On the added value of multi-scale modeling of concrete

Abstract

This review of the added value of multi-scale modeling of concrete is based on three representative examples. The first one is concerned with the analysis of experimental data, taken from four high-dynamic tests. The structural nature of the high-dynamic strength increase can be explained by using a multi-scale model. It accounts for the microstructure of the specimens. The second example refers to multi-scale thermoelastic analysis of concrete pavements, subjected to solar heating. A sensitivity analysis with respect to the internal relative humidity (RH) of concrete has underlined the great importance of the RH for an assessment of the risk of microcracking of concrete. The third example deals with multi-scale structural analysis of a real-scale test of a segmental tunnel ring. It has turned out that multi-scale modeling of concrete enables more reliable predictions of crack opening displacements in tunnel segments than macroscopic models taken from codes of practice. Overall, it is concluded that multi-scale models have indeed a significant added value. However, its degree varies with these examples. In any case, it can be assessed by means of a comparison of the results from three sources, namely, multi-scale structural analysis, conventional structural analysis, and experiments.

Graphical abstract

Keywords

experiments / multi-scale analysis / conventional structural analysis / concrete / reinforced concrete

References

[1] GeersM G D, KouznetsovaV G, BrekelmansW A M. Multi-scale computational homogenization: Trends and challenges. Journal of Computational and Applied Mathematics, 2010, 234( 7): 2175– 2182

[2] WriggersP, MoftahS O. Mesoscale models for concrete: Homogenisation and damage behavior. Finite Elements in Analysis and Design, 2006, 42( 7): 623– 636

[3] OskayC, FishJ. Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. Computer Methods in Applied Mechanics and Engineering, 2007, 196( 7): 1216– 1243

[4] MoulinecH, SuquetP. A numerical method for computing the overall response of nonlinear composites with complex microstructure. Computer Methods in Applied Mechanics and Engineering, 1998, 157(1–2): 69– 94

[5] ZaouiA. Continuum micromechanics: Survey. Journal of Engineering Mechanics, 2002, 128( 8): 808– 816

[6] AuriaultJ L. Heterogeneous medium. Is an equivalent macroscopic description possible? International Journal of Engineering Science, 1991, 29( 7): 785– 795

[7] PopperK. Conjectures and Refutations: The Growth of Scientific Knowledge. London: Routledge, 2014

[8] ZhangY, PichlerC, YuanY, ZeimlM, LacknerR. Micromechanics-based multifield framework for early-age concrete. Engineering Structures, 2013, 47 : 16– 24

[9] Irfan-ul-HassanM, PichlerB, ReihsnerR, HellmichC. Elastic and creep properties of young cement paste, as determined from hourly repeated minute-long quasi-static tests. Cement and Concrete Research, 2016, 82 : 36– 49

[10] PichlerB, ScheinerS, HellmichC. From micron-sized needle-shaped hydrates to meter-sized shotcrete tunnel shells: Micromechanical upscaling of stiffness and strength of hydrating shotcrete. Acta Geotechnica, 2008, 3( 4): 273– 294

[11] UllahS, PichlerB, ScheinerS, HellmichC. Influence of shotcrete composition on load-level estimation in NATM‐tunnel shells: Micromechanics-based sensitivity analyses. International Journal for Numerical and Analytical Methods in Geomechanics, 2012, 36( 9): 1151– 1180

[12] FischerI, PichlerB, LachE, TernerC, BarraudE, BritzF. Compressive strength of cement paste as a function of loading rate: Experiments and engineering mechanics analysis. Cement and Concrete Research, 2014, 58 : 186– 200

[13] BinderE, ReihsnerR, YuanY, MangH A, PichlerB L A. High-dynamic compressive and tensile strength of specimens made of cementitious materials. Cement and Concrete Research, 2020, 129 : 105890–

[14] Hlobil M. Micromechanical analysis of blended cement-based composites. Dissertation for the Doctoral Degree. Vienna: Tu Wien and Prague: Czech Technical University, 2016

[15] KühnT, SteinkeC, SileZ, ZreidI, KaliskeM, CurbachM. Dynamic properties of concrete in experiment and simulation. Concrete and Reinforced Concrete, 2016, 111(1): 41– 50 (in German)

[16] ZhangM, WuH J, LiQ M, HuangF L. Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests. Part I: Experiments. International Journal of Impact Engineering, 2009, 36( 12): 1327– 1334

[17] MihashiH, WittmannF H. Stochastic approach to study the influence of rate of loading on strength of concrete. Heron, 1980, 25( 3): 5– 54

[18] BažantZ P, CanerF C, AdleyM D, AkersS A. Fracturing rate effect and creep in microplane model for dynamics. Journal of Engineering Mechanics, 2000, 126( 9): 962– 970

[19] WangX F, YangZ J, YatesJ R, JivkovA P, ZhangC. Monte Carlo simulations of mesoscale fracture modelling of concrete with random aggregates and pores. Construction & Building Materials, 2015, 75 : 35– 45

[20] GaryG, BaillyP. Behaviour of quasi-brittle material at high strain rate. Experiment and modelling. European Journal of Mechanics. A, Solids, 1998, 17( 3): 403– 420

[21] HaoY, HaoH, LiZ X. Influence of end friction confinement on impact tests of concrete material at high strain rate. International Journal of Impact Engineering, 2013, 60 : 82– 106

[22] Flores-JohnsonE A, LiQ M. Structural effects on compressive strength enhancement of concrete-like materials in a split Hopkinson pressure bar test. International Journal of Impact Engineering, 2017, 109 : 408– 418

[23] KühnT. Experimental fundamentals for the meso and macroscopic modeling of concrete at high loading velocities: A critical review of the strain rate effect. Dissertation for the Doctoral Degree. Dresden: Technische Universität Dresden, 2020

[24] LuD, WangG, DuX, WangY. A nonlinear dynamic uniaxial strength criterion that considers the ultimate dynamic strength of concrete. International Journal of Impact Engineering, 2017, 103 : 124– 137

[25] ZhouX Q, HaoH. Modelling of compressive behaviour of concrete-like materials at high strain rate. International Journal of Solids and Structures, 2008, 45( 17): 4648– 4661

[26] TangT, MalvernL E, JenkinsD A. Rate effects in uniaxial dynamic compression of concrete. Journal of Engineering Mechanics, 1992, 118( 1): 108– 124

[27] GebbekenN, GreulichS. A new material model for SFRC under high dynamic loadings. In: Proceedings of 11th International Symposium on Interaction of the Effects of Munitions with Structures (ISIEMS 2003). Mannheim: ISIEMS, 2003

[28] BraraA, KlepaczkoJ R. Experimental characterization of concrete in dynamic tension. Mechanics of Materials, 2006, 38( 3): 253– 267

[29] LiQ M, LuY B, MengH. Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split hopkinson pressure bar tests. Part II: numerical simulations. International Journal of Impact Engineering, 2009, 36( 12): 1335– 1345

[30] MATLAB. Version R2018. Natick, MA: MathWorks. 2018

[31] OnlineEtymology Dictionary. Predict (v.). Available at the website of OnlineEtymology Dictionary. 2021

[32] EN1992-1-1. Eurocode 2: Design of Concrete Structures—Part 1-1: General Rules and Rules for Buildings. Brussels: European Committee for Standardization, 2011

[33] Euro-InternationalCommittee for Concrete. CEB-FIP model code 1990: Design Code. London: Thomas Telford Publishing, 1993

[34] NationalCooperative Highway Research Program. Guide for Mechanistic-empirical Design of New and Rehabilitated Pavement Structures. Final Report NCHRP Project 1-37A. 2004

[35] HuangH, AnM, WangY, YuZ, JiW. Effect of environmental thermal fatigue on concrete performance based on mesostructural and microstructural analyses. Construction & Building Materials, 2019, 207 : 450– 462

[36] ChenD, ZouJ, ZhaoL, XuS, XiangT, LiuC. Degradation of dynamic elastic modulus of concrete under periodic temperature-humidity action. Materials (Basel), 2020, 13( 3): 611–

[37] AnM, HuangH, WangY, ZhaoG. Effect of thermal cycling on the properties of high-performance concrete: Microstructure and mechanism. Construction & Building Materials, 2020, 243 : 118310–

[38] FuY F, WongY L, PoonC S, TangC, LinP. Experimental study of micro/macro crack development and stress–strain relations of cement-based composite materials at elevated temperatures. Cement and Concrete Research, 2004, 34( 5): 789– 797

[39] PichlerB, HellmichC. Estimation of influence tensors for eigenstressed multiphase elastic media with nonaligned inclusion phases of arbitrary ellipsoidal shape. Journal of Engineering Mechanics, 2010, 136( 8): 1043– 1053

[40] EmanuelJ, HulseyJ. Prediction of the thermal coefficient of expansion of concrete. Journal of the American Concrete Institute, 1977, 74( 4): 149– 155

[41] WangH, MangH, YuanY, PichlerB. Multiscale thermoelastic analysis of the thermal expansion coefficient and of microscopic thermal stresses of mature concrete. Materials (Basel), 2019, 12( 17): 2689–

[42] EN1992-1-1. Eurocode 2: Design of Concrete Structures—Part 1-1: General Rules and Rules for Buildings. Edition: 2015-07-31. Brussels: European Committee for Standardization, 2015

[43] WangH, HellmichC, MangH, PichlerB. May reversible water uptake/release by hydrates explain the thermal expansion of cement paste?—Arguments from an inverse multiscale analysis. Cement and Concrete Research, 2018, 113 : 13– 26

[44] Meyers S. Thermal expansion characteristics of hardened cement paste and of concrete. Highway Research Board Proceedings, 1951, 30: 193–203

[45] Mitchell L J. Thermal expansion tests on aggregates, neat cements, and concretes. Proceedings of the American Society for Testing and Materials, 1953, 53: 963–977

[46] Dettling H. Thermal expansion of cement pastes, aggregates, and concretes. Dissertation for the Doctoral Degree. Stuttgart: Technische Hochschule Stuttgart, 1962 (in German)

[47] WangH, HöllerR, AminbaghaiM, HellmichC, YuanY, MangH, PichlerB. Concrete pavements subjected to hail showers: A semi-analytical thermoelastic multiscale analysis. Engineering Structures, 2019, 200 : 109677–

[48] HöllerR, AminbaghaiM, EberhardsteinerL, EberhardsteinerJ, BlabR, PichlerB, HellmichC. Rigorous amendment of Vlasov’s theory for thin elastic plates on elastic Winkler foundations, based on the Principle of Virtual Power. European Journal of Mechanics. A, Solids, 2019, 73 : 449– 482

[49] KönigsbergerM, PichlerB, HellmichC. Micromechanics of ITZ-aggregate interaction in concrete, part I: Stress concentration. Journal of the American Ceramic Society, 2014, 97( 2): 535– 542

[50] KönigsbergerM, PichlerB, HellmichC. Micromechanics of ITZ-aggregate interaction in concrete, part II: Strength upscaling. Journal of the American Ceramic Society, 2014, 97( 2): 543– 551

[51] WangH, BinderE, MangH, YuanY, PichlerB. Multiscale structural analysis inspired by exceptional load cases concerning the immersed tunnel of the Hong Kong-Zhuhai-Macao Bridge. Underground Space, 2018, 3( 4): 252– 267

[52] LiuX, BaiY, YuanY, MangH A. Experimental investigation of the ultimate bearing capacity of continuously jointed segmental tunnel linings. Structure and Infrastructure Engineering, 2016, 12( 10): 1364– 1379

[53] LiuX, JiangZ, YuanY, MangH A. Experimental investigation of the ultimate bearing capacity of deformed segmental tunnel linings strengthened by epoxy-bonded steel plates. Structure and Infrastructure Engineering, 2018, 14( 6): 685– 700

[54] LiuX, JiangZ, ZhangL. Experimental investigation of the ultimate bearing capacity of deformed segmental tunnel linings strengthened by epoxy-bonded filament wound profiles. Structure and Infrastructure Engineering, 2017, 13( 10): 1268– 1283

[55] ZhangJ L, LiuX, RenT Y, YuanY, MangH A. Structural behavior of reinforced concrete segments of tunnel linings strengthened by a steel-concrete composite. Composites. Part B, Engineering, 2019, 178 : 107444–

[56] Liu X, Zhang J L, Jiang Z, Liu Z, Xu P, Li F. Experimental investigations of a segmental tunnel ring strengthened by using ultra-high performance concrete (UHPC). China Journal of Highway Transport, 2021, 34(8): 181–190 (in Chinese)

[57] ZhangJ L, SchlappalT, YuanY, MangH A, PichlerB. The influence of interfacial joints on the structural behavior of segmental tunnel rings subjected to ground pressure. Tunnelling and Underground Space Technology, 2019, 84 : 538– 556

[58] GalvánA, PeñaF, Moreno-MartínezJ Y. Effect of TBM advance in the structural response of segmental tunnel lining. International Journal of Geomechanics, 2017, 17( 9): 04017056–

[59] DoN A, DiasD, OresteP, Djeran-MaigreI. Three-dimensional numerical simulation for mechanized tunnelling in soft ground: The influence of the joint pattern. Acta Geotechnica, 2014, 9( 4): 673– 694

[60] WangZ, WangL, LiL, WangJ. Failure mechanism of tunnel lining joints and bolts with uneven longitudinal ground settlement. Tunnelling and Underground Space Technology, 2014, 40 : 300– 308

[61] LiuX, DongZ, BaiY, ZhuY. Investigation of the structural effect induced by stagger joints in segmental tunnel linings: First results from full-scale ring tests. Tunnelling and Underground Space Technology, 2017, 66 : 1– 18

[62] LiuX, DongZ, SongW, BaiY. Investigation of the structural effect induced by stagger joints in segmental tunnel linings: Direct insight from mechanical behaviors of longitudinal and circumferential joints. Tunnelling and Underground Space Technology, 2018, 71 : 271– 291

[63] LiuX, ZhangY M, BaoY H. Full-scale experimental investigation on stagger effect of segmental tunnel linings. Tunnelling and Underground Space Technology, 2020, 102 : 103423–

[64] ZhangJ L, MangH A, LiuX, YuanY, PichlerB. On a nonlinear hybrid method for multiscale analysis of a bearing capacity test on a real-scale segmental tunnel ring. International Journal for Numerical and Analytical Methods in Geomechanics, 2019, 43( 7): 1343– 1372

[65] ZhangJ L, VidaC, YuanY, HellmichC, MangH A, PichlerB. A hybrid analysis method for displacement-monitored segmented circular tunnel rings. Engineering Structures, 2017, 148 : 839– 856

[66] InternationalFederation for Structural Concrete. Fib Model Code for Concrete Structures 2010. Berlin: Ernst & Sohn, 2010

[67] JapanSociety of Civil Engineering (JSCE). Standard Specifications for Concrete Structures––2007 “Design”. Tokyo: JSCE, 2010

[68] GB50010-2010. Chinese Code for Design of Concrete Structures. Beijing: Ministry of Housing and Urban-Rural Development of China, General Administration of Quality Supervision, Inspection and Quarantine of China, 2010

[69] ZhangJ L, BinderE, LiuX, YuanY, MangH A, PichlerB L A. Assessment of the added value of multiscale modeling of concrete for structural analysis of segmental tunnel rings. Encyclopedia of Materials: Composites, 2021, 3 : 69– 78

[70] KönigsbergerM, HlobilM, DelsauteB, StaquetS, HellmichC, PichlerB. Hydrate failure in ITZ governs concrete strength: A micro-to-macro validated engineering mechanics model. Cement and Concrete Research, 2018, 103 : 77– 94

[71] HillR. Continuum micro-mechanics of elastoplastic polycrystals. Journal of the Mechanics and Physics of Solids, 1965, 13( 2): 89– 101

[72] ZhangJ L, LiuX, YuanY, MangH A, PichlerB L A. Transfer relations: useful basis for computer-aided engineering of circular arch structures. Engineering Computations, 2021, 38( 3): 1287– 1302

[73] ZhangJ L, HellmichC, MangH A, YuanY, PichlerB. Application of transfer relations to structural analysis of arch bridges. Computer Assisted Methods in Engineering and Science, 2018, 24 : 199– 215

[74] ZhangJ L, LiuX, ZhaoJ B, YuanY, MangH A. Application of a combined precast and in-situ-cast construction method for large-span underground vaults. Tunnelling and Underground Space Technology, 2021, 111 : 103795–

[75] JiangZ, LiuX, SchlappalT, ZhangJ L, MangH, PichlerB L A. Asymmetric serviceability limit states of symmetrically loaded segmental tunnel rings: Hybrid analysis of real-scale tests. Tunnelling and Underground Space Technology, 2021, 113 : 103832–

Acknowledgements

Financial support by the Ministry of Science and Technology of China (No. 2021YFE0114100) and by the Federal Ministry of Education, Science and Research (BMBWF) of Austria (No. CN 11/2021), jointly provided for the project “Intense Upgrades of the New Austrian Tunnelling Method (NATM) and Demonstration of its Applicability to High-Quality Urban Development”, is gratefully acknowledged. In addition, the authors are indebted to the National Natural Science Foundation of China (Grant Nos. 51908424, U1934210) and the Shanghai Pujiang Program (Nos. 19PJ1409700, 20PJ1406100) for financial support of this work.

Open Access

This article is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

RIGHTS & PERMISSIONS

2022 The Author(s) 2022. This article is published with open access at link.springer.com and journal.hep.com.cn.