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Stability of slopes in residual soilsEstabilidad de taludes en suelos residualesLaurence D. WesleyUniversity of Auckland (retired)New Zealand

AbstractThis paper examines and discusses a number of factors that make slope stability assessments, and slopeengineering in residual soils somewhat different fromsedimentary soils. In particular, slopes are generally steeperand of higher permeability. They are also likely to be more heterogeneous and thus less amenable to analyticalassessment than slopes in sedimentary soils. These factors are discussed in some detail. It is explained that climate

and weather influence is much greater in residual soils than sedimentary soils, and theoretical methods arepresented for taking this influence into account. It is shown also that traditional computer programme methods ofslip circle analysis can result in very large errors if applied to steep slopes in which seepage is occurring. Morerigorous treatment of the seepage state, especially the worst case state is needed in order to produce sensibleestimates of safety factor.

ResumenEste artculo analiza y discute una serie de factores que hacen que las evaluaciones de estabilidad del talud y laingeniera de taludes en los suelos residuales, sea algo diferente emla de los suelos sedimentarios. En particular,los taludes son generalemente ms pronunciados y de mayor permeabilidad. Tambin son probablemente msheterogneos y por lo tanto, menos susceptibles a evaluaciones analticas en comparacin con los taludes desuelos sedimentarios. Se discuten estos factores en un cierto grado de profundidad. Se explica que la influencia del

clima y el tiempo es mucho mayor en suelos residuales que en los suelos sedimentarios, y se presentan mtodostericos para tomar esta influencia en consideracin. Tambin se demuestra que los mtodos computacionalestradicionales de anlisis de crculo de deslizamiento pueden dar lugar a errores muy grandes si se aplican ataludes empinados en los que se estn produciendo filtraciones. Es necesario un tratamiento ms riguroso delestado de infiltracin, especialmente el estado para el "peor caso", con el objeto de producir estimacionesrazonables del factor de seguridad.

1 INTRODUCTION

The general principles of slope stability apply

equally to sedimentary soils and residual soils, butthere are various aspects of slope behaviour thatare peculiar to, or characteristic of, residual soils.These include the following:(a)Slopes in residual soils (excluding "black

cotton" soils) generally remain stable at muchsteeper angles than those in most sedimentarysoils. Slopes of 45o or steeper are notuncommon. Cuts in volcanic ash (allophone)clays can often be made as steep as 60o and10m high, without danger of slipping.

(b)Slope failures in residual soils, especiallywhen steep slopes are involved, are unlikelyto be deep seated circular failures. They aremore likely to be relatively shallow, oftenwith slightly curved or almost planar failuresurfaces. However, the volume of materialinvolved may still be very large.

(c)The value of c usually plays a significant rolein maintaining stability; it appears to be dueto some form of weak bonds betweenparticles.

(d)The residual strength is generally closer to thepeak strength than is the case with most

XIII Congreso Colombiano de Geotecnia - VII Seminario Colombiano de Geotecnia - ISBN 978-958-98770-2-9

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sedimentary soils, especially in clayscontinuing allophane or halloysite.

(e)The stability of many slopes in residual soils isdependent on the contribution to shearstrength arising from the zone of negativepore pressure above the water table.

(f) With some (possibly the majority) residualsoils, the presence of discontinuities may be

the factor governing the stability behaviour ofslopes.(g)The extent to which the stability of slopes in

residual soils can be evaluated by analyticalmethods is often very limited, because ofuncertainties in the soil strength parametersand in the seepage conditions.

(h)Slips and landslides in residual soils areagenerally triggered by heavy rainfall, and arethe result of temporary increases in the porepressure in the slope. This is an important

difference with sedimentary soils, wherewater tables tend to stay in a permanentequilibrium position unaffected by weather.

(i) Strong earthquakes may also be the trigger forslips or landslides.

(j)The actual cause (as distinct from the trigger)of a great many landslides in residual soils isin fact human activity. Excavations intoslopes, the placing of fill on slopes, theinterference with natural drainage and seepagepatterns, and deforestation are all factors that

to reducing stability and possibly lead tofailures, especially in urban areas.

2 FAILURE MODES

As mentioned above, slope failures in residualsoils, especially when steep slopes are involved,are unlikely to be deep seated circular failures.They are more likely to be relatively shallow, withfairly planar failure surfaces. In large slopes witha limited depth of weathered material overlyingsound rock, they are likely to be predominantly

translational slides. Also, it is not uncommon involcanic areas for volcanic material to slide at theinterface between volcanic deposits and theunderlying sedimentary soils. The slip surface inthis case may be fairly linear so that the slide isessentially a translational slide. However, thevolume of material involved may still be verylarge. Some modes of failure are illustrated inFigure 1.

It should not be imagined that assessing thestability of natural slopes is essentially ananalytical exercise. There are severe limitations on

the extent to which analytical methods can beapplied to natural slopes. They may or may not bean important part of slope stability assessment,depending on the nature of the slope, in particularits geology, topography, soil conditions and pasthistory.

Figure 1 Failure modes in residual soils.

3 THE PLACE OF ANALYTICAL AND NON-ANALYTICAL METHODS

Other, non-analytical methods, however, arealways an essential part of any assessment of the

stability of natural slopes. These methods mayappear primitive and not technically satisfying,but that does not lessen their importance. Theyinclude the following:(a) Visual inspection of the slope(b) Geological appraisal of the slope and

surrounding area(c) Inspection of aerial photos(d) Inspection of existing slopes in similar

materials to the slope in questionCareful visual inspection of slopes, along with

geological knowledge can give a very good guideas to whether a particular slope is stable or not.Slopes with smooth contours, as shown in Figure2, indicate that they have been formed by surfaceerosion processes, without slip movement. On theother hand irregular surfaces suggest the someform of slip movement may have been involved.

Inspection of aerial photographs can often showfeatures of a site that are not evident from a directvisual inspection. They can show scarp lines orchanges of vegetation indicating old slip

Shallow circularslide (very common)

Large translational slide

(common)

Deep seatedcircular slide(very unlikely)Norm

alwatertable

Peakwaterta

ble

Hardlayer

Hardlayer


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movement. Inspection of any existing cuts in thearea of interest can tell us two things how thecut slope itself is performing, and what sort ofmaterial it is made of.

Figure 2 Stability indications from surfacefeatures of slopes.

It is probably true that most assessments of thestability of a natural slope are based 80% or moreon (a) to (d) above and less than 20% onanalytical procedures.

4 LIMITATIONS OF ANALYTICALMETHODS.

The limitations of applying analytical methodsto residual soil slopes arise from uncertainties inthe shear strength parameters and in the seepageconditions. With respect to the strengthparameters, it is convenient to divide slopes intothree categories, as follows:1. Slopes consisting of uniform, homogeneous

materials.

2. Slopes containing distinct continuous planesof weakness

3. Slopes of heterogeneous material, but withoutdistinct planes of weakness, as for example ina weathering profile of the Little kind.

4.1 Slopes consisting of uniform materials:With such slopes, the determination of accurate

safety factors by conventional slip circle analysiswould appear to be a reasonable expectation.

However, there are still uncertainties that cannoteasily be eliminated. These uncertainties relate tofirstly the shear strength of the soil and secondlythe seepage and pore pressure state in the ground,as explained in the following paragraphs.

With respect to shear strength, the followingpoints should be noted:

-The value of can usually be determinedwith reasonable accuracy using normal

measurement methods, such as triaxialtesting.

-The value of c is often very significant,(due to weak bonds between particles) butcannot easily be determined with the samedegree of reliability as . Very carefultriaxial testing at low confining stresses isneeded to accurately determine c.

-The residual strength is likely to be fairlyclose to the peak strength, especially inclays continuing allophane or halloysite.

With regard to the seepage pattern and porepressure state in the slope, the relatively highpermeability of most slopes in residual soilsmeans that the seepage state is continuouslychanging depending on the weather conditions.The worst case seepage pattern is clearly the onethat governs the long-term stability of the slope.Unfortunately there is no reliable way todetermine this pattern, although there are somemethods that we can adopt to try to estimate thisworst case.

4.2 Slopes containing distinct, continuous,planes of weakness:The behaviour of many slopes in residual soils

is likely to be dominated by the presence ofrandom discontinuities in the form of distinctplanes of weakness. This is likely to be the casewith soils that have been subject to tectonicdeformations and shearing, or derived from rockssubject to such deformation. The presence of thesediscontinuities makes the determination of thelikely failure mode, and the values of the soilstrength parameters, extremely difficult, and thus

reduces the likelihood that analytical methods willproduce reliable results. Only in rare situations isit likely to be possible to determine the location,orientation, and strength of discontinuities withthe degree of reliability needed for the use ofanalytical methods.

Figure 3 Possible discontinuity patterns and

Smoot contoursindicate stability

Irregular contourssuggest instability

?

?

?

Shape is formed bysteady surface erosion

Shape appears to be formeby mass movement

Possible slip orslump movement


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influence on slope stability.

The exception to this observation is thesituation when the fissures are generallyorientated in a particular direction. Some residualsoils derived from sedimentary soils may containplanes of weakness that reflect particular weaklayers in the parent material. In this case it may bepossible to determine the shear strengthparameters within these weak layers and make use

of them in sensible stability analysis. Possiblepatterns of discontinuities are illustrated in Figure3.

4.3 Slopes of heterogeneous material, butwithout distinct planes of weakness:

The weathering of igneous rocks such asgranite, does not generally create distinct planesof weakness, so that this is quite a differentsituation to that just described above. The soilprofile consists of zones of partly weatheredmaterial containing remnants of the parent rock,

and zones of fully weathered material (soil).Determination of the strength parametersapplicable to the material as a whole is still verydifficult, if not impossible, by conventionalsampling and laboratory testing. This may notentirely rule out the use of analytical methods, asit may still be possible to determine the strengthparameters from back analysis methods applied toexisting slips or slopes. Some examples of thesemethods are given in a later section.

5 INFLUENCE OF CLIMATE.

Slips and landslides in residual soils aregenerally triggered by periods of prolonged orintense rainfall, and are the result of temporaryincreases in the pore water pressure in the slope.This is an important difference in behaviourbetween residual and sedimentary clays. Withsedimentary clays of low permeability (such as

London clay) the pore pressures can be measuredand the assumption safely made that they willremain approximately the same indefinitely(except very close to the surface), provided thereare no significant changes in external conditions.With residual soils, any measurement of porewater pressure in the slope is valid only at thetime it is made and cannot be assumed to berelevant to long term stability estimates. For suchestimates, it is the worst seepage condition likelyto occur in the future which will determine thelong term stability of the slope.

One important reason (which should be clearlyrecognised) that slopes in residual soils remainstable at steep angles is because the phreaticsurface (water table) is often deep, and the porepressure above the surface is negative (suctionor pore water tension) as described elsewhere.This zone of pore water tension may include mostof the slope, and increases the effective normalstress across any potential failure surface, thusincreasing the shear strength and the safety factorof the slope. The influence of intense rainfall on

this zone is to increase the pore pressure from itsnegative value towards zero (ie to reduce ordestroy the suction above the water table), orpossibly to turn it into a positive value if thephreatic surface rises. However, it is not necessaryfor the phreatic surface to rise at all for rainfall toinduce failure in a slope. The reduction in thenegative pore pressure without change in watertable my induce failure in the slope. An exampleof such a situation is given later.

5.1 Response of pore pressure to rainfall

The influence of rainfall on the water table andthe pore pressure state in a slope arises from twodistinct weather effects, as follows:(1) Regular seasonal influence. This is cyclical in

nature, and for many climates is reasonablypredictable, as described elsewhere.

(2) Isolated storm events. These are generallyunpredictable, both in timing and intensity,and are more likely to be the direct trigger oflandslides than normal seasonal changes.

(a) random discontinuities- indeterminate influence on stability

(b) regular discontinuities- quantifiable influence on stability

Planes of weakness


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The place where the most study has been givento the response of slopes to periods of heavyrainfall is Hong Kong, a part of China. HongKong, along with many parts of the Far East, issubject to extremely intense rainfall from time totime, because it is in the path of typhoons; thesetyphoons have been the trigger for many largedisastrous landslides, resulting in severe damageto property, and even loss of life. For about the

last four decades, Hong Kong has had a specialistgeotechnical unit responsible for investigatingslope failures and setting up guidelines for all newdevelopments close to, or actually on, slopingsites. Considerable data has been obtained fromfield monitoring of the way pore pressures inslopes respond to periods of rainfall, and this hasbeen used to develop empirical or semi-empiricalmethods for predicting pore pressurescorresponding to particular return period storms.The pore pressure response measured in stand-

pipe piezometers was found to be quite variable,and could be considered to be of two types. Thefirst is response to seasonal changes (ie wetseason to dry season), and the second is responseto intense short duration storms. The forms ofresponse are shown in Figure 4, taken from theHong Kong Manual for Slopes (2000). Thisinformation is very informative, as it shows thatground water regimes respond in quite differentways to the same storm event, so that anymodelling of pore pressure response to rainfallevents requires a very good understanding of the

factors governing the seepage conditions,especially detailed geological knowledge of thesoil layers.

Figure 4 shows that some piezometers respondonly to seasonal effects, and some respond only tostorm events, some do not respond at all, and thereis a range of responses made up of combinationsof these. Comments on the differing behaviourinclude the following:

- Piezometers that show no response of anysort may be located in places where thephreatic surface is fixed by nearby

boundary conditions, such as proximity toa drain or a lake. It is also possible thatthey may be in very low permeabilitymaterial.

- Piezometers that show seasonal responsebut no storm response are likely to belocated in layers of low permeability,where a long period of changed boundaryconditions is needed before thegroundwater system shows any change

- Piezometers that show no seasonalresponse but some storm response are

likely to be in soils of relatively highpermeability, so that in normal seasonalconditions water entering the slope canfind a way out just as quickly as it entersthe slope. It is only in very intenserainstorms that the rate of entry exceeds therate of exit with the consequence that thepore pressures increase and the water tablerises.

1 - Little or None 2 - Multiple Peaks 3 - Single Peaks

Seasonalresponse

Stormresponse

A - MultiplePeaks

B - SingleSym-metrical

Peak

C - SingleAsym-metricalPeak

D - Slight

E - None

Legend:Seasonal response P - Piezometric level Storm eventStorm response T - Time

P

P

P

P

P

T

T

T

T

T

Figure 4 Piezometer responses to seasonal andstorm influence (Geotechnical Manual for Slopes,Second Edition, 1984).

Whatever the explanation of the differingbehaviour, it clearly shows the difficultiesinvolved in any attempt to model pore pressureresponse to seasonal weather changes and to stormevents. We should note that the soils involved inthe Hong Kong measurements werepredominantly weathered granites, which arerelatively coarse grained (silty sands) and involvemajor variations in properties depending on thedegree of weathering. The mechanism by whichthe pore pressure changes in the Hong Kong soilsis probably a combination of that for a granularmaterial and that for a moderate permeability clay.


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In true clays, such as those normally found in wettropical climates, the response can be expected tobe that of a clay. In this case the response or theclay is governed by the coefficients ofpermeability (k) and one dimensionalcompressibility (mv), or in their combined formthe coefficient of consolidation (cv

). Themechanism of pore pressure change is similar tothat in normal consolidation or swelling of soils.

Figure 5 Summary of pore pressure response toclimate effects in clay slopes.

An approximate summary of the trends shownin Figure 4 is presented in Figure 5. This isintended for reasonably homogeneous clay slopes.Near the surface, influence from both seasons andisolated storm events is to be expected. As depthincreases, this influence declines, especially thatfrom storm events. There will be a maximum

depth beyond which neither seasonal not storminfluence will be felt.

5.2 Transient analysis of rainfall Influenceon the stability of a homogeneous clayslope

An example of a clay that generally belongs inhomogeneous soil category above is the tropicalred clay found widely in the island of Java inIndonesia. It is not completely homogeneous, butthe variations in its properties are sufficientlysmall that for practical engineering purposes it canoften be considered to be homogeneous. Theauthor has previously described and analysed ariver bank slope in this clay (Wesley, 1977). Thestability analysis was limited to examining theslope with the relatively deep water table that waspresent at the time of the investigation. No attemptwas made to establish the most probable seepagepattern, or the worst case. Our present purpose isto re-analyse the slope in greater detail, takingaccount of changing pore pressures resulting fromrainfall, and at the same time illustrate that

theoretical transient analysis in uniform slopes canproduce sensible and informative results. Figure8.8 shows a series of cross-sections along the riverbank that were actually measured, together withthe idealised section used in the analysis.The computer program Seep/W is used here to

carry out the transient seepage analysis. This isbased on the conventional transient form of thecontinuity equation (Lam, Fredlund and Barbour,

1987) expressed as follows:

t

hmQ

y

h

x

hk ww

=+

+

2

2

2

2

......... (1)

Where Q is the rate of flow into a soil elementfrom an external source.

mw

The volumetric water content () is the volumeof water per unit volume of soil. It is directlyrelated to the water content as normally defined insoil mechanics.

is the slope of the volumetric water contentwith change in pore pressure u.

Hence umw

=

For fully saturated soils it is easily shown thatmw =mv

For the case we are studying here the term Qdisappears as the rate of flow into the soilelements is determined by the hydraulicconductivity of the soil and the hydraulic gradientat the soil surface, and does not have a pre-determined value.

, the coefficient of compressibility of thesoil.

+

=

2

2

2

2

y

h

x

h

m

k

t

h

wv ....... .. (2)

Readers will recognise Equation 2 as having avery similar form to the well known Terzaghi

consolidation equation. The only difference ofsubstance is its two-dimensional form. Thesimilarity is to be expected, since the soilparameters controlling the mechanics in the twosituations are the same, namely the coefficient ofpermeability, k, and the compressibilitycoefficient, mv, or their combined form, thecoefficient of consolidation cv

. The Terzaghiequation is simply a special case of transient flow.

Dry season Wet season

Pore

pres s ure

Time (one year)

No climatic influence

Seasonalinflue

nce only

Seasonal and storm influence

Storm influence

Seasonalinfluence

Expec

tedtr

en

dw

ith

inc reas

ing

dep

th


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Figure 6 Transient analysis of the stability of a river bank slope in tropical red clay

The objective of the analysis is to determinehow the pore pressures the safety factor of theslope change as a result of continuous rainfall onthe slope and surrounding ground. The analysisincludes both transient states and the ultimatesteady state.The transient seepage states at a sequence of

time intervals obtained from the Seep/W analysisare transferred to a Slope/W analysis to obtain

safety factors. The soil properties used are those inthe original (1977) analysis, namely:

Unit weight =16.2 kN/m3

c =14kPa, =37,

o

.

The above equation then becomes:

t

hm

y

h

x

hk ww

=

+

2

2

2

2

(b) Initial and final pore pressure conditions

Final stateSF = 0.81

Initial stateSF = 2.14

Long term steadystate flow net

10m

15m

70o

(a) Measured river bank cross sections

10m70

o Red clay

Mottled red and

grey clay

Reddish grey clay

Assumedinitialwa

tertable

a

b

Idealized crosssection


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which with a little manipulation becomes:

In addition, for the transient analysis, thefollowing parameters were adopted:

Coefficient of permeability, k = 0.01 m/day,Coefficient of compressibility, mv =0.0001kPa

-1

.

The results are shown in Figures 7 and 8. Figure

7 shows graphs of pore pressure on one particularvertical section through the slope, namely sectiona-b in Figure 6, at a series of time steps. Thesimilarity of these curves to Terzaghiconsolidation curves is clearly evident. There is anotable difference however, as the finalequilibrium situation is not one of hydrostaticequilibrium. It is an equilibrium seepage state, sothat the pore pressures are well below thehydrostatic values. This is an example of a pointmade in a later section regarding the errorinvolved in the common vertical interceptassumption method used by computerprogrammes to calculate pore pressures.

Figure 7 Pore pressure changes with time onSection a-b of Figure 6.

These contours illustrate an important pointabout the way the water table rises. It does not riseat a uniform rate; instead it rises slowly at firstand then very rapidly in its final stages. This isbecause of the shape of the contours. From thestart until time step 1.1 it rises from its initialdepth of 10m to 8m, but then rises from 8m to thesurface between time step 1.1 and 2.7. Figure 8shows the rise in water table with time as well asthe rise in pore pressure at a depth of 15m. Thewater table reaches the surface after only 2.7 years

while the pore pressure at 15m takes about 20years to reach an equilibrium steady state.

Figure 8 also shows the change in safety factorwith time. The initial value of safety factor is 2.14taking into account the negative pore pressureabove the water table. It falls to unity in about 3years and continues to decline to reach its steadystate value of 0.81 in 20 years. If the long termstability is estimated assuming a worst-casecondition with the water table at the surface andusing a conventional computer stabilityprogramme the safety factor is only 0.11. Thisarises because of the unrealistic assumptioninherent in almost all conventional computerprogrammes, namely that the pore pressure can becalculated from the vertical intercept between thewater table (ground surface in this case) and theslip surface.

Figure 8 Safety factor, water table and headchanges with time.

Table 1 Details of the analysis and correspondingsafety factors:

SituationSafetyfactor

Comment

Initial condition,

water table asshown in Figure

6(b)

2.14

Analysis includes

effect of negativepore pressure above

water tableAfter three time

steps (days)1.03

Slope on point offailure.

Pore pressureratio ru

1.01=0.07

This is the ru

Long term

valueequivalent to theseepage patternafter three time

steps0.81 The most probable

-60 -40 -20 0 20 40 60 80 1000

10

2

12

4

14

6

16

8

20 (final steady state)

0.1

2.7

0.20.4

1.10.6

6.2

Pore pressure Pa

ep

m

Hydrostaticstate

Hydrostatic

state

Figures on contoursare time steps (days)

Finalwater table

Initialwater table

0 5 10 15 20

0 5 10 15 200

2

4

6

8

10

15

13

11

9

7

5

1.0

1.4

1.8

2.2

0.6

Depthofwatertable(m)

Pressureh

eadatbaseoflayer(m)

Saetyacto

r

Wate

rtable

Pressurehead

Time steps (years)


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SituationSafetyfactor

Comment

steady state flownet shown inFigure 6(b)

worst case porepressure state

Water table atground surfaceand verticalintercept

assumption. ru

0.11

=0.60

Normal softwaremethod, whichimplies vertical

equipotentials and

horizontal flowlines.

The safety factors are summarised in Table 8.2.This example of an actual field situation,illustrates a number of important points:1. The analysis produces a sensible result, as it

indicate that three days of continuous heavyrainfall is necessary for the safety factor to fallto unity and initiate failure. The island of J avadoes have very heavy rainfall, but it is most

unlikely to be continuous for three days, so thelikelihood of the worst case pore pressure stateactually occurring is very low.

2. Adopting a worst case condition of the watertable at the ground surface, and carrying out astability analysis using routine computerprogrammes that incorporate the verticalintercept assumption to estimate porepressure produces a hopelessly unrealisticresult. The banks of the stream concerned herehave been stable for years and an analysis thatproduces a safety factor of 0.11 is clearly

nonsensical.3. The results of the analysis are essentially thesame as those in the authors 1977 paper, inthat it shows the slope to have a safety factorof unity when the value of ru is quite low. The1977 paper states: the safety factor falls tounity when the ru value rises to just under0.1. The current analysis gives the value of ru

4. In the 1977 paper the statement is made thatthe groundwater level could rise substantiallyduring periods of heavy rainfall to give higher

values of r

as 0.07, which is not too different.

u

5. The shear strength parameters, c and , usedin this study are believed to be reliable, as alsois the assumption that the soil is reasonablyhomogeneous. However, the parameters, m

, a statement that reflects theauthors (mistaken) belief at the time that thepore pressure was related directly to the levelof the water table (the vertical interceptassumption).

v

(of permeability and compressibility) arebased on conventional oedometer tests. Thesituation involved here is one where the soilhas been subject to endless cycles ofseasonally changing effective stresses, andmuch more detailed laboratory testing isneeded to establish reliable values of theparameters. The time steps in the aboveanalysis could be in error by an order of

magnitude. It is generally the case that c

and k, used in the steady state analysis are ofmuch less certain reliability. Both coefficients

v

The above example is not intended to suggestthat theoretical analysis of this kind can predictwhen a slope is likely to fail. However, in thisparticular situation of a homogeneous soil it doesprovide useful information, namely that the slopeis unlikely to fail as a result of prolonged rainfall.

values measured in the laboratory tend to be apoor representation of those that apply in thefield, so this cannot be ruled out in the presentcase.

5.3 5.3 Prediction of long term worst casepore pressure state

As already noted, the long term stability isdependent on the worst pore pressure state in theslope, which cannot be predicted with anycertainty. One approach is to assume that thewater table rises to the ground surface, which isnot unreasonable, but it still leaves open thequestion of what exactly the pore pressures arebelow the water table. The last example illustratesthis issue. Even on a long term steady state basis,

the pore pressures are not hydrostatic beneath thewater table and the use of computer programmesthat assume this to be the case (ie the equipotentiallines are vertical) can give a very erroneousestimate of stability.

Figure 9 shows the results of an analysisinvestigating this issue. Stability estimates aremade of a range of slopes of varying inclinations,using two different pore pressure states, bothassuming the water table is at the ground surface.The assumption is that equipotentials are vertical,in line with most computer programmes. The

second assumption is of a flow net compatiblewith the water table at the surface, and thestability analysis repeated using pore pressuresfrom this flow net. We should note in passing thatthe only way the water table can exist at theground surface is for rain to be continuouslyfalling on the surface.


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0.25:1 0.5:1 1:1 1.5:1 2:1 2.5:1Slope inclination

0.25:1 0.5:1 1:1 1.5:1 2:1 2.5:1Slope inclination

0.6

0.4

0.2

0

1.6

1.2

0.8

0.4

0.5

0.3

0.1

1.4

1.0

0.6

0.7

Sa

ety

ac

or

Pore

pressure

ratio

(r)

u

r =0.61 - Water table at surface,vertical equipotentialsu

Based on r =0.61- water table at surface,vertical equipotentials

u

Equivalent values of r to givesafety factors based on flow net

u

Based on flow net duringcontinuous rainfall

(a) Flow net with continuous rainfall on surface (b) Flow net assumed in computer analysis wheninput is phreatic surface at ground surface

1:11:1

Unit weight =16kN/mc =30kPa

3

= 40

SF =1.22SF =0.81

30m

20m

(d) Values of r equivalent to the flow net from

continuous rainfall on the ground surface.u

( c ) Safety factors versus slope angle

Figure 9 Influence of pore pressure assumptions on the calculated safety factor.

Details of the slopes analysed and the assumedsoil properties are:

Height: 20 m

Inclination: from 0.25:1 to 2.5:1(0.25:1 means 0.25 horizontal and 1 vertical)Unit weight: 16 kN/mShear strength: from c =70 kPa, =45

3o, to c

=13 kPa, =30o

, as given in Table 2.

Table 2 Shear strength parameters.Slopeangle

0.25:1 0.5:1 1:1 1.5:1 2:1 2.5:1

c kPa 70 50 30 16 15 13

deg.45 45 40 35 33 30

The shear strength parameters have beenselected to give an average safety factor of unity,(or close to unity) for each slope angle from thetwo pore pressure cases analysed. This means

varying the strength parameters from large tosmall as the slope angle is decreased. Theparameters are believed to be representative ofresidual soils with slopes of these inclinations.The results of the analysis are shown in Figure 9.Figures 9(a) and 9(b) show typical results for oneof the slopes analysed, namely the 1:1 slope. InFigure 9(a) a flow net has been created using theSeepW programme and then used in SlopeW tocalculate the safety factor. The cross sectionactually used in the seepage study extended in thehorizontal distance well beyond the boundaries


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shown (in Figure 9(a)) in order to minimise edgeeffects. Figure 9(b) shows the situation used inmany computer programmes (verticalequipotentials), which in this case means an ru

Figures 9(c) and (d) summarise the results forall the slopes. The dramatic difference in safetyfactor with steep slopes is clearly illustrated inFigure 9(c). With the 0.25:1 slope the assumptionof vertical equipotentials gives a safety factor of0.5 while that with the flow net gives a value of1.5. Figure 9(c) shows the actual values of r

value = 9.8/16.0 = 0.61. The position of thecritical circles determined by the slip circleanalysis is not very different, but there is a largedifference in the safety factor. The value using theflow net is 50% higher than the value assuming

hydrostatic pore pressures.

u

Figure 10 summarises what has been said aboveand emphasises the differences in behaviourbetween residual and sedimentary soils.

thatcorrespond to the flow net seepage state. Theconclusion from this analysis is that estimating theworst case pore pressure state in steep slopes byassuming the phreatic surface rises to ground leveland the equipotential lines are vertical can easilylead to extremely erroneous results.

Figure 10 Pore pressure and safety factor changesin cut slopes in sedimentary and residual soils.

6 SLOPE DESIGN

6.1 Selection of the profile for a new cutslope.

It is perhaps appropriate to revisit and re-emphasise what was said earlier, namely that theselection of an appropriate profile for a new cutslope in residual soil is a matter of judgment based

more on non-analytical approaches, than onanalytical estimation. Despite this, much of thechapter has been spent looking at theory andanalytical methods, particularly in relation to theinfluence of climate and rainfall on slope stability.This has not been done to stimulate the use ofanalytical methods as a design process inpreference to non-analytical methods. Rather, ithas been done because estimating the influence ofrainfall is a predominant issue in selecting stableslopes, and knowledge of the theoreticalmechanism (or mechanisms) by which rainfallinfluences stability ought to be an aid in theprocess of using judgement to determine slopeprofiles

A further point that should be emphasised hereis that the use of non-analytical methods should inno way diminish the importance of siteinvestigations, especially investigations aimed atproviding a comprehensive picture of the geologyof a site. A simple illustration of the importance ofthis is given in Figure 11. The prime objective of asite investigation in relation to the design of cut

slopes must be to determine an accurate soilprofile at the location of the cut, especially inweathered igneous rocks such as granite. In manysituations, especially in highway construction, it isinevitable that slopes will be steep and safetyfactors will not be high. In this situation it isimperative to take maximum advantage of thestronger materials, especially any unweatheredrock. The cut should be vertical or near vertical incompetent rock, in order to minimise earthworks,and to make room for more gentle slopes in thesoil layers in the upper levels of the cut, as

indicated in Figure 11.Profiles of the sort illustrated in Figure 11 are

common in weathered granites, such as thosefound in Hong Kong and Malaysia. It is highlydesirable to determine the profiles prior tocommencement of construction raher than duringexcavation. For practical reasons slopes are cutfrom the top down in their final profile, and anyadjustments to this profile made necessary by soilconditions revealed during excavation posesconstruction difficulties. It is not an easy mattergetting excavation equipment back up to the top

Time

Time

Time

Pore

pressure

E

ective

stress

Safety

factor

End

ofco

nstruction

Longter

m

Long term steady state- typical of low permeability(sedimentary) clays

Fluctuating water table- typical of medium to highpermeability (residual) clays

Sedimentary clays

Residual clays

P

otenta a uresurface

Stormevents Seasonal

influence


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of a cut slope to re-shape the profile. Fordetermining the surface of the sound rock,geophysical methods can be a better approachthan conventional boreholes.

Figure 11 Profile of a cut slope in weatheredigneous rock such as granite

In volcanic materials, the increase in strengthwith depth found in weathered granites may be

very small or insignificant, in which case auniform slope angle is likely to be the mostappropriate. However, volcanic material is likelyto be rather unpredictable, which againemphasises the need for thorough siteinvestigations.

6.2 To bench or not to bench a slope?Figure 12 shows a slope which has incorporated

benches, or berms, into its design. These are notinfrequently considered to be an aid to improvethe stability of a slope, or at least a means tocontrol and minimise erosion.

Figure 12 Benched slope versus un-benchedslope.

Whether benches (berms) really are a desirablefeature of slope design is a question that is almostinvariably raised during discussions orpresentations on the design of cut slopes, at leastin the countries of the wet tropics. There is nosimple or single answer to this question, but thefollowing comments may be useful:

(a)Benches do not normally have a significantinfluence on the general stability of the slope.If the slope is cut without benches but with thesame average inclination as the benched slope(as indicated in Figure 12) the stability wouldbe the same. It can be argued that benchesmay have an adverse influence on stabilitybecause water will tend to pond on thebenches and result in greater infiltration into

the slope.(b)The only useful function that benches can

have is to control erosion and provide a meansof access to the slope. Their usefulness incontrolling erosion will depend very much onthe installation of properly designed sealedsurface drains on the benches and on regularmaintenance to keep the drains functioning asintended.

(c)The author is a somewhat less thanenthusiastic advocate of benches on slopesbecause he has inspected a very large numberof benched slopes in which the benches areclearly not performing any useful function.The drains that were incorporated at the timeof design have become blocked with erodedmaterial or vegetation, and in many casessurface slips of the benches have renderedthem ineffective. Where such slips occur theytend to promote concentrations of surface run-off and lead to rapid increases of surfaceerosion.

(d)For highly erodible soils such as weathered

granite, it is undoubtedly the case that controlmeasures are needed and benches may be themost practical measure available. However, itis imperative that measures are adopted toensure regular and effective maintenance ofthe benches.

(e)For erosion resistant soils, such as allophoneclays, there is no benefit to be gained from theuse of benches, and they probably do lessgood than harm.

6.3 A Note on vegetation cover on slopes

Vegetation generally has a positive effect inhelping to stabilise slopes. Its influence isthreefold:a)vegetation reduces the amount of water

seeping into the ground, and thus helps tominimise pore pressures.

b)vegetation also extracts moisture from theground, which also assists in minimising porepressures.

c)vegetation helps to minimise surface erosion.This may not have a direct influence on the

Original ground surface

Completelyweatheredsoillayer

Surfaceofsoundrock

Saprolite-weatheredrock

Steep slope in sound rockminimises earth works and

allows gentler slopes in softerlayers near the surface

10m

3m

Benches - to intercept run-offand control surface erosion


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stability of the slope, but is beneficial as awell vegetated surface is much less likely toallow seepage into the slope than a bareeroded surface.

7 BACK ANALYSIS METHODS FORDETERMINING STRENGTHPARAMETERS

7.1 Back-analysis of a single slip or asingle intact slope

Consider the slope shown in Figure 13. If thereis an existing slip in the slope, then we can assumethe safety factor is unity and by a back analysis ofthis circle we can determine shear strengthparameters c and that give SF =1. However,there is not a unique combination that satisfies thiscriterion, only a range of combinations of values.

Figure 13 Back analysis to determine the strengthparameters c and.

Even if there was not an existing slip in theslope, we could still assume it to have a safetyfactor of unity and by back analysis obtain anotherset of combinations of c and that give SF =1.The two sets of values obtained in this way areshown in Figure 14. It is seen that the values aredifferent, although they coincide at one point. Wewould not expect to get the same range of values

because the first set (from the known slip) hasbeen obtained from a single fixed slip - the oneshown in the figure. The second set has beenobtained without any constraints on the location ofthe slip circle, so that this set represents a range ofdifferent circles.This graph suggests the means by which we can

obtain a unique set of values from the analysis ofthe slope with the actual slip in it.

Figure 14 Combinations of c and obtained byback analysis of an intact and a failed slope.

Figure 15 Circles corresponding to ombinationsof c and.

If we take each of the sets of values obtainedfrom the actual slip, and then re-analyse the slopeassuming it is an intact slope (no existing slip init) seeking to determine the critical circle, we willobtain a series of critical circles in differentlocations. This is illustrated in Figure 15.The values obtained in this way are c =18kPa

and = 30o

Centre o s ip circ e

Position of

slip circle.

Ground surface andphreatic surface

. There are several other ways inwhich to determine the true values of c and .For example, they are given by the point at whichthe two graphs coincide in Figure 8.19, althoughthis point is poorly defined because of thetangential nature of the intersection. Othermethods are described by Wesley and Lelaratnam(2001).

(b) Intact slope

0.5 1.0 1.5tan/

20

40

60

Co

hesioninterceptc

(kPa)

/

(a) Slope withactual slip

0

=5o

15o

45o

35o

25o

=450

35o

25o

15o

5o

Line of centres of slip circlesshowing corresponding f values.

Centre of actual slip circle

Position of actualslip circle.

Ground surface andphreatic surface


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7.2 Analysis of a number of slips in thesame material

It is a big advantage when more than one slip isavailable in the same material. To obtain thestrength parameters c and we could apply themethod described above to each slip individuallyand then use an averaging procedure to obtain themost representative values. A better way is thatillustrated in Figure 16, which is for brown

London clay (after Chandler and Skempton,1974). This is not a residual soil but the method isequally valid for residual soils. In this exampledata is available from seven different sites in thesame material. By back analysis the average shearstrength needed to maintain stability, and also theaverage normal stress on the slip surface on whichfailure has taken place, have been determined.

Figure 16 Values of c and obtained from back-analysis of slips in brown London Clay (after

Chandler and Skempton, 1974).

These values have then been plotted on a graphof shear stress against effective normal stress, anda best fit line drawn to establish the Mohr-Coulomb failure line, and the c and values. Thehorizontal line through some of the data points inthe graph reflects uncertainty about the seepagecondition and pore pressures in the slope. The lineindicates the range of possible effective normalstress values arising from this uncertainty.

7.3 Analysis of a large number of intactslopes (no previous slips)

It is possible to collect data on slope heights andslope angles for a particular geological formationor soil type, that is, for any material that isreasonably homogeneous, and use this data todeduce the strength parameters by a curve fittingprocedure.The data should be gathered from those slopes

considered to be closest to failure, in other wordsthe steepest slopes for any particular height. The

data is then plotted in graphical form as shown inFigure 17(a) and a curve drawn defining the upperlimit of combinations of slope height and anglethat will remain stable. In addition to the curvefitted to the field data, two curves are also shownin Figure 17 to indicate the way in which theshape of the curves varies with the relativemagnitude of c and.

For any given values of c and , and fixed

seepage condition (defined by an ru

For example we can select two or three pointson the curve, such as A, B, and C, and then usethe procedure in Section 7.1 to determinecombinations of c and for each point and plotthese as graphs on a common graph, as shown inFigure 17(b). The intersection of these graphs (thepoint P) defines the values common the wholecurve and thus the values we are seeking.

value), therewill be a unique combination of slope heights andslope angles that will be stable. A procedureinvolving trial and error can then be used to fit acurve to the field data. This procedure can bequite tedious, but systematic methods can be usedto avoid time consuming trial and errorprocedures.

All of these methods are of limited value,because of the practical difficulties involved inapplying them in practice. Nature does not oftenprovide the tidy geometry or materials of uniformproperties needed to make the methods feasible

Figure 17 Curve fitting to height and slope datato determine c and.

BROWN LONDON CLAYFirst-time Slides

Long-term Equilibration may not be complete

r =0.35 0.3 0.25uGrangeHill

CuffleyHadley Wood

Sudbury Hill

Crews HillWest Acton

30

20

10

0 10 20 30 40 50Effective normal stress (kPa)

S

e a r

str

e n

g th

(kP

a )

c =1.0kPa

=20

o

c =0 =20 o

Northolt

S

ope

e

g

t

Slope angle

Best fit envelope ofavailable data

- upper limit of stableheight and anglecombinations

High low c/ /

Low high c/ /

A

B

C

tan

Cohesion

interceptc

PointA

PointBPointC

P

(a) the plotted data

(b) analysis to determinec and tan


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8 REMEDIAL MEASURES

Engineering involvement with slope stabilityissues frequently arises after failure has occurred.The engineer may be required to determine thecause of failure; his most important role, however,is likely to be determination of appropriateremedial measures to stabilise the slope. Tostabilise a slip after it has occurred, or to increase

the safety factor of a marginally stable slope wecan do one of more of the following:1. Decrease the disturbing forces

(a)flatten the slope(b)decrease the height(c)add a toe weight (berm)

2. Increase the shear resistance(a)lower the pore water pressure (drainage)(b)use mechanical keying such as piling(c)grout the soil

It is difficult to generalise as to which of theabove should be used in a particular case. All ofthe possibilities under (1) are usually practical andrelevant if the slope geometry is suitable; of thepossibilities under (2) the first (a) is by far themost relevant and practicable. 2(b) and 2(c) canonly rarely be used. The choice of measure to useis very dependent on the type of slip. There aretwo basic kinds of slips:1. Rotational typical of cuttings and

embankments usually in slope of low tomoderate height.

2. Translational typical of natural slopes

often in very large slopes of indefiniteextent.

8.1 Rotational slipsIt is generally possible and effective to decrease

the disturbing forces, as indicated in Figure 19.

Flatten slope

Decrease e g t

Add toe weight

Figure 18 Remedial, or stabilising measures,involving changing the geometry of the slope.

It may also be possible to increase the shearingresistance by installing drainage measures tolower the pore pressure. Two types of drainage,illustrated in Figure 20, are common.

Figure 19 Drainage measures to reduce porepressures in slopes.

8.2 Translational slipsIn this case it is usually not possible to reduce

the disturbing forces by flattening the slope or byadding a toe weight, because of the size of theslope and slide.

Generally the installation of drainage measuresis the only practical possibility, and trench drainsare by far the most effective method of doing this.The concept is illustrated in Figure 21. It isimportant to check that the ground water level inthe slope is high and that the drains will therefore

lower the pore pressures.

Figure 20 Drainage measures in translationalslides.

Ideally, the drains should be taken below thefailure surface but this is not essential. Thespacing should be in the range of 3 to 5 times thedepth.

It should be noted that in many remedialsituations, especially those involving large

Trench backfilledwith drainage material

Perforated pipe totake away inflow

Perforated pipesin drilled holes

(a) Trench or buttress drains

(b) Bored horizontal drains

Trenches backfilledwith drainage material

Perforated pipe totake away inflow

D

Spacing=(4 to 6)D

PLAN

CROSS SECTION

Horizontal drains could also beused - can be deeper but areless reliable than trench drains


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translation slides in residual soils, the safetyfactor is often very low, and it is usuallyimpractical to increase the value by more than say0.1 or 0.2, i.e. we can only hope to raise a safetyfactor of 1.0 to a value of 1.1 or 1.2. At a dam site(the Clyde Dam) in the South Island of NewZealand, half a billion dollars was spentstabilising landslides in most cases the safetyfactors were raised by only 0.1 or 0.2.

8.3 Mechanical methods, such as piling orgrouting.

The forces involved in most slips are very largein comparison to the resistance which can beprovided by pile installation. Figure 21 illustratesthe relative effectiveness of drainage measuresand bored piles on stability. It is evident thatdrainage measures are likely to be the preferredmethod for stabilising this particular slope.

Figure 21 Relative influence of drainage measuresand shear piles on safety factor.

Grouting cannot generally be used on clayslopes, because conventional cement grouts willnot flow into the pore space of clays. Groutingwould be a possibility in sandy or gravelymaterials. Various types of grouts that dont usecement are available on the market, but even thesemay not be very effective unless the clay is orrelatively high permeability.

REFERENCESGeotechnical Engineering Office, Civil Engineering

Department, The Government of Hong Kong (1984).Geotechnical Manual for Slopes, Second Edition.

Chandler, R.J ., and A.W.Skempton (1974) The designof permanent cutting slopes in stiff fissured clays.Geotechnique, 24 (4): 457- 466.

Wesley, L.D. and Lelaratnam, V. (2001). Shearstrength parameters from back-analysis of singleslips. Geotechnique, 51(4): 373 374.

40m

Potential slip surface

2:1Wate

rtable

Soil properties: Unit weight =16kN/mFriction angle =25

Cohesion intercept =15 kN/m

3

o

2

Safety factor =1.04

Groundwater level lowered 5m using drainage measures

Safety factor =1.33

Safety factor =1.16 (approx)

Six bored piles, 1m dia, penetrating through theslip surface, at 2m spacing along the slope

heavily reinforced,

5m


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