A Stochastic Differential Equation Approach to Studying Landslide Failure and Size Distributions

研究滑坡破坏和规模分布的随机微分方程方法

• 批准号: 0229846
• 负责人: Colin Stark
• 金额: $ 21.42万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-05-15 至 2006-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0229846&HistoricalAwards=false
• 关键词: Stochastic; Differential; Equation; Approach; Studying

A major unsolved problem in geomorphology is this: when a slope begins to fail, how big will the ensuing landslide be? The span of possible landslide sizes is enormous, with potential failures ranging in scale from meters to kilometers - so it's unfortunate, particularly for hazard assessment, that we remain unable to predict such sizes. This inability persists despite the fact that we now have rather good constraints on the size-frequency distribution of landslides at a regional scale. This project takes a new theoretical tack, one that involves the use of stochastic differential equations, to address in concert the issues of individual landslide propagation and ensemble landslide sizedistribution. We have found that a simple, stochastic calculus model for slope failure can explain the full size-frequency distribution of landslides, including the mean landslide size and both the power-law scaling and non-scaling components of the distribution. We are developing this theory in order to address the following key questions: (1) how does the mean landslide size in an ensemble distribution relate to reality? - if it is not an artifact of mapping resolution, does it relate to physical properties such as soil depth, cohesion, and lithology, or is it simply a function of mean hillslope scale? (2) are the physical assumptions of the stochastic theory borne out by field observations? (3) can we be more precise in our data analysis and modeling of different slope failure mechanisms? (4) do rockfalls occur by an entirely different stochastic process with an altogether different size-frequency distribution? The outcome of our efforts will be a deeper understanding of the stochastic behavior of hillslope failure and landslide hazard.

地貌学中尚未解决的一个主要问题是：当一个斜坡开始坍塌时，随之而来的滑坡会有多大？可能的滑坡规模跨度是巨大的，潜在的破坏范围从米到公里不等——所以不幸的是，特别是对于危害评估，我们仍然无法预测这样的规模。这种无能仍然存在，尽管我们现在在区域范围内对滑坡的大小-频率分布有相当好的限制。该项目采用了一种新的理论方法，其中包括使用随机微分方程来解决单个滑坡传播和总体滑坡尺寸分布的问题。我们发现，一个简单的边坡破坏随机演算模型可以解释滑坡的全尺寸-频率分布，包括平均滑坡尺寸以及分布的幂律标度和非标度分量。我们发展这一理论是为了解决以下关键问题：(1)总体分布中的平均滑坡大小如何与现实相关联？-如果它不是绘图分辨率的产物，它是否与物理性质有关，如土壤深度，凝聚力和岩性，或者它只是平均山坡尺度的函数？(2)现场观测是否证实了随机理论的物理假设？(3)对不同边坡破坏机制的数据分析和建模是否能够更加精确？(4)岩崩的发生是否具有完全不同的随机过程和完全不同的大小-频率分布？我们努力的结果将是对边坡破坏和滑坡灾害的随机行为有更深入的了解。