Explicit extension of the p–y method to pile groups in cohesive soils

doi:10.1016/j.compgeo.2012.07.004

Computers and Geotechnics

Volume 47, January 2013, Pages 28-41

https://doi.org/10.1016/j.compgeo.2012.07.004 Get rights and content

Abstract

Although simplified numerical methods are reliable for evaluating the response of a single pile under horizontal load, their application is questionable for assessing the response of pile groups. The notion of “p–y” curves has been considered with the aim of establishing a transformation relationship able to provide the “p_G–y_G” curves of soil resistance around a pile in a group from the well-known curves of soil resistance around the single pile.

This transformation extends the applicability of the “p–y” method to pile groups, without the need for time consuming numerical computations, rendering the proposed method efficient and attractive. Comparative examples demonstrated the applicability and the effectiveness of the proposed method. In addition, the method can be straightforwardly extended to account for varying soil resistance, according to the particular location of a pile in a group. It can therefore be used to estimate accurately force and bending moment distributions along the characteristic piles of a group, which are required for the efficient design of foundations.

Introduction

An accurate design of structures based on piled foundation subjected to lateral loads requires the lateral response of the piles under such loads. Although simplified numerical methods are reliable for predicting the response of a single pile under horizontal loading, their application is questionable for assessing the response of pile groups. As it is commonly accepted, for the same mean load, not only the pile group exhibits significantly higher deflection than an identical single pile, but also the response of each pile of the group differs, depending on its position in the group. The unequal distribution of load to the piles constituting a group is due to the overlap of shear resisting zones termed as ‘shadowing effect’. The diverse response of the pile group, attributed to the interaction between the piles of the group, has been examined experimentally [1], [2], [3], [4] and numerically [5], [6], [7]. The evaluation of experimental results reveals the stiffer behaviour of the single pile, as well as the unequal distribution of the applied load to the piles in a group. Available data from experiments and numerical analyses indicate that the load carried by the internal piles is less than that carried by the external piles, while corner piles in the leading row exhibit the higher resistance. Brown et al. [8] have introduced the notion of p-multipliers to scale down “p–y” curves for piles and account for the aforementioned effects of piles interaction on pile group response. Specific values for p-multipliers have been proposed Rollins et al. [3] in tabular form, resulting from experience gained through in situ load tests. Although the method provides a satisfactory approach of pile group behaviour for the cases experimentally examined, the restricted range of data renders the extrapolation of the method and the application of the estimated values of p-multipliers to different soil conditions and pile group configurations rather ambiguous. In addition, the fact that the values for p-multiplier are given per rows reduces the accuracy of the method given that the central pile and the corner leading piles demonstrate unequal behaviour than that of the other piles in their rows.

Considering the aforementioned lack of data, which has inevitably led to a variation in p-multiplier recommendations, the results of an extensive parametric numerical analysis has been used to establish a relationship with the ability to define the “p–y” curves for pile groups in clayey soils. To achieve this goal several pile group configurations in clayey soils have been examined, ranging from soft to very stiff clays, with the aim to evaluate the influence of all the parameters (i.e. piles’ number, piles’ spacing, deflection level, soil shear strength) affecting “p–y” values. To improve the comprehension of pile group behaviour, the ratio of the load carried by each pile in the group to that of the single pile load, for the same deflection, is computed. The results are afterwards used to derive a transformation relationship providing the “p_G–y_G” curves of soil resistance around a pile in a group from the well-known curves of soil resistance around the single pile. The process can be considered as an extension of the widely applied “p–y” method. The fact that it can provide the response of both the single pile and a pile group at the same time, without the need for time consuming numerical computations, renders the proposed method extremely attractive.

Section snippets

Response of a single pile

Various approaches have been proposed for single piles with the aim to take into account nonlinearities arising from soil–pile interaction. A simplified 1-D analysis, considering the pile as a beam element and substituting the soil by a family of curves as a function of deflection, is used to evaluate the response of a single pile. The simplicity of the method, in conjunction with the well-defined procedures for establishing the aforementioned curves termed as “p–y” curves [9], [10], [11], [12]

Response of pile groups

According to Papadopoulou and Comodromos [6] and Comodromos and Papadopoulou [7] the response of a pile group under lateral loading is of a similar form to that of a single pile. They investigated the variation of the deflection amplification factor, R_a, which is introduced when comparing the response of a pile group to that of a single pile (considering the same pile dimensions and soil profile). The R_a factor can be defined as the ratio of the group deflection at the pile cap y_mG to the

Applicability – verification

Given that available data from experimental results of pile groups under lateral loading are extremely rare, the applicability of the proposed method is verified on both numerical and experimental results.

Conclusions

A simplified and effective method has been previously proposed for predicting the response of pile groups, provided that the response of a similar single pile is known [7]. Straightforwardly, the method can be used to replace the pile foundation by a stiffness matrix within the process of the analysis and design of a superstructure. However the lack of force and bending moment distribution along the piles limits the efficiency and attractiveness of the method. With the aim of proposing a new

Acknowledgement

The authors gratefully acknowledge Prof. M. Georgiadis for his advice and helpful comments.

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Explicit extension of the p–y method to pile groups in cohesive soils

Abstract

Introduction

Section snippets

Response of a single pile

Response of pile groups

Applicability – verification

Conclusions

Acknowledgement

Comput Geotech

Cyclic lateral loading of a large-scale pile group

J. Geotech Eng – ASCE

Evaluation of laterally loaded pile group at Roosevelt Bridge

J Geotech Geoenviron Eng – ASCE

Lateral load behaviour of full-scale group in clay

J Geotech Geoenviron Eng – ASCE

Pile spacing effects on lateral pile group behaviour: load tests

J Geotech Geoenviron Eng – ASCE

Response evaluation of horizontally loaded fixed-head pile groups using 3-D nonlinear analysis

Int J Numer Anal Methods Geomech

Response evaluation of horizontally loaded fixed-head pile groups in clayey soils

Géotechnique

Lateral load behavior of pile group in sand

J Geotech Eng – ASCE

Lateral loadings of deep foundations in stiff clay

J Geotech Eng – ASCE