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-
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
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