Researches into fracture and fragmentation in rocks have been one of the leading topics of rock mechanics

and also an important theoretical base of many engineering practices such as mining

resource development

hydropower

traffic and earthquake. The catastrophes in rock engineering such as rockbursts

coal and gas bursts

roof caving

water bursts

slope failures

dam instability

ground surface subsidence and earthquakes are closely related to fracturing in rocks. As is well known

rock has a variety of complex characteristics atypical of other solids

say

metal; the complexity of mechanical behavior arises from complexity of its structures on a variety of length scales. In terms of the complex structure of rocks

there exist a large number of defects in rocks such as dislocations

crystal boundaries

secondary phases

twin crystallites

fissures

pores

inclusions and precipitates. As a result

rock appears to be discontinuous

strongly heterogeneous and anisotropic. In addition

the scale effect is also an inherent feature of rock.The classical theory of fracture mechanics

assuming rock to be homogenous and continuous

can not describe the inherent features of rocks. Fractal geometry originally defined by Mandelbrot supplies an alternative tool to describe quantitatively the rock features. This paper discusses special challenges posed for fractal geometry by rock fracture and fragmentations and recent advances made by applications of. fractal geometry to rock fracture and fragmentations

especially the authors’ contributions to the applications of fractal geometry to fracture and fragmentation in rocks

including rock fracturing at meso scale

dynamic propagation of macro rock cracks and size distribution of rock fragmentations. In addition

a case study subjected to engineering application is given in the paper. The paper also briefly sketches a selected promising area of current researches

focusing on the physical meaning of fractals and definition of mechanical variables in fractal space.