What Is a Pressure Bulb?

In geotechnical engineering, the pressure bulb—also referred to as a stress isobar—is a conceptual tool used to visualize how a structural load applied at the ground surface disperses vertically and laterally into the underlying soil mass. Essentially, a pressure bulb is a three-dimensional imaginary surface that connects all points in the soil where the vertical stress is equal due to an applied load.

The shape of this surface typically resembles an inverted bulb or onion. As the stress intensity decreases with both depth and radial distance from the point of application, the contours of the bulb spread downward and outward. These bulbs help engineers identify zones within the soil where load effects are significant—commonly referred to as the zone of influence.

Understanding the pressure bulb is critical in geotechnical design, as it provides a framework for evaluating how stress distributes under footings, rafts, piles, and other foundation types. This, in turn, informs decisions about foundation size, depth, spacing, and soil exploration requirements.

Why Are Pressure Bulbs Important in Foundation Engineering?

The real value of the pressure bulb lies in its ability to bridge theory and practice in soil-structure interaction. When a load is applied to a footing, not all the stress is absorbed at the surface; it penetrates into the soil, diminishing with depth. The pressure bulb concept helps engineers determine:

• How deep the soil should be explored during site investigations
• Where settlement may occur and how it could affect structural performance
• Whether adjacent foundations will interact, especially when built close together
• How much of the stress is carried by the upper soil layers versus the deeper strata

For example, if a building is constructed with shallow foundations, but soft clay exists within the pressure bulb’s extent, excessive or differential settlement may occur—leading to cracks, tilting, or even structural failure. This is particularly important in urban development projects, where multiple buildings are constructed in close proximity.

Mathematical Foundation: Boussinesq’s Equation

The foundation of pressure bulb analysis is derived from Boussinesq’s theory of stress distribution in a semi-infinite, elastic, homogeneous, and isotropic soil mass. This equation allows engineers to compute vertical stress (σ\sigma_σz​) at any point below a surface point load.

\sigma_z = \frac{3Q}{2\pi z^2} \cdot \frac{1}{\left(1 + \left(\frac{r}{z}\right)^2\right)^{5/2}}

\begin{aligned}
\sigma_z & : \text{Vertical stress at depth } z \\
Q & : \text{Point load applied at the surface} \\
z & : \text{Depth below the point load} \\
r & : \text{Horizontal distance from the load axis}
\end{aligned}

What the Equation Tells Us

• The closer you are to the point load, the higher the stress in the soil.
• As you move deeper (increase zzz), or further away horizontally (increase rrr), the stress decreases rapidly.
• This pattern helps us draw isobars (lines of equal stress), which form the pressure bulb shape under the load.

Why This Is Useful in Practice:

• Engineers use this formula to find out how deep and wide the soil is affected under a footing or a column.
• The stress values help decide:
  • How deep soil tests (boreholes) should go
  • If nearby foundations might interfere with each other
  • Whether soft soil layers inside the bulb could lead to settlement or failure

Example Application

Suppose a 1000 kN point load is applied at the surface.
You want to find the vertical stress exactly 2 meters below the load.

Since you’re right under the load (i.e., r=0), the formula simplifies to:

\begin{aligned}
\sigma_z &= \frac{3Q}{2\pi z^2} \\
&= \frac{3 \times 1000}{2\pi \times 2^2} \\
&= \frac{3000}{8\pi} \\
&\approx \frac{3000}{25.13} \\
&\approx 119.38 \, \text{kN/m}^2
\end{aligned}

So, the stress at that depth is 119.38 kN/m² — and this value can be used to check if the soil can safely support it.

Understanding Isobars and the Zone of Influence

An isobar is a line (or in 3D, a surface) connecting points of equal vertical stress. When these are drawn at values such as 10%, 20%, or 40% of the applied surface stress, they form closed contours that illustrate how far and deep the load effect extends into the soil.

The zone of influence is the region where soil stress from the foundation load is significant. It is typically defined using the 20% isobar—where the vertical stress equals 20% of the applied stress at the surface.

Inside the bulb: stress is greater than the isobar value
On the bulb: stress equals the isobar value
Outside the bulb: stress is lower than the isobar value

By identifying this zone, engineers can ensure that:

• Soil investigation includes all affected strata
• Foundation design avoids overstressing any weak layers
• Stress from multiple footings does not combine and cause failure

Application in Design and Soil Investigation

Pressure bulbs play a direct role in determining:

• The depth of boreholes and sampling
• The depth to which settlement and bearing capacity calculations should extend
• Whether isolated footings or combined foundations are suitable
• How to address potential overlap of stress zones in group foundations

As a rule of thumb, the pressure bulb for a shallow footing can extend to 1.5 to 2 times the width of the footing in depth. For example, a footing with a width of 2 meters may have a pressure bulb extending to 3–4 meters beneath the surface.

In complex projects, engineers use software like PLAXIS, STAAD Foundation, or Geo5 to simulate stress contours more accurately, particularly when the soil is layered or non-homogeneous.

Solved Numerical Problem Using Boussinesq’s Equation

Problem: A concentrated point load of 1000 kN is applied vertically at the surface. Calculate the vertical stress 2 meters directly below the load.

Solution:

\text{Given:} \\
Q = 1000 \, \text{kN} \\
z = 2 \, \text{m} \\
r = 0 \quad (\text{Point is directly beneath the load}) \\[10pt]

\text{Using Boussinesq's Equation:} \\
\sigma_z = \frac{3Q}{2\pi z^2} \\[10pt]

\text{Substitute values:} \\
\sigma_z = \frac{3 \cdot 1000}{2\pi \cdot 2^2} \\[10pt]

\sigma_z = \frac{3000}{8\pi} \\[10pt]

\sigma_z \approx \frac{3000}{25.13} \\[10pt]

\sigma_z \approx 119.38 \, \text{kN/m}^2

Real-Life Case Study: Foundation Settlement Due to Pressure Bulb Overlap

Project Location: NCR (Noida, India)
Project Type: Residential Apartment Complex

Problem:
An eight-storey building was constructed adjacent to a four-storey structure with shallow footings. The design did not account for pressure bulb overlap between the two foundations. The additional stress from the taller building caused significant loading in the zone of influence of the smaller building’s foundation.

Result:

• Excessive and differential settlement
• Wall cracks and column tilting
• Expensive retrofitting measures

Engineering Lesson:
Never assume that loads from different buildings act independently when they are close together. Pressure bulb analysis must be part of the geotechnical evaluation to prevent these issues.

Conclusion

The pressure bulb is not merely an academic theory; it is the core of real-world foundation behavior. It helps engineers visualize stress paths, identify vulnerable zones, and ensure that the soil can support the structure above safely and effectively. Whether designing isolated footings, raft foundations, or evaluating pile groups, understanding the stress distribution in the soil is non-negotiable.

📘FAQs: Pressure Bulb in Geotechnical Engineering