Numerisk simulering af temperatur- og spændingstilstanden i hærdnende betonkonstruktioner

Abstract

I dette projekt er der udviklet en metode til numerisk bestemmelse af massive betonkonstruktioners temperatur- og spændingstilstand under hærdning, baseret på det kommercielle elementmetodeprogram Abaqus. Simuleringerne er valideret ved forskellige eksperimentelle metoder. I den første del af projektet er der er arbejdet med endimensional varmetransport i et geometrisk simpelt hærdnende betonemne, idet der er anvendt eksperimentelle, analytiske og numeriske metoder. Der er gennemført et forsøg, hvor det blev forsøgt at sikre en endimensional varmetransport vha. isolering og formplader. Til dette blev der anvendt en beton med en høj varmeudvikling, så temperaturforskellen mellem middel- og randtemperaturen blev størst muligt efter afformningen. Desuden er der udført en adiabatisk kalorimetermåling, hvor betonens varmeudvikling er bestemt som funktion af modenheden. Idet forsøget er udført med endimensional varmetransport, er det muligt at anvende en analytisk løsning til varmeledningsligningen samt programmet TempSim, der er udviklet af Aalborg Portland, til at bestemme temperaturforløbet i betonen. Den endimensionale varmetransport er ligeledes bestemt numerisk i Abaqus, hvor der i første omgang er anvendt en todimensional model. Idet varmetransporten i forsøget viste sig ikke at være fuldstændig endimensional, var det nødvendigt at anvende en 3D model for at få sammenlignelige resultater mellem forsøget og de numeriske beregninger. I simuleringerne er nødvendigheden af at modellere formsystemet og varmeudstråling ligeledes undersøgt. I den anden del af projektet er der udført forsøg med en betonterning med dimensionerne 0,4 x 0,4 x 0,4 m, hvor varmetransporten er tredimensional. Forsøget er ligeledes simuleret i Abaqus med en 3D model, hvor resultatet giver god overensstemmelse med forsøgsresultatet. Temperaturforskellen mellem forsøget og simuleringen antyder dog, at betonens ændring af varmefylden under hærdning har en betydning for resultatet, hvorfor det er forsøgt at anvende en aftagende varmefylde i simuleringen. Generelt kan det konkluderes, at det er muligt at simulere temperaturtilstanden i en massiv betonkonstruktion under hærdning. I den tredje del af projektet er der gennemført eksperimentelle og numeriske analyser af tøjnings- og spændingstilstanden i betonterningen. Indledningsvis blev der udført et forsøg med den hærdnede betonterning, som blev opvarmet til en høj, ensartet fordelt temperatur, hvorefter tøjningerne blev målt under afkøling af betonen. Der blev anvendt et optisk målesystem, kaldet Aramis, der kan måle materialets overfladedeformationer og -tøjninger. Det er fundet, at målesystemet er i stand til at detektere et revnemønster på betonens overflade, men ikke revnevidden. I Abaqus er der udarbejdet en model svarende til forsøget, hvor tøjnings- og spændingstilstanden i betonterningen bestemmes. Til dette anvendes materialemodellerne Concrete damaged plasticity og modificeret Mohr-Coulomb. I Abaqus er det ikke muligt at simulere revner, i stedet angiver Abaqus en tøjningslokalisering som kan indikere en revnedannelse. Videre er det undersøgt, hvilken betydning det har for tøjnings- og spændingsresultatet, hvis der i stedet for anvendes en betonterning med dimensionerne 0,8 x 0,8 x 0,8 m eller 1,6 x 1,6 x 1,6 m. Til sidst er der udført en simulering af temperatur- og spændingstilstanden i et massivt hærdnende betonelement, der anvendes i en bølgebryder ved et aktuelt havneprojekt. I simuleringen er ændringen af betonens mekaniske materialeparametre som funktion af modenheden medtaget. Spændings- og tøjningsresultatet viser, at der med den aktuelle udførelsesmetode er mulighed for revnedannelse i betonen. En alternativ udførelsesmetode, hvor termorevnerne kan reduceres eller helt undgås, kan derfor med fordel evalueres i de udviklede numeriske metoder i Abaqus.

The present thesis deals with numerical simulations of temperature and stress development in massive concrete structures during hardening. The numerical computations were executed by means of the commercially available finite element software Abaqus. The results obtained have been validated through various experimental work. The first part of the thesis contains a one-dimensional heat transfer analysis for a plain concrete member by means of experimental, analytical, and numerical methods. An experiment was carried out where the one-dimensional heat transfer was implemented through the formwork and heat insulation arrangement. The employed concrete had a high heat of hydration generation, causing a high temperature level and a large temperature difference between the mean and surface temperatures. The heat development in the concrete was measured by adiabatic calorimetry, by converting the measured adiabatic temperature into heat generation as a function of the maturity. Due to the one-dimensional heat transfer, the temperature development can be computed by analytical methods. In the thesis the temperature development was computed by solving Fourier's general one-dimensional heat equation as a boundary-value problem manually as well as by using the finite-difference program TempSim developed by the company Aalborg Portland. The one-dimensional heat transfer can also be computed numerically by means of a two-dimensional model in Abaqus. However, in the laboratory it is difficult to ensure a completely one-dimensional heat transfer. Therefore, it was necessary to apply a three-dimensional model in Abaqus in order to obtain identical results from the experiment and the numerical simulation. In the simulations the necessity of modelling the formwork in Abaqus was investigated as well as the influence of thermal radiation. In all simulations of the heat transfer the thermal properties of the concrete were assumed constant, except the heat generation as determined by adiabatic calorimetry. The second part of the thesis presents the results of a three-dimensional heat transfer study on a concrete cube with the dimensions 0.4 x 0.4 x 0.4 m. The three-dimensional heat transfer was analysed by means of experimental work and by three-dimensional analysis using Abaqus. In the numerical simulations it was attempted to take a varying specific heat capacity into account. In the end of part two it is concluded that it is possible to simulate the temperature development and heat transfer in a massive concrete structure during curing. The third part of the thesis is concerned with experimental and numerical analyses of the stress state in the concrete cube. In the experiment the cured cube was heated to an initially high temperature. When the concrete cube subsequently was cooled the strains of the cube were measured using an optical device called Aramis. The optical device was also capable of detecting a crack pattern on the cube surface, although it did not provide exact crack widths. The development of stresses and strains during cooling of the cube have been simulated by means of Abaqus. The material models Concrete Damaged Plasticity and Modified Mohr-Coulomb have been employed. The strains computed by Abaqus were compared with the test results. In Abaqus it is not possible to simulate the cracks which were actually seen in the experiment. Instead, Abaqus results show a strain localisation that may indicate a crack. In addition, the effect of using a cube with the dimensions 0.8 x 0.8 x 0.8 m and 1.6 x 1.6 x 1.6 m was analysed. Finally, the temperature and stress development was simulated in a large massive concrete cube during hardening. Such concrete cubes are used in a breakwater structure at an ongoing harbour project. In the simulations the variation of the concrete mechanical properties with maturity are taken into account. The simulations showed that the formwork and curing procedures used did not prevent thermally induced cracking in the concrete. However, the Abaqus facilities developed in the present thesis could be used for evaluating possibilities to avoid or reduce the extent of thermally induced cracking by choosing different execution procedures.

A master thesis from Aalborg University

Numerisk simulering af temperatur- og spændingstilstanden i hærdnende betonkonstruktioner

[Numerical simulation of temperature and stress development during concrete curing]