Revista de la Facultad de Ingeniería U.C.V., Vol. 31, N°3, pp. 40-48, 2016
doi:10.21311/002.31.3.04
Numerical Analysis on Deformation Behavior of GeosyntheticReinforced Slopes
Fei Song1, Haibo Chai2, Liqiu Ma3, Hongbing Hu4
3
1
Institute of Geotechnical Engineering, School of Highway Engineering, Chang’An
University, Xi’an 710064, China;
2
Institute of Geotechnical Engineering, School of Highway Engineering, Chang’An
University, Xi’an 710064, China;
Guizhou Electricity Engineering Construction Supervise Company, Guiyang 550005,
China;
4
Guizhou Electric Power Design Institute and Research Institute, Guiyang 550002,
China.
Abstract
Geosynthetic-reinforced slopes are widely used in engineering practices because of its
unique advantages. In this paper, the deformation behavior of geosynthetic-reinforced
slopes is numerically investigated by employing geotechnical software Plaxis. The effects
of the location, the lengths and the normal stiffness of the reinforcement layer are
studied based on the analysis of the results. Study results indicate that the small spacing
of reinforcement layer within the range from one sixth to one half of the slope height can
significantly reduce the horizontal displacement of the slope. After the length of the
reinforcement layer increases up to the height of the slope, its contribution to the
reduction of the horizontal displacement becomes less significant. The reinforcement
effect becomes less after the normal stiffness of the geosynthetic material becomes
greater than 18×103kN/m.
Keywords: Geosynthetic-reinforced slopes; Deformation behavior; Spacing; Length;
Normal stiffness; Reinforcement layer
1. INTRODUCTION
In recent years, increasing numbers of geosynthetic reinforced slopes have been
constructed because of the advantages including reliability, aesthetics, cost, simple
construction techniques and good seismic performance. A lot of researchers proposed
methods for the stability analysis of geosynthetic-reinforced slopes on the basis of limit
equilibrium theory. Some valuable work associated with such analysis has been
conducted by Jewell, 1982, 1986 and 1991; Milligan and Rochelle, 1984; Rowe and
Soderman, 1985; Leshchinsky and Reinschmidt, 1985; Leshchinsky et al. 1986; Hird,
1986; Chouery et al., 1989; Leshchinsky and Boedeker, 1989; Koerner, 1990; Low et
al., 1990; Greenwood, 1990; Mandal and Labhane, 1991; Wright and Duncan, 1991;
Greenwood and Zytynski 1993; Sabhahit et al., 1994; Leshchinsky et al. 1995; Mandal
and Joshi, 1996; Low and Tang, 1997; Palmeira et al., 1998; Shahgholi et al. 2001.
Centrifuge model tests have been conducted by Zornberg et al. (1998 & 2003),
Viswanadham and Mahajan (2007) to investigate the mechanical behaviour of reinforced
slopes both at failure and in pre-failure states.
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Revista de la Facultad de Ingeniería U.C.V., Vol. 31, N°3, pp. 40-48, 2016
In this paper, numerical simulation on the deformation behaviour of geosyntheticreinforced slopes is carried out by employing the geotechnical software Plaxis. The
optimum layout of the reinforcement layers is initially addressed. Subsequently, the
effects of the length and the normal stiffness of the reinforcement material on the
horizontal deformation of the reinforced slope are investigated on the basis of the
analysis of the numerical simulation results. The study results can provide theoretical
references for the design of geosynthetic-reinforced slopes in engineering practices.
2. MODEL AND PARAMETERS OF CALCULATION
Mohr-Coulomb elastic-plastic model is adopted for the soil. The calculation parameters of
the soil are listed in Table 1. Geosynthetic materials are flexible elastic elements with a
normal stiffness but with no bending stiffness. They can only sustain tensile forces and
no compression and are generally used to model soil reinforcement. Linear elastic model
is selected to simulate the behaviour of the geosynthetic materials. The only material
property of the geosynthetic material is an elastic normal (axial) stiffness EA, which can
be determined from diagrams where the elongation of the geosynthetic material is
plotted against the applied force in a longitudinal direction. The axial stiffness is the ratio
of the axial force per unit width and the axial strain ( l / l where l is the elongation
and l is the length).
EA 
F
l / l
(1)
The elastic normal stiffness EA of the geosynthetic material in this study is 1×10 4kN/m.
In addition, the interface element is set between the geosynthetic material and the soil.
Table 1 Calculation parameters of the soil
Elastic
modulus
E(MPa)
Unit weight
γ(kN/m3)
Saturated
unit weight
γsat(kN/m3)
Poisson’s ratio
μ
Cohesion
c(kPa)
Internal
friction angle
φ(°)
35
18
20
0.35
35
20
Due to the restriction of the length of the paper, only the sketch and the mesh
generation of the calculation model with seven reinforcement layers are illustrated in
Figure 1 and Figure 2 respectively. If the left is selected as coordinate origin, the
coordinates of the five points from the slope top to the bottom are A(13,18), B(12,14),
C(11,10), D(10.5,8), and E(10,6)respectively.
Figure 1. Sketch of calculation model with 7 reinforcement layers (unit: m)
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Revista de la Facultad de Ingeniería U.C.V., Vol. 31, N°3, pp. 40-48, 2016
Figure 2. Mesh generation of calculation model with 7 reinforcement layers
3. EFFECT OF LOCATION OF REINFORCEMENT
Effect of location of reinforcement on the deformation behaviour is investigated and the
calculation cases include the slopes with single, two, six and seven reinforcement layers.
3.1 Single layer of reinforcement
The cases of unreinforced slopes, a=0, H/3, H/2 and 3H/4 are numerical simulated and
analyzed, in which a and H represent the distance between the bottom of the slope and
the reinforcement layer and the height of the slope, respectively. The horizontal
deformation of different cases is illustrated in Figure 3, from which it can be observed
that the horizontal deformation of the unreinforced slope is the largest and that of the
reinforced slope with a=H/3 is the smallest, indicating that the effect of reinforcement is
the best for a=H/3. The maximum horizontal displacement of the slope has been
reduced by 36.36%, 46.06%, 43.94%, and 40.60% for the cases of a=0, H/3, H/2 and
3H/4, respectively. The horizontal deformation is the largest at the place on the slope
surface, locating H/3 from the slope toe. Therefore, the effect of reinforcement is most
significant for the case of a=H/3.
Figure 3. Horizontal displacement of the slope surface with one reinforcement layer
3.2 Two layers of reinforcement
The horizontal deformation of slope surface with two layers of reinforcement is presented
in Figure 4, in which 0+H/6 represents the distance between the two reinforcement
layers and the bottom of the slope are 0 and H/6, respectively. The meanings of other
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Revista de la Facultad de Ingeniería U.C.V., Vol. 31, N°3, pp. 40-48, 2016
legends can be inferred in the same way as 0+H/6. The horizontal deformation of slope
surface can be reduced by 42.7%, 43.9%, 48.5%, 49.7%, 47.3%, 43.9% and 40.9% for
the cases of 0+H/6, 0+H/3, H/4+H/2, H/6+H/3, H/3+H/2, H/2+2H/3 and 2H/3+5H/6,
respectively. In comparison with the case in which the reinforcement layers are located
at the upper half of the slope, the horizontal displacement of the slope surface is smaller
when they are located at the lower half of the slope, showing the reinforcement effect is
most significant when the reinforcement layers are placed at the lower half of the slope.
The horizontal displacement is reduced most significantly for the case of H/6+H/3 and it
is reduced least for the case of 2H/3+5H/6. In addition, when the reinforcement layer is
located at the bottom of the slope, the reinforcement effect is not so obvious.
Figure 4. Horizontal displacement of the slope surface with two reinforcement layers
3.3 Six layers of reinforcement
The cases of six layers of reinforcement in this study are listed in Table 2. The horizontal
displacement of the slope surface is illustrated in Figure 5. The maximum horizontal
displacement of the slope surface can be reduced by 41.2%, 43.6%, 42.6%, 47.8% and
54% in cases a, b, c, d, and e, respectively, compared with that of the unreinforced
slope. The reinforcement effect is quite different when the locations of the reinforcement
layers are different even though the number of the reinforcement layers is the same. It
can be observed from Figure 5 that the reinforcement effect is best for case e and worst
for case a.
Table 2 Calculation cases of slope with six reinforcement layers
Cases
a
b
c
d
e
The distances between the reinforcement layers and the bottom of the slope
0, H/8, H/4, 3H/8, H/2, 5H/8
H/8, H/4, 3H/8, H/2, 5H/8, 3H/4
H/4, 3H/8, H/2, 5H/8, 3H/4, 7H/8
0, H/6, H/3, H/2, 2H/3, 5H/6
H/6, H/4, H/3, 5H/12, H/2, 2H/3
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Figure 5. Horizontal displacement of the slope surface with six reinforcement layers
3.4 Seven layers of reinforcement
Table 3 presents calculation cases of slope with seven reinforcement layers. The
horizontal displacements of the slope surface for different cases are shown in Figure 6.
The horizontal displacement of case h is the smallest and that of case f is the largest,
indicating that the horizontal displacement can be reduced effectively when the
reinforcement layers in the range of H/6-H/2 are at small spacing.
Table 3 Calculation cases of slope with seven reinforcement layers
Cases
f
g
h
The distances between the reinforcement layers and the bottom of the slope
0, H/8, H/4, 3H/8, H/2, 5H/8, 3H/4
H/8, H/4, 3H/8, H/2, 5H/8, 3H/4, 7H/8
H/6, H/4, H/3, 5H/12, H/2, 2H/3, 5H/6
Figure 6. Horizontal displacement of the slope surface with seven reinforcement layers
4. EFFECT OF REINFORCEMENT LENGTH
The horizontal displacements of the slope with different reinforcement lengths of single
layer and seven layers are computed and analyzed. In the calculation the distance
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between the single reinforcement layer and the bottom of the slope is H/3 and the case
of the slope with seven reinforcement layers is the case e in the previous section. In
addition, the reinforcement length, l, is H/3, H/2, 2H/3, 5H/6, H, 7H/6, 4H/3, 3H/2 and
5H/3 in different cases. The horizontal displacement along the height of the slope with
seven reinforcement layers is shown in Figure 7, from which it can be seen that the
horizontal displacement gradually decreases with the increase of the length of the
reinforcement layer. However, after the length of the reinforcement layer increases up to
the slope height, the horizontal displacement does not decrease any longer and
maintains a constant. The same trend can be observed in Figure 8, which illustrates the
variation of the maximum horizontal displacement with the reinforcement length.
Figure 7. Horizontal displacement of the slope surface with different reinforcement
lengths
Figure 8. Variation of maximum horizontal displacement with reinforcement length
5. EFFECT OF REINFORCEMENT STIFFNESS
The horizontal displacements of the slope with different reinforcement stiffness of single
layer and seven layers are computed and analyzed. The reinforcement stiffness, EA, is
2×103kN/m, 4×103kN/m, 6×103kN/m, 8×103kN/m, 10×103kN/m, 12×103kN/m,
14×103kN/m, 16×103kN/m, 18×103kN/m, 20×103kN/m, 22×103kN/m and 24×103kN/m
in different cases. The horizontal displacement along the height of the slope with seven
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reinforcement layers is shown in Figure 9. The variation of the maximum horizontal
displacement with the reinforcement stiffness is shown in Figure 10. The horizontal
displacement gradually decreases with the increase of the reinforcement stiffness.
However, after the reinforcement stiffness increases up to the value larger than
18×103kN/m, the horizontal displacement does not decrease significantly.
Figure 9. Horizontal displacement of the slope surface with different reinforcement
stiffness
Figure 10. Variation of maximum horizontal displacement with reinforcement stiffness
6. DISCUSSIONS
In this paper, only the cases of single layer, two layers, six layers and seven layers are
calculated and analyzed. The cases of other layers will be the future research work,
which can provide more theoretical references for the design engineering practices. In
addition, the stiffness of the reinforcement generally increases with the reinforcement
strength. However, the exact relation between the reinforcement stiffness parameter EA
in this study and reinforcement strength in the design will be studied furthermore.
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7. CONCLUSION
In this paper, by employing the geotechnical FEM software Plaxis, the effects of the
length and the normal stiffness of the reinforcement material on the horizontal
displacement of the slope surface are investigated and some conclusions are drawn
primarily on the basis of analysis of the numerical simulation results:
(1) The effect of reinforcement is most significant when the reinforcement layer is placed
above H/3 from the bottom of the slope for the case of single reinforcement layer. The
horizontal displacement can be reduced effectively when the reinforcement layers in the
range of H/6-H/2 are at small spacing.
(2) The horizontal displacement gradually decreases with the increase of the length of
the reinforcement layer. However, after the length of the reinforcement layer increases
up to the slope height, the horizontal displacement does not decrease any more.
(3) The horizontal displacement gradually decreases with the increase of the
reinforcement stiffness. However, after the reinforcement stiffness increases up to the
value larger than 18×103kN/m, the horizontal displacement does not decrease
significantly.
ACKNOWLEDGEMENTS:
The authors wish to express their sincere gratitude to the Key Industrial Science and
Technology Project of Shaanxi Province (No. 2015GY149) and the Scientific Project
funded by the Ministry of Housing and Urban-Rural Development of the People’s Republic
of China Council (No. 2015-K2-008).
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