Contents lists available at ScienceDirect Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo Research Paper Numerical simulation of two-tier geosynthetic-reinforced-soil walls using two-phase approach Ehsan Seyedi Hosseininia a, ⁎ , Ahoo Ashjaee b a Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, Iran b Civil Engineering Department, Mazandaran Institute of Technology, Iran ARTICLE INFO Keywords: Reinforced soil Two-tier walls Two-phase model Numerical simulation Deformation Performance ABSTRACT In this study, the mechanical behavior of two-tier Geosynthetic-Reinforced Soil walls is investigated numerically by using the concept of two-phase systems. Comparison of the results of this approach with those of discrete numerical models and centrifuge tests indicates that the approach has the ability to consider the interaction between tiers, predict the reinforcement load and wall-face displacement. Furthermore, it is more cost-effective. The limitations of this approach pertain to the prediction of the failure surface and the wall deformation regime. Totally, the two-phase approach can be properly applied in a fast, effective and safe manner. 1. Introduction Geosynthetic-Reinforced Soil (GRS) walls are now widely used in civil engineering practice. In some cases, GRS walls are designed and constructed in tier configurations rather than utilizing them as single walls due to wall stability, construction constraints, space requirements for drainage along the height of the wall, and aesthetics. The wall de- sign with tier configuration is more complicated than a single wall since the upper and lower tiers mutually interact over wall deformation and reinforcement loads. There are generally two approaches for design and analysis of multi- tier GRS walls. A lateral earth pressure method, which is based on an empirical extension of single-tier GRS walls, is introduced by the NCMA [1] and FHWA guidelines [2,3]. This method results in an over- estimation of design requirements [4–8]. The limit equilibrium (LE) method whose applicability has been examined and approved in [4,5,9,10] is another approach. These two approaches are only yield wall stability and no information about wall deformation and re- inforcement load distribution can be obtained. Thus, numerical ana- lyses should be implemented in the design procedure. Numerical methods have been widely used in order to study the performance of multi-tier GRS walls as well as the interactions between the tiers. Yoo and Song [11] performed plane-strain finite element si- mulation of two-tier GRS segmental retaining walls. The results indicate that an unexpected yield in the foundation may affect both internal and external stability of the lower tier owing to the absence of toe re- sistance. In addition, upper-tier reinforcement length has a significant influence on lower-tier lateral deformation. Yoo and Kim [12] cali- brated a three-dimensional finite element (FE) model of a full-scale test wall to further investigate load carrying capacity and relevant perfor- mance of the test wall under surcharge load. Stuedlein et al. [9] si- mulated a four-tier 46-m-tall reinforced wall using the finite difference code FLAC. Although the overall design in this work was based on the LE method, they utilized numerical simulations in order to assess wall performance and predict wall displacements at times of soil liquefac- tion. Yoo et al. [8] carried out a series of finite element (FE) analyses in order to investigate internal stability of small-scale two-tier GRS walls with various offset distances and reinforcement distributions. They showed that the lower-tier reinforcement length has a greater effect on overall wall stability than the upper-tier reinforcement length. Re- cently, Mohamed et al. [6] compared the results of numerical simula- tions of two-tier GRS walls with those of a centrifuge modeling series which included different offset distances. They concluded that there is an excellent agreement for slip surfaces and reinforcement loads be- tween the LE/FE methods and centrifuge tests. Generally, it can be said that in comparison with the LE method, numerical methods offer more comprehensive information about stress, strain, force, and displacement at any location of interest. We can consider the reinforced soil medium as a composite which behaves, at the macroscopic level, as a homogenous but anisotropic composite material [e.g. 13–16] due to the existence of repeated layers of soil and reinforcing elements in a periodic manner. For reinforced soil medium, a new concept called the ‘‘Multiphase Model’’ has been introduced by de Buhan and Sudret [17] which is an extension of the https://doi.org/10.1016/j.compgeo.2018.04.003 Received 9 October 2017; Received in revised form 28 February 2018; Accepted 2 April 2018 ⁎ Corresponding author. E-mail addresses: eseyedi@um.ac.ir (E. Seyedi Hosseininia), ashjaee.a@gmail.com (A. Ashjaee). Computers and Geotechnics 100 (2018) 15–29 0266-352X/ © 2018 Elsevier Ltd. All rights reserved. T