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# Methods for Nonhomogeneous Slopes

• Yang H. Huang

## Abstract

The application of earth pressure theory can be illustrated by the simple example shown in Fig. 12.1. By assuming the active force, P A , and the passive force, P p as horizontal, it can be easily proved by Rankine’s or Couloumb’s theory that the failure plane inclines at an angle of 45° + ø/2 for the active wedge and 45° − ø/2 for the passive wedge. From basic soil mechanics
$${{P}_{A}}\,=\,\frac{1}{2}\,\gamma \,\mathop{H}_{A}^{2}\,{{\tan }^{2}}\,\left( 45{}^\circ \,-\,\frac{\phi }{2} \right)\,-\,2c{{H}_{A}}\,\tan \,\left( 45{}^\circ \,-\,\frac{\phi }{2} \right)$$
(12.1)
$${{P}_{P}}\,=\,\frac{1}{2}\,\gamma \,\mathop{H}_{P}^{2}\,{{\tan }^{2}}\,\left( 45{}^\circ \,-\,\frac{\phi }{2} \right)\,-\,2c{{H}_{P}}\,\tan \,\left( 45{}^\circ \,-\,\frac{\phi }{2} \right)$$
(12.2)
in which H A and H p are the height of active and passive wedges, respectively. The factor of safety can be determined by
$$F\,=\,\frac{cl\,+\,W\,\tan \,\phi }{{{P}_{A\,}}\,-\,{{P}_{P\,}}}$$
(12.3)
in which l is the length of failure surface at middle block, and W is the weight of middle block.

## Keywords

Shear Strength Earth Pressure Failure Surface Failure Plane Passive Force
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Van Nostrand Reinhold Company Inc. 1983

## Authors and Affiliations

• Yang H. Huang
• 1
1. 1.University of KentuckyUSA