NUMERICAL MODEL FOR PREDICTION OF CRACKS IN CONCRETE STRUCTURES A. van Beek FEMMASSE B.V., Geldermalsen, The Netherlands B.E.J. Baetens INTRON B.V., Geldermalsen, The Netherlands E. Schlangen INTRON B.V., Geldermalsen, The Netherlands Abstract Crack free concrete is often demanded for durability reasons. Obtaining crack free concrete requires not only knowledge about the materials and the structure but also a tool that delivers this knowledge to the engineer. In this paper the use of the program HEAT of FEMMASSE is outlined. Background information is given. An example from practice is presented to show that this program is a helpful tool for engineers. This example shows how knowledge of science and practice has been combined to obtain a crack free water retaining wall. 1. Introduction For durability reasons, crack widths in concrete structures should be limited. Prevention of cracks is often required in water retaining structures like tunnels. Numerical models are a helpful tool to prevent cracks or limit crack widths of young concrete. INTRON uses and developed together with FEMMASSE a model called HEAT. HEAT is developed as calculation tool for engineers. With this model the engineer can simulate the hydration process of young concrete and the effect of environment on the changing material properties and on the structural behaviour. 2. HEAT the engineering tool FEMMASSE designs its programs especially to be used by engineers. FEMMASSE delivers and develops software for reliable, efficient and effective design of structures and structure-related products. The products of FEMMASSE are developed in close corporation with their clients. HEAT was designed especially for contractors to optimise the building process so cracks can be prevented. Information about the materials, the structure and the results of the analysis is easily obtained due to a user-friendly interface (figure 1). 39
2.1 State parameter approach Most properties of civil engineering materials are not absolute, but depend on the state of the material. This can be described with parameters such as temperature and moisture content. For concrete the age is also a parameter, expressed as maturity or hydration degree. The relation between state parameters and material properties is called the stateparameter concept. This approach is used in HEAT in order to make realistic analysis. 2.2 Material database Information of different types of concrete and soil are stored in a database. The information belonging to each material in this database is obtained with experiments. The materials in the database can be used to show the differences in the risk of cracking of the different types of concrete in a structure. 2.3 Design panel Cracks in concrete do not only depend on the material properties. Even more important is the structure itself. If the deformations due to shrinkage and/or temperature are restrained by the structure this can lead to cracks. In the HEAT model it is possible to draw a two dimensional picture of the structure. The temperature and moisture conditions can be placed on the boundaries of this structure. 2.4 Results The computer simulates the hydration process in the structure and calculates the stresses and strength in the concrete structure. The results can be presented in 2D-planes and in graphs. Figure 1 The user-interface of HEAT 40
3. Material models The simulations of HEAT are based on a number of material models to calculate the effect of the environment on the material in a structure. A database contains a number of concrete mixtures and their material properties necessary for these models. Models incorporated in the HEAT are: Maturity Relaxation Authogeneous Shrinkage Hygral Shrinkage Thermal dilatation etc. In the following paragraphs, the models that are important to determine cracks in young concrete will be outlined. 3.1 Heat transport The mathematical theory of heat transfer in isotropic media is based on the hypothesis that the rate of heat transfer through a unit area of a section is proportional to the temperature gradient normal to the section (Fick's first law): q r = λ T T xx Eq. 1 q T λ T = heat flux = temperature = thermal conductivity The partial differential equation describing the heat transfer under transient conditions is (Fick's second law): c T λ T H = 0 Eq. 2 T t T xx t c T H t =heat capacity =heat source Eq. (2) can be derived from Eq. (1) taking the heat balance into consideration (1). 3.2 Aging of concrete In order to describe the age dependent physical and mechanical processes a maturity model has been implemented. The maturity, M, (or also called equivalent hydration period) is defined as: 41
M ( t) = t tcon e Q ( R Tref + 1 273 T + 1 273 ) 1+ ( a c 1 a h) c bc dt Eq. 3 t t con Q R T ref T h a c b c = actual time = time at casting = activation energy = universal gas constant = reference temperature = temperature = moisture potential (relative humidity) = coefficient = coefficient This expression was first given by Bazant (2). The first part under the integral is the well-known Arrhenius expression to take the influence of the temperature history on the maturity in consideration. With the second part the influence of moisture potential h (0 =< h =<1 ) on the maturity process is described. Properties related to maturity are: Tensile strength Compressive strength Modulus of elasticity Creep etc. 3.3 Temperature increase due to hydration Effectively 2 different heat source models have been implemented to describe the liberation of heat of hydration of concrete. The first model is based on a shrinkage core model and has been applied successfully in many consulting projects (3). The second model is more a empirical model, developed by the Danish concrete industry, and also applied successfully to e.g. the east and west Storebaelt Bridges and the Øresund Tunnel (4). For projects in the Netherlands mostly the shrinkage Core Model is used. The mathematical expression for the Shrinkage Core Model is: a( M d) H t ( M ) = H T Eq. 4 1+ a( M d) H T d a = total heat of hydration = dormant period (reaction rate very slow) = function coefficient 42
4. Example of HEAT used in practice This example describes the ramps on the north side of the Western Scheldt tunnel. For the whole ramp the stresses due to temperature in the early age have been analysed. The aim of this analysis was to prevent cracks in the water retaining walls. This example deals with one of the cross sections as presented in figure 2. 500 500 ± 5-16 m ± 5-16 m 1000 800-1000 800-1000 1000 Figure 2 Characteristic cross section 4.1 Geometry and phases 29950 This analysis mainly concerns the connection between wall and base slab. The base slab is a floor build in two stages. In the first stage the concrete is cast under water. In the second stage the water has been pumped from the floor and the constructive floor was cast. The concrete of the two phases was modelled as one solid floor. The time between cast of the base slab and cast of the walls was 4 weeks. In the analysis it is assumed that both walls are cast at the same time. Therefore a vertical axis of symmetry was used. 4.2 Materials properties Table 1 Materials properties Composition Amount Strength Type cement Amount of cement Additives Aggregates w/c-ratio B35 (f 28 days ) = 35 N/mm² CEM III/B 42,5 LH HS 340 kg/m 3 BV/FM en LP-Bildner River sand and gravel (4-32 mm) 0.45 43
4.3 Kinematical boundaries Figure 3 shows the system of axis. In the analysis only the strains in the X-Y-plane (ε xx, ε yy en γ xy ) and perpendicular to this plane (ε zz ) are taken into account. ε zz is defined as: zz ( x, y) = ε(0,0) + κ y + κ x ε Eq. 5 x y with κ x as the rotation around the X axis and κ y is the rotation around the Y axis. Rotation around the Y-axis is restrained due to symmetry. Mechanical analyses had shown that the rotation κ x and dilation ε(0,0) were not restrained. y Figure 3 System of axis with respect to the structure z 4.4 Physical boundaries Climate The average ambient temperature is 15 C. Day temperature was 18 C at maximum and the night temperature 12 C at minimum. The wind speed is set on 5 m/s. Initial temperature The initial temperature of the concrete is 20 C for the wall and 15 o C for the base slab. Formwork and insulation The formwork is removed 4 days after casting. The formwork is a 18 mm plywood plate. With a wind speed of 5 m/s, the heat transfer coefficient in combination with the plywood is 7 W/m²K. After the formwork is removed the heat transfer coefficient is 25 W/m²K. x 44
5. Analysis without measures The temperature differences in the structure are the main reason for cracks. In figure 4 it is shown that after 36 hours the centre of the wall has a temperature of 45ºC. While the concrete is the floor has a temperature of 15ºC. Even in the wall a temperature difference of 13ºC was found. Figure 4 Distribution of temperature and temperature development in the structure. Temperature on it self will not cause cracks. The deformations of the structure due to thermal dilation can cause cracks. The different dilations within a structure will cause stresses as presented in figure 5. If these stresses exceed the tensile strength cracks will occur. Figure 5 Distribution of stresses and stress and strength development in the structure. Figure 5 shows that the stress (σ zz ) in the wall exceeds the limit of 50% of the tensile strength. This means that there is a high risk on cracking. The stresses are caused by the average temperature difference between the wall and the base slab during hardening of the concrete. Measures must be taken to lower this temperature difference. 45
Cooling was used as a useful and economical way to prevent cracks because: Pouring of base slab and walls in one pour (for example the Øresund tunnel) could be a solution but due to construction reasons a change of phasing was not possible. A less insulating formwork (for example steel) is not useful due to the large thickness of the walls. The average temperature will hardly decrease and the local gradient will increase unfavourable. Reinforcement that limits the crack width was not possible due to leakage limits. Other measures such as heating up the base slab, lowering the initial mix temperature and adjustments of the concrete mix composition were technically not possible. 6. Analysis with internal cooling 6.1 Design of the cooling system The largest tensile stresses occur at the base of the wall. It is, therefore, not necessary to cool the entire wall. A cooling system with diverging distances as shown in figure 6 gives the best results. outlet 4 * 800 2 * 600 inlet 3 * 400 Figure 6 Position cooling pipes and thermocouples in the wall The design of a cooling system is an iterative process. The combination of the results of the simulations and practical consideration, which were obtained in discussions with the contractor, has lead to the following scenario and details: Positioning the cooling pipes in the middle of the wall according to figure 5 The cooling pipes are made of plastic with a diameter of 32 mm and a thickness of 3 mm 46
The cooling pipes are in one system with the inlet on the bottom and the outlet on the top part of the wall. The inlet temperature of the water is 10 C. The flow of the cooling water is 1.0 m 3 /hours. The duration of the cooling is 50 hours. 6.2 Results of the analysis The cooling of concrete in the wall has resulted in smaller temperature differences between the slab and the wall and in the wall itself (figure 7). By optimising the distance between the cooling pipes, period of cooling and the cooling capacity of the system the temperature can be controlled so that the stresses will not exceed the tensile strength (figure 8). Figure 7 Distribution of temperature at the maximum temperature and development of the temperature in the core of the wall. Figure 8 Distribution of stresses (σ zz ) in the wall at the maximum stress and the stress development in the core of the wall. 47
7. Future developments The programs of FEMMASSE have always been developed in co-operation with Universities. This co-operation assures that HEAT incorporates the latest know-how of science. Even at this moment development of the FEMMASSE products continues. Models that describe moisture transport in inhomogeneous materials are under development. HEAT is used for predicting moisture transport in multi-layered systems like floors already (5). Modelling concrete structures with the effect of reinforcement on the stresses and on the crack formation (6) is one of the topics that has to be incorporated in the near future. With these developments HEAT will become a tool for the engineer with which he can design not only on forces and stresses but also on durability aspects. 8. Conclusions With the HEAT module, the effect of cooling of concrete, application of insulation, low heat cements etc. can be simulated to obtain crack free and thus durable concrete structures. In this paper the background of the models and some applications of the HEAT module on structures in practice has been demonstrated. In a structure without measures, it was shown that cracks are likely to occur while the concrete is still young. By using a measure which is not focussed on decreasing temperatures alone, but mainly on decreasing the chance of cracking (stresses compared with tensile strength) an economical solution was found. It is shown that with a user-friendly user-interface science from university can be made available to the engineer. In the future this type of software will be used to determine the durability of structures without having to perform extensive testing. 9. References 1. Crank, J., The mathematics of diffusion, Oxford University Press, 2 nd edition (1979). 2. Bazant, Z.P., Creep and shrinkage of concrete, Mathematical Modeling, Fourth Rilem International Symposium, Evanstone, Illinois 60201, USA, (1986). 3. Roelfstra, P.E., A numerical approach to investigate the properties of concrete, Numerical Concrete, Ph.D.Thesis, EPF -Lausanne, Switzerland, (1989). 4. J. Visser, T.A.M. Salet, P.E. Roelfstra, Temperature control of young concrete based on computer models, Cement nr. 9, pp. 16-22, (1992). 5. A. van Beek, E. Schlangen, Simulating the effect of shrinkage on concrete structures, Rilem Workshop, Shrinkage 2000, (2000). 6. M. Sule, K. van Breugel, Cracking behaviour of reinforced concrete subjected to early-age shrinkage, Rilem Workshop, Shrinkage 2000, (2000). 48