Fragmentation of rocks upon impact during rockfall is a phenomenon that is poorly understood, scarcely researched and difficult to predict. However, to adequately predict the outcomes of rockfall events, it is essential to know whether a given block is likely to fragment given the impact conditions and what will be the outcome of the fragmentation process; that is, the number, size and trajectory of fragments. To date, there is no model or data that can be used to fully answer these questions. This paper presents the first theoretical model that can predict the fragmentation survival probability of brittle spherical blocks upon dynamic impact (i.e. drop tests) from the statistical distribution of material properties, determined from a range of standard quasi-static tests. Considering that survival probabilities tend to follow a Weibull distribution, the model focuses on predicting the two Weibull parameters, commonly known as the shape parameter (m) and the scale parameter (here, the critical kinetic energy). The model is based on theoretically-derived conversion factors used to turn the critical work required to fail disc samples in quasi-static indirect tension into the critical kinetic energy to cause failure of spheres at impact in drop tests. The mechanistic conversion factors specifically account for the shape and size of the specimens tested and the increase of strength under dynamic loading (strain rate effect). Three series of drop tests were conducted (on spheres of three different diameters) and complemented by extensive material characterisation testing in order to validate the novel predictive model. The variability of material properties was characterised, and it was found that the material strength found by the characterisation tests generally follows a Weibull form, but the survival probability distribution of the drop tests seems to be linear. The predicted conversion factors were first compared against their experimental counterparts before validating the prediction of survival probability of the spheres upon dynamic impact (in drop tests). It was found that it is possible to predict the survival probability of artificial rock of three different diameters (50 mm, 75 mm, 100 mm) and two different strengths upon impact solely from the statistical information coming from Brazilian tests and with an average relative error of less than 9%.

岩石在崩塌时因撞击而碎裂是一种知之甚少，很少研究且难以预测的现象。但是，要充分预测落石事件的结果，必须知道在给定的冲击条件下给定的区块是否有可能破碎，破碎过程的结果将是什么；即碎片的数量，大小和轨迹。迄今为止，还没有可以用来完全回答这些问题的模型或数据。本文提出了第一个理论模型，该模型可以根据一系列标准准静态试验确定的材料特性统计分布，预测在动态冲击（即跌落试验）下脆性球形块的碎片存活概率。米）和比例参数（此处为临界动能）。该模型基于理论上得出的转换因子，用于将准静态间接张力下使圆盘样品失效所需的关键工作转变为临界动能，从而在跌落试验中导致球体失效。机械转换因子专门考虑了测试样品的形状和尺寸以及动态载荷下的强度增加（应变率效应）。进行了三个系列的跌落试验（在三个不同直径的球体上），并辅以广泛的材料表征试验，以验证新型预测模型。表征了材料性能的可变性，发现通过表征测试发现的材料强度通常遵循威布尔形式，但是掉落测试的生存概率分布似乎是线性的。首先将预测的转换因子与实验转换因子进行比较，然后再验证球体在动态冲击下的存活概率的预测（在跌落测试中）。已经发现，仅根据巴西试验的统计信息并具有平均相对误差，就有可能预测三种不同直径（50 mm，75 mm，100 mm）和两种不同强度的人造岩石的存活概率。少于9％。