Nonlinear Behavior of Single Vertical Pile Under Lateral Loads
Authors: Mohan Dinesh , Shrivastava S.P. 
Published: October 2008

Abstract
A field study on instrumented as well as non instrumented piles was carried out, in loose sandy soil, to investigate the behavior of single vertical piles. Piles were tested with different stiffness?s and length to diameter ratio. One pile was instrumented with electric wire resistance strain gauges to determine the moment, shear and soil pressure along the depth of pile. A detailed programmed for soil exploration was chalked out to determine the value of modulus of sub grade reaction.
The study showed that the load-deflection characteristic of a single vertical pile under lateral load can re better predicted by nonlinear theories, provided the value of modulus of sub grade reaction is properly assessed. A need for standardization of test technique has also been felt since there is wide variation in the values of soil parameters determined by different existing tests.

Introduction
The soil is generally assumed as linearly deformable in the analysis of vertical pile subjected to lateral loads mainly because an exact solution is readily available for such cases. Winkler's hypothesis, according to which the reaction offered by soil is linearly proportional to its deformation, forms the basis of this approach. Terzaghi7 has also shown that, corresponding to a particular deformation, the modulus of sub grade reaction increases linearly with depth for sand but for clays it remains constant.
The validity of Winkler's hypothesis has been questioned by a few 3')0rkers and 5) recent investigations of Kubo3, Sawaguchi and Gill1,2 have shown that the load deformation characteristic of a single vertical pile under lateral load is essentially nonlinear. ubo3) has proposed a parabolic relation between soil reaction and def0rrration based on his model tests. Sawaguchi5 has used this concept to check a few field piles. Gill used the concept of a rectangular hyperbola to describe the stress ..strain relation of soil. He checked his method against a few field tests on non-instrumented piles.

(a) Kubo?s method
Based)n model tests on instrumented piles, Kubo3 proposed the following relation between soil reaction and pile deflection.(MATHEMATICAL EQUATION IN FULL PAPER)
Following Terzaghi?s7 recommendations, value of m is unity for sandy soil and zero for over consolidated clay. The value of n for both sand and clay is111
To evaluate Ks, Kubo suggested the following relations(MATHEMATICAL EQUATION IN FULL PAPER)
The standard penetration test value (N) increases linearly with depth and the relation between N, the value of Nat a depth of 1 meter and Ks is given by(MATHEMATICAL EQUATION IN FULL PAPER)
The N value is constant with depth and the relation between N and Ks is given by(MATHEMATICAL EQUATION IN FULL PAPER)

(b) Gill's method
Gill1,2) developed a new test technique, called the segmental pile test to determine the soil parameters and proposed the use of rectangular hyperbola for des cribbing the load deformation response of soils. He proposed the following relation between the modulus of sub grade reaction and the deflection of pile at a particular depth