Prediction/Mitigation of Subsidence
Damage to Hazardous Waste Landfill Covers
(U.S.) Army Engineer Waterways Experiment
Station, Vicksburg, MS
Prepared for

Environmental Protection Agency, Cincinnati, OH
Mar 87
                                                         EPA 600-2-87-025
                                                            PB87-175386

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                                            «. — 3 / ~ ' 7 J J

                                            ;:i'.\."v;n, 4-  •,,
 P:ttUlCrH)N/MlTloATlUN  OF  SUBS I!*.NCt  UAMAtih
        HAZARDOUS  UASTK L,\NUKILL CUVtKS
                       by

                Paul  A.  Gilbert
                      and
               William L. Murphy
            Geotechnlcal Laboratory
U. S. Army Engineer Waterways Experiment St^tton
     PO Box 631, Vicksburg, MS  39180-0631
               Agreement Mo. DW21930680-01-0
                Project Officer

               Robert P. Hartley
        Land Pollution Control Dlvisioa
Hazardous Waste Engineering Research Laboratory
             Cincinnati, Gd
HAZARDOUS WASTE ENGINEERING RESEARCH LABORATORY
       OFFICE OF  RESEARCH  AND DEVELOPMENT
     U. S. ENVIRONMENTAL PROTECTION AGENCY
             CINCINNATI. OH  45268

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                            ,B,      TECHNICAL REPORT DATA
                            If lease rnu ,'niirjctiont on me went be/ore cample ti/it.1
                                                           3 REIlPiyjT S ACCESSION NO.
                                                              rioT    1 ( ~ 3 £
  •^••^•^^•••••^^^^^^^^^^••••^fcfc^^^B^m^^S^^—^^__
4 TITLE ANO SU8TITI.C
   Prediction/Mitigation  of  Subsidence  Damage to
   Hazardous Waste  Landfill  Covers
                                                           S. REPORT DATE
                                                             March 1987
                                                           6. PERFORMING ORGANIZATION COOe
  AuTHOR(S)

   Paul  A.  Gilbert and William L< Murphy
                                                           • . PERFORMING ORGANISATION REPORT SO
 PERFORMING ORGANIZATION NAME ANO AOOOESS
  l.S.  Army  Waterways Experinent Station
  P.O.  Box &:i
  Vicksburg. Mississippi  39180
                                                           10. PROGRAM ELEMENT NO.
                                                           1 1. CONTRACT /GRAN TNO.

                                                             DW 21930680-01-0
 2. SPONSORING AGENCY NAME AND ADDRESS
   Hazardous Waste Engineering Research  Laboratory
   Office of Research and Development
   U.S.  Environmental Protection Agency
   Cincinnati, Ohio  45268
                                                           13. TYPE OF REPORT AND PERIOD COVERED
                                                           14. SPONSORING AGENCY COOE


                                                             EPA/600/12
IS. SUPPLEMENTARY NOTES
  ^natatteristics  of  Resource Conservation and Recovery Act  hazardous waste landfills
    and of landfilled hazardous wastes have been described  to  pen.it development of
    models and other *;ialytical techniques for predicting,  reducing, and preventing
    landfill settlement  and  related cover damage by subsidence.   Differential settle-Ben
    across short distances  is  more threatening than relatively uniform settlement
    across longer  distances.   The potential for differentiallll settlement is considers
    to be greater  in heterogeneous landfills than in monofills.   Settlement of bulk
    waste landfills  is  relatively predictable and is expected  to be  essentially
    complete before  final closure.  Settlement of landfills with containerized
    wastes is more difficult to predict because the containerized wastes may remain
    relatively undeformed until the containers degrade and  collapse.  Bulk waste
    (monofill) landfills can be analyzed by consolidation theory.  The potential for
    differencial settl»--ent  can be analyzed by treating the final cover as a beam
    and determining  the  tensile stresses.  Differential settlement can also be
    analyzed by determining  the deformation of two or more  central columns.  Damage
    to the final cover  by differencial settlement can be minimized by compacting
    wastes during placement, by eliminating void space within  the landfill, by
    stabilizing liquids  before placement, by not disposing  of  waste  in containers,
    and by adjusting cover  component specifications to minimize the  effects of
                               KfV WORDS ANO DOCUMENT ANALYSIS
                 DESCRIPTORS
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  f*rm 2239-1 (»•». 4-77)   mcviou* COITION n o«o«.«TC

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     This report has been revioved  in accordance  with  the  U.S. Environmental
Protection Agency's peer and administr-itive  review  policies  and  approved  for
presentation and publication.  Mention  of  trade names  or commercial  products
does act constitute endorsement  ,>r  reeoimnendation for  use.
                                      II

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                                  FUREW'JKD
     Today's rapidly dev*l->ping aru* c' >nSing technologies and industrial
products and practices  frequently carry with them the  increased generation of
solid and hazardous wastes.  These materials, if impr >p-irly dealt with, can
threaten both public health and the environment .  Abandoned wast>» s-ltes and
accidental releases of  toxic and hazardous substances  to the environment also
have important environmental and public health Implications.  Th* Hazardous
Waste Engineering Research Laboratory  assists in providing an authoritative
and defensible engineering basis for assessing and solving these problems.   Its
products support the policies, programs and regulations of the Environmental
Protection Agency, the  i>e rmi ". c ' nj? and  other responsibilities of the State and
local governments, and  the needs of both  large and snail businesses in  handling
their wastes responsibly and economically-

     This repcrt describes the causes  and effects, prediction methods,  and
technologies that may be applied for  the  prevention  of subsidence In  hazardous
waste landfills.  The information should  be of assistance to those Involved
in evaluating landfill  permit applications.  The goal  is to help prevent
damage to, and resulting leaks through, landfill covers caused by subsidence-
induced stresses.
                                      Thomas R.  Haus=r,  Director
                          Hazardous Waste Engineering  Research  Laboratory
                                      iii

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                                   ABSTRACT

     Characteristics of Resource Conservation and Recovery Act  hazardous waste
landfills and of landfilled hazardous wastes have been described to  permit
development of models and other analytical techniques for predicting,  reduc-
ing, and preventing landfill settlement and related cover damage by  subsi-
dence.  Landfill settlement results from the consolidation and secondary
coar«»«io« of the waste nass and from the collapse of voids In the  fill and
of containers and other debris by corrosion, oxidation, combustion or biochem-
ical decay.  Landfills may be described a? containing a single type of waste,
a mnoflll. or as containing different types of wastes heterogeneously such as
bulk, in containers, and 35 c'elris.  referential settlement across short dis-
tances is more threatening thar relatively uniform settlement across  longer
distances.  The potential  for differential settlement is considered to be
greater in heterogeneous landfills than in ironofills.  Settlement of  bulk
waste landfills is relatively predictable and is expected to be essential y
complete before final closure- if adequate provisions are made for internal
drainage of fluids.  Settlement of landfills with contairerized wastes  is more
difficult  to predict because the containerized wastes may remain relatively
urdeformed until the containers degrade and collapse.  The void space arnjnd
nnd  in containers can be a major contributor to  total postclosure settlement.
Accordingly, steps should  be taken to  minimize the void component of  settle-
ment by backfilling voids  during waste placement or by eliminating  the dis-
posal c-f drums and other vaste  containers.  Settlement of  some  landfills can
be  predicted by analyzing  the deformation of a central col-imn consisting of
layers of  wastes and  intermediate  cover material.  Bulk waste  (monoflll) land-
fills can  be analyzed by crnsclidation theory.   The potential  for differential
settlement can be analyzed by  troafing the  final cover as a  bean and  determin-
ing the  tensile stresses that develop  in  the cover  layers.   Differential set-
tlement can alsc be  Analyzed by determining  the  •'eformation  of  two  or more
central  columns.  Damage to the final  cover by differential  settlement  can  be
nlniaized  by compacting wastes  during  placement, by  eliminating void  space
within  the landfill,  by stabilizing  liquids before  placement,  and by  adjusting
cover component specifications  to  minimize  the effects  of tensile strain.
                                        IV

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                                   CUNftNTS
                                                                          Page
Abstract ................................  xv
Figures  ................................  vl
Tables .................................  vil
Acknowledgments  ............................  vtii

    1.  Infodm-t ion .........................
             Fip.ck ground  .......................
             Purpose .........................
    2 .   Conclusion* arJ Recommend at ions  ...............     '
    1.   Landfill Ch ir.icteristics ...................     5
             Current landfill designs   ................     5
             Characteristics of  landfill wastes   ...........     9
    4.   An.ilvsis of Potentinl Settlement and Subsidence   .......     15
             Sett 1 eirent-causinp  mechanisms ..............     '5
             Trtdtctine landfill settlement  .............     20
             Analvsis of differential cover subsidence  ........     32
    5.   Vittpacien of Settlement ?nd Efferts of Settlement  ......     i4
             Landfill treatment  to reduce settlement potential  ....     ^4
             DesipTi and ror?truction of covers to
                .Tcconw'ij ite subsidence   ................     ^°
             Correcfive action  for subsidence  ............     53

Referrncer.  ..............................     57
Appendixes

    A.   Characteristics of Selected  Haznrdous Waste  Landfills   ....     59
    B.   Cl assi f ir.vtirn of f.eomenbranes  ................     ^^
    C.   Field  experimental F.xample of  Settlement  Analysis
          bv Standard Consolidation  Theorv  ..............     71
    D.   Consolidation Equation  ....................     80

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                                  F1CVRF.S

bo£                                                                    "age

:     Final  covers of  actual  RCRA landfills 	       ?

.'     EPA-recorwerJed  RCKA landfill cover	       R

3     Thickness .ind volume relationship for
        A soil  tnnss of thickness  H  and volume  V^	      IS

i     Constrain*-: elastic roduius of waste
        siirulater. h\ "Virtv litter"	
 5    Stress-str.iin characteristics of kitty litter . .

 6    Stress-strain data fit by oscillating polynomial

 7    Beam repre«entadci of a cover svstem	
 P    ^tress-strain behavior of clav sfectmens at
        different compaction condition   	      35

 1    Mo.inls of beams on the elastic foundations	      37

10    ." / •   versus avernjre tend«»x	      ^>

12    ? 'nd densfi'icat ion usin? vibratorv  rollers	      4fi

13    >nil compaction curve	      49

C-!   Hxperimental Inncftll, plar view	      7ft

C-2   Tvpical crr-ss section of experimental  landfill	      77

C-3   Load-depth diagram  	      79

C-i   fc»ad increment added to n sludge laver	      *8

C-5   Consol4dation characteristics of sample  sludge  	      79

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                                     TABLE?

NuirK-r

   I     Reported  Wa-te  fVnsities  for ..and;'. lied
           Hn.'artious  Wastes
        Fraineering Char.ii'ferl sties .ind Physical Properties
           of  Selected Un<=te« and Simulated Wastes	
         Settlement r>ue to Linear nnd Nonlinear Stress
           Strain Properties ir. Kittv Litter  .............   -  '

         Orrpnrt ion Kquipn-.ent nnd Methous ...............

         Rnnkir.R  of I'Sf^ Soil Tvpes bv Performance
           of  Tover Functions .....................
         Soil  Conservation Services Recommended
           Bentonire Application Rate for F.-.nn Ponds   .........     55

         Characteristics of Selected Hazardous Waste  Landrllls   ....     59

         Phv^ual Properties of P.iper-Xi1!  Sludee  ...........     75
                                       vii

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                                   ACKNOVLFIM'.MFNTS

     This study was authorized  by  the  U.S.  tnviroiunental Protection Agency
(hl'A), Hazardous Waste um-inmTing Research Laboratory, Cincinnati, Uhio, by
Interageney Agreement No.  UW.119]u6St)-01-
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                                   SECTION 1

                                 INTRODUCTION
BACKCROUND

     Section' 3004 of the Resource Conservation and Recovery Act (RCRA)  of 1976
requires Che Administrator of Environmental Protection Agency (EPA)  to  estab-
lish standards applicable to owners and operators of hazardous waste treat-
ment, storage, and disposal (TSD) facilities.  Among the standards are
requirements for "treatment, storage, or disposal of all such waste received
by the facility pursuant to such operating methods, techniques, and practices
as may be satisfactory to the Administrator."  The Implementing regulations
for landfill cover? are found in 40 CFR 264.310, "Closure and postclosure
care," which states that the final cover must be designed and constructed to
(H provide long-term minimization of migration of fluids through the closed
landfill; (2) function with minimum maintenance; (3) promote drainage and
minimize erosion or abrasion of the cover; (4) accommodate settling and sub-
sidence so that the cover's Integrity is maintained; snd (5) have a permeahli-
lt v less than or equal to the permeability of any buttom liner system or
natural soils present.

     Monitoring and maintenance, including necessary cover repairs, are also
required throughout the postclosure period.  The postclosure period is des-
ignated in 40 CFR 264.117 as 30 years after completion of closure.

     EPA recognizes the need to provide guidance In implementing the cover
requirements.  This document addresses the fourth  requirement  listed above
regarding settlement and cover subsidence.

PfRPOSE

     This report presents technical guidance directed at predicting, reducing,
and preventing landfill settlement and related cover damaged by subsidence.
The report is Intended to be used by regulatory personnel and by operators of
hazardous waste landfill?.

SCOPE

     The Information  in this report pertains to hazardous waste landfills
designed, constructed, and operated within the t'nited States under  the RC7A
regulations.  Landfills constructed and capped before the passage of RCRA  in
1976 may not meet RCRA's relatively stringent waste placement,  liquid wast,e
limitations, liner specifications, and leachate collection and  control
requirements, and thus may not be amenahle to the  analytical,  construction,
and remedial guidance presented  in this report.

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                                   SECTION 2

                        CONCLUSIONS AND RECOMMENDATIONS


     Hazardous waste landfills meeting RCRA requirements have physical  charac-
teristics that influence their potential for settlement and subsidence.
Attention to those characteristics can minimize postclosure subsidence  damage.

     Data on physical properties of real and simulated hazardous waste  are
available to assist the landfill operator or permitting agency in assessing
long- and short-term settlement potential.

     Landfill subsidence results from primary consolidation and secondarv com-
pression of the waste mass, and from collapse of voids or cavities in the fill
and around c~ir.-.lners by corrosion, oxidation, combustion, or biochemical
decay of landfllled materials.

     Rarely, a landfill may be a monoflll, that is it may contain uniform
layers of drummed wastes or uniformly placed bulk wastes.  More often,  the
landfill will consist of different types of wastes placed nonuniformly across
the landfill in layers separated by Intermediate covers of soil.  The poten-
tial for differential settlement must be considered to be greater in landfills
with nonuniform wastes and waste placement procedures.

     Bulk wastes behave differently from containerized (e.g., drummed)  wastes
in settlement characteristics.  Bulk wastes behave relatlvelv predictably,
much like soils, becoming increesingly consolidated with time, but at a
decreasing rate.  Containerized wastes may remain relatively undeformed until
the containers degrade and collapse, at which time voids will be created, and
consolidation will begin.

     Settlement by consolidation and secondary compression of bulk waste  land-
fills in which drainage layers are provided will probably be essentially  com-
plete before final closure.  Compaction of waste materials and Installation of
drainage layers are recommended to lessen the potential for postclosure set-
tlement and cover subsidenca.

     The approximate time required for primary consolidation to occur  can be
estimated for a waste or soil layer if the liquid limit is known for the mate-
rial and if the shortest distance to a drainage path  (e.g., a drain layer) is
known.  Time, for any degree of consolidation, can be computed more precisely
if the compressibility or coefficient of consolidation has beer, determined for
the mat«r:'al.

     Of the controlling factors, the distance to a drainage path has the most
pronounced effect on consolidation time for a waste layer.  This fact

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Indicates the desirability of including frenuent drainage layers and  of  remov-
Ir? liquid from the landfill mas* so that most of the consolidation will  occur
before closure.

     The time required tor ultimate settlement of containerized (drummed)
waste to occur cannot he computed without knowledge of the drum deterioration
time.  The time carrot be determined, although it is expected to be several
vears, perhaps several decades, if water infiltration is prevented by an
impervious can and  liner system.

     The void space around drurrs or other containers in a landfill can be a
major contributor to  total postclosure settlement and should be filled with
solidifying agents  or a free-flowing backfill to minimize the void component
of total settlement.

     The surest way of avoiding problems associated with postclosure deterior-
ation of drums and  the delayed settlement and cover subsidence associated with
it may be to ban drums from  landfills.   Instead, drums can be emptied and
crushed or reclaimed.  Drum  contents can be  treated and disposed as bulk
waste.

     Equations for  calculating settlement time  should be used more to identify
operational landfilling and  waste  treatment  procedures that will minimize  set-
tlement tine than to  predict precise values  from theory.

     Differential settlement across  relatively  short distances  that may  occur
within subcells comprising  a larger  landfill cell  is. more threatening than
relatively uniform  settlement across longer  distances that may  occur across
large monofills.  For the  former,  tenslonal  stresses may be sufficient  to
cause cracks in the cover  resulting  in leakage  of  water  into  the  landfill.
Those tensional stresses may not  develop over longer  distances, but ponding  of
water may occur on  the cover barrier,  weakening its  ability to  repel water.

     Similarly, tensional  stresses are anticipated to cause few or no problems
with flexible membrane barriers  over large  subsidence areas.   Locally severe
differential subsidence  can cause strain sufficient  to  rupture  a  flexible  mem-
brane or otherwise  cause  its premature failure.

     Two or more  central  column  models for  analyzing landfill deformation
 (settlement) can  be used  to predict  differential settlement between  columns
and  thereby  to determine  the effect  of differential  subsidence on the  final
cover.

     Expressions  for analyzing the deflection of a beam can be used  to  iden-
tify parameters  controlling the  deformation of a landfill cover subjected  to
differential  settlement.   Once identified,  the parameters can be  adjusted  by
cover  design  and  construction procedures to minimize distress to  cover
components.

      Differential settlement can be minimized by compacting wastes during  .
placement,  eliminating void space within the landfill,  stabilizing liquids
before placement, and othsr considerations.  The length of the cover (repre-
 sented as  a beam) subjected to subsidence can be raduced by placing wastes as

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uniformly as possible to provide uniform support to the cover.   The cover poll
components can le rc.irle more resistant to distress by compacting the cover har-
rier soils wet ot optimum water content.

     Final cover components will stretch under differential settlement and
must be constructed  Co withstand tensile strain.  The average tensil- strain
in the cover can be  computed, and  the maximum value of the differential set-
tlement that can he  tolerated bv the cover soils can be estimated  from that
computation.

     Plastic soils  (soils with high plasticity indexes) should be  selected  for
use as cover components  to produce a cover resistant  to tensile  strain.

     Laboratory  investigations by  others Indicate  the  flexible membrane  lin-
ers (FML's)  (components  of the barrier  layer  in  covers) may  fail at  lower
strains than would  be expected from manufacturer's data.   Every  effort  should
he made to  reduce differential settlement potential of the landfill  and  to
design the  cover to resist tensile strain.

     I.andfilled  wastes  should be compacted or  treated  where  possible to reduce
potential settlement.   Compaction  methods  include  standard compaction tech-
niques, vibratory rollers, and precompression (preloading and  surcharging).
Waste  treatment  methods include  addition of  fixative agents  to render the
wastes permanently  less compressible.

     The  stabilization  of  liquid wastes with pozzolanic materials has been
shown  to  increase  compressive strength "and lessen  settlement potential.  Such
stabilization  could be  especially  beneficial for containerized wastes.

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                                   SECTION 3

                           LANDFILL CHARACTERISTICS


     Landfill settlement and subsidence can always be related to the physical
design characteristics of the landfill, the character of the emplaced wastes,
and hov the filling process was conducted.  Careful attention to these factors
can minimize subsidence damage.  Typical aspects of currert characteristics
and practices are outlined below.

CURRENT LANDFILL DESIGNS

     Hazardous waste landfills that meet RCRA requirements have the following
characteristics:

     -  Pits (cells) are excavated in native soil or rock of low permeability
        (aboveground facilities enclosed by soil embankments are less common).

     -  Single- or multicell construction is practiced, the cells isolated by
        berns and the multicell groups Isolated by benns, liners, and cov.rs.

     -  Depths are commonly 15 to 50 feet but are as great as 100 feet.

     -  The base of the cell is usually above the water table or aquifer.

     -  Cells are lined with single or multiple natural or synthetic barriers
                                          —7      -*8
        with low permeability to water (10   to 10   cm/sec).

          Cells are equipped with leachate collection and monitoring systems.

          A final cover (cap) of more than one layer is installed; the cover
          includes a synthetic and/or natural barrier layer.

          Wastes are placed with some care in layers generally 3 feet thick or
          less and covered with less than 2 feet of crushed rock or soil fill
          (intermediate cover).  Waste and intermediate covers are alternated as
          the cell is filled.

          Compaction of liners and caps is usually controlled and monitored;
          compaction of waste and fill Is limited and is that obtained by pas-
          sage of tracked and wheeled waste placement vehicles.

          Final cover caps on closed cells are grassed and may be equipped wlfh
          settlement plates for subsidence monitoring.

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          Operators are required to solidify all liquids enclosed  within the
          cell (no free liquids are permitted).

     Several types of landfills are commonly found in the United States.
Characteristics of landfills for which descriptive information has been'
obtained are tabulated in Appendix A.  One of the most common is excavated
with the vaste fill almost entirely below the original ground surface and only
the cover above ground.  Another type is built essentially above ground with
the waste enclosed within embankments or dikes.  These two types may be com-
bined to maximize the waste volume in a limited area.  In hilly terrain and
more commonly in the western United States, cut-and-fill landfills may be con-
structed by partial excavation of natural valleys and gullies with the con-
struction of an embankment or retaining wall at the  lower end.  Tn the past,
it was common to take advantage of abandoned quarries or gravel pits, where a
lar^e excavation had been created for other reasons.  Unfortunately, many
quarry or pit types became uncontrolled dump sites.

     Hazardous waste landfills vary greatly in areal size.  Those observed by
the authors range from 1 to 37 acres for a single landfill under one cover.   A
single facility may contain several landfills under  separate covers, collec-
tively enclosing hundreds of acres.  Landfill depths are commonly less  than
50 feet  (fill and liner thickness) but are as great  as  100 feet.  Associated
landfill volumes of the largest fills are as much as  1,250 acre-feet or more
than 2 million cubic yards of waste and soil fill.   Landfill size is an impor-
tant parameter in developing models for analysis of  settlement and subsidence.

     All RCRA-permitted landfills have been required  to be lined with natural
or synthetic materials capable of preventing contact of vaste and leachate
with the ground water.  The "minimum technology requirements" of the Hazardous
and Solid Waste Amendments of  1984 require that new  landfills be double-lined
with a leachate collection layer between the liners.  Draft guidance from
EPA's Office of Solid Waste has suggested a membrane  liner as the top part and
a membrane on a clay layer as the bottom part of the double  liner.

     Further minimum technology requirements dictate that the landfill  cover
(cap) be no more permeable than the bottom liner.  EPA  has interpreted  this to
mean that the cover must include at least both a membrane and a clay component
as the barrier layer.

     Existing Itners and covers vary substantially from the  new requirements
and from site to site.  Liners may vary from none  (relying on  the  impermeabil-
ity of the cut soil) to elaborate and thick clay layer  and membrane  combina-
tions.  Covers on recent landfills also vary but are commonly a combination of
layers including both a membrane and clay.  A classification of geomembranes
is presented in Appendix B.  Figure 1 illustrates the variety of  existing
cover configurations, and Figure 2 illustrates a cover  that  will  meet  the  cur-
rent RC&A regulations.

     As-bull  final cover surface slopes vary from 1  to  30 percent but  are •
commonly 2, 5, or 8 percent.  Draft guidance from EPA's  Office  of  Solid Wastes
recommends from 3 to 5 percent.

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              TOTAL
            THICKNESS
                                       TOTAL
                                      THICKNESS
                                                      TOTAL
                                                     THICKNESS
   8FT
                                    FT
   4FT

                        FML
                                   .„
                                  /2 FT
                      "! GEOTEXTILE


  4FT
3-1/2 FT
  4FT
                        FML
                                   6FT
                                31/2 FT
                                                                   4 FT
                                                                 12-U FT
                                                         SOIL/BENTONITE
                                                              N0101V£N
                                                                                         I Ml
                                                                                  •.j»j FML
GEOTEXTILE FML   ^_^_^_^_^^^__
           1FT   '/S////77/7*
                                                                I"*" - •  '•• 1
                                                                  *   '   1
                                                                               LEGEND
                                                                                  TOP SOI LOR
                                                                                  SOIL BUFFER
                                                                                  DRAINAGE
                                                                                  BLANKET
                                                                                  GRAVEL
W////////.
                        FML
                                4-1/2 FT
                                                                                  COMPACTED
                                                                                  CLAY
                                                                                  FML
                      Figure  1.   Final covers of actual RCRA landfills.

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                    VEGETA TED TOPSOIL. 2 FT MIN
                — FIL T£a CLOTH OR FIL TER
                	DRAINAGE LAYER. J FT MIN
                I— SYNTHETIC MEMBRANE IFMLi. 20 MIL
                         CLA Y SOIL. 2 FT
                         SAND BUFFER. 6 IN. MIN
                     SECTION THROUGH LANDFILL
Figure 2.  EPA-reconnaended RCRA landfill  cover.

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     Settlement and cover subsidence analysis must consider the effects  of
settlement on the clav and membrane barriers of the cover.  Th« clay portion
Is potentially subject to tensile cracking, thinning, and ponding.   The  mem-
brane portion is subject to stretching and ponding.  The final cover surface
slope Is subject to being decreased by cover subsidence.  Anv of these changes
increases the possibility of cover leakage and infiltration of water Co the
waste below.

     All landfills meeting RCRA requirements incorporate a leachate collection
system Into the base of  the landfill.  Systems vary considerably but commonly
consist of plastic perforated pipe imbedded  in a  granular drainage blanket or
in drainage trenches which slope  toward a  sump for monitoring and removal of
leachate via a riser through the  fill and  cover.  The riser most often used
appears to be 4-foot sections of  concrete  sewer pipe added to each lift.  Geo-
textiles are emplaced  over the collection  pipe of some  systems  to filter out
fines and prevent  clogging of the collection lines.  In a  few landfills accom-
modations are made to  drain the upper portion  of  the fill  by  installation of
additional drainage  arrays within the fill as  the landfilling progresses.
Commonlv. however, the leachate  collection array  is  emplaced  only along the
base of the  landfill.

     Good drainage of  leachate  is desirable for several reasons, including
 lessening the  potential  for  long-range  settlement by allowing more  rapid pr- -
closure consolidation  and  by decreasing pore water pressure.

CHARACTERISTICS  OF LANDFILLED WASTES

     Commonly,  hazardous wrste  landfills accept  a variety of  wastes from  sev-
 eral types  of  industries.   Soire of the  more frequently occurring and abundant
wastes  include paint waste;  eleclroplatlng waste; wastewater  treatment
 sludges:  baghouse (collector)  dust; fly ash; intact, damaged, and  crushed
 steel  drums;  waste oil and oil-contaminated soil; electric arc furnace dust;
 filter  cake  from various dewatering operations;  and steel mill pickling
 liquor.

      Hazardous waste landfills may also contain,  generally in lesser quanti-
 ties,  more  noxious organic chemical wastes such  as polychlorlnated
 biphenyls (PCB's) and pesticide waste.

 Waste  Texture

      The liquid content of wastes is extremely important  in evaluating settle-
 ment potential,, for it  is often  deliqueficatlon  or  the  squeezing out of liquid
 that accounts for a great part of consolidation.

      Hazardous wastes since about  1980 have been treated  with  solidification
 (absorption) agents or  other materials before being landfilled.  Older land-
 fiUs may contain wastes with much  higher liquid volumes, some or most of
 which may have been in  drums.  When released, the drainage of  the  liquids may
 initiate significant  subsidence. Even  recent landfills contain liquids from
 precipitation and nin-on  that occur during filling.

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     The recent general ban on free liquids in landfills has been  interpreted
and enforced in different ways by the regulating agencies.   Some  stat«s  use
the EPA-recommended paint filter test to determine whether a waste is  a  liq-
uid.  Several other less sophisticated methods are in use,  such as rappinz a
drum and interpreting the sound, or measuring the "free liquid" over the
solids in a drum.  From a leachate standpoint, the determination by these
methods of whether a waste is a liquid may have merit, but from the srandpoint
of landfill settlement analysis, it may be more beneficial to evaluate consis-
tency on the basis of compressibility.

     Landfilled bulk wastes usually resemble soils in  that they can in most
cases support  the heavy vehicles used to place them within the landfill.  Some
treated wastes have pozzolanic qualities and "set up"  to relatively strong
materials of low compressibility.  Some solid landfilled materials  such  as
wood and metal products, including steel drum containers, have  initially high
strengths and  compressibilities but are presumed  to degenerate  and  corrode to
conditions  of  lew strength and high compressibility with  time vithin  the land-
fill.   Prediction of settlement  in landfills must consider  the  delayed  com-
pressibility potential of the landfilled materials as  well  as the short-term
potential.  The delayed potential may,  in  fact, be much more significant, as
will be seen later.

Waste Densities

     Density  Is  an  important  property of wastes  in evaluating the settlement
and subsidence potential.   In general,  greater  density means less void  space
and *nus  less  settlement potential.   Densifying the  waste Is one way  of reduc-
ing that  potential.

     Table  1  lists  densities  for some landfilled bulk wastes and wastes in
drums,  presumed  to  be  as delivered and  measured at  the landfill before  place-
ment and  compaction.

Engineering Properties of  Selected Wastes

      Reported  properties important to settlement analyses include natural
 (as-delivered) or optimum  (laboratory-determined) water content, unit weight,
unccnfined compressive strength, elastic modulus, shear strength (trlaxial
compression)  data,  ami compressibility and consolidation data.  Table 2 pre-
sents  selected data for several wastes and simulated wastes.  A  full report
presenting the results of  these tests and others is in preparation by the
authors.   Materials 1 through 12 of Table 2 were laboratory-tested before and
 after being enclosed in large lysimeters for a number of years and are  desig-
 nated "prelysimeter" and "postlyslmeter," accordingly.  The  three  industrial
wastes used in the lysimeter tests were an electroplating waste  sludge, a
 chlorine production brine sludge, and a glass etching sludge.  Both  raw
 (untreated) and stabilized (treated by mixing with portland  cement and  fly
 ash) samples of the wastes were tested.

      Materials 13 through 17 are mixtures simulating wastes  and  consist of '
 mixtures of fly ash and water, fly ash and oil, "kitty  litter"  and oil, and
 "kitty litter" and water.  Material  18 is an electroplating  waste  sludge
 treated with a pozzolanic (portland  cement-like) fixation  agent.   Data  for


                                        10

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      T*BLE 1.  REPORT^ u*cyTf nirvSITIES FOR LANDFI1.LEP HAZARDOUS WASTES
                       Waste
        Density
Wastewater treatment plant sludge press cake
  (bull:, 762 nonvolatile ash, 24Z volatiles)
Vastewater treatment sludge  (hard, dry cake)
Lime sludge (55Z total solids)

Metal hydroxide sludge
Electric arc furnace dust  (dry)
Electric arc furnace dust  (dry powder)
                           (pellets)
Enamel powder (ury)
Fly ash
Cement manufacture kiln dust
Cement manufacture baghouse  dust
Wastes In Drums
Lab pack (inorganic oxidizers in jars, cans)
Lab pack (oxides, salts in containers)
Lab pack (salts, alkalines,  solids,  and pastes
  in jars, cans)
Lab pack (organic solids, solids, and pastes
  in jars, cans)
Lab pack (organic acids, solids, and pastes
  in Jars, cans)
Sludge
Lab Pack (organlcs in glass  bottles)
Sludge
Lab pack (mixed wastes)
Hydroxide waste
Paint sludge (dry cake)
Cured polyester resin still  bottoms  (moist gel)
Waste placing sludge (mud filter case)
 85 Ib/cu  ft

 37
 86 (wet unit  weight)
 44 (dry unit  weight)
 69
 62
 70
100
 74
 63
 80*
 40*

250 Ib/drum
300 Ib/drum
SCO Ib/drum

500 Ib/drum

350 Ib/drum

450 Ib/drum
400 lb/drvm
300 Ib/drum
300 Ib/drum
425 Ib/drum
500 Ib/drum
600 Ib/drum
545 Ib/drum
*  Boynton, Robert S.,  1980.  Chemistry  and  Technology  of  Lime  and  Limestone,
  John Wiley and Sons,  Inc., NY, p  305.
                                       11

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                                                                                   ' '"• MH» .*
      «Ht* tttlffr  * %OI *ll
      f!*••«:«•t«r
                                                                                   . J «(c#r 1 <
                                                                                   I It cttcr *.'
                                                                                      «tt*r  ,t *«••
. i.    ra >I^M •* •^•ff-
      :<•»«•»' - > O.M O.M
                                                                  12

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material  18 were  reported by Webster  .  Materials  19 through 24 were two
limestone scrubber  flue  gas desulfur^zaC1011  (FGD>  sludges treated with differ-
ent proportions of  sludge solids,  fly Jsh and/or port land cenent, and water
and tested for unconfined comprespive strengths  (UCS) at optimum water con-
tents.  Data  for  materials  19  through 21 were for  one FGD sludge and 22
through 24 for another.  Compression  tests were  performed on remolded (com-
pacted) samples.  Table  2 also  shows values  for  UCS after varying setup times
after mixing.

     The values presented in Table 2  are not a comprehensive collection of
war.te property data but  do  represent  some common and abundant  landfilled waste
materials.  As such,  the values can supply approximate unit weight, strength,
and compressibility data for estimating initial  and long-tern  settlement of
landfills.  Unconfined compressive strength  values for treated sludges also
show the  tendency for wastes mixed with pozzolanic agents to gain strength
rapidly with  time.

Waste Placement Characteristics

     In most  hazardous waste landfills, the  wastes are placed  in rather stan-
dard configurations.  Unless the landfill is a monofill  (containing only one
general type  of waste),  it  will be divided into  cells  for wastes of different
chemical, character.  This segregation is usually to prevent the possibility of
•Detrimental chemical reactions among  the materials.  The cells will ordinarily
be separated  by clay berms  that are maintained as  the  landfill progresses
upward.

     The area and depth  of  the monofill or the cells are important  in  their
influence on  potential cover damage from subsidence.   Shorter  horizontal
dimensions and deeper depths tend to  accentuate  tensile  stresses in the cover.
Cellular  subdivision of  the landfill  acts similarly  in shortening horizontal
dimensions.   But  this subdivision will also  usually segregate  the waste into
masses of different physical characteristics,  separated  by berms with  still
another set of physical  characteristics.  All  of these differences  will tend
to accentuate differential  settlement and cover  subsidence.

     Wastes are generally placed in the  landfill in "lifts" that are  simply
layers of wastes.  It is probably rare  that  a  lift is  totally  uniform in  its
physical  characteristics across a landfill or  a  cell.   It is probably unreal-
istic to  require  uniformity, although that would be  ideal for  the evaluation
and prediction of settlement.

     A lift of bulk waste will generally be  comprised  of many  loads of mate-
rial dumped and spread across  the cell.  Spreading is  most  likely  to  be done
by relatively heavy equipment  which simultaneously compacts  the  waste.  The
lift of bulk  material may be a foot or nore  thick.  In some  landfills,  bulk
waste and containerized  (most  often in steel drums) waste will be  found in the
same cell, and sometimes in the same  lift.   Usually  drummed wastes  will be
grouped together, but the horizontal  locations of the  drum  groups may change
from one  lift to  the next.   However,  in  some landfills,  containerized waste
may comprise  an entire cell or even the  entire landfill. On  the other hand,
some operators disallow  drummed waste altogether and,  if it  is received,  the
drums will be emptied and crushed and landfilled separately.


                                       13

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     Intercell and intracell configuration of bulk and containerized  waste  Is
one of the most important considerations in evaluating the potential  for  cover
subsidence.  In general, bulk waste Is the easiest to manage to eliminate a
danger of Its contributing to postclosure subsidence.  This is not  to say that
It Is impossible to contro'  he potential danger from postclosurr settlement
of containerized waste, but it will be much more difficult.

     Waste lifts are often separated by soil layers, especially where lifts
are containerized waste.   Tn this case, the primary purpose of the soil layer
Is to provide a working surface for the next lift.  A conscious effort may or
may not be f;iven to filling the void space between containers.  Bulk wastes
may not be separated by soil layers.  It does not appear  that a great deal of
attention is given to the  properties of soils that may be used, even though
such attention could have  a dramatic effect on the amount and rate of ensuing
settlement.  For example,  free-draining soil layers  in bulk wastes can accel-
erate settlement during the preclosure period before the  cover  is placed.
Pozzolanic solidification  of drummed waste and the placement of pozzolanic
material between drums might eliminate the danger of postclosure settlement
and damaging cover subsidence by permanently increasing the compressive
strength of those waste layers.

     Most hazardous waste  landfills are equipped with vertical  riser pipes, as
noted earlier, extending completely through the waste mass and  cover.  These
riser pipes help  to drain  run-on and leachate from the waste mass, thus  accel-
erating settlement to some extent during and after the filling  process.  The
riser pipes also help ro vent gases that may be generated in the waste,
although several vent«: specifically for gas venting  are features of  some
covers.

     Preloading of the waste mass with a  temporary soil cover for a  period of
time before the installation of the final  cover has  been  suggested and occa-
sionally used as a means of promoting  settlement prior to  final closure.

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                                   SECTION 4

                ANALYSIS OF POTENTIAL SETTLEMENT AND SUBSIDENCE


SETTLKMFNT-CAt'SING MECHANISMS

     Several mechanisms have been "recognized to cause subsidence at sanitary
and low-level nuclear waste landfills.  These include primary consolidation
and secondary compression, raveling or piping of fill soils or debris into
voids or cavities, and enlarging and subsequent collapse of voids or cavities
in waste fill bv corrosion, oxidation, combustion, or biochemical decay.  All
of these mechanisms are not perMnent to hazardous waste landfills constructed
according to current RCRA requirements.  Those considered important in hazard-
ous waste landfills, and discussed herein,  Include primary consolidation,
secondary compression, collapse of voids created by waste container deteriora-
tion, and decav of waste debris.  Primarv  consolidation and secondary compres-
sion are the dominant mechanisms of  settlement in soil-like bulk wastes.

     The settlement mechanisms cause changes in the waste volume which  in turn
cause stresses and strains In the overlying cover that may result  in surface
subsidence.

Framework of the Analysis and Evaluation of Assumptions

     Real world situations involving in  situ stress,  strain,  deformation,
material properties, and  time dependent  factors which Influence  these quanti-
ties can never .be completely known  or modeled  precisely.  Additionally,  there
is an element of uncertainty  In  the  Reometrv of structures such  as  hazardous
waste landfills.  Therefore,  in  the  development of  a  model to predict behavior
in such structures,  certain  simplifying  assumptions must be made.   The  assump-
tion will typically  be  those made in the development  of  rhe  theory of consoli-
dation, and it may be  important  to  state these assumptions because  the
conditions  within a  hazardous waste  landfill may  be worse  than those within a
compacted earthen embankment.   Additionally,  it  should be  stated that predic-
tions made  on the behavior of well  controlled  compacted  earthen  embankments
using consolidation  theory can  be in considerable error simply because  real
world sltuatipns  rarely conform to  Idealized  theory.

     The  assumptions made for this  analysis are discussed  below.

     -  The material under analvsls Is homogeneous.  Homogeneity is never
         fully  realized In the very heterogeneous  mass of a hazardous waste
         landfill.   The mass  is  spatially heterogeneous and violates the
        assumption  of homogeneity.
                                       15

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     -  The material under consideration is saturated with  liquid.   Saturation
        tn hazardous waste landfills Is seldom complete,  but  complete  satura-
        tion influences the rate of settlement and subsidence.   Settlement
        occurs more rapidlv in an unsaturated fill, so time predictions  made
        with the assumption of complete saturation are conservative.

     -  One-dimensional compression does occur within a large portion  of a
        landfill which Is large in areal extent compared with the depth. How-
        ever, one dimensional compression does not occur in rones in which
        there are appreciable shear stresses, such as areas in close proximity
        to physical boundaries.

     -  The mass is isotropic.  The materials involved are generally soil-like
        materials which are not isotropic; that is the properties of the mate-
        rials may vary with direction.  Applied compaction may increase the
        anisotropy of the materials.  However, laboratory tests performed on
        representative materials should be performed on material treated in
        such a way as to duplicate, as closely as possible, the placement and
        hence the anisotropy of the material in the  landfill.

     -  Darcy's law is valid, and one-dimensional flow occurs in the landfill.
        Both  f these conditions are in general violated because of inhoreoge-
        neity and anisotropy of the materials in question.

     -  The material is linearly elastic.  The materials involved are soils
        which are not linearly elastic.  However, effort Is made to develop a
        treatment which accounts for the nonlinear behavior of the materials
        in question.

     -  The action of an infinitesimal mass is no different than that of the
        larger representative mass.  This assumption relates to the fact that
        a representative small specimen of material  may be tested to determine
        properties which may be used to predict the  behavior of rhe mass.
        Realistically, the accurate representation of the mass by a small
        specimen is unlikely because of the heterogeneous nature of a hazard-
        ous waste landfill.

     The serious violation of many of  the stated  fundamental assumptions is
fully recognized.  Similar violations of fundamental assumptions are recog-
nized for beam models (presented later in this section) because beam theory is
based on the assumption of small strains, and there  Is no  insur.-.nce that
strains will remain small in hazardous waste  landfills.  Evidence will  be pre-
sented to show that strains may become large.  However, it must be  realized
that in general these models will not be used to  quantify  the various factors
associated with distress in  the structures under  analysis.   Instead the models
will be used to identify parameters associated with  distress, how these param-
eters relate to each other, and how they may  be manipulated  to minimize the
effects of distress.  The models will be used for qualitative rather than
quantitative analysis.  In this light, the assumptions necessary for the   •
development of the models become less disturbing.
                                       16

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Primary Consoliddtion

     CorifolidatIon of a soil (or w;iste) is Che decrease in void ratio (the
ratio of the- volume of voids to the volume of solids) bv expulsion of fluids
from the voids under excess hydrostatic pore pressure (primary consolidation)
and by deformation of the skeleton of the mass and compression of gases in the
voids (secondary compress ion).  The decrease in void ratio by consolidation
represents a decrease in volume of the mass and can cause the surface of the
mass to subside.

     The classic Terzaghi theorv for one-dimensional consolidation of a soil
assumes that the soil is saturated and that deformation of the soil mass is by
change in volume caused bv expulsion of water from the consolidation.

     If a mass of soil of thickness  H , diagrammed in Figure 3, is com-
pressed, the change in its thickness,  AH , can be expressed as a change in
the void ratio,  Ae .  An estimate of settlement expected to occur in a soil
bv consolidation can be obtained by combining field data with laboratory data
on soil compressibility in the equation
where
     AH » amount of settlement
     C  - laboratory-determined coefficient of compressibility
     e£ * initial void ratio
     p  » initial overburden or self-weight stress  in the field

     ip * increase in strers by the  added  load

     Equation  1 might be used to compute the  subsidence  in a hazardous waste
landfill.  However, Equation 1 is developed from  the t' -;ory of consolidation
md therefore  suffers the limitations  resulting from the assumptions made in
rh2 development of the theorv.  These  assumptions and ' .-.e associated limita-
tions are listed and discussed separately  in  Section 3.  A procedure to com-
pute settlement based on the integration of measured stress-strain properties
circumvents some of the assumption of  the  consolidation  theory.

     Consolidation of soils by lowering of the water table has been identified
as a possible  cause of ground subsidence in some  locations.  The effect of
lowering the water table in a soil is  to surcharge  the  soil by increasing the
effective stress (the vertical stress  minus the pore water pressure) through a
decrease in pore pressure.  Similar  effects can be  expected in soil and waste
materials in a hazardous waste landfill where the extraction of landfilled
fluids through the leachate collection system would result in compression of
the mass.

Secondary Compression                                                      ,

     Settlement from secondary compression (deformation  of the soil mass)
occurs later in the loading history  of a fill as  the applied stress is
                                       17

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V

1

K
aT

«2




Ae
T
VOIDS


SOLIDS
A/y
T

H


Figure 3.  Thickness and volume relationship  for a.
    soil mass of thickness  H  and volume  V   .
                        18

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transferred from  the pore  fluids to the soil skeleton.  Secondary compression
       raa>' be calcill;1t*d from tht? following equation:
                                               "sec \

                                               W
where    C  » coefficient of secondary compression from lab
       'sec * tlm«  for which settlement is significant
       t   . » time  to completion of  100 percent primary consolidation

     The total settlement in bulk waste is the sum of the primary consoHd. -
tion and the secondarv compression settlements.  It is likely that most bulk
wastes initially contain a significant Amount of liquid.  If that is the case,
primary consolidation will .be a greater contributor to total settlement than
will secondary compression in bulk vnste  landfills.

     Appendix C provides an example  of the calculation of total settlement for
a landfill.

Container and Fill  Deterioration and Cavity Collapse

     The dominant settlement mechanism for heterogeneous landfills containing
mixtures of debris, bulk, and containerized wastes is not expected to be con-
solidation.  Instead, long-term settlement of heterogeneous hazardous waste
landfills should be analyzed on the  basis of deformation of the waste layers
and .Deteriorating waste containers.

     Most of this type of settlement is likely to take place after, perhaps
long after, closure of the landfill.  THUS, settlement caused by the collapse
of containerized waste may have more potential for subsidence damage to the
cover than consolidation settlement, much of which can occur, or can be made
to occur, prior to  closure.  However, it must be emphasized that there is no
documentation of subsidence-related  problems in controlled (RCRA-regulated)
landfills, probably because none are old  enough for deterioration to have
occurred.

     Settlement should result from later  filling of larger structural voids
witnin the la: dfill that remain through the filling process or are created by
waste degradation.  These voids are  expected to survive the primary consolida-
tion and secondary  compression because they are supported by initially very
stiff materials.  Drummed wastes are the  most significant case in point.

     Initial structural voids consist of  unfilled landfill space.  Incomplete
filling of containers and the space  between them is probably the most preva-
lent example of how such voids are created.  Random space in large debris and
space created by decay of organic materials are other exairp es.

     The maximum amount of potential settlement should approximate the volume
of the larger voids.  A small additional  amount should result from the consol-
idation of wastes after they are released from rigid containers.
                                       19

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     It should not uc construed that the potential settlement resulting from
the filling of larger voids will necessarily be significant.  Careful place-
ment of containers and debris-type materials with attention to filling voids
with lift (intermediate) cover material will keep cavity size small.  Sinkhole
development by piping should not occur because liner systems preclude the
development of escape paths or pipes, and leachate removal systems prevent
excessive heads and gradients that might trigger cavity collapse or growth.

PREDICTING LANDFILL SETTLEMENT

     A layer  or zone of waste or fill soil within a hazardous waste  landfill
possesses engineering properties that control  its deformation (strain) under
the  load  (stresses) imposed on  it by materials above and  around  it  In  a  con-
tinuum mechanics model of  the landfill.  Variable properties  including stiff-
ness (Young's modulus), unit weight of materials, and  Poisson s  ratio  (ratio
of  transverse normal strain to  the longitudinal  strain in a sample  compressed
longitudinally) reduce waste layers or zones  to  units  that can be mathemati-
callv analyzed  (if  the landfill satisfies  the  requirements of the mathematical
model).   Thus the .mount of settlement to  expect in  initial and  degraded waste
fill conditions may be estimated.  Values  of  the variables can be changed to
reflect  changing  conditions of  stress and  material properties in the landfill
with corresponding  charges in  the  deformation or settlement.  Material proper-
ties such as  unit weight,  modulus, and Poisson's ratio can b« determined in
the laboratory  for  actual  waste materials  and container* or can  be  estimated
from tests on simulated waste  materials- and  standard containers.

      Mathematical models  constructed  to  aid  analysis of deformation of land-
 fills should recreate  the  stress  conditions  and  loading history of  the fill.
 For example,  because wastes  and fill  are placed  in th« landfill gradually over
 a period of months  or years,  and  the  fill depth  increases gradually, deeper
 fill materials are  compressed at  different rates and under increasing loads as
 the filling progresses.   A model  should be used  that sinulates the process,
 building up the total structure by stacking one  layer at a time on top of the
 preceding layer ->nd allowing vertical stress and lateral confinement  to
 increase in a systematic manner as the layers are placed.  Deformation after
 closure is controlled by changing strengths and  stiffnesses of  the waste mate-
 rials as they degrade and deteriorate,  with relatively constant vertical
 stresses.  This later or postclosur* settlement  can be analyzed based on sud-
 den loading or "gravity release" loading whereby the load  to the entire land-
 fill is applied all at once.  Such a loading  condition would apply after
 closure (cessation of filling and application of final cap to the fill), after
 the landfill has undergone initial settlement.  Deformation  of  the post-
 closure landfill then depends on decreasing elastic moduli of the deteriorat-
 ing fill contents.  Earlier Investigations of settlement  in  hazardous waste
 landfills used these approaches to predict settlement.

 Settlement in Bulk Waste  Landfills

      In bulk waste disposal, liquid and solid wastes  are deposited  in the
 landfm and stabilized if necessary, then compacted  into the landfill  using.
 some pr&ctlcal, effective, economic compactiv*  effort.   Liquid  content  and
 compaction effort  applied to the waste will determine  the amount of settlement
 which will occur,  and there may be a certain  economic  pressure  on  the landfill


                                       20

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operator to maximize liquid waste content and minimize compaction effort.
Such an approach m?v lead to postclosure settlement problems if taken to
extreme.  Central column analysis mav be used to estimate postclosure set-
tlement based on assumed in situ stress and strain conditions and the abilifv
to select waste samples from which stress-strain properties representative of
the mass may be measured.  In using the central column model for estimating
settlement, stress-strain data from one-dimensional compression tests are
required.  In using this approach for the analysis of drum disposal, it was
convenient and conservative to assume stress-strain linearity.  Such linearity
may also be assumed for bulk waste disposal analysis, bur a more precise
method based on actual stress-strain data will be presented..

     Assume that stress-strain data from a one-dimensional compression  test
can be presented in the functional form

                                   e - ((a)                                 O)

where
     e « vertical strain
     a * vertical stress

The typical shape of such  stress-strain  data  is  seen  in  Figure 4.   The  "soil"
in question is again "kitty  litter," a material  often used  to  stabilized haz-
ardous waste.

     Assume further  that  the  stress-strain  curve may  be  leas'-squares  fitted
to he  represented by a polynomial  of degree  four.   (Note:   Many computer codes
exist  which will curve fit polynomials.)   From the  least squares polynomial
fit, the stress-strain data may  be written  as

                       E  - aQ +  ajO  +  a2a2  +  a-jj  + a^a                     (4)

where   an, a.,  a,,  a., a,   are the  coefficients  of  the curve fit.   The  instan-
taneous  change  in  stiffness may  be obtained by differentiating Equation 4 and
is

                        Jj£ - a.  + 2a,a + 3a.CT2 + 4a,o3                     (5)
                         do    1      I       -1        *

Substituting   a -  YY  into Equation  5

where
        Y - material density, assumed initially constant
        y - vertical distance below the surface

results in
                                                ry          f\

                                                                             •


 Substituting Equation 6 into
                                       21

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 60 r
                                                    ^1 MOIST "866PCF
                      8        12-16
                          P6RCENT 3TRAIN
                                                           24
Figure A.  Constrained elastic modulus  of waste simulated  by
           "kitty  litter."
                              22

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                                    C    de
                                   J  Yyd^
AL -  /  YV -j- dv                             (7)
and Integrating, the result
                                                                         (8)
is obtained where
       AL •» subsidence in a central column with r.onlinear stress-strain
            properties
        L - depth of landfill

To compare the results obtained  from  the  linear modulus  (Equation 3) versus
the nonlinear modulus (Equation  8) Table  3 was prepared  showing predicted sub-
sidence in a bulk landfill having  the stress-strain characteristics of kitty
litter.

     Stress-strain data for kitty  litter  are  shown in Figure 5.  Table 3 shows
how the two models predict different  values of settlement for different land-
fill depths and material densities.   The  table shows that settlement predicted
by the nonlinear model is always less than that predicted by the linear model.
The nonlinear model predicts  less  settlement  because the stress-strain stiff-
ness modulus of soil increases as  soil  is deformed in confined compression.
Because of the shape of this  curve, the secant stiffness modulus value is
always less than the average  tangent  stiffness modulus of the nonlinear curve,
and therefore the subsidence  predicted  by the nonlinear  model will be less
than that predicted by the linear  model.  However for shallow depths of land-
fills  (represented by the initially flat  part of the curve) the linear and
nonlinear models will predict essentially the same value of subsidence.  As
the landfill becomes deeper and  the stress-strain modulus increases, subsi-
dence  predicted by the more precise mode] will diverge,  as shown in Table 3.
Figure (5 also shows actual data  and the data  which would be predicted by the
polynomial and demonstrate that  there can be  good agreement between actual and
fitted stress-strain data.

     Assumptions made in developing this  model are that  the density at all
points along the column element  was initially homogeneous, the stress-strain
properties used are representative of the entire column, and the column was
suddenly "released to gravity"  from a weightless state.  The last assumption
will never be physically approached except in the case of a column  in a satu-
rated  landfill with very low  permeability which was  filled rapidly.  As was
mentioned above, subsidence begins to occur  as soon  as the first layer of
material is deposite ' in a landfill.  This nonlinear central column model will
predict the tota1 amount of subsidence  which  will occur  in columns  of the
waste, in short, an upper bound  of subsidence.  If this  upper bound of subsi-
dence  can be tole ated, then  the amount of subsidence which is likelv to occur
                                       23

-------
        TABLE 3.  SETTLEMENT DUE TO LINEAR AND NON-LINEAR STRESS STRAIN
                  PROPERTIES IN KITTY LITTER


      0.0168557
a* - -0.0005803
_ ^ _  i  nnft i i P_
a« " i »uvwi, i i-—^
a? . .6.47878 E-8
4
r
pcf
84
86
88
90
92
84
86
88
90
92
84
86
88
90
92
L
ft
30
3C
30
30
30
50
50
50
50
50
70
70
70
70
70
0
max
psi
17.5
17.9
18.3
18.8
19.2
29.2
29.9
30.6
31.3
31.9
40.8
41.8
42.8
43.8
44.7
Ed - v)
DSl
109
109
109
109
109
150
150
150
150
150
191
191
191
191
191
Linear
£L
ft
2.40
2.46
2.52
2.58
2.63
4.86
4.97
5.09
5.21
5.32
7.48
7.66
7.83
8.02
8.19
Nonlinear
AL
ft
1.93
1.94
1.95
1.95
J.96
3.27
3.26
3.26
3.25
3.25
4.60
4.61
4.63
4.65
£.67
                                       24

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50  -
40
                    LEGEND
          •  OBSERVED DATA
          O  DATA PREDICTED BY CURVE FIT
                                                                             0.25
          Figure 5.  Stress-strain characteristics  of  kitty litter.
                                       25

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will be less severe since some of the subsidence invariably occurs during
filling/construction.

     It must be mentioned that the curve fit of stress-strain properties imjst
be carried out with caution since higher order polynomial curves will oscil-
late between data points.  A high coefficient of correlation may be  indicated,
and the polynomial may predict points on the curve  with a high degree of
accuracy.  However between points the polynomial nay oscillate in an undesir-
able manner as is shown  in Figure 6.  If *nch a polynomial wera used to pre-
dict subsidence, incorrect and meaningless  results  would be obtained.
Oscillation occurs on this stress-strain plot because a  few widely  spaced
points are being fitted  with a high degreo  polynomial.  This problem will  be
avoided if enough closely spaced points on  the  stress-strain curve  are  used
such  that there  is no room between points for oscillation.  Finally, it may be
a good idea  to plot  the  polynomial fit against  the  actual  data to ensure that
no undesirable oscillation  is  occurring and the desired  stress-strain data are
accurately fit.

      Time is not  addressed  in  this nonlinear model.  The amount of settlement
 predicted is the maximum amount  which may occur in an unspecified time inter-
val.   If the steps  outlined  below are taken to  minimize the time for consoli-
 dation and the wastes are properly  treated  and  compacted so as to minimize
 settlement,  then the element of  tire  may  be eliminated as a point of consider-
 ation.  Operating such that  time for  primary consolidation is minimized may be
 the only effective means of dealing  with  time  since  time effects are poorly
 understood and therefore very difficult  to  model.

 Settlement in Containerized Waste Landfills

       It is the settlement occurring after closure  that causes surface  subsi-
 dence and possible cover (cap) damage.  Although,  as indicated previously,  the
 landfill can and should be constructed so that most  of the settlement will
 occur before closure, it is inevitable that some will occur later.

       Pcstclosure settlement is likely to be .dominated by compression resulting
 from  the closure of  structural voids.  Only a minor  amount will  result  from
 the continuation of  primary consolidation and secondary compression of  bulk
 wastes.  A relatively small amount of postclosure  settlement  may also  occur
 due to the primary consolidation of wastes  released  from deteriorated,  but
 formerly rigid, containers.

       Structural voids,  as noted earlier, are likely to  result from the close
 placement of  containers, usually drums, and the inability  to  completely fill
 both  the drums and  the  space  between them.  Some,  probably lesser, void space
 may result  from degradation of  organic materials and from  the unfilled space
  characteristic of coarse debris waste.  The amount of settlement to be
  expected  from closing of structural  voids  will  approximate  the total  of the
  structural void space.

       It  was  shown previously  (Equation  1)  that the void space around drums may
  be as much  as 10.73  percent by  volume  for  drums disposed by  burial on their
  sides and 9.31  percent  by  volume for drums disposed by on-*nd (upright)
  burial.  Void space  inside  drums is  difficult  to quantify,  but current


                                        25

-------
  50  i-
_ 30
v)
a.
  10
                        LEGEND


              A OBSERVED DATA

              • POLYNOMIAL FIT PREDICTION
                                             0.4


                                           STRAIN
                                                      0.5
                                                                0.6
                                                                          0.7        0.8
          Figure  6.  Stress-strain  data fit  by oscillating polynomial.
                                           27

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regulatory practice limits it to !0 percent.  Assuring that this void  space  is
filled completely with a solidifying agent is an obvious way to reduce event-
ual settlement.  Free-flowing backfill such as dry sand or gravel will be the
most effective material to fill the void spaces under and between drums to
minimize the void component of settlement.

     Subsidence caused by the change in stiffness of the waste material inside
the drum, after drum collapse, is difficult to quantify accurately.  The
expression developed from Equation 1 was


                            ,L , ^ l_^v I_l2v                          (9)
where
               AL - the subsidence due to the change  in stiffness between the
                    barrel and waste
                Y • density of the waste material
                L » thickness of  the combined waste layers
(l+v/l-v)(l-2v/E) ~ reciprocal of the slope of  the constrained modulus  from
                    one-dimensional compression of the material  in question

     The  subsidence predicted by  Equation 9 will be conservative (more  than
actually  occurs) because  it assumes linearity of the  constrained modulus.
Actually  the  stress-strain curve  is nonlinear,  with the rate of  strain
increase  diminishing as stress increases  (see Figure  5).

     nrums  are usually placed  in  layers, one to three drums  thick, with an
intermediate  cover of soil separating the layers.  The intermediate  cover lay-
ers  are generally well-compacted  during construction  and  do  not  pose a  long-
term consolidation problem.  However, with  tine, the  mild steel  of which most
waste  drums are made will corrode and may weaken to the point  of total  col-
lapse, subjecting the contents of the drum  to compression and  volume change
which  will  cause subsidence  in  the  landfill.  In this light,  the use of drums
may  create  the problem of prolonging  the  time over which  subsidence  occurs.

     It  is  not possible  to predict  the  time of  drum collapse.  Maintaining  the
integrity of  the landfill cap,  liner, and leachate  collection  system will tend
to keep  the drums dry and extend  their  lifetime.  However,  the contained mate-
rial  may be  more or  less corrosive in  themselves.   In addition, there  is no
reason to expect that containers  will all degrade  uniformly.   It would  seem
more likely that they would  degrade,  each on  its own  schedule, over  an
extended  period.  The beginning  of  deterioration might begin with the first
drum perhaps  a decade after  closure,  while  the  last might occur  a century or
more later.  The surest  way  of avoiding problems with drums  is to ban drums
from landfills, or  to ban intact  drums.   Drums  of  waste can  and  have been
emptied  of  their content, crushed,  and  then placed  in the landfill.   The drum
contents  are  fixed  or  treated  and then  applied  to  the landfill where they are
less of  a problem.   Drums can  also  be emptied  and  recycled (reclaimed).  Drum
recycling center or services are  available  in  some states.

     Intentionally  increasing  the compressive  strength of the contained mate-
rials  and the fill  materials between the  drums  scy prevent compression  and


                                       28

-------
subsidence from this cause even if the drums fall.  Mixing the waste and fill-
ing void spaces with pozzolanic materials such as lime and fly ash could pro-
vide Che needed strength.

Analysis of Settlement Time

     An analysis of time is necessary to estimate the portion of total settle-
ment that occurs prior to closure.  Any preclosure settlement reduces the
amount that can occur after closure and is therefore beneficial in preventing
cover subsidence.  In addition, preclosure settlement benefits the operator by
allowing more space for disposal of additional wastes.  As indicated earlier,
preclosure settlement is likely to be limited to consolidation of the bulk
waste and soil portions of the fill material.  Preclosure settlement goes
largely unobserved and unmeasured, and thus it is difficult to quantify.

     Consolidation time can be estimated.  If it is less than the time
required for waste placement, consolidation of the bulk wastes and intermedi-
ate soil layers can be assumed to have occurred prior Co capping and will not
contribute to subsidence.  An expression to estimate the time required  for
90 percent consolidation was derived  from the theory of consolidation and is
as follows:

                          t^-H^x  10(0.0168LL-2.2)                     (IQ)

where
      C • Cime in days for 90 percent primary consolidation
     H  - shortest path to drainage in a saturated medium, cm
      c«
     LL • the liquid limit of the material, percent

Certain simplifying assumptions were  necessary in Equation 1C, the details of
which are given by Murphy and Gilbert.   However, the Cime computed using
Equation 10 will.be conservative because the theory assumes complete water
saturation which will be slower than  for the case of partial saturation, and
the curve fit incorporating liquid  limit into the equation was chosen as an
upper (conserva. ive) bound.

     If, as : n example, a waste or  soil  layer is  18 inches thick and has
access to drainage (e.g., a drainage  layer) on either side, than  H   in the
equation is 9 inches or 23 centimetres.  If the liquid  limit of the soil is
60 percent, then the time computed  for 90 percent primary consolidation from
Equation 3 is 34 days, meaning that 90 percent of the settlement which  will
occur in that layer will take place in 34 days.  Therefore, most of the com-
pression which will occur in layers of a landfill to which drainage is  pro-
vided will probably occur during construction.

     Varying the thickness of the waste or soil layer or the distance between
drainage layers illustrates the great afreet that layer  thickness has on the
time of consolidation.  Halving the thickness cuts  the  consolidation time by  a
factor of it.

     More precise  (but still approximate) estimates of  primary consolidation
time may be made by performing laboratory consolidation  tests on  the actual


                                      29

-------
 materials to determine  the  coefficient of conso)idacion.   Then  the  time    t
 to  achieve an average  percent  consolidation,   U .  can be  predicted  wj-h'rhe
 equation
 where
       T - a dimensionless  time factor which is a direct result  of  the  mathe-
           matical  solution of  the partial  differential equations describing
           the  consolidation process.
     H^ - length of  drainage path for expulsion of water from the  soil voids
           (for single  drainage,  as with  soil overlying an impervious harrier,
           H^ " H ; for double  drainage,  as with soil bounded  above and below
           by pervious  zones,  HC - H/2 ; for multiple drainage  paths,  as with
           soil interspersed with alternate layers of pervious zones,  Hr *
           fraction of   H).                                              c
     Cv - coefficient  of consolidation,  a  laboratory-determined value
           dependent  on the soil's compressibility, permeability, and density
           (void ratio).

 The exact values of  T must be  determined by evaluating a rather  complex
 series  expression by trial  and error.  However,  this is not necessary  since it

 has been found that  T may be  evaluated  with high precision using the empir-
 ical expression



                             T"  i (rib)  (u *60Z)                        (12>
                                   \   /


                T -  -0.9332  Iog1() (l  - yM - 0.0851  (U > 60T)             (13)

 where U - percent consolidation  desired.

     Consequently, if  the  coefficient  of consolidation.   C , is determined
 for a material  in a  hazardous  waste landfill,  then the  time for any desired
 percent  of  consolidation may be  computed from Equation  11.  In  a more  general
 form. Equation 11 may  be written  (see  derivation  in Appendix  D).
where
         Y. * dry density of the waste material
              slope of the dry density versus pressure relationship determined
              from a one-dimensional compression tast on the waste material
                                      30

-------
         vw - density of water

          It - coefficient of permeability of the waste material

The various factors of Equation 14 may be evaluated to determine how they will
affect the time to achieve desired percentages of primary consolidation.
Obvously the factors in the numerator of Equation 14 must be minimized and
factors in the denominator must be maximized to minimize the time for
consolidation.

     The time factor,  T , and the density of water,  y  , cannot be changed
in the equation, but the other factors may be manipulated to achieve consoli-
dation In the shortest possible time.  For example,  H   may be manipulated to

advantage by installing drainage layers within the landfill.  It should be
mentioned again that  H   has the most pronounced direct effect on consolida-
tion time.             c

     The compressibility of the waste material is given in this treatment as
dy./dp , and this quantity will be minimized as the strength and density  y,
of the material are maximized.  This can be accomplished by applying compac-
tion effort to the landfill wastes and cover layers; selecting a material of
low compressibility (low plasticity index) to serve as intermediate cover
where possible; stabilizing the wastes and intermediate cover with pozzolanic
agents to increase their compressive strength; and compacting the intermediate
cover layers dry of optimum if they are clay-like, also to Increase their
compressive strength (a caution here is that subsequent wetting can cause
collapse* of low plasticity material).

     Finally, the time for consolidation may be minimized if the coefficient
of permeability,  k , of the landfill materials is maximized.  Since perme-
ability generally decreases as density increases, efforts to maximize both may
be counterproductive.  A good compromise may be to compact the soil or waste
to optimum density for the effort applied.

     In order to calculate time from Equation 11,  C   must be determined.
This parameter Is usually evaluated using a curve-fitting orocedure applied to
the time—consolidation curves from one-dimensional compression tests.  The. ,
procedure (logarlthm-of-time method) Is given in many standard references. '

     The values of  C^   are different for each load Increment and therefore
must be evaluated for all load increments used in the compression test.  To
compute the time for various degrees of consolidation for layers of material
in the field, an appropriate value of  C  , corresponding to the average

*  Collapse is a phenomenon which can occur in- low plasticity soils at low
  density (compacted dry of the optimum water content) when exposed to water.
  Wetting such a low plasticity soil may soften clay binder between larger
  silt and sand size particles causing a loss in strength which is accompanied
  by a large volume decrease.  Collapse usually occurs rapidly when compared
  to th« time for comparable volume change due to the process of
  consolidation.
                                       31

-------
pressure in the field situation Is selected and the time for field consolida-
tion is computed from Equations Jl, 12, and 13.

     Because of the simplifying assumptions made in the development of the
theory and uncertainty in the evaluation cf  C^ , time predicted by the theorv

is at best approximate and at worst only an order oj magnitude estimate.  The
problem of selecting an appropriate value of  GV  is additionally complicated

by the inhomogeneous nature of the contents of a hazardous wants landfill and
the difficulty of representatively sampling these materials for testing.  The
problem is additionally complicated because of the  inherent differences in
behavior between laboratory samples and in situ soil.

     Rather than trying to predict precise values from  the  theory,  it may be
much more practical to use the geometric and material properties  dictated by
the theory to identify general operational procedures that  will minimize  set-
tlement time.  Drainage layers to control the  effective thickness  of  waste
layers  (H ) appear to be a practical measure to monitor and control the
internal movement of fluid within  the  facility and  to eliminate extended  peri-
ods of settlement.  Previous  soil drains and,  in more recent  time,  geotextile

fabric drains4'6*7 have been  used  to relieve pressure and control  flow within
earthen embankments.  The same techniques may  b« used  to great  advantage  in
hazardous waste landfills.

Differential  Settlement

     Problems with differential  (uneven) settlement may occur if  drummed  waste
must be disposed  of  in a  landfill  with bulk waste.   The time  for  deterioration
of  the  steel  drum may be  quite  long  and drummed  waste layers  may  remain very
stiff  in  the  Interim.   In such  instances,  if  there are not  many drums for dis-
posal  In  a  landfill,  they may be dispersed  about  the landfill,  or emptied,  the
contents  stabilized,  and  the  drums crushed  or  reclaimed.  Obviously drums of
unstabilized  liquid  are  to  be avoided  because  once the drum is corroded,  the
entire  volume of  the drum becomes a  large  void.

     As discussed below,  differential  settlement is aggravated if stiff and
undeformlng columns  o* material  are  placed in  close proximity to flexible
deformable columns.   Since  the central column  model is actually based on
column elements,  If  spatial properties within  the landfill are known with
sufficient confidence,  the  subsidence  of two columns may be computed with the
central column model.   The difference  between  th« subsidence of the two col-
umns la the quantity described below.   Knowing the distance  I  between the
columns,  the index of the differential settlement,  4/A , may be computed and
 the methods used to analyze the effect of this amount of differential  settle-
ment on the cover system.

ANALYSIS OF DIFFERENTIAL COVER SUBSIDENCE

 Identification of Causative Factors

      Settlement of the waste mass In a hazardous waste  landfill will result in
 subsidence (sinking) of the cover (cap).  Differential  settlement  can  lead to
 cover damage and leakage caused by the tensile stresses created.   In such a


                                       32

-------
case, the cover system would be required  to brtdge  the zone of lost support.
For this reason,  It  is reasonable to  formulate a model to determine rhe impor-
tant factors involved in differential settlement using elementary beam theory.
The model assumes  that the cover system will lose support over a length,  {. ,
and as a result will undergo a differential settlement.  The model representa-
tion is therefore  a  beam with fixed supports at either end and is distorted
when one support  settles an amount  a  (see Figure  7).

     Expressions  for vertical shear,  moment, slope, and deflection of the ide-
                                                                           o
alized cover may  be  determined by integration using elementary beam theory.
The mathematical  expressions for maximum  stress due to shear and moment in the
beam model in Figure 7 are
and
                          ashear  "'-' IT/  ^"Tl                       (15)
                          °moment
where
  o .     , o       " maximum  stress  due  to  shear, moment
   shear   moment        ____,	
                i - length of beam
                E » Young's modulus  of the  cover material
                h - cover thickness

Although these  expressions were developed  using small-deflection beam theory
and may not be  appropriate for the  large deflections observed in soil struc-
tures, the expressions  identify parameters which quantify  distress caused by
differential settlement.  For example,  Equations 15 and 16 suggest that stress
is minimized if  A/J  ,  E ,  and  h/1  are  minimized.  Obviously  A/I  is mini-
mized if the differential settlement,   A  > is minimized.   This may be accom-
plished by minimizing total  settlement  and involves compacting wastes during
placement, eliminating  void  space within the landfill, stabilizing liquids
before drum disposal and other considerations  (Equation 7).

     Additionally,  A/Z mav be minimized  by maximizing   I .  This will reduce
cover stress by spreading the distortion over a greater length and therefore
reducing the effect of  the distortion.  The  I  may be maximized by placing
the landfill wastes as  homogeneously as possible to give uniform support to
the cover.

     Minimizing Young's Modulus,  E , of the cover material can be accom-
plished by compacting the cover soil wet of  the optimum water content.  This
will result in  a cover  with  lower strength but with greater pliability and
capacitv to distort without  rupture.  This is shown in Figure 8 which is taken
                      4
from Lambe and  Whitman  .  The figure shows that samples 1  and 2, which are
compacted dry of optimum water content, offer high strength and stiffness    .
(Young's Modulus) but exhibit brittle behavior in that they develop maximum
strength and fail at  relatively small strain.  Samples 5 and 6, compacted wet
                                       33

-------
                                   BEFORE
                                   SETTLEMENT
                                   AFTER
                                   SETTLEMENT
Figure  7.  Beam representation of a cover systen.

-------
               20  22  24   26  28  3O  32  34  38

                   MOLDING WATER CONTENT. %
                     S   8  10  12   14  16  18  20

                        AXIS STRAIN, %
Figure  8.   Stress-strain behavior of  clay specimens
            at different  compaction condition.
                          35

-------
of the optimum water content, show low strength .ind stiffness but exhibit
ductile/pliable behavior.

     High strength is seldom required in the cover system of 3 hazardous waste
landfill; therefore, wet-of-optimum compaction of the cover system would be
desirable since it would result in a material which would be more able to
yield and flew without rupture.  It thus would be able to conform to nonunl-
forra settlement In the foundation soil underneath.  An addition.il "free" bene-
fit of the wet-of-optimum compaction is a lower cover permeability.

     Finally Equations 15 and 16 suggest that the ratio  h/i  should ^t min-
imized.  This should be done by maximizing  i •  A thick cover is necessary to
control diffusion as well as to prevent the intrusion of animals and plant
roots into the landfill.  A thick cover also offers the advantage of more
resistance to desiccation due its large mass and thickness.

     The beam model shown in Figure 7 is a very simplified model, but  is use-
ful in that it is not used for analysis but rather to identify parameters  sig-
nificantly affecting the behavior of cover systems.  That is, the model  is
used in a qualitative rather than a quantitative sense.  However, a more com-
plex model consisting of a beam supported by an elastic foundation is  worth-
while considering if only to verify that significant parameters have not
been overlooked or omitted by the simpler model.  For completeness, three  con-
ditions were investigated considering beans supported by a Winkler foundation.
A Winkler foundation is a linearly elastic foundation consisting of springs of
constant sfffness, all in close proximity (adjacent) to each other but  all of
which behave independently of the influence of neighboring springs.  This  rep-
resentation more closely approaches the behavior of soil supported structures
but departs from actual behavior in that soils are not elastic, and elements
of soil are influenced by the behavior of neighboring elements.

     Three cases are considered and are shown schematically  in Figure  9.   They
are a case where the cover beam bridges a zone where interior support  is truch
less than that at the edges, a case where the cover beam bridges a zone  where
interior support is completely lost under the central span but the bean  is
fully supported (clamped) at the edges, and a case where the cover beam
bridges a zone where interior support is lost and the edges  have less  than
total support.

     For all three cases the beams in question have stiffness,  El , and
                                                               g
density,  y •  Solutions for cases 1 and 3 are given by Hetenyi  .  Case  2  is
the case of a beam with no rotation or deflection allowed at the ends.

Case 1 —
     For the configuration of case I the maximum moment and  shear are  located
at points A and B as shown in Figure 9.  Values of the maximum moment  and
shear are
i«
 max
                                 ybh /sinh  Xjt - sin  Xt\
                                 2.2 Isinh  XI + sin  \tj
                                       36

-------
    1
                                       K <=»
                        CASE  1
                         CASE  2
                   -El
                                                            K * <*>

/


1
/ /
I ^^ f • ^-— —
"^s^^ ~^^^^
^^••^^^^ ^^^^
*~*~~- — "^^
V

\
•
•
A K=0 B


«



e


^ «i^
< - o
L
3
(


                         CASE 3
Figure 9.  Models  of  beams on the elastic foundations.

-------
                        n      Ybh /cosh Xi - cos  xA
                        Snax *  X  I sinh Xi + sin  Xi J
where
       Y - density of (soil) beam
       b » width of the bean
       h « thickness of the beam

       X - fylCMEI
       K * foundation modulus (frora plate load test)
       I * length of beam supported by foundation of modulus  K

       I - (1/12) bh3

     From Equations 17 and  18 the maximum stresses due  to moment and shear may
be computed  to be
                                      ^sinh AI + sin

and
                                      /
                                      \
                                            Xi — sin />*, |                  (19N
                        _   y  Vbh t/^/cosh  Xi -  cos  Xi\                 (7^
                    °s ' C2  T   \r£*  ^sinh  Xi »  sin  Xij                 (20)
where  C.   and  C.  are constants.  From Equations 19 and  20  It  is  observed
that distress will be minimized  If  Y ,  bh  ,   E   and the  trigonometric
expression  are minimized and  K   Is maximized.  This seems consistent  with
intuition since induced stress will increase  if the density (unit weight)  of
the beam increases over a  span with less than complete support.  However,  the
density of  the beam and its depth,  h , are  largely uncontrollable, density
being essentially constant and   h is usually dictated by  factors outside  the
realn of soil mechanics.   E   should be minimized  as predicted by the simpler
model, and   f  should be maximized since the  greater the foundation support,
the lesser  will be the beau distress.  The trigonometric expressions in  Equa-
tions 19 and 20 are bounded between zero and  one.   If  X£  is zero  then  the
expression  becomes zero.   However,   X* is generally not equal to zero,  so  I
 must be zero which reduces the  problem to a .trivial case.  If  \t  > w ,  then
the trigonometric expression  approaches one.  The condition  \i >  ir  repre-
sents the case of a long beam.

     The conclusion reached by this analysis  is that case  1 is consistent  and
compatible  with the beam model.

Case 2 —
     For case 2, the maximum  stress due to shear  and moment becomes
and                                                                        .

                                    a  -   yt                              (22)
                                       38

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Case 2 may represent  the case of a cover fully supported until it loses sup-
port over a length,   I  such as if a single drum or series of drums collapsed
within a landfill  causing cover support  oss, or if settlement occurred in the
waste material underneath the cover.  Distress due to both moment and shear
may be minimized by minimizing the unsupported length   Z  which may be accom-
plished by providing  adequate compact^.n of wastes so that foundation support
is not lost over a  larger distance   «.  , or not burying  drums which otherwise
would ultimately collapse with the consequent loss of cover support.

Case 3—
     In case 3 the  maximum  stresses  due to shear and moment are
                                                                           (23)
                             m    W  W\2A +  X'L/

and

                                     a  - ^ YL                              (24)
                                      s   4

Both Equations  23  and  24  surest  that  Y   and   L   should  be minimized  for  min-
imum cover distress, but  these  limits lead to trivial  examples.   From  Equa-
tion 23, however,  it may  be  determined  that distress due  to moment  Is

minimized if  the product   ^L •  6 , which  produces the very interesting  result
that the relationship  between unsupported  length   L ,  the foundation constant
KI , and the  beam   E   and geometric parameters  b   and h for minimum dis-
tress are
                                                                           (25)


Equation 25  suggests  that  a  certain  degree  of  foundation  flexibility  may  be
desirable because  if  the  foundation  modulus becomes  infinitely  large, case 3
degenerates  to  case 2,  which is  that of a cover with fixed  ends and represents
a condition  of  more severe distress  than that  of case 3.  A gradual transition
In foundation support to  minimize distress  in  the beam (cove.')  is  suggested by
Equation 25  along  with  :ne comparison of cases 2 and 3 and  reinforces the
suggestion of the  earlier  simple model that distress is aggravated in a cover
system  if there is a  sudden  change in stiffness of the foundation, i.e.,
wastes  of great differences  in stiffness should not  be placed in close proxim-
ity to  each  other.

Tensile Strain

     The cover  system will be required to increase in length and therefore
carries tensile strain  as  differential settlement occurs  in a hazardous waste
landfill.  The  cover  will  crack  if tensile  strain becomes excessive.   Gener-
ally soils are  not able to withstand high levels of  tensile strain without
cracking.
                                                                           s
     The average tensile  strain  developed within the cover  may  be  computed
using the simple beam model.  This procedure Involves integrating  over the


                                       39

-------
deflected beam shape  to determine the arc length of the bean after deflection.
An expression to compute  the arc length of the deformed section of the beam
Model shown in F^ure 7 may be determined by integration, and is
                                                                        (26)
 where
        I -  length of the deformed cover  element
        & -  differential settlement
        I -  length of the cover element
        x -  coordinate along the cover element

 r:^r^T,:^^^^
 Figure 10 and are presented as the dimensionless q«««tlty  A/ *
   £  increases .
      If the maximum tensile strain which can be sustained  by a given soil is
 measured, estimated,  or  otherwise obtained, then the mwimurn value of   til
 which can be tolerated in  a cover system of that soil -ay  be estimated  from
 Figure 10.

      Figure 11 is a plot of maximum  tensile strain reported by several  inves-

 tigators9'10 versus soil plasticity  Index.  Figure 11 also suggests  that rhe
 capacity for tensile strain  increases as plasticity index  of a soil  increases.
 For cc^leteness. more research on th.  tensile strain capacity «*••"*•
 neededTbut the trend for  Figure 11  is  clear, showing that, for  similar condi-
 tion, of compaction (water content and  dry density), the tensile capacity of a
 soil  increases as the plasticity index  increases.  Therefore,  since  soil  that
 Ire able to withstand higher levels  of  tensile strain are preferred  for the
 instruction of cover sy«e« of hazardou, waste landfills, the  s.lectior , of
 soils with higher plasticity indices is indicated  if a selection is  possible.
       Additionally, it should be stated that  it would be highly <••*'««•
  nerform a laboratorv study of th. tensile properties of potential soils of
  Tichthl covtr system of a hazardou. wast,  landfill will be constructed.
  Inv.,tlg.tio«'should include (for th. -oil selected  for the c ov.r) sever a
  molding condition, to d.t.rmin. th. condition which  °Jf«edi.^e^"' ;°""?
  M«n of ten.ll. strain. «cono«v, and .... of placement for the differential
                                    2 sss
  be considered.
  Effects of Differential  Subsidence on th. FML
       Th. discussion of subsidence and settl.rn.nt effects has thus  far
  on d.£r«tion of th. soil  portion of the cov.r.  Effects of settlement on the

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I  00
0.73
0.90
0.23
                                    I    i   i  I  i i  i i
                                                           i    i   i  I  I  I i I
                           10                      10.0
                               TENSILE STRAIN, X
100.0
              Figure 10.  A/I   versus average tensile strain.

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3.5
                         LEGEND
             LEONARD ( BEAM FLEXURE TESTS )
                                                    T	T
          O  TSCHEBOTARIOFF ( DIRECT TENSION TESTS )
          D  WES DATA ( DIRECT TENSION TESTS )
                        10                    100
                           PLASTICITY INDEX, %
7
       1000
          Figure 11.  Tensile strain versus plasticity index.

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FML of the cover must also he considered.  Field data on FML performance In
hazardous waste landfills are not available, but laboratory tests have been

conducted on FML's under simulated fill and embankment conditions11'12.
Flexible membranes can elongate  substantially before failing, and little prob-
lem is anticipated for cover FML failure in the case of cover subsidence over
a large ar2a.  Locally severe subsidence, however, may produce substantial
differential settlement and much greater elongation of the FML.  Several
investigators have shown through multidimensional stress-strain analyses that
allowable strains reported by manufacturers of FMLs may be much higher  than
the actual strain at  failure of  FML's  in field conditions.  Manufacturers'
elongation data are generally for one-dimensional strain stretch tests  wherein
strain is distributed evenly within  the grip points of a tensile test  device.
In situ conditions can be expected to  produce multidimensional stresses and
uneven distribution of strain and cause thinning and possible  tearing  and
premature failure of  FML's.

      Steffen11 tested several geomembranes  in a pressure vessel  designed  to
stress the antire surface of a  3-foot  diameter  specimen of  the geomemhrane.
He reported  strains at failure  of 9  percent  for 90 mil HOPE  and  15  percent  for
80 mil HDPE, which  is about  1 percent  of  the  strain  reported  from manufactur-
ers'  one-dimensional  stress-strain  tests.   (His tests  on PVC,  CPE,  EPC, and
EPDM  produced higher  strains, from  40  to  70+ percent.)  Tests  conducted on
varying thicknesses of HDPE  indi-ated  that  thicker  FMLs were  able  to achieve

higher strains before  failing.   Strong   showed  through  tests  of membranes
stressed over artificial  fissures and  hard  points  in  a pressure  cell that high
localized elongations  could  be  minimized  by using  thicker  membranes and by
incorporating a  geotextile  (a woven fabric)  into  the  geomembrane application.
The investigations  indicate  that failure  of FML's  In areas of  severe differen-
tial  settlement  may occur  at lower  strain values  than would be expected from
FML manufacturers'  test  data.   Furthermore,  thicker FML's  may  allow greater
strains  to occur before  failure.

      Because the FML  is  secluded within the cover,  it cannot easily be
inspected and  its condition  determined.   Every effort should be  made when
placing wastes  in the landfill  to reduce the potential for differential set-
tlement, particularly in the upper  layers where local subsidences of the cover
may severely strain the  FML component.

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                                    SECTION 5

               MITIGATION OF SETTLEMENT AND EFFECTS OF SETTLEMENT


 LANDFILL TREATMENT TO REDUCE SETTLEMENT POTENTIAL

      Section 4 discussed the philosophy and theory behind controlling the
 amount of and total time for settlement of a hazardous waste landfill.  Prac-
 tices that optimize the variables of Equation 4 reduce the time to maximum
 settlement and make the landfill more manageable after closure.  This subsec-
 tion describes potential ways of treating the landfill contents to reduce aid
 hasten ultimate settlement.   Because soils and soil-like sludges and other
 materials constitute a major part of all hazardous waste landfills, it is not
 unreasonable to suggest adaptation of soil stabilization techniques to land-
 fills.  This subsection presents methods for fill compaction and waste
 fixation.

 Fill Compaction

      The following discussion makes reference to cohesive and .loncohesiv*
 soils.  Cohesive soils are generally those consisting of grain diameters pass-
 ing  the  No.  200 US Standard  sieve,  or 0.074 millimetre (silts and clays), and
 coarse grained materials are those  with substantial amounts of fines in the
 matrix such  as clayey sands.   Cohesionless soils are coarse grained soils such
 as sand  and  gravel,  the grains of which are more free to move within the soil
 mass than are  the grains of  cohesive soils.

 Standard Compaction Methods—
      Standard  compaction methods for soils include  the use of specially
 designed motorized compaction equipment and  laboratory and field monitoring
 procedures to  achieve  desired soil  density,  plasticity,  and permeability.   The
 reader Is referred to  the discussion of soil  compaction  methods  and procedures
 regarding the  application of  the methods to  landfill  cover preparation.   The
 same methods and  equipment are applicable  to  compaction  of some  hazardous
waste fills  to achieve greater preclosure  settlement  and to lessen  the poten-
 tial  for postclosure  settlement  and  subsidence.

Vibrocowpaction--
      Vibrocompaction methods  in  use  in  civil  engineering include blasting,
vibrating prob«, and vibratory rollers  and have  been  used  for rapid  densifica-
tron  of  saturated  cohesionless  soils.   The  range of grain-size distributions
suitable  for treatment  by vibrocompaction  is  generally  from coarse  to  fine
sand  (noncohesive  soils).  The effectiveness  of  the vibratory methods  is
greatly  reduced if  the  percent  finer  than  the No. 200  sieve  exceeds  about '
20 percent or  if more  than about  5 percent  is finer than 0.002 -am,  primarily
because  the hydraulic  conductivity of such materials  is  too  low  to  prevent

-------
rapid drainage following liquefaction.  Only the vibratory roller could  he
considered for compacting hazardous waste landfills.  The other methods  are
considered coo risky or are inappropriate for use in hazardous waste
landfills.

     Where dry or saturated coheslonless fills are being placed, vibratory
rollers are likely to he the best and most economical means for achieving high
density and strength.  The effective depth of densifIcation may be 6  feet or
more for the heaviest vibratory rollers (Figure 12a).  For a fill placed in
.successive lifts, a density-depth distribution similar to that in Figure 12b
results.  A properlv matched system of lift thickness, soil type, ard roller
type can yield compacted layers at a relative density of 90 percent or more
(relative density is a comparison of the existing void ratio of a soil with
the range of possible void ratios for the soil, and is expressed by
(e    - e)/(e    - e   ) where  e    is the void ratio in its loosest state
  max        max    min          max
and  e  .   the void ratio in Its densest state).
      mm

Precompression—
     Preloading—Earth fill or other material is placed over the landfill
prior to final closure in amounts; sufficient to produce a stress in the soft
soil equal to that anticipated from the final structures  (or in the case of
landfills, the final cover).  As the time required  for consolidation of the
soft soil may be long (months to years), varying directly as the square of the
layer thickness and inversely as the hydraulic conductivity, preloading alone
is likely to be suitable only for stabilizing thin  layers and with a long
period of time available prior to final development of the site.

     Surcharging—If the thickness of the fill placed for preloading is
greater than that of the expected structure-induced loading (the final cover
and appurtenances), the excess fill is termed a surcharge fill.  The amount  of
consolidation varies approximately in proportion to the stress Increase.  The
preloading fill plus surcharge can cause a given amount of settlement In
shorter time than can the preloading fill alone.  Thus, through the use of
surcharge fills, the time required for preloading can be redured signifi-
cantly.  Both primary consolidation and most of the secondary compression
settlements can be taken out in advance bv surcharge  fills.  Secondary com-
pression settlements may be the major part of the total settlement of highly
organic deposits or of old landfill sites.  The landfill operator will prob-
ably have to ask the pennitter for an extension of  closure time to perform the
surcharging.

     Vertical drains—The required preloading time  for most soft clay deposits
more than about '0 feet thick will be large.  The consolidation time may be
reduced by providing a shorter drainage path by installing vertical sand
drains.  Sand drains are typically 10 to 15 inches  in diameter and are
installed at spacings of 5 to 15 feet.  Perforated  risers can also be used as
vertical drains.  Horizontal drainage layers facilitate internal drainage.  As
discussed previously, any system that removes leachate from within the land-
fill helps reduce the time to achieve maximum settlement and adds to the long
range stability of the landfill.                                         ,

-------
              DRY DENSITY, PC F
             100              lOi
             DRY DENSITY, PCF
                 NOTE. SINGLE LOOSE LIFT OR
                       NATURAL DEPOSIT OF
                       THICKNESS >% FT
             60              60

         RELATIVE DENSITY. PERCENT


a.  DENSITY VERSUS 0£PTH FOR DIFFERENT NUMBERS
            OF ROLLER PASSES
1
' ••
k
f "
ki
0
4.1
t.o
IO IOO lOi II
"" — --^,


NOTE: 2-FT LlF
S ROLLE
^N

<
T HEIGHT \
R PASSES. \

)


»o 6o ao 100
       RELATIVE DENSITY. PERCENT


b. DENSITY VERSUS DEPTH RELATIONSHIP FOR A
         SERIES OF 2-FT LIFTS
               Figure 12.   Sand d^nsifIcatIon using  vibratory  rollers.
                                                                                !  I

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Waste Fixation

     Waste fixation describes a variety of processes bv which fluid or liquid
wastes are strenpth-ned or made solid by mixing with other agents.   Similar
terms often used are waste solidification or waste stabilization.  The two
processes most commonly used hv operators of hazardous waste landfills to fix
wastes are absorption  lor adsorption) and cementation.  Some fixation pro-
cesses absorb the  liquid waste and make the mixture appear as a solid.  The
liquid may or may  not  be immobilized.  Other processes, such as cementation,
produce a chemical and physical change in the mixture and impart considerable
strength relative  to the original  substance.  Two goals of fixation are gain
in compressive strength and binding  or retention of liquids.  Increase in com-
pressive strength  reduces compression of the waste and limits settlement of
the  landfill.  Retention of liquids  prevents the production of leachate within
the  landfill but if not completely effective may increase the time  to ultimate
consolidation.

      Fly ash primarily from coal-fired power plants,  kiln-dust from cement
manufacture, and absorptive clays  are often-used absorbents  in the  waste dis-
posal industry because of their  relatively  low  cost and availability.  Some
fly  ashes and kiln dust have pozzolanic qualities,  that is,  they react with
calcium hydroxide  in the presence  of water  to  form  cementitious  compounds.
Fly  ash and kiln dust  serve both  as  an absorbent and  in some  cases  as
strengthened when mixed with  manv liquid hazardous wastes.   Their  effective-
ness as stabilizers depends both -orT'tnepropertles  of the absorbents  and  of
the  materials being stabilized.   Tests must be  run  on potential  mixes to
determine effectiveness.

      Absorptive  clays  such  as  fullers  earth are used  in more limited  quanti-
ties in landfill waste stabilization because of higher materials oost.   A com-
mon  use is  as an  additive  to  drums of  liquid wastes to reduce the  amount  of
free liquids entering  the  landfill.   Adsorptive clays are  rarely used in
solidifying large  volumes  of  hulk wastes,  whereas  fly ash  and kiln dust  are
commonly used  for  that purpose.   Engineering characteristics of  mixtures of
fly  ash and absorptive clays  and water and  oil (simulated  liquid wastes), and
of real wastes  traated with pozzolanic material,  are  presented  in  Section 3 of
this manual.

      Chemical  grouts  and  plastlcizers have been introduced  to the  growing
waste fixation  market.  The long-term effectiveness of particulate additives
to retain  liquids  within  the waste under consolidation pressures and after
chemical breakdown of  the  mixture in a landfill environment has not been
determined,  but  Is suspected.

      Boutwell1* reported  on a process whereby a small quantity of  a polymer is
added to  a  waste-dust  mixture to render the mix less porous by blocking the
pores. Technological  advances- will surely be made in the field of waste fixa-
tion in the next few years and should be monitored for application to hazard-
ous  waste  landfill operations.

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DESIGN AND CONSTRUCTION OF COVERS TO ACCOMMODATE SUBSIDENCE

     This subsection discusses consldera'ions  in designing and constructing
final covers to withstand deformations resulting from settlement and
subsidence.

Compaction of Cover Soils

Coals of Compaction—
     The barrier  soils of final  landfill covers are usually compacted to
achieve desired low permeability to liquids, a primary  concern of hazardous
waste landfills.  Consideration  must also be given to preserving the plastic-
ity and flexibility of the cover soil to protect it when  it is subjected to
deformation.  Inflexible or  stiff cover soils  are more  likely to crack when
deformed  than are soils of low stiffness.  The desired  flexibility  can be
achieved by compacting the cover soils at a water content that  is wet  of opti-
mum.  Figure  13 is a soil's  compaction curve.  The curve  is made up of points
representing  the  dry densities of soils compacted at  increasing water  con-
tents.  The maximum density  that csn be achieved is represented by  the peak  of
the curve.  The water content at the peak  is called the optimum water  content
for the soil.  Any more water added to the soil will  produce  only  lower  com-
paction densities.  Cover soils  compacted wet  of optimum  water  content are
more plastic  and  less^sJtiff  and  brittle than they would be if compacted  at
lower water content, and are less likely  to develop zones of  tensile stress
than are  soils compacted dry of  optimum.   Fortunately,  soils  compacted wet of
optimum also  exhibit low permeability, and  the goals  are  compatible.

Standard  and  Modified Compaction--
     The  specification of compactive effort  to b«  performed on  a  soil  Is
determined  from  laboratory  tests conducted  on  a sample  of the soil.  Two com-
mon  laboratory tests are  the standard  Proctor  and  the modified  compaction
tests.   In  the standard  Proctor  test,  samples  of  the  soil at  increasing  water
contents  are  compacted by hand  in a mold  using a  5.5  pound hammer falling
 12 Inches  per blow  and applying  25  blows  per  layer  for 3  layers.   The  dry
density of  the  sample  after  compaction at  each water  content  is recorded and a
curve  like  that  in  Figure  13 ts  produced.   The standard Proctor test was con-
sidered  to  reproduce  compactive  efforts  similar to  those  of compaction equip-
ment  in use when  the  test was developed.   Compaction  specifications were made
based  on  a  percentage  of the maximum density achieved in the Proctor test
 (say  90,  95,  or  100 percent  of  standard  Proctor).

      Some prolerts  required  higher  compaction efforts.   A modified compaction
 test  was  developed  using greater laboratory compaction effort.  The modified
 test  uses a 10 pound  hammer falling 18 inches per blow, with 25 blows applied
 to each  of 5  layers.   A job  specification of 95 percent modified compaction
would then produce  an in-place soil of higher density than one compacted at
">5 percent of standard Proctor.

      Compaction specifications  further indicate the water content  relative  to
 optimum at which the soil should be compacted, because soils have  different
 characteristics at  water contents above,  at, or below  the optimum  water con-
 tent  (Figure 13).  Clays compacted on the wet side of  the optimum  water con-
 tent are less parmeable than those compacted on the dry  side.  Clays compacted


                                       48

-------
              MAX DRY DENSITY
    (J
    &

    >"
    K
    {/)


    8


    X
    Q
                             WATER CONTENT. X
Figure 13.  Soil compaction curve.   Each point on the curve represents

            a sample of  the soil compacted to a particular dry density

            at a given water content.

-------

 wet of optimum are more compressible at low stresses and less
 high stresses than are clays compacted dry of optimum.  Cl*s  ccr   d    f
 optimum are stronger and have a higher stress-strain modulus thaTdo cUvs
 compacted wet of optimum.  Because the characteristics desired  in  clavs of ch*
 covers of landfills are primarilv low permeability and low stif ^ss  compac-
 tion of cover clays should logical lv be specified at lower companion e?fort
 at wet or optimum (generally not to exceed 3 percent wet of optimum).

      Control of the compaction effort of soils in the field consists of con-
 ducting in-place or laboratory tests to determine the field density and water
 content of the soil after compaction to assure compliance with  specifications.
 Soils that are too loose require additional compaction effort which can be
 accomplished by increasing the weight of ballast or the number  of  passes  of
 the compacting unit or by reducing the thickness of the spread  layer.   Compac-
 tion effort can also be increased by using heavier or different types of
 equipment.

      If the water content of the soil is above the desired value,  it  can  be
 reduced by aerating the soil through scarifying or tilling. If the water con-
 tent is too low, water can be added to the fill and distributed or mixed  with
 the soil in the borrow area.

      Soils of the final covers of hazardous waste landfills require special
 precautions and considerations.   Care oust be  exercised in placing soils  over
 an FML to prevent damage to the  FML.   A buffer layer of granular material like
 sand should be placed over the FMT, to protect  it (see Figure 2) .   The in-place
 density and water "content of the compacted soil should b«s carefully checked  to
 ensure compliance with compaction specifications.  If subsidence or differen-
 tial settlement of the cover is  expected or predicted, the soil portion of the
 cover should be flexible and of  low stiffness  to withstand the  deformations.

 Compaction Equipment —
      The principal  types of compacting equipment are the smooth wheel roller,
 the rubber-tired roller,  the sheepsfoot  roller,  and  the vibratory  compactor.
 Vibratory rollers are the least  effective  compactors for cohesive  soils,  the
 kind of soil  used in  the barrier portion of landfill covers.  Rubber-tired
 rollers with high tire pressures and  sheepsfoot  rollers are effective for
 cohesive soils.   Sheepsfoot  rollers  are  particularly effective  at  bonding of
 lifts during compaction of  cohesive  soils.   Footed  rollers were in use at

 several RCRA landfills inspected in  a previous  investigation .  Table 4 sum-
marizes the  capabilities  and characteristics of  compaction equipment.

Compaction Characteristics  of Soils —
      Suitability of soils  for embankments  is similar to that for fill covers
because the  desired characteristics  for  both applications  include  accommoda-
tion of deformations  and  low permeability.  The  clay-rich  soils (SC, CL,  and
CK)  yield  the  lowest  permeabilities and  highest  plasticities when  compacted
and  are  the  soil  types  commonly  used  to  construct  the  soil barrier portion of
landfill  covers.  Reference  16 discusses soil  types  and compaction
characteristics.
                                      50

-------
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                         51

-------
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                                                           52

-------
 Other Construction Considerations

      The RCRA hazardous wast* landfill cover Is made up of layers which
 include materials other than the soil barrier, as illustrated in Figure  2.
 This subsection discusses considerations in the design and construction  of  the
 cover as a layered unit, following the basic component arrangement shown in
 Figure 2.

 Suitability of Various Soil* as Covers—

      LuCton et al.   evaluated and ranked soils for their performance as land-
 fill covers.  Table 5 lists the rankings for selected performance character-
 istics.  Rankings are 1 (best) through 13 (poorest).  Since this report
 concerns itself with the soil barrier portion of the cover of a hazardous
 waste landfill, some of the characteristics in Table 5 are not directly
 applicable.  Soils with fines in the matrix and clay soils perform well  in
 impeding percolation of water and migration of gases (columns A and B).   Ero-
 sion control (column C) is not a primary consideration for the barrier portion
 because the barrier is not normally exposed.

      Rankings for column D (crack resistance) are based on expansion and con-
 traction with accompanying cracking controlled by the clay mineralogy of the
 soils.  Fine grained and clayey soils accordingly rank low in resistance to
 that kind of cracking.  Final cover barrier-soils, "however, are covered
 Immediately after emplacement and are not allowed to undergo change in water
 content.  Cracking by expansion/contraction is not normally a problem.  From
 the standpoint of resistance to cracking during deformation from settlement '
 and subsidence, the clay soils rank high, as discussed in earlier sections.
 If the cover layers overlying the barrier portion are compromised, and the
 clay portion is exposed to the atmosphere, drying or water infiltration  can
 occur, and the barrier may well be subject to cracking by desiccation and
 shrinkage as suggested in column D of Table 5.  The table might best be  used
 as a guide to selection of other layers that make up the cover and less  to
 evaluate soils for the construction of the cover soil barrier.

 Use of Soil Additives and Soil Stabilization—
      Where appropriate soils for use as cover are not available on site, it
 may be necessary to bring in clay rich soils or to add bentonite (a swelling
 clay) to available soils to achieve the desired characteristics of low perme-
 ability and plasticity in the cover.  Table 6 presents recommended application
^•ates for sodium bentonite to reduce permeability of soils in farm ponds.  It
 can be used to estimate the amount of bentonite required for soils of landfill
 covers.  The use of soil stabilization techniques such as addition of lime  or
 pozzolanic materials or grouts is not anticipated to be of use in cover  soils
 because the techniques tend to great-^y stiffen the treated soils, an undesired
 quality in landfill covers.

 CORRECTIVE ACTION FOR SUBSIDENCE

      Corrective actions for subsidence events in a hazardous waste landfill
 are beyond the scope of this report, but seme points are worthv of mention'.

      Cover damage caused by subsidence will require repair and will likely
 require correction of the cause.  Damage is expected to be corrected hy


                                       53

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TABLE 5.  RANKING OF USCS SOIL TYPES BY PERFORMANCE OF COVER FUNCTIONS
                                                                      13
Soil Type
CW
GP
CM
GC
SW
SP
SM
SC
ML
CL
OL
MH
CH
OH
Pt
Column A
Impede Water
Circulation
10
12
7
5
9
11
8
6
4
2
—
3
1
—
—
Column R
lupede Gas
Migration
10
9
7
4
8
7
6
5
3
2
—
—
1
—
--
Column C
Water Erosion
Control
1
1
4
3
2
2
'I
'
"1
12
11
10
9
8
5
Column D
Crack (
Resistance
1
1
3
5
1
1
2
4
6
8
7
9
10
9
—
Column E
Reduce Frost
Heave
1
1
4
7
2
2
5
6
10
8
8
9
3
—
—

-------
       TABLE 6.  SOIL CONSERVATION SERVICES RECOMMENDED SODIUM BENTONITE
                APPLICATION RATE FOR FARM PONDS
                                                              Application Rate
	Soil                    Application Method            	psf	
Clay                       Pure membrane or mixed layer            1.0-1.5
Sandy silt                 Mixed layer                             1.0-1.5
Silty sand                 Mixed layer                             1.5-2.0
Clean sand                 Mixed layer                             2.0-2.5
Open rock or gravel        Clay or sand mixed  layer                2.5-3.0
                                       55

-------
excavation and exposure of the barrier layer, removal of the damaged part,
refilling of the underlying foundation, and replacement of the barrier layer.

     Correction of the cause of subsidence mav  require Increasing the strength
of the underlying waste materials.  Of the measures expected to be applicable,
grout Injection to increase the compresfive strength may be the most cost-
effective.  However, various methods of deep  compaction may also be applica-
ble, such as vlbrocowpaction, vibrodisplacement compaction, and heavy tamping.
Excavation and  replacement of the waste itself  is  not  a feasible measure  at
this time.
                                        56

-------
                                  REFERENCES

     •LCTW cF> W' C"  "R°le of Flxntion Processes in the Disposal  of  Wastes,"
     ASTM Standardization News, 1984, pp 23-25.

 2.  Hagerty.^j., Ullrich. R., and Thacker, B.  "Engineering Properties of  FGD
     Sludges,  Proceedings of the Conference on Geotechnical Practice for Dis-
     posal of Solid Waste Materials. June 13-15, Univ. of Michigan,  Ann Arbor,
     Specialty Conference of the Ceotechnical Engineering Division,  ASCE,
     1977.

 3.  Murphy, W. L., and Gilbert, P. A.  "Settlement and Cover Subsidence of
     Hazardous Waste Landfills," Report No. EPA-600/2-85/035, U.S. EPA Munic-
     ipal Environmental Research Laboratory, Cincinnati, Ohio, 1985.

 4.  Lambe, T., and Whitman, R.  Soil Mechanics, John Wiley and Sons, Inc.,
     New York. 1969. p 522.

 5.  Taylor. D. W.  Fundamentals of Soil Mechanics. John Wiley and Sons,
     New York, 1948.

 6.  Horz, R. C. Geotextiles for Drainage, Gas Venting and Erosion Control  at
     Hazardous Waste Sites, I' S. Army Engineer Waterways Experiment  Station,
     Vicksburg, Mississippi, 1986.

 7.  Harr, M. E.  Groundwater and Seepage. McGraw-Hill Inc., New York, 1962.

 8.  Hetenyi, M. Beams on Elastic Foundations, University of Michigan Press,
     Ann Arbor, Michigan, 1946.

 9.  Leonards, C. A., and Narin, J.  "Flexibility of Clay and Cracking of
     Hams," Journal of the Soil Mechanics and Foundations Division,  American
     Society of Civil Engineers, Vol 89, No. SM2. 1963.

10.  Tschebotarioff, G. P., Ward, E. R.. and DePhillippe, A. A.  "The Tensile
     Strength of Disturbed and Recompacted Soils," Proceedings of the Third
     International Conference on Soil Mechanics and Foundations Engineering,
     Vol 1,  Zurich, Switzerland, 1953.

11.  Steffen, H.   "Report on Two Dimensional Strain Stress Behavior  of Geomem-
     bran-ss  With and Without Friction," in Proceedings. International Confer-
     ence on Geomemhranes. Vol 1, Denver, Colorado, 1984, pp 181-185.

12.  Strong, A. G.  "Longevity Aspects of Polymeric Linings for Water Contain-
     ment, "  in Proceedings, International Conference on Geomembranes. Vol 1,
     Denver, Colorado,  1984, pp 281-285.-

13.  Headquarters, Departments of the Army and the Air Force.  Soils and Geol-
     ogy, Procedures for Foundation Design of Buildings and Other Structures
     (Except Hydraulic  Structures), Army TM 5-818-1, Air Force AFM 88-3,
     Chap 7, pp 16-1 through 16-17, 1983.
                                      57

-------
14.  Boutwell, G. P., .'r.  "Fixation in Land Disposal," paper preprint  pre-
     sented at Air Pollution Control Association Workshop on Hazardous  Waste,
     Baton Rouge, Louisiana, 1985.

15.  U.S. Department of  Che Army, Office, Chief of Engineers, Earth and Rock
     Fill Dams. General  Construction Considerations, Engineer Manual EM 1110-
     712300.  1971.

16   U.S. Department of  the Anny, Office, Chief of Engineers.  "The Unified
     Soil Classification System," Technical Memorandum No.  3-357, U.S. Army
     Waterways  Experiment Station.  Vicksburg,  Mississippi,  1960.

 17.  Lucton,  R.  J..  Re*an.  G.  L., and  Jones.  L. W    "Design and  Construction
     of Covers  for  Solid Waste Landfills,"  Report  No.  EPA-600/2-'9-t65,
     Municipal  Environmental  Research  Lab.  U.S. Environmental Protection
     Agency,  Cincinnati. Ohio, 1979.
                                         58

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                                  APPENDIX R

          CLASSIFICATION OF CEOMEMBRANES (reprinted from Proceedings,
                   International Conference on Geomembranes,
                       Denver, Colo., June 20-24, 1984)

Geonembrane:

Synthetic membranes, polymeric membranes, flexible membrane liners, plastic
liners, and Impervious sheets are n. few examples of the many names given to
these relatively new materials.  Although m-iny users of these materials often
prefer to use trade names, this practice is deeded inappropriate because it
creates considerable confusion.

Geomembrane is Che generic term proposed to identify these liner and barrier
materials.  Geomembranes are impermeable membrane liners and barriers used in
civ^l engineering for geotechnical projects.  They can be either sprayed on a
surface or prefabricated and transported to the construction site.  Sprayed-on
geomembranes are composed predominantly of asphalt.  They are either sprayed
directly on a surface (earth, concrete, etc.) or onto a geotextile.  Prefabri-
cated geomembranes are usually composed of synthetic polymers, elastomers
(rubbers), or plastomers (plastics); some are reinforced with a fabric.  There
are also prefabricated asphaltic geomembranes.

Classification of Geomembranes

Geomembranes can be classified according to production process and
reinforcement:

1.  Made In situ, non-reinforced geomembranes are made by spraying or other-
    wise placing a hot or cold viscous material directly onto the surface  to
    be lined (earth, concrete, etc.).  The non-reinforced geomembranes made by
    spraying are called "sprayed-on (or spray-applied, or sprayed in situ)
    non-reinforced geomembranes."  Typical materials used are based on
    asphalt, asphalt-elastomer compound, or polymers such as polyurethane.
    Due to the spray application, the final thickness of such geomembranes is
    not eas.y to control and may vary significantly from one location to
    another.  Typically, required thicknesses range between 3 and 7.5 mm
    (120 .-md 300 mils).

2.  Made in situ, reinforced geomembranes are made by spraying or otherwise
    placing a hot or cold viscous material onto a fabric.  The reinforced  geo-
    meatbranes made by spraying are called "sprayed-on  (or syray-applied, or
    sprayed in situ) reinforced geomembranes."  Typical materials used are the
    sa-ne as for the made in situ non-reinforced geomembranes described above.
    Typical fabrics used are the needle-punched nonwoven geotextiles because
    they can absorb viscous materials.  As discussed Above, the final thick-
    ness of such geomembranes is not easy to control.  Typically, required
    thicknesses range between 3 and 7.5 mm (120 and 300 mils).
 Giroud, J. P. and Frobel, R. K.  "Geotnembrane Products" Geotechnical Fabrics
Report, Vol I, number 2 (1983).

                                      69

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3.  Manufactured, non-reinforced geomembranes are made in a plant  by extrusion
    or calendering of a polyneric compound, without any faSrlc reinforcement,
    or by spreading a polvwer on a sheet of paper removed at the  end of  the
    manufacturing process.  Typical thicknesses range from 0.25 to 4 mm  (10  to
    160 rails) for geomembranes wade by extrusion and 0.25 to 2 mm (10  to
    80 mils) for geotnembranes made by calendering.  Typical roll  width for
    geomembranes made by extrusion is 5 to 10 m (16 to 33 ft), although  some
    are narrower.  Tynical roll width for geowembranes made by calendering is
    1.5 m (5 ft), with some manufacturers producing 1.8 to 2.4 m (6 to 8 ft)
    vide rolls.

 4.  Manufactured, reinforced geomembranes are made in a plant, usually by
    spread  coating or calendering.  In spread-coated geomerabranes, the rein-
    forcing fabric  (woven or nonwoven) is impregnated and coatee on one or
    both sides with  the compound, either polymeric or asphaltic.   In  calen-
    dered reinforced geomembranes, the reinforcing fabric  is  usually  a  scrim.
    Calendered geomembranes are always made with polymeric  compounds  and  are
    usually made us  of  three plies:  compound/scrim/compound.  Sometimes  they
    are made of  five plies:  compound/scrim/compound/scrim/compound.  Geomem-
    branes  with  additional plies can be made on a custom basis.   Typical
    thicknesses  of  asphaltlc spread-coated geomembranes ars 3 to  10 mm  (1/8 to
    3/8  inch).   Typical  thicknesses for polymeric spread-coated  and three-ply
    calendered geomembranes are 0.75 to  1.5 mm  (30 to 60 mils).   Typical
    thicknesses  for five-ply calendered geomembranes are  1  to 1.5 mm  (40  to
    60 mils).

 5.  Manufactured  reinforced geomembranes  laminated with  a fabric are made  bv
    calendering  a manufactured  geomembrane  (usually a non-reinforced  geomem-
    •brane previously made by calendering  or extrusion) with a fabric  (usually
    a nonwoven)  which remains  apparent  on  one  face of  the  final  product.

 Classification of Geomembrane  Polymers
   (National Sanitation Foundation):

 1.  thermoplastics'  Polyvinyl Chloride (PVC);  Oil  Resistant PVC  (PVC-OR);
    Thermoplastic Nltrlle-PVC  (TN-PVC);  Ethylene Interpolymer Alloy  (EIA);

 2.  Crystalline  Thermoplastics'-  Low Density  Polyethylene (LDPE); High Density
    Polyethylene (HOPE); High  Density Polyethylene-Alloy (HDPE-A); Poly-
    propylene;  Elasticized Polyolefin;

 3.  Thermoplastic Elastomers'   Chlorinated Polyethylen (CPE); Chlorinated
    Polyethylene-Alloy (CPE-A); Chlorosulfonated Polyethylene (CSPE), also
    commonly referred to as "Hypalon;" Thermoplastic Ethylene-Propylene Dlene
    Mono««r (T-EPDM);

 4.  Elastomers'-   Isoprene—Isobutylene Rubber (IIR), also commonly referred to
    as Butyl Rubber; Ethylene-Propylene Diene Monomer (EPDM); Polychloro-
    prene  (CR),  also commonly referred to as "Neoprene;" Epichlorohydrin Rub-
    ber  (CO).
                                        70

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                                 APPENDIX C

              FIELD EXPERIMENTAL EXAMPLE OF SETTLEMENT ANALYSIS
                      BY STANDARD CONSOLIDATION THEORY


RETAINING STRUCTURES AND FILL PLACEMENT

    An experimental paper-mill sludge landfill was cons.ructed and monitored
for a 2-year period to obtain engineering information essential to developing
procedures for the design and operation of pulp and paper-mill waste land-
fills.*  The landfill site was an old gravel pit.  The experimental fill con-
sisted of two sludge layers, initially 10 feet thick, with 1-foot-thick sand
drainage blankets at the top, middle, and bottom.  An earth dike provided lat-
eral confinement of the sludge, and a surcharge load consisting of 3 feet of
natural soil was used.  A lysimeter study provided information on changes in
quality of the leachate when passed through selected natural soils.  Fig-
ures C-l and C-2 show the landfill in a plan view and typical cross section,
respectively.

SLUDGE MATERIAL

    The dewatered sludge used in the landfill had the physical properties
shown in Table C-l.  The Consistency Limits are the water contents at  the
liquid and plastic limits, respectively.  These properties were determined
from -sample!; taken at various elevations as the sludge was placed.  Therefore,
the properties represent the initial, as-placed sludge conditions.

CONSOLIDATION AND SETTLEMENT

     Figures C-3 and C-4 give th«j initial average effective stress,  P'
                -»                                                      o
- 138 pound/foot' for each 10-foot-thick layer.  The total load acting on the
lower sludge layer,  AP,     , is calculated as follows:
                        lower
     Weight of sludge (design thickness) above lower layer » 10 ft

     x 70 lb/ft3 - 700  lb/ft2

     Top sand layer weight - 1 ft *  100 lb/ft3 -  100 lb/ft2

     Surcharge weight - 3 ft * 130 lb/ft3 - 390 lb/ft2

     AP. w   - (700 + 100 + 390) lb/ft2 - 1,190 lb/ft2

     Average effective  stress  P}ower " P0 + APiower "  (I38 +  1'190) lb/ft;2

     - 1,328 lb/ft2 - 0.664 ton/ft2 s: 0.64 kg/cm2
*  From Ledbetter. Richard H.,  "Design Considerations  for Pulp and  Paper-Mill
Sludge Landfills," EPA 600/3-76-111, December,  1976.

                                      71

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The total load acting on the upper layer,   PUpper  »  is tne weight of the sand


blanket and surcharge.  The sand blanket weight  Is  Included In  P' .   There-

                                   32°
fore,  AP      - 3 ft « 130 Ib/foot  -  390  Ih/foot  - surcharge weigh: .   The
         upper                                                          7

average effective stress is  P'     - P1 +  ^P  „   *  (138 + 390) Ib/foot~
                              upper     o     upper

             2                  '             2
« 528 Ib/foot  - 0.264 ton/foct"  0.264 kg/cm  .



     Figure C-5 shows the consolidation characteristics  for the sludge used  i;.

the experimental landfill.  Using the settlement equation




                                                                          (C-l)
 the primary settlement for each  layer  can be calculated as follows:



     Lower layer properties.


                                   C  - 1.65
                                   c


                                   HC - 10 ft



                                   e  - 4.85 at P*
                                   o             o


                                   P' - 138 lh/fr2
                                   o


                              .:P,     - ;ir- ib/ft2
                                lower


                                 /                 •>'
                   (1.65)(10  ft)  /,       1328 lb/ft~


        "Blower  "    l^-85     P10   138 Ib/ft2



                 -  2.82  ft  *  0.9833



                 *  2.77  ft  -  33.28 in.



     Upper layer properties.
C -
c
H -
t
e m
o
P1 -
o

AP
upper
1,65

10 ft

4.85 at P'
o
138 Ib/ft2

2
390 Ib/ft


-------
AH _       . n.frsuio ft:)

     upper
Pri	     I  -t- 4.85~
                                       A:s ih/ft2\

                                       \13S Ih/ff/
                - 2.*2 ft « 0.582



                • I.h4 ft - 19.72 in.



     Secondary settlement, defined as
                           *H,ec - CaHt




vrtiere C    » coefficient of secondary compression, from lab

      t    - time for which settlement is significant

      t"   « tine to completion of 100 percent primary consolidation.



can be calculated ns follows:



     Lower layer C  - 0.018 from Figure C-5 laboratory tests con" spending to
                  3


                            P.'     - 0.664 ton/ft2
                             1 owe r
                                  H  - !0 ft
     For one cycle of log *lme
                               AH         « C H
                                 sec.        a t
                                    lower
                             0.018 x 10 ft - 0.18 ft



                                 • 2.16 in.
     I'pper .'aver  C  » 0.016 from Figure C-5 laboratory tests corresponding to
                   a
                           P'     « 0.264 ton/ft2.
                            upper
                                  HC - 10 ft
     For one cvcle of log time
                               AH         « C H
                                 sec         a t
                                    upper



                           » C.C16 « 10 ft - 0.16 ft



                                 - 1.92 in.



Total settlement for the landfill is calculated as follows:
                                      73

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Lower Inver  AH            -  AH   .  •»• AH     .  33  2a  <„  A ,  ,
                     lower     P       sec                  16 In>

                         - 35.44  In.

Upper laver  ^^       ,  ,9.72  in. *  1.92 in. . 21.M lp>
                    upper

Total for the landflJ1


                '"total * ^total.     + ^total
                                 lower          upper

                        - 35.44 in. + 21.64 in.  - 57.08 in. - 4.76
ft
                               74

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TABLF C-l.   PHYSICAL PROPERTIES OF PAPER-MILL SLUDGE
Sludge Sample
Elevation Consistency
ln Lav°r Limits
N'o. ft (LL-PL)
1-0 5 325.4-141.6
L-t* 2.5 257.3-102.7
L-2* 7.5 247.7-105.6
U-l** 2.5 184.5- 86.0
U-2** 4 218.5-101.6
U-3** 5 297.5-133.0
U-4** 7.5 287.4-122.1
U-5** 10 302.8-138.6
Ash
Content
percent
35.7
42.2
43.3
59.4
46.5
36.5
34.2
32.2
Solids
Content,
Percent
bv Weight
28.5
27.2
28.2
34.4
31.9
26.9
29.0
28.4
Specific
Gravity
of Solids
2.01
2.05
.2.07
2.24
2.07
1.91
1.87
1.92
* Average of three samples.
** Average of three tests per sample location.
Sludge unit weight as placed, y * 70 pcf.
Soil surcharge unit weight, Y a: 130.4 pcf.
Laboratory test sample locations.
Laboratorv test
.:• •• - -
^^ss
XX" i-'cper sluice
$$^^
sample locations.

x^
layer V\
^N>
, 'f. U-5
! X U-2
X. U-2
' -f. u-i

         \
v\
                                '

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EXISTING GRAVEL
    PIT WALL
                  '  /L—J~—GRAVEL POCKET  \
LIMITS OF BOTTOM
 SAND BLANKET
                                                        LEGEND

                                               *   INSTRUMENT GROUPS

                                             	EARTH SURCHARGE LIMIT

                                             	BOTTOM SANO BLANKET LIMIT

                                               •   ELEVATIONS
            Figure C-l.  Experimental landfill, pl?.n  view.
                                   76

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                                             INSTRUMENT GROUP 4 ^    INSTRUME A T GROUP 5~
                                          EARTH SURCHARGED       \
         14-OH 20-
                1
                                     UPPER SLUDGE LAYER
                                     (INITIALLY 10'THICK)
           WWIDE GRAVEL DRAIN  ^»v«N
             NOR TH SIDE ONL YJ
I                                     LOWER SLUDGE LAYER
                                     (INITIALLY 9.6* THICK)
                                                                              PIPE
v...
« 0A4//V />//>f WOA r« SIDE ONL Y)
   LEGEND

SETTLEMENT FLAST
PIEZOMETERS

SAND DRAINAGE BLANKETS

GRAVEL
         Figure C-2.  Typical cross section of experimental landfill.

-------
00
           to
TOTAL VERTICAL
1 FT SAND. 100 PCF STRESS
s ' '
10 FT SLUOG
70 PCF
' / y >
/ y / y
' ; / ;
,' ] $\>-""2
^ y 4SOPSF\.
J) » \
' SOOPSF \
1 FT SAND. 100 PCF
Figure C-3. Load-depth d
LOAD INCREMENT. AP
Mil 11 111 111
DEPTH Z. FT
J W 0


1 FT SAND. 100 PCF
/ y / ^ y ) f
10 FT SLUDGE
y 70 PCF ' ^ ^
/^ ;ol
y x y
/v/^,1
1 FT SAND. IOO PCF

0
lagr
/OO
138
PS'F
176
•"•• •
HYDROSTATIC EFFECTIVE STRESS.
PRESSURE SLUDGE
\ U = 7W « 2 >00 PL - P0 - 0
\ PSF
312\ 13A
PSF \ >SF\
624, "IF \ 176
am.
EFFECTIVE STRESS. P'0
AP
AP
*-»>
                               Figure  C-4.   Load Increment added to a sludge layer.

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          5.o
         45
         4.0
       I 3.5
       o
       >
         3.0
         7.5
         2.0
        0.015  —
        0.005
      a
      o
        0.03
    5£
    iw 3
    9 g  o.ois
    ik
    ik >
     o  0.010

     ••
f0' 138PSF » 0.069 T/FT*


•o " 4 85

Ce • 1.65
                              i     iii  it11
           OM       0.1       0.2       0.4   04     1         23
           0.06       0.1       OJ       0.4   0.6     1        23
           0.05      0.1       0.2       0.4   04


                                PRESSURE*. T/Fr2
                                                           2    3
Figur» C-5.   Consolidation characteristics  of sample  sludges.

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                                   APPENDIX D

                             CONSOLIDATION EQUATION

      The consolidation equation may be expressed as


                                        THc2
                                    : " ~Cv~                           (D-D

 where
      t  - time required for consolidation
      T  • a dimensionless time factor
      He • length of the longest drainage path
      Cv - coefficients of consolidation

 The coefficient of consolidation may be expressed in the form


                                                                       (D-2)
                                         •VTW

 where
      k  - coefficient  of  permeability.of the soil medium
      e  - void ratio of the soil medium
           -de
      3v * "do  '  n"8*tlve  slope of the void  ratio versus pressure relationship
           for  the soil  in question

      Substituting Equation D-2 into  Equation D-l ,
                                         >•  e)

Differentiating  the well known weight volume  equation

                                      G  rw


where
     GS - specific gravity of the soil solids
     >d -' dry density of the soil

yields
                                             YW
                                                                       /D ox
                                                                       (D~3)
                                de . -c
Finally substituting Equations D-4 and D-5 into Equation D-3 gives
                                      80

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