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.

地貌学中一个尚未解决的主要问题是：当斜坡开始塌陷时，随之而来的滑坡会有多大？ 可能发生的滑坡规模范围巨大，潜在的滑坡规模从米到公里不等，因此不幸的是，特别是对于灾害评估而言，我们仍然无法预测此类规模。尽管我们现在对区域范围内滑坡的规模频率分布有相当好的限制，但这种无能仍然存在。该项目采用了一种新的理论策略，涉及使用随机微分方程，以协调解决个体滑坡传播和整体滑坡规模分布的问题。 我们发现，一个简单的边坡失稳随机微积分模型可以解释滑坡的完整尺寸频率分布，包括平均滑坡尺寸以及分布的幂律缩放和非缩放分量。 我们正在发展这一理论，以解决以下关键问题：（1）集合分布中的平均滑坡规模与现实有何关系？ - 如果它不是测绘分辨率的伪影，它是否与土壤深度、粘聚力和岩性等物理特性有关，或者它只是平均山坡比例的函数？ (2) 随机理论的物理假设是否被现场观察所证实？ （3）我们能否更精确地对不同边坡破坏机制进行数据分析和建模？ (4) 落石是否是通过具有完全不同的尺寸频率分布的完全不同的随机过程发生的？ 我们努力的结果将是对山坡破坏和滑坡灾害的随机行为有更深入的了解。