J. Cent. South Univ. (2020) 27: 267-276

DOI: https://doi.org/10.1007/s11771-020-4294-1

Quantitative investigation on micro-parameters of cemented paste backfill and its sensitivity analysis

LIU Lang(刘浪)^{1, 2}, ZHOU Peng(周鹏)¹, FENG Yan(冯岩)^{3, 4}, ZHANG Bo(张波)¹, SONG Ki-il(宋基一)⁵

1. Energy School, Xi’an University of Science and Technology, Xi’an 710054, China;

2. Key Laboratory of Western Mines and Hazards Prevention, Ministry of Education,Xi’an 710054, China;

3. School of Resource and Safety Engineering, Central South University, Changsha 410083, China;

4. Division of Minerals and Metallurgical Engineering, Lule University of Technology,Lule 97187, Sweden;

5. Department of Civil Engineering, Inha University, Incheon 402-751, Korea

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract: The mechanical properties of cemented paste backfill (CPB) depend heavily on its pore structural characteristics and micro-structural changes. In order to explore the variation mechanisms of macro-mechanical characteristics and micro-structure of CPB. CPB specimens with different mass concentrations prepared from the full tailings of Xianglushan Tungsten Ore were micro-tests. Moreover, acquired pore digital images were processed by using the pores (particles) and cracks analysis system (PCAS), and a sensitivity analysis was performed. The results show that as the mass concentration of CPB increases from 70% to 78%, the porosity, the average pore area and the number of pores drop overall, leading to a decline in the pores opening degree and enhancing the mechanical characteristics. As the mass concentration of CPB increases, the trend of fractal dimension, probability entropy and roundness is reduced, constant and increased, which can result in an enhancement of the uniformity, an unchanged directionality and more round pores. According to the definition of sensitivity, the sensitivities of various micro-parameters were calculated and can be ranked as porosity > average pore area > number of pores > roundness > fractal dimension > probability entropy.

Key words: cemented paste backfill; mass concentration; sensitivity analysis; micro-parameters

Cite this article as: LIU Lang, ZHOU Peng, FENG Yan, ZHANG Bo, SONG Ki-il. Quantitative investigation on micro-parameters of cemented paste backfill and its sensitivity analysis [J]. Journal of Central South University, 2020, 27(1): 267-276. DOI: https://doi.org/10.1007/s11771-020-4294-1.

1 Introduction

Backfill mining is arousing a great deal of attention and has become the mainly development tendency in underground mining technology. It has lots of advantages, including the effective regulation of gob via filling, the abatement of environmental pollution from mines and the reduction of ore dilution and loss indexes [1-8]. Full-tailings CPB is a type of novel filling material, which also possesses a lot of unique engineering superiority, since it has a wide source and is inexpensive. Therefore, investigating the compressive strength of full-tailings CPB is of great significance to backfill mining [9-12].

In recent years, scholars have conducted a great deal of research on the mass concentration proportions and micro-structures of CPB. For example, SHENG et al [13] examined the compressive strength of CPB under dynamic loads. YAO et al [14] employed the splitting method for testing backfill specimens with different proportions and concentrations, and acquired a peak load, peak displacement and stress/strain curves under different conditions. WOLFGANG et al [15] investigated the effects of cement types, water consumption and the curing period on the strength of CPB. QI et al [16-18] established an intelligent framework, through a series of papers, for predicting the mechanical properties of CPB. CARLOS et al [19] using an X-ray diffraction (XRD) and micro-structural analysis, analyzed the effect of the magnesium sulfate’s content on the micro-structural properties of MOS cement. XU et al [20] ascertained some micro-structural rules in the gelatinization and diagenesis of ultra-fine full-tailings under different conditions using an XRD, energy spectrum analysis and scanning electron microscopy (SEM). WANG et al [21] performed a quantitative analysis on soil micro- structures via image processing, and discussed the quantitative evaluation indexes for characterizing some structural elements, including the sizes, morphology and directionality of structural units and pores. XUE et al [22] explored the consolidation mechanism of saturated soft clay and measured its porosity with the aid of different microscopic means and tools. CHEN et al [23] investigated the compressive strength of specimens with different cement-tailings ratios and slurry concentrations after different curing periods, and analyzed the effects of various factors on the production of hydrates using the SEM scanning technique. CAO et al [24] employed the SEM and pores (particles) and cracks analysis system (PCAS) for examining the micro-structures of soft soil specimens under dynamic loads with cyclic stress ratios at different frequencies, and revealed the micro influencing mechanism of the cyclic stress ratio and frequency on the soil macro-deformation under wavy loads. ZHOU et al [25] performed laboratory consolidation tests, quantitatively analyzed the variation rules of porous characteristics under consolidation pressure by using SEM and computer image processing, and found that the change of consolidation pressure can significantly change the soft soil’s pore size, distribution, arrangement and morphology.

In summary, the previous studies have an emphasis on the mechanical properties of CPB from a macroscopic perspective, and the quantitative properties of soil and qualitative analysis of backfill from a microscopic perspective, but they have neglected the related correlation between the micro-structure and macroscopic mechanical properties of CPB. Furthermore, the sensitivity of micro-parameters of CPB has not been investigated in the literature.

This study focuses on the full-tailing CPB and analyzes the effect of different mass concentrations on the micro-structure of CPB. By SEM and the uniaxial compressive strength (UCS) tests, scanning images are processed by the PCAS micro quantitative analysis system to acquire the micro- structural parameters of CPB. Furthermore, micro- structural characteristics of CPB specimens with different mass concentrations, including the pore scale, arrangement and morphology, are quantitatively investigated, and the effect of the micro-parameters on macro-mechanical properties is characterized through a sensitivity analysis.

2 Materials and method

2.1 Test materials

In this study, the filling test used mainly full tailings from Xianglushan tungsten Ore, ordinary Portland cement at a strength grade of 425# (P.O42.5) and urban tap water. Using a laser diffraction particle size analyzer (MASTERSIZER 2000), the particle size distribution of full tailings from Xianglushan Tungsten Ore was measured in accordance with the basic particle size characteristics of tailings. Specifically, the specimens were collected from the dried full tailings via multi-point sampling; by means of an ultrasonic dispersion, the mortar was poured into the test chamber of the laser particle size analyzer via a pump, and the particle sizes were measured based on the principle of laser diffraction; finally, the data were processed using a computer and the test results were produced. Figure 1 displays the test results, which can be easily observed that the value of d₁₀, d₅₀ and d₉₀ is 11.8, 80.3 and 212.6 μm respectively, and the specific surface area (SSA) is 212.4 μm². The particle size non uniformity coefficient (d₆₀/d₁₀) is found to be 8.55. Optimal grading of the tailing particles should accord to the Thabo equation and ranges from 4 to 6. According to the measured particle size curve, the tailings specimens in the test include a small proportion of coarse particles, and these can be seen as the tailings that lack coarse particles. The natural grading is a relatively discontinuous grading. The measured results of the tailings proportions, unit weight, porosity and natural repose angle are listed in Table 1.

Figure 1 Grain size distribution of tailings

Table 1 Physical properties of tailings

When using an XRD for a phase qualitative analysis, the diffraction patterns are represented by the data of d and I (specifically, d represents the lattice spacing for the characterization of the diffraction line’s position, and I denotes the relative intensity of the diffraction line). In order to characterize the types of tailings qualitatively, the d-I curve was used as the fundamental basis for the qualitative phase analysis; and the measured d-I data set was compared with the standard d-I data set of the material with a known structure (i.e., the PDF card) to identify the existing phases in tailings. An X-ray diffractometer (D/MAX-RC, Rigaka Corporation, Japan) was used for the component analysis of tailings, which used a Cu target and the sample was taken via continuous scanning. Additionally, the operating voltage and current were set as 40 kV and 30 mA, respectively; both the emission and scattering seams were set as 1.0°; the receiving seam was set as 0.3000 mm; and the step width was set as 0.02°(2θ), the scanning speed was set as 0.1 (°)/s, and the scanning angle range was set as 10°-80° (2θ). Figure 2 displays the measured XRD pattern of tailings.

Figure 2 XRD pattern of tailings

2.2 Test process

During the test in this study, 4 identical CPB specimens were prepared, out of which 3 specimens were put under uniaxial compressive test and the remaining one was used for the SEM experiment. Firstly, referring to Table 2, the masses of cement, tailings and water in CPB were calculated. Next, the same amounts of tailings, cement and water were weighed and mixed uniformly. After stirring by hand for 5 min, the mixtures were poured into a cylindrical standard cast iron mold with a diameter of 50 mm and a height of 100 mm. It should be noted that the inner surface of the mold was coated with a layer of lubricating oil in advance, and a releasing agent with a concentration of 1.64% was also added in the release agent to demold easily. CPB slurry then finally and naturally compacted without any vibration. After the filling, CPB specimens were left for 24 h and demolded until it was fully formed. Prepared CPB specimens were labeled and placed in a constant temperature and humidity curing box for curing (temperature (20±1) °C, humidity (95±1) %). After curing for 28 d, CPB specimens were removed from the curing box for the SEM and UCS tests. The specific flow chart of the test is shown in Figure 3.

Table 2 Experimental design of CPB

Figure 3 Flow diagram of experiment

2.3 Preparation of SEM samples

SEM gets the advantages of high resolution, large magnification, wide field of view and strong sense of three-dimensional. Therefore, this study intends to produce SEM specimens [26]. CPB specimens were taken out from the curing box, and a small cylindrical electron microscope sample (diameter× mm×5 mm) was selected at the appropriate position. After the specimens were subjected to gold spray treatment for 180 s, an electron microscope scanning observation experiment was performed.

2.4 Quantitative analysis system

The SEM images consist of a series of pixels in a rectangular arrangement. In order to quantitatively characterize the micro-porous characteristics of CPB specimens with different mass concentrations, a digital image processing technique was used for extracting image information from a pixel matrix and accurately distinguishing the boundary between the skeleton particles and pores. In this study, using the microscopic quantitative test technique of the particle and pore identification and analysis system developed by Xi’an University of Science and Technology. SEM images were analyzed quantitatively in combination with the related theories in fractal geometry. After image processing, some quantitative statistical parameters, including the porosity, average pore area, the number of pores, roundness, probability entropy and fractal dimension, were obtained.

2.5 UCS test

After a 28-day curing period, CPB specimens were removed from the curing box. Both the upper and lower surfaces were polished, and the height and diameter of the specimens were measured by a Vernier caliper. The computer controlled 20 kN pressure was loaded at a constant rate of 1 mm/min to the CPB specimens up to destruction, the data were compiled and the uniaxial compressive strength of the CPB specimens was calculated, and the average of the three test pieces was taken as the final result.

3 Results and discussion

3.1 Analysis of relationship between porous structure and strength

Depending on the different mass concentration of CPB, the corresponding micro-parameters were obtained. Microstructure characteristics and variation rules of CPB were studied from the aspects of pore scale, morphology and arrangement. The relationship between microstructure parameters of cemented backfill and its uniaxial compressive strength was analyzed.

3.1.1 Change of pore scale

The porosity is equal to the ratio of the total pore area of the total area of the SEM image of CPB specimens. Figure 4 displays the variation characteristics of the UCS and porosity of CPB specimens with a mass fraction. Apparently, as the mass fraction increases, the porosity drops gradually and the UCS increases, suggesting that the porosity is negatively correlated with the UCS.

Figure 4 Relationship between porosity, UCS and mass fraction of CPB

The increase of mass fraction makes the hydrated gel particles increase, and the hydration product is usually stable at 28 d, and only a few needles are on the surface. Most of them are covered by flocs, and the gelation of the gel makes the CPB more compact, thus enhance the UCS [27, 28].

The average pore area of CPB specimens can reflect the pore size distribution [29]. Figure 5 displays the variations of the UCS and average pore area of CPB specimens with mass fraction. As the mass fraction increases from 70% to 78%, the average pore area drops and the UCS increases, with a maximum of 1.704 MPa. The reduction of the average pore area in CPB specimens can be attributed to the increasing mass of solids in CPB specimens, thereby reducing the pore spacing and making the micro-structure more complete. Accordingly, as the concentration of CPB increases, the pore spacing drops gradually, and therefore, the average pore area drops and the UCS increases. Therefore, for CPB specimens, the average pore area is negatively correlated with the UCS.

Figure 5 Relationship between average pore area, UCS and mass concentration of CPB

As showed in Figure 6, with the increase of the mass concentration of CPB, the number of pores decreases and the UCS increases. A smaller number of pores can be found since the backfill particles got close and were embedded in each other, and some pores were gradually compacted. Accordingly, the structure in CPB becomes more complete and cannot be easily destroyed, thereby leading to the increase of the UCS.

Figure 6 Relationship between number of pores, UCS and mass fraction of CPB

3.1.2 Change of pore morphology and its arrangement

The fractal dimension is a key parameter for characterizing the fractal properties quantitatively [30]. Figure 7(a) displays the variations of the fractal dimension with mass concentration and UCS. The calculated fractal dimension ranges from 1.10 to 1.22, which gradually drops as the mass concentration of CPB increases, accompanied by the gradual decrease of the pore spacing. At a mass fraction of 70%-74%, the calculated fractal dimension drops slowly; and as the mass fraction increases from 74% to 78%. The fractal dimension drops significantly. The main reason for the decrease of the fractal dimension is the increase of the pore uniformity due to the increasing mass fraction and decreasing pore spacing. As the mass fraction of CPB increases, the fractal dimension drops gradually and the UCS increases, suggesting that the fractal dimension is negatively correlated with the UCS [10].

Roundness, with a range of [0, 1], is a parameter for characterizing pore and particle shapes quantitatively [31]. A greater roundness suggests that the particle moves closer to a circle. Figure 7(b) shows the relationship between roundness, the UCS and the mass fraction. As the mass fraction increases, both the roundness and UCS increase gradually. Roundness is significantly correlated with the UCS. The particles with a denser arrangement formed more perfectly around the particle skeleton; correspondingly, pores became more circular and the compressibility of CPB dropped, which then resulted in the increases of the roundness and UCS.

Figure 7 Relationship between macro and micro-morphology of CPB:

Probability entropy can reflect the orderliness of the arrangement of the micro-structural units and also describe in the overall arrangement pattern of the pores [32]. Figure 8 displays the variations of the probability entropy and UCS with a mass fraction. At a mass fraction of 70%-78%, the probability entropy is large and exceeds 0.970 overall, suggesting that there is a disordered pore arrangement and no obvious directionality. As the mass fraction increases, the probability entropy drops gradually, while the orderliness and directionality of the pore arrangement increase;accordingly, the pores exhibit a more ordered arrangement and a more stable structure, thereby resulting in the decline in compressibility and the increase of the UCS of CPB.

Figure 8 Relationship between probability entropy, UCS and mass concentration of CPB

3.2 A sensitivity analysis of micro-parameters

3.2.1 Sensitivity analysis method

The micro-parameters of CPB specimens exhibit changes to varying degrees with different mass fractions. In order to explore the effects of the micro-parameters on the UCS, this study used the sensitivity as the index and analyzed the sensitivities of the micro-parameters quantitatively; the results are listed in Table 3.

Sensitivity refers to the ratio of the relative variation amplitude of micro-parameter to the relative variation amplitude of the UCS:

                    (1)

where S denotes the sensitivity of the parameter, Y denotes micro-parameters after a change, Y₀ denotes the state variable under a reference condition, P denotes the UCS after a change and P₀ denotes the value of parameter under a reference condition.

A positive sensitivity coefficient suggests that both the variate and parameter exhibit identical variation tendencies; in other words, the variable increases or decreases with the increase or decrease of the parameter. A negative sensitivity coefficient suggests that the variation and parameter exhibit opposite variation tendencies.

3.2.2 Results of sensitivity analysis

Using the initial variables as the reference, the relevant parameters change constantly with the variation of the mass concentration. Through sensitivity analysis on 6 sets of micro-parameters, 24 sensitivities can be acquired, which fall within a range of [-0.219, +0.097]. Due to a great fluctuation, the data of sensitivities were averaged for a further analysis and comparison. More conveniently, the calculated sensitivities were classified into four levels from insensitivity (Level 1) to most sensitivity (Level 4), with the detailed classification method presented in Table 4. The corresponding plus/minus sign represents the positive/negative correlation between the micro- parameter and UCS.

Table 3 Sensitivity of micro-parameters of CPB

CPB’s porosity is the most sensitive, with a calculated sensitivity of -0.138, which can be deemed to be Level 4. Accordingly, the porosity imposes the most significant effect on CPB’s strength. The porosity and compressive strength of CPB exhibit opposite variation tendencies, and therefore, the sensitivity of the porosity of strength is negative. The lower CPB’s porosity, the higher the UCS. This is due to the fact that CPB with a lower porosity has a more complete inner structure and is more difficult to crush.

Table 4 Sensitivity classification of micro-parameters

Sensitivity of CPB’s average pore area is -0.083, suggesting that the average pore area is quite sensitive to the UCS and can be classified as Level 3. A change of the pore area can have a significant effect on the CPB strength. With the decrease of the average pore area, the spacing between the particles in CPB also drops to ensure that the micro-structure more uniform and enhance its strength. Therefore, the average pore area is negatively correlated with the UCS, i.e., the calculated sensitivity of the average pore area is negative.

The number of pores in CPB is also sensitive to the UCS, with a sensitivity of -0.078, which can also be classified as Level 3. With a decreasing pore number, the small pores are compacted by the backfill particles, and CPB’s UCS increases. Accordingly, the sensitivity of the number of pores in the UCS is negative.

CPB’s probability entropy is the most insensitive to the UCS, with a sensitivity of -0.005. Apparently, probability entropy is a Level 1 index and imposes the least effect on CPB’s UCS. The calculated probability entropy has no obvious change. However, the pore arrangement became more directional and the UCS was affected slightly. Probability entropy and UCS of CPB underwent the variations in opposite directions, and therefore, the sensitivity of the probability entropy of the UCS is negative.

CPB’s fractal dimension is also a Level 1 index in terms of sensitivity, which is also insensitive to the UCS, with a sensitivity of -0.027. The fractal dimension imposes a slight effect on CPB’s UCS, but greater effects on the probability entropy. The fractal dimension of CPB and UCS exhibit opposite variation tendencies, and therefore, the sensitivity of the fractal dimension to the UCS is negative. This can be attributed to a reduced pore spacing and enhanced uniformity with the decrease of the fractal dimension.

Sensitivity of CPB’s roundness is 0.070, suggesting that the roundness is less sensitive and can be classified as Level 2. Accordingly, the roundness imposes a slight effect on CPB’s UCS. The roundness and UCS exhibit identical variation tendencies, so the sensitivity of the roundness is positive. Accordingly, if the pores are closer to standard circles in shape, the compressibility is lower and the UCS is greater.

UCS of CPB is subjected to a lot of micro-parameters. For an easier comparison, the proportions of the sensitivities of the various parameters of the total sensitivity were calculated to display the effects of the above 6 micro-parameters on the uniaxial compressive sensitivity. Figure 9 shows the comparison results of the sensitivity.

Figure 9 Sensitivity ratio of micro-parameters

4 Conclusions

1) The mass concentration of CPB can affect the porosity and average pore area greatly. As the mass concentration increases from 70% to 78%, the porosity and average pore area of CPB specimens drop overall. With the decreases in the total porosity and average pore area, the pore opening drops and the mechanical properties increase.

2) The mass concentration of CPB also affects the fractal dimension, probability entropy and roundness. With an increase in the mass concentration, the fractal dimension decreases, probability entropy exceeds 0.97 overall, and the roundness also increases. Moreover, the size difference among the pores drops, the distribution of pores exhibits no obvious directionality and orderliness, while the pores are closer to circles in shape.

3) The effects of the micro-parameters of CPB on the UCS were also examined. The porosity’s sensitivity is the greatest, followed by the average pore area, the number of pores, the roundness and the fractal dimension, whilst the probability entropy’s sensitivity is the lowest.

In future studies, we will consider some factors such as cement-tailings ratio, curing time, curing temperature and phase change material to study the response relationship between the microstructure and macroscopic mechanical properties of CPB. The research results of this paper have guiding significance for promoting the research, development and further improvement of CPB.

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(Edited by HE Yun-bin)

中文导读

胶结充填体微观参数定量分析及敏感度试验研究

摘要：胶结充填体的力学性能很大程度上取决于其孔隙结构特征及微观结构的变化。为探究胶结充填体的宏观力学特性和微观结构的变化机理，以香炉山钨矿的全尾砂为试验材料，通过对不同质量浓度的胶结充填体开展微观试验，获得的孔隙数字图像采用颗粒及孔隙识别与分析系统(PCAS)进行处理并进行敏感度分析。结果表明：随着胶结充填体质量浓度的增大(由70%增大到78%)，孔隙率、平均孔隙面积、孔隙数的总体变化趋势减小，导致孔隙张开的程度变小使其力学特征增强；随着胶结充填体的质量浓度对分形维数、概率熵和圆形度总体的趋势是减小、不变和增大导致均一化程度提高、定向性保持不变和孔隙更接近圆形。按照敏感度的定义，计算微观参数敏感度，其敏感度排序为孔隙率>平均孔隙面积>孔隙数>圆形度>分形维数>概率熵。

关键词：胶结充填体；质量浓度；敏感度分析；微观参数

Foundation item: Projects(51674188, 51874229, 51504182) supported by the National Natural Science Foundation of China; Project (2018KJXX-083) supported by Shaanxi Innovative Talents Cultivate Program-New-star Plan of Science and Technology, China

Received date: 2018-11-17; Accepted date: 2019-05-21

Corresponding author: LIU Lang, PhD, Professor; Tel: +86-15829310227; E-mail: liulang@xust.sn.cn; ORCID: 0000-0001-9536-0508; FENG Yan, PhD, Lecturer; Tel: +86-15874166544; E-mail: yan.feng@csu.edu.cn; ORCID: 0000-0002-8187- 8872