Slovak Journal Vol. 30, 2022, No.
3, 1 – 8
of Civil Engineering DOI: 10.2478/sjce-2022-0015
ANALYSIS OF STATIC AND CYCLIC TRAFFIC LOADING
OF AN EMBANKMENT SUPPORTED BY A GEOGRID
RETAINING STRUCTURE
Jakub, STACHO 1 * , Monika, SULOVSKA 1
Abstract Address
The article deals with a deformation analysis of a road embankment 1
Dept. of Geotechnics, Faculty of Civil Engineering, Slovak
under different types of static and cyclic loading. A typical cross-sec- University of Technology in Bratislava, Bratislava, Slovakia
tion of a road embankment supported by geogrid retaining struc-
tures is considered. In the case of a design, the load is usually applied * Corresponding author: jakub.stacho@stuba.sk
as a distributed static load. The analysis presented in the paper in-
cludes all the most loading methods used. Because there are only a
Key words
few measurements for these types of construction in a given region,
the analysis also includes a cyclic loading that aims to simulate real ● Traffic loading,
traffic loading. The cyclic loading considered the weights of cars and ● Static loading,
trucks and the distances between them, based on traffic intensity ● Cyclic loading,
measurements. The study results showed how significant the differ- ● Road embankment,
ences in vertical and horizontal deformations of an embankment ● Geogrid retaining structure.
are when the different types and methods of static loading are used
in a design. The results of the cyclic loading showed the deforma-
tions that can be expected from current real traffic.
1 INTRODUCTION presented is focused on vertical and horizontal deformations of
an embankment supported by a GRS. The simple analytical and
The design of a road embankment supported by a geogrid re- semi-empirical methods for determining the deformations of these
taining structure (GRS) is a type of construction increasingly used structures have been presented by, e.g., Wu (1994) and Holtz and
for expanding road infrastructures in Slovakia. In suitable condi- Lee (2002). The numerical modelling, which is based on the finite
tions, the design of a road embankment supported by a GRS can element method (FEM) or the distinct element method (DEM), was
lead to more effective, economical, and less time-consuming alter- presented by, e.g., Scotland et al. (2016); Drusa and Vlcek (2016);
native to conventional methods. The typical applications of these and Wang et al. (2014). The modeling of any traffic loading on an
types of constructions in Slovakia are discussed in, e.g., Dolinajova embankment is a separate problem. A traffic load is mostly applied
and Snahnican (2015); Adamec and Snahnican (2016); Silber-Has- according to Eurocode 1: Actions on structures, Part 2: Traffic loads
slacher and Snahnican (2019); and Sulovska and Stacho (2019). on bridges (EN 1991-2). Loading Model 1 (LM1) is used. The LM1
The study presented in this article focuses on road embankments defines the magnitude of the loads for the individual loading lanes
supported by a wrapped GRS with a passive facing system. In in a tandem system (TS) and a uniformly distributed load (UDL).
the case of a wrapped GRS, the geogrid is on the side of the face According to this standard, the load from a TS and ULD can be
returned back into the soil/embankment, see, e.g., Scotland et al. distributed to an equivalent distributed load. This method is usu-
(2014). In the case of a passive facing system, the wrapped GRS ally used in the case of the design of a construction supported by
is built to a total height in the first step; then, an independent fac- GRS. The load is applied as a design static load and represents the
ing system is constructed and given the final form of the structure, most critical situation during the life of a construction. It is used in
see, e.g., Silber-Hasslacher and Snahnican (2019). The analysis different verifications of the ultimate limit state (ULS); however,
© 2022 The Author(s). This is an open access article licensed under the Creative Commons Attribution 4.0
License (https://creativecommons.org/licenses/by/4.0/). 1
Slovak Journal of Civil Engineering Vol. 30, 2022, No. 3, 1 – 8
the traffic load is not applied in verifications of the serviceability for the stress-level dependency of the stiffness; G0ref - the initial
limit state (SLS). When the static load according to LM1 is used, small-strain shear modulus; and g0.7 - the shear strain level of the
the deformation of the embankment seems to be too great. The real secant shear modulus. Gs is reduced to about 70% of G0. The sub-
traffic loading is variable, acts dynamically, and has a smaller mag- soil was modelled as A-type undrained, and the material of the
nitude, which means that real deformations of the embankment are embankment was modelled as drained, see, e.g., the Plaxis manual
significantly smaller. There is not enough permanent monitoring of (2021). The basic properties used in the model are stated in Tab. 1,
the deformations of an embankment supported by GRS in Slova- where γ is the unit weight, gsat is the saturated unit weight; j´ is the
kia. For this reason, cyclic loading, the aim of which is to simulate drained angle of the shear strength; y´ is the angle of the dilation,
a typical real traffic loading, was modelled. The magnitude of the and c´ is the drained cohesion. Based on the engineering-geologi-
loads and loading frequency were determined according to the traf- cal survey, the subsoil consists of clayey sand. The body of the em-
fic intensity measurements in the given road section. bankment was designed from silty gravel. The properties, such as
γ, gsat, j´, c´, and Eoed were determined according to, e.g., Sulovska
and Stacho (2019). In this study, it was assumed that E50ref = Eoedref,
2 C REATING THE NUMERICAL MODEL FOR THE CASE and Eurref = 4 . Eoedref in the case of the clayey sand and Eurref = 3 .
STUDY Eoedref in the case of the gravels. The angle of the dilatancy of the
gravel was determined as y´ = j´ - 30°, see e.g., PLAXIS 2D CE
The numerical model of the embankment supported by GRS V21.01:1 (2021). Other parameters required for the HSs material
was done using the Plaxis geotechnical software. The calculations model, such as g0.7 and G0ref, were determined according to recom-
are based on FEM. This software permits modeling a construction mendations made by Ladicsova (2017).
process and executes a detailed deformation analysis of an em- The compacted gravel between the facing blocks and wrapped
bankment and subsoil under different types of loads. The scheme main body of the embankment, gravel bed, and base course, are
of the model focused on an embankment supported by GRS is usually created of compacted poorly graded gravel. Although the
shown in Fig. 1. The embankment has a height of 5.2 to 5.96 m grain size of the material may vary in the backfill, gravel bed,
above the terrain level. The width of the embankment at the top and base course, the same relatively conservative properties are
was 13.5 m. The whole dimensions of the model were 70 x 30 m, usually used in a practical design, see, e.g., Sulovska and Stacho
which was appropriate for the type of task. The model was created (2019). Gravel properties, i.e., silty gravel as well as poorly grad-
as a plane strain model using triangular 6-node elements, which ed gravel, were determined according to STN 72 1001: Classifi-
were required to reduce the calculation time for the analysis of cation of soil and rock.
the cyclic loading. The mesh of the finite elements was refined The foundation strips, facing blocks, and asphalt pavement
especially close to the facing of the wrapped GRS to obtain its were modelled using only the standard Linear elastic (LE) material
adequate horizontal deformation of the embankment. A view of the model, which adequately simulates the behaviour of these elements.
connectivity plot, the finite element mesh, is shown in Fig. 2. The The concrete had the following properties: Young’s modulus, E
soils were modelled using the Hardening small-strain (HSs) mod- = 35 GPa, and Poisson’s ratio, ν = 0.2. The wearing course of the
el, see Benz (2007). This constitutive model extends the “classic” pavement had the following properties: an axial stiffness E.A = 97.8
Hardening soil (HS) model and permitts taking into account the MN.m-1; a bending stiffness E.I = 326 MN.m-2.m-1; and ν = 0.35.
very small-strain soil stiffness and its non-linear dependency on The geogrid was modelled using an elastoplastic, isotropic geogrid
the strain amplitude. The parameters describing the deformation type of material. The elastic stiffness Egeogrid.Ageogrid was defined at a
behavior of the soil are as follows: E50ref - secant stiffness in a stan- value of 1100 kN.m-1, and the plastic threshold Np was applied at a
dard drained triaxial test; Eoedref - tangent stiffness for the primary value of 80 kN.m-1. The property of the interface between the geog-
oedometer loading; Eurref - unloading/reloading stiffness; m - power rid and soil is given by the Rinter parameter. The Rinter was assumed
Fig. 1 Scheme of the road embankment supported by GRS
2 ANALYSIS OF STATIC AND CYCLIC TRAFFIC LOADING OF AN EMBANKMENT SUPPORTED BY...
Slovak Journal of Civil Engineering Vol. 30, 2022, No. 3, 1 – 8
Fig. 2 Detail of the finite element mesh of the embankment
at a value of 1.0, which was determined from the study results pre- consolidation phases, and the time of each stage was given accord-
sented by Stacho et al. (2020). The same consideration was given ing to the real construction time of a similar embankment on the
by Mirmoradi and Ehrlich (2015). The connection between the two same motorway. The initial phases were focused on the landscap-
geogrids was modeled as rigid. The active length of the geogrid was ing and the construction of the concrete foundation strips. Subse-
4.0 m. The placing of the geogrids is also shown in Fig. 1. quently, the wrapped body of the embankment was constructed
step by step to its full height. The construction of the wrapped
Tab. 1 Properties of the soils used in the calculations
GRS was simulated according to a layer-by-layer formwork
Material / Soil
method. In this part of the calculations, the pure wrapped em-
bankment had relatively significant deformations. After the com-
Parameter Unit Embankment Poorly graded Subsoil plete consolidation phase, the deformations were set to zero, and
(Silty gravel) gravel (Clayey sand) the construction of the facing system and road construction was
γ (kN.m-3) 19 19 20.3 modelled. The facing blocks were placed 0.3 m from the wrapped
GRS body. The space between them was filled by compacted
gsat (kN.m-3) 19 19 20.3 gravel. The facing blocks were connected with the wrapped GRS
E50 (MN.m-2) 84 95 11.7 using the activation of the connecting geogrids. Subsequently, the
Eoed (MN.m )-2
84 95 11.7 construction of the road was modelled. The complete consolida-
tion phase ended the modelling of the construction of the embank-
Eur (MN.m )-2
252 285 46.8 ment. This numerical model was later used in the analysis, where
m (-) 0.5 0.5 0.7 different static and cyclic load types were applied.
G0 (MN.m )-2
157.5 178.0 60.84
g0,7 (-) 0.0002 0.0002 0.0003 2.1 Determining the load from the traffic
j´ (°) 28 35 24 In the first part of the analysis, the static load was applied in
y´ (-) 0 5 0 the numerical modelling. The traffic load was used according to
c´ (kN.m-2) 5 0 12 Eurocode 1: Actions on structures, Part 2: Traffic loads on bridges
(EN 1991-2). The loads for the individual lanes in the form of
Drainage TS (acting as the point load) and UDL (acting as the distributed
(-) Drained Drained Undrained A
Type
load) were applied according to LM1; see Tab. 2. According to
this standard, the load from TS and ULD could be distributed to
an equivalent distributed load.
The process of the construction of the embankment supported
by GRS was modelled in 19 phases. The phases were modelled as
Tab. 2 Application of the load according to LM1 of the EN 1991-2 standard
Loading type Width of the lane TS UDL Coefficients for the road category
Marking (Unit) (m) Qi,k (kN) qi,k (kN.m )
-2
aQ,i (-) aq,i (-)
Lane No.1 3 300 9 0.9 0.9
Lane No.2 3 200 2.5 0.9 1
Location
Lane No.3 3 100 2.5 0.9 1
Remaining area - - 2.5 - 1
ANALYSIS OF STATIC AND CYCLIC TRAFFIC LOADING OF AN EMBANKMENT SUPPORTED BY... 3
Slovak Journal of Civil Engineering Vol. 30, 2022, No. 3, 1 – 8
According to the standard, the loading lanes must be placed to Tab. 3 Loads applied in the numerical modeling in the different models
achieve the most critical situation for the design; however, it is not
exactly clear how the load must be applied in the given type of con- Loading Loading Characteristic distributed load
Model
struction when the different conditions require placing the load in type scheme f1,k f2,k f3,k
various positions. For this reason, two options are used in the prac-
Model S1 31.9 - -
tical design. The first option considers placing Lane No.1 on both Scheme 1
sides of the road and the remaining area between them, see Loading Model S2 64.21 - -
model A (Fig. 3). The second option considers the loading on one Model S1 44.1 2.5 -
side, i.e., Lanes Nos. 1 and 2, and the remaining area on the other Static Scheme 2
side of the road, see Loading model B (Fig. 3). In the case of Loading Model S2 89.92 2.5 -
model A (Fig. 3), two schemes were used, i.e., Scheme 1, where all Model S1 44.1 26.5 2.5
the loads were distributed to a single load fk, and Scheme 2, where Scheme 3
Model S2 89.92 57.04 2.5
the loads in the loading lanes were distributed to load fk,1, while the
load in the remaining area q2,k corresponds to f2,k. In Loading model Cyclic Scheme 4 Model D1 *changing (Fig. 4) - -
B, the loads in the loading lanes and the remaining lanes are directly
distributed to loads f1,k; f2,k; and f3,k (Fig. 3). The EN 1991-2 standard soidal course, see, e.g., Zhuang and Li 2015; Han et al. 2015; Pham
recommends a load distribution from TS to an area of 6.6 m2. This and Dias (2019). Other ways of modelling the cyclic load have been
option can lead to determining relatively significant deformations, presented by, e.g., Zheng et al. (2012), who used a semisine course,
which are often assumed to be unreal. For this reason, the load from or Abdelkrim et al. (2003) and Liu et al. (2017), who demonstrated
TS is distributed to an area of 15 m2 in the practical design. Both a simulation of a moving strip or point load, respectively.
options were used in the study presented in this paper. The charac- In the case of the analyzed embankment supported by GRS, the
teristic distributed loads for each scheme are summarized in Tab. 3. real traffic intensity was considered. The traffic intensity measure-
In the second part of the analysis, the load was modelled as ments in the given road section showed that five small passenger
cyclic and simulated the real traffic load. The numerical modelling cars and one truck passed through the section of the road in one
of cyclic loading can be done in different ways. An analysis of an minute. The average weight of the passenger cars at a value of 2.5
embankment or platform under dynamic/cyclic and cyclic load- t was taken into account. In the case of the truck, the weight of the
ing has been presented by, e.g., Abdelkrim et al. (2003); Zheng et whole truck of 44.0 t was assumed (Fig. 4). The load was modelled
al. (2012); Xuecheng et al. (2010); and Zhuang and Li (2015). In as a distributed load acting as a step (jump) load for loading the
the case of a dynamic analysis, the common problem in numerical road only for the time required to pass a car or truck, respectively,
modelling is the time required for the calculations and the heavy when the nominal speed of 90 km.h-1 is taken into account. These
demands on a computer’s hardware. Adam et al. (2000) present- times and the times between the cars or between the cars and the
ed a 3D modelling approach performed with a coupled boundary truck are stated in Fig. 4. In this way, one loading cycle, which was
element-boundary element method and a 2D modelling approach repeated in numerical simulations, was defined. In this case, the
performed by a coupled boundary element-finite element method. real situation was modelled; as a result, the distributed load of the
They demonstrated effective algorithms for reducing the time and average width of 2.5 m was modelled in the middle of each lane,
system requirements for the calculations. Another important aspect see Loading Model C and corresponding Scheme 4 in Fig. 3.
of the modeling is the way in which the dynamic/cyclic load is de-
fined. In most analyses, the load is specified using a traditional sinu-
Fig. 3 Schemes of the loading models and load distributions applied in the numerical modeling
4 ANALYSIS OF STATIC AND CYCLIC TRAFFIC LOADING OF AN EMBANKMENT SUPPORTED BY...
Slovak Journal of Civil Engineering Vol. 30, 2022, No. 3, 1 – 8
Fig. 4 One-load cycle used in the cyclic loading
3 THE RESULTS OBTAINED IN THE STUDY
The results of the study focus on a comparison of the vertical
deformations on the top and bottom of the embankment, the hori-
zontal deformations of the side of the embankment, and the passive
facing system of the embankment, respectively, see Fig. 2. The total
deformations are presented in Fig. 5 for the bottom of the embank-
ment, Fig. 6 for the top of the embankment, and Fig. 7 for the side
of the embankment. The first model marked Initial stage - No traf-
fic load, represents a situation when no traffic load is applied on the
embankment. The deformations are caused only by the construction
of the top of the embankment and the construction of the road, re- Fig. 5 Vertical deformation of the base of the embankment
spectively, and the construction of the passive facing system. Sub-
sequently, combinations of the different static loads applied were
assembled. The application of the loading in Schemes 1, 2, and 3, is
shown in Fig. 3. Model S1 takes the distribution of the load from TS
to an area of 15 m2 into account, and Model S2 takes the distribution
of the load from TS to an area of 6.6 m2 into account. The following
combinations of models and loading were assembled:
● Model S1 - Scheme 1,
● Model S1 - Scheme 2,
● Model S1 - Scheme 3,
● Model S2 - Scheme 1,
● Model S2 - Scheme 2, Fig. 6 Vertical deformation of the top of the embankment
● Model S2 - Scheme 3,
The results are presented for a situation when the static load
acted on the embankment for the time required for complete con-
solidation. This permitted determining the final permanent defor-
mation of the embankment, which was loaded by a different type
of static loading. The results obtained for the cyclic loading are
marked Model D1 - Scheme 4. In this case, the cyclic load was
applied according to Scheme 4 of Loading model C. The greatest
permanent deformation of the embankment was achieved after
324 loading cycles. The results of the deformation of the embank-
ment under cyclic loading are stated in section 3.1 in more detail. Fig. 7 Horizontal deformation of the embankment
The results showed that the vertical deformations determined
in Model D1 - Scheme 4 are slightly greater than those reached in Scheme 3. The vertical deformation of the bottom of the embank-
the Initial stage. The difference is about 3 mm at the bottom of the ment was about 33 - 37 mm, and the vertical deformation of the top
embankment and about 11.5 mm at the top of the embankment. In of the embankment was about 53 - 54 mm. The horizontal defor-
Model D1 - Scheme 4, the horizontal deformation increased from mation of the embankment was about 15 mm in the case of Model
6.1 mm (Initial stage) to about 11.0 mm. These results showed that S1 - Scheme 1 and about 16 mm in the case of Model S1 - Scheme
small deformations of the embankment only occur when simulating 2. In the case of Model S1 - Scheme 3, the horizontal deformation
the actual traffic loading. Applying the static loading typically used achieved was about 22.7 mm. In all three cases, the distribution
in the design led to determining significantly greater embankment area of 15 m2 was applied to the TS. When the distribution area of
deformations. In Model S1, the vertical deformations of the top and 6.6 m2 was used on the TS (Model S2), significantly greater vertical
bottom of the embankment are similar for all the loading schemes and horizontal deformations were achieved. The greatest vertical
applied, except for the lesser loading side of the embankment in deformations of the top and the bottom of the embankment were
ANALYSIS OF STATIC AND CYCLIC TRAFFIC LOADING OF AN EMBANKMENT SUPPORTED BY... 5
Slovak Journal of Civil Engineering Vol. 30, 2022, No. 3, 1 – 8
achieved when the load was applied according to Scheme 1; howev-
er, in the case of the horizontal deformations, the greatest value was
achieved when the load is applied according to Scheme 3.
3.1 D eformation of the embankment under cyclic
loading
The cyclic loading was applied according to the scheme in
Fig. 4, which tries to simulate real traffic loading according to
actual traffic intensity measurements. The loads were defined ac-
cording to Scheme 4 of Loading model C (Fig. 3). The vertical
deformations of the top and bottom of the embankment over time
are presented for the initial 180 cycles in Figs. 8 and 9, respec- Fig. 8 Vertical deformation of the top of the embankment over time -
tively. A significant increase in the deformations was achieved in initial 180 cycles
the initial cycles; then, the incremental displacement was reduced
over time. After 324 cycles, the stable value of the deformations
was achieved. It was assumed that the stable value of the defor-
mations was achieved when the excess pore pressure decreased
below 1 kPa. The change in the maximum pore pressure over time
for the initial 180 cycles is shown in Fig. 10.
The vertical deformations of the top and bottom of the em-
bankment and the horizontal deformation of the side of the em-
bankment, which is reached after 10, 100, and 324 cycles, are
shown in Figs. 11, 12, and 13. The results presented also include
the deformations determined in the initial stage. In the case of cy-
clic loading, the deformations increase significantly in the initial
cycles, but this increase decreases over time or on the number of
cycles, respectively. Fig. 9 Vertical deformation of the base of the embankment over time
- initial 180 cycles
Fig. 10 Course of the maximum pore pressure over time - initial 180
cycles
Fig. 11 Vertical deformation of the base of the embankment in the
case of cyclic loading
Fig. 12 Vertical deformation of the top of the embankment in the
Fig. 13 Horizontal deformation of the embankment in the case of
case of cyclic loading
cyclic loading
6 ANALYSIS OF STATIC AND CYCLIC TRAFFIC LOADING OF AN EMBANKMENT SUPPORTED BY...
Slovak Journal of Civil Engineering Vol. 30, 2022, No. 3, 1 – 8
The results more or less confirm that the deformations of the scheme have a significant impact on the deformations achieved.
embankment are mainly caused by truck traffic. In the analysis pre- Different schemes based on the Load Model 1 of the EN 1991-
sented, the subsoil of the embankment is relatively stiff and perme- 2 standard were applied in the case of the static loading. If the
able. Based on the average traffic intensity, only one truck passes load distribution from a tandem system (TS) to an area of 15 m2
through the road section per minute. All these parameters lead to a (which is often used in the practical design of given types of con-
relatively small number of cycles required to achieve a stable defor- structions) is applied, the vertical deformations of the top and bot-
mation. In the clayey subsoil, which requires a longer consolidation tom of the embankment are similar for all the loading schemes
time and a greater intensity of truck traffic, the time and number of applied. In the horizontal deformations, the loading according to
cycles needed to achieve a stable deformation can be significantly Scheme 3 led to determining the greatest horizontal deformations.
longer. The results also showed that in the case of the embankment If the load distribution from TS to an area of 6.6 m2 is applied,
design supported by GRS, the simulation of the cyclic loading per- according to the recommendations of the standard, the vertical
mitted obtaining a magnitude of the estimated deformations that and horizontal deformations of the embankment are significant-
could occur under expected or design traffic loading. ly greater. The greatest vertical deformations of the embankment
were achieved when the load was applied according to Scheme 1,
and the greatest horizontal deformations were achieved when the
4 CONCLUSIONS load was used according to Scheme 3. The cyclic loading simu-
lated the real traffic loading determined according to the traffic
The design of a road embankment supported by a geogrid re- intensity measurements of the given road section. A one-minute
taining structure (GRS) with a passive facing system is based on segment included five personal vehicles and one truck. The re-
verifications of the ultimate and serviceability limit states. The sults showed that in the given boundary conditions and proper-
verification of the deformations of the embankment, as part of ties of soil, the stable deformation of the embankment is reached
the serviceability limit state verifications, usually does not con- after 324 cycles. The results showed that the deformation of the
sider the acting variable traffic load. The visual monitoring of embankment is only a little higher than the deformation deter-
such constructions shows that some deformations from a traffic mined in the initial stage and visibly less than the deformation
load occurs; however, the permanent monitoring for a given type determined when different permanent static loading schemes were
of construction in the given region is missing. The results of the applied. The method presented can be suitably used in determin-
deformation analysis of the embankment supported by GRS un- ing the estimated deformations from a traffic load that can occur
der different types of loading showed that the type of loading and under expected or design traffic loading.
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