Geosynthetics August/September 2020 - 9

Comparing the calculated bubble
shape predicted by the FEA analysis
with the approximate static-equilibrium
approach developed by Thiel (2016)
indicated very close agreement for the
same bubble height, width and depth of
water. For the example investigated, the
agreement was closest when an interface
friction angle of 20° between the geomembrane and the subgrade was implemented in the FEA. A comparison of the
results for a single case is presented in
Figure 2. In addition to the predicted
bubbles' shapes that were very close,
the following quantitative comparison
of results of calculated pressures and
strains was also obtained:
*	 The calculated internal bubble pressure, P, by the approximate Thiel
(2016) approach was 0.15 psi (1.03
kPa) compared to 0.14 psi (0.95 kPa)
by the FEA method (8.4% difference).
*	 The calculated volume of the bubble,
V, by the approximate Thiel (2016)
approach was 21,613 cubic feet (612
m3) compared to 22,884 cubic feet (648
m3) by the FEA method (5% less).
*	 The strain estimated by the Thiel
(2016) method for the zone above the
waterline was 3.95%, while FEA results
show the strain varying from 3.0% at
the pole to 3.7% at the waterline.
*	 Thus, the "simplistic spreadsheet
model" is more conservative than the
FEA model, but still relatively accurate,
at least for the investigated example.
It is remarkable that the simplified
spreadsheet approach, Thiel (2016), is
similar to the FEA method, given that the
two methods were based on completely
unique and independent approaches. The
Thiel (2016) method could only assume
average strains in discrete zones of the
bubble, with unrealistic step functions
in the strain estimates along the bubble
profile, and unrealistic values of strains in
certain portions of the bubble. However,

FIGURE 2 Thiel (2016) method vs. FEA bubble shape. Note that FEA assumed interface
friction angle of 20°, whereas the Thiel method assumes interface friction angle of 0°.

the FEA method (i) takes into account
bottom friction of the liner with the
subgrade, and (ii) describes a continuity
of strain throughout the bubble profile
extending it into the free-field geomembrane surrounding the bubble. The correspondence between the two methods to
describe the shape, pressure and strains
in geomembrane bubbles provides a validation of their relative accuracy, which is
also corroborated by field observations.
Additional updates on the FEA
method for pond bubble analysis and
parametric studies are being submitted
as a paper for the upcoming EuroGeo7
conference scheduled to occur in Warsaw,
Poland, in May 2021.
References
Thiel, R. (2016). "Analysis of stresses and strains in
geomembrane gas bubbles that occur in surface
impoundments." Proc., Geo-Chicago 2016, American
Society of Civil Engineers, Chicago, Ill.
Thiel, R. (2017). "Design of exposed geomembrane
lined ponds: Controlling uplifting gas bubbles," Part I.
Geosynthetics, 35(5), 42-49.
Thiel, R. (2018a). "Design of exposed geomembrane
lined ponds: Controlling uplifting gas bubbles," Part II.
Geosynthetics, 36(1), 36-42.
Thiel, R. (2018b). "Design of exposed geomembrane
lined ponds: Controlling uplifting gas bubbles," Part III.
Geosynthetics, 36(2), 10-18. G

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Geosynthetics August/September 2020

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