To resolve problem of poor convergence in open-close iteration of discontinuous deformation analysis

an improved DDA method based on approximated step function and Lagrange interpolation is developed based on the relationship between the state of contact constraints within blocks and the block displacement. Hyperbolic tangent function is used to approximate the step function. The state of contact constraints within blocks is represented by block displacement using step function

which replaces the function of open-close iteration and avoids the problem of poor convergence in open-close iteration. The potential energy function of block system only containing the block displacement as unknown variable is derived with the principle of Lagrange interpolation. The extremum of general potential energy function is analyzed to obtain the block displacement. With the model of sliding block and underground chamber respectively

computational accuracy and computational speed of the improved DDA method are analyzed

and the correctness and the iterative stability of the improved DDA method is verified. Research shows that the improved DDA method based on approximated step function and Lagrange interpolation produces high precision

and it has a more stable and more robust computing convergence compared with the traditional DDA. Therefore

the improved DDA method based on approximated step function and Lagrange interpolation is a stable and effective numerical method and it provides a new approach for solving the problem of poor convergence in open-close iteration of discontinuous deformation.