Experimental Investigation on the Dynamic Flexural Performance of High-Strength Rubber Concrete

Abstract

Traditional concrete suffers from high energy consumption during production and low flexural strength, making it prone to flexural failure under impact loading. To address these issues, an eco-friendly non-autoclaved rubber concrete (NARC) was developed. The dynamic flexural performance of NARC was systematically investigated using a 100 mm diameter split Hopkinson pressure bar (SHPB) apparatus, with variations in rubber content (0%, 5%, 10%, 15%, and 20%). The results demonstrate an inverse correlation between dynamic flexural strength and rubber content. A replacement level exceeding 10% resulted in strengths inadequate for practical applications. At a 5% rubber content, the strain rate sensitivity was the most pronounced, where both dynamic strength and mid-span displacement exhibited a significant positive correlation with increasing strain rate. This enhanced performance is attributed to the high strength and dense microstructure of NARC, which facilitates more effective aggregate fracture under high-energy, short-duration impacts, thereby improving its dynamic load resistance. These findings provide valuable insights for promoting the practical and environmentally friendly production of rubber concrete.

1. Introduction

The construction industry faces increasing pressure to align socio-economic development with environmental sustainability, driving the adoption of greener concrete technologies [1,2,3,4,5]. Among these, non-autoclaved concrete (NAC) has gained attention for its reduced carbon footprint, achieved by eliminating energy-intensive high-pressure steam curing [6,7]. NAC is widely used in precast concrete pipe piles, which are frequently subjected to repeated impact loads during construction [8,9,10]. If the concrete lacks sufficient impact resistance, damage or cracking may occur, exposing reinforcement to corrosion and compromising the structural integrity and long-term durability of the pile—and ultimately, the safety of the entire building [11,12,13,14,15,16].

Simultaneously, the rapid expansion of China’s automotive industry has led to the accumulation of vast quantities of waste tires, whose main component, recycled rubber, poses serious environmental challenges due to its resistance to natural degradation [17,18,19,20]. Incorporating this waste rubber into concrete offers a dual benefit: it mitigates solid waste pollution while improving the material’s mechanical behavior. Rubber particles are known to reduce concrete brittleness and enhance deformation capacity and energy absorption, thereby improving impact resistance [21,22,23]. However, the dynamic flexural performance of non-autoclaved rubber concrete (NARC) remains insufficiently studied, despite its relevance to practical applications involving impact loading. This study aims to address this gap by systematically investigating the dynamic flexural properties of NARC, with the goal of supporting both sustainable material development and improved structural resilience.

Some scholars have made improvements and proposed non-autoclaved concrete. Liu et al. [24] investigated the impact resistance of environmentally friendly non-autoclaved concrete. The results showed that the impact resistance of non-autoclaved concrete was similar to that of autoclaved concrete and that it had prospects for practical application. Wang et al. [25] added slag powder and silicate hydrate to rubber concrete to solve the problem of thermal damage and expansion and deformation of concrete by the traditional curing process, and they proposed a steam-free curing system to save energy and reduce environmental pollution. Liu’s group [26] studied the durability of rubber concrete manufactured using the non-autoclaved curing method. The results showed that non-autoclaved concrete had better durability because they optimized the mix ratio, and therefore, they are more advantageous for use in marine environment and underground foundations. Although non-autoclaved concrete has shown excellent mechanical properties, its high brittleness and weak impact resistance still limit its practical application.

Other studies have found that an appropriate amount of rubber can improve the toughness [27,28] and impact resistance [29,30] of concrete. Rubber concrete has better impact resistance than ordinary concrete. The ability of a material to withstand impact loads relies on its toughness and capacity to absorb such loads. Experimental evidence indicates that rubber concrete exhibits better mechanical properties under impact loads compared to static loads. Atahan et al. [31] evaluated the energy dissipation impact of rubber by conducting dynamic drop hammer tests on rubber concrete. According to the experimental findings, an augmentation in the rubber proportion leads to a decrease in the compressive strength and elastic modulus of concrete, but it notably enhances the impact duration and capacity for energy dissipation. It has been determined that concrete with a rubber content of 20–40% significantly reduces the degree of damage under impact, while maintaining good strength and fracture resistance. Liu et al. [29]. conducted a study on the dynamic properties of rubber particle concrete with mass fractions of 5%, 10%, 15%, and 20%. It was discovered that the elastic strength of rubber-infused concrete rises as the strain rate increases, leading to notable improvements in impact resistance, toughness, and overall energy absorption capacity compared to regular concrete. Feng et al. [32]. conducted dynamic bending tests on concrete with different rubber admixtures (0%, 10%, 20%, 30%, 40%, 50%) using a Hopkinson bar with a diameter of 100 mm. According to the test outcomes, rubberized concrete with a substitution percentage of 30% exhibited superior durability against impacts and a reduced rate of cracking. Rubberized concrete exhibits a greater susceptibility to strain rate effect under impact loading [32,33], and the concrete’s strength escalates as the strain rate rises.

Currently, there is a notable research gap concerning the impact resistance and dynamic flexural behavior of non-autoclaved rubber concrete (NARC). To address this, the present study systematically investigates the mechanical properties and failure mechanisms of NARC under dynamic loading conditions. The primary objectives are to evaluate the dynamic flexural performance of NARC across a range of strain rates and to explore the potential of rubber incorporation in enhancing the durability and sustainability of non-autoclaved concrete. Using a 100 mm diameter split Hopkinson pressure bar (SHPB) setup (Liwei Technology Co., Ltd., Luoyang, China), dynamic flexural tests were conducted on NARC specimens with rubber volume fractions of 0%, 5%, 10%, 15%, and 20%. The influence of rubber particles and the non-autoclaved preparation process on the flexural behavior under impact was critically analyzed. The findings are expected to facilitate the practical application of waste rubber in concrete and promote the adoption of non-autoclaved production methods, thereby contributing to more sustainable construction practices.

2. Experimental Program

2.1. Raw Materials and Mix Proportions

As shown in

Table 1. Proportion of NARC (kg/m³).

Mixture	NAC	NARC5	NARC10	NARC15	NARC20
W/C	0.3	0.3	0.3	0.3	0.3
Cement	240	240	240	240	240
Sand	740	704	669	644	599
Coarse aggregate	1280	1280	1280	1280	1280
Water-reducer	9.2	9.2	9.2	9.2	9.2
Water	72	72	72	72	72
Mineral powder	160	160	160	160	160
Rubber particle	0	9.04	18.08	27.12	36.16
Slump (mm)	38	50	38	28	20

, fine aggregates were replaced with rubber particles at concentrations of 0%, 5%, 10%, 15%, and 20% (referring to the proportion of rubber particles relative to the total mass of fine aggregates). The non-autoclaved rubber concrete is named NAC, NARC5, NARC10, NARC15 and NARC20, respectively.

The raw materials used for the NARC are as follows. We utilized Ordinary Portland cement (Shijing Cement Company, Guangzhou, China) with a strength grade of 42.5 MPa. The mechanical properties of the cement were as follows: a flexural strength of 6.3 MPa (3-day) and 9.2 MPa (28-day), and a compressive strength of 36.0 MPa (3-day) and 58.2 MPa (28-day). Sand was used as the fine aggregate, with a maximum particle size of 4.8 mm, a fineness modulus of 2.59, and an apparent density of 1552 kg/m³. The coarse aggregate consisted of two different particle sizes in a ratio of 1:1. One particle size was between 0 mm and 10 mm and had an apparent density of 2650 kg/m³. The second particle size ranged from 0 mm to 20 mm, with an apparent density of 3047 kg/m³. The S95 mineral powder served as a mineral admixture, enhancing both the durability and workability of the concrete. The specific surface area of the mineral powder was 412 m²/kg, and the sphere density was 2.9 g/cm³. Ordinary tap water was used as the mixing water, while a high-efficiency water-reducing agent (manufactured by Jiangmen Qiangli Building Material Technology Co., Ltd., Jiangmen, China) made of high-performance polycarboxylate was employed. The rubber was made from waste tires without any pretreatment with a bulk density of 539 kg/m³. The particle size of 0.85 mm (20 mesh) was selected based on the existing results [33].

2.2. Experiment Preparation and Curing System

Five sets of rectangular samples measuring 40 mm × 40 mm × 160 mm were cast in iron molds and made into rubber concrete for flexural tests. Furthermore, five groups of cylinders measuring 150 mm in diameter and 300 mm in height were prepared and underwent quasi-static uniaxial compression tests in order to acquire the modulus of elasticity of NARC.

As shown in Figure 1, taking only autoclaved specimens requires pressure to be applied during curing, and the curing of autoclaved concrete specimens requires atmospheric steam curing before high-pressure curing. Specifically, one of the commonly used high-strength autoclaved concrete is used to exhibit the curing regime, which is raised to 85 °C for 1.5 h and then maintained at a constant temperature for 2.5 h. Next, the formwork was removed. Then, the high-temperature and high-pressure autoclave curing were performed. Specifically, the pressure was boosted for 2 h to 0.90 MPa, and then, the air intake of the boiler was stopped after constant temperature and pressure for 3 h, such that the autoclave was in the natural pressure reduction and cooling state for 1 h. Finally, the test piece was naturally cured to the test age. The curing process of non-autoclaved concrete specimens omits the step of autoclave curing. First, the temperature is maintained at 55 °C for 3 h. Then, it is increased at 5 °C/10 min for 1 h. After that, it was maintained at a constant temperature of 85 °C for 3.5 h. Finally, the specimens were naturally cured to the test curing age after the formwork removal.

According to the Chinese standard “Assessment Methods and Requirements for Low-Carbon Ready-Mixed Concrete Products (T/CBMF 27-2018)”, the total carbon emissions of traditional autoclaved concrete and non-autoclaved concrete were calculated (Table 1), including C1 (production and transportation), C2 (production and construction), C3 (carbon emissions from coal combustion during the curing process), C4 (carbon emissions from natural gas combustion during the curing process), and C5 (carbon emissions from electricity consumption). Therefore, compared to traditional autoclave-cured concrete, non-autoclave-cured concrete reduces carbon emissions by 92.82 kg per cubic meter (20.7%, coal combustion) or 70.28 kg per cubic meter (17.2%, natural gas combustion).

3. Quasi-Static Test

3.1. Compressive Performance

The concrete specimen used for uniaxial compression testing of concrete, which is typically conducted in accordance with the American specification ASTM C469 [34], is a cylinder with a height-to-base diameter ratio of 2:1. The quasi-static compression test was conducted on a cylinder measuring Ø 150 × 300 mm using a compression tester (Matest C088-01, Italy) with a capacity of 4000 kN. Prior to the examination, we attached four resistance strain gauges to the circumference of the cylinder to be tested.

During the test, we employed a pair of longitudinal and circumferential strain gauges to measure the corresponding strains in the longitudinal and circumferential directions. To prevent any potential impact on the accuracy of the test, we utilized the two longitudinal strain gauges to fine-tune the fit of the specimen to the machine’s loading surface during the pre-stressing phase. This was necessary because strain gauges exhibit greater sensitivity towards specimen deformation compared to displacement gauges, thus helping us avoid any localized stress concentrations. Zhejiang Huangyan Testing Instruments Factory produced the strain gauges, which have a resistance of 120 ± 0.1 Ω, a sensitivity factor of 2.08 ± 1%, and lengths of 100 mm and 80 mm for the longitudinal and transverse strain gauges, respectively. The final installation sketch is shown in Figure 2. Using a multi-channel static acquisition instrument (JM3841, Jin Ming Technology Co., Ltd., Guangdong, China), we collected data from all the strain gauges and displacement transducers. The loading was displacement-controlled. The loading speed was adjusted to 0.18 mm/min, corresponding to a strain rate of around 1 × 10⁻⁵ s⁻¹.The modulus of elasticity E and Poisson’s ratio v of the concrete material were obtained according to ASTM C469 [34] using Equations (1) and (2):

$$E={\displaystyle \frac{{\sigma }_2-{\sigma }_1}{{\epsilon }_2-0.000050}}$$

(1)

$$\nu ={\displaystyle \frac{{\epsilon }_{c2}-{\epsilon }_{c1}}{{\epsilon }_2-0.000050}}$$

(2)

where σ₁ represents the stress value at a longitudinal strain of 0.000050. σ₂ = 0.4σ_CM, σ_CM is the peak stress, and ε₂ is the strain corresponding to σ₂. ε_C1 and ε_C2 are the longitudinal strains of 0.000050 and ε₂ corresponding to the transverse strain. In addition, the compressive strength was calculated with the American specification ASTM C39 [35].

3.2. Flexural Performance

For the quasi-static flexural test, we employed an AG-Xplus flexural compression testing machine (Beichen Construction Engineering Testing Instrument Factory, Tianjin, China) with a capacity of 100 kN. The quasi-static flexural test was conducted following the guidelines of ASTM C293 [36]. A flexural test fixture, along with a pressure tester, was utilized to carry out the test, as depicted in Figure 3. By setting the loading rate to 0.10 MPa/s, we can calculate the quasi-static flexural strength using Equation (3), as follows:

$$f_f={\displaystyle \frac{3PL}{2b{h}^2}}$$

(3)

where P is the maximum force; L, b, and h are the length, width, and thickness of the specimen, respectively.

3.3. Quasi-Static Test Results and Discussion

3.3.1. Modulus of Elasticity

Figure 4 shows the stress–strain response of NARC specimens. Rubber concrete is a brittle material. Under compressive load, the internal pore of concrete is prone to experiencing stress concentration at its tip. The concrete is destroyed directly after reaching the peak stress. Using rubber as a replacement for the fine aggregate can greatly decrease the stress concentration at the void’s tip. In addition, rubber can produce tensile stress during the deformation of the rubber concrete, the time for stress declines after the yielding of the rubber concrete increases, and the ultimate strain is larger than that of the conventional rubber concrete.

The NARC yielded comparable outcomes to ordinary concrete in the quasi-static uniaxial compression test, as demonstrated in

Table 2. Carbon emission from pipe piles of two curing types.

Emission Type	Autoclaved Curing (kg/m3)		Non-Autoclaved Curing (kg/m3)
	Coal	Natural Gas	Coal	Natural Gas
C1	345.86	345.86	307.76	307.76
C2	0.41	0.41	0.41	0.41
C3	81.61	-	32.89	-
C4	-	43.85	-	17.67
C5	19.66	-	19.66	-
Total	447.54	409.78	354.72	339.50

. As the rubber content increases, the compressive strength and elastic modulus of concrete decrease, while the Poisson’s ratio drops from 0.22 to 0.16. This may be attributed to the high deformability of rubber particles themselves, their low permeability, and their smooth surfaces, which result in insufficient interfacial bonding between rubber and cement. The interfacial transition zone functions like pre-existing microcrack nuclei. Due to the weak bonding performance between rubber particles and mortar, the porosity of NARC is higher than that of NAC. These pores become buffer zones for deformation, absorbing longitudinal deformation energy and reducing the need for lateral expansion. Therefore, during axial compression, rubber particles can significantly increase the longitudinal deformation of concrete, resulting in a decrease in Poisson’s ratio. With a rubber content of 5%, there is a slight decrease in both compressive strength and modulus of elasticity. The explanation for this phenomenon is that the hydration degree of NARC is not as complete as that of ordinary concrete. There are many voids in the concrete during curing, and the rubber fills these voids, making the concrete structure more compact. At the same time, silica fume undergoes a reaction with calcium hydroxide to produce C-S-H gel, thereby mitigating the issue of poor interfacial adhesion between rubber and cement. The compressive durability of NARC primarily relies on the physical and mechanical characteristics of its component materials.

In general, the deformation capacity of NARC is better than that of ordinary concrete. This may be due to the deformation ability of rubber being relatively high, and replacing the fine aggregate improves the deformation ability of concrete. As a result of incorporating carbon powder and silica fume, the NARC exhibits enhanced concrete strength compared to regular concrete, albeit with increased brittleness. The inclusion of rubber particles is anticipated to have a more pronounced effect on the rubber structure, potentially leading to a significant decrease in concrete strength when utilizing the traditional autoclaved high-temperature and high-pressure curing technique. The non-autoclaved curing method has relatively less impact on the rubber. Therefore, NARC is more suitable for adding rubber particles to improve its brittleness; however, the amount of rubber replacement should be controlled within 10%.

3.3.2. Quasi-Static Flexural Strength

The results of the quasi-static flexural experiments are summarized in

Table 3. Quasi-static test results.

Specimen	Elastic Modulus E0, (GPa)	Compressive Strength fcs, (MPa)	Poisson’s Ratio v
NAC	50.90 ± 1.12	101.97 ± 5.42	0.22
NARC5	48.78 ± 2.23	99.74 ± 2.23	0.19
NARC10	45.82 ± 1.65	92.30 ± 1.53	0.17
NARC15	41.72 ± 2.36	80.42 ± 8.35	0.17
NARC20	38.08 ± 2.71	64.69 ± 7.36	0.16

. The flexural strength of NARC decreases with increasing rubber admixture. Simultaneously, the pozzolanic influence of silica fume can mitigate the influence of rubber on the strength of concrete. The reason for this is the utilization of a water-saving agent with high efficiency during the manufacturing procedure, which helps decrease the ratio of water to binder. Additionally, the inclusion of a mineral admixture is also responsible for this outcome. By enhancing the density of concrete, these mineral additives elevate the flexural strength of NARC in comparison to regular concrete.

Furthermore, the fragility of rubber concrete can be indicated by the proportion of compressive strength to flexural strength [37]. As shown in Figure 5, the brittleness of NARC decreases with increases in rubber content. This demonstrates that rubber particles enhance the durability of rubber concrete when subjected to quasi-static loading. Rubber particles fill the voids in concrete, generating tensile stress in the transition zone of the aggregate. As a result, the deformation capacity of concrete is significantly enhanced. As the rubber content increases, the effectiveness of crack inhibition improves. By incorporating rubber, it is possible to enhance the toughness of NARC.

3.3.3. Microscopic Morphology of NARC

To further examine the microstructure of NARC, this research employed a LYRA 3 XMU focused ion beam field emission scanning electron microscope for microscopic analysis of the concrete’s structural density. From Figure 6, it is evident that NARC contains numerous empty spaces and stratified crystals, yet the general arrangement remains fairly organized. The incomplete reaction of cement is due to the low water/cement ratio of NARC.

By incorporating silica fume and mineral powder, the cement paste surrounding the interface undergoes complete hydration, resulting in the formation of a significant amount of C-S-H gel. The hydration products are closely connected from the interface, and there is no obvious transition zone. Some generate needle columnar ettringite (AFt) crystal groups, interwoven with C-S-H gel, making the concrete structure become dense. The inclusion of silica fume (SF) in concrete allows for a secondary hydration reaction to occur with cement hydrates, resulting in a more comprehensive hydration process. This reaction leads to the formation of needle-shaped hydrated calcium silicate gel, which fills the pre-existing voids and flaws in the concrete, ultimately enhancing its strength.

3.4. Dynamic Experimental Establishment

We performed dynamic flexural experiments using the SHPB instrument. Figure 7 and

Table 4. Quasi-dynamic test results.

Specimen	Flexural Strength, ffs (MPa)	fcs/ffs
NAC	22.75 ± 1.25	4.48
NARC5	22.35 ± 1.54	4.46
NARC10	20.86 ± 1.58	4.42
NARC15	19.93 ± 1.68	4.03
NARC20	19.64 ± 2.04	3.29

show the dimensions and materials of the SHPB instrument used for dynamic flexural tests. We fitted customized three-point flexural devices to the ends of the incident and transmission bars and used semiconductor strain gauges. We attached two semiconductor strain gauges to the middle of the incident and transmission bars to collect the strain signals during the dynamic experiments. Each of the strain gauges had a resistance measuring 120.0 ± 0.1 Ω and a sensitivity coefficient of 110 ± 5%. The dynamic flexural test measured the strain using the dynamic strain acquisition instrument (DH5960, Guangdong, China) with an acquisition frequency of 1 MHz.

By controlling the air pressure, we conducted dynamic flexural tests to determine the dynamic flexural strength of NARC under varying strain velocities. Rubber concrete exhibits a strain rate effect on its flexural performance, leading to an enhancement in flexural strength as the strain rate increases. To maintain consistency, we used the same dimensions for the dynamic flexural experiments as the quasi-static flexural experiments, employing a rectangular specimen measuring 40 mm × 40 mm × 160 mm. Furthermore, a red copper metal sheet measuring 20 mm in diameter and 2 mm in thickness was employed as a shaper to diminish the high-frequency elements produced by the incident loading pulse [38].

3.5. Theoretical Derivation of the Dynamicflexural Test

The flexural strength is a significant mechanical characteristic of rubberized cement materials, and the SHPB method is frequently employed to examine the mechanical attributes of high-strain rate concrete. The analysis of SHPB experiments relies on two fundamental principles: the one-dimensional stress wave principle and the assumption of homogeneity [39]. Upon collision of the impact bar with the incident bar, the strain gauge signal of the incident bar captures the pulse generated, followed by the compression of the specimen upon contact with the incident bar. Subsequently, the incident bar signal records the reflected wave once more. The force F(t) and velocity v(t) across the specimen during impact can be obtained from Equations (4) and (5). The displacement u(t) at the point of impact across the specimen can be obtained by integrating the velocity v(t), as in Equation (6).

$$F\left(t\right)=E_b{A}_b\left[{\epsilon }_i\right(t)+{\epsilon }_r(t\left)\right]$$

(4)

$$v\left(t\right)=C_b\left[{\epsilon }_i\right(t)-{\epsilon }_r(t\left)\right]$$

(5)

$$u(t)=\int C_b[{\epsilon }_i(t)-{\epsilon }_r(t)]dt$$

(6)

For the dynamic flexural experiments, we used an apparatus modified by Feng at SHPB [32]. The strain–time curves obtained from the experiments can be analyzed to show that the transmitted waves are zero, which indicates that the stress waves cannot be transmitted directly to the base of the support during the impact but can only be reflected and transmitted repeatedly inside the specimen. In other words, the beam support is not subjected to any force during the dynamic three-point flexure experiment, and the specimen can be regarded as infinite. This satisfies the Euler–Bernoulli elastic beam assumption [40], as shown in Figure 8 and Equation (7). This assumption allows the shear deformation of the beam during the force to be neglected, and only the effect of flexural deformation is considered.

$${\displaystyle \frac{{\mathsf{\partial }}^{4}u\left(x,t\right)}{\mathsf{\partial }{x}^4}}+{\displaystyle \frac{{\rho }_0{S}_0}{E_0{I}_0}}{\displaystyle \frac{{\mathsf{\partial }}^{2}u\left(x,t\right)}{\mathsf{\partial }{t}^2}}=0$$

(7)

where I₀ is the moment of inertia, S₀ is the area of the beam section, and E₀ and ρ₀ are the modulus of elasticity and density of the specimen, respectively.

Delvare et al. [41] and Hanus et al. [42] first proposed and established the infinite beam model. The time Laplace transformation can be used to express the transient dynamic elastic response of the specimen using force F(t) and velocity v(t), as expressed in Equations (8) and (10).

$$u\left(x,t\right)={\int }_0^t{G}_1\left(t-\tau \right){\mathsf{\Omega }}_1\left(x,\tau \right)d\tau -{\int }_0^t\left(G_1\left(t-\tau \right)+G_2\left(t-\tau \right)\right){\mathsf{\Omega }}_2\left(x,\tau \right)d\tau$$

(8)

$${\mathsf{\Omega }}_1\left(x,\tau \right)={\displaystyle \frac{1}{\sqrt{\pi t}}}\mathrm{c}\mathrm{o}\mathrm{s}\left({\displaystyle \frac{{\alpha }^2{x}^2}{2t}}\right)\hspace{1em}{\mathsf{\Omega }}_2\left(x,\tau \right)={\displaystyle \frac{1}{\sqrt{\pi t}}}\mathrm{s}\mathrm{i}\mathrm{n}\left({\displaystyle \frac{{\alpha }^2{x}^2}{2t}}\right)$$

(9)

$$G_1\left(t\right)={\int }_0^t{\displaystyle \frac{v\left(\tau \right)}{\sqrt{\pi \left(t-\tau \right)}}}d\tau \hspace{1em}{G}_2\left(t\right)={\int }_0^t{\displaystyle \frac{F\left(\tau \right)}{4EI{\alpha }^3}}d\tau$$

(10)

where $\alpha =\sqrt[4]{{\rho }_0{S}_0/4E_0{I}_0}$ is a constant. The time–course relationship for stress in the span of the specimen (x = 0) can be derived from the dynamic impact test, as expressed in Equation (11). Because the strain rate effect of the elastic modulus of concrete is not obvious, the modulus of elasticity of the concrete material is assumed to be constant [43]. The strain rate corresponding to each test can be calculated from Equation (12).

$$\sigma \left(t\right)=h_0{\alpha }^2{E}_{0}v\left(t\right)$$

(11)

$$\dot{\epsilon }\left(t\right)=h_0{\alpha }^2{\displaystyle \frac{dv\left(t\right)}{dt}}$$

(12)

3.6. Failure Modes

Figure 9 shows the damage patterns of NARC with different rubber content, respectively. The primary crack in the beam extends from the bottom to the top surface. In the quasi-static flexural experiments, the NARC exhibit similar toughness. As the rubber replacement rate increases, the NARC specimens become tougher.

Rubber particles can be observed in the NARC sections, indicating their distribution. If the rubber admixture exceeds 10%, the concrete will clearly exhibit the dispersion of rubber particles. The distribution of coarse aggregates can be seen in the NARC sections. The aggregate distribution in the NARC section is more uniform, and the damaged section is flatter. Due to the elimination of high-pressure steam curing, the degree of concrete hydration is not complete, and the concrete color is darker than ordinary concrete. As shown in Figure 9a, when the rubber content is 15% and 20%, the cross-sectional area of the cement matrix (dark color in the cross-section) is significantly larger than when the rubber content is less than 10%. In other words, when the rubber content is below 10%, the aggregate (light color in the cross-section) is more susceptible to penetration. If the rubber mixture is below 10%, the specimen experiences damage at the transition zone of the aggregate interface, leading to a decrease in flexural strength as the rubber mixture increases. If the rubber mixture exceeds 10%, the specimen will experience damage in the vulnerable transition area between the aggregate and rubber interface, leading to a reduction in flexural strength. Hence, it is suggested that the ideal rubber proportion for NARC should be below 10%, as it has minimal impact on the flexural strength of concrete while enhancing the strain rate sensitivity.

As the strain rate increases, the severity of damage to the NARC under impact loading intensifies; nevertheless, the primary cracking continues to occur along the mid-span. At lower rates of deformation, the sample fractures into two equal parts at the center of the distance. This is because the impact load is weak and the test duration is long. Concrete has a lower tensile strength compared to its compressive strength, causing cracks to form in the tension zone of the specimen. Under conditions of moderate and high strain rates, the specimens experience powerful impact loads and continuous reflection of stress waves. Due to the limited duration of the load and the inadequate time to circumvent the majority of aggregates, a greater number of aggregates will be destroyed. Furthermore, as the strain rate increases, the severity of aggregate crushing will intensify. Because the impact load is brief and has a significant amount of energy, the cracks are unable to bypass the aggregate within the limited time and can only traverse through it, leading to damage to the aggregate. Consequently, the flexural resistance of NARC escalates as the strain rate rises. Because of the inclusion of silica fume, NARC exhibits a greater overall compressive strength compared to regular concrete. This leads to the compression zone’s contribution to the flexural properties at high strain rates, ultimately resulting in an increased flexural strength for NARC.

3.7. Dynamic Experimental Results and Discussions

Figure 10 shows the dynamic flexural test results of NARC at different strain rates. The analysis focuses on the average rate of strain observed during the rubber concrete selection experiment.

3.7.1. Example: Tests on NARC at Strain Rate of 0.43 s⁻¹ and 3.20 s⁻¹

Figure 10a shows the raw strain data collected by the dynamic strain gauge. When the strike bar and the incident bars collide, the incident wave (ε_i) is first collected; then, the stress wave is repeatedly reflected and diffused inside the concrete specimen. The reflected waves (ε_r) are then collected again by the strain gauges on the incident bar. During this process, the strain gauges on the transmission bar do not pick up any signal; this is because the stress wave is damaged during the reflection from the concrete, and the force at the support is zero. This proves that the shear deformation during the impact test can be neglected, and the dynamic flexural experiment satisfies the principle of the dynamic Euler–Bernoulli elastic beam model.

Due to the issue of strain rate determination, dynamic three-point flexural experiments are unable to maintain a constant loading rate during loading. Some scholars use the maximum strain rate in the experiment as the strain rate of the specimen [44]; the majority of scholars consider the average strain rate during the impact test to be the accurate representation of the specimen’s true strain rate [45]. Figure 10b depicts the velocity–time curve at the point of impact, from which the stress–time and strain–time curves can be derived. We used the average strain rate as the strain rate of dynamic experiment. According to the strain rate calculation method proposed by Guo [46], the average strain rate of the sample can be determined by analyzing the gradual section [t₁, t₂], where the strain–time graph shows an increase. During this period, the strain–time relationship can be represented by a linear curve, where the inclination of the curve is considered as the average rate of strain for the sample. As shown in Figure 10, the average strain rates are 0.43 s⁻¹ and 3.20 s⁻¹, respectively.

Figure 10e–f shows the relationship between the impact force and the flexural stress and the ultimate displacement in the span, with the impact force showing a trend of increasing to a peak and then decreasing. The specimen is considered to be damaged when the impact force decreases in phase and is separated from the incident bar when the impact force decreases to zero. Due to the significantly short dynamic three-point flexure action time, the ultimate displacement across the specimen is considered to be the displacement corresponding to the reduction in the impact force to zero. For the specimens in Figure 10e–f, the ultimate displacements are 0.57 mm and 1.78 mm, respectively.

3.7.2. Experimental Results

Table 5. Physical characteristics of the SHPB apparatus.

Parameters	Value
Incident bar length	5500 mm
Striker length	1000 mm
Transmission bar length	3500 mm
Bars diameter, Db	100 mm
Bars young’s modulus, Eb	5169 m/s
Velocity of elastic wave, Cb	206 GPa

presents the findings from the dynamic flexural tests conducted on NARC with various rubber additives. Figure 11 shows the relationship between the dynamic increase factor (DIF) and strain rate for different rubber admixtures of rubber concrete. The NARC exhibited similar strain rate effects, the NARC has a more reasonable material particle size distribution due to the addition of mineral admixtures, which increases the compactness and strength of the concrete. By contrast, the pozzolanic effect of mineral admixtures produces a large amount of C-S-H gel to fill the voids left after the concrete loses water. Therefore, the internal structure of NARC becomes more compact.

Table 6. Dynamic flexural test results of NARC.

Specimen	Quasi-Static Flexural Strength	Strain Rate (s−1)	Dynamic Flexural Strength (MPa)	DIF	Displacement (mm)
NAC-1	22.75	0.57	22.55	1.00	0.72
NAC-2		1.65	23.85	1.15	0.76
NAC-3		3.20	75.55	2.76	1.78
NAC-4		4.15	95.32	2.14	2.20
NAC-5		5.32	119.83	3.55	2.62
NAC-6		7.45	139.50	4.18	2.86
NARC5-1	22.35	1.20	26.16	1.17	0.71
NARC5-2		2.53	32.91	2.20	0.83
NARC5-3		3.47	91.80	2.93	2.19
NARC5-4		3.18	78.15	4.46	2.01
NARC5-5		4.88	130.18	4.69	2.80
NARC10-1	20.86	0.30	26.95	1.18	0.62
NARC10-2		0.39	29.01	1.27	0.65
NARC10-3		0.89	35.52	1.56	0.83
NARC10-4		3.06	69.05	3.03	1.84
NARC10-5		3.78	89.71	3.94	2.22
NARC10-6		3.84	105.56	4.64	2.47
NARC10-7		5.14	120.93	5.31	2.71
NARC15-1	19.93	2.32	29.68	1.49	0.91
NARC15-2		2.88	59.84	3.00	1.76
NARC15-3		3.02	76.01	3.81	2.03
NARC15-4		6.50	108.02	5.42	2.69
NARC15-5		5.96	102.78	5.23	2.45
NARC20-1	19.64	1.25	21.26	1.08	0.82
NARC20-2		0.98	20.47	1.04	0.69
NARC20-3		3.24	65.24	3.32	1.64
NARC20-4		5.38	74.72	3.80	2.13
NARC20-5		5.77	84.63	4.31	2.26
NARC20-6		6.51	112.12	5.71	2.74

summarizes the fitting values of the rubber concretes. Each set of the DIF experimental data is linearly related. We proposed an empirical correction formula, as expressed using Equation (13), to fit the strain rate effect for different rubber admixtures of NARC.

$$DIF=alg\left(\dot{\epsilon }\right)+b$$

(13)

Figure 12 shows that the relationship between ultimate displacement at midspan and strain rate for NRAC is logarithmically linear.

Table 7. The fitting results of DIF and $\dot{\epsilon }$ of NARC.

Specimen	a	b	R2
NAC	2.81	1.20	0.79
NARC5	5.76	0.54	0.77
NARC10	3.09	2.38	0.88
NARC15	5.67	0.80	0.98
NARC20	4.96	0.81	0.92

summarize the fitting values of the rubber concretes. Therefore, this relationship is nonlinearly fitted like the strain rate effect of DIF [32], as expected in Equation (14). The mechanism of strain rate effect in ultimate deformation is that when NARC is at a high strain rate, the load is applied instantaneously, and the inertial force generated by the mass of the beam will resist the downward deformation at the mid-span in the opposite direction, making the beam unable to quickly undergo brittle fracture. The growth rate of load is much faster than the expansion rate of microcracks. In the tensile zone, microcracks do not have enough time to expand and penetrate separately, but multiple microcracks emerge and develop simultaneously, requiring greater mid-span deformation for fracture failure. In addition, the concrete material in the tensile zone exhibits strain rate effect [33], which means that the beam needs to withstand greater tensile stress to reach the failure threshold, and the ultimate deformation increases accordingly. The flexural resistance of NARC for dynamic loads is better. When the rubber admixture exceeds 5%, the NARC’s strain rate sensitivity decreases. The strain rate effect of rubber concrete may increase due to the ability of a small quantity of rubber to fill the gaps in the concrete material without compromising its strength. Once the rubber is mixed at a level greater than 5%, it introduces excess air to increase the voids in the concrete, causing a reduction in concrete strength and making the NARC more susceptible to cracking.

$$u=\eta lg\left(\dot{\epsilon }\right)+\lambda$$

(14)

Figure 12 shows the relationship between mid-span displacement and strain rate. We used the same linear growth equation as the dynamic increased factor analysis for fitting. All the experimental data were in agreement with the linear growth, which can be fitted using Equation (14). In the case of the 5% rubber admixture, the effect of strain rate on the mid-span ultimate displacement of NARC is the most evident. As shown in

Table 8. The fitting results of ultimate displacement and $\dot{\epsilon }$ of NARC.

Specimen	η	λ	R2
NAC	2.11	0.88	0.87
NARC5	3.53	0.15	0.79
NARC10	1.69	1.29	0.93
NARC15	3.12	0.16	0.83
NARC20	2.25	0.62	0.96

, an increase in the rubber content beyond 5% leads to a reduction in the strain rate impact on the mid-span ultimate displacement of the concrete. This is because the concrete material with more than 5% rubber content has more internal voids and the bonding surface of the aggregate is weak. Therefore, the bonding surface is easily damaged under impact load, resulting in poor deformation capacity. Nevertheless, as a result of carbon powder and silica fume filling the gaps in the concrete, the bonding of hydration substances in NARC becomes robust under elevated temperatures. Therefore, the influence of rubber quantity on the strain rate effect of NARC is minimal. The strain rate effect of NARC is demonstrated to be higher than that of regular concrete, with the most noticeable impact observed when the rubber content reaches 5%.

4. Conclusions

We performed quasi-static and dynamic flexural experiments on NARC with different rubber admixtures. We obtained the following conclusions from the analysis of the experimental specimens:

(1)

NARC has achieved environmental benefits without compromising performance. Non-autoclaved curing reduces carbon emissions by approximately 20% compared to steam curing. Coal-based curing decreases from 447.54 kg/m³ to 354.72 kg/m³. Quasi-static testing indicates that NARC5 exhibits a flexural strength of 22.35 MPa, comparable to ordinary concrete (22.75 MPa). However, the brittleness ratio (compressive strength/flexural strength) decreased from 4.48 to 4.46, demonstrating enhanced toughness.

(2)

Although rubber particles can reduce the fragility of NARC as a flexible material, they significantly decrease the strength of NARC and are not suitable for the excessive addition of rubber particles. As the rubber content increased from 0% to 20%, the dynamic flexural strength decreased significantly. The weak interfacial adhesion between rubber particles and the cement matrix acts as a microcrack nucleus, leading to reduced strength. For example, at a strain rate of 7.45 s⁻¹, the dynamic flexural strength of NAC (0% rubber) was 139.50 MPa, while that of NARC20 (20% rubber) decreased to 74.72 MPa.

(3)

Rubber particles dissipate impact energy, synergistically improving flexural strength and ultimate deformation. At a rubber replacement rate of 5%, the impact of strain rate on DIF becomes more pronounced, and the strain rate effect is also evident in the mid-span displacement during flexural tests. The mechanism is that at high strain rates, the large impact energy causes coarse aggregates to fracture rather than being bypassed, thereby enhancing flexural strength. As a flexible material, rubber particles positively enhance the NARC’s ultimate deformation capacity by dissipating part of the impact energy. At appropriate rubber content levels, they can improve the strain rate sensitivity of strength on NARC.

(4)

Future research should focus on optimizing rubber–cement interfacial bonding to enable higher rubber content without strength loss and investigating NARC’s impact resistance under harsh environments (e.g., fires, oceans, and cold regions).