Cracking and fracturing of overlying strata are attributed to transformation of continuum medium into discontinuum medium or to evolution of discontinuum from the mechanical viewpoint. Accurate modeling of the motion process of overlying strata is especially important to control stability of strata and to predict and prevent some disasters. In the developed combined Lagragian-discrere element method (the continuum-discontinuum method)

potential contact forces are reliable only if the normal stiffness coefficient is accurate. To model the mining process with long time and to solve the problem that assemblies composed of discrete elements of coal seams can still possess the excessive load-carrying capacity

a quasi-static calculation mode and a stress drop method were adopted. To accurately select the normal stiffness coefficient applicable to modeling of interactions of strata

the coefficient was firstly standardized to check errors due to the embedded amount between elements

then four groups (the upper relatively soft-lower relatively hard

the upper relatively soft-lower relatively soft

the upper relatively hard-lower relatively soft and the upper relatively hard-lower relatively hard) of numerical tests of contact and equilibrium processes of two rock blocks were designed

and one group as an example was analyzed in detail. Through examining evolution of the following quantities

such as the penetration of two blocks

the averaged stress at the lower end of the top block

and the duration from motion to equilibrium

a universal result was obtained

and the appropriate ratio of the normal stiffness coefficient to the elastic modulus was determined to be 15 m−1. In order to check reasonability of the suggested value for modeling the motion process of overlying strata in the stope

the working face 1141 in a coal mine was taken as an example. It is found that when the normal stiffness coefficient was selected as the suggested value

the calculation result is reasonable and the calculation efficiency is high.