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Article

Study on Blast Mitigation Protection of Underground Station Structures Using Phononic Crystals

by
Jihu Wu
1,
Chuqiao Bo
2,
Dai Wang
3,*,
Zhongxian Liu
4,
Filip Broniewicz
5,* and
Miroslaw Broniewicz
5
1
China Railway Design Corporation, Tianjin 300308, China
2
School of Civil Engineering, Tianjin Chengjian University, Tianjin 300384, China
3
Tianjin Key Laboratory of Civil Structure Protection and Reinforcement, Tianjin 300384, China
4
Tianjin Key Laboratory of Soft Soil Properties and Engineering Environment, Tianjin 300384, China
5
Department of Building Structures and Structural Mechanics, Faculty of Civil Engineering and Environmental Sciences, Bialystok University of Technology, 15-351 Bialystok, Poland
*
Authors to whom correspondence should be addressed.
Buildings 2025, 15(21), 4006; https://doi.org/10.3390/buildings15214006
Submission received: 10 August 2025 / Revised: 21 October 2025 / Accepted: 31 October 2025 / Published: 6 November 2025
(This article belongs to the Special Issue Advances in Modern Structural Engineering: From Materials to Building Structures)
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Abstract

Urban subways, as critical strategic spaces, require underground structures with sufficient blast-resistant capabilities. To evaluate the blast resistance performance of underground station structures under ground-level nuclear explosion air shock waves, a three-dimensional finite element model of an underground station was developed using LS-DYNA. The blast mitigation effects of phononic crystals are primarily analyzed and the influence of parameters such as spatial arrangement, buried depth, and material properties of phononic crystals on the blast resistance of underground station structures is systematically examined. The results indicate that a denser configuration of phononic crystals enhances the blast mitigation effect, while the maximum displacement of the structure is increased. Considering the structure’s maximum response and economic feasibility, a spacing of 2 m between phononic crystals is recommended. Additionally, the blast mitigation effect stabilizes when the number of phononic crystal layers exceeds a certain threshold, with two layers being optimal. The buried depth of the phononic crystals has a limited effect on blast mitigation; therefore, positioning them midway between the ground surface and the structure at a depth of 2 m is advised. The material properties of the phononic crystals also have a significant impact on the blast protection. Rubber was found to yield the lowest dynamic response of the station structure, providing the best protective effect. These findings offer insights for designing phononic crystal-based blast protection in underground station structures.

1. Introduction

Urban subways and utility tunnels, which serve both civil defense and public infrastructure functions, are regarded as essential spatial resources for enhancing urban resilience and promoting sustainable urban development. These underground spaces face various uncertain disaster risks, including explosions and earthquakes, which place significant demands on a city’s response and recovery capabilities. With the spread of international terrorism and the increasing frequency of chemical explosion incidents, the accuracy and destructive power of modern airstrikes have improved significantly. Consequently, underground structures such as subway stations and tunnels must possess comprehensive protection capabilities for both peacetime disaster mitigation and wartime air defense. Due to high population density, evacuation difficulties, and susceptibility to attacks, any explosion that induces vibrations or collapses can lead to transportation paralysis, mass casualties, and significant social and economic impacts. These factors make underground structures prime targets for terrorist attacks. To mitigate the risk of accidental explosions from industrial incidents or terrorist attacks, underground structures must have adequate blast resistance. Therefore, research on blast protection for underground station structures is crucial for enhancing urban safety and resilience.
In general, the impact of explosions on underground structures can be categorized into surface explosions and internal explosions. For internal explosions, factors such as distance from the blast, the location of the explosion, and the presence of nearby underground structures can significantly influence the degree of damage. In recent years, scholars worldwide have conducted extensive experimental and numerical studies on the dynamic response of underground structures to internal explosions and have examined various factors, including the shape of the lining [1,2], material properties [3], soil type [4], soil parameters [5], explosive placement [6], explosive mass [7], and standoff distance [8], to understand their effects on internal explosion responses.
A primary focus in current research is protecting existing tunnels by reducing the effective intensity of shock waves. According to Kasilingam’s review [9], appropriate blast resistance and blast mitigation measures can significantly reduce damage from internal explosions to underground structures. Under explosive loads, damage often occurs in columns or lining structures. Various strategies have been proposed to protect these vulnerable areas, including the use of blast-resistant materials [10], blast-resistant components [11,12,13,14,15,16,17], blast-resistant structures [18,19,20,21,22,23,24], and blast-resistant configurations [25,26,27,28,29,30].
Comparative studies of internal and external explosions have shown that surface explosions pose a significantly higher risk than internal explosions due to their larger target areas and higher peak blast loads. Experimental research on surface explosions has been conducted by scholars, but full-scale tests are costly and challenging to control. Therefore, scaled-down experiments have been widely employed [31,32], and the influence of various factors, such as structural type [33,34,35,36,37,38,39,40,41,42], structural shape [43,44,45,46], and blast location [47,48], on the dynamic response of structures to surface explosions has been examined.
A review of previous research indicates that appropriate blast mitigation measures can significantly reduce the impact of external explosions. Effective blast resistance and mitigation strategies for surface explosions can be categorized into structural protection and environmental protection measures. In terms of structural protection, the installation of protective doors can effectively block blast waves from entering and reduce damage [49,50]. For environmental protection, protective structures such as ultra-high-performance reinforced concrete panels [51,52], aluminum foam materials [53], and geotechnical foam barriers [54] applied to linings have proven effective in resisting explosive impacts.
The installation of blast mitigation layers is also an effective approach. Dadkhah et al. [55] validated that the peak blast pressure can be reduced by using layers of shredded tire mixtures of varying thicknesses through simulations with ABAQUS software. Peng et al. [56] demonstrated through shake table tests that rubber–sand isolation layers can reduce the peak acceleration and strain increments in tunnel linings. Ichino et al. [57] incorporated expanded polystyrene (EPS) boards into soil as a blast mitigation layer, showing that appropriate thicknesses of sand and EPS layers effectively reduced blast wave intensity and peak structural pressure. Zhao et al. [58] proposed a sacrificial foam cementitious layer made of expandable polystyrene (EPS) particles and a cement matrix for tunnel linings, which provided significant blast mitigation. Wang [59] discovered that embedding a foam concrete layer over buried structures effectively reduced the impact of restrained explosions, with protection improving as foam concrete strength and thickness increased. Wang [60] further investigated metakaolin-based foam geopolymer (MKFG) as a sacrificial protective coating through experiments and numerical simulations, finding that sacrificial layers lowered peak lining pressure and that MKFG density correlated positively with protective performance. Mohammad Momeni et al. [61] present an improved calculation method, based on structural reliability analysis, to evaluate the minimum SSD for steel columns under dynamic blast loads. A parametric study is thus carried out to obtain curves of probability of low damage for a range of H-shaped steel columns with different sizes and boundaries.
In summary, many scholars have conducted experimental research and computational analyses on the blast resistance and protection of underground structures. The impact of explosions on structures can be categorized into external and internal explosions based on the point of load application. The influence of structural forms, soil conditions, and types of explosives have been examined in existing studies. Blast mitigation measures are generally divided into structural protection and environmental protection approaches. Under high peak loads, such as those from nuclear blasts, installing blast mitigation layers in the surrounding environment has been proven effective in countering blast effects. However, research on blast response analyses and blast mitigation measures remains limited, with many potential areas for further investigation concerning different structures and mitigation techniques under nuclear blast conditions.
Subway stations, as large underground structures with enclosed environments and complex designs, have been minimally studied in the context of blast response analysis. Current studies often use polymer composite materials or concrete layers as blast mitigation covers. Phononic crystal structures, which exhibit low-frequency attenuation due to their periodic foundation, can suppress seismic waves from propagating to upper structures. Yet, there has been limited research on using phononic crystals as blast protection structures. Hirsekorn et al. [62,63] investigated wave propagation characteristics and localized resonant attenuation properties in two-dimensional periodic structures, verifying their vibration reduction characteristics and bandgap behavior through finite element models. Kushwaha et al. [64,65,66] introduced the theoretical concept of phononic crystal periodic structures and presented the theoretical and experimental findings on one-, two-, and three-dimensional periodic isolation foundations, eventually extending the bandgap theory of periodic structures to the civil engineering field, proposing new structural mitigation and isolation foundations.
Given the current international situation marked by increased global conflicts and escalating military tensions worldwide, the study of the dynamic performance and nuclear blast resistance of underground subway stations under nuclear blast loads holds significant implications for civil defense. This study employs the LS-DYNA software (version R9.2.0) to conduct numerical simulations and parameter analysis on the nuclear blast resistance of underground subway stations equipped with phononic crystal protection measures, contributing to blast mitigation research for underground structures.

2. Physical Model

2.1. Establishment of the Finite Element Model

A three-dimensional finite element model of a double-layer underground subway station structure is created using LS-DYNA. The structure has a width of 22 m, a height of 15 m, and is buried under a 5 m thick overburden (buried depth) D = 5 m. Figure 1 shows the standard cross-sectional frame diagram of the underground station, while Figure 2 illustrates the finite element model of subway station–surrounding soil structure system. In the station–soil finite element model, both the soil and the structure are modeled using the three-dimensional solid element SOILD164, with a computational domain of 100 m × 55 m × 20 m and all units expressed in the m-kg-s system.
In the finite element model with the phononic crystal arrangement, the crystals are positioned with the following parameters: radius R = 0.25 m, center-to-center distance L = 2 m, and buried depth (distance from the center to the surface) d = 2 m. The arrangement includes two rows covering twice the width of the structure.
Following the approach detailed in reference [67], extensive trial calculations are performed to strike a balance between computational accuracy and efficiency, which leads to the specific mesh element sizes used throughout our model.
The underground subway station is discretized using hexahedral elements with dimensions of 250 mm × 250 mm × 1000 mm or 250 mm × 300 mm × 1000 mm. Each phononic crystal is modeled as a quarter-circle with a 250 mm radius in the XY plane, extending 1000 mm along the Z-axis. To improve calculation speed through mesh alignment, the soil domain is divided into different regions. The soil adjacent to the station’s sides and below its base slab is meshed with hexahedral elements measuring 250 mm × 1000 mm × 1000 mm or 300 mm × 1000 mm × 1000 mm. For the far-field soil, the cubic elements of 1000 mm × 1000 mm × 1000 mm are used. The mesh sizes in the soil layer above the station roof varied due to the presence of complex, circular phononic crystals. In the XY plane, we refined the mesh near these units, using triangular or quadrilateral soil elements with side lengths ranging from 80 mm to 300 mm. The rest of the soil in this layer is meshed with triangular or quadrilateral elements with side lengths from 250 mm to 1000 mm.
The interaction between the soil and the structure is modeled using shared node contact. In LS-DYNA, discontinuous media interfaces are commonly modeled using methods such as shared-node contact, fluid–structure coupling, and cohesive elements [68,69,70]. The shared-node model is chosen for its ease of use and computational efficiency. This method requires the meshes of the two adjacent media at the interface to be coincident, ensuring that both forces and deformations are completely equal across the interface [71].
The upper surface of the model is treated as a free boundary, while all other surfaces are simulated with non-reflective boundaries to model the semi-infinite soil domain. Since the soil surrounding underground structures is a semi-infinite medium, it is computationally impractical to model the entire domain. However, when analyzing soil–structure interaction under load, the effect of the load on the soil far from the structure is negligible. Therefore, a virtual boundary at a sufficient distance is introduced to truncate the soil into a finite region for simulation. Artificial boundary conditions, such as artificial transmitting or damping boundaries, are then applied to this virtual boundary. The damping coefficient is calculated based on the soil’s material properties, enabling the truncated finite soil domain to exchange energy with the external infinite medium. This ensures that outward-propagating waves can either penetrate the boundary and radiate to infinity or be dissipated at the boundary without reflecting back into the simulated finite domain.
In LS-DYNA, a transmitting boundary is implemented by applying normal and tangential viscous forces. The *BOUNDARY_NON_REFLECTING keyword command is used to set this condition, which eliminates stress wave reflections and effectively simulates the response of an infinite soil medium.
Reinforced concrete can be modeled through three approaches: the smeared model (integral model), embedded model (composite model), and discrete model (separated model). In this study, we adopt the integral modeling technique, which applies the principle of equivalent strength to homogenize the effects of the steel reinforcement throughout the concrete matrix. This method effectively simulates the overall material properties of the reinforced concrete element. To better simulate the actual conditions, the finite element model employs the Plastic Kinematic model (*MAT_PLASTIC_KINEMATIC) within LS-DYNA’s blast simulation analysis framework to simulate the material properties of reinforced concrete, a model widely utilized in engineering practice [72,73,74,75,76,77]. The soil medium is modeled using the Drucker–Prager model (*MAT_DRUCKER_PRAGER), which employs a generalized von Mises yield criterion. The main parameters for the soil are provided in Table 1. For the phononic crystal, steel is selected as the material, with its primary material parameters detailed in Table 2.
In structural calculations, the overpressure waveform of the surface air shockwave from a nuclear explosion can be simplified either as a tangent waveform at the peak pressure (t1) or as a triangular waveform with no overpressure rise, based on equivalent impulse (t2) (Figure 3) [79]. According to the Chinese national standard “Design Code for Civil Air Defense Engineering” (GB50225-2005) [80], the maximum overpressure for the nuclear explosion’s surface air shockwave is set at 1.5 MPa in this model. The duration of the effect, t, is taken as 0.1 s for the tangent simplified waveform (t1), with the total calculation time set to 1 s.

2.2. Validation of the Finite Element Model

To validate the chosen material models, element types, the existing literature is consulted to ensure the accuracy of numerical model.
This study first refers to the method validated using theoretical formulas. For instance, Zhang [5] referenced the U.S. Air Force Manual TM5-1300 [81] to calculate the effects of ground contact explosions on underground structures. The LS-DYNA finite element model’s numerical results for the peak pressure wave in soil showed good agreement with the theoretical calculations.
Based on the selection of mesh size in the previous section, this section validates the correctness of the three-dimensional numerical modeling, material selection, and mesh generation by comparing with the experiment conducted by Zeng et al. [82]. The structure has a height of 2.25 m and a width of 3.1 m. The arrangement of the experimental setup is shown in Figure 4. In this experiment, a 10 kg TNT charge was buried underground at a distance of 20 m from the structure and at a buried depth of 2 m. Sensors were installed on the ground and the structure to measure the vibration velocity. The finite element model was established as shown in Figure 5, and the results at the corresponding reference points were examined and compared with the experimental results, as presented in Table 3. Through the comparative analysis with the experimental data, it can be observed that the numerical simulation results agree well with the experimental findings, thereby validating the modeling approach, mesh generation, and the materials adopted.
Based on these validations, the modeling approach, mesh division, and material selection were thereby verified. Consequently, the finite element model can be used to simulate the dynamic response of underground structures subjected to ground blast loads, thereby providing a reliable representation of real-world engineering conditions.

3. Numerical Analysis

3.1. Influence of Phononic Crystal Presence on the Dynamic Response of Underground Stations

The dynamic response of an underground station structure with and without phononic crystals is analyzed, with a buried depth of 5 m. The arrangement of the phononic crystals is as follows: radius R = 0.25 m, center-to-center distance L = 2 m, buried depth d = 2 m, and two rows of crystals. The comparison is made under the impact of a surface nuclear explosion load.
Figure 6 shows the effective stress clouds of the underground station structure. From the figure, it is evident that the effective stress contour map accurately reflects the overall structural variation, allowing identification of weak regions under nuclear explosion effects. The map reveals that, without phononic crystals, the peak stress occurs at the roof slab, reaching 1.413 × 108 Pa. In contrast, with the phononic crystals, the peak stress gradually spreads towards the corners, with the stress peak shifting to the junction of the roof and side walls and decreasing to 4.057 × 107 Pa.
Figure 7 shows the displacement comparison of the underground station structure. From the figure, it can be observed that when phononic crystals are absent, the overall displacement of the structure is large, with the maximum displacement concentrated at the center of the roof slab reaching 11.08 cm. Displacements at the side walls and floor are slightly smaller than at the roof slab, and the displacement at the edge columns of the first platform is minimal.
When phononic crystals are present, the displacement of the roof slab spreads more uniformly outward, with the largest displacement now occurring at the side walls and the peak displacement reducing to 5.40 cm. The overall peak displacement of the structure is reduced by 50%.
The reason for this behavior can be analyzed as follows: without phononic crystals, the surface blast force is concentrated in the soil, causing the structure to bear most of the load. However, with phononic crystals in place, these crystals are able to absorb a significant portion of the load above the structure, resulting in a considerable reduction in the displacement. Therefore, in practical engineering, it is essential to reinforce the region above the structure to reduce the propagation of the explosion wave and ensure the safety of the entire structure.
Figure 8 shows the effective plastic strain clouds of the underground station structure. From the figure, the failure locations and extent of damage to the structure can be observed. Without the protection of phononic crystals, the plastic deformation primarily occurs at the corner points of the middle columns on the second floor. With the phononic crystal protection in place, the plastic zone gradually spreads to the corner points of the roof and floor slabs, and the plastic damage significantly decreases. However, the damage remains concentrated around the structural corner points.
The reason for this behavior can be analyzed as follows: The surface load has a direct impact on the station structure, and without any protective measures, the roof slab is the first to experience damage. With the introduction of protection above the structure, the corner points, being more vulnerable, become the primary locations for damage transfer. In such cases, both local and overall damage may occur in the structure. Therefore, reinforcement of the structure, particularly at the corners, is necessary in engineering practice.
The results above indicate that the phononic crystal reinforcement can provide effective blast protection for the structure. From the clouds, it can be seen that with the presence of phononic crystals, the maximum displacement and maximum stress of the structure gradually shift from the roof slab to the junction between the roof and side walls. In the subsequent discussion of the impact of the spatial arrangement of the phononic crystals, the observation point is uniformly selected at the junction between the roof and side walls, node A, for further analysis (Figure 9).

3.2. Influence of Phononic Crystal Density on the Dynamic Response of Underground Stations

The effect of phononic crystal density on the dynamic response of the underground station structure is primarily investigated by varying the center-to-center distance of the phononic crystals. The trends observed in the contour maps are similar to those discussed previously and will not be elaborated further. Instead, the analysis focuses on the time history curves. The peak load and structural buried depth are consistent with those discussed earlier.
For this study, the radius of the phononic crystals is fixed at R = 0.25 m, with the center-to-surface distance d = 2 m, and two rows of crystals are arranged. The center-to-center distance between the crystals is varied from sparse to dense with values of L = 1 m, L = 2 m, and L = 3 m to compare the structural response of the underground station under nuclear explosion loading.
Figure 10 presents a comparison of the effective stress in the underground station structure under different conditions. It can be seen that the stress in the structure increases as the center-to-center distance of the phononic crystals increases. Specifically, when the center-to-center distance is 1 m, the maximum effective stress is 4.039 × 107 Pa; when the distance is 2 m, the maximum effective stress is 4.057 × 107 Pa; and when the distance is 3 m, the maximum effective stress is 4.202 × 107 Pa. In this case, the stress propagates more rapidly, and the diffusion effect is more pronounced, covering a larger area.
The reason is that a larger center-to-center distance (i.e., a more sparse arrangement) is less effective at blocking the propagation of the explosion wave. When the center-to-center distance is set to 1 m, the closer arrangement offers better protection to the structure, allowing it to share the explosion load more effectively.
Figure 11 shows the displacement comparison of the underground station structure under different conditions. From the figure, it can be observed that when the center-to-center distance is 1 m, the maximum displacement is 6.583 cm; when the distance is 2 m, the maximum displacement is 5.403 cm; and when the distance is 3 m, the maximum displacement is 5.86 cm. The smallest structural deformation occurs when the center-to-center distance is 2 m, and the displacement is nearly the same as when the distance is 3 m. In this case, the maximum displacement occurs at the side walls and central columns. The displacement distribution is similar for all three conditions, with the structure being more prone to localized damage and losing stability. Therefore, in engineering practice, the center-to-center distance of the phononic crystals should be kept as small as possible. However, considering the overall economic efficiency, the spacing should not be too dense. To ensure the safe operation of the underground station, the optimal phononic crystal spacing is determined to be 2 m.
Figure 12 shows the time history curves at point A for different phononic crystal spacing configurations. From subfigures (a) and (b), it can be seen that the maximum stresses for L = 1 m, 2 m, and 3 m are 38.2 MPa, 38.3 MPa, and 38.2 MPa, respectively, indicating that the maximum stress is nearly the same for all three cases. However, the overall response of the structure for L = 1 m is noticeably greater than for L = 2 m and 3 m. The maximum displacements for L = 1 m, 2 m, and 3 m are 6.58 cm, 5.37 cm, and 5.81 cm, respectively, with L = 1 m exhibiting the largest displacement, which is 1.23 times that of L = 2 m. This indicates that the denser the arrangement of the phononic crystals, the more impact wave energy can be absorbed, making the underground station safer. Given the minimal difference between the three cases and considering the economic efficiency, L = 2 m is selected as the optimal center-to-center distance. The subsequent discussion will build on this configuration.

3.3. Influence of Phononic Crystal Arrangement on the Dynamic Response of Underground Stations

The impact of varying the number of phononic crystal layers on the structural response is studied. The phononic crystals have a radius of R = 0.25 m, with a center-to-center spacing of L = 2 m and a distance from the crystal center to the ground surface of d = 2 m. The number of rows varies from one to three, and the structural responses of the underground station under nuclear blast loading are compared accordingly.
Figure 13 shows a comparison of the effective stress in the underground station structure under different configurations. The results indicate that when there is one row, the maximum effective stress reaches 4.638 × 107 Pa. With two rows, the maximum effective stress decreases to 4.065 × 107 Pa, and with three rows, it remains at approximately 4.063 × 107 Pa. The stress propagation becomes slower as the number of rows increases. It is suggested that varying the number of phononic crystal rows, while maintaining the same crystal size and spacing, can effectively impede the propagation of blast waves. When arranged in three rows, the phononic crystals provide better structural protection by sharing the blast load. However, with larger spacings, the blast load from the nuclear explosion can more uniformly fill the structure, leading to higher stress levels.
Figure 14 illustrates the displacement comparison of the underground station structure under different configurations. It can be observed that when only one row is arranged, the maximum displacement reaches 7.049 cm, occurring at the side walls, with noticeable displacement also affecting the central column. For two rows, the maximum displacement decreases to 5.404 cm, and for three rows, it further reduces slightly to 5.195 cm, with the maximum displacement still occurring at the side walls, similar to the results for center distances of 1 m and 2 m. Comparing these scenarios reveals that the two-row configuration results in slightly larger displacement than the three-row setup. However, considering economic efficiency, it is essential to minimize the number of phononic crystal units. To ensure the structural safety of the underground station, the optimal configuration is recommended as the use of two rows of phononic crystals.
Figure 15 illustrates the time history curve at Point A under different numbers of phononic crystal rows. From subfigures (a) and (b), it can be observed that the maximum stress for configurations with one, two, and three rows are 45.6 MPa, 38.3 MPa, and 37.8 MPa, respectively. The maximum stress when three rows are arranged is 1.21 times higher than when only one row is used. The maximum displacements for one, two, and three rows are 7.05 cm, 5.37 cm, and 4.53 cm, respectively, with the largest displacement occurring in the one-row configuration, which is 1.56 times greater than the three-row configuration. The structural analysis shows that the underground station enters a plastic state in all cases, with the three-row arrangement exhibiting the highest plastic strain. However, the extent of damage is similar for the one-row and two-row setups. Considering displacement responses, this section concludes that the optimal configuration is a two-row arrangement, which will be used as the basis for further discussion in subsequent sections.

3.4. Influence of Phononic Crystal Buried Depth on the Dynamic Response of Underground Stations

The impact of the buried depth of phononic crystals on the structural response is primarily investigated. The radius of the phononic crystals is fixed at R = 0.25 m, with an inter-center distance of L = 2 m, and the number of rows is set to two. Buried depths of d = 1 m, d = 2 m, and d = 3 m are considered to compare the structural responses of the underground station under nuclear blast loading.
Figure 16 shows the peak effective stress distribution for the underground station structure at different buried depths. From the figure, it is observed that the effective stress initially appears at the corner of the underground station structure and gradually diffuses outward the entire structure. The effective stress accurately reflects the overall trend of the structural changes, which helps identify the weak zones in the structure under explosive load and guide engineering reinforcement. It can also be seen that, despite changes in buried depth, the overall effective stress of the structure does not vary significantly. The reason for this is that, under the same protective structure and load conditions, the intensity of the shockwave affecting the structure remains roughly constant. When d = 1 m, the maximum effective stress is 33.829 × 107 Pa, when d = 2 m, it is 4.057 × 107 Pa; and when d = 3 m, it is 5.094 × 107 Pa. This shows that as the buried depth of the phononic crystals increases, the peak effective stress also increases.
Figure 17 shows the displacement distribution of the underground station structure with phononic crystals at different buried depths. From the figure, it can be seen that the maximum displacement occurs at the two side walls and their vicinity. Specifically, when d = 1 m, the maximum displacement is 5.336 cm; when d = 2 m, it is 5.403 cm; and when d = 3 m, it is 5.496 cm. The displacement is similar across all three scenarios. Based on the analysis of the structure’s effective stress and displacement, it can be concluded that, under the condition of a reasonable phononic crystal density arrangement, the buried depth has a negligible impact on the explosive effects on the underground station structure. This arrangement typically does not lead to significant damage. Therefore, phononic crystals can be placed at an intermediate position between the surface and the structure, with a buried depth of 2 m from the surface.
Figure 18 presents the time history curves at point A for phononic crystals at different buried depths. From panels (a) and (b), it can be observed that the maximum stress values are 31.5 MPa, 38.3 MPa, and 48.8 MPa for buried depths of d = 1 m, d = 2 m, and d = 3 m, respectively. As the buried depth increases, the stress gradually increases, with the stress at d = 3 m being 1.55 times higher than that at d = 1 m. The maximum displacements at these depths are 5.19 cm, 5.37 cm, and 5.52 cm, with the maximum displacement occurring at d = 3 m. However, the maximum displacements are similar across all three scenarios. Given the relatively shallow buried depth and minimal difference in damage levels between d = 1 m and d = 2 m, this study prioritizes d = 2 m as the optimal buried depth for further analysis.

3.5. Influence of Phononic Crystal Materials on the Dynamic Response of Underground Stations

Since phononic crystals serve as the medium for the propagation of explosive loads, they can influence the transmission of such loads. The effect of different materials (concrete, steel, and rubber) for phononic crystals on the propagation of explosive loads is explored, with the finite element model being the same as in previous sections (structure buried depth of 5 m). The material parameters for the phononic crystals using concrete, steel, and rubber are as follows:
The steel material parameters are as provided in Table 2.
Rubber, as an elastic material, has a Young’s modulus of 4.38 × 106 MPa, a Poisson’s ratio of 0.461, and a density of 1300 kg/m3 [83].
For the concrete structure, C40 concrete is used, and the H-J-C material model (material number 111) available in LS-DYNA is applied. The material parameters are provided in Table 4.
Figure 19 presents the displacement contour maps of the underground station structure under different materials. From the figure, it can be observed that significant displacement occurs around the two sidewalls of the station, gradually spreading outward. When the phononic crystal material is concrete, the displacement is the largest, reaching 10.82 cm, followed by steel, with a maximum displacement of 5.403 cm. The smallest displacement occurs when the material is rubber, at 4.93 cm. This indicates that concrete as the phononic crystal material provides the weakest protection against explosions, while rubber offers the best mitigation of structural damage. The reason for this is that the material used for protective structures affects the explosion impact on the structure. Among the materials, the soft and elastic rubber is most effective, demonstrating significant reflection and attenuation of the shockwave. This allows more energy to be dissipated into the surrounding soil, minimizing structural damage. To optimize the protective effect, it is important to reinforce the structure where possible. In the absence of ideal conditions, appropriate protective measures should be implemented to ensure the overall safety of the underground station.
Figure 20 shows the time history curves at point A for different materials used in the phononic crystal. From panels (a) and (b), it can be observed that the maximum stress values for concrete, steel, and rubber are 69.3 MPa, 38.3 MPa, and 26.3 MPa, respectively. The stress for concrete is the highest, 2.63 times greater than that for rubber. Similarly, the maximum displacement for concrete, steel, and rubber is 7.41 cm, 5.37 cm, and 3.44 cm, respectively, with concrete causing the largest displacement, which is 2.15 times greater than rubber. As seen in panel (c), the underground station structure enters a plastic state when concrete and steel are used, while no plastic deformation occurs when rubber is used. This indicates that the structure experiences minimal damage when rubber is used, demonstrating its superior ability to absorb impact energy and providing the best protective effect for the structure.

4. Conclusions

This study utilized an LS-DYNA-based 3D finite element model of the underground station–soil system to investigate the dynamic response of the underground station under nuclear explosion loads. The following conclusions can be drawn:
(1) Plastic Zone Behavior: The cloud plot results indicate that the plastic zone of the underground station structure first appears at the corner of the middle platform. As the nuclear explosion load increases, the plastic zone gradually expands from the corner of the second-floor platform towards the corners of the top and bottom slabs, with the area of the plastic zone gradually increasing. However, the plastic damage primarily concentrates around the structural corner points.
(2) Effect of Phononic Crystal Configuration: When considering different phononic crystal configurations, the maximum displacements for circle center distances L = 1 m, 2 m, and 3 m are 6.58 cm, 5.37 cm, and 5.81 cm, respectively. The displacement is greatest when L = 1 m, being 1.23 times greater than at L = 2 m. For different numbers of rows (one, two, and three), the maximum displacements are 7.05 cm, 5.37 cm, and 4.53 cm, respectively, with the maximum displacement occurring when one row is used, which is 1.56 times greater than for three rows. The maximum displacements for distances d = 1 m, 2 m, and 3 m are 5.19 cm, 5.37 cm, and 5.52 cm, respectively, with the largest displacement occurring at d = 3 m. Based on a comprehensive evaluation of economic considerations, the optimal configuration is L = 2 m, two rows, and d = 2 m.
(3) Impact of Buried depth on Dynamic Response: The study on the effect of different buried depths on the dynamic response of the underground station shows that the maximum stresses for depths d = 1 m, 2 m, and 3 m are 38.3 MPa, 40.6 MPa, and 50.9 MPa, respectively, with the stress at d = 3 m being 1.33 times greater than at d = 1 m. The maximum displacements at depths d = 1 m, 2 m, and 3 m are 5.18 cm, 5.37 cm, and 5.55 cm, respectively, with the largest displacement occurring at d = 3 m. The buried depth has a significant effect on the underground station’s response to a nuclear explosion. Therefore, a reasonable buried depth should be considered in practical engineering to minimize damage, based on the most favorable economic conditions.
(4) Influence of Phononic Crystal Materials: The material used in the phononic crystal has a considerable impact on the structure’s performance. The maximum displacements for concrete, steel, and rubber are 7.41 cm, 5.37 cm, and 3.44 cm, respectively. The use of rubber as the material results in the best protection for the structure, followed by steel, while concrete provides the least effective protection. Compared to concrete, rubber greatly reduces structural damage, and it is recommended to prioritize the use of rubber in the phononic crystal design for enhanced structural protection in practical engineering.

Author Contributions

Conceptualization, D.W. and Z.L.; Data curation, J.W.; Formal analysis, C.B.; Funding acquisition, D.W.; Investigation, C.B.; Methodology, J.W. and F.B.; Software, Z.L.; Visualization, F.B. and M.B.; Writing—original draft, J.W. and C.B.; Writing—review & editing, D.W., F.B. and M.B. All authors have read and agreed to the published version of the manuscript.

Funding

This study is supported by the Tianjin Municipal Science and Technology Bureau (Grant Nos. 23JCYBJC00390, 23YDTPJC00670), which is gratefully acknowledged.

Data Availability Statement

Some or all the data supporting this study’s findings are available from the corresponding author upon reasonable request.

Conflicts of Interest

Author Jihu Wu was employed by the company China Railway Design Corporation. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Figure 1. Typical cross-section dimensions of subway station structure (unit: mm).
Figure 1. Typical cross-section dimensions of subway station structure (unit: mm).
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Figure 2. Finite element model of subway station–surrounding soil structure system.
Figure 2. Finite element model of subway station–surrounding soil structure system.
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Figure 3. Simplified waveforms of ground-level air shock waves from nuclear weapon explosions.
Figure 3. Simplified waveforms of ground-level air shock waves from nuclear weapon explosions.
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Figure 4. Test equipment arrangement [82]. In (b), W1–W4 represent acceleration sensors installed on the wall, while P1–P3 are acceleration sensors mounted on the columns. Reproduced with permission from Zeng, Y., Bai, C., & Wang, Z., Vibrating Response of a Residential Structure to Blast Based on HHT, J. Vib. Shock; published by Journal of Vibration and Shock, 2014.
Figure 4. Test equipment arrangement [82]. In (b), W1–W4 represent acceleration sensors installed on the wall, while P1–P3 are acceleration sensors mounted on the columns. Reproduced with permission from Zeng, Y., Bai, C., & Wang, Z., Vibrating Response of a Residential Structure to Blast Based on HHT, J. Vib. Shock; published by Journal of Vibration and Shock, 2014.
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Figure 5. Finite Element Model in LS-DYNA. In the finite element model, the blue regions represent the soil, while the black regions represent the structure.
Figure 5. Finite Element Model in LS-DYNA. In the finite element model, the blue regions represent the soil, while the black regions represent the structure.
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Figure 6. Effective stress clouds of underground stations with and without protection.
Figure 6. Effective stress clouds of underground stations with and without protection.
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Figure 7. Clouds of peak displacements of underground stations with and without protection.
Figure 7. Clouds of peak displacements of underground stations with and without protection.
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Figure 8. Effective plastic strain clouds for underground stations with and without protection.
Figure 8. Effective plastic strain clouds for underground stations with and without protection.
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Figure 9. Underground Station Observation Point A Location.
Figure 9. Underground Station Observation Point A Location.
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Figure 10. Effective stress clouds at different sparsity levels of phononic crystals.
Figure 10. Effective stress clouds at different sparsity levels of phononic crystals.
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Figure 11. Displacement clouds of phonon crystals at different degrees of sparsity.
Figure 11. Displacement clouds of phonon crystals at different degrees of sparsity.
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Figure 12. Time history curves of observation points at different sparsities of phonon crystals.
Figure 12. Time history curves of observation points at different sparsities of phonon crystals.
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Figure 13. Effective stress clouds for phononic crystals with different row numbers.
Figure 13. Effective stress clouds for phononic crystals with different row numbers.
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Figure 14. Displacement clouds of phononic crystals with different row numbers.
Figure 14. Displacement clouds of phononic crystals with different row numbers.
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Figure 15. Time history curves of observation points at different rows of phononic crystals.
Figure 15. Time history curves of observation points at different rows of phononic crystals.
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Figure 16. Effective stress clouds at different spacings of phonon crystals from the surface.
Figure 16. Effective stress clouds at different spacings of phonon crystals from the surface.
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Figure 17. Displacement clouds when phonon crystals are spaced differently from the surface.
Figure 17. Displacement clouds when phonon crystals are spaced differently from the surface.
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Figure 18. Time history curves of observation points at different spacings of phonon crystals from the ground surface.
Figure 18. Time history curves of observation points at different spacings of phonon crystals from the ground surface.
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Figure 19. Displacement clouds of subway structures at different materials.
Figure 19. Displacement clouds of subway structures at different materials.
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Figure 20. Time history curves of observation points at different materials of phononic crystals.
Figure 20. Time history curves of observation points at different materials of phononic crystals.
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Table 1. Material parameter values [67].
Table 1. Material parameter values [67].
reinforced concreteRO (Kg/m3)E
(Pa)		PRSIGY
(Pa)		ETAN (Pa)BETASRCSRPFS
25003.78 × 10100.23.5 × 1073.78 × 1091.099.31.941 × 1020
soilRO (Kg/m3)GNOD (Pa)RNURKFPHICVALSTR LIM
20501.3 × 1070.281.00.561.3 × 1070.005
Here: RO is the material density; E is the elastic modulus; PR is Poisson’s ratio; SIGY is the yield strength; ETAN is the tangent modulus; BETA is the hardening parameter; SRC and SRP are strain rate parameters, corresponding to C and P in the Cowper–Symonds model; FS is the failure strain; GNOD is the shear modulus; RKF is the shape parameter; PHI is the friction angle; CVAL is the cohesion; and STR LIM is the minimum shear strength. Reproduced with permission from Sun, R., Dynamic Response Analysis of Typical Upper Cover Structure under Explosion in Subway Station; published by Tianjin University, 2019.
Table 2. Values of steel material model parameters [78].
Table 2. Values of steel material model parameters [78].
RO (Kg/m3)E (Pa)PRSIGY (Pa)ETAN (Pa)BETASRCSRPFS
78302.08 × 10110.32.92 × 1082.1 × 10904050.2
Here: RO is the material density; E is the elastic modulus; PR is Poisson’s ratio; SIGY is the yield strength; ETAN is the tangent modulus; BETA is the hardening parameter; SRC and SRP are strain rate parameters, corresponding to C and P in the Cowper–Symonds model; and FS is the failure strain. Reproduced with permission from Qu, S., Structural Response and Damage and Ground Vibration of Subway Station under Internal Explosion; published by Tianjin University, 2012.
Table 3. Comparison of Numerical Simulation and Experimental Results for Peak Vibration Velocity.
Table 3. Comparison of Numerical Simulation and Experimental Results for Peak Vibration Velocity.
Reference Point IdentificationNumerical Simulation Results (mm/s)Experimental Results (mm/s)Relative Error (%)
P158.768.614.43
P225.930.815.91
P322.125.613.67
W199.2113.712.75
Table 4. H-J-C model parameters [78].
Table 4. H-J-C model parameters [78].
ROG (MPa)ABCNFC (MPa)T (MPa)EPSOEFMIN
240014,8600.791.60.0070.614040.0010.01
SFMAX (MPa)PC (MPa)UCPL (MPa)ULD1D2K1 (MPa)K2 (MPa)K3 (MPa)
7160.0018000.10.041.08.5 × 104−1.71 × 1052.08 × 105
Here: RO (material density), G (shear modulus), A (normalized viscosity strength), B (normalized hardening coefficient), C (strain rate coefficient), N (hardening exponent), FC (quasi-static uniaxial compressive strength), T (maximum tensile hydrostatic pressure), EPSO (reference strain rate), EFMIN (total plastic strain before failure), SFMAX (normalized equivalent maximum strength), PC (crushing pressure), UC (crushing volumetric strain), PL (compaction pressure), UL (compaction volumetric strain), D1 and D2 (damage parameters), and K1, K2, and K3 (pressure parameters). Reproduced with permission from Qu, S., Structural Response and Damage and Ground Vibration of Subway Station under Internal Explosion; published by Tianjin University, 2012.
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Wu, J.; Bo, C.; Wang, D.; Liu, Z.; Broniewicz, F.; Broniewicz, M. Study on Blast Mitigation Protection of Underground Station Structures Using Phononic Crystals. Buildings 2025, 15, 4006. https://doi.org/10.3390/buildings15214006

AMA Style

Wu J, Bo C, Wang D, Liu Z, Broniewicz F, Broniewicz M. Study on Blast Mitigation Protection of Underground Station Structures Using Phononic Crystals. Buildings. 2025; 15(21):4006. https://doi.org/10.3390/buildings15214006

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Wu, Jihu, Chuqiao Bo, Dai Wang, Zhongxian Liu, Filip Broniewicz, and Miroslaw Broniewicz. 2025. "Study on Blast Mitigation Protection of Underground Station Structures Using Phononic Crystals" Buildings 15, no. 21: 4006. https://doi.org/10.3390/buildings15214006

APA Style

Wu, J., Bo, C., Wang, D., Liu, Z., Broniewicz, F., & Broniewicz, M. (2025). Study on Blast Mitigation Protection of Underground Station Structures Using Phononic Crystals. Buildings, 15(21), 4006. https://doi.org/10.3390/buildings15214006

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