Retaining wall

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Retaining wall
Ex retaining wall.png
author Leif Roschier
pdf File:Ex retaining wall.pdf

Theory and background

Classic example of nomograph found in Ref [1] is the formula connecting the proportions of retaining walls according to picture.

Retaining illustrated.png

The picture can be scaled horizontally and vertically so that the wall cross-section is in general a rectangle as illustrated. The nomograph calculates equal retaining walls: one having straight faces (texture in figure) and one with on sloping faces (blue color). The problem follows equation


that can be written as

[math] \begin{vmatrix} 2(L^2-1) & 3L(L+1) & -L(L-1) \\ 2(2p+1) & 3(p+1) & -(p+1)(2p+1) \\ h & 1 & -h^2 \end{vmatrix} =0, [/math]

where p is defines as (density of earth)/(density of masonry). Similar nomograph is also found in Ref.[2]


  1. H.J. Allcock, J.R. Jones and J.G.L. Michel, The Nomogram. Sir Isaac Pitman & Sons, Ltd., 4nd Edition, 1952.
  2. d'Ocagne, Traité Nomographie, Gauthier-Villars (1899)

Construction of the nomograph

The underlying equation is expressed as determinant and type 9 has to be used. This equation has to be transformed so we use


Note that we have set the points at scale to be transformed with


in scale definitions.

Generated nomograph

Retaining wall
Ex retaining wall.png
Generated portable document file (pdf): File:Ex retaining wall.pdf

Source code

    Retaining wall.
          | 2*(u*u-1) | 3*u*(u+1) | -u*(u-1.0)    |
          |      v    |     1     |    -v*v       | = 0
          | 2*(2*w+1) | 3*(w+1)   |-(w+1)*(2*w+1) |
    Copyright (C) 2007-2012  Leif Roschier
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    GNU General Public License for more details.
    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <>.
from pynomo.nomographer import *
        'f':lambda u:2*(u*u-1.0),
        'g':lambda u:3*u*(u+1.0),
        'h':lambda u:(-u*(u-1.0)),
        'f':lambda v:v,
        'g':lambda v:1.0,
        'h':lambda v:(-v*v),
        'f':lambda w:2.0*(2.0*w+1.0),
        'g':lambda w:3.0*(w+1.0),
        'h':lambda w:(-(w+1.0)*(2.0*w+1.0)),
              'transformations':[('scale paper',)]