Stability Analysis of Steep Nailed Slopes Under Seismic Condition Using 3-D Finite Element Method
Stability Analysis of Steep Nailed Slopes Under Seismic Condition Using 3-D Finite Element Method
Stability Analysis of Steep Nailed Slopes Under Seismic Condition Using 3-D Finite Element Method
Model No. Slope angle/u Nail length/m Nail inclination/u Frequency amplification factor Input peak amplitude of accelerations/g
2 Typical history of input acceleration where the duration of the earthquake compressed by a frequency amplication factor
of ve (time history of the acceleration in the eastwest direction at observatory station TCU074 during the 1999 Chi-Chi
earthquake)
2 is shown in Fig. 1. The other four models are also TCU074 during the 1999 Chi-Chi earthquake with
developed similar to this model by adopting the same different peak amplitudes of acceleration for each model
mesh type as well as same element size. In this paper, two slope using the FE software, MIDAS GTS. Figure 2 is a
types of boundary conditions are considered: free-roller plot of the input acceleration with frequency amplification
and full-fixity. The free-roller and the full-fixity boundary factor of five. The duration of the earthquake applied to
condition are considered for the side soil boundary nodes all models, except model 4, has been compressed by a
and the bottom soil boundary nodes, respectively. At the frequency amplification factor of five, i.e. 9018 s. These
free-roller boundary, which is usually used to represent a data are used in FE analysis to provide unidirectional
far field boundary condition, soil particles are free to move (horizontal) seismic excitation, which is similar to the
in the direction ,which is parallel to the wall boundary. On laboratory shaking table test.
the other hand, at the bottom of the slope models, the
elements are fully fixed, and hence, all kind of movements
are restrained.
Results and discussions
All the five models developed using the FE method with The comparison study from the plot between the normal-
different slope and nail arrangements are analyzed with ized accumulated displacements of the facing at the end of
the input peak amplitude of accelerations (g) as mentioned each seismic excitation and the slope height at every
in Table 1. The time history analyses are carried out on all measured location for all the five model slopes has been
the developed FE model slopes using the earthquake divided mainly into two parts as shown in Fig. 3a and b,
history, i.e. the eastwest direction at observatory station which are as follows:
a Effect of different parameters from finite element (FE) analyses and b test results v FE results
3 Normalized accumulated displacements of the facing at the end of each seismic sequence for all the models
(i) The effect of various parameters has been obtained displacement at all the measured points is greater in case
from the results of FE analyses, which has been of the model slope having slope angle of 90u than that of
shown in Fig. 3a for all the input peak amplitude of model slope having slope angle of 80u at all the input peak
accelerations (g) as depicted in Table 1. amplitude of accelerations. The difference in magnitude of
(ii) A comparison study has been made between the facing displacement at all the measured locations increases
shake table test results and the FE results as with increase in input peak amplitude of acceleration.
depicted in Fig. 3b for the respective input peak Therefore, it can be concluded from these plots that the
amplitude of accelerations (g). steep slope having slope angle of 80u is safer than slope
having slope angle of 90u.
Effect of various parameters
Effect of nail inclination Comparison of FE analysis and shake table test
The effect of nail inclination on the seismic response of results
steep slopes is studied from model 1 and model 2 at the The comparison of test results with the FEM results from
end of each seismic excitation as shown in Fig. 3a having the plot between the normalized accumulated displace-
two different nail inclinations, i.e. 0u and 30u, respectively, ments of the facing and the slope height at every measured
keeping all other parameters as constant. The outward location for all models is shown in Fig. 3b. It can be seen
convex tendency shown in both the models is an evidence that there is no or a very less variation found in the
of a combination of translational and rocking movement magnitude as well as the deformation pattern of facing
with rocking movement as more predominant at all input displacement between the FEM results and the shaking
loading conditions. It can also be seen from the plot that table test results for model 3 than the rest of the models.
the magnitude of facing displacement at all the measured There is a large variation found in the magnitude as well as
points is greater in case of horizontally placed nails than the deformation pattern of facing displacement between
that of inclined nails at higher input peak amplitude of the FEM results and the shaking table test results for
acceleration. Therefore, it can be concluded from these model 2 than the rest of the models. It can also be seen
plots that the inclined nail for steep slopes is a better that the magnitude of facing displacement of the FEM
option than the horizontally placed nails. results is found ahead of the test results for model 4 while
Effect of length of nails for model 1, model 2, and model 5, it is vice versa. From
the plots of all these five models under the respective peak
The effect of nail length on the seismic response of slopes
amplitude of accelerations (g), it has been found that there
is studied from model 1 and model 3 at the end of each
is a variation in the magnitude of facing displacement as
seismic excitation as shown in Fig. 3a having two different
well as in the deformation pattern between the FEM
nail lengths, i.e. 0?4 and 0?5 m, respectively, keeping all
results and the shaking table test results. It has been shown
other parameters as constant. It has been found that there
in the results of FE modeling (Cai and Bathurst, 1995;
is no variation in the magnitude as well as pattern of
Segrestin and Bastick, 1988) that the seismic response of
facing displacement though there is a combination of
reinforced soil walls is a function of peak ground acce-
translational and rocking movement with rocking move-
leration, peak velocity, duration of the ground motion,
ment as more predominant in both the slopes at all input
frequency content, distance from the source, and other
loading conditions.
factors. Hence, the variation in the results of shake table
Effect of frequency amplification factor test and the current numerical analysis may be due to
The effect of frequency amplification factor on the seismic the variation in any one or more of these parameters
response of slopes is studied from model 1 and model 4 at considered during the FE analysis and shake table testing.
the end of each seismic excitation as shown in Fig. 3a The initial and final displacement diagram of model 2 at
having two different frequency amplification factors, i.e. the end of the final sequence of seismic excitation during
5?0 and 3?5, respectively, corresponding to 18?0 and 25?7 s shake table test and at the end of the seismic sequence
of excitation keeping all other parameters as constant. It having apeak50?818g during FE analysis has been depicted
has been found that there is no variation in the magnitude schematically in Fig. 4a and b, respectively. The critical
as well as pattern of facing displacement though there is a amplitude of acceleration for the model 2 at the end of a
combination of translational and rocking movement with range of seismic sequences has already been found as
rocking movement as more predominant in both the 0?805g from the shaking table test. In the FE analysis, the
slopes at all input loading conditions. peak amplitude of acceleration is considered as
apeak50?818g, which is greater than the critical amplitude
Effect of slope angle of acceleration (0?805g) obtained from the test. This may
The effect of slope angle on the seismic response of two be the reason for the variation in the deformation pattern
model slopes such as model 1 and model 5 at the end of of the model slope obtained in FE analysis.
each seismic excitation having slope angle of 80u and 90u,
respectively, keeping all other parameters same is shown in
Fig. 3a. The outward convex tendency shown in both the
Conclusions
models is an evidence of a combination of translational The FE analysis has been conducted on the nailed soil
and rocking movement with rocking movement as more slope models as per the geometry as well as the material
predominant at all input loading conditions. It can also parameters adopted in shaking table test (Hong et al.,
be seen from the plot that the magnitude of facing 2005). Some of the important conclusions drawn on the
a At the end of the final sequence of seismic excitation during shake table test (Hong et al., 2005) and b at the end of the
seismic sequence having apeak50?818g during finite element (FE) analysis (displacement in x-direction)
4 Initial and nal displacement diagram of model 2
basis of the results obtained from the FE analysis and Cornforth, D. 2005. Landslides in practice: investigation, analysis,
remedial and preventive options in soils.
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