Over the course of the 2022 and 2023, I and my previous colleague Sercan Kerem Tomac have been working on several different projects that include deep and wide shafts with secant piles. Although traditionally structural checks are limited to compressive strength check in hoop direction, we have worked together to create a more thorough approach. This article is our joint work on this issue.

Secant Piles as Plates

In a 3D FEM software (we are using Plaxis 3D, but it applies to most of the available software in the market), secant piles can be modelled as plates, if you do not go into the volume element calculations. As we know, plates in 3D FEM are rectangular strips. Fortunately, Plaxis 3D allows users to enter different elasticity modulus in 2 directions for this rectangular strip. The inputs are:

• Thickness of the plate (deq)
• E in vertical direction (E1)
• E in hoop direction (E2)

Looking at the available inputs, we can clearly see that a realistic modelling of secant piles is not possible. Because, we have only one thickness for the plate, however, secant piles have completely different behaviour on vertical direction and hoop direction.

So, here comes our first dilemma: Out of four results, we need to sacrifice one of them.

It all comes to the deq. Because in vertical direction, traditionally, the primary (soft) piles are disregarded and assumed only the secondary (hard) piles are working for vertical bending. However, in hoop direction, the critical problem is the primary piles. The thicknesses to express these behaviours are not same. That’s why we need to sacrifice one of four.

For a secant pile analysis, most of the axial forces is derived from the self-weight and axial force has minimum effect compared to others since tolerances and reduced bite length increases the demand in hoop direction significantly while in vertical direction, tolerance does not have any effect. Therefore, axial behaviour in vertical direction will not be used for equivalent plate calculations. Sacrifice: Axial behaviour in vertical direction.

How to Select the Plate Parameters?

This is the flow chart of calculation of plate parameters. Summarizing briefly:

1. We calculate the bite thickness of the secant piles after tolerance.
2. That bite thickness gives us the minimum rectangle we can fit on the secant piles. The thickness of that rectangle = bite thickness = deq for our plate.
3. E2 can be selected as either the elasticity modulus of primary piles or an average of the primary and secondary piles. The effect is not very high.
4. Afterwards, we need to have correct bending behaviour in vertical direction (EI), but we are not thinking about axial behaviour in vertical direction (EA) anymore.
   1. Calculate the EI of the vertical secondary piles.
   2. Calculate the I of the minimum rectangle (deq).
   3. Using (a) and (b), calculate the equivalent elasticity modulus to get the correct EI. That modulus will be used as E1.

See the formulation and flow of this system.

Bite Thickness