil between the piles is lifted up for pile spacing 3d, 4.5d, 6d. The vertical component of the earth pressure coefficient ’k’ governing the uplift resistance generated along the central portions of the pile groups is assumed as
k = (1  sinf) tand / tanf 
At d = f, k = 1  sinf. For other values of d k is a function of d and f. The assumption of k has been made for the pile group spacing varying from 3d to 6d and includes the influence of soilpile friction angle, d, on the uplift capacity.
The central portions of the groups are shown in Figure 5. These are ‘lnoq’ for 2 x 1, lnpr for 3 x 1, lqrx for 2 x 2 and lqrsyz for 3 x 2 groups.
Uplift Resistance Offered by the Edge Portions
The uplift resistance governed by the edge portions of the pile groups, lmn & opq for 2x1, lmn & pqr for 3 x 1, lmn, opq, rst & wvx for 2 x 2, lmn, opq, stw, vxy for 3 x 2 is taken as equivalent to that contributed by half of the piles. Taking the slenderness ratio, l, angle of shearing resistance, f, and soilpile friction angle, d, it is evaluated by the expression given by Chattopadhyay and Pise(1986) for a single pile (Figures App. III(a) to III(e)).
(3) 
where Q_{ue} = uplift resistance offered by the edge portions of the pile groups
n = number of half piles in the edge portions
The values of net uplift capacity factor A1 for different slenderness ratios, l, and pile friction angle, d, could be determined from the charts given by Chattopadhyay and Pise (1986)
The gross uplift capacity of a pile group ‘Q_{ug}’ can be expressed as
(4) 
Therefore, the gross uplift capacity of the line pile groups, 2 x 1, 3 x 1 is,
(5) 
where W_{q} = weight of piles, pile cap and weight of the soil enclosed in the central portion.
Similarly for a square 2 x 2,and rectangular pile groups 3 x 2, the gross uplift capacity is arrived at combining the two line pile groups 2 x 1 or 3 x 1 as
(6) 
The net uplift capacity of the pile groups could be found out by subtracting the weight of piles, pile cap from the gross uplift capacity.
COMPARISON OF EXPERIMENTAL AND PREDICTED RESULTS
Typical experimental results of the writers on the net uplift capacity of pile groups for L/d=12 have been compared with the predictions made by the proposed analysis (Table 1). They have also been compared with the predictions made by using Meyerhof and Adams’(1968) approach. The comparison is depicted in Table 1. The predicted values of the net uplift capacity using Meyerhof and Adams’ (1968) approach are much higher than the observed experimental results. The predictions from the present analysis are in closer agreement with the experimental values.
Table 1. Comparison with Writers’ Experimental Results
Net Uplift Capacity values shown (N)
PILE GROUPS (L/d=12) (1) 
Pred. Meyerhof et al (1968) Method (2) 
Pred. Proposed Method (3) 
Observed (4) 

Single pile  40  40  35  
2x1Pilegroup  3d  78.18  62.83  45 
4.5d  105  71  55  
6d  120  80  65  
3x1Pile group  3d  113.4  87  80 
4.5d  150  106  110  
6d  200  126  125  
2x2Pile group  3d  112.8  120  120 
4.5d  158.5  150  135  
6d  214  180  150  
3x2Pile group  3d  157  150  150 
4.5d  205  200  170  
6d  322  260  180  
The experimental results of Das et. al. (1976), Chattopadhyay (1994) and Siddamal (1989) have also been analyzed by the proposed analysis.
Figure 5.
Schematic Diagram of Pile Groups showing Different Zones
Model Test Results of Das et al. (1976)
Das et al. reported net uplift capacity in terms of efficiency of pile groups of size 1x1, 1x2, 1x3, 1x4, 2x2, 2x3, 3x3. Rough wooden piles of diameter 0.0127 cm and L/d=24 were used as model piles. Medium condition of sand having g =15.10 kN/m^{3}, (31^{o}) and D_{r} = 21% was used as the soil media. Soilpile friction angle d was taken as 30^{o} for the rough wooden piles. The measured values of the net uplift capacity of pile groups were indirectly evaluated from the reported efficiency diagram. The theoretical uplift capacities were predicted from Equations 5 and 6. Measured values of the uplift capacities for different groups are plotted against the predicted values in Figure 6. The ideal line having an equation of P_{measured} = P_{predicted} is also plotted. To find out the variation of the predicted values from the measured values an average line is plotted through the cluster of points. The predicted values are generally more than the experimental values by about 30% in most of the cases.
Figure 6. Comparison with Model Test Results of Das et al (1976)
Model Test Results of Siddamal (1989)
Siddamal reported axial uplift test results on model mild steel groups of size 1x1, 1x 2 and 2 x 2 having, L/d=7, 20 and 40. He used spacing 2, 4 and 6 times the pile diameter for 1x 2 pile group and 2 and 4 pile diameter for 2x2 pile group. The diameter of the pile was 20 mm. Dry sand having g = 16.1 kN/m^{3}, f = 40.5^{o} and d = 23^{o} was used as the foundation medium. The theoretical and observed net uplift capacities are shown in Table 2. The observed nonlinear variation of the uplift capacity with length is satisfactorily (about +/10% predicted by the proposed theory for L/d = 7 and 20. However, for L/d = 40, the predictions are about 30% less than the measured values.
Table 2. Comparison with Experimental Results of Siddamal (1989)
Net Uplift Capacity values shown (N)
Piles/Pile Groups (1) 
Spacing (2) 
L/d (3) 
Obs. by Siddamal (1989) (4) 
Pred. by Proposed Analysis (5) 
Single Pile  7 20 40 
21.69 114.51 441.63 
24.9 128.6 300 

2x1 Pile Group  2d 4d 6d 
7 7 7 
34.9 40.52 41.4 
31.8 34.07 38.01 
2x1 Pile Group  2d 4d 6d 
20 20 20 
166.3 176 166.3 
160 183.6 204.3 
2x1 Pile Group  2d 4d 6d 
40 40 40 
795.3 845.95 866.12 
427.6 510.0 427.6 600.0 
2x2 Pile Group  2d 4d 
7 7 
44.7 49.0 
39.5 54.72 
2x2 Pile Group  2d 4d 
20 20 
282.72 320.0 
323.2 370.0 
2x2 Pile Group  2d 4d 
40 40 
1102.80 1211.64 
784.3 989.5 
Model Test Results of Chattopadhyay (1994)
Chattopadhyay (1994) reported uplift test results on model pile groups of size 1x1, 2x1, 3 and 2x2 and L/d= 15.78, 23.68 and 31.57. Aluminium tubes of outer diameter 19 mm were used as piles. The groups were tested for spacing 2.3d, 4d, 5d and 6d. The soil was locally available brownish grey dry morga sand. The sand was coarse to medium with D_{60} = 0.95 mm, D_{10 } = 48mm and c_{u} = 1.98. The unit weight of sand was g = 17.00 kN/m^{3}. Typical load displacement diagrams of single pile, 2x1 and 2x2 pile groups at spacing 2.3d for L/d=15.78, 23.68, 31.57 were presented by him. From the load displacement diagrams the measured values of the net uplift capacity of pile and pile groups were evaluated. For theoretical calculations f = 40^{o} and d = 25^{o} (2/3 f) were considered. The theoretical and measured net uplift capacities are plotted in Figure 7. The predictions are very close to the line having an equation P_{measured} = P_{predicted}.
Figure 7. Comparison with Test Results of Chattopadhyay (1994)
SCALE EFFECTS
Turner and Kulhawy (1994) have shown the nonlinearity in the failure envelop and soil dilation at low effective confining stress can combine to cause apparent scale effects. They concluded that the effect of curvature in the failure envelop (high friction angles) at low effective confining stresses is insignificant for depth greater than 600mm. The authors used two lengths of piles, L/d=12, L/d=38. For all long pile groups, the piles were installed for greater depths (722mm).
CONCLUSIONS
Following conclusions are drawn from the present study.
The ultimate uplift capacity of the pile group depends on the embedment length to diameter ratio of a pile, pile group configuration, soilpile friction angle, spacing of piles in a group, and angle of shearing resistance of soil.
The load–displacement curves are nonlinear. At a particular value of displacement the rough pile groups offer significantly more resistance than smooth pile groups at all spacings.
The ultimate uplift capacity per pile increases linearly with an increase in spacing. The ultimate uplift capacity occurred at a pile head displacement of about 0.5 to 2.5% of pile diameter for smooth pile groups and 1 to 5% of pile diameter for rough pile groups.
In general, for L/d=12 smooth pile groups, the ultimate uplift capacity per pile is less than the single pile capacity. It is more than the single pile value for rough pile groups.
For L/d=38, rough pile groups, the ultimate uplift capacity per pile decreases with an increase in number of piles in a group and also with the change in pile group configuration from a line to square or to rectangular group.
The group efficiency increases roughly linearly with an increase in spacing. For pile groups with L/d=12 it is about 65 to 80 % for 2x1, 80 to 120% for 3x1, 50 to 100% for 2 x 2, and 50 to 85 % for 3x2 groups.
For pile groups having L/d=38 the efficiency is about 80 to 180 % for 2x1, 65 to 135 % for 3x1, 75 to 120 % for 2x2 and 60 to 150% for 3x2 pile groups. Lower and higher values are associated with 3d and 6d spacing respectively. For long rough pile groups, the group efficiency decreases with an increase in number of piles in a group and change in pile group configuration from a line to square or to a rectangular group. The efficiency decreases with an increase in length of piles for all rough pile groups.
Experimental values of the net uplift capacity of pile groups of the present investigation have been compared with the predictions made by the proposed analysis and also by Meyerhof and Adams’ (1968) approach. The predicted values using Meyerhof and Adams’ (1968) approach are much higher than the observed experimental results. The predictions from the proposed method are in closer agreement with the observed experimental values.
The test results on model pile groups reported by Das, Seeley and Smith (1976), Siddamal (1989), Chattopadhyay (1994) have also been compared with the predictions from the present analysis. Closer agreement between the experimental and predicted values has been noted.
REFERENCES
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