---
title: "Finite and infinite slopes"
subject: "Soil Mechanics"
chapter: 11
key: "semester_4/soil_mechanics:finite-vs-infinite-slope"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/finite-vs-infinite-slope
site: BCT Engineering
---

# Finite and infinite slopes

Soil Mechanics · Chapter 11: Stability of Slopes

- Asked in: 2075 Bhadra, 1 marks; 2074 Bhadra, 2 marks (asked 2 times)
- Video: [Finite and Infinite slope | Soil Mechanics | Unit 5 - Lec - 01 | Civil Tutor](https://www.youtube.com/watch?v=eSEx0FSAtz0) — CIVIL TUTOR
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/finite-vs-infinite-slope
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-11

## Question

Differentiate between finite and infinite slopes (explain finite slope and infinite slopes in regard to slope stability).

## Short answer

An infinite slope is very long with uniform soil, failure plane parallel to the surface, analyzed on a unit slice ignoring end effects. A finite slope has limited height with a curved or planar failure surface through the toe, analyzed by method of slices or Swedish circle.

## Answer

An **infinite slope** is a slope of very large extent whose length is much greater than the depth of the failure surface and which has uniform soil along its length. A **finite slope** has a limited height and length, with a definite top and toe.

| Point | Infinite slope | Finite slope |
|---|---|---|
| Extent | Very long; end effects ignored | Limited height $H$, with a toe and crest |
| Failure surface | Plane, parallel to the slope surface (shallow) | Curved (circular arc) or plane through the toe |
| Soil | Usually uniform, often cohesionless | Cohesive or $c$-$\phi$ soil |
| Analysis | A single slice of unit width; forces on its sides cancel | Method of slices, Swedish circle, Taylor's chart |
| Factor of safety | $F = \dfrac{c}{\gamma z\sin\beta\cos\beta} + \dfrac{\tan\phi}{\tan\beta}$ | Depends on geometry, e.g. $F = \dfrac{c_u L_a R}{W x}$ ($\phi=0$) |
| Depth of failure | Independent of slope height | Related to slope height $H$ |
| Examples | Natural hillside, long embankment surface | Earth dam, road cutting, embankment |

## Check yourself

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

1. What is the typical failure surface of an infinite slope?
   A. A deep circular arc through the toe
   B. A log spiral
   C. A vertical plane
   D. A plane parallel to the slope surface, shallow
   Answer: D. Finite slopes usually fail along a curved arc. (Key point: Failure surface)

2. What is the factor of safety of an infinite slope?
   A. F = c_u L_a R/(W x)
   B. F = tan beta/tan phi
   C. F = c/(gamma z sin beta cos beta) + tan phi/tan beta
   D. F = c/(gamma H)
   Answer: C. The slice analysis with side forces cancelling gives this expression. (Key point: Infinite FS)

3. How does failure depth relate to slope height?
   A. Both depend on H
   B. Infinite slope depth is independent of height; finite slope depth is related to height H
   C. Infinite depends on H only
   D. Neither depends on H
   Answer: B. End effects are ignored in infinite slopes. (Key point: Dependence on height)

4. Which method suits finite slopes?
   A. Method of slices, Swedish circle, or Taylor's charts
   B. Single slice with side forces cancelling
   C. Only tan phi/tan beta
   D. Rankine theory
   Answer: A. The infinite slope uses a single slice; finite slopes need circle-based methods. (Key point: Analysis method)

## Related in Soil Mechanics

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