Programming for simulation of hygro- thermal

Programming for simulation of hygrothermal deformation in concrete Qian Chunxiang, Chen Depeng and Liu Yujun

Deformations in concrete due to temperature and moisture (condition) always develop simultaneously and interactively. The examination of hygro-thermal deformation of concrete is necessary for better serviceability, durability estimation and life prediction. In this paper, a numerical simulation procedure is proposed for hygro-thermal deformation of concrete based on the principle of heat and moisture transfer in porous medium. The procedure comprises of an analytical solution of heat and moisture transfer, a calculation of moisture induced stress and a finite element analysis (FEM) of hygro-thermal deformation. The methodology of a software named Combined Temperature and Moisture Simulation System for concrete (CTMSoft) is developed. Visual Basic 6.0 programme was used for the graphical user interface (GUI) and the numerical calculation was developed using Matlab and ANSYS. The working of CTMSoft has been validated by a case analysis Keywords: Hygro-thermal deformation, concrete, mix programming, heat and moisture transfer. Literature about volumetric deformation of concrete are based on autogeneous shrinkage, drying shrinkage and hydration heat induced thermal shrinkage. Using these variations a few prediction models have been developed combining experimental work and statistical

analysis. Bažant and Najjar (Bažant and Najjar 1972) studied concrete deformation based on heat transfer and moisture diffusion in concrete. Fick’s second law for drying shrinkage and Fourier’s heat conducting equation for thermal shrinkage are the basic equations used to calculate deformation in concrete. As temperature and moisture act simultaneously and interactively to develop deformation synergistic simulation of hygro-thermal behavior is necessary for better serviceability, durability and life prediction. Shrinkage or cracking of concrete induced by the combined effect of heat and moisture has been investigated at high temperature to analyse the behaviour of concrete in fire (Chung and Consolazio 2005; Gerard and Marchand 2000; Ichikawa and England 2004; Isgor and Razaqpur 2004; Martin-Perez, Pantazopoulou, and Thomas 2001). However, research at normal temperature are rare. This is so despite the fact that mechanism of heat and moisture transfer in concrete are different at different temperatures. Research information on hygrothermal deformation with time-dependent boundary condition are even more scarce. Further, application of moisture effects as load on nodes while using finite element method has not been attempted before. In the light of the above, computer-programming technique to develop software for numerically calculating the heat and moisture transfer in porous materials like

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concrete and the deformation induced by the combined effect of these transfer mechanisms assume significance. The program provides an interface between user and computer using GUI. The software quantitatively evaluates heat and moisture distribution, stress induced by variation of relative humidity, and hygro-thermal deformation of concrete with different boundary conditions. This paper describes the development of CTMSoft and its evaluation with time-dependent boundary conditions using an under-lake tunnel concrete as an example.

Analytical method for simulating temperature and moisture distribution As material properties are considered to be uniform throughout whole material body, the heat and moisture transfer equations resulting from mass and energy conservation during the transfer process can be expressed as Equations (1) and (2).

…...(1)



……(2)

The methodology of CTMSoft

CTMSoft comprises of calculation processes containing finite element analysis as shown in Figure 1. An analytical procedure based on the mechanism of heat and moisture transfer in porous medium as an original methodology for predicting and estimating the heat and moisture transfer in porous media, was defined as a stand-alone and comprehensive frame for a real simultaneous solution. This was connected to the expressions for heat and moisture transfer inside the materials. Expressions of environmental temperature and moisture also formed part of the solution. In developing CTMSoft, FEM (Finite Element Method) was necessary to calculate the hygrothermal deformation of concrete. Before applying load on nodes of FEM, the moisture distribution should be transformed to moisture induced stress. However, no existing FEM software capable of directly transforming moisture load to deformation could be identified. This necessitated the development of CTMSoft capable of calculating the moisture induced deformation of concrete.

where r is the density of the material, cp is the specific heat of constituent, T is the temperature, l is the thermal conductivity, r is the phase change factor, M is the moisture content, hlv is the heat of phase change, Dmk is the moisture diffusion coefficient considering the effect of Knudsen diffusion, x is location variable, t is time variable and d is the thermal gradient coefficient. Laplace transformation and transfer function were used to simplify the partial differential equations of heat and moisture transfer into a single fourth-order ordinary differential equation (ODE), which could be easily solved by conventional methods. The inverse Laplace transformation yielded the moisture and the temperature distribution in time domain (Chang and Weng 2000; Chen and Qian 2007; Qin and Belarbi 2005) .

FEM for simulating hygro-thermal deformation The deformations induced by temperature changes can be calculated by direct application of temperature loads to the nodes in the FE analysis. In fact, with the current FEM approach it is not possible to directly apply moisture loads to the nodes. It must first be transformed into a moisture-induced stress. Fortunately, KelvinLaplace equation and Mackenzie formula described in Equations (3) and (4) make this possible. (Bentz, Garboczi, and Quenard 1998; Chen and Qian 2007; Grasley and Lange 2007). While on one hand Equation (3) describes the relationship between the negative pore fluid pressure and the internal relative humidity in the pore structure. On the other hand Equation (4) expresses the relationship between the hydrostatic pressure and the associated strain. Further, the relative humidity and its variation in concrete can be calculated based on the



The Indian Concrete Journal .....2009

moisture content, which is derived from the experimental water loss and dry weight of the specimen.

……(3)



……(4)

In Equations (3) & (4), p is the pore fluid pressure, RH is the relative humidity in concrete, vm is the molar volume of water, R is the universal gas constant, T is the Kelvin temperature, ε is the linear strain, Δp is the average of hydrostatic pressure caused by the variation of temperature or moisture, and K and K0 are bulk modulus of porous solid and bulk modulus of solid skeleton of the material respectively. The stress on each node can be imagined as the arithmetic product of strain and elastic modulus. Consequently, the stress induced by moisture changes, namely sh , can be calculated by Equation (5)[9] where Va /Vc is the volume fraction of the aggregate in the concrete, c is the porosity of concrete, G0 is the shear modulus, vm is the molar volume of water, and Ti and Tf denote the initial and final temperatures respectively, other notations have been explained earlier.

……(5)

menu bar, command buttons and figure viewer, etc. The graphical user interface (GUI) makes data entry user friendly. Program running and results display modules are also easy to use. The entry of parameters, boundary condition definition and environmental temperature and moisture settings are all active in GUI. The core task of performing the numerical simulation, which is written in and complied with Matlabor APDL of ANSYS, executes the virtual calculation process when triggered by the click of the mouse in the related menu or command buttons. The displaying and saving of figures of numerical results are performed at the main user interface. Although the program is clear and simple, a number of help features are included to make it more user friendly. This comprehensive help function provides the user with a variety of information, including an introduction to the CTMSoft, details of its methodology, how to get started and many useful techniques to effectively use the program. (2) Main interface of CTMSoft In the numerical simulation, data entry, saving and transferring of basic parameters, the definition and selection of element type, size, initial and boundary conditions, the use of Matlab and ANSYS, and the saving and displaying of numerical simulation results were all involved. At the main interface of CTMSoft, the positions for arranging the command menu, shortcut buttons, the element definition and meshing, the basic

CTMSoft CTMSoft structure Figure 1 shows schematic of the numerical simulation for hygro-thermal deformation of concrete. The software uses both Matlab and ANSYS based on Visual Basic. CTMSoft was developed by mix programming. Figure 2 shows the holistic structure of the CTMSoft with different parts and approaches. The CTMSoft was developed as an advanced Windows application by using the features of Visual Basic (VB) programming to offer the user a graphical interface including the

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conditions definition, the graphic display of numerical results appear as shown in Figure 3.

Deformation analysis on concrete for an under-lake tunnel Boundary conditions A concrete block of 30 m × 1.0 m × 4.5 m (see Figure 4) cut from an under-lake tunnel wall was used for the deformation analyses. The temperature and moisture at one side (Side A) of the concrete block with the changing ambient temperature over one year was used in the study. The other side (Side B) of the concrete represented moisture insulation and temperature condition corresponding to two situations namely adiabatic (tagged as “BC-1”) and non-adiabatic (tagged as “BC-2”). In the numerical simulation, the environmental temperature and moisture in the lake tunnel were measured and used as the boundary conditions of Side A, see Figures 5 and 6. The heat and moisture transfer boundary conditions could be expressed as Equations (6) & (7).



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……(6)



……(7)

It is noteworthy that the measured temperature and moisture levels were interpolated when used in the numerical simulation. This approach leads to a better correlation and more reasonable numerical results than applying high-order curve fitting. At Side B of the wall element, the boundary moisture and thermal insulation can be expressed as Equations (8) and (9).

……(8)



……(9)

The boundary of Side B in terms of moisture insulation and temperature variation, can be expressed as Equation (10) and Equation (11). The temperature change was the same as expressed in Figure 7.

……(10)

……(11) temperature on RH thermo-physical properties and moisture diffusivity respectively were also included.

where ao = heat transfer coefficient. Initially, temperature of 12°C and moisture content of 12% (95%RH) were assumed uniformly distributed over the wall panel. This was in agreement with the actual construction conditions of the concrete wall element selected.

……(12)

The time dependent ambient temperature, moisture levels, as well as their on site variations over one year were considered in the computation. The effect of

Basic parameters Table 1 summarises the mix proportions of the concrete. Parameters, which were considered constant because of the small variation in this study are given in Table 2. The thermal properties of concrete were calculated by weighted mean (applied to data from experiments or from the literature) for the components of the hardened concrete, namely cement paste, fine and coarse aggregates (Chen, Qian, Wang, and Liu 2007), see Figures 8 and 9. The relationship between RH and moisture content (Figure 10) was assessed by the test procedure described in the work of Kim and Lee (Kim and Lee 1998) .

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Table 1. Mix proportion of concrete Water Cement PFA Sand Aggregate (kg/m3) (kg/m3) (kg/m3) (kg/m3) (kg/m3) 140

285

80

740

Superplasticiser c×%

1200

1.0

Table 2. Parameters for simulation Parameters

Symbols

Values

Heat of phase change (kJ/kg)

hlv

2443.6

Thermal gradient coefficient (K )

d

0.001

Phase change factor

r

0.09

Density of concrete (kg/m )

r

2450

Knudsen diffusion influence coefficient

Kf

0.9271

-1

3

Comparison of results The time-dependent deformation of concrete was obtained by finite element analysis using temperaturemoisture distribution calculated by analytical method. The deformation variations at different depths in the two boundary conditions (BC-1 and BC-2) are shown in Figure 11. It is clear from Figure 11 that the more the depth from the surface (A) the smaller the effect of environmental temperature and moisture variation. A comparison of deformations between BC-2 and BC-1, shows that deformation at the near inner surface (Side A), which is subjected to the environmental variation, is higher, than that at the inner surface (Side B). This is attributed the difference in conditions between BC-1 and BC-2. Compared to the assumed constant temperature at soil side (Side B), the time-dependent temperature (BC-2, see Figure 7) reduces the deformation of concrete near soil surface and increases it at air side (Side A). The increase of temperature accelerates the moisture transfer, which in turn shrinks the specimen. This shrinkage induced by moisture reduction exceeds the expansion caused by temperature increase. These effects make the concrete BC-2 show a higher deformation near air (Side A) than near soil (Side B). Figure 12 compares the results from the hygrothermal coupling model with the experimental results (Chen 2007). The numerically predicted results have a similar trend as the field tested results, but most numerical results exceed the measured ones. The hygrothermal deformation induced from different boundary conditions, is almost the same in early ages, but the difference gradually increases with time. The difference between the numerical and the measured results may be



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attributed to the model neglecting the stress of concrete in structure. The numerical results calculate the moisture and the heat distribution in concrete induced by the transfer with time-dependent boundary conditions, while the field results are inevitably affected by the stress in concrete. A more detailed work is therefore needed for improving the comparison.

Conclusion

The numerical simulation method, which comprises of analytical method and FEM, is proposed in the paper. It is based on the theory of heat and moisture transfer in porous medium. Accordingly, CTMSoft developed by mix programming using Matlab and ANSYS is reported. A formula for calculating the stress induced by moisture changes in concrete was incorporated so that moisture effects can be applied directly to the FEM nodes. The efficiency of CTMSoft was validated by a case analysis of hygro-thermal deformation of concrete for a lake tunnel. The numerically predicted results give similar trend as the field test data with the predicted results slightly exceeding the measured ones.

Acknowledgements

Authors are thankful for the financial support from Education Ministry of China under Excellent Scholar Plan (No.NCET-05-0473) and Key Project of National Natural Science Foundation of China (50539040).

References

1. Bažant, Z.P., and Najjar, L.J. Nonlinear water diffusion in nonsaturated concrete, Materials and Structures, 1972, 5(1), pp. 3-20. 2. Chung, J.H., and Consolazio, G.R., Numerical modeling of transport phenomena in reinforced concrete exposed to elevated temperatures, Cement Concrete Research, 2005, 35(3), pp. 597-608.

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3. Gerard, B., and Marchand, J., Influence of cracking on the diffusion properties of cement-based materials: Part I: Influence of continuous cracks on the steady-state regime, Cement Concrete Research, 2000, 30(1), pp. 37-43.

13. Chen, D.P., Qian, C.X., Wang, H., and Liu, J.H., Research on determination and calculation method of specific heat capacity of cement-based materials, Journal of Building Materials, 2007, 10(2), 127-131 (in Chinese).

4. Ichikawa, Y., and England, G.L., Prediction of moisture migration and pore pressure build-up in concrete at high temperatures, Nuclear Engineering and Design, 2004, 228(1-3), pp. 245-259.

14. Kim, J.K. and Lee, C.S., Prediction of differential drying shrinkage in concrete, Cement and Concrete Research, 1998, 28(7), pp. 985-994.

5. Isgor, O.B. and Razaqpur, A.G., Finite element modeling of coupled heat transfer, moisture transport and carbonation processes in concrete structures, Cement Concrete Composites, 2004, 26(1), 57-73.

Dr. Chunxiang Qian, PhD, is a professor and director of the Research Institute of Green Construction Materials, School of Materials Science and Engineering, Southeast University, Nanjing, China.

6. Martin-Perez, B., Pantazopoulou, S.J., and Thomas, M.D.A., Numerical solution of mass transport equations in concrete structures, Computers & Structures, 2001, 79(13), pp. 1251-1264. 7. Chang, W.J. and Weng, C.I. , Analytical solution to coupled heat and moisture diffusion transfer in porous materials, International Journal of Heat and Mass Transfer, 2000, 43(19), pp. 3621-3632. 8. Chen, D.P. and Qian, C.X., Numerical simulation of concrete shrinkage based on heat and moisture transfer in porous medium, Journal of Southeast University, 2007, 23(1), pp. 75-80. 9. Chen, D.P. (2007), Study on Numerical simulation of hygro-thermal deformation of concrete based on heat and moisture transfer in porous medium and its application [D]. Southeast University, Nanjing. 10. Qin, M.H., and Belarbi, R., Development of an analytical method for simultaneous heat and moisture transfer in building materials utilizing transfer function method, Journal of Materials in Civil Engineering, 2005, 17(5), pp. 492-497. 11. Bentz, D.P., Garboczi, E.J., and Quenard, D. A. , Modelling drying shrinkage in reconstructed porous materials: Application to porous Vycor glass, Modelling and Simulation in Materials Science and Engineering, 1998, 6(3), pp. 211-236. 12. Grasley, Z., and Lange, D., Thermal dilation and internal relative humidity of hardened cement paste, Materials and Structures, 2007, 40(3), 311-317.



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Dr. Depeng Chen, PhD, is an associate professor in the School of Architectural and Civil Engineering, Anhui University of Technology, Maanshan City, Anhui Province, China

Yujun Liu is doing his masters at the School of Materials Science and Engineering, Southeast University, Nanjing, China.