Coupled chemical shrinkage and consolidation: some benchmark solutions

Mixtures of cement and mine waste are used as backfill in underground mines to provide support, which enables increased mineral extraction. Unlike most cemented material, the properties of mine backfill are relied upon immediately after cement is added and the material deposited underground. It is not only just the properties of the final cemented product but also the behaviour of cemented backfill during the hydration process that is important. During the hydration process, the backfill experiences chemically induced volume changes. These volume changes can lead to the development of effective stresses, which control the loads generated on barricade walls and the subsequent stability of unsupported faces. Although the processes that interact during cement hydration appear complex, the governing equation can be derived in terms of a small number of dimensionless parameter groups. The equation is simply the diffusion equation with a time-dependent source/sink term for which an analytical solution can be obtained under certain simplifying geometries. Approximate solutions can be obtained using a technique of analysis in which the mode shape of the spatial pore pressure variation is assumed. Such solutions provide benchmarks for simplified problems against which results of finite element modelling (for example) can be compared in order to confirm that the controlling mechanisms have been correctly identified.