One of the many threats to human life in fire is a premature collapse of the building structure. In recent years considerable attention has been paid to the problem of the design of residential and industrial buildings where one of the main requirements is that the construction is able to sustain the applied load in a fire situation for the period of time defined by the building standards.
The principal sheeting component of wall and ceiling assemblies of the building constructions is gypsum plasterboard. The main utilisation of the plasterboard lies in its ability to act as a barrier to fire. The plasterboard can withstand excessive heating without burning and provides the necessary fire resistance to the whole structure. It does not present any hazard in starting or propagating a fire even though it has combustible surfaces. The main characteristic of the plasterboard is its chemical composition. The primary component of the plasterboard is gypsum plaster which contains 21% of chemically combined water by weight. When the temperature reaches $100^oC$ the gypsum material undergoes dehydration which is a process of dissociation of chemically combined water from the crystal lattice followed by vaporisation of water. A certain amount of energy must be absorbed so that the dehydration can take place (Mehaffy et al.\/ , 1994). The absorption of energy slows down the process of heat transfer through the plasterboard drastically and prevents other members of the assembly from overheating. It was found by Luikov (1966) that in porous bodies containing free or absorbed water the heat transfer is accompanied by moisture transfer due to high pressure gradients. Since the plasterboard contains a significant amount of voids it is supposed that the migration of steam will increase the temperature of the part which is not exposed to fire.
Gypsum plaster is a brittle material that does not exhibit good response to loading and shrinks in fire to a marked degree. Fire-rated plasterboards are produced with an addition of vermiculite and chopped glass fibres to gypsum plaster. Vermiculite prevents the plasterboard from shrinkage as it expands at high temperatures, and the glass fibres enable the plasterboard to sustain the load and retain some structural integrity after the dehydration (Hannant, 1978).
Before the computer era and even until recently the only way to draw conclusions about the fire resistance of plasterboard assemblies has been through a series of full-scale tests. However, this method can not be considered as an effective one, because of its high cost and time outlay. An alternative approach is the development of mathematical models and computer programs that will be able to predict fire performance of the plasterboard. It can be evinced that only a few works are known where an attempt was made to describe mathematically some aspects of the processes which cause the structural collapse of plasterboard. Fuller {\sl et al.} (1992) examined the thermo-mechanical performance of the gypsum-wood stud nailed joints and Mehaffy et al. (1994) developed a numerical model of the heat transfer process through the plasterboard. The development of a comprehensive mathematical model that will be able to assess correctly the behaviour of the plasterboard assemblies in fire is now being conducted at the Centre for Environmental Safety and Risk Engineering and at the Department of Civil and Building Engineering of the Victoria University of Technology.
Since the structural failure of the plasterboard assembly in fire is a result of several physical and chemical processes, the only way to tackle this problem is to apply various numerical techniques. The finite element method has been chosen because it demonstrates a very good performance on the problems of heat transfer and solid state mechanics. First of all, a thorough analysis of the temperature distribution in the plasterboard must be carried out, because the changes in material properties of the gypsum plaster are strongly temperature dependent (Harmathy, 1983). The investigation is complicated by the necessity to include into the model the process of dehydration. Moisture transfer through the plasterboard must also be taken into account. The processes of heat and mass transfer together with the evaporation of moisture are governed by a set of partial differential equations that are solved using a sophisticated numerical implementation of the finite element method. After obtaining the temperature fields inside the plasterboard, changes in the material properties and temperature deformations can be calculated and used as initial data for the study of the structural behaviour of the entire plasterboard assembly. In the structural model the stress, displacement and strain fields are calculated from the complete system of differential equations for the general solid state mechanics theory. Again, since the simulation algorithm and software must involve simultaneous modelling of various thermomechanical processes, the development of a fully original software complex is required. As soon as stress fields have been obtained, the failure criteria can be applied, which makes it possible to ``trace'' the behaviour of the plasterboard over the whole process.
The development of the first two original versions of the mathematical model and software program for the one-dimensional analysis of heat and moisture transfer through the plasterboard has been completed recently. Numerical results obtained during the simulation can be briefly outlined as follows. The process of dehydration of the plasterboard is modelled as the movement of a thin layer of material (called the dehydration front) across the plasterboard in the direction orthogonal to its surfaces. The evaporation of water takes place only within the dehydration front. Behind the dehydration front all water has been evaporated while the non-dehydrated part of the plasterboard is assumed to be chemically and structurally intact. In the numerical experiments the left surface of the examined plasterboard was exposed to the heat source in which temperature followed the standard fire curve for small scale tests (Drysdale, 1990). The software program solves the heat transfer equation and, as a result, a user obtains a series of diagrams of ``temperature versus time'' at the surface exposed to fire, at the unexposed surface, and at an arbitrary surface within the plasterboard which can be chosen at the user's discretion. All geometrical and material parameters of the examined plasterboard were taken from experimental data (Cuerrier, 1993).
The numerical results calculated using a version of the mathematical model which did not take into consideration the process of steam migration through the plasterboard still exhibited good coincidence with the experimental data. However, at the unexposed surface the slope of the curve $T(t)$ between $50^oC$ and $100^oC$ was smaller than was detected during the experiment. The mathematical model was redeveloped, and a simple original procedure that could take into account the influence of moisture transfer on the temperature distribution was introduced into the program. Both the curves $T(t)$ at the unexposed surface are presented in figures 1 and 2 where temperature and time are given in $C^o$ and minutes respectively.
\caption{ Figure 1: Temperature $T(t) (x = L)$. No moisture transfer. }
It can be seen that the temperature of $100^oC$ is achieved more quickly in the case of moisture transfer. This happens because of the difference in temperature of steam and the surrounding non-dehydrated gypsum plaster which induces condensation of water vapour. The energy released in the condensation process raises the gypsum plaster temperature. Figure 2 was found to have much better coincidence with the experimental results than the curve presented by Cuerrier (1993).
\caption{ Figure 2: Temperature $T(t) (x = L)$. With moisture transfer. }
Computer simulation of such complex phenomena as the behaviour of materials and structures in fires, applied to real industrial projects, will be of great significance to the entire civil and building engineering community. An accurate numerical prediction of such complex processes can help to save not only time and money but also can help to save human lives, the most valuable resource on our planet.