Limits on the validity of infinite length assumptions for modelling shallow landslides
Limits on the validity of infinite length assumptions for modelling shallow landslides
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DOI：
10.1002/esp.3235
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发表时间：
2012-09
影响因子：
3.3
通讯作者：
D. Milledge;D. V. Griffiths;S. N. Lane;J. Warburton
中科院分区：
文献类型：
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作者：
D. Milledge;D. V. Griffiths;S. N. Lane;J. Warburton
无限坡度法被广泛用作地貌和景观演化模型的岩土工程组成部分。浅层滑坡无限长（沿下坡方向）的假设通常被认为对于自然滑坡是有效的，因为它们通常相对于其深度来说是长的。然而，这很少是合理的，因为边缘效应变得重要的临界长度/深度 (L/H) 比率是未知的。我们通过将无限边坡稳定性预测与一组合成二维边坡的有限元预测进行基准比较，建立了这个临界 L/H 比，假设预测之间的差异是由于无限边坡方法中的误差造成的。我们测试了六种不同的 L/H 比率的无限斜率方法，以找到其预测值与有限元方法的预测值的误差在 5% 以内的临界比率。我们对 5000 个合成斜坡进行了重复这些测试，这些斜坡具有一系列破坏面深度、孔隙水压力、摩擦角、土壤粘聚力、土壤单位重量和自然斜坡的斜坡角度特征。我们发现：(1) 对于较小的 L/H 比，无限边坡稳定性预测始终过于保守； (2) L/H 比为 25 时，预测始终收敛于有限元基准的 5% 以内（即，对于长于深度 25 倍的滑坡，无限坡度假设是合理的）；但是（3）它们可以以低得多的比率收敛，具体取决于坡度特性，特别是对于低粘性土壤。流域规模稳定性模型的含义是，如果网格分辨率较粗（例如 >25 m），则无限长度假设是合理的。然而，即使在更精细的网格分辨率（例如 1 m）下，它也可能有效，因为预测的孔隙水压力场中的空间组织降低了短时滑坡的可能性，并将预测滑坡的 L/H 比小于 25 的风险降至最低。 版权所有 © 2012 John Wiley & Sons, Ltd.
The infinite slope method is widely used as the geotechnical component of geomorphic and landscape evolution models. Its assumption that shallow landslides are infinitely long (in a downslope direction) is usually considered valid for natural landslides on the basis that they are generally long relative to their depth. However, this is rarely justified, because the critical length/depth (L/H) ratio below which edge effects become important is unknown. We establish this critical L/H ratio by benchmarking infinite slope stability predictions against finite element predictions for a set of synthetic two‐dimensional slopes, assuming that the difference between the predictions is due to error in the infinite slope method. We test the infinite slope method for six different L/H ratios to find the critical ratio at which its predictions fall within 5% of those from the finite element method. We repeat these tests for 5000 synthetic slopes with a range of failure plane depths, pore water pressures, friction angles, soil cohesions, soil unit weights and slope angles characteristic of natural slopes. We find that: (1) infinite slope stability predictions are consistently too conservative for small L/H ratios; (2) the predictions always converge to within 5% of the finite element benchmarks by a L/H ratio of 25 (i.e. the infinite slope assumption is reasonable for landslides 25 times longer than they are deep); but (3) they can converge at much lower ratios depending on slope properties, particularly for low cohesion soils. The implication for catchment scale stability models is that the infinite length assumption is reasonable if their grid resolution is coarse (e.g. >25 m). However, it may also be valid even at much finer grid resolutions (e.g. 1 m), because spatial organization in the predicted pore water pressure field reduces the probability of short landslides and minimizes the risk that predicted landslides will have L/H ratios less than 25. Copyright © 2012 John Wiley & Sons, Ltd.