﻿ 无黏性颗粒柱坍塌流动的尺寸效应分析
 上海理工大学学报  2023, Vol. 45 Issue (6): 567-573 PDF

Analysis of size effect in the collapse and flow of cohesionless granular columns
SUN Yinghao, NIU Zhiyang, WANG Dengming
College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China
Abstract: In order to analyze the size effect in discrete material flow and reveal transient behaviors of the mass flows in engineering practice at different scales, the experiment systematically investigated the collapse and flow process of the cohesionless granular columns driven by gravity using the particle high-speed measurement device and a constructed quasi-2D particle collapse experimental platform. The influences of column aspect ratio, as well as initial system size on the mobility and deposit morphology of the collapsing material were mainly analyzed by the particle image velocimetry（PIV）technique. The results showed that the flow front position of the granular columns with different initial lengths exhibited similar evolving characteristics with time, but the size change of the system had a significant effect on its final deposit morphology, especially the flow distance. By analyzing the critical length at which the size effect disappears, a scaling law of flow distance of a granular column with its aspect ratios and initial length was proposed, which can be used to accurately characterize the effect of column size on the mobility of collapsing material.
Key words: granular material     collapse     flow distance     size effect     PIV technique     scaling law

1 实验平台和测量方法 1.1 实验装置和方法

 图 1 颗粒柱坍塌的实验装置示意图 Fig. 1 Experimental device for the collapse of granular columns

1.2 数据测量和分析

2 不同尺寸颗粒柱坍塌后的流动和沉积 2.1 基本坍塌动力学行为

 图 2 不同瞬时时刻颗粒柱坍塌过程中颗粒的堆积构型 Fig. 2 Deposit configuration of granular columns during the collapse at several instantaneous moments

 图 3 典型纵横比下不同初始长度颗粒柱的归一化流动前端随时间的变化 Fig. 3 Normalized flow front position over time for the collapse of granular columns with different initial lengths and representative aspect ratios

2.2 沉积形态的尺寸效应

 图 4 不同初始长度的颗粒柱坍塌后的堆积形态 Fig. 4 Stacking patterns of the granular columns with different initial lengths after collapse

 图 5 不同纵横比a的颗粒柱体坍塌后归一化流动距离随着柱体初始长度${L}_{\mathrm{i}}/d$变化的规律 Fig. 5 Variation of the normalized flow distance with initial column length ${L}_{\mathrm{i}}/d$ after the collapse of granular columns with different aspect ratios
2.3 考虑尺寸效应的形态标度律

 图 6 不同初始长度的颗粒柱坍塌后归一化流动距离随柱体纵横比$a$的变化 Fig. 6 Variation of the normalized flow distance with the aspect ratio of the column with different initial lengths

 ${L}^{\mathrm{*}}=\left\{\begin{array}{c}{\lambda }_{1}a,\;\;a < 3\\ {\lambda }_{2}{a}^{\beta },\;\;a\geqslant 3\end{array}\right.$ (1)

 ${L}^{*}={L}_{\infty }^{*}\left(1-{{\rm{e}}}^{-\left({L}_{\mathrm{i}}/d\right)/A}\right)$ (3)

3 结　论

 [1] 厚美瑛, 陆坤权. 奇异的颗粒物质[J]. 新材料产业, 2001(2): 26-28. [2] IVERSON R M, VALLANCE J W. New views of granular mass flows[J]. Geology, 2001, 29(2): 115-118. DOI:10.1130/0091-7613(2001)029<0115:NVOGMF>2.0.CO;2 [3] PITMAN E B, NICHITA C C, PATRA A, et al. Computing granular avalanches and landslides[J]. Physics of Fluids, 2003, 15(12): 3638-3646. DOI:10.1063/1.1614253 [4] HU Y X, LI H B, LU G D, et al. Influence of size gradation on particle separation and the motion behaviors of debris avalanches[J]. Landslides, 2021, 18(5): 1845-1858. DOI:10.1007/s10346-020-01596-z [5] DENLINGER R P, IVERSON R M. Granular avalanches across irregular three-dimensional terrain: 1. Theory and computation[J]. Journal of Geophysical Research: Earth Surface, 2004, 109(F1): F01014. [6] LUBE G, HUPPERT H E, SPARKS R S J, et al. Collapses of two-dimensional granular columns[J]. Physical Review E, 2005, 72(4): 041301. [7] LAJEUNESSE E, MONNIER J B, HOMSY G M. Granular slumping on a horizontal surface[J]. Physics of Fluids, 2005, 17(10): 103302. DOI:10.1063/1.2087687 [8] WARNETT J M, DENISSENKO P, THOMAS P J, et al. Scalings of axisymmetric granular column collapse[J]. Granular Matter, 2014, 16(1): 115-124. DOI:10.1007/s10035-013-0469-x [9] CABRERA M, ESTRADA N. Granular column collapse: analysis of grain-size effects[J]. Physical Review E, 2019, 99(1): 012905. DOI:10.1103/PhysRevE.99.012905 [10] MAN T, HUPPERT H E, LI L, et al. Deposition morphology of granular column collapses[J]. Granular Matter, 2021, 23(3): 59. DOI:10.1007/s10035-021-01112-7 [11] MAN T, HUPPERT H E, LI L, et al. Finite-size analysis of the collapse of dry granular columns[J]. Geophysical Research Letters, 2021, 48(24): e2021GL096054. DOI:10.1029/2021GL096054 [12] YANG G C, JING L, KWOK C Y, et al. Size effects in underwater granular collapses: experiments and coupled lattice Boltzmann and discrete element method simulations[J]. Physical Review Fluids, 2021, 6(11): 114302. DOI:10.1103/PhysRevFluids.6.114302 [13] LUBE G, HUPPERT H E, SPARKS R S J, et al. Static and flowing regions in granular collapses down channels[J]. Physics of Fluids, 2007, 19(4): 043301. DOI:10.1063/1.2712431 [14] BALMFORTH N J, KERSWELL R R. Granular collapse in two dimensions[J]. Journal of Fluid Mechanics, 2005, 538: 399-428. DOI:10.1017/S0022112005005537 [15] XU X R, SUN Q C, JIN F, et al. Measurements of velocity and pressure of a collapsing granular pile[J]. Powder Technology, 2016, 303: 147-155. DOI:10.1016/j.powtec.2016.09.036 [16] SARLIN W, MORIZE C, SAURET A, et al. Collapse dynamics of dry granular columns: from free-fall to quasistatic flow[J]. Physical Review E, 2021, 104(6): 064904. DOI:10.1103/PhysRevE.104.064904 [17] DOYLE E E, HUPPERT H E, LUBE G, et al. Static and flowing regions in granular collapses down channels: insights from a sedimenting shallow water model[J]. Physics of Fluids, 2007, 19(10): 106601. DOI:10.1063/1.2773738 [18] TAPIA-MCCLUNG H, ZENIT R. Computer simulations of the collapse of columns formed by elongated grains[J]. Physical Review E, 2012, 85(6): 061304. DOI:10.1103/PhysRevE.85.061304 [19] CHOU H T, LEE C F. Falling process of a rectangular granular step[J]. Granular Matter, 2011, 13(1): 39-51. DOI:10.1007/s10035-010-0221-8 [20] POLANÍA O, CABRERA M, RENOUF M, et al. Collapse of dry and immersed polydisperse granular columns: a unified runout description[J]. Physical Review Fluids, 2022, 7(8): 084304. DOI:10.1103/PhysRevFluids.7.084304 [21] 满腾, 葛转, HUPPERT H E, 等. 颗粒柱塌落中的尺寸效应和瞬态流变性研究[J]. 计算力学学报, 2022, 39(3): 381-388. DOI:10.7511/jslxCMGM202215 [22] LAI Z Q, JIANG E H, ZHAO L J, et al. Granular column collapse: analysis of inter-particle friction effects[J]. Powder Technology, 2023, 415: 118171. DOI:10.1016/j.powtec.2022.118171 [23] GIROLAMI L, HERGAULT V, VINAY G, et al. A three-dimensional discrete-grain model for the simulation of dam-break rectangular collapses: comparison between numerical results and experiments[J]. Granular Matter, 2012, 14(3): 381-392. DOI:10.1007/s10035-012-0342-3 [24] CROSTA G B, IMPOSIMATO S, RODDEMAN D. Numerical modeling of 2-D granular step collapse on erodible and nonerodible surface[J]. Journal of Geophysical Research: Earth Surface, 2009, 114(F3): F03020.