Numerical modeling of a retaining wall subjected to earthquake loads
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Current seismic design criteria for retaining wall structures suggested by different organizations are based on estimating seismic earth pressure of the wall using analytical solutions (e.g. AASHTO 2012; Campos 2008). Different guidelines including AASHTO and Caltrans consider pseudo-static analytical solutions to identify seismic earth pressure (AASHTO 2012; Campos 2008). The first analytical attempt as a pseudo-static method to evaluate seismic earth pressure of retaining walls was suggested by Okabe (1926) and the method was verified in retaining walls with unsaturated and cohesionless soil material by Mononobe and Matsuo (1929) using shake table test results. The method developed by these investigators is known as Mononobe-Okabe (MO) method and is still widely used to determine seismic earth pressure of retaining walls. MO procedure is an extension of Coulomb theory and is based on limit equilibrium method and assumes an occurrence of a failure wedge in the backfill. MO method considers the earthquake acceleration is uniform in the backfill and is applied to the center of gravity of the failure wedge.
There are also many studies that evaluated the total seismic earth thrust (Pae) experimentally (Agusti and Sitar 2013; Al-Homoud and Whitman 1999; Atik and Sitar 2009; Nazarian and Hadjian 1979; Prakash 1981; Seed and Whitman 1970) and numerically (Atik and Sitar 2009; Bui et al. 2014; Elgamal and Alampalli 1992; Green et al. 2008; Green and Ebeling 2003; Psarropoulos et al. 2005; Scotto di Santolo and Evangelista 2011; Wilson and Elgamal 2010; Woodward and Griffiths 1996). Specifically, Seed and Whitman (1970), hereafter abbreviated as S&W, conducted different centrifuge tests on retaining walls with cohesionless backfill materials and provided a simple equation for determining Pae, which linearly correlates with horizontal earthquake peak ground acceleration (PGA). Their experimental-based estimation has been used in design guidelines for evaluating Pae, e.g., US Army Corps of Engineers (Whitman and Liao 1985). It is worth mentioning that the earthquake acceleration intensities for the mentioned numerical and experimental studies were limited to PGA ground motions of 0.2g to 0.4g. In most of these studies, the cohesion factor of backfills and hysteretic behavior of soil were also neglected.
Guidelines by AASHTO and state Departments of Transportations require the use of granular materials as backfill for retaining wall constructions as backfills with fine and cohesive material are sensitive to swell, shrinkage, and degree of saturation (AASHTO 2012; Campos 2008; Murinko 2010). However, according to field observations in several cases, backfill materials have a various amount of cohesion (Kapuskar 2005). Kapuskar (2005) conducted field observations of more than 100 retaining wall and abutment backfills used in 20 different bridge sites in the State of California. It was concluded that out of 20 bridge sites, 15 of them had sandy backfills with low plasticity fines that had cohesion up to 95 kPa.
Seismic response of retaining walls considering backfill cohesion has been taken into account analytically (Das and Puri 1996; Prakash and Saran 1966; Shukla et al. 2009; Shukla and Bathurst 2012; Vahedifard et al. 2014). Most of these approaches were developed based on an extension of MO method with consideration of backfill cohesion, wall adhesion, and tension cracks in cohesive backfill materials. The MO-based methods have restrictions to be used for backfills with different soil layers and complex geometries. Therefore, analytical methods based on trial wedge procedure has been proposed for backfills with various layers of soil or complex geometries (Anderson et al. 2008).
In addition to analytical solutions, some experimental and numerical investigations have also been conducted to evaluate the effects of backfill cohesion on seismic response of retaining walls there are some limited experimental and numerical studies are available that assessed the effect of cohesion on seismic response of retaining walls (Agusti and Sitar 2013; Mikola et al. 2014; Wilson and Elgamal 2010, 2015, Zamiran and Osouli 2014, 2015). The limitations of these studies are: 1) the wall response with a variation of backfill cohesion was not considered; 2) the Pae, its point of action, and induced moment under full seismic analyses were not considered; 3) the representative hysteretic damping and shear reduction of the backfill materials have not been considered. Also, these studies focused on the effect of either single soil cohesion parameter or single PGA.
In this study, seismic response of retaining walls is evaluated for cantilever walls with cohesive sandy backfill materials via fully dynamic analysis (FDA). A constitutive model accounting the hysteretic behavior of soil during dynamic loading excitation is utilized. A validated numerical approach based on centrifuge test results is used to conduct the FDA. The effect of three earthquake ground motions and backfill with various cohesions on seismic earth pressures, total seismic earth thrust coefficient (Kae), incremental seismic earth thrust coefficient (ΔKae), the location point of action of Pae, and wall moment variations during the shaking event are studied. The results of FDA are compared to estimations based on current analytical solutions. Finally, recommendations are provided for considering the effects of backfill cohesion in seismic response of cantilever retaining walls.
There are also many studies that evaluated the total seismic earth thrust (Pae) experimentally (Agusti and Sitar 2013; Al-Homoud and Whitman 1999; Atik and Sitar 2009; Nazarian and Hadjian 1979; Prakash 1981; Seed and Whitman 1970) and numerically (Atik and Sitar 2009; Bui et al. 2014; Elgamal and Alampalli 1992; Green et al. 2008; Green and Ebeling 2003; Psarropoulos et al. 2005; Scotto di Santolo and Evangelista 2011; Wilson and Elgamal 2010; Woodward and Griffiths 1996). Specifically, Seed and Whitman (1970), hereafter abbreviated as S&W, conducted different centrifuge tests on retaining walls with cohesionless backfill materials and provided a simple equation for determining Pae, which linearly correlates with horizontal earthquake peak ground acceleration (PGA). Their experimental-based estimation has been used in design guidelines for evaluating Pae, e.g., US Army Corps of Engineers (Whitman and Liao 1985). It is worth mentioning that the earthquake acceleration intensities for the mentioned numerical and experimental studies were limited to PGA ground motions of 0.2g to 0.4g. In most of these studies, the cohesion factor of backfills and hysteretic behavior of soil were also neglected.
Guidelines by AASHTO and state Departments of Transportations require the use of granular materials as backfill for retaining wall constructions as backfills with fine and cohesive material are sensitive to swell, shrinkage, and degree of saturation (AASHTO 2012; Campos 2008; Murinko 2010). However, according to field observations in several cases, backfill materials have a various amount of cohesion (Kapuskar 2005). Kapuskar (2005) conducted field observations of more than 100 retaining wall and abutment backfills used in 20 different bridge sites in the State of California. It was concluded that out of 20 bridge sites, 15 of them had sandy backfills with low plasticity fines that had cohesion up to 95 kPa.
Seismic response of retaining walls considering backfill cohesion has been taken into account analytically (Das and Puri 1996; Prakash and Saran 1966; Shukla et al. 2009; Shukla and Bathurst 2012; Vahedifard et al. 2014). Most of these approaches were developed based on an extension of MO method with consideration of backfill cohesion, wall adhesion, and tension cracks in cohesive backfill materials. The MO-based methods have restrictions to be used for backfills with different soil layers and complex geometries. Therefore, analytical methods based on trial wedge procedure has been proposed for backfills with various layers of soil or complex geometries (Anderson et al. 2008).
In addition to analytical solutions, some experimental and numerical investigations have also been conducted to evaluate the effects of backfill cohesion on seismic response of retaining walls there are some limited experimental and numerical studies are available that assessed the effect of cohesion on seismic response of retaining walls (Agusti and Sitar 2013; Mikola et al. 2014; Wilson and Elgamal 2010, 2015, Zamiran and Osouli 2014, 2015). The limitations of these studies are: 1) the wall response with a variation of backfill cohesion was not considered; 2) the Pae, its point of action, and induced moment under full seismic analyses were not considered; 3) the representative hysteretic damping and shear reduction of the backfill materials have not been considered. Also, these studies focused on the effect of either single soil cohesion parameter or single PGA.
In this study, seismic response of retaining walls is evaluated for cantilever walls with cohesive sandy backfill materials via fully dynamic analysis (FDA). A constitutive model accounting the hysteretic behavior of soil during dynamic loading excitation is utilized. A validated numerical approach based on centrifuge test results is used to conduct the FDA. The effect of three earthquake ground motions and backfill with various cohesions on seismic earth pressures, total seismic earth thrust coefficient (Kae), incremental seismic earth thrust coefficient (ΔKae), the location point of action of Pae, and wall moment variations during the shaking event are studied. The results of FDA are compared to estimations based on current analytical solutions. Finally, recommendations are provided for considering the effects of backfill cohesion in seismic response of cantilever retaining walls.
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