# Geosynthetics August/September 2021 - 23

```systems and project-specific site conditions.
portable dams need to be designed to
resist sliding, tipping and overturning.
For the manufacturer's dam to move as a
result of the pressure exerted on one side,
it must either be tipped over or slid across
the surface on which it rests. In order to
tip, the water pressure must lift the first
inner tube up and over the second. The
following calculation verifies the dam's
resistance to tipping.
Assumptions
The inner tubes are rectangular when
filled to facilitate the calculations. The
water level on one side will reach the top
of the cofferdam to simulate the worstcase
scenario.
The force exerted on the side of the
water structure is defined as Equation 1.
(1)
F = Y - hlh
2
Once the force on the side of the cofferdam
has been determined, the tendency
of the cofferdam to tip can be
evaluated. Point A is assumed to be the
pivot point and movements are calculated
by each force is a measure of how much
the force contributes to rotating the first
column of water around point A. The
two formulas (Equations 2 and 3) follow.
∑ MA = W - D - F - = 0
1
2
∑ MA = ph - l - - p - l - = 0
D D
2 2
h2
2
h
3
n
3
(2)
(3)
EQUATION 2 Formula for calculating tipping forces
EQUATION 3 Optional formula for calculating
tipping forces
Simplifying the expression, it is
observed that the stability of the dam is
dependent on the relationship between its
width, D, and the depth of water it must
resist. The relationship above indicates
the minimum width of the dam to prevent
it from tipping when resisting water
with a depth, h, equal to the height of
the dam itself. The design height for the
water structures to prevent tipping would
be described as D > (.82) h.
To quantify the stability of the dam,
the dimensions of the standard dam for
D and h are substituted into Equation 1.
The results are expressed in terms of a
safety factor. The safety factor indicates
how many times greater the water pressure
or water depth must be in order to
roll the dam.
Based on the current dam designs, the
safety factor against tipping when water
levels are to the top of the structure, as
per Table 1, is:
B
36 inches
48 inches
72 inches
84 inches
Inflated Width (in inches)
68
120
186
282
TABLE 1 Design factor of safety for water level at top of manufacturer's dams
Safety Factor Against Tipping
2.3
3.48
3.15
4.12
FIGURE 4 6-foot (1.8-m) geosynthetic cofferdams for pipeline repair in Manitoba, Canada
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23
```
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# Geosynthetics August/September 2021

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