Compensation grouting involves making grout injections at close neighboring locations so as to replace ground loss, due to tunnelling for example. Since the objective of the technology is to match volume changes so as to eliminate subsidence, the tendency of ground to dilate or compress around the injection becomes a very significant consideration. Furthermore, the effects of different sequences of grout injection, and the zoning of injection relative to the tunnel centreline, are of interest when devising grouting schemes. This paper investigates these issues using centrifuge and numerical modelling in dense and loose dry sand. It is found that the profile of surface heave and the tunnel lining deformation is dependent on the relative injection position, as well as injection history. Ground stiffening due to the compaction arising from previous injection permits larger pressures to be developed from a given injection volume. These larger pressures eventually cause upward heaving and lining deformation. In conclusion, the most favourable and unfavourable injection sequence are identified in relationship to the induced centre surface heave and tunnel lining deformation.