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Citation: Yuan, Y.‑L.; Hu, C.‑M.;
Xu, J.; Mei, Y.; Wang, F.‑F.; Wang, G.
Experimental Research on the Creep
Behavior of the Interface of
Compacted Loess and High‑Density
Polyethylene Geogrid. Buildings 2023,
13, 1353. hps://doi.org/10.3390/
buildings13051353
Academic Editor: Erwin Oh
Received: 2 January 2023
Revised: 2 May 2023
Accepted: 8 May 2023
Published: 22 May 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Swierland.
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4.0/).
buildings
Article
Experimental Research on the Creep Behavior of the Interface of
Compacted Loess and High‑Density Polyethylene Geogrid
Yi‑Li Yuan 1,2 ,*, Chang‑Ming Hu 1 ,2, Jian Xu 1,2 , Yuan Mei 1,2, Fang‑Fang Wang 1,2 and Ge Wang 1
1School of Civil Engineering, Xi’an University of Architecture & Technology, Xi’an 710055, China
2Shaanxi Key Laboratory of Geotechnical and Underground Space Engineering, Xi’an 710055, China
*Correspondence: yiliyuan@xauat.edu.cn; Tel.: +86‑13087540698
Abstract: The stability of geogrid‑reinforced soil structure is closely related to the interface char‑
acteristics between geogrid and soil. However, the creep behavior of the soil–geogrid interface is
still unrevealed. In this study, using a modied stress‑controlled pullout device, inuence of the
normal pressure, dry density, and water content on creep behavior of interface of compacted loess
and high‑density polyethylene (HDPE) geogrid is investigated. A three‑parameter empirical model
and a Merchant element model were established through ing analysis. Analysis results show that
the normal pressure, dry density, and water content have signicant eects on the creep shear dis‑
placement of the reinforced soil interface. Under the same pullout level, creep displacement of the
interface increases with the increase of water content and decreases with the increase of dry density
and normal pressure. Both the three‑parameter empirical model and Merchant element model can
describe the creep characteristics of the reinforced soil interface. The Merchant model is more accu‑
rate in the early stage, while the three‑parameter empirical model is more suitable for predicting the
long‑term creep deformation of the interface of compacted loess and geogrid.
Keywords: geogrid; pullout test; creep behavior; reinforced soil; component model
1. Introduction
In engineering practice, as an eective reinforcement material, geogrid has been widely
used in embankments [1–3], railway foundations [4–6], lling slopes [7,8], and retaining
walls [9–12] due to its good engineering properties and low cost. It was proven that the
engineering behavior of the geogrid‑reinforced soil structures is inuenced by property of
soil (the density, grain size and shape, water content, and strength) [13–15] and geogrid
(geometry, type, stiness, and roughness) [16,17] as well as their interface. The geogrid is
mostly made of polymer which has stable behavior [18]. On the other hand, the property
of the interface of soil and geogrid are more uncertain and less predictable.
The mechanical property of the interface of soil and geogrid plays an important role
in the stability and performance of reinforced soil structures [19,20]. Several experimental
and numerical studies have been performed to investigate the strength and deformation
properties of the soil–geogrid interface. Hatami et al. [21] investigated the pullout perfor‑
mance and interactions of geogrids with base layer aggregates in roadway applications un‑
der dierent in‑isolation properties of dierent geogrids. Esmaeili and Pourrashnoo [22]
investigated the eect of encasement of ballast with geogrid on shear behavior using a
large‑scale direct shear apparatus. Mirzaeifar et al. [23] studied the possibility of using ne‑
grained soil as backll material of geosynthetic‑reinforced walls and slopes through a lab‑
oratory study on pullout behavior of geogrids in granular layers. Moreover, with the help
of Particle Image Velocimetry (PIV), the soil–geogrid interactions at dierent gravimetric
water contents (GWC) values were investigated. Pullout resistance oered by geogrid de‑
pends primarily on the properties of structural ll, geometrical and mechanical properties
Buildings 2023,13, 1353. https://doi.org/10.3390/buildings13051353 https://www.mdpi.com/journal/buildings
Buildings 2023,13, 1353 2 of 15
of the geogrid, and normal stress at which the test is conducted [24]. The relationship be‑
tween soil properties and geogrid properties with pullout resistance is nonlinear and com‑
plex. To predict the behavior of the soil–geogrid interface, Pant and Ramana [25] proposed
a prediction method for pullout interaction coecient using data driven machine learning
regression algorithms. Their proposed model gives 90% accuracy in prediction of pullout
interaction coecient compared to laboratory test results. Using test data of large‑scale
direct shear tests, He et al. [26] established a nonlinear hyperbolic model to describe the
relationship between shear stress and shear displacement of the clay–geogrid interfaces.
As a result, the relation between water content and shear strength at the clay–geogrid in‑
terfaces was revealed.
In lling foundations and lling slopes, the geogrids in reinforced soil are mostly in
time‑varying tensile state due to the construction process and selement deformation of
soil. Under the long‑term tensile state, the interface slip strain may increase over time,
which is called the shear creep behavior. If the creep deformation of the soil–geogrid inter‑
face grows too large, the stress in soil structure may be redistributed, which could lead to
instability or collapse of the soil structure due to excessive deformation. Creep behaviors
of dierent soils have been fully investigated in previous studies [27]: Lian et al. [28] con‑
ducted triaxial creep tests and scanning electron microscopy (SEM) tests on intact loess to
investigate the inuence of the dry–wet cycle on the creep characteristics and microstruc‑
tural evolution. Zhu et al. [29] studied the spatial–temporal variations of the postconstruc‑
tion selement of high ll embankments based on an empirical formula ed by in situ
monitored data. Construction recommendations were also given. Based on a test section
of a high lling airport constructed on a thick loess foundation, Zhu and Li [30] investi‑
gated the creep behavior of both intact compacted loess under high pressure and dierent
initial conditions [31]. As for the creep behavior of geogrid, considering the inuence of
the reinforced soil on the creep characteristics of the geogrid, Wang et al. [32] carried out
a series of creep tests using a self‑developed pullout test device, and found that compared
with unconstrained conditions, the creep deformation of geogrid under the constraint of
reinforced soil is reduced by 11.5% at most, and the ability to resist the creep deformation is
beer. Yeo and Hsuan [33] performed an experimental study on the tensile creep behavior
of polyethylene‑terephthalate (PET) and high‑density polyethylene (HDPE) geogrids us‑
ing ve test methods: the short and long‑term stepped isothermal method (SIM), the short
and long‑term time–temperature superposition (TTS), and the conventional method. They
concluded that the Weibull model was able to predict the linear and non‑linear creep be‑
havior up to 100 years based on 10 h creep testing data and ing analysis. Zou et al. [34]
investigated the creep behavior and stress relaxation of HDPE geogrids under four sus‑
tained load levels. Research results showed that the working stress of geogrids should be
less than 40% of ultimate tensile strength.
Most of the existing studies were focused on the creep properties of soil or geogrid
using laboratory tests (direct shear test, pullout test) and numerical simulation methods.
Nevertheless, there is no study on creep behavior of the interface of soil and geogrid as far
as we know, which is also an important inuencing factor of the stability and strength of
reinforced soil structure.
In this paper, a modied pullout test device was used to conduct the creep defor‑
mation pullout test of the interface of compacted loess and HDPE geogrid. The eects
of normal pressures, dry density, and water content on the creep property of interface of
compacted loess and HDPE geogrid were studied. A three‑parameter empirical model and
a Merchant model for the interface creep behavior were studied through ing analysis.
Research results can provide reference for the prediction of the engineering behavior of
reinforced soil structure.
Buildings 2023,13, 1353 3 of 15
2. Materials and Methods
2.1. Soil and Test Device
To reveal the interface creep behavior between compacted loess and geogrid, a stress‑
controlled pullout test device was needed. In our study, an oedometer was modied to
achieve the above objectives. As shown in Figure 1, the modied pullout test device con‑
sisted of the following components: a normal pressure application system, a constant ten‑
sile load system, a measurement system, and a soil sample mold that is compatible with
geogrid specimen. The normal pressure application system is provided by the original
oedometer device. The constant tensile load system is realized through a pulley block
and counterweights. The original consolidation container is modied to serve as a sample
mold. The eective size of the mold is 7.98 cm in diameter and 2 cm in height, which is the
most commonly used dimension for both consolidation tests and direct shear tests. A 1 cm
long and 0.3 cm high narrow slit is cut in the middle of the height of the mold, so that the
geogrid can stretch out from the mold through the slit and connect with the load system.
Such dimension is big enough for the strip to pass through, and not too big to inuence the
stress state of the soil sample. The measurement system uses a dial indicator and a data
collecting system to record the displacement of the pullout length of the geogrid. The data
measurement system can automatically collect data at any time interval. In the initial stage
of the test, the data are collected every 30 s, and gradually increased to 1–5 h according to
the change rate of the deformation.
The test soil sample is collected from the high ll project in the new campus of Yan’an
University, Yan’an City, Shaanxi Province. The soil sample is mainly composed of silt,
containing a small amount of silty clay, which belongs to Q3loess (also known as “Malan
Loess”) [35]. Basic geotechnical tests were conducted to obtain the basic properties of the
soil samples. Table 1shows the resulting physical and mechanical properties. The grading
curve is shown in Figure 2. According to the Unied Soil Classication System (USCS),
the sampled soil was classied as lean silt (ML). Based on X‑ray diraction analysis ac‑
cording to test standard (GB/T 50123) [36], the chemical composition of the sampled soil
was obtained. The content of SiO2ranged from 50 to 60%, Al2O3ranged from 9 to 12%,
CaO ranged from 7 to 10%, MgO ranged from 1 to 3%, Fe2O3ranged from 4 to 5%, and
K2O ranged from 2%. The mineral composition is mainly composed of quar, feldspar,
and carbonate minerals. Through a laboratory compaction test, the optimal water content
and maximum dry density of soil samples were obtained as 13.50% and 1.785 g/cm3, re‑
spectively. In the tests of the present study, samples with dierent water content were
prepared by water lm transfer method [37] for humidication and placed in a moisturiz‑
ing cylinder for 48 hours before use [38].
High density polyethylene (HDPE) one‑way geogrid is used in the test, as shown in
Figure 3. The width of the transverse rib and the width of the longitudinal rib of the geogrid
are 19 mm and 5 mm, respectively. The thickness of the transverse rib and the thickness of
the longitudinal rib are 3.3 mm and 1 mm, respectively. The peak strain is 11.28%. Other
basic mechanical properties are shown in Table 2. The single geogrid used in the test is
cut from the unidirectional geogrid sample, and the actual length of the single geogrid is
determined by the specimen mold.
Table 1. Physical and mechanical properties of soil samples.
Specic
Gravity
Liquid
Limit/%
Plastic
Limit/%
Plasticity
Index/%
Cohesion
c/kPa
Internal Friction
Angle φ/(◦)
Particle Composition/%
>0.075 mm 0.075–0.005 mm <0.005 mm
2.70 29.7 18.4 11.3 38.20 27.14 1.05 78.43 20.52
Buildings 2023,13, 1353 4 of 15
Buildings 2023, 13, x FOR PEER REVIEW 4 of 15
(a)
(b)
Figure 1. Modified pullout test device. (a) Overall, (b) Detailed design.
Dial Gauge
Oedometer
Beam
Soil
Container
Geogrid
Slit
Measurement
System
Sheet
Metal
Geogrid
Fixture
Guide
Rail
Wire Rope
Connectin
g Loading
System
Dial
Gauge
Supporting
Bracket
Rope
Fixture
Figure 1. Modied pullout test device. (a) Overall, (b) Detailed design.
Buildings 2023,13, 1353 5 of 15
Buildings 2023, 13, x FOR PEER REVIEW 5 of 15
0.01 0.1 1 10 100 1000
0
10
20
30
40
50
60
70
80
90
100
Finer by weight /%
Particle size /μm
Figure 2. Grain gradation curve.
Table 1. Physical and mechanical properties of soil samples.
Specific
Gravity
Liquid
Limit
/%
Plastic
Limit
/%
Plasticity In-
dex/%
Cohesion
c/kPa
Internal Friction
angle φ/(°)
Particle Composition/%
>0.075 mm
0.075–0.005 mm
<0.005 mm
2.70
29.7
18.4
11.3
38.20
27.14
1.05
78.43
20.52
High density polyethylene (HDPE) one-way geogrid is used in the test, as shown in
Figure 3. The width of the transverse rib and the width of the longitudinal rib of the ge-
ogrid are 19 mm and 5 mm, respectively. The thickness of the transverse rib and the
thickness of the longitudinal rib are 3.3 mm and 1 mm, respectively. The peak strain is
11.28%. Other basic mechanical properties are shown in Table 2. The single geogrid used
in the test is cut from the unidirectional geogrid sample, and the actual length of the sin-
gle geogrid is determined by the specimen mold.
Figure 3. HDPE one-way geogrid.
Table 2. Basic mechanical properties of geogrid.
Figure 2. Grain gradation curve.
Buildings 2023, 13, x FOR PEER REVIEW 5 of 15
0.01 0.1 1 10 100 1000
0
10
20
30
40
50
60
70
80
90
100
Finer by weight /%
Particle size /μm
Figure 2. Grain gradation curve.
Table 1. Physical and mechanical properties of soil samples.
Specific
Gravity
Liquid
Limit
/%
Plastic
Limit
/%
Plasticity In-
dex/%
Cohesion
c/kPa
Internal Friction
angle φ/(°)
Particle Composition/%
>0.075 mm
0.075–0.005 mm
<0.005 mm
2.70
29.7
18.4
11.3
38.20
27.14
1.05
78.43
20.52
High density polyethylene (HDPE) one-way geogrid is used in the test, as shown in
Figure 3. The width of the transverse rib and the width of the longitudinal rib of the ge-
ogrid are 19 mm and 5 mm, respectively. The thickness of the transverse rib and the
thickness of the longitudinal rib are 3.3 mm and 1 mm, respectively. The peak strain is
11.28%. Other basic mechanical properties are shown in Table 2. The single geogrid used
in the test is cut from the unidirectional geogrid sample, and the actual length of the sin-
gle geogrid is determined by the specimen mold.
Figure 3. HDPE one-way geogrid.
Table 2. Basic mechanical properties of geogrid.
Figure 3. HDPE one‑way geogrid.
Table 2. Basic mechanical properties of geogrid.
Geogrid Ultimate Tensile
Strength/(kN/m)
Percentage
Elongation/%
Tensile Strength at 2%
Strain/(kN/m)
Tensile Strength at 5%
Strain/(kN/m)
HDPE90 98.38 11.5 33.25 60.54
2.2. Test Method
In order to investigate the inuence of normal pressure, dry density, and water con‑
tent on interface creep behavior between compacted loess and geogrid, three groups of
pullout tests were designed as shown in Table 3. Disturbed loess at the required dry den‑
sity and water content was statically pressed into mold in two layers, and a strip of geogrid
was buried between two soil layers and reaching out from the slit in the middle of the mold.
The geogrid is placed on the guide rail to ensure a constant tension direction and connected
to the counterweights through a xture and wire rope. A sheet metal was bonded to the
beginning of the extended geogrid to install the probe of the displacement sensor. Thus,
the pullout displacement can be automatically recorded by the data measurement system
connected with the sensor. The pullout process is stress controlled by applying dierent
counterweights during 3–6 stages. During the test, it was found that when the pullout
stress is smaller than 40% of the ultimate pullout stress, creep deformation may not oc‑
cur. On the other hand, if the pullout stress is greater than 70% of the ultimate pullout
stress, the geogrid will be pulled in a rather short time. Therefore, the stress level in the
tests was controlled at 45%, 55%, and 65% of the ultimate pullout stress for each condi‑
tion. The convergence criterion of the test was set such that the deformation is smaller
than 0.01 mm increment within 24 h. It should be noted that the maximum deformation
Buildings 2023,13, 1353 6 of 15
of geogrid under ultimate pullout load was 0.0008 mm, which is far less than the conver‑
gence criterion. Hence, the inuence of the deformation of the geogrid was ignored. The
observed creep deformation will be treated as the relative slip deformation between soil
and geogrid. Standard GB/T 50123 (published by Ministry of Housing and Urban Rural
Development of China) was used for the above tests in our study.
Table 3. Test setup.
Group Sample No Normal
Pressure/kPa
Dry
Density/(g/cm3)Water Content/% Ultimate Pullout
Stress/kPa
1
S1 50
1.5 10
93.71
S2 100 173.33
S3 150 212.28
S4 200 234.25
2
G1
100
1.4
10
138.63
G2 1.5 173.33
G3 1.6 219.65
G4 1.7 267.71
3
H1
100 1.5
10 173.33
H2 15 143.45
H3 20 109.92
3. Results
3.1. Frictional Behavior of the Contact Interface
Before the creep test, the ultimate pullout stress was obtained through tests. Results
are shown in Figure 4. It can be seen that normal pressure, dry density, and water con‑
tent aect the ultimate pullout stresses greatly. Their relations are approximately linear.
Ultimate pullout stress increases with the increase of dry density of the compacted loess
because a denser soil means that more particles will be in contact with the surface of the
geogrid causing a higher surface friction and mechanical occlusion. An increase in water
content diminishes the friction properties of the interface of soil and geogrid leading to
a lower ultimate pullout stress [39]. Finally, ultimate pullout stress increases with the in‑
crease of normal pressure [40]. This is due to the friction property of the interface of the
two materials. These conclusions are similar to those found in the literature [23].
Furthermore, direct shear tests were conducted to make a comparison of the inter‑
face property of soil–soil and soil–geogrid. Figure 5shows the relation curve of shear
and pullout stress displacement relationship curve of the soil–soil and the soil–geogrid
interfaces. The shear stress and pullout stress of the interface were calculated through
Equations (1) and (2), respectively:
τs=Ts
As
(1)
τp=Tp
2Ap
(2)
where, Tsand Tpare the shear force obtained from shear tests and pullout tests, respec‑
tively; Asand Apare the area of contacted faces of soil and geogrid in direct shear test and
pullout test, respectively.
Buildings 2023,13, 1353 7 of 15
Buildings 2023, 13, x FOR PEER REVIEW 7 of 15
because a denser soil means that more particles will be in contact with the surface of the
geogrid causing a higher surface friction and mechanical occlusion. An increase in water
content diminishes the friction properties of the interface of soil and geogrid leading to a
lower ultimate pullout stress [39]. Finally, ultimate pullout stress increases with the in-
crease of normal pressure [40]. This is due to the friction property of the interface of the
two materials. These conclusions are similar to those found in the literature [23].
(a)
(b)
(c)
Figure 4. Ultimate pullout stress. (a) Dry density, (b) water content, (c) normal pressure.
Furthermore, direct shear tests were conducted to make a comparison of the inter-
face property of soil–soil and soil–geogrid. Figure 5 shows the relation curve of shear
and pullout stress displacement relationship curve of the soil–soil and the soil–geogrid
interfaces. The shear stress and pullout stress of the interface were calculated through
Equations (1) and (2), respectively:
s
s
s
T
A
=
(1)
2
p
p
p
T
A
=
(2)
where, Ts and Tp are the shear force obtained from shear tests and pullout tests, respec-
tively; As and Ap are the area of contacted faces of soil and geogrid in direct shear test
and pullout test, respectively.
It can be seen from Figure 5 that the pullout force of the reinforced soil interface in-
creases nonlinearly with the increase of the horizontal displacement. With the increase of
normal pressure, the pullout force required under the same horizontal displacement of
1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75
120
140
160
180
200
220
240
260
280
Ultimate pullout strength (kPa)
Dry density (g/cm3)
912 15 18 21
100
110
120
130
140
150
160
170
180
Ultimate pullout strength (kPa)
Water content (%)
40 60 80 100 120 140 160 180 200 220
80
100
120
140
160
180
200
220
240
Ultimate pullout strength (kPa)
Normal pressure (KPa)
Figure 4. Ultimate pullout stress. (a) Dry density, (b) water content, (c) normal pressure.
Buildings 2023, 13, x FOR PEER REVIEW 8 of 15
the soil–geogrid interface gradually increases. Under all normal pressure, the relation-
ship curve of shear stress and shear displacement of direct shear test show a strain sof-
tening pattern. The greater the normal pressure applied, the greater the shear displace-
ment needed for a given peak shear stress. Both peak values and residual values of the
results of direct shear tests were recorded and their relations with normal pressure are
shown in Figure 6. On the other hand, the displacement–stress curves of the pullout tests
were of the strain-hardening type. The relationship between pullout strength and nor-
mal pressure is also shown in Figure 6. The cohesion and internal friction angle of loess
through direct shear test are 38.20 kPa and 27.14°, respectively, for peak strength, and for
the residual strength, the indexes are 9.6 kPa and 30.6°, respectively. As for the pullout
strength of the interface of compacted loess and geogrid, the cohesion is 41.47 kPa, and
the internal friction angle is 32.44°. It is clear that the internal friction angle of the four
test results is similar while cohesion varied greatly. The internal friction angle of the re-
sidual strength is closer to pullout strength. This is because the residual strength can bet-
ter reflect the frictional behavior of the soil.
0 2 4 6 8 10 12
0
40
80
120
160
200
50 kPa
100 kPa
150 kPa
200 kPa
τp /kPa
Lp /mm
0.0 0.9 1.8 2.7 3.6 4.5
0
25
50
75
100
125
150
50kPa
100 kPa
150 kPa
200 kPa
τs /kPa
Ls /mm
(a)
(b)
Figure 5. L-τ curve of pullout tests and direct shear tests. (a) Pullout test results, (b) direct shear
test results.
20 40 60 80 100 120 140 160 180 200 220
20
40
60
80
100
120
140
160
180
Soil-soil(Peak value)
Soil-soil(Residual value)
Soil-geogrid
Fitting line
Strength τ /kPa
Normal pressure /kPa
y = 0.59x+9.6
R2 = 0.9642
y = 0.64x+41.47
R2 = 0.9764
y = 0.51x+38.20
R2 = 0.9959
Figure 6. P-τ curve.
3.2. Creep Behavior of the Interface of Compacted Loess and Geogrid
In order to investigate the influence of normal pressure, dry density, and water con-
tent on the time-varying behavior of the interface of compacted loess and geogrid,
pullout tests were conducted under four normal pressures, four dry densities, and three
water content levels. Three tensile levels were considered in the tests, and the graded
Figure 5. L‑τcurve of pullout tests and direct shear tests. (a) Pullout test results, (b) direct shear
test results.
It can be seen from Figure 5that the pullout force of the reinforced soil interface in‑
creases nonlinearly with the increase of the horizontal displacement. With the increase
of normal pressure, the pullout force required under the same horizontal displacement of
the soil–geogrid interface gradually increases. Under all normal pressure, the relationship
curve of shear stress and shear displacement of direct shear test show a strain softening pat‑
tern. The greater the normal pressure applied, the greater the shear displacement needed
for a given peak shear stress. Both peak values and residual values of the results of direct
shear tests were recorded and their relations with normal pressure are shown in Figure 6.
Buildings 2023,13, 1353 8 of 15
On the other hand, the displacement–stress curves of the pullout tests were of the strain‑
hardening type. The relationship between pullout strength and normal pressure is also
shown in Figure 6. The cohesion and internal friction angle of loess through direct shear
test are 38.20 kPa and 27.14◦, respectively, for peak strength, and for the residual strength,
the indexes are 9.6 kPa and 30.6◦, respectively. As for the pullout strength of the interface
of compacted loess and geogrid, the cohesion is 41.47 kPa, and the internal friction angle is
32.44◦. It is clear that the internal friction angle of the four test results is similar while cohe‑
sion varied greatly. The internal friction angle of the residual strength is closer to pullout
strength. This is because the residual strength can beer reect the frictional behavior of
the soil.
Buildings 2023, 13, x FOR PEER REVIEW 8 of 15
the soil–geogrid interface gradually increases. Under all normal pressure, the relation-
ship curve of shear stress and shear displacement of direct shear test show a strain sof-
tening pattern. The greater the normal pressure applied, the greater the shear displace-
ment needed for a given peak shear stress. Both peak values and residual values of the
results of direct shear tests were recorded and their relations with normal pressure are
shown in Figure 6. On the other hand, the displacement–stress curves of the pullout tests
were of the strain-hardening type. The relationship between pullout strength and nor-
mal pressure is also shown in Figure 6. The cohesion and internal friction angle of loess
through direct shear test are 38.20 kPa and 27.14°, respectively, for peak strength, and for
the residual strength, the indexes are 9.6 kPa and 30.6°, respectively. As for the pullout
strength of the interface of compacted loess and geogrid, the cohesion is 41.47 kPa, and
the internal friction angle is 32.44°. It is clear that the internal friction angle of the four
test results is similar while cohesion varied greatly. The internal friction angle of the re-
sidual strength is closer to pullout strength. This is because the residual strength can bet-
ter reflect the frictional behavior of the soil.
0 2 4 6 8 10 12
0
40
80
120
160
200
50 kPa
100 kPa
150 kPa
200 kPa
τp /kPa
Lp /mm
0.0 0.9 1.8 2.7 3.6 4.5
0
25
50
75
100
125
150
50kPa
100 kPa
150 kPa
200 kPa
τs /kPa
Ls /mm
(a)
(b)
Figure 5. L-τ curve of pullout tests and direct shear tests. (a) Pullout test results, (b) direct shear
test results.
20 40 60 80 100 120 140 160 180 200 220
20
40
60
80
100
120
140
160
180
Soil-soil(Peak value)
Soil-soil(Residual value)
Soil-geogrid
Fitting line
Strength τ /kPa
Normal pressure /kPa
y = 0.59x+9.6
R2 = 0.9642
y = 0.64x+41.47
R2 = 0.9764
y = 0.51x+38.20
R2 = 0.9959
Figure 6. P-τ curve.
3.2. Creep Behavior of the Interface of Compacted Loess and Geogrid
In order to investigate the influence of normal pressure, dry density, and water con-
tent on the time-varying behavior of the interface of compacted loess and geogrid,
pullout tests were conducted under four normal pressures, four dry densities, and three
water content levels. Three tensile levels were considered in the tests, and the graded
Figure 6. P‑τcurve.
3.2. Creep Behavior of the Interface of Compacted Loess and Geogrid
In order to investigate the inuence of normal pressure, dry density, and water con‑
tent on the time‑varying behavior of the interface of compacted loess and geogrid, pullout
tests were conducted under four normal pressures, four dry densities, and three water
content levels. Three tensile levels were considered in the tests, and the graded loading
method was adopted. The Bolmann superposition principle [41] was used to obtain the
separated creep curve of the test results. Figure 7shows the typical pullout creep displace‑
ment curves of the specimens under dierent conditions.
It can be seen from Figure 7that during the early stage of the test, pullout displacement
grew rapidly, slowed down over time, and became stable when a certain time was reached.
This is very similar to the creep deformation behavior of compacted loess, which is not
surprising since these two processes are both related to interfacial friction characteristics
of compacted loess [30]. Compared to compacted loess, the creep behavior of the interface
of soil and geogrid has fast convergence speed since its frictional property is more implicit.
With the increase of loading level, the convergence time became longer.
According to the results shown in Figure 7b–d, normal pressure, dry density, and
the water content of compacted loess have notable eects on the creep property of the
interface of compacted loess and geogrid. When pullout load level and other conditions
remain unchanged, the creep displacement of the soil–geogrid interface decreases with
the increase of normal pressure, decreases with the increase of dry density, and increases
with the increase of water content. These results indicate that in practical engineering, the
potential of creep displacement of the soil–geogrid interface can be greatly reduced by
increasing the degree of compaction of soil and improving drainage, so as to improve the
stability and safety of the lling foundation and lling slope.
Buildings 2023,13, 1353 9 of 15
Buildings 2023, 13, x FOR PEER REVIEW 9 of 15
loading method was adopted. The Boltzmann superposition principle [41] was used to
obtain the separated creep curve of the test results. Figure 7 shows the typical pullout
creep displacement curves of the specimens under different conditions.
It can be seen from Figure 7 that during the early stage of the test, pullout dis-
placement grew rapidly, slowed down over time, and became stable when a certain time
was reached. This is very similar to the creep deformation behavior of compacted loess,
which is not surprising since these two processes are both related to interfacial friction
characteristics of compacted loess [30]. Compared to compacted loess, the creep behav-
ior of the interface of soil and geogrid has fast convergence speed since its frictional
property is more implicit. With the increase of loading level, the convergence time be-
came longer.
According to the results shown in Figure 7b–d, normal pressure, dry density, and
the water content of compacted loess have notable effects on the creep property of the
interface of compacted loess and geogrid. When pullout load level and other conditions
remain unchanged, the creep displacement of the soil–geogrid interface decreases with
the increase of normal pressure, decreases with the increase of dry density, and increases
with the increase of water content. These results indicate that in practical engineering,
the potential of creep displacement of the soil–geogrid interface can be greatly reduced
by increasing the degree of compaction of soil and improving drainage, so as to improve
the stability and safety of the filling foundation and filling slope.
(a)
(b)
(c)
(d)
Figure 7. Shear displacement and time creep curve of reinforced soil interface. (a) Influence of
pullout loading levels, (b) influence of normal pressure, (c) influence of dry density, (d) influence
of water content.
4. Discussion
4.1. A Three-Parameter Empirical Model for the Interface Creep Behavior
0500 1000 1500 2000 2500
1
2
3
4
5
6
7
8
9
10
Displacement /mm
Time /min
Pullout load level = 45%
Pullout load level = 55%
Pullout load level = 65%
0500 1000 1500 2000 2500
1
2
3
4
5
6
7
Displacement /mm
Time /min
s=50kPa Pullout load level = 55%
s=150kPa Pullout load level = 55%
s=200kPa Pullout load level = 55%
s=100kPa Pullout load level = 55%
0500 1000 1500 2000 2500
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
Displacement /mm
Time /min
r=1.4g/cm3
r=1.5g/cm3
r=1.6g/cm3
r=1.7g/cm3
0500 1000 1500 2000 2500
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
水平位移 /mm
Time /min
w=10%
w=15%
w=20%
Figure 7. Shear displacement and time creep curve of reinforced soil interface. (a) Inuence of pull‑
out loading levels, (b) inuence of normal pressure, (c) inuence of dry density, (d) inuence of
water content.
4. Discussion
4.1. A Three‑Parameter Empirical Model for the Interface Creep Behavior
To predict the creep behavior of the interface of compacted loess and geogrid based on
acquired deformation data, a R‑Q‑λthree‑parameter empirical model was introduced. A
ing analysis was conducted on the test results. Based on the creep test data with normal
pressure, dry density, and water content at 100 kPa, 1.5 g/cm3, and 10%, respectively, the
hyperbolic relationship of ln(L/t)−ln(t) was established. It can be seen from Figure 8that
at any tension level, ln(L/t)−ln(t) shows a good linear relationship, which can be expressed
as follows:
ln(L/t) = G+ (λ−1)ln(t)(3)
where Gis the intercept of ln(L/t)−ln (t) curve, λ−1 is the absolute value of the curve
slope, representing the aenuation rate of ln(L/t) with ln(t).
According to Figure 9,Gincreases with the increase of ln(τ), showing a good linear
relationship, as shown in Equation (4):
G=Qln(τ) + R(4)
Expression of the R‑Q‑λempirical model can be obtained by substituting Equation (4)
into Equation (3) as:
L=eRτQtλ(5)
where Q,R, and λare all the ing parameters. The results of the above test parameters
are as follows: λis in the range (0.0137, 0.0334), Q= 4.5312, R=−19.2911. Using this
three‑parameter model, the ing parameters for the test results under dierent inuenc‑
Buildings 2023,13, 1353 10 of 15
ing factors are calculated through ing analysis. Inuence of the normal pressure, dry
density, and water content on the model parameters are shown in Figure 10.
Buildings 2023, 13, x FOR PEER REVIEW 10 of 15
To predict the creep behavior of the interface of compacted loess and geogrid based
on acquired deformation data, a R-Q-λ three-parameter empirical model was intro-
duced. A fitting analysis was conducted on the test results. Based on the creep test data
with normal pressure, dry density, and water content at 100 kPa, 1.5 g/cm3, and 10%, re-
spectively, the hyperbolic relationship of ln(L/t) − ln(t) was established. It can be seen
from Figure 8 that at any tension level, ln(L/t) − ln(t) shows a good linear relationship,
which can be expressed as follows:
ln( / ) ( 1)ln( )L t G t
= + −
(3)
where G is the intercept of ln(L/t) − ln (t) curve, λ − 1 is the absolute value of the curve
slope, representing the attenuation rate of ln(L/t) with ln(t).
02468
-8
-6
-4
-2
0
2
4
74.94kPa
93.67kPa
112.40kPa
Fitting result
ln(L/t)
ln(t)
Figure 8. ln(L/t) − ln(t) Curve.
According to Figure 9, G increases with the increase of ln(τ), showing a good linear
relationship, as shown in Equation (4):
ln( )G Q R
=+
(4)
Expression of the R-Q-λ empirical model can be obtained by substituting Equation
(4) into Equation (3) as:
RQ
L e t
=
(5)
where Q, R, and λ are all the fitting parameters. The results of the above test parameters
are as follows: λ is in the range (0.0137, 0.0334), Q = 4.5312, R = −19.2911. Using this
three-parameter model, the fitting parameters for the test results under different influ-
encing factors are calculated through fitting analysis. Influence of the normal pressure,
dry density, and water content on the model parameters are shown in Figure 10.
Figure 8. ln(L/t)−ln(t) Curve.
Buildings 2023, 13, x FOR PEER REVIEW 11 of 15
4.3 4.4 4.5 4.6 4.7 4.8
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
parameter combination
Fitting line
G
ln(τ) /kPa
2
4.53ln( ) 19.29
0.9720
G
R
=−
=
Figure 9. G-ln(τ) curve.
(a)
(b)
(c)
Figure 10. Fitting results. (a) Normal pressure (b) dry density, (c) water content.
As shown in Figure 10, parameters Q and λ almost remain unchanged under differ-
ent normal pressure, dry density, and water content. On the other hand, parameter R de-
creases with the increase of normal pressure and dry density and increases with the in-
crease of water content. This shows that normal pressure, dry density, and water content
have a small influence on parameters Q and λ, but parameter R is greatly influenced. Pa-
rameter Q reflects the change trend of relative slip displacement with pullout stress per
unit time. The values of Q under different influencing factors are basically the same, in-
dicating that the shape of the curve is similar. Parameter R is the logarithm of secant
40 60 80 100 120 140 160 180 200 220
-30
-25
-20
-15
-10
-5
0
5
10
Q
R
λ1
λ2
λ3
Parameters
Confining pressure /kPa
1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75
-30
-25
-20
-15
-10
-5
0
5
10
Q
R
λ1
λ2
λ3
Parameters
Dry density /g∙cm-3
912 15 18 21
-15.0
-7.5
0.0
7.5
Q
R
λ1
λ2
λ3
Parameters
Water Content /%
Figure 9. G‑ln(τ) curve.
As shown in Figure 10, parameters Qand λalmost remain unchanged under dier‑
ent normal pressure, dry density, and water content. On the other hand, parameter R
decreases with the increase of normal pressure and dry density and increases with the in‑
crease of water content. This shows that normal pressure, dry density, and water content
have a small inuence on parameters Qand λ, but parameter Ris greatly inuenced. Pa‑
rameter Qreects the change trend of relative slip displacement with pullout stress per
unit time. The values of Qunder dierent inuencing factors are basically the same, indi‑
cating that the shape of the curve is similar. Parameter Ris the logarithm of secant strain
rate at unit time and unit shear stress. When the dry density of soil is small, the water con‑
tent is large, or the applied normal pressure is small, the shear failure of the interface of
compacted loess and geogrid is more likely to occur, the value of Ris thus larger. Param‑
eter λreects the hyperbolic relationship between the shear displacement rate and time.
Parameter λfor the test results in this paper have small uctuation which is ranged from
0 to 0.11.
Buildings 2023,13, 1353 11 of 15
Buildings 2023, 13, x FOR PEER REVIEW 11 of 15
4.3 4.4 4.5 4.6 4.7 4.8
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
parameter combination
Fitting line
G
ln(τ) /kPa
2
4.53ln( ) 19.29
0.9720
G
R
=−
=
Figure 9. G-ln(τ) curve.
(a)
(b)
(c)
Figure 10. Fitting results. (a) Normal pressure (b) dry density, (c) water content.
As shown in Figure 10, parameters Q and λ almost remain unchanged under differ-
ent normal pressure, dry density, and water content. On the other hand, parameter R de-
creases with the increase of normal pressure and dry density and increases with the in-
crease of water content. This shows that normal pressure, dry density, and water content
have a small influence on parameters Q and λ, but parameter R is greatly influenced. Pa-
rameter Q reflects the change trend of relative slip displacement with pullout stress per
unit time. The values of Q under different influencing factors are basically the same, in-
dicating that the shape of the curve is similar. Parameter R is the logarithm of secant
40 60 80 100 120 140 160 180 200 220
-30
-25
-20
-15
-10
-5
0
5
10
Q
R
λ1
λ2
λ3
Parameters
Confining pressure /kPa
1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75
-30
-25
-20
-15
-10
-5
0
5
10
Q
R
λ1
λ2
λ3
Parameters
Dry density /g∙cm-3
912 15 18 21
-15.0
-7.5
0.0
7.5
Q
R
λ1
λ2
λ3
Parameters
Water Content /%
Figure 10. Fiing results. (a) Normal pressure (b) dry density, (c) water content.
4.2. Merchant Model for the Interface Creep Behavior
The above empirical model is capable of describing the creep characteristics of the in‑
terface of compacted loess and geogrid. However, the model is not universal. The physical
meaning of the model parameters is not intuitive and is thus more suitable for application
in specic engineering projects. On the other hand, the component model has a clear physi‑
cal meaning and is thus more widely used in the modeling of creep behavior. In this paper,
a Merchant component model, which is composed of Hooke component and Kelvin com‑
ponent in series, was selected to study the creep deformation property of the interface of
compacted loess and geogrid. The model equation is:
L(t) = τ0
E0
+τ0
E1[1−e(−E1
η1t)](6)
where L(t) is the creep displacement value of the interface at arbitrary time. τ0is the pullout
load. E0is the elastic coecient of the Hooke model. E1and η1are the elastic coecient
and viscosity coecient of the Kelvin model, respectively. Using data analysis software
Origin, ing analysis was carried out for all test data. Fiing results for the conditions of
normal pressure at 100 kPa, dry density at 1.5 g/cm3, and water content at 10% is shown in
Figure 11. The correlation coecient of the model ing is above 0.98, indicating that the
element model can beer describe the creep property of the interface of compacted loess
and geogrid.
Here, the three‑parameter empirical model and the merchant model were compared
using the ing results of the condition of P= 100 kPa, ρd= 1.5 g/cm3, and ω= 10%. The
comparison results are shown in Figure 12 and Table 4(the pullout load is kept at 45% of
the ultimate strength). It can be seen from the comparison results that, in the early stage
of creep deformation, the prediction curve calculated by the Merchant model is closer to
the curve of the laboratory test value than that calculated by the three‑parameter empiri‑
Buildings 2023,13, 1353 12 of 15
cal model. In the late stage of creep, the calculated value of the Merchant model is basi‑
cally unchanged indicating that the Merchant model has a strong convergence, while the
calculated value of the three‑parameter empirical model is closer to the actual test value.
Its relative error is within 2%. This shows that the three‑parameter empirical model can
provide beer reference for the study of long‑term creep displacement of the interface of
compacted loess and geogrid in practical engineering.
Buildings 2023, 13, x FOR PEER REVIEW 12 of 15
strain rate at unit time and unit shear stress. When the dry density of soil is small, the
water content is large, or the applied normal pressure is small, the shear failure of the in-
terface of compacted loess and geogrid is more likely to occur, the value of R is thus
larger. Parameter λ reflects the hyperbolic relationship between the shear displacement
rate and time. Parameter λ for the test results in this paper have small fluctuation which
is ranged from 0 to 0.11.
4.2. Merchant Model for the Interface Creep Behavior
The above empirical model is capable of describing the creep characteristics of the
interface of compacted loess and geogrid. However, the model is not universal. The
physical meaning of the model parameters is not intuitive and is thus more suitable for
application in specific engineering projects. On the other hand, the component model
has a clear physical meaning and is thus more widely used in the modeling of creep be-
havior. In this paper, a Merchant component model, which is composed of Hooke com-
ponent and Kelvin component in series, was selected to study the creep deformation
property of the interface of compacted loess and geogrid. The model equation is:
1
1
00
01
( ) 1
Et
L t e
EE
−
= + −
(6)
where L(t) is the creep displacement value of the interface at arbitrary time. τ0 is the
pullout load. E0 is the elastic coefficient of the Hooke model. E1 and η1 are the elastic co-
efficient and viscosity coefficient of the Kelvin model, respectively. Using data analysis
software Origin, fitting analysis was carried out for all test data. Fitting results for the
conditions of normal pressure at 100 kPa, dry density at 1.5 g/cm3, and water content at
10% is shown in Figure 11. The correlation coefficient of the model fitting is above 0.98,
indicating that the element model can better describe the creep property of the interface
of compacted loess and geogrid.
Here, the three-parameter empirical model and the merchant model were com-
pared using the fitting results of the condition of P = 100 kPa, ρd = 1.5 g/cm3, and ω =
10%. The comparison results are shown in Figure 12 and Table 4 (the pullout load is kept
at 45% of the ultimate strength). It can be seen from the comparison results that, in the
early stage of creep deformation, the prediction curve calculated by the Merchant model
is closer to the curve of the laboratory test value than that calculated by the three-
parameter empirical model. In the late stage of creep, the calculated value of the Mer-
chant model is basically unchanged indicating that the Merchant model has a strong
convergence, while the calculated value of the three-parameter empirical model is closer
to the actual test value. Its relative error is within 2%. This shows that the three-
parameter empirical model can provide better reference for the study of long-term creep
displacement of the interface of compacted loess and geogrid in practical engineering.
0500 1000 1500 2000 2500
1
2
3
4
5
6
7
8
9
10
74.94kPa
93.67kPa
112.40kPa
Fitting curve
Displacement /mm
Time /min
Figure 11. Merchant model ing curve.
Buildings 2023, 13, x FOR PEER REVIEW 13 of 15
Figure 11. Merchant model fitting curve.
0500 1000 1500 2000 2500
1
2
3
4
5
6
7
8
9
10
74.94kPa
93.67kPa
112.40kPa
three-parameter empirical model
Merchant model
Displacement /mm
Time /min
Figure 12. Comparison between model calculation value and test value.
Table 4. Error analysis of calculated values of two creep models.
Horizontal
Tension/kPa
Time/min
Test Value/mm
Empirical Mod-
el Value/mm
Relative Er-
ror/%
Merchant Model
Value/mm
Relative Er-
ror/%
93.67
5
4.67
4.3558
6.728
4.9014
4.955
60
4.89
4.7743
2.366
4.9218
0.650
120
4.95
4.7874
3.285
4.9229
0.547
300
5.01
4.9157
1.882
4.9239
1.719
960
5.01
5.0893
1.583
4.9241
1.715
According to the comparison analysis, it can be concluded that both the three-
parameter empirical model and the Merchant model are capable of reflecting the creep
behavior of the interface of compacted loess and geogrid. The Merchant model is more
accurate in the early stage of the creep deformation, while the three-parameter empirical
model is more suitable for predicting the long-term creep deformation of the interface of
compacted loess and geogrid.
5. Conclusions
In this study, to investigate the creep behavior of the interface of compacted loess
and high-density polyethylene (HDPE) geogrid, a series of laboratory pullout creep tests
were carried out. A new stress-controlled pullout testing device was invented by modi-
fying the oedometer. The influence of the normal pressure, dry density, and water con-
tent on the creep behavior of the compacted loess–geogrid interface was studied. An
empirical creep model and a component creep model were applied to the test results and
comparatively studied. According to test results, normal pressure, dry density, and wa-
ter content affects the creep behavior of the interface of compacted loess and geogrid
significantly. Under the same pullout level, creep displacement of the interface increases
with the increase of water content and decreases with the increase of dry density and
normal pressure. The established three-parameter empirical model and Merchant model
can both describe the creep behavior of the interface of compacted loess and geogrid
well. The Merchant model is more accurate in the early stage, while the three-parameter
empirical model is more suitable for predicting the long-term creep deformation of the
interface of compacted loess and geogrid. In practical engineering, the potential of creep
deformation of soil–geogrid can be greatly reduced by increasing the degree of compac-
tion of soil and improving drainage, and the stability and safety of filling foundation or
filling slope can be improved.
Figure 12. Comparison between model calculation value and test value.
Table 4. Error analysis of calculated values of two creep models.
Horizontal
Tension/kPa Time/min Test
Value/mm
Empirical Model
Value/mm
Relative
Error/%
Merchant Model
Value/mm
Relative
Error/%
93.67
5 4.67 4.3558 6.728 4.9014 4.955
60 4.89 4.7743 2.366 4.9218 0.650
120 4.95 4.7874 3.285 4.9229 0.547
300 5.01 4.9157 1.882 4.9239 1.719
960 5.01 5.0893 1.583 4.9241 1.715
According to the comparison analysis, it can be concluded that both the three‑
parameter empirical model and the Merchant model are capable of reecting the creep
behavior of the interface of compacted loess and geogrid. The Merchant model is more
accurate in the early stage of the creep deformation, while the three‑parameter empirical
model is more suitable for predicting the long‑term creep deformation of the interface of
compacted loess and geogrid.
Buildings 2023,13, 1353 13 of 15
5. Conclusions
In this study, to investigate the creep behavior of the interface of compacted loess and
high‑density polyethylene (HDPE) geogrid, a series of laboratory pullout creep tests were
carried out. A new stress‑controlled pullout testing device was invented by modifying the
oedometer. The inuence of the normal pressure, dry density, and water content on the
creep behavior of the compacted loess–geogrid interface was studied. An empirical creep
model and a component creep model were applied to the test results and comparatively
studied. According to test results, normal pressure, dry density, and water content aects
the creep behavior of the interface of compacted loess and geogrid signicantly. Under
the same pullout level, creep displacement of the interface increases with the increase of
water content and decreases with the increase of dry density and normal pressure. The
established three‑parameter empirical model and Merchant model can both describe the
creep behavior of the interface of compacted loess and geogrid well. The Merchant model
is more accurate in the early stage, while the three‑parameter empirical model is more suit‑
able for predicting the long‑term creep deformation of the interface of compacted loess and
geogrid. In practical engineering, the potential of creep deformation of soil–geogrid can
be greatly reduced by increasing the degree of compaction of soil and improving drainage,
and the stability and safety of lling foundation or lling slope can be improved.
Author Contributions: Y.‑L.Y.: Conceptualization, Writing—original draft. C.‑M.H.: Methodol‑
ogy, Supervision. J.X.: Data curation, Formal analysis. Y.M.: Funding acquisition, Investigation.
F.‑F.W.: Data curation; G.W.: Visualization. All authors have read and agreed to the published ver‑
sion of the manuscript.
Funding: This research was nancially supported by the National Natural Science Foundation of
China (Grant No. 52178302), the Key R & D Projects in Shaanxi Province (No. 2020SF‑373), and the
Natural Science Basic Research Program of Shaanxi [grant number 2022JQ‑375].
Data Availability Statement: The data presented in this study are available on request from the
corresponding authors.
Acknowledgments: We are grateful for the generous support provided by National Natural Science
Foundation of China, the Key R & D Projects in Shaanxi Province, and the Natural Science Basic
Research Program of Shaanxi. We thank the reviewers for their valuable feedback.
Conicts of Interest: The authors declare no conict of interest.
References
1. Koo, H.; Kim, Y. Lifetime Prediction of Geogrids for Reinforcement of Embankments and Slopes. Polym. Test. 2005,24, 181–188.
[CrossRef]
2. Pan, G.; Liu, X.; Yuan, S.; Wang, Y.; Sun, D.; Feng, Y.; Jiang, G. A Field Study on the Arching Behavior of a Geogrid‑Reinforced
Floating Pile‑Supported Embankment. Transp. Geotech. 2022,37, 100795. [CrossRef]
3. Jyothi, B.D.; Krishna, V.R. Optimal Arrangement of Geogrids in Road Embankment Using Dierent Fill Materials. Mater. Today
Proc. 2021,46, 8507–8512. [CrossRef]
4. Kim, U.J.; Kim, D.S. Load Sharing Characteristics of Rigid Facing Walls with Geogrid Reinforced Railway Subgrade During and
After Construction. Geotext. Geomembr. 2020,48, 940–949. [CrossRef]
5. Esmaeili, M.; Zakeri, J.A.; Babaei, M. Laboratory and Field Investigation of the Eect of Geogrid‑Reinforced Ballast on Railway
Track Lateral Resistance. Geotext. Geomembr. 2017,45, 23–33. [CrossRef]
6. Uchimura, T.; Tateyama, M.; Tanaka, I.; Tatsuoka, F. Performance of a Preloaded‑Prestressed Geogrid‑Reinforced Soil Pier for a
Railway Bridge. Soils Found. 2003,43, 155–171. [CrossRef]
7. Ke, H.; Ma, P.; Lan, J.; Chen, Y.; He, H. Field Behaviors of a Geogrid Reinforced Msw Slope in a High‑Food‑Waste‑Content Msw
Landll: A Case Study. Geotext. Geomembr. 2021,49, 430–441. [CrossRef]
8. Alamshahi, S.; Hataf, N. Bearing Capacity of Strip Footings on Sand Slopes Reinforced with Geogrid and Grid‑Anchor. Geotext.
Geomembr. 2009,27, 217–226. [CrossRef]
9. Batali, L.; Klompmaker, J.; Tronac, B. Geosynthetic Reinforced Soil Structure—Problems Faced and Lessons Learned.
Case Studies from Romania. In Proceedings of the EuroGeo 6, 6th European Geosynthetics Congress, Ljubljana, Slovenia,
25–28 September 2016.
10. Mirmoradi, S.H.; Ehrlich, M. Experimental Evaluation of the Eects of Surcharge Width and Location on Geosynthetic‑
Reinforced Soil Walls. Int. J. Phys. Model. Geotech. 2019,19, 27–36. [CrossRef]
Buildings 2023,13, 1353 14 of 15
11. Liu, Y.; Zhao, Y.; Zhang, D.; Liu, Z. The Long‑Term Mechanical Performance of Geogrid‑Reinforced Soil Retaining Walls Under
Cyclic Footing Loading. Case Stud. Constr. Mater. 2022,17, e1642. [CrossRef]
12. Wang, H.; Yang, G.; Wang, Z.; Liu, W. Static Structural Behavior of Geogrid Reinforced Soil Retaining Walls with a Deformation
Buer Zone. Geotext. Geomembr. 2020,48, 374–379. [CrossRef]
13. Useche‑Infante, D.; Martinez, G.A.; Arrúa, P.; Eberhardt, M. Experimental Study of Behaviour of Circular Footing on Geogrid‑
Reinforced Sand. Geomech. Geoengin. Int. J. 2022,17, 45–63. [CrossRef]
14. Suksiripaanapong, C.; Horpibulsuk, S.; Udomchai, A.; Arulrajah, A.; Tangsuhinon, T. Pullout Resistance Mechanism of Bear‑
ing Reinforcement Embedded in Coarse‑Grained Soils: Laboratory and Field Investigations. Transp. Geotech. 2020,22, 100297.
[CrossRef]
15. Ferreira, F.B.; Vieira, C.S.; Lopes, M.D.L. Pullout Behavior of Dierent Geosynthetics—Inuence of Soil Density and Moisture
Content. Front. Built Environ. 2020,6, 12. [CrossRef]
16. Brown, S.F.; Kwan, J.; Thom, N.H. Identifying the Key Parameters that Inuence Geogrid Reinforcement of Railway Ballast.
Geotext. Geomembr. 2007,25, 326–335. [CrossRef]
17. Moraci, N.; Recalcati, P. Factors Aecting the Pullout Behaviour of Extruded Geogrids Embedded in a Compacted Granular Soil.
Geotext. Geomembr. 2006,24, 220–242. [CrossRef]
18. Baadiga, R.; Saride, S.; Balunaini, U.; Madhira, M.R. Inuence of Tensile Strength of Geogrid and Subgrade Modulus on Layer
Coecients of Granular Bases. Transp. Geotech. 2021,29, 100557. [CrossRef]
19. Yuan, Y.L.; Hu, C.M.; Mei, Y.; Wang, X.Y.; Wang, J. Slope Reliability Analysis Based on Curvilinear Local Averaging of a 2‑D
Random Field. Comput. Geotech. 2021,137, 104247. [CrossRef]
20. Mei, Y.; Zhang, X.; Nong, X.; Fu, L. Experimental Study of the Comprehensive Technology of Grouting and Suspension Under
an Operating Railway in the Cobble Stratum. Transp. Geotech. 2021,30, 100612. [CrossRef]
21. Hatami, K.; Mahmood, T.; Ghabchi, R.; Zaman, M. Inuence of in‑Isolation Properties of Geogrids On their Pullout Performance
in a Dense Graded Aggregate. Indian Geotech. J. 2013,43, 303–320. [CrossRef]
22. Esmaeili, M.; Pourrashnoo, A. Experimental Investigation of Shear Strength Parameters of Ballast Encased with Geogrid. Constr.
Build. Mater. 2022,335, 127491. [CrossRef]
23. Mirzaeifar, H.; Hatami, K.; Abdi, M.R. Pullout Testing and Particle Image Velocimetry (Piv) Analysis of Geogrid Reinforcement
Embedded in Granular Drainage Layers. Geotext. Geomembr. 2022,50, 1083–1109. [CrossRef]
24. Moraci, N.; Cardile, G.; Giorè, D.; Mandaglio, M.C.; Calvarano, L.S.; Carbone, L. Soil Geosynthetic Interaction: Design Param‑
eters from Experimental and Theoretical Analysis. Transp. Infrastruct. Geotechnol. 2014,1, 165–227. [CrossRef]
25. Pant, A.; Ramana, G.V. Prediction of Pullout Interaction Coecient of Geogrids by Extreme Gradient Boosting Model. Geotext.
Geomembr. 2022,50, 1188–1198. [CrossRef]
26. He, Z.; Mo, H.; Siga, A.; Zou, J. Research on the Parameters of Nonlinear Hyperbolic Model for Clay‑Geogrid Interfaces Based
On Large Scale Direct Shear Tests. Transp. Geotech. 2019,18, 39–45. [CrossRef]
27. Sven, S.; Ulrich, T.; Danny, O.; Andrey, P.; Daniil, T. Comparison of Pullout Test Results Carried Out on Steel Grid and Geosyn‑
thetic Materials. In Proceedings of the 11th International Conference on Geosynthetics 2018, ICG 2018, Seoul, Republic of Korea,
16–21 September 2018.
28. Baoqin, L.; Xingang, W.; Zhan, H.; Jiading, W.; Jianbing, P.; Tianfeng, G.; Rongsen, Z. Creep Mechanical and Microstructural
Insights Into the Failure Mechanism of Loess Landslides Induced by Dry‑Wet Cycles in the Heifangtai Platform, China. Eng.
Geol. 2022,300, 106589.
29. Zhu, C.; Zhou, X.; Wang, S.; Sara, <