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 water (ρw).

Specific (or mineral) density of dry particles (ρm).

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

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

3,140 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