Granular Matter最新文献

{"title":"Incremental shear strain chain: a mesoscale concept for slip lines in 2D granular materials","authors":"Jiaying Liu,&nbsp;Antoine Wautier,&nbsp;Wei Zhou,&nbsp;François Nicot,&nbsp;Félix Darve","doi":"10.1007/s10035-022-01258-y","DOIUrl":"10.1007/s10035-022-01258-y","url":null,"abstract":"<p>Constitutive behaviors of granular materials are driven by both particle interactions and geometric arrangements of contact network. To bridge the gap between the grain scale and the sample scale, the mesoscale is of great importance as it corresponds to the smallest scale at which geometrical effect can be accounted for. Meso shear structures (sometimes called microbands) have been observed frequently on incremental strain maps in granular materials under shearing, while the Rudnicki and Rice localization criterion for shear band is not fulfilled yet. These meso structures are thin, quasi-linear and they involve a few grains as well as their surrounding voids. This paper introduces the concept of “incremental shear strain chain” (simply called “shear chain”) to provide a specific quantitative definition of such mesostructures. “Shear chains” are defined based on incremental deviatoric strain fields in 2D biaxial simulations. Particular attention is paid to demonstrate that the shear chain orientation is a material scale property, insensitive to boundary conditions, loading paths and sample densities. Since shear chains are shown to be closely related to sliding mechanisms, they can stand for a mesoscale definition of the concept of slip lines as defined in the standard elasto-plasticity theory.</p>","PeriodicalId":582,"journal":{"name":"Granular Matter","volume":"24 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5024109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of particle holdup on bubble formation in suspension medium by VOF–DPM simulation","authors":"Huiting Chen,&nbsp;Ying Li,&nbsp;Yuandong Xiong,&nbsp;Han Wei,&nbsp;Henrik Saxén,&nbsp;Yaowei Yu","doi":"10.1007/s10035-022-01276-w","DOIUrl":"10.1007/s10035-022-01276-w","url":null,"abstract":"<div><p>A numerical simulation based on volume-of-fluid and discrete particle method has been accomplished to analyze the effect of particle holdup on bubble formation in suspension medium. A two-way coupled model involving some essential interphase forces (liquid-particle suspension inertial force, particle-bubble contact force, Basset force, bubble inertial force, virtual mass force, pressure gradient force, etc.) is firstly set up and validated with the experimental and simulation results. On the basis of the analysis on two-stage bubble formation, some potential influence factors (bubble neck length, bubble detachment size and period, bubble shape and wakes) are discussed. The results show that the neck length of bubble detachment increases with the increase of particle holdup due to the greater drag coefficient. For 0.6% &lt; <span>({varepsilon }_{p})</span> &lt; 0.8%, the neck length at <span>(t/{t}_{det})</span> = 1 varies greatly due to a significant increase in apparent viscosity at <span>({varepsilon }_{p})</span> = 0.55%. Additionally, the trajectory instability of the bubble is attributed to the increase of bubble aspect ratio, leading to a strong entrainment ability and transport enhancement in gas–liquid–solid medium. The particles can weaken the entrainment of bubble-induced flow to the surrounding fluid, thus the influence of shortening the detachment period caused by the wake weakening is weakened.</p><h3>Graphic abstract</h3>\u0000 <figure><div><div><div><picture><source><img></source></picture></div></div></div></figure>\u0000 </div>","PeriodicalId":582,"journal":{"name":"Granular Matter","volume":"24 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5442190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of sediment form and form distribution on porosity: a simulation study based on the discrete element method","authors":"Christoph Rettinger,&nbsp;Ulrich Rüde,&nbsp;Stefan Vollmer,&nbsp;Roy M. Frings","doi":"10.1007/s10035-022-01275-x","DOIUrl":"10.1007/s10035-022-01275-x","url":null,"abstract":"<p>Porosity is one of the key properties of dense particle packings like sediment deposits and is influenced by a multitude of grain characteristics such as their size distribution and shape. In the present work, we focus on the form, a specific aspect of the overall shape, of sedimentary grains in order to investigate and quantify its effect on porosity, ultimately deriving novel porosity-prediction models. To this end, we develop a robust and accurate simulation tool based on the discrete element method which we validate against laboratory experiments. Utilizing digital representations of actual sediment from the Rhine river, we first study packings that are composed of particles with a single form. There, porosity is found to be mainly determined by the inverse equancy, i.e., the ratio of the longest to the smallest form-defining axis. Only for small ratios, additional shape-related properties become relevant, as revealed by a direct comparison to packings of form-equivalent but smooth ellipsoids. Since sediment naturally features form mixtures, we extend our simulation tool to study sediment packings with normally-distributed forms. In agreement with our single form studies, porosity is found to depend primarily on the inverse of the mean equancy. By supplying additional information about a second form factor and the standard deviations, we derive an accurate model for porosity prediction. Due to its simplicity, it can be readily applied to sediment packings for which some measurements of flatness and elongation, the two most common form factors, are available.</p>","PeriodicalId":582,"journal":{"name":"Granular Matter","volume":"24 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2022-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10035-022-01275-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4876877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Point process statistics improves particle size analysis","authors":"Dietrich Stoyan,&nbsp;Georg Unland","doi":"10.1007/s10035-022-01278-8","DOIUrl":"10.1007/s10035-022-01278-8","url":null,"abstract":"<p>This paper re-considers the foundations of particle size statistics. While traditional particle size statistics consider their data as samples of random variables and use methods of classical mathematical statistics, here a particle sample is treated as a point process sample, and a suitable form of statistics is recommended. The whole sequence of ordered particle sizes is considered as a random variable in a suitable sample space. Instead of distribution functions, point process intensity functions are used. The application of point process data analysis is demonstrated for samples of fragments from single-particle crushing of glass balls. Three cases of data handling with point processes are presented: statistics for oversize particles, pooling of independent particle samples and pooling of piecewise particle data. Finally, the problem of goodness-of-fit testing for particle samples is briefly discussed. The point process approach turns out to be an extension of the classical approach, is simpler and more elegant, but retains all valuable traditional ideas. It is particularly strong in the analysis of oversize particles.</p>","PeriodicalId":582,"journal":{"name":"Granular Matter","volume":"24 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10035-022-01278-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4664149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Doublet craters originated by low speed impact experiments in granular matter","authors":"M. Jiménez-Valdez,&nbsp;E. Tomay,&nbsp;J. O. Marston,&nbsp;F. Pacheco-Vázquez","doi":"10.1007/s10035-022-01279-7","DOIUrl":"10.1007/s10035-022-01279-7","url":null,"abstract":"<p>We studied the formation of doublet craters generated by binary projectiles (steel beads or granular agglomerates) impacting simultaneously at low speed against a sand bed. For impacts of two solid beads, we observed different morphologies depending on the initial separation between the projectiles: two well defined craters, overlapping craters, or a single larger circular crater produced when the separation between projectiles is negligible. Doublet craters are characterized by an extended ridge between the depressions produced by the collision of the ejected curtains. When there is a slight delay between both impacts, the ridge and the ejecta curtains are not symmetric, and the delayed projectile penetrates deeper than its partner due to the bed fluidization and material displacement induced by the first impact. For experiments with sand agglomerates that are destroyed by the collision, doublets are also generated, but their morphology is considerably affected by the ejection of the projectiles debris. The resulting morphologies are similar to those found in numerical simulations (Miljković et al. in Earth Planet Sci Lett 363:121–132, 2013. https://doi.org/10.1016/j.epsl.2012.12.033) and experiments reported at considerably higher impact energies (Oberbeck and Aoyagi in J Geophys Res (1896–1977) 77(14):2419–2432, 1972. https://doi.org/10.1029/JB077i014p02419; Oberbeck in Moon 6(1–2):83–92, 1973. https://doi.org/10.1007/BF02630653), showing that the main features of doublet impact cratering can also be reproduced at low-energy scale.</p>","PeriodicalId":582,"journal":{"name":"Granular Matter","volume":"24 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4667756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence of particle size and packing on the thermal conductivity of carbonate sand","authors":"Huan He,&nbsp;Yong He,&nbsp;Guojun Cai,&nbsp;Yingfan Wang,&nbsp;Guozhu Zhang","doi":"10.1007/s10035-022-01277-9","DOIUrl":"10.1007/s10035-022-01277-9","url":null,"abstract":"<div><p>Carbonate sands (CS) have the potential to be utilized as construction materials, and their porous particles may bring unique thermal properties, which is critical for the thermal design of geosystems; however, this area of research is highly understudied. The present work provides a new contribution in this field by investigating the thermal conductivity (<i>λ</i>) of five uniform fractions of CS from the South China Sea, with emphasis on the influence of particle size and relative density of the sand. The impact of the size of particles on the index void ratios and thermal conductivity of the samples was profoundly different from that of silica sands. Contrary to silica sands, the extreme void ratio (<i>e</i>_max, <i>e</i>_min), which is critical for calculation of relative density, of the CS increased as the mean grain size increased. The maximum thermal conductivity of each fraction was negatively correlated with the particle size, and the thermal conductivity of the finer fractions exhibited higher sensitivity to the packing density. Literature models were found to be ineffective in predicting the thermal conductivity of the CS given the unique thermal energy transferring mechanisms of the porous particles. Two thermal conductivity models, stemming from semi-analytical and empirical approaches, were proposed in the light of providing useful guidance for the thermal designs that include CS.</p></div>","PeriodicalId":582,"journal":{"name":"Granular Matter","volume":"24 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4960596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Efficient DEM simulations of railway ballast using simple particle shapes","authors":"Bettina Suhr,&nbsp;Klaus Six","doi":"10.1007/s10035-022-01274-y","DOIUrl":"10.1007/s10035-022-01274-y","url":null,"abstract":"<div><p>For complex shaped materials, computational efficiency and accuracy of DEM models are usually opposing requirements. In the literature, DEM models of railway ballast often use very complex and computationally demanding particle shapes in combination with very simple contact laws. In contrast, this study suggests efficient DEM models for railway ballast using simple particle shapes together with a contact law including more physical effects. In previous works of the authors, shape descriptors, calculated in a shape analysis of two types of ballast, were used to construct simple particle shapes (clumps of three spheres). Using such a shape in DEM simulations of compression and direct shear tests, accurate results were achieved only when the contact law included additional physical effects e.g. edge breakage. A parametrisation strategy was developed for this contact law comparing DEM simulations with the measurements. Now, all the constructed simple particle shapes are parametrised allowing to study their suitability and relating their shape descriptors to those of railway ballast. The most suitable particle shapes consist of non-overlapping spheres, thus have a high interlocking potential, and have lowest sphericity and highest convexity values. In a micromechanical analysis of the four best performing shapes, three shapes show similar behaviour on the bulk and the micro-scale, while one shape differs clearly on the micro-scale. This analysis shows, which shapes can be expected to produce similar results in DEM simulations of other tests/load cases. The presented approach is a step towards both efficient and accurate DEM modelling of railway ballast.</p><h3>Graphic abstract</h3>\u0000 <figure><div><div><div><picture><source><img></source></picture></div></div></div></figure>\u0000 </div>","PeriodicalId":582,"journal":{"name":"Granular Matter","volume":"24 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2022-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10035-022-01274-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4557324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence of Methocel cellulose ether additive on micro-scale friction, abrasion and energy dissipation of rough-heterogeneous particles","authors":"Jing Ren,&nbsp;Haiwen Li,&nbsp;Kostas Senetakis,&nbsp;Gao-Feng Zhao","doi":"10.1007/s10035-022-01261-3","DOIUrl":"10.1007/s10035-022-01261-3","url":null,"abstract":"<div><p>Understanding and modeling the contact behavior of particles provides enhanced constitutive laws in discrete-based simulations as well as a strong linkage between micro- and macroscopic behavior of granular materials. In the present study, we studied the influence of a polymer-based additive composed of Methocel cellulose ether on the tribological response of rough particles with grain-scale experiments. We performed both monotonic and cyclic tests on pairs of particles subjected to repeated shearing so that to explore the additional influence of abrasion in relation to previous loading history. Each sample was tested at first in a dry state and consecutively was immersed into the polymer-based fluid. The test results indicated increased friction at the contacts of the particles when immersed in the polymer-based additive, suggesting promising applications of the Methocel cellulose ether in improving the stability of geo-systems. For the shearing tests in a dry state, abrasion influences were amplified at higher magnitudes of normal load, whereas the polymer additive acted as a fluid film (or thin coating) mitigating in this way the continuous abrasion due to repeated shearing. We incorporated the Mindlin and Deresiewicz (M–D) contact model in a modified form to analyze the tangential response of the particles. It was found that the power of the modified M–D model was directly correlated with the natural logarithm of the microslip displacement threshold, when this threshold was normalized with respect to the normal load. Based on the analysis of the closed loops from the cyclic tests, the energy dissipation was found to be reduced when the samples were immersed in the polymer fluid compared with the tests in a dry state. The test results from the present work offer some insights into the micromechanical-based analysis of particulate materials and the interactions of rough particles in the presence of polymeric fluids with potential applications in contact mechanics modeling using discrete-based tools. These results also contribute to unveiling the prevailing micromechanisms in order to understand (or interpret) bulk behavior, thus the database from the present work may provide helpful guidance in understanding granular material behavior and the interactions between particles with polymer-based additives.</p></div>","PeriodicalId":582,"journal":{"name":"Granular Matter","volume":"24 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2022-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10035-022-01261-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4560534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Small-strain shear modulus (Gmax) and microscopic pore structure of calcareous sand with different grain size distributions","authors":"Shao-Heng He,&nbsp;Meisam Goudarzy,&nbsp;Zhi Ding,&nbsp;Yifei Sun,&nbsp;Tao Xu,&nbsp;Qiong-Fang Zhang","doi":"10.1007/s10035-022-01270-2","DOIUrl":"10.1007/s10035-022-01270-2","url":null,"abstract":"<div><p>The maximum shear modulus (<i>G</i>_max) is a key material characteristic that is incorporated in advanced soil constitutive models. Numerous experimental studies have been conducted to describe the effects of particle sizes and packing characteristics on <i>G</i>_max. However, most of these studies were conducted on quartz-based sands. A review of the literature revealed that few studies have described the effects of grain size distribution (GSD) on <i>G</i>_max in calcareous sands. Therefore, bender element (BE) tests were performed on calcareous sands with different mean grain sizes (<i>d</i>₅₀), uniformity coefficients (<i>C</i>_u), and void ratios to obtain <i>G</i>_max. The BE results revealed that the <i>G</i>_max of calcareous sand increases slightly with increasing <i>d</i>₅₀ but decreases significantly with increasing <i>C</i>_u. A modified model of <i>G</i>_max incorporating the effects <i>C</i>_u and <i>d</i>₅₀ was therefore developed for calcareous sand. Moreover, microscopic observations of pore size distributions (PSD) obtained from nuclear magnetic resonance (NMR) tests were presented to demonstrate the effect of GSD on PSD and its correlation with <i>G</i>_max. The NMR results revealed that the interaggregate pore structure proportion and uniformity of the PSD decreased significantly with increasing <i>C</i>_u but increased slightly with increasing <i>d</i>₅₀. The underlying mechanism for the effect of GSD on <i>G</i>_max was related to its substantial impact on microstructure. The significant decrease in <i>G</i>_max with increasing <i>C</i>_u can be attributed to the remarkable reduction in the ratio of the interaggregate void ratio to the intraaggregate void ratio. Additionally, <i>G</i>_max was enhanced as the heterogeneity of the microporosity structure distribution decreased.</p><h3>Graphic abstract</h3>\u0000 <figure><div><div><div><picture><source><img></source></picture></div></div></div></figure>\u0000 </div>","PeriodicalId":582,"journal":{"name":"Granular Matter","volume":"24 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10035-022-01270-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4520041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the mean square displacement of intruders in freely cooling granular gases","authors":"Enrique Abad,&nbsp;Santos Bravo Yuste,&nbsp;Vicente Garzó","doi":"10.1007/s10035-022-01256-0","DOIUrl":"10.1007/s10035-022-01256-0","url":null,"abstract":"<div><p>We compute the mean square displacement (MSD) of intruders immersed in a freely cooling granular gas made up of smooth inelastic hard spheres. In general, intruders and particles of the granular gas are assumed to have different mechanical properties, implying that non-equipartition of energy must be accounted for in the computation of the diffusion coefficient <i>D</i>. In the hydrodynamic regime, the time decay of the granular temperature <i>T</i> of the cooling granular gas is known to be dictated by Haff’s law; the corresponding decay of the intruder’s collision frequency entails a time decrease of the diffusion coefficient <i>D</i>. Explicit knowledge of this time dependence allows us to determine the MSD by integrating the corresponding diffusion equation. As in previous studies of self-diffusion (intruders mechanically equivalent to gas particles) and the Brownian limit (intruder’s mass much larger than the grain’s mass), we find a logarithmic time dependence of the MSD as a consequence of Haff’s law. This dependence extends well beyond the two aforementioned cases, as it holds in all spatial dimensions for arbitrary values of the mechanical parameters of the system (masses and diameters of intruders and grains, as well as their coefficients of normal restitution). Our result for self-diffusion in a three-dimensional granular gas agrees qualitatively, but not quantitatively, with that recently obtained by Blumenfeld [arXiv: 2111.06260] in the framework of a random walk model. Beyond the logarithmic time growth, we find that the MSD depends on the mechanical system parameters in a highly complex way. We carry out a comprehensive analysis from which interesting features emerge, such a non-monotonic dependence of the MSD on the coefficients of normal restitution and on the intruder-grain mass ratio. To explain the observed behaviour, we analyze in detail the intruder’s random walk, consisting of ballistic displacements interrupted by anisotropic deflections caused by the collisions with the hard spheres. We also show that the MSD can be thought of as arising from an equivalent random walk with isotropic, uncorrelated steps. Finally, we derive some results for the MSD of an intruder inmersed in a driven granular gas and compare them with those obtained for the freely cooling case. In general, we find significant quantitative differences in the dependence of the scaled diffusion coefficient on the coefficient of normal restitution for the grain-grain collisions.</p><h3>Graphic abstract</h3>\u0000 <figure><div><div><div><picture><source><img></source></picture></div></div></div></figure>\u0000 </div>","PeriodicalId":582,"journal":{"name":"Granular Matter","volume":"24 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2022-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10035-022-01256-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4514331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}