Extended Abstract

Slope Stability in the Beira Alta Railroad Under the Action of Railway

Traffic

Ana Rita de Carvalho Faria Costa

June, 2019

Abstract

To connect the Atlantic coast seaports to the north of Europe and to align Portuguese transport strategy with

the European Union, the modernization of the existing railways becomes necessary. The modernization of

these centenary railroads will allow the increase of train traffic and speed. Therefore, the study of rock slopes

stability on these railroads, to comply with the proposed objectives, is necessary.

The present study refers to the Modernization of Beira Alta railway, namely Mangualde-Guarda section.

Beira Alta track aims to improve the connection between Aveiro region and the border with Spain in Vilar

Formoso. The section under study is developed mainly on porphyry granites and presents excavated rock

slopes with heights between 5 and 30 m. This study proposes the static analysis of the stability of those rock

slopes using three different methodologies. Also slope dynamic analysis is considered, taking into account

ground vibrations induced by train traffic.

Static analyses are performed by cinematic analysis with DIPS, SWedge and RocPlane and by two- and

three-dimensional finite element analysis using RS2 and RS3 from Rocscience. The results show that

cinematic static analysis offers the lowest safety factors compared to the other methodologies and three-

dimensional finite elements analysis the higher safety factors.

As for the dynamic analysis, when compared to the static analysis, a reduction of the safety factors is

observed, which shows that train traffic in the Beira Alta rail track influences the neighbor slopes stability.

Keywords: dynamic analysis; finite element method; slope stability; railroad; trains.

1. Introduction

Beira Alta railroad was built in 1979 and it’s

considered as one of the main rail tracks in

Portugal due to the high transportation of

merchandise and passengers. Several works

have been taken on, however, given the need to

improve railway international connection between

the Portuguese Atlantic coast seaports with the

North of Europe, the Portuguese government has

proposed a Strategic Plan of Infrastructures and

Transportation that seeks the modernization of

the track under study. Due to the conditions of the

rock mass, as well as other constrains that may

be related to the rail traffic, such as the axle load,

load dimension and required train speed, slope

stability analysis becomes necessary.

Many different types of instabilities may occur in

rock slopes, like rock fall, rock slide and toppling.

Excavation slopes along the train track section

are essentially rock slopes, where the main risk

for the rail infrastructure are the loose blocks or

ruptures by mechanisms of the planar type or

wedge (Figure 1). In case of these types of

ruptures, the structure has a dive that follows the

face of the slope.

These instabilities result from the natural

decompression of the rock mass, which are

related to the geodynamic agents (atmospheric

and biological).

a) b)

Figure 1 – Schematic representation of the types of rupture: a) Planar; b) Wedge (Lima & Menezes,

2012).

Slope stability analysis type should be chosen

depending on the ground conditions, on the

potential fault and taking into account the

limitations of each methodology (Eberhardt,

2003).

According to Eberhardt (2003), the main

objectives of the slope stability analysis are:

− Determine the stability conditions of the

slope;

− Identify the potential failure

mechanisms;

− Determine the sensibility/susceptibility

of the slope to different triggering rupture

mechanisms;

− Test and compare several techniques of

stabilization;

− Design ideal slopes in terms of safety,

reliability and cost.

Different methods for rock slope stability are

used, such as the kinematic approach, the limit

equilibrium method and finite element method.

1.1 Ground vibrations induced by train

traffic

Train circulation induce vibrations on the railway

track and therefore transmitted to the ground

where it propagates and when reaches nearby

structures, depending on the amplitude and

frequency, it can cause severe damages on those

structures (Xia, Zhang & Gao, 2005). These

vibrations are the result of the impact of the

wheels on the rails. The energy released is then

transferred to the railway and the magnitude will

depend on the quality of the track and the type of

train, circulation speed, etc. Ground foundation in

which lies the railway will absorb the generated

energy that may reach the surroundings (Figure

2) by stress waves that propagates through the

soil/rock layers or even structures (Monteiro,

2009).

Figure 2 - Schematic representation of the induced vibrations generated by the passage of a train.

(adapted from Hall, 2013).

Several factors may influence ground vibration

levels generated by train circulation. These

factors include (for example):

● Several types of components (such as

weight per axle, types of loads, speed,

suspensions, type of traction,

maintenance of wheelsets, among

others);

● Quality of the track and periodic

maintenance checks;

● Types of materials in which the

vibrations will propagate (type of

soil/rock, stratification, water table, etc).

In recent years, ground vibrations induced by

train traffic on the railways has been monitored,

both by the ownerships of these infrastructures

(especially those who allow higher speeds), as

well as by the increasing awareness of people

regarding these phenomena vibrations. So, the to

attest to the international standards that set the

limits of ground vibration amplitudes is one of the

reasons why vibrations in railways have been

studied.

Analytical and numerical methods, such as the

finite element method and the contour elements,

a) Vehicle response

b) Track structure response

c) Excitation of dynamic forces

d) Ground surface response

e) Generation of stress waves

f) Surface waves

g) Excavation slope

h) Propagation of stress waves

i) Primary body waves

j) Secondary body waves

l) Reflection and refraction at

different soils or bedrock

have been developed to predict the propagation

of stress waves induced by train traffic (Degrande

& Schillemans, 2001).

Xu et al. (2017) considered that train-induced

vibrations are undoubtedly one of the causes of

instability of slopes in the nearby area of the

railways. To verify this, these authors have

monitored the effects of such vibrations on slopes

with instability risk.

Several numerical models were classified

according to the surrounding material and the soil

modeling.

Krylov e Ferguson (1994) carried out the first

studies regarding the ground vibrations induced

by railway loads, using the conditions proposed

by Green. Krylov (1994, 1998), Sheng et al.

(1999) and Kaynia et al. (2000), considered loads

in a single axis (Figure 3).

Maldonado et al. (2008) also modelled the

interactions between train, railway and ground

foundation), which until then had rarely been

considered. In 2006, Lu et al. studied the

vibrations in the soil, caused by random loads that

are distributed along the railway at a constant

speed.

Datoussaïd et al. (2010) e Sheng et al. (2003)

were the pioneers in multi-body vehicles

modeling, which consisted in the combination of

rigid, flexible or rotating bodies, and

interconnecting elements (springs and dampers).

These models include a wagon attached to a

bogie through a secondary suspension. With the

upgrade of the models, Xia et al. (2000)

developed an integrated model of dynamic train-

railway-ground interaction (Figure 4) in order to

predict the vibration induced by a moving train.

The advances in technology began to put aside

analytical methods and highlighted now two-

dimensional and three-dimensional numerical

models, using methods such as finite elements

and boundary elements.

In 2003, Paolucci et al. introduce the finite

element (2D and 3D) numerical models to try to

understand the advantages and limitations of

these methods. To calculate the spatial load

distribution of train circulation, a series of static

forces were dynamically in the railway track

(Figure 5).

Figure 5 – Spatial distribution of the loading of a train in motion (Paolucci et al., 2003).

Along the years, many studies of finite element

(namely three-dimensional analysis) were carried

out to understand the propagation of train-

induced vibrations. These studies were lead by

Yang et al. (2003), Yang et al. (2009), Hall (2003),

Anastasopoulos et al. (2009), Ju (2009),

Stupazzini and Paolucci (2010), Zhai et al.

(2010), Banimahd et al. (2011), Wang et al.

Figure 4 – Rheological model train-railway-ground of a moving train (Xia et al., 2010).

Figure 3 – Model where the vibrations are generated by a single load axis (Kaynia et al., 2000).

Railway

Soil

(2012), Kouroussis e Verlinden (2013) and

Connolly et al. (2013).

Besides the two and three dimensional finite

element analysis, other methods are used to

model the propagation of waves in the ground,

such as the contour element method. In many

studies, O’Brien and Rizos (2005), Sheng et al.

(2006), Galvín et al. (2010) used this method to

predict ground vibrations caused by train loads.

In these studies, the ground was modeled using

the boundary element method and the railroad

with the finite element method (Figure 6). The

combination of both these methods allowed

taking advantage of each method and minimizing

the limitations of each.

2. Case study

2.1. General considerations

As referred before the case study of the present

work refers to the Beira Alta Railway

Modernization Project.

This study focuses on determining excavation

slopes stability with the use of static and dynamic

analysis verified in the Magualde-Guarda section,

which includes the Pk 164+300 to the Pk

200+150, comprising a total of 10 slopes.

For these analyses, the following rock index

properties presented on Table 1 were taken into

account (TPF, 2018).

For slope stability analysis it is necessary to

define rock mass properties, particularly those

from discontinuities, since they are responsible

for the main instabilities (TPF, 2018).

Table 1 – Index properties of the rock materials analyzed (TPF, 2018).

Index properties Coarse grained porphyry

granite

Specific weight 𝛾 (kN∙m-3) 26

Porosity 𝑛 (%) 0,12

Uniaxial compressive strength (MPa) 106

The following Table 2 presents the parameters

used to define the Barton-Bandis criterion, as well

as the intervals of values for the approximate cut-

off angle (TPF, 2018).re criterion.

Table 2 - Basic friction angle according to Hoek and Bray (1981).

JRC Friction

angle (𝜑𝑏′ )

Extension of the

discontinuity

plan (𝐿𝑛)

Normal strength

(𝜎𝑛)

Angle of shear

strength

obtained (𝜑′)

7 - 11 31º - 35º 5-10m 26-520 kPa 38º- 41º

For calculation purposes, it has been considered

that the shear angle is 40 degrees.

2.1. Methodology

With the information obtained from the field work,

the kinematic analysis was performed using DIPS

(from Rocscience). This software allows the

analysis of slides, using stereographic

projections, from discontinuities planes and

poles. Once the geological information is

obtained, all that remains is to combine and

evaluate these same discontinuities with rock

mass strength parameters.

Once the kinematic analysis is concluded, and

the slopes with global kinetic mechanisms are

identified as planar or wedge rupture, it is

necessary to proceed to the evaluation of slope

instability in the present conditions, to determine

the overall safety factor (SF) using SWedge and

RocPlane, both from Rocscience.

To assess a more accurate safety factor, a two

and three-dimensional static analysis were

performed, using RS2 and RS3 from Rocscience.

Figure 6 – Model ground-railway line (O'Brien & Rizos, 2005).

For slopes stability analysis through finite element

method, the software’s mentioned above use the

Shear Strength Reduction (SSR).

The SSR is a simple approach used to reduce

(systematically) the shear strength of the material

for a safety factor and calculate the finite element

models of the slope until the deformations are

unacceptably large or the solutions fail to

converge (Figure 8).

Figure 8 – Geometric interpretation of shear strength envelope reduction.

For the present study the Mohr-Coulomb criterion

was used. The following equation represents the

original expression from Mohr-Coulomb:

𝜏 = 𝑐′ + 𝜎′𝑡𝑎𝑛∅

This approach lowers the shear strength through

the safety factor (SF), which is determined by:

𝜏 =𝑐′

𝐹+𝜎′𝑡𝑎𝑛∅

𝐹

To understand the influence of the load on the

railway and on the nearby slopes it is necessary

to take into account train compositions that

circulates in these tracks. For the dynamic

analysis, only freight trains are considered

(Figure 9 and Figure 10) with wagons similar to

those observed in Figure 11.

Figure 10 – Side display of the Euro4000 locomotive.

Figure 11 – Wagons considered in the studies.

For the analysis, the time-domain dynamic Force

(in kN) for train. Thos was constructed

considering “Diretório da Rede” 2019, from

“Infraestruturas de Portugal”, from which it was

noted that the railroad in study (according to UIC-

700-0) has a maximum load per axle of 22.5 tons.

So the Euro4000 was considered to have 40

wagons with the total assembly of a maximum

length of 317.6 meters (less than the maximum

length of the line – 515 meters).

Figure 12 gives the graphic that relates the

information obtained on the following table.

In these studies, train circulation has been

considered as a dynamic force applied on one

specific point on the track, which is normally

associated to the area where the slope in the

static analysis is more unstable.

Figure 9 - Euro4000 locomotive.

0

50

100

150

200

250

0 5 10

F (k

N)

t (s)

Figure 12 - Force vs. Time graph resulting from the passage of a freight train.

4. Results and Discussion

4.1 Static analysis

Figure 13 presents the comparison of the results

between the global stability analysis and the static

analysis from the finite elements (in two and three

dimensions).

It is possible to verify that the global stability

analysis are those that represent the most

unfavorable results, attending to the fact that, in

comparison with the finite element analyses, they

had the lower safety factor values.

However, with the exception of some slopes, the

three-dimensional analysis with finite elements

originated higher safety factor values compared

to the others analyses, which is related to the fact

that they are able to better adjust to the real

geometry of the slopes.

Regarding the three-dimensional analysis, it is

verified that two of them present lower safety

factors than the two-dimensional analysis, which

is the case of the Slope 6. This may be due to the

fact that the two-dimensional analysis from this

slope may be compromised by the surrounding

conditions (Figure 14), as well as because of the

two-dimensional cut chosen corresponds to the

area where the slope is higher and with a bigger

inclination (Figure 15). These were considered as

the main factors that influence the slope stability.

Figure 14 – Influence of the surrounding conditions in 2D static analysis of the Slope 6.

Figure 15 – Side-cut of the Slope 6 used in the two-dimensional analysis (marked in red).

However, on the three-dimensional analysis, it

was verified that perhaps there was a loose block

on the center of the slope, which wasn’t include in

the area of study for this two-dimensional analysis

(Figure 16). Considering that the entire slope is

included in the 3D analysis, it is possible to

observe all the details, where, as on a 2D analysis

there isn’t this advantage. In this case, the

stability condition so without a doubt the

highlighted block, ignoring the height and

inclination of the slope, hence the fact that the

safety factor is lower in the three-dimensional

analysis than on two dimensions.

Figure 16 – Front view of the Slope 6 where the transverse profile used in two-dimensional analysis is identified in red and in the black the outstanding slope

block verified in the three-dimensional analysis.

Figure 13 - Comparison the results of the static analyses

Sa

fety

Fa

cto

r

Slopes

4.1 Dynamic analysis

The safety factors related to the dynamic analysis

from finite elements (2D and 3D) are displayed on

Figure 17.

Figure 17 – Comparison of the results of the dynamic analysis in RS2 and RS3.

In the Slope 1, for instance, it is possible to verify

a decrease of the safety factor in both analysis.

In Figure 18 there is an area marked as red which

represents the maximum shear strength on the

Slope 1 during the passage of the train. In order

to understand the influence of this passage in the

stability of the slope, it was selected a point where

the shear strength was higher, making it possible

to verify the variation along the passage of the

train on the specific track.

The graphic illustrated on Figure 19

demonstrates the variation of strain along the

various stages of the passage of the freight train.

From observing this graphic, we may conclude

that the strain increases while the train passes by,

taking into account that on stage 1 there is no

influence of the train load on the track, where on

stage 6 it reaches the maximum strain.

Analyzing the Figure 17 and comparing these

results with the safety factors from the static

analysis it is possible to conclude that the

passage of the train components will affect the

stability of the slopes who are closest to the

railway track.

4. Conclusions

Firstly, given the limitations of the global stability

analysis, it was confirmed that the low safety

factors obtained are mainly due to surface

wedges, which are not large breakages.

Regarding the two-dimensional finite element

analyses made, there were noted that some

limitations. These may include the choice of cut-

sections used for the geometry, because there

were chosen based on the highest sections

and/or higher slopes (which are the biggest

constrains).

After the three-dimensional analyses, it was

verified that the definition of this parameter wasn’t

the most accurate. This is supported by the fact

that, for instance, the Slope 6 (Pk 196+700 to the

Pk 196+850) had an unstable area that

corresponded to the highlighted block, which

wasn’t included in either area of the slope in

study, making it impossible to choose the

profile/section with greater height and inclination.

For this reason, it was obtained a higher safety

factor in the two-dimensional than the three-

dimensional analysis, because in the greater

Figure 19 - Variation graph of strain during the various stages corresponding to the passage

of a freight train.

Figure 18 - Place where the maximum shear strength was verified and where a point was placed to observe the variation of shear strength during the passage of a

train.

Sa

fety

Fa

cto

r

Slopes

height and inclination there isn’t any evidence of

instability.

Another limitation from this two-dimensional

analysis against the three-dimensional are the

surrounding limits, from where the results of the

safety factor are significantly lower in the two

dimensional analysis.

Regarding the software, the finite element

analysis in 3D revealed some difficulties in the

modeling of the slopes, both in the geometry and

in the definition of the meshes.

Because of the complex geometry, with several

irregularities, when submitted in the software,

some errors were encountered and could

definitely compromise the results. Looking to

solve this problem, in the CAD software (to model

the slopes), the surfaces had to be simplified.

However, this did not solve the entirely the

problem.

To pick the right meshes also revealed some

difficulties namely on the slopes with big lengths.

In these cases, the software didn’t allow to

choose freely the type of mesh. To solve this,

came the need to restrict the slopes to areas that

only presented higher risk of instability (which

decreased to almost half).

Instead of the 2D analysis, in this software, the

discontinuities weren’t possible to model. They

were included together with the rock mass.

Concerning the dynamic analysis (and attending

to the parameters established in this study), the

main objective for the modernization of the track

(for maximum speeds of 120km/h for commercial

trains and the loads which it integrates) was

accomplished and it may be said that the passage

of the train does indeed influence the slope

stability in the nearby area. In these analyses, the

passage of train components was simulated in a

simplistic matter, having in consideration only the

strength in the middle of the track.

In both two and three-dimensional dynamic

analysis it was verified that in all slopes the safety

factor decreased in comparison with the static

analysis.

In general, global stability analyses are the most

used because they present immediate results

and do not require slope modeling, thus

presenting the fastest analyses. Two-dimensional

finite element analyses require a much longer

lead time both in the choice of cross profiles for

the analysis as well as in the processing time of

the analysis. The same happens in the three-

dimensional analyses, whose modeling of the

slopes requires a time still higher to the one of the

two-dimensional analyses due to the necessity to

model the slopes in a CAD software, as well as

the processing time of the analyses is much

higher to the one of the two-dimensional

analyses. In terms of results, as previously seen,

the three-dimensional analyses are the ones that

present the best results, since they represent the

reality of the slope since they take into account

the confinement, which does not happen in the

two-dimensional analyses. On the other hand, the

global stability analyses are very conservative,

resulting in higher costs in the stability solutions

to be used.

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