This dissertation describes the development of a multiscale mathematical model to predict the effective thermal conductivity (ETC) of fiber-reinforced lightweight cement composites. At various stages in the development of the model, the results are compared to experimental values and the model is calibrated when appropriate. Additionally at each stage the proposed model and its results are compared to physical upper and lower bounds placed on the ETC for the different types of structural models. Fiber-reinforced lightweight cement mortar is a composite material that contains various components at different scales. The model development begins with a study of neat cement paste and is then extended to include normal weight fine aggregate, lightweight aggregate, and reinforcing fibers. This is accomplished by first considering cement mortar, then models for lightweight cement mortar and fiber-reinforced cement mortar are considered separately, and finally these two are joined together to study fiber-reinforced lightweight cement mortar. Two different experimental techniques are used to determine the ETC of the different materials. The flash method is used to determine the ETC of the neat cement paste and cement mortar samples, and a recently developed transient technique is used for the remainder of the samples. The model for the ETC of cement paste is derived from a lumped parameter model considering the water-cement ratio and saturation of the paste. The results are calibrated using experimental data generated during this project and are in good agreement with values found in the literature. The models for the ETC of cement mortar, fiber-reinforced cement mortar, lightweight cement mortar, and fiber-reinforced lightweight cement mortar are all based on a differential multiphase model (DM model). This is capable of predicting the ETC of a composite material with various ellipsoidal inclusion phases. It is shown how the DM model can be modified to include information about the maximum volume fraction of the inclusions. A linear packing model is introduced which allows the gradation of the different inclusion phases to be considered. Additionally other factors that affect the ETC are discussed, including the presence of an interfacial transition zone around the inclusions and the relative size of the different constituent phases. The model developed in this report is not only able to predict the effective thermal conductivity for a material, but it can also be used to minimize the effective thermal conductivity by optimizing the structure of the composite. This is done through proper selection of the types and amounts of the various constituents, along with their size, shape, and gradation.
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