Behind a smooth wall with level ground, the tilt of the stress can only be vertical or horizontal, so it is
one number, C, and K = σh′/σv′ = (1 − C)/(1 +
C). Friction stops C at ± sin φ′: the active and passive states. Drag along the
dial, or move the wall.
What you are seeing
The dial.K = (1 − C)/(1 + C) against the tilt
C, on a log scale. The curve is solid blue between friction's two stops and dotted
beyond them, where the shaded regions are out of reach. The dots mark passive (purple), water,
K = 1 (blue), at rest (green) and active (orange); the large dot is the dial now, and
the arrow is the trip from rest to here. Drag along it to move C.
The wall. The grains push on the wall with Kγz: the
pressure diagram grows with depth, with the at-rest diagram dashed in green for comparison. At
a stop, the sliding wedge and its slip plane are drawn, at 45° + φ′/2 (active) or 45° − φ′/2
(passive). The arrow at the top shows which way the wall has moved from rest.
The Mohr circle. The stress at the base of the wall, between σv′
and σh′, with the friction lines in blue. At a stop the circle touches them.
The status bar. Whether the soil is between the stops or at one.
The model
The two stops are Rankine's active and passive states. At rest the soil sits wherever deposition
left it, C0 = (1 − K0)/(1 + K0). Water
has no tilt, and sits at C = 0, K = 1. The soil is dry.