Proceedings of the International rilem conference Materials, Systems and Structures in Civil Engineering 2016

58

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures 

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

solutions indicate a separating crack over the whole height in the symmetry axis of the wall 

with L/H = 7 as well as a further stopping crack in the distance of l

cr

 

=(1.25

 

±

 

0.05)

   

h

W

 with a 

height of ~2/3 h

W

. A questionable continuation of the analytical approach would indicate 

another stopping crack at L/H = 2.3 with a height of 1/2

 

h

W

, but this is unlikely due to the 

weaknesses of the remaining wall length.  

From the authors’ point of view the achieved consistency between the numerical and 

analytical approach confirms the appropriateness of the included simplifications. In detail this 

refers to the role of Eigenstresses, which are remarkably reduced when any microcracking 

occurs, so that the process of macrocrack formation is driven predominantly by the stress 

resultants of the uncracked state AND the conceptual model to derive the distance between 

the primary cracks from the height reached by the previous crack is adequate. Of course, 

reinforcement will decrease this distance slightly and cracks which just reached full 

separation without reinforcement might be stopped somewhat before. 

Apart from the comparison between the two models, the insight into the structural behaviour 

of a wall on a foundation is very valuable for deformation based design concepts as presented 

by Schlicke and Tue in [3] or Knoppik-Wróbel in [4]. 

 

References 

 

[1]  Knoppik-Wróbel, A. and Klemczak B., Degree of restraint concept in analysis of early-

age stresses in concrete walls, Engineering Structures 102 (2015), 369-386, DOI: 

10.1016/j.engstruct.2015.08.025 

[2] Schlicke, D. and Tue, N. V., Minimum reinforcement for crack width control in 

restrained concrete members considering the deformation compatibility, Structural 

Concrete 16 (2015), 221-232, DOI: 10.1002/suco.201400058 

[3] Schlicke, D. and Tue, N. V., Crack width control – verification of the deformation 

compatibility vs. covering the cracking force, Proceedings of MSSCE2016/Service Life 

Segment, Lyngby, Denmark (2016) 

[4] Knoppik-Wróbel, A., Analysis of early-age thermal–shrinkage stresses in reinforced 

concrete walls, PhD thesis, Silesian University of Technology (2015) DOI: 

10.13140/RG.2.1.2970.8407 

[5]  Rostasy, F. S. and Henning, W., Zwang und Rissbildung in Wänden auf Fundamenten, 

Heft 407. Deutscher Ausschuss für Stahlbeton (1990) 

[6] Schlicke, D., Tue, N. V., Klausen, A., Kanstad, T. and Bjøntegaard, Ø., Structural 

analysis and crack assessment of restrained concrete walls – 3D FEM-simulation and 

crack assessment, Proceedings of the 1st Concrete Innovation Conference, Oslo, Norway 

(2014)  

[7] Klemczak, B., Adapting of the William–Warnke failure criteria for young concrete, 

Archives of Civil Engineering 53(2) (2007), 323-339 

[8]  Majewski, S., MWW3 – elasto–plastic model for concrete, Archives of Civil Engineering 

50(1) (2004), 11-43 

[9] Schlicke, D., Mindestbewehrung für zwangbeanspruchten Beton, PhD thesis, Graz 

University of Technology (2014) 

 http://lamp.tugraz.at/~karl/verlagspdf/buch_schlicke_25052016.pdf 

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59

International RILEM Conference on Materials, Systems and Structures in Civil Engineering 

Conference segment on Service Life of Cement-Based Materials and Structures

22-24 August 2016, Technical University of Denmark, Lyngby, Denmark 

 

SOME EXAMPLES ON SHRINKAGE RESTRAINT EFFECTS ON 

CONCRETE AND CONCRETE STRUCTURES 

 

Farid Benboudjema

(1)

 

 

(1) LMT-Cachan/ENS-Cachan/CNRS/Université Paris Saclay 

 

 

 

 

 

 

 

Abstract 

Although concrete is the most widely-used materials in construction in the world, its delayed 

behavior (shrinkage and creep) is still poorly understood. Shrinkage has negative impacts on 

concrete structures: cracking, prestress  loss etc. Shrinkage (autogeneous, drying and thermal) 

restraint occurs at different scales. At the mesoscopic scale, shrinkage of cement paste is 

restrained by aggregates: debonding at cement paste/aggregate interface and inter-granular 

cracks may occur. At the macroscopic scale, gradients of temperature and relative humidity, 

restraint by adjacent elements (previously cast slabs, concrete lift etc.) and by reinforcement 

may induce also debonding and cracking. Effects are various. A decrease of stiffness and load 

bearing capacity occurs. Penetration of aggressive species (carbonation, chloride etc.) is 

promoted due to the increase of transport properties (permeation and diffusivity). Finally, if a 

tightness is required and ensured only by concrete (nuclear reactor containment, tunnel lining, 

dams, wastewater treatment plant, etc.), it can be compromised. Some examples will be 

presented through experiments and numerical simulations, and will concern early-age and 

long term behavior, at different scales. A focus will be addressed on some issues still 

unresolved.  

 

 

1. Introduction 

 

At early-age in massive concrete structures, cracking may occur during hardening. Indeed, 

hydration is an exothermic chemical reaction (temperature in concrete may overcome 60°C 

[1-3]. Therefore, if autogenous and thermal strains are restrained (self restraint, construction 

joints), compressive stresses and then tensile stresses rise, which may reach the concrete 

strength and induce cracking in a real structure. For instance, Ithuralde [3] observed several 

crossing cracks (opening up to 0.5 mm) in a 1.2m width concrete wall (representative of 

French nuclear power plant containment), cast on a concrete slab. At long term, since drying 

is not uniform, gradient of drying shrinkage induces tensile stresses at the surface equilibrated 

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