---
title: "Earth pressure coefficients and types"
subject: "Foundation Engineering"
chapter: 3
key: "semester_5/foundation_engineering:earth-pressure-coefficients-types"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/earth-pressure-coefficients-types
site: BCT Engineering
---

# Earth pressure coefficients and types

Foundation Engineering · Chapter 3: Lateral Earth Pressure Theories and Retaining Walls

- Asked in: 2081 Baisakh, 2 marks; 2074 Chaitra, 2 marks (asked 2 times)
- Video: [Different types of earth pressure.](https://www.youtube.com/watch?v=0M54_m5DHUs) — Civil Engineer Mahadev Das
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/earth-pressure-coefficients-types
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-3

## Question

Explain earth pressure coefficient and its types (relative wall movements and lateral earth pressure coefficients).

## Short answer

Earth pressure coefficient K = σ′h/σ′v. At-rest K0 ≈ 1−sinφ (no movement). Active Ka = tan²(45°−φ/2) (wall moves away). Passive Kp = tan²(45°+φ/2) (wall moves into soil). Ka < K0 < Kp; for smooth vertical wall KaKp = 1. For φ=30°: Ka=0.33, K0=0.5, Kp=3.

## Answer

The **earth pressure coefficient** $K$ is the ratio of the horizontal effective stress to the vertical effective stress at a point in the soil:
$$
K = \frac{\sigma_h'}{\sigma_v'}
$$
Its value depends on the soil strength and on how much the wall moves.

| Type | Wall movement | Value |
|---|---|---|
| **At rest** $K_0$ | No movement (rigid, fixed wall) | $K_0 \approx 1-\sin\phi'$ (normally consolidated); larger if over-consolidated |
| **Active** $K_a$ | Wall moves **away** from soil (about 0.001-0.005 H) | $K_a = \tan^2(45^\circ-\phi/2) = \dfrac{1-\sin\phi}{1+\sin\phi}$ |
| **Passive** $K_p$ | Wall moves **toward** soil (about 0.01-0.05 H) | $K_p = \tan^2(45^\circ+\phi/2) = \dfrac{1+\sin\phi}{1-\sin\phi}$ |

Relation: $K_a < K_0 < K_p$ and $K_a K_p = 1$ (for horizontal backfill and smooth vertical wall). For example, for $\phi = 30^\circ$: $K_a = 0.333$, $K_0 = 0.5$, $K_p = 3$.

## Check yourself

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

1. The earth pressure coefficient K is:
   A. Vertical effective stress / horizontal effective stress
   B. Horizontal effective stress / vertical effective stress
   C. Cohesion / unit weight
   D. Shear stress / normal stress
   Answer: B. K = sigma_h'/sigma_v'. (Key point: Definition of K)

2. Which relation is correct?
   A. Kp < K0 < Ka
   B. K0 < Ka < Kp
   C. Ka < K0 < Kp
   D. Ka = K0 = Kp
   Answer: C. Ka < K0 < Kp. (Key point: Order of coefficients)

3. For phi = 30 degrees, Ka and Kp are:
   A. 0.5 and 2
   B. 0.333 and 3
   C. 3 and 0.333
   D. 0.25 and 4
   Answer: B. Ka = (1-sin30)/(1+sin30) = 1/3 and Kp = 3, so Ka Kp = 1. (Key point: Numerical example)

## Related in Foundation Engineering

- [Wall movement versus earth pressure plot](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-movement-pressure-plot) — Foundation Engineering, chapter 3
- [Active pressure on wall, cohesive soil](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acohesive-wall-pressure-diagram) — Foundation Engineering, chapter 3
- [Active pressure, 8 m wall, table of layers](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-8m-two-layer-table) — Foundation Engineering, chapter 3
- [Active thrust, 7.5 m wall, 4.5 m sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atwo-layer-wall-7-5m-4-5m-sand) — Foundation Engineering, chapter 3, asked 4×
- [Active thrust, 7.5 m wall, 3 m sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atwo-layer-wall-7-5m-3m-sand) — Foundation Engineering, chapter 3, asked 4×
- [Active thrust, 7.5 m wall, 5 m sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atwo-layer-wall-7-5m-5m-sand) — Foundation Engineering, chapter 3, asked 4×

## Related in other subjects

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- [Design process for masonry wall under lateral loads](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Adesign-wall-lateral-loading) — Concrete Technology and Masonry Structure, chapter 9
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