针对非连续变形分析中开合迭代难以收敛的难题，基于块体接触约束状态和块体位移之间的关系，提出了基于逼近阶跃函数和拉格朗日插值的改进DDA方法。采用双曲正切函数来逼近阶跃函数，利用阶跃函数将块体接触约束状态用块体位移来表达，以此来替代开合迭代，避免了开合迭代难以收敛的难题。利用拉格朗日插值原理，推导得到只含有块体位移为未知量的块体系统势能函数，并利用变尺度法来求解总体势能函数的极值以得到块体位移。分别结合滑块模型和地下洞室模型，分析了改进DDA方法的计算精度和计算速度，验证了文中提出的改进DDA方法的正确性和稳定性。研究表明：基于逼近阶跃函数和拉格朗日插值的改进DDA方法具有较高的精度，且相比较传统DDA方法而言，具有更为稳定的和更为强健的计算收敛性。因此，基于逼近阶跃函数和拉格朗日插值的改进DDA方法是一种稳定有效的数值计算方法，为解决非连续变形中开合迭代难以收敛的问题提供了新思路。

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.