The Newmark sliding block method combined with block theory (referred to as the dynamic Newmark method) can be used to calculate the dynamic safety factor and the permanent displacement, which provides a quantitative tool to evaluate the dynamic stability of a rock block under seismic action. Frequent changes in the position of a rock block under seismic action may lead to the changes in contact areas and modes of contact between sliding faces. These problems that are not considered in the original dynamic Newmark method are solved to extend the dynamic Newmark method. First, the loop analysis method is introduced to obtain the contact polygonal faces of a sliding surface, and the simplex integration method is used to calculate the contact areas. Second, the reference point method is defined to identify the mode of contact between a structural plane and the surrounding rock mass, and the possible mode of motion of the rock block is determined. Based on these extensions of the dynamic Newmark method, an Extended Newmark Method (ENM) program is developed, and a verification example, three comparison cases, and an application are used to validate the correctness and effectiveness of the extended method. The results show that the ENM program can be used to calculate the effects of the change in contact areas and modes of contact on block motion, which better reflects the dynamic response of a rock block under seismic action compared with the original dynamic Newmark method.

中文翻译：

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动态Newmark方法在岩块地震稳定性分析中的扩展

结合块体理论的Newmark滑块法（简称动态Newmark法）可用于计算动力安全系数和永久位移，为评价地震作用下岩块的动力稳定性提供了量化工具。地震作用下岩块位置的频繁变化可能导致滑动面接触面积和接触方式的变化。解决了原动态Newmark方法中没有考虑的这些问题，扩展了动态Newmark方法。首先引入环分析法求出滑动面的接触多边形面，并采用单纯形积分法计算接触面积。第二，定义参考点法来识别结构面与围岩之间的接触方式，并确定岩块可能的运动方式。基于动态Newmark方法的这些扩展，开发了扩展Newmark方法(ENM)程序，并通过一个验证实例、三个对比案例和一个应用程序来验证扩展方法的正确性和有效性。结果表明，ENM程序可用于计算接触面积和接触方式的变化对块体运动的影响，与原始动态Newmark方法相比，能更好地反映地震作用下岩石块体的动力响应。基于动态Newmark方法的这些扩展，开发了扩展Newmark方法(ENM)程序，并通过一个验证实例、三个对比案例和一个应用程序来验证扩展方法的正确性和有效性。结果表明，ENM程序可用于计算接触面积和接触方式的变化对块体运动的影响，与原始动态Newmark方法相比，能更好地反映地震作用下岩石块体的动力响应。基于动态Newmark方法的这些扩展，开发了扩展Newmark方法(ENM)程序，并通过一个验证实例、三个对比案例和一个应用程序来验证扩展方法的正确性和有效性。结果表明，ENM程序可用于计算接触面积和接触方式的变化对块体运动的影响，与原始动态Newmark方法相比，能更好地反映地震作用下岩石块体的动力响应。