The analyses of soil slope in arc slipping need to search three parameters of radius and coordinates of the arc center. By moving the slipping arc horizontally

it is found that the slipping arc must pass through the slope foot or the horizontal coordinate of its center is determined by the radius. It is proved that the slipping arc of vertical slope must pass through the slope foot

where the slipping angle is greater than the internal friction angle. For pure cohesion soil or no friction soil

when the slope angle is greater than

the slipping arc passes through the slope foot; otherwise its center on the perpendicular line through the middle point of the slope face and the critical height is for the arc with infinite radius and slipping angle ? 66.78? at the slope bottom. Based on the numerical calculation

the slipping arcs do not pass through the slope foot when the slope angles are less than 40?

34? and 22? for internal friction coefficient 0.05

0.1 and 0.2 respectively; but their critical heights are only 2 % less than the slipping arcs through slope foot. When internal friction coefficient is greater than 0.3

the slipping arcs pass through the slope foot. So only the arcs passing through slope foot are needed to calculate for the critical height of soil slope.