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Tons Dry Solids (TDS)
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Figure 8. TDS sensitivity analysis
ERDC TN-DOER-T6
September 2004
generally apply to TDS measurement. Additional requirements include incorporating the dry
solid specific density and the in situ water density into the TDS equation.
TDS involves the measurement of the hopper-load's volume and weight in order to determine its
average density and the quantity of "dry solids" that it contains. The equation used to calculate
TDS is derived in Welp and Rosati (2000), as well as a more detailed description of TDS
measurement. The data requirements for computing TDS are:
Density of in situ waterw).
Specific (or mineral) density of dry particlesm).
Hopper volume (Vh).
Hopper weight (Wh).
The in situ water and mineral densities are determined from representative samples collected
from the dredging prism.  The hopper volume and weight are measured by the methods
previously described in this TN. How well TDS can be measured depends on how accurately
and consistently the four factors presented above are measured, as well as the validity of the
principals used to calculate it. The following sensitivity and uncertainty analyses illustrate the
individual effects that each of these four factors have on TDS measurement accuracy.
TDS Sensitivity Analysis. A sensitivity analysis was conducted on the TDS equation using
dredge McFarland as the presentation platform (TDS data were collected on the USACE dredge
McFarland, see Welp and Rosati (2000) for details). The McFarland is a medium-sized hopper
dredge with a rated hopper capacity of 2,400 m3 (3,140 yd3) and a loaded displacement (in fresh
water) of 12,475 long tons.  The sensitivity plot in Figure 8 graphically illustrates the relative
effects that each of the four required data inputs (parameters) have on the final calculated TDS
value on a hopper dredge of this size. In a sensitivity analysis, the value for each parameter is
varied over a practical range of values while the other three TDS equation parameters are held
constant. This process is then repeated for the other three parameters. For example, the mineral
density curve in Figure 8 is plotted by holding the water density and hopper volume and weight
parameters constant (1,250 kg/m3, 3,140 yd3, 2,834 long tons (LT), respectively), while the
mineral density is varied from 2,600 kg/m3 to 2,800 kg/m3 (or specific gravities of 2.6 and 2.8,
respectively). Sands and gravel range between 2,650 kg/m3 and 2670 kg/m3, while cohesive
sediments such as silts and clays can vary from about 2,680 kg/m3 and 2750 kg/m3 (Scott 2000).
For the water density curve, this parameter is varied between 980 kg/m3 and 1030 kg/m3. Values
3
of an average hopper density of 1,200 kg/m3 and full hopper volume of 3,140 yd were held
constant for the mineral and water density curves. In the hopper (dredged material) volume
curve, the volumes range "above and below" the most accurate, or "true" value of a full hopper of
3
3,140 yd and the hopper weight curve varies over a range of 500 LT.
Looking at the mineral density curve, when this parameter is varied between values typically
encountered in the field of 2,650 kg/m3 and 2,750 kg/m3 (with respective calculated TDS values
between 672 LT and 657 LT), the TDS value changes by about 15 LT. On the water density
curve, when this parameter's (water density) value is varied from 980 LT to 1,030 LT, (with
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