Submarine pipelines are critical components of ocean engineering, and serves as essential infrastructures for energy transportation [1,2], deep-sea resource development [3,4], and transoceanic communication [5]. These pipelines operate in complex marine environments, where they must endure long-term exposure to ocean currents and corrosion, as well as sudden extreme events such as underwater explosions. A prominent example is the Nord Stream pipeline incident in 2022, where a suspected underwater explosion led to catastrophic pipeline rupture, leading to major environmental and geopolitical consequences. Understanding the dynamic response of submarine pipelines to underwater explosions is essential for improving blast-resistant designs and ensuring the reliability of key national infrastructures [6].

Underwater explosions are typically categorized into far-field [7] or near-field [8] scenarios on the basis of the distance between the explosion source and the submarine structure [9]. In far-field explosions [7], the explosion-induced shock wave gradually attenuates into linear acoustic waves during propagation. This phenomenon primarily induces global structural responses through hydrodynamic impact loading. To assess potential damage, researchers often simplify these shock waves via one-dimensional hydrodynamic models [8,10]. In contrast, near-field explosions are far more complex and involve three primary loading mechanisms: the initial shock wave, pressure pulsations from bubble oscillation, and high-speed jets formed during nonspherical bubble collapse [11,12]. Moreover, the shockwave-bubble-structure interaction further generates rarefaction waves [13], creating an intermediate cavitation zone with subatmospheric pressures [14]. The subsequent collapse of cavitation bubbles within this region produces secondary impacts that impose cyclic loads on nearby structures. Experimental investigations by Brett et al. [15,16] have quantitatively demonstrated the critical role of cavitation-induced loads in governing the deformation patterns of submerged cylindrical structures.

In near-field scenarios, jet pressures generated by bubble collapse [17] can exceed the initial shock wave magnitude. Such extreme loading often leads to severe deformation in submarine pipelines accompanied by nonlinear material phenomena, including yielding and fracturing [18–22]. Although the collapse mechanisms of cylindrical shells under hydrostatic compression have been extensively investigated [23–26], their dynamic response to near-field blast loading remains less explored. Gupta et al. [18] performed experiments on the collapse of 6061-T6 aluminum pipes in a confined environment, where the samples were subjected to combined loading from preapplied hydrostatic pressure and longitudinal explosion. Their results revealed that the pressure pulse induced by the initial collapse of the explosion bubble exerted a non-negligible influence on the structure. Later, Sun et al. [27] conducted numerical simulations and theoretical modeling to reveal how the initial hydrostatic pressure and fluid-structure interaction influence the stability of cylindrical metal shells. Their findings demonstrated that pre-existing hydrostatic pressures degrade structural stiffness, triggering a progression from axisymmetric vibration to secondary vibration modes. A critical pressure threshold was identified, beyond which shell implosion occurred abruptly. More recent experimental work by Mao et al. [28] further investigated the role of internal pressures and wall thicknesses on thickness in the deformation and damage of pressurized cylindrical shell pipes. They revealed that higher initial internal pressures enhanced the structural resistance, whereas increased wall thickness unexpectedly reduced it. Research [29] revealed a two-stage deformation pattern of the pipe: minor initial distortion during the shock wave stage, followed by significantly amplified deformation during the bubble pulsation stage. Recently, Ma et al. [9] conducted numerical studies on the dynamic coupling mechanisms between underwater explosion bubbles and unrestrained pipes, analyzing the bidirectional interaction between bubbles and structural dynamics. They reported that at relatively low amplitudes, cylindrical shells collapsed in a counterintuitive manner and noted that the collapse time did not monotonically decrease with increasing explosion amplitude.

While significant progress has been made in understanding pipeline dynamics. Most existing studies—primarily aimed at enhancing structural blast resistance via modifications in structural configurations and material properties [30,31]—have relied on idealized models and have not fully accounted for three critical factors relevant to practical applications: seabed constraints, the two-way interaction between bubble dynamics and the pipe response, and structural support configurations. These factors introduce substantial complexity into the fluid-structure interaction behavior of the pipe. To fill this knowledge gap, this study investigates the dynamic response of a seabed-mounted pipe subjected to near-field explosions. We employed a recently developed multiphase fluid-structure interaction solver to capture the two-way interaction between bubble dynamics and the structural response. For a given explosion pressure, we systematically analyze the effects of the internal pipe pressure, pipe wall thickness, and support angle on the implosion resistance of seabed pipes. These findings provide a theoretical foundation for optimizing pipeline design and enhancing structural resilience under explosive loading. The paper is organized as follows: Section 2 introduces the physical model and numerical methods, including a mesh convergence analysis for verification. In Section 3, we analyze the dynamic response of pipes under different underwater explosion bubble pressures. Section 4 explores the implosion resistance of seabed pipes with varying internal pressures, wall thicknesses, and support angles under near-field underwater explosions. Finally, concluding remarks are presented in Section 5.

In an underwater explosion, the explosive charge determines the initial internal pressure of the bubble, which in turn affects the bubble’s expansion dynamics, including volume evolution, maximum radius, and oscillation period. The resulting pressure waves and fluid motions then govern the impact force and collapse behaviors of nearby pipes. Hence, a systematic analysis is carried out to investigate how varying the initial pressure of a bubble affects the structural response of the pipe. Seven different pressures are examined: P_b = 10, 25, 30, 35, 50, 75, 100, 150, and 200 MPa. This study focuses on the fluid-structure interaction following bubble formation without explicitly modeling the detonation process. To represent varying explosion intensities in a parametric manner, swe use the Jones–Wilkins–Lee (JWL) equation [51] to map bubble internal pressures to equivalent TNT charges:where A₁, R₁, B₁, R₂, and ω are material-specific constants; and V and E are the dimensionless specific volume and internal energy, respectively. The values of these parameters are taken from Wang et al. [30]. On the basis of this model, the selected internal pressures correspond to TNT charge equivalents of 4.171 g (10 MPa), 10.429 g (25 MPa), 12.514 g (30 MPa), 14.600 g (35 MPa), 20.857 g (50 MPa), 31.286 g (75 MPa), 41.714 g (100 MPa), 62.567 g (150 MPa), and 83.324 g (200 MPa). In addition, the pipe geometric parameters in all test cases follow the baseline values listed in Table 1. Moreover, to simulate a deep-water environment, the ambient water pressure is set to P_w = 1 MPa. At the same time, for the convenience of analysis, we nondimensionalize the pressure parameters on the basis of P_w: P_b^* = P_b/P_w, P_i^* = P_i/P_w. Additionally, we nondimensionalize the size parameters on the basis of R_s, for example, δ^* = δ/R_s.

Figure 6 presents a comparison of the time evolution of bubble dynamics and the associated structural response under 4 representative initial pressures. Two distinct dynamic response regimes of the pipe can be observed: an elastic oscillation regime (P_b^* ≤ 30) and an implosive collapse regime (P_b^* ≥ 35). These regimes differ not only in the extent of deformation but also in the bubble shape, jet formation, and energy transfer patterns.

Specifically, at P_b^* = 25, the bubble exhibits quasispherical oscillations with only minor flattening at its lower boundary. The pipe undergoes elastic oscillations with decreasing amplitude. Neither significant denting nor irreversible deformation is observed. During the bubble collapse phase, the elastic rebound of the pipe provides an upward pushing effect on the lower bubble boundary. In this case, the bubble’s impact on the pipe is limited, and the amplitude of pipe vibrations diminishes over time.

At P_b^* = 50, the interaction enters a transitional regime. In the early expansion phase, the bubble rapidly grows and emits a strong expansion wave. The impact of the expanding bubble induces a downward concavity on the upper surface of the pipe by t = 27 ms. As the bubble collapses, the pipe begins to rebound but fails to recover its original shape, marking the onset of large-scale plastic deformation. In the subsequent bubble re-expansion phase, the concavity on the pipe acts as a geometric trap, concentrating the bubble’s loading on the midsection. This results in intensified deformation of the pipe, eventually resulting in a flattened collapse.

At P_b^* = 75, the bubble-pipe interaction exhibits a more intensified deformation process than that at P_b^* = 50. During the bubble expansion phase, a stronger expansion wave is produced, which leads to significant compression on the upper wall of the pipe. By t = 18.6 ms, a deeper downward concavity has formed. The bubble’s lower boundary is pulled into a “bulb-like” shape. In the following process, despite not being subjected to the jet’s direct impact, the pipe continues to deform inward owing to a buckling-folding instability, eventually resulting in a flattened and irreversible collapse. Notably, during the bubble’s first expansion, the pipe’s concavity acts as a geometric trap that focuses the expansion wave, leading to localized high-pressure accumulation. The focus of compressive energy at this concavity amplifies the downward load on the structure. At t = 37.2 ms, elastic rebound subsequently occurs in the compressed region, imparting upward momentum to the lower bubble interface. This initiates the formation of a distinct upward-directed bubble jet, which becomes clearly visible at t = 55.8 ms. This jet illustrates a feedback mechanism in which structural deformation modifies the local pressure field of the bubble, reinforcing the two-way coupling between pipe collapse and bubble dynamics. A similar concavity-induced pressure accumulation can also be observed that at P_b^* = 50, the resulting pressure gradient during the second bubble cycle is relatively weak. At t = 80.8 ms, although the pipe collapse zone experiences elevated pressure, the reduced intensity and gradient are insufficient to trigger an upward jet.

At P_b^* = 100, the process accelerates significantly: the pipe enters plastic deformation almost immediately and collapses into a curly shape before the bubble completes its expansion. Unlike the lower-pressure cases, the process bypasses the typical rebound-collapse sequence entirely. Additionally, during collapse, the bubble’s lower boundary is significantly elongated under a high-pressure gradient, forming a more pronounced “bulb-like” shape. Owing to the premature structural collapse of the pipe before the bubble completes its full expansion, no reverse jet is observed. However, a distinct high-pressure accumulation still forms at the concave region on the upper surface of the pipe. At t = 9.2 ms, the expanding bubble induces an early and intense pressure concentration in this region. Compared with lower-pressure scenarios, the focused pressure region emerges more rapidly and with greater intensity. From the above representative case, it is worth noting that in similar configurations, Ma et al. [9] observed three main deformation modes of pipes in the absence of rigid seabeds and structural supports: oscillation, axisymmetric collapse, and curling collapse. In our study, however, the presence of boundaries and supports inhibited the occurrence of axisymmetric collapse. These structural constraints limit large-scale displacement and deformation between supports, causing the impact to concentrate in localized regions and increasing the likelihood of asymmetric curling.

Interestingly, the rate and mode of pipe implosion vary considerably with the initial explosion pressure. To further quantify the morphological changes and dynamic mechanisms of pipe implosion, we compare several implosion-related parameters across the tested initial pressures. Figure 7(a) compares the final morphologies of the collapsed pipe. The changes of corresponding width and height with respect to the initial pressure are plotted in Fig. 7(c) and (d). As the initial pressure increases, the width decreases progressively whereas the height increases. These trends illustrate a transition from flat denting to narrow, deep folding as the bubble-induced loading intensifies. The change in the pipe’s implosion time is illustrated in Fig. 7(b). It is expected that the implosion time decreases significantly as P_b^* increases.

The above results suggest a pressure-dependent transition in the implosion mechanism. When P_b^* < 100, the bubble’s maximum volume and loading intensity are limited, preventing the pipe from implosing during the initial expansion phase. In this regime, implosion is driven primarily by the bubble’s secondary collapse. Specifically, the second collapse generates a localized high-pressure region near the upper wall of the pipe, inducing downward deformation. The resulting morphology is typically a flattened, column-like shape. In contrast, when P_b^* ≥ 100, the first expansion of the bubble is sufficient to trigger substantial implosive deformation. The implosion process becomes dominated by top collapse, while the pipe’s sidewalls curl inward due to tensile effects. The implosion morphology gradually evolves into a shape characterized by minimal deformation at the ends and pronounced vertical compression at the center.

Furthermore, bubble migration and pipe deformation are critical for understanding the underlying fluid-structure interaction mechanisms [52,53]. Figure 8 presents the temporal evolution of three key indicators across a range of P_b^* values: bubble centroid migration (Fig. 8(a)), pipe top displacement (Fig. 8(b)), and plastic zone development (Fig. 8(c)). The corresponding spatial distributions of the plastic regions are schematically summarized in Fig. 8(d).

As shown in Fig. 8(a), low-pressure cases (P_b^* = 10, 25, and 30) exhibit periodic centroid oscillations with short durations and limited amplitudes, reflecting restrained bubble expansion due to lower energy release. Among them, P_b^* = 10 features the shortest period and smallest amplitude, resulting from its minimal internal pressure, which restricts the bubble volume. The bubble remains nearly spherical, generating symmetric pressure waves and resulting in limited structural impact. These periodic motions induce synchronized oscillations in the pipe top displacement (Fig. 8(b)). As depicted in Fig. 8(c), P_b^* = 10 produces negligible deformation, with the plastic strain remains near zero. In contrast, P_b^* = 30 triggers localized plasticity due to larger displacements near the bubble-facing apex, where alternating bending stresses begin to exceed yield thresholds.

At intermediate pressures (P_b^* = 35, 50, and 75), the system becomes significantly more complex and nonlinear. The centroid trajectory becomes nonmonotonic, descends initially, briefly rebounds upward, and then accelerates downward again. This reflects a two-stage interaction: during initial expansion, the bubble induces localized pipe concavity without full collapse, which compresses the lower bubble surface and causes the reverse jet. Additionally, this rebound is mirrored in the displacement of the pipe top (Fig. 8(b)), which shows initial downward motion, brief elastic recovery, and subsequent intensified deflection. As the energy input increases, elastic recovery becomes less effective and plastic deformation initiates earlier, as confirmed by the rapid rise in plastic strain (Fig. 8(c)). Particularly for P_b^* = 75, the plastic ratio escalates quickly and saturates at a relatively high level, indicating reduced structural recoverability under relatively strong fluid-structure coupling. In the high-pressure regime (P_b^* = 100 and above), asymmetric collapse dominates. The bubble centroid follows a sharp, monotonic descent toward the structure with no rebound, signifying direct impact. With increasing P_b^*, the centroid’s downward velocity, pipe deflection rate, and structural failure onset all intensify. The pipe top rapidly reaches a normalized displacement of −2, indicating complete implosion.

Figure 8 (d) further reveals the spatial evolution of the plastic zones with increasing pressure. At P_b^* = 10, plastic deformation is negligible and limited to regions near the supports. When P_b^* = 25, the plasticity extends toward the apex, reflecting accumulated stress from repeated oscillations. At P_b^* = 50, the plastic deformation becomes more pronounced across the top wall, with the central region fully yielding. However, the collapse pattern remains relatively flat, resulting in partial preservation of elasticity near the flanks. When P_b^* = 100, the entire upper span between the supports is almost completely plastified, leaving only narrow bands between the supports that remain elastic.

To further investigate the structural behavior of the pipe under varying operating and design conditions, we conduct a series of parametric studies based on the baseline case with P_b^* = 100. Specifically, the effects of the internal pipe pressure, wall thickness, and support angle are analyzed. Unless otherwise specified, all the geometric and explosion parameters follow the baseline configuration listed in Table 1, and only the parameter under investigation is varied in each case.

This study develops a fluid-structure coupling simulation framework by integrating a multiphase compressible fluid dynamics solver with a nonlinear structural dynamics solver. By examining the flow field, bubble dynamics, and transient stress-strain responses of the pipe, the interactions between the bubble, the surrounding water, and the pipe are thoroughly analyzed. In contrast to most previous studies based on idealized models [9], this work accounts for three critical factors relevant to practical applications: seabed constraints, the two-way interaction between bubble dynamics and the pipe response, and structural support configurations.

First, we investigate the pipe response under different explosion pressures (10 MPa, 4.171 g of TNT → 200 MPa, 83.324 g of TNT) and identify two response types: periodic oscillation (≤30 MPa, 12.514 g of TNT) and downward collapse (≥35 MPa, 14.6 g of TNT). At lower initial pressures, the bubble expansion pressure is weak, resulting in only minor elastic responses of the pipe without significant plastic deformation. At moderate initial pressures, significant concavities are observed at the top of the pipe, which lead to plastic deformation under the influence of bubble pulses. At higher initial pressures, the strong pressure waves and jets emitted by bubble pulsation act together, causing rapid pipe implosion characterized by significant collapse from the top surface. In addition, as the initial pressure increases, the bubble’s lower edge elongates during the expansion phase, forming a characteristic “bulb-like” shape, whereas the jet intensity, and the pressure wave amplitude increases significantly. The pipe deformation transitions from overall flat compression to vertical compression at the center, with the implosion time decreasing progressively. Simultaneously, analysis of bubble migration and structural plastic deformation reveals that the pipe’s concavity acts as a geometric trap, concentrating compressive energy and leading to localized pressure amplification in the fluid. The subsequent elastic rebound of the structure destabilizes the lower bubble interface, triggering the formation of the reverse jet.

We subsequently conduct a systematic analysis of factors such as the internal pipe pressure (1 × 10⁵ → 2 × 10⁵ Pa), wall thickness (10→20 mm) and support angle (0º → 120º) to reveal the dynamic response characteristics of the pipe under different conditions. Increasing the internal pressure markedly delays collapse and redistributes deformation, transitioning from top-localized collapse to a flatter mode with increased width and reduced height. For pipe thickness, thinner pipes feature localized top denting, whereas thicker pipes exhibit greater resistance and more uniform deformation, along with prolonged collapse times. The support angle introduces a nonmonotonic effect: the collapse time initially decreases and then reaches a minimum at 60º. These findings provide valuable insights into the structural design of submarine pipelines for enhancing the resistance to explosive loading.