Numerical Modeling of Granular Anchor Pile System in Loose Sandy Soil Subjected to Uplift Loading
Abstract
During the last few decades various researchers have proposed appropriate experimental and numerical methods to estimate the uplift capacity of granular anchor piles (GAPs) in expansive soils. Surprisingly, very few studies have been performed to determine the uplift capacity of GAPs in loose sands. This paper presents the results of the numerical study to estimate the ultimate uplift capacity of group piles. Numerical analysis is performed using finite element software PLAXIS3D. The foundation system is assumed to consist of a different number of regularly spaced GAPs installed in loose sandy soils. The analysis examines the influence of factors such as number of piles n and length L to width D ratio, and properties of the granular pile material and compares the efficiency of group of GAP systems of different configurations.
Keywords
Granular anchor pile Finite element method Loose sand Group piles Uplift capacityNotations
 L
Length of a pile (m)
 D
Diameter of a pile (m)
 γ
Total unit weight of soil above the water table (kN/m^{3})
 γ_{sat}
Saturated unit weight of soil (kN/m^{3})
 ϕ
Angle of internal friction of soil (°)
 c
Cohesion of soil (N/m^{2})
 ν
Poisson’s ratio
 E_{s}
Elastic modulus of surrounding soil (kPa)
 E_{p}
Elastic modulus of pile material (kPa)
 E
Elastic modulus of plate element (kPa)
 d
Thickness of a plate element (m)
 S
Centre to centre spacing between piles in group piles (m)
 n
Number of piles in a pile group
 η
Efficiency
Introduction
The construction of structures in the coastal areas consisting of weak soils at shallow depths requires due attention to be given on safety and stability of surrounding structures which may be under question due to poor engineering properties of weak soils. So, proper attention must be required in designing the foundation of structures in such conditions. Soil in these areas has to be improved using an efficient and economical ground improvement technique.
Ground improvement of loose cohesionless soils can be achieved by different methods such as excavation and replacement, compaction piles, compaction with explosives, vibroflotation, well point system, dynamic compaction, grouting, etc. The selection of the most suitable method depends on different factors, including soil conditions, maximum depth of the compaction, required degree of the compaction, type of structures to be supported, etc.
On the other hand, ground improvement techniques are normally preferred for economical considerations. Out of several available techniques, granular piles have been widely used. Granular piles reinforce the surrounding soil and improve the engineering properties of the soil. It provides an effective drainage condition so that resistance offered to the liquefaction in loose saturated soils can be enhanced. This method also improves the stability of embankments, raise the consolidation rate, improve the bearing capacity of the soil, and reduce the settlements [1, 2]. Recently, the performance (behaviour) of stone columns is analyzed both experimentally and numerically by several researchers in soft soils with or without providing geosynthetics around the granular pile [3, 4, 5].
Recently there is marked increase in the construction of the transmission towers, high raised buildings and tall structures. The design of these engineering structures requires that the foundation system should also resist vertical uplift forces. In such situations, the granular pile alone cannot help much in the case of tensile/uplift force, and hence an attractive and economical design solution may be required. It can be achieved with the slight modification in granular pile. A base plate is provided at the bottom of pile and it is connected with an anchor rod to resist the uplift forces coming to the foundation. The concept of having compressible piles to resist the uplift loads is relatively new, economical and efficient ground improvement technique [6] and it is known as granular anchor pile (GAP) system.
GAP system is suitable for soft soils or weak soils. When the loose sandy soils are required to withstand compressive loads as well as tensile loads coming to the foundation, the GAP system provides an economical and safe solution. These piles are ideally suitable for expansive soils too.
A welldocumented study on the GAP system has been carried out in the laboratory and field study before its application to actual field conditions [6, 7, 8, 9, 10]. The parametric analysis was performed to determine the ultimate pullout capacity of GAP in homogenous and nonhomogenous soft ground [11, 12]. A smallscale numerical analysis was performed on GAP in expansive soils [13, 14]. A very few field studies have been performed on GAP system in loose cohesionless soils in literature [1, 15]. Kranthikumar et al. [16] analyzed GAP system in loose cohesionless soils using Plaxis3D and presented a detailed parametric study for single pile system.
A critical review of the literature pointed out very limited attempts [13, 14] towards the numerical modeling of GAP system in expansive soils. However, no numerical study seems to be available to analyze the performance of a group of GAPs in loose sandy soils subjected to the uplift loading. In this study, the performance of a group of GAPs under uplift loading condition is examined by using threedimensional finite element analysis with PLAXIS 3D software. An attempt is made to investigate the influence of factors such as number of piles n, spacing of piles S, and soil–pile properties on the uplift capacity of GAP system. The group efficiency of the GAP system in loose sandy soils under uplift loading is also determined.
Numerical Modelling of Gap System
Validation
The accuracy of the proposed numerical modeling in PLAXIS 3D was validated by comparing the field results of GAP system performed on cohesionless soils [1]. The size of the soil test bed assumed in the analysis was 5 m × 5 m × 5 m. The dry unit weights of the granular pile and cohesionless soil were 22 and 17 kN/m^{3}, respectively [1]. The pile and soil modulus were 12.3 and 4.3 MPa respectively [1]. The diameter of anchor plate was same as the diameter of the pile and thickness was 0.0254 m. The length of anchor rod was same as the length of pile with diameter 0.016 m. For both anchor rod and anchor plate, the mild steel material with a high flexural rigidity was used for avoiding buckling and deformations.
Parametric Study
Material properties of soil elements used in the numerical model
Parameters  γ (kN/m^{3})  γ _{sat} (kN/m^{3})  c (kN/m^{2})  ϕ (°)  E (MPa)  ν 

Loose sand  17  19  0  29  3800  0.3 
Pile material  22  24  0  36  15,000  0.3 
Material properties of plate elements used in the numerical model
Model type  Parameters  d (m)  E (GPa)  ν 

Linear elastic  Anchor plate  0.025  200  0.15 
Footing  0.01  200  0.15 
Analysis of a Single Pile
Uplift capacity of a GAP system for different R _{inter} values of soil and pile (D = 0.5 m, L/D = 10)
R _{inter} of pileplate  Uplift capacity (kN) of a single pile for R _{inter} values of pilesoil  

1.00  0.95  0.90  0.85  0.80  
1.00  112.534  110.361  107.971  105.379  102.643 
0.95  112.474  110.304  107.931  105.329  102.595 
0.90  112.390  110.236  107.867  105.274  102.539 
0.85  112.304  110.155  107.791  105.202  102.472 
0.80  112.213  110.058  107.699  105.317  102.391 
Uplift capacity and efficiency of a GAP system for a given diameter D = 0.5 m
Diameter (m)  Length (m)  L/D  Upilft capacity (kN)  Efficiency (%)  

1 pile  2 piles  3 piles  4 piles  2 piles  3 piles  4 piles  
0.5  2.50  5.0  62.49  119.32  174.25  230.72  95.47  92.94  92.30 
0.5  3.75  7.5  92.59  181.65  265.96  350.19  98.09  95.75  94.56 
0.5  5.00  10.0  112.53  221.55  326.48  431.59  98.44  96.71  95.88 
0.5  6.25  12.5  128.70  254.36  375.36  497.17  98.81  97.22  96.57 
0.5  7.50  15.0  144.08  284.68  420.59  557.80  98.79  97.30  96.79 
Effect of Group Piles
Uplift capacity of the GAP system of different pilegroup configurations for different L/D ratios is summarized in Table 4 alongwith efficiency in each case. It is observed that group efficiency of a GAP system decreases with increase in the number of piles in a given pile group on the account of interaction effects. As number of piles in the group increases, the load carrying capacity of the group piles may reduce due to the overlapping of the stresses transmitting in the piles to the surrounding soil. For upward movement of 0.1D, the group efficiency of GAP system ranges from 0.9 to 1.0 for a given spacing.
Effect of arrangement of piles in a group on the efficiency of GAP system
Diameter (m)  Length (m)  L/D  Efficiency (%)  

3 piles  4 piles  
Line pattern  Triangle  Line pattern  Square  
0.5  2.5  5  93.04  92.94  91.56  92.30 
0.5  5.0  10  96.87  96.71  96.01  95.88 
Effect of Depth of Water Table
Effect of GAP Construction
The uplift capacity of a GAP system mainly depends on soil and pile properties and also depends on the degree of compaction used for the granular pile. During the compaction of granular pile, the surrounding loose soil also undergoes compaction. So the shear strength properties of the loose soil around the granular pile get modified. The change in the state of strength while installing the GAP into the soil can be estimated by cylindrical cavity expansion theory (CCET) as proposed by Randolph et al. [17]. Randolph et al. [17] have revealed from the numerical study that expanding a cavity by doubling the radius is adequate to simulate expansion of cavity from a zero initial diameter. McCabe et al. [18] have concluded that if a lateral strain of 10 % is applied to the granular pile in PLAXIS 3D then the radial stresses generated in the surrounding soil closely follow the CCET formulation developed by Gibson and Anderson [19].
Uplift capacity and efficiency of a GAP system considering effects of construction
Diameter (m)  Length (m)  1 pile  Uplift capacity (kN)  Efficiency (%)  Lateral strain  

2 piles  4 piles  2 piles  4 piles  
0.5  5  112.534  221.548  431.588  98.436  97.403  0 
0.5  5  177.490  340.219  646.786  95.842  95.054  10 % 
0.45  5  155.635  290.211  564.529  93.234  97.262  10 % 
Conclusions

The uplift resistance of the GAP system in a loose sandy soil increases with increase in the length and diameter of the pile.

The uplift capacity of GAP system increases around more than 25 % when L/D ratio increases from 5 to 7.5 and 7.5 to 10. However further increment in L/D ratio from 10 to 12.5 and 12.5 to 15 results marginal increase (15 %) in the uplift capacity.

The efficiency of pile group decreases with increase in the number of piles for constant spacing, because if number of piles in a group increases, the load carrying capacity of pile group may reduce due to the overlapping of the stresses transmitting in the piles to the surrounding soil.

The uplift capacity of GAP system is observed to be higher by considering the effects of construction due to densification of the surrounding soil.

Efficiency of group piles of GAP system lies between 0.9 and 1.0 for different number of piles with different diameters and L/D ratios.

The variation of uplift capacity of a GAP system with depth of water table is almost linear. The uplift capacity decreases with increasing the depth of water table.
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