Forest Hydrology and Watershed Management - HydrologieForestiere et Amenagement des Bassins Hydrologiques(Proceedings of the Vancouver Symposium, August 1987; Actesdu Co11oque de Vancouver, Aout 1987):IAHS-AISHPubl.no.167,1987.

Evaluation of the effect of deforestation onslope stability and its application to watershedmanagement

YOSHINORI TSUKAMOTO & HIROHIKO MINEMATSU

Department of Forestry, Tokyo University ofAgriculture and Technology, Fuchu, Tokyo 183,Japan

ABSTRACT The effect of tree roots on slope stability isevaluated with the upper bound theorem. The greatesteffect is indicated in mature forests where the surface

soil depth is less than 100 cm. The critical soil depthis estimated as an index of instability of surface soils.All major factors affecting the stability of surfacesoils are discussed and summarized in a table for practi-cal watershed management.

Effet du deboisement sur la stabilite de la pente etconsequence dans l'amenagement des bassins hydrologiquesRESUME L'effet des racines d'arbres sur la stabilitedes sols est evaluees au moyen du theoreme de la limitesuperieure. L'effet maximum se retrouve sous foretmature au Ie sol est de moins de 100 cm d'epaisseur.L'epaisseur critique de sol est estime comme indexd'instabilite des sols. Un tableau pour un amengementpartique des bassins resume et discute de tous lesfacteurs affectant la stabilite des sols.

INTRODUCTION

One of the largest hydrological events in a watershed with forestedsteep slopes is the occurrence of numerous debris slides in heavystorms, resulting in serious devastation of hillslopes, torrents anddownstream channels. The occurrence of debris slides is greatlyaffected by forest cutting (Gray & Megahan, 1981; Tsukamoto &Kusakabe, 1984). The former investigations on the effect of defor-estation on slope stability are conducted mostly with statisticalanalysis. In this paper, the effects of forest treatments on slope

stability are discussed analytically by making use of the conceptofcritical soil depths, zero order basins and the upper bound theorem.The research results are applied to practical watershed management.

181

182 Yoshinori Tsukamoto & Hirohiko Minematsu

FACTORSAFFECTING SLOPESTABILITY

In this paper, the writers deal with the debris slide which is afailure of a surface soil layer within the depth of tree root zone

or in slightly deeper zones (Tsukamoto et al., 1982). According to

the infinite slope model, safety factor (Fs) is determined by the

following parameters:

Fs = f(Cu, Cr, 4>,H, h, i, 11) (1)

where Cu, Cr, 4>,H, h, i and 11denote soil cohesion, pseudo cohesionby tree roots, internal friction angle, soil depth, saturated waterdepth, weight of a unit soil mass and slope angle, respectively.

One of the characteristics of debris slides is the short recur-

rence period of the failure of surface soils. It can be pointed outthat the degradation of surface bed materials and formation of sur-face soils as potential sliding materials are of great importance.It must not be overlooked that, as surface weathering and soil form-ation proceed, Cu, Cr and H change keeping close relationships. Astime elapses, Cu of surface soil decreases while Cr increases withtree growth. Hand h increase as weathering proceeds. The primalcauses of debris slides on a vegetated slope are the increase ofsoil depth, pore pressure in the surface soil layer and the effectof tree roots. The latter affects the soil strength in two ways,that is, the decrease of soil strength by biological (tree roots)weathering and the increase of soil strength by tree root networks.

ANALYSIS OF THE EFFECT OF THREE FACTORS ON SLOPE STABILITY

Soil depth

Accumulating processes of the surface soil on granite slopes weremeasured by Shimokawa (1984). The result of his measurements showsthe existence of the maximum surface soil depth on a creeping (mid-dle) slope. In this report, the writers present the concept of acritical soil depth as an index of the degree of instability ofsurface soils on a slope. Under the given values of Cu, 4>and 11,the slope has the critical soil depth, when 4>and 11satisfy 4>< 11

which frequently occurs in saturated clayish soil. In this study,the simple cone penetration test is employed to measure N values ofsurface soils. The apparatus consists of three parts, that is, atop cone with 600 sharp angle and 3 cm diameter, a rod and a weightof 50 kg. N10 values are measured by counting the number of timesof dropping of the weight from the height of 50 cm to drive the cone10 cm down into the soil. N10 = 5 to 10 (5 to 10 times are requiredto drive the cone 10 cm down) is the limiting hardness of tree rootgrowth which corresponds to the maximum possible depth of B soilhorizon. N10 = 20 is assumed to correspond to the heavily weathereddepth based on actual field observations. Fig.l is the result ofmeasurements of surface soil depths on various slopes of three dif-ferent geologies. Fig.l indicates the existence of a maximum criti-cal soil depth for a given slope gradient. If this concept is

Deforestation effects on slope stability 183

valid, the ratio of the present soil depth (DD) to the critical

depth (Dnmax)' DD/DDmax, gives an approach to the estimation ofdegree of instability of the surface soil on a slope with thegradient,D.

soilthe

s-.c:

+J0.. 4.0Q)rtj

r-!.r-!0UJ

. PaleozoicGraniteTertiary

0

b.

600 50° 10°

2.0Q)u('{j~~::JU) 0

Slope gradient

FIG.l An example of the relationship between slopegradients and critical surface soil depths.

Pore pressure

The writers classified slope profiles into four types as shown inFig.2 (Tsukamoto & Kusakabe, 1984). The classification is based onthe surface soil depth and the possibility of the growth of treeroots into the underlying materials. It is presumed that the largerthe possibility of growth of vertical roots, the larger the per-meability of the underlying layers on creeping middle slopes decrea-ses in the order of B, C, and A. The pore pressure in the surfacesoil will decrease in the reverse order, that is A, C and B.

The magnitude of pore pressure is linearly related to the waterdepth on a sliding plane. Microtopography on a slope surface exertsa great effect on the formation of pore pressure in the surfacesoil. In the previous paper, the writers point out the importanceof a converging slope unit (zero order basin) as a unit of conver-gence of saturated throughflow and debris slide occurrence(Tsukamoto et al., 1982). According to the analysis, debris slidesoccur with high probability at the following sites:

(a) on the centre line of a zero order basin,(b) on a creeping slope segment which is the steepest part of the

slope near the turning point of slope curvatures.

Tree roots

The writers employed the following formula (Gray & Megahan, 1981) toevaluate the reinforcement of soil strength by tree roots.

b.

b.

b.

b.

0 b. b.b.a

Ob.b.

a , I

40° 30° 20°

184 Yoshinori Tsukamoto & Hirohiko Minematsu

CXCu = Cu + Crh (2)

l3Cu = Cu + Crv (3)

Crh or Crv = 1.12 E qi (4)

qi = O.493di1.246 (5)

Where Crh and Crv are the reinforcement of soil strength by lateralroots and vertical roots and qi is tensile strength of a tree rootwith the diameter di(mm) in situ under saturated conditions. Crhand Crv are obtained from the simulation model for sugi plantations(Tsukamoto & Minematsu, 1986). The simulation model gives thenumber and the diameters of roots on a given soil profile forlateral roots and on a given depth for vertical roots.

A Type C Type

~\lj#;.

LL /' -' $LMJ-// ",,/ ~.~..\""

" ~~ Surface ~ h:'\'"A SOiL".l<,J~ed rockTransitional,l1

la~ Bed rock

,/~t;~~aCkS

L~1f1 ~ .

~ ~};;= =;~:~}~.~

FIG.2 Classification of slope profiles into four types.

According to the upper bound analysis (Tsukamoto & Kusakabe,1984), a soil is assumed to behave as a perfectly plastic materialobeying Tresca's yield criterion under undrained conditions.Following this assumption, the strength of soil is expressed by anundrained shear strength and the law of incompressibility is used.For the computation, a failure of surface soils is assumed toconsist of three blocks as illustrated in Fig.3.

The three blocks slide down in the direction as shown in Fig.3satisfying vocos0 = Vi = v2cos0. The safety factor is computed with

the total energy dissipation on the surface of velocitydiscontinuity on the three blocks divided by the work done by thegravitational field. The total energy dissipation (E) is writtenas:

Deforestation effects on slope stability 185

E = Cuvocos0{[2ad(1/sin8cos0 + sin0/cos0) + 6~]w+ 2ad(d/sin0 +~)} (6)

The total work done (W) is equal to:

W = VoTdwcos0sinD [(d+2a/T)Cot0+(~+a/T)(~/d)] (7)

Then, safety factor Fs is given by:

Fs = E/W (8)

A A'

F,B B',F'

E,e

D D'

FIG.3 Division of a sliding mass into three blocks forcomputation.

Fig.4 is the result of computation of safety factors of a C-typeslope profile of Fig.2 with the parameters shown in Table 1.

In Fig.4A, the safety factor is calculated on three types ofsurface soil conditions, that is, soil without tree roots (Fss,calculated by the upper bound theorem), soil with vertical roots(Fsv, calculated by the infinite slope model) and soil with verticalroots and lateral roots (FsvLl for living roots and FsvLd fordecaying roots, calculated by the upper bound theorem). The resultsare summarized as follows:

(a) Tree roots reinforce soil strength remarkably, following theincrease in the safety factors. The magnitude of increase suggeststhat no sliding plane would be formed in a densely distributed rootzone.

(b) Deforestation greatly reduces the safety factors.(c) The pattern of the change of safety factors with tree ages

is similar with the result reported by Ziemer (1981) until the ageof twenty. However, in this study, the safety factors decline grad-ually after the twentieth year.

Fig.4B is the result of computation of safety factors indifferent surface soil depths by using the parameters in Table 1 andthe simulation models of tree root distributions (Tsukamoto &

--- W --

186 Yoshinori Tsukamoto & Hirohiko Minematsu

Minematsu, 1986). The effect of vertical roots and lateral roots onthe reinforcement of soil strength is greatly affected with thesurface soil depths, since the root area ratio of vertical roots onthe bottom of the sliding plane and that of lateral roots on thevertical profiles decrease as the surface soil depths increase.

TABLE 1tion

Values of the parameters used in the upper bound calcula-

Length of debris slide (~)Width of debris slide (w)Surface soil depth (d)Depth of transitionallayer

Ratio of vertical rootvolume to the total volume

0.2 kg cm-230°

60m30m70cm

Soil cohesion (Cu)

Slope gradient (n)

Angle of a sliding

plane to the slopesurface (e)

Weight of saturated

soil (T) 1 . 5 t m-3

50cm 45°

0.5

A

'"f,.,

FSVLl

FSVLlor---

V;-FSVLd FSS

~v ,;-- .-.-0

0 20 40Tree age

60

FIG.4 Change of safety factors by forest cutting (A)and with the surface soil depths (B).

According to Fig.4B, the results are summarized as follows:(a) The remarkable difference in the effect of surface soil

depths on the reinforcement of soil strength by tree roots is recog-nized.

(b) The rapid decline of the reinforcement is observed insurface soils deeper than 100 em. The reinforcement by tree rootsbecomes very small in the soil with 150 cm depth and almostnegligible in the soil with 200 cm depth.

(c) It is presumed on the slope with mature forest cover that nosliding plane would be formed within the surface soil less than100 cm depth.

SYNTHESIS OF THE EFFECT OF THREE FACTORS

Slope stability is determined with the synthesis of the effect ofthree factors above stated. Fig.5 is a schematic illustration ofthe yearly change of the safety factors with the change of magnitudeof three factors.

B2.0

50

701.0

'"f,.,-300

00 20 40 60

Tree age

Deforestation effects on slope stability 187

As the years proceed after the appearance of a bed layer on thesurface, the safety factor of soil itself on the potential slidingplane decreases with the increase of the surface soil depth by wea-thering and the growth of vegetation (Fig.5B). The reinforcement ofsoil strength by tree roots increases during the first several de-cades, decreasing afterwards as the soil depth increases (Fig.5C).The magnitude of pore pressures on a slope is determined with thesurface soil depth while the soil is shallow. As soil depth in-creases, however, the effect of soil depths on pore pressures de-creases (Fig.5D).

l::=~ob

A

ld:tJ:~-~B E ; B + C + D

OCcun."c. of ".". .a,..., fo," CU,,,",-

C

~CU"'"'0 100 200 300

Year

...

1.0

,00 200Year

300

FIG.5 A schematic illustration of the change ofmagnitude of three factors, and the decrease of thesafety factors after appearance of bed materials on theground: (A) Increase of the surface soil depth byweathering; (B) Decrease of the safety factor of soilitself at the surface soil bottom; (C) Change ofmagnitude of the reinforcement of soil strength by treeroots; (D) Change of magnitude of pore pressures in thesurface soil; (E) Synthesis of B, C and D, which showsthe change of the safety factor at the surface soilbottom.

PREDICTION OF HAZARDOUS SLOPE SEGMENTS

The writers attempted to make a matrix expression of the parametersaffecting slope stability as shown in Table 2. Numbers in thematrix are given with the writers' experiences basin on theobservations and the results of the aforementioned analyses. Thecomparative importance and the weight of the parameters for debrisslide occurrence will be evaluated with the analysis byquantification, though not mentioned in this paper. The matrixitself will provide much information for the planning of actualforest cuttings which do not reduce slope stability. The matrixshows the importance of the surface soil depth and the properties ofthe underlying layers for debris slide occurrence.

Application of the matrix to actual watershed slopes shows thatconverging slope segments on deeply weathered granite slopes are

most hazardous in three geologies in Japan, that is, granite, ter-tiary and paleozoic. This coincides with the results of statisticalanalyses of debris slide occurrence after forest cutting and the

188 Yoshinori Tsukamoto & Hirohiko Minematsu

results of debris slide disasters (Tsukamoto & Kusakabe, 1984). Thewriters observed that some of tertiary slopes and clayish paleozoicslopes have the similar properties of the underlying layers withthose of granite slopes.

TABLE 2 A matrix to evaluate unstable slope segments

Slope stability Surface Soil

Slope Critical depthtype (D~/D~ax)

Pore Pressure

Slope Slopeprofile type topography

Unstable

ResidualColl uvial

Creeping

0.3>

0.3 - 0.60.6<

BD

A,D

DivergingPlane

Converging

Stable

Slope stability Tree rootEffect ofSurface

soil depth(m)

reinforcement

vertical roots*

Slope profile

type**

Forest

Cuttingtype

treatmentPlanted

tree ageyears

Stable

Unstable

0.70.7 - 1.5

1.5

BC

A,D

thinning 20<

clear cutting 20>

*Under the condition of mature forest; **The order is reversed byforest cutting

REFERENCES

Gray, P.H. & Megahan, W.F. (1981) Forest vegetation removal andslope stability in the Idaho Batholith. USDA Res. Pap. INT-271,11-19.

Shimokawa, E. (1984) Natural recovery process of vegetation on land-slide scars and landslide periodicity in forested drainagebasins. Proc. Symp. on Effect of Forest Land Use on Erosion andSlope Stability, Hawaii, 63-72.

Tsukamoto,Y., Ohta, T. & Noguchi,H. (1982)Hydrologicalandgeomorphological studies of debris slides on forested hillslopesin Japan. IAHS Publ. No. 137, 89-98.

Tsukamoto, Y. & Kusakabe, O. (1984) Vegetative influences on debrisslideoccurrenceson steepslopesin Japan. Proc. Symp. onEffect of Forest Land Use on Erosion and Slope Stability, Hawaii,63-72.

Tsukamoto, Y. & Minematsu, H. (1986) Evaluation of the effect oflateral roots on slope stability. (Presented at XVIII IUFROWorld Congress, Yugoslavia) Beitrage zure Wildbach erosions-undLawienenforschung IUFRO subject group Sl.04-00 (in press).

Deforestation effects on slope stability 189

Ziemer, R.R. (1981) The role of vegetation in the stability of for-ested slope. Proc. XVII IUFRO World Congress, Tokyo, Div. 1,297-308.