Vertical Stress Increase Under L-Shaped Raft Foundation
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A flexible L-shaped raft foundation (figure below) applies a uniform pressure of $60$ kN/m$^2$ to the underlying soil. Find the vertical stress increase at $4$ m below points A, B, and C.
This question includes visual content: A technical diagram shows an L-shaped shaded area within a larger rectangle. The overall rectangle is formed by points D, H, C, and B. Dashed lines divide the rectangular area. Point A is an internal intersection point. Vertical dimensions: The distance from D to K is not explicitly labeled, but from H to F is $4$ m, and from F to C is $8$ m. Horizontal dimensions: The distance from D to E is $6$ m, and from E to H is $8$ m. The shaded L-shaped foundation consists of three rectangular sections: D-E-A-K, K-A-J-B, and A-F-C-J. Section E-H-F-A is unshaded (empty). The dimensions indicate the L-shape has a total width of $14$ m ($6$ m + $8$ m) at the base and a total height of $12$ m ($4$ m + $8$ m) along the left side. Point A is located at the inner corner of the L-shape.
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Hi arjan, let's look at this geotechnical problem where we calculate the vertical stress increase under an L-shaped raft foundation.
Vertical Stress Calculation
Method: Newmark's Influence Method for Rectangular Areas
The foundation exerts a uniform pressure, lowercase q, of sixty kiloNewtons per square meter. We need to find the stress increase at a depth, z, of four meters.
The general formula for vertical stress under a corner of a rectangular area is q multiplied by an influence factor, capital I sub s.
To use this formula, we must break the L-shape into rectangles where the point of interest is a corner. Let's start with point A.
Stress at Point A
Point A is a common corner for three rectangles: A E D K, A K B J, and A J C F. We'll find the influence factor for each.
| Rectangle | L (m) | B (m) | m = B/z | n = L/z |
|---|---|---|---|---|
| AE D K | 4 | 6 | 1.5 | 1.0 |
| AK B J | 8 | 6 | 1.5 | 2.0 |
| AJ C F | 8 | 8 | 2.0 | 2.0 |
Using the Fadum influence chart or the analytical equation, we find the influence factors. For rectangle one, I sub s is zero point one nine three six. For rectangle two, it's zero point two two zero two. For rectangle three, it's zero point two three two eight.
The total stress at point A is the sum of these factors times the pressure.
Now let's find the stress at point B. For point B, the entire L-shape can be seen as one large rectangle D H C B minus the empty rectangle E H F A.
Stress at Point B
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