Multi-scale Modeling and Parameter Analysis of Cement-based Materials Based on Micromechanics

WU Lang, CHENG Wen-nuo, CHEN Fen-fen, LEI Bin

Journal of Changjiang River Scientific Research Institute ›› 2026, Vol. 43 ›› Issue (1) : 155-163.

PDF(8253 KB)
PDF(8253 KB)
Journal of Changjiang River Scientific Research Institute ›› 2026, Vol. 43 ›› Issue (1) : 155-163. DOI: 10.11988/ckyyb.20241210
Hydraulic Structure and Material

Multi-scale Modeling and Parameter Analysis of Cement-based Materials Based on Micromechanics

Author information +
History +

Abstract

[Objective] Current micromechanical models pay limited attention to parameter uncertainty and interactions, which makes it difficult for their response results to reflect the dispersed nature of the properties of cement-based materials. Therefore, it is necessary to explore an analysis method that can simultaneously capture the effects of multiple parameters and their interactions on the responses of micromechanical models of cement-based materials. [Methods] To address the discrete distribution of response results in existing micromechanical models and to identify and control the influencing factors causing this phenomenon, a multi-scale micromechanical model of cement-based materials was constructed in this study. Cement-based materials were divided into four scales: calcium silicate hydrate gel, cement paste, cement mortar, and concrete. Considering the mineral composition of cement phases, aggregates, and the ITZ, a multi-scale micromechanical model capable of accounting for the randomness of input parameters was proposed. Meanwhile, probabilistic methods were applied to the constructed micromechanical model, and global sensitivity analysis was employed to quantify the effects of input parameter uncertainty on the elastic modulus of cement-based materials. [Results] The results showed that the proposed model exhibited good applicability in simulating the relationship between elastic modulus and hydration degree of cement-based materials across multiple scales and showed good agreement with experimental results. The discreteness of the model response results mainly originated from the cross-scale propagation of input parameter uncertainty, indicating that uncertainty at the concrete scale incorporated the uncertainties of input parameters at the mortar and cement paste scales. The total-order sensitivity indices, ranked from largest to smallest, were the elastic modulus of sand and coarse aggregates, the volume fraction of sand and coarse aggregates, the elastic modulus of hydration products, the volume fraction of cement clinker, and the elastic modulus of cement clinker. To identify the dominant sources of uncertainty within the model framework, particular attention should be paid to the elastic modulus of sand and coarse aggregates, whereas the volume fraction and elastic modulus of cement clinker can be regarded as insensitive factors. [Conclusion] Screening the number of input parameters has important practical significance for reducing computational complexity and improving the efficiency of model response analysis.

Key words

cement-based materials / micromechanics / multi-scale / hydration products / elastic modulus

Cite this article

Download Citations
WU Lang , CHENG Wen-nuo , CHEN Fen-fen , et al. Multi-scale Modeling and Parameter Analysis of Cement-based Materials Based on Micromechanics[J]. Journal of Changjiang River Scientific Research Institute. 2026, 43(1): 155-163 https://doi.org/10.11988/ckyyb.20241210

References

[1]
杨华, 李宗利, 惠弘毅. 基于随机骨料模型的混凝土弹性模量预测研究[J]. 长江科学院院报, 2016, 33(2):100-105.
Abstract
为确定混凝土的弹性模量,基于细观层次假定混凝土是由骨料、砂浆和两者之间的粘结界面组成的三相复合材料,借助蒙特卡罗方法和瓦拉文公式,在二维平面上建立了随机骨料模型。通过有限元法预测混凝土的弹性模量,并将数值计算结果与试验结果进行比较,验证了该细观有限元模型的有效性。在此基础上研究了混凝土各细观组成成分的弹性模量、骨料体积率、骨料最大粒径、骨料级配、界面厚度以及孔隙等因素对混凝土弹性模量的影响规律。结果表明:在混凝土的各细观组成成分中,砂浆弹性模量对混凝土弹性模量的影响最大;连续级配的混凝土弹性模量在相同条件下大于间断级配的混凝土;孔隙的存在以及界面层厚度的增大均会使混凝土的弹性模量减小。研究结果为混凝土配合比的设计及力学性能的优化提供参考。
(YANG Hua, LI Zong-li, HUI Hong-yi. Prediction of Elastic Modulus of Concrete Based on Random Aggregate Model[J]. Journal of Yangtze River Scientific Research Institute, 2016, 33(2): 100-105.) (in Chinese)
In the assumption at mesoscopic level, concrete materials are assumed as three-phase composites consisting of aggregate, mortar and the bonding interface between mortar and aggregate. In order to determine elastic modulus of concrete (EMC), on the basis of the assumption, we establish a random aggregate model in the two-dimensional plane with Monte Carlo method and Walraven formula. Meanwhile, we predict EMC by using finite element method and compare the numerical calculated results with test results to verify the effectiveness of this mesoscopic finite element model. Furthermore, we discussthe impacts of several parameters (elastic modulus, aggregate’s volume content, aggregate’s maximum size, aggregate’s gradation, interface thickness and pores) of mesoscopic component on EMC. Test results show that 1) as for mesoscopic components of concrete, impact of elastic modulus of mortar on EMC is the biggest; 2) under given conditions, EMC with continuous gradation is bigger than that with uncontinuous gradation; 3) EMC decreases with the increasing of interface thickness and the existence of pores. The research results offer reference for the design of concrete’s mix proportion and optimization of its mechanical properties.
[2]
SANAHUJA J, DORMIEUX L, CHANVILLARD G. Modelling Elasticity of a Hydrating Cement Paste[J]. Cement and Concrete Research, 2007, 37(10): 1427-1439.
[3]
PICHLER B, HELLMICH C. Upscaling Quasi-brittle Strength of Cement Paste and Mortar: A Multi-scale Engineering Mechanics Model[J]. Cement and Concrete Research, 2011, 41(5): 467-476.
[4]
王晨霞, 王金旭, 王宇飞, 等. 硅灰对再生混凝土抗盐冻性能及微观结构的影响[J]. 长江科学院院报, 2024, 41(6):171-177.
Abstract
为研究硅灰对内蒙河套盐碱地区的再生混凝土微观结构和抗盐冻性能的影响,以硅灰掺量为变量对再生混凝土(RAC)进行了冻融循环试验、抗氯离子渗透试验和电镜扫描试验(SEM)。结果表明:通过SEM能看出球状硅灰颗粒可以使结构变得致密,RAC的质量损失率、立方体抗压强度损失率和氯离子迁移系数均随硅灰掺量的增加呈现先减后增的趋势,但硅灰掺量为10%和15%的RAC相对动弹性模量却相差不大;综合来看硅灰掺量为10%时抗盐冻性能最好,90次冻融循环后RC10组的质量损失率、立方体抗压强度损失率和氯离子迁移系数分别仅为RC0组的54.3%、50.3%和49.81%;同时建立了以硅灰掺量和冻融循环次数为参数的冻融损伤模型,并对内蒙盐碱地区的RAC进行了寿命预测。研究成果有助于推动再生混凝土的合理利用。
(WANG Chen-xia, WANG Jin-xu, WANG Yu-fei, et al. Effect of Silica Fume on Salt Frost Resistance and Microstructure of Recycled Concrete[J]. Journal of Changjiang River Scientific Research Institute, 2024, 41(6): 171-177.) (in Chinese)
[5]
GARBOCZI E J, BENTZ D P. Analytical Formulas for Interfacial Transition Zone Properties[J]. Advanced Cement Based Materials, 1997, 6(3/4): 99-108.
[6]
VARGAS P, RESTREPO-BAENA O, TOBÓN J I. Microstructural Analysis of Interfacial Transition Zone (ITZ) and Its Impact on the Compressive Strength of Lightweight Concretes[J]. Construction and Building Materials, 2017, 137: 381-389.
[7]
CHEN B, RAO M, FENG Y. Effects of Curing Temperature and Supplementary Cementitious Materials on the Interfacial Transition Zone (ITZ) of High-ferrite Cement Products[J]. Construction and Building Materials, 2024, 425: 135920.
[8]
KIM S Y, KIM J S, KANG J W, et al. Construction of Virtual Interfacial Transition Zone (ITZ) Samples of Hydrated Cement Paste Using Extended Stochastic Optimization[J]. Cement and Concrete Composites, 2019, 102: 84-93.
[9]
KÖNIGSBERGER M, HLOBIL M, DELSAUTE B, et al. Hydrate Failure in ITZ Governs Concrete Strength: A Micro-to-macro Validated Engineering Mechanics Model[J]. Cement and Concrete Research, 2018, 103: 77-94.
[10]
范东林, 陈苏社, 李光斌, 等. 煤矸石混凝土三相细观力学性能及细观破坏机理[J]. 煤炭工程, 2024, 56(5):173-181.
(FAN Dong-lin, CHEN Su-she, LI Guang-bin, et al. Three-phase Meso-mechanical Properties and Meso-failure Mechanism of Coal Gangue Concrete[J]. Coal Engineering, 2024, 56(5): 173-181.) (in Chinese)
[11]
刘文君, 韩海涛, 鲁芹, 等. 基于细观力学的石墨烯复合材料导热性能分析[J]. 兵器装备工程学报, 2024, 45(7):259-266.
(LIU Wen-jun, HAN Hai-tao, LU Qin, et al. Analysis of Thermal Conductivity of Graphene Composites Based on Mesomechanics[J]. Journal of Ordnance Equipment Engineering, 2024, 45(7):259-266.) (in Chinese)
[12]
童良玉, 刘清风. 纤维增强混凝土氯离子扩散系数的多尺度预测模型[J]. 复合材料学报, 2022, 39(11): 5181-5191.
(TONG Liang-yu, LIU Qing-feng. Multi-scale Prediction Model of Chloride Diffusivity of Fiber Reinforced Concrete[J]. Acta Materiae Compositae Sinica, 2022, 39(11): 5181-5191.) (in Chinese)
[13]
刘平, 史朝悦, 陈庞, 等. 纤维增强碱矿渣轻骨料混凝土宏细观力学性能[J]. 混凝土, 2023(8): 43-47.
(LIU Ping, SHI Zhao-yue, CHEN Pang, et al. Macroscopic Mechanical Properties and Microstructure Characteristics of Fiber Toughened Alkali-activated Slag Lightweight Aggregate Concrete[J]. Concrete, 2023(8): 43-47.) (in Chinese)
[14]
BAO S, ZHANG Y, LI C, et al. Interfacial Bonding Behavior of Steel Fibers when Using Fine Glass Powder as Partial Substitution of Silica Fume/Cement[J]. Construction and Building Materials, 2024, 411: 134516.
[15]
黄乐, 苏凯栋, 高奔浩, 等. 低碳超高性能混凝土单轴受压力学性能[J]. 长江科学院院报, 2025, 42(4):183-192.
Abstract
为解决超高性能混凝土水泥用量成倍增加所带来的高碳排放问题,采用高炉矿渣、粉煤灰和硅灰等材料大掺量替代硅酸盐水泥,制备了一种低水泥含量的低碳超高性能混凝土(LC-UHPC)。考虑水泥替代率、钢纤维体积掺量和水胶比等3个因素,设计制作了11组共154个试件,通过不同龄期的立方体抗压试验、抗折试验与单轴受压试验研究了LC-UHPC破坏形态、基本强度与变形能力等力学性能的变化规律,并根据试验结果建立了单轴受压应力-应变全曲线数学方程。结果表明:LC-UHPC轴心受压破坏形态为剪切破坏,钢纤维掺入能明显改善LC-UHPC各项力学性能指标;与传统UHPC相比,LC-UHPC的水泥替代率最高可达70%,其28 d单轴抗压强度可达149.09 MPa;建立的轴心受压应力-应变曲线方程能够较好地预测LC-UHPC单轴受压下的力学响应全过程,可为LC-UHPC力学性能研究及其结构构件的设计计算提供有益参考。
(HUANG Le, SU Kai-dong, GAO Ben-hao, et al. Mechanical Properties of Low Carbon Ultra-high Performance Concrete under Uniaxial Compression[J]. Journal of Changjiang River Scientific Research Institute, 2025, 42(4): 183-192.) (in Chinese)
[16]
ORTEGA PELAYO R E, EL BOUZIDI S, TROTTIER A, et al. Structural Integrity Assessment of CANDU Pressure Tubes Using Sobol Indices for Global Sensitivity Analysis[J]. Nuclear Engineering and Design, 2024, 428: 113499.
[17]
KOZIELS, PIETRENKO-DABROWSKA A, LEIFSSON L. Improved Efficacy Behavioral Modeling of Microwave Circuits through Dimensionality Reduction and Fast Global Sensitivity Analysis[J]. Scientific Reports, 2024, 14: 19465.
Behavioral models have garnered significant interest in the realm of high-frequency electronics. Their primary function is to substitute costly computational tools, notably electromagnetic (EM) analysis, for repetitive evaluations of the structure under consideration. These evaluations are often necessary for tasks like parameter tuning, statistical analysis, or multi-criterial design. However, constructing reliable surrogate models faces several challenges, including the nonlinearity of circuit characteristics and the vast size of the parameter space, encompassing both dimensionality and design variable ranges. Additionally, ensuring the validity of the model across broad geometry/material parameter and frequency ranges is crucial for its utility in design. The purpose of this paper is to introduce an innovative approach to cost-effective and dependable behavioral modeling of microwave passives. Central to our method is a fast global sensitivity analysis (FGSA) procedure, which is devised to identify correlations between design parameters and quantify their impacts on circuit characteristics. The most significant directions identified through FGSA are utilized to establish a reduced-dimensionality domain. Within this domain, the model may be constructed using a limited amount of data samples while capturing a significant portion of the circuit response variability, rendering it suitable for design purposes. The outstanding predictive capability of the proposed model, its superiority over traditional techniques, and its readiness for design applications are demonstrated through the analysis of three microstrip circuits of diverse characteristics.© 2024. The Author(s).
[18]
VU-BAC N, RAFIEE R, ZHUANG X, et al. Uncertainty Quantification for Multiscale Modeling of Polymer Nanocomposites with Correlated Parameters[J]. Composites Part B: Engineering, 2015, 68: 446-464.
[19]
VENKOVIC N, SORELLI L, SUDRET B, et al. Uncertainty Propagation of a Multiscale Poromechanics-hydration Model for Poroelastic Properties of Cement Paste at Early-age[J]. Probabilistic Engineering Mechanics, 2013, 32: 5-20.
[20]
XIN L, XU J, LI Z, et al. A Mori-Tanaka Method Based Theoretical Approximation for Functionally Graded Thick Wall Tube under Combined Thermal and Mechanical Loads[J]. Journal of Thermal Stresses, 2023, 46(3): 229-250.
[21]
NOYELJ P, HAJJAR A, DEBASTIANI R, et al. Impact of Viscoelasticity on the Stiffness of Polymer Nanocomposites: Insights from Experimental and Micromechanical Model Approaches[J]. Polymer, 2024, 309: 127443.
[22]
SIMEONOV P, AHMAD S. Effect of Transition Zone on the Elastic Behavior of Cement-based Composites[J]. Cement and Concrete Research, 1995, 25(1): 165-176.
[23]
ACKER P. Micromechanical Analysis of Creep and Shrinkage Mechanisms[C]//Creep, Shrinkage and Durability Mechanics of Concrete and Other Quasi-brittle Materials:Proceedings of the Sixth International Conference. Cambridge(MA), USA: MIT. August 20-22, 2001.
[24]
BERNARD O, ULM F J, LEMARCHAND E. A Multiscale Micromechanics-hydration Model for the Early-age Elastic Properties of Cement-based Materials[J]. Cement and Concrete Research, 2003, 33(9): 1293-1309.
[25]
ZHENG Q S, DU D X. An Explicit and Universally Applicable Estimate for the Effective Properties of Multiphase Composites which Accounts for Inclusion Distribution[J]. Journal of the Mechanics and Physics of Solids, 2001, 49(11): 2765-2788.
[26]
ESHELBY J D. The Determination of tne Elastic Field of An Ellipsoidal Inclusion,and Related Problem[C]// Proceeding of the Royal Society of London A: Mathematical,Physical and Engineering Sciences. London, UK: The Royal Society, 1957: 376-396.
[27]
MEHTA P K, MONTEIRO J M. Concrete: Microstructure Properties and Materials[M]. New York: McGraw-Hill Professional, 2014.
[28]
KÖNIGSBERGER M, PICHLER B, HELLMICH C. Micromechanics of ITZ-aggregate Interaction in Concrete Part Ⅱ: Strength Upscaling[J]. Journal of the American Ceramic Society, 2014, 97(2): 543-551.
[29]
MORI T, TANAKA K. Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions[J]. Acta Metallurgica, 1973, 21(5):571-574.
[30]
BENVENISTE Y. A New Approach to the Application of Mori-Tanaka’s Theory in Composite Materials[J]. Mechanics of Materials, 1987, 6(2): 147-157.
[31]
ZHENG Q S, DU D X. An Explicit and Universally Applicable Estimate for the Effective Properties of Multiphase Composites which Accounts for Inclusion Distribution[J]. Journal of the Mechanics and Physics of Solids, 2001, 49(11): 2765-2788.
[32]
LEE K M, PARK J H. A Numerical Model for Elastic Modulus of Concrete Considering Interfacial Transition Zone[J]. Cement and Concrete Research, 2008, 38(3): 396-402.
[33]
SALTELLI A, RATTO M, ANDRES T, et al. Global Sensitivity Analysis: The Primer[M]. New York: Wiley-Interscience, 2008.
[34]
ABBAS T, MORGENTHAL G. Framework forSensitivity and Uncertainty Quantification in the Flutter Assessment of Bridges[J]. Probabilistic Engineering Mechanics, 2016, 43: 91-105.
[35]
CONSTANTINIDES G, ULM F J. The Effect of Two Types of C-S-H on the Elasticity of Cement-based Materials:Results from Nanoindentation and Micromechanical Modeling[J]. Cement and Concrete Research, 2004, 34(1): 67-80.
[36]
VELEZ K, MAXIMILIEN S, DAMIDOT D, et al. Determination by Nanoindentation of Elastic Modulus and Hardness of Pure Constituents of Portland Cement Clinker[J]. Cement and Concrete Research, 2001, 31(4): 555-561.
[37]
KÖNIGSBERGER M, HELLMICH C, PICHLER B. Densification of C-S-H Is Mainly Driven by Available Precipitation Space, as Quantified through an Analytical Cement Hydration Model Based on NMR Data[J]. Cement and Concrete Research, 2016, 88: 170-183.
[38]
吴浪, 宋固全, 雷斌. 基于细观力学模型水泥浆体弹性力学性质预测[J]. 华中科技大学学报(自然科学版), 2011, 39(3): 39-42.
(WU Lang, SONG Gu-quan, LEI Bin. Prediction of Elastic Properties of Cement Pastes Using Micromechanics[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2011, 39(3): 39-42.) (in Chinese)
[39]
YANG C C. Effect of the Transition Zone on the Elastic Moduli of Mortar[J]. Cement and Concrete Research, 1998, 28(5): 727-736.
[40]
BER VEILLER M, PAPE Y L, GIORLAJ S A. Sensitivity Analysis and Uncertainty Propagation in Multiscale Modeling of Concrete[C]// Poromechanics IV: Proceedings of the 4th Biot Conference on Poromechanics. New York, United States. June 8-10, 2009.
PDF(8253 KB)

Accesses

Citation

Detail

Sections
Recommended

/