The fundamental formula for calculating the stress exerted by a foundation on the soil is derived from the definition of stress, which is force per unit area.
Understanding Foundation Stress
Foundation stress, also known as bearing pressure or contact pressure, is the pressure exerted by the foundation's load onto the underlying soil. Calculating this stress is a critical step in geotechnical engineering to ensure the soil can safely support the structure without excessive settlement or bearing capacity failure.
The core concept is straightforward: dividing the foundation load by the contact area between the foundation and the soil.
The Formula
Based on the provided reference, the formula for calculating foundation stress is:
$$ \text{Foundation Stress} = \frac{\text{Foundation Load}}{\text{Contact Area}} $$
- Foundation Load: The total vertical load transferred from the structure (and the foundation's own weight) to the foundation.
- Contact Area: The total area of the bottom of the foundation that is in direct contact with the soil.
Applying the Formula: An Example
Let's use the example provided in the reference to illustrate the calculation:
- Scenario: A strip foundation with a specific width and length carries a certain load.
- Foundation Dimensions: Width = 1 m, Length = 10 m
- Contact Area Calculation: The contact area is the product of the width and length.
- Contact Area = Width × Length = 1 m × 10 m = 10 m²
- Foundation Load: The reference gives the load as a load per unit length, which is common for strip foundations: Load per unit length = 170 kN/m. For a 10 m length, the total load would be 170 kN/m * 10 m = 1700 kN.
- Foundation Stress Calculation: Using the formula, divide the total load by the contact area.
- Foundation Stress = Total Load / Contact Area = 1700 kN / 10 m² = 170 kPa
Wait: The reference states the stress is 17 kPa, not 170 kPa. Let's re-read the reference: "If the foundation load per unit length is 170 kN/m, the foundation stress is 17 kPa." This implies the stress calculation uses the load per unit area, not the total load divided by the total area in this specific example. For a strip foundation, the stress is often calculated as the load per unit length divided by the width.
Let's verify this:
- Load per unit length = 170 kN/m
- Width = 1 m
- Stress = (Load per unit length) / Width = 170 kN/m / 1 m = 170 kN/m² = 170 kPa.
This still doesn't match the reference's "17 kPa". There seems to be a discrepancy in the numbers provided in the reference example itself. Let's assume the stress value (17 kPa) and the area (10 m²) are correct and calculate the implied load:
- Implied Total Load = Stress × Area = 17 kPa × 10 m² = 170 kN.
- Implied Load per unit length = Implied Total Load / Length = 170 kN / 10 m = 17 kN/m.
Or, assume the load per unit length (170 kN/m) and width (1m) are correct, and the stress value is derived:
- Stress = 170 kN/m / 1m = 170 kPa.
Given the reference explicitly states "dividing the foundation load by the contact area between the foundation and the soil" as the calculation method, and then gives an example where 170 kN/m load results in 17 kPa stress with a 1m width, there is likely a numerical error in the example's final stress value provided in the reference itself.
However, sticking strictly to the formula given by the reference ("dividing the foundation load by the contact area"), the calculation should be:
- Foundation Load (Total): For a 10m length strip foundation with 170 kN/m load, the total load is 170 kN/m * 10 m = 1700 kN.
- Contact Area: 1 m * 10 m = 10 m².
- Calculated Stress: 1700 kN / 10 m² = 170 kPa.
The reference's text formula is clear, even if the example's final numerical result is inconsistent with its own inputs. We will present the formula as stated and include the reference's example details, noting the calculated stress based on the stated formula differs from the example's final value.
Key Components of the Formula
Understanding the components is crucial:
- Foundation Load (P or F): This includes the weight of the structure above, the weight of the foundation itself, and any live loads (people, furniture, etc.) or environmental loads (snow, wind, seismic) that contribute to the vertical force at the foundation level. It is typically measured in Kilonewtons (kN) or Newtons (N).
- Contact Area (A): This is the geometric area of the foundation base that is in contact with the soil. For simple shapes like rectangles or circles, this is straightforward to calculate (Length × Width for a rectangle, π × radius² for a circle). It is measured in square meters (m²) or square feet (ft²).
- Foundation Stress (σ or q): This is the resulting pressure on the soil. It is typically measured in Kilopascals (kPa), Pascals (Pa), or pounds per square inch (psi). 1 kPa = 1 kN/m².
Visualizing the Formula
| Component | Symbol | Units (Common) | Description |
|---|---|---|---|
| Foundation Stress | σ or q | kPa, psi | Pressure exerted on the soil |
| Foundation Load | P or F | kN, N, lbs | Total vertical force applied by the foundation |
| Contact Area | A | m², ft² | Area of foundation base touching the soil |
Practical Considerations
While the formula Foundation Stress = Foundation Load / Contact Area provides the average stress, the actual pressure distribution under a foundation can be complex and influenced by factors like:
- Foundation rigidity
- Soil type and stiffness
- Location of the load (concentric vs. eccentric)
However, for basic understanding and initial calculations, the average stress calculated by this formula is a fundamental parameter. This calculated stress is then compared against the soil's allowable bearing capacity to determine if the soil can safely support the load. The foundation's size (and thus contact area) is often adjusted to ensure the calculated foundation stress is less than the soil's capacity.
Example from Reference:
The reference provides an example illustrating the calculation based on the formula:
- A strip foundation with a width of 1 m and a length of 10 m.
- The contact area is calculated as 1 m × 10 m = 10 m².
- If the foundation load per unit length is 170 kN/m, the calculated stress using the formula (interpreting the reference's formula as Total Load / Total Area, with Total Load = 170 kN/m 10 m = 1700 kN) would be 1700 kN / 10 m² = 170 kPa. Note: The reference states the resulting stress is 17 kPa, which does not align with the provided load and area figures based on the stated formula. The formula itself, however, remains Load divided by Area.*
This formula is a cornerstone in the initial assessment of how a foundation interacts with the ground beneath it.
