Experimental study and statistical analysis of lean iron ore concrete with high impact resistance

ABSTRACT

Impact tests were conducted using a specially made drop hammer impact device on concrete specimens (C60–C90) containing lean iron ore from mine waste as coarse aggregate to realize enhanced impact resistance in applications such as pile driving. Impact resistance tests were also conducted on equivalent conventional limestone concrete specimens for comparison. The statistical analysis results show that the number of impacts at the initial and final cracking of lean iron ore concrete conformed to the Weibull distribution of the strength grade. The impact resistance of lean iron ore concrete was ~0.65–2.03 times greater than that of conventional limestone concrete. In this study, as the impact fracture energies of the C80 and C90 specimens were the maximum and the damage to the lean iron ore aggregate was obvious, the properties of the lean iron ore were completely utilized. Consequently, a linear relationship between the failure resistance of lean iron ore concrete and its strength grade was identified. Finally, the use of lean iron ore as a coarse aggregate in concrete was shown to effectively reduce the probability of the precast concrete pile head bursting during driving.

KEYWORDS:

• Lean iron ore
• concrete
• drop hammer impact
• high impact resistance
• statistical analysis

1. Introduction

Following the rapid advancement of the construction industry, unpredictable impact loads have begun to affect the integrity of engineering components in different applications, and must therefore be properly accounted for. Under repeated dynamic impact loading, concrete components are subjected to repeated compression and tension, which continually induces and spreads microcracks. In particular, when a concrete component is connected to a fixed support, the shock wave generated after impact loading continuously reverberates inside the component, significantly reducing its service life. For example, in the case of precast pile installation, the pile top can burst after being subjected to multiple hammer blows (Figure 1); this adversely affects the continued use of precast piles. Many scholars have accordingly studied the impact resistance of different concrete materials using the drop-hammer impact tester; for example, Li and Yu (2019) and Zhidan, Yali, and Maopeng (2021) studied the impact response and resistance of ultra-high-performance fiber-reinforced concrete; Gopinath, Prakash, and Ahamed (2020), Weiguang, Lumin, and Huailiang (2022), Alrshoudi et al., Fahed, Hossein, and Rayed (2020), Yuan et al., Feng, Seok, and Hwi (2022), and Jian, Bojian, and Wei (2022) studied the synergistic effects of different types of fiber reinforcement in concrete under impact loads; Yang, Yang, and Zhang (2020) studied the impact resistance of concrete in composite structures; Srikanth, Murthy, and Rao (2021), Rahul and Nirendra (2021), Xiaoe (2019), and Vijayaprabha, Siva, and Mugahed (2021) studied the impact resistance of concrete containing different aggregates; Sadi, Han, and Wenlixia (2021) studied the impact resistance of reinforced concrete; and Nv et al., Linnv, Yisa, and Yijia (2021) studied the influence of curing methods on the impact resistance of concrete. In recent years, numerous studies have applied the drop-hammer impact test. At present, ordinary concrete is mainly taken as the research object, and the influence of adding fibers and replacing aggregate on the impact resistance of concrete is discussed. Studies on the properties of concrete materials and the methods used to enhance their impact resistances are currently research hotspots.

Figure 1. Hammer failure of precast pile: (a) pile top burst and (b) post-burst pile.

China’s open-pit iron mines strip hundreds of millions of tons of lean iron ore every year. This ore is discharged as waste to dumping grounds, not only occupying land but also presenting safety hazards (Bie 2002). To protect the environment and reduce the potential for harm, China has conducted assorted preliminary research into the treatment and utilization of such mine waste resources. Chen, Ni, and Wu (2015) reported that hematite iron ore, which accounts for ~10% (by mass) of the available iron (herein referred to as lean iron ore) can be used as a coarse aggregate in high-strength concrete after being crushed into particles. Wang, Kang, and Han (2015) used lean iron ore sand to replace natural river sand as a fine aggregate in concrete; the resulting product could replace conventional concrete in many structures. Furthermore, Zhang, Tang, and Liu (2021) studied the gelling activity of lean iron ore, Zhao et al. (2021) studied the characteristics of lean iron ores, and Cheng et al. (2016) studied the influence of lean iron ore on the compressive strength of concrete. Although these studies reported meaningful research results, the efficient and comprehensive development and utilization of lean iron ore remains a vital research topic for effectively utilizing mine waste resources in construction materials.

Therefore, in this study, lean iron ore was crushed into a coarse aggregate following the coarse particle size standard. Such aggregate materials have previously been applied in experimental studies of concrete in its early curing stages to improve the relevant theory and associated applicability (Zhu 2018); however, the results showed that the failure phenomena observed in previous experiments fail to account for the characteristics and contributions of lean iron ore coarse aggregate and its contribution to the performance of high-strength concrete. Using lean iron ore as coarse aggregate to improve the mechanical properties of high-strength concrete is a novel approach. At present, only few studies have been conducted on the impact resistance of high-strength concrete at home and other foreign countries, especially on strengthening the impact resistance of high-strength concrete from the perspective of hard coarse aggregates.

To discuss the feasibility of improving the impact resistance of high-strength concrete using lean iron ore coarse aggregate, based on the existing literature, in this study, high-strength concrete specimens (C60–C90) containing lean iron ore as a coarse aggregate were examined under impact tests using the standard free-drop hammer method recommended by the ACI 544 Committee. The experimental data and analysis results of this study can provide a reference for the effective utilization of lean iron ore and the performance optimization of high-strength concrete.

2. Materials and methods

2.1. Experimental materials

The cement used in this study was P.O52.5 ordinary Portland cement; its parameters all satisfied the requirements of the National Standard of Ordinary Portland Cement (GB 175-2007 2007). The crushed particle size of the lean iron ore coarse aggregate was 4.75–25 mm, thereby conforming to the requirements for continuous gradation; the physical and mechanical properties of the lean iron ore coarse aggregate are compared in Table 1 against the various specifications for coarse aggregates. The data in the table indicate that the apparent density of the coarse aggregate slightly exceeds that of the ordinary aggregate; meanwhile, its void ratio, locking effect, hardness, crushing value, abrasion value, and impact value are all smaller. Comparing the coarse aggregate requirements (GB/T 14685-2011 2011; JTG/T, F30-2014 2014; JTT/T F50-2011 2011) expressed in different specifications, it can be concluded that lean iron ore can be treated as a Grade I material when applied as a coarse aggregate. The harmful chemical components and iron content in the aggregate are shown in Table 2, which indicates that the contents of Fe, MgO, and Na₂O in the lean iron ore were considerably low, satisfying the requirements for use as a coarse aggregate. The aggregate is shown in Figure 2(a). The coarse aggregate used in the benchmark concrete was ordinary limestone macadam with an apparent density of 2706 kg/m³, hardness of 1.39%, crushing value of 18.79%, abrasion value of 19.4%, and impact value of 13.2%; these properties specify it as a Grade I coarse aggregate. The aggregate is shown in Figure 2(b). The fine aggregate in all mixes was river sand, with a fineness modulus of 2.73, apparent density of 2610 kg/m³, and silt content of 1.8%. The gradation curve of coarse aggregate and fine aggregate is shown in Figure 3. A polycarboxylate water-reducing agent was selected as the admixture to realize a water reduction rate of 30% in all mixes. The water used in all mixes was tap water, which meets the appropriate standard of water for concrete.

Figure 2. Coarse aggregate used in the experiment: (a) lean iron ore coarse aggregate and (b) limestone coarse aggregate.

Figure 3. Gradation curve of aggregate.

Table 1. Physical and mechanical properties of various coarse aggregates.

Parameter	Grade I coarse aggregate for buildings	Grade I coarse aggregate for concrete pavement	Grade I coarse aggregate for concrete bridges	Properties of lean iron ore aggregate
Apparent density (kg/m^3)	>2500	≥2500	>2500	3080
Stacking density (kg/m^3)	>1350	≥1350	>1350	1687
Water absorption (%)	<1	≤1	<1	0.76
Void ratio (%)	<47	≤47	<47	45.2
Hardness (%)	<5	≤5	<5	0.24
Crushing value (%)	<10	≤18	<10	6.13
Abrasion value (%)	-	≤28	-	11.12
Impact value (%)	-	≤28	-	8.8
Silt content (%)	≤0.5	≤0.5	<0.5	0.37
Mud content (%)	0	≤0.2	0	0
Needle sheet particulates (%)	<5	≤8	<5	4.1

Note: “-“ Indicates a lack of specified requirements.

Table 2. Statistical distribution of harmful chemicals and iron content in lean iron ore.

Chemical	Na2O	MgO	BaO	P	S	TiO2	Fe	Zn	Sc	Cl
Compositional distribution (%)	0.2938	0.7153	0.5988	0.1054	0.1159	0.0427	10.23	0.0305	0	0.016

2.2. Sample preparation and strength testing

2.2.1. Preliminary mix design

The high-strength concrete mix used in this study was designed according to the JGJ55-2011 Specification for the Mix Proportion Design of Ordinary Concrete and the related technical specifications (JTG E42-2005 (2005), JGJ/T, 281–2012 (2012)). The absolute volume method was used to calculate the preliminary mix proportions presented in Table 3. As shown in the table, two mix types were prepared: Type A mixes used lean iron ore as the coarse aggregate to prepare C60, C70, C80, and C90 strength grade concrete specimens, whereas i Type B mixes used the conventional limestone coarse aggregate instead to prepare the same concretes.

Table 3. Preliminary mix proportions.

Mix	Strength grade	Coarse aggregate type	Water cement ratio	Sand content (%)	Water (kg/m^3)	Cement (kg/m^3)	Water reducing agent (kg/m^3)	Fine aggregate (kg/m^3)	Coarse aggregate (kg/m^3)
A1	C60	Lean iron ore	0.36	29	150	412.5	2.06	566.3	1372.9
A2	C70	Lean iron ore	0.32	28	146	457.1	2.29	538.2	1359.9
A3	C80	Lean iron ore	0.29	27	142	483.9	2.42	516.8	1370.6
A4	C90	Lean iron ore	0.28	26	138	483.3	2.42	501.9	1378.0
B1	C60	Limestone	0.36	32	150	412.5	2.06	566.3	1205.9
B2	C70	Limestone	0.32	31	146	457.1	2.29	538.2	1194.8
B3	C80	Limestone	0.29	30	142	483.9	2.42	516.8	1204.2
B4	C90	Limestone	0.28	29	138	483.3	2.42	501.9	1210.7

2.2.2. Strength testing

Compressive strength test specimens for the mixes reported in Table 3 were prepared by manual mixing followed by casting in 100 mm cubes on a shaking table, demolding after 24 h, and 28 d of curing. The temperature and relative humidity of the concrete specimens in the laboratory during curing were 20°C and 95%, respectively. Each mix was then tested using the standard test method on three identical specimens; the results are shown in Table 4. The measured compressive strengths of both concrete mix types were found to be higher than the specified value. Because the strengths of these mixes clearly satisfied the requirements, the impact resistance tests were conducted following the mix proportions shown in Table 3.

Table 4. Compressive strengths of mixes.

s	A1	A2	A3	A4	B1	B2	B3	B4
28 d compressive strength (MPa)	67.3	83.5	118.3	124.2	60.8	71.0	87.4	100.5

2.3. Experimental method

Following the standard test method recommended by the ACI 544 Committee (American Concrete Institute (ACI) 1988), a multifunctional drop-hammer impact testing apparatus was developed for use in this study, as shown in Figure 4. The bottom of the instrument comprised a steel base plate. The instrument itself fixed the specimen in place and helped it to maintain its shape during impact. A 63.5 mm diameter steel ball was placed in the center of the upper surface of the specimen and fixed with a specially designed fixing pad. Prior to the installation of the fixing pad, the central region of the specimen was checked to ensure that it was flat and free of concavity or convexity. During the test, a steel hammer weighing 4.55 kg fell freely from a height of 460 mm to impact the steel ball; this then transferred energy to the specimen. Twelve specimens, 150 mm in diameter and 63.5 mm thick, were prepared for each concrete mix, resulting in a total of 96 trials.

Figure 4. Self-made drop hammer impact test device.

The following test procedure was followed until specimen destruction: The impact was repeatedly applied to the specimen; when the first crack was observed on the specimen surface, the number of impacts N₁ and the length L, width c, and depth d of the crack were recorded using a reading microscope; the impact testing was repeated and the surface of the specimen was observed after each impact; when the number of cracks on the specimen surface no longer increased from impact to impact, the specimen was considered to be completely destroyed; meanwhile, the number of impacts to destruction (final cracking) N₂ was recorded together with the corresponding L, c, and d. The crack depth at this time was defined as the full thickness of the specimen, in accordance with phenomena observed during the tests.

An impact test evaluates the impact resistance of a specimen using the number of impacts to initial cracking, N₁; the number of impacts to final cracking, N₂; the difference between N₁ and N₂, ΔN; the energy absorbed by the initial or final cracking of the specimen, W^’; and the resistance of the specimen to initial or final cracking, P.

According to ACI 544, the impact energy of concrete can be calculated as

(1) $W=Nmgh$(1)

where N is the number of impacts, h is the drop height, m is the hammer mass, and g is the acceleration due to gravity (9.81 m/s²).

The resistance of the specimen to initial and final cracking can be determined using

(2) $P=\frac{W^{\prime }}{\mathrm{\Delta }s}$(2)

where Δs is the crack volume, calculated as

(3) $\mathrm{\Delta }s=Ldc$(3)

3. Results and statistical analysis

3.1. Experimental phenomenon

The photographs showing the initial cracking for Type A and B concrete mix specimens in Figures 5 and 6, respectively, were selected from among the specimens exhibiting clear cracks and representative test values. During each experiment, repeated impacts first resulted in the formation of a dent in the center of the specimen; then, an initial crack spread outward from this dented region. The initial cracks formed in the two concrete mix types were similar; however, only one initial crack formed on the surface of the Type A specimens in all grades, whereas multiple initial cracks formed on the benchmark Type B concrete specimens. These cracks were scattered across the specimen surface, causing severe surface damage.

Figure 5. Initial cracking of lean iron ore concrete: (a) A1, (b)A2, (c) A3, and (d) A4.

Figure 6. Initial cracking of benchmark concrete: (a) B1,(b) B2, (c) B3, and (d) B4.

Figures 7 and 8 show the final crack failure modes for the Type A and B concrete mix specimens, respectively. As shown in Figure 7, the final cracks on the surface of the Type A specimens were approximately straight lines. During the test, the sound of the hammer impacting these specimens was clean and crisp, and when the initial crack appeared, this sound gradually decreased. If the sound is crisp and high pitched, it indicates that the hammered concrete is in good condition internally; if the sound becomes softer and the intensity becomes weaker, it indicates that the hammered concrete is internally deteriorated and broken. As shown in Figure 8, the final cracks on the surfaces of the Type B specimens randomly spread across the specimens according to the different initial crack positions, exhibiting an irregular radial pattern.

Figure 7. Final cracking of lean iron ore concrete: (a) A1, (b) A2, (c) A3, and (d) A4.

Figure 8. Final cracking of benchmark concrete: (a)B1, (b) B2, (c) B3, and (d) B4.

Because of the use of recycled aggregate, the final crack of the specimens in Nune Srikanth, Murthy, and Rao (2021)’s study presents a “T” shape similar to the final crack failure of the benchmark concrete. For the experimental specimen of Fahed, Hossein, and Rayed (2020), the use of polypropylene fiber indicated that when the final crack appeared, the radial shape was more notable. In contrast, the number of final cracks in the lean iron ore concrete was the lowest, which clearly indicates the brittleness of this concrete.

The internal section characteristics of each group of concrete specimens also differed after failure, as indicated by the fractures observed in the coarse aggregate. This phenomenon is closely related to the properties of the coarse aggregate in the two concrete types. Therefore, to study the influence of the degree of coarse aggregate fracture on the crack propagation and impact resistance of the concrete mixes, the ratio of surface fractures in the coarse aggregate to those in the hardened cement paste (referred to as the “fracture ratio” in this study) was statistically determined for each specimen (Table 5).

Table 5. Surface fracture ratio of coarse aggregate to hardened cement paste.

Mix type	C60	C70	C80	C90
A	1:3	2:3	3:1	5:2
B	3:2	4:3	2:1	2:1

It can be observed in Table 5 that the fracture ratio of the A3 specimen was the largest; as shown in Figure 9, the surface of its damaged section was relatively flat, and the broken coarse aggregate was symmetrical about that section. The fracture ratios of the Specimens A1 and A2 were smaller than that of Specimen A3, the surfaces of their damaged sections were unevenly distributed, and failure cracks were clearly observed to propogate through the hardened cement paste and coarse aggregate at their interfaces, as shown in Figure 10. The damaged sections of Type B concrete specimens were similar for all strength grades. Coarse aggregate and mortar-aggregate interface fractures were clearly visible in all sections, as shown in Figure 11. When the strength grade increased, the surface fracture ratio also gradually increased. This phenomenon is related to the crushing value and particle shape of the coarse aggregate. Coarse aggregate particles of iron tailings primarily exhibited crushing value characteristics in A1 and A2. In A3 and A4, the crushing value characteristics of coarse aggregate particles were not obvious, exhibiting flaky blocks and clear brittle fracture. The crushing value of limestone coarse aggregate was lower than that of iron tailings coarse aggregate, and the particle shape outperformed that of the iron tailings aggregate. In Specimen B, the crushing value and particle shape characteristics of the coarse aggregate are reflected together. Therefore, the fracture surface ratios of the benchmark concrete specimens were similar.

Figure 9. C80 lean iron ore concrete (A3) section.

Figure 10. C60 lean iron ore concrete (A1) section.

Figure 11. C70 benchmark concrete (B2) section.

3.2. Statistical analysis of experimental results

A total of 96 specimens were tested to determine their impact resistances. Table 6 lists the N₁,N₂, and ΔN index values for the specimens of Mix Types A and B, in which it can be clearly observed that the test results exhibit a certain discreteness. This could be caused by the different orders followed during the feeding of aggregate materials while preparing the concrete mix, or the formation of uneven surfaces due to vibration during preparation.

Table 6. Test results for each mix.

Specimen	N1/N2 (number of impacts)
	A1	A2	A3	A4	B1	B2	B3	B4
1	33/37	170/188	377/382	392/400	110/127	160/188	180/212	200/230
2	106/126	150/176	307/312	403/410	85/107	150/178	199/237	296/325
3	10/12	155/175	380/395	260/271	90/115	130/160	196/236	305/344
4	102/121	180/205	400/402	482/490	180/210	165/195	190/227	265/298
5	110/129	175/195	427/432	462/470	30/53	150/179	175/221	230/262
6	96/109	166/190	440/445	395/403	70/93	155/180	182/219	105/121
7	86/102	159/180	360/368	415/423	70/94	148/175	201/238	290/311
8	120/138	173/193	415/420	421/429	60/81	149/180	200/237	302/330
9	123/140	154/175	405/412	438/446	83/107	151/182	195/235	206/231
10	100/121	165/185	390/397	427/438	98/117	148/172	195/232	256/284
11	105/129	160/188	366/376	486/490	77/103	140/168	193/230	260/285
12	101/156	257/262	365/370	435/442	53/77	190/215	246/281	189/303
Mean value	91/110	172/193	386/393	418/426	84/107	153/181	196/233	242/277
Standard deviation	34.3/42.7	28.3/23.6	35.5/35.1	58.6/57.5	37.0/38.2	14.6/14.0	17.8/17.0	59.3/61.0
Coefficient of variation	0.38/0.39	0.16/0.12	0.09/0.09	0.14/0.13	0.44/0.36	0.10/0.08	0.09/0.07	0.24/0.22

To ensure that the test results were representative, the average index value for each mix type was taken as the basis for the corresponding analysis. To ensure the accuracy of the average test results, the Grubbs method was used to determine the number of impacts at initial and final cracking. The average of the valid data was taken as the analysis result, as shown in Table 7. The loading conditions in Nv et al., Linnv, Yisa, and Yijia (2021)’s experiment were the same as those used in this study. The energy absorbed by the C60 specimen at initial cracking was 1900 J, which is very close to those of Specimens A1 and B1 in this study. This suggests that the impact test data presented here have certain credibility.

Table 7. Average results of impact test indexes.

Mix	Number of impacts at initial cracking N1	Number of impacts at final cracking N2	Difference between N2 and N1ΔN	Energy absorbed by specimen at initial cracking (J)	Energy absorbed by specimen during failure (J)
A1	91	110	19	1868	2259
A2 A3 A4 B1 B2 B3	172 386 418 84 153 196	193 393 426 107 181 233	21 7 8 23 28 37	3526 7913 8569 1784 3137 4018	3963 8069 8747 2197 3716 4784
B4	242	277	35	4961	5687

At present, the application of reliability theory in engineering is particularly popular and has yielded significant advances. Numerous experimental studies have shown that the impact lifespan of concrete obeys the Weibull distribution (Wang, Wang, and Liu 2010). Therefore, a Weibull distribution failure probability analysis was performed for the impact resistance of lean iron ore concrete, as described in this section.

First, the distribution laws describing the impact resistances of Specimen Types A and B were expressed using the following Weibull density function:

.

(4) $\begin{array}{rl}& f(N)=\frac{b}{N_a-N_0}{\left(\frac{N-N_0}{N_a-N_0}\right)}^{b-1}\\ & \times exp\left[-{\left(\frac{N-N_0}{N_a-N_0}\right)}^b\right](N_0\le N<\mathrm{\infty })\end{array}$(4)

Here, N₀ is the minimum life parameter, N_a is the characteristic life parameter, and b is the Weibull shape parameter.

To simplify the calculation model, let the minimum life N₀ = 0; then, Equation. (4)(4) $\begin{array}{rl}& f(N)=\frac{b}{N_a-N_0}{\left(\frac{N-N_0}{N_a-N_0}\right)}^{b-1}\\ & \times exp\left[-{\left(\frac{N-N_0}{N_a-N_0}\right)}^b\right](N_0\le N<\mathrm{\infty })\end{array}$(4) can be simplified to a two-parameter Weibull distribution as follows:

(5) $f\left(N\right)=\frac{b}{N_a}{\left(\frac{N}{N_a}\right)}^{b-1}\times exp\left[-{\left(\frac{N}{N_a}\right)}^b\right]\left(N_0\le N<\mathrm{\infty }\right)$(5)

Based on Equation. (5(5) $f\left(N\right)=\frac{b}{N_a}{\left(\frac{N}{N_a}\right)}^{b-1}\times exp\left[-{\left(\frac{N}{N_a}\right)}^b\right]\left(N_0\le N<\mathrm{\infty }\right)$(5) ), the failure probability function P(N) of the Weibull distribution can be determined using

(6) $P\left(N\right)=exp\left[-{\left(\frac{N}{N_a}\right)}^b\right]$(6)

which can be transformed into

(7) $\frac{1}{P(N)}=exp{\left(\frac{N}{N_a}\right)}^b$(7)

Applying logarithms on both sides of Equation. (7)(7) $\frac{1}{P(N)}=exp{\left(\frac{N}{N_a}\right)}^b$(7) yields

(8) $lnln\left(1/p\right)=blnN-bln{N}_a$(8)

$Thenlettingy=lnln\left(1/p\right),x=ln\left(N\right),a=b,\beta =bln\left(N_a\right)$

(9) $y=\alpha x-\beta$(9)

The statistical properties of the data indicate that the expectation estimation of the average ranking method can be used to obtain the failure probability function P(N) of the Weibull distribution as follows:

(10) $P(N)=1-\frac{i}{n+1}$(10)

where i is the serial number of a given sample and n is the total sample size.

The failure probability functions were calculated for each specimen according to Equation. (10)(10) $P(N)=1-\frac{i}{n+1}$(10) . The resulting fitting functions are shown in Figures 12 and 13, in which the scatter points were fitted using the least squares method to obtain the corresponding regression parameters α and β in Equation. (9)(9) $y=\alpha x-\beta$(9) as well as the correlation coefficient R. The Weibull fitting results for the N₁ and N₂ of the lean iron ore concrete specimens are listed in Table 8, exhibiting a clear linear relationship with good correlation. The average correlation coefficient of initial crack impact time was 0.862. The average correlation coefficient of final crack impact time was 0.865. The linear relationship for the A3 specimen was the most obvious; the presence of clearly abnormal data in the impact test results for Specimens A1 and A2 resulted in slightly smaller R values than Specimens A3 and A4.

Figure 12. Linear regression results for number of impacts N₁ at initial cracking: (a) A1, (b) A2, (c) A3, and (d) A4.

Figure 13. Linear regression results for number of impacts N₂ at final cracking: (a) A1, (b) A2, (c) A3, and (d) A4.

Table 8. Weibull fitting results.

Index	Mix	α	β	R
N1	A1	1.165	5.581	0.832
	A2	5.470	28.603	0.751
	A3	10.477	62.860	0.973
	A4	5.627	34.402	0.890
N2	A1	1.165	5.793	0.846
	A2	5.701	29.993	0.752
	A3	10.690	64.313	0.969
	A4	5.902	36.178	0.892

Thus, the fitting results show that N₁ and N₂ for each grade of lean iron ore concrete can be determined using the Weibull distribution. As a result, the impact resistance of lean iron ore concrete can be considered highly reliable throughout its life, regardless of the concrete strength.

3.3. Enhancement mechanism analysis

According to statistical analyses of the impact test results, the relationships between N₁, N₂, ΔN, W^’, and the strength grade for each concrete mix type were identified, as shown in Figures 14, 15, and 16.

Figure 14. Relationship between strength grade and number of impacts.

Figure 15. Relationship between strength grade and fracture energy.

Figure 16. Relationship between strength grade and number of impacts between initial and final cracking.

From these figures, it can be concluded that the increase in strength grade corresponds to marked increases in N₁, N₂, and W^’ for both types of concrete, which follow approximately consistent change rules. The data indicate that the N₁, N₂, and W^’ of all lean iron ore concrete strength grades were consistently 0.65–2.03 times higher than those of the benchmark concrete. When the strength reached that of the C90 grade, the N₁, N₂, and W’ for lean iron ore concrete exhibited their largest values. For the C80 grade concrete, the improvement ratio of lean iron ore concrete was the largest. In terms of the damage degree, the fracture ratio was relatively high for the C80 grade. Furthermore, between Grades C70 and C80, the slope corresponding to Type A in Figures 14 and 15 indicates a general increasing trend.

As shown in Figure 16, the ΔN of the benchmark concrete consistently exceeded that of the lean iron ore concrete. When the concrete strength grade increased, the difference between the ΔN values of the Type A and B concretes gradually increased; this difference was the largest between the two C80 concretes. When an initial crack failure occurred during the test process, the final failure of the specimen occurred quickly thereafter, indicating that when lean iron ore is applied in high-strength concrete, the impact resistance of the concrete is enhanced, though its brittleness is also increased. This result was confirmed by the observed change in the hammering sound during the experiment. To reflect the influence of ΔN on the impact resistance of concrete more intuitively, the ductility index β was used to evaluate the concrete performance as follows:

(11) $\beta =\frac{\mathrm{\Delta }N}{N_1}$(11)

The results obtained using Equation. (11)(11) $\beta =\frac{\mathrm{\Delta }N}{N_1}$(11) are presented in Table 9 and show that the ductility of each lean iron ore concrete strength grade was ~1.31–10.44 times smaller than the equivalent benchmark concrete strength grade. However, owing to the considerable difference between ΔN and N₁, the β values compared for the two concrete types were fairly small, indicating that ΔN has a smaller influence on the impact resistance of lean iron ore concretes for all grades.

Table 9. Ductility index.

Mix type	C60	C70	C80	C90
A	0.208	0.122	0.018	0.019
B	0.273	0.183	0.188	0.144

Rahul and Nirendra (2021) added 10% rubber powder into concrete, and the impact resistance was consequently improved by 7.3%. Through experimental research, Cong, Wenchang, and Xiangqing (2021) found that the ductility index β of C40 ordinary concrete under impact is 0.13–0.22. In contrast, in this study, the impact resistance of concrete mixed with lean iron ore coarse aggregate exceeds that with rubber powder, and the ductility index decreases with the increase in concrete grade.

Each specimen’s ability to resist initial and final cracking was calculated using Equation. (2)(2) $P=\frac{W^{\prime }}{\mathrm{\Delta }s}$(2) and the measured crack L, d, and c. The regression results shown in Figure 17 indicate a linear correlation between the impact resistance index and strength grade of the two types of concrete: when the strength grade increased, the ability of both concrete types to resist impact damage improved. However, the lean iron ore concrete exhibited a stronger impact resistance to both initial and final cracking than the benchmark concrete. Furthermore, when the strength grade increased, the impact resistance of the lean iron ore concrete was primarily realized through its ability to resist initial cracking.

Figure 17. Relationship between impact resistance and strength grade according to different concrete mix types (conventional and lean iron ore mix).

Because the two concrete types investigated in this study are solid materials, their dynamic responses under impact load will differ substantially from those under static loads; this difference is primarily reflected in the rate effect (Cui, Wang, and Zhang 2017). When a solid material is either combined with or transformed into a rigid body in an ideal state, all the energy inputted to it from the outside can be converted into kinetic energy. However, in the non-ideal state, the external input energy can be converted into solid kinetic energy and solid potential energy. The physical equilibrium equation for a solid rigid body under impact load can therefore be expressed as

(12) $W_i-W_k-W_p=0$(12)

(13) ${\int }_{\mathrm{\Omega }}\rho \nu \bar{x}\mathrm{d}V-{\int }_S\sigma \nu \bar{x}\mathrm{d}S-\int \int { }_{\mathrm{\Omega }}f\mathrm{d}S\mathrm{d}V=0$(13)

where W_i,W_k, and W_p are the input energy, kinetic energy, and potential energy, respectively; $\bar{\mathrm{x}}$ is the unit vector of the spatial position of the micro-element; ρ is the continuous medium density; $\nu$ is the velocity of the micro-element medium in the load field; $\sigma$ is the stress per unit cell of the medium $\mathrm{\Omega }$; s is the surface area of the unit cell; V is the medium volume; and f is the viscous force counteracting the interfacial dislocation fracture of the microelements.

Solid microscopic particles exhibit poor performance when transforming external kinetic energy into internal energy. By neglecting the internal energy effect and considering practicality and operability, the energy conservation equation of the particle field for a solid microscopic material under impact can be expressed as

$\mathrm{\Delta }W=\rho \nu \bar{x}\mathrm{d}V+\sigma \nu \bar{x}\mathrm{d}S+\frac{\mathrm{\partial }f(\dot{\epsilon },\rho ,\bar{x},U_d,D)}{\mathrm{\partial }t}\mathrm{d}V$

(14) $=\mathrm{\Delta }{W}_{\nu }+\mathrm{\Delta }{W}_{\rho }+\mathrm{\Delta }{W}_{\tau }$(14)

where $\dot{\epsilon }$ is the material strain rate, D is the medium damage coefficient, U_d is the thermal activation energy during the process of micro-damage, W is the kinetic energy inputted by the impact load into the solid, W is the inertial energy of the material particles, W_ρ is the plastic energy of the particles, and W_τ is the material damage fracture energy.

Particle velocity attenuation is caused by external constraints, material deformation, and friction between particles at fracture. It is a macroscopic representation of the transformation from external impact kinetic energy to the potential energy of a material (Einav 2007). The potential energy of a material can be expressed as

$W_{\nu }=\int \int \int \rho \nu \bar{x}\mathrm{d}V=\frac{1}{2}\varphi {\psi }^2=\frac{1}{2}\varphi (\frac{\mathrm{\Delta }l}{t}.\frac{l}{l}{)}^2$

(15) $=\frac{1}{2}\varphi {\left(\frac{\epsilon }{t}\cdot l\right)}^2=\frac{1}{2}\varphi {\dot{\epsilon }}^2{l}^2$(15)

(16) $W_{\rho }=\int \int \int \sigma \nu \bar{x}\mathrm{d}S=(1-D_t){\int }_0^t{\int }_0^{\epsilon }\sigma (\epsilon ,t)d\epsilon dt$(16)

where $\varphi$ is the equivalent mass of the solid medium, ψ is the nominal equivalent velocity of the particle, Δl is the displacement of the particles under impact load, D_t is the damage coefficient of the material at moment t, and σ(ε,t) is the stress function of the material under impact load.

Many scholars have derived theoretical equations describing the fracture energy of solid materials from the perspectives of thermal activation and damage degree (Einav 2007; Petrov et al. 2017). The “G-formula” for fracture energy, as recommended in the CEB-FIP (1993), is given by

(17) $G=\alpha {\left(\frac{f_c}{10}\right)}^{0.7}$(17)

where f_c is the compressive strength of the material and α is the related coefficient for the properties of the cementitious matrix; generally, α = 0.03 for aggregate concrete.

The fracture energy released by impact fracture damage (1993) can be expressed by w_τ, which is obtained as

(18) $W_{\tau }=\alpha \hspace{0.17em}{\left(\frac{{\mathrm{f}}_{\mathrm{d}}}{10}\right)}^{0.7}=\alpha {\left(\frac{\mathrm{D}\mathrm{I}\mathrm{F}\cdot {\mathrm{f}}_{\mathrm{s}}}{10}\right)}^{0.7}$(18)

where DIF is the dynamic enhancement coefficient, f_d is the dynamic compressive strength of the material, and f_s is its static compressive strength.

Multiple scholars have concluded that DIF is related to the loading rate, and is usually in the range 1.25–1.92 (Watstein 1953; Atchley and Furr 1967; Hughes and Watson 1978). In view of the low loading rate applied in the impact tests conducted in this study, DIF was set to 1.25. By combining Equations. (17)(17) $G=\alpha {\left(\frac{f_c}{10}\right)}^{0.7}$(17) and (18(18) $W_{\tau }=\alpha \hspace{0.17em}{\left(\frac{{\mathrm{f}}_{\mathrm{d}}}{10}\right)}^{0.7}=\alpha {\left(\frac{\mathrm{D}\mathrm{I}\mathrm{F}\cdot {\mathrm{f}}_{\mathrm{s}}}{10}\right)}^{0.7}$(18) ), the fracture energy values of the two types of concrete under quasi-static load and impact fracture damage were calculated, with the results shown in Figure 18.

Figure 18. Relationship between fracture energy and fitted values according to strength grade.

Figure 18 shows that the fracture energy of the two types of concrete evaluated in this study increased with increasing strength grade. Compared with the benchmark (Type B) concrete, the static and impact fracture energies of lean iron ore (Type A) concrete were noticeably stronger. The impact fracture energy of the Type A concrete essentially reached its maximum for the C80 concrete strength grade. The impact fracture energy of this concrete was 1.236 times that of the benchmark concrete and 1.169 times that of its own static fracture energy. The change laws describing the curves in Figure 18 are similar to those describing the curves in Figures 14 and 15, all showing that lean iron ore aggregate is the main factor enhancing the impact fracture energy of concrete at Grades C80 and above. Equation (18)(18) $W_{\tau }=\alpha \hspace{0.17em}{\left(\frac{{\mathrm{f}}_{\mathrm{d}}}{10}\right)}^{0.7}=\alpha {\left(\frac{\mathrm{D}\mathrm{I}\mathrm{F}\cdot {\mathrm{f}}_{\mathrm{s}}}{10}\right)}^{0.7}$(18) can therefore be used to calculate the impact fracture energy of different concrete grades containing lean iron ore.

3.4. Engineering feasibility analysis

A high-strength precast concrete pile driving example was used to conduct a lifespan assessment and analysis of lean iron ore aggregate concrete in application. A high-strength precast concrete pile with a diameter of 550 mm and a section length of 10 m was used. The vertical pullout and bearing capacity of the single pile were 400 kN and 2000 kN, respectively. After foundation treatment, a geological survey of the soil underlying the subject construction area was conducted; the obtained soil data are presented in Figure 19.

Figure 19. Construction soil survey data.

Following the geological survey results (as well as the relevant requirements of the pile driving project), the constructor used a #50 diesel hammer machine to drive the precast pile by dropping an 11 metric ton hammer at a distance of 2 m. The resulting construction records are provided in Table 10. Several piles driven under normal construction conditions were selected from these records to analyze their damage phenomena after driving. According to the recorded data and field construction situation, the penetration rates of Piles 8, 9, 12, and 17 decreased notably when they entered the medium sand layer. Furthermore, clear cracks (~50 mm long and 1 mm wide) occurred at the head of the second pile section; indeed, the main damaged parts of all four piles were located at their heads. The total numbers of hammer blows applied to the damaged piles were generally higher than those of the piles that exhibited intact bodies after installation; a maximum of 955 impacts were applied. When Piles 13 and 19 penetrated the coarse sand, they burst in their third sections and the damage to the pile head was significant; hence, the construction was stopped immediately.

Table 10. Construction records.

Pile number	Number of pile connections	Penetration depth (mm)	Total hammer impacts	Post-construction pile condition
7	3	306	890	Good
8	3	310	945	Pile top fracture
9	3	298	951	Pile top fracture
10	3	290	873	Good
11	3	302	886	Good
12	3	322	960	Pile top fracture
13	3	312	957	Pile top fracture
14	3	300	906	Good
15	1	120	126	Pile fracture
16	3	308	890	Good
17	3	326	960	Pile top fracture
18	2	236	812	Improper pile connection
19	3	309	956	Pile top fracture

According to the statistical and failure analyses of the above-mentioned pile-driving cases, when an ordinary high-strength concrete precast pile was used, the probability of breakage at the pile head was ~60%. This represents a technical problem that occurs frequently during precast pile driving. Furthermore, these results indicate that the use of lean iron ore concrete has a much larger influence on the impact life of a pile than the initial crack shape or ductility. For piles, impact life is defined in terms of the number of hammer blows that can be withstood before failure. According to test experience and the engineering lifespan theory, the impact life of a precast iron ore concrete pile can be expressed in terms of the impact life of a conventional benchmark concrete pile as

(19) $N\approx {\left[N_b\cdot {\left({\int }_{e_0}^{e_1}\left(\zeta e+{\beta }_1\right)de\right)}^{0.5}{\beta }_2\right]}^k\left(e_0\le e\le e_1\right)$(19)

where N is the estimated impact life of the iron ore concrete pile, N_b is the impact life of a benchmark concrete pile, e is the impact resistance parameter of the concrete, e₀ is the minimum enhancement factor, e₁ is the maximum enhancement factor, k is the engineering construction safety coefficient, ζ is the impact reliability correlation enhancement coefficient, β₁ is the impact reliability correlation ductility coefficient, β₂ is the ductility of the concrete material (where β₂ = 1 – β, in which β is the ductility index).

The impact life of a lean iron ore concrete pile was then estimated using Eq. (19(19) $N\approx {\left[N_b\cdot {\left({\int }_{e_0}^{e_1}\left(\zeta e+{\beta }_1\right)de\right)}^{0.5}{\beta }_2\right]}^k\left(e_0\le e\le e_1\right)$(19) ); the results indicated that the use of lean iron ore as coarse aggregate enhances the impact resistance of high-strength concrete by a factor of ~0.65–2.03. For the iron ore concrete piles investigated in this study, k was determined to be 0.95, α and β₁ were both 0.9, and β₂ was calculated using the β values reported in Table 9. The probability of pile head bursting failure was found to decrease by ~8.6–51.2% when using lean iron ore concrete. However, pile heads can fail because of geological conditions. The reference values for the impact life of precast piles comprising lean iron ore concretes of various grades are shown in Table 11.

Table 11. Lifespan extension of precast lean iron ore concrete piles under harsh geological conditions.

Concrete grade	C60	C70	C80	C90
Lifespan extension (%)	8.6	13.5	51.2	48.9

4. Conclusions

The results obtained from an experimental study on the impact resistance of lean iron ore concrete were compared with those of a conventional limestone benchmark concrete to draw the following conclusions.

(1) In terms of the number of impacts at initial and final cracking for each grade of lean iron ore concrete, the fitting results of the Weibull probability distribution show a linear function relationship. The average correlation coefficient of initial crack impact times was 0.862. The average correlation coefficient of final crack impact time was 0.865. This is a good correlation and can pass the Weibull probability distribution test.

(2) Compared with benchmark concrete, lean iron ore concrete exhibited low ductility and clear brittle fracture. The ductility was reduced by a factor of ~1.31–10.44. At the initial cracking, the surfaces of most specimens exhibited one crack; at the final cracking, the specimen surface crack was almost a straight line with no radial characteristics. After the initial crack, the lean iron ore concrete broke along the initial crack and failed quickly.

(3) The impact resistance of the lean iron ore concrete was significantly enhanced compared to the conventional benchmark concrete. When the number of impacts at failure and the impact fracture energy were evaluated, the impact resistance of the lean iron ore concrete was found to be ~0.65–2.03 times greater than that of the benchmark concrete, with the C80 and C90 concrete specimens exhibiting the maximum impact resistance. When the strength of concrete was between C70 and C80, the impact energy balanced by lean iron ore exhibited a general increasing trend, and C80 represented the cut-off point for the coarse aggregate of lean iron ore to be fully utilized.

(4) A linear relationship was observed between the impact fracture resistance of the lean iron ore concrete and its strength grade. The C80 lean iron ore concrete exhibited the greatest impact fracture energy (1.236 times that of the corresponding benchmark concrete and 1.169 times its own static fracture energy) and its aggregate characteristics were observed to be fully utilized. However, whilst the application of lean iron ore in high-strength concrete was found to considerably enhance the impact resistance of concrete, it also increased its brittleness. Lean iron ore coarse aggregate is the main factor to enhance the impact fracture energy of concrete.

(5) In a field application experiment, pile-driving activities were observed to frequently break conventional concrete pile heads, owing to geological conditions. The probability of pile-head bursting failure was reduced by ~8.6–51.2% when using lean iron ore as the coarse aggregate in precast pile concrete. For precast piles with C60–C70 concrete, the life extension rate was 8.6–13.5%; for precast piles with C80–C90 concrete, the life extension rate was 48.9–51.2%.

Acknowledgments

This work was supported by the scientific research project of Liaoning Education Department under Grant [2020LNJC02]; and the Excellent Talents training project of Liaoning University of Science and Technology Grant [2019RC01].

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the scientific research project of Liaoning Education Department [2020LNJC02]; Excellent Talents training project of Liaoning University of Science and Technology Grant [2019RC01].