Calculation and strength distribution of Rankine earth pressure on inclined surface

According to stress state of one point on an inclined surface, we derived the formula of Rankine active and passive earth pressure on inclined surface by means of graphic method of Mohr Circle. The formula can be seen as two parts in the linear equation and non-linear equation of the filling depth z. By analyzing the part of nonlinear equation, we find that strength distribution of Rankine active and passive earth pressure on inclined surface is related to the relationship between internal friction angle φ and angle of inclined surface β. We obtain the forms of strength distribution of Rankine active and passive earth pressure on inclined surface and draw the graphics of distribution of earth pressure strength with 3 situations β > φ, β=φ and β < φ. The graphics of distribution is nonlinear. Rankine active earth pressure does not have solution in the case of β < φ below certain depth z>2. Finally, the presented formulas are applied in practical engineering. The experimental results in this instance can be well described by the presented formulas. The presented formulas are proven to be effective.