A continuum-discontinuum method is proposed to model a series of complex mechanical behaviors of quasi-brittle materials（rocks

concretes

etc.）

such as deformation

cracking

contact

friction and rotation.The method benefits from the Lagrange element method

the discrete element method and the fictitious crack model.Compared with the continuum method

the proposed method can model true cracking phenomena without remeshing.Compared with the discontinuum method

the proposed method can well treat the continuum medium before cracking.A numerical study is conducted to model the cracking and caving of horizontal strata induced by the excavation of a single stratum in long-wall mining.Results show that as the work face advances

the bed separation and cracking continuously occur in the roof.Rock blocks also continuously cave

and the region with lower vertical stresses in the roof is trapezoidal

whose size increases gradually until reaching a stable value.At two lateral sides and the top of the trapezoid

obvious cracks are observed;at other positions of the trapezoid

cracks are compacted.At two lateral sides of the trapezoid

rock blocks are obliquely arranged in the form of masonry structures.If the size of the ore body in an excavation and the number of timesteps between two adjacent excavations are increased

the caving of the roof arrives later

and the trapezoid tends to be more symmetric.These differences are related to the dependence on the loading/unloading history for a non-liner dynamic system.It has to be noted that shear fractures and the effects of hydraulic supports have not been considered in the present simulation.