Three-dimensional discontinuous deformation analysis method (3D.DDA) is a dynamic calculation method based on the implicit solution. Inertial force is introduced in the solution process to ensure that the time variable is the real time variable, and springs are applied at the block boundary to avoid mutual intrusion between blocks. Therefore, the value of time step and contact spring stiffness directly affect the accuracy of 3D.DDA calculation results. Firstly, we analyzed the effects of the time step and contact spring stiffness on the numerical calculation results of the 3D.DDA method based on the theoretical formula derivation. Secondly, we studied the influence mechanism of time step on the simulation results of the 3D.DDA method individually based on the double block free falling model. And we determined the reasonable value area of time step. Then, considering the contacts between blocks, we studied the joint influence mechanism of time step and contact spring stiffness on the 3D.DDA simulation results based on the double block sliding model. And we analyzed the error between the 3D.DDA simulation value and the theoretical value under the conditions of different time step and contact spring stiffness. Based on that, we divided the combined value area of time step and contact spring stiffness into four regions (Q1, Q2, Q3, and Q4) and determined the optimal value area of time step and contact spring stiffness. At last, we carried out the slope rockfall model experiment and numerical simulation, and the trajectory of the falling rock in the numerical simulation was basically consistent with the experiment results, which verified the effectiveness of the optimal value area of time step and contact spring stiffness. The research results can provide a reference for the choice of the value of time step and contact spring stiffness in the numerical simulation based on the 3D.DDA method.

中文翻译：

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三维间断变形分析方法中时间步长和弹簧刚度的参数化研究

三维不连续变形分析法（3D.DDA）是一种基于隐式解的动态计算方法。在求解过程中引入惯性力，保证时间变量为实时变量，并在块体边界处施加弹簧，避免块体间相互侵入。因此，时间步长和接触弹簧刚度的大小直接影响 3D.DDA 计算结果的准确性。首先，在推导理论公式的基础上，分析了时间步长和接触弹簧刚度对3D.DDA方法数值计算结果的影响。其次，我们基于双块自由落体模型分别研究了时间步长对3D.DDA方法仿真结果的影响机制。并确定了时间步长的合理值域。然后，考虑块与块之间的接触，研究了时间步长和接触弹簧刚度对基于双块滑动模型的3D.DDA模拟结果的联合影响机制。并分析了不同时间步长和接触弹簧刚度条件下3D.DDA仿真值与理论值的误差。在此基础上，我们将时间步长和接触弹簧刚度的组合值区域划分为四个区域（Q1、Q2、Q3和Q4），确定了时间步长和接触弹簧刚度的最优值区域。最后我们进行了边坡落石模型实验和数值模拟，数值模拟中落石的轨迹与实验结果基本一致，验证了时间步长和接触弹簧刚度最优值区域的有效性。研究结果可为基于3D.DDA方法的数值模拟中时间步长和接触弹簧刚度取值的选择提供参考。