---
title: "SPT corrected N-value, dense sand"
subject: "Foundation Engineering"
chapter: 2
key: "semester_5/foundation_engineering:spt-dilatancy-20m"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/spt-dilatancy-20m
site: BCT Engineering
---

# SPT corrected N-value, dense sand

Foundation Engineering · Chapter 2: Soil Exploration

- Asked in: 2081 Bhadra, 4 marks
- Video: [Calculate Correct N Value of a Soil Using Overburden and Dilatancy Correction|SPT Solved Problem](https://www.youtube.com/watch?v=mUR8UjnWPSY) — Master Civil Engineering
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/spt-dilatancy-20m
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-2

## Question

A SPT was performed at a depth of 20 m in a dense sand deposit with a unit weight of $17\ \text{kN/m}^3$. If the number of blows were found to be 18, 21 and 22 for each 150 mm penetration, what is the N-value corrected for overburden and dilatancy?

## Short answer

Observed N = 21+22 = 43 after seating drive. Overburden stress 340 kN/m², CN=0.77log10(2000/340)=0.593 gives N'=25.5. Dilatancy correction N''=15+0.5(N'−15) = 20.2, so corrected N-value ≈ 20.

## Answer

**Method:** Terzaghi-Peck corrections. First the overburden correction $N' = C_N N$ with $C_N = 0.77\log_{10}(2000/\sigma_v')$, then the dilatancy correction $N'' = 15 + \tfrac12(N'-15)$ for $N' > 15$.

**Observed N:** the first 150 mm is the seating drive, so
$$
N = 21 + 22 = 43
$$

**Overburden stress:** no water table is given, so
$$
\sigma_v' = \gamma z = 17 \times 20 = 340\ \text{kN/m}^2
$$

**Overburden correction:**
$$
\begin{aligned} C_N &= 0.77\log_{10}\frac{2000}{340} = 0.593 \\ N' &= 0.593\times 43 = 25.48 \end{aligned}
$$

**Dilatancy correction** ($N' > 15$):
$$
N'' = 15 + \tfrac12(25.48-15) = 20.24
$$

**Answer: corrected N-value $\approx 20.2$, say 20.** (If the dilatancy correction is applied first, $15+0.5(43-15)=29$ and $29\times0.593=17.2$; the order recommended by Terzaghi-Peck, overburden then dilatancy, is used here.)

## Check yourself

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

1. From blows 18, 21, 22, the observed N is
   A. 61
   B. 43
   C. 39
   D. 22
   Answer: B. Ignore the first 150 mm: 21 + 22 = 43. (Key point: Observed N)

2. With no water table, sigma_v' at 20 m with gamma = 17 kN/m^3 is
   A. 170 kN/m^2
   B. 20 kN/m^2
   C. 340 kN/m^2
   D. 34 kN/m^2
   Answer: C. 17 x 20 = 340. (Key point: Overburden stress)

3. The recommended order of corrections is
   A. dilatancy first, then overburden
   B. no order, any
   C. overburden first, then dilatancy
   D. only dilatancy
   Answer: C. Terzaghi-Peck order gives N' = 25.48 then N'' = 20.24. (Key point: Order)

4. The final corrected N is about
   A. 43
   B. 25
   C. 29
   D. 20
   Answer: D. N'' = 15 + 0.5(25.48 - 15) = 20.2. (Key point: Final)

## Related in Foundation Engineering

- [SPT corrected N-value, submerged sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aspt-corrected-6m-submerged) — Foundation Engineering, chapter 2
- [Mat 18 m × 22 m, safe building weight](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amat-18x22-clay-ucs75) — Foundation Engineering, chapter 7, asked 2×

## Related in other subjects

- [Two-layer sand, plot stresses (bulk 18)](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Atwo-layer-sand-stress-plot) — Soil Mechanics, chapter 6