Abstract
Prediction of the critical seismic yield acceleration coefficient and the seismic permanent displacement of soil nail reinforced slope under seismic loading has been playing an important role in helping design in the earthquake-prone areas. In this paper, the seismic stability of soil nail reinforced slope is analyzed using the kinematic theorem of limit analysis. The log-spiral failure mechanism is considered and the corresponding analytical expressions are derived to calculate the critical seismic yield acceleration coefficient and the permanent displacement of slope subjected to earthquake loading. A series of calculations are carried out to illustrate the influence of inertial force on the stability of a nail-reinforced slope. Parametric studies indicate that the strength and geometry of slope as well as characteristic parameters of soil nail have a significant effect on the critical seismic yield acceleration coefficient and the permanent displacement of soil nail reinforced slope.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- a :
-
\( H/r_{0} \)
- c :
-
Soil cohesion
- d :
-
Diameter of soil nail
- \( \dot{D}_{1} \) :
-
Energy dissipation rate during rotational failure due to soil nail
- \( \dot{D}_{2} \) :
-
Energy dissipation rate during rotation failure along the sliding surface
- \( f_{1} \sim f_{6} \) :
-
Functions depend on the angle of \( \theta_{0} ,\,\theta_{h} ,\,\,\varphi \) and \( \beta \)
- \( F_{i} \) :
-
Boundary traction
- g :
-
Gravity acceleration
- H :
-
Height of slope
- \( H_{\text{in}} \) :
-
Space distance of soil nail in vertical direction
- \( k_{h} \) :
-
Seismic acceleration coefficient input
- \( k_{y} \) :
-
Seismic yield acceleration coefficient
- \( k_{yc} \) :
-
Critical seismic yield acceleration coefficient
- \( L_{i} \) :
-
Length of the ith soil nail
- n :
-
Number of soil layers
- \( r_{0} ,\,r_{h} \) :
-
Radius of the log-spiral with respect to angles \( \theta_{0} \) and \( \theta_{h} \)
- S :
-
Boundary area of the sliding soil mass
- \( T_{i} \) :
-
Force of the ith layer unit width
- V :
-
Volume of the sliding soil mass
- \( v_{i} \) :
-
Kinematically admissible velocity field
- \( \dot{W} \) :
-
Rate of work due to soil weight and inertial force
- \( X_{i} \) :
-
Body forces
- \( \ddot{x} \) :
-
Acceleration of the sliding block relation to the slip surface
- \( z_{i} \) :
-
Depth of the ith layer measured downwards from the top of the slope
- α :
-
incline angle of soil nail
- β :
-
inclination angle of the slope
- γ :
-
unit weight of soil
- φ :
-
internal friction angle of soil
- θ :
-
polar coordinate, m
- \( \theta_{0} ,\,\theta_{h} \) :
-
magnitudes of θ used to describe the log-spiral failure surface
- \( \omega ,\dot{\omega },\ddot{\omega } \) :
-
rotational angle, angular velocity and acceleration of the rotation mass
- \( [\tau ] \) :
-
bond strength between soil nail and surrounding soil
- \( \dot{\varepsilon }_{ij} \) :
-
strain rate field compatible with v i
- \( \sigma_{ij} \) :
-
stress field relating to X i and F i
Reference
Ausilio E, Conte E, Dente G (2000) Seismic stability analysis of reinforced slopes. Soil Dyn Earthq Eng 19(3):159–172
Ausilio E, Conte E, Dente G (2001) Stability analysis of slopes reinforced with piles. Comput Geotech 28(8):591–611
Chang C, Chen WF, Yao JTP (1984) Seismic displacements in slopes by limit analysis. J Geotech Eng 110(7):860–874
Chen WF (1975) Limit analysis and soil plasticity. Elsevier, Netherlands, pp 35–39
Cheuk CY, Ng CWW, Sun HW (2005) Numerical experiments of soil nails in loose fill slopes subjected to rainfall infiltration effects. Comput Geotech 32(4):290–303
Derek H (2005) Landslide in practice: investigation analysis remedial and preventive options in soils. Wiley, New York
Giri D, Sengupta A (2009) A kinematic limit approach for the stability analysis of nailed soil slopes. Asian J Civil Eng (Build Housing) 10(2):163–176
Juran I, George B, Khalid F, Elias V (1990) Kinematical limit analysis approach for the design of soil nailed structures. J Geotech Eng 116(1):54–71
Martin J (1997) The design and installation of soil nail slope stabilization scheme using ‘Snail’. In, Proceeding of third international conference on ground improvement geosystems, London, pp 399–406
Michalowski RL, You L (2000) Displacements of reinforced slopes subjected to seismic loads. Geotech Geoenviron 126(8):685–694
Newmark NM (1965) Effects of earthquakes on dams and embankments. Geotechnique 15(2):139–159
Ng CWW, Lee GTK (2002) A three-dimensional parametric study of the use of soil nails for stabilising tunnel faces. Comput Geotech 29(8):69–673
Nouri H, Fakher A, Jones C (2006) Development of horizontal slice method for seismic stability analysis of reinforced slopes and walls. Geotext Geomemb 24(3):175–187
Patra CR, Basudhr PK (2005) Optimum design of nailed soil slopes. Geotech Geologi Eng 23(3):273–296
Topal T, Akin M (2009) Geotechnical assessment of a landslide along a natural gas pipeline for possible remediations. Environ Geol 57(3):611–620
Yang MZ, Drumm EC (2000) Numerical analysis of the load transfer and deformation in a soil nailed slope. Geotech Spec Publ 96:102–116
Zhou YD, Cheuk CY, Tham LG (2009) An embedded bond-slip model for finite element modelling of soil-nail interaction. Comput Geotech 36(6):1090–1097
Acknowledgments
This research was funded by the National Technology Support Project of China (GrantNo.2011BAK12B03), the National Natural Science Foundation of China (GrantNo.40872181) and West Light Foundation of the Chinese Academy of Sciences. The writers appreciate the financial support.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
He, S., Ouyang, C. & Luo, Y. Seismic stability analysis of soil nail reinforced slope using kinematic approach of limit analysis. Environ Earth Sci 66, 319–326 (2012). https://doi.org/10.1007/s12665-011-1241-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12665-011-1241-3