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