Let us now investigate limiting cases and then compare results to the Coulomb solution for a vertical wall with no interface friction.

**Comparison to the Coulomb Solution (**Ï•=0**)**

Let us now investigate
limiting cases and then compare results to the Coulomb solution for a vertical
wall with no interface friction.

From Equations (12.23)
and (12.24) for

and theoretically no
wall friction develops. Thus we obtain the failure surface and stress
distribution identical to Coulomb's solution, Ïƒ* _{w}* = Î³

At
the other extreme for:

b. *N =** N*_{min}* *;* T =** T *_{max}

for a very rough wall along which the
shear strength is fully mobilized. Thus *T*, *N*, and Î´ are functions of Ïˆ, which defines the
failure surface.

In practice, however,
the average angle of wall friction, Î´,
is usually selected on the basis of the possibilities of wall movement and the
relative roughness of the wall (e.g., steel is relatively smooth compared to
concrete). For a known Î´,
*T*, *N*, *P*, the angle Ïˆ and the point of
application of the resultant thrust are uniquely defined. The complete solution
for a vertical wall is shown in Figure 12.12 where it can be seen that wall
friction always helps both by reducing *P _{A}* and lowering the
point of its application. The total thrust for Î´=0 given by Coulomb is a maximum. Friction is often neglected in design in
soil mechanics to help compensate for the unsafe assumption of tension capacity
in the upper portion of the active wedge.

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Civil : Principles of Solid Mechanics : Slip Line Analysis : Comparison to the Coulomb Solution (Ï•=0) |

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