The traditional numerical manifold method (NMM) is restricted to the cases of no structure damage when dealing with the discontinuous deformation problems. To overcome the limitation

a high-order NMM for modelling structure damage is further developed by adding the enriched displacement functions for modeling the stress singularity to the physical patches around the crack tips. Then it is applied to the simulation of the fracture process of the gravity dam from continuum to discontinuum. Firstly

sensitivity analysis of the gravity dam with a single crack is conducted; it is found that the crack growth paths are nearly the same as the results in the references

under the conditions of different crack growth lengths or mesh densities. Based on this

the analysis of the multiple cracks growth is conducted; the results indicate that only one dominant crack propagates

which again is quite the same as the result in the references. At last

it is used for the crack growth analysis of Koyna gravity dam

in which the changes of crack growth paths are studied by setting different overflow heights. The results show that the crack growth paths tend to propagate in the horizontal direction and the ability of the resistance to failure of the dam is gradually diminishing. In general

NMM has the good numerical stability and robustness in treating the real engineering problems.