Effect of depositional environment differences on micro-macro rheological behavior of sedimentary soft rocks

Abstract

Although significant progress has been made in micromechanical characterization and upscaling of homogeneous materials, systematic investigations into deposition-controlled micro–macro rheological relationships in heterogeneous sedimentary soft rocks remain limited, particularly concerning time-dependent viscous parameter upscaling. This study investigates six typical fluvial and lacustrine microfacies from the Ordos Basin, China, including riverbed lag, natural levee, floodplain lake, point bar, sheet sand, and shallow lake mud. Mineral composition and microstructure are characterized, and nanoindentation creep tests quantify viscoelastic properties. A micro–macro upscaling method that transforms the time-domain Burger model into the frequency domain and utilizes three traditional homogenization schemes: dilute approximation, Mori-Tanaka, and self-consistent methods, for comparative estimation of macroscopic rheological parameters is proposed. Microstructural analysis demonstrates distinct fabric patterns controlled by depositional energy. Floodplain lake and sheet sand microfacies show superior rheological stability due to dense quartz skeletons, whereas riverbed lag and shallow lake mud perform poorly, caused by skeleton relaxation and clay-dominated slip, respectively. The point bar microfacies exhibits a “rigid-soft hybrid” behavior, with high long-term stability but reduced transient stability. Comparatively, the frequency-domain upscaling framework developed in this study, incorporating the Mori-Tanaka scheme, demonstrates satisfactory agreement with experimental data, validating its capability to predict macroscopic viscoelastic properties from microstructural features.

Keywords

Sedimentary soft rocks / Depositional environment / Microstructure / Rheological properties / Upscaling method

Acknowledgments

This work was financially supported by the National Natural Scienc e Foundation of China (No. 42472334), DeepEarth Probe and M ineral Resources Exploration-National Science and Technol-ogy Major Project (No.2024ZD1004208), and the China Postdoc-toral Science Foundation (No.2025M771774).

References

[1] Fan KF, He JH, Li WP, Chen WC. Dynamic evolution and identification of bed separation in overburden during coal mining. Rock Mech Rock Eng 2022; 55 (7):4015-30.

[2] Liu MN, Qiao W, Zhao SL, Cheng XG. Stress intensity factor-based prediction method and influential factors of roof water inrush under longwall mining. Arab J Geosci 2022; 15(3):215.

[3] He CC, Lu WY, Zha WH, Wang F. A geomechanical method for predicting the height of a water-flowing fractured zone in a layered overburden of longwall coal mining. Int J Rock Mech Min Sci 2021;143:104798.

[4] Huang XL, Qi SW, Guo SF, Zheng BW, Zhao Q, Sha P, Wang TZ, Yao XL, Liang N, Chang JY, Rong XY. Effect of the crystal habit on micromechanical extensile behaviors of the crystalline rock during compression. Eng Geol 2022;310:106874.

[5] Chu ZF, Wu ZJ, Wang ZY, Weng L, Liu QS, Fan LF. Micro-mechanism of brittle creep in saturated sandstone and its mechanical behavior after creep damage. Int J Rock Mech Min Sci 2022;149:104994.

[6] Sharma A, Ouyang M, Hintsala ED, Stauffer D, Zhong W, Yang Y, Trelewicz JR, Snead LL, Sprouster DJ. High-temperature nanoindentation creep studies on castable and sintered nanostructured low-activation ferritic-martensitic alloys. J Nucl Mater 2025;611:155804.

[7] Zaborowska A, Kurpaska Ł, Zielin´ ski M, Xu Q, Wyszkowska E, O’Connell J, Neethling JH, Di Fonzo F, Frelek-Kozak M, Papanikolaou S,Diduszko R, Jagielski

[8] J. High-temperature behavior of amorphous alumina coatings: Insights from in-situ nanoindentation and X-ray diffraction studies. Ceram Int 2025;51:12918-31.

[9] Li ZZ, Nguyen S. Modelling flow and transport in fractured crystalline rocks by an upscaled equivalent continuous porous media method. Geomech Energy Environ 2025;41:100625.

[10] Yang YQ, Xiao YF, Zhou W, Jiskani IM, Luan BY. Strength analysis of geopolymer-rock interface: Mohr-Coulomb shear and interface transition zone (ITZ) nanoindentation testing. Constr Build Mater 2025;458:139544.

[11] Manjunath GL, Jha B. Geomechanical characterization of gondwana shale across nano-micro-meso scales. Int J Rock Mech Min Sci 2019;119:35-45.

[12] Liu YW, Liu A, Liu SM, Kang Y. Nano-scale mechanical properties of constituent minerals in shales investigated by combined nanoindentation statistical analyses and SEM-EDS-XRD techniques. Int J Rock Mech Min Sci 2022;159:105187.

[13] Yang Y, Peng RL, Li JH, Chen XW, Zhang HY, Zhao J, He YH, Liu ZW. Elastic-plastic properties of ceramic matrix composites characterization by nanoindentation testing coupled with computer modeling. Ceram Int 2024;50:185408.

[14] Liu XY, Xu DP, Duan SQ, Li SJ, Jiang Q. Investigation on the microscale creep behavior of constituent minerals in granite using nanoindentation and a novel creep model. Measurement 2025;245:116666.

[15] Shi X, Jiang S, Yang L, Tang MM, Xiao DS. Modeling the viscoelasticity of shale by nanoindentation creep tests. Int J Rock Mech Min Sci 2020;127:104210.

[16] Ma ZY, Zhang CP, Pathegama Gamage R, Zhang GL. Uncovering the creep deformation mechanism of rock-forming minerals using nanoindentation. Int J Min Sci Technol 2022; 32(2):283-94.

[17] Ying JW, Xie ZM, Jiang ZJ, Li ZA, Chen BX.Microscale fracture and creep analysis of 3D porous graphene-based cementitious material by nanoindentation test and energy-based method. Constr Build Mater 2023;409:133992.

[18] Feng W, He JM, Dai Z, Chang XZ, Shi XT, Xu F, Liu B. Creep behavior of epoxy adhesives subjected to different hygrothermal aging conditions—nanoindentation creep tests and theoretical study. Polym Degrad Stab 2024;229:110926.

[19] Liu YW, Zhang GP, Qiao JM, Tang XH. Micromechanical testing and property upscaling of planetary rocks: a critical review. Int J Min Sci Technol 2024; 34 (9):1217-41.

[20] Gottron D, Henk A. Upscaling of fractured rock mass properties-an example comparing Discrete Fracture Network (DFN) modeling and empirical relations based on engineering rock mass classifications. Eng Geol 2021;294:106382.

[21] Jiang H, Arns C, Yuan YJ, Qin CZ.SVM-based fast 3D pore-scale rock-typing and permeability upscaling for complex rocks using Minkowski functionals. Adv Water Resour 2024;183:104605.

[22] Sun CL, Li GC, Xu JH, Rong HY, Sun YT. Rheological characteristics of mineral components in sandstone based on nanoindentation. Chin J Rock Mech Eng 2021; 40(1):77-87. In Chinese.

[23] Wang JF, Liu YK, Yang C, Zheng YC, Jiang WM, Luca Menegon, François Renard, Peng PA, Xiong YQ. Upscaling the creep behavior of clay-rich and quartz-rich shales from nanoindentation measurements: application to the Wufeng-Longmaxi shale. China Int J Rock Mech Min Sci 2023;171:105580.

[24] Wu ZX. Advance review on occurrence state and leaching of lithium in sedimentary bauxite (aluminum) deposits. China Ore Geol Rev 2024;164:105851.

[25] Lin MR, Xi KL, Cao YC, Niu XB, Ma WJ, Wang XJ, Xu S. Palaeoenvironmental changes in the late Triassic lacustrine facies of the Ordos Basin of Northwest China were driven by multistage volcanic activity: Implications for the understanding the Carnian Pluvial Event. Palaeogeogr Palaeoclimatol Palaeoecol 2024;637:112012.

[26] Gong S, Li Z, Zhao YY. An extended Mori-Tanaka model for the elastic moduli of porous materials of finite size. Acta Mater 2011;59:6820-30.

[27] Bhaskar LK, Moharana N, Holz H, Ramachandramoorthy R, Hari Kumar KC, Kumar R. Probing elastic isotropy in entropy stabilized transition metal oxides: Experimental estimation of single crystal elastic constants from polycrystalline materials. Acta Mater 2025;288:120871.

[28] Lange S, Warkentin A, Ricoeur A. Scale transition and residual fields in modeling of polycrystalline ferroelectrics based on the internal energy potential and a Voigt-Reuss approximation. Eur J Mech A Solids 2024;103:105161.

[29] Zhang GQ, Mi LD. Sedimentary facies of clastic-platform carbonate sediment strata of epicontinental sea in the Daniudi Gasfield. Ordos Basin Nat Gas Ind B 2021; 8(3):239-51.

[30] Xian BZ, Wang JH, Gong CL, Yin Y, Chao CZ, Liu JP, Zhang GD, Yan Q. Classification and sedimentary characteristics of lacustrine hyperpycnal channels: Triassic outcrops in the south Ordos Basin, central China. Sed Geol 2018;368:68-82.

[31] Schumm AS. The fluvial system. New York: Wiley Interscience; 1977.

[32] Liu BJ.Sedimentary petrology. Beijing: Geology Press; 1980.

[33] Qiao W, Liu MN, Li WP, Wang QQ, Cheng XG, Li XQ. Proceedings, Chengdu. China Singapore: Springer Nature Singapore 2023;2024:541-70.

[34] Wang ZY, Lu SF, Zhou NW, Liu YC, Lin LM, Shang YX, Xiao GS, Wang J. Diagenesis as a control on the tight sandstone reservoir quality of the upper Carboniferous strata in the northeastern Ordos basin. China Mar Petrol Geol 2023;158:106565.

[35] He YN. Inverse modeling for subsidence history in southern Ordos Basin from Jurassic to Early Cretaceous, vol. China University of Geosciences for Master Degree, China University of Geosciences (Beijing); 2019.

[36] Ma ZY, Pathegama Gamage R, Zhang CP. Application of nanoindentation technology in rocks: a review. Geomech Geophys Geo Energy Geo Resour 2020; 6(4):60.

[37] Sun CL, Li GC, Elgharib GM, Xu JH, Rong HY. Experimental investigation on the mechanical properties of crushed coal samples based on the nanoindentation technique. J China Coal Soc 2020;45:682-91.

[38] Meng JQ, Niu JX, Xia JK, Kan LH. Study on mechanical properties and failure mechanisms of coal at the nanometer scale. Chin J Rock Mech Eng 2020; 39 (1):84-92.In Chinese.

[39] Berbenni S, Capolungo L. A Mori-Tanaka homogenization scheme for non-linear elasto-viscoplastic heterogeneous materials based on translated fields: an affine extension. Comptes Rendus Mécanique 2015; 343(2):95-106.

[40] Abou-Chakra Guéry A, Cormery F, Shao JF, Kondo D. A comparative micromechanical analysis of the effective properties of a geomaterial: effect of mineralogical compositions. Comput Geotech 2010; 37(5):585-93.

[41] Stefaniuk D, Kachanov M. Voigt-Reuss and Hashin-Shtrikman bounds revisited. Int J Eng Sci 2023;191:103903.

[42] Lee H, Liu X, Lan KC, Tan H, Pan X, Zhang X, Park JS, Li MM, Almer J.Evaluation of elastic constants of M23C6 and M7C3 embedded in Fe-Cr-C alloys using in-situ XRD tensile test and self-consistent model. Materialia 2024;38:102274.

[43] Zhao D, Chen C, Khong SZ. A frequency-domain approach to nonlinear negative imaginary systems analysis. Automatica 2022;146:110604.

[44] Gentile FS, Moiola JL, Paolini EE. Nonlinear dynamics of internet congestion control: a frequency-domain approach. Commun Nonlinear Sci Numer Simul 2014;19:1113-27.

[45] Huang Y, Hu KX, Wei X, Chandra A. A generalized self-consistent mechanics method for composite materials with multiphase inclusions. J Mech Phys Solids 1994; 42(3):491-504.

[46] Cheng YT, Cheng CM, Ni WY. Methods of obtaining instantaneous modulus of viscoelastic solids using displacement-controlled instrumented indentation with axisymmetric indenters of arbitrary smooth profiles. Mater Sci Eng A 2006; 423(1-2):2-7.

[47] Ni ZJ, Qiao JM, Zhang JK, Tang XH. Determining mechanical property and wave velocity of sandstone by accurate grain-based model and microscale mechanics experiments. Rock Soil Mech 2025; 46(6):1865-80.

[48] Zhang ZP, Zhang SC, Shi SZ, Zou YS, Li JM, Ma XF, Xiao FC. Evaluation of multi-scale mechanical properties of conglomerate using nanoindentation and homogenization methods: A case study on tight conglomerate reservoirs in southern slope of Mahu sag. Chin J Rock Mech Eng 2022; 41(5):926-40. in Chinese.