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Oct 31, 2024

Assessment of dynamic responses and impact resistance of corrugated plate-reinforced concrete tunnels under irregular rockfall scenarios | Scientific Reports

Scientific Reports volume 14, Article number: 26157 (2024) Cite this article Metrics details This article presents a composite tunnel rockfall protection structure (CPRC) employing galvanized

Scientific Reports volume 14, Article number: 26157 (2024) Cite this article

Metrics details

This article presents a composite tunnel rockfall protection structure (CPRC) employing galvanized corrugated steel plates as the inner formwork for reinforced concrete structures. It addresses the threats posed by frequent rockfall disasters in mountainous regions with complex geology. The research investigates impact damage from various rockfall shapes through numerical simulations and experiments on five representative forms, comparing traditional reinforced concrete structures RC with CPRC. The study highlights both structures’ dynamic responses and damage characteristics across different impact scenarios, introducing the Residual Resistance Index RRI as a measure of post-impact safety performance. Results show that the numerical simulations align with laboratory tests, with discrepancies within 10%, validating the simulation method’s accuracy in predicting impact resistance. Following impacts, both structures primarily displayed brittle concrete damage; however, the CPRC structure demonstrated a 79.46% reduction in concrete damage and an 86.31% decrease in reinforcement damage. The energy-dissipating properties of the corrugated plates significantly lowered rockfall penetration depth and impact energy transfer ratio, with an RRI exceeding 0.88 post-event. Additionally, the study reveals varying damage effects from different rockfall shapes, further supporting the CPRC structure’s superior impact resistance and its effectiveness in preventing secondary disasters in tunnel engineering within mountainous terrains.

As human activity expands into mountainous regions, the development of essential transportation infrastructure has rapidly escalated. Correspondingly, the frequency of rockfall disasters has increased. The shapes of falling rocks exhibit a high level of complexity and unpredictability. In mountainous areas, the public transportation system is increasingly vulnerable to the destruction caused by rock collapses and the impact of falling rocks1,2,3. Furthermore, the collapse and spalling of concrete structures due to brittle failure following impact and the degradation of building material performance beyond its intended service life pose significant challenges4,5,6. Conventional masonry and monolithic reinforced concrete structures have become obsolete in harsh engineering environments. Therefore, devising a system of high-safety and easily constructed disaster protection structures is paramount in mountainous transportation engineering protection.

Among the existing protective measures, traditional approaches predominantly involve the construction of reinforced concrete sheds as the primary protective structure. The advantages of this type of structure lie in its relative cost-effectiveness and commendable durability, making it suitable for permanent applications. However, under the impact of large-volume and high-velocity falling rocks, it becomes apparent that even when the impact stress remains below the load-bearing capacity of the concrete structure, the material is susceptible to cracking7,8. This phenomenon aligns with Herrmann’s “scabbing” theory9, which posits that prolonged exposure to such stress conditions can result in brittle fractures and localized collapses.

In general, the design of protective structures often incorporates an additional layer above the reinforced concrete framework to enhance its protective capabilities. This cushioning layer primarily serves as a shock absorber, capable of dissipating a portion of the impact force and distributing contact stresses. Initially, tunnel cushion layers evolved from backfilled earth materials post-excavation to more porous and loose sand layers10, and subsequently to composite material layers. The incorporation of expanded polystyrene (EPS) particles and geotextiles serves to bolster the overall impact resistance11.

However, in the narrow exit locations of tunnels in the mountainous regions of western China, the feasibility of constructing side retaining walls is significantly limited. Under prolonged dynamic loading or the erosive action of water flow, the cushioning layers are susceptible to lateral loss, making it challenging to maintain adequate protection over time. Crucially, the presence of a thicker cushion layer can impede the inspection of structural damage and complicate the replacement of underlying structures, thereby posing a potential risk to the safety and maintenance of the overall system.

In recent years, galvanized corrugated steel sheets have garnered considerable attention as a novel reinforcement material across various fields12,13,14, finding extensive applications, particularly in bridge engineering. Sui et al. introduced an innovative corrugated steel plate damper (CSPD) designed for installation on the piers and trusses of steel arch bridges15. Through simulations analyzing vibrational displacement and mechanical responses, they revealed the energy dissipation capabilities of corrugated plate-reinforced structures under seismic influences. Moreover, Maleska et al. proposed the incorporation of corrugated plates in combination with reinforced concrete structures for tunnel engineering applications16, significantly accelerating construction processes and achieving cost savings exceeding 50%. This composite structure exhibits remarkable resilience against vibrations and energy dissipation characteristics, maintaining a commendable level of structural integrity even under intense seismic activity. Sun et al. conducted a comparative analysis of traditional reinforced concrete tunnel structures and corrugated plate-reinforced concrete composite structures, elucidating the superior performance of the latter under static loading conditions as tunnel linings17. According to relevant studies, prefabricated modular steel-concrete composite structures can substantially enhance the tensile bearing capacity of structural systems while reducing the overall weight18,19, thereby providing a theoretical foundation for lightweight construction approaches and affirming the viability of corrugated plate structures.

It can be proven that the corrugated plate structure can form a new type of impact protection structure with complementary material advantages by combining with the reinforced concrete structure, which has substantial practical value. Specifically, (1) Enhancement of Structural Strength: The unique structural characteristics of corrugated plates allow for a tighter integration with reinforced concrete, thereby providing superior resistance to bending and increased load-bearing capacity20,21,22. The corrugated shape enhances the plate’s rigidity, reducing structural deformations under external loads and improving overall structural stability. (2) Strengthening of Structural Durability: Galvanized corrugated plates exhibit strong corrosion resistance23,24, effectively extending the structure’s service life and reducing damage caused by environmental factors. (3) Enhancing Construction Efficiency: When used as internal formwork during construction, corrugated plates can be rapidly installed and simplify the support system for formwork. This fixed assembly feature reduces preparation work on the construction site and subsequent formwork removal procedures, significantly improving construction speed. This is particularly crucial for projects requiring timely completion, as it can dramatically shorten the construction period and reduce labor costs.

(4) Substantial Reduction in Engineering Carbon Emissions: Using corrugated plate-reinforced concrete composite structures reduces reliance on timber and other disposable formwork materials, helping decrease natural resource consumption and mitigate environmental impacts25,26,27.

Incorporating corrugated plate-reinforced concrete composite structures presents a novel solution for mitigating rockfall hazards. This composite method involves prefabricating Q345 galvanized corrugated steel plates, assembling them onsite post-fabrication, and utilizing them as formwork for the concrete exposed openings. This approach offers advantages such as enhanced on-site construction efficiency, minimal environmental disturbance, and the potential for lightweighting the exposed opening structure. Additionally, it bolsters the overall structure’s stability and safety, resulting in significantly improved strength and impact resistance performance.

The present study is based on the reinforcement and renovation project of a tunnel in the western mountainous region of China. Utilizing LS-DYNA software, a three-dimensional numerical simulation was conducted on the impact process of falling rocks with five representative shapes on traditional reinforced concrete tunnels and corrugated plate-reinforced concrete composite tunnels. The accuracy of the results was verified through indoor experiments. The study ultimately revealed the damage mechanisms of various rock shapes on the structure and the dynamic response results of the two types of structures. A concise summary highlights the enhanced impact resistance of corrugated plate-reinforced concrete composite structures, providing a theoretical foundation for subsequent engineering applications and theoretical studies.

The focal point of this study is the improvement and restoration project for the exposed tunnel section located in the western mountainous region of China’s existing railway line. The upper part of the tunnel exit is predominantly comprised of severely wind-eroded granite and basalt rock formations, while the lower portion consists of vast layers of large cobblestones. Moreover, vertical joints are prevalent in the foundation rock layer above the tunnel, and due to the region’s frequent seismic activity, intense rainfall, and prolonged weathering effects, the overall structure is significantly impacted by external disturbances. Despite multiple attempts at remediation, no practical results have been achieved, and the entrance of the tunnel section is highly susceptible to collapse and rockfall disasters. The existing protective structure in the lower part is an aged reinforced concrete tunnel, which is ineffective in safeguarding against significant rockfall incidents.

To mitigate the threat of rockfall damage to structures, minimize construction interference with the environment, and enhance driving safety and stability, a prefabricated corrugated plate-reinforced concrete (CPRC) structure was chosen as the main load-bearing body for the improved protective structure. The actual engineering situation is shown in Fig. 1. To ensure that the corrugated plate and reinforced concrete (RC) structure share loads and deform together, increasing the rigidity and stability of the overall composite structure, shear studs and locking reinforcement bars are used to connect the corrugated steel plate to the reinforcing mesh framework within the concrete. The circumferential centerline is flush with the bottom of the concrete, as shown in Fig. 2.

Structure diagram.

Connection detail.

The pre-processing of the model was conducted using the HyperWorks software platform, with the corrugated plate-reinforced concrete composite structure constituting the primary component of the model. Upon establishing the model, a detailed meshing process was undertaken, as illustrated in Fig. 3. Most of the concrete, foundation, and rockfall elements were discretized utilizing stable hexahedral meshes with single-point integration at their centers28.

To accurately simulate the damage behavior of the concrete elements under impact, the mesh dimensions for the concrete elements were set at 0.08 m × 0.25 m × 0.20 m (longitudinal × transverse × vertical). In comparison, the foundation elements were discretized into hexagonal prisms with dimensions of 0.3 m. The corrugated plate structure was divided using Belytschko-Tsay shell elements, characterized by single-point integration in the plane, which offers enhanced computational efficiency; this approach is notably stable and effective for problems involving large deformations, with a mesh size of 0.10 m × 0.20 m. Additionally, various reinforcing steel elements within the structure were simulated using Hughes-Liu beam elements with a single integration point, all featuring a uniform mesh size of 0.05 m.

Connection detail.

Due to the brittle nature of concrete, its compressive strength and damage under impact are significantly influenced by the impact velocity. To accurately simulate the structure’s stress transmission and structural cracking damage under impact load, the continuous surface cap model in LS-DYNA (MAT_159_CSCM_CONCRETE) is chosen to define the concrete material parameters. The parameter values are listed in Table 1. The continuous surface cap model describes the yield condition of concrete material based on a yield surface in stress space. This model consists of a shear failure surface, a cap surface, and a smooth transition surface between them, as shown in Fig. 4. Three stress invariants constitute the definition of the yield surface. According to the research findings of Dikshant et al.29, the yield surface definition equations are provided in Eqs. 1 to 4:

Where \({I_1}\)represents the first invariant of stress tensor; \({J_2}\) represents the second invariant of stress tensor; \({J_3}\) represents the third invariant of stress tensor; \(k\) represents cap hardening coefficient; \(\Re ({J_3})\) represents rubin third invariant reduction factor; \({F_c}({I_1},k)\)represents hardening cap surface equation; \({F_f}({I_1})\) represents shear yield surface equation is calculated as follows:

Where \(\alpha\)、\(\lambda\)、\(\beta\)、\(\theta\) are parameters obtained from triaxial compression tests on concrete cylindrical specimens.

The corrugated plate material is Q345 galvanized steel with design parameters of 300 mm × 110 mm × 7 mm (wavelength × height × thickness). The reinforcing steel bars are HRB400 ribbed rebar. The material parameters are listed in Tables 2 and 3. This study uses the bilinear elastoplastic model (MAT_003_PLASTIC_KINEMATIC) in LS-DYNA to simulate the corrugated plate and rebar. This model accurately reproduces the deformation and failure under impact, considering dynamic hardening and strain rate effects30. The behavior of the model can be described by Eqs. 5 and 6:

Where \({\sigma _y}\) represents yield strength; \({\sigma _0}\) represents initial yield strength; \(Q\)、\(C\) are strain rate related parameter; \(\eta\) represents hardening parameters, used to describe different hardening models, \(\eta =0\) represents model is dynamically hardened, with no change in the size of the yield surface, and moves along the direction of plastic strain,

\(\eta =1\) represents model is isotropic hardening, with the yield surface position unchanged and the size varying with strain, \(0<\eta <1\) represents mixed hardening, represents plastic hardening modulus; the calculation formula is as follows:

Where \(E\) represents elastic modulus represents tangent modulus; \(\varepsilon\) represents material strain; \({\varepsilon _{eff}}\) represents effective plastic strain.

Given that the structural degradation of the rockfall itself is not the focal point of this analysis, the study disregards the deformation of the rock mass, treating it as a rigid body. Consequently, a rigid material model (*MAT_rigid) represents the rockfall. Based on extensive field investigations, it has been determined that the tunnel entrance segment is situated within a granite geological zone, which is particularly prone to rockfall incidents. The rock mass is considered to possess a density range of 2.5 to 3.0 g/cm³, with material parameters detailed in Table 4.

The shape of falling rocks directly determines the contact type and stress transmission form between the falling rock and the structure during impact. To study the different impact effects that complex and diverse shapes of falling rocks in mountainous areas might cause on structures, this paper focuses on common falling rock shapes in southwestern mountainous areas. According to Peng’s research31, large falling rocks formed due to weathering and rain erosion usually have smooth curved surfaces, strong mobility, and typically appear spherical, as shown in Fig. 4(a). Falling rocks from weathered and fragmented layered rock masses usually have relatively regular shapes with edges and corners, approximating a cube, as shown in Fig. 4(b). Besides, based on actual statistical results, polyhedrons are one of the most observed falling rock shapes in mountainous regions, as shown in Fig. 4(c).

Typical rockfall shape.

This study focuses on the impact effects of differently shaped rockfalls on RC and CPRC structures, investigating how the geometric characteristics of the rockfall influence structural damage. To maintain consistency within this research, the impact energy of the rockfall is fixed at 1040 KJ32,33. Based on the findings of Lu et al.34, it was determined that among 5,500 simulated rockfall scenarios in mountainous regions, the most representative shapes are the sphere, cube, and columnar forms. Additionally, variations in aspect ratio and modes of impact are considered, leading to the introduction of cuboid and rhombohedron shapes. Thus, the common rockfall forms are represented by five standard geometries. To quantitatively assess shape characteristics, the concept of sphericity is employed as an evaluative metric, defined as the ratio of the surface area of an object to the surface area of a sphere that possesses the same volume as the object in question, as shown in Table 5. The calculation method is detailed in Eq. 7:

Where \({K_s}\) represents sphericity index; \({A_s}\) represents the surface area of a sphere with the same volume as the fallen rock, m2; \(A\) represents the actual surface area of rockfall, m2.

The hourglass phenomenon is a unique state that is mathematically stable but physically unachievable. It manifests in LS-DYNA simulations as a condition where the mesh elements undergo shape distortion without strain energy35. It leads to unrealistic stress distribution and displacement states and causes spurious energy dissipation, affecting the model’s actual response. For the impact analysis of the CPRC structure, it is essential to minimize non-physical hardening responses of the model elements without overly constraining the normal deformation of the structural elements. Based on the hourglass control theory proposed by Flanagan and Belytschko, stiffness-based hourglass control is more effective than viscous control36. A chosen hourglass control coefficient of 0.03 can effectively suppress the increase of hourglass energy.

The impact of falling rocks on wave patterns in reinforced concrete structures represents a highly nonlinear extensive deformation process. In this context, LS-DYNA characterizes the dynamic relationships between objects by defining subordinate and primary components. The falling rock mass is treated as a subordinate entity within the contact settings. At the same time, its interaction with the primary surfaces, such as the upper surface of the reinforced concrete structure, is established through the automatic surface-to-surface contact keyword (CONTACT_AUTOMATIC_SURFACE_TO_SURFACE). Since the falling rock is modeled as a rigid body, the material stiffness significantly diverges from the granular substratum or concrete. The constraint parameters are configured to employ a soft constraint penalty formula (SOFT = 1) to ensure the contact simulation’s accuracy and the computations’ stability.

Assuming no relative sliding exists between the concrete and the reinforcement, this study employs a penalty function coupling constraint approach (CONSTRAINED_BEAM_IN_SOLID_PENALTY) to simulate the connection between steel reinforcement and concrete. This method is analogous to introducing a spring between the steel reinforcement and the concrete, which generates a penalty resistance proportional to their relative motion. Consequently, kinetic energy is converted into elastic potential energy stored within the constraining spring, mitigating kinetic energy loss and fulfilling the principle of energy conservation.

Similarly, in the case of the corrugated wave plate-reinforced concrete structure, the corrugated plate serves as the internal mold for the reinforced concrete. Following the welding of shear studs to the outer side of the wave plate and the subsequent anchoring to the rebar cage before pouring the concrete—as illustrated in Fig. 2—this connection method ensures that the various components of the composite structure undergo uniform loading. In the computational model, the initial state of potential gaps or relative displacements between the two components is disregarded, thus maintaining a close bond between the wave plate structure and the reinforced concrete. Furthermore, a tied surface-to-surface contact (CONTACT_TIED_SURFACE_TO_SURFACE) simulates the coordinated deformation between the concrete and the corrugated plate.

Due to constraints imposed by the venue and the volume of work, considering the dimensions and scaling factors employed in the relevant indoor experiments from the study by Martin et al.37. led to the selection of spherical rockfalls as the focal point of this investigation.

A spherical rockfall body is selected as the research object, as well as the model length similarity ratio \({C_L}=1:10\), elastic modulus similarity ratio \({C_E}=1:1\), and heavy similarity ratio \({C_p}=1:1\).

In order to faithfully replicate the actual conditions of the tunnel protective structure, we opted to utilize C35 concrete for the model, thereby accurately representing the concrete components of the tunnel. To simulate the rebar mesh in the actual structure, high-strength steel wires were employed. Furthermore, the model’s dimensions and thickness were scaled down according to a predetermined ratio, while maintaining all other parameters constant, to ensure the acquisition of precise simulation data.

The experiment is to simulate the protection model of the reinforced concrete scaled tunnel with rockfall impact. The model atmosphere is divided into the loading control and data acquisition devices. Among them, the loading control device is a steel ball with a weight of 30 kg fixed on the loading frame through an electromagnet. The experimental diagram and open-hole model are shown in Figs. 5 and 6. The data acquisition device includes an acceleration sensor and a dynamic strain acquisition device. The acceleration sensor uses the IEPE piezoelectric acceleration sensor of model 1A531E produced by Donghua Testing Co., Ltd. It is installed on the upper surface of the loading steel ball, as shown in Fig. 7. The dynamic strain signal acquisition instrument uses JM3840 dynamic strain acquisition equipment of Yangzhou Jingming Technology Co., LTD., China, as shown in Fig. 8.

Experimental loading structure.

Shelter model.

Load device.

Dynamic strain indicator.

In the design of impact protection structures, the most crucial design load is the maximum impact force. This essential factor cannot be overlooked when assessing safety performance. One must apply Newton’s second law to calculate the instantaneous maximum impact force during a rockfall event. Monitoring the falling rock’s acceleration variations throughout the impact process can ascertain the instantaneous maximum acceleration at the moment of impact. This subsequently allows for deriving the instantaneous maximum impact force at that precise moment. Hence, accurate measurements of acceleration are vital for estimating the peak force.

In numerical simulations, the LS-DYNA software can facilitate this process by configuring the *DATABASE output option, enabling the export of acceleration time history curves of the falling rock. Similarly, in laboratory experiments, acceleration time history curves can be captured using an acceleration sensor affixed to a spherical body, thereby permitting the derivation of the instantaneous maximum impact force38.

Compared to the Chinese Railway Tunnel Manual method derived from the impulse law and the Chinese Highway Subgrade Specification method derived from the deformation depth of the underlying structure39, this method achieves a more accurate actual value of the maximum impact force rather than an average impact force. This provides a precise reference design basis for the safety performance design of structures under extreme conditions, avoiding potential safety hazards caused by inaccurate impact force calculations. The detailed results of the maximum impact force obtained by each method are shown in Table 6.

From Table 6, it can be observed that the maximum impact forces of spherical falling rocks on CPRC structures and RC structures collected through experiments are 44.62 MN and 43.91 MN, respectively. The maximum impact forces obtained through numerical simulations for CPRC and RC structures are 41.03 MN and 38.84 MN, respectively. The numerical simulation results are slightly lower than the experimental results, with errors of 8.05% and 9.25%, respectively. This small error rate reflects a certain degree of correspondence between experiments and numerical simulations, proving the simulation parameter values’ correctness and the results’ validity. The subsequent results can meet the high requirements of engineering theoretical calculations.

Additionally, the maximum impact force of falling rocks is greatly influenced by the material properties of the protective structure. When the materials of the impacted parts of the falling rocks and the protective structures are the same, the maximum impact forces on CPRC and RC structures under the impact of falling rocks of the same shape are very close (0.55–5.34%). The impact force on the CPRC structure may even slightly exceed that on the RC structure. This phenomenon is due to the supporting effect of the lower corrugated plate structure, which provides greater equivalent concrete stiffness, limiting the downward protrusion deformation of the concrete. Consequently, the instantaneous impact force can exceed that of ordinary reinforced concrete structures that have not been reinforced with corrugated plates.

Interestingly, from the perspective of the shapes of falling rocks, it can be observed that cube and cuboid rocks generate the highest impact forces due to their rectangular impact contact areas with sharp edges. Spheres and cylinders have moderate contact areas but almost no sharp points and produce approximately equal impact forces. In contrast, rhombohedron rocks, which have point-to-surface contact due to their sharp points, generate the smallest impact forces. This phenomenon occurs because falling rocks with similar cross-sectional shapes and areas produce similar impact forces. The two sets of cubic rocks have the highest impact forces due to the edges of their impact surfaces. On the other hand, rhombohedron rocks experience point-to-surface contact during impact. Because the penetration effect is significant, the structure’s resistance to this rock shape is limited, resulting in a smaller impact reaction force.

Since rockfall protection structures are primarily composed of concrete, their brittle failure characteristics are pretty significant in the impact resistance performance of the structures. To conduct an in-depth comparative study on the impact resistance of RC structures and CPRC protection structures, it is necessary to provide comprehensive feedback on the integrity and functionality of the structures after impact. Ls-dyna provides different damage cloud map output options based on different concrete material parameters. Due to the use of the CSCM constitutive model in this concrete structure, brittle damage (history var # 4) is used as the evaluation index for structural damage status, as shown in Figs. 9 and 10.

RC shelter structure damage nephogram.

CPRC shelter structure damage nephogram.

Through comparative analysis, it is clear that after reinforcement with corrugated plates, the structures exhibit smaller ranges and lower degrees of brittle damage under impacts from rockfalls of various shapes. Specifically, after the impact of a spherical rockfall, the RC structure experiences severe damage at its center, and the underside view reveals significant dent deformation at the lower end. In contrast, the CPRC structure shows a smaller damaged area with lower central deformation.

Notably, the damage cloud diagrams indicate that the RC structure suffers through-thickness failure under the impact of a rhombohedral rockfall. This suggests that the rockfall has penetrated the protective structure, causing the central part of the structure to lose its protective capability entirely. This penetration leads to stress concentration in subsequent loadings, which can result in further structural damage and even collapse. The corrugated plate in the CPRC structure provides significant uplift support to the reinforced concrete part. Even with the strongest penetrating effect from a rhombohedral rockfall, it fails to cause through-thickness damage, and the damaged area remains confined within a certain range. During impacts from rockfalls of other shapes, due to surface-to-surface contact, the penetrating effect of the rockfall is less pronounced, and the damage tends to spread across a broader area rather than inward into the structure.

To quantify the specific structural damage status, the concrete damage volume and steel bar damage ratio of the RC structure and CPRC shelter structure under different rockfall shape impact conditions are summarized in Table 7.

During the simulation of impacts, when the strain in concrete or reinforcement elements exceeds the material’s ultimate strength due to the impact, the elements fail and are removed from the calculation. The extent of these failures can serve as an indicator of the degree of structural cracking and damage. According to the table above, the distribution pattern of concrete and reinforcement element damage closely corresponds to the brittle damage nephogram. The rhombohedral rockfall causes through-thickness damage to the RC structure, resulting in the largest volume of concrete damage, amounting to 3.424 m³. Similarly, the proportion of reinforcement damage is the highest among all conditions, at 4.17%. After reinforcing with a corrugated plate structure, the penetrating effect of the rhombohedral rockfall is significantly suppressed, reducing the volume of concrete damage to 0.336 m³ and the reinforcement damage proportion to 0.35%, decreasing by more than 90%. Under the same point-to-surface contact impact from a spherical rockfall, the quantity of damaged concrete elements and the proportion of damaged reinforcement elements decrease by more than 82%. For other rockfall conditions with lower penetration effects, the reduction in concrete damage volume is over 73%, and the reduction in reinforcement damage proportion ranges from 79 to 91%.

This parameter effectively illustrates that the CPRC open-cut tunnel structure can significantly reduce the extent of structural damage under the same impact conditions. It ensures that the structure maintains a certain degree of integrity even under severe rockfall disasters, inhibits the development of rockfall impact craters and cracking damage, and confines the damage to the upper surface of the concrete. This containment provides a safeguard for post-disaster repair work.

An important factor affecting the state of structural damage is the penetration depth of the rockfall into the protective structure40. The term “penetration depth” was originally used in civil engineering to evaluate the penetrative effects of weaponry. Significant contributions in this area include Young’s formula and the Forrestal formula, developed by the Sandia National Laboratories, as well as the ACE formula introduced by the U.S. Army Corps of Engineers. This index is used to evaluate the distance that the contact point of the falling body intrudes into the protective structure after the impact of the falling body. Due to their strong correlation with both the thickness of these protective structures and the presence of corrugated plate supports, the current understanding of penetration depth should be regarded as a provisional metric for evaluating the destructive impacts of rockfall, as well as the reinforcing efficacy of corrugated plate structures under similar conditions.

This indicator is crucial for assessing the safety and impact resistance of the structure, as it allows for a direct prediction of the potential damage a rockfall may cause41,42. Given that the initial velocity was applied solely in the Z-axis direction to the falling rock mass, this study defines the penetration depth in the numerical simulations as the maximum displacement along the negative Z-axis of the lowest node of the rock mass (the first point of contact) after it engages with the protective structure.

The distribution of penetration depths for different shapes of rockfalls into the RC and CPRC structures is shown in Fig. 11.

Penetration depth.

Under the impact conditions of five different rockfall shapes, only the rhombohedral rockfall, representing sharp contact, exhibited the strongest penetration effect. The penetration depth into the RC structure was 1.21 m, exceeding the structural thickness, causing through-thickness damage to the RC structure and posing a severe threat to the safety of the lower structure and personnel. Under the same conditions, the penetration depth into the CPRC structure was reduced to 0.22 m, a decrease of 81.82%. Next, the penetration depths of spherical rockfalls into the RC and CPRC structures were 0.28 m and 0.08 m, respectively, a difference of 71.41%. The penetration depths of other rockfall shapes were controlled within a lower range, and after reinforcement with corrugated plates, the penetration depths were further reduced, with decreases ranging from 33.33 to 57.14%.

The results indicate that conventional RC structures are insufficiently resilient against the risks posed by rockfall disasters in mountainous regions. This is particularly true for the large, angular debris represented by the polyhedral shapes discussed in this paper, which can penetrate the structures and directly impact the transportation infrastructure beneath them. Other shapes of rockfalls also cause varying degrees of surface damage to the structure, reducing the actual effective thickness of the structure. The CPRC structure significantly reduces the penetration depth caused by various shapes of rockfalls, lessening the extent of damage to the protective structure and preventing it from being penetrated and losing its function. It is worth mentioning that the corrugated plate, used as the lower structure of reinforced concrete, not only enhances the impact resistance of the structure but also effectively prevents the cracked and damaged concrete fragments from falling and collapsing due to impact, thereby ensuring the integrity of the underlying structures and the safety of traffic.

A preliminary analysis of the enhanced damage resistance of CPRC structures was conducted through a comparative study of structural damage. However, when rockfalls and collapses occur, there is a high likelihood of secondary impacts or structural collapse disasters43,44,45, posing a significant threat to the normal passage of underlying transportation facilities and the safety of passing personnel. This paper introduces the Residual Resistance Index (RRI) to evaluate the residual strength of the structure after impact46,47,48,49. The RRI calculation formula is as follows:

In the initial intact state of the structure, a rigid plate with both length and width of 2000 mm is placed at the impact point of the structure. The rigid plate applies a surface load to the structure by specifying displacement in the Z direction, as shown in Fig. 12. The maximum load-bearing capacity of the structure in its intact state, denoted as PU, is obtained from the load-displacement curve. After completing the impact process, the LS-DYNA software’s restart function is used to save the model, excluding damaged elements (the cracked model post-impact). The maximum residual load-bearing capacity of the damaged state denoted as PR, is obtained using the same method.

Rigid plate loading mode.

The RRI changes of RC and CPRC structure under the shape of multiple rockfalls are shown in Fig. 13.

RRI.

The above figures indicate the following: (1) For RC shelter structures, the impact of rockfalls of different shapes on the protective structure varies slightly, consistent with the distribution patterns of the damaged areas. Specifically, the rhombohedral rockfall exhibits the strongest penetration effect and has an RRI of 0.24. This indicates that after the structure experiences through-type damage, the central part’s load-bearing capacity significantly decreases, almost failing to ensure the protective function of the shelter structure after the first impact. Next, the spherical rockfall reduces the RRI of the structure to 0.47, showing that this shape also greatly affects the internal load-bearing capacity of the structure. Furthermore, when the rockfall shapes are cuboidal, rectangular, or cylindrical, the RRI remains above 0.61, indicating that the structure retains a certain load-bearing capacity after the impact.

The CPRC structure, reinforced with corrugated plates, shows an RRI increase of above 0.88 under the same impact conditions, with the maximum increase being 72.80%. This proves that the corrugated plate material significantly enhances the impact resistance of the shelter structure. After the initial rockfall disaster, the CPRC structure still possesses a high load-bearing capacity, capable of withstanding subsequent multiple rockfalls and collapse disasters, ensuring that the structure does not suffer severe secondary damage due to the initial impact.

This section will compare and analyze the load-bearing entities such as concrete parts, corrugated plate parts, and reinforced foundation parts based on different structures.

Whether the main protective structure is RC or CPRC, the concrete component remains the primary element resisting impact. Comparative analysis of the effective stress variation time-history curves and their maximum values during the impact process, as shown in Fig. 14; Table 8, is crucial for understanding the dynamic response of the structure under impact and identifying the damage and failure modes. This analysis can help improve the safety performance of impact-resistant designs.

Effective stress of concrete.

During rockfall events, the stress surge in protective structures resisting rock impacts is influenced by impact velocity, material properties, geometry, and contact area factors. The figure above clearly shows the similarities and differences in the effective stress-time history curves of the two structures during the impact process. The stress-time history curves of RC and CPRC structures exhibit highly similar trends under the same rock shape. Within 0.03 s after impact, the effective stress in the concrete rapidly rises to its peak value. It then quickly decreases as the concrete elements fail and stress propagates downward.

Among the shapes, the rhombohedron involves point contact with the protective structure, resulting in the smallest contact area and, under identical conditions, the highest impact stress. The sphere initially has point contact, quickly transitioning to arc contact. Other rock shapes maintain face-to-face contact throughout the impact process, with a constant contact area. Based on the contact area characteristics during impact, the maximum effective stress values from highest to lowest are Rhombohedron, Sphere, Cube, Cuboid, and Cylinder.

The distribution of maximum effective stress values for RC and CPRC structures under various impact conditions indicates that the corrugated plate provides higher stiffness and damping to the CPRC structure due to its material properties. Compared to the RC structure, the maximum effective stress is reduced by 15.84–26.64%.

The impact stress transmitted by the reinforced concrete structure in the CPRC structure is mainly borne by the corrugated plate structure. As an internal mold of the structure, the corrugated plate must have extremely high stability and safety. The stress time history curve of the corrugated plate structure is shown in Fig. 15, and the maximum value and arrival time are shown in Table 9.

Effective stress of corrugated plate.

Based on the trends in the effective stress-time history curves, they can be roughly divided into two groups. The first group consists of spherical and rhombohedral rocks, which transmit impact stress to the corrugated plate relatively quickly, at 5.60 ms and 4.80ms, respectively, but have smaller maximum stress values of 15.36 MPa and 18.16 MPa, maintaining a constant value after that. The second group includes cubic, cuboid, and cylindrical rocks, where the impact stress transmission is slower, with the maximum effective stress on the corrugated plate occurring approximately 10 ms later than in the first group. The maximum effective stress for this group ranges from 30.36 MPa to 32.95 MPa, about 1.89 times that of the first group, followed by two slow oscillations downward.

Interestingly, this distribution is the opposite of the maximum stress distribution observed in concrete under impact. This phenomenon occurs because the point-to-face contact of spherical and rhombohedral rocks results in greater initial impact stress, causing more severe concrete damage and penetration effects, consuming most of the impact energy, and significantly weakening the stress transmission to the lower parts. However, the face-to-face contact of the other three rock shapes results in poorer penetration and penetration effects, allowing most of the impact stress to be retained and transmitted downward through the overall subsidence of the contact center area, placing higher demands on the load-bearing capacity of the lower structure.

Similarly, the change in maximum vertical displacement of the corrugated plate shows that the second group of rocks causes greater deformation. Still, overall, it is controlled within 6 mm, much less than the minimum value of 100 mm required by the standards. This demonstrates that the CPRC structure has high safety performance under rockfall impact and will not result in parts intruding into the building clearance.

Figure 16; Table 10 show the changes in the foundation’s effective stress.

Effective stress of subgrade.

The overall variation in subgrade effective stress is insignificant, with the maximum value distribution nearly identical to that of the corrugated plate stress. In the RC structure, the maximum subgrade stress ranges from 5.10 MPa to 6.23 MPa under various conditions. In contrast, in the CPRC structure, the maximum value ranges from 3.93 MPa to 4.61 MPa, showing an overall reduction of over 23.07% compared to the RC structure. Since the reinforced subgrade primarily bears the compressive stress transmitted from the superstructure, the impact stress transmitted to the top of the subgrade is much lower than the compressive strength of C35 concrete, which is 23.4 MPa. Therefore, the structure has a high safety margin and will not experience subgrade instability or failure.

The energy absorption mechanism of the corrugated plate operates through the effective conversion and dissipation of kinetic and internal energy, thereby diminishing the impact energy transmitted downward and mitigating the “scabbing” phenomenon in the structure. The temporal variations of kinetic and internal energy in the corrugated plate structure under five distinct working conditions are illustrated in Fig. 17.

Corrugated plate energy time history curve.

Following the contact of falling rocks with the protective structure, it is evident that the shock wave traverses the concrete units and reaches the corrugated panel in an exceedingly brief interval. This phenomenon is manifested in the rapid escalation of the kinetic energy of the corrugated panel, which surges to its peak value within 5.59 ms before experiencing a swift decline. The impact energy dissipates in two distinct components: one segment, as kinetic energy, is transmitted to the foundation structure, as illustrated in Table 11, while the other segment is converted into internal energy within the corrugated panel through the damping effect of the steel material. Specifically, both the spherical and polyhedral corrugated panels absorb 34.69% of the energy through energy dissipation mechanisms, whereas, under various other conditions concerning the falling rocks, this ratio varies between 28.51% and 28.81%.

The shock wave transmitted to the foundation structure after being weakened by the upper structure has been significantly reduced, and the foundation energy of the CPRC structure has decreased more than that of the RC structure under all working conditions. According to Table 11, the energy dissipation effect of corrugated plates is very significant, which can significantly reduce impact energy and improve the structural impact resistance performance. Interestingly, the impact energy generated by spheres and rhombohedrons, which have strong penetration effects, is transmitted to the lower structure less than other shapes of falling rocks. This phenomenon occurs because, in the initial contact, the kinetic energy of falling rocks is converted into damage to the concrete part, and the remaining impact energy transmitted downward is slightly lower than in other working conditions.

This paper employs numerical simulation methods to investigate the impact processes of five representative irregular rockfall bodies on both standard reinforced concrete shelters and corrugated plate-reinforced concrete composite shelters. The results of maximum impact force are compared with those obtained from indoor experiments to validate the reliability of the parameter selections. Subsequently, based on the insights garnered from the numerical simulations, more in-depth exploration is undertaken to discuss the damage distribution characteristics inflicted by various shapes of rockfall bodies on the opening structures and the dynamic response characteristics of those structures. The primary conclusions are as follows:

​(1) For spherical rockfall bodies, the maximum impact force calculated by model test methods on RC and CPRC structures has an error within 10% compared to the numerical simulation results, indicating that the numerical simulation parameters are reasonably accurate and effective, meeting engineering calculation requirements. The maximum impact force generated by rockfall impacts is closely related to material properties. The impact contact surfaces for RC and CPRC structures are concrete materials, resulting in very similar maximum impact forces for the exact shape of rockfall bodies. However, the CPRC shelter structure has greater stiffness and material deformation resistance, resulting in slightly higher instantaneous impact reaction forces than the non-reinforced RC structure.

(2) Under rockfall disasters of the same shape, the damage area distribution and damage degree of the CPRC open shed structure is significantly lower. Due to the supporting role of the corrugated plate, the damage amounts of concrete units and reinforcement units in the structure are reduced by 73.02–90.19% and 79.68–91.67%, respectively, compared to the RC structure. After the initial impact, the residual resistance index (RRI) of the CPRC open shed structure remains above 0.88, indicating a high residual bearing capacity, which can resist subsequent multiple rockfalls and collapse disasters, preventing severe secondary disasters.

(3) The penetration ability of rockfall bodies is positively correlated with the damage amount of the upper structure and negatively correlated with the impact stress transmission ability. Particularly for rhombohedral rockfall bodies with sharp edges that contact surfaces in a point-to-face manner, the penetration effect is much stronger than other rockfall shapes, causing through-type damage to the RC structure. The number of concrete failure units and the proportion of reinforcement failure are much higher than for different shapes of rockfall bodies, and the residual resistance index (RRI) can even drop to 0.24. However, the damage process to the RC structure consumes a large amount of impact energy, reducing the maximum effective stress transmitted to the corrugated plate and subgrade structure by 52.13% and 26.44%, respectively, resulting in relatively minor damage to the lower structures.

(4) The corrugated panels mitigate the immense impact of high-energy rockfalls on singular points through their flexible deformation capabilities. They exhibit remarkable resistance to perforating failures even under extreme disaster conditions. In contrast to traditional rigid concrete structures, this composite configuration effectively diminishes the risk of extensive cracking and structural collapse. Furthermore, it enhances the structure’s durability under repetitive impacts, significantly reducing the difficulty of maintenance and the costs associated with repairs following an incident.

This article conducts a comparative analysis of the dynamic response results of RC and CPRC structures under the impact of five representative rockfall shapes. A detailed investigation has been performed regarding structural damage, variations in structural stress, and energy dissipation. However, this study does have certain limitations:

This study augments numerical simulation analysis with an experimental approach through indoor model testing to validate the accuracy of the numerical simulations. The ultimate goal is to enhance the impact resistance and durability of the protective structure via the reinforcement effect of corrugated plates. Unfortunately, due to the high costs and substantial workload involved in model fabrication, as well as the destructive nature of the tests that prevents the reuse of models, the indoor experimental section of this study was limited to a comparative analysis of the damage inflicted by spherical rockfalls on the structure. In experiments, the substantial debris and concrete cracking resulting from impacts currently lack standardized quantification methods, preventing us from generating accurate structural damage data. This issue urgently needs to be addressed.

Moreover, no optimization or comparative analysis of the structural design parameters was performed. Future research should prioritize the lightweight modification of the reinforced concrete structure above the corrugated plates, such as reducing concrete thickness and reinforcement ratios. Additionally, it would be advantageous to explore the substitution of conventional Portland cement with lightweight, high-strength modified concrete materials, further reducing the overall weight of the structure.

The primary focus of this research is the corrugated plate-reinforced concrete composite cavern structure. The models employed in this study are consistent with real-world engineering applications, utilizing the corrugated plate structure as internal formwork, with shear studs connecting the rebar mesh before pouring concrete to form the structural core. To meet the demands for rapid construction and ease of disassembly, future research directions should lean towards exploring prefabricated systems based on existing designs, which would allow for the installation and dismantling of protective structures under a wider range of complex construction and geological conditions.

At present, research in tunnel protective structures primarily focuses on the probability of rockfall occurrence and associated damage risks. However, there exists a significant gap in predicting the extent of damage and failure of RC and CPRC structures following rockfall events. A comprehensive and accurate evaluation system to assess the severity of structural damage resulting from rockfall disasters is still lacking, leaving a considerable void in reference data during the design phase of protective structures. Developing such an evaluation framework requires extensive experimental research and field case studies to ensure the reliability and accuracy of the results. Our current body of work remains limited in this regard, and we are committed to advancing this area of research, with the sincere hope of addressing this critical issue in future studies.

All generated simulation data used in this research institute can be obtained from Professor Wang, and there is currently no confidential data involved in the submitted manuscript. If you need to provide relevant data, please contact Professor Wang at [email protected].

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CCCC Special Engineering Co., Ltd, 430000, Wuhan, China

Zhu Peilin & kai Li

School of Civil Engineering, Lanzhou Jiaotong University, 730070, Lanzhou, China

Wang jinghe & Yan songhong

Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, 730000, China

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Mr. Zhu Peilin is responsible for the numerical simulation and manuscript writing of this paper, Professor Wang is responsible for the review and revision of the content of the article, Professor Yan is responsible for providing financial support and the content of engineering cases Dr. Lin and Dr. Li are responsible for the statistics of relevant tunnel protection engineering cases in the mountainous areas of western China. All authors reviewed the manuscript.

Correspondence to Wang jinghe.

The authors declare no competing interests.

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Peilin, Z., jinghe, W., songhong, Y. et al. Assessment of dynamic responses and impact resistance of corrugated plate-reinforced concrete tunnels under irregular rockfall scenarios. Sci Rep 14, 26157 (2024). https://doi.org/10.1038/s41598-024-77976-5

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Received: 02 August 2024

Accepted: 28 October 2024

Published: 30 October 2024

DOI: https://doi.org/10.1038/s41598-024-77976-5

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