---
title: "Newmark's influence chart and its use"
subject: "Soil Mechanics"
chapter: 8
key: "semester_4/soil_mechanics:newmark-influence-chart-use"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/newmark-influence-chart-use
site: BCT Engineering
---

# Newmark's influence chart and its use

Soil Mechanics · Chapter 8: Vertical Stresses Below Applied Loads

- Asked in: 2074 Bhadra, 3 marks; 2073 Bhadra, 2 marks (asked 2 times)
- Video: [Newmarks Influence Chart | Vertical Stress distribution | vertical stress in soil | Soil Mechanics](https://www.youtube.com/watch?v=nQu7qiIlds8) — Civil Engineering Exam
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/newmark-influence-chart-use
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-8

## Question

What is Newmark's influence chart? What is the main use of this chart?

## Short answer

Newmark’s chart consists of concentric circles and radial lines dividing it into elements of equal stress influence (I=0.005). Its primary use is determining vertical stress increase at any depth below an irregularly shaped loaded area by counting covered elements and using Δσz = I·N·q.

## Answer

**Newmark's influence chart** is a diagram made of concentric circles divided by radial lines into a number of small areas (elements), each of which causes the same vertical stress at the centre point at a given depth $z$ when loaded with a uniform pressure. It is based on Boussinesq's equation for a uniformly loaded circular area.

```text
        \  |  /
      ---(   O   )---   circles: R/z = 0.27, 0.40,
        /  |  \          0.52, 0.64, 0.77, 0.92, 1.11,
                         1.39, 1.91, ∞  (influence 0.1 each)
```

The chart has 10 circles (stress ratio 0 to 1 in steps of 0.1) and 20 radial lines. Each element then has an influence value $I = \dfrac{1}{10\times20} = 0.005$.

#### Use

To find the vertical stress increase $\Delta\sigma_z$ at any point below a loaded area of **irregular shape** (any plan shape):

$$
\Delta\sigma_z = I \times N \times q
$$

where $N$ is the number of elements covered by the plan of the loaded area (drawn to a scale such that the length OQ equals the depth $z$ and the point is placed at the centre of the chart), and $q$ is the uniform load intensity.

## Check yourself

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

1. What is Newmark's chart based on?
   A. Boussinesq's equation for a uniformly loaded circular area
   B. Westergaard's equation
   C. The 2:1 method
   D. Terzaghi's theory
   Answer: A. Concentric circles from Boussinesq circular-area stress. (Key point: Chart basis)

2. With 10 circles and 20 radials, I is:
   A. 0.1
   B. 0.05
   C. 0.005
   D. 0.02
   Answer: C. I = 1/(10 x 20) = 0.005. (Key point: Influence value)

3. What is its main use?
   A. Stress below loaded areas of irregular shape
   B. Bearing capacity
   C. Settlement time
   D. Soil classification
   Answer: A. It handles any plan shape. (Key point: Main use)

4. Which is the stress formula?
   A. I N q
   B. I q / N
   C. N / (I q)
   D. q / I
   Answer: A. Delta sigma_z = I N q. (Key point: Formula)