Bandung Paper 6

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Invited Lecture. National Seminar Slope 2000, 27 April 2002, Bandung, Indonesia.In Paulus P Rahardjo (edt.) Slope 2002.

Proceedings of the National Seminar, Slope 2002. 27-April 2002. Bandung, Indonesia. 1529.

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1 INTRODUCTIONThe occurrence of rainfall-induced landslides in re-

sidual soil slopes is a problem encountered in manytropical regions with abundant rainfalls. Further-more, the increasing rate of urbanisation has in-creased hillside developments for engineered and fillslopes in many regions in the tropics. The analysesof the stability of these slopes involve unsaturatedsoils because the water table is usually deep. Cli-matic changes directly affect the unsaturated soilzone. It is important to note that rainfall-inducedslope failure involves infiltration through the unsatu-rated zone above the ground water table. Therefore,

a slope should be considered as an integral system ofunsaturated-saturated soils in the stability analyses.

The objective of this paper is to outline the basicprocedure for assessing stability of residual soilslopes involving saturated-unsaturated soils. Therelevant theory and measurements associated withthe unsaturated soil for slope stability assessment are

briefly introduced. Characterization of soil proper-ties, flux boundary conditions, field instrumentationand interpretation of field measurements for slopestability assessment are discussed through example

applications.

2 THEORY2.1

Stress State Variables

Stress state variables are stress variables that definethe stress condition in a soil and it allows the trans-fer of theory between saturated and unsaturated soilmechanics. There are two independent stress statevariables for an unsaturated soil; namely net normalstress, (ua), and matric suction, (uauw), where is total stress, ua is pore-air pressure, and uw is

pore-water pressure. Under a special condition,when a soil is saturated, the pore-water pressureequals the pore-air pressure and the matric suction,

(uauw), diminishes. The stress state variables thenrevert to a single effective stress, (uw). The stressstate variables control the shear strength and volumechange behavior of the soil.

2.2 Soil-Water Characteristic CurveThe soil-water characteristic curve (SWCC) relatesthe water content of a soil to matric suction and it isan important relationship for an unsaturated soil.The SWCC essentially shows the ability of an un-saturated soil to retain water under various matric

suctions. It has a similar role as the consolidationcurve of a saturated soil that relates void ratio or wa-ter content to effective stress. The SWCC of a soildictates the manner by which the permeability, shearstrength and volume change of the soil will behave

Studies of rainfall-induced slope failures

H. Rahardjo, E.C. Leong & R.B. Rezaur

School of Civil and Environmental Engineering, Nanyang Technological University, Singapore

ABSTRACT: Rainfall-induced slope failures are common problems in steep residual soil slopes in the trop-ics. The characteristics of water flow, pore-water pressure changes, and shear strength of soils are the main

parameters associated with slope stability analysis involving unsaturated soils which are directly affected by

the flux boundary condition (infiltration, evaporation) at the soil-atmosphere interface. Procedures for slopestability analyses considering unsaturated-saturated soils as an integral system are presented. The paper alsohighlights procedures and the importance of characterizing soil properties, flux boundary conditions, spatialand temporal variability of pore-water pressures and instrumentation for slope stability assessment. It has also

been shown through examples how these procedures can be used to generate stability assessment charts forlocal slopes under local environmental considerations.


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at different matric suctions upon drying and wetting(Fredlund andRahardjo, 1993a).

The SWCC of a soil can be obtained using a pres-sure plate extractor as shown in Figure 1 and the

principle of pressure plate test involving surface ten-sion of water is explained in Figure 2.

2.3 Shear StrengthThe shear strength of an unsaturated soil can be ex-

pressed in terms of the independent stress state vari-ables as follows (Fredlund et al., 1978):

( ) ( ) bfwafafff uuuc ++= tantan (1)

where: c' = intercept of the 'extended' Mohr-Coulomb failure envelope on the shear stress axiswhere the net normal stress and the matric suctionare equal to zero (It is also referred to as 'effectivecohesion'); (fua)f = net normal stress at failure;

(uauw)f= matric suction at failure; ' = angle ofinternal friction associated with the net normal stress(fua); and

b= an angle indicating the rate of in-crease in shear strength relative to matric suction,(uauw).

The extended Mohr-Coulomb failure envelope isdefined as a three-dimensional surface tangent to the

Mohr circles at failure with the shear stress, , as theordinate and the two stress state variables, (ua)and (uauw) as abscissas. At saturation, the matricsuction becomes zero because the pore-water pres-sure, uw approaches the pore-air pressure, ua. As aresult Equation 1 reverts to the shear strength equa-tion for saturated soils. The extended Mohr-Coulomb failure envelope can be obtained by con-ducting triaxial tests using a modified triaxial cell(Figure 3) for testing unsaturated soils.

2.4 PermeabilityThe flow of water through an unsaturated soil can bedescribed by Darcys law (Childs and Collis-George,1950):

y

hkv www

= (2)

where: vw = flow rate of water; kw= coefficient ofpermeability with respect to the water phase;hw/y = hydraulic head gradient in the y-direction;hw = hydraulic head (i.e., the sum of the elevationand pore-water pressure heads ory + uw/(wg); w =density of water;g= acceleration due to gravity.

Because the ability of an unsaturated soil to retain

water varies with the matric suction, unlike the satu-rated zone the coefficient of permeability kw, in anunsaturated zone is not a constant, it is rather a func-tion of matric suctions. The unsaturated water coef-ficient of permeability can be indirectly estimated

Figure 1.Schematic diagram of a pressure plate extractor (fromRahardjo et al., 2001)

Figure 2. Schematic diagram of air-water interface in apressure plate test (from Aung et al., 2001)

Figure 3. Modified triaxial cell for testing unsaturated soils(from Rahardjo et al., 2001)


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from the SWCC and the saturated coefficient ofpermeability, ks. As SWCC can be determined withgreater reliability and in a shorter time this indirectmethod of obtaining the permeability is attractive.Since water can only flow through the water-filled

pores, the SWCC therefore, essentially indicates thespace available for the water to flow through the soilat various matric suctions. Therefore, the shape ofthe SWCC can be used to estimate the variation inthe water coefficient of permeability with respect tomatric suction or the permeability function. Indirectmethod of obtaining the permeability function is de-scribed in detail by Fredlund and Rahardjo (1993b).A permeability function estimated using the SWCCand ks is shown in Figure 4. Relationship betweensoil-water characteristic curve and shear strength fora sand and a clayey silt is shown in Figure 5.

2.5 Seepage AnalysisSeepage analyses are performed to calculate the

pore-water pressure changes in a slope due to rain-fall. The governing equation for the flow of water

through an isotropic soil can be formulated usingDarcy's law as follows (Fredlund and Rahardjo1993b):

t

hgm

y

hk

yx

hk

x

ww

www

ww

=

+

2 (3)

where: x andy = cartesian coordinates in the x- andy-direction, respectively; w = density of water; g=gravitational acceleration; wm2 = coefficient of watervolume change with respect to a change in matric

suction (uauw), or the slope of the SWCC.

A soil slope can be considered as an unsaturated-saturated soil system. The changing pore-water pres-sures in the slope under the influence of infiltration

can be analyzed using Equation (3). The computedpore-water pressures can then be input to a slopestability analysis, in order to assess the variation inthe factor of safety of the slope under different rain-fall conditions.

2.6 Stability AnalysisOnce the possible range of pore-water pressurechanges in a slope during a rainfall is establishedeither from seepage analyses or from field monitor-ing, the stability of a slope can be assessed using the

limit equilibrium analyses. The factors of safety withrespect to moment equilibrium,Fm and force equilib-rium, Ff can be written as follows (Fredlund and Ra-hardjo 1993b):

Figure 4. Relationship between soil-water characteristic curveand coefficient of permeability for a sand and a clayey silt(from Fredlund & Rahardjo, 1993b)

Figure 5. Relationship between soil-water characteristic curveand shear strength for a sand and a clayey silt (from Fredlund

& Rahardjo, 1993b)


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NfWx

RuNRc

F

b

w

m

+

=

'tan'tan

tan'

(4)

+

= sin

cos'tan'tan

tancos'

N

uNc

F

b

w

f (5)

where: c' = effective cohesion, = sloping distanceacross the base of a slice,R = the radius for a circu-lar slip surface or the moment arm associated withthe mobilised shear force on the base of each slice,N= the total normal force on the base of the slice, W=the total weight of a slice of width b and height h,

x = the horizontal distance from the centreline ofeach slice to the centre of rotation or to the centre ofthe moments, f= the perpendicular offset of the

normal force from the centre of rotation or from thecentre of moments, =the angle between the tan-gent to the centre of the base of each slice and thehorizontal.

The slope is again treated as an unsatu-rated-saturated soil system. The b angle describesthe change in shear strength as a result of matric suc-tion changes that can occur during a rainfall. The bangle is equal to ' when the soil is saturated or the

pore-water pressure is positive. The bangle gener-ally decreases when the soil is unsaturated or the

pore-water pressure is negative. Both Equations (4)and (5) indicate a decrease in factor of safety as thepore-water pressure, uw, increases during rainwaterinfiltration.

3 CHARACTERISATION OF SOILSoil properties effect the SWCC, permeability, shearstrength and hence the stability of a residual soilslope. Therefore, it is essential to characterize thesoil properties for stability assessment. A typical six-grade soil profile characterization for residual soil

based on bedrock information and weathering pro-file condition, proposed by Little (1969) is explainedin Figure 6. A comprehensive characterization for aresidual soil is illustrated in Figure 7.

Six residual soil slopes were selected for rain-fall-induced slope failure studies in Singapore. Thelocations of the slopes are shown in Figure 8.Yishun, Mandai, NTU-CSE, NTU-ANX and

NTU-IHPT93 slopes were intended for comprehen-sive instrumentation while NTU-FYP slope was se-lected for small scale point measurement studies.

Yishun and Mandai slopes were located in the BukitTimah granitic formation. The other four slopeswere located in the Jurong sedimentary formation.(Figure 8). For illustration, only results from the Ju-

rong sedimentary formation are presented in the sub-sequent sections.

Figure 6. Typical weathering profile of residual soil (fromLittle, 1969)

Figure 7. Porous saprolite soil from basalt near Londrina, Bra-zil (from Vargas, 1985)

Figure 8. Location of the study slopes, generalized geologicalmap of Singapore, schematic diagram of relative position andarrangement of field instruments (from Rezaur, et al. 2002)


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Ground investigations were performed in theseslopes by drilling boreholes to establish the strati-graphy of the slope, locate the groundwater table andobtain undisturbed soil samples for laboratory test-ing. At least one borehole was located at both thecrest and toe of the slopes. Additional boreholeswere drilled on the slope face depending on thelength of the slope face and the uniformity of thesoil in the slope. At least one of the boreholes wasadvanced to the depth of the groundwater table or tothe bedrock interface to identify the bedrock forma-tion. Continuous undisturbed sampling was per-formed in each borehole using a Mazier sampler.

By combining the information of both field inves-tigations and laboratory tests, simplified soil profileswere produced to provide convenient reference forsoil layering and soil properties at the researchslopes. An example of a simplified soil profile forthe NTU-CSE slope is shown in Figure 9.

3.1 Ground investigation resultsThe variation of index properties with depth andhence with the degree of weathering of residual soilsfrom the Jurong sedimentary formation are shown inFigure 10. This section illustrates how the groundinvestigation results are assessed for use in the seep-age analyses.

3.1.1 Specific GravitySpecific gravity depends on the mineralogy of soiland it can reflect the history of weathering (Tuncerand Lohnes, 1977). The mineralogy of residual soilsvaries considerably depending on parent rocks and

weathering process. Specific gravity of residual soilsfrom the Jurong sedimentary formation ranges from2.65 to 2.75 and its value increases slightly withdepth (Figure 10). This could be accounted for bythe presence of minerals other than Quartz in deeperlayers that have a higher specific gravity than Quartz(Aung, 2001).

3.1.2 Void Ratio and Total DensityWeathering leads to a porous structure due to con-siderable leaching of minerals in the soil. Void ratioappears to decrease with depths (Figures 10) reflect-ing the variation in the degree of weathering. Waterand air replace the soluble minerals resulting in a

porous structure. In the upper layers of residualsoils, porosity and void ratio are higher thereforewater and air phase occupy more space as comparedto the lower layers. As a result total density is lowernear the surface. At deeper depths, porosity de-creases resulting in an increase in total density.Therefore, the variation in total density as well asvariation in dry density reflects the variation in de-gree of weathering. The total density of residualsoils from the Jurong sedimentary formations rangesfrom 1.9 to 2.5 Mg/m3.

3.1.3 Atterberg LimitsIn general, plasticity index (liquid limit minus plas-tic limit) of residual soils decreases with depth as thedegree of weathering decreases. In addition, naturalwater content is very close to or less than plasticlimit throughout the depth indicating the unsaturated

Figure 9. Idealized soil profile of the NTU-CSE slope (from

Lee et al., 1999)

Figure 10. Results of index property tests on residual soils fromdifferent depths of the sedimentary Jurong formation (fromRahardjo et al. 2002)


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condition of the residual soils. However, the de-creasing trend of plastic limit and water content withdepth is not obvious in the Jurong sedimentary for-mation (Figure 10). This could be due to less weath-ering in the soil profiles of the Jurong sedimentaryformation at this particular site.

3.1.4 Soil-water characteristic curve & permeabil-ity function

The soil-water characteristic curve (SWCC) is ameasure of the water storage capacity of soil at vari-ous suction values. The ability of a soil to retain wa-ter varies with soil suction. Therefore, the coefficientof permeability is not a constant in unsaturated soils

but is a function of soil suction because water canonly flow through water-filled pores. Suction atwhich a soil starts to become unsaturated is calledair-entry value. The air-entry value of a soil dependson the soil structure. Its value varies with grain sizedistribution as well as pore size distribution. Thecoarser the grain size and the larger the inter-particleand intra-particle pores of a soil, the lower is theability of the soil to retain the saturated condition.When a soil becomes more weathered, more clayminerals are formed and the ability of the soil to re-tain water under high matric suctions increases orthe air-entry value of the soil increases. Therefore,the SWCC of a soil reflects its pore size distributionand hence the degree of weathering.

The SWCCs of the residual soils from differentdepths of the Jurong sedimentary formation are

shown in Figure 11. Figure 11 shows that the satu-rated volumetric water content and the air-entryvalue decrease with depth as the degree of weather-ing decreases or the pore sizes decrease except forthe soil from 13-14m depth. This inconsistency may

be due to the difference in the parent rock type. Theair-entry value of the residual soils from the Jurongsedimentary formation was found to be around 300kPa. The void ratio varies with depth from 0.5 to0.2. The permeability functions for residual soilsfrom different depths of the Jurong sedimentaryformations estimated using the SWCC of Figure 11and ks are shown in Figure 12.

3.2 Shear strengthA summary of shear strength parameters of residualsoils from the Jurong sedimentary formations isshown in Table I. The shear strength parameters ingeneral show an inverse relationship with the degreeof weathering. While the degree of weathering gen-erally decreases with depth, the shear strength pa-rameters of residual soils appear to increase withdepth.

The effective cohesion c' of Grade IV residualsoils at 3 m to 4 m depths was found to be very high(i.e., 125 kPa) and the corresponding effective fric-tion angle is 42 (Table I). This could be attrib-uted to the very high bond strength among individ-

Figure 11. Soil-water characteristic curves of residual soils

from different depths of the Jurong sedimentary formation(from Rahardjo et al. 2002)

Figure 12. Permeability functions for residual soils from the

Jurong sedimentary formation at different depths (fromRahardjo et al. 2002)

Table I. Summary of shear strength parameters for residualsoils from different depths of the Jurong sedimentary

formation (from Rahardjo et al. 2002)Depth

(m)

Soil type Grade c

(kPa)

()

b

()

Jurong Sedimentary Formation

3-4 Purple Silty Sand IV 125 42 N.A4.5-5.5 Purple Silty Sand IV 55 51 40

9-10 Orange Silty Sand IV 35 45 3522-24 Purple Silty Sand III 225 50 N.A


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ual particles of the weathered rocks of Grade IV. Forthe weathered rocks between 4.5 m to 5.5 m depths,the effective cohesion decreases to 55 kPa and theeffective friction angle increases to 51. This de-crease in effective cohesion and corresponding in-crease in effective friction angle could probably bedue to a change in grain size between these two lay-ers (34 m and 4.55.5 m depths). The shearstrength parameters of Grade IV highly weatheredsandstone at 9 m to 10 m depths are lower than thoseat 4.5 m and 5.5 m depths, perhaps due to a weaker

bond strength. The shear strength of Grade III mod-erately weathered sandstone is very high. The effec-tive cohesion for this weathered sandstone is as highas 225 kPa and the effective friction angle is 50.

4 FLUX BOUNDARY CONDITIONSFlux boundary conditions control the response of a

slope to climatic changes. Infiltration, runoff, evapo-ration and subsequent changes in pore-water pres-sure, shear strength of soil, groundwater table fluc-tuation and subsurface water movement are influ-enced by the flux boundary conditions. Therefore, itis important to evaluate these parameters for slopestability assessment.

4.1 InfiltrationPrior to the full-scale instrumentation of a slope it isdesirable to have a preliminary qualitative under-standing of the infiltration capacity and transient re-sponse of matric suctions to an advancing wettingfront in the instrumented slopes. This could beachieved by performing a double-ring infiltrationtest in conjunction with a few quick draw tensiome-ters as shown in Figures 13 and 14. The layout of the

infiltrometer and tensiometers is shown in Figure 15.The study can be performed on a vegetated and a

bare surface simultaneously. Results from such ex-periments on a flat grass-covered surface are shownin Figure 16. Figure 16a shows the cumulative infil-

tration rate at various times obtained from the dou-ble-ring infiltrometer test. Figure 16b shows the re-sponse of the tensiometers at different depths to theadvancing wetting front. Such tests are useful to as-sess the infiltration rate and permeability of the soilat shallow depths. For example, from the responsetime of the tensiometers to the infiltrating water attwo different depths (Figure 16b) it is possible tocalculate the velocity of water movement in the ver-tical direction. The permeability of the soil can becalculated from Darcy's law.

Figure 13. Schematic diagram of an open double-ring infiltra-tion test (from Agus et al., 1999)

Figure 14. Double-ring infiltrometer and quick draw tensiome-ter assembly to study infiltration capacity and transient re-sponse of matric suction to an advancing wetting front inNTU-CSE slope (from Kumar & Ganesh, 1996)

Figure 15. Plan view and sectional view of layout of

double-ring infiltrometer and quick draw tensiometers for asynchronised measurement of infiltration capacity and matricsuction response to an advancing wetting front (from Kumar &

Ganesh, 1996)


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It is not always feasible to conduct a detailed andfull-scale comprehensive field instrumentation forlong-term monitoring because of budget constraints.Under such circumstances point measurements withsimulated rainfalls can be performed. Such studiesalthough are not comprehensive and lack the fea-tures of a full-scale study can still provide meaning-ful results from small plots within a short time. Suchrainfall simulations speed up the process of data col-lection, as it is not necessary to wait for a naturalrainfall. The installation of tensiometers can be con-fined to a small plot (1 1 m2) as shown in Fig-ure 17 rather than covering the entire slope. Resultsfrom a point measurement study on a small plot withsimulated rainfalls at the NTU-FYP slope are shownin Figure 18.

4.2 RunoffField tests can also be carried out on the instru-mented slopes in order to measure the infiltrationcharacteristics on a slope surface. The rainfall-

runoff-infiltration characteristics of a slope can bestudied on an isolated plot of the slope (Figure 19).The runoff is measured using a calibrated flume witha capacitance water depth probe (Figure 20). Thestudy can be conducted under a simulated rainfallusing sprinklers (Figure 19) or a natural rainfall. Theuniformity in rainfall application (simulated) can beassessed by collecting rainfall in a number of smallcans spread randomly over the area and comparingthe rainfall collected in the cans for a fixed period ofrainfall application.

(a) Cumulative infiltration versus time

(b) Matric suction versus time

Figure 16. Cumulative infiltration rates from a double-ringinfiltration test on a flat grass-covered surface and tensiometer

responses at various depths to the advancing wetting front dueto infiltration (from Kumar & Ganesh, 1996)

Figure 17. Small scale point measurements with simulated

rainfall (from Teo & Yap, 1993)

Figure 18. Typical results from small scale point measurementstudies at NTU-FYP slope. Illustration shows total head varia-tions with time at different depths subjected to a simulated

rainfall of 196 mm h1 for a period of 32 minutes (from Teo &Yap, 1993)


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Figures 21 and 22 show the runoff hydrographfrom a simulated and a natural rainfall, respectively.Such runoff measurements and hydrographs allowfor indirect assessment of total infiltration into theslope resulting from rainfall events. The infiltrationrates shown in Figure 21 were derived as the differ-ence between rainfall and runoff rates assuming in-terception losses to be negligible. Such hydrographsresulting from several rainfall events can then beused to assess infiltration into a slope as a percent-

age of rainfall amounts as shown in Figure 23. InFigure 23, infiltration (as a percentage of total rain-fall) is plotted against rainfall amount records fromnatural rainfalls monitored in the NTU-CSE slope. Itappears from Figure 23 that rainfall events which

produce small total amount of rainfall may contrib-ute fully to infiltration.

Figure 23 also suggests the existence of a thresh-old rainfall amount. Any rainfall below this amountwill not produce any runoff and the whole rainfallmay end up as infiltration. With reference to Figure

23 (dotted line) this threshold appears to be about 10mm of total rainfall. Beyond the threshold rainfall,the percentage of rainfall contributing to infiltrationdecreases with increasing total rainfalls. The infiltra-tion amount could decrease to about 40% of the rain-

fall (Figure 23) for rainfall events producing ahigher total amount. This however, does not meanthat the total infiltration amount is less with rainfallevents producing high total rainfall than rainfallevents producing small total rainfalls. For example,with 40% of the rainfall contributing to infiltration a100 mm rainfall (higher total amount) would resultin 40 mm total infiltration. While with 100% of therainfall contributing to infiltration a 10 mm rainfallwould produce only 10 mm of total infiltration.

The data suggest that in residual soil slopes totalinfiltration could range between 40% to about 100%of the total rainfall depending on the rainfall amount.The relationship (Figure 23) derived from the rain-fall records in the residual soil slope has practicalsignificance. If the rainfall amount is known, Figure23 could indicate the fraction of the rainfall thatcould become infiltration. This information can then

be used in seepage analyses as flux boundary condi-tions.

Figure 19. Field plot for studying rainfall, runoff and infiltra-tion processes (from Lee et al., 1999)

Figure 20. Field installation of a flume with water depth probefor runoff measurement (from Lee et al., 1999)

Figure 21. Runoff measurements from a simulated rainfallevent (from Lee et al., 1999)

Figure 22. Runoff measurement from a natural rainfall event(from Lee et al., 1999)


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4.3 EvaporationEvaporation from a slope also plays an importantrole in matric suction recovery. Potential evapora-tion from a slope can be measured using a Penman

pan shown in Figure 24. However, the actual evapo-ration depends on the negative pore-water pressurenear the soil surface (Figure 25).

5 INSTRUMENTATIONInstrumentation is an important aspect of stabilityassessment against rainfall-induced slope failures.The instruments involved are a rain gauge, piezome-

ters and tensiometers for measuring positive andnegative pore-water pressures, respectively. Aschematic diagram of relative position and arrange-ment of field instruments in one of several instru-mented slopes in Singapore is shown in Figure 8.

The mechanism of water flow within a slope dur-ing evaporation and infiltration can be observed

through continuous real-time monitoring of the pore-water pressure and rainfall events as illustrated inFigure 26a. The groundwater table plays an impor-tant role in governing the suction profile in thedeeper soil layers. Typical results from piezometerreadings in conjunction with rainfall at the

NTU-CSE slope are shown in Figure 26b. The pore-water pressure distribution can then be used to as-sess the stability of the slope over a period of time(Figure 27).

Figure 23. Percentage of infiltration as a function of rainfallamount (from Lee et al., 1999)

Figure 24. Evaporation pan (from Rahardjo, 2001)

Figure 25. Ratio of actual evaporation (AE) and potentialevaporation (PE) versus total suction for different soils (fromWilson et al., 1997)

(a) Pore-water pressure variation with rainfall

(b) Ground water table variation with rainfall

Figure 26. Time series of pore-water pressure, rainfall and

ground water table from NTU-CSE slope (from Hritzuk, 1997)


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The effect of soil cover can also be studied fromthe instrumented slopes. Figure 28 shows the re-sponses of NTU-IHPT93 slope under three differentsurface covers to the same rainfall events. The effectof vegetation on negative pore-water pressures in aslope can be observed from the cyclic pattern of the

pore-water pressure within the root zone of a tree(01.4 m depth) as illustrated in Figure 29.

Spatial and temporal variability in data causesdifficulty in representing the soil profile with a de-terministic or a precisely defined set of hydraulic

parameters. Time series of pore-water pressure data

from an instrumented slope can also be used to ex-amine the spatial and temporal variability inpore-water pressures across the slope profile asshown in Figure 30. Using autocorrelation analysesthe 'range' (a measure of the length of influence, for

Figure 27. Variation in factor of safety with time and rainfall

(from Rahardjo et al., 2000)

Figure 28. Changes of in situ total head profiles in response torainfall under different conditions of slope cover (from Lim etal., 1996)

Figure 29. Effect of a Rain Tree on pore-water pressures (fromGasmo et al., 1999)

(a) Distribution of range along slope length (c) Distribution ofsill along slope length

(b) Distribution of range along slope depth (d) Distribution ofsill along slope depth

Figure 30. Distribution of range and sill parameters along theslope length and depth in NTU-CSE slope (from Rezaur et al.,2002)


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time series data) and 'sill' (a measure of temporalvariability, for time series data) were calculated forthe time series of pore-water pressures in NTU-CSEslope. The spatial distribution of range and sillacross slope length and depth are shown in Fig-ure 30.

6 ASSESSMENT OF SLOPE STABILITYA parametric study was performed to examine theeffect of infiltration on the stability of unsaturatedresidual soil slopes by Rahardjo et al. (1999, 2000).A finite element seepage program, SEEP/W(Geo-Slope, 1998a), was used to simulate rainwaterinfiltration into a slope and generate transient

pore-water pressure distributions for different com-binations of slope angle and height. The limit equi-librium slope stability model, SLOPE/W(Geo-Slope, 1998b), was then used to determine the

critical slip surface and the factor of safety for thetransient pore-water pressure distributions calculatedby SEEP/W. This provided information about theeffect of infiltration on slope stability. The resultsfrom the parametric study were used to developcharts to provide preliminary assessments of slopestability against rainfall-induced slope failure fortypical residual soil slopes in Singapore.

In the parametric study a combination of four dif-ferent slope angles of 18, 27, 45 63 (3H:1V,2H:1V, 1H:1V, 0.5H:1V) and three different slope

heights of 10, 20, and 40 m were analyzed. A gener-alized geometry of the slope model used in the pa-rametric study is shown in Figure 31. The slope ma-terial was assumed to be homogeneous, single lay-ered with a saturated permeability of 1.0104 m s1.The shear strength properties of the slope materialare given in Table II. The SWCC and the permeabil-ity function are shown in Figures 32 and 33, respec-tively.

The initial pore-water pressure distribution for

each slope configuration was defined as a hydro-static pore-water pressure profile with a limitingnegative pore-water pressure of 75 kPa. This limitwas selected based on field measurements of nega-tive pore-water pressures. The top boundary wasspecified as a flux boundary. A rainfall intensity of80 mm hr1 (2.2105 m s1, a typical rainfall rateduring heavy rainfalls in Singapore) was appliedfrom time equal to 0 hour until time equal to 4hours. A rainfall intensity of about zero (1.01012m s1) was then applied for a further period of 10

days to allow the water that infiltrated into the slopeto redistribute. The top boundary condition and allother parameters (except slope angle and height)were the same for all analyses.

Figure 31. Generalized geometry of slope model for parametric

study (from Rahardjo et al., 2000)

Table II. Shear strength parameters for the parametric study

Combination c(kPa)

(deg)

b

(deg)

kN/m3

1 10 26 26 20

Figure 32.Soil-water characteristic curve of residual soil fromJurong sedimentary formation (from Rahardjo et al., 2000)

Figure 33. Permeability function computed from the dryingsoil-water characteristic curve of Figure 33 (from Rahardjoet al., 2000)


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The results from the seepage analyses of the pa-rametric study show that the slope height, slope an-gle and the transient pore-water pressure distributioninfluence the stability of a slope. Infiltration charac-teristics were similar for each of the slopes. Exam-

ples of pore-water pressure and hydraulic head dis-tribution in a slope (angle 27 and height 10 m) afterfour hours of rainfall are shown in Figures 34a and34b, respectively.

Figures 35a and 35b show the critical slip surfacefor the 10 m, 27 slope before the rainfall event (i.e.,time equal to 0 hours) and after four hours of rain-fall. The critical slip surface was located at a depthof about 9.4 m at time equal to zero hour (Figure35a) and the factor of safety was about 2.9 (Figure35b).

The factor of safety and the respective depth ofcritical slip surface over time for 27 slopes with dif-ferent heights are shown in Figures 36a and 36b, re-spectively. A few trends are apparent from these

plots. Prior to the commencement of rainfall, slopes

with lower heights had a higher factor of safety(Figure 36a) and the depths of critical slip circles aredeeper for slopes with greater heights (Figure 36b).As rainfall continued, positive pore-water pressuresdeveloped (between 1 and 4 hours) and these trendschanged.

Both the stability and the depth of critical slipsurface decreased over time during rainfall due toinfiltration and reached minimum values at the endof four hours, and increased over time during

pore-water pressure redistribution (between 4 and 28

hours, see Figures 36a and 36b). It is also evidentthat after the development of positive pore-water

pressures (time = 4 hours) due to infiltration, all 27oslopes regardless of their heights had about the samefactor of safety and the same depth of critical slip

(a). Pressure contours

(b). Total head contours

Figure 34. Pore-water pressure (kPa) and total hydraulichead (m) distributions in the parametric slope model after four

hours of rainfall with an intensity of 80 mm hr

1

(fromRahardjo et al., 2000)

(a). Time = 0 hour

(b). Time = 4 hours

Figure 35. Location of critical slip circle for the parametricslope model at different times subjected to a rainfall intensity

of 80 mm hr1



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28

surface. This implies that once positive pore-waterpressures have developed, slope height has little ef-fect on the factor of safety and the depth of criticalslip surface.

These examples show that the transientpore-water pressure distribution appears to be a keytriggering mechanism behind rainfall-induced slopefailures. Infiltration may lead to the development of

positive pore-water pressure zones in a slope. After a

period of time when the positive pore-water pressurezone has developed, the critical slip surface of theslope becomes shallow passing through the positive

pore-water pressure zone.

The results of the parametric study were used todevelop preliminary assessment charts for slope sta-

bility against rainfall. As an example for a typicalresidual soil slope in Singapore of 10 m height andslope angle of 27, the assessment charts are shownin Figure 37. Figure 37a shows the transient

pore-water pressure distributions in the slope sub-

jected to a rainfall of 80 mm hr1 for different dura-tion. Figures 37b and 37c show the respective fac-tors of safety for different slope angles and heights,respectively.

(a). Factor of safety

(b). Depth of critical slip circle

Figure 36. Time series of factor of safety and depth of criticalslip circle during rainfall and redistribution for a 27

oslope


(a) Transient pore-water pressure distributions in a 10m slope

standing at 27 subjected to rainfall of 80 mm hr1 and variousduration.

(b) Respective factor of safety versus slope angle calculatedusing (a).

(c) Respective factor of safety versus slope height calculated

using (a)Figure 37. Charts for preliminary assessment of slope stability(from Rahardjo et al., 2000)


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7 CONCLUSIONSSlope responses to rainfall, infiltration and evapo-transpiration processes are variable in space andtime and are largely influenced by the dynamicclimatic conditions, soil properties and vegetation.Instrumented slopes can provide an understanding ofslope responses to such processes over a long-time

which is essential for advancing rainfall-inducedslope failure studies.

Slope stability against rainfall should be analyzedas a dynamic problem involving environmentalchanges instead of a static problem as convention-ally considered. The unsaturated soil zone is the cru-cial interface between environment and the slopeand unsaturated soil mechanics principles can beused for realistic assessment of slope stabilityagainst rainfall. The slope itself should be analyzedas an integral system of unsaturated-saturated soil

where saturated soil is a special case of unsaturatedsoil.

ACKNOWLEDGEMENTS

The work was funded by research grants from Na-tional Science and Technology Board, Singapore(Grant NSTB 17/6/16: Rainall-Induced Slope Fail-ures) and the Nanyang Technological University(NTU), Singapore (Grant RGM 11/96: Slope Stabil-ity in Tropical Soils). The field assistance from theGeotechnics Laboratory staff, School of Civil & En-

vironmental Engineering, NTU, in carrying out thisresearch is gratefully acknowledged.

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