Design of waterfront retaining wall for the passive case under earthquake and tsunami

Stability of Waterfront Retaining Wall Subjected to Pseudo-Dynamic Earthquake Forces and Tsunami

“…The design charts presented in the analysis, obtained by keeping the parameters in non-dimensional form can be readily used for the practical design purposes. Clear differences between the present methodology and the one adopted by previous researchers who used pseudo-static approaches, but respectively with a planar and curved rupture surfaces (Ebeling and Morrison (1992), and Choudhury and Ahmad (2007a)) have been highlighted through the present study and depending upon which it can be safely recommended that the pseudo-dynamic approach is certainly an improvement over previous approaches; the incorporation of which would lead to an economic yet safe design. Fukui et al, (1962) approaches for the estimation of the tsunami wave pressure F S oC , F S oF : Factor of safety in overturning mode of failure of the wall by respectively considering the CRATER (2006) and Fukui et al, (1962) approaches for the estimation of the tsunami wave pressure F r : Total resisting force F S sC , F S sF : Factor of safety in sliding mode of failure of the wall by respectively considering the CRATER (2006) and Fukui et al, (1962) approaches for the estimation of the tsunami wave pressure g : Acceleration due to gravity h t : Tsunami water height on the upstream side of the wall h wd , h wu : Height of the water on the downstream and upstream sides of the wall respectively H d : Point of application of the dynamic component of the total seismic passive earth pressure (P pe ) k h , k v : Seismic acceleration coefficients in the horizontal and vertical directions respectively k * h : Modified seismic acceleration coefficient in the horizontal direction K : A constant as described in text K p : Passive earth pressure coefficient under static conditions K pe : Seismic passive earth pressure coefficient m,n : Constants as described in text m w (z) : Mass of the thin rectangular element of the wall having thickness dz, and located at a depth z below the top of the wall m 1 ,m 2 ,m 3 ,m 4 : Constants as described in text P dyn : Hydrodynamic pressure P p : Total passive earth pressure under static conditions P pe : Total seismic passive earth pressure P std , P stu : Hydrostatic pressure on the downstream and upstream sides of the wall respectively P tC , P tF : Tsunami wave pressure by respectively considering the CRATER (2006) and Fukui et al, (1962) approaches for the estimation of the tsunami wave pressure Q hw , Q vw : Seismic inertia force on the wall in the horizontal and vertical directions respectively r u : Pore pressure ratio t : Time T : Period of lateral shaking V p , V s : Respectively, the velocity of the primary and shear waves propagating through the soil V pw , V sw : Respectively, the velocity of the primary and shear waves propagating through the wall W w : Weight of the wall z : Depth below the top of the wall α, α MO : Angle which the failure wedge plane makes with the horizontal at the base of the wall, calculated using the pseudo-dynamic approach as described in the text and Mononobe-Okabe approach respectively γ c , γ s , γ w : Unit weight of concrete, soil, and water respectively γ d , γ sat : Dry and saturated unit weight of the soil respectively γ we ,γ : Respectively the equivalent unit weights of water and the soil, modified due to submergence of the backfill δ : Wall friction angle η, λ : Constants, respectively equal to T V p and T V s κ, ξ : Constants, respective...…”

“…No previously existing work was found, which was identical to the present methodology, however only two research works, which were found to be somewhat closer to the approach described by the present methodology, at least in terms of the forces/pressures considered for the stability of the waterfront retaining wall are of Choudhury and Ahmad (2007a) and Ebeling and Morrison (1992) but using the conventional pseudo-static approach. Also, the work of Ebeling and Morrison (1992) makes a mention of assessing the stability of waterfront retaining wall under different forces as have been considered in the present methodology, except for the consideration of the tsunami wave pressure.…”

“…Similarly, the comparison of the factor of safety, both in sliding and overturning modes of failure is shown in Figs. 10. It is observed that for a typical value of the horizontal seismic acceleration coefficient (k h ) of 0.2, and by using the present methodology, in which pseudo-dynamic approach has been adopted for the calculation of both the seismic passive earth pressure and the seismic wall inertia force, the factor of safety in sliding mode of failure is about 16% more than the one calculated by considering the pseudo-static approach proposed by Choudhury and Ahmad (2007a). This 16% increase in the factor of safety can be attributed to the less conservative nature of the pseudo-dynamic approach (as has been observed by Steedman and Zeng (1990); Choudhury and Nimbalkar, (2005)) than the traditional pseudo-static approach.…”

“…Also, the work of Ebeling and Morrison (1992) makes a mention of assessing the stability of waterfront retaining wall under different forces as have been considered in the present methodology, except for the consideration of the tsunami wave pressure. It is however to be noted, that like the study of Choudhury and Ahmad (2007a), Ebeling and Morrison (1992) also adopted the pseudo-static approach for the calculation of the seismic passive earth pressure, thus both suffering from the inherent drawbacks as have been pointed out by Steedman and Zeng (1990) and recently by Choudhury and Nimbalkar ((2005), (2007)). The comparison of the present study, thus, has been made by these two works.…”

“…The literature archives show that there have not been many studies in the past, in which the stability and the behavior of such waterfront retaining walls had been assessed under the mentioned combination of forces/pressures. Whatever is present in the literature is either by considering only one force/pressure or just a combination of a few of these forces/pressures at a time, except for the work reported by Choudhury and Ahmad (2007a) who considered all these forces/pressures, but in which the seismic earth pressure was calculated using the conventional pseudo-static approach, which can be regarded to be too conservative as it has got several drawbacks as has been reported by Steedman and Zeng (1990), Choudhury and Nimbalkar (2005, 2006, 2007, Choudhury and Ahmad (2008), Ahmad and Choudhury (2008), and Nimbalkar and Choudhury (2008). The effect of the hydrodynamic pressure along with the seismic active earth pressure was studied by Ebeling and Morrison (1992) and Ahmad (2007b, 2008).…”