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<span id='_Hlk529003922'></span>

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==Analysis of damage failure in uniaxial compressive of cemented paste backfill by ultrasonic pulse velocity test==

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Bingwen Wang<sup>1</sup>  Lin Li<sup>1 </sup>  Yao Yu<sup>1</sup>  Benyong Huo<sup>1</sup>  Jian Liu<sup>1</sup>  Jie Liu<sup>2</sup>

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<span style="text-align: center; font-size: 75%;">1</span> <span style="text-align: center; font-size: 75%;">School of Energy and Mining Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China</span>

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2 Linglong Gold Mine, Shangdong Gold Group Co.Ltd, Zhaoyuan Shangdong, 265406, China

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'''Abstract:''' Cemented paste backfill (CPB) is prepared by mixing cementitious materials, tailings and water. Uniaxial compressive strength (UCS) is one of the most commonly used indicators for evaluating the mechanical performance of CPB. Ultrasonic pulse velocity (UPV) testing which is a non-destructive measurement, can also be applied to determine the mechanical properties of cement-based materials such as CPB. In order to study the failure mechanism of CPB,144 CPB samples prepared at different mass fraction and cement-tailing ratios were subjected to the UCS and UPV tests at 7,14 and 28 days of curing age. The effect of cement-tailing ratio and mass fraction on the UCS and UPV of CPB samples were obtained, the UCS values were correlated with the corresponding UPV data. Microstructural analysis was also performed on CPB samples to understand the effect of microstructure on the UCS data. The results show that the UCS and UPV values of CPB increased with cement-tailing ratio, mass fraction and curing time. Based on the experimental results, the damage constitutive equations and the damage evolution equations of different backfills were proposed on the basis of damage mechanics. Moreover, comparative analysis of constitutive model and experimental results were made to verify the reliability of the damage model. The results acquired by this paper provide a scientific basis for the rational strength design of backfill mine.

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'''Key words:''' Cemented paste backfill; Uniaxial compressive strength; Ultrasonic pulse velocity; Failure mechanism

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<span id='_Hlk500425389'></span>

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==1. Introduction==

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Underground mining is a significant way to extract mineral resources from earth. Meanwhile, plenty of solid waste (e.g. waste rock, tailings) and underground gobs are created [1]. The discharge of tailings on ground may contaminate the environment or even become a potential hazard. Besides, the underground gobs can result in land surface subsidence [2]. During the underground mining, it is necessary for the underground gobs to fill timely with filling material that have a certain physical and mechanical properties. Filling mining stope with tailings has numerous advantages, such as controlling ground pressure, enhancing resource recovery and realizing sustainable development of mining industry [3-5].

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As to metal mines, cemented paste backfill (CPB) is an engineered mixture of dewatered tailings, cementitious materials and water [6-9]. The UCS of CPB is one of the most significant parameters because CPB structure must remain stable during the extraction of adjacent stopes to ensure the safety of the miners and avoid ore dilution. The mechanical performance of CPB samples is commonly measured with UCS test [10,11]. Ultrasonic pulse velocity (UPV) test, a non-destructive and easy method to apply in both laboratory and in situ conditions, has increasingly been conducted to assess the geotechnical properties of rock or cement-based materials. Numerous studies have been practiced on the use of UPV test. Previous researchers used UPV test to estimate the mechanical and engineering properties of rocks and concrete. And it can also be applied to determine the cracks or defects in the material [12-15]. Wang and Li [16] reported that the cracking characteristics (i.e. crack width) of rock and earth mass can be evaluated by measuring the UPV in these media. Some others used UPV test to characterise in situ microcrack damage resulted from tunnel excavation and the state of decay of wall rock [17]. As to CPB, Diezd’Aux [18] and Galaa et al [19] have obtained various UPV values in CPB samples with different binder dosage (3-5 wt.%), but they have not used the UPV testing results to evaluate the strength of CPB. Consequently, Yilmaz et al [20] have conducted a study to take advantage of the UPV measurement to predict the strength of CPB samples.

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The objective of this research is to analyse damage failure in uniaxial compressive of CPB samples prepared with different cement-tailing ratio and mass fraction by UPV test. The USCs of CPB samples were correlated with the UPV. As a result, this paper attempt to establish significant relationship between UCS and UPV of CPB. After the stress reaches the UCS, the UPV values of CPB rapidly decreases. On the basis of these experimental, this paper put forward damage mechanism of CPB tentatively. Besides, the relationship between damage value and strain was obtained according to the damage evolution equations. Additionally, the scanning electron microscope (SEM) analysis was performed for the determination of microstructural properties of CPB samples.

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==2. Materials and methods==

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<span id='_Hlk500425498'></span>

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===2.1 Unclassified-tailings and Cementitious materials===

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Gold mining tailings, cementitious materials and water were used to prepare the CPB samples. The unclassified tailings and cementitious materials used in this study are both provided by Ling-Long gold mine in the east of China. The chemical properties of the unclassified tailings and cementitious materials are shown in Table 1.

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

Table 1. Chemical composition of the unclassified-tailings and cementitious materials</div>

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{| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;" 

|-

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Chemical component

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|SiO<sub>2</sub>

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Al<sub>2</sub>O<sub>3</sub>

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|K<sub>2</sub>O

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Na<sub>2</sub>O

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|CaO

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Fe<sub>2</sub>O<sub>3</sub>

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|MgO

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|S

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|TiO<sub>2</sub>

|-

|  style="border-top: 1pt solid black;text-align: center;"|Unclassified

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tailings(wt.%)

|  style="border-top: 1pt solid black;text-align: center;"|66.90

|  style="border-top: 1pt solid black;text-align: center;"|18.06

|  style="border-top: 1pt solid black;text-align: center;"|4.70

|  style="border-top: 1pt solid black;text-align: center;"|2.85

|  style="border-top: 1pt solid black;text-align: center;"|2.27

|  style="border-top: 1pt solid black;text-align: center;"|1.51

|  style="border-top: 1pt solid black;text-align: center;"|0.88

|  style="border-top: 1pt solid black;text-align: center;"|0.25

|  style="border-top: 1pt solid black;text-align: center;"|0.17

|-

|  style="border-bottom: 2pt solid black;text-align: center;"|Cementitious materials(wt.%)

|  style="border-bottom: 2pt solid black;text-align: center;"|20.40

|  style="border-bottom: 2pt solid black;text-align: center;"|9.33

|  style="border-bottom: 2pt solid black;text-align: center;"|0.58

|  style="border-bottom: 2pt solid black;text-align: center;"|0.28

|  style="border-bottom: 2pt solid black;text-align: center;"|53.08

|  style="border-bottom: 2pt solid black;text-align: center;"|1.27

|  style="border-bottom: 2pt solid black;text-align: center;"|4.51

|  style="border-bottom: 2pt solid black;text-align: center;"|3.21

|  style="border-bottom: 2pt solid black;text-align: center;"|1.25

|}

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According to the data from Table 1, the content of Al<sub>2</sub>O<sub>3</sub> and SiO<sub>2</sub> contained in the unclassified tailings is respectively 18.06 wt.% and 66.90wt.%, indicating that the unclassified tailings samples in the test can be suitable to make cemented paste backfill (CPB). In addition, SiO<sub>2</sub> content in the unclassified tailings is high, which provides activity for the unclassified tailings to participate in hydration. Table 2 shows the particle size composition of unclassified tailings and cementitious materials.

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

Table 2. Particle size composition of the unclassified-tailings and cementitious materials</div>

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{| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;" 

|-

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;vertical-align: bottom;"|Element

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;vertical-align: bottom;"|D<sub>10</sub>(μm)

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;vertical-align: bottom;"|D<sub>25</sub>(μm)

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;vertical-align: bottom;"|D<sub>50</sub>(μm)

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;vertical-align: bottom;"|D<sub>75</sub>(μm)

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;vertical-align: bottom;"|D<sub>90</sub>(μm)

|-

|  style="border-top: 1pt solid black;text-align: center;vertical-align: bottom;"|Unclassified

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tailings

|  style="border-top: 1pt solid black;text-align: center;vertical-align: bottom;"|8.46

|  style="border-top: 1pt solid black;text-align: center;vertical-align: bottom;"|28.06

|  style="border-top: 1pt solid black;text-align: center;vertical-align: bottom;"|101.52

|  style="border-top: 1pt solid black;text-align: center;vertical-align: bottom;"|188.99

|  style="border-top: 1pt solid black;text-align: center;vertical-align: bottom;"|245.32

|-

|  style="border-bottom: 2pt solid black;text-align: center;vertical-align: bottom;"|Cementitious materials

|  style="border-bottom: 2pt solid black;text-align: center;vertical-align: bottom;"|5.07

|  style="border-bottom: 2pt solid black;text-align: center;vertical-align: bottom;"|23.93

|  style="border-bottom: 2pt solid black;text-align: center;vertical-align: bottom;"|61.60

|  style="border-bottom: 2pt solid black;text-align: center;vertical-align: bottom;"|154.68

|  style="border-bottom: 2pt solid black;text-align: center;vertical-align: bottom;"|236.71

|}

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===2.2 Preparation of cemented unclassified tailings backfill===

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Mixing unclassified tailings and cementitious materials, a series of samples (mass fraction of 65%,68%,70% and 72%) were made at cement-tailing ratios of 0.250:1, 0.125:1, 0.100:1 and 0.083:1 respectively. The required amount of unclassified-tailings, cementitious materials and water

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are mixed and homogenized in a mixer until obtaining the desired mixtures. Afterwards, the produced cemented unclassified tailings backfill mixtures are poured into curing cubes of 7.07 <math display="inline">\times</math> 7.07 <math display="inline">\times</math> 7.07cm in length <math display="inline">\times</math> width <math display="inline">\times</math> height to form cubics CPB samples. Then, these samples are cured in YH-40B standard curing chamber (Fig. 1) at temperature of 20 <math display="inline">\pm</math> 1 <math display="inline">℃</math> and for period of 7,14 and 28 days.

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===2.3 UCS and UPV tests ===

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After the specific curing age (7,14 and 28 days), the uniaxial compressive strength (UCS)tests were conducted with MTS rigid apparatus according to ASTM C 109-02[21]. The ultrasonic pulse velocity tests were carried out simultaneously (as shown in Fig. 1). The samples are subjected to the UPV tests according to ASTM C 597[22]. By taking advantage of the ultrasonic pulse method, the UPV testing measures longitudinal P-wave velocities in the test media. Fig.2 schematically demonstrates the UPV testing of CPB samples in this study. Before the UCS and UPV testing, the end surfaces of the test samples (face1 and 2 in Fig. 2) are made smooth and flat. And then two thin films of Vaseline are separately coated on these two surfaces (faces 3 and 4 in Fig. 2) of the transducers (transmitter and receiver), in order to ensure favorable contact of the transducers and the samples. During the UPV testing, the longitudinal P-wave velocity (''V<sub>P</sub>'') in the sample is investigated and recorded, as well as visually displayed on the screen. The longitudinal P-wave velocity is calculated by the following equation:

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<div style="text-align: right; direction: ltr; margin-left: 1em;">

''V<sub>P</sub>=d/t ''                                (1)</div>

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Where ''d'' is the distance between the transmitter and receiver, ''t ''is the travel time.

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

{|

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| [[Image:Review_156654264638-image1.jpeg|192px]]

| [[Image:Review_156654264638-image2.jpeg|center|264px]]

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(a)                                    (b)

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

 [[Image:Review_156654264638-image3.jpeg|282px]] </div>

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

(c)</div>

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Fig. 1. Preparation and testing of CPB samples: (a)mixing; (b)CPB samples; (c)UPV and UCS tests.

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

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{|

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| [[Image:Review_156654264638-picture- 1.svg|center|52px]]

| [[Image:Review_156654264638-picture- 2.svg|center|54px]]

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{|

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| [[Image:Review_156654264638-picture- 3.svg|center|51px]]

| [[Image:Review_156654264638-picture- 4.svg|center|52px]]

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{|

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| [[Image:Review_156654264638-picture- 5.svg|center|99px]]

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| [[Image:Review_156654264638-picture- 7.svg|center|99px]]

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 [[Image:Review_156654264638-image4.png|438px]] </div>

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

Fig. 2. Schematic diagram for UPV testing of the cubic CPB sample.</div>

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==3. Results and discussions==

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===3.1 Strength and ultrasonic properties of CPB samples===

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The USC development of the CPB samples with different mass fraction and cement-tailing ratio is illustrated in Fig.3. From this figure, it can be found out that USC values of the CPB samples increase with the increase of the cement-tailing ratio on the condition of the same mass fraction. This is because of the physical and chemical effects of the cementitious materials. Physically, a portion of the cementitious materials fills the pores or cracks within the CPB samples. Chemically, the other portion of the cementitious materials reacts with calcium hydroxide to form hydration products. Increasing binder dosage produces more hydration products which can improve the microstructure of CPB by reducing total porosity [23]. A Scanning Electron Microscope (Hitachi S-3400N) is used to conduct SEM observations on the CPB samples. The typical examples of the results of these SEM observations is illustrated in Fig. 4. On the microscopic view, the hydration products increases the strength of CPB in microscopic scale. Therefore, a larger dosage of the cementitious materials can lead to a higher USC value of CPB (eg. when preparing the CPB at the same mass fraction (72%) and curing time (28 days), cement-tailing ratio of 0.250:1 results in 4.96 MPa USC value while cement-tailing ratio of 0.100:1 leads to 2.05 MPa).

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It can also be observed from Fig. 3 that UCS values increase with the extension of curing time. This is because more and more hydration products (C-S-H and ettringite) are generated as the curing time increases. These products will fill the pore space within CPB and improve bonding between particles of tailings, leading to the increase of the strength of CPB [24].

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{|style="text-align: center;"

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| style="text-align: center;padding:10px;"|[[Image:Review_156654264638-image5-c.png|382px]]

| style="text-align: center;padding:10px;"|[[Image:Review_156654264638-image6-c.png|center|394px]]

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| style="text-align: center;font-size: 75%;"|(a)

| style="text-align: center;font-size: 75%;"|(b)

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| colspan="2" style="text-align: center;padding:10px;"|[[Image:Review_156654264638-image7-c.png|376px]]

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| colspan="2" style="text-align: center;font-size: 75%;"| (c)

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Fig. 3. Uniaxial compressive strength of CPB samples (a) curing time of 7 days(b) curing time of 14 days(c) curing time of 28 days

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

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{|style="text-align: center;"

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| style="text-align: center;padding:10px;"|[[Image:Review_156654264638-image8.png|222px]]

| style="text-align: center;padding:10px;"|[[Image:Review_156654264638-image9.png|center|228px]]

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|style="text-align: center;font-size: 75%;"|(a)  

| style="text-align: center;font-size: 75%;"|(b)

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| colspan="2" style="text-align: center;padding:10px;"|[[Image:Review_156654264638-image10.png|240px]]

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| colspan="2" style="text-align: center;font-size: 75%;"| (c)

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</div>

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Fig. 4. SEM images of CPB samples (mass fraction of 70%, cement-tailing ratio of 0.250:1) at different curing time: (a) curing time of 7 days; (b) curing time of 14 days and (c) curing time of 28 days.

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Figure 5 describes the stress and UPV of CPB samples prepared from different mass fraction and cement-tailing ratio on the condition of 28 days curing time. The UPV values of CPB samples increased with increasing cement-tailing ratio on the condition of the same mass fraction and the curing time. For instance, at the same mass fraction (72%), the CPB samples prepared at 0.250:1 of the cement-tailing ratio produce higher UPV values than those prepared at 0.100:1 of the cement-tailing ratio. The proportional relationship between the cement-tailing ratio and UPV can be ascribed to the fact that raising the content of cementitious materials results in generating more hydration products to fill the pore structures (UPV in air is lower than that in any mineral skeleton such as rock and cementitious materials),which in turn increases the UPV in CPB [25、26].

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From Fig. 5, it can also be discovered that the UPV values of CPB varies with the increase of the load stress. Before the stress reaches the USC, the fluctuation of UPV values is very small. After the stress reaches the USC, the UPV values of CPB rapidly decreases with the "cliff type" falling Characteristics. This is because the original crack and newly generated crack in the CPB samples lead to the fluctuation of the UPV values before peak stress. While after peak stress, a large number of microcracks expand greatly and the macroscopically fractured joints are formed rapidly. These phenomenons lead to the decline of pulse velocity in CPB samples, since the UPV values in air is lower than that in any mineral skeleton.

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{|style="text-align: center;"

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| style="text-align: center;padding:10px;"|[[Image:Review_156654264638-image11-c.png|376px]]

| style="text-align: center;padding:10px;"|[[Image:Review_156654264638-image12-c.png|center|376px]]

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|style="text-align: center;font-size: 75%;"|(a)  

| style="text-align: center;font-size: 75%;"|(b)

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| style="text-align: center;padding:10px;"|[[Image:Review_156654264638-image13-c.png|382px]]

| style="text-align: center;padding:10px;"|[[Image:Review_156654264638-image14-c.png|center|376px]]

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|style="text-align: center;font-size: 75%;"|(c)  

| style="text-align: center;font-size: 75%;"|(d)

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Fig. 5. Ultrasonic pulse velocity of CPB samples: (a) Ultrasound test results (0.250:1); (b) Ultrasound test results (0.125:1); (c) Ultrasound test results (0.100:1); (d) Ultrasound test results (0.083:1).

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===3.2 Damage constitutive equations of different backfills===

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Assuming the CPB is isotropic, according to the Lemaitre theory of strain equivalent [27], we have:

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<div id="_Hlk528854603" style="text-align: right; direction: ltr; margin-left: 1em;">

''σ=E ε(1﹣D)''                               (2)</div>

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Where ''σ'' is the effective stress; ''E'' is the elastic modulus;'' ε'' is the strain; ''D'' is the damage value. When ''D''=0, the backfill is no damage state; when ''D''=1, the backfill is in the course of absolute damage or failure.

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Due to the complicated damage mechanism, the morphology and distribution of microscopic defects in the composite materials are random. The strength of the material obeys the Weibull statistical distribution [28].

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From the relationship between the damage parameter ''D'' and the effective stress ''σ'', it can be seen that the damage parameter ''D'' of the CPB also obeys the Weibull statistical distribution. From the Weibull distribution of parameter ''D'', ''σ'', the statistical distribution equation of damage parameters can be obtained:

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<div style="text-align: right; direction: ltr; margin-left: 1em;">

{| class="formulaSCP" style="width: 100%; text-align: center;" 

|-

| <math>\, D\, =1-exp\left[ -{\left( \frac{\epsilon }{n}\right) }^{m}\right] \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \, (3)</math>

|}

</div>

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Where ''m'' is Weibull distribution shape parameters, ''n'' is the Weibull distribution scale parameters (where'' m, n'' <math display="inline">\geq</math>  0). Inserting Eq. (3) into Eq. (2):

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<div style="text-align: right; direction: ltr; margin-left: 1em;">

{| class="formulaSCP" style="width: 100%; text-align: center;" 

|-

| <math>\, \sigma \, =E\, \epsilon \, exp\left[ -{\left( \frac{\epsilon }{n}\right) }^{m}\right] \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (4)</math>

|}

</div>

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On the basis of stress-strain curves and considering boundary conditions, we can obtain:

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<div style="text-align: right; direction: ltr; margin-left: 1em;">

{| class="formulaSCP" style="width: 100%; text-align: center;" 

|-

| <math>\, \left\{ \begin{matrix}{\left. \sigma \right| }_{\epsilon ={\epsilon }_{p}}={\sigma }_{p}\\d\sigma /{\left. d\epsilon \right| }_{\epsilon ={\epsilon }_{p}}=0\\{\left. D\right| }_{d\sigma /d\epsilon =E}=0\\{\left. \epsilon \right| }_{\sigma =0}=0\end{matrix}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (5)\right.</math> 

|}

</div>

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Where ''ε<sub>p</sub>'' is the corresponding peak strain when the stress reaches the highest point at ''σ<sub>p</sub>'' in the Fig.6.

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There are two unknown variables in Eq. (4). By solving Eq. (5), we have:

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<div style="text-align: right; direction: ltr; margin-left: 1em;">

{| class="formulaSCP" style="width: 100%; text-align: center;" 

|-

| <math>\, m{\left( \frac{{\epsilon }_{p}}{n}\right) }^{m}=</math><math>1\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (6)</math>

|}

</div>

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<div style="text-align: right; direction: ltr; margin-left: 1em;">

{| class="formulaSCP" style="width: 100%; text-align: center;" 

|-

| <math>\, n=\frac{{\epsilon }_{p}}{{\left( \frac{1}{m}\right) }^{\frac{1}{m}}}\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \, (7)</math>

|}

</div>

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Combining boundary conditions and inserting Eq. (7) into Eq. (6):

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<div style="text-align: right; direction: ltr; margin-left: 1em;">

{| class="formulaSCP" style="width: 100%; text-align: center;" 

|-

| <math>\, m=\frac{1}{ln\left( \frac{E{\epsilon }_{p}}{{\sigma }_{p}}\right) }\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \, (8)</math>

|}

</div>

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Inserting Eq. (7) and Eq. (8) into Eq. (3):

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<div style="text-align: right; direction: ltr; margin-left: 1em;">

{| class="formulaSCP" style="width: 100%; text-align: center;" 

|-

| <math>\, D=1-exp\left[ -\frac{1}{m}{\left( \frac{\epsilon }{{\epsilon }_{p}}\right) }^{m}\right] \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (9)</math>

|}

</div>

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Eq. (9) is the damage evolution equation of the CPB material under uniaxial compression.

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Inserting Eq. (9) into Eq. (2), we can obtain damage constitutive equations of CPB:

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<div style="text-align: right; direction: ltr; margin-left: 1em;">

{| class="formulaSCP" style="width: 100%; text-align: center;" 

|-

| <math>\, \sigma =E\, \epsilon \, exp\left[ -\frac{1}{m}{\left( \frac{\epsilon }{{\epsilon }_{p}}\right) }^{m}\right] \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \, \, (10)</math>

|}

</div>

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According to experiment data and by solving Eq.(9) and Eq.(10),we can obtain the damage constitutive equations of different backfills (Table 3)

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According to the stress-strain curves above achieved by experiment, we can obtain the values of the elastic modulus'' E'', the peak stress ''σ<sub>p</sub>'' and the peak strain ''ε<sub>p</sub>'' By inserting these data into Eq (9) and Eq (10), we can obtain the damage constitutive equations (Table 3) and damage evolutions of different backfills (Table 4). And by calculating with these equations, we can obtain the stress-strain curves of different backfills (dashed lines of Fig.6). Compared with experiment curves ,the calculated results agree well with experiment data.

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

Table 3. Damage constitutive equation (70% mass concentration, curing 28days)</div>

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{| style="width: 100%;border-collapse: collapse;" 

|-

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Cement-tailing ratio

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Elastic modulus

​

''E''/Mpa

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Damage constitutive equation

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|The range of ''ε''

|-

|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|0.250:1

|  rowspan='2' style="border-top: 1pt solid black;text-align: center;"|471.38

|  style="border-top: 1pt solid black;text-align: center;"|471.38(''ε-''0.0100) exp[-0.178((''ε''-0.0100)/0.0148)<sup>5.56</sup>]+1.26

|  style="border-top: 1pt solid black;text-align: center;"|''ε''≤0.0248

|-

|  style="text-align: center;"|471.38''ε ''exp[-0.502 (''ε''/0.0248)<sup>1.99</sup>]

|  style="text-align: center;"|''ε''<span style="text-align: center; font-size: 75%;">></span>0.0248

|-

|  style="text-align: center;"|0.125:1

|  style="text-align: center;"|180.15

|  style="text-align: center;"|180.15(''ε''-0.0028) exp[-0.543(''ε''-0.0028)/0.0205)<sup>1.84</sup>]

|  style="text-align: center;"|

|-

|  rowspan='2' style="border-bottom: 2pt solid black;text-align: center;"|0.100:1

|  rowspan='2' style="border-bottom: 2pt solid black;text-align: center;"|111.66

|  style="text-align: center;"|111.66(''ε''-0.0059) exp[-0.280((''ε''-0.0059)/0.0191)<sup>3.57</sup>]

|  style="text-align: center;"|''ε''≤0.0250

|-

|  style="border-bottom: 2pt solid black;text-align: center;"|111.66''ε ''exp[-0.549(''ε''/0.0250)<sup>1.82</sup>]

|  style="border-bottom: 2pt solid black;text-align: center;"|''ε''>0.0250

|}

​

​

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

 [[Image:Review_156654264638-image15-c.png|396px]] </div>

​

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

Fig. 6. ''τ-σ'' curve of 3 kinds of cement-tailing ratio (70% mass concentration, curing 28d)</div>

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===3.3 Damage laws of different backfills===

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It is manifest in Table 4 that damage peak values (''D<sub>p</sub>'') of different backfills range from 0.395 to 0.422, and it increases with the increase of cement-tailing ratio.

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<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

Table 4. Damage evolution equation (70% mass concentration, curing 28days)</div>

​

{| style="width: 100%;margin: 1em auto 0.1em auto;border-collapse: collapse;" 

|-

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;vertical-align: top;"|Cement-tailing ratio

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Elastic modulus

​

''E''/Mpa

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Damage evolution equation

​

''D=''

|  style="border-top: 2pt solid black;border-bottom: 1pt solid black;text-align: center;"|Damage peak value ''D<sub>p</sub>''

|-

|  style="border-top: 1pt solid black;text-align: center;vertical-align: top;"|0.250:1

|  style="border-top: 1pt solid black;text-align: center;"|471.38

|  style="border-top: 1pt solid black;text-align: center;"|1- exp[-0.50205(''ε''/0.0248)<sup>1.99182</sup>]

|  style="border-top: 1pt solid black;text-align: center;"|0.395

|-

|  style="text-align: center;vertical-align: top;"|0.125:1

|  style="text-align: center;"|180.15

|  style="text-align: center;"|1- exp[-0.54257(''ε''/0.0205)<sup>1.84308</sup>]

|  style="text-align: center;"|0.419

|-

|  style="border-bottom: 2pt solid black;text-align: center;vertical-align: top;"|0.100:1

|  style="border-bottom: 2pt solid black;text-align: center;"|111.66

|  style="border-bottom: 2pt solid black;text-align: center;"|1- exp[-0.27998(''ε''/0.0191)<sup>3.57166</sup>]

|  style="border-bottom: 2pt solid black;text-align: center;"|0.422

|}

​

​

According to the damage evolution equations of different backfills, we can obtain the relationship between damage value and strain (shown in Fig.7). It can be observed from Fig.7 that the damage values grow gently with the increase of strain. To be more precise, the larger the cement-tailing ratio is, the more slightly the damage value increases. While after peak stress, the damage values go up steeply with the increase of strain, and the damage peak values get large with decreasing the ratio.

​

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

 [[Image:Review_156654264638-image16-c.png|348px]] </div>

​

<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">

Fig. 7. Relationship between damage value(''D'') and strain </div>

​

<span id='_Hlk500234948'></span>

​

==4. Conclusions==

​

In this study, the effects of mass fraction and cement-tailing ratios on the mechanical performance and ultrasonic properties of CPB samples are investigated. A total of 144 CPB samples (70.7 <math display="inline">\times</math> 70.7 <math display="inline">\times</math> 70.7mm) prepared at different mass fraction and cement-tailing ratio were subjected to the UPV and UCS tests at 7,14 and 28 days of curing times. Based on the experimental results, the following conclusions can be drawn:

​

(1) The USC values increased with the mass fraction and cement-tailing ratio as well as the extension of curing time. Increasing contents of cementitious materials produce hydration products which in turn improve the USC values of CPB.

​

(2) The evolution of UPV in CPB is similar with the development of the crack in CPB during loading stress. When the stress stands at its peak, the UPV values drop rapidly. Furthermore, the ultrasonic properties of CPB samples were consistent with their respective USC properties.

​

(3) There are different mechanical characteristics and damage laws in different backfills. Exactly, the larger the cement-tailing ratio is, the more slightly the damage value increases before the peak stress. The damage grows faster and breakage appears more suddenly after peak stress.

​

(4) Considering the difficulties of taking core samples from in situ CPB stopes for the determination of CPB strength with conventional compressive strength test, UPV test will allow mine operators/ owners for the rapid estimation of their in situ CPB characteristics.

​

==Declarations==

​

==Author contribution statement==

​

Bingwen Wang, Jian Liu: Analyzed and interpreted the data; Wrote the paper.

​

Lin Li, Yao Yu, Benyong Huo: Conceived and designed the analysis; Analyzed and interpreted the data; Contributed analysis tools or data.

​

Jie Liu: Contributed analysis tools or data.

​

==Funding==

​

<span id='OLE_LINK3'></span><span id='OLE_LINK4'></span><span id='OLE_LINK5'></span>This work was supported by National Key Research & Development Project of China [grant number 2018YFC0808403].

​

==Competing interest statement==

​

The authors declare no conflict of interest.

​

==Additional information==

​

No additional information is available for this paper.

​

==Acknowledgement==

​

The writers are thankful to the reviewers and the editor for their valuable suggestions to improve

​

the quality of the manuscript.

​

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