Abstract
Rigidity gain can be observed in sand aging but is usually accompanied by minute densification. This phenomenon is inconsistent with the conventional diagram of rigidity/jamming transition for granules and therefore too enigmatic to be utilized in the field by engineers. Therefore, this study aims to reveal the mechanism of rigidity gain and reconcile the inconsistency in sand aging. The aging processes of two sand packings with the same mono-sized spheres but different initial densities were reproduced via discrete element method simulations. In the simulations, sudden increases in the solid fraction destroyed the similarity between the evolution processes of rigidity gain and densification, confirming the inadequacy of explaining this gain considering densification alone. The bond-orientational order remained almost unchanged, while the contact-force order generally increased over time with distinct drops, similar to the change in rigidity gain. This evolution pattern is attributed to the laws of thermodynamics, which require the Gibbs energy of the sand packing to decrease over time, and contact-force order reduction assists with this decrease. Simultaneously, this reduces the nonaffinity under shear and rigidity demolition, consequently dominating the rigidity gain mechanism in sand aging. Based on these findings, the conventional diagram of rigidity transition was modified to jointly consider the effects of the solid fraction and structural orders. The proposed diagram can depict how the sand packing rigidity is enhanced over time and can better guide the consideration of the sand aging effect in the field.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Al-Sanad HA, Ismael NF (1996) Effects of aging on freshly deposited or densified calcareous sands. Transportation Research Record 1547(1):76–81, DOI: https://doi.org/10.1177/0361198196154700111
ASTM D854 (2014) Standard test methods for specific gravity of soil solids by water pycnometer. ASTM D854, ASTM International, West Conshohocken, PA, USA
ASTM D4253 (2016) Standard test method for maximum index density and unit weight of soils using a vibratory table. ASTM D4253, ASTM International, West Conshohocken, PA, USA
ASTM D4254 (2016) Standard test methods for minimum index density and unit weight of soils and calculation of relative density. ASTM D4254, ASTM International, West Conshohocken, PA, USA
Augustesen A, Liingaard M, Lade PV (2004) Evaluation of time-dependent behavior of soils. International Journal of Geomechanics 4(3):137–156, DOI: https://doi.org/10.1061/(ASCE)1532-3641(2004)4:3(137)
Aziz M, Sheikh FN, Qureshi MU, Rasool AM, Irfan M (2021) Experimental study on endurance performance of lime and cement-treated cohesive soil. KSCE Journal of Civil Engineering 25(9): 3306–3318, DOI: https://doi.org/10.1007/s12205-021-2154-7
Bagi K (2003) Statistical analysis of contact force components in random granular assemblies. Granular Matter 5(1):45–54, DOI: https://doi.org/10.1007/s10035-002-0123-5
Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: An explanation of the 1/f noise. Physical Review Letters 59(4):381–384, DOI: https://doi.org/10.1103/PhysRevLett.59.381
Baxter CD, Mitchell JK (2004) Experimental study on the aging of sands. Journal of Geotechnical and Geoenvironmental Engineering 130(10): 1051–1062, DOI: https://doi.org/10.1061/(ASCE)1090-0241(2004)130:10(1051)
Born M, Huang K (1956) Dynamical theory of crystal lattices. Clarendon Press, Oxford, UK
Bowman ET, Soga K (2003) Creep, ageing and microstructural change in dense granular materials. Soils and Foundation 43(4):107–117, DOI: https://doi.org/10.3208/sandf.43.4_107
Bureau L, Baumberger T, Caroli C (2001) Jamming creep of a frictional interface. Physical Review E 64(3):031502, DOI: https://doi.org/10.1103/PhysRevE.64.031502
Chang L, Chen Q (2021) Simulation on the process of contact erosion between cohesionless soils. KSCE Journal of Civil Engineering 25(9):2884–2892, DOI: https://doi.org/10.1007/s12205-021-2154-7
Chikkadi V, Schall P (2012) Nonaffine measures of particle displacements in sheared colloidal glasses. Physical Review E 85(3):031402, DOI: https://doi.org/10.1103/PhysRevE.85.031402
Chow JK, Tai P, Li J, Li Z, Wang W (2021) Over-stiff and over-damped problem of multi-sphere approach for ellipse-wall collision using discrete element method. Powder Technology 394:735–747, DOI: https://doi.org/10.1016/j.powtec.2021.09.008
Corwin EI, Jaeger HM, Nagel SR (2005) Structural signature of jamming in granular media. Nature 435(7045):1075–1078, DOI: https://doi.org/10.1038/nature03698
Dagois-Bohy S, Tighe BP, Simon J, Henkes S, Van Hecke M (2012) Soft-sphere packings at finite pressure but unstable to shear. Physical Review Letters 109(9):095703, DOI: https://doi.org/10.1103/PhysRevLett.109.095703
Errington JR, Debenedetti PG (2001) Relationship between structural order and the anomalies of liquid water. Nature 409(6818):318, DOI: https://doi.org/10.1038/35053024
Gao Y, Chen Z, Airey D (2019) Compression index versus natural water content relationships for China’s coastal soft clays. KSCE Journal of Civil Engineering 23(11):4611–4620, DOI: https://doi.org/10.1007/s12205-019-1652-3
Goldenberg C, Tanguy A, Barrat JL (2007) Particle displacements in the elastic deformation of amorphous materials: Local fluctuations vs. non-affine field. Europhysics Letters 80(1):16003, DOI: https://doi.org/10.1209/0295-5075/80/16003
Howie JA, Shozen T, Vaid YP (2002) Effect of ageing on stiffness of very loose sand. Canadian Geotechnical Journal 39(1):149–156, DOI: https://doi.org/10.1139/101-085
Jardine RJ, Standing JR, Chow FC (2006) Some observations of the effects of time on the capacity of piles driven in sand. Géotechnique 56(4):227–244, DOI: https://doi.org/10.1680/geot.2006.56.4.227
Joshi RC, Achari G, Kaniraj SR, Wijeweera H (1995) Effect of aging on the penetration resistance of sands. Canadian Geotechnical Journal 32(5):767–782, DOI: https://doi.org/10.1139/t95-075
Karimpour H, Lade PV (2013) Creep behavior in Virginia Beach sand. Canadian Geotechnical Journal 50(11):1159–1178, DOI: https://doi.org/10.1139/cgj-2012-0467
Kawasaki T, Tanaka H (2014) Structural evolution in the aging process of supercooled colloidal liquids. Physical Review E 89(6):062315, DOI: https://doi.org/10.1103/PhysRevE.89.062315
Kim BS, Sakakibara T, Park SW, Kato S (2021) Effects of grain shape on mechanical behavior of granular materials using DEM analysis. KSCE Journal of Civil Engineering 25(6):1939–1950, DOI: https://doi.org/10.1007/s12205-021-0582-z
Kim HK, Santamarina JC (2018) Spatially varying small-strain stiffness in soils subjected to K0 loading. KSCE Journal of Civil Engineering 22(4):1101–1108, DOI: https://doi.org/10.1007/s12205-017-0547-4
Koeze DJ, Hong L, Kumar A, Tighe BP (2020) Elasticity of jammed packings of sticky disks. Physical Review Research 2(3):032047, DOI: https://doi.org/10.1103/PhysRevResearch.2.032047
Komurka VE, Wagner AB, Edil TB (2003) Estimating soil/pile set-up. Report No. 03–05, Highway Research Program, Madison, WI, USA
Kuhn M, Bagi K (2009) Specimen size effect in discrete element simulations of granular assemblies. Journal of Engineering Mechanics 135(6):485–492, DOI: https://doi.org/10.1061/(ASCE)0733-9399(2009)135:6(485)
Kuhn MR, Mitchell JK (1993) New perspectives on soil creep. Journal of Geotechnical Engineering 119(3):507–524, DOI: https://doi.org/10.1061/(ASCE)0733-9410(1993)119:3(507)
Leung CF, Lee FH, Yet NS (1997) The role of particle breakage in pile creep in sand. Canadian Geotechnical Journal 33(6):888–898, DOI: https://doi.org/10.1139/t96-119
Li YW, Ciamarra MP (2004) Accurate determination of the translational correlation function of two-dimensional solids. Physical Review E 100(6):062606, DOI: https://doi.org/10.1103/PhysRevE.100.062606
Li Z, Wang YH, Chow JK (2018) Density effect and associated unjamming events on the aging-induced stiffness increase in sand. International Journal of Geomechanics 18(12):04018173, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001320
Li Z, Wang YH, Ma CH, Mok CMB (2017) Experimental characterization and 3D DEM simulation of bond breakages in artificially cemented sands with different bond strengths when subjected to triaxial shearing. Acta Geotechnica 12(5):987–1002, DOI: https://doi.org/10.1007/s11440-017-0593-6
Liu AJ, Nagel SR (1998) Nonlinear dynamics: Jamming is not just cool any more. Nature 396(6706):21–22, DOI: https://doi.org/10.1038/23819
Liu Y, Xu C, Xu G, Mao H, Xiao Z (2021) Macro-micro mechanical behavior of crushable granular materials under generalized stress conditions. KSCE Journal of Civil Engineering 25(5):1634–1644, DOI: https://doi.org/10.1007/s12205-021-1035-4
Mesri G, Feng TW, Benak JM (1990) Postdensification penetration resistance of clean sands. Journal of Geotechnical Engineering 116(7): 1095–1115, DOI: https://doi.org/10.1061/(ASCE)0733-9410(1990)116:7(1095)
Michalowski RL, Nadukuru SS (2012) Static fatigue, time effects, and delayed increase in penetration resistance after dynamic compaction of sands. Journal of Geotechnical and Geoenvironmental Engineering 138(5):564–574, DOI: https://doi.org/10.1061/(ASCE)GT.1943-5606.0000611
Mickel W, Kapfer SC, Schröder-Turk GE, Mecke K (2013) Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter. The Journal of Chemical Physics 138(4):044501, DOI: https://doi.org/10.1063/1.4774084
Mitchell JK (1986) Practical problems from surprising soil behavior, 20th Terzaghi Lecture. Journal of Geotechnical Engineering 112(3): 259–289, DOI: https://doi.org/10.1016/0148-9062(86)90076-8
Mitchell JK (2008) Aging in sand — A continuing enigma? Proceedings of the 6th international conference on case histories in geotechnical engineering, August 11, Arlington, VA, USA
Morgan JK, Boettcher MS (1999) Numerical simulations of granular shear zones using the distinct element method: 1. Shear zone kinematics and the micromechanics of localization. Journal of Geophysical Research: Solid Earth 104(B2):2703–2719, DOI: https://doi.org/10.1029/1998JB900056
Ngan AHW (2004) On distribution of contact forces in random granular packings. Physica A: Statistical Mechanics and its Applications 339(3–4):207–227, DOI: https://doi.org/10.1016/j.physa.2004.03.068
O’Hern CS, Langer SA, Liu AJ, Nagel SR (2001) Force distributions near jamming and glass transitions. Physical Review Letters 86(1): 111, DOI: https://doi.org/10.1103/PhysRevLett.86.111
O’Sullivan C, Bray JD (2004) Selecting a suitable time step for discrete element simulations that use the central difference time integration scheme. Engineering Computations 21:278–303, DOI: https://doi.org/10.1108/02644400410519794
Ostojic S, Panja D (2006) Elasticity from the force network ensemble in granular media. Physical Review Letters 97(20):208001, DOI: https://doi.org/10.1103/PhysRevLett.97.208001
Palombo M, Gabrielli A, Servedio VDP, Ruocco G, Capuani S (2013) Structural disorder and anomalous diffusion in random packing of spheres. Scientific Reports 3:2631, DOI: https://doi.org/10.1038/srep02631
Park KH, Jung YH, Chung CK (2017) Evolution of stiffness anisotropy during creep of engineered silty sand in South Korea. KSCE Journal of Civil Engineering 21(9):2168–2176, DOI: https://doi.org/10.1007/s12205-016-1105-1
Rycroft C (2009) Voro++: A three-dimensional Voronoi cell library in C++. Chaos 19:041111, DOI: https://doi.org/10.2172/946741
Schlegel M, Brujic J, Terentjev EM, Zaccone A (2016) Local structure controls the nonaffine shear and bulk moduli of disordered solids. Scientific Reports 6:18724, DOI: https://doi.org/10.1038/srep18724
Schmertmann JH (1991) The mechanical aging of soils. Journal of Geotechnical Engineering 117(9):1288–1330, DOI: https://doi.org/10.1061/(ASCE)0733-9410(1991)117:9(1288)
Squire DR, Holt AC, Hoover WG (1969) Adiabatic elastic constants for argon. theory and Monte Carlo calculations. Physica 42(3):388–397, DOI: https://doi.org/10.1016/0031-8914(69)90217-1
Steinhardt PJ, Nelson DR, Ronchetti M (1983) Bond-orientational order in liquids and glasses. Physical Review B 28(2):784–805, DOI: https://doi.org/10.1103/PhysRevB.28.784
Suarez NR (2012) Micromechanical aspects of aging in granular soils. PhD Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
Tatsuoka F, Uchimura T, Santucci de Magistris F, Hayano K, Di Benedetto H, Koseki J, Siddiquee MSA (1999) Time-dependent deformation characterisitcs of stiff geomaterials in engineering practice. Proceedings of the second international conference on pre-failure deformation characteristics of geomaterials, Balkema, Torino, Italy
Torquato S, Truskett TM, Debenedetti PG (2000) Is random close packing of spheres well defined? Physical Review Letters 84(10): 2064–2067, DOI: https://doi.org/10.1103/PhysRevLett.84.2064
Toyota H, Takada S (2021) Mechanical properties of cementitious sand and sand with small cyclic shear strain to assess aging effects on liquefaction. Acta Geotechnica, DOI: https://doi.org/10.1007/s11440-021-01368-6
Trappe V, Prasad V, Cipelletti L, Segre PN, Weitz DA (2001) Jamming phase diagram for attractive particles. Nature 411(6839):772–775, DOI: https://doi.org/10.1038/35081021
Wang YH, Gao Y, (2014) Examining the behavior and mechanisms of structuration in sand under the K0 condition. Granular Matter 16(1):55–68, DOI: https://doi.org/10.1007/s10035-013-0457-1
Wang YH, Gao Y, Leung G (2016) Experimental characterizations of an aging mechanism of sands. Journal of Geotechnical and Geoenvironmental Engineering 142(2):06015016, DOI: https://doi.org/10.1061/(ASCE)GT.1943-5606.0001413
Wang J, Xiao M, Evans JC, Qiu T, Salam S (2019) Time-dependent cone penetration resistance of a postliquefaction sand deposit at shallow depth. Journal of Geotechnical and Geoenvironmental Engineering 145(6):04019021, DOI: https://doi.org/10.1061/(ASCE)GT.1943-5606.0002049
Wang Z, Michalowski RL (2015) Contact fatigue in silica sand — Observations and modeling. Geomechanics for Energy and the Environment 4:88–99, DOI: https://doi.org/10.1016/j.gete.2015.07.003
Wang YH, Yun ML, Yan G (2014) Examining the mechanisms of sand creep using DEM simulations. Granular Matter 16(5):733–750, DOI: https://doi.org/10.1007/s10035-014-0514-4
Wu M, Wang J (2020) A DEM investigation on crushing of sand particles containing intrinsic flaws. Soils and Foundations 60(2): 562–572, DOI: https://doi.org/10.1016/j.sandf.2020.03.007
Yao W, Hu B, Zhan H, Ma C, Zhao N (2019) A novel unsteady fractal derivative creep model for soft interlayers with varying water contents. KSCE Journal of Civil Engineering 23(12):5064–5075, DOI: https://doi.org/10.1007/s12205-019-1820-5
Yoshino H, Mézard M (2010) Emergence of rigidity at the structural glass transition: A first-principles computation. Physical Review Letters 105(1):015504, DOI: https://doi.org/10.1103/PhysRevLett.105.015504
Yuan Q, Li Z, Gao Y, Wang YH, Li X (2019) Local responses in 2D assemblies of elliptical rods when subjected to biaxial shearing. Acta Geotechnica 14(6):1685–1697, DOI: https://doi.org/10.1007/s11440-019-00844-4
Zhang L, Guo Z, Liang Z (2020) Tri-axial confining numerical test and settlement analysis of the gravel layer. KSCE Journal of Civil Engineering 24(9):2572–2580, DOI: https://doi.org/10.1007/s12205-020-0952-y
Zhang F, Li M, Peng M, Chen C, Zhang L (2019) Three-dimensional DEM modeling of the stress—strain behavior for the gap-graded soils subjected to internal erosion. Acta Geotechnica 14(2):487–503, DOI: https://doi.org/10.1007/s11440-018-0655-4
Zhang Z, Wang YH (2014) Examining setup mechanisms of driven piles in sand using laboratory model pile tests. Journal of Geotechnical and Geoenvironmental Engineering 141(3):04014114, DOI: https://doi.org/10.1061/(ASCE)GT.1943-5606.0001252
Zhang Z, Wang YH. (2016) DEM modeling of aging or creep in sand based on the effects of microfracturing of asperities and evolution of microstructural anisotropy during triaxial creep. Acta Geotechnica 11(6):1303–1320, DOI: https://doi.org/10.1007/s11440-016-0483-3
Acknowledgments
This research was supported by the Guangdong Basic and Applied Basic Research Foundation (Grant Nos. 2020B1515120083 and 2019A1515110512) and Shenzhen Science and Technology Program (Grant Nos. RCBS20200714114855326 and GXWD 20201230155427003-20200824104811001).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, C., Tai, P., Li, Z. et al. Mechanism of Packing Rigidity Gain in Sand Aging: From the Perspective of Structural Order Evolution. KSCE J Civ Eng 26, 2641–2652 (2022). https://doi.org/10.1007/s12205-022-1460-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-022-1460-z