---
title: "Significant depth and isobar"
subject: "Soil Mechanics"
chapter: 8
key: "semester_4/soil_mechanics:significant-depth-isobar"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/significant-depth-isobar
site: BCT Engineering
---

# Significant depth and isobar

Soil Mechanics · Chapter 8: Vertical Stresses Below Applied Loads

- Asked in: 2078 Poush, 4 marks
- Video: [Isobar | Pressure Bulb | Vertical Stress](https://www.youtube.com/watch?v=CTnIfCG9FJo) — Civil Engineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/significant-depth-isobar
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-8

## Question

Define significant depth and its importance. Construct an isobar for significant depth.

## Short answer

Significant depth is where Δσz falls to 10% of contact pressure, typically 1.5–2B for square and 4–6B for strip footings; it determines exploration depth. The 0.1q isobar is built by computing points with Δσz=0.1q at various depths and radial distances using Boussinesq, then connecting them.

## Answer

**Significant depth** is the depth below a foundation up to which the increase in vertical stress due to the load is large enough to cause significant settlement. Below it the stress increase is negligible. It is commonly taken as the depth at which the vertical stress increase falls to **10% of the contact pressure** ($0.1\,q$), or 20% of $q$ in some practice (or where $\Delta\sigma_z = 0.1\,\sigma'_{v0}$ for the overburden).

**Importance:**

- It fixes the depth of exploration (boreholes should reach at least this depth).
- It fixes the soil thickness to be included in settlement and consolidation calculations. Layers below it can be neglected.
- For footings, the depth is approximately $1.5B$ to $2B$ for a square footing and $4B$ to $6B$ for a strip footing.

#### Construction of an isobar for significant depth

An isobar is a contour of equal vertical stress.

1. Select the stress level, e.g. $\Delta\sigma_z = 0.1\,q$.
2. For a chosen set of depths $z$ below the footing, compute $\Delta\sigma_z$ at various horizontal distances $x$ from the centre using Boussinesq or the strip/circular/rectangular footing equations (or charts).
3. At each depth, mark the points where $\Delta\sigma_z = 0.1\,q$ on both sides of the axis.
4. Join the points by a smooth curve to get a bulb-shaped isobar.
5. The depth of the lowest point of the 0.1q isobar, on the axis, is the significant depth.

```text
   |<---- B ---->|
   ▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇  q
    (   0.5 q   )
     (  0.2 q  )
      ( 0.1 q )  <-- isobar
        \___/    significant depth below this
```

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the significant depth below a foundation?
   A. The depth of the foundation base below ground
   B. The depth below which the stress increase is negligible and causes no significant settlement
   C. The depth at which the water table is met
   D. The depth at which the soil becomes rock
   Answer: B. Significant depth is the depth beyond which the load-induced stress increase is too small to cause significant settlement. (Key point: Definition of significant depth)

2. Which criterion is commonly used to fix the significant depth?
   A. Where the stress increase falls to 50% of q
   B. Where the stress increase falls to 10% of the contact pressure q
   C. Where the stress increase equals q
   D. Where the stress increase becomes zero exactly
   Answer: B. It is commonly taken at the depth where the vertical stress increase is 0.1q (20% of q in some practice). (Key point: Common criterion)

3. Why is significant depth important in design?
   A. It gives the bearing capacity directly
   B. It fixes the footing width
   C. It fixes the borehole exploration depth and the soil thickness included in settlement calculations
   D. It determines the unit weight of soil
   Answer: C. Boreholes should reach it and layers below it can be neglected in settlement and consolidation calculations. (Key point: Importance)

4. How is the 0.1q isobar constructed?
   A. Plot points at various depths where the stress increase equals 0.1q on both sides of the axis and join them by a smooth curve
   B. Draw a straight line at 45° from the footing edge
   C. Plot the points where total stress is 0.1q
   D. Join the points of equal settlement
   Answer: A. The stress is computed at various depths and offsets, points with 0.1q are marked, and joined to give a bulb; its lowest axis point gives the significant depth. (Key point: Constructing the isobar)

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