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

55

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 

 

reach whole height and no further primary cracks are formed. Besides, a horizontally running 

damage intensity concentration can be observed near the edge of the wall due to shear. 

 

 

 

 

a) yz, x = 0 (interior) 

b) xy, z = 0 (axis of symmetry) 

Figure 5. Map of DIF in the L = 10.5 m wall at the age of wall t = 15.5 days 

 

 

 

a) yz, x = 0 (interior) 

b) yz, x = 0.5 b

W

 (surface) 

b) xy, z = 0  

Figure 6. Final map of DIF in the L = 10.5 m wall at the age of wall t = 18 days 

 

Figures 7 to 9 present analogical simulation of damage development in a long wall with the 

length of 21 m (L/H = 7, so twice of the reference case). In Fig. 7 it can be seen again that 

when the first primary crack develops, softening occurs in its vicinity. It must be noted that 

the crack in the long wall starts to develop sooner than in the short wall, at the age of wall of 

4.5 days. The crack progresses at the thickness of the wall and at its height. It gets its final 

shape at the age of 8.7 days when it reaches whole height of the wall, which was to be 

expected for the higher L/H. 

 

 

 

a) yz, x = 0 (interior) 

b) xy, z = 0  

Figure 7. Map of DIF in the L = 21 m wall at the age of wall t = 5 days 

 

Figure 8 shows the DIF map at the age of 12 days. Intensive damage was indicated in the 

interior of the wall which represents microcracks due to Eigenstresses. Besides, a fully-

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56

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 

 

developed separating crack is visible at the surface in the symmetry axis which “splits” the 

wall in two halves. After the first primary crack, the remaining half of the wall still has an L/H 

of 3.5 so ongoing cooling forms another primary crack at the age of 12.7 days (Fig. 9).  

 

 

 

a) yz, x = 0 (interior) 

b) xy, z = 0  

 

 

c) yz, x = 0.5 b

W

 (surface) 

 

Figure 8. Map of DIF in the L = 21 m wall at the age of wall t = 12 days 

 

 

 

a) yz, x = 0 (interior) 

b) xy, z = 4 m  

 

 

c) yz, x = 0.5 b

W

 (surface) 

 

Figure 9. Final map of DIF in the L = 21 m wall 

 

The distance from the axis of symmetry to this crack amounts ~4 m, which is ~1.3·h

W

. 

Softening is observed in the vicinity of this crack, too. In contrast to the corresponding wall of 

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57

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 

 

L/H = 3.5, this crack reaches on average ~80 % of the height of the wall. This difference may 

result from the fact that the crack is formed earlier, so the strength of the concrete is lower.  

 

 

3.  Analytical prediction of hardening-induced macrocrack formation in walls  

 

The analytical approach to determine the macrocrack pattern of walls on foundations was 

comprehensively explained by Schlicke and Tue in [2]. The basic idea is to relate the distance 

between primary cracks to the length needed to build up the restraint stresses again. From the 

theoretical point of view, this length strongly correlates with the height which the primary 

crack reaches. Thus, the stress at the top of the macrocrack 

R

 will be determined according to 

the remaining concrete area above the top of the crack h

R

 to compare the resulting curve with 

the present tensile strength f

ct

. In all cases where 

R

(h

R

) falls below the tensile strength, a stop 

of the cracking will be assumed at this height; in any other case a continuous crack over the 

wall height will be assumed. 

If the crack height is known, the distance between the geometrically set primary cracks will 

be assumed to have a size of l

cr

 = 1.2 h

cr

. The application of this approach for the numerically 

studied systems is shown in Fig. 10. The considered stress resultants were determined fully 

analytically on the basis of an equivalent deformation impact 

0

 taking into account the 

temperature field changes due to hydration heat release uniformly distributed in the cross 

section, stiffness evolution and viscoelasticity for the given material parameters in Tab. 1. 

Details on the approach used are given by Schlicke in [9]. 

 

Figure 10. Analytically determined primary crack patterns of the numerically studied cases 

 

 

4. Discussion 

and 

conclusions 

 

The paper presents a comparative study on early-age cracking process with two independent 

methods recently proposed by the authors [1, 2]. Although the proposed models accept a 

certain level of simplification, the comparative study gives an acceptable agreement. Both 

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