Surface Load Characteristics of High-Pile Steel Tube Columns Under Shallow Water Explosion

Literature Overview

This paper by Zhuang Tieshuan, Wang Mingyang, Wu Jun, Zhang Tao, Yang Chengyu, and Yan Minhua, published in Journal of Vibration and Shock in 2020, presents experimental results on the surface pressure characteristics and spatial distribution of shock waves acting on high-pile steel tube columns under shallow water explosion conditions. The research was funded by the National Natural Science Foundation of China (grant 51578543). The study is of significant importance for the design of marine and naval structures subjected to underwater explosive loading, such as ship hulls, offshore platforms, and submarine structures.

Experimental Configuration and Test Matrix

The authors conducted water explosion model tests with varying parameters to systematically investigate the influence of explosive charge mass, explosion distance, and detonation depth on the shock wave loading characteristics. The test matrix is summarised below:

Test Parameter	Variation Range	Purpose
Explosive charge mass	Multiple levels	Study effect of energy input on peak pressure
Explosion distance	Multiple levels	Study effect of stand-off distance on pressure decay
Detonation depth	Multiple levels	Study effect of water surface proximity on reflection and diffraction

The high-pile steel tube column serves as the target structure, and pressure sensors were mounted on the column surface to record the shock wave loading history. The use of a high-pile column (a column with significant height relative to the water depth) allows the study of three-dimensional wave propagation effects including reflection from the water surface and diffraction around the column edges.

Shock Wave Interaction Mechanisms

The paper identifies two primary shock wave interaction mechanisms acting on the steel tube column surface:

Reflected shock wave: The incident shock wave from the explosion reflects off the column surface, creating a reflected wave with higher pressure than the incident wave. The reflection coefficient depends on the impedance mismatch between water and steel.
Diffracted shock wave: The shock wave diffracts around the column edges, creating complex wave patterns on the column surface, particularly on the shadow side.

Key Experimental Findings

The experimental results reveal several important characteristics:

Temporal coincidence: The reflected and diffracted shock waves act approximately simultaneously on the column surface, which simplifies the loading model but complicates the separation of individual wave contributions.
Non-uniform pressure distribution: The peak pressure varies along the height of the column, with higher pressures near the mid-height where the shock wave energy is concentrated.
Water surface effect: The influence of the water surface on the shock wave peak pressure is relatively small, but the secondary bubble pulsation is significantly affected by the water surface proximity. This is because the shock wave is a high-frequency phenomenon with short duration, while the bubble pulsation is a lower-frequency phenomenon with longer duration.
Scaling law: For the same scaled distance (Z = R/W^(1/3), where R is the distance and W is the charge mass), the reflected shock wave peak pressure is consistent, but the diffracted shock wave peak pressure is relatively lower for smaller charges at closer distances. This suggests that the diffraction mechanism is not purely governed by the scaled distance and may be influenced by the absolute charge mass and distance.

Engineering Design Formula

A particularly valuable contribution of this paper is the proposed engineering calculation method for the actual shock wave pressure acting on the steel tube column surface. The key finding is:

When the scaled distance Z ≥ 1.71, the actual shock wave peak pressure on the column surface can be approximated as 1.37 times the free-field shock wave peak pressure.

This factor of 1.37 represents the combined effect of reflection and diffraction, and provides a simple design multiplier for engineers. The formula is of practical value for blast-resistant design of marine structures.

Reflection and Diffraction Coefficients

The paper provides expressions for the shock wave reflection coefficient and diffraction coefficient as functions of scaled distance. Both coefficients decrease with increasing scaled distance, which is consistent with the physics of shock wave decay. The reflection coefficient represents the amplification of pressure due to reflection off the steel surface, while the diffraction coefficient represents the attenuation of pressure as the wave wraps around the column.

Structural Response and Welding Considerations

From a structural engineering perspective, the shock wave loading on the steel tube column induces dynamic bending, membrane stretching, and local buckling. The non-uniform pressure distribution along the column height creates a complex bending moment diagram that must be accounted for in the design. The dynamic loading also induces high strain rates in the steel, which affects the material properties according to the Johnson-Cook or Cowper-Symonds constitutive models.

For the steel tube column itself, the welding quality of longitudinal and circumferential welds is critical under blast loading. The high strain rates and complex stress states can initiate cracks at weld defects. According to MIL-STD-132 and API 5L, welds in blast-resistant structures should be inspected by ultrasonic testing (UT) and magnetic particle testing (MT), with acceptance criteria at least at level II. The heat-affected zone (HAZ) of the welds should be examined for microstructural changes that could reduce the dynamic fracture toughness.

FMEA Analysis of Failure Modes

Applying Failure Mode and Effects Analysis (FMEA) to the steel tube column under water explosion loading:

Failure Mode	Cause	Severity	Detection	Mitigation
Local buckling	Excessive compressive stress on column wall	High	Visual/UT	Increase wall thickness, add stiffeners
Weld cracking	Stress concentration at weld toe	Critical	MT/PT	Post-weld heat treatment, weld toe grinding
Global bending failure	Excessive moment from non-uniform pressure	High	Strain gauges	Increase column diameter, add lateral bracing
Fatigue cracking	Repeated shock loading	Medium	UT/ET	Limit number of shock events, inspect periodically

Study Insights and Reflections

This paper provides valuable experimental data on the complex shock wave interactions that occur when underwater explosions impinge on cylindrical structures. The finding that the water surface has limited effect on shock wave peak pressure but significant effect on bubble pulsation is important for the design of structures in shallow water environments. The engineering design formula with the 1.37 multiplier is a practical tool for preliminary design, although detailed design should use the full reflection and diffraction coefficient expressions.

The scaled distance finding is particularly interesting: the fact that the diffraction peak pressure is not purely a function of scaled distance suggests that absolute geometry and wave interaction effects play a role beyond simple geometric similarity. This has implications for the scaling of model tests to full-scale structures, which is a common practice in blast engineering.

Summary

The paper provides comprehensive experimental data on shock wave loading characteristics for high-pile steel tube columns under shallow water explosion conditions. The identification of reflection and diffraction mechanisms, the development of engineering design formulas, and the quantification of water surface effects are all valuable contributions. Engineers designing marine structures for blast resistance should use these findings for load estimation, while paying close attention to weld quality, material strain rate sensitivity, and the complex pressure distribution patterns revealed in the study.