Keywords: piles, closed-form solutions, lateral loading, soil-structure interaction.

In this paper, elastic-plastic solutions are developed for laterally loaded piles. The solutions can be reduced to the available solutions for some simple cases. Various explicit expressions were developed, which compare fairly well with published (experimental and numerical) results under different load levels. The solutions allow the effect of interface yielding (also the effect of a lower layer) to be explored, which should be accounted for in general pile design.

Lateral pile response has been analysed widely using the load transfer () approach, by simplifying the pile-soil interaction as a series of independent springs distributed along the pile shaft and at the base [1]. Using this approach, the key is to determine the load transfer curve at any a depth, and the profile of the ultimate resistance along the pile length. The analysis is generally recourse to numerical method [2]. With the popular usage of spreadsheet software, an expedite analysis can be readily performed if closed form expressions are available [3,4,5]. Such expressions (mainly for free- head piles) were developed using Winkler model, and have been reported to compare well with experimental data [6]. However, these good predictions could be achieved through adjusting relevant parameters, because (1) within elastic state, using Winkler model, the maximum bending moment could be overestimated by up to 40 comparison with more rigorous numerical approaches [7]; (2) within plastic state, the adopted profile of the ultimate resistance vary among each researchers. These two points needs to be clarified, in order to facilitate the practical application of the approach.

In this paper, as a direct extension of the elastic solution [8], elastic-plastic solutions are firstly developed for free-head piles due to lateral loading by assuming the independent springs of an ideal elastic-plastic force-displacement relationship. A generalised profile of limiting force is adopted in plastic state, and the load transfer approach is used in elastic state to represent both the Winkler springs (subgrade modulus, ) and the coupled effect (a fictitious tension, for a strectched membrane) among the individual springs. The soil is assumed as a homogeneous medium, but the limiting force itself may vary with depth [9,10].

The load transfer factors (, ) are adopted since they are valid for any pile length and pile-soil relative stiffness. The measured load transfer () curve may generally behave as a hyperbolia or parabolia [11]. However, only the current simplified model allows pile response to be expressed explicitly right up to failure. The current solutions can be reduced to available solutions. Parametric study shows that the effect of interface yielding is at least as equally important as the limiting force profiles, which has not been well quantified previously. The solutions are sufficiently accurate in comparison with a numerical approach and relevant measurement [12]. The yield normally occurs at a rather lower loading level, thus elastic-plastic solution should be adopted in general design.

1

H. Matlock, L.C. Reese, "Generalized solutions for laterally loaded piles." J. of Soil Mech. and Found. Engrg. Div. 86(5), 63-91, 1960.

2

D.P. Coduto, Foundation design. Prentice Hall, Englewood Cliffs, N. J., 1994.

3

M.F. Randolph, "The response of flexible piles to lateral loading." Geotechnique, 31(2), 247-259, 1981.

4

S.E. Yamada, "Beam on partially yielded foundation." J. of Engrg. Mechanics, ASCE, 114(2), 353-363, 1988. doi:10.1061/(ASCE)0733-9399(1988)114:2(353)

5

B.B. Rajani, N.R. Morgenstern, "Pipelines and laterally loaded piles in elastoplastic medium." J. of Geotech. Engrg. Div., ASCE, 119(9), 1431-1447, 1993. doi:10.1061/(ASCE)0733-9410(1993)119:9(1431)

6

R.F. Scott, Foundation analysis. Prentice Hall, Englewood Cliffs, N. J. 1981.

7

W.D. Guo, "Subgrade modulus for laterally loaded piles." Proc. 8th Int. Conf. Civil and Structural Engrg Computing, CIVIL-COMP2001, Eisenstadt, nr Vienna, Austria. 2001. doi:10.4203/ccp.73.112

8

W.D. Guo, F.H. Lee, "Theoretical load transfer approach for laterally loaded piles. " Int. J. Num. & Analy. Methods in Geomechanics, 2001, in press.

9

B. Brom, "The lateral response of piles in cohesionless soils." J. of Soil Mech. and Found. Engrg. Div. 90(3), 123-56, 1964b.

10

J.D. Murff, J.M. Hamilton, "P-Ultimate for undrained analysis of laterally loaded piles." J. of Geotech. Engrg. Div., ASCE, 119(1), 91-107, 1993.

11

M. Jimiolkwoski, A. Garassino, "Soil modulus for laterally loaded piles." Proc. 9th Int. Conf. Soil Mechanics and Foundation Engrg., Speciality session 10, Tokyo, 43-58, 1977.

12

H. Kishida, S. Nakai, "Large deflection of a single pile under horizontal load." Proc. 9th Int. Conf. Soil Mechanics and Foundation Engrg., Speciality session 10, Tokyo, 87-92, 1977.

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