Analytical solution for active earth pressure of c–φ soil considering arching effect

ABSTRACT

The current study was undertaken to study the effect of soil arching on active earth pressure distribution in retaining walls with c–φ backfill. An analytical approach is presented to develop a general solution considering the effects of surcharge, backfill soil cohesion and slip surface inclination. The magnitude and height of the application of lateral active force is also derived. The results from the proposed equation corresponded to the measured results from a full-scale test, shows non-linear pressure distribution with zero pressure at wall base and less pressure in deeper heights compared to Coulomb’s method. According to the results of parametric analysis, the proposed equation predicts the active earth thrust nearly equal to that of the Coulomb’s equation, however, the surcharge-induced soil pressure is obtained approximately 50% greater than the conventional equation. Moreover, the height of application of active thrust is located at the height of 0.4H from the wall base. These indicate that using the Coulomb’s active equation for retaining walls design, is not in the safe side.

KEYWORDS:

• Active pressure
• arching
• cohesion
• surcharge
• analytical solution

List of Notations

The following symbols are used in this paper:

${\theta }_x$	=	inclination of principal stresses at any arbitrary point (degree)
${\theta }_w$	=	inclination angle of the principal stresses at the wall surface (degree)
${\theta }_s$	=	inclination angle of the principal stresses at the slip surface (degree)
$B_z$	=	length of the flat element at depth z (m)
$c_w$	=	wall-soil cohesion (kPa)
H	=	total height of the rigid retaining wall (m)
h	=	point of application of active thrust from the base of wall (m)
Ka	=	coefficient of the active earth pressure (nondimensional)
M	=	total moment acting on the wall (kN/m)
P	=	active total force (kN)
$\alpha$	=	slip surface inclination (degree)
γ	=	unit weight of the backfill soil ($kN/m^3$)
δ	=	wall–soil friction angle (degree)
${\sigma }_{hw}$	=	horizontal stress in an element just behind the wall (kPa)
${\bar{\sigma }}_v$	=	average vertical stress acting on the differential element of the sliding wedge (kPa)
${\sigma }_1$	=	major principal stress (kPa)
${\sigma }_3$	=	minor principal stress (kPa)
$\phi$	=	friction angle of backfill soil (degree)

Disclosure statement

No potential conflict of interest was reported by the authors.