Subgrade Modulus

One of the key material properties when designing a foundation is the coefficient of subgrade reaction, k. This is more commonly known as the soil subgrade modulus which in its simplest form is defined as follows:

k = q / delta

In the above equation, q is a load per unit area and delta is a settlement.

If you look at the units of k you will see that this value is a measure of force per unit area per length. This value can be reduced to a spring constant if the area that it acts over is known.

If the spring constant is known, spring supports can be added to a finite element mesh to simulate the reaction of the soil under a foundation. In VisualFoundation, the tributary area of the plates surrounding each node is multiplied by the subgrade modulus k to determine the spring constant for each node in the finite element mesh. This is done on a per-node basis because the size of the plate elements surrounding each node can vary. Remember, soil springs in VisualFoundation carry only compressive forces and have zero stiffness in tension.

For a detailed discussion of subgrade modulus (specifically for foundation design), refer to the following:

• ACI Committee 336, "Suggested Analysis and Design Procedures for Combined Footings and Mats (ACI 336.2R-88)," American Concrete Institute, 1988
• Bowles, Joseph E., 1996. Foundation Analysis and Design, 5th Edition, McGraw-Hill Book Co. New York

The Portland Cement Association's "Concrete Floors on Ground" publication reports a subgrade modulus for different soil types. These values are meant for slab-on-grade design, and may not be appropriate for foundation design. However, these tables may provide a useful starting place. Site specific values, from a geotechnical engineer, will provide the most accurate solution.

The analysis results will generally be sensitive to the subgrade modulus. In light of this and the uncertain nature of soil parameters, it may be wise to vary the subgrade modulus over a range of possible values during design.

Soil Bearing

Assuming a size (plan dimension and thickness) has been chosen to guarantee uplift and overturning stability, the next step is ensuring the size will not result in excessive bearing pressures between the footing and soil. Traditionally, this has been done assuming the footing is infinitely rigid relative to the soil. This results in a linearly varying bearing pressure when some overturning exists. For rectangular footings this bearing pressure calculation is not difficult. When the shape becomes more complex these calculations become much more tedious.

Many footings are of a thickness which causes them to have some flexibility relative to the soil and linearly varying bearing pressures do not exist. The interaction of soil stiffness and footing stiffness becomes an important analysis consideration. Use of the finite element method as employed by our VisualAnalysis computational engine provides a fast and accurate way to deal with soil-structure interaction. VisualFoundation uses the finite element method creating a model of plate elements as well as beam or wall stiffening elements. Compression-only linear spring supports are used to model the soil. Accurate bearing pressures result from the analysis which can be compared to allowable or ultimate values specified by geotechnical engineers.

You will specify one bearing pressure value to use for unity checking. This is located in the Modify, Project Settings panel. It is up to you to use either a service level or a strength level value for this number.