Plate Load Test Calculations: Pressure and Modulus

Calculation guidance for plate contact pressure, load-settlement increments and modulus of subgrade reaction, including scale limitations.

Table of contents

A plate load test records applied load and plate movement to characterise load-settlement response at a test location. The arithmetic is straightforward, but interpretation depends on plate geometry, test setup, stress range, seating, ground conditions and the selected method.

Topic guide: For background, method selection and related checks, see Plate Load Testing.

Applied contact pressure

For applied load \(P\) and plate area \(A\):

$$ q=\frac{P}{A} $$

For a circular plate of diameter \(D\):

$$ A=\frac{\pi D^2}{4} $$

For a rectangular plate:

$$ A=BL $$

Settlement increment

For two readings:

$$ \Delta s=s_2-s_1 $$ $$ \Delta q=q_2-q_1 $$

The load and settlement readings used must be identified. Seating movements and unload-reload cycles should not be removed or combined without following the nominated interpretation method.

Modulus of subgrade reaction

A secant or incremental modulus of subgrade reaction may be written as:

$$ k_s=\frac{\Delta q}{\Delta s} $$

The units are pressure divided by displacement, such as kPa/mm or kN/m3.

The selected stress interval must be reported. A single \(k_s\) value is not an intrinsic soil property. It depends on plate size, stiffness, stress level and test conditions.

Worked example

Assume:

  • plate area \(A=0.25\) m2
  • applied load \(P=100\) kN
  • settlement from the nominated origin \(s=5\) mm

Pressure:

$$ q=\frac{100}{0.25}=400\ \mathrm{kPa} $$

Using \(s=0.005\) m:

$$ k_s=\frac{400}{0.005} =80{,}000\ \mathrm{kN/m^3} $$

This may also be written as 80 MN/m3.

The result applies to the selected origin and stress interval. It is not automatically a design subgrade modulus for a different foundation or slab.

Load-settlement curve

The calculation record should preserve every stage:

Stage Time Load Pressure Settlement Corrected settlement

Useful outputs may include:

  • pressure at each stage
  • settlement increments
  • secant values over nominated ranges
  • unload and reload response
  • residual settlement
  • plot of pressure versus settlement
  • test-stage duration

Important corrections and controls

The interpretation may need to consider:

  • plate seating
  • datum and reference-frame movement
  • reaction-system movement
  • time-dependent settlement
  • plate rigidity
  • non-level contact
  • disturbance during test preparation
  • groundwater and moisture
  • nearby boundaries
  • stress bulb relative to layer thickness

These should not be hidden inside an unexplained correction.

Scale effect

A plate tests a limited volume of ground. A larger footing or slab influences a larger and deeper zone. Directly transferring a plate response to another loaded area requires an appropriate method and engineering review.

Calculation validation

The tool should:

  • verify plate dimensions and area
  • use compatible load and area units
  • retain raw readings
  • identify seating correction
  • require the selected stress interval
  • display the resulting units clearly
  • flag zero or negative settlement increment
  • prevent an unexplained conversion to bearing capacity
  • distinguish measured curve data from derived values

Related resources

Authoritative references

Plate-load interpretation and transfer to design require the nominated method and review by a suitably qualified geotechnical professional.