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

51

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 

 

parts the stiffness of the foundation will reduce the crack width considerably. Only if the 

macrocrack proceeds over the height of the wall, they become visible. For an efficient design 

it is very desirable to know whether these macrocracks will stop at a certain height or proceed 

over the whole wall as well as what is the distance to the next macrocrack. Thus, significant 

factors influencing these aspects are discussed in the following section. 

 

1.3  Relevant influences on the final macrocrack pattern 

The material, technological and environmental conditions determine mostly the magnitude of 

strains and strain rate, and as such define whether the cracks form or not. The final pattern of 

cracks depends mostly on geometry, dimensions and restraint conditions. 

In general, the maximum tensile stresses in a base-restrained element occur in the plane of 

symmetry in length direction. This is also where first cracks are formed and where they reach 

the greatest heights. For the same material, technological and environmental conditions the 

height of this crack would depend solely on the restraint situation dependent on the EA and EI 

as well as L/H ratios.  

Depending on the cracking potential of hardening concrete and geometrical characteristics of 

the wall, further primary cracks can successively develop in the wall. In shorter walls, these 

cracks reach lower heights due to a smaller effective L/H ratio. The cracks are usually vertical 

in the central part of the wall and slanted near the edges where the rotational restraint 

becomes more significant. Horizontal cracks can be formed at the joint if shear stresses at the 

joint exceed the bond strength. A comprehensive description of cracking pattern in walls on 

foundations is presented in chapter 2 of [4]. 

 

1.4  Modelling 

The modelling of hardening-induced macrocrack patterns of walls on foundations is a 

complex matter. The major challenge is to combine complex time- and stress-dependent 

material behaviour with crack formation on structural level. Only a modest number of 

contributions exist, whereby the fundamental work by Rostasy and Henning [5] is certainly to 

be seen as one of the most important ones. Next to this, the authors of this paper proposed two 

approaches independently of each other. Other pertinent proposals are not known.  

 

 

2.  Numerical prediction of hardening-induced macrocrack formation in walls 

 

2.1 Model used 

The model used was based on the proposal of Knoppik-Wróbel and Klemczak [1]. 

Calculations were performed with a computer implementation of this phenomenological 

model that allows for thermo–mechanical analysis of walls on foundation taking into account 

the effect of hydration heat, temperature development, ageing, creep, soil–structure 

interaction and behaviour of concrete after damage.  

The analysis was performed in two steps. In the first step non-linear and non-stationary 

thermal fields were determined in concrete elements and subsoil, respectively: 

 

 

(1)

 

(2)

 

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52

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 

 

where   is temperature, K; 

 is specific heat, kJ/(kg·K);   is density, kg/m

3

;   is thermal 

conductivity, W/(m·K) and 

 is the rate of hydration heat generated per unit volume of 

concrete, W/m

3

. The function of hydration heat time-development was described with the 

approximation function of equivalent age,  : 

 

 

(3)

 

where 

 is the total amount of hydration heat, J/g, and 

 are calibration coefficients 

dependent on the type of cement. 3

rd

 type boundary conditions were used. The aim of this 

study was to investigate mechanical behaviour of the wall, thus physical analysis was limited 

to thermal analysis. The authors are, however, aware that other influences such as autogenous 

and drying shrinkage as well as coupling of these phenomena are not less important. 

The imposed thermal strains were treated as volumetric strains and they were calculated based 

on the changes of temperature: 

 

 

(4)

 

(5)

 

where 

 is the coefficient of thermal expansion, 1/K.  

Viscoelasto–viscoplastic material model with the modified 3-parameter Willam–Warnke 

failure criterion (MWW3) was used for hardening concrete following Klemczak [7] and 

elasto–plastic material model with the modified Drucker–Prager failure criterion was used for 

soil (see [4]). Detailed formulations of these models are given in [1] and [4]. The possibility 

of crack occurrence was defined with the damage intensity factor (

): 

 

 

(6)

 

Graphical interpretation of 

 is shown in Fig. 3. When DIF = 1, it is equivalent to 

formation of a crack in the direction perpendicular to the direction of the principal tensile 

stress. Smeared cracking pattern was used. When failure is reached, material exhibits 

softening behaviour. In the model, deviatoric and volumetric softening was applied with 

hardening and softening laws adopted following Majewski [8]. 

 

 

Figure 3. Graphical interpretation of damage intensity factor (DIF) 

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