Dynamic Response and Energy Dissipation Mechanisms of Soil–Lightweight Foam Composite Protective Layers Under Impact Loading

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript “Dynamic Response and Energy Dissipation Mechanisms of Soil-Lightweight Foam Composite Protective Layers under Impact Loading” by Jianping Gao et al. presents the results of experimental studies of the dynamic response and energy dissipation characteristics of polystyrene and polyethylene foam samples, as well as foam-soil composites. The experiments were carried out under impact loading of samples at different speeds in the range from 9.5 to 15.4 m/s. The obtained results may be of interest to specialists practicing in the field of creating composite protective coatings designed to absorb impact mechanical loads. The manuscript corresponds to the focus of the journal; the experimental studies were conducted at an acceptable methodological level. However, reading the work raises certain questions that should be answered before deciding whether to publish.

1. In my understanding, Figures 8, a and 8, b are almost identical. The authors should explain what the “waveform improvement” is.
2. The authors used the instrumental “pulse shaper” to improve the forms of acquired pulses. According to Fig. 7, the introduction of such a unit is equivalent to low-pass filtering of the recorded signals. Why couldn't this be done using software filtering of the recorded signals at the post-processing stage?
3. Please provide an analysis of the physical or instrumental reasons for the linear decrease in peak stress velocity with increasing length of foam samples and the differences in these parameters for EPS and EPE foams (Fig. 10).
4. Figure 13 is physically inconsistent because the transmitted energy exceeds the incident energy. The text fragment “Both the reflected and transmitted energies increase simultaneously, but their magnitudes are significantly lower than that of the incident energy.” (lines 393-394) contradicts the presented graphs. Further, following from Fig. 13, the energy absorption can hardly be called effective, despite the authors’ statement (“….indicating that the specimen has a strong energy absorption capacity.”, line 397).

5. Figures 17 - 19 are difficult to percept; the amount of data presented is small. It is better to provide them in the form of bar diagrams (like Fig. 16).

Author Response

Comments and Suggestions for Revising the Paper “Dynamic Response and Energy Dissipation Mechanisms of Soil-Lightweight Foam Composite Protective Layers under Impact Loading”

Dear Editors,

I wish to express my sincere gratitude to the editorial team and the reviewers for their meticulous and comprehensive revisions of this manuscript. Each comment has significantly contributed to both the authors and the overall quality of the manuscript. To facilitate the review process, I have highlighted the corrections and key sections. While some minor issues, including wording and typographical errors, were not specifically noted in the revision comments, they have been rectified in the revised manuscript. Additionally, I have meticulously reviewed the entire content of the manuscript once again. The revised manuscript and the accompanying response to comments have been submitted for your review.

Thank you for your attention, and I look forward to your feedback.

Review:

(1) In my understanding, Figures 8, a and 8, b are almost identical. The authors should explain what the “waveform improvement” is.

Answer: Thank you for your valuable suggestion. Regarding this issue, the following explanation is provided:

In SHPB tests conducted on solid materials, it is not necessary to use sample holding devices, as the load is applied directly. However, since the study involves particulate materials, it is necessary to incorporate rigid sleeves and plates. The test results shown in Figure 8 primarily serve to verify whether the addition of the sleeve and plate device affects the test results.

As shown in Figure 8(a), the test was conducted without the sleeve, representing the unloaded case. Figure 8(b) represents the unloaded test results with the addition of the sleeve and plate. A comparison reveals that the results of Figure 8(a) and Figure 8(b) are almost identical, indicating that the influence of the sleeve and plate on the test results is minimal. Therefore, the similarity of the results between Figure 8(a) and Figure 8(b) is a normal finding. If the results between the two figures had differed significantly, it would have suggested that the addition of the sleeve and plate had a substantial impact on the test results. The waveform improvement mentioned in the paper refers specifically to the effect of the waveform shaper, which will be addressed further below.

(2) The authors used the instrumental “pulse shaper” to improve the forms of acquired pulses. According to Fig. 7, the introduction of such a unit is equivalent to low-pass filtering of the recorded signals. Why couldn't this be done using software filtering of the recorded signals at the post-processing stage?

Answer: Thank you for your valuable suggestion. Regarding this issue, the following explanation is provided:

 (a) Numerous studies have confirmed the following functions of the waveform shaper: (1) It adjusts the shape of the incident stress wave to achieve constant strain rate loading and reduce high-frequency oscillations, thereby improving the accuracy of the experimental results; (2) It prolongs the wave propagation time. The correction results shown in Figure 7 demonstrate that the wave propagation time is significantly extended with the use of the waveform shaper compared to when it is not used (as indicated by the blue line in Figure 7); (3) The waveform shaper can smooth the voltage signal.

(b) Regarding the expert's comment that the same effect can be achieved through software filtering during the post-processing phase, it is true that low-pass filtering can be implemented using post-processing software. However, one of the main functions of the deforming device is to achieve constant strain rate loading, which cannot be accomplished through post-processing software.

(c) Specifically, from a quantitative perspective, when no waveform shaper is used, the duration of the incident wave pulse is approximately 0.319 ms, whereas with the waveform shaper, it increases to 0.508 ms. This means the incident signal duration is extended by 59.2%.

(d) In conclusion, the waveform shaper not only performs low-pass filtering and smooths the voltage signal but also has other significant effects. This is one of the most commonly used methods in SHPB experiments.

In accordance with the expert's suggestion, we have added a description of the waveform shaper's impact on the signal duration in the revised manuscript. The specific revision is as follows:

Overall, compared to tests without a pulse shaper, the application of the pulse shaper in-creased the pulse duration by 60%, greatly enhancing the reliability of the experiment.

Figure 7. Effect of shapers on waveform.

(3) Please provide an analysis of the physical or instrumental reasons for the linear decrease in peak stress velocity with increasing length of foam samples and the differences in these parameters for EPS and EPE foams (Fig. 10).

Answer: Thank you for your valuable suggestion. Regarding this issue, the following explanation is provided:

(a) Foam is an elastoplastic material, and the stress wave incident on the foam will dissipate energy during propagation, leading to attenuation.

(b) General research results indicate that an increase in sample thickness further reduces the peak stress, as the stress wave is attenuated over a longer propagation path.

(c) EPE (Expanded Polyethylene) is softer, recoverable, and exhibits strong viscoelastic properties. It has closed cells, but its skeleton is more extensible, providing higher damping/energy dissipation. As a result, it filters the impact more effectively, leading to lower peak stresses and better recovery.

(d) The peak stress velocity c is proportional to, where E is the modulus and is the density. Since the modulus of EPE is generally lower than that of EPS, the wave speed is lower, the rise is slower, and high frequencies are more easily attenuated within the same length, resulting in a lower peak stress velocity.

In response to the expert's comment, we have added relevant content regarding the differences in peak stress velocity between EPS and EPE in the manuscript. The specific revision is as follows:

In addition, the difference in peak stress velocity between EPS and EPE is primarily attributed to the attenuation of stress waves during propagation through the materials (Figures 10(b) and 10(d)). As the sample length increases, the propagation path of the stress wave becomes longer, leading to greater energy dissipation. Moreover, EPE foam, compared to the more rigid and brittle EPS foam, exhibits greater flexibility, resilience, and a closed-cell structure, providing higher damping and cushioning capabilities. Consequently, at the same thickness, EPE foam is more effective in absorbing and attenuating shock waves, resulting in a lower peak stress velocity.

(4) Figure 13 is physically inconsistent because the transmitted energy exceeds the incident energy. The text fragment “Both the reflected and transmitted energies increase simultaneously, but their magnitudes are significantly lower than that of the incident energy.” (lines 393-394) contradicts the presented graphs. Further, following from Fig. 13, the energy absorption can hardly be called effective, despite the authors’ statement (“….indicating that the specimen has a strong energy absorption capacity.”, line 397).

Answer: Thank you for your valuable suggestion. We apologize for the translation error in the legend of Figure 13 due to a typographical mistake.

As the expert correctly pointed out, transmitted energy cannot exceed incident energy, as the incident energy is the largest among all energy types. Additionally, the expert raised concerns about the effectiveness of energy absorption, which may not be considered substantial. In fact, in SHPB tests, nearly all non-metallic materials face significant reflection energy due to the large impedance mismatch between the bars and the specimen. We have taken this issue into account in the study. Therefore, in Section 3.3.2, Equation (8) was modified to quantitatively describe energy absorption by defining the energy absorption coefficient as the incident energy minus the reflected energy. This adjustment helps reduce the influence of reflection energy on the results to some extent.

In response to the expert’s suggestion, the description of Figure 13 has been revised in the revised manuscript. The specific revision is as follows:

Figure 13. Typical energy change time course curve.

Figure 13 illustrates the variation of energy with time for a typical specimen during the SHPB test, reflecting the material's energy absorption characteristics. During the test, incident energy rapidly increases with loading time and stabilizes after 0.032 ms. Both reflected and transmitted energies rise synchronously, but their amplitudes are much lower than that of the incident energy. Absorbed energy shows a continuous increase with time, indicating the specimen’s dissipation effect on incident energy. Furthermore, soil particles are a low wave impedance material, resulting in most of the incident energy being converted into reflected energy, with relatively small proportions of transmitted and absorbed energies.

(5) Figures 17 - 19 are difficult to percept; the amount of data presented is small. It is better to provide them in the form of bar diagrams (like Fig. 16).

Answer: Thank you for your valuable suggestion. We greatly appreciate your input. Figures 17–19 are three-dimensional plots that involve two variables. If converted into two dimensions, the impact of the two variables on the results would not be properly represented. Based on your suggestion, we have revised the figures into three-dimensional bar charts.

Therefore, your suggestion was excellent, and we have updated most of the figures accordingly. However, due to the stacking of data points along the Y-axis, the display effect of Figure 18 is unsatisfactory. Therefore, we sincerely hope that the figure will retain its original lollipop chart format in the manuscript. The specific revision is as follows:

 

Figure 17. Stress attenuation coefficient in foam: (a) EPS cushion layer; and (b) EPE cushion layer.

Figure 18. Effect of density variation ratio on energy absorption coefficient: (a) EPS cushion layer; and (b) EPE cushion layer.

Figure 19. Effect of density variation ratio on energy absorbing density: (a) EPS cushion layer; and (b) EPE cushion layer.

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

The paper is clearly and well written. She would suggest some minor revision to the paper before publication. I hope that the given comments will be useful for avoiding mistakes and improving the quality of work.

Review:

Title: Dynamic Response and Energy Dissipation Mechanisms of Soil-Lightweight Foam Composite Protective Layers under Impact Loading

The abstract is too long, see the templates.

The introductory part should emphasize the innovation in the work.

In paragraph 2.1, state the origin of the materials you used in your work, and also state the origin of the device.

In the title of Figure 2, descriptions for a, b, c... should be added. Why are there references in the title of image 2 if they are images of your samples?

Add a description of the method used to obtain the particle diameter distribution

Figure 4 requires either mass or atomic % of elements. In the text you only mentioned the elements, not how many there are.

In the headings of paragraphs 2.2. and 2.3, write in a little more detail about your test equipment and test procedures.

In the captions for pictures 10 and 11, you should describe what a, b, c, d... represent to you. Put the explanation in the caption, not next to a or b.

Figures 18 and 19 are not clear, especially on the z axis.

Author Response

Comments and Suggestions for Revising the Paper “Dynamic Response and Energy Dissipation Mechanisms of Soil-Lightweight Foam Composite Protective Layers under Impact Loading”

Dear Editors,

I wish to express my sincere gratitude to the editorial team and the reviewers for their meticulous and comprehensive revisions of this manuscript. Each comment has significantly contributed to both the authors and the overall quality of the manuscript. To facilitate the review process, I have highlighted the corrections and key sections. While some minor issues, including wording and typographical errors, were not specifically noted in the revision comments, they have been rectified in the revised manuscript. Additionally, I have meticulously reviewed the entire content of the manuscript once again. The revised manuscript and the accompanying response to comments have been submitted for your review.

Thank you for your attention, and I look forward to your feedback.

 

The paper is clearly and well written. She would suggest some minor revision to the paper before publication. I hope that the given comments will be useful for avoiding mistakes and improving the quality of work.

Review:

(1) The abstract is too long, see the templates.

Answer: Thank you for your valuable suggestion. We have revised the abstract as per your recommendation. The specific modification is as follows:

Abstract: Engineering structures often face safety risks under impact or explosion loading, making the design of lightweight and efficient cushioning systems crucial. This study investigates the dynamic response and energy dissipation characteristics of Expanded Polystyrene (EPS), Expanded Polyethylene (EPE), and soil–foam composite cushion layers under impact loading, using a Split Hopkinson Pressure Bar (SHPB) testing apparatus. The tests include pure foam layers (lengths ranging from 40 to 300 mm) and a soil-foam composite layer with a total length of 60 mm (soil/foam ratio 1:1 to 1:3), subjected to impact velocities of 9.9–15.4 m/s. The results show that the stress wave propagation velocity of EPE is 149.6 m/s, lower than that of EPS at 249.3 m/s. At higher velocities, the attenuation coefficient for the 40 mm EPE sample reaches as low as 0.22, while EPS is 0.31. Furthermore, the maximum energy absorption coefficient of EPE exceeds 98%, with better stability at high impact velocities. In composite cushion layers, both soil and foam collaborate in energy ab-sorption, but an increased proportion of soil leads to a decrease in energy absorption efficiency and attenuation capacity. Under equivalent ratios, the soil-EPE combination performs better than the soil-EPS combination. By constructing a comprehensive evaluation system based on three indices: stress wave attenuation coefficient, energy absorption coefficient, and energy absorption density, this study quantifies the impact resistance performance of different cushioning layers, providing theoretical and parametric support for material selection in engineering design.

(2) The introductory part should emphasize the innovation in the work.

Answer: Thank you for your valuable suggestion. In response to the expert’s comment, we have addressed the limitations of current research in the introduction and highlighted the innovations of this study. Additionally, a description of the existing gaps in the current research has been added. The specific revision is as follows:

Excerpt 1: However, shock tubes and drop-weight devices face challenges in obtaining the mechanical response of materials under medium-to-high strain rate conditions [18], while model experiments typically rely on embedded pressure gauges to capture stress data. Due to the significant difference in wave impedance between the pressure gauges and the materials, as well as the interference caused by the gauges on the stress waves, this can result in the transmitted stress being greater than the incident stress, leading to calibration difficulties [19]. For instance, Hampton et al. [20] found that the transmitted stress measured by pressure gauges was higher than the actual incident pressure due to interactions between the gauges and the soil, with the maximum deviation reaching 50%. Schindler [21] pointed out that the placement of the pressure gauges could cause significant sample disturbance, making calibration within the sample difficult. The Split Hopkinson Pressure Bar (SHPB) resolves the issue of simultaneously measuring stress and strain at the same position in the sample over time by measuring the elastic deformation at the ends of the incident and transmission bars. This approach provides more accurate results than embedded pressure gauges and allows high strain-rate loading by varying bar diameter and increasing projectile velocity.

Excerpt 2: Overall, significant progress has been made in understanding the energy absorption characteristics of lightweight cushion layers under dynamic loading. However, most studies compare the energy absorption performance of different materials based on experimental observations, lacking a unified mathematical model to describe the quantitative relationship between the material's energy absorption properties, sample length, and loading conditions. This limitation hinders a deeper understanding and efficient design of lightweight cushion materials.

Excerpt 3: Innovative mathematical models for the stress attenuation coefficient, energy absorption coefficient, and energy absorption density have been proposed, enabling multidimension-al quantification and comprehensive evaluation of the cushioning energy absorption performance of different materials. These models provide experimental evidence and a theoretical foundation for the design and protective applications of composite structures under dynamic loading.

(3) In paragraph 2.1, state the origin of the materials you used in your work, and also state the origin of the device.

Answer: Thank you for your valuable suggestion. We have added information regarding the sources of the experimental materials and equipment in Sections 2.1 and 2.2, as requested. The specific revision is as follows:

Excerpt 1: Soil used for testing was collected from Zibo, Shandong Province. According to the geotechnical test results, the natural moisture content of the soil sample is 32.3%.

Excerpt 2: EPS and EPE materials used in this study were both commercially available light-weight foams.

Excerpt 3: Experiments were conducted using the Split Hopkinson Pressure Bar (SHPB) system provided by the Archimedes Dynamic Testing Laboratory in Tianjin, with modifications made to the setup to accommodate testing of particulate materials (Figure 5).

(4) In the title of Figure 2, descriptions for a, b, c... should be added. Why are there references in the title of image 2 if they are images of your samples?

Answer: Thank you for your valuable suggestion. We provide the following explanation regarding this issue:

(a) In the original manuscript, Figures 2(e), 2(f), and 2(h) are figures sourced from other papers. However, since we did not obtain the copyright for these images, we followed the editor’s instructions and have referenced them in text form. Furthermore, considering that these images serve only as supplementary illustrations, switching to text references will not impact the overall content of the paper.

(b) Since the two images in the figure are cited, they are accompanied by the corresponding references. However, due to the issue of not obtaining the image copyrights, we have revised the manuscript to describe these images in text form. The specific revision is as follows:

EPS and EPE materials used in this study were both commercially available lightweight foams. EPS has a density of 15 kg/m³. According to the study by Sarmiento et al. [46] on the microscopic characteristics of EPS, foam cell morphology is regular, with distinct boundaries, representing a typical closed-cell structure. Thin walls separate the cells, forming the unique 'foam skeleton' of EPS material, which deforms, collapses, and ruptures during compression, playing a key role in its energy absorption performance. Based on the experimental design, 18 groups of EPS samples with different lengths were tested in this study.

EPE foam used in the experiment has a density of 20 kg/m³. According to Tan's study [47], EPE material exhibits a typical foam cell structure, with polyhedral closed cells and a relatively uniform pore size distribution. Additionally, the cells are large, and the cell walls are thick, providing good deformation stability. The cells are interconnected through the cell walls, forming a complex spatial network skeleton. To compare the energy absorption performance with that of EPS, 18 groups of EPE samples with different lengths were also tested in this study.

(5) Add a description of the method used to obtain the particle diameter distribution.

Answer: Thank you for your valuable suggestion. Particle sieving tests are standard geotechnical experiments. We have added the relevant information in Section 2.1, as per your suggestion. The specific revision is as follows:

The sand used in the tests was sourced from Zibo City, Shandong Province. According to the results of the geotechnical tests, the natural water content of the soil sample was 32.3%. As this study does not consider the impact of water content on stress wave propagation, the soil was dried at 105°C for 48 hours during preparation. Subsequently, sieve analysis was conducted using sieves with apertures of 5 mm, 2.5 mm, 1.25 mm, 0.6 mm, 0.3 mm, and 0.08 mm. Based on the particle size distribution curve (Figure 3), particles larger than 2 mm accounted for 5.0% of the total mass, while particles larger than 0.075 mm constituted 67.0% of the total mass.

(6) Figure 4 requires either mass or atomic % of elements. In the text you only mentioned the elements, not how many there are.

Answer: Thank you for your valuable suggestion. The original manuscript used EDS for auxiliary analysis of the soil composition. However, the authors have since conducted XRD analysis, which provides higher accuracy than EDS. Therefore, in the revised manuscript, the EDS spectrum has been replaced with the XRD test results, and an analysis of the XRD results has been included. The specific revision is as follows:

XRD analysis results (Figure 4) indicate that quartz and albite are the main mineral com-ponents in the soil samples, with a relatively high intensity of quartz diffraction peaks, accompanied by multiple sets of feldspar diffraction peaks.

 

Figure 4. XRD Spectrum of the soil sample.

(7) In the headings of paragraphs 2.2. and 2.3, write in a little more detail about your test equipment and test procedures.

Answer: Thank you for your valuable suggestion. We have supplemented and revised the test equipment and testing procedure as per your suggestion. Additionally, we have modified the titles of Sections 2.2 and 2.3. The specific revision is as follows:

2.2. SHPB Testing Apparatus and Improved Sleeve

2.3. Sample Preparation and Testing Procedure

(8) In the captions for pictures 10 and 11, you should describe what a, b, c, d... represent to you. Put the explanation in the caption, not next to a or b.

Answer: Thank you for your valuable suggestion. We have made revisions to all the headings in the manuscript as per your suggestion.

Figure 10. Effect of EPS layer specimen length on stress wave propagation characteristics: (a) wave velocity in EPS cushion layer; (b) peak stress velocity in EPS cushion layer; (c) wave velocity in EPE cushion layer; and (d) peak stress velocity in EPE cushion layer.

Figure 11. Effect of composite cushion layer on stress wave propagation characteristics: (a) wave velocity in soil–EPS cushion layer; (b) peak stress velocity in soil–EPS cushion layer; (c) wave velocity in soil– EPE cushion layer; (d) peak stress velocity in soil–EPE cushion layer.

(9) Figures 18 and 19 are not clear, especially on the z axis.

Answer: Thank you for your valuable suggestion. We apologize for the unclear images, which may have been caused by compression during the document preparation. We have uploaded high-resolution vector images for all figures in the system, and we kindly ask the reviewer to refer to them.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Presented problem has significant, practical meaning and is scientifically valuable. I recommend publishing very good organized manuscript after small corrections:

• the new, original scientific elements should be underlined,
• the number of the examined samples with the same material and geometrical parameters should be presented,
• 5 needs a more detailed descriptions,
• the parameters in equations (4),(5), (6) should be described,
• the type of letters in equation (8) should be checked,
• 14 the parameter a should be added,
• 15 the parameter W_p should be added,
• the future investigations should be presented.

Author Response

Comments and Suggestions for Revising the Paper “Dynamic Response and Energy Dissipation Mechanisms of Soil-Lightweight Foam Composite Protective Layers under Impact Loading”

Dear Editors,

I wish to express my sincere gratitude to the editorial team and the reviewers for their meticulous and comprehensive revisions of this manuscript. Each comment has significantly contributed to both the authors and the overall quality of the manuscript. To facilitate the review process, I have highlighted the corrections and key sections. While some minor issues, including wording and typographical errors, were not specifically noted in the revision comments, they have been rectified in the revised manuscript. Additionally, I have meticulously reviewed the entire content of the manuscript once again. The revised manuscript and the accompanying response to comments have been submitted for your review.

Thank you for your attention, and I look forward to your feedback.

 

Review:

(1) the new, original scientific elements should be underlined.

Answer: Thank you for your valuable suggestion. In response to the expert’s comments, this paper highlights the current limitations of existing research in the introduction section and outlines the innovations of this study. Additionally, a description of the shortcomings of current research has been added. The specific modifications are as follows:

Excerpt 1: However, shock tubes and drop-weight devices face challenges in obtaining the mechanical response of materials under medium-to-high strain rate conditions [18], while model experiments typically rely on embedded pressure gauges to capture stress data. Due to the significant difference in wave impedance between the pressure gauges and the materials, as well as the interference caused by the gauges on the stress waves, this can result in the transmitted stress being greater than the incident stress, leading to calibration difficulties [19]. For instance, Hampton et al. [20] found that the transmitted stress measured by pressure gauges was higher than the actual incident pressure due to interactions between the gauges and the soil, with the maximum deviation reaching 50%. Schindler [21] pointed out that the placement of the pressure gauges could cause significant sample disturbance, making calibration within the sample difficult. The Split Hopkinson Pressure Bar (SHPB) resolves the issue of simultaneously measuring stress and strain at the same position in the sample over time by measuring the elastic deformation at the ends of the incident and transmission bars. This approach provides more accurate results than embedded pressure gauges and allows high strain-rate loading by varying bar diameter and increasing projectile velocity.

Excerpt 2: Overall, significant progress has been made in understanding the energy absorption characteristics of lightweight cushion layers under dynamic loading. However, most studies compare the energy absorption performance of different materials based on experimental observations, lacking a unified mathematical model to describe the quantitative relationship between the material's energy absorption properties, sample length, and loading conditions. This limitation hinders a deeper understanding and efficient design of lightweight cushion materials.

Excerpt 3：Innovative mathematical models for the stress attenuation coefficient, energy absorption coefficient, and energy absorption density have been proposed, enabling multidimension-al quantification and comprehensive evaluation of the cushioning energy absorption performance of different materials. These models provide experimental evidence and a theoretical foundation for the design and protective applications of composite structures under dynamic loading.

(2) the number of the examined samples with the same material and geometrical parameters should be presented.

Answer: Thank you for your valuable suggestion. In fact, Table 1 shows the number of test samples corresponding to different materials, lengths, and velocities. In response to the expert's comment, the revised manuscript includes additional descriptions regarding the number of samples tested. The specific modification is as follows:

EPS and EPE materials used in this study were both commercially available lightweight foams. EPS has a density of 15 kg/m³. According to the study by Sarmiento et al. [46] on the microscopic characteristics of EPS, foam cell morphology is regular, with distinct boundaries, representing a typical closed-cell structure. Thin walls separate the cells, forming the unique 'foam skeleton' of EPS material, which deforms, collapses, and ruptures during compression, playing a key role in its energy absorption performance. Based on the experimental design, 18 groups of EPS samples with different lengths were tested in this study.

EPE foam used in the experiment has a density of 20 kg/m³. According to Tan's study [47], EPE material exhibits a typical foam cell structure, with polyhedral closed cells and a relatively uniform pore size distribution. Additionally, the cells are large, and the cell walls are thick, providing good deformation stability. The cells are interconnected through the cell walls, forming a complex spatial network skeleton. To compare the energy absorption performance with that of EPS, 18 groups of EPE samples with different lengths were also tested in this study.

(3) 5 needs a more detailed descriptions.

Answer: Thank you for your valuable suggestion. We have provided more detailed additions and explanations for Figure 5, in accordance with your advice. The specific modification is as follows:

An improved Split Hopkinson Pressure Bar (SHPB) system with a diameter of Φ40 mm was used, as shown in Fig. 5, and a sleeve clamping structure suitable for granular media was designed. The system consists of three main modules: the power module, the pressure bar system, and the data acquisition module. The power module compresses nitrogen gas, stores it, and drives a metal projectile to impact the incident bar, generating a compressive stress wave. The projectile speed is controlled by adjusting the nitrogen pressure, allowing for loading at different strain rates. The bar system comprises a 2.4 m long incident bar and a 2.0 m long transmission bar, both made from 7075 aluminum alloy, with an elastic modulus of 71 GPa and a stress wave propagation speed of approximately 5000 m/s. Due to the significant wave impedance mismatch between the specimen and the bars, semiconductor strain gauges were selected for signal acquisition. The strain gauges have a nominal resistance of 120 Ω and are amplified by a factor of 1000. The strain gauges are positioned 850 mm from each end of the specimen. Data acquisition is performed at a frequency of 10 MHz, ensuring accurate capture of the entire stress wave propagation process under impact loading, thus guaranteeing data timeliness and integrity. (This paragraph provides a comprehensive summary of the compression bar system and the data acquisition system in Figure 5.)

The specimen housing sleeve consists of an outer sleeve, an inner sleeve, and front, rear, and support plates. The outer sleeve is made from high-strength steel, with a total length of 360 mm, an inner diameter of 40.1 mm, and a wall thickness of 2.0 mm, providing ideal lateral confinement. The sleeve is pre-equipped with a series of threaded holes for in-stalling and adjusting the plate positions, allowing for precise control of the specimen's initial length and density before loading. All bolts must be removed during loading to prevent interference with the propagation of the stress wave. The inner sleeve is made of the same material as the outer sleeve, with a diameter of 25 mm, and its primary function is to further restrict the specimen's length and packing density, enhancing the repeatability and consistency of the test. The front and rear plates are made from the same material as the SHPB bars, with a diameter of 40.0 mm and a thickness of 15 mm. These plates help reduce wave impedance mismatch caused by interface discontinuities and prevent specimen particle leakage. The support plate is 10 mm thick and made from high-strength steel, positioned below the rear plate to ensure the plates do not tilt when bolted. (This paragraph provides a comprehensive description of the sleeve and plate in Figure 5.)

This study primarily tests different lengths of EPS and EPE, as well as soil–EPS and soil–EPE composite specimens with varying proportions under a fixed length. The experimental procedure is as follows:(1) Positioning the Plates: Place the support plate on a level working surface and stack the rear plate. Secure the outer sleeve and the rear plate with bolts to ensure the bottom structure is stable and reliable; (2) Filling the Test Material: For pure EPS and EPE materials, place them directly inside the sleeve according to the de-signed length, and position a plate on top of the test material before applying the impact load. For composite material layers, first place the designed length of EPS or EPE foam material on the rear plate, then fill the calculated amount of soil on top of the foam material to form a layered structure with a total length of 60 mm. The foam-to-soil layer length ratios are 1:1, 1:2, and 1:3; (3) Density Control for Composite Layers: To ensure uniform density of the soil across different impact conditions, a constant mass filling method is used. The soil density is maintained at 1.6 g/cm³ through multiple pre-compression and leveling adjustments. It is important to note that the applied pre-compression is minimal and does not alter the initial density of the foam. When the top of the inner sleeve is aligned with the end of the outer sleeve, the limiting plate should be in contact with the outer sleeve, ensuring that the specimen length is precisely set; (4) Assembly and Impact Loading: The assembled specimen is placed between the SHPB incident and transmission bars. The sleeve's orientation is adjusted to maintain a horizontal position, ensuring full contact between the plate ends and the bar ends. The fixing bolts are then removed, and impact loading is applied. To reduce interface friction and improve experimental accuracy, graphite powder is evenly applied on the contact surfaces between the incident bar and the front plate, and between the transmission bar and the rear plate. (This paragraph provides a comprehensive summary and description of the experimental loading steps in Figure 5.)

(4) the parameters in equations (4), (5), (6) should be described.

Answer: Thank you for your valuable suggestion. We have added parameter symbol explanations for all the formulas in the article, in line with your advice. The specific modification is as follows:

(4)	(4)
(5)	(5)
(6)	(6)
(7)	(7)

Where W_I, W_R, W_T, and W_S represent the incident energy, reflected energy, transmitted energy, and absorbed energy, respectively. A_C and E_C are the cross-sectional area and the elastic modulus of the bar, respectively. C_C is the propagation velocity of the compressive stress wave in the bar. ε_I and ε_R are the incident and reflected strains, respectively, and ε_T is the transmitted strain. t represents time.

(5) the type of letters in equation (8) should be checked.

Answer: Thank you for your valuable suggestion. We have revised equation (8) according to your advice. The specific modification is as follows:

where α is the energy absorption coefficient, is the absorbed energy, and  and  are the incident energy and reflected energy, respectively.

(6) 14 the parameter α should be added.

Answer: Thank you for your valuable suggestion. We have provided parameter symbol explanations for all the formulas in the article, in accordance with your suggestion. The specific modification is as follows:

(8)

(8)

where α is the energy absorption coefficient, is the absorbed energy, and  and  are the incident energy and reflected energy, respectively.

(7) 15 the parameter W_p should be added.

Answer: Thank you for your valuable suggestion. We have provided parameter symbol explanations for all the formulas in the article, in accordance with your advice. The specific modification is as follows:

(9)

(9)

Where  represents the energy absorption density, W_S denotes the absorbed energy, and V is the sample volume. The energy absorption density is a measure of the material's efficiency in absorbing impact energy. The higher its value, the greater the proportion of incident energy effectively absorbed by the material, indicating better energy absorption performance.

(8) the future investigations should be presented.

Answer: Thank you for your valuable suggestion. We have added a description of future research directions in the conclusion section, as per your advice. The specific modification is as follows:

(4) The SHPB testing method employed in this study is suitable for investigating the dynamic behavior of different cushioning materials at high strain rates. However, the small size of the specimens does not fully account for the effects of specimen size and the influence of macroscopic structures on the overall response. Future research should integrate SHPB testing with large-scale model experiments to more comprehensively evaluate the dynamic protective performance of material systems under real engineering conditions.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

In my opinion, the authors provided comprehensive answers and explanations to all the questions that arose. The quality of the manuscript has improved after the changes and additions were made. In its present form, the manuscript fits the criteria of publication.