**1. Introduction**

Gravity quay walls are the most common type of construction for docks and harbours because of their durability, ease of construction and capacity to reach deep seabed levels. Gravity quay walls are designed for three main criteria; sliding, overturning and allowable bearing stress under the base of quay wall. Although the design of gravity quay walls has been reasonably well understood for static loads, but analysis under seismic loads is still in being developed. During strong ground shaking, the pore water pressure of cohesionless saturated backfill soils builds up. This pressure increase not only causes the lateral forces on the wall (which leads to wall failure), but also reduces the effective stress of backfill soil which may result in liquefac‐ tion. The occurrence of liquefaction in backfill soil was the main reason of damages from past earthquakes to gravity quay walls (e.g., in 1964 at Nigata Port (Hayashi et al. 1966), in 1993 at Kushiro-oki, and in 1994 at Hokkaido Toho-oki (Sasajima et al. 2003)). Moreover, observations of 24 marine structures in 1999 earthquake at Kocaeli, Turkey showed the seaward movement of quay walls due to the liquefaction of backfill soils (Sumer et al. 2002). The same observations were reported in 1999 during the Chi Chi earthquake in Taiwan (Chen and Hwang 1999).

The seismic coefficient method containing Mononobe-Okabe's formula is usually used in the design of gravity-type quay walls to resist earthquake damages but this design method does not take into account the liquefaction of backfill soil and its associated deformations (Sasajima, et al. 2003). Furthermore, conventional design method of quay walls is based on providing capacity to resist a design seismic force, but it does not provide information on the performance of a structure when the limit of the force-balance is exceeded. In this regard, gravity quay walls failures have caused much progress in the development of deformation-based design methods for waterfront structures. Accordingly, much significant experimental and theoretical research works have been done (Sugano et al. 1996; Inagaki et al. 1996; Iai 1998; Iai et al. 1998; Iai and

© 2013 Ebrahimian; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Ebrahimian; licensee InTech. This is a chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Ebrahimian; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Sugano 2000; Ichii et al. 2000; Inoue et al. 2003; Nozu et al. 2004; Mostafavi Moghadam et al. 2009 and 2011). A new design methodology, named performance-based design, has born from lessons learned caused by earthquakes in 1990's to overcome the limitations of conventional seismic design (PIANC 2001). In this framework, lateral spreading of the saturated backfill and foundation soils along with the effect of quay wall as the supporting structure (saturated soil-structure interaction) are taken into account as a more logical design.

numerical results in terms of seaward movement, settlement and inclination of wall as well as the total pressure recorded behind the caisson wall were compared with 1g shaking table tests results. It was demonstrated that the numerical results appropriately supports the experimen‐

Numerical Modelling of the Seismic Behaviour of Gravity-Type Quay Walls

http://dx.doi.org/10.5772/55027

259

In this chapter, firstly some aspects related to calibration of a numerical model are discussed. Then, the numerical results are verified by comparing the calculated values with correspond‐ ing ones obtained from 1g shaking table tests. A series of two dimensional fully coupled effective stress dynamic analyses are carried out in order to study the deformation of quay wall, liquefaction potential and failure mechanisms of soil-wall system during seismic loading. The Finn and Byrne model Byrne (1991) is used with some minor modifications to model pore pressure build up during seismic loading. Afterwards, computational parametric studies are performed to investigate the effects of backfill soil properties and input excitation character‐ istics on the seismic behaviour of gravity-type quay walls including the residual deformation

Several 1g shaking table tests have been executed to verify the obtained numerical results. It is found that the extent of liquefaction and the deformation pattern of soil-wall system that includes seaward displacement, tilting and settlement (as typical failure modes of quay walls due to earthquake) resulted from numerical analyses agree reasonably well with the actual observations in shaking table tests. During seismic excitation, no evidence of liquefaction has detected near the quay wall but liquefaction occurs at some landward distance from the wall. Based on the current results, it seems possible to develop a safer design of gravity-type quay

In this research, a two-dimensional (2D) reference model is developed to simulate the seismic performance of gravity-type quay walls in a rational way. Nonlinear time history dynamic analysis is conducted using computer program FLAC 2D (Itasca 2004). FLAC 2D is an explicit finite difference program for modeling soil-structure interaction analysis under static and seismic loading conditions. Here, numerical approach is based on a continuum finite difference discretization applying Lagrangian approach (Itasca 2004). Every derivative in the set of governing equations is directly replaced by algebraic expression written in terms of field variables (e.g., stress or displacement) at discrete point in space. Regarding dynamic analysis, explicit finite difference scheme is applied to solve the full equation of motion using the lumped grid point masses derived from the real density of surrounding zone. The calculation sequence first invokes the equations of motion for deriving new velocities and displacements from stresses and forces; then, strain rates are derived from velocities, and new stresses from strain rates. Every cycle around the loop corresponds to one time step. Each box updates all grid variables from known values which are fixed over the time step being executed (Figure 1).

of wall, liquefaction potential and failure modes of soil-wall system.

walls by using lessons learned from the present numerical analyses.

**2. Description of the numerical method**

tal results obtained by model tests.

Predicting the response of a structure retained a liquefiable soil during an earthquake is highly dependent on adequately accounting for the effects of pore water pressure development, stress-strain softening and strength reduction in the soil on the system behavior. Thus, it is required to perform dynamic analyses that account for the saturated soil-structure interaction effects using numerical modeling techniques. Several researchers have reported the use of numerical analysis for predicting the behavior of liquefiable soil measured in laboratory tests or field case histories. Iai et al. (1998) reported that FLIP code can successfully predict the seismic behavior of port structures. Yang and Parra developed CYCLIC code and reported successful predictions of the seismic behavior of gravity quay wall placed on liquefiable sand and calibrated the numerical results with centrifuge tests (Parra 1996; Yang 2000). Both the codes DYSAC2 and DYNAFLOW are reported by Arulanandan (1996) as having adequately predicted the response of a submerged embankment subjected to dynamic loading in a centrifuge test. According to Madabhushi and Zeng (1998), the code SWANDYNE successfully predicted the seismic response of a gravity quay wall rested on liquefiable sand modeled in the centrifuge. Finn reported the successful validation of TARA-3 using centrifuge tests results (Finn et al. 1991). The successful use of FLAC package for prediction of the behavior of caisson retaining walls in liquefiable soils was reported by Dickenson and Yang (1998). They used a nonlinear effective stress analysis method based on the Mohr-Coulomb constitutive model and a pore water pressure increment scheme based on the work of Seed and his co-workers (e.g. Martin et al. 1975; Seed and DeAlba 1986). Likewise, McCullough and Dickenson, who used the same analysis method and soil model in FLAC, reported fairly good agreement between predicted and measured permanent horizontal displacements at top of five anchored sheet pile bulkhead walls in liquefiable soils subjected to different earthquakes in Japan between 1987 and 1993 (McCullough and Dickenson 1998). It should be noted that the assumption of the Yang and McCullough was that the foundation soil is non-liquefiable. A hyperbolic type stress-strain formulation developed by Pyke (1979) along with the pore water pressure build up model proposed by Byrne (1991) was implemented in FLAC code by Cooke (2001). They concluded that Pyke-Byrne model over-predicts the horizontal displacement of gravity quay walls modelled in centrifuge within a factor of approximately two.

Recently, Ebrahimian et al. (2009) have carried out a series of two dimensional fully coupled effective stress dynamic analyses in order to study the deformation of quay walls and the liquefaction potential of backfill soils. Additionally, several 1g shaking table tests have been executed to verify the obtained numerical results. They showed based on the lessons learned obtained from numerical results, a safer design of gravity-type quay walls can be developed. Correspondingly, Mostafavi Moghadam et al. (2009) conducted finite difference effectivestress analyses to investigate the seismic performance of caisson quay walls. Their obtained numerical results in terms of seaward movement, settlement and inclination of wall as well as the total pressure recorded behind the caisson wall were compared with 1g shaking table tests results. It was demonstrated that the numerical results appropriately supports the experimen‐ tal results obtained by model tests.

In this chapter, firstly some aspects related to calibration of a numerical model are discussed. Then, the numerical results are verified by comparing the calculated values with correspond‐ ing ones obtained from 1g shaking table tests. A series of two dimensional fully coupled effective stress dynamic analyses are carried out in order to study the deformation of quay wall, liquefaction potential and failure mechanisms of soil-wall system during seismic loading. The Finn and Byrne model Byrne (1991) is used with some minor modifications to model pore pressure build up during seismic loading. Afterwards, computational parametric studies are performed to investigate the effects of backfill soil properties and input excitation character‐ istics on the seismic behaviour of gravity-type quay walls including the residual deformation of wall, liquefaction potential and failure modes of soil-wall system.

Several 1g shaking table tests have been executed to verify the obtained numerical results. It is found that the extent of liquefaction and the deformation pattern of soil-wall system that includes seaward displacement, tilting and settlement (as typical failure modes of quay walls due to earthquake) resulted from numerical analyses agree reasonably well with the actual observations in shaking table tests. During seismic excitation, no evidence of liquefaction has detected near the quay wall but liquefaction occurs at some landward distance from the wall. Based on the current results, it seems possible to develop a safer design of gravity-type quay walls by using lessons learned from the present numerical analyses.
