---
title: "Earthquake effect and strain for active state"
subject: "Foundation Engineering"
chapter: 3
key: "semester_5/foundation_engineering:earthquake-effect-active-strain"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/earthquake-effect-active-strain
site: BCT Engineering
---

# Earthquake effect and strain for active state

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

- Asked in: 2072 Chaitra, 1+2 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/earthquake-effect-active-strain
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-3

## Question

What is the earthquake effect on earth pressure? What is the order of horizontal strain required to produce the active state in (i) coarse grained soil and (ii) fine grained soil?

## Short answer

Earthquake shaking adds pseudo-static horizontal (kh) and vertical (kv) inertia forces to the wedge, increasing active thrust (Kae > Ka) and raising the resultant to about 0.6H above base; passive resistance decreases. Coarse-grained soils reach active state at 0.001–0.005 H strain, fine-grained soils at 0.01–0.04 H.

## Answer

#### Earthquake effect on earth pressure
Ground shaking adds inertia forces to the soil wedge behind the wall. In the pseudo-static (Mononobe-Okabe) method these are taken as horizontal $k_h W$ and vertical $k_v W$ forces, where $k_h$ and $k_v$ are seismic coefficients.
- The **active thrust increases** to $P_{ae} = \tfrac12\gamma H^2(1-k_v)K_{ae}$, with $K_{ae} > K_a$.
- The **passive resistance decreases**.
- The resultant acts higher (the dynamic increment about $0.6H$ above the base), increasing overturning moment.
- Water-saturated loose sand may liquefy, causing large extra pressure. Walls in seismic zones must be designed for these forces.

#### Horizontal strain needed to reach the active state
- (i) Coarse-grained soil (sand): very small, about 0.001 to 0.005 times $H$ (0.1 to 0.5%) of wall movement; dense sand needs less, loose sand more.
- (ii) Fine-grained soil (clay): much larger, about 0.01 to 0.04 times $H$ (1 to 4%).

## Check yourself

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

1. Earthquake effect on active thrust (Mononobe-Okabe) is that:
   A. It decreases
   B. It increases, with Kae > Ka
   C. It is unchanged
   D. It becomes zero
   Answer: B. Pseudo-static inertia forces increase active thrust and reduce passive resistance. (Key point: Seismic active thrust)

2. The dynamic increment of thrust acts about:
   A. 0.33H above the base
   B. 0.6H above the base, raising overturning moment
   C. At the base
   D. At the top
   Answer: B. The dynamic increment acts higher, about 0.6H. (Key point: Point of application)

3. Movement required for the active state in sand is about:
   A. 0.001 to 0.005 H
   B. 0.01 to 0.04 H
   C. 0.1 to 0.5 H
   D. Zero
   Answer: A. Sand needs about 0.1-0.5% of H. (Key point: Strain in coarse soil)

4. Compared with sand, active state in clay needs:
   A. Less movement
   B. Much larger movement, about 0.01 to 0.04 H
   C. The same
   D. No movement
   Answer: B. Clay needs about 1-4% strain. (Key point: Strain in fine soil)

## Related in Foundation Engineering

- [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, sloping backfill and water table](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-sheet-pipe-sloping-backfill) — 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
- [Tension crack and active pressure, layered clay](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Awall-cohesive-tension-crack) — Foundation Engineering, chapter 3
- [Why design for active pressure only](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apassive-pressure-neglect) — Foundation Engineering, chapter 3, asked 4×
- [Earth pressure coefficients and types](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aearth-pressure-coefficients-types) — Foundation Engineering, chapter 3, asked 2×

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- [Capacitance with and without earth effect](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Acapacitance-with-earth-effect-13m) — Power System Analysis I, chapter 4
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