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Discussion |
CSIRO, Division of Applied Geomechanics, , P.O. Box 54, Mount Waverly, Victoria 3149, Australia.
M. DUNBAVAN writes: Evans used the assumption of two discrete basal support columns of different moduli in developing his stress distribution equations. An alternative assumption is that the Young's modulus varies continuously across the base of the column and the following equations were derived for a linear variation.
The general form of the linear relationship for Young's modulus, E, is:
where x is the distance from the inside edge of the column towards the free face along the base (see inset of Fig. 1) and E0 is the value at the inside edge of the column. In comparing the variation of modulus with the two discrete values used by Evans, two interpretations for the value of m arise as shown in Fig. 1. One case assumes that the moduli for the two columns are the values at each end of the base, giving:
The second case assumes that the moduli for the two columns are average values for the half base width, giving:
The stress distribution across the base for linear variation in settlement then becomes:
with the notation being the same as that used by Evans. Using integration methods with the independent variable x, vertical force and moment equations when solved yield:
and
For
For
Evans' data was used for calculations so that a comparison of results could be made:
and the values are given in Table 1
The first interpretation for the linear variation of Young's modulus is more practical, indicating that any other functional would best be
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