Abstract: Coarse-grained soils are susceptible to particle breakage under high stress, which leads to changes in soil gradation and affects their stiffness and deformation characteristics. This study investigates the impact of particle breakage on the stiffness and deformation of coarse-grained soils by analyzing their stress-strain behavior across different gradations. Based on the particle breakage law identified through experiments, we propose evolution equations for the isotropic compression line and the critical state line. The breakage ratio within the yield function is treated as a constitutive variable, integrated with the consistency condition, to account for the additional volumetric strain resulting from particle breakage. Utilizing non-orthogonal plasticity theory, we establish the relationship between the particle breakage ratio and the dilatancy parameter through a state variable, which determines the direction of plastic flow under particle breakage conditions. Finally, we develop a non-orthogonal elastoplastic constitutive model for coarse-grained soils to characterize the effects of particle breakage. The validity of this model is assessed using conventional triaxial drainage test data from Changhe rockfill and Cambria sand. The results indicate that the proposed model accurately reflects the transformation of volumetric strain in coarse-grained soils from dilatancy to contractancy as confining pressure increases from low to high, demonstrating enhanced predictive capability under high-stress conditions.
[1] YAO Y P,LIU L,LUO T. A constitutive model for granular soils[J]. Science China Technological Sciences,2018,61:1 546–1 555.
[2] VESI? A S,CLOUGH G W. Behavior of granular materials under high stresses[J]. Journal of the Soil Mechanics and Foundations Division,1968,94(3):661–688.
[3] EINAV I. Breakage mechanics—Part I:Theory[J]. Journal of the Mechanics and Physics of Solids,2007,55(6):1 274–1 297.
[4] HARDIN B O. Crushing of soil particles[J]. Journal of Geotechnical Engineering,1985,111(10):1 177–1 192.
[5] TONG C X,ZHAI M Y,LI H C,et al. Particle breakage of granular soils:changing critical state line and constitutive modelling[J]. Acta Geotechnica,2022,17(3):755–768.
[6] 马鹏程. 骨架可降解土体本构模型研究及应用初探[博士学位论文][D]. 杭州:浙江大学,2022.(MA Pengcheng. Study on constitutive models for soils with degradable solid skeleton and their applications[Ph. D. Thesis][D]. Hangzhou:Zhejiang University,2022.(in Chinese))
[7] SALIM W,INDRARATNA B. A new elastoplastic constitutive model for coarse granular aggregates incorporating particle breakage[J]. Canadian Geotechnical Journal,2004,41(4):657–671.
[8] WANG G S,LI Z H,LIANG J Y,et al. A state-dependent non-orthogonal elastoplastic constitutive model for sand[J]. Computers and Geotechnics,2024,166:105960.
[9] 石北啸,刘赛朝,吴鑫磊,等. 考虑颗粒破碎的堆石料剪胀特性研究[J]. 岩土工程学报,2021,43(7):1 360–1 366.(SHI Beixiao,LIU Saichao,WU Xinlei,et al. Dilatancy behaviors of rockfill materials considering particle breakage[J]. Chinese Journal of Geotechnical Engineering,2021,43(7):1 360–1 366.(in Chinese))
[10] 贾宇峰. 考虑颗粒破碎的粗粒土本构关系研究[博士学位论文][D]. 大连:大连理工大学,2008.(JIA Yufeng. Coarse granular soil constitutive model incorporating particle breakage[Ph. D. Thesis][D]. Dalian:Dalian University of Technology,2008.(in Chinese))
[11] 汪 稔,孙吉主. 钙质砂不排水性状的损伤–滑移耦合作用分析[J]. 水利学报,2002,33(7):75–78.(WANG Ren,SUN Jizhu. Damage-slide coupled interaction behavior of undrained calcareous sand[J]. Journal of Hydraulic Engineering,2002,33(7):75–78.(in Chinese))
[12] SUN D A,HUANG W X,YAO Y P. An experimental study of failure and softening in sand under three-dimensional stress condition[J]. Granular Matter,2008,10(3):187–195.
[13] ZHANG J,SALGADO R. Stress-dilatancy relation for Mohr-Coulomb soils following a non-associated flow rule[J]. Géotechnique,2010,60:223–226.
[14] YU M H,YANG S,FAN S C,et al. Unified elasto-plastic associated and non-associated constitutive model and its engineering applications[J]. Computers and Structures,1999,71(6):627–636.
[15] LU D C,LIANG J Y,DU X L,et al. Fractional elastoplastic constitutive model for soils based on a novel 3D fractional plastic flow rule[J]. Computers and Geotechnics,2019,105:277–290.
[16] LU D C,ZHOU X,DU X L,et al. A 3D fractional elastoplastic constitutive model for concrete material[J]. International Journal of Solids and Structures,2019,165:160–175.
[17] LIANG J Y,LU D C,DU X L,et al. A 3D non-orthogonal elastoplastic constitutive model for transversely isotropic soil[J]. Acta Geotechnica,2022,17(1):19–36.
[18] LU D C,MENG F P,ZHOU X,et al. A dynamic elastoplastic model of concrete based on a modeling method with environmental factors as constitutive variables[J]. Journal of Engineering Mechanics,2023,149(12):04023102.
[19] 刘映晶. 颗粒材料的级配相关临界状态力学特性模拟[博士学位论文][D]. 上海:上海交通大学,2014.(LIU Yingjing. Modeling the influence of the particle size distribution on the critical state mechanical behavior of granular material[Ph. D. Thesis][D]. Shanghai:Shanghai Jiaotong University,2014.(in Chinese))
[20] MARSAL R J. Large scale testing of rockfill materials[J]. Journal of the Soil Mechanics and Foundations Division,1967,93(2):27–43.
[21] LIANG J Y,LU D C,ZHOU X,et al. Non-orthogonal elastoplastic constitutive model with the critical state for clay[J]. Computers and Geotechnics,2019,116:103200.
[22] COOP M R,SORENSEN K K,FREITAS T B,et al. Particle breakage during shearing of a carbonate sand[J]. Géotechnique,2004,54(3):157–163.
[23] TURCOTTE D L. Fractals and fragmentation[J]. Journal of Geophysical Research:Solid Earth,1986,91(B2):1 921–1 926.
[24] MCDOWELL G R,BOLTON M D. On the micromechanics of crushable aggregates[J]. Géotechnique,1998,48(5):667–679.
[25] LADE P V,YAMAMURO J A,BOPP P A. Significance of particle crushing in granular materials[J]. Journal of Geotechnical Engineering,1996,122(4):309–316.
[26] HU W,YIN Z Y,SCARINGI G,et al. Relating fragmentation,plastic work and critical state in crushable rock clasts[J]. Engineering Geology,2018,246:326–336.
[27] YU F W. Particle breakage and the critical state of sands[J]. Géotechnique,2017,67(8):713–719.
[28] WOOD D M,KIKUMOTO M,RUSSELL A. Particle crushing and deformation behaviour[C]// Proceeding of the Prediction and Simulation Methods for Geohazard Mitigation. [S. l.]:[s. n.],2009:263–268.
[29] YAO Y P,LIU L,LUO T,et al. Unified hardening(UH) model for clays and sands[J]. Computers and Geotechnics,2019,110:326–343.
[30] LI X S,DAFALIAS Y F. Dilatancy for cohesionless soils[J]. Géotechnique,2000,50(4):449–460.
[31] VERDUGO R,ISHIHARA K. The steady state of sandy soils[J]. Soils and Foundations,1996,36(2):81–91.
[32] BEEN K,JEFFERIES M G. A state parameter for sands[J]. Géotechnique,1985,35(2):99–112.
[33] 刘恩龙,覃燕林,陈生水,等. 堆石料的临界状态探讨[J]. 水利学报,2012,43(5):505–511.(LIU Enlong,QIN Yanlin,CHEN Shengshui,et al. Investigation on critical state of rockfill materials[J]. Journal of Hydraulic Engineering,2012,43(5):505–511.(in Chinese))
[34] YAMAMURO J A,LADE P V. Drained sand behavior in axisymmetric tests at high pressures[J]. Journal of Geotechnical Engineering,1996,122(2):109–119.