Performance-based analysis of cantilever retaining walls subjected to near-fault ground shakings

Abstract

Considering the devastating damages of ‘forward-directivity’ on structures, a series of finite element models were conducted to evaluate the seismic performance of cantilever retaining walls under near-fault excitations. The wavelet approach was used to extract the velocity pulse of near-source motions, and a semi-artificial records reagent far-field earthquake was produced. Both were then imposed on the model, separately. The results indicated a vivid difference in lateral displacement, in which some cases up to differences of experienced 85% and forces along the walls were approximately equal. In view of this finding, a wide range of PGAs was applied to the near-fault scenarios of the models. The captured movements were compared with the recommended criteria for performance-based aseismic design of retaining structures. According to the numerical analysis, in most earthquakes, for accelerations exceeding 0.4 g, lateral displacement of the wall had a higher value than the permissible proposed limits. Also, accelerations exceeding 0.6 g for both near and far-field records resulted in wall failure (>5% H). The final section of this research presents a comprehensive parametric study on the effects of ground motion characteristics and soil mechanical properties on system performance.

Introduction

Earthquake ground motions recorded close to a fault plane recognized as near-fault ground motions can be extremely different from motions captured far from the ruptured source. While there are different opinions regarding the near-fault zone location, the most common is restricted within a 20 km distance of the ruptured fault (Bray and Rodriguez-Marek, 2004). Baziar and Rostami (2017) mentioned that the near-fault region is limited by the magnitude of a seismic event that is equal to $R_t(km)=0.3M_w^2$. Wave propagation effects or the so-called ‘forward-directivity’ (FD) affect near-fault sites. The fault rupture propagation toward a site at a speed that nears the shear wave velocity, oriented perpendicularly to the fault plane, form the FD effect (Somerville, 2003). Most seismic energy demands in FD pulses accumulate at the beginning of the record, which is evident in the large-period pulses in the velocity time history. It is worth noting that the ratio of seismic energy of directivity pulses to the energy of the whole earthquake in near-fault records can be up to 80%. This indicates the importance of near-fault excitations (Mukhopadhyay and Gupta, 2013).

Also, ground shaking in the near-fault zone, parallel to the fault strike with strike-slip mechanism or in the fault-normal direction for dip-slip faults may be affected by a permanent static movement called the ‘fling-step’ (Somerville et al., 1997). The FD effect is a dynamic phenomenon that does not leave permanent ground movements; as observed in the time history, FD produces two sided velocity pulses, while the fling-step, caused by permanent earth displacements, makes one-sided velocity pulses (Bray and Rodriguez-Marek, 2004).

All of the above explanations reveal that near-fault records are inherently different from larger site-to-source recorded shakings and, therefore, require special consideration when designing geotechnical and structural systems. Bertero was the first to report the devastating failure capacities of near-source earthquakes (Bertero et al., 1978). The catastrophic earthquakes of the 1990s such as the Northridge (1994), Kobe (1994) and Chi-Chi (1999) earthquakes led to a wide range of research efforts, aimed at assessing the performance and damage potential of various geotechnical and structural systems subjected to near-fault pulse shakings (Hall et al., 1995, Alavi and Krawinkler, 2000, Garini and Gazetas, 2013, Davoodi et al., 2013).

Gazetas et al. (2009) presented a numerical study on a rigid block that was supported by a frictional contact surface and charged by motions having forward-directivity or fling-step effects. They concluded that the upper-bound sliding displacements from near-source excitations may substantially exceed the values obtained from some of the currently available design charts. Song and Rodriguez-Marek (2014) developed a coupled method for analyzing the sliding-blocks of slopes under near-fault pulse-like and nonpulse-like ground motions. The authors found that the slope is expected to experience larger displacements when near-fault ground motions have pulse-like characteristics. Zou et al. (2017) conducted a numerical analysis and found that the seismic response of concrete face rockfill dams increased with an increasing ratio of the peak ground velocity to the peak ground acceleration (PGV/PGA). Higher values of crest displacement as well as intense damages to the concrete face were among the consequences of near-fault shakings.

It is evident from the literature that near-fault ground motions are susceptible to inducing large displacements on different types of geotechnical structures. Hence, the role of these types of excitations is crucial to consider when designing by performance-based procedures. Retaining walls are an example of a one such system and are widely used for stabilizing excavations in roads and highways, especially for urban areas. Extensive applications lead to constructing retaining structures in seismic regions and areas that are close to active faults. The seismic response of retaining walls is a complicated problem because it involves dynamic soil-structure interactions. Seismically induced lateral displacements, dynamic bending moments and pressures behind the retaining structures are multi-dimensional problems that depend on wall foundation and backfill soil, the inertial and rigidity of the wall itself, and the nature of input excitations.

The classic methods proposed by Okabe, 1924, Mononobe and Matsuo, 1929, known as the Mononobe–Okabe (M-O) as later developed by Seed (1970), are still the main approaches for the design of retaining walls. This method recruits the pseudo-static equilibrium by simplifying earthquake loading as an inertial force, without considering the dynamic characteristics of input earthquake loads and retaining walls. Since then, various researches have been conducted to assess the seismic performance of retaining walls by means of experimental (Nakamura, 2006, Kloukinas et al., 2014, Jo et al., 2017, Candia et al., 2016); numerical and analytical approaches (Veletsos and Younan, 1997, Psarropoulos et al., 2005, Nimbalkar and Choudhury, 2007, di Santolo and Aldo, 2011, Brandenberg et al., 2017, Bakr et al., 2019).

Gazetas et al. (2004) used finite-element modeling to explore the magnitude and distribution of dynamic earth pressure forces on several types of flexible retaining systems. By using dynamic centrifuge experiments performed on cantilever walls and following two-dimensional nonlinear finite-element analysis, Atik and Sitar (2010) concluded that the current design methods based on the M-O theory significantly overestimated the captured dynamic earth pressure forces and moments and mentioned that seismic earth pressures along with cantilever retaining walls can be neglected at accelerations below 0.4 g. By focusing on displacements, Conti et al. (2012) showed that maximum accelerations smaller than the critical limit equilibrium value increase the structural loads, thereby, subjecting the retaining walls to significant permanent displacements. Cakir (2013) analyzed the effect of earthquake frequency content on the seismic response of retaining structures and reported that wall responses are highly dependent on the$\mathit{PGV}/PGA$ ratio and can cause a spiked increase or decrease in system displacement by the frequency content variation. Bakr and Ahmad (2018) developed charts and correlated between seismic earth pressure and wall movement. The authors reported that accelerations greater than 0.4g enabled the retaining wall to continue moving without enhancing the dynamic passive earth pressure forces. Mikola et al. (2016) recorded distribution of the seismic earth pressures on cantilever retaining structures using centrifuge tests. Salem et al. (2020) performed a series of two-dimensional finite element methods for analyzing the seismic response of cantilever retaining walls. The sensibility of the system response to the soil constitutive model was studied. A Rigid perfectly plastic (M-C) and an advanced nonlinear elastoplastic model (HSSMALL) were used. The results of the analysis showed that in the M-C model, a larger force than HSSMALL was captured. Furthermore, a higher value of lateral displacement for the 1989 Loma Prieta-UCSC earthquake was recorded in the M-C model. Conti and Caputo (2019) investigated the dynamic response and phase shift between soil and the inertia forces under a real earthquake. Jadhav and Prashant (2020) proposed displacement-based design procedures for cantilever retaining walls. The authors reported that using shear key placed at the heel of cantilever retaining wall was reduced the transitional displacement by 40%. Santhoshkumar et al. (2019) investigated the earth pressure behind cantilever retaining walls using a pseudo-dynamic approach. Zamiran and Osouli (2018) correlated the free-filed PGA to the relative displacement of the wall under real earthquakes. They reported that 50% of walls experienced failure state when input PGA reached to 0.47g for cohesionless backfill.

Reviewing the literature shows that most dynamic studies on retaining walls are limited to the earth pressures and forces that act along with the structures. The number of displacement-based studies of retaining walls is rare. Also, the performance of cantilever retaining walls under near-fault excitations is not yet well understood. The conformity of seismic wall movements in real earthquake scenarios with failures and permissible states are also unknown. So, further research about response and seismic forces behind retaining walls that are motivated by near source motions are needed. Qualitative insight into the performance analysis of retaining walls under near-fault strong ground motions will emphasis on the importance of displacement-based designs.

In this regard, the present research evaluated the results of a series of dynamic 2D finite element (FE) numerical models based on the performance of cantilever retaining structures under near-fault excitations with a focus on seismically induced lateral displacements. Due to the higher damage potential of FD over fling step (Bray and Rodriguez-Marek, 2004, Kalkan and Kunnath, 2006), this research was mainly focused on FD shakings and used fully dynamic time-domain analyses in the process. In the first section and to illustrate the importance of the discrepancies in wall responses under near and far-field ground motions, FD pulses were extracted from the velocity time series of near-fault, main, and residual records and imposed on the verified model. Then, near-fault strong ground motions with a wide range of PGAs from 0.1 g to 0.6 g were applied for different shaking scenarios. The captured movements were compared with the recommended criteria for the performance-based aseismic design of soil retaining structures in the literature. A comprehensive parametric study was applied to assess the effect of different parameters. The effect of the mechanical properties of backfill/foundation soil as well as the frequency content of the ground motion was investigated.