A simple analytical model is developed to describe the mechanics of cemented granular material. The two-dimensional problem of the deformation of an arbitrarily shaped cement layer has been reduced to an ordinary differential equation of the second order. A simple analytical solution is obtained to model the normal and shear deformation of a cement layer with straight boundaries. The problem of the normal compression of two contacting circular elastic grains and an elastic cement layer between them has been reduced to a linear integral equation. This problem has been solved both for two-dimensional (cylindrical grains) and three-dimensional (spherical grains) cases. The elastic modulus of such a combination is strongly increased by cementation compared to the case of a classic Hertzian contact.
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Dvorkin et al. (1991) studied this question.