Estimating shear strength of high-level pillars supported with cemented backfilling using the HoekeBrown strength criterion

Deep metal mines are often mined using the high-level pillars with subsequent cementation backfilling(HLSCB)mining method.At the design stage,it is therefore important to have a reasonable method for determining the shear strength of the high-level pillars(i.e.cohesion and internal friction angle)when they are supported by cemented backfilling.In this study,a formula was derived for the upper limit of the confining pressure σ3max on a high-level pillar supported by cemented backfilling in a deep metal mine.A new method of estimating the shear strength of such pillars was then proposed based on the Hoek eBrown failure criterion.Our analysis indicates that the horizontal stress σhh acting on the cemented backfill pillar can be simplified by expressing it as a constant value.A reasonable and effective value for σ3max can then be determined.The value of s3max predicted using the proposed method is generally less than 3 MPa.Within this range,the shear strength of the high-level pillar is accurately calculated using the equivalent MohreCoulomb theory.The proposed method can effectively avoid the calculation of inaccurate shear strength values for the high-level pillars when the original HoekeBrown criterion is used in the presence of large confining pressures,i.e.the situation in which the cohesion value is too large and the friction angle is too small can effectively be avoided.The proposed method is applied to a deep metal mine in China that is being excavated using the HLSCB method.The shear strength parameters of the high-level pillars obtained using the proposed method were input in the numerical simulations.The numerical results show that the recommended level heights and sizes of the high-level pillars and rooms in the mine are rational.

Vertical transportation system of solid material for backfilling coal mining technology

For transportation of solid backfill material such as waste and fly ash from the surface to the bottom of the shaft in a fully mechanized backfilling coal backfilling coal mining technology, we developed a new vertical transportation system to transport this type of solid backfill material. Given the demands imposed on safely in feeding this material, we also investigated the structure and basic parameter of this system. For a mine in the Xingtai mining area the results show that: (1) a vertical transportation system should include three main parts, i.e., a feeding borehole, a maintenance chamber and a storage silo; (2) we determined that 486 mm is a suitable diameter for bore holes, the diameter of the storage silo is 6 m and its height 30 m in this vertical transportation system; (3) a conical buffer was developed to absorb the impact during the feeding process. To ensure normal implementation of fully mechanized backfilling coal mining technology and the safety of underground personnel, we propose a series of security technologies for anti-blockage, storage silo cleaning, high pressure air release and aspiration. This vertical transporting system has been applied in one this particular mine, which has fed about 4 million tons solid material with a feeding depth of 350 m and safely exploited 3 million tons of coal.

Mechanical properties and damage characteristics of solidified body-coal combination in continuous driving and gangue backfilling

Recovery of the coal buried under buildings,railways and water bodies and the residual coal in irregularly arranged fully mechanized mining faces is a common engineering problem facing underground coal mining.In this study,a mining technology of continuous driving and gangue backfilling(CDGB)was proposed.The technology,which can not only alleviate ground subsidence and gangue discharge,but also release the above-mentioned coals,contributes to green and efficient sustainable development of mining.The stability of the system of the solidified body-reserved coal pillar combination(S-C combination)is crucial to the CDGB technology.Therefore,it is of great significance to explore the mechanical and damage characteristics of S-C combination in the synergistic bearing process.First,four sets of differentshaped S-C combination specimens were fabricated and a S-C combination bearing structure in CDGB was constructed to explore the differences in mechanical characteristics and damage modes of different-shaped S-C combination specimens during CDGB.Subsequently,their surface strain field evolutions and acoustic emission(AE)response characteristics in the load-bearing process were obtained with the aid of the digital image correlation technique and the AE signal monitoring system.Furthermore,a damage evolution model based on AE parameters and mechanical parameters was established to clarify the damage evolution law.The following results were obtained:(1)The free area of S-C combination can serve as a quantitative index to evaluate the stability of the overburden control system;(2)The concept of critical value k of the free area was first proposed.When the free area exceeds the critical value k(free area ratio greater than 1.13),the deformation resistance and the free area changes becomes negatively correlated;(3)As the free area expands,the failure of the S-C combination specimen evolves from tensile failure to shear failure.The distribution characteristics of the axial strain field also verified such a change in the failure mode;(4)When the free area expands,the peak AE count gradually changes from“double peaks”to“a single peak”.In this process,the expansion of free area shortens the time for accumulating and releasing energy during loading.Micro cracks generated in the specimen change from a phased steep growth to a continuous increase,and the process in which micro cracks develop,converge,intersect and connect to form macro cracks accelerates.The damage evolution law concluded based on AE parameters and mechanical parameters can well characterize the damage evolution process of S-C combination,providing certain reference for the study on the synergistic bearing of S-C combination during CDGB.

Systematic review of mixing technology for recycling waste tailings as cemented paste backfill in mines in China

The development of industry is inseparable from the support of mining.However,mining processes consume a large amount of energy,and increased tailing emissions can have a significant impact on the environment.In the past few decades,the mining industry developed many technologies that are related to mineral energy management,of which cemented paste backfill(CPB)is one of the representative technologies.CPB has been successfully applied to mine ground control and tailings management.In CPB technology,the mixing process is the key to achieving materials with good final quality and controlled properties.However,in the preparation process,the mixed homogeneity of the CPB is difficult to achieve because of fine tailings,high solid volume fraction,and high viscosity.Most research focused on the effect of mixing ingredients on CPB properties rather than on the preparation process of the CPB.Therefore,improving the performance and reducing the production cost of CPB by optimizing the mixing process are important.This review summarizes the current studies on the mixing technology of CPB and its application status in China.Then,it compares the advantages and disadvantages of multiple mixing equipment and discusses the latest results and research hotspots in paste preparation.Finally,it concludes the challenges and development trends of mixing technology on the basis of the relevant application cases in China to promoting cement-based material mixing technology development.

Rheological properties of a multiscale granular system during mixing of cemented paste backfill:A review

The technology of cemented paste backfill(CPB)is an effective method for green mining.In CPB,mixing is a vital process aiming to prepare a paste that meets the non-stratification,non-segregation,and non-bleeding requirements.As a multiscale granular system,homogenization is one of the challenges in the paste-mixing process.Due to the high shearing,high concentration,and multiscale characteristics,paste exhibits complex rheological properties in the mixing process.An overview of the mesomechanics and structural evolution is presented in this review.The effects of various influencing factors on the paste's rheological properties were investigated,and the rheological models of the paste were outlined from the macroscopic and mesoscopic levels.The results show that the mechanical effects and structural evolution are the fundamental factors affecting the rheological properties of the paste.Existing problems and future development trends are presented to change the practice where the CPB process comes first and the theory lags.

Failure characteristics and the damage evolution of a composite bearing structure in pillar-side cemented paste backfilling

A backfilling body-coal pillar-backfilling body(BPB)structure formed by pillar-side cemented paste backfilling can bear overburden stress and ensure safe mining.However,the failure response of BPB composite samples must be investigated.This paper examines the deformation characteristics and damage evolution of six types of BPB composite samples using a digital speckle correlation method under uniaxial compression conditions.A new damage evolution equation was established on the basis of the input strain energy and dissipated strain energy at the peak stress.The prevention and control mechanisms of the backfilling body on the coal pillar instability were discussed.The results show that the deformation localization and macroscopic cracks of the BPB composite samples first appeared at the coal-backfilling interface,and then expanded to the backfilling elements,ultimately appearing in the coal elements.The elastic strain energy in the BPB composite samples reached a maximum at the peak stress,whereas the dissipated energy continued to accumulate and increase.The damage evolution curve and equation agree well with the test results,providing further understanding of instability prevention and the control mechanisms of the BPB composite samples.The restraining effect on the coal pillar was gradually reduced with decreasing backfilling body element's volume ratio,and the BPB composite structure became more vulnerable to failure.This research is expected to guide the design,stability monitoring,instability prevention,and control of BPB structures in pillar-side cemented paste backfilling mining.

Revisiting factors contributing to the strength of cemented backfill support system:A review

This paper provides a review of the intrinsic and extrinsic factors affecting the uniaxial compressive strength(UCS)of cemented tailings backfill(CTB).The consideration is that once CTB is poured into underground stopes,its strength is heavily influenced by factors internal to the CTB as well as the surrounding mining environments.Peer-reviewed journal articles,books,and conference papers published between 2000 and 2022 were searched electronically from various databases and reviewed.Additional sources,such as doctoral theses,were obtained from academic repositories.An important finding from the review is that the addition of fibers was reported to improve the UCS of CTB in some studies while decrease in others.This discrepancy was accounted to the different properties of fibers used.Further research is therefore needed to determine the“preferred”fiber to be used in CTB.Diverging findings were also reported on the effects of stope size on the UCS of CTB.Furthermore,the use of fly ash as an alternative binder may be threatened in the future when reliance on the coal power declines.Therefore,an alternative cementitious by-product to be used together with furnace slag may be required in the future.Finally,while most studies on backfill focused on single-layered structures,layered backfill design models should also be investigated.

Subsidence prediction method based on equivalent mining height theory for solid backfilling mining

Based on the characteristics of strata movement of solid backfilling mining technology, the surface subsidence prediction method based on the equivalent mining height theory was proposed, and the parameters selection guideline of this method was also described. While comparing the parameters of caving mining with equivalent height, the subsidence efficient can be calculated according to the mining height and bulk factor of sagging zone and fracture zone, the tangent of main influence angle of solid backfilling mining is reduced by 0.2-0.5（while it cannot be less than 1.0）. For sake of safety, offset of the inflection point is set to zero, and other parameters, such as horizontal movement coefficient and main propagation angle are equal to the corresponding parameters of caving mining with equivalent height. In the last part, a case study of solid backfilling mining subsidence prediction was described. The results show the applicability of this method and the difference of the maximum subsidence point between the prediction and the observation is less than 5%.

Using cemented paste backfill to tackle the phosphogypsum stockpile in China:A down-to-earth technology with new vitalities in pollutant retention and CO_(2) abatement

Phosphogypsum(PG),a hard-to-dissipate by-product of the phosphorus fertilizer production industry,places strain on the biogeochemical cycles and ecosystem functions of storage sites.This pervasive problem is already widespread worldwide and requires careful stewardship.In this study,we review the presence of potentially toxic elements(PTEs)in PG and describe their associations with soil properties,anthropogenic activities,and surrounding organisms.Then,we review different ex-/in-situ solutions for promoting the sustainable management of PG,with an emphasis on in-situ cemented paste backfill,which offers a cost-effective and highly scalable opportunity to advance the value-added recovery of PG.However,concerns related to the PTEs'retention capacity and long-term effectiveness limit the implementation of this strategy.Furthermore,given that the large-scale demand for ordinary Portland cement from this conventional option has resulted in significant CO_(2) emissions,the technology has recently undergone additional scrutiny to meet the climate mitigation ambition of the Paris Agreement and China's Carbon Neutrality Economy.Therefore,we discuss the ways by which we can integrate innovative strategies,including supplementary cementitious materials,alternative binder solutions,CO_(2) mineralization,CO_(2) curing,and optimization of the supply chain for the profitability and sustainability of PG remediation.However,to maximize the co-benefits in environmental,social,and economic,future research must bridge the gap between the feasibility of expanding these advanced pathways and the multidisciplinary needs.

一种简化的基于First-Fit的Backfilling调度策略——RB-FIFT

机群作业管理系统是机群系统的重要组成部分,而作业调度策略又是机群作业管理系统的核心内容。作业调度策略的选择不仅关系到机群系统的利用率,还决定用户作业的响应速度和平均执行时间。在节点分配基于空间共享策略(Space-Sharing)的机群系统中,传统的基于先来先服务的First-Fit调度策略虽然能够提高机群系统的利用率,却容易引起饥饿问题。文章基于传统的先来先服务的调度策略,提出了一种简化的Backfilling算法,简要叙述了该算法的设计和实现,最后根据模拟实验结果,从用户和系统的角度分析了该算法的性能。

Reinforcing effects of polypropylene on energy absorption and fracturing of cement-based tailings backfill under impact loading

Polypropylene(PP)fiber-reinforced cement-based tailings backfill(FRCTB)is a green compound material with superior crack resistance and has good prospects for application in underground mining.However,FRCTB exhibits susceptibility to dynamic events,such as impact ground pressure and blast vibrations.This paper investigates the energy and crack distribution behavior of FRCTB under dynamic impact,considering the height/diameter(H/D)effect.Split Hopkinson pressure bar,industrial computed tomography scan,and scanning electron microscopy(SEM)experiments were carried out on six types of FRCTB.Laboratory outcomes confirmed fiber aggregation at the bottom of specimens.When H/D was less than 0.8,the proportion of PP fibers distributed along theθangle direction of80°-90°increased.For the total energy,all samples presented similar energy absorption,reflectance,and transmittance.However,a rise in H/D may cause a rise in the energy absorption rate of FRCTB during the peak phase.A positive correlation existed between the average strain rate and absorbed energy per unit volume.The increase in H/D resulted in a decreased crack volume fraction of FRCTB.When the H/D was greater than or equal to 0.7,the maximum crack volume fraction of FRCTB was observed close to the incidence plane.Radial cracks were present only in the FRCTB with an H/D ratio of 0.5.Samples with H/D ratios of 0.5 and 0.6 showed similar distributions of weakly and heavily damaged areas.PP fibers can limit the emergence and expansion of cracks by influencing their path.SEM observations revealed considerable differences in the bonding strengths between fibers and the FRCTB.Fibers that adhered particularly well to the substrate were attracted together with the hydration products adhering to surfaces.These results show that FRCTB is promising as a sustainable and green backfill for determining the design properties of mining with backfill.

Paste-like self-flowing transportation backfilling technology based on coal gangue

A paste-like self-flowing pipeline transportation backfilling technology with coal gangue as aggregate is proposed to remove the potential damage caused by coal gangue piles. As well, the difficult problems of recovering high quality safety coal pillars and deep mining of the Suncun Coal Mine （SCM）, Xinwen Coal Group, Shandong are resolved. The physical-chemical properties of coal gangue, optimized proportion of materials, backfilling system and craft in the SCM were studied in the laboratory and then an industrial test was carried out on high quality coal pillars under a town. The results show that finely crushed kaolinized and fresh gangue with granularity less than 5 mm can be used as aggregate with fly ash to replace part of the cement and a composite water reducer as an additive, accounting for 1.0%-1.5% of the total amount of cement and fly ash. The recommended proportion is l（cement）：4（fly ash）： 15（coal gangue）, with a mass fraction of 72%-75%, rheoiogical paste-like properties and a strength of more than 0.7 MPa at 7 d. The sequence of adding cement, fly ash, water reducer and then coal gangue ensures that the suspended state of the slurry, reducing the wear and jam of pipelines. The working face is advancing continuously by the alternating craft of building block walls with coal gangue and backfilling mined-out gobs with paste-like slurry. The recovery rate is as high as 90% with a backfilling cost of 36.9 YuarffL good utilization of coal gangue and no subsidence on the surface. This technology provides a good theoretical basis and application experience for coal mines, cement backfilling with paste-like slurry.

Damage evolution of rock-encased-backfill structure under stepwise cyclic triaxial loading

Rock-encased-backfill(RB)structures are common in underground mining,for example in the cut-andfill and stoping methods.To understand the effects of cyclic excavation and blasting activities on the damage of these RB structures,a series of triaxial stepwise-increasing-amplitude cyclic loading experiments was conducted with cylindrical RB specimens(rock on outside,backfill on inside)with different volume fractions of rock(VF=0.48,0.61,0.73,and 0.84),confining pressures(0,6,9,and 12 MPa),and cyclic loading rates(200,300,400,and 500 N/s).The damage evolution and meso-crack formation during the cyclic tests were analyzed with results from stress-strain hysteresis loops,acoustic emission events,and post-failure X-ray 3D fracture morphology.The results showed significant differences between cyclic and monotonic loadings of RB specimens,particularly with regard to the generation of shear microcracks,the development of stress memory and strain hardening,and the contact forces and associated friction that develops along the rock-backfill interface.One important finding is that as a function of the number of cycles,the elastic strain increases linearly and the dissipated energy increases exponentially.Also,compared with monotonic loading,the cyclic strain hardening characteristics are more sensitive to rising confining pressures during the initial compaction stage.Another finding is that compared with monotonic loading,more shear microcracks are generated during every reloading stage,but these microcracks tend to be dispersed and lessen the likelihood of large shear fracture formation.The transition from elastic to plastic behavior varies depending on the parameters of each test(confinement,volume fraction,and cyclic rate),and an interesting finding was that the transformation to plastic behavior is significantly lower under the conditions of 0.73 rock volume fraction,400 N/s cyclic loading rate,and 9 MPa confinement.All the findings have important practical implications on the ability of backfill to support underground excavations.

基于Backfilling调度算法的“扩履适足”改进算法

在众多的并行作业调度算法中,Backfilling通常被广泛认为是有效提高CPU利用率的一种算法。该算法是在FCFS算法的基础上,将队列中较小的作业回填(Backfill)到空闲CPU,以提高CPU利用率。但是,当空闲CPU数量仍然无法满足Backfilling算法中小作业的回填要求时,系统仍有部分CPU闲置,因而也难以达到更好地提高CPU利用率的目的。对于共享内存体系结构的并行计算机系统,本文提出了基于Backfilling算法的“扩履适足”的改进算法。该算法以正在运行的作业的CPU利用率为依据,通过动态调整正在运行作业的CPU数,扩大可供回填(backfill)的CPU空间,使得Backfilling算法无法回填的作业得到运行,弥补了Backfilling算法的不足,大大提高了共享内存体系结构并行计算机系统的CPU利用率。

结合Backfilling和空闲资源调度的云工作流调度方法

针对云计算中工作流的科学调度问题,提出了一种快速且有效的调度方案.首先,根据计算速度将所有的资源节点以降序方式排列;然后,调度程序通过深度优先搜索,检查任务之间的依赖关系,并根据截止期限对待执行任务进行加权排序;接着,计算每个待执行任务所使用的资源的时隙.如果当前可用资源不能满足当前任务,则采用Backfilling策略,对该任务所需资源进行预留,并跳到下一个任务执行.如果当前资源满足当前任务,则执行提出的空闲资源调度(IRS)策略,尽量安排空闲资源来执行该任务.仿真结果表明:与当前云工作流调度技术相比,本文调度策略具有更低的任务完成时间与任务执行延迟,以及更高的资源利用率.

Paste-like cemented backfilling technology and rheological characteristics analysis based on jigging sands

To make backfilling body meet strength requirement,physical-chemical evaluation and proportioning tests were conducted on several backfilling materials.Jigging sands,#32.5 cement and fly ash were determined as backfilling aggregate,binding material and modified material,respectively.An optimized proportion of backfilling materials with a solid mass fraction of 78%and cement:fly ash:jigging sands mass ratio of 1:2:14,was suggested to Jiangan Pyrite Mine,China.The slurry made by optimized proportion produced obvious shear thinning phenomena,and was confirmed as paste-like slurry.To analyze its rheological characteristics,L-type pipeline test and Haake VT550 rotational viscometer test were conducted.Bingham and Casson fluid models were applied to several paste-like slurry samples to simulate flow and stress states;Casson fluid model was proved to have better simulation effect on paste-like slurry with shear thinning phenomena;rheological parameters of backfilling slurry made by suggested proportion were measured.Initial yield stress,average apparent viscosity and limiting viscosity are 55.35 Pa,1.216 Pa-s and 0.48 Pa-s,respectively.Compared with Bingham fluid model,Casson fluid model has a better simulation effect on paste-like slurry with shear thinning phenomena,through calculating the residual standard deviations.

Mechanical properties and damage evolution characteristics of waste tire steel fiber-modified cemented paste backfill

During the process of constructional backfill mining,the cemented paste backfill(CPB)typically exhibits a high degree of brittleness and limited resistance to failure.In this study,the mechanical and damage evolution characteristics of waste tire steel fiber(WTSF)-modified CPB were studied through uniaxial compression tests,acoustic emission(AE)tests,and scanning electron microscopy(SEM).The results showed that the uniaxial compressive strength(UCS)decreased when the WTSF content was 0.5%,1%,and 1.5%.When the WTSF content reached 1%,the UCS of the modified CPB exhibited a minimal decrease(0.37 MPa)compared to that without WTSF.When the WTSF content was 0.5%,1%,and 1.5%,peak strain of the WTSF-modified CPB increased by 18%,31.33%,and 81.33%,while the elastic modulus decreased by 21.31%,26.21%,and 45.42%,respectively.The addition of WTSF enhances the activity of AE events in the modified CPB,resulting in a slower progression of the entire failure process.After the failure,the modified CPB retained a certain level of load-bearing capacity.Generally,the failure of the CPB was dominated by tensile cracks.After the addition of WTSF,a gradual increase in the proportion of tensile cracks was observed upon loading the modified CPB sample to the pore compaction stage.The three-dimensional localization of AE events showed that the WTSF-modified CPB underwent progressive damage during the loading,and the samples still showed good integrity after failure.Additionally,the response relationship between energy evolution and damage development of WTSF-modified CPB during uniaxial compression was analyzed,and the damage constitutive model of CPB samples with different WTSF contents was constructed.This study provides a theoretical basis for the enhancement of CPB modified by adding WTSF,serving as a valuable reference for the design of CPB constructional backfill.

Microstructural evolution and strengthening mechanism of aligned steel fiber cement-based tail backfills exposed to electromagnetic induction

Cemented tailings backfill(CTB)not only boosts mining safety and cuts surface environmental pollution but also recovers ores previously retained as pillars,thereby improving resource utilization.The use of alternative reinforcing products,such as steel fiber(SF),has continuously strengthened CTB into SFCTB.This approach prevents strength decreases over time and reinforces its long-term durability,especially when mining ore in adjacent underground stopes.In this study,various microstructure and strength tests were performed on SFCTB,considering steel fiber ratio and electromagnetic induction strength effects.Lab findings show that combining steel fibers and their distribution dominantly influences the improvement of the fill’s strength.Fill’s strength rises by fiber insertion and has an evident correlation with fiber insertion and magnetic induction strength.When magnetic induction strength is 3×10^(-4) T,peak uniaxial compressive stress reaches 5.73 MPa for a fiber ratio of 2.0vol%.The cracks’expansion mainly started from the specimen’s upper part,which steadily expanded downward by increasing the load until damage occurred.The doping of steel fiber and its directional distribution delayed crack development.When the doping of steel fiber was 2.0vol%,SFCTBs showed excellent ductility characteristics.The energy required for fills to reach destruction increases when steel-fiber insertion and magnetic induction strength increase.This study provides notional references for steel fibers as underground filling additives to enhance the fill’s durability in the course of mining operations.

Roughness characterization and shearing dislocation failure for rock-backfill interface

Shearing dislocation is a common failure type for rock–backfill interfaces because of backfill sedimentation and rock strata movement in backfill mining goaf.This paper designed a test method for rock–backfill shearing dislocation.Using digital image techno-logy and three-dimensional(3D)laser morphology scanning techniques,a set of 3D models with rough joint surfaces was established.Further,the mechanical behavior of rock–backfill shearing dislocation was investigated using a direct shear test.The effects of interface roughness on the shear–displacement curve and failure characteristics of rock–backfill specimens were considered.The 3D fractal dimen-sion,profile line joint roughness coefficient(JRC),profile line two-dimensional fractal dimension,and the surface curvature of the frac-tures were obtained.The correlation characterization of surface roughness was then analyzed,and the shear strength could be measured and calculated using JRC.The results showed the following:there were three failure threshold value points in rock–backfill shearing dis-location:30%–50%displacement before the peak,70%–90%displacement before the peak,and 100%displacement before the peak to post-peak,which could be a sign for rock–backfill shearing dislocation failure.The surface JRC could be used to judge the rock–backfill shearing dislocation failure,including post-peak sliding,uniform variations,and gradient change,corresponding to rock–backfill disloca-tion failure on the field site.The research reveals the damage mechanism for rock–backfill complexes based on the free joint surface,fills the gap of existing shearing theoretical systems for isomerism complexes,and provides a theoretical basis for the prevention and control of possible disasters in backfill mining.

Particle aggregation and breakage kinetics in cemented paste backfill

The macroscopic flow behavior and rheological properties of cemented paste backfill(CPB)are highly impacted by the inherent structure of the paste matrix.In this study,the effects of shear-induced forces and proportioning parameters on the microstructure of fresh CPB were studied.The size evolution and distribution of floc/agglomerate/particles of paste were monitored by focused beam reflection measuring(FBRM)technique,and the influencing factors of aggregation and breakage kinetics of CPB were discussed.The results indicate that influenced by both internal and external factors,the paste kinetics evolution covers the dynamic phase and the stable phase.Increasing the mass content or the cement-tailings ratio can accelerate aggregation kinetics,which is advantageous for the rise of average floc size.Besides,the admixture and high shear can improve breaking kinetics,which is beneficial to reduce the average floc size.The chord length resembles a normal distribution somewhat,with a peak value of approximate 20μm.The particle disaggregation con-stant(k_(2))is positively correlated with the agitation rate,and k_(2) is five orders of magnitude greater than the particle aggregation constant(k1).The kinetics model depicts the evolution law of particles over time quantitatively and provides a theoretical foundation for the micromechanics of complicated rheological behavior of paste.