Several retaining wall deformations and failures have been reported during historical earthquakes. The most well-known method for predicting the seismic deformation of retaining wall is known as Newmark sliding block method. The Newmark sliding block method requires the acceleration time history of an earthquake in the free-field. However, as the acceleration time history might not be available for a practical design, some investigators including Richards and Elms (1979) developed empirical correlations to evaluate maximum retaining wall displacement in seismic conditions. The Richards and Elms empirical correlation (R&E) has been suggested in different design guidelines including Army Corps (Whitman and Liao 1985) and AASHTO LRFD Bridge Design Specifications (AASHTO 2007). In a more recent study conducted by Anderson et al. (2008) and as part of The National Cooperative Highway Research Program (NCHRP) study, an updated correlation was provided based on various Newmark analyses. The updated NCHRP equation has been embedded in the recent guidelines including Caltrans. More advanced Newmark based pseudo-static methods have also been developed to evaluate the sliding deformation of the retaining walls. Examples include works performed by Biondi et al. in 2014 and Conti et al. in 2013. However, it is noteworthy that the above-mentioned studies only consider the sliding deformation of the retaining wall and the rotational and tilting deformation are neglected. Some investigators including works performed by Nadim and Whitman (1984), Rafnsson (1991), Prakash et al. (1995), and Wu and Prakash (2001) adopted analytical approaches to predict the seismic deformation of the retaining walls considering tilt and rotation of the retaining wall. However, due to the complexity of these analytical procedures, the approaches have not been adopted in design guidelines for practical purposes.
The deformational behavior of gravity and cantilever retaining walls in seismic conditions, have been studied both numerically and experimentally. The main scope of most of these studies was evaluating sliding and rotational displacement of retaining wall systems during earthquake events. In a few studies, seismic earth pressure and retaining wall motion responses were also investigated. In addition, Huang et al. (2009) and Wu and Prakash (2001) proposed a wall displacement criterion for identifying the level of damage for seismic performance of retaining walls.
There are some limitations with these studies. For example, most of the mentioned studies focused on retaining walls with cohesionless backfill materials. A few studies considered backfill cohesion, however, their main focus was not displacement behavior of retaining walls. Moreover, specific backfill cohesion was selected in these studies. Therefore, the effects of cohesion variation on seismic response of the walls were not considered. In addition, only limited number of seismic events and shaking intensities were used in these studies.
There is limited information about the seismic deformational response of retaining walls with cohesive backfills. However, field inspections by Kapuskar (2005) show low to high level of cohesiveness in backfill materials. The study conducted by Caltrans (Kapuskar 2005) investigated 20 different bridge sites in the State of California. It was found that in 18 cases, the backfill material of bridge abutments contains some level of cohesiveness. In 9 cases, backfill materials with up to 95 kPa cohesion were observed.
The other critical factor is the stochastic nature of earthquake and its related damages, which is often characterized by the probability of occurrence or failures. For example, fragility analyses have been used to evaluate the probability of failures of different structures (Baker 2015) and caisson quay walls (Ichii 2004; Jafarian et al. 2014). However, there has been a lack of knowledge in determining the fragility functions of cantilever retaining wall structures especially with cohesive backfills.