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About this WWW Demo

The simulation engine behind this demo is of course DuCOM, which is executed from a wrapper that is actually a simple CGI (common gateway interface) script. The options for the web demo have been kept at bare minimum, owing to the short response time required for the web. On its own DuCOM can handle any shape and size of concrete structures for any history of boundary conditions applied over the life cycle of a typical structure. Current web technology and inherent difficulties in providing a proper user interface restrict us to implement the full fledged version of DuCOM on the web. However, executable binaries of DuCOM for HP-UX are available for download to those who have the proper computational muscle at their disposal.

The future versions of DuCOM would include the coupling with several other deterioration and transport phenomenon's like chloride and oxygen diffusion, corrosion of reinforcement; carbonation etc. Furthermore, efforts are underway to integrate the material durability simulation tools like DuCOM with their structural analysis counterpart like COM3 so that a homogenous system of concrete service life span simulation could be achieved. In the authors viewpoint such an integrated approach is more rational and certainly feasible provided concerted efforts are undertaken in this direction.

A brief technical discussion about the overall scheme is given below.

 
 

 
 

General

As noted in the introduction, DuCOM is a computer program that uses FE (Finite Elements) to solve the heat and mass transport problems of a porous media. It is the result of ongoing research being carried out at the Concrete Laboratory of the University of Tokyo. The generic differential equation that could be solved by DuCOM can be stated as :

(1)

where, is an independent variable. DuCOM is capable of solving above differential equation for any number of independent variables simultaneously (1 to N). This has been achieved by implementing an alternate solving scheme where, latest iterate level values of an independent variable are obtained by using previous iterate level values of other variables in the same time step.

 

The Coupled Computational Scheme

The microstructure development, hydration and moisture transport in the concrete is quite complex and inter-related. These can be however, formulated as a set of simplified analytical models. One of the practical ways to make a good use of such an analytical system is to combine them into a unified computational framework. This would enable us to study the overall early age development phenomenon under generic conditions from a material scientist point of view. Also, from an engineer's view point - the computational approach would enable us to apply these models to real life structures and study the effects of mix-proportions, curing conditions and environments etc., on the overall structural durability. This process would probably help the concrete community in making more informed guesses for the performance based durability design methods.

For the computational integration, finite-element based methods are adopted because of the versatility in their scope of applications. The entire theoretical formulation framework of micro structure formation, moisture transport and hydration phenomenon's is integrated into a finite element based computational program; code named DuCOM (Durability Model of COncrete). The method is applied both in time and space domains to obtain the solutions of primary variables, pore water pressure P and temperature T. As a part of the framework, solutions are also obtained for the development of pore structure in terms of microstructure distribution and porosity of various phases, the average pore water content, hydration degree of individual mineral components and the strength of the paste. Input required in this scheme of solution is - initial mix proportions, powder material characteristics (density, and mineral compositions), initial temperature, the geometry of target structure and the boundary condition to which the structure will be exposed during its life cycle. To know more about the basics of material modeling and the integrated computational scheme, please refer to this online paper.

 

Outline of Material Modeling in DuCOM

For heat and moisture transport modeling in concrete, eqn. (1) can be degenerated to a simpler form as given in eqn (2). The conservation equations for temperature and pressure in concrete can be simply stated as

(2)

where, the material parameters and various other terms are obtained considering the constitutive laws of powder material hydration, microstructure formation and path dependent moisture transport based on microstructure. The material modeling summary table given below gives a summary of the physical phenomenon's that have been considered in obtaining relevant material parameters. It might serve as a good starting point to explore the details of the constitutive material models of moisture and heat transport in concrete. It is important to stress the immense significance of various experimental data that have been greatly useful in benchmarking and validation of the models that describe the material behavior. Furthermore, the experimental results would always serve to enhance and refine the basic aspects of these material modeling in the future also.


 

Nuts and Bolts of FE Implementation

Standard Galerkin procedure is used to obtain the space discretizations of the system of partial differential equation given by eqn. (2). Since, the temperature and pressure fields are inherently coupled in this system, we have adopted an alternate staggered scheme of solution. In this scheme, temperature and pressure fields are obtained alternatively in a given step of time, until complete convergence is achieved. This alternate scheme of solution has been recommended for coupled systems, since it leads to many interesting possibilities of applications, for example:

  1. Completely different methods could be used in each part of the coupled system.
  2. Independent codes dealing efficiently with single systems could be combined
  3. Parallel computation with its inherent advantage could be used
  4. Efficient iterative solvers could be developed in the systems of same physics.

Perhaps, the computational time might increase by small amounts in such cases, but a stable convergence is guaranteed as compared to the direct simultaneous solution schemes. Due to the alternate solution schemes, the finite element discretizations can be illustrated for the variable X and can be identically applied to T and P. By applying a one step time discretization to eqn (2) following system of equations can be obtained

(3)

with the usual meaning of symbols. The C, K and f matrices are obtained as

(4)

The algebraic system of equations in (3) are solved using skyline substitution method. Convergence of the system is based on the limitation of relative error of P and T. Moreover, for stability of the solutions and spurious oscillation's removal, especially under rapid change situations and start of the solution procedure, a complete diagonalization of C based on mass lumping parameters has been adopted. Also, for the guaranteed stability, is usually taken as 2/3 for time discretizations. The material models are implemented as library's that are external to the main solver and can be maintained and developed independently. These material subroutines are basically accessed only during the formation of core stiffness matrix. Also, most of the material models have been currently implemented as is, without much simplifications. This ensures a high degree of accuracy in the results, however there is a price to be paid in terms of the computational efficiency. In the computations, boundary conditions are specified either as a known value of the primary variable or in the terms of a convective condition; where the ambient value of the variable and convective transfer coefficients as hX should be specified.

For example, in the case of moisture transport boundary conditions could be specified as a given pore pressure head directly or in the terms of the ambient relative humidity at any given time, i.e.

(4)

where, qs represents the flux of moisture into the porous media at the surface. Ps is the specified pore pressure head, hs is the environmental humidity corresponding to a pore pressure of Ps. A value of 10-5 m/s for surface moisture emmissivity coefficient, convective moisture transfer conditions at the surface.


The In's and Out

In the computational framework described above, the only basic input required are mix-proportions, the properties or type of cement and powder materials, the geometry of the structure, the initial casting temperature and the boundary conditions specified in terms of history of exposure of the structure to the environment. All other parameters are intrinsically computed based upon micromodels of material behavior. For example, the critical parameters required to evaluate various transport coefficients in the moisture transport formulations are the pore distribution parameters and the total porosity of interlayer, gel and capillary components. During the course of simulations, these parameters are actually obtained as an output of the hydration degree dependent microstructure development model. For a fully mature concrete however, these can also be estimated approximately from the experimental measurements of porosity and pore distributions as obtained by MIP (Mercury Intrusion Porosimetry) methods. In this integrated simulation scheme, the interdependency of seemingly different physical phenomenon's can be rationally taken into account.