American Concrete Institute ACI Structural Journal May 2019
A New Model for Crack Control in Reinforced Concrete (RC) Tank Walls (Part I and Part II)
by Mariusz Zych and Andrzej Seruga
Newswise — New research is focusing on a model for calculating crack width in the case of cracks caused by progressive cooling of the wall (for example, at the stage of concrete hardening or during ambient temperature changes), the concrete shrinkage, and the subsequent service loads. This research paper addresses crack control and water-tightness of semi-massive reinforced concrete (RC) tank walls (Fig.1), in which cracking may occur at the construction stage and develop later as a result of imposed deformation or external loads.
In RC tanks, cracks of excessive width cause leaks that prevent the proper use of concrete tanks, as well as the loss of durability and consequent loss of load-bearing capacity. This aspect frequently determines the degree of horizontal reinforcement in the walls. In the Eurocode standards there is some doubt about the lack of any entrance regarding the need to determine the change in the crack widths caused by imposed loads due to the loads occurring later, especially external loads.
In the proposed model, the coefficients of the degree of wall relaxation were defined after concrete cracking. The coefficients of the degree of external restraint are used only for checking the criterion of cracking. In the presented approach, the degree of relaxation depends primarily on the:
- Level of cracking initiation h1/H
- Stiffness D11 defining the stiffness of the cracked section (for example, the influence of the degree of reinforcement ρ)
- Geometry of the wall, whether the wall is straight or circular (in the case of the latter one, also includes the influence of the radius and wall thickness)
The model includes three basic stages for the development of crack width. The first stage covers the formation of early-age cracks occurring as a result of imposed loads acting during concrete hardening. The second concerns the formation of a stabilized spacing of first-order cracks (refer to Fig. 2), as well as the early period of imposed loads acting on a structure. The third involves sufficiently high values of imposed loads or, more frequently, service loads that result in the occurrence of second-order cracks, with a simultaneous increase in the width of cracks formed in previous stages. In addition, instead of the degree of restraint, an average degree of relaxation was suggested as the basic parameter to determine the crack width and spacing.
The stepwise development of the crack width is not defined in the European Standard EN 1992-3 or in the world literature, and is a new concept of the proposed model. The results of this study can serve as a basis for future code changes for crack control derived from hydration temperatures, elevated temperatures, shrinkage, and external load effects on crack propagation.
The second part of the paper includes a calculation example, using the proposed model, of the wall segment restrained along three edges. The example features a wall segment, implemented and tested on a semi-massive tank in Żywiec, Poland. Stages of the segment cracking included the period of concrete hardening in winter, and after the water-tightness tests were presented. The measured temperature changes over a period of four months from the concreting of the segment were presented, as well as the changes in concrete strains and stresses in the reinforcement bars.
A very important aspect of the increase in the modulus of elasticity of concrete was analyzed that, in the early stages of hardening, turns out to be much slower than specified in the guidelines of the European Standard EC2-1-1. The research also provided the basis for the verification of a new crack control model, which considers the influence of the staging of imposed loads on changes in the crack width––an issue that was previously unrecognized in the world literature or current standards. A satisfactory consistency of the calculated and measured crack widths was demonstrated, both for the early stage of concrete hardening and after nine months, which was after the concreting of the segment. In the analyzed case, a significantly greater impact of the imposed load than that of the external load was demonstrated on the stress and cracking of the wall segment. The results obtained are also presented with reference to the currently applicable provisions of the European standards. The results can serve as a basis of future code changes for crack control coming from hydration temperature, elevated temperature, shrinkage, and external load effects.
The research can be found in a paper titled, “A New Model for Crack Control in RC Tank Walls, published by ACI Structural Journal.
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