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 interrelated. 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 mixproportions, 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, finiteelement 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:
 Completely different methods could be used in each part of the coupled
system.
 Independent codes dealing efficiently with single systems could be
combined
 Parallel computation with its inherent advantage could be used
 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
h_{X} 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, q_{s} represents the flux of moisture into the porous media at
the surface. P_{s} is the specified pore pressure head, h_{s}
is the environmental humidity corresponding to a pore pressure of P_{s}. 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
mixproportions, 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.
