general slope stability concepts

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PB051-01 5168F-Abramson August 2, 2001 16:39

CHAPTER 1

GENERAL SLOPESTABILITY CONCEPTS

1.1 INTRODUCTION

The evolution of slope stability analyses in geotechnical engineering has followedclosely the developments in soil and rock mechanics as a whole. Slopes either occurnaturally or are engineered by humans. Slope stability problems have been facedthroughout history when men and women or nature has disrupted the delicate balanceof natural soil slopes. Furthermore, the increasing demand for engineered cut and fillslopes on construction projects has only increased the need to understand analyticalmethods, investigative tools, and stabilization methods to solve slope stability prob-lems. Slope stabilization methods involve specialty construction techniques that mustbe understood and modeled in realistic ways.

An understanding of geology, hydrology, and soil properties is central to apply-ing slope stability principles properly. Analyses must be based upon a model thataccurately represents site subsurface conditions, ground behavior, and applied loads.Judgments regarding acceptable risk or safety factors must be made to assess theresults of analyses.

The authors have recognized a need for consistent understanding and applica-tion of slope stability analyses for construction and remediation projects across theUnited States and abroad. These analyses are generally carried out at the beginning,and sometimes throughout the life, of projects during planning, design, construc-tion, improvement, rehabilitation, and maintenance. Planners, engineers, geologists,contractors, technicians, and maintenance workers become involved in this process.

This book provides the general background information required for slope sta-bility analyses, suitable methods of analysis with and without the use of computers,and examples of common stability problems and stabilization methods for cuts and

1

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2 GENERAL SLOPE STABILITY CONCEPTS

fills. This body of information encompasses general slope stability concepts, engi-neering geology principles, groundwater conditions, geologic site explorations, soiland rock testing and interpretation, slope stability concepts, stabilization methods,instrumentation and monitoring, design documents, and construction inspection.

Detailed discussions about methods used in slope stability analyses are given,including the ordinary method of slices, simplified Janbu method, simplified Bishopmethod, Spencer’s method, other limit equilibrium methods, numerical methods, totalstress analysis, effective stress analysis, and the use of computer programs to solveproblems. This book is intended for individuals who deal with slope stability problems,including most geotechnical engineers and geologists who have an understanding ofgeotechnical engineering principles and practice.

1.2 AIMS OF SLOPE STABILITY ANALYSIS

In most applications, the primary purpose of slope stability analysis is to contributeto the safe and economic design of excavations, embankments, earth dams, landfills,and spoil heaps. Slope stability evaluations are concerned with identifying criticalgeological, material, environmental, and economic parameters that will affect theproject, as well as understanding the nature, magnitude, and frequency of potentialslope problems. When dealing with slopes in general and slope stability analysis inparticular, previous geological and geotechnical experience in an area is valuable.

The aims of slope stability analyses are

(1) To understand the development and form of natural slopes and the processesresponsible for different natural features.

(2) To assess the stability of slopes under short-term (often during construction)and long-term conditions.

(3) To assess the possibility of landslides involving natural or existing engineeredslopes.

(4) To analyze landslides and to understand failure mechanisms and the influenceof environmental factors.

(5) To enable the redesign of failed slopes and the planning and design of preven-tive and remedial measures, where necessary.

(6) To study the effect of seismic loadings on slopes and embankments.

The analysis of slopes takes into account a variety of factors relating to topography,geology, and material properties, often relating to whether the slope was naturallyformed or engineered.

1.3 NATURAL SLOPES

Many projects intersect ridges and valleys, and these landscape features can be proneto slope stability problems. Natural slopes that have been stable for many years

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1.4 ENGINEERED SLOPES 3

may suddenly fail because of changes in topography, seismicity, groundwater flows,loss of strength, stress changes, and weathering. Generally, these failures are notunderstood well because little study is made until the failure makes it necessary. Inmany instances, significant uncertainty exists about the stability of a natural slope.This has been emphasized by Peck (1967), who said:

Our chances for prediction of the stability of a natural slope are perhaps best if thearea under study is an old slide zone which has been studied previously and may bereactivated by some human operations such as excavating into the toe of the slope. Onthe other hand, our chances are perhaps worst if the mechanism triggering the landslideis (1) at a random not previously studied location and (2) a matter of probability suchas the occurrence of an earthquake.

Knowing that old slip surfaces exist in a natural slope makes it easier to understandand predict the slope’s behavior. Such slip surfaces often result from previous land-slides or tectonic activities. The slip surfaces may also be caused by other processes,including valley rebound, glacial shove, and glacial phenomena such as solifluctionand nonuniform swelling of clays and clay–shales. The shearing strength along theseslip surfaces is often very low because prior movement has caused slide resistance topeak and gradually reduce to residual values. It is not always easy to recognize land-slide areas (while postglacial slides are readily identified, preglacial surfaces may lieburied beneath glacial sediments). However, once presheared strata have been located,evaluation of stability can be made with confidence.

The role of progressive failure in problems associated with natural slopes has beenrecognized more and more as time goes on. The materials most likely to exhibitprogressive failure are clays and shales possessing chemical bonds that have beengradually disintegrated by weathering. Weathering releases much of the energy storedin these bonds (Bjerrum, 1966). Our understanding of landslides involving clay andshale slopes and seams has increased largely due to the original work by Bishop(1966), Bjerrum (1966), and Skempton (1964).

1.4 ENGINEERED SLOPES

Engineered slopes may be considered in three main categories: embankments, cutslopes, and retaining walls.

1.4.1 Embankments and Fills

Fill slopes involving compacted soils include highway and railway embankments,landfills, earth dams, and levees. The engineering properties of materials used inthese structures are controlled by the borrow source grain size distribution, the meth-ods of construction, and the degree of compaction. In general, embankment slopesare designed using shear strength parameters obtained from tests on samples of theproposed material compacted to the design density. The stability analyses of embank-ments and fills do not usually involve the same difficulties and uncertainties as naturalslopes and cuts because borrow materials are preselected and processed. Because fills

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are generally built up in layers, analyses are required for all steps in the life of theproject including:

(1) All phases of construction

(2) The end of construction

(3) The long-term condition

(4) Natural disturbances such as flooding and earthquakes

(5) Rapid drawdown (for water-retaining structures like earth dams)

Debris and waste landfills differ from other engineering slopes in that they typicallyhave an extreme variety of material types, sizes, and characteristics. These materialsare extremely difficult to characterize and analyze.

Constructed fills have been used since antiquity with varying degrees of successand failure. In ancient times, they were used to construct earth fill dams for storingirrigation water. One of the oldest recorded earth fill dams is the dam completed inCeylon in the year 504 BC, which was 11 miles long, 70 feet high, and containedabout 17 million cubic yards of embankment (Schuyler, 1905).

It is well known and documented that compaction of soils increases their strength.Tools and methods for compacting soils were developed long before the principlesof compaction were discovered in the 1930s. For a long period of time, before thebuilding of the first road compaction roller in the 1860s, cattle, sheep, and goats wereused to compact soils. For example, in the United States, the 85-foot high Santa Fewater supply dam of New Mexico was compacted by 115 goats in 1893 (HighwayResearch Board, 1960).

Although mechanical equipment has been used to compact soil since the late 1860s,the engineering literature prior to the 1930s gave no evidence that anyone had estab-lished the relationships between moisture content, unit weight, and the compactioneffort, relationships that are now documented as the fundamental principles of soilcompaction. Between the 1930s and 1940s, the principles of compaction were widelyknown and discussed among engineers. The “Proctor curve” was a result of thesestudies. Following the work by Proctor, numerous investigations and reports wereprepared to increase knowledge of compaction principles, which, through modifica-tions and upgrading, resulted in widely used compaction testing standards.

Today, as in the past, earth materials continue to be used for embankment fillsand backfill behind retaining structures because of their widespread availability andrelative economy. Backfill is compacted in lifts that vary from 6 inches to 3 feet,depending on the types of soils and proposed use. Different types of compactors,ranging from large sheep’s foot and vibratory rollers to small hand-operated tampers,have been developed and used to compact soils.

Embankment fills generally consist of:

(1) Cohesionless soils (sands and gravels)

(2) Cohesive soils (silts and clays)

(3) A mixture of cohesionless and cohesive soils, gravels, and cobbles (hereincalled earth–rock mixtures).

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Figure 1.1 The moisture–density relationship (Proctor curve).

Organic soils, soft clays, and silts are usually avoided. The range of particle sizesof embankment fills is governed, for economic purposes, by the availability of thematerials from nearby borrow areas.

The density of the materials after being excavated from borrow areas is usually verylow and can be increased by compaction with mechanical equipment. In general, whenthe moisture content of the compacted soil is increased, the density will increase undera given compaction effort, until a peak or maximum density is achieved at a particularoptimum moisture content. Thereafter, the density decreases as the moisture contentis increased. The variations of moisture contents with density of the compacted soilis generally plotted in curves (Proctor curves) similar to Figure 1.1. The point of100 percent saturation is called the saturation line, which is never reached since someair (pore space) always remains trapped in the soil material.

Cohesionless and cohesive soils behave differently when being compacted andhave different compaction curves under the same compaction effort. Engineering char-acteristics of fills are discussed in the following sections. Typical engineering prop-erties for compacted soils include maximum dry unit weight (standard compaction),optimum moisture content, typical strength, and permeability characteristics.

In general, soil shear strength varies with soil type and compaction conditions.Samples compacted dry of optimum moisture content appear stronger and more stablethan those compacted wet of optimum moisture content. Increasing the compactioneffort on soil reduces the permeability by reducing the amount of void space betweenthe soil particles. When soil is compacted dry of optimum moisture content, thepermeability is increased with an increase in water content. There is a slight decreasein permeability if the water content exceeds the optimum value.

Cohesionless Fills Cohesionless soils generally consist of relatively clean sandsand gravels that remain pervious when compacted. These soils are represented by

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Unified Classification System soil groups SW, SP, GW, GP, and boundary groups ofany of these.

During the compaction process, compacted cohesionless soils are not affectedsignificantly by water content because they are relatively pervious. The Proctor curve,as depicted in the dry density versus optimum moisture content graph, is usuallyround. Hence, their compactness is usually evaluated based on their relative density,as introduced by Terzaghi (1925) and defined as

Dr = emax − e

emax − emin(Eq. 1-1)

where Dr = relative density expressed as a percentageemax = void ratio of the soil in its loosest state

e = void ratio of the soil being testedemin = void ratio of the soil in its densest state

Since void ratio is related to dry density for a given specific gravity, Equation 1-1 canbe written as

Dr = γdmax(γd − γdmin)

γd (γdmax − γdmin)(Eq. 1-2)

where γdmax = dry density of the soil in its densest stateγdmin = dry density of the soil in its loosest state

γd = dry density of the soil being tested

The loose or dense state of cohesionless soils is usually judged by relative densityas defined by Terzaghi. Typical ranges of relative density of sand are

0 < Dr < 13 Loose sand

13 < Dr < 2

3 Medium dense sand23 < Dr < 1 Dense sand

Terzaghi further defined compactibility as

F = emax − emin

emin(Eq. 1-3)

where F is very large for well-graded cohesionless soil such as SW and GW soils.Table 1.1 presents a list of compactibility values (F) for cohesionless soils.

Cohesive Fills Cohesive soils consist of those that contain sufficient quantitiesof silt and clay to render the soil mass relatively impermeable when properly com-pacted. Unlike compacted cohesionless soils, whose physical properties are generallyimproved by compaction to the maximum dry unit density, the physical propertiesof cohesive soils are not necessarily improved by compaction to a maximum unit

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TABLE 1.1 List of Compactibility Factor F

MaximumClassification γmin γmax emin emax Size D10 Cu Cc F

SP-SM 90 108 0.54 0.84 #16 0.058 6.1 2.2 0.555SM 75 97 0.83 1.36 3

4

′′0.0065 31.0 5.5 0.638

SP 92 112 0.48 0.80 #4 0.15 3.0 0.93 0.667SP 93 113 0.46 0.77 1 1

2

′′0.16 2.4 0.92 0.674

SP 95 116 0.43 0.74 #4 0.30 3.7 1.0 0.721SP-SM 92 113 0.46 0.80 3

4

′′0.08 3.0 0.88 0.739

SP 85 107 0.54 0.94 #30 0.10 2.3 1.3 0.740SP 97 118 0.40 0.70 1 1

2

′′0.11 3.2 1.2 0.750

SP 99 120 0.38 0.67 1 12

′′1.8 4.4 0.76 0.763

SM-ML 83 108 0.62 1.11 #4 0.012 8.3 1.5 0.790SP-SM 79 103 0.60 1.08 #30 0.09 2.4 1.5 0.800SP 103 124 0.33 0.60 3

8

′′0.17 5.0 0.75 0.818

SM 105 126 0.31 0.57 5′′ 0.02 350.0 0.30 0.838SP-SM 87 112 0.48 0.90 #4 0.08 3.0 1.3 0.875SM 82 108 0.54 1.02 #16 0.023 6.5 1.4 0.889SW-SM 95 119 0.39 0.74 3′′ 0.05 10.0 1.4 0.897SP 98 122 0.36 0.69 #4 0.37 5.1 1.2 0.917SW-SM 98 125 0.34 0.71 3′′ 0.07 6.8 1.0 1.088SP-SM 97 124 0.33 0.70 3

4

′′0.10 5.0 1.4 1.121

SP-SM 84 115 0.44 0.97 1 12

′′0.085 4.7 1.4 1.205

SP-SM 94 123 0.34 0.76 1 12

′′0.12 4.4 1.3 1.235

SM 99 128 0.31 0.70 3′′ 0.02 240.0 1.8 1.258SP-SM 80 114 0.44 1.06 #16 0.07 3.7 1.6 1.409SW-SM 80 116 0.42 1.07 1 1

2

′′0.074 6.6 2.4 1.547

SM 83 120 0.38 0.99 #4 0.015 26.0 6.1 1.605SM 102 134 0.23 0.62 3

4

′′0.01 120.0 1.9 1.695

GN-GM 113 127 0.31 0.47 3′′ 0.14 86.0 1.2 0.517GP-GM 112 129 0.32 0.52 3′′ 0.03 200.0 0.50 0.625GW-GM 116 133 0.26 0.44 5′′ 0.17 171.0 2.2 0.692GP-GM 110 128 0.30 0.51 3′′ 0.11 191.0 15.0 0.700GP-GM 117 133 0.24 0.41 5′′ 0.125 160.0 4.0 0.708GW-GP 111 130 0.27 0.49 3′′ 0.20 105.0 7.5 0.815GP 116 134 0.23 0.43 5′′ 0.27 111.0 6.2 0.870GW 119 139 0.24 0.45 3′′ 0.51 45.0 2.2 0.875GW 120 139 0.20 0.39 3′′ 0.45 51.0 1.6 0.950GW 119 139 0.21 0.41 3′′ 0.18 94.0 1.1 0.952GW 111 132 0.25 0.49 3′′ 2.9 9.7 1.8 0.960GP 115 136 0.22 0.44 5′′ 0.38 29.0 0.61 1.000GP 114 135 0.22 0.45 3′′ 2.0 11.0 0.77 1.045GW-GM 121 141 0.19 0.39 3′′ 0.30 77.0 2.3 1.052GM 122 141 0.17 0.36 1 1

2

′′0.025 381.0 3.0 1.118

GW-GM 114 137 0.21 0.45 3′′ 0.60 16.0 1.2 1.143GW 112 138 0.20 0.48 3′′ 2.0 12.0 1.3 1.400GW 109 137 0.21 0.52 3′′ 2.0 14.0 2.6 1.476

(Continued )

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TABLE 1.1 (Continued )

MaximumClassification γmin γmax emin emax Size D10 Cu Cc F

GP 114 140 0.18 0.45 3′′ 1.7 10.0 0.76 1.500GM 101 132 0.25 0.64 1 1

2

′′0.03 260.0 12.0 1.560

GW-GM 111 139 0.19 0.49 3′′ 1.8 13.0 2.3 1.578GP 115 142 0.17 0.44 3′′ 0.31 87.0 8.2 1.588GW 123 146 0.13 0.34 3′′ 0.21 124.0 1.1 1.615GW-GM 110 139 0.19 0.50 5′′ 0.42 43.0 2.1 1.631GW-GM 115 142 0.17 0.45 3′′ 0.15 133.0 1.1 1.647GP-GM 112 140 0.18 0.48 3′′ 0.42 26.0 4.2 1.667GW-GM 112 140 0.18 0.48 5′′ 0.25 56.0 1.0 1.667GW-GM 114 142 0.16 0.45 3′′ 1.2 15.0 1.7 1.812GP 112 141 0.17 0.48 3′′ 1.4 7.1 0.73 1.823GW-GM 118 147 0.12 0.40 3′′ 1.3 19.0 1.1 2.333

Source: Hilf (1991).

density. For example, Figure 1.2 indicates that the strength of compacted silty claydecreases with increasing molding water content (Seed and Chan, 1959).

Whether compacted cohesive soils should be placed dry or wet of optimum for thesame density depends on the type of construction. During construction of a fill slope,data (Lee and Haley, 1968) indicate that it is better to place cohesive soils dry ofoptimum. Such data are presented in Figures 1.3 and 1.4. Nevertheless, for earth damconstruction, there is an increasing tendency to compact the cores of earth dams onwet of the optimum moisture content to minimize crack development and subsequentformation of seepage channels. A balance must be struck between the resultant lowerstrength and potential pore pressure problems caused by using a higher initial watercontent.

By changing the moisture content of compacted clays, a pronounced change in theirengineering properties results. The effects of compaction dry and wet of optimum onthe shear strength, permeability, compressibility, and structure of cohesive soils areshown in Table 1.2.

Earth–Rock Mixtures There has been a considerable increase in the usage ofearth–rock mixtures in the fills of high embankments over the last 40 years. Such soilsare heterogeneous mixtures of particles that may range in size from large boulders toclay. The mixing of the larger size particles enhances the workability of the soil inthe field and increases the overall strength of the soil.

Past research studies by the Bureau of Reclamation (Holtz and Gibbs, 1956) sug-gested that the strength of earth–rock mix fill depends on the amount of rock to bemixed with the in situ soils. The strength will increase with the amount of rock untilsome threshold percentage, for instance about 50 to 68 percent for sand–gravel mix-tures, is reached. Further increase in gravel contents produces little to no increase instrength. Variations in friction angle with gravel contents of earth–rock mixtures forcoarse-grained soils are shown in Figure 1.5.

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Figure 1.2 Strength of compacted clay versus moisture content. (From Seed and Chan, 1959,reproduced by permission of ASCE.)

Embankments on Weak Foundations Embankments are sometimes builton weak foundation materials. Sinking, spreading, and piping failures may occurirrespective of the stability of the new overlying embankment material. Considera-tion of the internal stability of an embankment-foundation system, rather than just theembankment, may be necessary. A simple rule of thumb based on bearing capacitytheory can be used to make a preliminary estimate of the factor of safety against

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Figure 1.3 Compaction and unconfined compression characteristics of Higgins clay. (a) Un-confirmed compression tests. (b) Compaction curves. (From Lee and Haley, 1968, reproducedby permission of ASCE.)

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Figure 1.4 Unconsolidated-undrained tests on compacted Higgins clay. (a) Stress–straincurves = 250 psi. (b) Strength versus confining pressure. (From Lee and Haley, 1968, repro-duced by permission of ASCE.)

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TABLE 1.2 Comparison between Dry of Optimum and Wet of OptimumCompaction of Cohesive Soils

Physical Properties Effects of Compaction

Shear Strength

As moldedUndrained Dry side much higherDrained Dry side somewhat higher

After saturationUndrained Dry side somewhat higher if swelling

prevented; wet side can be higher ifswelling permitted

Drained Dry side about the same or slightly higherPore-water pressure at failure Wet side higherStress–strain modulus Dry side much greaterSensitivity Dry side more apt to be sensitive

Permeability

Magnitude Dry side more permeablePermanence Dry side permeability reduced much more

by permeation

Compressibility

Magnitude Wet side more compressible in low stressrange, dry side in high stress range

Rate Dry side consolidates more rapidly

Structure

Particle arrangement Dry side more randomWater deficiency Dry side more deficient, therefore more water

imbibed, more swell, lower pore pressurePermanence Dry-side structure more sensitive to change

Source: Table extracted from Soil Mechanics, by Lambe and Whitman (1969).

circular arc failure for an embankment built over a clay foundation. The rule is (Cheneyand Chassie, 1982)

FOS = 6c

γfill × Hfill(Eq. 1-4)

where FOS = factor of safetyc = cohesion of foundation clay (pounds per square foot)

γfill = unit weight of embankment fill (pounds per square foot)Hfill = height of embankment fill (feet)

The factor of safety computed using this rule serves only as a rough preliminaryestimate of the stability of an embankment over a clay foundation and should not be

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Figure 1.5 Total stress angle of internal friction versus gravel contents. (Donaghe and Torrey,1985.)

used for final design. The simple equation does not take into consideration factorssuch as fill strength, strain incompatibility between embankment fill and the underly-ing foundation soils, and fill slope angle. In addition, it does not identify the locationof a critical failure surface. If the factor of safety using the rule-of-thumb equa-tion is less than 2.5, a more sophisticated stability analysis is required (Cheney andChassie, 1982).

Figure 1.6 shows the variations in safety factor, strength, pore pressures, load, andshear stresses with time for an embankment constructed over a clay deposit. Overtime, the excess pore pressure in the clay foundation diminishes, the shear strengthof the clay increases, and the factor of safety for slope failure increases.

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Figure 1.6 Stability conditions for an embankment slope over a clay foundation. (FromBishop and Bjerrum, 1960, reproduced by permission of ASCE.)

Embankment fills over soft clay foundations are frequently stronger and stifferthan their foundations. This leads to the possibility that the embankment will crackas the foundation deforms and settles under its own weight and to the possibility ofprogressive failure because of stress–strain incompatibility between the embankmentand its foundation. Design charts developed by Chirapuntu and Duncan (1977), usingfinite element method analyses, depict the effects of cracking and progressive failureon the stability of embankments on soft foundations. These charts may be used as asupplement to conventional stability analyses. The use of geosynthetic reinforcementin the fill may prevent the initiation of cracking and subsequent failure in these cases.Alternatively, it may be necessary to remove the soft foundation materials or locatethe fill at another site.

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Figure 1.7 Example of stress–strain incompatibility.

Peak strengths of the embankment and the foundation soils cannot be mobilizedsimultaneously because of stress–strain incompatibility (Figure 1.7). Hence, a stabil-ity analysis performed using peak strengths of soils would overestimate the factor ofsafety. Many engineers perform stability analyses using soil strengths that are smallerthan the peak values to allow for possible progressive failure.

Shale Embankments Embankments constructed of shale materials often haveslope stability and settlement problems. According to DiMillio and Strohm (1981),the underlying causes of shale fill slope failures and excessive settlement frequentlyappear to be:

(1) Deterioration or softening of certain shales over time after construction

(2) Inadequate compaction of the shale fill

(3) Saturation of the shale fill

These types of failures have been found to be typical in many areas from the Ap-palachian region to the Pacific coast. In general, severe problems with shales inembankments are found in states east of the Mississippi River rather than west of theriver (DiMillio and Strohm, 1981). Embankments can use fill originating from shaleformations successfully if the borrow source is not particularly prone to long-termdecomposition and if adequate compaction and drainage are required. In addition,shale embankments should be keyed into any sloping surfaces by using benches andinstalling drainage measures to intercept subsurface water that may enter the foun-dation area. Guidelines for design and construction of shale embankments have beenestablished by Strohm et al. (1978).

1.4.2 Cut Slopes

Shallow and deep cuts are important features in any civil engineering project. Theaim in a slope design is to determine a height and inclination that is economical

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and that will remain stable for a reasonable life span. The design is influenced bythe purposes of the cut, geological conditions, in situ material properties, seepagepressures, construction methods, and the potential occurrence of natural phenomenasuch as heavy precipitation, flooding, erosion, freezing, and earthquakes.

Steep cuts often are necessary because of right-of-way and property line con-straints. The design must consider measures that will prevent immediate and suddenfailure as well as protect the slope over the long term, unless the slope is cut fortemporary reasons only. In some situations, cut stability at the end of constructionmay be a critical design consideration. Conversely, cut slopes, although stable in theshort term, can fail many years later without much warning.

To a certain degree, the steepness of a cut slope is a matter of judgment not relatedto technical factors. Flat cut slopes, which may be stable for an indefinite period, areoften uneconomical and impractical. Slopes that are too steep may remain stable onlyfor a short period of time. A failure may pose a danger to life and property at a laterdate. Failures could involve tremendous inconvenience and the expense of repairs,maintenance, and stabilization measures.

Figure 1.8 shows the general variations of factor of safety, strength, excess porepressure, load, and shear stresses over time for a clay cut slope. The initial shearstrength is equal to the undrained shear strength on the assumption that no drainageoccurs during construction. In contrast to embankment slopes, the pore pressure withinthe cut increases over time. This increase is accompanied by a swelling of the clay,which results in reduced shear strength. Thus the factor of safety decreases over timeuntil an unstable condition is reached. This, for the most part, explains why clayeycut slopes sometimes fail a long time after initial excavation.

For cuts in overconsolidated clays, the in situ shear strength is a direct function ofthe maximum past overburden pressure. The higher the maximum past overburdenpressure, the greater the shear strength. However, if the clay is subjected to long-termunloading conditions (permanent cuts), the strength of the clay no longer dependson the prior loading. The strength of a cut slope will decrease with time. The lossin strength is attributed to reduction of negative pore pressure after excavation. Thisloss in strength has been observed to be a time-dependent function related to the rateof dissipation of negative pore pressure.

In practice, the loss in strength after cuts are made is not easily determined. Ac-cording to McGuffey (1982), the time dependency of clay cut slope failures can behypothesized to be a function of the Terzaghi hydrodynamic lag model. The estimatedtime to failure can be expressed as (McGuffey, 1982)

t = h2T90

Cν

(Eq. 1-5)

where t = time to failureh = average distance from the slope face to the depth of the maximum

negative pore pressureT90 = time factor for 90% consolidation = 0.848Cν = coefficient of consolidation (square feet per day)

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Figure 1.8 Stability conditions for a cut slope. (From Bishop and Bjerrum, 1960, reproducedby permission of ASCE.)

This model was used with some success by McGuffey (1982) to determine andback-analyze the time for stress release leading to slope failures in clay cuts in NewYork.

Long-term cut slope stability is also dependent on seepage forces and, therefore, onthe ultimate groundwater level in the slope. After excavation, the free-water surfacewill usually drop slowly to a stable zone at a variable depth below the new cut surface.This drawdown usually occurs rapidly in cut slopes made in sand but is usually muchslower in clay cut slopes. Although typical rates and shapes of groundwater draw-down curves have been proposed for cut slopes, none has proved useful for correctlypredicting the time or rate of drawdown of preconsolidated clays. The main obstacleto such prediction comes from the difficulty in correctly modeling the recharge of thearea in the vicinity of the cut slope.

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Figure 1.9 Cut and fill slopes used for landfills. (From Mitchell and Mitchell, 1992, repro-duced by permission of ASCE.)

1.4.3 Landfills

Landfills are a special case where both cut and fill slopes are involved (Figure 1.9) andwhere the fill materials are much less than optimum. To make matters worse, exceptfor very old landfills, zones of clay barriers and, more recently, geosynthetic barriers(Figure 1.10) are placed between the fill materials and the natural ground, creatingan extra zone that must be characterized and analyzed with respect to short-term andlong-term stability. Also, the plethora of environmental regulations that are imposedon existing and new landfills places an extremely heavy burden on the engineersand geologists to accurately characterize and analyze the short-term and long-termbehavior of landfills for the life of the project and beyond.

Landfills may contain organic materials, tree limbs, refuse, and a variety of debristhat are commonly dumped, pushed, and spread by bulldozers, and then compactedby refuse compactors. Compaction of landfills is somewhat different from the com-paction of soils, particularly with respect to crushing. Compaction crushes (collapses)hollow particles, such as drums, cartons, pipes, and appliances, and brings the crushedparticles closer together. It may be expected that landfills, compacted at the top only,will be relatively loose. Landfill materials are commonly soft, and large voids can beencountered.

The evaluation of landfill slope stability is similar to the analysis of other typesof slope stability problems. Selection of proper values for the strengths of the wasteand foundation materials, and of proper shearing resistances along the interfaceswithin the liner and cover systems, is the most critical part of any stability study. Thegreatest difficulties and uncertainties are associated with evaluation of the strengthand stress–strain properties of the liner system materials and interfaces, and of thewaste fill.

Very little is known about the geotechnical engineering properties of landfills. Thepaucity of data results in part from the difficulties in credible sampling and testingof refuse. This difficulty is further compounded by the fact that refuse compositionand properties are likely to change erratically within a landfill and are also likely todecompose with time.

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The unit weight of landfill is highly dependent on a number of factors, includ-ing initial composition, compactive effort, decomposition, settlement, and moisturecontent. Although the density of the landfill will typically increase with depth, con-siderable variability should be expected within relatively short distances (Landva andClark, 1987).

The moisture content of landfill materials is also dependent on a number of in-terrelated factors, such as the initial composition, landfill operating procedures, theeffectiveness of any leachate collection and removal systems, the amount of moisturegenerated by biological processes within the landfill, and the amount of moistureremoved with landfill gas (Mitchell and Mitchell, 1992). The water content of thelandfills in the United States ranges from 10 to 50 percent.

Shear strengths of the landfills may be estimated by means of:

(1) Laboratory testing

(2) Back-calculation from field tests and operational records

(3) In situ testing

Laboratory samples are usually reconstituted from landfills before they are tested.Direct shear tests have been commonly used to determine shear strength parametersof the landfill materials. Back-calculation of an existing landfill based on field loadtests also can be made to estimate the shear strengths of the landfill (Converseet al., 1975). However, the back-calculated strengths are usually conservative by anunknown amount because the back-calculation assumes failure of the slope (that is, afactor of safety equal to 1). Vane shear and standard penetration tests have been usedto estimate the shear strength of refuse in a landfill near Los Angeles, California(Earth Technology Corporation, 1988). The shear strength data obtained by thesein situ testings may not be representative of the actual conditions because both thevane shear device and the standard penetration sampler are small compared with theinclusions (for example, tires, wood, carpet) that make up the landfill.

True cohesion or bonding between particles is unlikely in landfills. However, theremay be a significant cohesion intercept that results from interlocking and overlappingof the landfill constituents. This interpretation is supported by some laboratory test re-sults and the common observation that vertical cuts in landfills can stand, unsupported,to considerable heights (Mitchell and Mitchell, 1992).

Alshunnar (1992) proposed the following design considerations for landfill slopes:

(1) Groundwater conditions before and after construction of the landfill

(2) Subsurface conditions

(3) Construction sequence

(4) Adjacent site conditions and history

(5) Site topography

(6) External loads such as from construction equipment, stockpiles, earthquakes,and so on

(7) Liner geometry and configuration

(8) Filling sequence

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It is extremely difficult to reconcile the uncertainties implicit in landfill sitecharacterizations (e.g., landfill material types and characteristics, future land use atand around the site, the probability of severe natural phenomena like earthquakes,tsunamis, sinkholes, etc.) with the guarantees that regulatory agencies require of oper-ators and owners related to siting, operations, and closure. Seed and Bonaparte (1992)stated:

There are some considerable uncertainties with respect to material properties and dy-namic response characteristics associated with both: (a) waste fill masses, and (b) baseliner systems and final cover systems. As a result, current analysis and design methodsare generally based on a sequence of conservative assumptions at various stages of theanalyses, with the resulting cumulative level of conservatism generally selected so asto offset the possible impact(s) of uncertainties at each stage of analysis and design. Inthe opinion of the authors, the compounding of conservative assumptions, both in termsof property/parameter selection and analysis/evaluation methodology, at multiple stagesduring the overall analysis and design process should provide a conservative final resultwhen carefully implemented.

An example of how modern regulations and construction methods of landfillssurpassed analytical characterization and design methods is the case of the KettlemanHills Landfill B-19 Phase IA failure. On March 19, 1988, there was a failure in LandfillB-19, Phase IA at the Kettleman Hills Class I hazardous waste treatment, storage,disposal facility (Byrne et al., 1992). Approximately 580,000 cubic yards of wasteand other material had been placed to a height of 90 feet above the base at the time ofthe failure (Figure 1.11). The entire mass slid a horizontal distance of about 35 feettoward the southeast, and vertical slumps of up to 14 feet along the sideslopes ofthe landfill were observed after the failure (Figure 1.12). Initial study of the failureindicated that it had most likely occurred within the liner system and identified bothgeomembrane/clay and various synthetic/synthetic interfaces as candidate slidingsurfaces. The characteristics of the landfill base and sideslope liners are shown inFigure 1.13. Further study, testing, and two- and three-dimensional slope stabilityanalyses after the failed waste and liner materials were excavated concluded that

(1) The mechanism of failure consisted of slip along multiple interfaces withinthe landfill liner system.

(2) Low liner interface strengths (residual friction angles as low as 8 degrees)relative to the constructed geometry of the landfill were clearly the underlyingcause of the failure.

(3) The predominant surface of sliding during the failure appeared to be the ge-omembrane/clay interface of the secondary liner system that apparently be-haved in an essentially undrained mode during the approximately one year ofwaste loading prior to failure.

(4) Undrained shear strength testing of the clay/geomembrane interface indicatedthat the shear strength was sensitive to the as-placed moisture and densityconditions of the clay.

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Figure 1.11 Kettleman Hills landfill layout. (From Byrne et al., 1992, reproduced by per-mission of ASCE.)

Figure 1.12 Slope failure at Kettleman Hills Landfill. (From Byrne et al., 1992, reproducedby permission of ASCE.)

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Figure 1.13 Kettleman Hills landfill liner characteristics. (From Byrne et al., 1992, repro-duced by permission of ASCE.)

(5) The calculated factor of safety using a three-dimensional model and residualshear strengths was 0.85. This was consistent with the observed occurrence oflarge displacements following failure initiation and the attainment of residualstrength conditions over the entire slip surface.

(6) The failure demonstrated that specifications for the placement of liner claymust focus not only on achieving specific permeability requirements, butalso on developing liner shear strengths that are adequate to support both theinterim and final geometric configurations of the landfill.

It should be noted here that three-dimensional analysis was required for this case be-cause of the complex geometry and difficulty in selecting a typical two-dimensionalsection to analyze. However, as Duncan (1992) states, “The factor of safety cal-culated using 3D analyses will always be greater than, or equal to, the factor ofsafety calculated using 2D analyses.” This is true for all cuts and fills, not justlandfills.

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1.4.4 Retaining Structures

Retaining structures are frequently used to support stable or unstable earth masses.The different types of retaining structures, as shown in Figure 1.14, are:

(1) Gravity walls (e.g., masonry, concrete, cantilever, or crib walls)

(2) Tieback or soil-nailed walls

(3) Soldier pile and wooden lagging or sheet pile walls

(4) Mechanically stabilized embankments including geosynthetic and geogrid re-inforced walls

Figure 1.14 Types of retaining structures. (a) Gravity retaining wall. (b) Tieback retainingwall. (c) Sheet pile cantilever wall or soldier pile. (d ) Mechanically stabilized embankment.

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1.5 LANDSLIDES 25

Retaining structures are used in seven principal ways, as shown in Figure 1.15. Thedesign of retaining structures requires three primary considerations:

(1) External stability of the soil behind and below the structure

(2) Internal stability of the retained backfill

(3) Structural strength of retaining wall members

1.5 LANDSLIDES

When a slope fails, it is often called a landslide or a slope failure. Several classificationmethods and systems have been proposed for landslides. The one adopted in thisbook and most consistently around the world is the one proposed by the InternationalAssociation of Engineering Geologists (IAEG) Commission on Landslides.

1.5.1 Features and Dimensions of Landslides

Typical features of a landslide are shown schematically in Figure 1.16. The observablefeatures of a landslide are

(1) Crown The practically undisclosed material above the main scarp

(2) Main Scarp A steep surface on the undisturbed ground at the upper edgeof the landslide

(3) Top The highest point of contact between the displaced material and mainscarp

(4) Head The upper parts of the landslide between the displaced material andmain scarp

(5) Minor Scarp A steep surface on the displaced material produced by differ-ential movements

(6) Main Body The part of the displaced material that overlies the surface ofrupture

(7) Foot The portion of the landslide that has moved beyond the toe

(8) Tip The point on the toe farthest from the top

(9) Toe The lower margin of the displaced material

(10) Surface of Rupture The surface that forms the lower boundary of the dis-placed material

(11) Toe of Surface of Rupture The intersection between the lower part of thesurface of rupture and the original ground surface

(12) Surface of Separation The original ground surface now overlain by the footof the landslide

(13) Displaced Material Material displaced from its original position by land-slide movement

general slope stability concepts

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