Brine Pond Appendix-F

102 Pages·2011·1.71 MB·English

APPENDIX F
Geotechnical References
Geosynthetics International, 2005, 12, No. 1
Analysis and design of veneer cover soils
R. M. Koerner1 and T.-Y. Soong2
1EmeritusProffesor,DrexelUniversityandDirector,GeosyntheticResearchInstitute,475Kedron
Avenue,Folsom,PA19033-1208,USA,Telephone:[phone],Telefax:[phone],
E-mail:[email protected]
2CTIandAssociates,12842EmersonDrive,Brighton,MI48116,USA,Telephone:[phone],
Telefax:[phone],E-mail:[email protected]
Received 10 July 2003, accepted 10 July 2003
ABSTRACT: Cover soil sliding on slopes underlain by geosynthetics is obviously an unacceptable
situation and, if the number of occurrences becomes excessive, can eventually reflect poorly on the
entire technology. Steeply sloped leachate collection layers and final covers of landfills are
situations where incidents of such sliding have occurred. Paradoxically, the analytic formulation of
the situation is quite straightforward. This paper presents an analysis of the common problem of a
veneer of cover soil (0.3 to 1.0m thick) on a geosynthetic material at a given slope angle and
length. The paper then presents different scenarios that create lower FS (factor of safety) -values
than the gravitational stresses of the above situation, e.g. equipment loads, seepage forces and
seismic loads. As a counterpoint, different scenarios that create higher FS-values also are presented,
e.g. toe berms, tapered thicknesses and veneer reinforcement. In this latter category, a subdivision
is made into intentional reinforcement (using geogrids or high-strength geotextiles) and non-
intentional reinforcement (cases where geosynthetics overlay a weak interface within a multilined
slope). A standard numeric example is used in each of the above situations to illustrate the various
influences on the resulting FS-value. In many cases, design curves are also formulated. Suggested
minimum FS-values are presented for final closures of landfills, waste piles, leach pads, etc.,
which are the situations where veneer slides of this type are the most serious. Hopefully, the paper
will serve as a vehicle to bring a greater awareness to this situation so as to avert such slides
from occurring in the future. Note: This paper was initially published as the Giroud Lecture in the
Proceedings of the Sixth International Geosynthetics Conference held in Atlanta, USA, in 1998.
KEYWORDS: Geosynthetics, Analysis, Design, Limit equilibrium methods, Steep slopes, Veneer
stability
REFERENCE: Koerner, R. M. & Soong, T-Y. (2005). Analysis and design of veneer cover soils.
Geosynthetics International, Special Issue on the Giroud Lectures, 12, No. 1, 28–49
liners (CCL), are the particular materials of concern.
1. INTRODUCTION
These situations represent a major challenge due (in part)
There havebeen numerous coversoil stabilityproblemsin tothefollowingreasons:
thepast,resultinginslidesthatrangefrombeingrelatively
small (which can be easily repaired), to very large • The underlying barrier materials generally represent a
(involving litigation and financial judgments against the low interface shear strength boundary with respect to
parties involved). Furthermore, the number of occurrences thesoilplacedabovethem.
appears to have increased over the past few years. Soong • The liner system is oriented precisely in the direction
and Koerner (1996) report on eight cover soil failures ofpotentialsliding.
resulting from seepage-induced stresses alone. While such • The potential shear planes are usually linear and are
slides can occur in transportation and geotechnical appli- essentiallyuninterruptedalongtheslope.
cations, it is in the environmental applications area where • Liquid (water or leachate) cannot continue to percolate
they are most frequent. Specifically, the sliding of rela- downward through the cross-section owing to the
tively thin cover soil layers (called ‘veneer’) above both presenceofthebarriermaterial.
geosynthetic and natural soil liners, i.e. geomembranes
(GM), geosynthetic clay liners (GCL) and compacted clay When suchslopesare relativelysteepand uninterruptedin
1072-6349 # 2005 Thomas Telford Ltd 28
Analysis and design of veneer cover soils 29
their length (which is the design goal for landfills, waste
piles and surface impoundments so as to maximize 2.1. Limit equilibrium concepts
containment space and minimize land area), the situation The free body diagram of an infinitely long slope with
isexacerbated. uniformly thick cohesionless cover soil on an incipient
There are two specific applications in which cover soil planar shear surface, like the upper surface of a geomem-
stability has been difficult to achieve in light of this brane, is shown in Figure 1. The situation can be treated
discussion; quite simply. By taking force summation parallel to the
slopeandcomparingtheresistingforcewiththedrivingor
mobilizingforce,aglobalfactorofsafety(FS)results:
• leachate collection soil placed above a GM, GCL and/
or CCL along the sides of a landfill before waste is
Resisting forces
placedandstabilityachievedaccordingly;
• final cover soil placed above a GM, GCL and/or CCL FS¼X
Driving forces
inthecaporclosureofalandfillorwastepileafter the (1a)
wastehasbeenplacedtoitspermittedheight. X
Ntanä Wcosâtanä
¼Wsinâ¼ Wsinâ
For the leachate collection soil situation the time frame is
generally short (from months to a few years), and the Hence:
implications of a slide may be minor in that repairs can
tanä
sometimes be done by on-site personnel. For the final FS (1b)
¼ tanâ
coversoilsituationthetimeframeisinvariablylong(from
decades to centuries), and the implications of a slide can Here it is seen that the FS-value is the ratio of tangents of
be serious in that repairs often call for a forensic analysis, the interface friction angle of the cover soil against the
engineering redesign, separately engaged contractors and upper surface of the geomembrane (ä), and the slope
quite high remediation costs. These latter cases sometime angle of the soil beneath the geomembrane (â). As simple
involve litigation, insurance carriers, and invariably tech- as this analysis is, its teachings are very significant. For
nicalexperts,thusbecomingquitecontentious. example:
Since both situations (leachate collection and final
covers) present the same technical issues, the paper will • To obtain an accurate FS-value, an accurately
address them simultaneously. It should be realized, how-
determined laboratory ä-value is absolutely critical.
ever, that the final cover situation is of significantly
The accuracy of the final analysis is only as good as
greaterconcern.
theaccuracyofthelaboratory-obtainedä-value.
In the sections to follow, geotechnical engineering • For low ä-values, the resulting soil slope angle will be
considerations will be presented leading to the goal of proportionately low. For example, for a ä-value of 208,
establishing a suitable factor of safety against slope
and a required FS-value of 1.5, the maximum slope
instability. A number of common situations will then be angleis148.Thisisequivalenttoa4(H)on1(V)slope,
analyzed, all of which have the tendency to decrease
which is relatively low. Furthermore, many geomem-
stability. A number of design options will follow, all of braneshaveevenlowerä-valuesthan208.
which have the objective of increasing stability. A sum- • This simple formula has driven geosynthetic manufac-
maryandconclusionssectionwillcounterpointthevarious
turers to develop products with high ä-values, e.g.
situations which tend to either create slope instability or
textured geomembranes, thermally bonded drainage
aid in slope stability. It is hoped that an increased
geocomposites,internallyreinforcedGCLs,etc.
awareness of the analysis and design details offered here-
in,andelsewhere,willleadtoasignificantdecreaseinthe
Unfortunately, the above analysis is too simplistic to use
numberofveneercoversoilslidesthathaveoccurred.
in most realistic situations. For example, the following
situationscannotbeaccommodated:
2. GEOTECHNICAL ENGINEERING
CONSIDERATIONS
W
As just mentioned, the potential failure surface for veneer Wcosâ
cover soils is usually linear with cover soil sliding with Wsin â
respect to the lowest interface friction layer in the under-
Geomembrane
latyhllieonwgnescerfdoosrsfo-asrecstrttiiroaalnig.chTetfnhoteerwrpoaltoredcnatstiitaoalbnfisaliitalyunrdecadplcilfaufnelaerteibnoetninrgwadilitiihn,oeaausrt C over soil Nta n ä
with soil stability problems analyzed by rotational failure â N
surfaces. Furthermore, full static equilibrium can be
achieved without solving simultaneous equations or mak- Figure1. Limitequilibriumforcesinvolvedinaninfinite
ingsimplifieddesignassumptions. slopeanalysisforauniformlythickcohesionlesscoversoil
Geosynthetics International, 2005, 12, No. 1
30 Koerner and Soong
• a finite-lengthslopewith theincorporation of a passive
soilwedgeatthetoeoftheslope;
• theincorporationofequipmentloadsontheslope;
•• ccoonnssiiddeerraattiioonnooffsseeeispmagiceffoorrcceessawcittihnignotnhethceovceorvesorislo;il; stress ón (high)
• theuseofsoilmassesactingastoeberms; hear ón (middle)
• theuseoftaperedcoveredsoilthicknesses; S
• reinforcement of the cover soil using geogrids or high- ô ón (low)
p ô
strengthgeotextiles. r
Shear displacement
These specific situations will be treated in subsequent (a)
sections. For each situation, the essence of the theory will
be presented, followed by the necessary design equations.
This will be followed, in each case, with a design graph
(Peak)
andanumericexample.First,however,theimportantissue h, ô
of interfacesheartestingwillbediscussed. ngt äp
e
str (Residual)
2.2. Interface shear testing ar
e ä
h r
S
The interface shear strength of a coversoilwith respect to
the underlying material (often a geomembrane) is critical
to properly analyze the stability of the cover soil. This cap c
ar
value of interface shear strength is obtained by laboratory Normal stress, ó
n
testing of the project-specific materials at the site-specific (b)
conditions. By project-specific materials, we mean sam-
Figure2. Directsheartestresultsandmethodofanalysisto
pling of the candidate geosynthetics to be used at the site, obtainshearstrengthparameters:(a)directsheartestdata;
as well as the cover soil at its targeted density and (b)Mohr–Coulombstressspace
moisture conditions. By site-specific conditions we mean
normal stresses, strain rates, peak or residual shear
strengths and temperature extremes (high and/or low).
Note that it is completely inappropriate to use values of straightline, which istheMohr–Coulombfailurecriterion
interface shear strengths from the literature for final cover commontogeotechnicalengineering.Theconcept isread-
soildesign. ily adaptable to geosynthetic materials in the following
While the above list of items is formidable, at least the form:
type of test is established. It is the direct shear test which
ô c ó tanä (2a)
p ap n p
has been utilized in geotechnical engineering testing for ¼ þ
many years. The test has been adapted to evaluate ôr car óntanär (2b)
¼ þ
geosynthetics and is designated as ASTM D5321 or ISO
12957. The upper limit of ä when soil is involved as one of the
In conducting a direct shear test on a specific interface, interfaces is ö, the angle of shearing resistance of the soil
one typically performs three replicate tests, with the only component. The upper limit of the c value is c, the
a
variable being different values of normal stress. The cohesion of the soil component. In the slope stability
middle value is usually targeted to the site-specific condi- analyses to follow, the c term will be included for the
a
tion, with a lower and higher value of normal stress sake of completeness, but then it will be neglected (as
covering the range of possible values. These three tests being a conservativeassumption) in the design graphs and
result in a set of shear displacement against shear stress numeric examples. To utilize an adhesion value, there
curves: see Figure 2a. From each curve, a peak shear must be a clear physical justification for the use of such
strength (ô ) and a residual shear strength (ô) is obtained. values when geosynthetics are involved. Only unique
p r
As a next step, these shear strength values, together with situations such as textured geomembranes with physical
their respectivenormalstress values,are plotted inMohr– interlocking of soils having cohesion, or the bentonite
Coulomb stress space to obtain the shear strength para- component of a GCL, arevalid reasons for including such
metersoffrictionandadhesion:seeFigure2b. aterm.
The points are then connected (usually with a straight Note that residual strengths are equal to, or lower, than
line), and the two fundamental shear strength parameters peak strengths. The amount of difference is very depen-
are obtained. These shear strength parameters are: ä, the dent on the material, and no general guidelines can be
angle of shearing resistance, peak and/or residual, of the given. Clearly, material-specific and site-specific direct
two opposing surfaces (often called the interface friction sheartestsmustbeperformedtodeterminetheappropriate
angle); and c , the adhesion of the two opposing surfaces, values. Further, each direct shear test must be conducted
a
peak and/or residual (synonymous with cohesion when toarelativelylargedisplacementtodeterminetheresidual
testingfine-grainedsoils). behavior (Stark and Poeppel 1994). The decision as to the
Each set of parameters constitutes the equation of a use of peak or residual strengths in the subsequent analy-
Geosynthetics International, 2005, 12, No. 1
Analysis and design of veneer cover soils 31
sis is a very subjective one. It is both a materials-specific
and site-specific issue, which is left up to the designer 2.3. Various types of loading
and/or regulator. Even further, the use of peak values at There are a large variety of slope stability problems that
the crest of a slope and residual values at the toe may be may be encountered in analyzing and/or designing final
justified. As such, the analyses to follow will use an covers of engineered landfills, abandoned dumps and
interface ä-value with no subscript, thereby concentrating remediationsitesaswellasleachatecollectionsoilscover-
onthecomputational proceduresrather thanthisparticular ing geomembranes beneath the waste. Perhaps the most
detail. However, the importance of an appropriate and common situation is a uniformly thick cover soil on a
accurateä-valueshouldnotbeminimized. geomembrane placed over the subgrade at a given and
Owing to the physical structure of many geosynthetics, constant slope angle. This ‘standard’ problem will be
the size of the recommended shear box is quite large. It analyzed in the next section. Avariation of this problem
must be at least 300mm by 300mm, unless it can be will include equipment loads used during placement of
shown that data generated by a smaller device contain no cover soil on the geomembrane. This problem will be
scale or edge effects, i.e.that no bias existswith a smaller solved with equipment moving up the slope and then
shear box. The implications of such a large shear box movingdowntheslope.
should not be taken lightly. Some issues which should Unfortunately, cover soil slides have occurred, and it is
receiveparticularattentionarethefollowing: felt that the majority of the slides have been associated
with seepage forces. Indeed, drainage above a geomem-
brane (or other barrier material) in the cover soil cross-
• Unless it can be justified otherwise, the interface will section must be accommodated to avoid the possibility of
usually be tested in a saturated state. Thus complete seepage forces. A section will be devoted to this class of
and uniform saturation over the entire specimen area slopestabilityproblems.
must be achieved. This is particularly necessary for Lastly, the possibility of seismic forces exists in earth-
CCLs and GCLs (Daniel et al. 1993). Hydration takes quake-prone locations. If an earthquake occurs in the
relativelylong incomparison withsoils inconventional vicinity of an engineered landfill, abandoned dump or
(smaller)testingshearboxes. remediation site, the seismic wave travels through the
• Consolidation of soils (including CCLs and GCLs) in solid waste mass, reaching the upper surface of the cover.
largershearboxesissimilarlyaffected. It then decouples from the cover soil materials, producing
• Uniformity of normal stress over the entire area must a horizontal force, which must be appropriately analyzed.
be maintained during consolidation and shearing so as A section will be devoted to the seismic aspects of cover
toavoidstressconcentrationsfromoccurring. soilslopeanalysisaswell.
• The application of relatively low normal stresses, e.g. All of the aboveactions are destabilizing forces tending
10 to 30kPa simulating typical cover soil thicknesses, to cause slope instability. Fortunately, there are a number
challenges the accuracy of some commercially avail- of actions that can be taken to increase the stability of
able shear box setups and monitoring systems, slopes.
particularlytheaccuracyofpressuregages. Other than geometrically redesigning the slope with a
• Shear rates necessary to attain drained conditions (if flatter slope angle or shorter slope length, a designer can
this is the desired situation) are extremely slow, alwaysusegeogridsorhigh-strengthgeotextileswithinthe
requiringlongtestingtimes. cover soil acting as reinforcement materials. This tech-
• Deformations necessary to attain residual strengths nique is usually referred to as ‘veneer reinforcement’.
require large relative movement of the two respective Additionally, the designer can add soil mass at the toe of
halves of the shear box. So as not to travel over the the slope, thereby enhancing stability. Both toe berms and
edges of the opposing shear box sections, devices tapered soil slopes are available options and will be
should have the lower shear box significantly longer analyzedaccordingly.
than 300mm. However, with a lower shear box longer Thus it is seen that a number of strategies influence
than the upper traveling section, new surface is slope stability. Each will be described in the sections to
constantly being added to the shearing plane. This follow. First, the basic gravitational problem will be
influence is not clear in the material’s response or in presented, followed by those additional loading situations
thesubsequentbehavior. which tend to decrease slope stability. Second, various
• The attainment of a true residual strength is difficult to actions that can be taken by the designer to increase slope
achieve. ASTM D5321 states that one should ‘run the stability will be presented. The summary will contrast
test until the applied shear force remains constant with the FS-values obtained in the similarly crafted numeric
increasing displacement’. Many commercially available examples.
shear boxes have insufficient travel to reach this
condition.
3. SITUATIONS CAUSING
• The ring torsion shearing apparatus is an alternative
DESTABILIZATION OF SLOPES
device to determine true residual strength values, but is
not without its own problems. See Stark and Poeppel This section treats the standard slope stability problem
(1994) for information and data using this alternative and then superimposes upon it a number of situations, all
testmethod. of which tend to destabilize slopes. Included are gravita-
Geosynthetics International, 2005, 12, No. 1
32 Koerner and Soong
tional, construction equipment, seepage and seismic E sinâ W N cosâ NAtanäþCa sinâ (6)
forces. Each will be illustrated by a design graph and a A ¼ Aÿ A ÿ FS
numericexample.
Hencetheinterwedgeforceactingontheactivewedgeis
FS W N cosâ N tanä C sinâ
3.1. Cover soil (gravitational) forces E ð Þð Aÿ A Þÿð A þ aÞ
A
¼ sinâ FS
Figure 3 illustrates the common situation of a finite ð Þ
length, uniformly thick cover soil placed over a liner (7)
material at a slope angle â. It includes a passivewedge at
the toe and has a tension crack of the crest. The analysis The passive wedge can be considered in a similar
thatfollowsisafterKoernerandHwu(1991),butcompar- manner:
ableanalysesareavailablefromGiroudandBeech(1989),
ªh2
McKelveyandDeutsch(1991)andothers. W (8)
P ¼sin2â
The symbols used in Figure 3 are defined as: W
A
totalweight of the activewedge; WP ¼ totalweight of th¼e Np ¼WPþEPsinâ (9)
passive wedge; NA effective force normal to the failure ch
plane of the active¼wedge; N effective force normal to C (10)
P ¼ ¼sinâ
the failure plane of the passivewedge; ª unit weight of
¼
the cover soil; h thickness of the cover soil; L length By balancing the forces in the horizontal direction, the
¼ ¼
ofslopemeasured alongthegeomembrane;â soil slope followingformulationresults:
¼
anglebeneaththegeomembrane; ö friction angle ofthe
C N tanö
cover soil; ä ¼ interface friction an¼gle between cover soil EPcosâ¼ þ FSP (11)
and geomembrane; C adhesive force between cover
a
¼
soil of the active wedge and the geomembrane; c Hencetheinterwedgeforceactingonthepassivewedgeis
a
¼
adhesion between cover soil of the active wedge and the
C W tanö
geomembrane; C cohesive force along the failure plane EP þ P (12)
¼ ¼cosâ FS sinâtanö
of the passive wedge; c cohesion of the cover soil; EA ð Þÿ
¼
interwedge force acting on the active wedge from the By setting E E , the resulting equation can be
A P
¼ ¼
passive wedge; E interwedge force acting on the arranged in the form of the quadratic equation ax2 + bx +
p
¼
passive wedge from the active wedge; and FS factor of c 0,whichinourcase,usingFS-values,is
¼ ¼
safetyagainstcoversoilslidingonthegeomembrane.
2
a FS b FS c 0 (13)
The expression for determining the factor of safety can ð Þ þ ð Þþ ¼
bederivedasfollows.Consideringtheactivewedge:
where
L 1 tanâ
WA ¼ªh2(cid:18)hÿsinâÿ 2 (cid:19) (3) a¼(WAÿNAcosâ)cosâ
NA ¼WAcosâ (4) b¼ÿ[(WAÿNAcosâ)sinâtanö
h
Ca ¼ca Lÿsinâ (5) þ(NAtanäþCa)sinâcosâ (14)
(cid:18) (cid:19)
sinâ(C W tanö)]
P
By balancing the forces in the vertical direction, the þ þ
followingformulationresults: c (N tanä C )sin2âtanö
A a
¼ þ
The resulting FS-value is then obtained from the solution
Active wedge Cover soil ofthequadraticequation:
ã, c, ö
h
W b pb2 4ac
A FS ÿ þ ÿ (15)
¼ 2a
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
C
a Geomembrane When the calculated FS-value falls below 1.0, sliding of
Passive wedge WP EP NAtanä the cover soil on the geomembrane is to be anticipated.
E
A N Thus avalue of greater than 1.0 must be targeted as being
A
C
â L the minimum factor of safety. How much greater than 1.0
Nptanö the FS-value should be, is a design and/or regulatory
NP issue. The issue of minimum allowable FS-values under
different conditions will be assessed at the end of the
paper. In order to better illustrate the implications of
Equations 13, 14 and 15, typical design curvesfor various
Figure3. Limitequilibriumforcesinvolvedinafinitelength FS-values as a function of slope angle and interface
slopeanalysisforauniformlythickcoversoil friction angle are given in Figure 4. Note that the curves
Geosynthetics International, 2005, 12, No. 1
Analysis and design of veneer cover soils 33
gle, (degrees)ä456000 ãLLc e555g e 013n 80kd N:kmN/m5/m2:134öch:1a 5 55 33 30:S001 0lk°o Nmp/emm r2at2io:1 (H:V)F S F=S F2=.S 01=. 51.0 1:1 Acdceecleelreartiatoino/n }loGweomembrane
n
a
ction 30 Wbulldozer
M fri
G20
o- (a)
oil-t
s
er 10
v
o
C
0
0 10 20 30 40 50
Slope angle, â (degrees)
Fcoighuesrieo4n.leDssecsiogvnercusorivlessofnorlinsteaabrilfiatyiluorfeupnliafonrems-ftohricvkanrieosuss Acdceecleelreartiatoino/n } hig h Geomembrane
globalfactorsofsafety Wbulldozer
(b)
are developed specifically for the variables stated in the
legend of the figure. Example 1 illustrates the use of the Figure5. Constructionequipmentplacingcoversoilon
curves in what will be the standard example to which slopescontaininggeosynthetics:(a)equipmentbackfillingup
otherexampleswillbecompared. slope(therecommendedmethod);(b)equipmentbackfilling
downslope(methodnotrecommended)
Example 1
Given a 30m long slope with a uniformly thick 300mm
cover soil at a unit weight of 18kN/m3. The soil has a soil and working with an ever-present passive wedge and
friction angle of 308 and zero cohesion, i.e. it is a sand. stable lower portion beneath the active wedge. While it is
The cover soil is placed directly on a geomembrane as necessary to specify low ground pressure equipment to
shown in Figure 3. Direct shear testing has resulted in an place the soil, the reduction of the FS-value for this
interface friction angle between the cover soil and geo- situation of equipment working up the slope will be seen
membrane of 228 with zero adhesion. What is the FS- toberelativelysmall.
valueataslopeangleof3(H)-to-1(V),i.e.18.48? For soil placement down the slope, however, a stability
Substituting Equation 14 into Equation 15 and solving analysis cannot rely on toe buttressing, and a dynamic
for the FS-value results in the following, which is seen to stress should also be included in the calculation. These
beinagreementwiththecurvesofFigure4: conditions decrease the FS-value, in some cases to a great
extent. Figure 5b shows this procedure. Unless absolutely
a 14:7kN=m
¼ necessary, it is not recommended to place cover soil on a
b 21:3kN=m FS 1:25
¼ÿ 9 ¼ slope in this manner. If it is necessary, the design must
c 3:5kN=m
¼ = consider the unsupported soil mass and the dynamic force
In general, this is too low a value for a final cover soil of the specific type of construction equipment and its
;
factor of safety, and a redesign is necessary. While there mannerofoperation.
are many possible options for changing the geometry of For the first case of a bulldozer pushing cover soil up
the situation, the example will be revisited later in this from the toeof the slope to thecrest,the analysis uses the
section using toe berms, tapered cover soil thickness and free body diagram of Figure 6a. The analysis uses a
veneer reinforcement. Furthermore, this general problem specific piece of construction equipment (like a bulldozer
will be used throughout the main body of this paper for characterized by its ground contact pressure) and dissi-
comparison purposes to other cover soil slope stability pates this force or stress through the cover soil thickness
situations. to the surface of thegeomembrane. A Boussinesq analysis
is used (Poulos and Davis 1974). This results in an
3.2. Construction equipment forces equipmentforceperunitwidthasfollows:
The placement of cover soil on a slope with a relatively
W qwI (16)
e
low shear strength inclusion (like a geomembrane) should ¼
always be from the toe upward to the crest. Figure 5a where W equivalent equipment force per unit width at
e
shows the recommended method. In so doing, the gravita- the geomem¼brane interface; q W /(2 3 w 3 b); W
b b
¼ ¼
tional forces of the cover soil and live load of the actual weight of equipment (e.g. a bulldozer); w length
¼
construction equipment are compacting previously placed of equipment track; b width of equipment track; and
¼
Geosynthetics International, 2005, 12, No. 1
34 Koerner and Soong
w
Wba 5 0 (assu m e d) h Footprint of b
track
We W esin â Cover soil h
Geomembrane
N eta n ä Geomembrane
â Ne 5 We cosâ 1.0
(a) Ice, 0.9
a
erf
nt 0.8
e i
n
a
Wb W b(a/g) h omembr 00..67
e
g
WeW esin â F e Geomembrane ence factor at 00..45 NThoete v:ariation and influence of w
u 0.3 is small in comparision with b
N eta n ä Infl
0.2
0 1 2 3 4
â Ne 5 We cosâ Width of track, b
Thickness of cover soil, h
(b)
Figure7. ValuesofinfluencefactorIforuseinEquation16
todissipatesurfaceforcethroughcoversoiltogeomembrane
Figure6. Additional(togravitationalforces)limitequili-
interface(afterPoulosandDavis1974)
briumforcesduetoconstructionequipmentmovingoncover
soil(seeFigure3forthegravitationalsoilforcetowhichthe
aboveforcesareadded):(a)equipmentmovingupslope(load
withnoacceleration);(b)equipmentmovingdownslope(load
1.40
plusacceleration)
Legend:
L 5 30 m â 5 18.4°
ã 5 18 kN/m3 ö 5 30°
1.35 c 5 0 kN/m2 ca 5 0 kN/m2
I influence factor at the geomembrane interface (see w 5 3.0 m b 5 0.6 m
¼
Figure7). h 5 900 mm
e
Upon determining the additional equipment force at the u
interface between cover soil and geomembrane, the analy- S-val1.30
sis proceeds as described in Section 3.1 for gravitational F h 5 600 mm
forces only. In essence, the equipment moving up the
1.25
slope adds an additional term, We, to the WA-force in h 5 300 mm
Equation 3. Note, however, that this involves the genera-
tion of a resisting force as well. Thus the net effect of
increasing the driving force as well as the resisting force 1.20
0 10 20 30 40 50 60
is somewhat neutralized insofar as the resulting FS-value
Ground contact pressure (kPa)
is concerned. It should also be noted that no acceleration/
deceleration forces are included in this analysis, which is Figure8. Designcurvesforstabilityofdifferentthicknessof
somewhat optimistic. Using these concepts (the same coversoilforvariousconstructionequipmentgroundcontact
equations as used in Section 3.1 are used here), typical pressures
design curves for various FS-values as a function of
equivalent ground contact equipment pressures and cover
soilthicknessesaregiveninFigure8.Notethatthecurves has a friction angle of 308 and zero cohesion, i.e. it is a
are developed specifically for the variables stated in the sand. It is placed on the slope using a bulldozer moving
legend.Example2aillustratestheuseoftheformulation. from the toe of the slope up to the crest. The bulldozer
has a ground pressure of 30kN/m2 and tracks that are
Example 2a 3.0m long and 0.6m wide. The cover soil to geomem-
Given a 30m long slope with uniform cover soil of brane friction angle is 228 with zero adhesion. What isthe
300mm thickness at a unit weight of 18kN/m3. The soil FS-valueataslopeangle3(H)-to-1(V),i.e.18.48?
Geosynthetics International, 2005, 12, No. 1
Analysis and design of veneer cover soils 35
This problem follows Example 1 exactly except for the equipment (bulldozer) force per unit width at geomem-
addition of the bulldozer moving up the slope. Using the brane interface (recall Equation 16); â soil slope angle
¼
additional equipment load, Equation 16 substituted into beneath geomembrane; a acceleration of the bulldozer;
¼
Equations14and15resultsinthefollowing: andg accelerationduetogravity.
¼
Using these concepts, the new force parallel to the
a 73:1kN=m
¼ cover soil surface is dissipated through the thickness of
b 104:3kN=m9FS 1:24 the coversoil tothe interface of thegeomembrane. Again,
c ¼1ÿ7:0kN=m >>= ¼ a Boussinesq analysis is used (Poulos and Davis 1974).
¼ The expression for determining the FS-value can now be
While the resulting >>;FS-value is low, the result is best derivedasfollows.
assessed by comparing it with Example 1, i.e. the same Considering the active wedge, and balancing the forces
problem but without the bulldozer. It is seen that the FS- in the direction parallel to the slope, the following
value has only decreased from 1.25 to 1.24. Thus, in formulationresults:
general, a low ground contact pressure bulldozer placing
N N tanä C
cover soil up the slope with negligible acceleration/ EAþð eþ AFÞS þ a ¼ðWAþWeÞsinâþFe
deceleration forces does not significantly decrease the
(18)
factorofsafety.
For the second case of a bulldozer pushing cover soil where Ne effective equipment force normal to the
¼
down from the crest of the slope to the toe, as shown in failureplaneoftheactivewedgeaccordingto
Figure 5b, the analysis uses the force diagram of Figure
N W cosâ (19)
e e
6b. While the weight of the equipment is treated as just ¼
described, the lack of a passive wedge along with an Note that all the other symbols have been previously
additional force due to acceleration (or deceleration) of defined.
the equipment significantly modifies the resulting FS- The interwedge force acting on the active wedge can
values. This analysis again uses a specific piece of nowbeexpressedas
construction equipment operated in a specific manner. It
E W W sinâ F
A A e e
produces a force parallel to the slope equivalent to W ¼ð þ Þ þ
b
(aac/cge)l,erwathieorneoWfbthe¼buthlledowzeeirg,hatndofgthethbeulaldcoczeelerr,aatio¼ndthuee ÿðNeþNAFÞStanäþCa (20)
¼
to gravity. Its magnitude is equipment operator dependent
and related to both the equipment speed and the time to The passive wedge can be treated in a similar manner.
reachsuchaspeed;seeFigure9. The following formulation of the interwedge force acting
The acceleration of the bulldozer, coupled with an onthepassivewedgeresults:
influence factor I from Figure 7, results in the dynamic C W tanö
force per unit width at the interface between cover soil EP þ P (21)
¼cosâ FS sinâtanö
andgeomembrane,F.Therelationshipisasfollows: ð Þÿ
e
By setting E E , the following terms can be
a A ¼ P
F W (17) arrangedintheformofEquation13,inwhichthea,band
e ¼ e g
(cid:18) (cid:19) ctermsaredefinedasfollows:
where F dynamic force per unit width parallel to the
e a [(W W )sinâ F ]cosâ
¼ A e e
slope at the geomembrane interface; W equivalent ¼ þ þ
e
¼
b [(N N )tanä C ]cosâ
e A a
¼ÿf þ þ
10 [(W W )sinâ F ]sinâtanö
g A e e
05 þ þ þ
0.
d (s) 8 a 5 þ(CþWPtanö)g
nticipated spee 6 a 5 0a. 051 g0.1 5 g FEiqnucaal¼ltyio,[n(tNh1ee5.þrUeNssuiAnl)tgitnatgnheäFsþeS-cCvoaanl]ucseeinptâcsa,tnatnypböiecalobdteasiingendcuurs(2vin2egs)
ach a 4 a 5 0.20g fcoorntvaacrtiopuresssFuSr-evaalnudeseqausipamfeunntctaicocneloefraetiqounipcmanenbtegdroevuenld-
o re a 5 0.30g oped; see Figure 10. Note that the curves are developed
me t 2 specificallyforthevariablesstatedinthelegend.Example
Ti 2billustratestheuseoftheformulation.
0
0 5 10 15 20 25 30 35 Example 2b
Anticipated speed (km/h) Given a 30m long slope with uniform cover soil of
Figure9. Graphicrelationshipofconstructionequipment 300mm thickness at a unit weight of 18kN/m3. The soil
speedandrisetimetoobtainequipmentacceleration has a friction angle of 308 and zero cohesion, i.e. it is a
Geosynthetics International, 2005, 12, No. 1
36 Koerner and Soong
1.4 equipment be allowed to work down the slope. If it is
Legend: unavoidable, an analysis should be made of the specific
L 5 30 m â 5 18.4°
1.3 ã 5 18 kN/m3 ö 5 30° stability situation, and the construction specifications
h 5 300 mm c 5 c 5 0 kN/m2 should reflect the exact conditions made in the design.
a
w 5 3.0 m b 5 0.6 m The maximum weight and ground contact pressure of the
ue1.2 a 5 0.05g equipment should be stated, along with suggested operator
al movement of the cover soil placement operations. Truck
v
FS-1.1 a 5 0.10g traffic on the slopes can alsogive as high, or even higher,
a 5 0.15g stresses,andshouldbeavoidedinallcircumstances.
1.0 a 5 0.20g 3.3. Consideration of seepage forces
The previous sections presented the general problem of
a 5 0.30g slope stability analysis of cover soils placed on slopes
0.9
under different conditions. The tacit assumption through-
0 10 20 30 40 50 60
Ground contact pressure (kPa) out was that either permeable soil or a drainage layer was
placed abovethe barrier layerwith adequate flow capacity
Figure10. Designcurvesforstabilityofdifferentconstruc-
to efficiently remove permeating water safely away from
tionequipmentgroundcontactpressureforvariousequip-
the cross-section. The amount of water to be removed is
mentaccelerations
obviously a site-specific situation. Note that in extremely
arid areas, or with very low-permeability cover soils,
drainage may not be required, although this is generally
sand. It is placed on the slope using a bulldozer moving theexception.
from the crest of the slope down to the toe. The bulldozer Unfortunately, adequate drainage of final covers has
has a ground contact pressure of 30kN/m2 and tracks that sometimes not been available, and seepage-induced slope
are 3.0m long and 0.6m wide. The estimated equipment stability problems have occurred. The following situations
speed is 20km/h and the time to reach this speed is 3.0s. haveresultedinseepage-inducedslides:
The cover soil to geomembrane friction angle is 228 with
zero adhesion. What is the FS-value at a slope angle of • drainage soils with hydraulic conductivity (permea-
3(H)-1(V),i.e.18.48? bility)toolowforsite-specificconditions;
First, using the design curves of Figure 10 along with • inadequate drainage capacity at the toe of long slopes
Equations 22 substituted into Equation 15 thesolution can where seepage quantities accumulate and are at their
beobtained: maximum;
• fines from quarried drainage stone either clogging the
• From Figure 9 at 20km/h and 3.0s the bulldozer’s drainage layer or accumulating at the toe of the slope,
accelerationis0.19g. thereby decreasing the as-constructed permeabilityover
• From Equations 22 substituted into Equation 15 we time;
obtain • fine, cohesionless, cover soil particles migrating
through the filter (if one is present) either clogging the
a 88:8kN=m drainage layer or accumulating at the toe of the slope,
¼
thereby decreasing the as-constructed outlet permeabil-
b 107:3kN=m9FS 1:03
c ¼1ÿ7:0kN=m >>= ¼ • iftryeeozvinergtiomfet;he drainage layer at the toe of the slope,
¼
This problem solutio>>;n can now be compared with the wseheiplaegtehfeortcoepsoagfatihneststhloepiecethwaewdsg,ethatertehbeytome.obilizing
previoustwoexamples:
If seepage forces of the types described occur, a variation
Example 1: cover soil with no bulldozer loading FS in slope stability design methodology is required. Such an
¼
1.25 analysis is the focus of this subsection. Additional discus-
Example 2a:coversoilplusbulldozer movingupslopeFS sion is given by Thiel and Stewart (1993) and Soong and
1.24 Koerner(1996).
¼
Example 2b: cover soil plus bulldozer moving down slope Consider a cover soil of uniform thickness placed
FS 1.03 directlyaboveageomembraneataslopeangleâasshown
¼
in Figure 11. Different from the previous examples, how-
Theinherentdangerofabulldozermovingdowntheslope ever, is that within the cover soil there exists a saturated
is readily apparent. Note that the same result comes about soil zone for part or all of the thickness. The saturated
by the bulldozer decelerating instead of accelerating. The boundary is shown as two possibly different phreatic
sharp braking action of the bulldozer is arguably the more surface orientations. This is because seepage can be built
severe condition owing to the extremely short times up in the cover soil in two different ways: a horizontal
involved when stopping forward motion. Clearly, only in build-up from the toe upward, or a parallel-to-slope build-
unavoidable situations should the cover soil placement up outward. These two hypotheses are defined and
Geosynthetics International, 2005, 12, No. 1