Pseudo-dynamic methods for seismic passive earth pressure behind a cantilever retaining wall with inclined backfill

Abstract

The designing of retaining walls requires the complete knowledge of earth pressure distribution. Under earthquake conditions the design needs special attention to reduce the devastating effect, but under seismic conditions, the available literature mostly uses the pseudo-static analytical solution as an approximate to the real dynamic nature of the complex problem. This paper shows a detailed study on the seismic passive earth thrust behind a cantilever retaining wall with inclined backfill surface by pseudo-dynamic analysis. A planar failure surface has been considered. The effect of variation of parameters such as soil friction angle, wall friction angle and back fill inclination have been explored. A complete analysis shows that the time dependent non-linear behaviour of the pressure distribution obtained in the present method results in more realistic design values of earth pressures under earthquake conditions. Results are provided in tabular and graphical non-dimensional form and compared thoroughly with the existing values in the literature.

Keywords:

• pseudo-dynamic analysis
• cantilever retaining wall
• planer failure surface
• passive earth pressure

Nomenclature
ah(z,t):	=	Horizontal earthquake acceleration at any depth z and at any time t (m/s2).
av(z,t):	=	Vertical earthquake acceleration at any depth z and at any time t (m/s2).
H:	=	Height of the retaining wall (m).
i:	=	Backfill surface inclination (degree).
Pae(t):	=	Earth pressure in active state at any time t (kN/m2).
ρ:	=	Density of soil mass (kg/m3).
γ:	=	Unit weight of soil mass (kN/m3).
m:	=	Mass of failure soil wedge (kg).
W:	=	Total weight of soil wedge (kN).
ϕ:	=	Soil friction angle (degree).
δ:	=	Angle of wall friction (degree).
kh,kv:	=	Horizontal and vertical seismic coefficients respectively.
α:	=	Angle of wedge surface with horizontal (degree).
G:	=	Shear modulus of the backfill soil material (kN/m2).
ν:	=	Poisson’s ratio of backfill soil material.
Vs,Vp:	=	Shear wave and primary wave velocity in the backfill material (m/s).
t,T,ω:	=	Any time t within the time period T moving at an angular velocity ω (s, rad/s).
Qh(t):	=	Total horizontal seismic inertia force acting at the cg of the wedge (kN).
Qv(t):	=	Total vertical seismic inertia force acting at the cg of the wedge (kN).
λs:	=	Wave length of shear wave (m).
λp:	=	Wave length of primary wave (m).
Kpe:	=	Total seismic earth pressure coefficient due to the combination of kh and kv.