Influence of axial load on the lateral pile groups response in cohesionless and cohesive soil

Abstract

The lateral response of single and group of piles under simultaneous vertical and lateral loads has been analyzed using a 3D finite element approach. The response in this assessment considered lateral pile displacement and lateral soil resistance and corresponding p-y curve. As a result, modified p-y curves for lateral single pile response were improved with respect to the influence of increasing axial load intensities. The improved plots can be used for lateral loaded pile design and to produce the group action design p-multiplier curves and equations. The effect of load combination on the lateral pile group response was performed on three pile group configurations (i.e., 2×1, 2×2 and 3×2) with four pile spacings (i.e., s = 2D, 4D, 6D and 8D). As a result, design curves were developed and applied on the actual case studies and similar expected cases for assessment of pile group behavior using improved p-multiplier. A design equation was derived from predicted design curves to be used in the evaluation of the lateral pile group action taking into account the effect of axial load intensities. It was found that the group interaction effect led to reduced lateral resistance for the pile in the group relative to that for the single pile in case of pure lateral load. While, in case of simultaneous combined loads, large axial load intensities (i.e., more than 6H, where H is lateral load values) will have an increase in p-multiplier by approximately 100% and will consequently contribute to greater group piles capacities.

Keywords

piles / pile group / spacing / configuration / combined load

Introduction

According to current day practice, piles are independently analyzed first for the vertical load to determine their bearing capacity and settlement and then for the lateral load to determine the flexural behavior [ 1, 2]. This approach is valid only for small lateral loads, however, in case of pile groups, the lateral loads are significantly high and the order of 10%-20% of the vertical loads. In such cases, studying the interaction effects due to combined vertical and lateral loads is essential. Thus, a more systematic analysis is essential [ 1- 3]. In general, the pile group should not be only design or analyze to support vertical loads or lateral loads separately but always a simultaneous combination of the vertical and lateral loads.

Piles are always constructed within a group and the position of pile within the group directly affects the pile performance especially its lateral behavior. The piles in trailing (back rows) are thought to exhibit less lateral resistance because of interference with the failure surface of the row of piles in front of them. This group interaction effect is expected to become less significant as the spacing between piles increases because there is less overlap between adjacent failure planes [ 4]. One method which was presented by many researchers (e.g., [ 5- 9]) accounting for the group reduction effects is to reduce the modulus or the soil resistance, p, from a single pile p-y curve using a constant reduction factor or p-multiplier (f_m) which was proposed initially by Brown et al. [ 10]. Although this simple approach has provided relatively good estimates of measured pile group behavior [ 10, 11], p-multipliers are extremely restricted in their application. The values of the p-multiplier always depend only on the magnitude of lateral load.

Many investigators have studied assessments of the behavior of laterally loaded pile group using finite element method. Normally, the finite element method simulates the soil as a continuum. Pile displacements and stresses are evaluated by solving the classic beam bending equation using one of the standard numerical methods such as the models used by Kishida & Nakai [ 12], and Iyer & Sam [ 13]. Randolph [ 14] developed simple algebraic equation of interaction factors, based on results from finite element analysis, to account for the added displacements from the influence loads of neighboring piles. Muqtadir and Desai [ 15] used a three-dimensional (3D) finite element approach to evaluate the pile group behavior embedded in sandy soil. A 3D analysis was performed using von Mises surface was reported by Brown and Shie [ 16]. Trochanis et al. [ 17] studied a two-pile system subjected to lateral load using commercial program (ABAQUS), in 3D conditions. Another 3D finite element analysis for evaluating the lateral pile group response when Kimura et al. [ 18] reported carrying pure lateral loading. In addition, using a finite element package, GPILE-3D. In addition, other researchers used computational methods for soils performance (i.e., [ 19– 21]). Finalluy, Kahyaoglu et al. [ 22] used PLAXIS 3D Foundation to investigate the behavior of laterally loaded pile and pile group.

As previously mentioned, all lateral response on pile groups were studied by non-simultaneous actions of both axial and lateral loads. Thus, this study aim to assess the influence of simultaneous load combinations on the lateral pile group action using 3D finite element approach in PLAXIS 3D FOUNDATION software [ 23]. Two types of soil (a cohesionless and a cohesive soil) were used for comparison. The study includes three pile group configurations with four pile spacing. The main intention of this paper is to obtain improved p-y design curves taking into account the influence of pile spacing on the lateral pile response within group for different group configurations subjected to different loading combinations. In addition, a cohesionless and a cohesive soil were used to establish design curves that show p-multiplier values as a function of pile spacing. Finally, a design equation was derived to compute the value of p-multiplier as a function of both pile spacing and pile diameter.

Constitutive relationships

In this study, the elastic model used for modeling the pile structural material, while the elasto-plastic Mohr-Coulomb model used for the soils. In addition, a thin layer interface element used to model the interface zone between the soil and the pile material.

Structural members’ model

The use of the linear elastic model is quite common to model massive structures in the soil or bedrock layers that include piles etc. [ 23] This model represents Hooke’s law of isotropic linear elasticity used for modeling the stress-strain relationship of the pile material. The model involves two elastic stiffness parameters, namely the effective Young’s modulus, E', and the effective Poisson's ratio, ν'.

Soil model

The surrounding soil represented by Mohr-Coulomb’s model. This elasto-plastic model based on soil parameters that known in most practical situations. The model involves two main parameters, namely the cohesion intercept, c' and the friction angle, {\varphi }^{\prime } . In addition, three parameters namely Young’s modulus, E', Poisson’s ratio, ν', and the dilatancy angle, ψ' are needed to calculate the complete stress-strain (σ, ϵ) behavior. The failure envelope as referred by Potts & Zdravkovic [ 24] and Johnson et al. [ 25] only depend on the principal stresses ( {\sigma }_1^{\prime } , {\sigma }_3^{\prime } ), and is independent of the intermediate principle stress ( {\sigma }_2^{\prime } ).

Interface elements model

Interfaces are modeled as 16-node interface elements. Interface elements consist of eight pairs of nodes, compatible with the 8-noded quadrilateral side of a soil element. Along degenerated soil elements, interface elements are composed of six node pairs, compatible with the triangular side of the degenerated soil element. Each interface has a virtual thickness assigned to it which is an imaginary dimension used to obtain the stiffness properties of the interface. The virtual thickness is defined as the virtual thickness factor times the average element size.

Analysis methodology and layout

The analysis consists of modeling of single pile and pile cap using linear-elastic model with 15-node wedge elements. The cross-section of the pile is circle with a diameter of 1.0 m and length of 15 m. The baseline soil parameters used for the analysis of laterally loaded pile group are illustrated in Table 1. Two types of soil are used in the analysis.

Finite element analyses were performed using the software PLAXIS 3D FOUNDATION [ 23]. In the finite element method a continuum is divided into a number of (volume) elements. Each element consists of a number of nodes. Each node has a number of degrees of freedom that correspond to discrete values of the unknowns in the boundary value problem to be solved.

Analyses were performed with several trial meshes with increasing mesh refinement until the displacement changes very minimal with more refinement. The aspect ratio of elements used in the mesh is small close to the pile body, near to the pile cap and piles bases. All the nodes of the lateral boundaries (right and bottom of Fig. 1) are restrained from moving in the normal direction to the respective surface. The predicted results from the three-dimensional finite element simulation are compared with that from analyses involving a single isolated pile in the same typical condition.

The outer boundaries of soil body of cubic shape are extended 10D on the sides and 5D to the bottom of pile group. The 3D view of the finite element mesh of the pile groups and the surrounding soil mass are shown in Fig. 1. The outer dimensions of pile cap depend on the pile group arrangement. The pile cap extends of 0.5 m beyond the outside face of exterior piles. The finite element simulation includes the following constitutive relationships for pile, surrounding soil and interface element.

Results and discussion

This study deals with the effect of vertical load intensities on the lateral behavior of pile. The vertical load (V) applied started from zero (no vertical load) to 10 times the lateral load (H) and was increased in five stages (i.e., V = 2H, 4H, 6H, 8H and 10H). Lateral load magnitudes are 50, 250 and 450 kN. The slenderness ratio L/D = 15 is used throughout this study. The influence of these mentioned factors are summarized in the following sections.

Analysis of pile group 2×1

In general, in case of low axial loads (V = 2H and 4H) the single isolated pile under the action of simultaneous axial and lateral loads in both cohesionless and cohesive soils suffered less deflection (indicate high resistance) than the pile within group due to group action. While in case of high axial loads (more than 6H) the lateral pile displacement of the single isolated pile is greater than those obtained from the pile within group. This is possibly due to influence level of axial load intensities. This increase can be directly attributed to the increase in confining stress with increasing axial loads at different depths caused by the action of vertical load on the pile [ 1, 2]. In addition, it seems that the front pile (leading piles) within the group for a given row resist more load than the middle (2nd trailing piles) and back piles (trailing piles) in the row as shown in Fig. 2. This is possibly due to group action effect in which the group action is less influence on the leader row compared with other rows, this was also observed by Brown et al. [ 10], and Rollins et al. [ 8]. It can be observed that for the same magnitude of axial load, group interaction was made a regular change in lateral pile displacement and irregular in lateral soil pressure.

In the case of pile spacing effects, for all axial load intensities, the pile spacing below 6D give highest lateral pile displacement than the pile with wide pile spacing (i.e., s = 8D), This is because of the pile-to-pile action led to reduced lateral resistance for the piles in the group when reduce pile spacing [ 8]. From the results, the values of the lateral pile displacement and lateral soil pressure observed are closed with those obtained from the analysis of single isolated pile when the pile spacing is large (i.e., s = 8D) and vise versa which was also observed by Brown et al. [ 10], and Rollins et al. [ 4, 8].

The influence of axial load intensities on the ultimate lateral soil resistance along the depth for both cohesionless and cohesive soils with four different pile spacing is shown in Fig. 3. It can be seen that the magnitudes of axial load largely effect the lateral soil resistance. This effect can be directly attributed to the change in confining stresses with increasing vertical load at different depth caused by the action of axial load on the pile [ 1, 2]. Also it can be noticed that the ultimate soil resistance of laterally loaded piles decreases significantly with increase in pile spacing [ 4, 8, 10, 11].

Unequivocally, the p-y method remains an important technique for analysis and design of the laterally loaded piles and pile group. This method can used to evaluate the lateral pile response within the group when only the details of single isolated pile response are available. The traditional p-y methods to predict pile group response was improved by Brown et al. [ 10] from a single isolated pile p-y curve. The influence of axial load intensities on the group interaction and the predicted p-y curve for four pile spacing on both cohesionless and cohesive soils is illustrated in Fig. 4. The predicted p-y curves are evaluated at depth of 3 m because the maximum ultimate lateral soil pressure occurs at this depth. It can be observed that significant high variance of the observed p-y curve for the case of closed pile group (i.e., s = 2D). This is possibly due to influence of pile group interaction and axial load level which increases lateral pile displacement and at the same time reducing the lateral soil pressure. Therefore, it can be concluded that the level of axial load changes in the predicted p-y relation. This change directly affects the design curve of laterally loaded single piles and pile groups. In addition, it can also be seen that the pile within leading row has values of the lateral pile displacement and lateral soil pressure very close with the results obtained from single isolated pile. This is possibly due to reduction in the group action on the leading row unlike the piles within other rows (i.e., trailing row). This observation was also reported by Brown et al. [ 10] and Rollins et al. [ 4, 8, 11].

Analysis of pile group 2×2

The behavior of the 2×2 pile group is close to the behavior of previous group analyzed (i.e., 2×1). This was also supported by Patra & Pise [ 6]. This is due to the same number of pile in the direction parallel with load direction. The lateral pile displacement changed and redistribution on the lateral soil resistance was observed when increasing the axial load level and effected by the group interaction condition. In general, the lateral pile displacement within group (for all pile spacing) due to the influence of axial load level was less than the results observed from the single pile when the axial load less than 4H. These results were greater than the results obtained from assessment of single isolated pile for the axial load more than 6H. This is possibly due to increase in soil strength when high magnitude of axial load is applied as shown in Fig. 5.

The difference in ultimate soil resistance for different combinations of axial and lateral load and with varied pile spacing is illustrated in Fig. 6. This can be compared with the results obtained by Brown et al. [ 10] and Rollins et al. [ 4, 8, 11] for pure laterally loaded pile group. It can be observed that the low intensity of axial load (less than 4H) give similar results between those predicted by this study and those obtained from published cases. On the other hand for high magnitude of axial load (greater than 6H) it can be observed different results and the behavior become non-uniform. This is possibly due to redistribution of the front soil resistance when the levels of axial loads are increased.

The influence of axial load intensities on the predicted p-y curve for four pile spacing on both cohesionless and cohesive soils is illustrated in Fig. 7. It can be concluded that similar values are obtained for p-y curve predicted for 2×2 pile group and results obtained from group 2×1. In addition it can be observed that low axial load intensity (less than 4H) give close results with that obtained from pure lateral load analysis. While when axial load are increased (more than 4H), larger differences in the behavior are noted and the predicted p-y curve was greater than those obtained from pure lateral load analysis.

Analysis of pile group 3×2

The distribution of load between rows of the pile group is one of the issues for analysis and design the pile groups with such configuration. The location of the pile within group is very important when assessing the behavior of piles within group. In general, leading pile is most efficient because it resisted most loads in comparison with the single pile and the trailing piles. The 2nd trailing piles resist the least due to group interaction [ 4, 8, 10, 11].

The lateral pile displacement and lateral soil resistance have close values for both first and second trailing row which also observed by Zhang et al. [ 5] and Rollins et al. [ 4, 8]. It can be seen that the values observed for the first trailing row is significantly greater than the values observed for the second trailing row and similarly obtained by Brown et al. [ 10]. This is possibly due to the group interaction which has more effect on the intermediate rows as shown in Fig. 8. For the different axial and lateral load combinations, higher changes in the lateral pile displacement with depth are observed due to increased in the axial load level. This change is always less for the pile in first and second row compared with those obtained from trial row.

On the other hand, the axial load intensities made a redistributed in lateral soil pressure with depth for pile with group compared with that of single isolated pile as illustrated in Fig. 9. This is possibly due to the influence of load combinations influenced on the front soil pressure distribution. No conclusion available regarding this issue and only available investigation was done by [ 1, 2] for the single isolated pile which not closed with present study.

Finally, the predicted p-y relationship for pile group under the influence of axial load intensities and with four different pile spacing is shown in Fig. 10. It can be observed that low axial load intensity (less than 4H) produce close results with that obtained from pure lateral load analysis for first, second trailing and leading row. When axial load (greater than 4H) increases, the behavior changes significantly and the predicted p-y curved is greater than those obtained from pure lateral load analysis.

Prediction of the pile-to-pile modulus multiplier and proposed equation for analysis of pile groups

As reported by Rollins et al. [ 8, 11], one method of accounting for the shadowing or group action effects is to reduce the modulus or the soil resistance, p for the pure laterally loaded pile group. This module is named p-multiplier (f_m) which usually derived from a single isolated pile and pile within group p-y curve which earlier proposed by Brown et al. [ 10]. Although this simple approach has provided relatively good estimates of measured pile group behavior [ 10, 11], p-multipliers are extremely restricted in their application. The pile-soil-pile interaction is illustrated in Fig. 11. The previous researches obtained the pile-to-pile modulus multiplier only for pure lateral load. No reports are available for the influence of axial load intensities to the p-multiplier. Therefore, this section provides the development of the f_m with respect to pile spacing for both pure lateral loaded pile groups as well as pile groups subjected to combination of axial and lateral loads. The development is predicted in two types of soil (cohesionless and cohesive soil). The improvement includes:

1) Proposed design curve show p-multiplier values as a function of pile spacing.

2) Proposed design equation to compute the amount of p-multiplier (f_m) as a function of both pile spacing (c-c) and pile diameter (D).

Proposed design curve

The pile-to-pile modulus multiplier (f_m or p-multipliers) was evaluated by dividing the ultimate soil pressure of pile within group by the values obtained from single isolated pile at the given depth [ 8, 10]. Predicted p-y curve for pile within group can be obtained by multiplying the values of lateral soil pressure p by the value of f_m while keeping lateral pile displacement constant. The result of the predicted p-multipliers represent both cases of purely lateral loaded pile groups as well as pile groups carrying combination of axial and lateral loads are illustrated in Fig. 12.

In general, it can be observed that the values of f_m of leading pile is always greater that those measured for first and second trailing pile which was also observed previously by Brown et al. [ 10] and Rollins et al. [ 4]. Therefore the piles in the leading row carry load similar to that carried by single isolated pile. This is due to the less effect of group action on the leading pile compared with other piles. The piles in first and second trailing row also carry similar magnitudes of loads. It can be seen that for pile spacings between 2D to 5D the values of f_m are small. This means the large group action effect occur in this case of small pile spacing compared with the pile group of wide pile spacing (i.e., s is more than 5D). This indicate that the pile within the group for the case of wide spacing pile group can be designed according to the results obtained from single isolated pile.

The main finding from this comparison is the values of f_m obtained from the pile groups in cohesionless soil are larger than the f_m magnitudes obtained from pile groups in cohesive soil. This is possibly due to the increase in lateral pile group capacity resulted from the action of axial load. Other studies on this are unavailable for comparison. Similar reports are available only for the case of single isolated pile [ 1, 2]. Therefore, when compared to the phenomenon of the increasing in lateral pile capacities when applied axial load, it can be found that Karthigeyan et al. [ 1, 2] also observed that for piles in cohesionless soil, the vertical loads (when simultaneously applied with lateral loads) decreases the lateral deflection thus increasing the lateral load capacity of the piles. In addition, in cohesive soils, this study found that the axial loads decrease the lateral pile capacity.

Other important issue observed from this assessment is the improvement in the lateral capacity of pile within group compared with similar single isolated pile capacity. Available reports for pure laterally loaded pile group predicted the pile within group carry lower loads than the single isolated pile. Therefore, the values of f_m always is less than one [ 8, 10]. However, in this study it can be observed that the values of f_m are greater than one especially in the case of high axial load intensities (i.e., more than 8H). This is possibly due to decrease in lateral group action when applying high axial load. The lateral group action is small decrease in case of 2×1 and 2×2 pile groups and largely decreased in case of 3×2 pile groups. Therefore, it can concluded that the large size pile groups will be more resistive to the lateral load when taken into account the effect of simultaneous axial loads.

Proposed design equation

An equation have also been developed according to the design p-multiplier curves to compute the amount of p-multiplier (f_m) as a function of both pile spacing (c-c) and pile diameter (D) under the effect of the simultaneous combination of axial and lateral loads. The equation may applied for both cohesionless and cohesive soils, given in the form of:

(1) f_{\mathrm{m}}=A\mathrm{l}\mathrm{n}(s/D)+B,

where A and B are constant which can directly obtained from Table 2.

This table is limited for three pile group configuration (i.e., 2×1, 2×2 and 3×2) and four pile spacing (i.e., s = 2D, 4D, 6D and 8D). The values of the constants are calculated for five axial load magnitudes (i.e., V = 2H, 4H, 6H, 8H and 10H). The values of these constants for both soil types can extrapolate to other pile group configurations. The design method used only in one layered soil and no cap influenced

Example calculation of the pile group

The total lateral load resistance of one pile group’s configuration (i.e., 2×2) is to be determining according to the assumed single pile response reported by Karthigeyan et al. [ 2] for both cohesionless and cohesive soils. This group has spacing of 3.53D center to center in the direction of lateral load. This value of pile spacing also used by Rollins et al. [ 4]. For this example, the piles are 1.2 m and 10.0 m diameter and length, respectively. The predicted f_m magnitudes for this specific example calculated using Eq. (1) and the results are shown below.

1) Cohesionless soil:

Trailing row, spacing,

f_{\mathrm{m}(v=\mathrm{0})}=\mathrm{0.2075}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.2575}=\mathrm{0.52}

f_{\mathrm{m}(v=\mathrm{0.2}\mathrm{V})}=\mathrm{0.1618}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.2084}=\mathrm{0.41}

f_{\mathrm{m}(v=\mathrm{0.4}\mathrm{V})}=\mathrm{0.1726}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.2608}=\mathrm{0.48}

f_{\mathrm{m}(v=\mathrm{0.6}\mathrm{V})}=\mathrm{0.2032}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.6679}=\mathrm{0.92}

f_{\mathrm{m}(v=\mathrm{0.8}V)}=\mathrm{0.1485}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{1.1242}=\mathrm{1.30}

Leading row, spacing,

f_{\mathrm{m}(v=\mathrm{0})}=\mathrm{0.1867}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.4018}=\mathrm{0.64}

f_{\mathrm{m}(v=\mathrm{0.2}\mathrm{V})}=\mathrm{0.1346}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.4948}=\mathrm{0.67}

f_{\mathrm{m}(v=\mathrm{0.4}\mathrm{V})}=\mathrm{0.1903}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.4729}=\mathrm{0.71}

f_{\mathrm{m}(v=\mathrm{0.6}\mathrm{V})}=\mathrm{0.2580}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{1.0639}=\mathrm{1.39}

f_{\mathrm{m}(v=\mathrm{0.8}\mathrm{V})}=\mathrm{0.1501}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{1.4318}=\mathrm{1.62}

2) Cohesive soil:

Trailing row, spacing,

f_{\mathrm{m}(v=\mathrm{0})}=\mathrm{0.1973}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.1852}=\mathrm{0.42}

f_{m(v=\mathrm{0.2}\mathrm{V})}=\mathrm{0.2639}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.0375}=\mathrm{0.37}

f_{\mathrm{m}(v=\mathrm{0.4}\mathrm{V})}=\mathrm{0.2786}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.0764}=\mathrm{0.43}

f_{m(v=\mathrm{0.6}\mathrm{V})}=\mathrm{0.3169}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.3155}=\mathrm{0.72}

f_{\mathrm{m}(v=\mathrm{0.8}\mathrm{V})}=\mathrm{0.3869}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.4551}=\mathrm{0.94}

Leading row, spacing,

f_{\mathrm{m}(v=\mathrm{0})}=\mathrm{0.2292}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.2890}=\mathrm{0.58}

f_{\mathrm{m}(v=\mathrm{0.2}\mathrm{V})}=\mathrm{0.2189}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.2955}=\mathrm{0.57}

f_{\mathrm{m}(v=\mathrm{0.4}\mathrm{V})}=\mathrm{0.2482}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.3279}=\mathrm{0.64}

f_{\mathrm{m}(v=\mathrm{0.6}\mathrm{V})}=\mathrm{0.4207}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.3331}=\mathrm{1.86}

f_{\mathrm{m}(v=\mathrm{0.8}\mathrm{V})}=\mathrm{0.4325}\mathrm{l}\mathrm{n}(\mathrm{3.53})+\mathrm{0.4872}=\mathrm{1.03}

The computed load vs. deflection for single isolated pile with f_m values in case of cohesionless and cohesive soil and both load conditions (i.e., pile group subjected to pure lateral loads and combination of axial and lateral loads) are shown in Fig. 13.

Summary and evaluation of the results

From related literatures of studies related to pile groups embedded in cohesionless and cohesive soil, the analysis of pile groups are either subject to pure axial load or pure lateral load. These previous studies did not include any findings regarding simultaneous combination of loading influence on the pile group action. In fact, the axial load intensity largely changes the lateral pile and pile group response as reported by Karthigeyan et al. [ 1, 2] for single isolated pile. This change is neglected when analysis and design the piles and pile groups and also underestimates the foundation stiffness. Therefore, this study includes this effect of simultaneous load combinations on the lateral pile response within group. This research has made it possible to quantify many important aspects of pile and pile group behavior under combination of axial and lateral loads.

To satisfy the objective of this study, three-dimensional finite element approach was used to analyze this geotechnical problem. The geotechnical system included linear elastic, Mohr-Coulomb and 16-nodes interface elements constitutive models. Three pile group was used (i.e., 2×1, 2×2 and 3×2) with four varying pile spacings (i.e., 2= 2D, 4D, 6D and 8D). Cohesionless and cohesive soils were used in this study for comparison. Laterally applied loads were 50, 250 and 450 kN. In addition forces of 2H, 4H, 6H, 8H and 10H represent the axial loads

The analysis of the pile groups included lateral pile displacement and lateral soil resistance with pile depth as well as the corresponding p-y curves. On the first and second trailing rows as well as the leading row. The lateral pile displacement changes and the lateral soil pressure redistributed when the level of axial load was increases. This was also observed by Karthigeyan et al. [ 1, 2] for single isolated pile. The p-y curves obtained from this study take into account the influence of axial and lateral loads combination. Previous studies only depended on the pure lateral loads. The resultant p-y design curves can be used to produce the design parameters for laterally loaded pile design. In addition these curves can be used to create p-multiplier design curves. These curves can be used to predict the lateral behavior of pile within group when only the results of single isolated piles are available. The predicted p-multiplier design curves was used to developed design equation to compute the amount of p-multiplier (f_m) as a function of both pile spacing (c-c) and pile diameter (D) under the effect of combined axial and lateral load. This paper also provides a table containing the values of the design equation constants (i.e., A and B). This design equation was applied on the similar example that the problem parameters were assumed according to Rollins et. al. [ 4] and Karthigeyan et al. [ 2] reports. This calculation example show step by step application of this equation. This equation can used in order to produce design parameters for the pile within group from the results of single isolated pile.

Conclusions

The magnitudes of axial load have large effect on the lateral pile displacement and soil resistance. The lateral pile displacement significantly increased and lateral soil pressure significantly redistributed when the magnitudes of axial applied load are increased. The magnitude of axial load subsequently changes the predicted p-y relation and this change directly effect the design curve of laterally loaded piles and pile groups. High different on the p-y curve was observed in case of closed pile group (i.e., s is less than 4D). The pile within leading row has close values with that of single isolated pile. The behavior of the 2×2 pile group is close but not the same with the behavior of 2×1 pile group. In the case of 3×2 group, the lateral pile displacement and lateral soil resistance are similar to both first and second trialing row. The magnitude of axial load also significantly effect on the predicted f_m. The values of f_m can also be greater than one especially in case of high axial load intensities. The lateral group action is small in case of 2×1 and 2×2 pile groups and largely decreased in case of 3×2 pile groups.

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