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Interaction of armouring and particle weathering 1195

Copyright © 2006 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 31, 1195–1210 (2006)DOI: 10.1002/esp

Earth Surface Processes and LandformsEarth Surf. Process. Landforms 31, 1195–1210 (2006)Published online 3 August 2006 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/esp.1397

The interaction between armouring and particleweathering for eroding landscapesSaniya Sharmeen1,2 and Garry R. Willgoose1*1 School of Engineering, The University of Newcastle, NSW, 2308, Australia2 Ku-ring-gai Council, Locked Bag 1056, Pymble, NSW, 2073, Australia

AbstractThe interaction between particle weathering and surface armouring and its effect on erosionhas been investigated. The effect of soil armouring is to decrease sediment transport withtime by preferentially stripping away fine particles. On the other hand the effect of weather-ing, which breaks down the particles in the armour, is generally believed to increase erosion.By extending an existing armouring model, ARMOUR, and using a variety of publishedweathering mechanisms this interaction has been explored. The model predicts that whilethis is generally true, in some cases erosion can be decreased by weathering. When theparticles generated by weathering were approximately of equal diameter, erosion increasedwhile armouring decreased. When weathering produced very fine particles by spalling, ero-sion increased and armouring also increased. When weathering produced a range of particlesfrom fine to coarse, the armour layer broke down and erosion decreased relative to the no-weathering case. This latter decrease in erosion was due to the high entrainment of coarsertransportable materials from the bed decreasing the sediment transport capacity of the flow.In these studies clear regimes could be identified where erosion was limited by either theenergy of the flow alone (i.e. ‘transport-limited’), or the rate of weathering (‘weathering-limited’); however, for some mechanisms there was an interaction between the two, whichwe called ‘weathering/transport limited’. Copyright © 2006 John Wiley & Sons, Ltd.

Key words: erosion; weathering; landform evolution; armouring

*Correspondence to:G. R. Willgoose, School ofEngineering, The Universityof Newcastle, NSW, 2308,Australia. E-mail:[email protected]

Introduction

The long-term erosion performance of engineered landforms and subsequent containment of wastes is an outstandingenvironmental management issue for many industries generating potentially hazardous waste. The long-term perform-ance of rehabilitation structures is poorly understood. To evaluate the long-term performance of a rehabilitated minesite we need to know the temporal changes in the physical characteristics (and thus erosion) of the surface for periodsof up to 1000 years in the future (Willgoose and Riley, 1998). These physical characteristics, such as particle sizedistribution, are affected by (a) soil armouring as a result of fluvial erosion and (b) weathering. In this paper we ignorebiogenic effects such as the vertical mixing of soil particles by termites which are believed to be important on naturalsites in the region where our data have been collected (Paton et al., 1995). Rather we concentrate solely on two(important) components of the physical processes: armouring due to erosion, and armour breakdown due to surfaceweathering.

Soil armouring is the process of surface coarsening that occurs due to the selective removal of the finer transport-able materials from the soil surface by overland flow, leaving coarser, less mobile materials behind. As the finetransportable materials are progressively removed, the fine fraction of the soil becomes coarser and is more difficult toremove so that sediment transport decreases. If the flow continues with time eventually all fines are removed, a stablearmour layer is formed on the surface and sediment transport decreases to zero. This armour layer is at least one grainsize thick and protects the underlying material from being eroded if flow remains less than or equal to the armourforming flow (Proffitt, 1980). If a higher flow is applied the armour layer may be destabilized and a new, coarser,stable armour formed.

Received 24 June 2003;Revised 29 September 2005;Accepted 24 November 2005

1196 S. Sharmeen and G. R. Willgoose


By contrast, weathering is the process of physical or mechanical breakdown, and/or chemical alteration of rocks andminerals near the Earth’s surface. In this paper we consider the breakdown only of rock particles exposed on the soilsurface, not of any underlying bedrock. Surface weathering produces fine transportable materials that can potentiallybe removed by erosion (Ollier, 1984) and that are more in equilibrium with newly imposed physico-chemical condi-tions (Reiche, 1950; Ollier, 1984; Bland and Rolls, 1998). It occurs in place and does not directly involve movementof materials (Selby, 1982). The increasing availability of fine materials may subsequently increase sediment transport.Moreover, its effect on armouring may be that sediment transport no longer decreases to zero, a stable soil armourmay not form, and the maximum erosion rate may be limited by the weathering process’s ability to produce transport-able fines, rather than the energy of the overland flow.

The amount of fine materials produced by weathering depends on the weathering rate and characteristics of thebreakdown products. If weathering produces more fines than are needed to satisfy the transport demand of flow, thesediment transport rate will be ‘transport-limited’. By contrast, if the weathering produces less fines than are needed tosatisfy the transport capacity of flow, sediment transport will be limited by the ability to entrain fines and transportwill be ‘source-limited’. In this latter case soil armouring will occur. The rate of soil armouring in the presence ofweathering should also be inversely related to weathering rate.

While we can describe the interaction between weathering and armouring qualitatively, the quantitative effect,particularly on sediment transport, is poorly understood. In this paper we will quantitatively assess the effect of surfaceweathering on soil armouring. A quantitative understanding of this interaction will allow us to model the change inlong-term soil erodibility and erosion rates, an important component of predicting the long-term evolution of landforms.Because we have ignored biogenic effects we do not claim to fully model soil development, but only the interactionbetween armouring and weathering.

The Soil Armouring Model – ARMOUR

The soil armouring model ARMOUR (Sharmeen, 2000; Willgoose and Sharmeen, 2006) is used to simulate thedevelopment of soil armours caused by erosion. A simple weathering model of the armour particles is developed to (a)predict the amount of finer materials produced by weathering, and (b) modify the grading of the armour layer. Thismodified bed material grading is used in the ARMOUR model to estimate the sediment transport rate and subsequentarmouring and weathering. The ARMOUR model is described in detail elsewhere (Willgoose and Sharmeen, 2006).The description below concentrates on those aspects of the model of relevance to this paper.

The soil armouring model, ARMOUR, is a one-dimensional finite difference model in space and time that simulatessurface armour development down a hillslope. ARMOUR simulates erosion and deposition at each section for everytimestep. Sediment flux is estimated as a function of bed shear stress, τo, median diameter of the material in the water,d50f, slope, bed resistance and soil characteristics. The Shields stress is the threshold on sediment entrainment definingwhat range of particle diameters can be entrained into the flow. The transport capacity of the flow, qs, is given by (Grafand Suszka, 1987):

q

F

k g s d F F

k g s d

s

S

f Se

S

fe

( ) ( )

( )

=⋅ <⋅ − − < < ⋅

⋅ − > ⋅

−

− −

− −

0 0

10 4 1 0 068

10 4 1 0 068

1

503 1 1

503 1

ψψ ψ ψ

ψ ψ

(1)

where ψ −1 is the entrainment function (= τ γ0 501/[ ( ) ]s d f− ), e is the erosion non-linearity, k is the intrinsic erodibility,d50f is the median diameter of the material in the flow layer, g is the acceleration due to gravity and FS is the Shieldstransport threshold. An entrainment model describes the relative proportions of the soil size gradings that are entrainedinto the flow.

Three layers are modelled in ARMOUR: the flow, armour and subsurface parent material. The flow layer is thelayer in which suspended and bedload transport occurs. The armour layer is the upper soil layer, which interacts withthe flow by entrainment and deposition. The subsurface soil layer is a reservoir for the armour layer to (a) replenisheroded material or (b) store excess deposited material. The grading in each layer is modelled by dividing the sedimentinto discrete particle size fractions. These gradings allow modelling of the selective removal of the finer, moretransportable particles from the bed as a function of transport processes.

A range of entrainment processes can be used to estimate sediment entrainment from each size fraction. Inthis paper we use the hiding model of Andrews and Parker (1987) and Parker (1990) which models the relative ability



to be entrained as a function of how particles are exposed to the flow, i.e. the effect of hiding of finer particlesbehind the coarser ones. A previous study (Willgoose and Sharmeen, 2006) has shown this to be a goodmodel of sediment entrainment. The relative entrainment is parameterized by a hiding exponent β and rate α. Avalue of β = 0 implies perfect equal entrainability of sediments; β = 1 is size selective transport (Hoey and Ferguson,1994).

During deposition the model deposits materials at the maximum rate allowed by their settling velocity assuming auniform distribution of the sediment throughout the water column.

Using the amount of entrainment/deposition and the grading of the sediment, ARMOUR estimates the new armour,flow and subsurface layer grading calculating from the top node of the hillslope to the bottom. At any calculation nodeon the hillslope there is an interaction between the transport capacity (and thus the amount of erosion or deposition),the grading of the flow (itself a fraction of the grading of the sediment from upstream), and the entrained sediment.ARMOUR solves this non-linear interaction at each node by an iterative solver.

The input data required by the model are (1) the initial soil grading and specific gravity, (2) plot slope, width andlength, and (3) runoff hydrograph. The model process parameters are Manning’s n, intrinsic erodibility of the granularsediment k, erosion non-linearity e, armour depth, Shields shear stress entrainment threshold FS and hiding para-meters α and β. Manning’s n is required in the model for estimating flow depth, bed shear stress, sediment flux andthreshold particle size for sediment entrainment. It depends on the initial roughness of the bed and is not a functionof the changing armour grading during the simulation. The intrinsic erodibility k is a calibration parameter to adjustthe material erosion rate for a given bed grading to match erosion plot data. The erosion non-linearity e determinesthe non-linear dependence of sediment transport on changes in the bed shear stress. The Shields entrainment functionFS is the threshold for sediment movement and FS = 0·045 for non-cohesive sediment (Graf and Suszka, 1987). Forcohesive sediment it is calibrated. The armour depth is considered constant in space and time, and does not interactwith the armour grading. The hiding coefficient α and exponent β control the size selectivity of entrainment and arecalibrated.

Mechanics of Weathering

This section describes the development of the weathering model used in ARMOUR.

Weathering processThere are three types of weathering processes (Bland and Rolls, 1998; Ollier, 1984; Trudgill, 1983): (a) physical/mechanical, (b) chemical, and (c) biological. While it is convenient to consider these three processes separately, it isworth remembering that all these processes usually operate concurrently, so that there may be interactions between theprocesses and it may be difficult to distinguish the contribution of each process separately. For example, (a) chemicalweathering may induce internal stress as a result of volume changes (e.g. hydration processes) hastening the physicalbreakdown process due to stress fracturing or (b) physical weathering produces fresh rock surfaces that are inchemical disequilibrium, enhancing chemical weathering.

Physical weathering. Physical weathering is the physical breakdown of rocks into smaller fragments with nochemical alteration. It produces materials with the same mineralogical composition as their parent materials andprovides fresh surfaces on which chemical and biological weathering can act.

Physical weathering is most important for large rock fragments and as the initial breakdown agent. This processnormally proceeds fastest near the Earth’s surface because of the greater climatic extremes (e.g. heating/cooling,wetting/drying cycles), and at lesser rates below ground. It breaks down the coarser fragments into fine fragments thathave á higher specific area (surface area per kilogram of sediment). At some point in time when fragments are small(so specific area is large) chemical weathering starts to dominate.

Internal stresses, mainly tension, are the primary agent for this type of weathering. These internal stresses areproduced from forces that may: (a) originate within the rocks during temperature fluctuations, wetting and drying, orcrystallization of salts; (b) be applied externally during the creation of landforms; or (c) originate from stress unload-ing due to the removal of overlying rock.

Chemical weathering. Chemical weathering is the chemical alteration of the minerals in the rock. It produces newminerals, which are chemically more stable or nearer to equilibrium with the physico-chemical conditions of theEarth’s surface. Some of these new minerals are soluble and physically removed from the environment by soil waterleaching and soil erosion. Others are insoluble and may change volume, inducing internal stresses or collapse of thecrystal lattice to hasten disintegration of the rock by physical weathering.



Biological weathering. Biological weathering is the effect of plants, animals and bacteria. Biological weathering isoften not the immediate cause of rock and mineral breakdown. Rather it creates an environment that often facilitatesphysical and chemical weathering. For example the contribution of animals to weathering is repeated mixing of soilmaterials, exposing fresh material to air and water. Organic matter assists rock and mineral breakdown, normally atlower depths, by (a) exerting physical stress through the expansion and contraction of plant organic tissues duringwetting and drying, and/or (b) emitting substances (e.g. CO2, complexing agents, organic and inorganic acids).

Biological weathering may also assist physical and chemical weathering processes by (a) changing soil moisturecontent through root extraction and humus, (b) changing ground temperatures through shading provided by plants orthe production of heat during fermentation process, (c) transporting or relocating materials into zones of differentweathering agent, and/or (d) protecting materials from erosion, both water and wind erosion, reducing the exposure ofnew surfaces and reducing weathering (Ollier, 1984).

Weathering propertiesOur specific interest in weathering is determining the rate at which soil/rock fragments change and generate fines withtime. There are two properties that determine the amount of materials produced by weathering: (a) its rate, and (b)variation with depth in the soil.

Weathering rate. The weathering rate is the amount of breakdown or alteration of rock from its original state perunit time (Bland and Rolls, 1998) and depends on material properties (e.g. thermal conductivity, coefficient of thermalexpansion), the environment (e.g. climate, topography), soil water chemistry, and time.

Determining the weathering rate is difficult. The variability of Earth materials and environmental conditions, to-gether with the shortage of dated events in recent Earth history create problems in determining rates of naturallyweathered materials from field-based studies. In contrast, laboratory experiments, though easy to control and monitor(e.g. change of mineralogy, surface area), have difficulty replicating field conditions. Furthermore, experiments areperformed over a limited duration and consequently highly concentrated experimental solutions are often used asweathering agents in an attempt to accelerate chemical weathering processes.

Two types of studies have been reported: (1) field measurements of the amount of material removed within a setperiod of time (e.g. Corbel, 1959; Groom and Williams, 1965; Pentecost, 1991); and (2) the probability of breakdownof rock fragments under different conditions of applied stress (e.g. Manning, 1936; Gaudin and Meloy, 1962; Klimpeland Austin, 1965; Robertson et al., 1997). The two types of experiments measure different types of weathering. Thefirst type is representative of chemical weathering and/or physical weathering that occurs due to wearing or spalling ofparticles. The second type is representative of the physical fracturing of rock fragments. Weibull statistics are com-monly used to characterize the probability of a rock fragment breaking. The Weibull distribution implies that theprobability of a particle breaking decreases with decreasing size. The rationale for this is that smaller particles containfewer flaws.

Weathering depth. The weathering depth is ‘the vertical extent of a weathered rock sequence from the initial landsurface or originating surface down to unweathered parent rock’ (Senior and Mabbutt, 1979).

It is difficult to estimate the average depth of weathering of an area. Consequently, many researchers have tried todetermine only the maximum depth: 100 m in Nigeria (Thomas, 1965) and Uganda (Ollier, 1960), 45 m in Queens-land, 300 m in New South Wales, 80 m in Victoria, and 40 m in Western Australia (Ollier, 1965).

The weathering depth depends on the environment, climate and topography. For instance a shallow weatheringdepth is generally found on steep hillslopes and a greater depth on gentle hillslopes (Norton and Smith, 1930; Hadleyand Toy, 1977; Brunsden, 1979). It may be only a metre in temperate regions, but tens of metres in the tropics(Strakhov, 1967; Bland and Rolls, 1998). There are some exceptions to this rule with deep weathering profiles in non-tropical areas, like Germany and Dartmoor, which Ollier (1984) asserts is a result of historical tropical climateprevailing in the Tertiary, not the current-day climate.

Weathering products and fracturing mechanismsOur specific interest in this paper is the evolution of the particle size grading as a result of weathering processes andthe particles generated that are potentially transportable by erosion. Accordingly, we ignore weathering processes thatresult in dissolved products (e.g. leachate) except where the dissolution process leads to a change in the transportabil-ity of the particle by erosion. This could occur, for instance, by a reduction in the diameter of the particle or by areduction of the particle density due to extensive pitting.

Physical weathering produces small particles having the same mineral compositions as their parent materials.The breakdown mechanisms of particles are either: (a) from the weathering rind around the periphery – spalling



Figure 1. Breaking of a particle from a weathering rind along with the size of the fragmented particles (for do > 2dw).

(Figure 1); or (b) along the cracked surface – body fracture (Figure 2). The first mechanism is typical of the wearingof particles due to abrasion and the spalling of particles as a result of excessive tensile stress within a thin layer closeto the particle surface due, for instance, to large temperature fluctuations in a short time (e.g. during bush fire). Thesecond mechanism more typically results from diurnal temperature fluctuations or salt crystallization where repetitiveexpansion and contraction create cracks and rocks gradually split along the cracked surface. The smallest particlediameter that can break is about 0·02 mm with smaller particles being unlikely to fail by physical weathering (Ollier,1984; Kuenen, 1960).

The products of chemical weathering are soluble compounds, new precipitated gangue materials (e.g. clay minerals,oxides and hydroxides), and residual unweathered materials (e.g. quartz and gold). Particles are produced by (a)disintegration of a single particle into a number of smaller particles (Figure 3a), (b) dissolution of a particle by pittingof the surface (Figure 3b), and (c) dissolution of a particle by etching of the surface (Figure 1) (Lerman, 1979).

The Weathering Module in ARMOUR

The numerical modelThe weathering module in ARMOUR was developed to estimate the breakdown of armour particles into smallerparticles. The module explicitly simulates the breakdown of a particle of a given size into a number of product

Figure 2. Breaking of particles along the cracked surfaces.



Figure 3. Breaking of a particle into smaller particles (a) by disintegration and (b) by pitting of the surface.

particles, each with specified properties (e.g. diameter, see Figures 1 and 2). A particle has a probability of breakingper unit time of Pf. The weathering rate is then a function of the mean time scale Tf (= 1/Pf) of fracture of the particle.The weathering rate is assumed to be constant with time and depth in the weathering mantle. Only particles within theweathering mantle can fracture. Conservation of mass is applied during the fracturing process. The depth of theweathering mantle can be either equal to or greater than the armour depth. In this paper we assume that weathering depthis equal to the armour depth so that weathering occurs only in the armour layer and not in the underlying source material.

Two modes of breaking can be simulated. The particle may either (a) spall/wear/etch around the particle peripherygenerating one large particle and a number of fine particles (Figure 1) or (b) they may split into a number of particleswith specified sizes (Figure 2). No particle breaks if its diameter is less than 0·02 mm.

Fracture modesType I: spalling. In this mode particles break from a weathering rind of depth dw around the periphery of the parentparticle (Figure 1). The thickness of the weathering rind dw is input (in mm) and assumed to remain constant with timeand with the diameter of the parent particle.

The fragmented particle size is a function of the parent particle size do and volume Vo is estimated according to thefollowing.

• If do > 2dw (Figure 1), the diameter of the fragmented particles will be dw and the residual particle will be (do − 2dw).Nbr fragmented particles are generated.

• If 0·02 mm < do < 2dw, the parent particle will break into two equal pieces (Nbr = 2) with the fragmented andresidual particle volume Vo /2.

• If do < 0·02 mm, the particle will not break (Nbr = 1).

The number of generated fine particles, Nbr, is such that the generated fines have a total mass equal to that of therind around the original particle.

Type II: body fracture. In this mode the parent particle with diameter do splits into a number of smaller particleswhose size and number are estimated according to the following.

• Type IIa: the parent particle, volume Vo, splits into equal sized Nbr particles with volume Vo/Nbr (Figure 2). Thevalue of Nbr can either be input or can be a function of parent particle size (Lerman, 1979):

Nd

dbr

o

a

min

=

1

(2)

where a1 is a positive constant that increases with decreasing size of the fragmented particles, and dmin is theminimum size of particle that can break (= 0·02 mm) (Ollier, 1984; Kuenen, 1960). We assume that a1 is between0·1 and 0·35.

• Type IIb: the parent particle, volume Vo, splits into Nbr particles with a range of sizes according to (Lerman, 1979):

V

N N

V

N N N

V

N N N io

br br

o

br br br

o

br br br

1 1 1

1

1 1

11,

, . . . , . . .

. . . +

−

+ +− +

+ +

(3)

Like Type IIa, the value of Nbr can either be input or can be a function of parent particle size using Equation 2.



Table I. Value of the best parameter set of ARMOUR for the Rangerdata

Parameter Value

Erodibility k 0·0044Erosion non-linearity e 3·238Manning’s n 0·103Armour depth da (mm) 34·7Hiding coefficient α 0·045Hiding exponent β 1·102

Armouring Parameters

This study has been carried out for the non-cohesive stony metamorphic spoils of the Ranger Uranium Mine, NorthernTerritory, Australia. The armouring and transport parameters were calibrated in a previous study to data collected fromfield runoff–erosion plots (Sharmeen, 2000; Willgoose and Sharmeen, 2006).

The area of the study plot (plot1) was 113·5 m2, length 24 m, average width 4·7 m and average slope 2·1 per cent.The land surface is covered by a stony metamorphic spoil with specific gravity 2·65, size range 0 –19 mm, mediandiameter 3·3 mm. It included around 33 per cent of materials in the range 0·187–2 mm and 61 per cent in the range2–19 mm. In the computer simulation the plot was divided longitudinally into six sections, each 4 m long.

The input runoff series was estimated from the 18-year pluviograph record at Jabiru, located about 17 km southwestof Ranger, using a long-term infiltration rate of 6·5 mm h−1 for an unvegetated site (Willgoose and Riley, 1998). Theinitial infiltration rate was assumed to be zero, because all rainfall occurs in the wet season and the site can beassumed saturated before a rainfall event. These 18 years were repeated six times to generate 98 years of runoff data.

The erosion and armouring parameters adopted here are the best-fit results found by Willgoose and Sharmeen(2006) and reflect the rocky non-cohesive nature of the surface (Table I).

Weathering Parameters

The predominant spoil at Ranger is a schist that quickly weathers in the seasonally wet tropical environmentof Kakadu to produce a fine-grained material rich in clay (Riley, 1994). The weathering rate is increased bythe extreme environment, with day-time air temperatures regularly reaching more than 35 °C, rock temperatures ofup to 70 °C and yearly rainfall of around 1480 mm concentrated in four to five months of the year (Wells et al.2006a).

Weathering produces a large quantity of soluble materials, particularly MgSO4. The average solute concentrationsin runoff in the early phases of the wet season are often higher than 200 mg l−1 but decrease rapidly during thewet season (Riley, 1994). Riley explained this decrease as a combination of depletion of finer sediments, flushingof soluble materials, and a change in the chemistry of the weathering reactions. As the smaller particles wereeroded from the surface by the storm, the embedded rocks became exposed. Some of these exposed rocksweathered so rapidly that they broke down in one wet season. The solute concentrations on the minesite, as wellas the observed weathering rate, are several orders of magnitude higher than in the surrounding areas (Riley,1994).

During the dry season, the spoils were shattered by salt weathering, as salts accumulated on the surface of the spoilsduring wetting and drying with the early morning dew evaporating during the day. Hydration of clays and thermalexpansion and contraction of spoils have also been speculated to contribute to weathering. In summary, weatheringduring the dry season and in the inter-storm interval produces fine particles that accumulate on the top of theunderlying coarse rocks providing the source material for erosion.

Based on the observations of Riley (1994), we can summarize the dominant weathering processes at Ranger as:

• physical weathering: salt weathering, wetting and drying, and insolation weathering; this appears to be the domi-nant process;

• chemical weathering: solution, oxidation–reduction, and hydrolysis; this appears to be a second-order process.



Figure 4. Erosion rate for ‘no weathering’. From Sharmeen and Willgoose (2006).

Unfortunately we do not have the necessary information to quantitatively determine the rate or characteristics of thebreakdown products for weathering at Ranger. These studies are on going (Wells et al. 2005, 2006ab). The authorsbelieve, however, that there is merit in a series of desktop studies that allow us to assess the relative importance of theparameters in the weathering model and explore the interactions between armouring and weathering. Specificallysome questions that can be explored are: (a) Which parameters need to be determined accurately and which do not?(b) Are there qualitative differences in erosion prediction for the various models that might be the basis of laboratoryor field experiments? (c) Is there a range of values of parameters outside which realistic behaviour cannot be found?(d) Are there testable hypotheses that might be used as a basis for field studies to distinguish the effect of differentweathering modes (i.e. Figures 1 and 2)? We will explore some of these questions in the following sections.

Weathering and Armouring Interactions

The long-term erosion characteristics of hillslopes depend on the armouring and weathering processes of the surface.In the absence of weathering at Ranger, the erosion rate decreases with time (Figure 4). We wished to explore how thisrate changes if the armour particles are allowed to weather, and investigated the effect of (a) weathering-limitederosion, (b) the particle fragmentation process, (c) the size of the fragmented particles, and (d) changes in weatheringrate.

Weathering-limited erosionWe first explored the concept of ‘weathering-limited’ erosion. To generate initial conditions a stable armour with zeroerosion was formed by running ARMOUR continuously with a runoff of 0·007 l s−1 for a long period of time with noweathering so that as the finer transportable sediments were removed the erosion rate decreased asymptoticallyapproaching zero (negative times in Figure 5); once the erosion rate was small the erosion rate was forced to zero byremoving all bed material below the Shields threshold size for sediment entrainment (range 0–0·111 m). Because ofthe prior armouring this could be done without significantly changing the median size d50a of the armour (d50a = 3·34 mm).The armour thus formed had a zero erosion rate for any discharges less than 0·007 l s−1.

After forcing zero erosion, the weathering model was turned on (positive time in Figure 5). The armouring com-ponent of the model was operational as before.

In the first experiment (Figure 5a) Type IIa weathering with each particle breaking into two equal-sized fragmentswas considered. Any erosion that occurred was limited by weathering. The erosion rate increased with increasingweathering rate (decreasing Tf) and remained well below the original transport capacity of the flow (0·016 mm h−1).Not all weathered particles could be transported because only the fragments below the Shields threshold diametercould be entrained into the flow. There is a transient period of about 20 hours during which fine material wasgenerated but before significant transport could occur. As noted by Willgoose and Sharmeen (2006), the entrainmentmechanism and transport are dominated by the finest fraction of the sediment, and its takes a little time before theweathering process can generate fine enough material for significant transport to occur.

The second experiment was designed to eliminate the effect of gradual fines generation on particle entrainment inExperiment 1 and used Type I weathering (Figure 5b). In this mode, all fragmented particles produced were small



Figure 5. Weathering-limited erosion: (a) Type IIa weathering, particles break into two equal pieces; (b) Type I weathering, particlebreak from the weathering rind of thickness dw 0·02 mm.

enough to be able to be entrained into the flow immediately if the weathering rate remained below the transportcapacity of flow. In this case, the erosion rate is equal to the weathering rate. This was observed for Tf less than 145(Figure 5b) when the erosion rate asymptotes to a value of about 2·6 × 10−6 mm h−1. For a lower Tf (≤145 s), theamount of fines produced by weathering was more than could be transported by the flow and the erosion was‘transport-limited’.

The asymptotic value with Tf for erosion in Figure 5b for Tf less than 145 reflects the grading of the sedimentgenerated by the weathering. If the particles were smaller, so that the transport capacity of the flow was higher, thenthe asymptotic value with Tf would be larger, and vice versa for larger particles. The characteristic of Type I weather-ing is that the particles generated are fine enough to be entrained as soon as they are created so do not act as a sourceto generate even finer materials, and that the grading of the weathering products is solely a function of the depth of theweathering rind. Since the weathering rind depth does not change with time, and the number and size of the armourparticles changes only slowly with time, then the amount and grading of the material changes only slowly with timeresulting in the asymptotic convergence with time of erosion seen in Figure 5b.

For Type II weathering the weathering process does not immediately generate fine transportable particles after onlyone generation of weathering, but requires several generations of breaking. Over time the potentially transportablesediments will become finer, until the sediments are fine enough that the transport capacity equals the weatheringprocess generation. Thus we see in Figure 5a the amount of erosion gradually increasing with time with no asymptoteduring the simulation. We did not run the simulations long enough to see the inevitable asymptote of transport-limitation which will occur for all cases when the rate of removal of fines by entrainment into the flow exactly equalsthe generation of fines by weathering. This balance between erosion and weathering must occur. If transport removesmore fines than are being generated, the transportable fraction of the armour will coarsen slightly and the transportrate will drop because the grading of sediment entrained into the flow will become coarser as coarser sediment isentrained. On the other hand, if entrainment removes less fines than are generated, the transportable fraction of thearmour will become finer and transport will increase. This balance between transport-limitation and weathering-limitation is thus a stable equilibrium to which the process will converge.

It is thus apparent that Type I and Type II weathering processes are fundamentally different in the way the transportcapacity and weathering process interact. The above experiments also indicate that the effect of weathering onarmouring depends on both the rate of weathering and the size distribution of the weathering products. In thefollowing sections we examine these dependencies in detail.

Effect of weathered particle size distributionWe investigate the effect of the weathering product particle fragment size distribution on erosion. The rate of particlebreakdown is the same in all cases, Tf = 1. Armouring parameters are the same as for the weathering analysesdiscussed above.

Type I weathering: spalling. The effect of spalling of particles on erosion was investigated for rind thickness dw fortwo cases: (a) 0·02 mm and (b) 1 mm (Figure 6). For both values of dw, the erosion rate decreased with time, as it didwhen there was no weathering (Figure 6a). While weathering does increase the erosion at any given time, surface



Figure 6. Armour layer characteristics for Type I weathering and Tf = 1 year: (a) erosion rate; (b) median diameter d50a (Type Iweathering: particles break from the weathering rind of thickness dw with size of the fragmented particles dw and residual particled − 2dw. Particles split equally if they are smaller than 2dw).

armouring dominates with erosion rates decreasing with time. The erosion rate for all cases was approximately thesame over the first ten years. As the finer materials were removed by entrainment the erosion rate decreased. Thisdecrease was less when weathering produced finer material. The decrease over 100 years was around 50 per cent whendw = 1 mm, 62 per cent when dw = 0·02 mm, and 66 per cent for the no-weathering case. At 100 years the results donot appear to be asymptoting suggesting this relative difference will continue beyond 100 years.

The median diameter of the armour layer d50a became coarser in all cases (Figure 6b). However, the weatheringcases produced a median diameter coarser than the no-weathering case even though for the weathering cases theerosion rate was higher. At first glance this appears contradictory because erosion rate should decrease with increasingarmouring. However, for small dw a large number of fines were produced with size less than dw, while the residualparticle size remained approximately the same as the parent particles (i.e. d − 2dw ≈ d ). The higher availability of thefiner particles of size less than dw increased their entrainment, decreased the mean diameter of material in the flow andthus increased erosion rate because sediment flux is proportional to d f

eoe

5015⋅ − τ , where d50f is the median diameter of the

sediment in the flow and τo is the applied bed shear stress. At the same time, the erosion of finer particles, produced byweathering, reduced the entrainment of coarse particles. Coarse particles therefore accumulated on the bed and d50a

increased more than for the no-weathering case.Type II weathering: body fracturing. The effect of Type II weathering was investigated for two conditions: (a) Type

IIa: a particle breaks into two or four equal-sized particles; and (b) Type IIb: a particle breaks into a distribution ofdifferent-sized particles according to Equation 3.

Particle breaks into equal sizes (Type IIa). As for Type I weathering, the erosion rate decreased with time(Figure 7a). The effect of weathering was again insignificant for the first ten years. With time, as the erosion ratedecreased, the differences between the weathering cases became more pronounced. For instance, over 100 years theerosion rate for Nbr = 4 decreased by around 41 per cent, for Nbr = 2 by about 56 per cent and for no-weathering byabout 66 per cent.

However, by comparison with Type I weathering, the armour layer was completely destroyed (Figure 7b) with thed50 of the armour trending back to that of the underlying material. As the splitting of particles into equal sizesproduced more small-sized particles, the armour layer grading became finer. This contrasts with Type I weatheringwhere the large particles remain relatively unchanged.

Particle breaks into a distribution of sizes (Type IIb). For Type IIb weathering two cases were considered: (a)particles broke into four particles (i.e. Nbr = 4); and (b) the number of fragmented particles was dependent on theparent particle size following Equation 2. In both cases when the particle breaks the subsequent fragmented particleshave the range of sizes given by Equation 3. This contrasts with the previous section where the fragmented particleswere all of the same size.

In case (a) the erosion rate was unaffected by weathering (Figure 8a). If anything, the erosion rate decreased slightlyfaster when Nbr = 4 compared with the no-weathering case. This occurred because more coarse transportable particleswere produced from this particular breaking pattern and the median size of the materials being transported by the flow,d50f, was increased. The increase of d50f, on the other hand, decreased sediment flux and thus erosion. This fasterdecrease was not observed for higher Nbr where fragmented particles sizes were smaller.



Figure 7. Armour layer characteristics for Type IIa weathering with equal fragmented particle size and Tf = 1 year: (a) erosionrate; (b) median diameter d50a (Type II weathering: particles break along the cracked surface).

While the erosion rate was independent of weathering, the variation of median diameter d50a of bed materialsshowed that the armour layer with weathering was finer relative to the no-weathering case (Figure 8b). This fining wasless pronounced than that for equal splitting of particles (Figure 7b). The conclusion is that the effect of weathering onerosion is less when fewer fines are produced by particle breakdown.

Effect of weathering rateFigures 9 to 11 show the relationship between breaking time Tf (i.e. the weathering rate Pf) on erosion for the threedifferent fragmentation processes examined in the previous section. Three breaking times Tf were considered: 1, 0·166and 0·0833 years. The shorter the time the faster is the weathering.

The general result from all the simulations is that the faster the weathering the higher the erosion. For Type Iweathering (Figure 9) with dw = 0·02 mm, the erosion rate increased sharply for the higher weathering rates evenduring the initial years and before armouring had any significant impact. This is because all of the weathering productparticles were small enough to be immediately transportable. All three rates showed an armouring effect with decreas-ing erosion rates over time. However, for the higher weathering rates this decrease appears to be asymptotic to a non-zero value. This suggests that the coarse particles act as a large reservoir that is the source of the fine transportablematerial; as weathering does not significantly deplete that reservoir of coarse material, the rate of generation of finesdoes not diminish with time. The non-zero asymptote is then the erosion rate as limited by the rate of generation oftransportable fines by weathering, that is, ‘weathering-limited’ erosion.

Figure 8. Armour layer characteristics for Type IIb weathering with increasing fragmented particle size and Tf = 1 year: (a) erosionrate; (b) median diameter d50a (Type II weathering: particles break along the cracked surface).



Figure 9. Effect of particle breaking time Tf on erosion rate: (a) dw = 0·02 mm; (b) dw = 1 mm (Type I weathering: particles breakfrom the weathering rind).

Figure 11. Effect of particle breaking period Tf on erosion rate: (a) Nbr = 4; (b) Nbr = ( / )d dminα1, where a1 varied randomly between

0·1 and 0·35 (Type II weathering with increasing fragmented particle size).

Figure 10. Effect of particle breaking period Tf on erosion rate: (a) Nbr = 2; (b) Nbr = 4 (Type II weathering with equal fragmentedparticle size).



For Type IIa weathering with splitting into four equal-sized particles (Figure 10b), the erosion rate increased withtime approaching a constant value, with the equilibrium erosion rate determined by the ability of weathering to delivermaterial (i.e. weathering-limited). When the particles broke into two equal pieces (Figure 10a), the effect was lesspronounced than for the four-particle case, where the generated particles were smaller in size. The erosion ratefollowed the same trends for the no-weathering case up to about 20 years at which time the weathering products werefine enough to be transportable. After 20 years the erosion rate gradually increased to a constant value. This behaviourwas more pronounced for higher weathering rates. Notably, for both the Type IIa cases the effect of armouring isoverwhelmed by the weathering process, to the extent that a coarse armour layer is not formed, with the surfacearmour becoming finer with time than the underlying material. This fining relative to the underlying material may bean artefact of the model restricting weathering to the armour layer only.

For Type IIb weathering (Figure 11) armouring was again the dominant process. An apparently anomalous result isshown in Figures 9b and 11a. In these cases the weathering process was generating a lot of transportable material onlyslightly smaller than the Shields threshold and this generated material was able to change the size distribution of thearmour to such an extent that the erosion rates actually decreased slightly in the presence of weathering.

Discussion

We have studied the effect of weathering on erosion in the presence of armouring over a 100-year simulation. In theabsence of field data to calibrate the weathering rate of particles, or the diameter and number of the fragmentedparticles generated by weathering, a desktop parametric study was performed to explore the range of behaviourspossible in the field. It is important to note that we do not claim that this paper models surface evolution processes inthe field at the Ranger field site because (1) in the absence of site-specific data we are using hypothetical weatheringrates and process pathways, and (2) we are ignoring other processes that are known to be occurring in the field, suchas vertical mixing of the soil by termites.

The study showed that the erosion rate in the presence of weathering was sensitive to both the rate at whichweathering occurs and the size distribution of the particles that are generated by the weathering process. There werealso subtle and surprising interactions between armouring and weathering that could result in anomalous trends inerosion rates with changes in the weathering processes.

Broadly the behaviours observed with increasing weathering can be classified into three kinds.(1) Increased erosion, coarser armour. This was observed when particles weathered with a spalling-like process.

Spalling produces very fine fragments with only small changes in the diameter of the parent particles. These fineswere highly mobile and available for transport and were entrained into the flow leaving the coarse armour particles onthe bed. The consequence was increased erosion due to the higher availability of fines, and increasing bed armouringbecause of the relatively unchanged size of the parent particles and loss of fines.

(2) Increased erosion, finer armour. This was observed when particles split into a number of particles of broadlysimilar sizes, all significantly smaller than the original parent particle. Erosion increased due to the higher availabilityof finer transportable material, and armouring decreased due to the splitting of coarse armour particles into finerparticles. In cases where the weathering rate was low relative to the transport capacity, the erosion rate asymptoticallyreached a constant value that was a function of the weathering rate and process. This state was interpreted as being‘weathering-limited’.

(3) Decreased erosion, finer armour. In this case the erosion rate when weathering was active was less than the casewhere no weathering was occurring. This was observed when breaking produced a greater number of coarse, buttransportable, armour particles. The higher availability of coarse transportable particles increased their entrainment,which in turn decreased armouring as well as decreasing erosion because of the coarseness of the transported sedi-ment. This effect was a transient effect observed until weathering produced more fines available for transport.

It is thus clear that both the weathering rate and size distribution of the particles are important. The spalling processthat generated a large amount of small transportable particles led to a very significant increase in erosion rates withvery little impact on the armour layer grading. The body fracturing process, on the other hand, which destroyed thecoarse armour particles in the process of generating the fines, resulted in destruction of the armour layer in the processof generating the fines.

The interaction between transport processes can be summarized as shown in Figures 12 and 13. Figure 12 is aplot of the asymptotic with time erosion rates from Figure 5a, so shows the relationship between erosion and weath-ering rates for spalling-like weathering. Figure 13 shows the asymptotic with time erosion rates from Figure 9a,so shows the relationship when body fracture is the dominant weathering process. The trend in these figures isdifferent.



Figure 12. Erosion rate as a function of weathering rate for Type I weathering.

Let us consider spalling first (Figure 12). For a low weathering rate (the left-hand end of the figure) the limitingprocess is the rate at which fines are generated by weathering, with the transport process being energetic enough thatit removes all fines generated. In this case erosion is ‘weathering-limited’. As the weathering rate increases, and therate of fines generation increases, a point is reached where fines generation is just balanced by the rate of entrainmentby overland flow. For even higher weathering rates, fines generation is greater than the ability to remove them andfines begin to accumulate on the surface. In this case erosion is ‘transport-limited’.

There is an abrupt change in process dominance with the erosion rate, shown by the kink in the trend line inFigure 12. This abrupt change occurs because spalling generates large numbers of very small particles, whose size isindependent of the weathering rate. With an increase in the weathering rate only the number of particles changes andnot their size, so the transport-limited capacity (a function of the grading of the sediment transported) does notsignificantly change with the weathering rate.

Weathering by body fracture is fundamentally different (Figure 13). In this case the size of the weatheringproduct particles is a function of the original particle size. Evidence of a long-term balance between weathering andtransport was seen (Figure 9). Figure 13 does not show a sharp distinction between weathering- and transport-limitederosion. In fact for this weathering process the erosion rate for a given weathering rate is a function of boththe weathering process and the erosional armouring process, and there is no weathering rate at which the erosion isdominated by weathering alone, or erosion alone. This is seen by the lack of a flat section of the erosion–weatheringrelationship for high weathering rates, and the lack of an abrupt switch from weathering-limited to transport-limitederosion. In fact, for low weathering rates the transport process is limited by the coarse nature of the weatheringproducts, while for high weathering rates erosion rates are higher because the weathering products are finer. The exactform of the relationship in Figure 13 is probably a function of the details of the mathematics of the processes wemodelled and the grading of the armour layer, but the general monotonic increasing trend with weathering rate islikely to be a general feature. We call this type of erosion ‘weathering/transport-limited’ reflecting the importance ofboth processes.

Figure 13. Erosion rate as a function of weathering rate for Type II weathering.



There were surprising interactions between the grading of the material being generated by the weathering process(primarily a function of the weathering process and the grading of the coarse non-transportable sediments) and thegrading of the armour. It was possible for the combined erosion and weathering process to generate a particle sizedistribution that was coarser than the pre-existing armour, but because there were more fines in the armour layeravailable for transport (i.e. exposed at the surface) the transport rate increased. It is clear then that the erosion processin a weathering-limited environment may be a complex mix of the entrainment of the sediment as a result of erosion,the grading of the armour, and the size distribution of the weathering products, as well as the actual rate of theweathering process.

Nevertheless, we were able to identify cases where the erosion rate was clearly dominated by the weathering rate,so that it might be called ‘weathering-limited’ and other cases where erosion was limited by the interaction betweenweathering and armouring. It was equally apparent that no universal weathering rate, defined here as the rate ofgeneration of transportable particles, can be determined, because that rate depends on the size distribution of thetransportable material (and thus on the weathering process and the grading of the coarse, less transportable fraction ofthe armour layer), and the size selectivity of the sediment entrainment in the sediment transport process.

One way of looking of this process might be to think of the armour layer as having two interactive storages.Conceptually, the first storage contains the particles that can be transported by the flow (i.e. are available for entrain-ment) and the second storage contains the coarser particles that cannot be transported by the flow. There is a flux ofparticles into the transportable fraction of the armour from the non-transportable fraction by weathering, and a flux ofparticles out of the transportable fraction of the armour layer by the flow entrainment mechanism. In this way it ispossible to speculate that an equilibrium size distribution can develop in the transportable fraction of the armour layer.It would then be possible to define a weathering-limited grading to the transportable fraction of the armour layer, andthus a weathering-limited transport capacity of the flow via the entrainment process. The second author is currentlyinvestigating this line of thought.

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