22-EmbankmentSeismic201108

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Last Modified December 14, 2009

22. Seismic Risks for Embankments

Key Concepts

There are very few instances where an earthquake has damaged an embankment

dam enough to result in the uncontrolled release of reservoir water. Manyembankment dams are exposed to earthquake shaking each year, but either the

damage caused by the earthquake was not extensive enough, or in the rare cases

where damage was extensive, the reservoir was far below the damage and

uncontrolled releases did not happen. The failure probability estimationprocedures described below are built upon standard analysis techniques used to

predict responses of soil to dynamic loading and upon observations from case

histories of embankments that have been exposed to earthquakes.

Dynamic loading from an earthquake changes the stress states within an

embankment, causing permanent damage if the stress changes cause shear or

tensile strength to be exceeded. Loose, saturated, cohesionless soils, when subjectto earthquake shaking and initial shearing, can contract as the soil particles are

rearranged. Since the water within the pore spaces is virtually incompressible,this results in an increase in porewater pressure. If the pore pressure increase is

enough to reduce the effective stress to zero, the soil is said to have liquefied and

the soil experiences a significant reduction in shear strength. Extensive shear

strength reduction beneath an embankment slope can trigger a flow slide which,in turn, can result in a very rapid dam failure. Many cycles of low-amplitude

loading can also induce a fatigue-like shear strength loss in dense, saturated,

materials, a phenomenon some call 'cyclic mobility'.

Whether or not the soil of an embankment or its foundation liquefies completely,

pore pressure increases can still result in a decrease in shear resistance. If enoughreduction in shear resistance occurs, over a sufficient extent, large deformations

can result. A translational failure can occur if the entire foundation beneath an

embankment liquefies and the reservoir pushes the embankment downstream far

enough to create a gap in the vicinity of an abutment. Overtopping erosion failurecan occur if crest deformations exceed the freeboard at the time of the

deformations.

If the deformations do not result in an immediate release of the reservoir, the

embankment can be cracked or disrupted to the point where seepage erosion can

occur through the damaged remnant. This failure mechanism can occur with orwithout liquefaction. There are many ways in which cracking can occur due to

seismic shaking, such as differential settlement upon shaking, general disruption

of the embankment crest, offset of a foundation fault, or separation at spillwaywalls. See the section on Internal Erosion and Piping Risks for Embankments for

other conditions that may make a particular dam more susceptible to transverse

cracking and subsequent seepage erosion.

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Compacted embankments are typically not considered to be subject to

liquefaction upon shaking and initial shearing. Dense, cohesionless soils tend to

dilate upon shearing, which increases the pore space between soil particles andreduces the pore pressures. Most Reclamation embankment dams are compacted,

so the focus of liquefaction studies tends to be related to loose foundation soils.

However, hydraulic fill embankments may be susceptible to liquefaction or porepressure increases. Fine-grained soils, while not strictly 'liquefiable', may be

susceptible to strength loss during an earthquake. Two aspects of a fine-grained

soil's shear strength behavior can require investigation: the anticipated peakmagnitude of earthquake-induced shear loading when compared to a soil's

undrained shear strength determined from monontonic loading, and the potential

for a reduction in the undrained shear strength due to the effects of many shearingcycles.

If active faults or faults capable of co-seismic displacement cross an embankmentdam foundation, the potential exists for foundation displacement that cracks or

disrupts the dam core or water retaining element as well as transition zones or

filters. The cracking can initiate concentrated seepage, and the translationalmovement can create locations where there would be unfiltered exit points for theseepage. Both conditions would increase the likelihood for failure from internal

erosion or piping. Shearing of a conduit passing through an embankment dam as

a result of fault displacement can result in transmission of high pressure waterinto the dam, leading to increased gradients and potential for internal erosion.

Seiche waves can be generated by large fault offsets beneath the reservoir or byregional ground tilting that encompasses the entire reservoir. Sloshing can lead

to multiple overtopping waves from these phenomena.

Risk Analysis Methodology Appendix J (Reclamation, 2005) provides additionaldetails on these topics.

Seismically-Induced Potential Failure Modes

The following are generic descriptions of how a dam might fail due to these

potential failure modes. For a prototype dam, additional details would be needed

in the descriptions, as described in the section on Potential Failure ModeIdentification, Description, and Screening.

Liquefaction and OvertoppingSevere earthquake shaking would cause loose embankment or foundation

materials to contract under cyclic loading, generating excess pore water pressures

(liquefaction occurs). Pore water pressure increases would reduce the soils shearstrength. Loss of shear strength over an extensive area would lead to slope

instability and crest settlement. Crest deformation would exceed the freeboard

existing at the time of the earthquake. The depth and velocity of water flowing

over the crest would be sufficient to erode materials covering the downstreamslope. Headcutting action would carve channels across the crest. The channels

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would widen and deepen. Subsequent human activities would not be sufficient to

stop the erosion process. The embankment would breach and release the

reservoir.

Liquefaction and Transverse Cracking at the CrestSevere earthquake shaking would cause loose embankment or foundation

materials to contract under cyclic loading, generating excess pore water pressures(liquefaction occurs). Pore water pressure increases would reduce the soils shear

strength. Loss of Shear strength over an extensive area would lead to slope

instability, deformations, and crest settlement. However, crest deformation wouldnot exceed the freeboard existing at the time of the earthquake. Open and

continuous transverse cracks would form across the crest and through all zones of

the dam deep enough to intersect the reservoir. Water depth and velocity flowingthrough open cracks would be sufficient to erode the materials along the sides and

across the bottom of the cracks. Material from upstream zones would not be

effective in sealing the cracks (by being transported to a downstream zone orconstriction point where a filter would begin to form). Headcutting action would

carve channels across the crest. The channels would widen and deepen.

Subsequent human activities would not be sufficient to stop the erosion process.The embankment would breach and release the reservoir.

Liquefaction and Sliding Opening GapsSevere earthquake shaking would cause loose embankment or foundationmaterials to contract under cyclic loading, generating excess pore water pressures

(liquefaction occurs). Pore water pressure increases would reduce the soils shear

strength. Loss of shear strength would occur in a layer that is continuousupstream to downstream. Reservoir loading would exceed the shearing resistance

remaining in the layer and the entire embankment would slide downstream.Downstream deformation would open a gap at the crest deep enough to intersect

the reservoir. Water depth and velocity flowing through the gap would besufficient to erode the materials along the sides and across the bottom of the gap.Material from upstream zones would not be effective in sealing the gap (by being

transported to a downstream zone or constriction point where a filter would begin

to form). Headcutting action would carve channels across the crest. The channels

would widen and deepen. Subsequent human activities would not be sufficient tostop the erosion process. The embankment would breach and release the

reservoir.

Deep CrackingSevere earthquake shaking would cause differential settlement over stiffness

discontinuities, at near-vertical embankment/foundation contacts, or at contactsbetween embankment and concrete. Transverse cracks would form through the

core and concentrate seepage flow through the cracks below the reservoir surface

would occur. Seepage quantity and velocity would be sufficient to erode core

material and transport it beyond the downstream shell material. Upstream zoneswould not be effective in sealing the cracks (by a mechanism whereby material

from upstream zones would be transported to a downstream zone or constriction

point where a filter would begin to form).

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Deformation > Freeboard?

Crack Leads to Failure?

Liquefaction?

Crack Leads to Failure?

Earthquake Loading

0

etc.

etc.

etc.

Earthquake Event

0.5g

0.1g to 0.3g

0.3g to 0.5g

Yes

No

Yes

No

Yes

No

Yes

No

Figure 22-1. Typical Event Tree Model for Dam Failure due to Earthquake

Loading

Event Tree

Figure 22-1 shows an event tree typically used when only one slope is potentially

unstable (Reclamation dams frequently have their cutoff trenches offset upstream

of the centerline which makes the upstream slope more stable than thedownstream slope). The first node in Figure 22-1 splits the tree into several

branches representing different earthquake loading conditions with selected

ranges of peak horizontal acceleration (or other measure of earthquake shaking).The second node further separates situations where liquefaction is believed likely

or unlikely for a given a peak horizontal acceleration range. If liquefaction will

not take place, crest deformations usually do not lead to total freeboard loss, and

the final node in this branch assesses whether or not water flowing throughcracks, either at the dam crest or deep within the embankment, can lead to breach

formation. If liquefaction does take place, a subsequent node treats conditionswhere embankment deformations might lead to freeboard loss and failure by

overtopping. If in this case the dam is not overtopped, the possibility of failureinitiating with flow through cracks is again assessed.

Probabilities assigned to events or natural states are multiplied along each

branchs pathway, leading to a joint probability for the particular combination ofthe events or states along that path. Each branch ending in a failure condition

contributes to the total failure probability. Consequences are assigned to each

failure branch and an annualized probability of life loss is calculated (see alsosection on Event Trees).

Past situations where liquefaction has occurred resulted in significantly moreextensively damaged embankments. Therefore, failure modes are analyzed in

two categories: where liquefaction does and does not take place.

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The event tree is rather simple, but complex calculations are made outside the tree

and then brought back in. The steps needed to evaluate the event tree are

described in more detail below.

When both upstream and downstream slope stability must be considered, the

event tree becomes much more complex. Issues related to liquefaction probability

estimation involving joint probabilities, independence, and correlation requireconsideration for liquefaction and shear strength loss upstream alone, downstream

alone. These issues are discussed in more detail in Appendix J (Reclamation,

2005).

Continuous ZoneThe first item to be addressed is the likelihood that a continuous layer or zone ofpotentially liquefiable material exists within the dam or foundation. This may be

explicitly included as a node in the event tree. While simple in concept,

estimating the likelihood for continuity requires significant insight. It is typicallybased on exploratory information and knowledge of the geologic and dam

construction processes. For example, the extent of a potentially liquefiable

foundation layer is formulated from what is known about the foundation. If thefoundation is composed of lacustrine deposits, there would be reason to believesoil properties identified for a layer would in general be laterally continuous. The

same may not be true for alluvial stream deposits.

Borehole property data, such as Standard Penetration Tests (SPT), Becker-

Hammer Penetration Tests (BPT), Shear Wave Velocity Tests (SWV), and Cone

Penetrometer Tests (CPT) can provide insights into the potential for a continuouslayer. In this regard, the data should be reviewed looking for a continuous low

strength layer and not as a population lumped together for statistical analysis. Theextent of the loose layer can often be constrained to within some limits from this

type of data. Then it becomes a matter of judging the likelihood that theidentified layer is continuous enough to lead to a stability problem if it were toliquefy.

Typically, continuity parallel to the dam axis of 1 to 2 times the dam height is

needed to adversely affect stability without significant 3-dimensional effectscontributing to stability. If the continuity transverse to the dam axis underlies

most of the dam slope, it is probably of sufficient continuity to affect slope

stability. Shorter transverse continuity can also affect slope stability dependingon the geometry and strength. Slope stability analyses incorporating post

liquefaction shear strengths can be useful in determining how far low-strength

materials need to extend beneath a slope before stability becomes an issue.

When there are few of the insitu tests normally used to evaluate liquefaction

potential at a site, it has been common to first estimate the likelihood of

continuity, and then estimate the likelihood that the zone thought to be continuouscan liquefy. When there are many insitu tests, it is common to estimate a range of

values for some material property (SPT blowcount or shear strength) related to

liquefaction and thought to be 'representative' of a zone under the embankment

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slope that extends laterally two to three times the height of the embankment.

Again, the 'representative' value should be judged based on a critical evaluation of

the geology and insitu test data, taking care to look for weak zones which havecontinuity. It is best to avoid equating 'representative' with a statistical average

(unless there truly is a statistically-significant sample size from a known bad-

acting zone). A frequent mistake is to average all the available SPT blowcounts

in a given geologic unit, regardless of whether the unit appears to have arecognizable low-blow zone of sufficient extent. Another mistake is to average

all the available data in a unit when borehole spacing is much greater than two to

three times the dam height. In this case, a single low-blowcount interval in asingle borehole could be significant.

Seismic Load RangesLarger accelerations and longer durations are generally expected to occur less

frequently. Earthquakes can occur randomly within a region of similar seismic

activity, or can be associated with an identified seismogenic fault source.Perceived regional slip rates determine potential earthquake frequency on faults.

Statistical models determine earthquake frequency where not associated with a

fault. Seismic hazard is typically provided as a return period or an exceedanceprobability for peak horizontal acceleration or in spectral acceleration form atspecified periods or period ranges. Reclamation also uses acceleration time-

history records thought likely to represent specified return period ranges.

The selection and description of seismic load ranges is covered in the sections on

Seismic Hazard Analysis and Event Trees.

LiquefactionEstimating the likelihood of liquefaction for any given zone or layer depends onseveral factors and requires computations outside of the event tree. It is not the

intent of this section to provide a detailed discussion of liquefaction analysis.Please refer to the embankment dam draft seismic design standard (Reclamation,2001), Seed et al (2003), Bray and Sancio (2006), and Boulanger and Idriss

(2004) for more information on this type of analysis.

Several analyses need to be conducted before the risk analysis team activities takeplace. For example, the cyclic stress ratio will need to be calculated for each

particular load level and at key locations beneath the dam. In addition, raw

blowcount data will need to be normalized ahead of time. If CPT or shear wavevelocity data is to be also used, that information must also be reduced ahead of

time. The reader is referred to Seed et al (2003) for a discussion of these

methods.

Bray and Sancio (2006) report on how soils of differing Plasticity Index

demonstrate liquefaction susceptibility. Boulanger and Idriss (2004) provide

additional guidance on liquefaction and post-liquefaction behaivior of fine-grained soils.

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The basic probabilistic liquefaction models (Liao et al, 1988, Youd et al, 2002,

and Seed et al, 2003), have all been based on statistical regressions using

corrected SPT (N1)60blowcount, fines content or percent passing the #200 sieve(FC), and cyclic stress ratio (CSR) as the basic input parameters. These various

relationships can produce decidedly different liquefaction probability estimates.

Reclamation has typically considered the Seed et al relationship to be the most

reliable, since it is the most recent and the authors went to efforts to ensure onlydata of high quality was used in developing the model. However, some weight

has been given to the other two relationships in certain cases. The model of Youd

et al included only SPT samples known to be within geologic units that wereresponsible for lateral spreading as a result of liquefaction. It generally shows

more spread than the other two relationships, producing lower liquefaction

probabilities at higher blow counts and higher liquefaction probabilities at lowerblow counts. The model by Liao et al is the most general, being based on many

different manifestations of liquefaction behavior. Their regression associated the

observed liquefaction behavior with the lowest blowcount recorded in eachindividual borehole drilled in the vicinity of that behavior. They did not try to

identify a representative value for specific geologic units, amalgamating data

from several boreholes.

The risk analysis team typically develops a distribution of (N1)60 to represent the

potentially liquefiable layer or zone of interest. Since there typically is not

enough blow count information to develop reliable statistical distributions for agiven layer or zone, the simplest way is to develop a cumulative probability

distribution based on the degree of belief of the team. The seismic toolbox

(Reclamation, 2005) provides the appropriate questions to develop such adistribution based on a review of the available information, as follows: The

representative (N1)60 value is not likely to be less than _?_ (10th

percentile) and isnot likely to be more than _?_ (90

thpercentile). It cannot be less than _?_ (0

percentile) nor more than _?_ (100th percentile). It is equally likely to be more orless than _?_ (50

thpercentile). Using these data pairs, a cumulative probability

distribution can be defined in @Risk. It may be appropriate to examine more than

one distribution, depending on the available information. A similar approach can

be used to develop a probability distribution for fines content (percent passing the

No. 200 sieve).

A spreadsheet is then set up to calculate the probability of liquefaction using the

probabilistic liquefaction models selected to perform the analysis. A cell is set upwith the (N1)60 distribution and another with the fines content distribution. At

each load for which a cyclic stress ratio has been calculated or estimated, the

probability of liquefaction is calculated by referencing the cells containing thedistributions. These values are than converted to load range values (e.g.

conservatively by averaging the load range partition values, or by weighting in

some other fashion (see section on Event Trees) and returned to the event tree.

The equations for doing this are summarized below:

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Seed et al, 2003:)97.44*05.0)'ln(*7.3)ln(*53.29)ln(*32.13)*004.01(*60,1 +++= FCMCSRFCNg W

),7.2,( TRUEgNORMDISTPL =

where MW is the average moment magnitude of the earthquakes contributing to

the hazard (determined by de-aggregation of the hazard), is the effective

overburden stress (in lb/ft2

), and the probability of liquefaction, PL, is determinedfrom the standard cumulative normal distribution using the Excel function

NORMDIST. The fines content, FC, is capped at 35 percent.

Youd et al, 2002:

)/*65.0ln(*395.0*258.0*256.2633.7 ,60,1 KCSRNMQ CSWLY ++=

60,1

5.12

,60,1 *)1000/(99.0()/190(76.1( NFCFCEXPN CS ++=

4.2)1000/'16(*0007101.06.0

+=K

)718.21(1

LYQLP

+

=

where the correction for N1,60,CS applies only to FC>5 percent, and is capped at 35

percent.

Liao et al, 1988 (silty sand, K defined above):

( ) 60,1*1819.0)*/(*65.0ln*6854.24831.6 NKKCSRQ mLL += 56.2*173 = Wm MK

)718.21(1

LLQLP

+

=

(Note: more than one of these liquefaction models can be used and weightedaccording to the likelihood (summing to 1.0) that each is thought to represent thecase being evaluated.)

Deformation Exceeds FreeboardAn estimate of the undrained residual shear strength of the liquefied soil materials

is needed to estimate deformations. This is typically done using the relationship

developed by Seed and Harder (1990), and shown in Figure 22-2. Although the

curve is based on a limited number of case history back analyses, it is typicallyassumed that soils will tend to have strengths within the limits of the curves

drawn by Seed and Harder. For a given (N1)60 clean sand equivalent, a triangular

distribution is frequently assigned with its peak corresponding to approximatelythe midpoint between the two curves, and the upper and low limits corresponding

to the upper and lower curve, respectively. Olson and Stark (2002, 2003) may

also be considered (Figure 22-3). The relationship of Olson and Stark accountsfor the initial effective vertical stress in estimating the strength. Linear

extrapolation of these curves beyond a corrected blowcount of 15 is generally

considered to be conservative, since the relationships should be concave upward.

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Using only the Seed and Harder relationship would typically result in a slightly

more conservative estimate.

To obtain the clean sand equivalent blow counts for undrained residual shear

strength assessment of silty soils, blow counts are added to the (N1)60 value

according to interpolations form Table 22-1.

Table 22-1. Blowcount correction to obtain clean sand equivalent for

strength

Fines Content (%) Blow Counts Added to (N1)60

5 1

25 2

50 4

Figure 22-2. Undrained Residual Shear Strength as a Function of Corrected

Blowcount (adapted from Seed and Harder, 1990)

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Figure 22-3. Undrained Residual Shear Strength Determination (after Olsonand Stark, 2002)

Reclamation often uses the computer program FLAC to analyze seismically-induced deformation. FLAC is a two-dimensional explicit finite-difference

program. This program can be used to simulate the behavior of structures built of

soil, rock or other materials that may undergo plastic flow when their yield limitsare reached. Materials are represented by zones and regions that may be shaped

by the user to conform to the physical structure being modeled. Each zone is

assumed to behave according to a prescribed linear or nonlinear stress/strain law

in response to applied forces or boundary constraints. The represented material

can yield and flow, and the grid can deform and move with the material beingrepresented. However, caution and experience is needed when using such

sophisticated nonlinear computer programs to ensure the results are reasonable.The models should be thoroughly tested, validated, and verified to ensure

reasonable performance. The results of this testing should be documented so that

those reviewing the results of the analyses will have as much confidence as

possible in the results. Modeling using FLAC can therefore be quite time-consuming and expensive. Even so, model uncertainty can be included in the

probability estimates rather than strictly relying on the output numbers (e.g. to

account for three-dimensional effects if two-dimensional models were used).

Deformation can result from slope instability under gravity loading alone. If anearthquake can trigger liquefaction, pore water pressure increases reduce shear

strength and the slope might become unstable. After liquefaction triggering, aslope can continue to deform even though the earthquake shaking has ceased if

the static factor of safety is less than 1. Should liquefaction initiate early in the

earthquake, continued shaking provides inertial forces that add to deformation.Modeling experience using FLAC has shown that when the static factor of safety

is less than 1, the dynamic deformation portion is typically a small fraction of the

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total deformation. Intuitively, the dynamic component will be more significant

for earthquake acceleration records of long duration, particularly when the

earthquake provides strong accelerations at the dams natural frequency.

Resource constraints usually dictate that FLAC results are generated for a limited

number of loadings and assumed initial conditions. For the example in figures

22-4a and 22-4b below, a foundation layer beneath an embankment slope wasassigned residual shear strength values of 50, 100, and 200 psf. Gravity loading

alone produced the deformation values labeled Static. A relatively strong

earthquake was responsible for the additional deformation labeled Dynamic.Connecting the six model point-estimates with lines, as in figure 22-4a, is

reasonable. One could easily analyze the model with additional parameter

assumptions to fill in the spaces between previous runs. Likewise, extrapolating

the lines to the right, as in figure 22-4b, is appropriate and we would expectverification with additional analysis for higher shear strength values.

Extrapolation to the left in figure 22-4b is much more problematic. FLAC

becomes unstable with strengths this low. Also, it becomes questionable as towhether a plastic constitutive model as provided by FLAC is appropriate.

0

1

2

3

4

5

6

7

8

9

0 50 100 150 200 250

Residual Shear Strengt h (psf)

CrestDeformation(feet)

Static

Dynamic (>1.0g pha)

0

2

4

6

8

10

12

14

0 50 100 150 200 250 30

Residual Shear Strengt h (psf)

CrestDeformation(feet)

Static

Dynamic (>1.0g pha)

Figure 22-4a. Figure 22-4b.

Limit equilibrium modeling can be used to discern an approximate value for

maximum crest deformation when the embankment slope has a factor of safetyless than 1. Presumably, when an upstream slope is unstable there is a

downstream remnant where one would expect insignificant deformation.

Essentially, this remnant of relatively undisturbed embankment material wouldprovide the highest remaining barrier to uncontrolled reservoir release. The peak

of the undisturbed remnant would determine the maximum crest deformation

estimate used to gage overtopping likelihood. Figure 22-5a shows a series ofcircular and wedge-shaped failure surfaces analyzed using a limit equilibriummethod. Figure 22-5b shows the same cross section modeled using FLAC. The

deformation arrows are absent in 22-5b on the downstream slope at a point where

the figure 22-5a shows a failure surface that has a Safety Factor of 1.12. TheFLAC analysis shows highly deformed material remaining above the elevation of

the peak of the undeformed section. An upper bound crest deformation estimate

would result if one assumed that all the highly deformed material would slide into

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the reservoir. If a FLAC or an alternative deformation analysis does not exist,

potential failure surfaces that produce a Safety Factor of about 1.1 in a limit

equilibrium analysis might be interpreted to provide a crude estimate for thelocation of the highest remnant piece of undeformed dam. The likelihood of

attaining a safety factor along such a surface less than this can be estimated using

reliability analysis (see section on Reliability Analysis).

Figure 22-5a.

Figure 22-5b.

Often a cutoff trench located beneath the dam crest determines the location of the

remnant undisturbed block, particularly for analysis of downstream slopestability. If potentially liquefiable materials were removed during original

construction to create the cutoff trench, limit equilibrium analysis of post-

earthquake stability typically reveals Safety Factors well above 1.0 as the

analyzed failure surface geometries begin to intersect the cutoff trench. Thebottoms of wedge-shaped failure surfaces are limited by the point of intersection

between the modeled liquefiable layer and the cutoff trench. Back angles extend

up from these points at an approximate angle of (45+/2) from the horizontal forcritical failure surfaces, where is the friction angle of the embankment material.

A rough estimate for maximum crest displacement can be calculated from the

point where this extension intersects the upstream slope.

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The loss of freeboard needs to be compared to the reservoir elevation at the time

of the earthquake. To do this, a curve is prepared similar to that described in the

section on Reservoir Level Exceedance Curves for reservoir exceedanceprobability. A general distribution function can be assigned to the curve using the

RiskGeneral function in @Risk. The probability of failure due to overtopping is

then typically estimated as the probability of the reservoir exceeding the elevation

of the deformed dam crest.

If an evaluation using one of the simplified methods described above results in an

estimated annual failure probability or annualized loss of life that exceedsReclamations public protection guidelines, more refined studies are probably

justified. This requires detailed FLAC analyses to estimate the loss of freeboard

due to various seismic loads. Typically, enough FLAC analyses are run to

develop curves (high, median, and low) for freeboard loss as a function ofundrained residual shear strength of the liquefied layers or zones. Team judgment

incorporating model uncertainty is also included in the development of the curves.

These curves are then used in a fashion similar to that described in the precedingparagraph to estimate the probability of overtopping erosion failure.

Al ternate Approach The methods described above rely heavily upon formulaic means to obtain

estimates of liquefaction probability from SPT data and to choose representative

strength values. There are some instances when it may be preferable to use more

of a degree-of-belief approach. Such cases include: Sites where no SPT blow count information is available

Sites where many different approaches have been used to assess

liquefaction triggering, including shear wave velocity testing (which cantbe meaningfully converted to SPT blow counts) or in-situ density testing

Sites that have previously experienced a significant earthquake loading,

and the measured SPT blow counts may not correlate with the pastobserved signs of liquefaction or no liquefaction in terms of predicted

performance

Sites where qualitative arguments (such as questionable continuity,

questionable degree to which coarse materials can experience strengthloss, potential for drainage of excess pore pressures, etc.) may be used to

estimate a low (or in some cases a high) probability of liquefaction

Foundations that contain fine-grained soils that may be susceptible tostrength loss but not classical liquefaction

Foundations that contain very coarse-grained soils, which have few case

histories to draw upon to judge the value of empirical formulas for

liquefaction probability and residual strength

An alternate approach to estimating SPT blow count distributions is to use a

degree-of-belief estimating approach to the likelihood of liquefaction or strengthloss. The event tree is similar to that already described, and may consist of

branches following the earthquake load range probabilities that include:

The probability of sufficiently widespread susceptible soils (continuity)

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The probability that soils will lose strength under a specific load

increment

The probability that deformations will exceed available freeboard

Each of these branches, as well as possible variations, will be briefly discussed.

Continuity of susceptible materials

In cases where continuity is a critical issue, it may be helpful to have this initialbranch that estimates the probability (and uncertainty) of whether sufficiently

continuous susceptible soils exist beneath a dam to lead to instability or excessive

cracking. Factors including geologic deposition, presence of cutoff trenches or

natural barriers, effects of embankment loading, and results of available testing orexplorations will influence this probability distribution.

Probability of s trength loss

In this case, the probability that liquefaction or strength loss occurs is estimated

for each of the earthquake loading increments being considered. Risk analysts

make experience-based judgments given the available information on the site,

which may include performance during past loadings; laboratory test data;triggering analyses using shear wave velocities or penetration tests; and fine-

grained soil susceptibility based on vane shear tests or CPT values in clayey soils.

When SPT blow counts are available for sandy soils, probabilistic curves areconsulted (but not rigidly tied to the final estimates of probability).

Deformations exceeding freeboard

This probability is typically estimated by developing curves of expected

deformation. For example the team may estimate the range of absolute minimumcrest loss, reasonable minimum probable crest loss, best estimate or median crest

loss, reasonable maximum probable crest loss, and absolute maximum crest loss.

These values then form a probability distribution of crest loss for the strength lossvalue assumed to result from liquefaction or cyclic failure. If the reservoirremains relatively constant, the deformation curves represent the likelihood of

losing freeboard when compared to the operating conditions. When the reservoir

fluctuates considerably, the operations cycles are reviewed to get a feel for anannual mean reservoir level that can be used in the estimates.

In some cases, these three branches are combined by considering the probability

of a given strength scenario, and the resulting deformations given each strengthscenario. Specifically, the first two probabilities (probability of continuity and

probability of strength loss) are instead phrased as the probability that a given

strength will result from a given increment of earthquake loading. This isparticularly useful when a team has developed deformation models for several

different strength scenarios. The strengths assigned in these scenarios are meant

to model a likely range of values and include reasonable upper and lower bounds.

For example, if Newmark and/or FLAC analysis have been performed for threedifferent strength assumptions, the risk team estimates the likelihood of each of

the three strength assumptions, with the sum of the three probabilities adding to

1.0. Expected deformation curves for each of the three strength scenarios can

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than be developed as described above. This approach is useful in allowing teams

to reflect the (sometimes considerable) uncertainty in estimating the strength loss

(and corresponding deformations) that will result from earthquake shaking.

Internal Erosion through Cracks

If the embankment and foundation do not liquefy, and/or if the freeboard is noteffectively lost through seismic deformations, the dam will not fail due to

overtopping (or rapid erosion of the severely damaged dam crest), but there is still

the potential for a slower internal erosion through cracks in the embankment,

typically in the crest and upper portions of the dam. Fell et al (2008) includeconsiderations for internal erosion through seismically-induced cracks, based in

part on observed damage to embankment dams following large earthquakes. The

primary goal is to determine how deep the embankment is likely to crack, andhow open the cracks are likely to be relative to the possible reservoir elevation.

Once this is determined, the likelihood of internal erosion is assessed a similar

fashion as for static loading.

The first step in the procedure is to determine the damage class from figures 5.7

and 5.8 in Fell et al (2008). This may require asking the seismologists to de-

aggregate the seismic hazard to determine the magnitudes of the earthquakes thatcontribute most to the hazard at various peak horizontal ground accelerations. If

liquefaction occurs, assume Damage Class 3 or 4, depending on how severe the

liquefaction is judged to be. A Damage Class is determined for each earthquake

load partition, and the earthquake load partitions are selected to coincide with theDamage Class contours, if possible. For this reason, it is usually desirable to

develop a separate event tree to evaluate internal erosion through cracks (as

opposed to tacking it on to the end of the liquefaction tree at the non-failurenodes). If a separate tree is developed, care must be taken in combining these

risks with liquefaction overtopping risks (and other seismic risks), as discussed in

the section on Combining and Portraying Risks (common cause adjustment) so as

to not assign a combined conditional failure probability that is too high for a givenload range. Given the Damage Class, determine the likely settlement as a

percentage of dam height from Table 5.36 in Fell et al (2008). Cracking begins at

the new elevation of the crest after seismically-induced settlement and extendsdownward from there.

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Fell et al (2008) Figure 5.7 - Incidence of transverse cracking versus seismic intensity and

damage class contours for earthfill dams (Pells and Fell, 2003)

Fell et al (2008) Figure 5.8 - Incidence of transverse cracking versus seismic intensity and

damage class contours for earthfill and rockfill dams (Pells and Fell, 2003)

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Fell et al (2008) Table 5.36 Damage classification system (Pells and Fell, 2003)

Damage Class Maximum

Longitudinal

Crack Width (1)

mm

Maximum

Relative Crest

Settlement (2)

%

Number Description

0 No or Slight < 10 mm


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Fell et al (2008) Table 5.25 - Likely crack width at the depth shown versus

maximum crack width at the dam crest ( Depths in feet and metres)

Maximum crack

width at dam crest

Likely crack width at depth shown, (Crack width in

millimetres (inches)))1(

5 feet1.5

metres

10 feet3

metres

15 feet4.5

metres

20 feet6

metres

25 feet7.5

metres

30 feet10

metres

Inches Millimetres

0.5 10 1

1 25 2 1

2 50 20 5 1

3 75 40(1.6) 20 5 2

4 100 60(2.4) 35(1.4) 15 7 3 1

10 250 210(8) 180(7) 140(5.4) 110(4.4) 90(3.5) 60(2.4)

The likelihood of erosion in a crack is a function of the erodibility of the soil and

the average hydraulic gradient (and resulting traction shear stress). As reported in

Fell et al (2008), highly erodible soils such as silts, silty sands, or dispersive claysmay be likely to erode at a crack width of to inch under a hydraulic gradient

as low as 0.1, and at widths as small as 1 or 2 mm under hydraulic gradients of

0.5 or more. Clays may not be likely to erode until cracks reach 1 or 2 inches in

width and gradients approach 0.5 or more.

The likelihood of erosion initiation is the product of the likelihood of a transverse

crack forming, the likelihood of the crack extending beneath the reservoir (whichis determined in the same manner as likelihood for loss of freeboard, as discussed

above), and the likelihood that there is sufficient gradient across the crack to

initiate erosion given that the cracking extends beneath the reservoir. Typically, a

gradient is estimated that would result in erosion, and the likelihood of thereservoir reaching an elevation to create that gradient is estimated from the

reservoir exceedance curve. The rest of the event tree is evaluated using

applicable nodes from the event tree described in the section on Internal Erosionand Piping Risks for Embankments. An important consideration while evaluating

the rest of the tree is the likelihood that the upstream and downstream filters,transition zones, and/or shells are capable of sustaining a crack to the same depth

and width as the core. If this likelihood is high, the chances of a filtered exit(continuation) and upstream crack-filling (progression) may be low.

Foundation or Reservoir Fault Displacement

Where an active fault, or fault capable of coseismic displacement exists in the

foundation of a dam, offset along the fault can cause cracking of the embankmentand/or conduits passing through the dam. Since each dam and geometry is

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unique, a site specific event tree needs to be developed to evaluate this on a case-

by-case basis. The loading in this case involves fault offsets of various magnitude

ranges, and their associated probability. Input from Quaternary geologistsspecializing in fault and seismic source characterization is typically needed to

develop this input. An event tree is developed to describe the specific potential

failure mode being evaluated. Nodes on the tree include the potential impacts of

fault offset in leading to dam failure. For example, what is the likelihood thateach range of displacement is sufficient to develop an open crack through the

core, disrupt or offset a filter zone, and/or crack through a conduit.

Another possibility concerns an active fault passing through the reservoir of an

embankment dam. Fault offset within the reservoir could create a seiche wave

capable of overtopping and eroding the dam. Again, it is necessary to develop an

event tree, establish return periods for various levels of fault offset, assess thepotential for an overtopping wave to develop, and evaluate the likelihood of short

duration overtopping to lead to an erosional breach. An initial estimate of wave

height equal to the vertical fault offset is probably reasonably conservative inmost cases. The reader is referred to Wilson (1972) and Hammack (1973) for

additional discussion on modeling seiche waves. However, overtopping failure ofa dam due to seiche waves is a relatively improbable failure mode which is only

considered when seismotectonic specialists indicate a high likelihood fordevelopment of a seiche wave.

Accounting for Uncertainty

Uncertainty is accounted for in the distributions that are input in making the

calculations. Spreadsheet cells containing input values are described in terms of adistribution rather than a single value. Then, a Monte-Carlo analysis is

performed, typically with 10,000 iterations, to develop a distribution of annual

failure probability and annualized loss of life. Setting up spreadsheets to performseismic risk evaluation of embankment dams requires several calculations to be

made outside of the event tree; for example, probability of liquefaction, crest

deformation (settlement), and likelihood of deformation exceeding freeboard all

can involve calculations rather than just assigning probabilities to the event treenodes.

Relevant Case Histor ies

Relatively few dams have actually failed as a result of liquefaction, internal

erosion through seismically-induced cracks, or other seismically-related failuremodes. However, a few case histories provide relevant insights.

Lower San Fernando Dam: 1971The upstream slope of Lower San Fernando Dam failed during the 1971 SanFernando Earthquake (Seed et al, 1975). Intact blocks of embankment material

moved tens of feet on liquefied hydraulic fill shell material. There was evidence

to suggest the slope failure took place after the shaking had stopped. Fortunately,

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a remnant of the dam remained above the reservoir water level at the time, and the

dam did not breach.

Sheffield Dam: 1925Sheffield Dam failed during the Santa Barbara earthquake of 1925. Although

there were no witnesses to the breach, it was believed that the sandy foundationsoils which extended under the entire dam liquefied and that a 300-foot long

section of the dam slid downstream, perhaps as much as 100 feet (Seed et al,

1969). The dam was located quite close to the city of Santa Barbara, and a wall

of water rushed through town, carrying trees, automobiles, and houses with it. Amuddy, debris-strewn aftermath was left behind. Flood waters up to two feet

deep were experienced in the lower part of town before they gradually drained

away into the sea. No fatalities were reported.

Austrian Dam: 1989Austrian Dam was severely cracked and damaged by the 1989 Loma PrietaEarthquake (Forster and MacDonald, 1997), with peak ground accelerations

estimated at 0.5 to 0.6g from the nearby Magnitude 7 event. Longitudinal cracks

14 feet deep (based on trenching) formed just below the dam crest on theupstream and downstream slopes. Transverse cracks formed at both abutments, 1to 9 inches wide, and the embankment separated from the concrete spillway wall,

opening a gap of about 10 inches. Fortunately, the reservoir was low at the time

of the earthquake, and no subsequent internal erosion ensued.

San Fernando Powerplant Tailrace Dam: 1994A small embankment dam forming the tailrace for the San Fernando powerplantwas shaken by large ground motions during the 1994 Northridge earthquake. The

earthquake occurred early in the day, and the tailrace dam was intact whenpowerplant personnel left for the day. The next morning he dam had failed

(Davis, 1997). The tailrace concrete lining had buckled in several locations. Itwas suspected that a layer of loose sand beneath the dam, identified by CPT data,

liquefied, and piped through the gaps in the concrete lining undetected, slowlythroughout the day.

Cracking in Dams Exposed to the Loma Prieta Earthquake: 1989Harder, 1991, lists the damage that occurred to 35 dams exposed to the Loma

Prieta Earthquake. The completion date, maximum dam height, distance to the

epicenter, and estimated peak ground accelerations are included along with thedamage descriptions. The Loma Prieta Earthquake was a magnitude 7.0

earthquake with approximately 7 to 10 seconds of strong shaking. Dams exposed

to less than 0.2g did not experience damage. Dams exposed to peak groundaccelerations between 0.2g and 0.35g either experienced no damage or developed

longitudinal cracks. Transverse cracking was only noted in dams exposed to

greater than 0.35g, though 7 of 19 dams exposed to this level of shaking

experienced no damage, 7 of 19 dams experienced either minor or longitudinalcracking and only 5 of 19 dams experienced transverse cracking.

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Comprehensive Facility Review (CFR) Considerations

There is seldom time during a CFR to set up detailed spreadsheets incorporating

Monte Carlo simulations to perform the calculations described in this section.Therefore, simplified event trees are generally developed, and probabilities

estimated directly for each branch of the event tree using judgment and subjective

probability estimates (see section on Subjective Probability and ExpertElicitation) based on whatever information is available for a particular dam.

Table 22-3 below is one example typically used in CFRs.

Table 22-3

A second simplified spreadsheet analysis example would be structured to treat

uncertainty to a limited extent. This spreadsheet considers likely low, best, andhigh estimates for the key variables, giving weightings of 20% to the high and

low estimates, and 60% to the best estimates. The user-supplied information is

the dam's hydraulic height; 16th, 50th

, and 84th

percentile values for historicalfreeboard; representative SPT blowcount as a weighted percentile in each of five

blowcount ranges; 16th, 50th

, and 84th

percentile values of exceedance

probabilities for three ranges of earthquake loading; and an embankmenterodiblity factor.

Assumptions built into the spreadsheet are shown below. The liquefaction

probability as a function of blowcount for the three load ranges were assignedhigh, median, and low values roughly based upon Liao, et.al., with cyclic shear

stress taken as half the peak horizontal acceleration. The assumptions for crest

elevation change as a fraction of dam height are multiplied by the user-supplieddam height, and the user-supplied freeboard is subtracted to determine if the dam

remnant is overtopped. If freeboard remains, the probability of cracking failure is

assigned according to the amount of freeboard remaining, adjusted with a

multiplier to account for the magnitude of crest loss (the probability is reduced to1.0 if the multiplier increases the failure probability above 1.0). The erodibilty

factor is also multiplied by the assigned cracking failure probabilities, and can be

0.5, 1.0, or 2.0, depending upon the user-supplied assessment of low, medium orhigh degree of erodibility. All combinations of load range, blowcount range,

liquefaction probability, crest loss, and historical freeboard are multiplied across

the spreadsheet, according to the 0.2 and 0.6 weighting factors described above,

and the end columns are summed to obtain the best estimate for annual failure

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probability. Separate calculations are made multiplying-across and summing-

down only the rows containing the high values, and then all the rows containing

the low values in order to present a range for the annual probability of failureestimate. Figure 22-6 below shows some of the output from the spreadsheet.

Figure 22-6 Simplified Spreadsheet Output

Issue Evaluation Uncertainty Analysis

The process frequently used for Issue Evaluation risk analysis of embankment

dams subjected to seismic loading is depicted in figure 22-7 below. Note that the

curve representing failure likelihood as a function of post-earthquake residual

freeboard may include some probability of failure with positive freeboardremaining. This represents the likelihood of rapid erosion through a severely

damaged crest, rather than slower seepage erosion through earthquake-induced

cracks, which was covered earlier in this section.

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Figure 22-7 Summary of Probability Estimation Process

Available information is assessed to generate a belief about liquefaction

probability (Step 1 in figure 22-7 above). An understanding of site geology and

judgment regarding depositional environment, layering and material properties

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leads to selection of a representative distribution for standard penetration test

(SPT) blow count. The probability density function used to model SPT blow

count is more an amalgam of many pieces of information than it is a statisticalrepresentation of a large sample of blow count data. There may be extensive SPT

data for some sites, but more often there is limited SPT data or no SPT data at all.

Becker penetration tests (BPT), cone penetrometer tests (CPT), density or shear

wave velocity measurements and general geologic information all influencejudgment used to create the representative blow count distribution. An industry-

standard functional relationship between cyclic shear stress ratio (CSR) and SPT

blow count forms the basis of the liquefaction probability estimate (Step 1 inFigure 22-7).

A residual shear strength is assigned to each material assumed to be capable of

liquefaction (Step 2 in Figure 22-7 above). The functional relationship betweenresidual shear strength and SPT blow count used in traditional deterministic

analysis as a proxy for undisturbed sampling and shear strength testing is used

here. The uncertainty in residual shear strength for a given blow count is modeledusing a random variable that characterizes the following beliefs: The residual

shear strength is not likely to be more than the upper bound, not likely to be lessthan the lower bound, cannot be less than zero, and has a best estimate that is

about a third to half way up from the lower bound.

A functional relationship between residual shear strength and crest deformation is

constructed from the results of dynamic deformation analysis (Step 3 in Figure22-7). Residual shear strength is varied in a parametric study of seismically-

induced deformations to obtain estimates for potential crest deformations.Upstream and downstream slope instabilities are both considered, as is the

possibility that the entire embankment could be pushed downstream in a

translational shear failure.

The initial reservoir elevation could be anywhere in its operating range when an

earthquake occurs. Historical reservoir operation data indicates the frequency at

which the reservoir has been at a given elevation and is used to create thereservoir operating curve, which is used to predict how much freeboard is likely

to exist when an earthquake does occur. This difference between the dam crest

elevation and the reservoirs initial elevation is treated as a random variable.Given probability distributions for the pre-earthquake freeboard and the

likelihood for crest deformation, the likelihood for post-earthquake freeboard is

calculated as a joint probability of the two (Step 4 in Figure 22-7).

Given post-earthquake freeboard, the likelihood for continuing breachdevelopment by overtopping and down-cutting erosion is assessed using another

intuitive functional relationship (Step 5 in Figure 22-7). The reasoning used toform the shape of this relationship is as follows: If crest deformation is greater

than initial freeboard, overtopping and erosion is virtually certain. Failure from

this point would most likely take place rapidly, depending on the degree of

overtopping and the erodibility of the embankment materials. If crest deformationis only slightly less than initial freeboard, there may be interconnected cracks in

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the crest, open and deep enough to intersect the reservoir. Water flowing in these

cracks would have to flow fast enough and with sufficient quantity to be capable

of eroding and transporting embankment material. Upstream shell or crack-stopping materials would have to fail to perform a self-healing, filter-forming

operation and a functional downstream filter zone would have to be missing in the

original design or displaced/disrupted by crest deformation. Whether breach

formation would continue would depend on the depth and velocity of water in theopen cracks. Also, there is a possibility that human interventions might be

successful. The actual freeboard amount responsible for the various breach-

continuation likelihoods would also depend on the amount of crest deformation.Post-earthquake freeboard values transpiring from different amounts of pre-

earthquake freeboard pose different potential for erosional failure. If crest

deformation is much less than initial freeboard, the dam crest is not likely to be in

jeopardy, but internal erosion and piping failure modes at other locations withinthe dam or foundation could become an issue, particularly for embankments

already considered to be in marginally poor condition.

ExerciseGiven an effective overburden stress of 6,440 lb/ft

2, a maximum shear stress of

2,540 lb/ft2, and representative (N1)60 = 17, calculate the probability of

liquefaction using the relationship of Liao et al if the average earthquake is MW =

6.0.

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References

Bureau of Reclamation (2005), Risk Analysis Methodology Appendix J,

Estimating Risk from Seismic Loading of Embankment Dams andFoundations, Technical Service Center, Denver, Colorado.

Davis, C.A. (1997), Response of the San Fernando Power Plant Tailrace to the1994 Northridge Earthquake and Recommended Repairs, City of Los

Angeles, Department of Water and Power, Water Supply Division, publication

AX 215-48, DSR#68514.

Fell, R., M. Foster, J. Cyganiewicz, G. Sills, N. Vroman, and R. Davidson (Final

Draft 2008), Risk Analysis for Dam Safety, A Unified Method for

Estimating Probabilities of Failure of Embankment Dams by Internal Erosionand Piping, URS Australia Pty Ltd, Sydney, New South Wales, Australia.

Forster, I.R., and R.B. MacDonald (1997), Post-Earthquake Response

Procedures for Embankment Dams Lessons from the Loma PrietaEarthquake, Australian National Committee on Large Dams Annual

Conference.

Hammack, J.L. (1973), A Note on Tsunamis: Their Generation and Propagation

in an Ocean of Uniform Depth, Journal of Fluid Mechanics (Britain), Vol.

60, Part 4, pp. 769-799.

Liao, S.S.C.., D. Veneziano, and R.V. Whitman (1988), Regression Models for

Evaluating Liquefaction Probability, Journal of Geotechnical Engineering,

American Society of Civil Engineers, Vol. 114, No. 4, pp. 389-409.

Pells, S. and Fell, R. (2003). Damage and Cracking of Embankment Dams by

Earthquake and the Implications for Internal Erosion and Piping. Proceedings

21st Internal Congress on Large Dams, Montreal. ICOLD, Paris Q83-R17,International Commission on Large Dams, Paris.

Seed, R.B., K.O. Cetin, R.E.S. Moss, A.M. Kammerer, J. Wu, J.M. Pestana, M.F.Riemer, R.B. Sancio, J.D. Bray, R.E. Kayen, and A. Faris (2003), Recent

Advances in Soil Liquefaction Engineering: A Unified and Consistent

Framework, 26th

Annual ASCE Los Angeles Geotechnical Spring Seminar,

Long Beach, CA.

Seed, R.B., and L.F. Harder (1990), SPT-Based Analysis of Cyclic Pore Pressure

Generation and Undrained Residual Strength, H.B. Seed Memorial

Symposium, Berkeley, CA, BiTech Publishing, Ltd., Vol. 2, pp. 351-376.

Seed, H.B., K.L. Lee, I.M. Idriss, and F. I. Makdisi, (1975), The Slides in the

San Fernando Dams During the Earthquake of February 9, 1971, Journal of

the Geotechnical Engineering Division, American Society of Engineers, Vol.101, No. GT7.

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Seed, H.B., K.K. Lee, and I.M. Idriss, Analysis of Sheffield Dam Failure,

Journal of the Soil Mechanics and Foundations Division, American Society ofCivil Engineers, Vol. 96, No. SM6.

Wilson, B.W. (1972), Seiches, Advances in Hydroscience, Chow, U.T. (editor),

Academic Press, New York, New York, Vol. 8.

Youd, T.L., C.M. Hansen, and S.F. Bartlett (2002), Revised Multilinear

Regression Equations for Prediction of Lateral Spread Displacement, Journalof Geotechnical and Geoenvironmental Engineering, American Society of

Civil Engineers, Vo. 128, No. 12, pp. 1007-1017.

Olson, S. M. & Stark, T. D, Liquefied strength ratio from liquefaction casehistories, Canadian Geotechnical Journal, Volume 39, No. 3, pp 629647,

March, 2002.

Olson, S. M. & Stark, T. D., Yield strength ratio and liquefaction analysis of

slopes and embankments, American Society of Civil Engineers, Journal ofGeotechnical and Geoenvironmental Engineering, Volume 129, No. 8, pp

727737, August, 2003.

Boulanger, R.W. and Idriss, I.M., "Evaluating the Potential for Liquefaction or

Cyclic Failure of silts and Clays," Report No. UCD/CGM-04/01, Departmentof Civil and Environmental Engineering, University of California at Davis,

December, 2004.

Bray, J.D., and Sancio, R.B., "Assessment of the Liquefaction Susceptibility of

Fine-Grained Soils," American Society of Civil Engineers, Journal of

Geotechnical and Geoenvironmental Engineering, Volume 132, No. 9, pp11651177, September, 2006.

Harder, L.F. Jr., "Performance of Earth Dams During the Loma PrietaEarthquake," Paper LP05, Proceedings: Second International Conference on

Recent Advances in Geotechnical Earthquake Engineering and soil Dynamics,

Saint Louis, Missouri, March, 1991.

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