Abstract: Fault structure is one of the main geological factors influencing coal mining. In order to rapidly and accurately form and identify the fault at underground field to seek the location of tunnels, the paper proposes a state equation for faults which is deduced from fault spatial geometry relation and mathematical analysis using the basic principle of structural geology and the mathematical means, and discuses its application. According to the fault classification by the state equation, the geometry relation among faults can be clearly described, showing the basic fault types in nature. Using the macro-characteristics that is easy to observe and related to the states to identify the faults can rapidly and accurately solve some problems on the fault structures to guide production in time. 

Key words: Geological structure, Fault, 3D space, State, Equation, Application