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

49

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 

 

COMPUTATIONAL PREDICTION OF RESTRAINT-INDUCED 

MACROCRACK PATTERNS IN CONCRETE WALLS 

 

Agnieszka Knoppik-Wróbel 

(1)

, Dirk Schlicke 

(2)

 

 

(1) Silesian University of Technology, Gliwice, Poland 

(2) Graz University of Technology, Graz, Austria 

 

 

 

 

 

 

Abstract 

Two independent approaches to predict the restraint-induced macrocrack patterns in walls 

have been recently proposed by the authors [1, 2]. The model of Knoppik-Wróbel and 

Klemczak [1] is fully numerical whereas the approach of Schlicke and Tue [2] is a simplified 

engineering model on the basis of analytical considerations. Both approaches are macroscopic 

solutions aiming at a robust prediction of macrocrack patterns with respect to its main driving 

forces. Both accept a certain level of simplification to ensure a broad applicability, however, 

their reliability was verified by satisfying results of recalculations of practical observations, as 

presented e.g. in [4, 6].This contribution presents both approaches and compares the results of 

each for a given example. Besides computational aspects, mechanical background of the 

restraint-induced cracking is outlined with special regard to relevant material properties, 

geometry and restraint situations. 

 

 

1.  Fundamentals on hardening-induced macrocrack formation in walls on foundations 

 

1.1

 

Driving forces 

Concrete is a material which gains its strength and stiffness due to cement hydration. In 

concrete elements with significant dimensions this leads to remarkable temperature histories, 

beginning with self-heating due to the heat release of the highly exothermal hydration and 

limited conductivity of concrete. Subsequently, the hydration reaction rate decreases and the 

element cools down to the ambient temperature level. In case of walls on foundations, the 

accompanying temperature deformations are restrained by the rigid connection between both 

components, which leads in the warming phase to compression in the wall. By cooling down, 

the imposed compressive stresses are decreased again. However, since also the concrete 

stiffness evolves strongly at the same time, compressive stresses due to warming are 

significantly smaller than tensile stresses due to cooling down. Autogenous shrinkage, 

decreasing viscoelasticity of aging concrete and the difference between concrete temperature 

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50

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 

 

at setting and ambient temperature level increase these tensile stresses additionally. The final 

resultants of these stresses are a tensile force and a positive bending moment in the cross 

section of the wall (N

W

, M

W

) which are superimposed by negative bending moment over the 

combined cross section of the wall and foundation due to activation of self-weight (M

g

). 

Fig. 1 illustrates this context schematically. 

 

 

 

Figure 1. Hardening-induced stress resultants in a wall on a foundation 

 

Besides, transient influences on the temperature and moisture field of the cross section cause 

internal restraint. Temperature and drying differ significantly between the surface and the 

interior of the wall, but the accompanying deformations are fully restrained in the uncracked 

state since the cross section remains plane, which leads to self-balanced stresses or the so-

called  Eigenstresses. For better understanding, Fig. 2 shows the described parts of a 

hardening-induced stress distribution.  

 

 

Figure 2. Hardening-induced stress resultants in a wall on a foundation 

 

1.2  Crack formation process 

From macroscopic point of view, crack formation starts if the present tensile strength is 

exceeded in a single material point ( (y,z) > f

ct

(y,z)). As long as Eigenstresses are predominant 

in this stage, only microcracking – respectively small, locally restricted cracks – occur. 

However, this type of cracking comes along with softening of the cross-section and beneficial 

compressive Eigenstresses decrease. In the worst case, only stresses due to stress resultants 

remain. If these stresses reach the tensile strength of the cross-section, macrocracking is to be 

expected (

N

 + 

My

 + 

Mz

 > f

ctm

). Figure 4 in [3] illustrates this context. 

The risk of macrocracking is usually reduced by Eigenstresses, however, as soon as 

microcracking occurs, the risk of macrocracking increases. This effect is intensified by further 

Eigenstresses over the width, which are not illustrated in Fig. 2 for clearness reasons. 

With respect to the final stress distribution without Eigenstresses as shown in Fig. 1 (right), 

the formation of macrocracks starts theoretically in the bottom part of the wall. But in these 

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