A Numerical Modeling Method For Predicting The Elastic Modulus Of Cement Paste

Computer techniques have been widely applied to the simulation ofthe microstructures of cement-based materials. The studies of themicrostructural development of cement paste and its main influentialfactors by computer simulation to increase the overall properties ofcement-based materials have become an important research topic. Themacroscopic physico-mechanical properties of cement paste are dependenton the microstructures, such as pore structures, interfacial transition zone,and constituents and therefore are important parameter for the optimizationdesign of cement-based materials.A simulation algorithm is developed for the two-dimensionalsimulation of cement hydration. By introducing periodic boundaryconditions, the initial distribution of cement particles within a squareelement is implemented. In the cement hydration model, the reaction rate ateach point on the cement surface is assumed to be the same and eachcement particle is represented by three concentric circles. As cement hydration progresses, the mutual interference effect between neighboringcement particles is quantified by introducing three parameters and theincremental relationship between various constituents is established. Bycomparing with the experimental results obtained from the literature, thevalidity of the proposed numerical method is verified. The effects of themaximum cement diameter, water/cement ratio and temperature on thedegree of hydration are analyzed. As preliminary applications, thevariations of the area fractions of capillary pores, unhydrated cement, andhydrated products, the two-point probability function of capillary pores,and the capillary perimeter per unit area with time are evaluated in aquantitative manner.Based on the simulated microstructure of cement paste, a numericalmethod for predicting the elastic modulus of cement paste is proposedapplying the lattice model. By applying the transfer matrix method, ananalytical expression for the element stiff matrix of a heterogeneous beamis derived. By comparing with the experimental results collected from theliterature, the validity of the numerical method is verified. Based on thenumerical results, the effects of the degree of hydration, temperature,water/cement ratio, and maximum cement diameter on the elastic modulusof cement paste are analyzed.