the effect of riparian tree roots on the mass-stability of riverbanks

THE EFFECT OF RIPARIAN TREE ROOTS ON THE MASS-STABILITYOF RIVERBANKS

BRUCE ABERNETHY* AND IAN D. RUTHERFURD

Cooperative Research Centre for Catchment Hydrology, Department of Geography and Environmental Studies, The University ofMelbourne, Parkville, Victoria 3052, Australia

Received 22 July 1999; Revised 25 November 1999; Accepted 3 December 1999

ABSTRACT

Plants interact with and modify the processes of riverbank erosion by altering bank hydrology, flow hydraulics and bankgeotechnical properties. The physically based slope stability model GWEDGEMwas used to assess how changes in bankgeotechnical properties due to the roots of native Australian riparian trees affected the stability of bank sections surveyedalong theLatrobeRiver.Modelling bank stability againstmass failurewith andwithout the reinforcing effects ofRiverRedGum (Eucalyptus camaldulensis) or SwampPaperbark (Melaleuca ericifolia) indicates that root reinforcement of the banksubstrateprovideshigh levels ofbankprotection.Themodel indicates that the additionof root reinforcement toanotherwiseunstable bank section can raise the factor of safety (Fs) fromFs = 1�0up to aboutFs = 1�6.The additionof roots to riverbanksimproves stability even under worst-case hydrological conditions and is apparent over a range of bank geometries, varyingwith treeposition.Treesgrowingclose topotential failureplane locations, either lowon thebankoron the floodplain, realizethe greatest bank reinforcement. Copyright# 2000 John Wiley & Sons, Ltd.

KEYWORDS: riparian vegetation; root reinforcement; bank erosion; bank stability; mass failure

INTRODUCTION

There is wide agreement that riparian plants influence the stability of riverbanks (e.g. Hickin, 1984; Thorne,1990; Abernethy and Rutherfurd, 1998), yet discussion of the role of vegetation in the physical processes ofbank erosion has largely remained general and speculative (but see Shields and Gray, 1992; Hubble and Hull,1996; Abam, 1997). In large part, the difficulty of including vegetation in analyses of riverbank erosion lies inthe modifications to bank hydrology, flow hydraulics and bank geotechnical properties that the plantsintroduce. As Thorne and Osman (1988) argue, these modifications are difficult to predict and are, therefore,hard to incorporate into bank stability analyses. That the effects of vegetation change with season and plantlife cycle further complicates the matter.Empirical studies have demonstrated clearly that alluvial channels supporting well-developed riparian

vegetation are deeper, narrower and migrate more slowly than their cleared counterparts (Andrews, 1984;Hickin, 1984; Hey and Thorne, 1986). However, the utility of applying these results to other rivers is limited.Predicting the influence of vegetation on channel change requires an understanding of both the underlyingmechanisms of bank failure and the pertinent mechanical features of plants. In this paper, we develop a modelof the influence of vegetation on the mass stability of riverbanks formed in cohesive material typical oflowland floodplain reaches.The shape and size of mass failures in cohesive riverbanks are controlled by the geometry of the bank

section, the geotechnical and hydrological properties of the bank material and the type and density ofvegetation. Although data are lacking to characterize all aspects of plant behaviour in respect of bank erosion,root reinforcement of bank sediments is arguably the most important way that vegetation enhances mass

Earth Surface Processes and LandformsEarth Surf. Process. Landforms 25, 921±937 (2000)

Copyright # 2000 John Wiley & Sons, Ltd.

* Correspondence to: Dr B. Abernethy, Sinclair Knight Merz, PO Box 2500, Malvern Victoria 3144, Australia. E-mail:[email protected]/grant sponsor: Land and Water Resources Research and Development Corporation

stability. However, inability to account adequately for the magnitude and distribution of root reinforcementremains a major limitation of riverbank stability analyses. This restrains their physical basis and predictivecapacity.Research into the role of vegetation in landslides and other slope stability problems has demonstrated that

even low root densities can provide substantial increases in shear strength compared to non-root-permeatedsoils (Wu et al., 1979; Waldron and Dakessian, 1981; Ziemer, 1981; Gray and Leiser, 1982; Greenway, 1987;Riestenberg, 1994; Schiechtl and Stern, 1996). However, riverbank failure mechanisms are quite different tothose found on hillslopes; riverbanks tend to be steeper and shorter, with a more varied profile. Assumptionsunderpinning hillslope stability analyses are not often met by typical riverbank failure mechanisms. Theposition of trees and their root distribution throughout the bank profile strongly influence riverbank failuresbecause of the relatively small size of the failure blocks. Unlike large-scale hillslope stability analyses, it isinappropriate to apply an average value of root reinforcement throughout a riverbank profile when assessingbank stability.Abernethy and Rutherfurd (in press) explored the distribution and strength of the roots of Swamp

Paperbark (Melaleuca ericifolia) and River Red Gum (Eucalyptus camaldulensis). That study measured theadditional root reinforcement that these two native riparian tree species lent to bank sediments at sites alongthe Latrobe River in Gippsland, Victoria, Australia (Figure 1). Here, we compare the stability of LatrobeRiver bank-sections with and without the reinforcing effects of tree roots under a range of natural bankconditions. We model bank stability with the generalized wedge method of slope stability analysis (Donaldand Zhao, 1995b), modified to include the additional strength of tree roots.

BANK STABILITY MODEL

There are numerous methods for analysing the stability of slopes (Duncan, 1992). Most methods adopt limitequilibrium procedures where a safety factor, Fs, is defined as the ratio of the stresses resisting failure to thestresses required to bring the slope into a state of limiting equilibrium along a given failure surface:

Fs � s

��1�

where s = shear strength of the soil and � = shear stress acting along the failure surface. In this case, thedriving stresses result from the downslope component of the weight of bank material. The Mohr±Coulomb

Figure 1. Latrobe River field sites

Copyright # 2000 John Wiley & Sons, Ltd. Earth Surf. Process. Landforms 25, 921±937 (2000)

922 B. ABERNETHY AND I. D. RUTHERFURD

failure criterion describes the shear strength of a soil:

s � c� � tan� �2�

where c = soil cohesion, � = total stress normal to the shear plane and tan� = coefficient of internal friction.Soils reinforced by plant roots behave as composite materials in which elastic roots of relatively high

tensile strength are embedded in a matrix of relatively plastic substrate (Gray and Leiser, 1982). Thecontribution to soil shear strength from the intermingled roots of plants can be considered as an additionalapparent cohesion, cr (Waldron, 1977; Wu et al., 1979; O'Loughlin and Ziemer, 1982). Roots have anegligible influence on the frictional component of soil strength (Gray and Leiser, 1982). When water ispresent in the soil, and steady downslope seepage conditions prevail, the total normal stress is replaced by aneffective stress (�ÿu) where u is the pore-water pressure (Fredlund, 1987). Accounting for the effect of rootsand pore-water pressure, soil shear strength is described by:

s � c0 � cr � ��ÿ u� tan�0 �3�

where the primes denote effective stress parameters. (All units are kPa.)Although the various facets of limit equilibrium theory are well known (Duncan, 1992), all stability

analyses exhibit some deficiencies and difficulties in application. Most analyses are based on some form ofthe method of slices but some use multiple wedge analyses (e.g. Sarma, 1979, 1987). Conventional verticalslice methods such as those used by Morgenstern and Price (1965), Spencer (1973), Janbu (1973) andFredlund and Krahn (1977) are generally regarded as the best available for stability analyses, but they will notnecessarily produce a kinematically admissible failure mechanism. Often, these methods result in unbalancedforces and moments so that equilibrium conditions are not strictly satisfied (Donald and Zhao, 1995b).According to Donald and Zhao (1995b), the generalized wedge method (GWEDGEM) fully satisfies force

and moment equilibrium while maintaining a kinematically admissible failure mechanism. The slip mass isdivided into several wedges where the inter-surface between any two wedges is not necessarily vertical. Shearstrengths on the interfaces are mobilized to the same degree as on the slip surface.Various multivariable unconstrained search routines are included in GWEDGEM for the selection of

critical failure mechanisms. The failure mechanisms may be any multilinear shape. In addition, the user mayspecify homogenous or non-homogenous materials, partial submergence, external loading, tension crackingand pore-water pressures (Donald and Zhao, 1995a). Pitsch (1997) compared GWEDGEM with a number ofwell-known slope stability models. She concluded that GWEDGEM gave results at least as good or betterthan previously recognized accurate methods.

Model parameters

Data to describe model parameters were collected at sites along the lower Latrobe River near Rosedale(Figure 1). The lower Latrobe River has a sinuous channel about 30 m wide and about 5 m deep, with a lowgradient and extensive meanders formed in resistant fine-grained banks with a sand bed. The river flowsalong an alluvial ridge with steep natural levees, flanked by a broad floodplain that contains numerous cutoffmeanders and avulsed palaeochannels (Bird et al., 1979). The bankfull discharge of the Latrobe River at theRosedale gauge (Figure 1) is 100m3sÿ1, while the flood of record occurred in December 1934 with anestimated instantaneous peak discharge of 3505m3sÿ1 (Reinfelds et al., 1995).Reinfelds et al. (1995) provide a full description of the river and document a long history of human

intervention, beginning in the 1890s with snag removal, riparian clearing and artificial cutoffs. Mass failureof the banks is quite common through the study reach (Figure 1) occurring over a range of bank geometries.Current management of channel instability is to spot-treat failed bank sections with rock riprap along withwidespread planting of endemic riparian species.Observations of bank failure through the surveyed reach indicated that shallow sliding occurred over a

range of bank heights and angles. Some low, steep bank sections failed as a toppling slab while the higherbanks tended to fail by either deep-seated rotation or translation. Thorne's (1982) description of toppling slab


EFFECT OF TREE ROOTS ON BANK STABILITY 923

failures includes separation of the block from the intact bank by a vertical tension crack. Field observationindicated that tension cracks were most likely to occur at sites with depleted vegetation cover. However,isolating the influence of vegetation on tension cracking from other bank stability factors is difficult owing tothe highly variable effect of roots on the tensile strength of soil (Pizzuto, 1984).GWEDGEM can account for tensile stress in the upper-bank profile but we excluded this effect from all

stability simulations. With no data to constrain the problem, assessing the stability of banks prone to tensioncracking after the introduction of vegetation relies heavily on the assumption that root reinforcement negatestension crack development. Because we were unable to verify the effects of root reinforcement on tensioncracking, we could not apply such an assumption with confidence. Consequently, later stability predictions ofbare banks, where tension cracking is likely, may be somewhat overestimated and improvements in bankstability with the addition of vegetation may be somewhat underestimated. However, our analyses do accountfor root reinforcement with respect to shear strength, hydrostatic confining and pore-water pressures, bankmaterial properties and natural bank geometries.Root reinforcement. Because of their riparian association and their history in bank stability work, we

elected to investigate the bank-reinforcing properties of Swamp Paperbark (Figure 2) and River Red Gum(Figure 3). The two species provide a contrast in size and in distribution within the riparian corridor.Swamp Paperbark is a wetland species found throughout southeast Australia, widely occurring on the

lower portions of riverbanks. Because the seedlings remain flexible, their establishment is assisted by layingover during floods followed by a quick recovery as the river stage drops. In its mature form, SwampPaperbark is an erect shrub or small tree that suckers freely from the base to form dense, multistemmedthickets (Costermans, 1989; Holliday, 1996). Stands are typically dome-shaped with stems ranging in heightfrom 0�5 m on the fringe to 10 m in the centre.River Red Gum is found along, or near, almost all of the seasonal watercourses in arid and semi-arid

Australia and most streams and rivers in the southeast (Jacobs, 1955). However, River Red Gum seedlings are

Figure 2. Swamp Paperbark



sensitive to flooding in the first two years and the tree is found higher up the bank (Dexter, 1978), usually onthe bank top along the Latrobe River. Boland et al. (1989) describe the tree as medium-sized, commonlygrowing to 20 m tall and occasionally exceeding 45 m. The crown is large, in open formation, and the treeusually has a short thick bole.In another paper (Abernethy and Rutherfurd, in press) we assessed the root reinforcement of a mature River

Red Gum and Swamp Paperbark stand at sites on the Latrobe River (Figure 1). We mapped the size andlocation of all roots intersected by a number of vertical profile walls (BoÈhm, 1979) dug into the banksediments at various distances between the tree trunks and the canopy driplines. We measured the tensilestrength of individual roots in the laboratory and in the field, and we assessed root anchorage in the bankmaterial. Applying these data to a simple model (adapted from Wu et al., 1979) we estimated the magnitudeof root reinforcement for each 10 cm increment of depth at each profile wall:

cr �P

niaiti

Aw

�4�

where Aw = the area of the profile wall increment, ni = number of roots, ai = average cross-sectional area ofroots and ti is the tensile strength of roots in size-class i intersected by Aw.This technique produced an array of discrete cr values that defined root reinforcement at particular

distances, C, from the tree trunk (m) and depth, D, below the soil surface (m). Fitting a simple linearregression through the log-transformed cr data of each species yielded the following expressions of rootreinforcement (kPa). For River Red Gum:

cr � e4920ÿ0099Cÿ1333D R2 � 0 � 70 �5�

Figure 3. River Red Gum



while for Swamp Paperbark:

cr � e4769ÿ0540Cÿ1891D R2 � 0 � 63 �6�

Distance away from the trunk is always measured parallel to the bank surface, while depth is measurednormal to the bank surface.The two marked portions in Figure 4 indicate circumstances where the bank geometry precludes an explicit

definition of cr based on C and D. Points within the area A are defined by two possible coordinate pairs.Where points are defined by more than one coordinate pair the model calculates all potential values of cr andthen, for the sake of conservatism, sets the lowest value of reinforcement for that point. In circumstancesdescribed by the area B, no value of cr may be set, as C and D cannot be defined. Here the value of C at theinflection point is applied across the entire area while D is calculated along the axis that originates at theinflection and bisects area B.The root networks of River Red Gum and Swamp Paperbark are severely curtailed by the presence of

permanently saturated bank material. For modelling purposes, we set cr to zero wherever permanentlysaturated material occurred. We considered any point in a bank profile below the level of the summer baseflow to be permanently saturated and therefore not reinforced by roots. The gauge record at Rosedale (Figure1) indicated that the average February daily baseflow stage was 0�8 m above gauge-zero, which we set for allcross-sections.Other growth habits of Swamp Paperbark also dictate root distribution. Our observations of Swamp

Paperbark stands along the Latrobe River indicated that they grow up and over the bank from the channel(Figure 2). Typically, they cover the whole bank face from about the summer baseflow level to about 1 monto the floodplain. To reflect the distribution and strength of the roots under the stand, we set C to zero soroot reinforcement varied only with depth. Beyond the stand cr remained a function of both depth anddistance from the trees.Pore-water pressure. There is much anecdotal and published evidence to suggest that bank failures are

associated with periods of prolonged rainfall followed by drawdown of river stage (e.g. Twidale, 1964). Atsuch times, the strength of bank material is minimized and its weight maximized. Positive pore-waterpressures may also be produced which further weaken riverbanks. The Rosedale gauge record documents 18overbank floods where, on the falling limb of the hydrograph, the stage continued to fall for at least sevendays after it had dropped below bankfull. Decreases in stage following the floods ranged from 0�6 m to 2�6 min seven days.For the purposes of worst-case stability analysis, we assumed that the maximum seven-day flood recession

(2�6 m) represented maximum channel drawdown. Moreover, to represent the most critical bank hydrologyconditions during drawdown, we adopted a conservative groundwater configuration whereby the entire

Figure 4. Coordinate system to determine root reinforcement (cr). In area A, cr is calculated for both pairs of coordinates (C, D1 andC, D2)with the smallervalueadopted.NeitherD2norD3 intersect areaB, socr is calculatedwithC set to thedistanceof the inflectionpoint fromthe

trunk while D is measured along the axis that originates at the inflection and bisects the shaded area



riverbank below the bankfull stage level remained saturated. Under this regime, positive pore-water pressuresare developed throughout the profile. We assumed (after Morgenstern, 1963) that there was no dissipation ofpore-water pressure in the saturated bank following drawdown.To avoid overly detailed analysis of pore-water pressure, Bishop (1954) found that it was convenient to

express pore pressure as a function of the major principal stress. Although principal stress directions varyalong a potential slip surface, the vertical head of soil and water above any soil element is an adequateapproximation of the major principal stress. During force-equilibrium calculations, GWEDGEM determinesthe water force on any potential slip surface by quadratic integration of control points along the slip surface.The control points are interpolated from a pore pressure grid that we defined for points below the groundwatersurface (see Donald and Zhao, 1995b p. 6). We set all pore-water pressures in bank material above thegroundwater surface to zero. The free water weight in the channel is automatically transferred to hydrostaticpressure acting on the bank.Bank material. For our purposes, it was enough to describe the geotechnical properties of the bank material

in terms of its constituent particle-size fractions, bulk unit weight and shear strength. We collectedundisturbed samples from a range of soil depths at both field sites (Figure 1) and returned them to thelaboratory for analysis.Particle-size analysis indicated that the material of both sites was a silty loam with little variation in

particle-size distribution with depth through either of the profiles (Abernethy, 1999). The median particle sizedistribution of the samples was 21 per cent clay, 62 per cent silt, 16 per cent sand and 1 per cent gravel. Theaverage saturated bulk weight of the material, s, was 18�3 kN mÿ3.Slow (drained) direct shear tests of undisturbed saturated samples indicated that the effective strength

parameters of these sediments are c' = 15 kPa and �' = 16�. Owing to the lack of variation in the sediments wetested, we treated the soil strength parameters as uniformly distributed throughout the bank profile(Abernethy, 1999).Bank geometry. We analysed the stability of 24 bank profiles which had been previously surveyed in 12

channel cross-sections between the gauge at Rosedale and the River Red Gum site (Figure 1). Channelgeometries described by the cross-sections included straight sections and left and right meander bends with arange of bank angles and heights. The data were not specifically collected to assess bank erosion processes, sounstable bank sections may be under-represented in the data set. We numbered each section downstream withthe left and right bank profiles denoted by an L or an R, respectively.

Modelling procedure

The following paragraphs describe the process of combining bank geometry with bank material andhydrological properties, river stage data and root reinforcement to produce GWEDGEM assessments of bankstability. We set bankfull stage to the lowest bankcrest of each cross-section and set baseflow at 0�8 m abovethe lowest point in the bed. The location of points within the pore-water pressure grid is not constrained by theprogram, so we ensured that there were sufficient data points to describe bank hydrology around the bank toeand face (Figure 5).Along with points that describe the bank profile and hydrology, GWEDGEM users are also required to

identify those coordinates that represent the bank-toe and the bank-crest. GWEDGEM then generates threetrial failure surfaces ±shallow, medium and deep ±covering the full range of possible critical failures; eachtrial consists of three wedges. Using the trial failures as a starting point GWEDGEM automatically searchesfor the location of the failure surface that returns the lowest safety factor. During this optimization process,the trial failure mechanisms typically converge to about the same position within the profile. The three-wedgefailure mechanism with the lowest Fs is subjected to further calculation and finer subdivision. Final failuremechanisms are typically composed of nine wedges.We applied the above optimization and refinement process to stability analyses of all surveyed bank

profiles with and without root reinforcement. In addition, we fixed the failure mechanism predicted undernon-reinforced conditions to compute a safety factor for the bank profile when that failure plane was directlyreinforced. For simulations of bank stability with root reinforcement, we positioned the trees in locationstypical of those observed near our field sites. In the following stability analyses, the River Red Gum trunk and



the upper extent of the Swamp Paperbark thicket are located 1 m from the bank-crest, on the floodplainsurface.

BANK STABILITY ANALYSIS

We assessed the safety of Profile 1L with no root reinforcement and maximum drawdown of channel stage(Figure 6). The default three-wedge failure mechanism predicts that the bank profile is stable with Fs = 1�82(Figure 6a). Dividing the default three-wedge analysis into nine wedges improves the prediction, yieldingFs = 1�75 (Figure 6b).Simulations with root reinforcement introduced to Profile 1L predict larger slump blocks with higher

safety factors than the bare case (Figure 7). Swamp Paperbark roots yield Fs = 2�13, River Red Gum rootsimprove the safety factor to 2�15. When expressed as a percentage of the bare Fs, the increase in bank stabilitydue to Swamp Paperbark roots is 22 per cent, while the River Red Gum root reinforcement produced animprovement of 23 per cent. Reinforcing failure plane `a' in Figure 7 with Swamp Paperbark and River RedGum roots improved bank stability by 34 per cent and 70 per cent, respectively.

Figure 5. Pore-water pressure grid as applied to Profile 1L (pore pressures are calculated for each point marked�, see text)

Figure 6. Stability analysis of Profile 1L with no root reinforcement and stage set to 2�6 m below bankfull: (a) three-wedge analysis,Fs = 1�82; and (b) nine-wedge analysis, Fs = 1�75



Stability of surveyed bank profiles

We analysed the stability of each of the 24 profiles in the same way as described for Profile 1L (Table I).Cross-section dimensions do not vary greatly through the reach, but there was quite a range in bank geometry.Bank angles ranged from 24� to 56� while bank heights ranged from 2�9 m to 5�5 m. Similarly, there was arange of safety factors with Fs under bare conditions ranging from 1�3 to 2�4. The mean Fs was 1�7.Not surprisingly, changes in stability were associated with changes in bank geometry. GWEDGEM tended

to predict lower safety factors for the higher and steeper banks (Table I). We confirmed this through simplelinear regression of bank geometry against factor of safety. The factor of safety decreased with eitherincreased bank height:

Fs � 2 � 69ÿ 0 � 25H R2 � 0 � 45 �7�

Figure 7. Comparison of bank stability (Profile 1L)with differing root reinforcement: (a) failure plane for bare bank,Fs = 1�75; (b) failureplane with bank reinforcement due to Swamp Paperbark roots, Fs = 2�13; and (c) failure plane with bank reinforcement due to River RedGum roots, Fs = 2�15. Reinforcing failure plane a (no optimization) with Swamp Paperbark yields Fs = 2�26 and with River Red Gum

Fs = 2�74. For ease of interpretation, only the failure planes are shown

Table I. Comparison of the stability of surveyed bank pro®les with and without root reinforcement*

Cross-section Left bank Right bank

Opt. Fixed Opt. Fixed

No. Width(m)

Depth(m)

�(�)

H(m)

BareFs

PB(%)

RG(%)

PB(%)

RG(%)

�(�)

H(m)

BareFs

PB(%)

RG(%)

PB(%)

RG(%)

1 31�5 4�2 38 3�9 1�75 22 23 34 70 36 3�6 1�87 14 23 23 482 33�6 4�2 47 3�4 1�78 78 86 97 109 23 3�3 1�98 22 35 39 553 27�2 4�6 40 4�0 1�62 11 11 27 37 29 5�5 1�66 13 29 20 424 32�5 4�2 31 3�6 1�82 11 12 15 15 49 3�1 1�52 16 18 28 365 34�0 4�7 35 4�0 1�78 65 44 88 116 56 4�5 1�28 20 28 29 546 30�0 4�8 34 3�1 2�01 72 79 98 136 50 4�0 1�72 18 35 96 1197 27�7 4�2 41 5�4 1�49 15 18 21 33 55 3�6 1�54 97 110 132 1758 24�2 4�3 45 3�3 2�02 11 28 17 35 37 3�1 1�83 17 13 31 609 36�4 4�4 53 5�0 1�25 15 22 57 63 27 2�9 2�40 40 51 62 7910 30�0 4�2 35 4�1 1�70 8 10 24 28 31 3�6 1�98 13 38 24 4811 29�8 4�4 47 4�9 1�31 9 12 12 16 44 4�4 1�58 66 91 84 11812 29�0 4�4 39 3�8 1�52 16 20 25 28 48 3�7 1�49 20 39 30 60

*Bare Fs represents the computed safety factor of the bank profile with no root reinforcement. The figures listed in the SwampPaperbark (PB) and River Red Gum (RG) columns represent the difference between the Fs computed with the appropriate rootmodel and the bare Fs expressed as a percentage of the bare Fs (i.e. percentage increase). Values are presented for failure planesoptimized to the root reinforcement conditions and for reinforcement of the fixed non-reinforced failure plane.



or bank angle:

Fs � 2 � 55ÿ 0 � 02� R2 � 0 � 49 �8�

or a combination of height and angle

Fs � 3 � 21ÿ 0 � 02� ÿ 0 � 21H R2 � 0 � 78: �9�

When we added root reinforcement to the profiles the association between bank geometry and stabilitydeclined. For Swamp Paperbark:

Fs � 4 � 39ÿ 0 � 01� ÿ 0 � 44H R2 � 0 � 35 �10�

and for River Red Gum:

Fs � 4 � 61ÿ 0 � 01� ÿ 0 � 46H R2 � 0 � 34 �11�

Regardless of the reduced correlation between bank geometry and stability, adding root reinforcementfrom either species increased the predicted Fs of all bank profiles (Table I). When the failure plane wasoptimized for Swamp Paperbark reinforcement, stability improved by 8 per cent to 97 per cent, with a meanincrease of 29 per cent. Without optimization, Swamp Paperbark roots improved the stability of the originalfailure plane by 12 per cent to 132 per cent, with a mean of 46 per cent. The model produced similar, butslightly greater, increases in Fs with River Red Gum root reinforcement. Optimized failure planes werepredicted as 10 per cent to 110 per cent more stable, with a mean of 36 per cent. Reinforcing the failure planefixed at that derived under bare conditions increased the predicted Fs by 15 per cent to 175 per cent, with amean of 66 per cent.Hickin (1984) pointed out that root growth through the whole depth of floodplain is a very strong

reinforcing mechanism. The results presented here bear this out and partly explain the range in additionalstability due to root reinforcement. Dividing the profiles into groups based on whether or not the bank toeremained below the summer baseflow allowed distinction between complete and partial reinforcement of thebank profile. Such a distinction highlighted marked differences in the stabilizing influence of the tree roots.Where the toe remained below the baseflow, and was not reinforced, the mean Fs was 1�65 (N = 17).Improvement to the stability of these profiles with the addition of roots was on average 15 per cent for theSwamp Paperbark and 22 per cent for the River Red Gum. For profiles where the toe was not covered by thesummer baseflow, the mean Fs was 1�83 (N = 7) and the average additional reinforcement was 62 per centfrom the Swamp Paperbark and 70 per cent from the River Red Gum.While reinforcement of the bank toe explains some of the range in the safety factor values, it does not fully

account for the weakened correlation between bank geometry and safety factor after the introduction of rootsto the profile. Allowing cr to vary directly with finer-scale profile geometry produces a complex pattern ofroot reinforcement. This pattern introduces variation in stability that is not explained by the gross measures ofbank geometry: height and angle as indicated by the regressions above. Certainly, this complicatedinteraction between plants and riverbanks is borne out by even casual observation in the field.

Bank stability after basal scour

By definition, the bank profiles analysed above must have had safety factors greater than unity as they wereall standing at the time of survey. Consequently, analyses of these bank sections do not demonstrate thestabilizing influence that tree roots impart to an otherwise unstable bank. Of the results presented in Table I,Profile 9L has the lowest predicted safety factor and hence is the bank profile that is closest to its critical statefor the given conditions. Altering the surveyed bank profile allowed us to simulate lateral or vertical fluvial



erosion such that the non-reinforced bank stability (Fs = 1�25) was reduced to critical (Fs = 1). We theninvestigated the reinforcing effects of the tree roots on this unstable bank profile.Lateral scour. Profile 9L was surveyed on an outside bank of a right-hand meander bend. Simulating lateral

toe scour by simply moving the point representing the bank toe to the left causes the bank profile to steepen(Figure 8). Removing 2 m of bank at the toe increased the bank angle from 53� to 70� and produced criticalbank stability. The height remained unchanged at 5 m.Root networks respond to whatever conditions exist at the time of their growth, in this case the pre-scour

profile. However, our model framework precluded a description of cr distribution with values of C and D

other than those specifically associated with the bank profile under analysis. Hence, cr was somewhatartificially distributed by the post-scour bank geometry. This caveat notwithstanding, the roots of bothspecies improved stability, as expected (Figure 8, Table II). This result accords well with our observations ofbank failures in the field where degraded vegetation cover is typically a prerequisite for deep-seatedrotational or translational failure. However, oversteepening is not the only process responsible for reducingbank stability on the Latrobe River; undercutting leading to cantilever instability also produces bank failure.While undercutting is beyond the scope of GWEDGEM, simulations of further lateral scour of the profile

(beyond that depicted in Figure 8) indicate that root reinforcement will stabilize the bank at any angle, up tovertical, given the bank height of 5 m. While we have witnessed undercuts on well-vegetated banks in otherparts of the river, we are unsure of the extent of undercutting through the study reach. Flow obscured thelower portions of the banks during each of our field inspections. In addition to undercutting, bed scouradjacent to the bank may also cause bank destabilization owing to an increase in bank height. Reinfelds et al.(1995) report that bed lowering, particularly downstream of meander cutoffs, has led to substantial bankinstability along the Latrobe River.Vertical scour. To simulate bed scour, we lowered the level of the points representing the bank toe and the

riverbed adjacent to the bank. Bed scour of 1�3 m increased the height and angle of Profile 9L to 6�3 m and59� and produced critical stability conditions in the bank (Figure 9, Table II). Reinforcing the altered bankprofile with Swamp Paperbark and River Red Gum roots improved bank stability by 43 per cent and 48 per

Figure 8. Profile 9L after 2 m of lateral toe scour. The broken line represents the old bank profile. Failure planes: (a) bare bank,Fs = 1�00;(b) bank reinforced with Swamp Paperbark roots, Fs = 1�37; and (c) bank reinforced with River Red Gum roots, Fs = 1�41

Table II. Summary of the effect of scour on the stability (Fs) of bank pro®le 9L

Prior to scour Lateral scour Vertical scour

Opt. Fix. Opt. Fix. Opt. Fix.

Bare 1�25 ± 1�00 ± 1�00 ±Swamp Paperbark 1�44 1�96 1�37 1�84 1�48 1�55River Red Gum 1�53 2�04 1�41 1�91 1�43 1�54



cent, respectively. The addition of root reinforcement to the bank section ensured that it remained stable evenwith ongoing bed scour adjacent to the bank. With a Swamp Paperbark stand established on the bank face, afurther 2�6 m of scour, beyond the initial 1�3 m, was required to reduce the safety factor to unity anddestabilize the bank. In the case of a River Red Gum established on the bank top, a total of 3�2 m of bed scourwas required before unstable conditions ensued.That we did not observe vegetated banks up to 8�9 m in the study reach requires some comment. One

explanation of the discrepancy might lie in our application of the summer baseflow. With no data to model theeffect of vertical scour on the baseflow stage, we simply allowed the summer baseflow to remain at 0�8 mabove the bed for all simulations. Actual conditions may provide for a higher baseflow in summer, whichmight prevent the roots from penetrating bank portions near the toe. An alternative explanation is that, incommon with the lateral scour simulations above, undercutting might contribute to bank instability beforevertical scour can overheighten the banks.An interesting result of the simulations described by Figure 9 and Table II was that the Swamp Paperbark

increased the safety factor more than the River Red Gum. When compared with the River Red Gum, theSwamp Paperbark stand produced a greater value of cr around the lower portions of the bank. This increase inreinforcement near the bank toe pushed the failure plane deeper into the bank profile. That Swamp Paperbarkstands can be established low on the bank, such that high root densities reinforce potential failure planes nearto the toe, bears out the local river management authority's faith in the species as a bank stabilizing agent.

Bank stability with changing tree position

The above River Red Gum analyses with the tree located 1 m away from the bank crest, while realistic andconvenient for comparative purposes, are limited.RiverRedGums are found all over the floodplain, sometimeseven growing on the bankface. The analyses shown in Figure 10 and Table III reflect the effect on bank stabilityof a mature River Red Gum growing at various points on the bank and floodplain. The bank geometry adoptedfor this analysis was Profile 9L with 1�3m of bed scour where Fs = 1 under bare conditions.With the introduction of the roots of a River Red Gum, all potential failure surfaces illustrated in Figure 10

(positions marked a to g) are deeper than the critical failure surface under bare conditions. Even a River RedGum some 15 m away from the bank crest is able to reinforce the bank sediments and stabilize the bank(Fs = 1�26). Clearly, however, the greatest improvement in Fs occurred when we positioned the tree at aboutwhere the predicted failure planes intersect the floodplain surface. The factor of safety returned by the modelfor the River Red Gum in position c was markedly higher than the other simulations (Fs = 1�61) and thepredicted failure surface was forced well into the floodplain. Modelling the effect of River Red Gumsestablished on the bankface also produced high safety factors owing to the increased root reinforcement at thetoe.

Figure 9. Profile 9L after 1�3 m of bed scour. The broken line represents the old bank profile. Failure planes: (a) bare bank, Fs = 1�00; (b)bank reinforced with Swamp Paperbark roots, Fs = 1�48; and (c) bank reinforced with River Red Gum roots, Fs = 1�43



DISCUSSION

While it may be possible to identify statistically averaged stable states, river morphology is ultimatelydependent upon the local processes of erosion and deposition. Predicting the magnitude and direction ofchannel change brought about by short-term erosion processes, such as bank failure, superimposed on theexisting planform requires an understanding of the underlying mechanisms of bank recession. Assessment ofthe channel boundary as influenced by vegetation provides further insight into those mechanisms. However, itis only in exceptional cases that changes in channel form are observed directly, so physically based modelshave increasingly provided geomorphologists a means of interpreting field research (Kirkby, 1997).Here, modelling allowed us to incorporate explicitly root reinforcement within a framework that accounted

for the processes of bank failure and overcame the usual limitations of analysing natural riverbanks stability(see Darby and Thorne, 1996). Accounting for the points raised by Darby and Thorne, the shape of predictedfailure planes appeared to conform to those observed in the field (Figure 11) and were not constrained to passthrough the bank toe. The predicted position of the failure plane depends on the weight, strength andstratification (if applied) of the bank material and the geometry of the bank profile. Rather than ignoring theinfluences of bank hydrology, characterization of the pore-water may be as good as time and cost allow.Moreover, any failure plane that does not meet strict force and moment equilibrium and kinematicadmissibility criteria is rejected immediately. Thus, the final critical slip surface must be physicallyacceptable before a safety factor is computed.Future additions to the model will include other effects of vegetation that we have omitted here: surcharge

weight of trees on the bank, evapotranspiration and other plant alterations to bank hydrology, and the effect ofroots on tension cracks. Although the interaction between bank geometry and roots, alone, seems to explainthe scale and distribution of bank failures through the reach, only further work will reveal the extent of theinfluence of the other factors. However, because our results reflect what we see in the field, it is possible that

Figure 10. Profile 9L after 1�3 m of bed scour, showing the effect of River Red Gum position on critical failure plane position

Table III. The effect of River Red Gum position on the stability (Fs) of bankpro®le 9L with 1�3 m of basal scour

Simulation(Figure 10)

Tree position(distance from crest) Safety factor

bare ± 1�00a 15 m left 1�26b 10 m left 1�43c 5 m left 1�61d 1 m left 1�43e At crest 1�48f 1 m right 1�48g 2 m right 1�51



the effects that we have not incorporated are not as important as root reinforcement for bank stability alongthe lower Latrobe River.Regardless of the nature of the bank properties and the processes and mechanisms involved in bank retreat,

Thorne (1982) argues that the long-term rate of bank retreat at a section is fluvially controlled. That does notmean that bank properties are irrelevant: they control the stable bank height and angle. Thorne links thesedimentary processes operating exclusively on the banks and those operating in the channel, as a whole,through the concept of basal endpoint control. It is important to consider the stability of the outer bank whenanalysing the cross-sectional geometry and the migration rate of a river bend. Thorne (1991) contends thatmany riverbanks fail before the outer bank scour depth reaches its theoretical maximum as determined bybend flow hydraulics.Reinfelds et al. (1995) showed that the high-magnitude floods of the 1920 and, 30s had a low geomorphic

effectiveness on the lower Latrobe River. In response to these floods, a series of meander cutoffs wasestablished along with an extensive programme of desnagging. Relatively minor floods during the 1970scaused knick points to migrate upstream from the cutoffs, incising the bed and destabilizing the banks.Craigie et al. (1991) document the extensive bank clearing that had occurred by this time.The bed degradation that occurred through the lower reaches of the Latrobe River after the 1930s had two

impacts on the stability of the banks through the study reach. Firstly, deepening of the bed gave rise tounstable bank sections as the devegetated bank height passed the critical height for failure. Secondly, slumpblock survival times shortened owing to an increase of in-channel streampower. Larger flows were containedwithin the degraded channel and flow resistance was reduced following snag removal (Reinfelds et al., 1995;Abernethy and Rutherfurd, 1998).The scenario described by Reinfelds et al. supports our assessment of the channel stability of the lower

Latrobe River. Unstable sections with degraded riparian zones will respond well to the introduction ofvegetation. However, some bank sections directly affected by meander cutoffs and localized erosion continueto heighten and steepen. For vegetation to establish itself and produce the root networks capable of bankreinforcement, harder engineering options are required at those sites. Indeed, many of the cutoff meanderbends are currently being reinstated, which is likely to slow and stabilize the bed degradation. With the bed sostabilized, riparian revegetation through the reach will reinforce the banks. Revegetated bank sections willthen be able to resist mass failure even considering their present high and steep profiles (relative to historicalgeometries).The physical basis of the technique outlined here allowed a quantified assessment of the additional stability

that trees lend to riverbanks. In the usual sense of bank stabilization and protection works, project costs aredirectly related to the safety margin required of the bank. Hemphill and Bramley (1989) maintain that a safetyfactor marginally above unity (say 1�05 to 1�10) might be acceptable where the potential loss from bank

Figure 11. Comparison of `observed' and predicted mass failure of a degraded Latrobe River bank profile devoid of trees. The observedfailure plane and intact profile were surveyed in two separate transects some 3 m apart. We assume that the intact profile is a reasonablerepresentationof the failed sectionbefore failure.Thepredicted failureplanewas the result of aGWEDGEMsimulationusing the `typical'geotechnical and hydrological parameters described herein. As can be seen the predicted failure plane represents a reasonableapproximation of the observed failuremechanism.The survey formed part of a separate exercise to the study described here and the results

have not been included in the foregoing analysis



failure is small. In situations where extensive damage to property may result, Hemphill and Bramley arguethat a factor of safety as high as 1�40 or more may be necessary for an adequate level of protection. Clearly,the addition of healthy mature vegetation to the banks assessed here provides high levels of stability.The immediate implication of the above analyses is that otherwise unstable riverbanks might be reinforced

and stabilized with the introduction of mature woody vegetation. In terms of riparian management, ourassessment indicates a potential planting strategy for revegetation works designed to improve bank stability.Combining Swamp Paperbark, planted low on the bank face, with River Red Gum, established on thefloodplain where predicted failure surfaces intersect the floodplain, will achieve very high levels of stability.Moreover, this strategy is ecologically sound as it mimics the lateral sequence of species within naturalriparian forests in the region.Riparian vegetation does not, however, produce a permanent and unchanging riverbank. The magnitude

and distribution of root reinforcement will change over time as the plants grow and die and as fluvialprocesses continue to deform riverbeds and banks. Channel adjustment exerts an essential geomorphologicalconstraint on fluvial ecosystems that regulates riparian and aquatic habitat diversity and species richness(PieÂgay et al., 1997). Compared to traditional engineering measures based on inert materials, vegetation ismost likely to achieve the conflicting management goals of bank stability for economic concerns and bankdiversity for ecological concerns.

CONCLUSION

Vegetation is an integral part of the riparian landscape and plays a major role in stabilizing riverbanks andmoderating erosion. However, traditional bank stability analyses rarely consider botanical factors. In the past,the outcome of removing or introducing vegetation to a riverbank was forecast in terms of increasing ordecreasing stability but the magnitude of the effect was not precisely predicted. Here, we have explicitlyaccounted for the strength and distribution of the roots of mature riparian trees. Adapting the physically basedslope stability model, GWEDGEM, to include the spatial distribution of root reinforcement allowed us toquantify the influence of tree roots on the stability of bank sections surveyed along the Latrobe River.Bank erosion on the lower Latrobe River is the result of a combination of lateral and vertical scour at the

bank toe followed by mass failure of the overlying bank portions. The presence of mature trees on the banksincreases their stability against mass failure by reinforcing the bank sediment with roots. The effect of theroots is most apparent by analysing otherwise unstable bank sections. Roots prevent banks from failing due tooversteepening from lateral toe scour. Where vertical scour occurs, vegetated banks can stand up to 3�9 mhigher than their bare counterparts. However, it is likely that some degree of undercutting leads to thedestabilization of vegetated bank sections.Improvements in bank stability, achieved even with worst-case hydrological and geotechnical parameters,

were apparent over a range of bank geometries, and varied with tree position in relation to the bank. Thegreatest improvements to stability were realized when the trees were located close to where potential failureplanes intersected the profile surface, either on the floodplain or on the bank face. Assessment of a channelboundary as influenced by vegetation provides insight into the mechanisms that contribute to the magnitudeand spatial distribution of short-term channel change. The presence of vegetation growing on a riverbank hasthe potential to affect both the rate and distribution of bank erosion. This in turn may influence the speed anddirection of bend migration, or hydraulic geometry, and so alter the pattern of channel evolution. Ourobjective was to develop an explanation of the influence of vegetation on riverbank erosion processes byidentifying and studying the underlying causal mechanisms. By providing a means of interpreting fieldresearch, our model provides a link between the study of process and the study of form, within a frameworkthat may be generally applied to riverbank profiles.

ACKNOWLEDGEMENTS

During the study, the first author received an Australian Postgraduate Award and a CRCCH scholarship. Ourstudy was undertaken as part of the Australian National Riparian Zone Research Project, which is funded by



the Land and Water Resources Research and Development Corporation. We thank the Lake WellingtonRivers Authority for provision of channel cross-section data, and Ting Zhao, Ian Donald and Chris Haberfieldfor their assistance with geotechnical problems. Ting wrote the code that incorporated our root reinforcementmodel into the GWEDGEM package. Comments by Ian Prosser and Chris Gippel improved a previous draft.

REFERENCES

Abam TKS. 1997. Aspects of alluvial river bank recession: some examples from the Niger delta. Environmental Geology 31(3/4): 211±220.

Abernethy B. 1999. On the Role of Woody Vegetation in Riverbank Stability. PhD Thesis. Monash University: Melbourne.Abernethy B, Rutherfurd ID. 1998. Where along a river's length will vegetation most effectively stabilise stream banks?Geomorphology 23(1): 55±75.

Abernethy B, Rutherfurd ID. (in press) The distribution and strength of riparian tree roots in relation to riverbank reinforcement.Hydrological Processes.

Andrews ED. 1984. Bed-material entrainment and hydraulic geometry of gravel bed rivers in Colorado. Geological Society of AmericaBulletin 95: 371±378.

Bird ECF, Bird JF, Finlayson BL, McArthur J, McKay L. 1979. Bank Erosion of the Latrobe River and its Lower Tributaries.Environmental Studies Series, 267. Ministry for Conservation: Melbourne.

Bishop AW. 1954. The use pore-pressure coefficients in practice. GeÂotechnique 4: 148±152.BoÈhm W. 1979. Methods of Studying Root Systems. Springer-Verlag: Berlin.Boland DJ, Booker MIH, Chippendale GM, Hall N, Hyland BPM, Johnston RD, Kleinig DA, Turner JD. 1989. Forest Trees ofAustralia (4th edition). Nelson-CSIRO: Melbourne.

Costermans LF. 1989. Native Trees and Shrubs of South-Eastern Australia (revised edition). Weldon: Sydney.Craigie and Associates, Condina, P. 1991. Latrobe/Thompson Rivers Management Study: Report on Existing Conditions, Problemsand Restoration. Mid Gippsland Rivers Management Board: Traralgon, Victoria.

Darby SE, Thorne CR. 1996. Development and testing of riverbank-stability analysis. Journal of Hydraulic Engineering 122(8): 443±454.

Dexter BD. 1978. Silviculture of the river red gum forests of the central Murray floodplain. Proceedings of the Royal Society ofVictoria 90: 175±191.

Donald IB, Zhao T. 1995a. GWEDGEM: A Computer Program for Slope Stability Analysis Based on the Generalised Wedge Method.User's Manual. Department of Civil Engineering, Monash University: Melbourne.

Donald IB, Zhao T. 1995b. Stability analysis by general wedge methods. In The Ian Boyd Donald Symposium on ModernDevelopments in Geomechanics, Monash University, Melbourne, Haberfield CM (ed.). Monash University; 1±28.

Duncan JM. 1992. State of the art: static stability and deformation analysis. In Proceedings of the ASCE Specialty Conference on theStability and Performance of Slopes and Embankments II, Berkeley, Seed RB, Boulanger RW (eds). American Society of CivilEngineers, Geotechnical Special Publication No. 31; 227±266.

Fredlund DG. 1987. Slope stability analysis incorporating the effect of soil suction. In Slope Stability, Anderson MG, Richards KS(eds). Wiley: Chichester; 113±144.

Fredlund DG, Krahn J. 1977. Comparison of slope stability methods of analysis. Canadian Geotechnical Journal 14: 429±439.Gray DH, Leiser AT. 1982. Biotechnical Slope Protection and Erosion Control. Van Nostrand Reinhold Company: New York.Greenway DR. 1987. Vegetation and slope stability. In Slope Stability, Anderson MG, Richards KS (eds). Wiley: Chichester; 187±230.

Hemphill RW, Bramley ME. 1989. Protection of River and Canal Banks, a Guide to Selection and Design. CIRIA Water EngineeringReport. Butterworths: London.

Hey RD, Thorne CR. 1986. Stable channels with mobile gravel beds. Journal of Hydraulic Engineering 112(8): 671±689.Hickin EJ. 1984. Vegetation and river channel dynamics. The Canadian Geographer 28(2): 111±126.Holliday I. 1996. A Field Guide to Australian Native Flowering Plants: Melaleucas. Lansdowne Publishing: Sydney.Hubble T, Hull T. 1996. A model for bank collapse on the Nepean River, Camden Valley, NSW. Australian Geomechanics 29: 80±98.Jacobs MR. 1955. Growth Habits of the Eucalypts. Department of the Interior, Forestry and Timber Bureau: Canberra.Janbu N. 1973. Slope stability computations. In Embankment Dam Engineering; Casagrande Volume, Hirschfeld RC, Poulos SJ (eds).Wiley: New York; 47±86.

Kirkby MJ. 1997. A role for theoretical models in geomorphology? In The Scientific Nature of Geomorphology: Proceedings of the27th Binghamton Symposium in Geomorphology, Rhoads BL, Thorn CE (eds). Wiley: Chichester: 257±272.

Morgenstern NR. 1963. Stability charts for earth slopes during rapid drawdown. GeÂotechnique 13(2): 121±131.Morgenstern NR, Price VE. 1965. The analysis of the stability of general slip surfaces. GeÂotechnique 15: 79±93.O'Loughlin CL, Ziemer RR. 1982. The importance of root strength and deterioration rates upon edaphic stability in steepland forests.In Ecology of Subalpine Zones, Oregon State University, Corvallis, Waring RH (ed.). Proceedings International Union of ForestryResearch Organisations Workshop; 70±78.

PieÂgay H, Cuaz M, Javelle E, Mandier P. 1997. Bank erosion management based on geomorphological, ecological and economiccriteria on the Galaure River, France. Regulated Rivers: Research and Management 13(5): 433±448.

Pitsch S. 1997. Comparison of programs and methods of slope stability analysis. http://wasss.entpe.fr/steph/engstef/enghom.htm [16January 1998].

Pizzuto JE. 1984. Bank erodibility of shallow sandbed streams. Earth Surface Processes and Landforms 9: 113±124.Reinfelds I, Rutherfurd I, Bishop P. 1995. History and effects of channelisation on the Latrobe River, Victoria. AustralianGeographical Studies 33(1): 60±76.

Riestenberg MM. 1994. Anchoring of thin colluvium by roots of Sugar Maple and White Ash on hillslopes in Cincinnati. United States



Geological Survey Bulletin 2059-E: 1±25.Sarma SK. 1979. Stability analysis of embankments and slopes. Journal of the Geotechnical Engineering Division, ASCE 105(12):1511±1524.

Sarma SK. 1987. A note on the stability analysis of slopes. GeÂotechnique 37(1): 107±111.Schiechtl HM, Stern R. 1996. Ground bioengineering techniques for slope protection and erosion control (English edition translated byL. Iaklitsch). Blackwell: Boston.

Shields FD, Gray DH. 1992. Effects of woody vegetation on sandy levee integrity. Water Resources Bulletin 28(6): 917±931.Spencer E. 1973. The thrust line criterion in embankment stability analysis. GeÂotechnique 23: 85±100.Thorne CR. 1982. Processes and mechanisms of riverbank erosion. In Gravel-Bed Rivers: Fluvial Processes, Engineering andManagement, Hey RD, Bathurst JC, Thorne CR (eds). Wiley: Chichester: 227±271.

Thorne CR. 1990. Effects of vegetation on riverbank erosion and stability. In Vegetation and Erosion, Thornes JB (ed.). Wiley:Chichester: 125±143.

Thorne CR. 1991. Bank erosion and meander migration of the Red andMississippi Rivers, USA. Hydrology for theWater Managementof Large River Basins: 20th General Assembly of the International Union of Geodesy and Geophysics, Vienna. InternationalAssociation of Hydrological Sciences; 301±313.

Thorne CR, Osman AM. 1988. Riverbank stability analysis. II: application. Journal of Hydraulic Engineering 114(2): 151±172.Twidale CR. 1964. Erosion of an alluvial bank at Birdwood, South Australia. Zeitschrift fuÈr Geomorphologie 8: 184±211.Waldron LJ. 1977. The shear resistance of root-permeated homogenous and stratified soil. Soil Science Society of America Journal 41:843±849.

Waldron LJ, Dakessian S. 1981. Soil reinforcement by roots, calculation of increased soil shear resistance from root properties. SoilScience 132(6): 427±435.

Wu TH, Mckinnell III, Swanston DN. 1979. Strength of tree roots and landslides on Prince of Wales Island, Alaska. CanadianGeotechnical Journal 16(1): 19±33.

Ziemer RR. 1981. Roots and the stability of forested slopes. In Proceedings of the International Symposium on Erosion and SedimentTransport in Pacific Rim Steeplands, Christchurch, Davies TRH, Pearce AJ (eds). IAHS-AISH Publication No. 132; 343±361.



the effect of riparian tree roots on the mass-stability of riverbanks

Documents