Experimental study on dynamic compressive and splitting tensile properties of high strength expansive concrete

Abstract

Concrete shrinkage usually results in the decrease in bearing capacity, durability and impact resistance of Concrete-Filled steel tube (CFST) structures during its service life. High strength expansive concrete (HSEC) is recently developed to deal with the shrinkage cracking in CFST structures. In this study, dynamic compressive tests and dynamic splitting tensile tests on the developed grade C60, C70 and C80 HSEC were performed using a split Hopkinson pressure bar device. Test results show that the expansive concrete is a typical rate-sensitive material, and its dynamic compressive strength and dynamic splitting tensile strength both increase with the strain rate. The compressive strength dynamic increase factor (DIF_c) of HSEC is smaller than that of the ordinary concrete under the same strain rate, whereas the splitting tensile dynamic increase factor (DIF_t) is larger than that of the ordinary concrete. All the test data were classified to establish calculation models of DIF_c, peak toughness (R_p), specific energy absorption (SEA), and DIF_t, which provide a theoretical basis for the design and application of HSEC and CFST in engineering.

Keywords

expansive concrete concrete-filled steel tube split Hopkinson pressure bar dynamic increase factor splitting tensile

Introduction

Concrete is one of the most widely used construction materials. However, shrinkage cracking usually significantly affects the durability and impact resistance of concrete structures, especially the Concrete-Filled steel tube (CFST) structures. According to a large amount of engineering statistical data, the proportion of load cracks in concrete is only approximately 20%, whereas the proportion of non-load cracks, which result in reduced safety and high maintenance costs, is as high as 80% (Zhu, 1999). Expansive concrete can expand during hydration to make up for shrinkage and reduce cracks. Therefore, its use is a potentially effective way to solve the problem of shrinkage cracks, especially for the CFST structures.

Expansive cement was first proposed in the 1930s by H. Lossier (Nagataki and Gomi, 1998). It exploits the fact that the volume expansion of ettringite after hydration can compensate for the shrinkage of cement. However, owing to the limited technology at that time, the extent of expansion, as well as the balance between the strength and expansion could not be well-controlled, and thus this type of concrete was not widely used. It was not until the 1960s that Japanese companies developed calcium sulfoaluminate aluminate, and expansive concrete began to be mass-produced and applied (Zhong, 2006). Since then, many researches had confirmed that EA plays a positive role on the performance of concrete and tried to reveal its mechanism. The effect of the expansive agent (EA) on particle size was investigated by (Chen et al., 2012). It is found that as the particle size decreases, the specific surface area of the EA increases, and the early expansion effect improves. In the later expansion period, the hydration rate of large and small particles is roughly the same. (Li et al., 2020) confirmed that an EA in a concrete-filled steel tube can produce remarkable expansion and effectively limit the separation between the core concrete and steel tube. (Zhang et al., 2020) conducted four-point bending tests on specimens to induce cracks and found that an EA can significantly improve the crack healing efficiency of strain-hardening cement-based composites under water fog curing conditions. (Li et al., 2020) found that steel slag powder and hybrid EAs can effectively reduce the drying shrinkage deformation of ultrahigh-performance concrete (UHPC) with a slight decrease in strength. These studies analysed the components or amount of EA to explore its mechanism on concrete. However, the balance between the strength and expansion is still a severe technical challenge, especially for the high strength expansive concrete (HSEC) where EA might reduce the concrete strength significantly.

The influence of EA on the mechanical properties of concrete has also attracted the interests of many scholars. (Li, 2013) stated that the appropriate addition of a MgO EA can improve the durability and mechanical properties of concrete, such as compressive strength, flexural strength and elastic modulus. However, excessive EA addition may induce the opposite effect. (Qian et al., 2020) studied the effect of elevated curing temperatures on the mechanical properties of cement mortars containing an EA and found that the ratio of tensile strength to compressive strength increases with the EA content as well as the curing temperature. (Shen et al., 2020) investigated the combined use of lightweight aggregate and an EA in UHPC and found that the expansive UHPC exhibited high levels of expansion and high mechanical properties. (Li et al., 2020) found that the compressive strength, splitting tensile strength and elastic modulus of self-compacting steel-fibre-reinforced concrete increased when an EA was incorporated. (Cao et al., 2017) observed that the compressive strength of expansive self-consolidating concrete was improved at 7 days when an EA was added. It is clearly shown that expansive concrete has a certain potential to improve the performance of concrete. As demonstrated by the above studies, most current researches focussed on the expansion mechanism and mechanical properties, and most of the studies on the mechanical properties were conducted considering the static conditions. However, in occasional accidents, engineering structures may suffer seismic loads (Wang et al., 2022), impact (Ma et al., 2020), explosion and other extreme loads, which will induce the high strain rate effect on concrete material (Chen et al., 2015). Compared with static situation, dynamic load will often bring greater damage to structures. To deal with these problems, it is very necessary to study the dynamic mechanical properties of expansive concrete.

In this study, the dynamic compressive properties and dynamic splitting tensile properties of the recently developed grades C60, C70 and C80 HSEC are systematically investigated by using a split Hopkinson pressure bar (SHPB) device. The dynamic mechanical properties of HSEC in terms of the dynamic increase factor, impact toughness and energy absorption characteristics are studied. The relationship between dynamic increase factor and strain rates are provided. In addition, the difference of dynamic performance between HSEC and ordinary concrete is analysed by comparing their dynamic mechanical response, and a scientific basis and guidance for the design and application of expansive concrete in engineering is provided.

Experimental setup

Specimen preparation

PⅡ 52.5 Portland cement was used in the developed HSEC. The activity index of silica fume (SF) is 97%, and the grade of the mineral powder (MP) is S95. The physical parameters and chemical composition of the cement, SF and MP are shown in Table 1. The microbeads, a type of ultrafine fly ash, have a fineness of 1250 mesh, which is equivalent to a size of 0.01 mm. The water-reducing agent and EA were provided by Sobute New Materials Company. A general polycarboxylic acid water-reducing agent was used; its performance indices are shown in Table 2. The HME-type EA consists of calcined CaO and MgO, and its performance meets the requirements of GB/T 23,439–2017, Expansive agents for concrete. Granite gravel with a particle size of 15 mm was used as the coarse aggregate. The fine aggregate was obtained from river sand and had a fineness modulus of 2.6–3.0.

Table 1.

Physical parameters and chemical composition of some raw materials (Qin et al., 2021).

Raw material	Chemical composition/%								Specific surface area/(m²/kg)	Density/(g/cm³)
Raw material	CaO	SiO₂	Al₂O₃	Fe₂O₃	TiO₂	MgO	SO₃	Loss	Specific surface area/(m²/kg)	Density/(g/cm³)
Cement	63.23	19.32	4.41	2.77	0.26	1.34	2.42	3.12	344	3.05
SF	0.21	96.24	0.18	0.54	-	0.46	0.77	2.50	20,200	2.18
MP	42.10	30.40	14.80	1.21	0.62	6.33	0.59	0.65	354	2.80

Table 2.

Performance indices of polycarboxylic acid water reducer (Xia et al., 2019).

Solid content/%	Water reduction rate/%	Bleeding rate ratio	Cl⁻ content/%	pH	28 days compressive strength ratio
30	28	5.0	0.01	7.2	150

Three strength grades of HSEC, C60, C70 and C80 were designed, and the mixing proportions are shown in Table 3.

Table 3.

Mix proportion design of HSEC/(kg/m³).

Concrete grade	Cement	Silica fume	Mineral powder	Microbeads	Expansive agent	Sand	Stone	Water	Water reducer
C60	370	0	85	50	55	765	925	170	4.37
C70	399	19	30	83	59	732	1011	151	5.94
C80	442	27	33	58	62	690	1036	144	8.85

The unformed concrete was poured into steel ring moulds with a diameter of 50 cm and a height of 20 cm. The specimens were cured in a high-humidity environment for 28 days and then cut into cylindrical specimens with a diameter of 68 mm and a thickness of 34 mm (Figure 1). The upper and lower surfaces of the specimens were polished. A total of 43 specimens were processed: 23 for compressive testing and 20 for splitting tensile testing.

Test system

A hydraulic testing machine was used to perform static tests, and the schematic diagram is shown in Figure 2. The static properties of the specimens are presented in Static mechanical properties.

Dynamic compressive and splitting tensile tests were conducted in an SHPB device. A conventional SHPB consists of three parts: a loading system, bars and a data acquisition system, as shown in Figure 3. The gas gun applies pressure to the striker, giving it a certain initial velocity. The striker then hits the incident bar and produces a stress pulse, which propagates along the bar. As the stress pulse propagates to the specimen, which is sandwiched between the incident bar and transmission bar, the specimen is broken. Part of the stress wave is reflected back to the incident bar, and part propagates forward along the transmission bar. The SHPB used in this experiment is 74 mm in the diameter, and two strain gauges are attached to the trisection point of the incident and transmission bars (close to the specimen). To reduce the dispersion of the wave, copper pulse shapers were used, which extended the rising edge of the incident pulse.

Test principle

Figure 4(a) clearly shows that the specimen was sandwiched between the incident and transmission bars along its thickness direction in the dynamic compressive test. Loading pressures of 0.2, 0.4 and 0.6 MPa were applied in the experiment. Assuming that the Hopkinson bar is elastic, the propagation velocity of the wave in the bar is $c_{0} = \sqrt{E / ρ}$ . According to the assumption of uniform axial stress and strain within the specimen, the average stress σ_s, average strain rate ${\dot{ε}}_{s}$ and average strain ε_s of the specimen in the dynamic compressive test can be calculated according to the two-wave method (Ma et al., 2020) as follows

σ_{s} = \frac{E_{0} A_{0}}{A_{s}} ε_{t}

(1)

ε_{s} = - \frac{2 c_{0}}{l_{s}} \int_{0}^{t} ε_{r} d t

(2)

{\dot{ε}}_{s} = - \frac{2 c_{0}}{l_{s}} ε_{r}

(3)

where A₀ is the cross-sectional area of the incident and transmission bars; E₀ is the Young’s modulus of the bars; A_s and l_s are the cross-sectional area and thickness of the specimen, respectively; ε_i, ε_r and ε_t represent the incident, reflected and transmitted stress waves, respectively. The propagation velocity of the wave in the bars is

c_{0} = \sqrt{E_{0} / ρ}

, where ρ is the density of the bars. In this test, c₀ is 5172 m/s and l_s is 0.034 m.

As shown in Figure 4(b), the specimen was sandwiched between the incident and transmission bars along its diameter in the dynamic splitting test. The splitting tensile stress and strain rate can be calculated according to equations (4)–(7) (Shuai, 2013). To ensure the accuracy of the strain rate calculation, a strain gauge was pasted on the centre of the specimen to record the change in strain during the splitting tensile process. The loading pressures were the same as the compressive test

f_{td} = \frac{2 P}{π l_{s} D}

(4)

P = π R^{2} E_{0} ε_{t}

(5)

where D is the diameter of the specimen and R is the radius of the incident and transmission bars. The stress rate

\dot{σ}

and strain rate

\dot{ε}

of the specimen can be calculated according to the following formulas

\dot{σ} = \frac{f_{t d}}{τ}

(6)

\dot{ε} = \frac{\dot{σ}}{E}

(7)

where τ is the time required for the transmitted wave to reach its peak and E is the Young’s modulus of the specimen.

The determination of representative strain rate needs clarification. There are several ways to determine the representative strain rate of the specimen. One of the typical methods is to use the mean strain rate over the loading period. However, many studies have shown that this averaging definition cannot reflect the actual strain rate (Chen et al., 2013; Hu et al., 2019). In this study, the maximum strain rate will be used.

Results and discussion

Static mechanical properties

Cubic specimens with dimensions of 100 × 100 × 100 mm³ were used to measure the compressive strength and elastic modulus, and cylindrical specimens with a diameter and height of 68 mm were used to measure the static splitting tensile strength. The test results are presented in Table 4.

Table 4.

Static mechanical properties of specimens.

Concrete grade	Static compressive strength (MPa)	Static elastic modulus (GPa)	Static splitting tensile strength (MPa)
C60	69.9	44.62	3.93
C70	77.4	45.04	4.38
C80	86.6	46.57	4.92

Due to the limits of experimental conditions, the size and shape of specimens used in static test and SHPB test are different. In some studies, the static cube compressive strength will be multiplied by an empirical coefficient to eliminate the size effect of concrete. However, in addition to size and shape, the size effect is also affected by many factors, such as the type of concrete, aggregate gradation, strength and so on. Therefore, the multiplication of coefficient cannot eliminate the influence of size effect effectively. In addition, it has been observed that the shape of the cross section has little effect on the static strength of the specimen (Xin, 2015), the compressive strength of the cylinder after coring is very close to that of the cube (Huang, 2004). Consequently, the original cube compressive strength will be used in this study.

Dynamic compressive test

Failure patterns

As is shown in Figure 5, three groups of specimens with different strength grades were subjected to different degrees of damage in a strain rate range of 200–600 s⁻¹. The damaged specimens can be divided into two parts: fragments and powder. Larger fragments are usually irregular polyhedra with smooth failure surfaces, which are typically located at the bond between the aggregate and cement. Most of the smaller fragments are strips that are thin at the ends and thick in the middle, and broken aggregate is clearly visible on the surface of the strips. There are clearly more strips than polyhedra. When the strain rate was less than 350 s⁻¹, the powder consisted mainly of coarse particles, but when the strain rate exceeded 500 s⁻¹, it was finer. It is also observed that with the increase of concrete strength, the maximum size of fragments decreased and more powder was produced.

Dynamic compressive test results

Figure 6(a) shows the typical original waveform obtained in the dynamic compressive test. To validate the data, the stress balance of each group of data must be verified before the stress–strain curve is calculated. As shown in Figure 6(b), ε_i, ε_r and ε_t are intercepted, based on the three-wave equal relationship satisfied by the stress balance; if ε_i + ε_r is very close to ε_t, the test can be considered to satisfy the stress balance hypothesis, and the data are valid.

The dynamic stress–strain curve is a reflection of strength, energy and deformation of materials, which is of great significance (Chen et al., 2021). Figure 7 shows the dynamic compressive stress–strain curves of the three groups of HSEC specimens. The mechanical properties obtained from the test results are summarised in Table 5. A preliminary analysis of the test results reveals that the strength of all the specimens increases with the strain rate, indicating that the compressive strength of HSEC shows a clear strain rate effect; however, the critical strain corresponding to the peak stress has no significant relationship with the change in strain rate. In addition, it can also be observed that the compressive strength shows an increasing trend with the increase of concrete strength. It should be noted that the strain rate in this test ranges from 200 to 550 s⁻¹, which is higher than other SHPB compression tests. In previous studies, (Grote et al., 2001) conducted SHPB tests on mortar within the strain rate of 250–1700s⁻¹; the strain rate in Dong’s test (Dong et al., 2018) ranges from 94 to 926s⁻¹, so the results in this test are still credible. However, the SHPB test on expansive concrete is too few to explain the reason of high strain rate, which needs further researches to demonstrate.

Table 5.

Mechanical parameters of HSEC from dynamic compressive test.

No.	Static compressive strength/MPa	Strain rate/s⁻¹	Critical strain at peak stress	Dynamic compressive strength/MPa	DIF_c
C60	69.9	210.76	0.0123	82.3	1.18
		219.71	0.0124	111.9	1.60
		345.60	0.0073	114.7	1.64
		369.57	0.0192	116.7	1.67
		578.99	0.0142	169.5	2.43
C70	77.4	220.09	0.0101	109.6	1.42
		237.95	0.0075	119.0	1.54
		334.87	0.0069	120.7	1.56
		347.83	0.0065	124.6	1.61
		513.88	0.0145	114.1	1.47
C80	86.6	220.98	0.0068	125.4	1.45
		327.23	0.0056	143.9	1.66
		521.17	0.0154	131.7	1.52
		530.49	0.0100	173.1	2.00

Abbreviation: HSEC, High strength expansive concrete.

Impact toughness

The impact toughness indicates the energy absorption performance of materials under dynamic load. It is an important indicator of the impact resistance of a material in protective engineering. The impact toughness can be evaluated using the peak toughness (R_p) and specific energy absorption (SEA) (Frew et al., 2002). R_p represents the area enclosed by the stress–strain curve and the abscissa axis, in which the strain ranges from 0 to the critical strain, as shown in Figure 8. The SEA represents the energy absorbed by the specimen per unit volume during impact, which can be calculated using equations (8) and (9)

R_{p} = \int_{o}^{ε_{d}} σ (t) d ε (t)

(8)

SEA = \frac{A_{b} E_{b} C_{b}}{A_{s} l_{s}} \int_{0}^{t} [ε_{i} {(t)}^{2} - ε_{r} {(t)}^{2} - ε_{t} {(t)}^{2}] d t

(9)

where ε_d represents the critical strain, A_b is the cross-sectional area of the bar, E_b is the elastic modulus of the bar, C_b is the velocity of wave propagation in the bar, and A_s and l_s are the cross-sectional area and thickness of the specimen, respectively.

Before the maximum stress is reached, damage develops slowly, and the data are relatively accurate. Thus, R_p can precisely reflect the toughness of the material before failure. After the maximum stress is reached, the failure process accelerates, and the error of the test data increases, which makes the SEA less accurate than the peak toughness (Gao et al., 2015). Therefore, the two indexes, R_p and SEA, are used here to comprehensively evaluate the impact toughness of the HSEC.

As shown in Figure 9, the strain rate is in the ranges 200–240, 320–370 and 520–580 s⁻¹, and the R_p ranges are 0.42–0.52, 0.46–0.83 and 1.01–1.53 J/cm³, respectively. R_p increases with increasing $l g \dot{ε}$ , showing a significant strain rate effect. Moreover, the growth rate of R_p increases gradually with increasing $l g \dot{ε}$ . A comparison of the models reveals that the power function model can better reflect the variation law between $l g \dot{ε}$ and R_p. On the basis of the analysis, a calculation model of R_p is established, as shown in equation (10)

R_{p} = 0.0016 {(l g \dot{ε})}^{6.56} \dot{ε} > 200 s^{- 1}, R^{2} = 0.82

(10)

Figure 10 shows the variation of the SEA of C60, C70 and C80 concrete. During the loading of the specimens, the SEA exhibited stages of gradual change, rapid increase and gradual change, where the rapid increase stage reflects the appearance and expansion of cracks. A summary of the SEA data (Figure 11) reveals that with increasing $l g \dot{ε}$ , the SEA, like R_p, shows a clear strain rate effect; however, unlike R_p, the SEA is linearly correlated with $l g \dot{ε}$ . A model of the SEA is given in equation (11)

S E A = 4.766 l g \dot{ε} - 9.47 \dot{ε} > 200 s^{- 1}, R^{2} = 0.90

(11)

Dynamic increase factors

The dynamic increase factor (DIF_c) is another important index of the dynamic mechanical properties of concrete, which can reflect the increase in compressive strength under an impact load. Dynamic increase factor is defined as the ratio of dynamic compressive strength to static compressive strength. The formula is shown in equation (12)

{DIF}_{c} = \frac{f_{c,d}}{f_{c,s}}

(12)

Many studies have established the relationship between DIF_c and the strain rate of concrete. Among them, the fitting models of CEB (Comite Euro-International Du Beton, 1993), (Ross et al., 1996) and (Tedesco et al., 1997), (Fujikake et al., 2000) and (Hao et al., 2010) are typical.

Comite Euro-International Du Beton, 1993

D I F_{c} = {\begin{matrix} {(\frac{{\dot{ε}}_{d}}{{\dot{ε}}_{s}})}^{1.026 α} {\dot{ε}}_{s} < {\dot{ε}}_{d} \leq 30 s^{- 1} \\ γ {(\frac{{\dot{ε}}_{d}}{{\dot{ε}}_{s}})}^{1 / 3} {\dot{ε}}_{d} > 30 s^{- 1} \end{matrix}

(13)

where

α = {(5 + 9 f_{c s} / f_{c 0})}^{- 1}

; f_c0 = 10 MPa;

\lg γ = 6.156 α - 2

; f_cs and f_c0 are the dynamic and static compressive strength, respectively;

{\dot{ε}}_{d}

and

{\dot{ε}}_{s}

are the dynamic and static strain rates, respectively; and

{\dot{ε}}_{s} = 3 \times 10^{- 5} s^{- 1}

(Tedesco et al., 1997) and (Ross et al., 1996)

D I F_{c} = {\begin{matrix} 0.009651 l g {\dot{ε}}_{d} + 1.058 {\dot{ε}}_{d} \leq 63.1 s^{- 1} \\ 0.7581 l g {\dot{ε}}_{d} - 0.289 {\dot{ε}}_{d} > 63.1 s^{- 1} \end{matrix}

(14)

(Fujikake et al., 2000)

D I F_{c} = e x p (0.00126 \times l g {({\dot{ε}}_{d} / {\dot{ε}}_{s})}^{3.373})

(15)

(Hao et al., 2010)

D I F_{c} = {\begin{matrix} 0.04191 l g {\dot{ε}}_{d} + 1.2165 {\dot{ε}}_{d} \leq 30 s^{- 1} \\ 0.8988 {(l g {\dot{ε}}_{d})}^{2} - 2.8255 l g {\dot{ε}}_{d} + 3.4907 {\dot{ε}}_{d} > 30 s^{- 1} \end{matrix}

(16)

These four models have all been established for ordinary concrete. A comparison with the experimental data (Figure 12) shows that these models are not suitable for HSEC. However, the variation laws of the models of Tedesco et al. and Ross et al. are similar to that of the data in this study. Therefore, the parameters of this model can be refitted to calculate the DIF_c model of HSEC. The fitting results are shown in equation (17). The formula is applicable to HSEC of strength grades C60–C80, and the strain rate range is $\dot{ε} > 200 s^{- 1}$

D I F_{c} = 1.05 l g {\dot{ε}}_{d} - 1.00 \dot{ε} > 200 s^{- 1}

(17)

As the strain rate increases, more cracks are generated inside the concrete specimen, and more energy is required to support crack generation and propagation. However, during the very short impact time, the deformation and buffering ability of the material is insufficient for the required energy to accumulate. Therefore, according to the functional principle, the external energy can be counteracted only by increasing the stress (Wang et al., 2014).

Dynamic splitting tensile test

Failure patterns

Figure 13 shows the dynamic splitting tensile failure patterns of C70 specimens under different strain rates. The damaged concrete specimen can be divided into two parts. One part consists of two fragments with circular arc profiles, and the other part consists of debris and powder, as shown in Figure 14. The boundary between these two parts is not a straight line; it tends to expand at the loading point, forming a triangular area. Cracks develop along the diameter during impact, and aggregates are crushed or fall from the cement. Because the stress is concentrated near the loading point of the specimen, most of the formed fragments are fine particles or even powder. With increasing strain rate, more broken pieces are produced, and the volume of fragments becomes smaller.

Dynamic splitting tensile test results

A typical original waveform in the dynamic splitting tensile test is shown in Figure 15. The incident, reflected and transmitted waves are marked with arrows. It is clear that the transmitted wave is small, and the peak values of the incident and reflected waves are similar. This result can be attributed to the small contact area between the specimen and bars. A small amount of energy is transmitted to the transmission bar through the specimen, and most of it is reflected from the end of the incident bar to form the reflected wave.

Figure 16 shows the dynamic splitting stress–time curve of HSEC. The strain rate range is 3.176–4.96 s⁻¹, and the splitting tensile strength range is 15–25 MPa. As the strain rate increases, the splitting tensile strength also tends to increase. The splitting tensile strength of HSEC clearly shows a strain rate effect. In addition, the dynamic splitting tensile strength of concrete is approximately 15–25 MPa, whereas the dynamic compressive strength is approximately 90–180 MPa, which is much greater than the splitting tensile strength.

Dynamic increase factors

In the dynamic splitting tensile test, DIF_t can also be used to measure the strengthening effect of strain rate on concrete. Many researchers have established models to predict the DIF_t values of concrete. In this section, five ordinary cement models are compared with the experimental results, as shown in Figure 17.

(Malvar and Ross, 1998)

D I F_{t} = {\begin{matrix} {(\frac{{\dot{ε}}_{d}}{{\dot{ε}}_{s}})}^{1.016 δ} {\dot{ε}}_{d} \leq 1 s^{- 1} \\ β {(\frac{{\dot{ε}}_{d}}{{\dot{ε}}_{s}})}^{1 / 3} {\dot{ε}}_{d} > 1 s^{- 1} \end{matrix}

(18)

(Fujikake et al., 2006)

D I F_{t} = {(\frac{{\dot{ε}}_{d}}{{\dot{ε}}_{s}})}^{0.0013 {[l o g (\frac{{\dot{ε}}_{d}}{{\dot{ε}}_{s}})]}^{1.95}}

(19)

(Zhou and Hao, 2008)

D I F_{t} = {\begin{matrix} 0.0225 l o g {\dot{ε}}_{d} + 1.12 {\dot{ε}}_{d} \leq 0.1 s^{- 1} \\ 0.7325 {(l o g {\dot{ε}}_{d})}^{2} + 1.235 {\dot{ε}}_{d} + 1.6 0.1 s^{- 1} < {\dot{ε}}_{d} \leq 50 s^{- 1} \end{matrix}

(20)

(Hao and Hao, 2014)

D I F_{t} = {\begin{matrix} 0.26 l o g {\dot{ε}}_{d} + 2.06 10^{- 4} s^{- 1} \leq {\dot{ε}}_{d} \leq 1 s^{- 1} \\ 2 l o g {\dot{ε}}_{d} + 2.06 1 s^{- 1} < {\dot{ε}}_{d} \leq 2 s^{- 1} \\ 1.44331 l o g {\dot{ε}}_{d} + 2.2276 2 s^{- 1} < {\dot{ε}}_{d} \leq 150 s^{- 1} \end{matrix}

(21)

(Tedesco et al., 1997)

D I F_{t} = {\begin{matrix} 2.929 l o g {\dot{ε}}_{d} + 0.814 {\dot{ε}}_{d} > 2.32 s^{- 1} \\ 0.1425 l o g {\dot{ε}}_{d} + 1.833 {\dot{ε}}_{d} \leq 2.32 s^{- 1} \end{matrix}

(22)

The above models were established for ordinary concrete and are clearly not suitable for calculating the DIF of HSEC. Therefore, a new DIF_t formula based on the experimental results is proposed [Equation (23)], which is suitable for C60–C80 HSEC at strain rates above 3 s⁻¹

D I F_{t} = 3.29183 l o g {\dot{ε}}_{d} + 2.09537 {\dot{ε}}_{d} \geq 3 s^{- 1}

(23)

Figure 17 clearly shows that the DIF_t values of HSEC increase with increasing strain rate and are larger than those of ordinary concrete. This indicates that the dynamic tensile strength of HSEC is more sensitive to strain rate than ordinary concrete.

Comparisons of HSEC and ordinary concrete

In this section, the dynamic compressive and splitting tensile strengths of ordinary concrete are calculated according to (Comite Euro-International Du Beton, 1993). Because the formula of CEB underestimates the strengthening effect of strain rate on the dynamic tensile strength, the dynamic splitting tensile strength is calculated using equation (18), which has been revised by Malvar and Ross (Malvar and Ross, 1998). The results were compared with the measured strength of the HSEC to further illustrate the performance differences between expansive and ordinary concrete.

Figure 18 compares the dynamic compressive strength and dynamic splitting tensile strength of C60 concrete. The compressive strength of HSEC is less than that of ordinary concrete, whereas the splitting tensile strength is greater than that of ordinary concrete. In fact, the addition of an EA does not always increase the strength of concrete. (Zaichenko et al., 2014) found that when concrete reaches the maximum expansion, shrinkage will occur, which may cause compensation cracks to re-appear or even produce new cracks. In addition, the expansion pressure caused by the hydration of HSEC will also produce microcracks, resulting in strength reduction.(Yoo et al., 2012) found that the effect of an EA on the compressive strength of concrete was very small and even decreased slightly. (Zhao et al., 2020) also found that the compressive strength and splitting tensile strength of concrete with an EA decreased.

Sun, 2021 conducted experimental researches and theoretical analysis on expansive cement mortar under different constraint conditions. It is pointed out that the expansion effect of EA is related to the constraint direction, that is, the slurry expansion may show anisotropy. The expansion in the unconstrained direction is invalid because it cannot produce self-stress. In this test, the EA weakened the dynamic compressive strength of expansive concrete but enhanced the dynamic tensile strength. This may be because the specimens used in this experiment were cured in steel ring moulds, so they were unconstrained in axial direction and constrained in radial direction. Expansive agent generates solid products during hydration. Due to the existence of radial external constraints, the solid products effectively make up for the micro cracks in the concrete and reduce the porosity. Therefore, the effect of EA is significant in the radial direction, increasing the dynamic splitting tensile strength. However, the concrete expands freely in the axial direction. The internal void volume is not compensated, but more cracks may be generated due to shrinkage (Zaichenko et al., 2014), resulting in the decrease of strength. What is more, the addition of EA would affect the early hydration of concrete (Sun, 2021), and finally led to the reduction of dynamic compressive strength. In fact, the influence of EA on concrete strength is related to many factors, such as the type and amount of EA, the size and direction of restraint stress. More in-depth studies are needed to explore the strengthening law describing the effect of an EA on HSEC.

Conclusion

The dynamic compressive performance and dynamic splitting tensile performance of the developed HSEC were systematically studied using an SHPB device. The main conclusions are as follows.

(1) The dynamic compressive performance of HSEC shows a significant strain rate effect. The dynamic strength enhancement effect was revealed in terms of energy, and calculation models of DIF_c, R_p, and the SEA were established.

(2) Dynamic splitting tensile tests showed that the tensile strength of HSEC also shows a remarkable strain rate effect, and the sensitivity to strain rate is higher than that to compression, which matches the behaviour of ordinary concrete. A calculation model of DIF_t was established.

(3) The constrained direction during expansion has an important effect on the mechanical properties of specimens. A comparison of the dynamic compressive and splitting tensile strength of the HSEC and the ordinary concrete with the same strength grade revealed that EA does not always have a positive effect on the strength of HSEC. During the curing process, the constraint of ring moulds made the specimen expand effectively in the radial direction, so the dynamic splitting tensile strength is observed strengthened. However, there was no self-stress in the axial direction, and the internal micro cracks might increase instead of being compacted, resulting in the decrease of dynamic compressive strength.

Footnotes

Acknowledgements

The authors acknowledge financial support from the National Natural Science Foundation of China (Nos. 51978166 and 51738011) and the Fundamental Research Funds for the Central Universities (No. 2242021R10131).

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was partially supported by the National Natural Science Foundation of China and Central University Basic Research Fund of China.

ORCID iDs

Qiyao Li

Li Chen

References

Cao

Cheng

Cao

, et al. (2017) Workability, strength and shrinkage of fiber reinforced expansive self-consolidating concrete[J]. Construction & Building Materials 131(Jan.30): 178–185.

Chen

Gao

P W

Geng

, et al. (2012) Research on deformation of cement paste with MgO-expansive[J]. Bulletin of the Chinese Ceramic Society 31(03): 617–621. (in Chinese).

Chen

Zhou

(2013) Experimental and modeling study of dynamic mechanical properties of cement paste, mortar and concrete[J]. Construction and Building Materials 47: 419–430.

Chen

Fang

Jiang

X Q

, et al. (2015) Combined effects of high temperature and high strain rate on normal weight concrete[J]. International Journal of Impact Engineering 86: 40–56.

Chen

Yue

Zhou

, et al. (2021) Experimental and mesoscopic study of dynamic tensile properties of concrete using direct-tension technique[J]. International Journal of Impact Engineering 155: 103895.

Comite Euro-International Du Beton (1993) CEB-FIP Model Code 1990[S]. Trowbridge. Wiltshire, UK: Redwood Books.

Dong

Han

, et al. (2018) Dynamic impact behaviors and constitutive model of super-fine stainless wire reinforced reactive powder concrete[J]. Construction and Building Materials 184: 602–616.

Frew

D J

Forrestal

M J

Chen

(2002) Pulse shaping techniques for testing brittle materials with a split Hopkinson pressure bar[J]. Experimental Mechanics 42(1): 93–106.

Fujikake

Mori

Uebayashi

, et al. (2000) Dynamic properties of concrete materials with high rates of tri-axial compressive loads. J]. Structures and Materials 8: 511–522.

10.

Fujikake

Senga

Ueda

, et al. (2006) Effects of strain rate on tensile behavior of reactive powder concrete[J]. Journal of Advanced Concrete Technology 4: 79–84.

11.

Gao

Bai

, et al. (2015) Static and dynamic mechanical properties of high early strength alkali activated slag concrete[J]. Ceramics International 41(10): 12901–12909.

12.

Grote

D L

Park1

S W

Zhou

(2001) Dynamic behavior of concrete at high strain rates and pressures: I. experimental characterization[J]. International Journal of Impact Engineering 25: 869–886.

13.

Hao

(2014) Influence of the concrete DIF model on the numerical predictions of RC wall responses to blast loadings[J]. Engineering Structures 73: 24–38.

14.

Hao

(2010) Numerical analysis of lateral inertial confinement effects on impact test of concrete compressive material properties[J]. International Journal of Protective Structures 1(1): 145–168.

15.

Huang

Gao

, et al. (2019) Method of determining strain rate in SHPB experiment of concrete materials[J]. Explosion and Shock Waves 39(6): 1–9. (in Chinese).

16.

Huang

(2004) Study on Dimension Effect of Concrete Core[D]. Chongqing: Chongqing University. (in Chinese).

17.

Shang

, et al. (2020a) Shrinkage and mechanical properties of self-compacting SFRC with calcium-sulfoaluminate expansive agent [J]. Materials 13(3): 588.

18.

Wang

, et al. (2020b) Effect of CaO and MgO based expansive agent on deformation and mechanical properties of concrete-filled steel tubes[J]. Construction and Building Materials 250: 118723.

19.

Cheng

Deng

(2020c) Effects of steel slag powder and expansive agent on the properties of Ultra-High Performance Concrete (UHPC): based on a case study. J]. Materials 13(3): 683.

20.

(2013) Mechanical Properties and Durability Performance of Reactive Magnesia Cement concrete[D]. Cambridge: University of Cambridge.

21.

Yue

, et al. (2020) Experimental study and numerical simulation of impact compression mechanical properties of high strength coral aggregate seawater concrete[J]. International Journal of Impact Engineering 137: 103466.

22.

Malvar

Ross

(1998) Review of strain rate effects for concrete in tension[J]. ACI Materials Journal 95: 735–739.

23.

Nagataki

Gomi

(1998) Expansive admixtures (mainly ettringite) [J]. Cement and Concrete Composites 20(2–3): 163–170.

24.

Qian

Jiang

Song

, et al. (2020) Impact of elevated curing temperature on mechanical properties and microstructure of MgO-based expansive additive cement mortars[J]. Structural Concrete 21(3): 1082–1092.

25.

Qin

Han

Guang

, et al. (2021) Experimental study on mechanical properties of high performance concrete for railway bridges. J]. Concrete 377: 134–136. (in Chinese).

26.

Ross

Jerome

Tedesco

, et al. (1996) Moisture and strain rate effects on concrete strength[J]. ACI Material Journal 93(3): 293–300.

27.

Shen

Zheng

, et al. (2020) Expansive ultra-high performance concrete for concrete-filled steel tube applications[J]. Cement and Concrete Composites 114: 103813.

28.

Shuai

(2013) Mechanical Properties Experimental Study and Finite Element Analysis of Concrete under the Impact load[D]. Changsha: Hunan University. (in Chinese).

29.

Sun

(2021) Study on Expansion Performance of MgO Expansive Cement Mortar under Different Constraint Conditions[D]. Taian: Shandong Agricultural University. (in Chinese).

30.

Tedesco

Powell

Ross

, et al. (1997) A strain-rate-dependent concrete material model for ADINA[J]. Computers & Structures 64(5/6): 1053–1067.

31.

Wang

Liu

Jiang

(2014) Dynamic performance of concrete based on a Φ75mm SHPB system under high temperature[J]. Journal of Vibration and Shock 33(17): 12–17.

32.

Wang

Xiao

Zhang

,et al. (2022) Depth-consistent models for probabilistic liquefaction potential assessment based on shear wave velocity. Bulletin of Engineering Geology and the Environment 81(6): 1–14.

33.

Xia

Sha

Liu

,et al. (2019) Experimental study on properties of low shrinkage and high adhesion black high performance concrete[J]. China Concrete and Cement Products 12: 12–17. (in Chinese).

34.

Xin

(2015) Analysis of compressive strength relationship between concrete cylinder specimen and cube specimen [J]. China Water Power and Electrification 7: 59–62. (in Chinese).

35.

Yoo

Kwon

Sato

, et al. (2012) Analysis technique for autogneous shrinkage in high performance concrete with mineral and chemical admixtures[J]. Construction and Building Materials 34: 1–10.

36.

Zaichenko

Nazarova

Marshdi

(2014) Effect of expansive agent and shrinkage reducing admixture in shrinkage-compensating concrete under hot-dry curing environment[J]. Teka Commission of Motorization and Power Industry in Agriculture 14(2): 170–178.

37.

Zhang

Dai

Wang

, et al. (2020) Effects of magnesia expansive agents on the self-healing performance of microcracks in strain-hardening cement-based composites (SHCC)[J]. Materials Today Communications 25: 101421.

38.

Zhao

Liu

Wan

, et al. (2020) Mechanical properties and autogenous deformation behavior of early-age concrete containing pre-wetted ceramsite and CaO-based expansive agent[J]. Construction and Building Materials 267(10): 120992.

39.

Zhong

Y S.

(2006) Study on the Magnesia Concrete Expansion Additive of effect[D]. Nanjing: Nanjing University of Technology. (in Chinese).

40.

Zhou

Hao

(2008) Modelling of compressive behaviour of concrete-like materials at high strain rate[J]. International Journal of Solids and Structures 45: 4648–4661.

41.

Zhu

(1999) Thermal Stresses and Temperature Control of Mass concrete[M]. Beijing: China Electric Power Press. (in Chinese).