Giant landslides, topography, and erosion

Abstract

Distributions of slope angles in tectonically active mountain belts point to the development of threshold conditions, where hillslopes attain a critical inclination or height at which they fail readily because of limitations in material strength. It has been proposed that hillslopes adjust to rapid uplift and bedrock incision through an increase in the rate of relief-limiting landsliding rather than gradual slope steepening. Here we test this concept by investigating the relationship between mean local relief H¯, which we take to be a proxy of long-term erosion rates E, and the occurrence of over 300 of the largest (V > 10⁸ m³) terrestrial landslides on Earth. We find that nearly two-thirds of these giant landslides have occurred in the steepest 5% of the Earth's land surface, where relief is close to its proposed upper strength limit. They are primarily located in deeply incised valleys, along fault-bounded fringes of active mountain belts, and in volcanic arcs.

This distribution coincides with areas of high long-term erosion rates (∼ 4 mm yr^− 1), confirming that giant landslides contribute to rapid denudation of mountains. Most of the eroded volume is concentrated in the smallest, but steepest parts of mountain belts and volcanic arcs. First-order estimates of minimum erosion rates accomplished by the largest landslides are ≥ 0.01 mm yr^− 1; these rates are between 1% and 10% of the Late Pleistocene to Holocene mean erosion rates in a given area. Importantly, the landslide erosion rates show a nonlinear increase with mean local relief, suggesting that the contribution of giant landslides in total and per event increases significantly with increasing overall erosion rates. However, giant landslides also occur in areas of lower-than-average relief (H¯ ∼ 300–700 m), irrespective of whether threshold hillslopes have developed or not. Factors contributing to these failures include soft rocks, extensive low-angle discontinuities, high rates of fluvial bedrock incision, and tectonically driven deformation and slope loading.

Introduction

Catastrophic landslides are localised, but highly efficient agents of erosion in mountainous terrain, moving large masses of material over kilometre-scale distances in geologically instantaneous time (∼ 10² s) (Eisbacher and Clague, 1984). Because they are frequently triggered by earthquakes and high-intensity precipitation events, their study provides insight to tectonic and climatic forcing of hillslope adjustment to topographic relief produced by glacial erosion and fluvial bedrock incision.

It has been proposed that hillslopes in active mountain belts adjust to high rates of rock uplift and erosion by increases in the rate of landsliding rather than by progressive slope steepening (Montgomery and Brandon, 2002). This hypothesis implies that hillslopes attain a threshold angle characteristic of limit equilibrium conditions of slope failure that is insensitive to changes in uplift, climate, or lithology (Burbank et al., 1996, Montgomery, 2001). Hillcrests and divides are worn down at a rate that effectively maintains local hillslope relief.

Montgomery and Brandon (2002) argued that topographic relief cannot grow indefinitely, proposing a hyperbolic relationship between the long-term erosion rate E and orogen-scale mean local relief H¯ for tectonically active mountain belts throughout the world:

$$E=E_0+\frac{K\overline{H}}{[1-{(\overline{H}/H_c)}^2]}\text{,}$$

where E₀ is the erosion rate due to chemical weathering, K is a rate constant, and H_c is the limiting relief. This relationship implies that, for regions that have a mean local relief close to H_c, small increases in mean local relief require substantial increases in erosion rates. Montgomery and Brandon (2002) proposed that hillslope and relief adjustment to high rates of erosion is achieved through increases in the rate of landsliding rather than slope steepening.

From an engineering geological perspective, key controls on hillslope stability include material strength set by cohesion and internal friction, slope and discontinuity geometry, and transient loading imposed by water content and seismic ground acceleration. For simple solutions, limit equilibrium conditions of landsliding can be expressed as a maximum stable hillslope height, supporting the notion of landslide-limited relief (Schmidt and Montgomery, 1995). It has also been proposed that erosional unloading by valley incision or debuttressing during deglaciation alters topography-induced stress fields, focusing tensile stresses near valley floors and thus further disposing slopes of sufficient relief to catastrophic failure (Augustinus, 1995).

In numerical studies of landscape evolution, landslide triggering can be modelled in terms of attainment of a critical hillslope height or threshold hillslope angle at which slope failure will occur (Densmore et al., 1998). By implication, these thresholds of relief or slope angle cannot be exceeded (Eq. (1)), because they are maintained and limited by landsliding. Threshold hillslopes have been reported from the northwestern Himalaya (Burbank et al., 1996), the Olympic Mountains (Montgomery, 2001), the fringes of the Tibetan Plateau (Whipple et al., 1999), and the New Zealand Southern Alps (Korup, 2006a, Korup, 2006b). With few exceptions (Montgomery, 2001), however, there have been no attempts to further validate a causal link between threshold hillslopes and the rates and characteristics of landslides in these or other mountain belts.

Here, we provide one of the first regional-scale tests of the concept of failure-controlled relief limitation at the upper size limit of landsliding. We compiled data on over 300 of the largest catastrophic terrestrial landslides on Earth. We examine these giant landslides with respect to mean local relief and long-term, orogen-scale erosion rates in Earth's major mountain belts. The frequency of landslides is inversely and nonlinearly related to landslide size (Malamud et al., 2004), but the validity of this and other empirical statistical models is limited to inventories containing only a fraction of the landslide size spectrum, i.e. mainly small events. We use the apparent erosion rate of giant landslides as a proxy of their overall rate of landsliding. This approximation seems reasonable, as we are interested in the response of giant landslides to changes in topographic relief, rather than the general relationship between magnitude and frequency of landsliding itself.

We hypothesize that if the nonlinear relation between erosion rates and mean local relief is indeed governed by the rate of landsliding (Montgomery and Brandon, 2002), the contribution of large events should also increase with growing topographic relief (Fig. 1). In the alternative cases of invariant or declining rates of erosion by giant landslides, we would expect a higher contribution from smaller landslides in order to account for the necessary increases in erosion rates. Our study addresses several key questions of how topography and landslides dynamically interact: What are the relationships between topographic relief and the largest landslides on Earth? Is the spatial distribution of these giant slope failures fully explained by hillslope relief? How do these landslides contribute to relief adjustment and erosion? We first present results from a regional quantitative analysis. In the discussion, we refine these findings based on our field observations on giant landslides in various mountain belts.