Reinforced Soil Wall Analysis under Working Stress Conditions Using a Two Phase Model with the Introduction of a New Design Parameter

Document Type : Original Article


Engineering Faculty of Khoy, Urmia University, Urmia, Iran


A previously introduced two phase model was used to assess its capability in predicting the behavior of reinforced soil walls under working stress conditions. The two phase model is a homogenization method based on the virtual work theorem. The reinforced soil medium is considered as the superposition of two continuous phases, the reinforcement and matrix phases that interact within the medium. Application of the two phase model simplifies changes in the arrangement and properties of the inclusions and decreases the computation time considerably. This approach can be used to reduce the time needed for optimization in practical applications. The introduced approach was first validated by comparison with the filed measurements. Therefore, a full-scale reinforced soil wall that has been constructed and tested under working stress condition at the Public Works Research Institute in Japan was simulated using the two phase model. A finite difference code was used to implement the two phase model and simulate the model. A nonlinear elasto-plastic law and a linearly elastic, perfectly plastic constitutive law were employed for the matrix and reinforcement phases, respectively. Then an extensive parametric study including 125 reinforced soil wall models was conducted to show the capability and strength of the introduced approach for simulation of the reinforced soil walls under working stress condition. The effect of inclusion length and stiffness, inclusion spacing, and wall height on maximum lateral displacement of the models was investigated. Eventually, a new dimensionless design parameter was introduced to achieve a simple criterion for evaluating lateral displacements.


 1. de Buhan, P., and Sudret, B. “A Two phase elastoplastic model
for unidirectionally reinforced materials.” European Journal of
Mechanics A/Solids, Vol. 18, (1999), 995-1012. 
2. de Buhan, P., and Sudret, B. “Micropolar multiphase model for
materials reinforced by linear inclusions.” European Journal of
Mechanics A/Solids, Vol. 19, (2000), 669-687. 
3. Sudret, B., and De Buhan, P. “Multi-phase model for inclusionreinforced
geostructures Application to rock-bolted tunnels and
piled raft foundations.” International Journal of Numerical
Analytical Methods Geomechanics, Vol. 25, (2001), 155-182. 
4. Hassen, G., and de Buhan, P. “A two phase model and related
numerical tool for the design of soil structures reinforced by stiff
linear inclusions.” European Journal of Mechanics A/Solids,
Vol. 24, (2005), 987-1001. 
5. Hassen, G., and de Buhan, P. “Elastoplastic Multi-phase model
for simulating the response of piled raft foundations subject to
combined loadings.” International Journal of Numerical
Analytical Methods Geomechanics, Vol. 30, (2006), 843–864. 
6. Seyedi Hosseininia, E., and Farzaneh, O. “Development and
validation of a two phase model for reinforced soil by
considering nonlinear behavior of matrix.” Journal of
Engineering Mechanics, 10.1061/(ASCE)EM.19437889.0000111, (2009), 721–735.
7. de Buhan, P., and Hassen, G. “A multiphase model for assessing
the overall yield strength of soils reinforced by linear
inclusions.” Limit State of Materials and Structures, Springer,
Dordrecht, (2013), pp: 165-178. 
8. Nguyen, V. T., Hassen, G., and De Buhan, P. “Assessing the
dynamic stiffness of piled-raft foundations by means of a
multiphase model.” Computers and Geotechnics, Vol. 71,
(2016), 124-135. 
9. Karpurapu, R., and Bathurst, R. J. “Behaviour of geosynthetic
reinforced soil retaining walls using the finite element
method.” Computers and geotechnics, Vol. 17, No. 3, (1995), 279-299. 
10. Moghadasnezhad, F. “Non Linear Finite Element Analysis of
Reinforced and Unreinforeced Pavements.” International
Journal of Engineering-Transactions A: Basics, Vol. 17, No.
3, (2004), 213-226. 
11. Hatami, K., and Bathurst, R. J. “Development and verification of
a numerical model for the analysis of geosynthetic-reinforced
soil segmental walls under working stress conditions.”
Canadian Geotechnical Journal, Vol. 42, No. 4, (2005), 10661085.
12. Qhaderi, R., Vafaeian, M., & Hashemolhoseini, H. “A
parametric study of the behavior of geosynthetic reinforced soil
slopes.” International Journal of Engineering, Vol. 18, No. 4,
(2005), 371-389. 
13. Hatami, K., and Bathurst, R. J. “Numerical model for reinforced
soil segmental walls under surcharge loading.” Journal of
Geotechnical and Geoenvironmental Engineering, Vol. 132,
No. 6, (2006), 673-684. 
14. Vafaeian, M., & Abbaszadeh, R. “Laboratory model tests to
study the behavior of soil wall reinforced by weak reinforcing
layers.” International Journal of Engineering - Transactions
B: Applications, Vol. 21, No. 4, (2008), 361-374. 
15. Ling, H. I., and Liu, H. “Deformation analysis of reinforced soil
retaining walls—simplistic versus sophisticated finite element
analyses.” Acta Geotechnica, Vol. 4, No. 3, (2009), 203-213. 
16. Kibria, G., Hossain, M. S., and Khan, M. S. “Influence of soil 
reinforcement on horizontal displacement of MSE 
wall.” International Journal of Geomechanics, Vo. 14, No. 1,
(2013), 130-141.