1D FEA of laterally loaded pile: inclusion of moving soil

[LRJ]

Hi,

I've got a 1D finite element beam-column model working which I use to analyse laterally loaded piles. The only thing left that I want to implement is a way to model moving soil, e.g. from landslides. The usual way to do this is by including so-called 'y-shifts' in the model. My understanding of these 'y-shifts' is that they are simply an offset to the p-y springs. Is that correct?

I ask as I've also seen an implementation of y-shifts which involves an additional mass matrix. So the |m_M|.{y} term in the full FEM equation becomes:

|m_M|.{y - y₀}

Where:
|m_M| = Mass matrix
{y} = Displacement vector (y₁, θ₁, y₂, θ₂)
{y₀} = Displacement vector for moving soil (y₀₁, θ₀₁, y₀₂, θ₀₂)

Should I get the same result if I simply offset the p-y springs? Moreover, is that what {y - y₀} in the above equation means?

 

[LRJ]

After a bit more reading I've learned that the p-y soil spring stiffness is calculated according to the relative soil-pile displacement (i.e. y - y0). This implies that it is modelled as a modification to the input p-y spring.

Supposing that is correct, what I want to know is if that means when my pile is not loaded (so: y - y0 = 0), would I have soil reaction but no bending moment or shear force? This seems counter intuitive though could be a result of considering relative pile-soil movement as opposed to total movement.

Does this make sense? I realise my OP was a little confusing and this post might also be.

 

[LRJ]

I've figured out how to include the above in my model. In case anyone in the future would like to know, I'll document it here.

Essentially the moving soil is incorporated as an additional load. You multiply your shape functions (for each integration point with the relevant weighting) by your distributed load for that element to get the moving soil load vector (F1, M1, F2, M2). The distributed load is dependent on the amount the soil has moved (i.e. the y-shift). You can determine this load using the intersection of the y-shift on the p-y curve.

The form of the calculation is quite similar to the |m_M| matrix calculation except you don't multiply a shape function by another shape function and you multiply the vector by a distributed load rather than multiplying the matrix by the soil stiffness.

Doing the above ensures that, even when the pile is not loaded with a horizontal load or moment, there is still loading on the pile from moving soil. So my second post above can be ignored.

 

[LRJ]

Correction to the above: the distributed load for the Fshift vector should not be based on the intersection of the y-shift on the unshifted p-y curve; it should be the intersection of the y displacement value on the shifted p-y curve.