Volume Coupled Multi-Field Physics

Coupled chemical and mechanical processes in concrete structures with respect to aging

Accurate prognosis of the durability of concrete structures requires a detailed description of the continuously running aging processes and a consideration of the complete loading history. Therefore, in the framework of continuous porous media mechanics a model is developed, which allows a detailed analysis of the most important aging processes of concrete as well as a flexible coupling of the different processes via a monolithic algorithm. 

This requires a formal treatment and a general description of the different processes, including principal variables like deformation, relative humidity, temperature, concentration of substances dissolved in water or gas phase and the degree of hydration as well as principal processes which desribe the development of principal variables in space and time and required material models for transport, reaction and deformation behaviour.

The description of the degradation of the structure due to extreme environmental conditions requires the consideration of water and heat transport as well as the transport of substances like chloride or carbonate. Besides, chemical reactions arise in the cement paste. Here, the hydration process, dehydration under high temperatures, chloride binding and carbonation are considered.

Example: Column on Slab - exposure to salt solution

cramer fig7a

The figure shows the distribution of the degree of hydration after 100 days. Inside the structure m achieves nearly the final value. In contrast this the drying effect of the ambiance stopped the hydration process in areas near to the surface. Between the slab and the column, the degree of hydration is smaller because of the successively concreting of slab and column.

The distribution of mechanical damage D is depicted after 100 days. The damage results from the boundary conditions of the formwork for the concreting of the column and from differences in material properties due to the different age of the slab and the column. The distribution of water saturation indicates a lower saturation in the joint between the slab and the column although the corresponding relative humidity shows a uniform course. This is reasoned by the lower degree of hydration in this area which affects the saturation function.


Distribution of free chloride concentration is shown after 5 years and evolution of concentration is given over time at different depths. When the content of free chloride exceeds a critical value at the reinforcement, chloride-induced corrosion may occur, which leads to a decreasing resistance of the reinforcement and to damage of the surrounding concrete due to volume growth of the reaction products. 

Applications of the model to durability analysis of concrete structures under chloride and carbonate attack indicate, that the consideration of the loading history and therefore changes in material structure and material-dependent model parameters as well as principle variables influences strongly the depth of chloride penetration. Excluding these aging effects leads to an overestimation of material capabilities. 

The material model describes the stress-strain behaviour of concrete at external loadings as well as at exposures to internal volume-demanding attacks, e.g. at high temperatures and pore pressures due to fire or because of sulphate attack.

Numerical Simulation of Concrete at high temperature

The prognosis of the load bearing capacity and the knowledge of the fire resistance period of the complete construction are essential aspects at the evaluation of safety in case of fire.

Tunnels have a particular high potential of dangers due to their closed constructions where the temperature in the area on fire may rise up to 1500 K. Fumes and flue gas reach quickly life-threatening concentrations in the tunnel area. The computational model developed here basis on the balance equations for mass of water, steam and dry air as well as on balance equation for energy and on principle of linear momentum. The summarized balance equation for mass of pore water and steam employs the release of steam due to dehydration process. The balance equation for energy takes into account heat fluxes because of diffusion and convection as well as the enthalpy of reactions due to dehydration.

Example: Column subjected to high temperature defined ISO fire-curve


The vapour pressure reaches its maximum values at the edge. The evolution of the temperature leads to high stresses within the structure which are even increased due to high pore pressure resulting from released vapour. The large stresses lead to mechanical damage. Chemical damage from dehydration of cement minerals contributes to the increase of the total damage close to the heated boundary.

Deformation behaviour due to elevated pore pressure related to sulphate attack

In case of sulphate attack chemical reactions cause regeneration of phases, what results in higher pore pressures due to volume-demanding processes.

Example: Pillar exposed to sulphate attack

The volume strain is presented in dependence on content of ettringite.

Related to the increasing part of volume of ettringite we observe rising pore pressure, which reaches its maximum value shortly after the appearance of first deformations. The following distribution of damage is depicted in the right hand side figure. The orientation of the arising anisotropy corresponds to the direction of fracture.

Municipal Solid Waste Landfills

For landfill monitoring and aftercare, long-term prognoses of emission and deformation behaviour are required. Landfills may be considered as heterogeneous structures, in which flow and transport processes of gases and liquids interact with local material degradation and mechanical deformation.

Gekoppelte Prozesse beim Siedlungsabfall

Coupled THMC processes are described by means of a complex continuum mechanical approach. Prognosis of long-term behaviour of landfill structures can be investigated seriously only by considering the coupling of the most important processes on the landfill-site as well as the different scales in space and time to be observed. Balance equations of momentum, mass and energy consider stress deformation behaviour, transport phenomena and biochemical reactions.

The concept of effective stresses is included in the mechanical equilibrium and thus a separate description of different settlement phenomena is enabled. The compaction model combines stress-dependency of compaction rate with density-dependence. The creep rate is coupled to degradation by the solid dry bulk density.

In porous media, the degradation of organic matter leads to time-dependent deformations and to changes in pore structure. Heat generation from exothermic reactions is considered, whereas the temperature has the determining influence on the degradation kinetics. The emerging landfill gas emanates via the pore space.

Example: Degradation induced settlements

Long term analysis of a landfill structure is performed to investigate the influence of varying temperatures on settlements and degradation, regarding two variants with different heat conductivities of the solid phase resulting in different developments in time of the temperature.

Vertical Cauchy stresses of the basic matrix at different times are depicted at the deformed landfill structure.

Example: Analysis of gas extraction system

To investigate the influence of deformation on gas flow two variants with different permeabilities are compared. After 2.2 years the extraction system is activated. The simulations are performed under isothermal conditions, implying a higher decrease in permeability in variant 2 due to compaction. At  0.5 h after activation of gas collection, the effect of gas extraction is already visible from the negative pressure close to the extraction pipe. After 33 h a larger area of the landfill cross section is under negative pressure.

Efflux of gas is depicted over time regarding both variants of permeabilities. From the obtained gas production curve it is obvious that gas production is strongly related to degradation.

Example: Development of acetate in the landfill-site


The figures show the development in time of the content of acetate. Degradable organic matter is concentrated in the middle of the landfill structure. During degradation acetate is generated as an intermediate, see left hand side figure. Due to feeding by water from the upper boundary acetate is transported to the bottom line, see following figures. After feeding has been finished, concentration of acetate increases again, see right hand side figure.

Current Research Projects

  • T. Stein: Numerische Analyse von Stahlbetonbauteilen im Brandfall
  • K. Al-Kadry: Linear and nonlinear numerical investigation of reinforced concrete structures under dynamic loading and emphasis to earthquake loading

Completed Research Projects

  • F. Cramer: Mehrfeld-Modell für chemisch-physikalische Alterungsprozesse von Beton, Dissertation, TU Braunschweig, 2016
  • L. Ostermann: Hochtemperaturverhalten von Beton – Gekoppelte Mehrfeld-Modellierung und numerische Analyse, Dissertation, TU Braunschweig, 2011
  • S. Bente: Interaction of Degradation, Deformation and Transport Processes in Municipal Solid Waste Landfills, Dissertation, TU Braunschweig, 2010
  • V. Krase :  Stability of municipal solid waste landfills , Dissertation, TU Braunschweig, 2007
  • J. Kindlein: Gekoppelte Analyse von Reaktions- und Transpor tprozessen in Deponiestrukturen, Dissertation, TU Braunschweig, 2011
  • J. Hanel: Modell zur Analyse von gekoppelten Transport- und Stoffabbauprozessen in Deponien, Dissertation, TU Braunschweig, 2001
  • A. Steffens: Modellierung von Karbonatisierung und Chloridbindung zur numerischen Analyse der Korrosionsgefährdung der Betonbewehrung, Dissertation, TU Braunschweig, 2000
  • C.-X. Huang: Berechnung von Temperaturspannungen und Rißbildungen infolge Hydratation in 3D-Betonkonstruktionen, Dissertation, TU Braunschweig, 1999