Effects of width-height ratio and roof-floor strength on the mechanical characteristics of cemented gangue backfill pier-column

Cemented gangue backfill pier-column (CGBP) which was made of coal gangue, fly ash, cement, and water is the supporting component of the goaf in partial backfill mining or constructional backfill mining for controlling the surface subsidence of coal mining. The width-height ratio and roof-floor strength directly affect the bearing capacity of CGBP under axial compression, which is essential for the design of CGBP. Herein, the effect of width-height ratio (1:3–1:1) on the mechanical characteristics of CGBP with different curing ages under uniaxial compression was system studied through experiment, and the damage process was analyzed by ultrasonic equipment and DIC. Based on the experimental results and discrete element theory, a three-phase numerical model for CGBP was established, which considered the real aggregate shape and distribution and the mechanical characteristics of each phase. Then, the effects of the end friction coefficient and the strength ratio of roof-CGBP-floor combination on the strength and failure characteristics of CGBP (large width-height ratio: 1:1–4:1) were investigated. The results show that CGBP shows the width-height ratio effect obviously and the strength and ductility increase with the increase of the width-height ratio, and the width-height ratio effect increases with the increase of curing age and strength ratio. The end friction constraint is the main reason for the width-height ratio effect, and the higher the friction coefficient is, the larger the width-height ratio effect shows, and the width-height ratio effect disappears without end friction constraint. The increase of the width-height ratio of CGBP and the strength ratio of the roof-CGBP-floor combination increases the strength of the combination. Whether the strength of the combination is greater than that of CGBP may have a roof-floor strength threshold or a strength ratio threshold, which are between 31.44–54.11 MPa and 3.75–6.44, respectively. When the strength of the roof and floor is different, the strength of the combination is mainly controlled by the weak carrier and increases with the increase of the strength of the weak carrier. The peak strain energy of CGBP and combination increases with the increase of end friction coefficient, width-height ratio, and strength of roof and floor. The experimental and simulation results can be used to guide the design of CGBP in constructional backfill mining or partial backfill mining.


Introduction
The cemented gangue backfill material (CGBM) is a mixture made of coal gangue waste, fly ash waste, cement, and water (Zhang and Wang 2007). Owing to its relatively high strength and fine pumping performance, it has been extensively used in backfill mining for coal resources and controlling surface subsidence (Wu et al. 2015;Wang et al. 2021a;Chen et al. 2020a;Hou et al. 2020;Liu et al. 2021a;Li et al. 2020a;Sun et al. 2019;Wu et al. 2020;Wu et al. 2022). Backfill mining is also an effective mining method for the "Three Under" coal resources, under the building, water, and railway, which can minimize the impact of mining on the original environment (Sun et al. 2018;Zhang et al. 2021Zhang et al. , 2017Lu et al. 2017;Chen et al. 2016). However, because of the high cost of cement and fly ash and the limited raw material of coal gangue, full backfilling mined-out space faces a high cost which hinders the promotion of the backfill mining technology, and thus the partial backfill mining method and the constructional backfill mining method were proposed, and the roof of the goaf was supported by the pier columns made of CGBM, as shown in Fig. 1 (Zhu et al. 2017(Zhu et al. , 2019a(Zhu et al. , 2019bDu et al. 2019a;Feng et al. 2019;Liu et al. 2020;Xu et al. 2015Xu et al. , 2007. The strength of the cemented gangue backfill pier-column (CGBP) will grow quickly, preventing the deformation of overlying strata and controlling the surface subsidence (Zhang et al. 2021;Lu et al. 2017;Zhu et al. 2019b;Guo et al. 2022). Besides, the mining method using CGBP constructs a large amount of underground space in the goaf which could be used not only as an underground reservoir (Bian et al. 2021) but also for underground CO 2 storage (Wang et al. 2022a), which has broad application prospects. The CGBP in the goaf is usually not laterally constrained and only loaded by the roof Du et al. 2019bDu et al. , 2019c. Therefore, the mechanical properties of CGBP under axial compression are the key parameters for the design of partial backfill mining or constructional backfill mining.
Geometry as an external factor affecting the compressive strength of a pillar is an important variable in pillar design, and the geometry effect includes the size effect and shape effect (Moomivand and Vutukuri 1996). One of the main purposes of CGBP design is to determine the optimum geometry of CGBP, and thus, geometry effect of CGBP can not be ignored, including the size effect and the width-height ratio effect . The size effect of the CGBM specimen has been investigated by many researchers, and they tested the mechanical properties of the cubic or cylinder CGBM specimen with different sizes (Yilmaz et al. 2015;Cheng et al. 2019;Gan et al. 2018;Guo et al. 2021;Wang et al. 2020;Xu et al. 2016). They found that the uniaxial compressive strength of the CGBM specimen decreases with the increase in size, the failure mode of the CGBM specimen gradually changes from splitting failure to shearing failure with the increase in size, and the dissipated energy is an intrinsic factor affecting its compressive strength. According to the test results, the calculation formula of size effect for the compressive strength and the damage constitutive model of CGBM with different sizes are established, which can provide a reference for the CGBP design. For actual backfill mining engineering, however, the height of CGBP has been determined by the thickness of the coal seam, and therefore, the design of CGBP has to focus on the width-height ratio. As shown in Table 1, different width-height ratios of pillars are adopted in the design of the backfill mining, and thus, the mechanical properties of CGBP with different width-height ratios are essential for the design of the constructional backfill mining or partial backfill mining. The effect of height to diameter ratio (25-50:50 mm) on dynamic characteristics of cemented tailings backfills with fiber reinforcement through impact loading was studied (Wang et al. 2022b). However, the mechanical properties 1.5:0.9 (Sun et al. 2012) 60:2.7 (Zhu et al. 2019a) 7.1:0.82 (Xu et al. 2015) 6:2 (Xie et al. 2016) 5.6:0.82 (Zhu et al. 2017) of CGBP with different width-height ratios under axial compression are still unclear and need to be systematically investigated. For partial backfill mining or constructional backfill mining, CGBP needs to bear partial pressure from the roof at the early curing age, and then the pressure of the roof increases with the advancement of the mining face (Cao et al. 2020;Chen et al. 2020a;Lu et al. 2017;Ran et al. 2021;Guo et al. 2020;Feng et al. 2022;Ghirian and Fall 2016;Yilmaz et al. 2014;Yilmaz et al. 2009;Liu et al. 2021b). In other words, the pressure will increase with the increase of the curing age (Zhang and Zhang 2020). Therefore, the mechanical properties of CGBP at the early curing age are critical for the design of CGBP, and the width-height ratio effect of CGBP at the early curing age also needs to be studied (Chen et al. 2020a). On the other hand, the reason for the geometry effect of the rock attracted many researchers, forming two reasons to explain the geometry effect. One is that the geometry effect originates from the microscopic inhomogeneity of the rock material (You and Hua 1997;You and Zou 2000), and the other is that it originates from the constraints at the end of the specimen (Yang et al. 2005;Sun et al. 2014). For the large size of CGBP in the field, there is no structural face inside that can degrade the mechanical properties of CGBP. Therefore, the effect of end constraint on the width-height ratio effect of CGBP needs to be clarified.
As an important carrier of backfill mining engineering, the backfill structure does not refer to a separate backfill, but a system structure composed of the backfill and the surrounding rock (Fig. 1), supporting the overlying strata and maintaining the stability of the goaf. It is essential to study the failure mechanism of the roof-backfill-floor combination. Chen et al. studied the mechanical properties of the backfill-hard roof combination under uniaxial compression and found that the strength of the combination is larger than that of the backfill and is smaller than that of the hard roof (Chen et al. 2020b). He et al. studied the failure properties of the backfill-rock combination and found that the content of the tailings has a significant influence on the cracking process and AE characteristics of the backfill (He et al. 2021). Yin et al. studied the effect of interface angles on failure properties of rock-backfill under uniaxial compression and found that there are three macro-failure patterns, and with the increase of interface angle, the strength and elastic modulus decreased (Yin et al. 2021). Zhao et al. studied the synergistic deformation and mechanical properties of the backfill-rock combination and found that the overall strength of the combination is similar or smaller to that of the single backfill specimen, and the elastic modulus increases as the strength ratio of the two specimens decrease (Zhao et al. 2022). Besides the synergistic deformation of the backfillbackfill combination was also studied . The strength of the roof-backfill-floor combination is an essential index for the design of backfill mining. The existing researches focus on the different backfill and single strength of the roof; however, just as in the coal-rock combination (Yang et al. 2020a), the strength of the roof and floor have significant effects on the mechanical responses of the roof-backfill-floor combination. Therefore, the mechanical properties of the roof-backfill-floor combination under different strength ratios also need to be studied.
In this paper, the width-height ratio effect (small: 1:3-1:1) and the effect of curing age on the width-height ratio effect of CGBP were studied through the experiment, and the damage process was analyzed by ultrasonic equipment and DIC (digital image correlation). A three-phase CGBP simulation model based on discrete element theory and real coarse aggregate distribution and shape was established, and the experimental results were used to calibrate the meso-parameters of the CGBP simulation model. Then, the uniaxial compressions of CGBP (large width-height ratio: 1:1-4:1) and corresponding roof-backfill-floor combination were accurately simulated. The effects of the end constraint and the strength ratio of the combination on the mechanical properties of CGBP and combination were studied, respectively. Moreover, whether the strength of the roof and floor is the same or not may affect the mechanical properties of the combination, and thus both situations were investigated. Finally, the width-height ratio effect in the design of CGBP in the field was discussed and the failure mechanism of the combination was analyzed.

Raw material and specimen preparation
To satisfy the pumping and strength requirements, the cemented gangue backfill material (CGBM) was mixed with coal gangue waste (950 kg/m 3 ), class F fly ash waste (380 kg/m 3 ), ordinary Portland Type-42.5 cement (180 kg/ m 3 ), and tape water (350 kg/m 3 ) (Wang et al. 2021a;Guo et al. 2020). Fly ash waste was obtained from the power plant of the Fenxi mining group. Coal gangue waste was collected from Tunlan Colliery, Shanxi province, China. After the second class cracked, as shown in Fig. 2, coal gangue was divided into three groups (fine: 0-5 mm, medium: 5-10 mm, coarse: 10-15 mm) according to the nominal diameter, which counted for 30%, 35%, and 35% of the mass of the total aggregate, respectively. The fineness module of 0-5 mm aggregate was 2.69. The physical characteristics and chemical components of fly ash and cement are shown in reference (Ran et al 2021). The particle size distribution of fly ash and coal gangue was shown in reference (Ran et al. 2021). The diameter of the testing specimen should be larger than 5 times the diameter of the coarse aggregate, and thus the fresh CGBM was poured into three group molds with the dimension of 100 × 100 × 100 mm 3 , 100 × 100 × 200 mm 3 , and 100 × 100 × 300 mm 3 . Each group cast twelve specimens. The fresh CGBM was compacted on a vibrating table for 10 s. All specimens were demoulded after casting for 24 h and then placed in a curing room with a standard environment of 20 ± 3 ℃ for 3 days, 7 days, 14 days, and 28 days, respectively.

Testing process
A universal testing machine with a maximum load capacity of 100 kN (WDW-100) was utilized in the uniaxial compressive experiment with a displacement rate of 0.6 mm/min, as shown in Fig. 3. The ultrasonic pulse velocity (UPV) and DIC were used to study the damage process of the CGBP specimen during the loading process. Three specimens were repeated for each group under different curing ages and different width-height ratios. Before the uniaxial compression tests, the specimens were taken out from the curing room  The internal damage evolution process of CGBP was monitored by non-metallic ultrasonic equipment (NM-4B) (Jiang et al. 2020). Before the compression test, the positions (top, middle, and bottom) of the probes were fixed as shown in Fig. 2. The detection frequency of the ultrasonic detector at each position from top to the bottom was once every 10-15 s. The detectors of the ultrasonic equipment were handed by the same person to make sure the same detection standard (Fig. 3). To ensure good contact between the probes and the specimen surface, Vaseline was used as the coupling agent between the test specimen and transducers.
DIC is a surface monitoring method, which can be utilized to reflect the surface deformation and crack propagation of the specimen under loading (Wang et al. 2022c). To analyze the surface damage evolution process of CGBP under uniaxial compression, as shown in Fig. 3, black and white speckles were evenly spread on the surface, and the surface crack propagation of specimens was monitored by a DIC monitoring system which was constituted of a camera (Nikon D7100) and a computer. The camera's acquisition frequency was once every 5 s. Ncorr is an open-source 2D DIC MATLAB program, and the surface strain characteristics of the specimen were obtained by the MATLAB program (Blaber et al. 2015).

Numerical simulation
The discrete element method (DEM) can simulate large deformation, discontinuity, and material anisotropy. The basic principle of DEM is to express the discontinuity as a group of rigid circle particles, and derive the movement trend of the entire discontinuity through the motion equation of the rigid particles (Potyondy 2007;Potyondy and Cundall 2004). It has been widely used to simulate mechanical processes such as rock, concrete, and cemented material (Li et al. 2021a;Song et al. 2019). Different mesoscopic contact models can be assigned to the contact between rigid circle particles to express different macroscopic mechanical properties of the material, such as elasticity, plasticity, and viscosity.

Three-phase numerical simulation model for CGBP
Cemented gangue backfill material is the viscoelastic plastic body, and the linear parallel bond model can well reflect the elastoplasticity of cemented materials. In CGBP, the mortar acts as a bonding material between the coarse aggregates (coal gangue), and therefore force and moment can be transferred between the aggregates. When the stress caused by the relative movement between the aggregates exceeds the bonding strength, the linear parallel bond will break and a microcrack will form, and then the contact will degrade to the linear contact model (Li et al. 2021a;Ding et al. 2018). As shown in Fig. 4, the linear parallel bond model is a bonding model between particles, which is used to express the mechanical properties of CGBP.
To simulate the large width-height ratio of CGBP, the CGBP specimens with different sizes (100 × 100 × 100-100 × 100 × 400 mm 3 ) were cut along the long axis to collect the actual shape and distribution of the coarse aggregate in the Fig. 4 The simulation model of CGBP and roof-backfill-floor combination. a Actual aggregate shape and reconstructed aggregate shape. b Schematic diagram of CGBP three-phase material and microcracks.
c Calibration process of meso-parameters of CGBP with width-height ratio from 1:1 to 1:3. d Simulation model of CGBP with width-height ratio 4:1. e Simulation model of roof-backfill-floor combination CGBP specimen, as shown in Fig. 4a. The vertical photo of the section of the specimen was taken by a high-definition camera (Nikon D7100) and then CAD was used to obtain the outline of the coarse aggregate, and finally, the outline was used to group the particles generated by the initial numerical model. The initial numerical model of CGBP was generated by ball particles with a maximum radius of 0.48 mm and a minimum radius of 0.32 mm.
Cemented gangue backfill material is a multiphase combination material. According to the difference in the strength of each phase, the contact is divided into three types: the contact between coarse aggregate, the contact between cement mortar, and the contact between coarse aggregate and cement mortar. Figure 4b shows the microscopic morphology of the CGBP specimen between aggregate and mortar after uniaxial compression. The coarse coal gangue aggregate and cement mortar in the specimen is relatively complete without damage and microcrack. However, there are several microcracks at the interfacial transition zone (ITZ). Therefore, to imitate the mechanical properties of CGBP, the DEM model of the three-phase CGBM was established. Figure 4c shows the calibration models of the CGBP specimen with a width-height ratio from 1:1 to 1:3, which was the same as the experiments. Figure 4d shows the simulation model of the CGBP with a width-height ratio of 4:1. Figure 4e shows one of the simulation models of the roofbackfill-floor combination. The initial model of the roof and floor were created by ball particles with a maximum radius of 0.6 mm and a minimum radius of 0.4 mm. The widthheight ratio of CGBP is 4:1, and the height of the roof and floor is half of the height of CGBP. To simulate the mechanical properties of the interface transition zone between roof and CGBP and between floor and CGBP, the contact at the interface transition zone (Fig. 4e) was applied to a linear parallel bond model which can imitate the bonding of CGBM after the hydration of cement and fly ash.

Calibration of meso-parameters and realization of the loading process
The meso-mechanical parameters of the numerical model are calibrated according to the failure characteristics and stress-strain curve of CGBP with width-height ratios from 1:1 to 1:3. It is assumed that the meso-parameters and the macro-parameters are linear, and the mutual affection of the meso-parameters is ignored in the calibration process (Li et al. 2021a). After the preliminary calibration, the mesoparameters of the CGBP model are slightly modified to meet the experimental results. Figure 5 shows the stress-strain curve of the simulation CGBP model and the strength of the simulation CGBP model with width-height ratios of 1:1 to 1:3. It can be seen that the mechanical properties of the numerical model are similar to the real CGBP specimen. In addition, the failure modes of the numerical model of CGBPs are the same as the real CGBP specimen, which proves that the meso-parameters of CGBP can express the width-height ratio effect of the CGBP under uniaxial compression. Table 2 shows the meso-parameter calibration results of the numerical model of the CGBP specimen under uniaxial compression. Figure 6 shows the uniaxial compressive strength (UCS) and elastic modulus of CGBP under different curing ages and different width-height ratios. From Fig. 6a, the UCS of CGBP increases with the increase of curing age and increases with the increase of width-height ratio. Furthermore, the width-height ratio effect of strength increases with the increase of curing age. For example, the UCS of CGBP at the curing age 28 days with the width-height ratio of 1:1 is 1.29 times larger than that with the width-height ratio of 1:3; however, the UCS ratio at the curing age 7 days is 1.08. This means that the width-height ratio effect of CGBP affects by the curing age and the design of CGBP should consider this curing age effect, especially for CGBP which needs to bear the pressure of the roof at early curing age. From Fig. 6b, the elastic modulus of CGBP decreases with the increase in width-height ratio and increases with the increase of curing age. The elastic modulus of CGBP also shows the widthheight ratio effect, and the higher the curing age is, the more obvious the width-height ratio effect will be. Figure 7 shows the stress-strain curve of CGBP under uniaxial compression at different curing ages and different widthheight ratios. The stress-strain curve can be divided into four sections, including the initial compaction stage, elastic compression stage, plastic damage stage, and residual bearing stage. The UCS and elastic modulus of CGBP show the width-height ratio effect and the residual bearing strength and peak strain at the peak stress increase obviously with the increase in width-height ratio. The smaller the widthheight ratio is, the obvious brittle characteristics of CGBP will be. After the peak stress, the decreasing rate of the stress decreases with the increase in the width-height ratio, and CGBP with a large width-height ratio shows stronger  ductility performance. Furthermore, the ductility characteristics of CGBP are affected by the curing age, the smaller the curing age is, the stronger the ductility properties show, and the decrease rate of stress after peak stress is much slower. That is why the width-height ratio effect of CGBP increases with the increase of curing age. Figure 8 shows the failure pattern of CGBPs after uniaxial compression. Figure 8a shows the failure pattern of CGBP at curing age 28 days. The failure patterns of CGBPs with different width-height ratios are different. For the widthheight ratio of 1:3, because of the small tensile strength, the specimens have many macrolongitudinal splitting cracks which are parallel to the axial direction and a few specimens show the shear crack along with the whole specimen, which means that the failure pattern at a width-height ratio of 1:3 is mainly longitudinal splitting and accompanies with the single shear failure. When the width-height ratio is 1:2, the failure pattern is mainly single shear failure and partial conjugate oblique shear failure. However, for the widthheight ratio of 1:1, the failure pattern only shows the conjugate oblique shear failure. Overall, with the increase in the width-height ratio, the failure pattern of CGBP changes from splitting failure to single shear failure and then to the conjugate oblique shear failure. For Fig. 8b and c, the curing age affects the failure pattern of CGBP. The failure patterns of the specimens with the width-height ratio of 1:3 and 1:1 at the curing age 14 days are similar to the failure pattern at the curing age 28 days, respectively. However, for the with-height ratio of 1:2, the specimen at curing age 14 days shows more conjugate oblique shear failure and few specimens show single shear failure. For the curing age 7 days, the failure patterns of the specimens are basically similar to that at the curing age 14 days. However, for the width-height ratio of 1:3, the specimens show more single shear failure and conjugate oblique shear failure.

Failure characteristics
From the above analysis, there is a relation between the width-height ratio, strength, and failure pattern. The strength of the specimen with the conjugate oblique shear failure is larger than that of the single shear failure and is larger than that of the longitudinal splitting pattern. The larger the width-height ratio is, the stronger the restraint on the middle of the specimen from the lateral restraint on the end face of the specimen will be, which makes the specimen exhibit a conjugate oblique shear failure. The direct reason for the different failure patterns of the specimen is the different hoop effects caused by the ends friction constraint. The hoop  effect has a limit affecting zone, for the large width-height ratio, the middle of the specimen can be restrained by the surrounding friction stress, and the surrounding stress can be regarded as hoop restraint stress and increase the strength. On the other hand, the curing age can also affect the failure properties of CGBP, and the early the curing age is, the better the ductility shows, and the CGBP specimen shows better integrity and avoids structural damage, like splitting failure. Figure 9 shows the surface horizontal strain of CGBP with different width-height ratios under axial compression at the early curing age of 3 days. Through the DIC strain analyses, it can be seen how the cracks are generated and multiply under the cracks connection. As the pressure continues to be applied, the strain range continues to increase.

DIC surface strain characteristics
Comparison of the failure patterns of the CGBPs at different width-height ratios, the failure pattern of the specimen with a width-height ratio is 1:1 is a conjugate oblique shear failure, and the failure pattern of the specimen with a width-height ratio of 1:3 also shows a conjugate oblique shear failure, which can increase the strength of the specimen. The DIC monitoring results improve that, because of the better ductility of the CGBP at early curing age, the small width-heigh ratio CGBP will not show the splitting failure pattern and the bearing capacity of the CGBP can be increased. Therefore, the width-height ratio effect of CGBP is not obvious at the early curing age and will increase with the increase of the curing age. Figure 10 shows the change process of UPV of the testing specimens under uniaxial compression. Obviously, the UPV of CGBP increases with the increase of the curing age. Figure 10a-c shows the change process of UPV under different curing ages at a width-height ratio of 1:3. The change process of UPV includes three processes, the stable stage, the slowly decreasing process, and the quickly decreasing process. During the compaction and elastic stage, the UPV keeps stable with the increase of stress because no macrocracks produce. When the stress reaches the plastic stage, the UPV decreases gradually, and macrocracks produce inside the specimen. After the peak stress, the UPV drops rapidly with the increase of macrocracks. From the monitoring results of the UPV at different locations (top, middle, and bottom), the failure of the specimen results from the damage in the local position, and the failure of CGBP is a non-uniform damage process. Once a certain position is damaged, the crack at that position will continue to accumulate, forming two situations. One is that the damage increases rapidly, which leads to the rapid destruction of the position, forming the single shear failure, and then the entire CGBP is rapidly destroyed. The other is that the damage is transmitted to the adjacent position, and then the damage of the adjacent position also begins to increase, forming the splitting failure pattern and finally causing the instability of CGBP. The failure of CGBP with a width-height ratio of 1:3 is similar to structural instability, which causes a lower strength. This situation is gradually improved as the width-height ratio of CGBP increases. Compared with the CGBP specimens with the width-height ratio of 1:2 and 1:1, the larger the width-height ratio is, the better the integrity shows during the compression process.

Ultrasonic pulse velocity properties
For the effect of curing age on the damage process of CGBP (Comparision of Fig. 10a-i), the larger the curing age is, the more obvious brittleness shows during the damage process. After the peak stress, the UPV of the specimen at curing age 28 days drops more quickly than that of other curing ages, and the earlier the curing age is, the slower the dropping process of UPV will be. This proves that the early age CGBP shows better ductility properties and the expanding of cracks is slower than that at curing age 28 days. The curing age also affects the initial decreasing time of UPV. The smaller the curing age is, the UPV starts to decrease earlier. The microcracks are easier produced in the specimen at early curing age under uniaxial compression. With the increase of curing age, the bearing capacity of CGBP increases, the stiffness also increases, and the initial crack stress increases. However, the rapid decrease of UPV after the peak stress for the specimen at curing age 28 days also means that once the macrocracks occur in the specimen at curing age 28 days, these macrocracks expand quickly and CGBP lost its bearing capacity.

Effects of large width-height ratio and end friction coefficient
From the experimental results, the ends hoop effect affects the mechanical properties of CGBP, and therefore the mechanical properties of the CGBPs (large widthheight ratio: 1:1-4:1) under different ends friction coefficients (0.0-1.0) were investigated through the numerical simulation. Figure 11 shows the stress-strain curve of CGBP under different width-height ratios and different end friction coefficients. As shown in Fig. 11a-d, under the same width-height ratio, the higher the friction coefficient is, the larger the peak stress and correspondent peak strain show. In addition, the (a) before peak (b) after peak 1 (c) after peak 2 (d) after peak 3 (e) before peak (f) after peak 1 (g) after peak 2 (h) after peak 3 (i) before peak 1 (j) before peak 2 (k) after peak 1 (l) after peak 2 Fig. 9 The surface horizontal strain of CGBP under different widthheight ratios at different loading times. a Before peak. b After peak 1. c After peak 2. d After peak 3. e Before peak. f After peak 1. g After peak 2. h After peak 3. i Before peak 1. j Before peak 2. k After peak 1. l After peak 2 increase in friction coefficient can increase the ductility characteristics of CGBP. Especially, for the increase of friction coefficient from 0.0 to 0.25, the CGBP under the friction coefficient of 0.0 shows obviously brittle characteristics. Except for the friction coefficient of 0.0, the slope of the curves of other CGBPs in the elastic deformation stage before the peak does not change much. As shown in Fig. 11e-i, under the same friction coefficient, the increase in width-height ratio can increase the peak stress and peak strain of CGBPs except for the condition of friction coefficient of 0.0. Under the condition of a friction coefficient of 0.0, the mechanical properties of CGBPs do not affect by the width-height ratio, indicating that the hoop effect is a necessary condition for the mechanical properties of CGBPs to be affected by the width-height ratio. In addition, when the friction coefficient is larger than 0.5, the ductility properties of the CGBP increase firstly and then decrease with the increase of the width-height ratio, which proves that CGBP may fail in structural ways when the width-height ratio is excessively large. This means that the CGBP with a large width-height ratio may be separated into several parts after peak stress under axial compression because of the small tensile strength and cannot bear the pressure as a whole (Zhang et al. 2022). Figure 12 shows the strength of CGBP under different end friction coefficients. For the condition of friction coefficient 0.0, the effect of the width-height ratio on the strength of CGBP is not obvious, and the strength of CGBP shows a slight decrease with the increase in width-height ratio. However, with the increase in friction coefficient, the width-height ratio effect of strength of CGBP becomes more obvious. The larger the width-height ratio is, the higher the strength of CGBP shows and the higher the friction CGBPs under different friction coefficients is similar except for the friction coefficient 0.0, which means that when the width-height ratio decreases to some extent, the end friction does not affect the strength of CGBP. In practical engineering, the friction coefficient between the roof, backfill, and the floor can not be 0.0; therefore, the design of CGBP must consider the width-height ratio effect. Under the same load of the roof, using the large width-height ratio CGBP can reduce the use of raw material because of its high strength. In addition, the larger width-height ratio CGBP has a better ductility, which can avoid the sudden instability of the supporting system in the goaf. Figure 13 shows the failure characteristics of CGBP. With the increase in friction coefficient, more cracks formed in CGBP, and the CGBP is damaged more thoroughly and more fragments formed. For the condition of friction coefficient of 0.0, the number of cracks in CGBP is much less than that under other friction coefficients, and the CGBP shows structural damage and forms several big fragments, that is why CGBP under the friction coefficient of 0.0 shows the brittle failure.

Failure characteristics
The failure process of CGBP under axial compression is from outside to the middle except for the condition of friction coefficient of 0.0, and the production of cracks in the outside and inside of the CGBP without friction constraint is simultaneous, forming the oblique shear failure. Except for the condition of a friction coefficient of 0.0, the failure mode of CGBPs is conjugate oblique shear and peeling layer by layer from outside to the middle, forming a core bearing area that will increase with the increase of the width-height ratio. For the same condition of friction constraint, the larger the width-height ratio is, the closer the specimen is to the three-dimensional stress state, the greater the number of bond failures required to cause its failure, and the higher the strength shows. The influence of end friction is mainly concentrated in the area near the end face, forming a "triangular crack inhibition zone" (Li et al. 2021b). The inhibition zone can restrict the deformation of the area near the end face during compression. The existence of the inhibition zone can cause changes in the surrounding stress distribution but the influence range is limited. For the large width-height ratio, the end-face friction will make the stress concentration bands formed at both ends of the specimen cross and penetrate, resulting in a similar effect of confining pressure and a significant increase in the strength of the specimen. For the small width-height ratio, the proportion of the stress concentration zone in the entire specimen is small, and the specimen is damaged at a position far from the end face, which decreases the strength. Therefore, the end face friction has a greater impact on the strength of CGBP with a large width-height ratio. Compared to the force chain of the width-height ratio from 1:1 to 4:1, the bearing zone of the small width-height ratio specimen at the middle position is much smaller, which proves that the proportion of the triangular crack inhibition zone of the large width-height ratio specimen is larger than that of the small width-height ratio specimen. Figure 14 shows the crack number-strain curve and the AE count-strain curve of CGBP. As shown in Fig. 14a, when the acoustic emission occurs, the specimen with the widthheight ratio of 2:1 enters the gradual failure stage, but the peak of the number of events usually occurs after the peak of the curve, which also means the development of microcracks promotes the destruction of CGBP. After the CGBP is destroyed, more micro-cracks are generated until the specimen loses its bearing capacity completely and the acoustic emission stops (Xue and Yilmaz 2022).

Crack evolution process
Comparison of the crack number under different widthheight ratios (Fig. 14b-e), the crack number is near zero at the beginning, and then with the increase of strain, the crack number increases gradually and the increasing rate also increases. At a given width-height ratio, the larger the friction coefficient is, the slower the increasing rate of the crack number with the increase of strain will be, and the higher the total crack number shows when the stress decreases to 50% of the peak stress. This means that the hoop effect increases with the increase of friction coefficient, and the CGBP shows better integrity, and the greater the resistance of microcracks to develop into main cracks, forming better ductility properties.
Under the same friction coefficient, the increasing rate of crack number decreases with the increase of the widthheight ratio, and the total crack number increases with the increase of the width-height ratio. At the width-height ratio of 1:1, the increase of crack with the increase of strain shows the stepped feature, which means that the damage of CGBP shows the transient feature and the stress concentration can cause a large number of cracks. However, with the increase in the width-height ratio, the stepped feature of the crack number has been significantly improved, which proves that CGBP is damaged as a whole and the overall instability due to local damage is avoided.

Effect of roof-floor strength: same strength of roof and floor
In backfill mining engineering, the roof and floor are different kinds of rocks according to the geological conditions and have different mechanical properties. Therefore, the mechanical properties of the backfill may be affected by the mechanical properties of the roof and floor, and four different kinds of rocks were used to study the mechanical properties of the roof-backfill-floor combination through numerical simulation. Table 3 shows the meso-parameters of the rocks and the ITZ between roof and backfill and between floor and backfill. Figure 15 shows the stress-strain curve of the roof-backfill-floor combination under different strength ratios. The shape of the curve is different before the peak stress, and the increase in the strength of the roof and floor can increase the elastic modulus of the combination. For the Fig. 12 Effect of roof-floor friction coefficient on the strength of different width-height ratio CGBPs same width-height ratio, the peak stress and corresponding peak strain of the combination increase with the increase of the strength ratio. Under the same strength ratio of the roof-backfill-floor combination, the peak stress and peak strain at the peak stress increases with the increase of the width-height ratio.

Stress-strain curve
When the width-height ratio is from 1:1 to 3:1, the ductility of the combination increases with the increase of the strength ratio. For the width-height ratio of 4:1, the ductility of the combination increases firstly and then decreases at the strength ratio of 6.44 (54.11/8.39), and the combination with a strength ratio of more than 6.44 shows obvious brittle properties after the peak stress. This means that with the increase of the width-height ratio, the combination may be destroyed with the structural failure pattern under the relatively high strength ratio (Li et al. 2022b). Figure 16 shows the strength of the roof-backfill-floor combination. The strength of the combination increases with the increase in width-height ratio and strength ratio. It proves that the combination also shows the width-height ratio effect and the increase of the strength ratio can increase the width-height ratio effect of the combination. On the other hand, the strength of the roof and floor can affect the strength of the combination. When the strength of the roof and floor reaches 54.11 MPa, the strength of the combination is higher than that of CGBP, and the higher the strength ratio is, the larger the strength of the combination shows. However, when the strength of the roof and floor is 31.44 MPa, the strength of the combination is less than that of CGBP, and the lower the strength ratio is, the smaller the strength of the combination will be. This means that there may be a strength threshold (between 31.4 and 54.11 MPa) or a strength ratio threshold (between 3.75 and 6.44) for the strength of the roof-backfill-floor combination. When the strength or the strength ratio is larger than the threshold, the strength of the combination is larger than that of CGBP. Figure 17 shows the failure characteristics of the combination. Figure 17a shows the failure process of the combination with the width-height ratio of 3:1 of CGBP under the strength ratio of 6.44. It is clear that, under the axial compression, the stress transforms from the roof and floor to the backfill, and then the combination deforms together. When the stress reaches 2.8 MPa and 3.4 MPa, the CGBP deforms along the X axial because of the larger Poisson ratio while the combination deforms along the Y axial under the pressure. Therefore, the tensile stress occurs in the roof and floor, and the tensile stress decreases from the contact face between the backfill and roof to the ends. As the increase of the axial stress (9.2 MPa), the deformation of the backfill increases to some extent and the tensile stress in the roof or floor exceeds the tensile strength of the roof or floor. Finally, cracks produce in the roof and floor and then tensile stress will decrease while the undamaged roof or floor will continually bear tensile stress until the cracks produce again. And then, the combination will form a hyperbolic failure pattern and the core bearing area will bear the pressure. The tensile stress field will redistribute until the combination reaches a dynamic balance state, and then new cracks will generate when the stress exceeds the bearing capacity of the core bearing area. Finally, the combination will lose its bearing capacity. For the influence of the strength ratio, as shown in Fig. 17b-e, when the strength of the roof and floor is less than 54.11 MPa (strength ratio is less than 6.44), the damage is mainly focused on the roof or floor. When one of the sides is damaged, the pressure will destroy the remaining bearing area until the damaged side is destroyed totally, and then the combination loses its bearing capacity. When the strength ratio exceeds 6.44, the loss of bearing capacity of the combination is mainly due to the failure of the backfill. For the influence of the width-height ratio, when the strength of the roof and floor is less than 54.11 MPa, the failure pattern of the combination with a width-height ratio of 1:1 will not form a hyperbolic pattern. However, with the increase in the width-height ratio and strength ratio, the combination will form a hyperbolic failure pattern.

Table 3
The meso-parameters of the roof and floor with four different strengths (Yang et al. 2020a) Figure 18 shows the crack number-strain curve and AE counts-strain curve of the combination. As shown in Fig. 18a, the crack number increases with the increase of the strain, and there is a strain threshold for the crack number from slow increase to sharp increase. The strain threshold increases with the increase of the strength ratio, and the crack number at the strain threshold increases with the increase of the strength ratio, which proves that the increase of the strength ratio can increase the bearing capacity and coordination deformation capacity. Because of the large Poisson ratio of CGBP, the horizontal deformation of CGBP is larger than that of the roof and floor, and therefore the horizontal deformation of CGBP is constrained by the roof and floor. With the increase of the strength ratio, the resistance ability for the deformation increases, and the damage velocity of the combination with a large strength ratio is lower than that of the small strength ratio. Because the tensile strength of the low strength of the roof and floor is small, the mico-cracks in the roof or floor can extend to the main crack and the roof and floor with lower strength can damage much more quickly than that of the larger strength.

Crack evolution process
With the increase of the width-height ratio, the increase rate of the crack number can be more slowly, which means that the increase of the width-height ratio can improve the integrity of the combination and can increase the coordination deformation capacity, and then decrease the damage process. When the axial stress is greater than the crack initiation stress of the combination structure, the internal cracks of the structure begin to initiate and expand. Then, when the axial stress increases to a certain extent, macroscopic cracks form on the surface of the structure, and the corresponding axial stress is called the macroscopic fracture initiation stress, and the stress-strain curve shows a relatively obvious step-like fluctuation (Chen et al. 2017). Macroscopic failure initiation characterizes the onset of macroscopic failure of the combination structure. Table 4 shows the macroscopic crack initiation strength of the combination under axial compression. The macroscopic crack initiation stress of the combination increases with the increase of the strength ratio between roof, floor, and backfill. When the strength of the roof and floor is less than 54.11 MPa, the increase of the width-height ratio has no obvious influence on the macro-crack initiation stress. However, when the strength of the roof and floor are larger than or equal to 54.11 MPa, the crack initiation strength increases with the increase of the width-height ratio from 1:1 to 3:1 and then tends to be constant. Figure 19 shows the stress-strain curve and strength properties of the combination with the width-height ratio of 2:1 of the CGBP. For the strength of the roof of 20.01 MPa, the increase in the strength of the floor can little strengthen the mechanical properties of the combination. When the strength of the roof increases to 31.44 MPa, the increase in the strength of the floor can obviously increase the peak stress and peak strain of the combination. This means that the increase of the strength of the strong carrier can increase the strength and deformation properties of the combination. However, for the strength of weak carriers is much lower than the strength threshold, the increase of the strength of the strong carrier can not obviously increase the strength of the combination. On the other hand, the strength of the combination with a weak roof and a very hard floor is much less than that with the middle roof and middle floor. This demonstrates that the strength and deformation properties of the roof-backfill-floor combination are mainly controlled by weak carriers and the increase of the strength of the weak carrier can obviously increase the strength and deformation properties of the combination. Figure 20 shows the failure characteristics of the combination with different strengths of the roof and floor. Compared with the same strength of the roof and floor, the failure position of the combination with different strengths of the roof and floor is almost at the weak carriers and the backfill, and the instability of the combination is due to the failure of the weak carriers. The strong carries are in the tensile state, and the tensile force does not exceed the bearing capacity of the strong carries. Only when the strength of weak carriers and strong carriers are close, the strong carriers can produce main cracks. This means that the design of the combination should pay more attention to the combination between backfill and weak carriers. Figure 21 shows the changing process of crack number and strain under different strengths of roof and floor. For the lower strength of the weak carrier, the increase in the strength of the strong carrier can not obviously change the crack evolution process and the damage process is dominated by the weak carrier. However, when the strength of the weak carrier increases closer to the strength threshold, the increase of the strength of the strong carrier can increase the macrocrack initiation stress and the combination has better integrity to bear the axial pressure. On the other hand, the increase in the strength of the weak carrier can increase the macrocrack initiation stress obviously. When the difference of strength between the weak carrier and the strong carrier is too large, brittle failure after the peak stress is easy to occur in the combination.

Width-height ratio effect in the design of CGBP
For a given total area of the required CGBPs, the load of the roof that can be supported by the large width-height ratio CGBPs is greater than that of the small width-height ratio. In addition, the thickness of the coal seam is constant, and the amount of plastic deformation caused by yield weakening increases with the increase of the width-height ratio of CGBP. After one CGBP loses its bearing capacity, its original load is shared by the adjacent CGBPs or surrounding rock. If the roof can be effectively supported without subsidence, the recovery of the damaged CGBP only by its elastic strain will not cause an explosive collapse, and even  maintain its full shape. Large width-height ratio CGBPs produce large plastic deformation during the yielding process, that is, CGBPs bear large subsidence displacement of the roof in the transition state with almost constant bearing capacity, which improves the effective support of the roof. Overall, the design of the constructional backfill mining or partial backfill mining should adopt the large width-height ratio CGBP when the mechanical conditions of the surrounding rock allow it. The width-height ratio effect affects by the curing age and the end friction constraint. The increase in the curing age will increase the width-height ratio effect. Therefore, in the design of the backfill mining, the CGBP bearing the pressure of the roof at early curing age may not consider the width-height effect, and the long-term stability design of the CGBP should consider the width-height effect. On the other hand, the increase of the end friction coefficient can increase the width-height ratio effect of CGBP. Therefore, in the design of the backfill mining, the surface of the roof and floor should be rougher to increase the friction coefficient but should avoid excessive ups and downs which may cause stress concentration in CGBP and result in the degradation of the bearing capacity. In addition, some measures can be used to increase the adhesion (hydration reaction of cement and fly ash) between the backfill and the roof and floor, such as increasing the slurry concentration of CGBM, and reducing the bleeding rate of CGBM, and increasing the strength. The traditional CGBP is passively connected to the roof due to the subsidence characteristics of the fresh CGBM. Actually, curing stress at an early age can increase the strength of CGBP in the long-term bearing process Feng et al. 2022). Therefore, measures can be taken to allow CGBP to actively connect to the roof and increase the friction coefficient. Bieniawski proposed the calculation equation (Eq. (1)) of the coal pillar in the design of the geometry effect. As described in the "Numerical simulation results" section, the ends friction effect is the main reason for the width-height effect of CGBP, so we give the calculation equation of the key parameter of n (Eq. (2)), which considers the friction coefficient. Figure 22 shows the calculation results of the new model. It can be seen that this model can express the width-height ratio effect of the CGBP which considers the ends friction effect.
where p is the strength of CGBP; cu is the strength of the cubic specimen; w∕h is the width-height ratio of CGBP; n is the index of width-height ratio effect; f is the ends friction coefficient, and the friction coefficient varies between 0 and 1 and is not equal to 0.

Failure and instability mechanism of the roof-backfill-floor combination
As shown in Table 5, the phenomenon that the strength of the combination is smaller than the weak part in the combination is not only in the rock-backfill combination but also in the coal-rock combination. When the strength ratio between roof and backfill or between rock and coal is very small, the strength of the combination is smaller than the lowest strength in the combination. This proves that there may be a strength or strength ratio threshold in the roof-backfill-floor combination. Actually, the strength of the combination is also related to the height ratio between roof and backfill, and the higher the height ratio is, the larger the strength of the combination, and therefore, the strength of the combination needs more experiments to verify the real strength of the combination according to the real geological condition (Chen et al. 2017;Ma et al. 2021).
The roof and floor have an end-face friction effect on CGBP. Under the condition of the roof and floor that are relatively hard compared to CGBP, it plays a role in strengthening the stability of CGBP, but for the condition of the relatively soft roof and floor, it will greatly weaken the strength and stability of CGBP. As shown in Fig. 23, according to Eq. (3) of the plane strain problem, the influence of the roof and floor of various strengths on CGBP is deduced (Table 6) (Hu 1995).
where x is the horizontal strain; is the Poisson ratio; E is the elastic modulus; y is the stress at the axial direction.
The equivalent tensile stress exerted by CGBP on the roof and floor can be calculated by substituting the coordination condition of equal strain at the contact point between the CGBP and the roof and floor and considering the unidirectional stress state x .
where Δ x is the tensile stress in the roof; E roof is the elastic modulus; x is the horizontal strain of the roof under codeformation of the roof and CGBP.
(1) p = cu 0.64 + 0.36(w∕h) n (2) n = 0.21 + 0.42f It can be seen that (Table 6) the horizontal displacement of the relatively hard roof and the floor is much smaller than that of CGBP, so the hard roof and floor will limit the horizontal deformation of CGBP through the friction effect, thereby enhancing the strength and stability of CGBP. On the contrary, for the relatively soft roof and floor, the tensile strength of the roof and floor is small. After horizontal deformation with CGBP, when the horizontal stress is greater than the tensile strength of the roof and floor, the roof or the backfill will be rapidly destroyed, and the bearing capacity of the combination will be less than that of CGBP. At this time, the friction effect of the roof and floor does not limit the horizontal deformation, but generates horizontal tension in CGBP, weakens the strength of the original CGBP, and finally leads to the rupture of CGBP and the roof and floor (Figs. 17 and 20). The bearing capacity of the edge area of CGBP with small confinement is much smaller than that of the central part with large confinement. Therefore, as the width-height ratio increases, the core bearing area with large confinement also increases, and the strength of CGBP increases.
When the immediate roof and floor are hard and thick, the surrounding rock will constrain the deformation of the roof in the horizontal direction, which can increase the bearing capacity of the combination. However, when the immediate roof is relatively thin and weak, the unsupported position is easily broken, so the horizontal support of the roof and floor may be significantly weakened, and the situation described in the current article will occur (Zhu et al. 2022).

Energy evolution
The CGBP absorbs energy while restraining the subsidence of the overlying strata, which is the key parameter for the design of constructional backfill mining or partial backfill mining. Adjusting the energy between CGBP and the

Fig. 23
The frictional effect between roof as well as floor and cement gangue backfill pier-column overlying rock layer is the key to accurately controlling the movement of the strata. Without considering the dynamic action, the total energy absorbed by the CGBP includes the strain energy and the friction energy consumed by the structure to overcome the deformation (Wu et al. 2021). Figure 24 shows the effect of friction coefficient and width-height ratio on the full load-bearing strain energy of CGBP. The peak strain energy of CGBP increases with the increase of friction coefficient and width-height ratio. However, for the width-height ratio of 1:1, the peak strain energy does not increase significantly as the increase of friction coefficient after the friction coefficient of 0.25. Moreover, when the width-height ratio is 4:1, the peak strain energy does not change significantly when the friction coefficient increases from 0.75 to 1.0. It means that when the widthheight ratio is too large or too small, after the friction coefficient reaches a certain value, continuing to increase the friction coefficient will not significantly increase the peak strain energy. Figure 25 shows the effect of the strength of the roof and floor on the full load-bearing strain energy of the roof-backfill-floor combination. It can be seen that the increase in the strength of the roof and floor can significantly increase the peak strain energy of the combination. On the other hand, when the strength of the roof and floor reaches a certain value, increasing the strength of the roof and floor will cause the accumulated strain energy to be released instantaneously, and the combination will show structural failure characteristics. Figure 26 shows the variation of the full load-bearing strain energy of the roof-backfill-floor combination under different strength conditions of the roof and floor. When the strength of the weak carrier is low, increasing the strength of the strong carrier cannot significantly improve the peak strain energy of the combination. With the increase of the strength of the weak carrier, the peak strain energy increases obviously, and increasing the strength of the strong carrier can also improve the bearing capacity of the combination.

Conclusion
The width-height ratio effect of CGBP under different curing ages was studied through experiment. In addition, the effect of end friction coefficient and strength of roof and floor on the mechanical properties of CGBP under different large width-height ratios were studied through numerical simulation. The main conclusions can be drawn from the experimental and numerical simulation results: 1. A three-phase CGBP simulation model based on DEM, real aggregate shape and distribution, and different tio 2:1 (a) Width-height ratio 1:1 ( b) Width-height ra (c) Width-height ratio 3:1 ( d) Width-height ratio 4:1 Fig. 25 Effect of roof and floor (same strength) on the strain energy of combination. a Width-height ratio 1:1. b Width-height ratio 2:1. c Widthheight ratio 3:1. d Width-height ratio 4:1 strengths of each phase was established, and the uniaxial compression processes of CGBP and roof-backfillfloor combination were accurately simulated. The DEM model of CGBP can express the width-height ratio effect of CGBP under uniaxial compression. 2. The strength and elastic modulus of CGBP show the obvious width-height ratio effect and the width-height ratio effect increases with the increase of curing age. The strength of CGBP increases with the increase of the width-height ratio and curing age. The ductility, residual bearing strength, and peak strain increase with the increase in width-height ratio. The elastic modulus decreases with the increase of the width-height ratio and increases with the increase of curing age. The failure pattern of CGBP changes from conjugate oblique shear failure to single shear failure to splitting failure when the width-height ratio decreases from 1:1 to 1:3. The strength of the specimen with the conjugate oblique shear failure is larger than that of the single shear failure and is larger than that of the longitudinal splitting failure. 3. The end friction constraint is the main reason for the width-height ratio effect of CGBP, and the larger the friction coefficient is, the larger the width-height ratio effect will be, and the width-height ratio effect disappears without end friction constraint. The strength and peak strain of CGBP without friction constraint is much less than that with friction constraint. The strength, peak strain, and ductility of CGBP increase with the increase in width-height ratio and friction coefficient. 4. The increase in the strength ratio and width-height ratio of CGBP increases the strength and ductility properties of the roof-backfill-floor combination. The increase in strength ratio can increase the width-height ratio effect.
Whether the strength of the combination is greater than that of CGBP may have a roof and floor strength threshold or a strength ratio threshold, which are between 31.44-54.11 MPa and 3.75-6.44, respectively. When the strength and strength ratio is greater than the threshold, the strength of the combination is greater than that of CGBP. When the strength of the roof and floor is different, the strength of the combination is mainly controlled by the weak carrier and increases with the increase of the strength of the weak carrier. When the weak carrier is identified, increasing the strength of the strong carrier will also improve the strength of the combination. 5. The failure patterns of CGBP (large width-height ratio 1:1-4:1) with different ends friction coefficients and the corresponding combination is hyperbolic except for the friction coefficient of 0.0 and small strength ratio, and CGBP damages from left and right to the middle, forming a core bearing zone. The greater the strength of the roof and floor is, the more serious the damage of the backfill in the combination will be, and the more complete the roof and floor show. The peak strain energy of CGBP and combination increases with the increase of friction coefficient, width-height ratio, and the strength of the roof and floor. When the strength of the roof and floor reaches a certain value, the combination will show brittleness characteristics.
Although this paper investigated the mechanical properties of the roof-backfill-floor combination under different strength ratios through numerical simulation, the precise strength threshold or strength ratio threshold and mechanical responses need more experiments to determine according to real engineering.
Funding This work is supported by the National Natural Science Foundation of China (51974192). The research was conducted while the first author was in receipt of financial support from the China Scholarship Council.

Data availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

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