Effect of structural design on fundamental frequency of reinforced-soil retaining walls K. Hatami * , R.J. Bathurst Civil Engineering Department, Royal Military College of Canada, Kingston, Ont., Canada K7K 7B4 Accepted 5 March 2000 Abstract The results of a numerical study on the influence of a number of structural design parameters on the fundamental frequency of reinforced- soil retaining wall models are presented and discussed. The design parameters in the study include the wall height, backfill width, reinforcement stiffness, reinforcement length, backfill friction angle and toe restraint condition. The intensity of ground motion, character- ized by peak ground acceleration, is also included in the study as an additional parameter. The study shows that the fundamental frequency of reinforced-soil wall models with sufficiently wide backfill subjected to moderately strong vibrations can be estimated with reasonable accuracy from a few available formulae based on linear elastic wave theory using the shear wave speed in the backfill and the wall height. Numerical analyses showed no significant influence of the reinforcement stiffness, reinforcement length or toe restraint condition on the fundamental frequency of wall models. The strength of the granular backfill, characterized by its friction angle, also did not show any observable effect on the fundamental frequency of the reinforced-soil retaining wall. However, the resonance frequencies of wall models were dependent on the ground motion intensity and to a lesser extent, on the width to height ratio of the backfill.  2000 Elsevier Science Ltd. All rights reserved. Keywords: Fundamental frequency; Reinforced-soil; Retaining walls; Seismic response; Dynamic analysis; Geosynthetics; FLAC 1. Introduction Dynamic lateral earth pressure behind a reinforced-soil retaining wall subjected to an intensive ground motion can be significant. This additional (incremental) horizontal pres- sure may induce excessive wall lateral displacement and reinforcement load which can result in damage to—or collapse of—the structure. Damage to bridge superstruc- tures, as a result of excessive lateral movement of abutment retaining walls due to seismic loading has been reported [1–4]. An essential step in seismic design of both conventional and reinforced-soil retaining walls is to determine the natural frequencies of the structure. Reinforced-soil retaining walls of typical heights (e.g. H  10 m and backfill material are generally considered as short-period structures (e.g. see Ref. [5]). Soil damping also significantly reduces the contribution of higher modes in total dynamic response of retaining wall systems [6]. Therefore, the response of the wall to ground motion is dominated by the fundamental frequency of the structure (also, see Ref. [3]). The fundamental frequency of a retaining wall-backfill system is often estimated according to a one-dimensional shear beam analogy based on the height of the wall and the speed of shear wave in the backfill material [1,5–10]. In contrast to an infinitely long uniform soil layer, a reinforced-soil retaining wall system includes structural components such as reinforcement layers and a vertical-facing panel supported on a footing. The vertical wall face suggests that a two-dimensional approach to fundamental frequency response analysis may be more appropriate than the one- dimensional shear beam approach. Dynamic response of reinforced-soil retaining walls to ground motion has been the subject of several studies [11– 16]. However, little can be found in the available literature that specifically addresses the influence of structural design (e.g. reinforcement stiffness, length and spacing, facing panel type and thickness, and toe restraint condition at the panel footing), geometry and material properties of the backfill, intensity level of shaking and duration of excitation on the fundamental frequency of reinforced-soil retaining wall structures. Richardson and Lee [14] conducted a series of shaking table studies on small-scale (380 mm high) reinforced-soil wall models. They subjected the retaining wall models to harmonic motions with different amplitudes and frequen- cies. The maximum base acceleration varied between 0.02 Soil Dynamics and Earthquake Engineering 19 (2000) 137–157 0267-7261/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S0267-7261(00)00010-5 www.elsevier.com/locate/soildyn * Corresponding author. Tel.: + 1-613-541-6000, ext. 6347; fax: + 1- 613-545-8336. E-mail address: hatami-k@rmc.ca (K. Hatami).