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A bonded polyhedral DEM model for irregular cemented granular materials based on energy-conserving contact theory 基于节能接触理论的不规则胶结颗粒材料黏结多面体DEM模型
IF 2.9 3区 工程技术 Pub Date : 2025-07-16 DOI: 10.1007/s10035-025-01558-z
Ting Qiao, Siqiang Wang, Shunying Ji

Cemented granular materials, as unique granular substances possessing both permeability and load-bearing characteristics, have found extensive applications in chemical catalysis and geological engineering, and other fields. Given the significant impact of skeleton particle shape on the mechanical properties of cemented granular materials, this paper proposes a bonded polyhedral discrete element method adaptable to arbitrary skeleton particle shapes. Within this method, the adhesive surface is constructed from the contact geometry, and the interaction between particles of different shapes is described by employing an energy-conserving contact model based on strain energy density. The spring-damping model and bilinear constitutive model are utilized to characterize the elastic behavior and damage fracture behavior of cement, respectively. Moreover, the influence of skeleton particle shape on cemented granular materials is elucidated through both mesoscopic and macroscopic analyses using the proposed model. Mesoscopic results indicate that the area of the adhesive surface is a critical factor influencing the destructive force of bonding units. Variations in particle shape cause particles with identical volume and density to form adhesive surfaces with differing shapes and areas under the same conditions, leading to varied destructive forces in the bonding units. The macroscopic results reveal that both the sphericity and aspect ratio of the skeleton particles impact the strength of the cemented granular material. This effect predominantly arises from the differences in the coordination number of the accumulation bodies formed by skeleton particles of varying shapes.

Graphical Abstract

胶结颗粒材料作为一种具有渗透性和承载性的独特颗粒物质,在化学催化和地质工程等领域有着广泛的应用。鉴于骨架颗粒形状对胶结颗粒材料力学性能的重要影响,本文提出了一种适用于任意骨架颗粒形状的粘结多面体离散元方法。该方法根据接触几何构造粘接表面,采用基于应变能密度的能量守恒接触模型描述不同形状颗粒之间的相互作用。采用弹簧-阻尼模型和双线性本构模型分别表征水泥的弹性行为和损伤断裂行为。此外,利用所建立的模型,通过细观和宏观分析,阐明骨架颗粒形状对胶结颗粒材料的影响。细观结果表明,粘结面面积是影响粘结单元破坏力的关键因素。颗粒形状的变化使体积和密度相同的颗粒在相同的条件下形成形状和面积不同的粘接面,从而导致粘接单元中破坏力的变化。宏观结果表明,骨架颗粒的球度和长径比都影响胶结颗粒材料的强度。这种效应主要是由不同形状的骨架颗粒所形成的堆积体的配位数不同引起的。图形抽象
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引用次数: 0
Quantitative correlation analysis of 2D and 3D particle morphology of gravelly soils 砾质土二维和三维颗粒形态的定量相关分析
IF 2.9 3区 工程技术 Pub Date : 2025-07-16 DOI: 10.1007/s10035-025-01559-y
Jian Gong, Zehong Wu, Wenju Zhu, Zongrui Tu, Mingjie Jiang, Guoxiong Mei

Particle size and shape are critical for characterizing gravel soils, typically quantified through the analysis of two-dimensional (2D) images and three-dimensional (3D) models. However, obtaining 3D particle features can be challenging and time-consuming, often resulting in low efficiency. To address this, many researchers have recently attempted to estimate 3D morphological features from 2D data by establishing relationships between 2D image features and their 3D counterparts. Nevertheless, these methods generally focus on specific particle categories within a limited region, limiting their broader applicability. In response, this study proposes a method for acquiring extensive morphological data for gravelly soils in both 2D and 3D formats through multiple collections. Additionally, it introduces and validates a practical approach for deriving 3D information from 2D image analysis, offering a series of new equations that are compared with previously published models. The result demonstrates that 3D morphological features, including particle size and shape, can be effectively estimated from 2D data using linear and polynomial correlation equations.

粒度和形状是表征砂砾土的关键,通常通过分析二维(2D)图像和三维(3D)模型来量化。然而,获得三维粒子特征是具有挑战性和耗时的,往往导致低效率。为了解决这个问题,许多研究人员最近试图通过建立2D图像特征与3D图像特征之间的关系,从2D数据中估计3D形态特征。然而,这些方法通常只关注有限区域内的特定粒子类别,限制了它们更广泛的适用性。为此,本研究提出了一种通过多种采集获取二维和三维砂砾土形态数据的方法。此外,它还介绍并验证了一种从2D图像分析中获得3D信息的实用方法,并提供了一系列与先前发表的模型进行比较的新方程。结果表明,利用线性和多项式相关方程可以有效地从二维数据中估计三维形态特征,包括颗粒大小和形状。
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引用次数: 0
Impact of strain rate, free water, and aggregate fragmentation on the dynamic behavior of concrete in compression regime using a unique coupled DEM/CFD technique 采用独特的耦合DEM/CFD技术研究应变率、自由水和骨料破碎对受压状态下混凝土动态行为的影响
IF 2.9 3区 工程技术 Pub Date : 2025-07-08 DOI: 10.1007/s10035-025-01555-2
Marek Krzaczek, Michał Nitka, Jacek Tejchman

This paper examines the simultaneous impact of strain rate, aggregate fragmentation, and free water on the dynamic behavior of concrete in mesoscale uniaxial compression conditions. A concrete specimen measuring 50 × 50 mm2 and having a low porosity of 5% was the subject of extensive two-dimensional (2D) dynamic investigations (that is, a research limitation). Its mesostructure was based on laboratory micro-CT images. Concrete’s fracture patterns, strength, brittleness, and fluid pressure distributions were all investigated. A mesoscopic pore-scale hydro-mechanical model based on a unique fully coupled DEM/CFD technique with breakable aggregate particles was utilized to study the behavior of partially or fully saturated concrete. A four-phase material comprising aggregate, mortar, ITZs, and macropores was used to replicate concrete. Groups of small spherical particles were used to simulate the fragmentation of aggregate particles with various shapes and sizes, allowing for intra-granular fracturing among them. A network of fluid channels was assumed in a continuous region between discrete elements. A two-phase laminar compressible fluid flow (air and water) in pores and cracks was suggested for wet concrete. The accurate volumes of pores and cracks were computed for tracking the liquid/gas content. Dynamic numerical compressive tests were performed with strain rates ranging between 1 1/s and 1000 1/s. Strain rate, aggregate fragmentation, and free water flow increased the dynamic compressive strength. Because of free water confinement in pores and cracks, the pore fluid pressures retarded a fracture process, enhancing the concrete dynamic strength.

本文考察了应变率、骨料破碎和自由水对中尺度单轴压缩条件下混凝土动态行为的同时影响。一个尺寸为50 × 50 mm2,孔隙率为5%的混凝土试件进行了广泛的二维(2D)动态研究(即研究局限性)。其细观结构基于实验室显微ct图像。混凝土的断裂模式、强度、脆性和流体压力分布都进行了研究。基于独特的全耦合DEM/CFD技术,建立了含破碎集料颗粒的细观孔尺度水力学模型,研究了部分饱和和完全饱和混凝土的力学行为。一种由骨料、砂浆、ITZs和大孔组成的四相材料被用来复制混凝土。小的球形颗粒组被用来模拟不同形状和大小的聚集体颗粒的破碎,允许它们之间的颗粒内破裂。在离散单元之间的连续区域假定流体通道网络。提出了湿混凝土孔隙和裂缝中的两相层流可压缩流体(空气和水)流动。计算了孔隙和裂缝的精确体积,以跟踪液体/气体含量。动态数值压缩试验,应变速率范围为1 1/s ~ 1000 1/s。应变速率、骨料破碎和自由水流增加了动态抗压强度。由于孔隙和裂缝中的自由水约束,孔隙流体压力延缓了断裂过程,提高了混凝土的动强度。
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引用次数: 0
Low-velocity binary projectile impact cratering in loose granular media 低速二元弹丸在松散颗粒介质中的撞击
IF 2.9 3区 工程技术 Pub Date : 2025-07-08 DOI: 10.1007/s10035-025-01556-1
Yuxuan Luo, Xuegang Huang, Chun Yin, Jian Jin, Wenxue Li, Xiao Peng

Asteroid impacts are a significant area of study in astronomy; however, the specific impact properties of binary systems at close distances have not been extensively explored. This study employs a dual approach, combining low-velocity impact experiments with numerical simulations, to investigate the dynamic characteristics of binary projectiles at varying separation distances. Special focus is placed on how the initial separation distance affects the repulsion and attraction phenomena of the projectiles within granular media. Empirical evidence shows that smaller initial separation distances lead to significant repulsion between projectiles upon impact. Once a specific separation distance is reached, the binary projectiles exhibit attractive behavior post-impact. Quantitative simulations clarify the observed repulsive and attractive phenomena by considering the force chain, thereby providing a deeper understanding of the dynamic impact process.

Graphical Abstract

小行星撞击是天文学研究的一个重要领域;然而,近距离双星系统的具体撞击特性还没有得到广泛的研究。本文采用低速碰撞实验与数值模拟相结合的双重方法,研究了二元弹丸在不同分离距离下的动力学特性。特别关注的是初始分离距离如何影响颗粒介质中弹丸的排斥和吸引现象。经验证据表明,较小的初始分离距离会导致弹丸在撞击时产生显著的斥力。一旦达到一定的分离距离,二元弹丸在碰撞后表现出吸引行为。定量模拟通过考虑力链来澄清观察到的排斥和吸引现象,从而对动态碰撞过程有更深入的了解。图形抽象
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引用次数: 0
Constitutive model for soil-structure interface considering particle rearrangement 考虑颗粒重排的土-结构界面本构模型
IF 2.9 3区 工程技术 Pub Date : 2025-07-02 DOI: 10.1007/s10035-025-01546-3
Yifei Sun, Xingbo Huang

The strength-displacement behaviour of soil-structure interface should be carefully considered during slope stabilisation using soil nail. Experimental evidences have demonstrated that tangential displacement between the soil and structure could deteriorate the microstructure within the interface, resulting in a strength degradation of the soil-structure system. To capture such responses, an elastoplastic model is developed by adopting particle probabilistic entropy to characterise the evolution of particle rearrangement within the interface, where a microstructure-dependent plastic flow rule and a kinematic hardening law are proposed. The capability of the model is verified by simulating a series of interface direct shear tests, where the normal-dilatancy response and strain softening of the interface under low normal stress as well as the distinct normal-contraction under cyclic loads are well simulated. Then, the model is further implemented through FRIC subroutines for finite element (FE) simulation of the pull-out tests on a soil–nail under different overburden pressures. It is found that the FE model can reasonably simulate the pull-out behaviour of a soil nail. The stress and strain fields around the soil nail as well as the pull-out force and displacement response can be reproduced.

Graphical Abstract

土钉稳定边坡时,应充分考虑土-结构界面的强度-位移特性。实验证据表明,土-结构之间的切向位移会使界面内的微观结构恶化,从而导致土-结构体系的强度退化。为了捕获这种响应,通过采用颗粒概率熵来描述界面内颗粒重排的演变,建立了弹塑性模型,其中提出了微观结构相关的塑性流动规则和运动硬化规律。通过对一系列界面直剪试验的模拟,验证了该模型的有效性,模拟了低法向应力作用下界面的法向剪胀响应和应变软化,以及循环荷载作用下界面明显的法向收缩。然后,通过FRIC子程序对不同覆盖层压力下的土钉拔拔试验进行有限元模拟。结果表明,该有限元模型能较好地模拟土钉的拔拔过程。可以再现土钉周围的应力场、应变场以及拔拔力和位移响应。图形抽象
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引用次数: 0
Evolution of particle breakage during cyclic shear of sand 砂土循环剪切过程中颗粒破碎的演化
IF 2.9 3区 工程技术 Pub Date : 2025-06-30 DOI: 10.1007/s10035-025-01548-1
Andrzej Gluchowski, Magued Iskander

The evolution of particle breakage in sand with different mineralogy under cyclic shear loading is explored. The work focuses on the impact of factors such as the cyclic stress ratio (CSR), confining pressure, amplitude of shear stress and number of cycles. Direct shear tests were carried out at increasing stress levels and numbers of cycles. Specimens were recovered after each test and subjected to dynamic image analysis (DIA), which permitted capturing not only changes in the particle size distribution (PSD) but also evolution of particle shapes for approximately 4% of all particles tested at a fine scale. Detailed analysis of the PSD curve combined with an analysis of the evolution of particle shapes, demonstrates how soil gradation evolves during cyclic loading and how this impacts the mechanical behavior of sand. The study presents a novel framework for predicting particle breakage in sands subjected to cyclic loading using readily available stress–strain data, eliminating the need for complex and costly fine-scale particle size analyses. The method adapts the existing Loading Intensity (LI) framework, incorporating an efficiency factor that accounts for the diminishing effect of cyclic loading as the number of cycles and cyclic stress ratio increase. A strong correlation was established between the Particle Partition Potential (P3) and Hardin's Breakage Index (Br), enabling the prediction of particle breakage with generally small errors (< 2%) and remarkable accuracy at higher breakage levels. This framework offers a reliable and practical tool for assessing soil degradation under cyclic loading.

Graphical Abstract

探讨了不同矿质砂在循环剪切作用下颗粒破碎的演化规律。重点研究了循环应力比(CSR)、围压、剪应力幅值和循环次数等因素的影响。在不断增加的应力水平和循环次数下进行了直剪试验。每次测试后,样品都被回收,并进行动态图像分析(DIA),这不仅可以捕获颗粒尺寸分布(PSD)的变化,还可以捕获约4%的细尺度测试颗粒的颗粒形状的演变。对PSD曲线的详细分析结合颗粒形状的演变分析,展示了循环加载过程中土壤级配的演变以及这如何影响砂土的力学行为。该研究提出了一种新的框架,可以利用现成的应力应变数据预测循环加载下砂土中的颗粒破碎,从而消除了复杂且昂贵的细尺度粒度分析的需要。该方法采用了现有的加载强度(LI)框架,纳入了一个效率因子,该因子考虑了循环加载随着循环次数和循环应力比的增加而减小的影响。颗粒分割电位(P3)与哈丁破碎指数(Br)之间存在很强的相关性,使得预测颗粒破碎的误差通常很小(< 2%),在更高的破碎水平上具有显著的准确性。该框架为评估循环荷载下的土壤退化提供了可靠和实用的工具。图形抽象
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引用次数: 0
Experimental study of inverse-grading transport of single coarse particles of different shapes based on the YOLO algorithm 基于YOLO算法的不同形状单粒粗颗粒反分级输运实验研究
IF 2.9 3区 工程技术 Pub Date : 2025-06-30 DOI: 10.1007/s10035-025-01549-0
Aibing Jin, He Wang, Meichen Liu, Hao Sun, Lishan Zhao, Lichang Wei, Muya Li

The flow of granular particles is characterized by particle-size sorting called “inverse-grading transport”, and it is important to carry out a series of basic studies on the inverse-grading transport behavior of coarse particles for disaster prevention and mitigation and related theoretical study of particle separation. In order to investigate the influence of shape on the inverse-grading transport characteristics of a single coarse particle, a series of cyclic shear tests were conducted utilizing 3D sand printing technology alongside a self-constructed two-dimensional cyclic shear test device. Using the YOLO target detection algorithm, the inverse-grading transport trajectory, rotation characteristics, and local structure were analyzed. A kinematic equivalent analysis method classified transport behaviors of coarse particles, revealing correlations between single coarse particles of different shapes and macroscopic segregation patterns. The results indicate that: (1) Single coarse particles slowly ascend from the bottom center, with their vertical transport rate increasing until they reach the surface. (2) Particle shape significantly affects the inverse-grading transport of single coarse particles. The closer the coarse particles are to the free surface, the lower is the local volume fraction above them, while the volume fraction below them increases. (3) The inverse-grading transport of coarse particles is significantly correlated with their own rotation and with changes in the local structure of the granular medium around them. Our experiments thus show that the inverse-grading phenomenon of landslide-debris flow is mainly caused by changes in the local structure of the granular medium around the coarse particles.

颗粒颗粒的流动以粒径分选为特征,称为“反级配输运”,开展一系列粗颗粒反级配输运行为的基础研究和颗粒分离的相关理论研究对于防灾减灾具有重要意义。为了研究形状对单个粗颗粒反级配输运特性的影响,利用3D砂打印技术和自建的二维循环剪切试验装置进行了一系列循环剪切试验。利用YOLO目标检测算法,分析了反分级传输轨迹、旋转特性和局部结构。运动学等效分析方法对粗颗粒的输运行为进行了分类,揭示了不同形状的单个粗颗粒与宏观偏析模式之间的相关性。结果表明:(1)单个粗颗粒从底部中心缓慢上升,垂直输运速率逐渐增大,直至到达地表;(2)颗粒形状显著影响单个粗颗粒的反级输运。粗颗粒越靠近自由表面,其上方局部体积分数越低,下方局部体积分数越高。(3)粗颗粒的反级输运与其自身的旋转以及周围颗粒介质局部结构的变化有显著的相关性。因此,我们的实验表明,滑坡-泥石流的反级配现象主要是由粗颗粒周围颗粒介质的局部结构变化引起的。
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引用次数: 0
Multi-scale analysis of pore structure and permeability simulation of coral gravel under particle breakage using X-ray computerized tomography 基于x射线计算机断层成像的珊瑚砾石颗粒破碎孔隙结构多尺度分析及渗透率模拟
IF 2.9 3区 工程技术 Pub Date : 2025-06-30 DOI: 10.1007/s10035-025-01552-5
Lei Yan, Xianwei Zhang, Xinyu Liu, Haodong Gao, Zefeng Zhou, Gang Wang

Coral gravel soil, coral sand, and coral-derived mixed soil are common construction and building materials in coastal areas and islands, which are characterized by biologically formed fossilized sediments such as coral gravels (CG). The unique pore structures and irregular particle shapes of CG result in high porosity and significant breakage potential, influencing their mechanical properties and hydraulic behavior in engineering practice. However, the evolution of pore structures in CG during particle breakage and its impact on permeability remains poorly understood. This study employs a multi-scale analysis method, combining X-ray computed tomography and seepage simulations, to quantitatively investigate the evolution of pore structure and permeability in four types of CG: rod-shaped, branchlet, massive, and flaky during the particle breakage process. Test results categorized the internal pores of particles into intraparticle, blind, and through pores and demonstrated that as particle breakage occurs, intraparticle and blind pores decrease while through pores increase, leading to enhanced permeability. In the branchlet and flaky CG samples, intraparticle porosity decreases from 74.43% and 72.88% to 22.32% and 12.2%, respectively, while through porosity significantly increases with the progression of particle fragmentation. In addition, an exponential correlation between through porosity and permeability is established, supported by a regression model. This study proposes a framework for understanding multiscale pore evolution during particle breakage by analyzing changes in porosity and seepage behavior, improving the comprehension of the pore structure and hydraulic performance of fragmented granular materials. It provides valuable insights for the design and performance prediction of biological materials in offshore and geotechnical engineering applications.

Graphical Abstract

珊瑚砾石土、珊瑚砂和珊瑚源混合土是沿海地区和岛屿常见的建筑材料,其特征是珊瑚砾石(CG)等生物形成的化石沉积物。CG独特的孔隙结构和不规则的颗粒形状导致其孔隙率高,破坏潜力大,在工程实践中影响了其力学性能和水力行为。然而,颗粒破碎过程中孔隙结构的演化及其对渗透率的影响尚不清楚。本研究采用多尺度分析方法,结合x射线计算机断层扫描和渗流模拟,定量研究了颗粒破碎过程中棒状、小枝状、块状和片状四种类型孔隙结构和渗透率的演变。试验结果将颗粒内部孔隙分为颗粒内孔、盲孔和透孔,并表明随着颗粒破碎,颗粒内孔和盲孔减少,透孔增加,导致渗透率提高。在小枝状和片状CG样品中,颗粒内孔隙度分别从74.43%和72.88%降低到22.32%和12.2%,而通过孔隙度随着颗粒破碎程度的增加而显著增加。建立了孔隙度与渗透率的指数相关关系,并建立了回归模型。本研究通过分析颗粒破碎过程中孔隙和渗流行为的变化,提出了一个理解颗粒破碎过程中多尺度孔隙演化的框架,提高了对破碎颗粒材料孔隙结构和水力性能的认识。它为海洋和岩土工程应用中生物材料的设计和性能预测提供了有价值的见解。图形抽象
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引用次数: 0
Mesoscopic mechanics and microstructural evolution of triaxially compressed polydisperse pebbles: insights from DEM modeling 三轴压缩多分散卵石的细观力学和微观结构演化:来自DEM模型的见解
IF 2.9 3区 工程技术 Pub Date : 2025-06-27 DOI: 10.1007/s10035-025-01550-7
Deepak K. Pawar, Ratna Kumar Annabattula, Narasimhan Swaminathan

A computational framework that utilizes the discrete element method (DEM) was developed to conduct triaxial compression tests on lithium-based pebbles. In addition, the process for determining optimized simulation parameters for performing stress-controlled numerical hydrostatic and triaxial compression tests using LIGGGHTS has been outlined. This framework was employed to study the influence of the polydispersity of pebbles on the Drucker-Prager (D-P) parameter, which is the friction angle. The study revealed that the effect of polydispersity, measured by the polydispersity index ((lambda )) was negligible, as the value of friction angle ((beta )) remained constant at (approx 29^circ ) for (lambda le 0.5). However, in highly polydisperse samples with (lambda =0.8), (beta ) increased to (approx 31^circ ). Additionally the dilatancy angle ((psi )) decreases as (lambda ) increases. The difference between (beta ) and (psi ) increases with (lambda ), and thus, the associative flow rule is not suitable for highly polydisperse samples. To conduct a more detailed analysis of the mesoscopic mechanics, three parameters based on the mean number of contacts, which governed the microstructural similarity of the sample and the extent of particle participation, were examined. Additionally, two local parameters based on Voronoi tessellation were investigated. These parameters highlight how changing (lambda ) influences the local deformation and characterizes the local structural variation in the granular samples. In particular it was found that, the participation of particles to the total deformation was higher in samples with high polydispersity.

利用离散元法(DEM)开发了一个计算框架,对锂基鹅卵石进行三轴压缩试验。此外,还概述了使用lighghts进行应力控制的数值流体静压和三轴压缩试验确定优化模拟参数的过程。采用该框架研究了鹅卵石多分散性对摩擦角Drucker-Prager (D-P)参数的影响。研究显示,多分散性的影响,以多分散性指数((lambda ))可以忽略不计,因为摩擦角((beta ))保持不变 (approx 29^circ ) 为了 (lambda le 0.5). 然而,在高度分散的样品中 (lambda =0.8), (beta ) 增加到 (approx 31^circ ). 另外,膨胀角((psi ))随 (lambda ) 增加。两者的区别 (beta ) 和 (psi ) 随着 (lambda ),因此,联想流动规律不适用于高度多分散的样品。为了对细观力学进行更详细的分析,基于平均接触数的三个参数进行了检查,这些参数控制了样品的微观结构相似性和颗粒参与程度。此外,还研究了基于Voronoi镶嵌的两个局部参数。这些参数突出了变化的程度 (lambda ) 影响局部变形,表征颗粒状试样的局部结构变化。特别发现,在多分散性高的试样中,颗粒对总变形的参与程度更高。
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引用次数: 0
Representations of major physical statistics of windblown sand in the atmospheric surface layer 大气表层风沙的主要物理统计表示
IF 2.9 3区 工程技术 Pub Date : 2025-06-26 DOI: 10.1007/s10035-025-01544-5
Tian-Li Bo, Si-Jiang Liu

The streamwise and vertical wind speed fluctuations predicted by a multi-scale wind speed fluctuation prediction model were introduced into a one-dimensional windblown sand model to simulate windblown sand under different friction velocities and particle sizes. And the scaling relation of major physical statistics was studied. Our results show that the mean and standard deviation of sand transport rate and average saltation velocity are proportional to u*3/g. The mean and standard deviation of average saltation length are proportional to u*2/g. The mean and standard deviation of speed and angle distribution of lift-off sand particles over time also need to consider friction velocity (u*) and particle size. Here, g represents the gravitational acceleration. Empirical representations of mean and standard deviation of these five statistics were obtained based on the scaling relation, and the variations of coefficients with dimensionless particle size were mainly considered. Empirical representations provide a basis for simulating windblown sand over a large spatial range and introducing turbulent motions in the study of aeolian landforms.

Graphical abstract

Distribution of the mean of lift-off speed under different frictional wind speeds.

在一维风沙模型中引入多尺度风速波动预测模型预测的顺流和垂直风速波动,模拟不同摩擦速度和不同粒径下的风沙。研究了主要物理统计量的标度关系。结果表明,输沙速率和平均跃移速度的平均值和标准差与u*3/g成正比。平均跃变长度的均值和标准差与u*2/g成正比。提离砂粒速度和角度随时间分布的平均值和标准差还需要考虑摩擦速度(u*)和粒度。这里g代表重力加速度。根据标度关系得到了这五项统计量的均值和标准差的经验表示,并主要考虑了系数随无因次粒度的变化。经验表征为在大空间范围内模拟风沙和在风成地貌研究中引入湍流运动提供了基础。图示:不同摩擦风速下的平均起离速度分布。
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引用次数: 0
期刊
Granular Matter
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