Lateral response of pile due to combined load under free and fixed conditions

: (cid:3) Pile foundations are used to support both vertical and horizontal loads in many geotechnical projects, such as coastal and offshore engineering. In this project, the Finite Difference Method is proposed to solve the differential equation governing the lateral and axial pile response. Initially, the behaviour of the pile subjected to lateral load will be analysed. The effect of various parameters like pile head fixity, the cohesion of surrounding soil, pile diameter, and length of the pile on lateral pile response will be analysed. Finally with these conditions, the deflections profile of the pile subjected to both lateral and axial load is investigated. By using python code we can easily find out the increase in diameter of pile, cohesion of surrounding soil effect on pile head and effect of increase in combined load will be studied. The above stated parameters will be studied for combined loading also under the free and fixed head conditions.

1 Deflected shape and bending moment distribution of a laterally loaded fixed-head pile (a) first yield limit state, (b) second yield limit state, and (c) ultimate limit state. (Source: Song et. Al 2004)

Importance of the study
Some of the circumstances in which we will offer pile foundation include [3][4][5][6] • When there is a high groundwater table.
• The superstructure imposes heavy and irregular loads.
• Other foundations are either too expensive or impractical.
• When the soil is compressible at shallow depths.
• When scouring is a possibility because the area is close to a riverbed, the beach, etc.
• When a deep drainage system or canal is located close to the building.
• When bad soil conditions make it impossible to excavate dirt to the appropriate depth.
• When excessive seepage intake renders pumping or any other method of maintaining the foundation trenches dry impracticable.

Subgrade Reaction
In the Winkler soil model, it is assumed that the pressure p and deflection y at a site are connected via a subgrade response modulus, which for horizontal loading is symbolised by the symbol [7][8]. Thus,

P = kh*y
Where kh has the units of force/length. An equation has been restated frequently as The pile is usually assumed to act as a thin strip whose behaviour is governed by the beam equation [9] Ep*Ip (d 4 y/dz 2 ) = -y*d Where, Ep = modulus of elasticity of pile Ip = moment of inertia of pile section z = depth in soil d = width or diameter of the pile

Elastic Reaction
Here, we take into account the soil's continuous character. The elastic model also has the benefit of allowing for consistent study of both immediate movements and overall final motions.[10-11]

Objective
1) The objective of the present study is to find the effect of various soil parameters (Cohesion, modulus of Elasticity) and pile parameter (Moment of inertia, Grade of Concrete, Poison ratio, Length of pile, Diameter of pile).
2) The Effect of Combined load on lateral pile response is figured by using python algorithm code.

Algorithm
The algorithm for the lateral deflection of the pile under combined load is :

Code:
The Full project source code is uploaded in the Github, CLICK HERE The deflection profile of pile under the loading in given conditions and combined loading case is shown in figure 1.  The comparison between pile top deflection under fixed head condition and free head condition are shown below with variation of various parameters.  Moreover, other characteristics can be coupled to the deflection profile of the pile under combined loading as needed. The following are a few of the common relations that may be derived:

Influence of Moment on deflection profile of Combined loaded pile
i. In both instances, the pile top deflection rose by 90% while the lateral loading increased by a factor of ten. ii.
When the moment is raised three times, the pile top deflection for a free head pile rose by 67%. iii.
For free head piles, the pile top deflection falls by 48.6%, and when the diameter is raised by 60%, it falls by 99.95%. iv.
Also, in order to properly do the task that is expected of us, we may observe and compare the many relationships we have above.