appendix h geomembrane liner stability calculations · appendix h geomembrane liner stability...

APPENDIX H

Geomembrane Liner Stability Calculations

Interface Description:

Geocomposite overlying 60-mil HOPE Liner

a:b:c:

Cover Thickness (ft):Slope Angle (degrees):Length of Slope (ft):

Unit weight of Cover Soil (pcf):Friction angle of Cover Soil (°):Cohesion of Cover Soil (psf):Interface Friction Angle (°):Interface Adhesion (psf):Tensile Force (Ibs):

Wa (Ib/ft)Na (Hot)Wp (Ib/ft)C (Ib/ft)Ca (Iblft):

0.0287518.43 Radians:

135

0.4360 Radians:5

26 Radians:0

.0

1.691.600.000.450.00

0.16-0.380.00

0.32

0.00

0.45

Factor of Safety :

2.36


60-mil HDPE Liner overlying Geotextile wrap


0.032518.43 Radians:

1350.32

Unit weight of Cover Soil (pcf):Friction angle of Cover Soil (°):Cohesion of Cover Soil (psf):Interface Friction Angle (°):Interface Adhesion (psf):Tensile Force (Ibs):

Wa (Iblft)Na (Ib/ft)Wp (Ib/ft)C (lb/ft)Ca (Iblft):

a:b:c:

Factor of Safety :

0.6160 Radians:1

25 Radians:00

2.72.60.00.10.0

0.3-0.40.0

1.53

0.00

0.44


Non-woven geotextile over Subgrade


0.6718.43 Radians:

1020.32

a:b:c:

Unit weight of Cover Soil (pct):Friction angle of Cover Soil (°):Cohesion of Cover Soil (psf):Interface Friction Angle (°):Interface Adhesion (psf):Tensile Force (Ibs):

Wa (Ib/ft)Na (lb/ft)Wp (Ib/ft)C (Iblft)Ca (Iblft):

190.3925 Radians:

026.2 Radians:

00

12726.712073.9

142.50.00.0

1206.8-1990.4

276.9

0.44

0.46

Factor of Safety :

1.50


Non-woven geotextile over Subgrade

Cover Thickness (ft):

0.67Slope Angle (degrees):

18.43

Radians:

0.32Length of Slope (ft):

102

Unit weight of Cover Soil (pcf):

40.6

(Assume Saturated Conditions)Friction angle of Cover Soil (°):

25

Radians:

0.44Cohesion of Cover Soil (psf):

0Interface Friction Angle (°):

26.2

Radians:

0.46Interface Adhesion (psf):

0Tensile Force (Ibs):

0

Wa (Ib/ft)

2713.9Na (Iblft)

2574.7Wp (Iblft)

30.4C (lb/ft)

0.0Ca (Iblft):

0.0

a: 257.3b: -424.5c: 59.0

Factor of Safety :

1.50

Designing withGeosyntheticsFifth Edition

Robert M. KoernerDirector, Geosyn.thetic InstituteEmeritus Professor of Drexel University

Upper Saddle River, New Jersey 07458

382

Designing with Geogrids

Chap, 3

The expression for determining the factor of safety. considering the active wedge,can be derived as follows:

4V

h°tan (31

(3.15)-'yh sing 2 I'

NA = 4 TA cos (3 (3.16)

_

h(3,17)Ca -

-Cn L

sin

By balancing the forces in the vertical direction, the following formulation results:

NAtanE4 sin 13 = WA - NA cos (3

FS

-sin 13

r (3.18)p

sin 2(3Np = Wp + Ep sin 13 (3.19)

(^) O (3.20)C =

By balancing the forces in the horizontal direction, the following formulation results:

C + N.p tan

Hence the interwedge force acting on the passive wedge is

C+Wp tan 4P

cos I3(FS) - sin 13 tan

By setting EA = EP, the following equation can be arranged in the form ofax` + bx + c = 0, which in our case, using FS values, is

a(FS)2 +b(FS)+c=0 (3.21)

where

a=(4iA-NA.cos (3)cos (3, (322)b = -[(WA - NA cos (3) sin 13 tan 4 + (NA tan 8 + Ca)

sin 13 cos (3 + sin (3(C + Wi, tan c))], and (3.23)

c = (NA tan 8 + Ca) sin' 13 tan c[i (3.24)

Hence the interwedge force acting on the active wedge is

(FS)(WA - NA cos 13) - (NA tan + Ca) sin (3

sin 13 (FS)

The passive wedge can be considered in a similar manner:

EA _

Ep cos (3 =FS

Sec. 3.2

Designing for Geogrid Reinforcement

The resulting FS value is then obtained from the following equation:

,-b + 1/b 2 - 4 acFS=2a

where (in Figure 3.22a and in the above analysis)

WA = total weight of the active wedge,WP

total weight of the passive wedge,NA = effective force normal to the failure plane of the active wedge,Np = effective force normal to the failure plane of the passive wedge,y = unit weight of the cover soil,h

= thickness of the cover soil,L = length of slope measured along the geomembrane,

= soil slope angle beneath the geomembrane,= friction angle of the cover soil,

8 = interface friction angle between cover soil and geomembrane,Ca = adhesive force between cover soil of the active wedge and the

geomembrane,adhesion between cover soil of the active wedge and the geomembrane,

C = cohesive force along the failure plane of the passive wedge,c

= cohesion of the cover soil,EA = interwedge force acting on the active wedge from the passive wedge,Ep

interwedge force acting on the passive wedge from the active wedge, andFS = factor of safety against cover soil sliding on the geomembrane

When the calculated FS value falls below 1.0, a stability failure of the cover soil slidingon the geomembrane is to be anticipated.Thus a value greater than 1.0 must be target-ed as being the minimum factor of safety. How much greater than 1.0 the FS valueshould be is a design and/or regulatory issue. Example 3.12 illustrates the procedure.

Example 3.12Given a cover soil slope of

- 18.4° (i.e. 3H-to-1V), L = 30 m, h = 900 mm,= 18 kNlm3, c = 0, = 30°, c, - 0, 8 = 18°, determine the resulting factor of safety.

Solution:

=

2^LWA - ^h

h]

tan li)-sin 13

2

30(18.0)(0.90)

1

- t;an18.4 )

L`

(

D90 sin 18.4

2

= 14.58(33.3 - 3.17 - 0.17)

- 437 kN/m

383

(3.25)

550

Designing with Geomembranes

Chap. 5

For termination of double liner systems, the designer is faced with a number ofpossible choices.. Major considerations are to protect the integrity of both geomem-branes and to keep surface water out of the leak detection system. In this regard, thetwo geomembranes can enter separate anchor trenches or come together in a commonanchor trench. The primary geomernbrane can also be cut short of the anchor trenchand welded to the secondary geomenibrane along the horizontal runout distance. Easeismically active areas, consideration should be given to this latter approach with novertical anchor trench at all; the logic being that geomembrane pullout is more desir-able than geontenzbrane tensile failure somewhere along the side slope.

The terminus of the liner of a completed internal cell within a zoned landfill, withits eventual extension into an adjacent cell, is usually done by overlapping and seamingalong the horizontal ruizout length of an intermediate berm. When waste fills the sec-ond cell, the berm is entombed and the process is then continued from cell to cell.Shear stresses on the geomembranes in both cells over this berm have been evaluatedby large-scale laboratory models and found to be generally small and geomembrane-dependent (see Koerner and Wayne {79]). In high berms where higher stresses are gen-erated, an auxiliary (or sacrificial) geomembrane rub-sheet over the crest of the bermshould effectively dissipate the stresses before they propagate down to the underlyingprimary geomembrane.

5.6.9 Side Slope Subgrade Soil Stability

The design of the stability of the soil mass beneath the liner system of a solid-wastelandfill is carried out in exactly the same manner as was discussed for liquid contain-ment (reservoir) slopes and berms (recall Section 5.3.5). The process carl include thestrength of the covering liner materials, but if they are not included in the analysis, theerror is on the conservative side. Interior berms, with or without geosynthetic inclu-sions, are also handled in the same manner as previously described.

5.6.10 Multilined Side Slope Cover Soil Stability

The situation of a liner and its leachate collection cover soil stability, or slumping, be-comes quite complicated for multilined geomembrane and geonet collection systems ofthe type shown in Figure 5.40, Consider such a system, as shown in Figure 5.40e Theleachate collection system soil gravitationally induces shear stress through the system,thereby challenging each of the interface layers that are in the cross section. If all of theinterface shear strengths are greater than the slope angle, stability is achieved and theonly deformation involved is a small amount to achieve elastic equilibrium (Wilson-Fahmy and Koerner [80]). However, if any interface shear strengths are lower than theslope angle, wide-width tensile stresses are induced into the overlying geosynthetics.This can cause the failure of the geosynthetics or pullout from the anchor trench, or itcan result in quasistability via tensile reinforcement. If the last is the case, w'can referto the overlying geosynthetics as acting as nonintentional veneer reinforcement.

If the situation consists of the double liner system shown in Figure 5.45, all of theinterface surfaces can be made quite stable by proper selection of the geosynthetics.

Sec. 5.6

Solid Material (Landfill) Liners

55i

Figure 5.45 Geotexlile/geomernbranelgeonet eoinpositelgcomembrane above aCCL or GCL.

For example, textured geoinembranes could be selected, and these together with non-, woven needle-punched geotextiles will usually result in peak friction angles in excessof 25°. Furthermore, by thermally bonding the geotextiles in the leak detection systemto the geonet, these surfaces are also stable at relatively high slope angles. Thus, thecritical interfaces are at the upper (leachate collection sand or gravel) and the lower

(CCL or GCL) surfaces. The upper surface is analyzed exactly as described in Section3.2.7 for the case without geogrid reinforcement. The proper selection of cover soil

against a nonwoven needle-punched geotextile (acting as a protection material, recallSection 5.6.7) should also result in a peak friction angle in excess of 25°.This leaves the

lower surface of the secondary geomembrane against the clay liner as being the poten-tially low-interface surface. If the clay liner is a CCL, the concern is with the expelledconsolidation water lubricating the interface. This surface has been involved in a majorfailure of a hazardous waste liner system, as reported by Byrne et al. [81] with an inter-face friction angle of 10°. If the liner is a GCL, the concern is the hydrated bentonitebeing extruded out of the upper geotextile and lubricating the interface with an inter-face friction angle of 5 to 10°. This surface was involved in two slides of full-scale fieldtests both involving woven geotextiles on the GCL, by Daniel et a]. [82].

The analysis of multilined slopes of the type being discussed is a direct extensionof the veneer reinforcement model presented in Section 3.2.7 on geogrids. RecallingFigure 3.22b, the analysis results in equation (3.21):

a(FS)2 + b(FS) + c = 0

where

a= (V6A-NA cospTsinp)cos(3,b = -[(WA -- NA cos ( 3 - T sin 13) sin ;3 tan + (N tan 8 + Ca) sin p cos p

+ sin p(C' + Wp tan (k)], andc = (NA tan 8 + Ca) sin2I3 tan 4,

552

Designing with Geo membranes

Chap. 5

The resulting FS value is then obtained from equation (3.22):

-b+Vb2 -4ac

The variables and values of WA, NA, T, and Wp were defined in Sections 3.2,7 and 5.3.5.The critical parameter in the above equation is T, the allowable wide-width tensionstrength of the geosynthetic layers above the potential failure surface, For the crosssection shown in Figure 5.45, T represents the allowable strength of all of the geosyn-thetie materials above the critical interface, Not only is the issue of reduction factorsdifficult to assess for the liner materials per se, but the issue of strain compatibility isalso unwieldy. In this latter regard, the wide-width tensile strength of each geosynthet-ic material must be determined, plotted on the same axes, and assessed at a specificvalue of strain, That is, the liner system components cannot act individually and mustact as an equally strained unit. Example 5.20 illustrates the situation.

Example 5.20

For a 30 m long slope at 3(11) to 1(i i.e., = 18.4° - lined with a double liner systemconsisting of GT/GM!GC/GMICCL or GCL (as in Figure 5.45), the lowest friction angle isassumed to be the secondary geomembrarte to the underlying clay interface, which is 10°.All other interface friction angles are in excess of 18.4°.The wide-width tensile behavior ofthe various candidate geosynthetics is given in the following graph.The leachate collectioncover soil is 450 nun thick with a unit weight of 18.0 kN/m' and a friction angle of 30°.What is the factor of safety of the slope based on a cumulative reduction factor of 2.0?

Solution:

,_r L _ 1

tan 13^^ ^^ h sing

2

= (18.0)(0,45)2 30 -

1

- tan 18.40.45

sin 184

2= 3.65[63,3]= 231 kNlnn

NA = WA cos p= 231 cos 18,4= 219 kNitn

_,h2Wp

//= sin 213/ (18.0)(0.45) 2

sin 36.8= 6,03 kN/m

Tait taken at the first geosynthetic failure, which is the nonwoven needle-punched geotex-tile at 25 k%silm, is

FS =2a

mil'

e .4

T,,,1 = 25 + 2(22) + 36= 105 kN/m

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appendix h geomembrane liner stability calculations · appendix h geomembrane liner stability...

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