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
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