PFC-FDEM multi-scale cross-platform numerical simulation of thermal crack network evolution and SHTB dynamic mechanical response of rocks

Abstract

Underground engineering in extreme environments necessitates understanding rock mechanical behavior under coupled high-temperature and dynamic loading conditions. This study presents an innovative multi-scale cross-platform PFC-FDEM coupling methodology that bridges microscopic thermal damage mechanisms with macroscopic dynamic fracture responses. The breakthrough coupling framework introduces: (1) bidirectional information transfer protocols enabling seamless integration between PFC’s particle-scale thermal damage characterization and FDEM’s continuum-scale fracture propagation, (2) multi-physics mapping algorithms that preserve crack network geometric invariants during scale transitions, and (3) cross-platform cohesive zone implementations for accurate SHTB dynamic loading simulation. The coupled approach reveals distinct three-stage crack evolution characteristics with temperature-dependent density following an exponential model. High-temperature exposure significantly reduces dynamic strength ratio (60% at 800 °C) and diminishes strain-rate sensitivity, with dynamic increase factor decreasing from 1.0 to 2.2 (25 °C) to 1.0-1.3 (800 °C). Critically, the coupling methodology captures fundamental energy redistribution mechanisms: thermal crack networks alter elastic energy proportion from 75% to 35% while increasing fracture energy from 5% to 30%. Numerical predictions demonstrate excellent experimental agreement (±8% peak stress-strain errors), validating the PFC-FDEM coupling accuracy. This integrated framework provides essential computational tools for predicting complex thermal-mechanical rock behavior in underground engineering applications.

Keywords

Thermal geomechanics / Thermo-mechanical coupling phenomena / Fracture network propagation / PFC-FDEM / Dynamic mechanical response

Acknowledgements

This work has been supported by the National Natural Science Foundations of China (Nos. 12272411 and 42007259), the State Key Laboratory for GeoMechanics and Deep Underground Engi-neering, the China University of Mining & Technology (No. SKLGDUEK2207), and the Department of Science and Technology of Shaanxi Province (Nos. 2022KXJ-107 and 2022JC-LHJJ-16).

Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijmst.2025.08.013.

References

[1] Taylor SR, McLennan SM. The geochemical evolution of the continental crust. Rev Geophys 1995; 33(2):241-65.

[2] Qiao L, Hao JW, Liu ZY, Li QW, Deng NF. Influence of temperature on the transformation and self-control of energy during sandstone damage: Experimental and theoretical research. Int J Min Sci Technol 2022; 32 (4):761-77.

[3] Chen QJ, Chen YL, Xiao P, Du X, Pan YG, Azzam R. Mechanical properties and damage constitutive model of sandstone after acid corrosion and high temperature treatments. Int J Min Sci Technol 2023; 33(6):747-60.

[4] Zhang T, Yu LY, Su HJ, Zhang Q, Chai SB. Experimental and numerical investigations on the tensile mechanical behavior of marbles containing dynamic damage. Int J Min Sci Technol 2022; 32(1):89-102.

[5] Zeng L, Zhang JL, Liu S. Mechanical behavior and damage constitutive model of fractured granite after high-temperature treatment based on 3D digital image correlation. Theor Appl Fract Mech 2025; 138:104919.

[6] Liu S, Jia Y, Zhai Y, Hao SX. Mesoscopic fracture damage evolution and fractal damage constitutive model of heat-treated red sandstone under direct tensile impact loadings. J Rock Mech Geotech Eng 2025; 17(1):323-40.

[7] Zeng L, Liang XQ, Lu HQ, Liu S, Yuan H, Mohamed HS. Compressive behavior of seawater and sea sand concrete-filled FRP-steel composite multi-tube hollow columns. Constr Build Mater 2024; 438:137133.

[8] Lyu C, Liu JF, Ren Y, Liang C, Zeng Y. Mechanical characteristics and permeability evolution of salt rock under thermal-hydro-mechanical (THM) coupling condition. Eng Geol 2022; 302:106633.

[9] Yang Z, Yang SQ, Zheng WB, Tannant DD. Coupled thermal-hydraulic simulations of fracturing in granite under high temperature and high pressure treatment via peridynamic. Int J Rock Mech Min Sci 2022; 160:105247.

[10] Li ZB, Ren T, Li XC, Qiao M, Yang XH, Tan LH, Nie BS. Multi-scale pore fractal characteristics of differently ranked coal and its impact on gas adsorption. Int J Min Sci Technol 2023; 33(4):389-401.

[11] Lei QH, Latham JP, Tsang CF. The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks. Comput Geotech 2017; 85:151-76.

[12] Wu D, Li HB, Fukuda D, Liu HY. Development of a finite-discrete element method with finite-strain elasto-plasticity and cohesive zone models for simulating the dynamic fracture of rocks. Comput Geotech 2023; 156:105271.

[13] Wu ZY, Jiao YY, Zheng F, Huang GH, Liu CD. A new SDDA-based numerical approach for simulating rock cracking induced by temperature stresses. Comput Geotech 2023; 154:105113.

[14] Wang ED, Yao RY, Li Q, Hu XY, Sun GY. Lightweight metallic cellular materials: a systematic review on mechanical characteristics and engineering applications. Int J Mech Sci 2024; 270:108795.

[15] Wang YJ, Xu H, Pasini D. Multiscale isogeometric topology optimization for lattice materials. Comput Meth Appl Mech Eng 2017; 316:568-85.

[16] Fu XY, Liao YH, Zeng DL, Huang Y, Zhang XP, Ding XH. A probabilistic method for image enhancement with simultaneous illumination and reflectance estimation. IEEE Trans Image Process 2015; 24(12):4965-77.

[17] Matouš K, Geers MGD, Kouznetsova VG, Gillman A. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials. J Comput Phys 2017; 330:192-220.

[18] Munjiza A, John NWM. Mesh size sensitivity of the combined FEM/DEM fracture and fragmentation algorithms. Eng Fract Mech 2002; 69(2):281-95.

[19] Wu D, Li HB, Shao ZS, Chen SH, Zhou CB, Liu LW. Effects of infilling materials on mechanical behaviors and cracking process of pre-cracked rock: Insights from a hybrid continuum-discontinuum method. Eng Fract Mech 2021; 253:107843.

[20] Zhang SR, Qiu SL, Jiang Q, Yan CZ, Zhou LY, Li XH. Modeling damage evolution in granite under temperature using a thermo-mechanical grain-based FDEM model. Comput Geotech 2024; 169:106198.

[21] Lohar GK, Kumar A, Roy N. Numerical assessment of time-dependent deformation of a road tunnel: A case study. Transp Infrastruct Geotechnol 2024; 11(2):447-69.

[22] Jing H, Guo X, Yang PF. PFC-FLAC coupling-based numerical simulation of triaxial test on soybean granular material. part. Sci Technol 2024; 42 (4):527-40.

[23] Deng PH, Liu QS, Lu HF. FDEM numerical study on the mechanical characteristics and failure behavior of heterogeneous rock based on the Weibull distribution of mechanical parameters. Comput Geotech 2023; 154:105138.

[24] Xu CY, Liu QS, Tang XH, Sun L, Deng PH, Liu H. Dynamic stability analysis of jointed rock slopes using the combined finite-discrete element method (FDEM). Comput Geotech 2023; 160:105556.

[25] Brünig M. A thermodynamically consistent continuum damage model taking into account the ideas of CL Chow. Int J Damage Mech 2016; 25(8):1130-41.

[26] Tan L, Liu F, Huang Y, Crosta G, Frattini P, Cen XQ. Production-induced instability of a gentle submarine slope: Potential impact of gas hydrate exploitation with the huff-puff method. Eng Geol 2021; 289:106174.

[27] Lisjak A, Kaifosh P, He L, Tatone BSA, Mahabadi OK, Grasselli G. A 2D, fully-coupled, hydro-mechanical, FDEM formulation for modelling fracturing processes in discontinuous, porous rock masses. Comput Geotech 2017; 81:1-18.

[28] Diehl P, Prudhomme S, Lévesque M. A review of benchmark experiments for the validation of peridynamics models. J Peridyn Nonlocal Model 2019; 1 (1):14-35.

[29] Hao DH, Liu QQ, Hu YL, Madenci E, Guo H, Yu Y. Coupled neutronic-thermal- mechanical analysis of a nuclear fuel pellet using peridynamics. Eng Comput 2024; 40(4):2445-72.

[30] Mu DR, Zhang DY, Tang AP, Qu HG, Li ZM. Numerical simulation of rock thermal fracture considering friction effect in the framework of smooth particle hydrodynamics based on total Lagrangian formula. Rock Mech Rock Eng 2022; 55(3):1663-85.

[31] Wu L, Hou ZM, Xie YC, Luo ZF, Xiong Y, Cheng L, Wu X, Chen Q, Huang L. Fracture initiation and propagation of supercritical carbon dioxide fracturing in calcite-rich shale: A coupled thermal-hydraulic-mechanical-chemical simulation. Int J Rock Mech Min Sci 2023; 167:105389.

[32] Zhang TY, Zhu ZW, Ma Y, Cheng ZQ, Li T. Rate-dependent FDEM numerical simulation of dynamic tensile fracture and failure behavior in frozen soil. Comput Geotech 2025; 178:106916.

[33] Bu MH, Guo PY, Li XP, Zhang P, Wang JM. Thermo-mechanical behavior of granite rocks based on the analysis of 3D grain-based numerical models. Rock Mech Rock Eng 2025; 58(6):6115-43.

[34] Li JH, Yang LY, Xie HZ, Wei P, Li DZ, Xu YC, Zhang F. Research on impact toughness and crack propagation of basalt fiber reinforced concrete under SHPB splitting test. J Build Eng 2023; 77:107445.

[35] Hao SX, Zhai Y, Liu S, Jia Y. Mechanical properties and energy evolution of thermally damaged red sandstone in high-strain-rate impact tensile tests: Experimental and theoretical analyses. J Mater Res Technol 2024; 32:4028-47.

[36] Khan MM, Iqbal MA. Dynamic increase factor of concrete subjected to compression and tension by using split Hopkinson pressure bar setup: overview. Mech Solids 2023; 58(6):2115-31.

[37] Sun B, Yang P, Zhang ZH, Wang SY, Zeng S. Investigation of the fracture characteristics of rock mass after thermal-mechanical damage coupling. Rock Mech Rock Eng 2024; 57(7):4707-27.

[38] Lisjak A, Grasselli G. A review of discrete modeling techniques for fracturing processes in discontinuous rock masses. J Rock Mech Geotech Eng 2014; 6 (4):301-14.

[39] Bobet A, Fakhimi A, Johnson S, Morris J, Tonon F, Yeung MR. Numerical models in discontinuous media: Review of advances for rock mechanics applications. J Geotech Geoenviron Eng 2009; 135(11):1547-61.

[40] Boaga J. The use of FDEM in hydrogeophysics: A review. J Appl Geophys 2017; 139:36-46.

[41] Lin YX, Ma JJ, Lai ZS, Huang LC, Lei MF. A FDEM approach to study mechanical and fracturing responses of geo-materials with high inclusion contents using a novel reconstruction strategy. Eng Fract Mech 2023; 282:109171.

[42] Liu S, Xu JY. Mechanical properties of Qinling biotite granite after high temperature treatment. Int J Rock Mech Min Sci 2014; 71:188-93.

[43] Hoagland RG, Hahn GT, Rosenfield AR. Influence of microstructure on fracture propagation in rock. Rock Mech 1973; 5(2):77-106.

[44] Yang SR, Qu JM. Computing thermomechanical properties of crosslinked epoxy by molecular dynamic simulations. Polymer 2012; 53(21):4806-17.

[45] Kranz RL. Microcracks in rocks: A review. Tectonophysics 1983; 100(1- 3):449-80.

[46] Schöpfer MPJ, Abe S, Childs C, Walsh JJ. The impact of porosity and crack density on the elasticity, strength and friction of cohesive granular materials: Insights from DEM modelling. Int J Rock Mech Min Sci 2009; 46(2):250-61.

[47] Yang SQ, Ranjith PG, Jing HW, Tian WL, Ju Y. An experimental investigation on thermal damage and failure mechanical behavior of granite after exposure to different high temperature treatments. Geothermics 2017; 65:180-97.

[48] Liu XF, Yuan SY, Sieffert Y, Fityus S, Buzzi O. Changes in mineralogy, microstructure, compressive strength and intrinsic permeability of two sedimentary rocks subjected to high-temperature heating. Rock Mech Rock Eng 2016; 49(8):2985-98.

[49] Bažant ZP, Planas J. Fracture and Size Effect in Concrete and Other Quasibrittle Materials. London: Routledge; 2019.

[50] Fredrich JT, Wong TF. Micromechanics of thermally induced cracking in three crustal rocks. J Geophys Res Solid Earth 1986; 91(B12):12743-64.

[51] Sarııs¸ık G. Research on engineering properties of heat-treated volcanic rocks. Arab J Geosci 2021; 14(1):63.

[52] Weibull W. A statistical distribution function of wide applicability. J Appl Mech 1951; 18:293-7.

[53] Danzer R, Supancic P, Pascual J, Lube T. Fracture statistics of ceramics-Weibull statistics and deviations from Weibull statistics. Eng Fract Mech 2007; 74 (18):2919-32.

[54] Amadei B. Berlin, Rock Anisotropy and the Theory of stress Measurements. Heidelberg:Springer, Berlin Heidelberg; 1983.

[55] Karihaloo BL, Xiao QZ. Asymptotic crack tip fields in linear and nonlinear materials and their role in crack propagation. Phys Mesomech 2019; 22 (1):18-31.

[56] Olson JE. Joint pattern development: Effects of subcritical crack growth and mechanical crack interaction. J Geophys Res Solid Earth 1993; 98 (B7):12251-65.

[57] Nemat-Nasser S, Lori M, Datta SK. Micromechanics: Overall properties of heterogeneous materials. J Appl Mech 1996; 63(2):561.

[58] Griffith AAVI. The phenomena of rupture and flow in solids. Phil Trans R Soc Lond A 1921; 221(582-593):163-98.

[59] Liang HB, Chen HF, Guo JH, Bai J, Jiang YJ. Research on lithology identification method based on mechanical specific energy principle and machine learning theory. Expert Syst Appl 2022; 189:116142.