The bottom-hole differential pressure and the three-dimensional in-situ differential stress are the main factors during drilling that affect the distribution of the bottom-hole rock stress; and then affect the drilling speed. The purpose of the article is to quantitatively study the effect of the three-dimensional in-situ stress on the bottom-hole stress distribution under the overbalanced

balanced

underbalanced and air drilling condition. On the basis of the mechanical analysis of the bottom-hole rock

the fluid-solid coupling model with the factors of the three-dimensional in-situ stress of the normal fault

fluid column pressure and pore pressure is set up

without analytical solution of the model; and then the numerical solution method is used to resolve it. The results show that the maximum principal stresses of the bottom-hole surface under different drilling conditions are the same; the minor principal stress increases with the increase of the bottom-hole differential pressure. The minor principal stress decreases with the increase of the horizontal maximum in-situ stress

and keeps stable when the horizontal minimum in-situ stress changes under differential drilling condition. The maximum principal stress of the bottom-hole surface firstly decreases with the increase of the horizontal minimum in-situ stress and keeps stable with the existence of the differential pressure and it keeps stable during air drilling while the horizontal minimum in-situ stress changes

and keeps stable when the horizontal maximum in-situ stress changes under differential drilling condition. Distribution of the bottom-hole stress field of the reverse fault and strike-slip fault is to be studied. Quantitative study of the bottom-hole stress distribution with differential pressure of bottom-hole and three-dimensional in-situ stress provides a numerical stimulation method for study of bottom-hole stress field under actual drilling condition and is the theoretical basis for faster and more efficient drilling.