1

Study of coexistence measures against landslides, particularly

reinforced soil techniques

Catarina dos Santos Lopes Farias (1)

October 2014

(1) M.Sc. Student, Instituto Superior Técnico, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal; catarina.lopesfarias@gmail.com

Abstract: The landslides known as debris flows have been gaining notoriety for the devastating social-economic

consequences they are causing in many areas of the world. Since the last decades that numerous scientists have been

developing different researches focusing on three main purposes: the comprehension of the mass movement, the

development of mitigation measures and the prediction of future events. Unfortunately, due to the complexity of this type of

landslide, there is still a long way to go.

The present work aims to provide the reader with a detailed analysis of this type of mass movement and to demonstrate a

design method of one of the coexistence measures used against this type of landslide, the geosynthetic reinforced soil

embankments. At first, the main characteristics, the classifications and the parameters of a debris flow are introduced, as well

as the numerical and empirical methods used to estimate their effects. Follows an approach of a real event that occurred in Rio

de Janeiro, Brazil, for which the main parameters and characteristics are determined. Finally, the design method is applied to

this real case study, simultaneously with a limit equilibrium analysis and a stress-strain analysis. Moreover, the author has the

will to sensitize and attract new researchers to this field of development, which desperately needs.

KEYWORDS: debris flows; mitigation measures; impact force; geosynthetic reinforced soil slopes; limit equilibrium

analysis; stress-strain analysis.

1 Introduction

A long time ago, debris flows were known by the Japanese

people as Já-Nuke (the run off of the king snake), Yama-

tsunami (the tsunami at mountain) and Yama-shio (the

mountain tide). These names try to define the nature of

this type of landslide, which affects socioeconomically

villages and cities around the world (TAKAHASHI, 2007).

POLANCO (2010) describes them as a mixture of

sediments and water carried by gravity, that acquires a

large mobility, dragging all kinds of debris (rocks, trees,

soil, mud, and others). They exhibit certain characteristics

such as high speed, a large capacity of destruction and the

ability to transport great volumes of debris over long

distances in short periods of time.

More worrisome than the huge material and economic

consequences, is the number of casualties. According to

NUNES & SAYÃO (2014), previous studies point to a

number of deaths of 104000 people, caused by large

landslides, mostly debris flows. Unfortunately, the state of

Rio de Janeiro (Brazil) has been very affected by these

mass movements. One of the most powerful events

happened in January 2011 and will be discussed later in

this paper.

The main purpose of this study is to analyse the debris

flow mass movement, particularly the real case that

occurred in Rio de Janeiro, Brazil, for which the main

parameters are determined by empirical and numerical

methods. Furthermore, the article aims to describe the

design of one of the mitigation measures against debris

flows, using limit equilibrium and finite elements analysis.

Finally, the author wants to sensitize new researchers into

this field of development.

2 Landslides and mitigation measures

Landslides are caused by either external factors, the

increase of the shear stress for instance, or internal factors

such as the decrease of the shear strength. They are

divided into gravitational mass movements, where the

material moves due to the force of gravity, and mass

transport movements, where some liquid carries the soil,

usually water. VARNES (1978) proposed a slide

movements classification based on the type of material

and the mode of movement – Table 1.

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Table 1 – Classification of slide movements (VARNES, 1978)

Mode of movement

Type of material

Bedrock Predominantly coarse soil

Predominantly fine soil

Falls rock fall debris fall earth fall

Topples rock topple debris topple earth topple

Slides Rotational

rock slide debris slide earth slide Translational

Lateral Spreads rock spread debris flow earth spread

Flows rock flow (deep creep)

debris flow (soil creep) earth flow

Complex Combination of two or more main types of movement

Slope failures describe a large variety of processes, which

result in the downward and outward movement of slide-

forming materials including rock, soil or a combination of

these (VARNES, 1978). There are five main slope

ruptures: circular and planar failure, topple, rock fall and

debris flow. This paper will focus on the analysis and

description of debris flow.

2.1 Debris flow

Debris flow is a catastrophic mass movement. Usually, it

occurs due to the increase of the pore water pressure and

consequent decrease of the effective stress on the

discontinuities of a rock mass. In general, it happens after

an intense and prolonged rainfall or after an earthquake.

They are divided into three different zones: initiation,

transportation and deposition zones.

Characteristics and classifications

According to VANDINE (1996), a slope capable of initiating

a debris flow is divided in three parts:

o Initiation zone – areas with a slope angle larger than

25° (for lower inclinations, it may not have the required

energy to develop the movement);

o Transportation zone – areas with a slope angle larger

than 15°;

o Deposition zone – partial deposition areas (slope

angle smaller than 15°) and final deposition areas

(slope angle smaller than 10°).

Figure 1 shows the three mentioned zones.

As said by NETTLENTON et al. (2005), there are two

forms of debris flows, which may be distinguished by their

topographic and geological characteristics: hillslope (open-

slope) and channelized debris flows (Figure 2 and Figure

3, respectively). The first one forms its own path down the

valley before the deposition zone on lower slope gradients.

Figure 1 – Zones of a debris flow (VANDINE, 1996)

Figure 2 – Hillslope debris flow (NETTLENTON et al., 2005)

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Figure 3 – Channelized debris flow (NETTLENTON et al.,

2005)

Channelized debris flows follow an existing channel, for

instance, valleys or depressions (NETTLENTON et al.,

2005). Usually, in this kind of movement, there is a high

content of solid material (near 80%).

There are several debris flows classifications suggested by

different authors. This paper will describe two, proposed

by HUNGR et al. (2001) and JAKOB & HUNGR (2005).

Firstly, HUNGR et al. (2001) distinguish the soil type into

debris or earth, based on the percentage content of coarse

material. Earth has a content of gravel and coarser clasts

lower than 20% and involves clays and very soft rocks with

a consistency closer to the plastic limit. Contrary, debris

have more than 20% of coarse material and are defined as

loose material of low plasticity, produced by the

weathering (residual soil), for instance. Adding to that,

there is also mud, which refers to liquid or semi-liquid

clayey material. The mixture between mud and the surface

water may increase the water content above the liquid

limit, leading to the initiation of a very rapid flow.

After the type material distinction, HUNGR et al. (2001)

divide the flows into 4 types:

o Debris flow – “a very rapid to extremely rapid flow of

saturated non-plastic debris in a steep channel (IP <

5% in sand and finer fractions)”;

o Mud flow – “a very rapid to extremely rapid flow of

saturated plastic debris in a channel, involving

significantly larger water content relative to the source

material (IP > 5%)”;

o Debris flood – “a very rapid, surging flow of water,

heavily charged with debris, in a steep channel”;

o Debris avalanche – “a very rapid do extremely rapid

shallow flow of partially or fully saturated debris on a

steep slope, without confinement in an established

channel”.

On the other hand, JAKOB & HUNGR (2005) presented a

debris flow classification based on the magnitude of the

movement in order to allow the establishment of hazard

maps. They considered 9 classes, depending on the

volume, the peak discharge and the inundated area –

Table 2.

The six bottom classes indicate “not available” in the some

fields. “Not available” means that debris flows of this

magnitude have not been observed. However, the authors

believe they are possible.

Causes of debris flows

According to NUNES & SAYÃO (2014), there are two main

types of debris flows causes: the preparatory factors,

which make the slope vulnerable to failure without actually

inducing the flow (poor drainage and extreme climatic

conditions, for instance), and the triggering factors, that

initiate the movement by themselves (high pore water

pressure along the potential failure surfaces). The

combination of these two kinds of causes leads to a

landslide and controls the likelihood and the timing of

events at different sites.

There are also internal and external causes. The first ones

lead to a reduction in shear strength and the second ones

indicate the increase of the applied shear stress.

Main parameters of a debris flow

According to RICKENMANN (1999), the debris flow

volume (!) is one of the most important parameters, when

considering an evaluation of a potential hazard. It is

defined as the total mass transported from the top of the

slope until the deposition zone. As it will be shown later, it

can be estimated using empirical equations.

The values of the peak discharge, !! , and the

corresponding velocity are very important when it is

necessary to evaluate the conveyance capacity of a debris

flow. There are also empirical relationships used to

determine these two parameters.

Despite being a very important parameter on the

evaluation of the shear behaviour of different debris flow

materials (it may help to identify some of them), it is very

difficult to obtain the mean velocity (!) in the field. As it will

be presented later, this parameter is estimated based on

empirical data or measured in laboratory tests

(RICKENMANN, 1999).

The travel distance, ! , is defined as the horizontal

projection of the debris flow’s length. It is an essential

parameter when establishing potentially endangered areas

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Table 2 – Debris flow magnitude classification (adapt. JAKOB & HUNGR, 2005)

Class Volume (m3) Peak discharge (m3/s) Inundated area (m2) Potential consequences

1 < 102 < 5 < 4.102 Very localized damage, damage in small buildings

2 102 - 103 5 - 30 4.102 – 2.103 Can bury cars, destroy a small wooden building, break trees, derail trains

3 103 – 104 30 – 200 2.103 – 9.103 Can destroy larger buildings, damage concrete bridge piers, block or damage highways

4 104 – 105 200 - 1500 9.103 – 4.104 Can destroy parts of villages, block creeks, destroy sections of infrastructure corridors

5 105 – 106 1500 - 12000 4.104 – 2.105 Can destroy parts of towns, block creeks and small rivers

6 105 – 106 Not available > 2.105 Can destroy towns, obliterate valleys up to several tens of km2 in size

7 106 – 107 Not available Not available Can destroy cities, inundate large valleys up to 100 km2 in size

8 107 – 108 Not available Not available Vast and complete destruction over hundreds of km2

9 > 108 Not available Not available Vast and complete destruction over hundreds of km2

(RICKENMANN, 1999) and is easily estimated after a

debris flow event.

The runout distance on fan is also a very important

parameter for more detailed delineation of potentially

endangered zones (RICKENMANN, 1999). It defines the

distance between the fan apex and the lowest point of the

deposition zone.

Mitigation measures against debris flows

According to HUBL & SUDA (2008), there are two types of

mitigation measures. Active measures focus on the hazard

and intervene directly in the magnitude or the

characteristics of a debris flow. On the other hand, passive

measures focus on the potential damage. They do not stop

the soil failure but reduce the potential loss through

political and technical solutions.

This paper will approach an important passive measure,

whose goal is to dissipate the energy of a debris flow, by

slowing and depositing the surge front of de movement. It

will be presented the design of geosynthetic reinforced soil

embankments. The Geoguide – The New Guide to

Reinforced Fill Structures and Slope Design in Hong Kong

points numerous advantages of these structures over the

common concrete walls:

o The foundations of a reinforced embankment are at

shallow depths, comparing to those in a conventional

structure.

o Reinforced soil slopes represent very flexible

structures and, contrary to the conventional solutions,

they cope with differential displacements;

o This type of solutions also adapt to seismic waves

propagation, which is interesting because a debris flow

is a dynamic movement with an associated impact

force;

o Reinforced soil embankments are considered to be

“green” solutions, a very important characteristic

nowadays.

3 Case study – Debris flow of Córrego D’antas, Rio de Janeiro, Brazil

On the 11th of January of 2011, a tragedy happened in Rio

de Janeiro. Huge volumes of rain fell on that region,

triggering approximately 4000 mass movements. Several

people were affected and Brazilian entities point to costs

over R$4780 million (€1600 million, at the exchange rate

of 3/1). The Figure 4 shows two pictures, before and after

the debris flow of Córrego D’antas.

According to a report done by a local company, the

movement started at an elevation of 1300 m and the initial

volume was 500 m3. During its way down, it collected

debris and gained a lot of energy. Three zones were

distinguished according to VANDINE’s (1996)

classification:

Figure 4 – Before and after the debris flow of Córrego D’antas (left and right, respectively)

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Initiation zone – slope angle of 45°.

Transportation zone – areas with a slope angle between

40° and 60°.

Deposition zone – area with the slope angle of 26° (greater

than that established by VANDINE but, according to

PELIZONI (2014), the division between the transportation

and the deposition zone was made considering the area

where the velocity started to decrease).

Slope characteristics and soil

parameters

The field report written immediately after the debris flow,

enabled the estimation of some of the characteristics of the

slope: the initial and the final elevation of the movement,

the travel distance and the involved material – Table 3.

PELIZONI (2014) estimated the soil parameters based on

a retro analysis made on SLOPE program. The author

defined four different types of materials. The main

parameters, unit weight (γ) and friction angle of the soil

(ϕ′) are presented in Table 4.

Table 3 – Slope characteristics

Initial elevation

(m)

Final elevation

(m) L (m) Material

1300 880 800 Rocks + mud

Table 4 – Parameters of the materials considered

Material !′ (°) ! (kN/m3) Sound rock 35 26

Weathered rock 30 22 Residual soil 30 18

Deposit material 26 16

Estimation of the main parameters of the

debris flow

This section will provide the determination of the main

parameters of the debris flow in study, based on empirical

equations, the observed values, and the results of the

numerical analysis made by PELIZONI (2014). Table 5

shows the values.

As illustrated in the table, there is still a huge disparity

between the results of different empirical equations and

the observed values of the same parameter, for instance

for the inundated area. On the other hand, there are

parameters, which can be easily measured after the event

and, therefore, the existing correlations provide reliable

results. The numerical analyses of DAN3D (finite elements

program) made by PELIZONI (2014) were based on a

retro analysis, where after numerous iterations, the author

was able to present interesting and viable results.

Table 5 –Results of the observed values, the results of the empirical equations and the results of DAN3D

Volume (m3)

Observed - Not available

RICKENMANN (1999) ! = !

1.19!!.!"

!/!.!" 11588.79

POLANCO (2010) ! = 252.84 !!

!.!" 5292.90

MOTTA (2014) ! = !2.72

!/!.!" 1! 11179.68

DAND3D - 10000 - 17000

Peak discharge (m3/s)

Observed - Not available

RICKENMANN (1999) !! = 0.1!!.!" 236.13

MOTTA (2014) !! = 0.29!!.!" 33.66

!! = 0.14!!.!" 34.25

DAN3D - 6 - 13

Travel distance (m)

Observed - 790

RICKENMANN (1999) ! = 1.9!!.!"!!.!" 1277.31

POLANCO (2010) !! = 3.23!!!.!"! 800.70

MOTTA (2014)

! = 106.61.!!.!"#$ 938.12

! = !3.55

!/!.!" 1010.13

!!!á!= −0.83!"# + 11.20

121.29

!!!"#

= 0.06!"# − 0.52 10683.98

! = 2.29!!.!"!!.!" 1036.35

DAN3D - 700 - 778

Maximum velocity (m/s)

Observed - Not available

RICKENMANN (1999) ! = 2.1!!.!!!!.!! 38.28

MOTTA (2014) !!á! = 120.99!!!.!" 18.75

DAN3D - 15 - 18

Inundated area (m2)

Observed - 35600

POLANCO (2010) ! = 7!!.!! 2007.87

MOTTA (2014) ! = 187.6.!!/! 93831.30

! = 24.37!!.!! 31926.12

DAN3D - ~20000

!: volume (m3); L: travel distance (m); H: height of the debris flow (m); Qp: peak discharge (m3/s); !: velocity (m/s); S: slope angle (°); A: cross section area (m2); B: inundated area (m2)

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It is also interesting to notice that the empirical relations

developed by Brazilian authors (POLANCO and MOTTA)

provide, in general, results closer to the real values, since

they should be more adapted to the Brazilian dynamic of

soils.

Impact force estimation

Unfortunately, the impact force of the debris flow was not

measured during the event, and it was not one of the

output results of the DAN3D program. However, it is a very

important parameter when designing energy dissipation

structures.

This paper will use three different methods to estimate the

debris flow’s impact force: hydrostatic and hydrodynamic

models and a third one, which was proposed by HUBL et

al. (2009). The numerical expressions are given bellow,

where ( 1 ), ( 2 ) and ( 3 represent the hydrostatic, the

hydrodynamic and the HUBL et al. (2009) models,

respectively:

!!á! = !"#ℎ ( 1 )

!!á! = !"!! ( 2 )

!!á! = 5!!!,! !ℎ !,! ( 3 )

with ! and ! as emprirical factors, ! is the mass density of

the debris flow (kg/m3), ! is the gravity aceleration (m/s2),

ℎ represents the debris flow height (m), ! is the debris flow

velocity (m/s) and !!á! is the impact force (N/m2).

The adopted values for ! , ℎ and ! were based on the

extensive work of PELIONI (2014). The interval considered

for each of them is presented in Table 7. The empirical

factors ! and ! were estimated considering the values

adopted for real events and the Froude number (!"). !" is

a dimensionless value that describes different flow regimes

of a channel flow. It can be determined using expression (

4 ) and the interval determined is shown in Table 7.

!" = !!ℎ

( 4 )

It was considered that approximate Froude numbers

describe similar flow regimes. Therefore, the empirical

factors were determined averaging ! and ! of the real

events whose !" were identical to the interval determined.

Table 6 shows the real events that HUBL et al. (2009)

studied, with the corresponding !", ! and ! factors. Those

marked in blue represent the values chosen for averaging.

The average results are shown in the Table 7.

Table 6 – Fr, k and a for real events

Real event Fr ! !

Rio Reventado (Costa Rica) 0.5 4.67 18.67

Hunshui Gully (China) 1.90 8.33 2.31

Bullock Greek (New Zeeland) 1,26 6,50 4,06

Pine Creek (Australia) 7.56 21.43 0.38

Wrightwood Canyon (USA) 0.95 3.68 4.09

Wrightwood Canyon (USA) 0.87 5.21 6.94

Lesser Almatinka (Philippines) 0.84 4.29 6.12

Nojiri River (Japan) 2.71 10.07 1.37

Table 7 - Parameters considered in the estimation of the

impact force

! (m) ! (m/s) ! (kg/m3) !" ! !

4 - 6 10 – 12.5 2200 1.60 –

2.0 2.58 8.30

Table 8 presents the impact force results for the three

models.

Table 8 – Impact foce results

Hydrostatic Hydrodynamic HUBL et al. (2009)

!!á! (kPa) 716 - 1074 660 - 1031 627 - 956

The three intervals obtained are very similar, which gives a

certain ground to the realized approach. A value, 800 kPa,

was chosen for estimating the impact force.

4 Design of the reinforced soil embankment

This section of the paper aims to present the design of a

reinforced soil embankment with geosynthetics. At first, it

will be used a method proposed by the Federal Highway

Administration (FHWA, 2001), which uses a limit

equilibrium analysis based on a global safety factor. Next,

the designed slope will be simulated in a finite elements

program, where a stress-strain analysis is performed.

Location of the reinforced embankment

Considering the field report written after the event and not

having other information, it had been decided that the

reinforced soil embankment was located in the deposition

zone of the debris flow. Adding to that, along with the

reinforced embankment, the approved design includes a

flexible barrier to stop large volumes of debris. Hence, the

impact force estimated on 3 is no longer suitable due to

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two reasons: i) its density is now smaller and ii) on

deposition zones, the debris flow velocity is also smaller.

Given these two points, values of 1800 kg/m3 and 6 m/s

were considered for the density and the velocity of the

debris flow, respectively. The impact force acting on the

slope, !!á!!", is:

!!á!!" = 2,58×1800×6! = 167!kPa ( 5 )

Characteristics of the soil slope and the

reinforcements

Based on the materials defined by PELIZONI (2014) (see

Table 4), there were two types of soil selected: the residual

soil, to be the part of the slope and the weathered rock,

which is considered to be the foundation of the reinforced

embankment.

The reinforcement is a nonwoven geotextile, constituted by

polypropylene (PP) reinforced with polyester (PET) of high

resistance. Its tensile resistance is 50 kN/m.

Pre-design based on the sliding

resistance

Before the design of the reinforced embankment for its

weight, the author decided to verify if the slope is able to

self-support the impact force in terms of sliding. It was

considered a safety factor of 1,3. Figure 5 shows a generic

embankment, with the impact force, !!"#$%&' , which is

perpendicular to the slope’s face and distributed along the

slope’s length. !!"#$%&' was obtained by the product of

!!á!!" by the length of the slope’s face, !!"#$:

!!"#$%&' = !!á!!"!!"#$ = 1889!!"/! ( 6 )

Note that the vertical component of the impact force

contributes to the sliding resistance, while the horizontal

component is the destabilizing force. Table 9 shows the

adopted dimensions for the embankment, and the

calculations.

Figure 5 – Generic embankment

Table 9 – Verification of the sliding resistance

Data Values Calculations γ (kN/m3) 18 - ϕ’ (°) 30 - δ (°) (1) 30 ϕ′ H (m) 8 - ecrista (m) 3 - β (°) 45 - Lface (m) 11.31 H/senα W1 (kN/m) 216 γHe!"#$%& W2 (kN/m) 324 γH!/(2tgα) !!"#$%&'! (kN/m) 1338 F!"#$%&'cosα

!!"#$%&'! (kN/m)

1338 F!"#$%&'senα

FS 1.30 - (1) The interface slope-foundation friction angle was considered equal to ϕ’

4.1 Method proposed by FHWA

(2001)

Initially, the three most important slip surfaces were

defined using the SLOPE program: i) the circular surface

of the unreinforced slope with the safety factor of 1,3; ii)

the sliding surface of the unreinforced slope with the safety

factor of 1,3; iii) the circular failure surface that requires the

largest magnitude of reinforcement.

The equation bellow defines the total reinforcement

tension per unit width of slope:

!! = (!"! − !"!)!!! ( 7 )

Where !! is the total reinforcement tension per unit width, !"!

and !"! is, respectively, the reinforced and unreinforced slope

safety factor, !! represents the driving moment, and ! is the

radius of the slip surface.

In order to define the third slip surface described before, it

is necessary to define the maximum reinforcement tension,

!!,!á!. Note that the minimum safety factor usually does

not control the location of !!,!á! . Therefore, nine failure

surfaces were analysed. The results of four of them are

shown in Table 10.

Table 10 – Estimation of !!,!á!

!"! 1,3

!"! 0.608 0.797 0.863 0.886

!! (kNm/m) 1497 3867.9 4651.3 4969.7

! (m) 22.0 16.2 16.9 17.5

!! (kN/m) 47.1 119.9 120.3 117.7

ecrista

H

ß

W1

W2 W2

Lface

Fimpacto

8

Observing the table presented, it can be concluded that

the maximum reinforcement tension per unit width is

around 120 kN/m and the safety factor FSU of the

corresponding slip surface is near 0.863.

Figure 6, Figure 7 and Figure 8 show the three failure

surfaces which define the critical zone, i.e., the area that

needs to be reinforced.

According to FHWA (2001), the slope was divided into two

reinforcement zones of equal height (4 m), the bottom and

the top. ¼ of !!,!á! goes to the top zone and ¾ goes to the

bottom zone. Based on that, it was possible to define the

number of reinforcements in each zone (N), the maximum

reinforcement tension in each reinforcement (!!á!,!) and

the vertical spacing between them (!!,!). The results are

presented in Table 11, and Figure 9 shows the resultant

reinforced embankment.

The total length of the reinforcements (!) is determined by

the sum of the embedment length, !! and the active

length, !!. Table 12 summarizes the calculations for each

layer of reinforcement. FHWA (2001) suggests the

adoption of the larger ! obtained, in this case, 6 m.

Figure 6 – Slip surface with FSu closer to 1,3

Figure 7 – Slip surface with FSu closer to 1,3 (sliding)

Figure 8 – Slip surface corresponding to Ts,máx

Table 11 - Determination of the N, !!á!,! and !!,!

Data Bottom Top Calculations

!! (kN/m) 50 -

!!"#$ (kN/m) 90.2 30.1 -

!!"#$ (m) 4 4 -

!! 1 -

N 1.8 ! 2 0.6 ! 1 ≥ !!"#$!!!!

!!á!,! (kN/m) 45.1 30.1 !!"#$!

!!,! (m) 2.2 ! 2 6.7 (1) ≤ !!!!!!"#$!!"#$

(1) The only reinforcement of the top will be positioned in the

middle of the top zone. !!! is the tensile resistance, !!"#$ represents the maximum reinforcement tension required for

each zone, !!"#$ is the height of each zone and !! is the

coverage ratio of the reinforcement, which was considered 1.

Figure 9 – Reinforced soil slope

Three reinforcements were added to the simulation in

SLOPE and two parameters were defined: the tensile

resistance, and the interface friction (!!"), which depends

on the weight above each reinforcement. The pull-out

resistance (!"! ) is determined multiplying the interface

friction by 1 m length of the slope. Table 13 shows the

results. The face system was simulated with

reinforcements along the face of the slope. Figure 9 shows

the reinforcements R4, R5 and R6. R6 was not located at

the same depth as R3 because it would separate the slope

into two parts.

Table 12 – Determination of the reinforcements’ length

Data R1 R2 R3 Calculations

!!! (kN/m2) 126 90 36 -

!"! 1.5 -

!∗ 0.385 2/3!"∅′ !! 1.0 -

! (1) 1.0 -

!!á!,! (kN/m) 45.1 45.1 30.1 Previously

determined

!!(m) 0.77 !1 1.08 2.71

!!á!,!!"!2!∗!!!!!!

3

R3

R1

R2

2

3

3

R6

R4

R5

3

9

Data R1 R2 R3 Calculations

H (m) 8.0 -

!! (m) 7.0 5.0 2.0 -

!!(m) 0.58 1.73 3.46 ! − !! !"(45− !

!

2 )

!! (m) 1.58 2.81 6.17 !! + !!

A FHWA (2001) do not give K a specific value. It was considered to be 1 because the results are accordingly to what is expected. !!! is the effective stress, !∗ is a function of a embedment factor, !! is the depth, !"! is the embedment bearing capacity factor, Κ is a scale corrective factor and H is the height of the slope.

Table 13 – Determination of the skin bond friction and the pull-out resistance for each layer

Data R1 R2 R3 Calculations

!(m) 6 6 6 Previously determined

!! (kN/m) 50 -

!"! (kN/m2) 630 450 180 !!!!"#$

!"! (kN/m) 630 450 180 !!"×1!!

Where F is the interface factor, considered 1,5.

Finally, after the program ran, it was verified that the

minimum safety factor obtained was 1,338, higher than the

minimum stipulated by FHWA (2001) – Figure 10.

Furthermore, Figure 11 and Figure 12 show that the critical

area, defined previously, are reinforced as predicted.

Figure 10 – Slip surface corresponding to the minimum FS,

after the introduction of the reinforcements

Figure 11 – Slip surfaces corresponding to the FS 0,863

(yellow) and 1,3 (colours degrade)

. Figure 12 – Slip surface corresponding to the FS 1,3 (sliding)

4.2 Stress-strain analysis

Now, the reinforced soil slope defined in Figure 9 will be

simulated in a finite elements program, PLAXIS. The

properties of the soil material are defined in Table 14. It

was not possible to simulate the slope’s face using

geosynthetic and, hence, there were used concrete plates,

whose properties are defined in Table 15. It was assumed

a construction by phases of 1 m each. Table 14 - Soil properties

Soil slope

! (kN/m3) !′ (°) Material type ! (kPa) !

18 30 drained 80000 0.3

Table 15 - Properties of the concrete plates and the geotextile

Painéis de betão armado Geotêxtil CG50

!" (kN/m)

!" (kNm2/m)

! (kN/m2) !"!"% (kN/m)

6000000 20000 5 331

Figure 13 illustrates the axial forces on the reinforcements

right after the construction of the slope. Note that just the

right side is presented. As it is shown, the maximum force

is 0,38 kN/m, almost zero. That result is in agreement with

the expected. Being passive solutions, the reinforcements

will only be mobilized if the soil deforms.

Figure 13 – Axial forces in the reinforcements in the end of the

construction

In order to check if the slope is close to rupture, a Phi

reduction analysis was conducted. This type of analysis

gives the partial safety factor for which the !′ should be

divided, in order to get the slope failure. Running the

program, the partial safety factor was 2.1. Figure 14 shows

0,38 kN/m

10

the axial forces on the geotextiles, after the Phi reduction

analysis. The maximum force is 37.4 kN/m.

Figure 14 – Axial forces in the reinforcements after the Phi

reduction analysis

According to the design approach 1, combination 2 of the

Eucocode 7, only a partial factor of 1.25 should be applied

to the soil parameters, which indicates that the slope is

overdesigned. Tough, it is interesting to notice the total

displacements of the slope – Figure 15. The arrows

progress indicates a slip surface very similar to the one

defined in the limit equilibrium analysis (see Figure 10).

Figure 15 – Total displacements after the Phi reduction

analsysis

Out of curiosity, another Phi reduction analysis was

realized, but this time, it was stopped at the partial safety

factor 1.25. The maximum axial force is around 5 kN/m,

10% of the total tensile resistance of the reinforcements.

The last analysis include the impact force determined with

( 5 ). After running PLAXIS, it was verified that the total

displacements were less than 1 mm.

5 Conclusions

Debris flows are a very complex mass movement, which

involves great volumes and velocities. Adding to that, it

happens suddenly, without signs that indicate its initiation.

Unfortunately, many areas of the world are affected by this

landslide, for which numerous scientists have been

focusing their attention on the vulnerable areas

Various empirical correlations have been developed with

the purpose of determining where the phenomenon occurs

and how to predict future events. However and as shown

in this paper, there is still a large disparity between the

results. In addition, there is also a world effort in order to

develop stabilization and coexistence measures against

this flow, highlighting the reinforced soil embankments.

The design of the geosynthetic reinforced embankments

had two different approaches: a limit equilibrium analysis,

where the dimensions of the slope were defined, and a

stress-strain analyses, in order to verify the stresses on the

reinforcements and the strains in the slope.

The limit equilibrium analysis based on the FHWA (2001)

method proved to be very effective, because there was no

need for several iterations to get the expected result.

However, as shown by the Phi reduction analysis, it leads

to an overdesign of the structures. Therefore, it is

considered to be a good pre-design but it does not exempt

the application of the Eurocodes norms.

The most surprising and unexpected observed fact is the

low values obtained for the total displacements imposed by

the impact force. It is believed that those results derive

from the static analysis performed (using an equivalent

hydrostatic force), instead of a dynamic analysis.

Nowadays, the programs, which perform that kind of

studies, are still very limited.

6 References FHWA. (2001). Mechanically Stabilized Earth Walls and Reinforced

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HUNGR O., EVANS, S.G., BORIS, M. Y., HUTCHINSON, J.N.

(2001). Review of the classification of landslides of the flow type.

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JAKOB, M., HUNGR, O. (2005). Debris-flow Hazards and Related

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37.4 kN/m