Rapid filling of low-permeability cemented paste backfill into underground stopes results in the generation of significant excess pore pressures that are modified by the volume shrinkage accompanying the process of cement hydration. Gibson produced results of an analysis of the excess pore pressures in a simultaneously accreting and consolidating sediment. The dimensionless governing equation lends itself to finite-difference solution: results are presented for a typical rate of volumetric shrinkage and compared with Gibson's original isochrones of excess pore pressure to account for simultaneous conventional consolidation and chemical-induced volume changes in accreting sediment. The effect of time-dependent volume shrinkage can be directly added to Gibson's results for linear problems. The solution technique can be adapted to increase realism by allowing the stiffness of the backfill to increase or permeability to fall as a consequence of the shrinkage. Making a few idealisations, an apparently complex problem can be analysed with rather simple computational resources. Benchmark results can be provided against which more complex methods of analysis (such as finite-element analysis) can be validated.