Module 18 · Lesson 18.1
Rigid or flexible
Two mechanisms, and no way to tell which without checking.
Why this matters
Every other module in this course has had one mechanism to compute. This one has two, they predict different things, and choosing between them is not a matter of preference — a short pile and a long pile of identical section in identical soil fail in completely different ways.
By the end of this lesson you should be able to
- Compute the stiffness factor and the length ratio
- Classify the pile and identify its mechanism
- Say what happens in the range where neither solution applies
A laterally loaded pile is a beam on an elastic foundation. The competition is between the pile's flexural stiffness EI and the soil's resistance, characterised by a modulus of subgrade reaction kh. Their ratio has the dimensions of length to the fourth power, so
T = (EI / kh)^¼
is a length: the distance over which the pile and the soil influence one another. Everything then depends on how the pile's embedded length compares with it.
- L/T below about 2 — rigid, or 'short'. The pile is stiff relative to the soil and rotates essentially as a rigid body about a point some way down. It fails when the soil around it gives way.
- L/T above about 4 — flexible, or 'long'. The pile bends. The lower part barely moves, and failure occurs when a plastic hinge forms in the pile itself. Adding length beyond this achieves nothing at all.
- Between 2 and 4 — intermediate, where neither closed-form solution is trustworthy and a numerical analysis is warranted.
Worked example
Classifying one pile at three lengths
Given
- Concrete pile, D = 0.6 m, E = 30 GPa
- Modulus of subgrade reaction kh = 5000 kN/m³
Find
Whether the pile is rigid or flexible at 4 m, 5 m and 10 m
Check yourself
A pile has L/T = 5. Where does it fail?
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint