If a particular depth is chosen for z then a series of concentric circles can be drawn. In theory there will be ten circles, but one has an infinite radius, so that in practice only nine circles can therefore be drawn. If a set of equally spaced rays, say n in number, are now drawn emanating from the centre of the circles there will be 10 n enclosed areas or influence units. Each area will contribute erz/10n where a7 is the total vertical stress. If, for example, n = 8 then each influence unit contributes crz/80 = 0.0125<xz. The influence factor is 0.0125.

Construction of a Newmark chart

Choose a convenient dimension for z (say z = 20 m); the radii of the circles are then 5.4, 8.0, 10.4, 12.8 m, etc. Establish a scale (say 1:100) and draw the circles. Select a suitable number of rays (20 is the usual figure) and construct them at equally spaced intervals. The resulting diagram is shown in Fig. 4.8; on it is drawn a vertical line, AB, representing z to the scale used (AB = 200 mm). With n = 20, the influence factor is 1/200 = 0.005.

The diagram can be used for other values of z by simply assuming that the scale to which it is drawn alters: thus if z is to be 10 m the line AB now represents 10 m and the scale is therefore 1: 50 (similarly if z = 40 m the scale becomes 1:200).

Operation of a Newmark chart

The chart can be used for any uniformly loaded foundation of whatever shape. First a scale drawing is made of the foundation, generally on tracing paper, using a scale that corresponds with the length AB on the chart; the point at which the vertical stress is required is then placed over the centre of the circles and the number of influence units contained within the boundaries of the foundation, including fractions of units, are added together to give a total number of units N. <rz is simply equal to N x px influence factor.

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