ETL 1110-2-563
30 Sep 04
Appendix E
Empirical Method for Barge Impact Analysis for Rigid Walls
E-1. Introduction
In this appendix, an empirical correlation between the maximum force normal to the wall and the linear
momentum normal to the wall is presented. The maximum force Fw used in this correlation was obtained
from the models presented in Chapter 5 of Arroyo, Ebeling, and Barker (2003). Recall that no damage
occurred to the barge and no lashings failed during impact testing for the eight impact experiments used
to derive the empirical correlation described in this appendix. The experiments were also conducted to
eliminate both the transverse velocity component V0y and the rotational component. These both were
negligible in the results from the data processing.
E-2. Development of Empirical Correlation from Full-Scale Experiments
a. Using values for Fw(max), the maximum normal force Fw, and the linear momentum normal to the
wall given in the last column of Table E-1, a best-fit straight line was calculated for the eight experiments.
The velocity V0x listed in the third column of Table E-1 acts in the local barge x-axis. This approach
relates the Fw obtained from the energy method directly to the linear momentum. Figure E-1 shows the
velocity vector transformation from local (barge) axis) to global (wall) axis used for the experiments. It is
important to mention that only one data point of the whole Fw time-history for each of the eight
experiments was used to develop this empirical correlation. The velocity normal Vnorm and velocity
parallel Vpar shown in Figure E-1 relate the coordinate system of the barge train to the coordinate system
of the wall.
b. A least squares regression procedure was used to develop the best-fit straight line through the
eight data points (for the eight impact experiments) for the Figure E-2 empirical correlation. The line was
assumed to start at the origin (i.e., no intercept term was used for the linear equation). The resulting best-
fit equation for this set of eight data values is (Fw)max = 0.435*m*V0x*sin θ, where m is the mass in tons.
That is, a coefficient times the linear momentum normal to the wall determines the maximum force
normal to the wall.
Table E-1
(Fw)max Empirical Correlation
Approach
Measured
Velocity
Mvsin(θ)
Angle
(Fw)max
V0x
Mass
2
Exp No.
k-sec /ft
kips
deg
ft/sec
k-sec
29
12.63
2.2
1,865.59
286.63
897.42
30
12.19
2.35
1,865.59
369.15
925.73
31
10.60
1.61
1,865.59
236.2
552.52
37
10.29
1.95
1,865.59
327.27
649.84
38
11.94
1.83
1,865.59
230.29
706.32
39
14.12
1.61
1,865.59
271.07
732.74
41
8.76
2.86
1,865.59
419.37
812.59
42
17.48
1.83
1,865.59
577.44
1,025.48
2
2
Note: To convert kip-sec /ft to MN-sec /m, multiply by 0.135. To convert k-sec to MN-sec, multiply by 0.004450 MN-sec.
E-1
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