# Limits on the validity of infinite length assumptions for modelling shallow landslides

### Details

Serval ID

serval:BIB_6438C3ECE1E9

Type

**Article**: article from journal or magazin.

Collection

Publications

Fund

Title

Limits on the validity of infinite length assumptions for modelling shallow landslides

Journal

Earth surface processes and landforms

ISSN-L

0197-9337

Publication state

Published

Issued date

2012

Volume

37

Number

11

Pages

1158-1166

Language

english

Notes

ISI:000308443200003

Abstract

The infinite slope method is widely used as the geotechnical component

of geomorphic and landscape evolution models. Its assumption that

shallow landslides are infinitely long (in a downslope direction) is

usually considered valid for natural landslides on the basis that they

are generally long relative to their depth. However, this is rarely

justified, because the critical length/depth (L/H) ratio below which

edge effects become important is unknown. We establish this critical L/H

ratio by benchmarking infinite slope stability predictions against

finite element predictions for a set of synthetic two-dimensional

slopes, assuming that the difference between the predictions is due to

error in the infinite slope method. We test the infinite slope method

for six different L/H ratios to find the critical ratio at which its

predictions fall within 5% of those from the finite element method. We

repeat these tests for 5000 synthetic slopes with a range of failure

plane depths, pore water pressures, friction angles, soil cohesions,

soil unit weights and slope angles characteristic of natural slopes. We

find that: (1) infinite slope stability predictions are consistently too

conservative for small L/H ratios; (2) the predictions always converge

to within 5% of the finite element benchmarks by a L/H ratio of 25

(i.e. the infinite slope assumption is reasonable for landslides 25

times longer than they are deep); but (3) they can converge at much

lower ratios depending on slope properties, particularly for low

cohesion soils. The implication for catchment scale stability models is

that the infinite length assumption is reasonable if their grid

resolution is coarse (e.g. >25?m). However, it may also be valid even at

much finer grid resolutions (e.g. 1?m), because spatial organization in

the predicted pore water pressure field reduces the probability of short

landslides and minimizes the risk that predicted landslides will have

L/H ratios less than 25. Copyright (c) 2012 John Wiley & Sons, Ltd.

of geomorphic and landscape evolution models. Its assumption that

shallow landslides are infinitely long (in a downslope direction) is

usually considered valid for natural landslides on the basis that they

are generally long relative to their depth. However, this is rarely

justified, because the critical length/depth (L/H) ratio below which

edge effects become important is unknown. We establish this critical L/H

ratio by benchmarking infinite slope stability predictions against

finite element predictions for a set of synthetic two-dimensional

slopes, assuming that the difference between the predictions is due to

error in the infinite slope method. We test the infinite slope method

for six different L/H ratios to find the critical ratio at which its

predictions fall within 5% of those from the finite element method. We

repeat these tests for 5000 synthetic slopes with a range of failure

plane depths, pore water pressures, friction angles, soil cohesions,

soil unit weights and slope angles characteristic of natural slopes. We

find that: (1) infinite slope stability predictions are consistently too

conservative for small L/H ratios; (2) the predictions always converge

to within 5% of the finite element benchmarks by a L/H ratio of 25

(i.e. the infinite slope assumption is reasonable for landslides 25

times longer than they are deep); but (3) they can converge at much

lower ratios depending on slope properties, particularly for low

cohesion soils. The implication for catchment scale stability models is

that the infinite length assumption is reasonable if their grid

resolution is coarse (e.g. >25?m). However, it may also be valid even at

much finer grid resolutions (e.g. 1?m), because spatial organization in

the predicted pore water pressure field reduces the probability of short

landslides and minimizes the risk that predicted landslides will have

L/H ratios less than 25. Copyright (c) 2012 John Wiley & Sons, Ltd.

DOI

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30/01/2013 8:38

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18/11/2016 13:48