control, and higher flow events are not included in this example. The combination of various annual

events needs to be carefully considered and properly applied when performing a PBIA.

upper guide wall for the lock were taken from a 1:120-scale hydraulic modeling at ERDC. Fifty experi-

ments were conducted using a scale model rigid barge train (32 m (105 ft) wide by 297 m (975 ft)) and

remote control towboat. The experiments utilized two different separate operators that simulated twenty-

five approaches to the upper guide wall. These experiments were conducted at a river flow of 708 cu m/

sec (25,000 cu ft/sec). The raw data were recorded on a computer data acquisition system and post-

processed to determine the x-velocity and y-velocity components of the barge and the angle of impact to

the approach wall. Due to scaling effects of the water, the data for velocity and angle were processed prior

to the barge impacting the wall. The data from the fifty experiments are presented in Table D-1.

Figures D-1 through D-3 show the histograms from the experiments for longitudinal (*V*0*x*) velocity,

transverse (*V*0*y*) velocity, and impact angle, respectively.

(1) The data required for a PBIA are the longitudinal *V*0*x *and transverse *V*0*y *components, approach

angles, and the mass for the barge train. These data must be processed to define the statistical parameters

(i.e., mean, standard deviation, etc.) for the input to the PBIA model. The processing of the data may be

done in the form of either a discrete distribution (a probability density for a specific value) or a continu-

ous distribution (smoothed function that fits the data). These concepts will be explained in further detail

using the data for this example.

(2) The weight of the barge train was taken from OMNI database (LPMS) records from 1984 to

present for downstream barges transiting the adjacent lock chambers. From these data an annual histo-

gram was processed using Excel to produce a discrete distribution of the data. The annual histogram for

weight of the barge train is shown in Figure D-4. This figure shows that the data show two dominating

masses (2,700,000 and 27,000,000 kg (3,000 and 30,000 tons)) for the traffic at this lock. This type of

distribution is referred to as a double-humped camelback and is difficult to fit a continuous distribution.

In this case, a discrete distribution at specific intervals (1,000 tons) is more reasonable and acceptable to

use. The resulting input table for the discrete distribution for weight is shown in Table D-2.

(3) From the hydraulic model data in the previous sections, a continuous distribution and statistical

parameters are fitted using a commercially available program. The program used for this example is

called BestFit (Palisade Corporation 2003a). This program permits the fitting of data to numerous distri-

butions and ranks them based on statistical testing procedures. For simplicity, a lognormal distribution

was taken for the best fit to the raw data and the distributions are shown in Figures D-5 through D-7.

Table D-3 shows a summary of the statistical parameters used for the PBIA.

(4) For this example, the PBIA model is developed in Microsoft Excel using a commercial Monte

Carlo Simulation add-in package called @Risk (Palisade Corporation 2003b). @Risk allows the easy

simulation of numerous combinations of annual events, which develop an annual probability distribution

for the impact loads on the upper guide wall. For this example, 100,000 iterations were run to determine

the distribution for the impact load. This annual distribution of impact load is then used to calculate the

return periods for the impact loads to be used in design.

D-2