Closed-Form Solution for Seismic Earth Pressure on Bilinear Retaining Wall Using Method of Characteristics

ABSTRACT

This paper presents a simplified mathematical formulation for a set of closed-form solutions to compute static and seismic active and passive earth pressure on a retaining wall with bilinear backface. The concept of the method of stress characteristics in the framework of hyperbolic partial differential equations has been employed for the intended purpose. The advantage of varying the wall geometry for obtaining an economical design is briefly discussed. This mathematically robust but elementary procedure may be useful as a predecessor for obtaining an efficient and economical design of a retaining wall to palliate the earthquake damage.

KEYWORDS:

• Earth pressure
• earthquakes
• hyperbolic equations
• method of characteristics
• retaining wall
• stress plasticity

Notations

ah, av	=	Horizontal and vertical earthquake accelerations
D	=	Constant damping ratio of soil
fa	=	Amplification factor for seismic waves
FH1, FH2	=	Horizontal component of thrust P1 and P2
g	=	Acceleration due to gravity
H	=	Height of wall
H1	=	Height of upper part of wall
kh, kv	=	Horizontal and vertical earthquake acceleration coefficient
P1, P2	=	Thrusts acting on upper and lower part of wall
q	=	Uniformly distributed surcharge
t	=	Time
T	=	Period of lateral shaking
Vp, Vs	=	Primary and shear wave velocities
x, y	=	Axes in two dimensional Cartesian co-ordinate system
ϕ	=	Angle of internal friction of soil
γ	=	Unit weight of soil
σ	=	Distance on the Mohr stress diagram, between the centre of the Mohr circle and a point where the Coulomb’s linear failure envelope intersects the σ-axis
θ	=	Angle made by the major principal stress (σ1) with the positive x-axis
θg	=	Magnitude of θ along the ground surface
θw1, θw2	=	Magnitude of θ along upper and lower part of wall