Hillslope processes

Chapter structure

• Hillslope environments
• Hillslope transport processes and hillslope development
• Soil production, weathering processes

Hillslopes are an almost universal landform, occupying some 90% of the land surface. In hilly and mountainous regions, long-term downslope movement of soil on hillslopes can play a crucial role governing the rate at which landscape evolves through time. Although river incision is often considered to mainly drive landscape response to tectonic or climatic change, hillslope erosion processes produce and deliver sediments to channels, which are known to influence river incision rates either as tools for erosion or as a cover protecting the underlying bedrock from erosion. Considering weathering and hillslope transport processes is therefore vital to understand how landscape evolves in response to climatic variations.

Learning outcomes

• Recognise the different processes triggering hillslope processes and their terminology;
• Understand the importance of weathering and its products on the evolution of hillslope environments;
• Explore the mathematical expressions of regolith formation and hillslope processes

Hillslope environments

Note

This section is mainly based on R.J. Huggett book: Fundamentals of Geomorphology (3rd ed.), 2011 (link).

Hillslopes are an integral part of the drainage basin system, delivering water and sediment to streams. They range from flat to steep. Commonly, hillslopes form catenas – sequences of linked slope units running from drainage divide to valley floor. Given that climate, vegetation, lithology, and geological structure vary so much from place to place, it is not surprising that hillslope processes also vary in different settings and that hillslopes have a rich diversity of forms.

Nonetheless, geomorphologists have found that many areas have a characteristic hillslope form that determines the general appearance of the terrain. Such characteristic hillslopes will have evolved to a more-or-less equilibrium state under particular constraints of rock type and climate.

Hillslopes may be bare rock surfaces, regolith and soil may cover them, or they may comprise a mix of bare rock and soil-covered areas. Hillslopes mantled with regolith or soil, perhaps with some exposures of bare rock, are probably the dominant type. They are usually designated soil-mantled hillslopes. However, hillslopes formed in bare rock – rock slopes – are common. They tend to form in 3 situations:

1. First, rock slopes commonly form where either uplift or deep incision means that they sit at too high an elevation for debris to accumulate and bury them.
2. Second, they often form where active processes at their bases remove debris, so preventing its accumulation.
3. Third, they may form where the terrain is too steep or the climate is too cold or too dry for chemical weathering and vegetation to create and sustain a regolith.

More generally, bare rock faces form in many environments where slope angles exceed about 45°, which is roughly the maximum angle maintained by rock debris. In the humid tropics, a regolith may form on slopes as steep as 80° on rocks such as mudstones and basalts because weathering and vegetation establishment are so speedy. Such steep regolith-covered slopes occur on Tahiti and in Papua New Guinea where, after a landslide, rock may remain bare for just a few years.

Hillslope processes

Gravity, flowing water, and temperature changes are the main forces behind hillslope processes, with the action of animals and plants being important in some situations.

This section describes the processes involved in the transport of material over hillslopes. Hillslopes provide the gradients enabling material to be transported from the slopes themselves towards the valley bottoms, directly by gravity alone, or by water flowing down over the surface. Gravity has the potential to transfer material downslope if the material resistance to counteract it is insufficient. Similarly, water flowing along the surface exert a drag on soil particles and have the potential to entrain material. After the gradient has fallen below a critical threshold to keep the material in transport, deposition occurs.

Several hillslope processes serve to transport regolith and other weathering products. They range from slow and continual processes to rapid and intermittent processes. In the following, a brief overview is given of some of the main characteristics, morphologies of mass movements and erosion.

Terminology

Note

Conventionally, slope processes in which gravity alone is the dominant transporting agent are called mass movements. Processes in which other agents dominate are called erosion, e.g. wind or water erosion.

The terminology depends on what is moving and how it moves and is defined as: slide, fall, flow, and heave (note: not mutually exclusive categories):

1. Slide is when the material maintains continuous contact with the surface.
2. Fall refers to the free fall of material (looses contact with the surface).
3. Flow involves continuous movement with the material behaving in a plastic to liquid manner.
4. Heave is a slow movement where the particles are pushed up perpendicular to the sloping surface then “let down” in the direction of gravity.

Speed & type of movements

Slow movements

Fig. 16 Soil creep process and associated typical features.

Generally used for processes having speed ranging from 1 mm/yr to 1 mm/day. The most common of these movements is the downward motion of surface material called soil creep. This is the slowest type of mass wasting, requiring years of gradual movement to have a pronounced effect on a slope. Slopes creep due to the expansion and contraction of surface sediment, and the pull of gravity. The pull of gravity is a constant, but the forces causing expansion and contraction of sediment are not. The presence of water is generally required, but in a desert lacking vegetative ground cover even dry sediment will creep due to daily heating and cooling of surface sediment grains.

Two other types of slow movements are:

Frost heaving that occurs when water gets behind or underneath an object and freezes.

Solifluction that refers to the downslope movement of debris under saturated conditions. Solifluction is the mass movement of soil and regolith affected by alternate freezing and thawing. This process is characteristic of saturated soils in high latitudes, both within and beyond the permafrost zone. A number of features contribute to active solifluction:

1. frequent freeze-thaw cycles
2. saturated soils and regolith, after snow melt and heavy rainfall
3. frost-susceptible materials, with significant contents of silt and clay, at least at depth
4. extensive regolith across a range of slope angles

Moderate movements

It corresponds to speed ranging from 1 cm/day to 1 cm/sec. The main hillslope processes in this category are:

1. Slump: the downward and outward movement of earth traveling as a unit or as a series of units.
2. Earthflows are slow but perceptible movements.
3. Debris slide that involves the movement of comparatively dry unconsolidated material.

These types of movements like for example rock slide or landslide occur where there is a tilted, pre-existing plane of weakness within a slope which serves as a slide surface for overlying sediment/rock to move downward. Such planes of weakness are either flat sedimentary surfaces (usually where one layer of sediment or sedimentary rock is in contact with another layer), planes of cleavage (determined by mineral foliation) within metamorphic rocks, or a fracture (fault or joint) within a body of rock. Rock slides can be massive, occasionally involving an entire mountainside, making them a real hazard in areas where a surface of weakness tilts in the same direction as the surface of the slope (the video above illustrates the evolution of a coastal landslide at Mud Creek in California (Warrick et al., 2020)). Rock slides can be triggered by earthquakes or by the saturation of a slope with water.

At the top corner of the Summerfield’s triangle, the debris flows as the name implies, contains a variety of particles or fragments, mainly small to large rock fragments but also trees, animal carcasses, cars and buildings. Debris flows usually contain a high water content which enables them to travel at fairly high velocity for some distance from where they originated. Debris flows tend to follow the paths of pre-existing stream channels and valleys, but debris flows are much denser than water, so they can destroy anything in their paths such as houses, bridges, or highways.

Rapid movements

Fastest type of movements that can go quite fast (e.g., free fall).

A rock fall consists of one or maybe a few rocks that detach from the high part of a steep slope, dropping and perhaps bouncing a few times as they move very rapidly down slope.

Rock falls are very dangerous because they can occur without warning, and because the rocks are traveling at high velocity.

Tip

You can usually tell where rock falls are common by identifying talus at the base of steep slopes.

Transport-limited and supply-limited processes

It is common to draw a distinction between hillslope processes limited by the transporting capacity of sediment and hillslope processes limited by the supply of transportable material.

In transport-limited processes, the rate of soil and rock transport limits the delivery of sediment to streams. In other words, the supply of sediment exceeds the capacity to remove it, and transport processes and their spatial variation dictate hillslope form. Soil creep, through-wash, rainflow, rainsplash, and rillwash are all hillslope processes limited by transporting capacity.

On supply-limited (or weathering-limited) hillslopes, the rate of sediment production by weathering and erosional detachment (through overland flow and mass movement) limits the delivery of sediment to streams. In other words, weathering and erosional processes dictate hillslope form. Leaching of solutes, landsliding, debris avalanches, debris flows, and rockfall are all hillslope processes limited by sediment supply.

Mechanisms linking climate with landslides, erosion, and sediment transport

Temperature

High temperatures contribute to slope instability by enhancing the thermal breakdown of rock, decreasing the viscosity of groundwater( i.e more lubricating), and thawing frozen ground so more water infiltrates. Warm conditions can also cause increased evaporation, leading to drier soils and more stable conditions in deeper soils, especially in summer. Finally, warming can intensify the cycling between wet and dry periods, which may act to widen gaps in rock and soil, contributing to a decrease in slope stability.

Precipitation

Fig. 17 Rainfall (source: MetOffice) and landslides (source: BGS) in the UK.

Heavy rain events reduce slope stability by rapidly raising the water table (or groundwater elevation) and by enhancing water drainage through the soil to lower layers. In addition, intense rainfall can erode surface sediments, and higher streamflow during these events can transport more sediment downstream. Different patterns of rainfall will affect which slopes might be destabilized, and where erosion and sediment transport are most important.

Soil Water Content

Wetter soils are heavier, can absorb less precipitation (thus increasing runoff), and have greater lubrication among soil layers. Analysis from the landslides often indicates that the initial conditions of the soil prior to the triggering events are an important contributor to the mobility and, as a result, the severity of the landslide.

Snowpack and Glaciers

Higher snowlines can lead to exposure of unconsolidated (erodible) sediment, more ground surface erosion, greater soil saturation, and higher streamflows. Retreating glaciers uncover loose, unvegetated sediment that is vulnerable to mobilisation. Melting glaciers typically leave behind sediments that are then exposed to weather and erosion.

Earthquakes

Fig. 18 Japan earthquake: landslide traps residents in homes (the guardian)

Large earthquakes can trigger widespread landsliding. In addition to causing extensive socioeconomic disruption, earthquake-induced landslides play a key role in the evolution of mountain landscapes, increasing sediment flux through the fluvial networ and contributing to net erosion rates. While earthquake ground shaking triggers near-instantaneous landsliding, some slopes do not fully fail and are weakened, resulting in elevated susceptibility of hillslopes to landsliding during postseismic rainfall and subsequent seismicity. These legacy effects have been broadly attributed to landscape-scale weakening of hillslope substrates resulting from increased brittle (micro)fracturing and joint dilation (“damage”) caused by transient hillslope stresses experienced during earthquake ground shaking.

Weathering

Weathering is the breakdown of rocks at the Earth’s surface, by the action of rainwater, extremes of temperature, and biological activity. It does not involve the removal of rock material. There are three types of weathering, physical, chemical and biological.

Note

Many rocks form under high temperatures and pressures deep in the Earth’s crust. When exposed to the lower temperatures and pressures at the Earth’s surface and brought into contact with air, water, and organisms, they start to decay. The process tends to be self-reinforcing: weathering weakens the rocks and makes them more permeable, so rendering them more vulnerable to removal by agents of erosion, and the removal of weathered products exposes more rock to weathering. Living things have an influential role in weathering, attacking rocks and minerals through various biophysical and biochemical processes, most of which are not well understood.

Weathering products: regolith

The weathered mantle or regolith is all the weathered material lying above the unaltered or fresh bedrock. It may include lumps of fresh bedrock. Often the weathered mantle or crust is differentiated into visible horizons and is called a weathering profile (as shown in the figure below).

Fig. 19 Typical weathering profile in granite. The weathering front separates fresh bedrock from the regolith. The regolith is divided into saprock, saprolite, and a mobile zone.

The weathering front is the boundary between fresh and weathered rock. The layer immediately above the weathering front is sometimes called saprock, which represents the first stages of weathering. Above the saprock lies saprolite; this is more weathered than saprock but still retains most of the structures found in the parent bedrock. Saprolite lies where it was formed, undisturbed by mass movements or other erosive agents. Deep weathering profiles, saprock, and saprolite are common in the tropics. No satisfactory name exists for the material lying above the saprolite, where weathering is advanced and the parent rock fabric is not distinguishable, although the terms ‘mobile zone’, ‘zone of lost fabric’, ‘residuum’, and ‘pedolith’ are all used.

Fig. 20 Top: Example of regolith in the field (WA - Australia). Left: Regolith and weathering (rock decay) in the Critical Zone (Pope, 2015). Right: \(q_s\) is the downhill mass transport resulting from the action of multiple processes. \(P_s\) is rate of conversion of rock into soil. \(U\) is the apparent rate of uniform mass uplift (from Bovy 2012, modified from Dietrich et al. (1995)). Soil thickness \(h\) and depth below the ground surface \(h_\star\) are both measured vertically.

Soil production function

Note

As mentioned above, soil production, or rock weathering, is the result of a variety of chemical and mechanical processes. It is, however, difficult for geomorphologists to consider each of these processes separately while studying the form of the landscape. Bedrock weathering rates are thus usually estimated using empirical soil production functions, i.e., relationships between weathering rates and soil depth.

A minimum soil cover is needed for bedrock weathering, as soil acts as a reservoir of water essential to weathering processes such as freeze-thaw or solutional processes. At depths beyond which soil production is maximised, soil production is self limiting as thicker soil progressively buffers the underlying bedrock from weathering.

This behaviour can be represented by a humped function. This relationship has been assumed for 100 years, but has not been quantitatively tested until recently. Heimsath et al. (1997, 1999) have first applied field methods and cosmogenic dating to hillslopes in northern California to determine soil production rates as a function of soil depth. These observations suggest an exponential decrease in soil production with increasing soil depth, as proposed earlier by Dietrich et al. (1995).

Fig. 21 Schematic representation of the exponential soil production function proposed by Dietrich et al. (1995) and Heimsath et al. (1997, 1999), and the humped soil production function initially proposed by Gilbert (1877) (redrawn from Humphreys and Wilkinson, 2007).

Soil production equation

Bedrock weathering is modelled using the exponential soil production function used by Heimsath et al. (1997, 1999). The rate of weathering \(P_s\) (m/yr) is given by:

\[P_s = P_0 e^{(− \frac{h}{h_0})}\]

where \(P_0\) is expressed in (m/yr) and \(h_0\) (m) is a characteristic soil depth (soil production ‘damping’ depth) at which \(P_s = \frac{P_0}{e}\).

This soil production law has been calibrated at different sites (in northern California and southern Australia) using both soil thickness and cosmogenic radionucleides (CRN) measurements (Heimsath et al., 1999, 2000). For these sites, the authors reported values of \(P_0\) between \(5 \cdot 10^{−5}\) and \(8 \cdot 10^{−5}\) m/yr and a value of \(h_0 \simeq 0.5\) m.

Hillslope: the diffusion equation

Fig. 22 An explanation for the development of ridge-and-valley topography in soil-mantled terrain. Slope-dependent (diffusive) transport leads to convex hillslopes, and when the topography is laterally perturbed the transport direction (red arrows) causes the topographic highs to lower and topographic lows to fill in, resulting in smooth topography, as suggested by the dashed line. In contrast, advective transport, which depends on water flow and slope gradient, carries sediment downslope and produces concave hill slopes. Flow concentrations (blue flowpaths) resulting from lateral topographic perturbation lead to incision, as suggested by the dashed lines. The competition of these two processes leads to diffusion dominated ridges and advection-dominated valleys. Source: Adapted from Dietrich and Perron (2006)

Formulations for hillslope erosion are mainly derived considering hillslope form (e.g., convex, convex-concave, planar). In many models, sediment transport rate on hillslopes is assumed to be equal to a linear function of topographic gradient. Such an expression has its origin in the pioneering studies of convex hillslopes by Davis (1892) and Gilbert (1909). Combined with the application of mass conservation, this leads to the diffusion equation that describes the rate of elevation change \(\delta h/ \delta t\):

\[\frac{\delta h}{ \delta t} = - \nabla \cdot q_s\]

\[q_s = - \kappa \nabla z\]

\[\frac{\delta h}{ \delta t} = \kappa \nabla^2 z\]

where \(z\) is elevation, \(\nabla \cdot\) is the spatial divergence operator, \(\nabla z\) is the topographic gradient (i.e., the local slope), \(q_s\) is the soil flux in the positive direction of \(\nabla z\), and \(\kappa\) is the hillslope diffusivity.

Modelling soil transport

Although the linear dependence of soil transport on local slope has been widely assumed, only a few observations support this relationship. Morevover, it is well admitted that sediment transport on hillslopes result from a variety of processes, such as landsliding, rain-splash, depth-dependent creep, or overland flow. Other transport laws have therefore been proposed. These laws, still based on the process/form principle, state that transport rates depend non-linearly on local slope, on depth of soil movement and/or on drainage area or overland flow discharge. Some authors have proposed new parameterisation of soil transport which involves several processes, i.e., in which soil transport on slopes results from the combination of multiple geomorphic transport laws.

Considering no aeolian input nor significant loss by dissolution, the local rate of soil thickness change, \(\delta h/ \delta t\) (m/yr), is determined by the balance between soil production and soil transport:

\[\frac{\delta h}{ \delta t} = P_s - \nabla \cdot q_s\]

where soil thickness \(h\) (m) is measured vertically, \(P_s\) is the rate of bedrock weathering or soil production (m/yr), \(q_s\) is the total downhill soil flux, and \(\nabla \cdot\) is the spatial divergence operator.

Soil bulk (dry) density of most soils varies within the range of 1.1-1.6 g/cm3, while the density of soil particles (i.e., the bedrock weathered material) has a short range of 2.6-2.7 g/cm3 in most mineral soils. A value of  \(\simeq 2\) is therefore acceptable.

The local rate of surface elevation change, \(\delta z/ \delta t\) (m/yr), is related the rate of soil thickness change:

\[\frac{\delta z}{ \delta t} = \frac{\delta h}{ \delta t} - P_s + U\]

where \(U\) (m/yr) is a source term that can either represent the rate of incision of channel streams at the hillslope boundaries or uniform uplift.

Fig. 23 From CLICHE model (Bovy, 2012) snapshots of a specific simulation under Pleniglacial conditions (after 100 kyr of simulation, left hand-side) and present-day conditions (at the end of the simulation, right-hand side). A. Soil thickness. B. Local volumetric downhill soil flux (all processes). C-F. Contribution to the local downhill soil flux from transport by overland flow, simple creep, depth dependent creep and solifluction (unit-less). Note that the soil fluxes involved here are the averages over an entire elongated cycle in the simulation.

Simple creep

The parameterisation of soil transport used here includes the widely-used transport law which states that transport rate depends linearly on topographic gradient. This law—here termed as simple creep has in fact been used to represent a variety of transport processes such as creep or rain splash.

Downslope simple creep is commonly regarded as operating in a shallow superficial layer. We write:

\[q_d = - \kappa_d \nabla z\]

Note that because of the multi-process parameterisation of soil transport, the coefficient \(\kappa_d\) is not necessary equivalent to the coefficient of diffusion-based models. Its value is also clearly scale-dependent.

Depth-dependent creep

Beside linear creep, a few field observations but numerous laboratory and modelling studies have supported depth-dependent, viscous-like flow of soil. The general expression for depth-dependent creep is given by:

\[q_{dd} = - \kappa_{dd} h^p (\nabla z)^l\]

Different authors have provided different values for the soil thickness and topographic gradient exponents. For example, Heimsath et al. (2005) used p = l = 1, although, generally, the velocity of soil displacement declines exponentially with depth. Due to a lack of constraints, Braun et al. (2001) have adopted values from Manning’s equation for liquid flow (p = 1.67 and l = 0.5). In most cases, p ranges from 1.5 to 2.0 and l ranges from 0.5 to 1.0.