2002 Faustino Valero - Criterios Proyecto Estruc. Suelo Reforzado
2002 Faustino Valero - Criterios Proyecto Estruc. Suelo Reforzado
2002 Faustino Valero - Criterios Proyecto Estruc. Suelo Reforzado
Earthquake Evaluation
Guidance Document
TABLE OF CONTENTS
FOR
INTRODUCTION PAGE 2
APPENDIX I PAGE 15
APPENDIX II
INTRODUCTION
The promulgation and approval by the Environmental Protection Agency of the State of
Tennessee Solid Waste regulations has added an earthquake evaluation requirement for
Class I and Class II solid waste landfills located in Tennessee. Specifically, the
regulations state that "new Class I and Class II Solid Waste landfill facilities shall not be
located in seismic impact zones, unless the owner or operator demonstrates that all
containment structures, including liners, leachate collection systems, and surface water
control systems, are designed to resist the maximum horizontal acceleration in lithified
earth material for the site. The owner or operator must place the demonstration on the
Narrative Description of the Facility and Operations Manual." In order to comply with
this regulation it is first necessary to understand the meaning of the terms " maximum
horizontal acceleration", "lithified earth material" and "seismic impact zone", which are
defined in the regulations as follows;
"lithified earth materials" means all rock, including all naturally occurring and
naturally formed aggregates of masses of minerals or small particles of older rock that
formed by crystallization of magma or by induration of loose sediments. This term does
not include man-made materials, such as fill, concrete, and asphalt, or
UNCONSOLIDATED earth materials, soil, or regolith lying at or near the earth surface.
"seismic impact zone" means an area with a ten percent or greater probability that
the maximum horizontal acceleration in lithified earth materials, expressed as a fraction
of the earth's gravitational pull will exceed 0.10g in 250 years.
In order to implement the above stated regulation it is first necessary to determine the
maximum horizontal acceleration in the lithified earth materials at a proposed or at
an existing site so as to determine if the site is in fact within a "seismic impact zone".
2
DETERMINATION OF HORIZONTAL GROUND ACCELERATION
There are a number of seismic hazard maps that have been developed to depict horizontal
accelerations by means of contour lines. The United States Geological Survey has
developed a generalized map of the United States that depicts the expected horizontal
ground accelerations (with a 90 percent or greater probability that the acceleration will
not be exceeded in 250 years) for the entire United States referred to as Open-File No. 82-
1033 (Map 1). The regulations also state that the maximum horizontal acceleration may
also be determined by performing s site-specific seismic risk assessment which is based
upon a probablistic approach.
Basically, there are two potential mechanisms by which solid waste landfill facilities may
fail as a result of earthquake induced ground motions. These two potential failure
mechanisms are referred to as liquefaction and slope stability. Although this guidance
policy will present one procedure for evaluating liquefaction and one for evaluating
global slope stability, there is actually more than one procedure for evaluating the
potential of each of these phenomenon.
3
EVALUATION OF EARTHQUAKE FORCES ON THE SLOPE
STABILITY OF SOLID WASTE LANDFILLS
STEP 1. Develop a model of the landfill slope configurations to be used for pseudo-
static analysis.
STEP 2. Determine the maximum undrained shear strengths of the soil and waste layers
within the landfill mode.
STEP 3. Multiply the maximum undrained shear strengths of the soil and waste layers
within the landfill model.
STEP 4. Perform pseudo-static analyses on the landfill model substituting different
values for the horizontal acceleration so as to determine which acceleration results in a
factor of safety of one. The horizontal acceleration that yields a factor of safety of one
shall be referred to as the yield acceleration (ky). It should be noted that the Tennessee
Division of Solid Waste Management utilizes STABL5M to evaluate the stability of
landfill slopes.
4
NEWMARK PROCEDURE (CONTINUED)
I. a finite element analysis of the embankment section (Clough and Chopra, 1966;
Idress and Seed, 1967)
II. by a shear slice analysis (Ambraseys, 1960; Seed and Martin, 1966).
III. a simplified approach developed by Makdisi and Seed that lends itself to
hand calculations is presented in the following paragraphs.
STEP 5a. Determine the following embankment and subsurface soil properties;
5
STEP 5b. Perform First Iteration
I. Assume value of vs
2
II. Calculate G/Gmax = (VS/Vmax)
III. From Figure I determine the shear strain ( ) and damping, ( )
6
FIGURE 1: SHEAR MODULUS AND DAMPING CHARACTERISTICS USED IN
RESPONSE CALCULATIONS
7
STEP 5B. First Iteration for determining crest acceleration (continued)
IV. Calculated the values of the first natural frequencies ( ) and the associated
natural periods (T) as follows;
Using the periods determined in step IV, the percent damping from Figure 1, and the
maximum horizontal acceleration from the USGS Map (MF 2120), find the
corresponding spectral accelerations (San) from Figure 2.
VI. Calculate the maximum crest accelerations (umax) for the first three modes:
(NOTE: is referred to as a mode participation factor)
GIVEN:
FIND:
u 1 max = 1 (Sa1)
u 2 max = 2 (Sa2)
u 3 max = 3 (Sa3)
VII. Determine the maximum value of the crest acceleration by taking the square root of
8
the sum of the squares of the maximum accelerations of the first three modes.
2 2 2 1/2
[ (u 1 max) + (u 2 max) + (u 3 max) ] = u max
9
STEP 5B First Iteration for determining crest acceleration (continued)
VIII. Calculated the average equivalent shear strain ( ave)eq from the following
equation;
( ave)eq = 0.65 x 0.3 x (h / Vs2) (Sa1)
NOTE: The shear strain obtained from the above calculation is generally
different from the shear strain determined from using assumed velocity values and
entering Figure 1 as was done in step III of 5b. If there is a difference between the
assumed shear strain values and the calculated values, it will be necessary to perform a
new iteration using the value obtained from the above equation to determine a new set
of Modulus and damping parameters. Generally, it will take three iterations for the
strain compatible properties to converge.
Upon determining the maximum value of the crest acceleration u max proceed
with the Newmark Procedure so as to calculate the total deformation at the
site.
10
NEWMARK PROCEDURE (CONTINUED)
STEP 6. Determine the maximum of crest acceleration (k max) for any level within the
embankment using the maximum crest acceleration (u max) determined in Step 5 and
entering Figure 3.
[NOTE: THE NUMBER 0 IN THE y/h COLUMN IS THE CREST FOR THE
EMBANKMENT.]
11
NEWMARK PROCEDURE (CONTINUED)
STEP 7. Determine permanent displacement (U) for the yield acceleration (Ky) by
12
LIMITING SEISMIC SLOPE STABILITY DESIGN CRITERIA
The following limiting design criteria have been established so as to insure that the
landfill liner, leachate collection system and landfill appurtenances will remain functional
when subjected to earthquake induced forces.
13
VENEER STABILITY OF SOLID WASTE LANDFILL COVER SYSTEMS
In the event that geosynthetic type materials (geomembranes, geonets and geocomposites)
are incorporated into cover systems at solid waste landfills it will be necessary to perform
veneer stability type calculations. A quick basic check of the veneer stability of the cover
system can be accomplished with the following equation:
in which is the slope angle, is the limiting interface friction angle and amax is the
pseudo-static seismic coefficient.
Again this type of stability analysis must result in a factor of safety that exceeds one to
provide adequate stability against sliding. Presently, it is the opinion of the Solid Waste
Division that his type of failure mechanism will generally not result in a catastrophic type
of failure. Therefore, some flexibility will be given for the design of the stability of
landfill cover systems.
14
APPENDIX I
15
GLOSSARY OF TERMS
16
EXAMPLE PROBLEM ONE (Determining Crest Acceleration and Permanent
Deformation of a waste fill)
[Note: This example problem actually begins at Step 5 of the revised Newmark Method
outlined in the preceding sections.]
1/2
(Gmax / ) = V max
FIRST ITERATION:
2
and G/Gmax = (VS/Vmax) = 0.4
From Figure 1: for G/Gmax = 0.4 the shear strain = 0.06% and the damping ( ) = 13%
17
3 = 8.65 (Vs / h ) = rad/sec, T 1 = 2 / 3
18
EXAMPLE PROBLEM ONE (CONTINUED)
Use the value of the maximum horizontal acceleration ( amax) in combination with the
value of determined in STEP ONE and the periods (T) determined in STEP TWO to
enter Figure 2, to determine the spectral accelerations for each of the natural frequencies.
19
EXAMPLE PROBLEM ONE (CONTINUED)
2 2 2 1/2
[ (u 1 max) + (u 2 max) + (u 3 max) ] = u max
2 2 2 1/2
[ (0.416) + (0.335) + (0.249) ] = 0.59 g
Note: Since the shear strain calculated from the above equation does not match the
value determined in Step One it is necessary to perform a second iteration.
20
EXAMPLE PROBLEM ONE (CONTINUED)
SECOND ITERATION (CONTINUED)
Determine the Spectral Accelerations
Use the value of the maximum horizontal acceleration ( amax ) in combination with the
value of ( ) determined in STEP SEVEN as well as the periods (T) determined in STEP
SEVEN to enter Figure 2, to determine the spectral accelerations for each of the natural
frequencies.
Determine the Crest Accelerations (u) for each of the natural frequencies ( ):
Therefore substituting into the following equation the maximum crest acceleration (umax)
is;
2 2 2 1/2
[ (0.39) + (0.339) + (0.253) ] = 0.575g
Finally substituting into the equation for maximum shear strain produces the following
result;
U max = 0.57g
To = 0.7 sec
ave = 0.07%
G = 1270 ksf
= 14%
21
EXAMPLE PROBLEM ONE (CONTINUED)
STEP NINE: Determine the maximum value of average acceleration (kmax) for any level
within the embankment using the maximum crest acceleration (umax) determined in Step 8
and entering Figure 3. Since the height of the embankment is h = 150' y = (depth of
failure plane) = 128' then y / h = .85. Upon entering Figure 3 at 0.95 and reading to the
right yields a value for (kmax) / (umax) of 0.35. Since umax was found to equal .575g in the
previous step then:
NOTE: y is the depth of the sliding and h is the height of the embankment
22
EXAMPLE PROBLEM ONE (CONTINUED)
STEP NINE: Determine the permanent displacement (U) for the yield acceleration (Ky)
by entering Figure 4 with the appropriate values of kmax and To.
so that U = 0.025 [ kmax (To)] = 0.025 (0.201) (32.2) (0.7) = .113 feet
THEREFORE, FOR THE EXAMPLE PROBLEM THE AMOUNT OF
DEFORMATION WOULD BE 0.113 FEET WHICH WOULD BE CONSIDERED
ACCEPTABLE FOR LEACHATE COLLECTION SYSTEM WITH COLLECTION
PIPES.
23
DETERMINATION OF LIQUEFACTION POTENTIAL
AND
24
DETERMINATION OF LIQUEFACTION POTENTIAL
AND
ITS IMPACT ON WASTE FILLS
STEP 1. Determine the maximum horizontal acceleration (amax) in g's from the USGS
map number 2120 or from a site-specific seismic risk assessment.
STEP 2. Determine the total overburden pressure (Ptot) on the soil layer in question.
(See Example Problem Two)
STEP 3. Determine the effective overburden pressure (Po) on the soil layer in question.
(See Example Problem Two)
STEP 4. Use Figure 5 to correct the standard penetration resistance value (N) for the
effect of overburden pressure.
N1 = CN *N
STEP 6. Compute the cyclic stress ratio, (R ), developed in the field during design
earthquake:
STEP 7. Knowing the magnitude of the earthquake (M) and (N1) estimate the cyclic
stress ratio Rf required to cause liquefaction from Figure 7.
STEP 8. Calculate the factor of safety against liquefaction Fs for each layer, to obtain an
appropriate factor of safety which for earthen structures is generally between 1.2 and 1.5.
Fs = Rf / Ri
25
PROCEDURE FOR DETERMINATION OF LIQUEFACTION POTENTIAL AND
ITS IMPACT ON WASTE FILLS (CONTINUED)
STEP 9. If the preceding steps do indicate that there is a potential for liquefaction within
a particular layer it will be necessary to determine if the liquefaction will result in damage
to the solid waste facility. The occurrence of liquefaction within a layer does not
necessarily result in subsidence or deformation on the surface. In order to evaluate the
potential for damage at a facility it will be necessary to enter Figure 8 and determine if the
liquefaction will result in damaging movements on the surface.
26
Correlation Between CN and Effective Overburden Pressure
FIGURE 5
27
RANGE OF VALUES OF rd FOR DIFFERENT SOIL PROFILES
FIGURE 6
(FROM H. B. SEED)
28
Correlation Between Field Liquefaction Behavior of Sands for Level Ground Conditions
and Modified Penetration Resistance
FIGURE 7
(FROM NAVFAC 7.3)
29
THICKNESS OF SURFACE LAYER, H1 (m)
FIGURE 8
BOUNDARY CURVES FOR LIQUEFACTION SURFACE EVENT (Ishihara, 1985)
30
APPENDIX II
31
CALCULATE OVERBURDEN PRESSURE
EXAMPLE PROBLEM TWO
KEY TO SYMBOLS = unit weight of soil (lb. / cu. ft.)
wet = wet unit weight of soil (lb. / cu. ft. )
sub = submerged unit weight of soil (lb. / cu. ft.)
sub = weight of soil below water table
sub = wet - unit weight of water ( 62.4 lb. / cu. ft. )
Total overburden pressure (Ptot) is found by multiplying the wet unit weight of soil
( wet ) by the thickness of each soil layer and continuously summing the results with
depth.
Example: Determine (Po) at 20 feet below the ground surface in a silty clay deposit with
a wet unit weight of 127 lbs./cu. ft. and the water table at 10 feet below the ground
surface.
step one 10 ft. x 127 lb. / cu. ft. = 1270 lbs. / sq. ft. (Po above water table)
step two 10 ft. x (127 - 62.4) = 646 lb./sq. ft. (Po below water table)
step three Add the results for step one and step two
A plot of the effective overburden pressure versus depth is called a Po diagram and is
illustrated on the following page.
32
LIQUEFACTION EXAMPLE PROBLEM
STEP 1. Determine the maximum horizontal acceleration (amax) in g's from the USGS
map number 2120
STEP 2. & 3. Determine the total overburden pressure (Ptot) and effective overburden
pressure (Po) on the soil layer in question.
33
Correlation Between CN and Effective Overburden Pressure
FIGURE 5
(FROM NAVFAC 7.3)
34
RANGE OF VALUES OF rd FOR DIFFERENT SOIL PROFILES
FIGURE 6
( H. B. SEED )
35
LIQUEFACTION EXAMPLE PROBLEM (CONTINUED)
STEP 6. Compute the Cyclic Stress Ratio (Ri).
36
Correlation Between Field Liquefaction Behavior
of Sands for Ground Level Conditions and Modified
Penetration Resistance
FIGURE 7
(NAVFAC 7.3)
37
LIQUEFACTION EXAMPLE PROBLEM (CONTINUED)
STEP 9. Enter Figure 8 to determine if the predicted liquefaction at 10 feet will result in
damaging surface movements.
FIGURE 8
38
SUMMARY OF EVALUATION POLICY
The state of the art relative to the effect that earthquake induced forces have upon solid
waste landfills is still in its infancy. The procedure adopted in this policy is based upon
empirical data and has been generally adopted by the industry. However, the Division is
committed to stay current on any new findings relevant to earthquake analysis and will be
open to new ideas.
In summary, the following limiting design criteria have been adopted by the Division of
Solid Waste Management so as to insure that the landfill liner, leachate collection system
and landfill appurtenances will remain functional when subjected to earthquake inducted
forces.
III. In the event that liquefaction is predicted for a particular site it will be
necessary to utilize Figure 8 to determine if the liquefaction will result in damaging
movements on the surface. If damaging movements are predicted the site will be deemed
unacceptable unless a plan can be implemented to densify the liquefiable layer.
39
LIST OF REFERENCES
Algermissen, S.T., Perkins, D.M., Thenhaus, P.C., Hanson, S.L., and Bender, B.L.
(1990) "Probabilistic Earthquake Acceleration and Velocity Maps for the United
States and Puerto Rico", U.S.G.S. Miscellaneous Field Studies. Map MF2120.
Ambraseys, N.N. and Sarma, S.K. (1967) "The response of Earth Dams to Strong
Earthquakes, " Geotechnique 17"181-213, September.
Clough, R.W. and Chopra, A.K. (1966) "Earthquake Stress Analysis in Earth
Dams", Journal of the Engineering Mechanics Division, ASCI, Vol. 92, No. EM2,
Proceedings Paper 4793, April, pp. 197-212.
Makdisi, F.I. and Seed, H. Bolton (1977) "A Simplified Procedure for Computing
Maximum Crest Acceleration and Natural Period for Embankments, " In Press.
Makdisi, F.I. and Seed, H. Bolton (1977) "A Simplified Procedure for Estimating
Earthquake-Induced Deformation in Dams and Embankments", (In Press).
40
LIST OF REFERENCES (CONTINUED)
Seed, H. Bolton and I.M. Idress, 1971. A Simplified Procedure for Evaluating Soil
Liquefaction Potential, Journal Soil Mechanics and Foundation Engineering,
ASCE, Vol. 97 (SM9).
41