Expansión guerrillera, políticas de paz y eclosión paramilitar (1982-1996)

3-26. A linear regression on the shock peak strain data demonstrates that the L position had no effect on the severity of the shock response in these events (R2 value of -0.05). For the bubble responses, there was a weak linear correlation R2 value of 0.52, where the peak response was lower as the charge was positioned further from amidships (L = 0.0 m). The spread between the highest and lowest peak strain responses from bubble loading at each L position also reduced, despite the same W and R scenarios at each L position. This suggests that the bubble loading had a diminishing effect on the peak strain response after the shock wave, as the L

position was moved further from amidships. While it was noted that the results for E7 may have been slightly larger due to the strain gauge locations, this would only result in a stronger correlation between the L position and peak platform response from bubble loading. However,

further data is required to quantitatively determine a relationship between the L position and the peak strain response on a submerged platform.

Figure 3-26 The effect of L position on the peak strain responses from shock wave and bubble loading for all events

The effects of the L position on the platform response from bubble loading are further examined by comparing the IB from Table 3-7 and the peak strain measurements due to bubble loading in Figure 3-27. Here it is shown that while IB was similar for events with the same W and R (event sets E4, E6 and E8 (W = 43 g, R = 0.8 m), and E3, E5 and E7 (W = 250 g, R = 1.3 m)), the strain levels during the UNDEX induced whipping response varied significantly at each L

position.

The cause of these differences was purely due to the L position as all other variables remained the same for each similar event set. Due to this, the differences were attributed to the proximity of the bubble to the nodes and anti-nodes of the primary distortional mode shape of the submerged platform, which for this case was BM1. Events closest to the anti-node of the BM1 mode shape at L = 0.0 m, E3 (W = 250 g) and E4 (W = 43 g), induced the most severe whipping responses for their charge sizes, while those at the node of the mode shape at L = -4.3 m, E7 (W = 250 g) and E8 (W = 43 g), were 71 % and 58 % lower compared to their respective

L = 0.0 m events.

It is shown that the peak strain results follow a linear trend at each L position, as per the fitted lines in Figure 3-27, with an assumed intercept at point (0 MPa.ms, 0 µε). The trend is well

characterised for the amidships (L = 0.0 m) events E1 – E3 (W = 250 g) while lacking for E4 (W = 43 g). There is insufficient data to validate this trend for other charge sizes and L

positions. However, it is clear from the limited results that the L position had a significant effect on the submerged platform’s whipping response severity, where the gradient of the peak strain and IB relationship decreased by approximately 100 µε between each successive L position. This relationship suggests that the effects of the L position increase as IB increases, for the investigated bubble proximity ranges of 1.45 ≤ γ ≤ 2.00 and relative sizes of 2.5 ≤ λ ≤ 4.5. Considering a comparison of each event’s SF, previously noted in Table 3-4, this parameter is unable to differentiate between the three trends noted in Figure 3-27, most apparent by the large difference in the peak response from events E3, E5, and E7, which all have the same SF = 0.38. Furthermore, the shock factor would not be able to account for changes in the response due to depth of the event, while the pressure impulse is comparable at any depth, given it is a function

of it. For these reasons it is strongly suggested that the SF should not be used to predict whipping events on submerged platforms.

Figure 3-27 Peak strain responses from bubble loading compared to the bubble pressure impulse IB

3.4

Conclusion

A set of eight underwater explosion experiments were conducted to investigate the whipping response of a submerged 12 m long, 0.4 m diameter cylindrical platform. Two Pentolite charge sizes (250 g and 43 g) at stand-off distances from 1.8 m to 0.8 m, and at different longitudinal positions along the hull length were used in this experiment. All UNDEX events were conducted with the charge and the platform at a depth of 5 m.

Measured incident pressures showed good correlation with theory for the first bubble cycle. Similitude equations for the bubble period compared well with experimental measurements for a relative proximity of γ > 1.67. Beyond this limit the similitude results under or over predicted the period depending on the charge size. New K coefficients for bubble period calculations were identified and presented from this experimental dataset. Due to the limited data sets available, further experimental analysis of different bubble proximities would be required to determine the cause of these differences at bubble proximities of γ < 1.67.

Through integration of the incident pressure-time data, it was found for both Pentolite charge sizes that 35.1% and 64.9% of the total pressure impulse was associated with the shock wave and bubble respectively. Given the consistency across all conducted events, this relative contribution is likely a property of the explosive material.

The severity of whipping induced bending responses was shown to depend on the relative contribution of the first three distortional bending modes for the submerged platform. The contribution of a mode increased with the proximity of the bubble frequency to the submerged platform’s modal frequencies, and with the physical proximity of the UNDEX to the anti-node

of the primary distortional mode shape, which was the first bending mode for this platform. Charges of any size detonated in proximity to the anti-node of the first bending mode shape induced the most severe whipping responses. Charges detonated near the node of the first bending mode shape induced whipping response strains that were 71 % and 58 % lower than the respective 250 g and 43 g charge sizes detonated at the anti-node of the mode shape. It was observed that interaction of the multiple dominant mode shapes caused the peak bending response to occur at locations away from the charge stand-off point for some events. This generally occurred when the charge stand-off location was between the node and anti-node of the first bending mode shape.

It is suggested that if the stand-off location along the platform length can be influenced to occur at the node of the primary bending mode shape, the platform will be inherently hardened against a severe whipping response. Additionally, should a scenario occur where multiple bending modes are excited, the responses at locations away from the stand-off point may need to be assessed, as these can potentially undergo a more severe response than that at the stand-off point.

Comparison of the bubble pressure impulse to the peak strains measured during the whipping response suggest that as the impulse increases, the stand-off location in relation to the primary bending mode shape has a more pronounced effect on the whipping severity. This relationship appears valid for the 250 g charge size detonated at amidships for the investigated bubble proximity ranges of 1.45 ≤ γ ≤ 2.00 and relative size of λ = 4.5. Further work is required to determine if this is also valid for other charge sizes and stand-off locations. This will be investigated in the following chapters using a validated numerical model.

Chapter 4.

Numerical model development and