Calculation of Active Earth Pressure for Narrow Backfill with a Curved Slip Surface

Table 1

Various formulas for slip surface when in active state.

References	Theoretical essentials of slip surface	Backfill conditions
Coulomb [6]	The slip surface is a straight line with the angle from the horizontal plane.	Surcharge-free, flat top, cohesionless or cohesive
Rankine [5]	The slip surface is a straight line with the angle from the horizontal plane.	Surcharge-free, flat top, cohesionless or cohesive
Tsagareli [8]	The slip surface is an exponential curve.	Surcharge-free, flat top, cohesionless
Goel and Patra [7]	The slip surface is a parabolic curve that is diagonally across the bottom and top.	Surcharge-free, flat top, cohesionless
Xu et al. [21]; Xu et al. [22]	The slip surface can be divided into a logarithmic spiral segment and a Rankine straight segment.	Surcharge-free, flat top, cohesionless or cohesive
Xie and Leshchinsky [23]	The slip surface can be represented by a logarithmic spiral.	Surcharge-free, flat top, cohesionless or cohesive
Rao et al. [16]	The slip surface is a straight line with the angle from the horizontal plane.	Surcharge-free, flat top, cohesionless or cohesive
Khosravi et al. [24]	The shape of slip surface changes from log-spiral or parabolic to planar as the “planar ratio of slip surface” increases.	Surcharge-free, flat top, cohesionless