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## Operational Analysis |

Analysis of pile or minipile in normal operation is effected using Finite Elements Method (FEM).

Finite Elements Method models realistically foundation piles/minipiles subjected to transverse loads considering both displacements and rotation at nodes, to define the elastic line of the pile and thus is the most realistic and effective method available to analize this type of structure.

Below are recalled the broad lines of the method.

P is the matrix of external nodal forces. F is the matrix of internal forces. A is the matrix of influence factors which due to the equilibrium of internal and external forces binds the first two according to the well known relation:

P = AF

Internal displacements e (translation and rotation ) of the element in the generic node are linked to the external displacements X (translation and rotation ) applied to the nodes by the relation:

e = BX

where the matrix X is matrix A transposed.

On the other hand the internal forces F are linked to internal displacements by:

F = Se

Which by substitution gives:

F = SATX

and therefore:

P = AF = A SATX

Calculating the inverse of matrix A SAT one obtains the expression for external displacements:

X = (A SAT)-1P

When displacements X are known, it is possible to deduce the internal forces F required for the project structure.

The matrix A SAT is known as the global rigidity matrix in that it links nodal displacements and external forces. The method further has the advantage of permitting known rotations and displacements to be taken into account as boundary conditions.

The nodal reactions of the springs that represent the terrain are considered as global forces related to the modulus of subgrade reaction and to the area of influence of the node.In the pile/minipile solution by finite elements subjected to transverse loads, subgrade reaction modulus is considered in the form:

ks = As + BsZn

or alternatively, where it is desired to contain the growth of the modulus with increase in depth:

ks = As + Bstan-1(Z/B)

in which Z is the depth and B the diameter of pile/minipile.

The values of As e BsZn are obtained from the expression for bearing capacity (Bowles) with correction factorssi, di, & ii set to 1:

ks = qult/DH = C(cNc + 0.5γBNg)

BsZn = C(γNqZ1)

Where C=40 is obtained in relation to a maximum settlement of 25 mm.

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