# Experimental Study on Impact Absorption Capacity of Various Expanded Materials for Rock Shed

Authors: Yusuke Kurihashi; Naochika Kogure; Shin-ichi Nitta; Masato Komuro
Journal: Shock and Vibration
 (2020)

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## Abstract

In recent years, there has been a continuous increase in the intensity of natural disasters. Slope disasters such as rock falls occur along coastlines and in mountainous regions. Rock shed structures are implemented as measures to prevent rock fall damage; however, these structures deteriorate over time, and their impact resistance also decreases. As a supplementary measure, a method employing foam material as a cushioning material has been used in practical applications. However, the effect of the compressive strength characteristics on the cushioning performance of foamed materials has not been studied thus far. Therefore, in this study, falling-weight impact-loading tests involving various fall heights were performed to examine the absorption performance of various expanded materials. Moreover, we examined the case where core slabs were layered to effectively exploit the absorption performance of the expanded materials. The results of this study are summarized as follows: (1) the transmitted impact penetration stress-strain curves right under the loading points of various expanded materials exhibit properties similar to those obtained from the results of material testing. However, in the case of expanded materials with high compressive strengths, the compressive stress from the results of material testing tends to be lower. (2) In the case of expanded materials with high compressive strengths, with and without core slabs, the distribution of the transmitted impact stress is large, and the energy absorption capacity is high. (3) In this experiment, the energy absorption capacity was found to double when core slabs are layered, regardless of the type of expanded material used. This suggests that expanded materials with high compressive strengths may contribute towards a higher improvement in energy absorption capacities, by using layered core slabs.


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## Body

## 1. Introduction

Torrential rains occur around the world due to climate change caused by global warming, and large-scale slope disasters occur frequently. In recent years, natural disasters have continued to intensify [1]. Slope disasters such as falling rocks occur along the coast and in the mountains [2]. As road disaster prevention countermeasures against rock fall, methods such as reinforced concrete (RC) and/or prestressed concrete (PC) rock sheds, retaining walls, rock fall protection nets, fences, embankments, and other disaster prevention systems have been used [3]. At present, many structures have been in operation for more than 50 years. As the deterioration of structural performance due to aging may become apparent, it is necessary to urgently implement countermeasures [4].Among them, in the case of RC/PC rock shed (Figure1), a soil material (sand, locally generated soil, etc.) is installed as a cushioning material on the top slab to reduce the impact force caused by falling rocks [5–9]. When it is necessary to improve the impact resistance of the rock shed, a method has been applied in which the cushioning material on the top plate is replaced with a material having a high cushioning performance such as a foam material from a soil material [9–11]. Thus far, in addition to foam materials, techniques such as combining geogrids with steel materials and a three-layered absorption system, wherein reinforced concrete (RC) slabs and sand are installed on the foam material [9, 12] have been employed.Figure 1
Outline of rock shed and cushioning materials.In recent years, foam materials with various material properties for various applications have been developed [13, 14]. In general, foam materials with high compressive strength characteristics tend to increase the transmitted impact stress when an impact load is applied and also possess high energy absorption performance. Also, when applied to the abovementioned three-layered absorption system, there is a possibility that the distribution range of transmitted impact stress can be made wider. Thus, it is considered that the use of a material with different strength characteristics from the conventional foam material may improve the absorption performance of the three-layered absorption system. However, the effect of compressive strength characteristics on the cushioning performance of foamed materials has not been studied at present.Based on this perspective, in this study, falling-weight impact-loading tests were performed for various fall heights, with the aim of examining the absorption effects of various expanded materials with different compressive strength characteristics. Moreover, the tests were performed under the condition that the cores slabs were layered to diffuse the transmitted impact stress, to compare and examine the impacts of the compressive strength characteristics of the expanded materials on their absorption performance. We evaluated the degree of dispersion of the transmitted impact stress based on the energy conservation relationship.


## 2. Experiment Outline

### 2.1. Specimen Outline

Table1 lists characteristics of the expanded materials for comparison used in this study. The expanded materials were polystyrene expanded material (ST), polypropylene expanded material (PP), and polyethylene-polystyrene composite expanded material (EST). The polystyrene expanded material (ST) has been widely used as a countermeasure for weak ground and reducing falling rocks in civil engineering projects thus far.Table 1
Material property of the expanded material.
MarksMain componentExpanding magnification (times)Weight of unit volume (kN/m3)Primary applicationsSTPolystyrene500.212Measures for land subsidence and those for reducing falling rockPPPolypropylene450.195Fenders and car bumpersESTPolyethylene-polystyrene complex300.304Cushioning material of precision apparatus and home electric appliancesMoreover, polypropylene expanded material (PP) is superior in its dimensional stability, and it is capable of returning to its original shape even after a significant compressive deformation. Therefore, it is widely used in fenders and car bumpers. As the perseverance and compressive strength of the polyethylene-polystyrene expanded material (EST) are higher than those of other expanded materials, it is applied as a packaging material in precision apparatus and domestic electrical appliances.Figure2 depicts the compression test results for various expanded materials. The tests were performed for a cube with a side of 50 mm, according to ISO 884 (rigid cellular plastics—determination of compression properties) [15]. The figure indicates that the stress elastically increases to approximately 2% of compression strain in all the three expanded materials; it changes with a small increasing gradient until around 60–70% and then increases rapidly. However, the compressive stress with the same strain is different for each expanded material, which affects the transmitted impact stress when an impact load is applied.Figure 2
Results of compressive strength tests for each expanded material.The specimen list is presented in Table2. A total of 22 specimens were used. The expansion material and fall height were varied for both cases, i.e., with and without core slabs. Furthermore, impact-loading tests were performed for total nine kinds of expand materials with different raw materials and the expanding magnification prior to this experiment, and materials having compressive strength characteristics that significantly differ from those of general-purpose ST expand materials were selected.Table 2
Specimen list.
Name of specimenPresence of core slabType of expanded materialSet fall heightH (mm)Measurement impact velocityV (m/s)Input energyEk (J)N-ST-H50Without core slabST500.999.77N-ST-H1001001.4019.7N-ST-H1501501.7430.3N-ST-H2002001.9839.1N-PP-H50PP500.979.34N-PP-H1001001.4019.7N-PP-H1501501.7430.3N-EST-H50EST500.979.34N-EST-H1001001.4019.7N-EST-H1501501.8132.9N-EST-H2002001.9839.1N-EST-H3003002.5665.5C-ST-H200With core slabST2002.0742.9C-ST-H3003002.4258.4C-ST-H4004002.7273.9C-PP-H200PP2001.9839.1C-PP-H3003002.5665.5C-EST-H200EST2002.0742.9C-EST-H3003002.4258.4C-EST-H4004002.9084.1C-EST-H5005003.1196.5C-EST-H6006003.35112.0In Table2, Term 1 of the specimen name indicates the presence of core slabs (N, without core slabs and C, with core slabs). Term 2 indicates the type of material (see Table 1), and the numeric values attached to the alphabet H of Term 3 indicate the fall height (mm).


### 2.2. Method and Measurement Parameter

Figure3 shows outlines of the specimens and transmitted impact stress measurement. The plane dimension of the specimens is 240 mm on the four sides, with a thickness of 50 mm. In the case of the specimens with core slabs, a plaster board with a thickness of 12.5 mm (conforming to JIS A 6901 [16]) was installed on the expanded material. Furthermore, thickness of the plaster board was selected from specifications of the commercially available products in reference to the thickness ratio for EPS blocks and core RC slabs in three-layered absorption systems that are practically used [9].Figure 3
Outline of specimen and transmitted impact stress measurements. (a) A-A section. (b) Plan view.
(a)(b)In the weight fall impact test, a 20-kg steel weight with a tip diameter of 60 mm was allowed to free-fall from a predetermined height on the expansion material, through a linear rail. The expansion materials were installed on a steel bottom plate in which nine load cells were buried to measure the distribution of the transmitted impact stress.Figure4 depicts an experiment status. In the experiment, the points when the maximum penetration strain of the expanded materials exceeded 75% were defined as end states. Thus, the experiment was continued with gradually increasing falling heights until the weight penetration depth exceeded 37.5 mm (= 75% of 50 mm). This was based on the idea that (1) when a penetration strain exceeds 75%, as shown in Figure 2, the compressive stress suddenly increases and (2) the damage to expanded materials would become significant, as shown in Figures 5 and 6, which may lead to damage to the experimental apparatus, especially load cells (Figure 3).Figure 4
State of the falling-weight impact-loading test.Figure 5
State of expanded material cut area in the case of material without core slabs. (a) ST. (b) PP. (c) EST.Figure 6
Cut area of the expanded material in the case with core slabs. (a) ST. (b) PP. (c) EST.The dependent variables used in this experiment are falling-weight impact, weight penetration, and transmitted impact stress distribution. The weight impact force was measured using a load cell with a capacity of 25 kN, for measuring the impact load. The quantity of weight penetration was evaluated by vertically installing a laser-type displacement meter and measuring the distance to an L-shape angle steel on the weight. The transmitted impact stress distribution was measured using load cells with a capacity of 7 MPa; those were installed on the loading point and around it with an interval of 45 mm, as shown in Figure3.Moreover, the impact velocity was calculated by measuring the time required for a white plate of 30-mm length attached to the weight to pass through a laser sensor. In the experiment, these measured values were collected using a memory recorder at a sampling frequency of 2 kHz. After the experiment, the expanded materials were centrally cut to observe destruction properties.


## 2.1. Specimen Outline

Table1 lists characteristics of the expanded materials for comparison used in this study. The expanded materials were polystyrene expanded material (ST), polypropylene expanded material (PP), and polyethylene-polystyrene composite expanded material (EST). The polystyrene expanded material (ST) has been widely used as a countermeasure for weak ground and reducing falling rocks in civil engineering projects thus far.Table 1
Material property of the expanded material.
MarksMain componentExpanding magnification (times)Weight of unit volume (kN/m3)Primary applicationsSTPolystyrene500.212Measures for land subsidence and those for reducing falling rockPPPolypropylene450.195Fenders and car bumpersESTPolyethylene-polystyrene complex300.304Cushioning material of precision apparatus and home electric appliancesMoreover, polypropylene expanded material (PP) is superior in its dimensional stability, and it is capable of returning to its original shape even after a significant compressive deformation. Therefore, it is widely used in fenders and car bumpers. As the perseverance and compressive strength of the polyethylene-polystyrene expanded material (EST) are higher than those of other expanded materials, it is applied as a packaging material in precision apparatus and domestic electrical appliances.Figure2 depicts the compression test results for various expanded materials. The tests were performed for a cube with a side of 50 mm, according to ISO 884 (rigid cellular plastics—determination of compression properties) [15]. The figure indicates that the stress elastically increases to approximately 2% of compression strain in all the three expanded materials; it changes with a small increasing gradient until around 60–70% and then increases rapidly. However, the compressive stress with the same strain is different for each expanded material, which affects the transmitted impact stress when an impact load is applied.Figure 2
Results of compressive strength tests for each expanded material.The specimen list is presented in Table2. A total of 22 specimens were used. The expansion material and fall height were varied for both cases, i.e., with and without core slabs. Furthermore, impact-loading tests were performed for total nine kinds of expand materials with different raw materials and the expanding magnification prior to this experiment, and materials having compressive strength characteristics that significantly differ from those of general-purpose ST expand materials were selected.Table 2
Specimen list.
Name of specimenPresence of core slabType of expanded materialSet fall heightH (mm)Measurement impact velocityV (m/s)Input energyEk (J)N-ST-H50Without core slabST500.999.77N-ST-H1001001.4019.7N-ST-H1501501.7430.3N-ST-H2002001.9839.1N-PP-H50PP500.979.34N-PP-H1001001.4019.7N-PP-H1501501.7430.3N-EST-H50EST500.979.34N-EST-H1001001.4019.7N-EST-H1501501.8132.9N-EST-H2002001.9839.1N-EST-H3003002.5665.5C-ST-H200With core slabST2002.0742.9C-ST-H3003002.4258.4C-ST-H4004002.7273.9C-PP-H200PP2001.9839.1C-PP-H3003002.5665.5C-EST-H200EST2002.0742.9C-EST-H3003002.4258.4C-EST-H4004002.9084.1C-EST-H5005003.1196.5C-EST-H6006003.35112.0In Table2, Term 1 of the specimen name indicates the presence of core slabs (N, without core slabs and C, with core slabs). Term 2 indicates the type of material (see Table 1), and the numeric values attached to the alphabet H of Term 3 indicate the fall height (mm).


## 2.2. Method and Measurement Parameter

Figure3 shows outlines of the specimens and transmitted impact stress measurement. The plane dimension of the specimens is 240 mm on the four sides, with a thickness of 50 mm. In the case of the specimens with core slabs, a plaster board with a thickness of 12.5 mm (conforming to JIS A 6901 [16]) was installed on the expanded material. Furthermore, thickness of the plaster board was selected from specifications of the commercially available products in reference to the thickness ratio for EPS blocks and core RC slabs in three-layered absorption systems that are practically used [9].Figure 3
Outline of specimen and transmitted impact stress measurements. (a) A-A section. (b) Plan view.
(a)(b)In the weight fall impact test, a 20-kg steel weight with a tip diameter of 60 mm was allowed to free-fall from a predetermined height on the expansion material, through a linear rail. The expansion materials were installed on a steel bottom plate in which nine load cells were buried to measure the distribution of the transmitted impact stress.Figure4 depicts an experiment status. In the experiment, the points when the maximum penetration strain of the expanded materials exceeded 75% were defined as end states. Thus, the experiment was continued with gradually increasing falling heights until the weight penetration depth exceeded 37.5 mm (= 75% of 50 mm). This was based on the idea that (1) when a penetration strain exceeds 75%, as shown in Figure 2, the compressive stress suddenly increases and (2) the damage to expanded materials would become significant, as shown in Figures 5 and 6, which may lead to damage to the experimental apparatus, especially load cells (Figure 3).Figure 4
State of the falling-weight impact-loading test.Figure 5
State of expanded material cut area in the case of material without core slabs. (a) ST. (b) PP. (c) EST.Figure 6
Cut area of the expanded material in the case with core slabs. (a) ST. (b) PP. (c) EST.The dependent variables used in this experiment are falling-weight impact, weight penetration, and transmitted impact stress distribution. The weight impact force was measured using a load cell with a capacity of 25 kN, for measuring the impact load. The quantity of weight penetration was evaluated by vertically installing a laser-type displacement meter and measuring the distance to an L-shape angle steel on the weight. The transmitted impact stress distribution was measured using load cells with a capacity of 7 MPa; those were installed on the loading point and around it with an interval of 45 mm, as shown in Figure3.Moreover, the impact velocity was calculated by measuring the time required for a white plate of 30-mm length attached to the weight to pass through a laser sensor. In the experiment, these measured values were collected using a memory recorder at a sampling frequency of 2 kHz. After the experiment, the expanded materials were centrally cut to observe destruction properties.


## 3. Experimental Result of Expanded Material without Core Slab

### 3.1. Various Response Waveforms

Figure7 shows response waveforms for each weight fall height H with respect to weight impact force, weight penetration, and transmitted impact stress right under the loading point (simply called transmitted impact stress below) of materials without core slabs. In the figure, the weight impact force presents waveform with a duration time of 50–75 ms at peak amplitudes of around 1.5–2.5 kN. Moreover, in the event that compressive strength characteristics in the abovementioned material testing are large, rising gradient and maximum impact force tend to increase while the main wave motion duration time tends to decrease.Figure 7
Various time history response waveforms in the case of material without a core slab. (a) Impact force. (b) Weight penetration depth. (c) Transmitted impact stress.Regarding weight penetration, the material exhibited maximum weight penetration, returned to its original state, and rebounded higher than the impact point. Moreover, the maximum weight penetration declines with the duration of main wave motion, indicating larger compressive strength characteristics. The maximum weight penetration increased with an increase in the fall height, and the maximum fall height of the expanded materials exceeded 37.5 mm (ultimate state).The transmitted impact stress rose suddenly with weight impact, similar to the case of the weight impact force at 20 ms of elapsed time, and its gradient varied after that as its characteristic. Moreover, the transmitted impact stress when the gradient changed (20–25 ms) almost corresponds with the gradient turning point on the compressive strength test result shown in Figure2. However, in the case of the EST specimen, the transmitted impact stress at this time was greater than that at the inflection point of compressive stress (0.18 MPa) shown in the material testing result. The authors believe that it is necessary to examine this point in future works.Furthermore, the transmitted impact stress showed a tendency to rise with an increase in the weight fall heightH, and the maximum fall heights of the expanded materials showed a tendency to rise suddenly after 25 ms of elapsed time. This was caused by compressive stress increasing rapidly during the process such that strain of the expanded materials reached 75%.


### 3.2. Transmitted Impact Penetration Stress-Strain Hysteresis Loop

Figure8 shows the transmitted impact stress-penetration strain hysteresis loops in the case of materials without core slabs. The penetration strain was obtained by dividing the weight penetration depth by the thickness of the expansion material. The figure shows that the area enclosed by the transmitted impact stress-penetrating strain hysteresis loop tends to increase with an increase in fall height. Moreover, the transmitted impact stress was almost constant for the penetration strain up to around 40% whilst the rising gradient of the stress steepens after 50–60%, and its shape is almost similar to that seen in the compressive strength test result shown in Figure 2.Figure 8
Transmission impact stress-penetration distortion hysteresis loop for materials without a core slab. (a)H = 100 mm. (b) H = 150 mm. (c) H = 200 mm. (d) H = 300 mm.
(a)(b)(c)(d)However, in the case of the EST specimen, the transmitted impact stress for penetration strain of up to around 40% is greater than the compressive stress obtained by the material test. Although the above suggests the possibility that speed dependency of EST is high, it is necessary to accumulate data and examine them to verify it in the future [13].


### 3.3. Damage State of Expanded Material

Figure5 presents the cut areas of each specimen after the experiment for materials without core slabs. Furthermore, the cut areas are the faces obtained by cutting the materials along the center line, passing through the loading point, as shown in Figure 9. Each sketched cut area in the figure indicates the maximum penetration strain εp in the experiment.Figure 9
Location of cutting the expanded material.From the figure, it can be seen that the residual deformation area increases with an increase in the weight fall heightH in either expansion material. The cracking progressing diagonally downward is long, with a widening crack-width. Moreover, although the maximum penetration strain εp is greater in the PP specimen than that in the ST specimen, it is superior in the returning performance as the damage is minimal. On the contrary, as the deformation and damage for the same fall height are smaller in the EST specimen than those in the ST specimen, it is superior in the resistance and energy absorption capacity for impacts.


### 3.4. Transmitted Impact Stress Distribution at the Time of the Maximum Penetration

In Figure10, transmitted impact stress distributions at the time of the maximum penetration in the case of the materials without core slabs are compared for each fall height H.Figure 10
Transmission impact stress distribution at the maximum penetration in the case without core slabs. (a)H = 100 mm. (b) H = 150 mm. (c) H = 200 mm. (d) H = 300 mm.
(a)(b)(c)(d)The figure shows that the transmitted impact stress right under the loading point reaches its maximum in either specimen, regardless of the fall height. In the case of the ST and PP specimens, the transmitted impact stress of the loading point is prominently high. The tendency that the transmitted impact stress at the loading point becomes prominent is evident in the case ofH = 150 mm, and the PP specimen reaches the ultimate state at this time point. The ST specimen reaches its ultimate state at H = 200 mm.For the EST specimen, the distribution shape of the transmitted impact stress curve displays a pentagon shape with its base wider than the others untilH = 200 mm, and at H = 300 mm, it presents a shape whereby the transmitted impact stress at the loading point becomes prominent. It has been clarified from the above that the transmitted impact stress of the EST specimen with high compressive strength tends to disperse most widely.


## 3.1. Various Response Waveforms

Figure7 shows response waveforms for each weight fall height H with respect to weight impact force, weight penetration, and transmitted impact stress right under the loading point (simply called transmitted impact stress below) of materials without core slabs. In the figure, the weight impact force presents waveform with a duration time of 50–75 ms at peak amplitudes of around 1.5–2.5 kN. Moreover, in the event that compressive strength characteristics in the abovementioned material testing are large, rising gradient and maximum impact force tend to increase while the main wave motion duration time tends to decrease.Figure 7
Various time history response waveforms in the case of material without a core slab. (a) Impact force. (b) Weight penetration depth. (c) Transmitted impact stress.Regarding weight penetration, the material exhibited maximum weight penetration, returned to its original state, and rebounded higher than the impact point. Moreover, the maximum weight penetration declines with the duration of main wave motion, indicating larger compressive strength characteristics. The maximum weight penetration increased with an increase in the fall height, and the maximum fall height of the expanded materials exceeded 37.5 mm (ultimate state).The transmitted impact stress rose suddenly with weight impact, similar to the case of the weight impact force at 20 ms of elapsed time, and its gradient varied after that as its characteristic. Moreover, the transmitted impact stress when the gradient changed (20–25 ms) almost corresponds with the gradient turning point on the compressive strength test result shown in Figure2. However, in the case of the EST specimen, the transmitted impact stress at this time was greater than that at the inflection point of compressive stress (0.18 MPa) shown in the material testing result. The authors believe that it is necessary to examine this point in future works.Furthermore, the transmitted impact stress showed a tendency to rise with an increase in the weight fall heightH, and the maximum fall heights of the expanded materials showed a tendency to rise suddenly after 25 ms of elapsed time. This was caused by compressive stress increasing rapidly during the process such that strain of the expanded materials reached 75%.


## 3.2. Transmitted Impact Penetration Stress-Strain Hysteresis Loop

Figure8 shows the transmitted impact stress-penetration strain hysteresis loops in the case of materials without core slabs. The penetration strain was obtained by dividing the weight penetration depth by the thickness of the expansion material. The figure shows that the area enclosed by the transmitted impact stress-penetrating strain hysteresis loop tends to increase with an increase in fall height. Moreover, the transmitted impact stress was almost constant for the penetration strain up to around 40% whilst the rising gradient of the stress steepens after 50–60%, and its shape is almost similar to that seen in the compressive strength test result shown in Figure 2.Figure 8
Transmission impact stress-penetration distortion hysteresis loop for materials without a core slab. (a)H = 100 mm. (b) H = 150 mm. (c) H = 200 mm. (d) H = 300 mm.
(a)(b)(c)(d)However, in the case of the EST specimen, the transmitted impact stress for penetration strain of up to around 40% is greater than the compressive stress obtained by the material test. Although the above suggests the possibility that speed dependency of EST is high, it is necessary to accumulate data and examine them to verify it in the future [13].


## 3.3. Damage State of Expanded Material

Figure5 presents the cut areas of each specimen after the experiment for materials without core slabs. Furthermore, the cut areas are the faces obtained by cutting the materials along the center line, passing through the loading point, as shown in Figure 9. Each sketched cut area in the figure indicates the maximum penetration strain εp in the experiment.Figure 9
Location of cutting the expanded material.From the figure, it can be seen that the residual deformation area increases with an increase in the weight fall heightH in either expansion material. The cracking progressing diagonally downward is long, with a widening crack-width. Moreover, although the maximum penetration strain εp is greater in the PP specimen than that in the ST specimen, it is superior in the returning performance as the damage is minimal. On the contrary, as the deformation and damage for the same fall height are smaller in the EST specimen than those in the ST specimen, it is superior in the resistance and energy absorption capacity for impacts.


## 3.4. Transmitted Impact Stress Distribution at the Time of the Maximum Penetration

In Figure10, transmitted impact stress distributions at the time of the maximum penetration in the case of the materials without core slabs are compared for each fall height H.Figure 10
Transmission impact stress distribution at the maximum penetration in the case without core slabs. (a)H = 100 mm. (b) H = 150 mm. (c) H = 200 mm. (d) H = 300 mm.
(a)(b)(c)(d)The figure shows that the transmitted impact stress right under the loading point reaches its maximum in either specimen, regardless of the fall height. In the case of the ST and PP specimens, the transmitted impact stress of the loading point is prominently high. The tendency that the transmitted impact stress at the loading point becomes prominent is evident in the case ofH = 150 mm, and the PP specimen reaches the ultimate state at this time point. The ST specimen reaches its ultimate state at H = 200 mm.For the EST specimen, the distribution shape of the transmitted impact stress curve displays a pentagon shape with its base wider than the others untilH = 200 mm, and at H = 300 mm, it presents a shape whereby the transmitted impact stress at the loading point becomes prominent. It has been clarified from the above that the transmitted impact stress of the EST specimen with high compressive strength tends to disperse most widely.


## 4. Experimental Result in the Case with Core Slabs

### 4.1. Various Response Waveforms

Figure11 shows the time history response waveform for weight impact force, weight penetration, and transmitted impact stress in the case of the materials with core slabs. It is understood from the figure that the weight impact force, unlike the case without cores, suddenly increased to around 2 kN just after the impact. Then, it was once unloaded and reloaded. This is because the weight collided into the core slab, penetrated it, and deformed the expansion material as mentioned later. Furthermore, the maximum weight impact force for each weight fall height H was smallest in the PP specimen and greatest in the EST specimen, similar to the case without core slabs.Figure 11
Various time history response waveforms in the case with core slabs. (a) Impact force. (b) Penetration depth. (c) Transmitted impact stress.The response waveform for weight penetration and transmitted impact stress presented properties similar to those in the case without core slabs. This is because the core penetrated the expanded material just after the collision and presented deformation behaviors similar to those seen in the case without core slabs. The ST, PP, and EST specimens reached the ultimate state after loading with the fall heights ofH = 400, 300, and 600 mm, respectively.


### 4.2. Transmitted Impact Stress-Penetration Strain Hysteresis Loop

Figure12 presents the transmitted impact stress-penetration strain hysteresis loops in the case of the materials with core slabs. The penetrating strain was obtained by dividing weight penetration by the thickness of expanded material, without regard to the core thickness. This is because the destruction properties showed that the compressive deformation of the core was quite small.Figure 12
Transmission impact stress-penetrating distortion hysteresis loop in the case with a core slab. (a)H = 200 mm. (b) H = 300 mm. (c) H = 400 mm. (d) H = 500 mm. (e) H = 600 mm.
(a)(b)(c)(d)The figure shows that transmitted impact stress-penetration strain hysteresis loops create a large loop as the fall heightH increases, similar to the case without core slabs. The initial gradients are lower than those in the case without core slabs. This is because the transmitted impact stress was dispersed by core slabs and the transmitted impact stress right under the loading point decreases.Moreover, the hysteresis loops with a penetrating strain after 20% present properties that are similar to those obtained by the abovementioned material testing result. This was caused by the energy absorption characteristics that were almost similar to the case without core slabs after the core penetrated the material.


### 4.3. Damage State of Core and Expansion

Figure13(a) depicts core slab surface, Figure 13(b) core slab back side, Figure 13(c) expanded material surface after removing core slabs, and Figure 13(d) collapsed state of expanded material after the experiment of the C-ST-H400 specimen. Figures 13(a) and 13(b) show that the core slabs had holes with diameter that is almost equal to that of the weight tip, reaching to penetrating shear fracture. Moreover, Figure 13(c) presents a penetrating shear cone separated from the cone on the upper side of the expansion material. Moreover, it is understood from Figure 13(d) that the expansion material was compressively deformed in a wider range than the weight tip diameter due to the influence of penetrating shear fractures of the core slab. Such a tendency was seen in the weight fall impact test of a two-layered absorption system consisting of the existing RC slab and EPS [17].Figure 13
Damage state of the core slab and expanded material of the C-ST-H400 specimen after experiment. (a) Core slab surface. (b) Bottom surface of the slab. (c) Foam material surface after removing the slab. (d) Penetration condition of foam material.
(a)(b)(c)(d)Figure6 shows cut area of the expanded material after the experiment. The figure indicates that residual deformation area of the expanded material is greater in the case of ST and EST specimens than in the case without core slabs shown in Figure 5. This is because the impact force was dispersed by the effect of core slabs. This result indicates that the energy absorption capacity of the expanded materials is demonstrated effectively by installing cores, regardless of the type of expanded materials.Furthermore, in the case without core slabs, ST, PP, and EST specimens reached the ultimate states atH = 200, 150, and 300 mm, respectively, and in the case with core slabs, they reached the ultimate states at H = 400, 300, and 600 mm, respectively. This result indicates that energy absorption capacity was doubled when core slabs were layered in this experiment, regardless of the expansion materials. As the energy absorption capacity was doubled by core slabs rather than additively increased, it has been demonstrated that the effect of energy absorption capacity was improved by installing core slabs more effectively with greater compressive strength characteristics.


### 4.4. Transmitted Impact Stress Distribution at the Time of the Maximum Penetration

In Figure14, transmitted impact stress distribution at the time of the maximum penetration in the case with core slabs is compared for each fall height H.Figure 14
Transmitted impact stress distribution at the time of the maximum penetration with the core slab. (a)H = 200 mm. (b) H = 300 mm. (c) H = 400 mm. (d) H = 500 mm. (e) H = 600 mm.
(a)(b)(c)(d)(e)The results indicate that the transmitted impact stress distribution of the EST specimen displays a pentagon shape with an extended base in the case of the fall heightH = 300 mm, similar to the case of the core slab with H = 100 mm (Figure 10(a)); in the case of the ST and PP specimens, the transmitted impact stress at the loading point tends to be prominently high. Furthermore, the PP specimen reached the ultimate state at this time point and the ST specimen reached its ultimate state at H = 400 mm.On the other hand, in the case of the EST specimen, the transmitted impact stress distribution was in a pentagon shape with an extensive base untilH = 500 mm, and in triangle shape at H = 600 mm. The ESP specimen reached its ultimate state at H = 600 mm.The results clarify that the distribution range of the transmitted impact stresses for the same fall height became most extensive in the case of the EST specimen, which has the highest compressive strength in this study.


## 4.1. Various Response Waveforms

Figure11 shows the time history response waveform for weight impact force, weight penetration, and transmitted impact stress in the case of the materials with core slabs. It is understood from the figure that the weight impact force, unlike the case without cores, suddenly increased to around 2 kN just after the impact. Then, it was once unloaded and reloaded. This is because the weight collided into the core slab, penetrated it, and deformed the expansion material as mentioned later. Furthermore, the maximum weight impact force for each weight fall height H was smallest in the PP specimen and greatest in the EST specimen, similar to the case without core slabs.Figure 11
Various time history response waveforms in the case with core slabs. (a) Impact force. (b) Penetration depth. (c) Transmitted impact stress.The response waveform for weight penetration and transmitted impact stress presented properties similar to those in the case without core slabs. This is because the core penetrated the expanded material just after the collision and presented deformation behaviors similar to those seen in the case without core slabs. The ST, PP, and EST specimens reached the ultimate state after loading with the fall heights ofH = 400, 300, and 600 mm, respectively.


## 4.2. Transmitted Impact Stress-Penetration Strain Hysteresis Loop

Figure12 presents the transmitted impact stress-penetration strain hysteresis loops in the case of the materials with core slabs. The penetrating strain was obtained by dividing weight penetration by the thickness of expanded material, without regard to the core thickness. This is because the destruction properties showed that the compressive deformation of the core was quite small.Figure 12
Transmission impact stress-penetrating distortion hysteresis loop in the case with a core slab. (a)H = 200 mm. (b) H = 300 mm. (c) H = 400 mm. (d) H = 500 mm. (e) H = 600 mm.
(a)(b)(c)(d)The figure shows that transmitted impact stress-penetration strain hysteresis loops create a large loop as the fall heightH increases, similar to the case without core slabs. The initial gradients are lower than those in the case without core slabs. This is because the transmitted impact stress was dispersed by core slabs and the transmitted impact stress right under the loading point decreases.Moreover, the hysteresis loops with a penetrating strain after 20% present properties that are similar to those obtained by the abovementioned material testing result. This was caused by the energy absorption characteristics that were almost similar to the case without core slabs after the core penetrated the material.


## 4.3. Damage State of Core and Expansion

Figure13(a) depicts core slab surface, Figure 13(b) core slab back side, Figure 13(c) expanded material surface after removing core slabs, and Figure 13(d) collapsed state of expanded material after the experiment of the C-ST-H400 specimen. Figures 13(a) and 13(b) show that the core slabs had holes with diameter that is almost equal to that of the weight tip, reaching to penetrating shear fracture. Moreover, Figure 13(c) presents a penetrating shear cone separated from the cone on the upper side of the expansion material. Moreover, it is understood from Figure 13(d) that the expansion material was compressively deformed in a wider range than the weight tip diameter due to the influence of penetrating shear fractures of the core slab. Such a tendency was seen in the weight fall impact test of a two-layered absorption system consisting of the existing RC slab and EPS [17].Figure 13
Damage state of the core slab and expanded material of the C-ST-H400 specimen after experiment. (a) Core slab surface. (b) Bottom surface of the slab. (c) Foam material surface after removing the slab. (d) Penetration condition of foam material.
(a)(b)(c)(d)Figure6 shows cut area of the expanded material after the experiment. The figure indicates that residual deformation area of the expanded material is greater in the case of ST and EST specimens than in the case without core slabs shown in Figure 5. This is because the impact force was dispersed by the effect of core slabs. This result indicates that the energy absorption capacity of the expanded materials is demonstrated effectively by installing cores, regardless of the type of expanded materials.Furthermore, in the case without core slabs, ST, PP, and EST specimens reached the ultimate states atH = 200, 150, and 300 mm, respectively, and in the case with core slabs, they reached the ultimate states at H = 400, 300, and 600 mm, respectively. This result indicates that energy absorption capacity was doubled when core slabs were layered in this experiment, regardless of the expansion materials. As the energy absorption capacity was doubled by core slabs rather than additively increased, it has been demonstrated that the effect of energy absorption capacity was improved by installing core slabs more effectively with greater compressive strength characteristics.


## 4.4. Transmitted Impact Stress Distribution at the Time of the Maximum Penetration

In Figure14, transmitted impact stress distribution at the time of the maximum penetration in the case with core slabs is compared for each fall height H.Figure 14
Transmitted impact stress distribution at the time of the maximum penetration with the core slab. (a)H = 200 mm. (b) H = 300 mm. (c) H = 400 mm. (d) H = 500 mm. (e) H = 600 mm.
(a)(b)(c)(d)(e)The results indicate that the transmitted impact stress distribution of the EST specimen displays a pentagon shape with an extended base in the case of the fall heightH = 300 mm, similar to the case of the core slab with H = 100 mm (Figure 10(a)); in the case of the ST and PP specimens, the transmitted impact stress at the loading point tends to be prominently high. Furthermore, the PP specimen reached the ultimate state at this time point and the ST specimen reached its ultimate state at H = 400 mm.On the other hand, in the case of the EST specimen, the transmitted impact stress distribution was in a pentagon shape with an extensive base untilH = 500 mm, and in triangle shape at H = 600 mm. The ESP specimen reached its ultimate state at H = 600 mm.The results clarify that the distribution range of the transmitted impact stresses for the same fall height became most extensive in the case of the EST specimen, which has the highest compressive strength in this study.


## 5. Estimation of the Maximum Penetration Strain Based on Coefficient of Stress Dispersion

### 5.1. Coefficient of Stress Dispersion

Table3 shows a list of experimental results of energy balance in this experiment. Here, the input energy Ek was calculated with measured impact velocity. Moreover, the absorbed energy Ea1 of the expanded materials right under the weight was calculated as shown below based on the hysteresis loops of transmitted impact stress and penetrating strain right under the loading point shown in Figures 8 and 12:(1)Ea1=S×H×A,where S = integration value (MPa) until the maximum penetration strain in the transmitted impact penetrating stress-strain hysteresis loop (see Figure 15), H = expanded material height (mm), and A = area of the bottom face area of the weight (mm2).Table 3
List of experimental results of energy balance.
Name of specimenPresence of core slabType of expanded materialFalling height (mm)Input energyEk (J)Absorbed energy of expanded material right under the weightEa1 (J)Coefficient of stress dispersionα = Ek/Ea1N-ST-H50Without core slabST509.779.51.0N-ST-H10010019.716.61.2N-ST-H15015030.325.81.2N-ST-H20020039.136.51.1N-PP-H50PP509.346.31.5N-PP-H10010019.714.51.4N-PP-H15015030.326.81.1N-EST-H50EST509.3410.01.0N-EST-H10010019.717.01.2N-EST-H15015032.920.51.6N-EST-H20020039.127.91.4N-EST-H30030065.543.21.4C-ST-H200With core slabST20042.910.43.8C-ST-H30030058.416.73.5C-ST-H40040073.932.02.5C-PP-H200PP20039.110.43.8C-PP-H30030065.521.32.8C-EST-H200EST20042.916.62.6C-EST-H30030058.422.82.6C-EST-H40040084.126.82.9C-EST-H50050096.531.53.1C-EST-H600600112.038.63.0Figure 15
Integral values to the maximum penetration strain.The coefficient of stress dispersionα was obtained by the following equations under the assumption that the input energy Ek is equivalent to the absorbed energy Ea of the entire expanded materials:(2)Ek=Ea=α×Ea1,α=EkEa1.It is understood from these equations thatα is physical quantity obtained by dividing the total absorbed energy Ea of the expanded material (= input energy Ek) by the absorbed energy Ea1 of the expanded material under the weight. Therefore, it is thought that α is evaluable as an index indicating spread of the energy absorption range of the expansion material. Furthermore, energy absorption by core slabs was ignored based on the assumption that it is much smaller than that of the expanded materials. The table shows that the coefficient of stress dispersion α is 1.0–1.6 in the case without core slabs and 2.5–3.8 in the case with core slabs. It has been revealed quantitatively that the coefficient of stress dispersion α was increased by core slabs and the expanded materials absorbed energy effectively in a wide range.An estimation of the coefficient of stress dispersionα geometrically using the weight radius R and core thickness t, based on the assumption that the core punching shear fractures at 45 degrees, is shown in Figure 16, and it is expressed by the following equation:(3)αp=πR+t2πR2=1+tR2,where αp is the theoretical coefficient of stress dispersion for the punching shear model.Figure 16
Conception diagram of the punching shear fracture of the core slab (in the case that diagonal tension cracking the angle of the core slab is 45 degrees).In this experiment, as the weight radiusR = 30 mm and core thickness t = 12.5 mm, the coefficient of the stress dispersion αp = 2.01. The above suggests that transmitted impact stress disperses more widely than the assumptions, as outlined in Figure 16.


### 5.2. Estimation of the Maximum Penetration Strain

Here, the maximum weight penetration is calculated and compared with the experimental result, in accordance with the compression stress-strain relation (see Figure2) based on the coefficient of the stress dispersion α and material testing. Furthermore, values at the time of the maximum input energy were used for the coefficient of the stress dispersion α of each specimen.The experimental results of the maximum penetration strainεp for each input energy Ek are plotted in Figure 17 and compared with the penetration strain-input energy curve obtained by the calculation result. Here, the input energy E for the arbitrary penetration strain ε was obtained by the following equation and is expressed as an ε–E curve in the calculation result:(4)E=α×Saε×H×A.Figure 17
Weight penetration-input energy relationship. (a) ST. (b) PP. (c) EST.
(a)(b)(c)Here,Sa (ε) represents integral values to the arbitrary strain ε in the compression stress-strain relationship based on the material testing results (see Figure 2). The figure shows that penetration strain for the same input energy is smaller in the case with core slabs than in the case without them in both experimental and calculation results in either specimen. Moreover, the penetration strain with the same input energy is smallest and superior in energy absorption capacity to the EST specimen.Comparison of the experiment and calculation results shows that the calculation result is greater than the experimental result by around 30% in some cases, whilst on the other hand there is an increased tendency of the penetration strain to increase the input energy seen in both cases.Therefore, the maximum penetration strainεp can be evaluated by appropriately setting the stress dispersion coefficient α corresponding to various absorbents and core slabs and using the relationship between compressive stress and strain based on material tests. The safety factor under the conditions of this study is about 30%.In the case that expanded materials with high compressive strength such as the EST specimen are used, transmission impact force rises accordingly. Therefore, it is necessary to design absorption materials considering load-carrying capacity of existing rock shed. Moreover, in order to improve accuracy of the penetration evaluation method proposed in this paper, it is necessary to (1) clarify the difference between the material testing result and impact-loading test result in the stress-strain relation and (2) evaluateα corresponding to various expanded materials.


## 5.1. Coefficient of Stress Dispersion

Table3 shows a list of experimental results of energy balance in this experiment. Here, the input energy Ek was calculated with measured impact velocity. Moreover, the absorbed energy Ea1 of the expanded materials right under the weight was calculated as shown below based on the hysteresis loops of transmitted impact stress and penetrating strain right under the loading point shown in Figures 8 and 12:(1)Ea1=S×H×A,where S = integration value (MPa) until the maximum penetration strain in the transmitted impact penetrating stress-strain hysteresis loop (see Figure 15), H = expanded material height (mm), and A = area of the bottom face area of the weight (mm2).Table 3
List of experimental results of energy balance.
Name of specimenPresence of core slabType of expanded materialFalling height (mm)Input energyEk (J)Absorbed energy of expanded material right under the weightEa1 (J)Coefficient of stress dispersionα = Ek/Ea1N-ST-H50Without core slabST509.779.51.0N-ST-H10010019.716.61.2N-ST-H15015030.325.81.2N-ST-H20020039.136.51.1N-PP-H50PP509.346.31.5N-PP-H10010019.714.51.4N-PP-H15015030.326.81.1N-EST-H50EST509.3410.01.0N-EST-H10010019.717.01.2N-EST-H15015032.920.51.6N-EST-H20020039.127.91.4N-EST-H30030065.543.21.4C-ST-H200With core slabST20042.910.43.8C-ST-H30030058.416.73.5C-ST-H40040073.932.02.5C-PP-H200PP20039.110.43.8C-PP-H30030065.521.32.8C-EST-H200EST20042.916.62.6C-EST-H30030058.422.82.6C-EST-H40040084.126.82.9C-EST-H50050096.531.53.1C-EST-H600600112.038.63.0Figure 15
Integral values to the maximum penetration strain.The coefficient of stress dispersionα was obtained by the following equations under the assumption that the input energy Ek is equivalent to the absorbed energy Ea of the entire expanded materials:(2)Ek=Ea=α×Ea1,α=EkEa1.It is understood from these equations thatα is physical quantity obtained by dividing the total absorbed energy Ea of the expanded material (= input energy Ek) by the absorbed energy Ea1 of the expanded material under the weight. Therefore, it is thought that α is evaluable as an index indicating spread of the energy absorption range of the expansion material. Furthermore, energy absorption by core slabs was ignored based on the assumption that it is much smaller than that of the expanded materials. The table shows that the coefficient of stress dispersion α is 1.0–1.6 in the case without core slabs and 2.5–3.8 in the case with core slabs. It has been revealed quantitatively that the coefficient of stress dispersion α was increased by core slabs and the expanded materials absorbed energy effectively in a wide range.An estimation of the coefficient of stress dispersionα geometrically using the weight radius R and core thickness t, based on the assumption that the core punching shear fractures at 45 degrees, is shown in Figure 16, and it is expressed by the following equation:(3)αp=πR+t2πR2=1+tR2,where αp is the theoretical coefficient of stress dispersion for the punching shear model.Figure 16
Conception diagram of the punching shear fracture of the core slab (in the case that diagonal tension cracking the angle of the core slab is 45 degrees).In this experiment, as the weight radiusR = 30 mm and core thickness t = 12.5 mm, the coefficient of the stress dispersion αp = 2.01. The above suggests that transmitted impact stress disperses more widely than the assumptions, as outlined in Figure 16.


## 5.2. Estimation of the Maximum Penetration Strain

Here, the maximum weight penetration is calculated and compared with the experimental result, in accordance with the compression stress-strain relation (see Figure2) based on the coefficient of the stress dispersion α and material testing. Furthermore, values at the time of the maximum input energy were used for the coefficient of the stress dispersion α of each specimen.The experimental results of the maximum penetration strainεp for each input energy Ek are plotted in Figure 17 and compared with the penetration strain-input energy curve obtained by the calculation result. Here, the input energy E for the arbitrary penetration strain ε was obtained by the following equation and is expressed as an ε–E curve in the calculation result:(4)E=α×Saε×H×A.Figure 17
Weight penetration-input energy relationship. (a) ST. (b) PP. (c) EST.
(a)(b)(c)Here,Sa (ε) represents integral values to the arbitrary strain ε in the compression stress-strain relationship based on the material testing results (see Figure 2). The figure shows that penetration strain for the same input energy is smaller in the case with core slabs than in the case without them in both experimental and calculation results in either specimen. Moreover, the penetration strain with the same input energy is smallest and superior in energy absorption capacity to the EST specimen.Comparison of the experiment and calculation results shows that the calculation result is greater than the experimental result by around 30% in some cases, whilst on the other hand there is an increased tendency of the penetration strain to increase the input energy seen in both cases.Therefore, the maximum penetration strainεp can be evaluated by appropriately setting the stress dispersion coefficient α corresponding to various absorbents and core slabs and using the relationship between compressive stress and strain based on material tests. The safety factor under the conditions of this study is about 30%.In the case that expanded materials with high compressive strength such as the EST specimen are used, transmission impact force rises accordingly. Therefore, it is necessary to design absorption materials considering load-carrying capacity of existing rock shed. Moreover, in order to improve accuracy of the penetration evaluation method proposed in this paper, it is necessary to (1) clarify the difference between the material testing result and impact-loading test result in the stress-strain relation and (2) evaluateα corresponding to various expanded materials.


## 6. Conclusion

In this study, falling-weight impact-loading tests with various fall heights were performed for examining the absorption performance of various expansion materials. We examined the case wherein core slabs were layered for an effective utilization of the absorption performance of expanded materials. The findings of this study are summarized as follows:(1)
The transmitted impact stress-penetration strain curves right under the loading points of various expanded materials exhibit properties that are similar to those obtained from the results of the material testing. However, in the case of expanded materials with high compressive strengths, the compressive stress tends to be higher than that observed in the results of material testing.(2)
In the case of expanded materials with high compressive strengths, with and without core slabs, the distribution of the transmitted impact stress and energy absorption capacity is large.(3)
In this experiment, the energy absorption capacity doubles when core slabs are layered, regardless of the type of expansion material. This indicates that expansion materials with high compressive strengths may result in higher improvements in the energy absorption capacity by using layered core slabs.



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