an engineering geological characterisation of tropical clays - GBV

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The variation of so calculated percentage swelling (S%) with extent of external loading P%
(i.e., load decrements, P kPa, expressed as a percentage of respective swelling pressure, SP
kPa) is presented diagrammatically in Fig. (7.37a). The variation is also closely logarithmic
with a very strong correlation (R = 0,98), i.e.
P = -15,86Ln(S) + 29,84 (7.50)
where P = extent of loading (%)
S = cumulative swelling (%), derived w.r.t initial specimen height Ho
This relationship is also represented as a straight line graph in Fig. (7.37b) where percentage
swelling (S%) has been plotted on a logarithmic scale.
The second relationship could also be possibly used to estimate and/ or anticipate percentage
swelling (S%) and/ or swelling (S mm) that may arise from certain or chosen projected
external loading conditions. For instance, choosing zero loading conditions implies P (kPa)
and P% [i.e. (P/SP)*100] are also zero, so that from Equation (7.50),
0 = -15,86Ln(S) + 29,84 or Ln(S) = 29,84/15,86 = 1,88, so that
S = e^ 1,88 = 6,55%
Or for initial specimen thickness Ho of 11mm,
S = (6,55/100) * 11 = 0,72mm
On the average, therefore, the black clays would undergo a maximum percentage swelling of
6,55% (or swelling of 0,72 mm relative to the initial specimen thickness Ho of 11 mm), under
zero external loading conditions. Other values of percentage swelling and/ or amount of
swelling that may arise from selected external loading could be similarly calculated or just
read off from the curves of Figs. (7.37a &b).
The second relationship could also be possibly used for estimating the extent of external
loading (P%) and/ or external load (P kPa) necessary to give chosen or allowable percentage
swelling and/ or amount of swelling, as may be required by foundation designers. For
instance, a selected average percentage swelling of S% = 2 (or S = 0,22 mm for Ho = 11 mm)
would be exhibited by the clays when the extent of external loading P% is such that
P% = -15,86 * Ln(2) + 29,84 = -(15,86 * 0,693) + 29,84, or
P% = 18,85,
and this is the same value given by the curve of Fig. (7.37) for S% = 2.
For an average swelling pressure, SP = 50,29 kPa as calculated for tested samples of black
clays in Table (7.23), the external loading pressure is given by
P (kPa) = (P% * SP)/100 = (18,85 * 50,29)/100 or
P (kPa) = 9,48