Course · lesson 4 of 7

Rafts as a Winkler plate

When pads crowd the plan or the ground is soft, one slab under the whole building is the answer. This lesson models a raft as a plate on soil springs, finds the subgrade modulus, follows the pressure, settlement, moments and punching, and uses the STATIX raft calculator.

1. Learning outcomes

After this lesson you can:

say when a raft is better than separate footings;
choose a subgrade modulus k and know its limits;
explain how a plate on springs shares column loads, and how stiffness changes the pressure;
place the top and bottom steel of a raft and check punching at edge and corner columns;
state what the STATIX raft calculator assumes and read its results.

2. Before you start

Lesson 1 (allowable pressure, settlement and k = q_a/s) and lesson 3 (the base as an upside-down beam).
The free raft calculator; the raft Learn page as background.
About 55 minutes.

3. When a raft

When a raft. When pads would cover much of the plan, when the soil is weak or variable, or when the building cannot take the differential settlement of separate pads, one slab under the whole building (a raft) spreads the loads, bridges soft spots and evens out settlement.

4. The soil as springs

The Winkler model. The STATIX raft calculator treats the soil as a bed of independent springs under a thin plate: each node of the plate sits on a spring of stiffness k times its share of the area. Pressure at a point is k times the settlement there. It is a simple model; it gives no settlement trough beyond the loaded area.

Where k comes from. The raft calculator takes k directly, or a geotechnical engineer's allowable pressure q_a with the settlement it causes, and divides (lesson 1). k is not a pure soil property: it depends on the size of the loaded area and the stress level, so treat it as an estimate and try a range.

Stiff or flexible. A thick raft on soft soil acts almost rigidly and spreads the load evenly. A thin raft on stiff soil bends locally, so the pressure gathers under the columns. What matters is the stiffness of the plate relative to k; the calculator finds the actual pressure from the plate and the springs together.

How the load spreads. Under each column the plate is pushed down furthest and the springs there are compressed most; between and beyond the columns the plate rises and the springs carry less. The plate bends to share the load out.

spring at a node: k × tributary area; pressure q = k w; settlement w = q / k k from a report: k = q_a / s (e.g. the pressure and the settlement it causes)

5. Pressure, moments and punching

Contact pressure. The largest pressure under the raft at the service loads must stay within the allowable pressure. Where a load case would lift part of the raft, the calculator removes those springs and solves again, because the soil cannot pull.

Moments. A raft is a flat slab turned over: the columns are its supports and the soil is its load. Between the columns it bends upward, with tension at the top; under and around the columns the tension is at the bottom. The calculator designs four mats: bottom and top, in x and in y.

From plate moments to steel. The plate analysis gives bending and twisting moments; the Wood-Armer rules turn them into design moments for each mat. The calculator averages the peak over a width of 2h and leaves out the column footprints, and says so in each row (a practice choice).

Punching at the columns. Each column is checked like a flat slab column, with the net upward soil pressure inside the perimeter deducted. Columns near an edge or a corner have their perimeter cut by the edge, so they are usually the critical ones. If v is too high the calculator gives shear links where the punching rules allow them; otherwise deepen the raft.

6. What the calculator assumes

What the calculator assumes. A rectangular raft of uniform thickness, meshed with lines through every edge and column face; thin-plate elements with the short-term concrete stiffness; columns spread over their footprints; Winkler springs that take no tension. Walls and a floor load can be added as line and area loads.

7. In STATIX

In STATIX: the raft size and depth, the soil stiffness (k, or q_a with its settlement), the columns one per line with their position, size and loads, and any walls or floor load. The results give the pressure and settlement contours, the four mats and punching at every column.