Comparison
of Seismic Slope-Performance Models--Case Study of the Oakland East Quadrangle, California

By

Scott
B. Miles1
and David K. Keefer2

Open-File
Report 99-137

1999



This
report has not been reviewed for conformity with U.S. Geological
Survey editorial standards or with the North American Stratigraphic.
Code. Any use of trade, product, or firm names is for descriptive
purposes only and does not imply endorsement by the U.S. Government.

> 1Western Regions Earthquake Hazards Team, 345 Middlefield
> Rd., MS 977, Menlo Park, CA 94025, [email protected]





Abstract:Researchers,
emergency response and lifeline managers, and municipal planners are
beginning to recognize the utility of seismic landslide hazard
zonation. With this recognition, the decisions made based on
resulting maps could have widespread social and economic impact in
the event of a large earthquake. This report compares several popular
permanent displacement models for assessing seismic
slope-performance. The approaches are implemented in a raster GIS to
expose potential differences and assess the effects of using a
particular approach within a decision-making context. It is observed
that each approach forecasts notably different levels of
slope-performance. Thus, considering the variety of spatial seismic
landslide analysis approaches and the effect of basing a decision on
a map created using a single one of them, it is suggested that less
reliance be put on the traditional paper map format. Instead,
multiple approaches can be used to investigate many scenario
earthquakes under a variety of conditions in a computer-based spatial
decision support system.

INTRODUCTION

Keefer
(1984) observed that earthquakes of moderate to high magnitude can
cause landslides over an area as large as 500,000 km2.
These landslides also have large damage potential as illustrated by
the recent effects of the 1989 Loma Prieta and 1994 Northridge
earthquakes (Harp and Jibson, 1995; Keefer, 1998). Accordingly,
researchers, emergency response and lifeline managers, and municipal
planners are beginning to recognize the utility of seismic landslide
hazard and risk zonation. With this recognition, the decisions made
based on resulting hazard or risk maps could have widespread social
and economic impact in the event of a large earthquake. Therefore,
investigating and comparing several popular techniques for seismic
slope-performance zonation is important.

The
state of the art in seismic landslide hazard zonation using
geographic information systems (GIS) was summarized by Ho and Miles
(1997), who suggested several potential approaches using dynamic
permanent-displacement models. In the short time since then,
considerable effort has been spent improving seismic landslide hazard
zonation techniques using spatial technologies (Miles and Ho, 1999;
Jibson and others, 1998; McCrink and Real, 1996). This report extends
the study of Ho and Miles (1997) by implementing several seismic
slope-performance models using raster GIS to expose any differences
between the approaches and assess the potential effects of using a
particular approach within a decision-making context. The report
begins by summarizing the approaches that exist for determining
seismic landslide hazard. The general procedure of a
permanent-displacement analysis--the class of approaches chosen in the report for investigation--is then described. The report concludes by discussing the
implementation of each individual approach and the differences among
these approaches.

PERMANENT-DISPLACEMENT
ANALYSIS

Three
basic approaches exist for conducting seismic landslide hazard
analysis. These consist of the statistical, pseudo-static, and
permanent-displacement approaches. A statistical approach assesses
hazard by assuming the past predicts the future. Hazard is assessed
through correlation of past landslides with several influential
factors. Results of a statistically based analysis can range from an
estimated probability of failure to some index indicating degrees of
hazard. Pseudo-static analysis employs a traditional static
slope-stability analysis with the addition of a horizontal force
component that models the effects of earthquake-induced
ground-motions. A pseudo-static analysis yields a factor of safety
against seismic slope failure. This effectively provides a simple
binary index of whether a slope is expected to fail or not at a given
level of seismic acceleration. Permanent-displacement techniques
provide information regarding actual slope-performance through
calculation of some index of relative or actual displacement based on
commonly accepted characterizations of earthquake-shaking severity.
Permanent-displacement analysis is chosen for investigation because
of its higher information content, better modeling of ground-motion,
and increasing acceptance in the earthquake engineering community.

## Newmark's Sliding Block
Analogy

In
his landmark paper, Newmark (1965) noted that the transient effects
of earthquake motions can cause permanent deformation of slopes prior
to complete failure. Newmark proposed modeling a slope subjected to
earthquake-induced accelerations as a friction block resting on an
inclined plane subjected to the same accelerations as the modeled
slope (Figure
1). Therefore, in each instance when the sum of the static and
dynamic forces exceed the shear resistance of the sliding interface
the block will displace. The interface shear resistance is commonly
characterized by the critical acceleration (ac) of
the modeled slope, which is the base acceleration needed to overcome
the shear resistance. Newmark (1965) defined the following
relationship to calculate critical acceleration in the case of planar
slip:

(1)

where FS
is the static factor of safety of the slope andais the thrust angle of the landslide block, which can be approximated
by the slope angle. Total induced displacement can be determined by
summing the displacement resulting from each instance the shear
resistance is exceeded during ground shaking. This value must be
evaluated to assess the potential effect on the landslide block.
Newmark displacements should be considered indices that indicate
relative slope-performance during seismic shaking rather than a
precise prediction of slope deformation (Jibson and others, 1998).
Thus, to define the related hazard (i.e. damage potential) a
probability of failure should be determined through correlation with
actual landslides or by using a relationship, such as the one
presented in Jibson and others (1998).

The
sliding block analogy assumes the slope is rigid and perfectly
plastic and that shear strength remains constant during shaking. Each
assumption may only be valid for certain conditions and does not
represent general behavior. For example, assuming rigid, perfectly
plastic behavior will result in an over-estimation of Newmark
displacement for strain-hardening materials and an under-estimation
for strain-softening materials (Kramer, 1996). However, a Newmark
analysis has the advantage over more recent developments in
permanent-displacement analysis (i.e. finite element and finite
difference techniques) in that the only additional information beyond
that required for static slope-stability analysis is an appropriate
acceleration time history. Whereas with the more advanced approaches,
require defining several constitutive parameters and can require a
prohibitive amount of material testing for regional slope-performance
analysis.

## Double Integration
Approach

Newmark
originally employed an energy-based method for calculating cumulative
slope displacement. A less numerically cumbersome method was
developed by Wilson and Keefer (1983) where those parts of an
earthquake accelerogram that exceed the critical acceleration of a
slope are double-integrated (Figure
2). The numerical scheme is straightforward to implement as
illustrated by routines existing in BASIC, FORTRAN and C (Jibson,
1993; Sharma, 1996; Miles, 1997). Even so, application of the
double-integration algorithm can require significant time and
computing resources when used for spatial-analysis.

The two
major steps of the double-integration approach are calculation of the
critical acceleration of each slope of interest and selection of an
appropriate earthquake time history. Selection of a time history for
predictive hazard analysis can pose a major obstacle in using the
double-integration approach. Ideally, records of an earthquake that
occurred on the fault zone of interest having adequate magnitude are
used. Unfortunately in many3⁄4if
not most3⁄4cases, such records do not exist. The alternatives consist of
modifying actual records from the fault zone of interest (or another
fault system) or generating artificial time histories. This issue is
treated in greater detail by Miles and Ho (1999) and Kramer (1996).

## Simplified Approach

Citing
the numerical complexity and the difficulty associated with selection
of acceleration time histories, a handful of researchers have
developed simplified approaches to calculating Newmark displacements
(Franklin and Chang, 1977; Makdisi and Seed, 1978; Ambraseys and
Menu, 1988; Yegian and others, 1991; Jibson, 1993; Jibson and others,
1998). By and large, these approaches are based on numerical
regression of results obtained from double-integrating real or
synthetic time histories. Variations among approaches are typically
in the ground-motion descriptors used to correlate with Newmark
displacement and in the final means with which to conduct the
simplified analysis. Simplified approaches that are chart based are
clumsy and imprecise when applied to regional analysis and, thus, are
not considered in this report. The balance of the simplified
approaches take the form of simple mathematical equations, which are
developed from regression analyses. It is relatively straightforward
to apply any of the approaches that follow this style to
slope-performance zonation.

SUBJECT
LOCATION

In
order to compare the various slope-performance analyses when applied
to a real-life problem, the 7.5 minute 1:24,000 Oakland East
quadrangle, California was selected as the region on which to conduct
seismic slope-performance zonation. This particular area has been the
subject of previous seismic landslide studies (Herbel, 1994; Miles
and Barrera, unpub. data, 1995; Miles and Ho, 1999). The Oakland East
quadrangle is located in the San Francisco Bay area and contains the
eastern parts of the cities of Oakland and Berkeley (Figure
3). The quadrangle is bisected by the Hayward fault, the
predominant seismic source in the region, which strikes
southeast-northwest. The hilly areas northeast of the fault exhibit
moderate to steep slopes (Figure
4). Because of the large amount of existing infrastructure and
areas of dense population, seismic landslide hazard within the
Oakland East quadrangle is of great interest to lifeline managers and
municipal planners.

SEISMIC
SLOPE-PERFORMANCE ZONATION

Four
approaches to seismic slope-performance zonation using Newmark's
analysis were implemented using raster GIS. The majority of the
models were applied using the Arc/Info GRID module, which facilitates
algebraic manipulation of raster coverages (i.e. map or grid
algebra). All analysis was performed at a 10-meter resolution. All of
the approaches follow the same general procedure. The four steps
involved are data collection, seismic landslide susceptibility
assessment, seismic shaking characterization, and lastly,
permanent-displacement analysis. The various approaches differ in the
methods used in conducting the latter two steps. The implementation
of the four different approaches are discussed later in this section.
The common steps of data collection and seismic landslide
susceptibility assessment are described below in reverse order.

## Seismic Landslide
Susceptibility Analysis and Data Collection

Regional
susceptibility to earthquake-triggered landslides can be assessed by
determining the critical acceleration of each slope in the area. In
the case of spatial-analysis using GIS, this is typically done for
each pixel in the coverage. As previously noted, determination of
critical acceleration requires the calculation of the static factor
of safety for each slope. The most common approach to conducting
regional static slope-stability analysis is to apply the infinite
slope model to each pixel in the coverage. However, neighborhood
analysis can be employed to account for inter-pixel interaction. Such
a method is referred to as a focal analysis, as opposed to local
analysis where each pixel is treated individually. Using the infinite
slope model, the static factor of safety of a slope (FS) can
be expressed as:



(2)



where c'
is the effective cohesion,f'
is the effective angle of internal friction,gis the material unit weight,gwis the unit weight of water,ais the angle of the slope from the horizontal, d is the normal
depth to the failure surface, and m is a ratio of d
indicating the location of the ground water table. For this report, a
local analysis using the infinite slope model was conducted. The
slope-stability analysis was performed for completely dry (m=0)
and saturated (m=1) conditions to bound possible water table
elevations in lieu of real data.

The
data collection step comprises gathering representative values for
each parameter of the infinite slope model. This step is crucial to
the remaining steps of any permanent-displacement analysis. Even so,
as the goal of this report is the comparison of slope-performance
models, simple estimates of material property values were used.
Therefore, the resulting slope-performance maps presented later in
this report are not fit for use as a critical decision-making tool.
Material property estimates were made during a previous study of the
Oakland East quadrangle (Miles and Barrera, unpub. data, 1995). Soil
strength values were produced through overlay of the engineering
geology map (Radbruch 1969) and the USDA soil survey map of the
quadrangle (Welch, 1981). USCS classifications specified in the soil
survey were assigned to each geologic unit polygon. Thus, different
polygons of the same geologic unit could have different USCS
classifications. Actual values were then obtained using relationships
of friction angle or cohesion to USCS classification from Bell
(1981), the NAVFAC Design Manual, and engineering judgment. This
approach will underestimate strength in areas where soils are shallow
and sliding occurs in the underlying bedrock. However, static
stability was ensured for all slopes in the analysis area. The areal
distribution of estimates for drained cohesion and friction angle are
shown in Figures 5
and 6,
respectively.

The final
two parameters needed to perform a seismic landslide susceptibility
analysis are slope angles and the depth to failure for each potential
landslide (pixel). Slope angles were calculated from a USGS format
1:24,000 10-meter DEM of the Oakland East quadrangle. For estimation
of landslide failure depth, a single value of 10 feet was assumed
throughout the quadrangle. The value of 10 feet is considered
representative for the most abundant types of earthquake-induced
landslides (Keefer, 1984). Based on the data collected, maps showing
the areal distribution of critical acceleration under dry and
saturated conditions were produced for use in subsequent Newmark
analysis. The maps are shown in Figures 7 and 8, respectively.

## Ambraseys and Menu (1988)

One of
the first well-known simplified approaches to Newmark's analysis was
developed by Ambraseys and Menu (1988). They developed a suite of
regression equations based on actual ground-motion records that
express Newmark displacement (DN)
as a function of critical acceleration ratio, which is the ratio of
critical acceleration (ac)
to peak ground acceleration (amax).
The equation used for this report does not consider up-slope movement
and is expressed as:

(3)



When
critical acceleration ratio is greater than one, the result will be
complex. Application of the model requires that peak ground
accelerations (PGA) be calculated for the coverage. This was
accomplished using the attenuation relationship of Abrahamson and
Silva (1997) as suggested in Sitar and Khazai (unpub. data). For
moment magnitudes (M) greater than 6.4 the relationship
takes the following form:

(4)



where
amaxis expressed in units of gravity and R is epicentral distance
in kilometers. In order to apply the attenuation relationship, the
distance to the epicenter must be calculated for each pixel in the
coverage. This was accomplished by digitizing the trace of the
Hayward fault from Radbruch (1969) and calculating the euclidean
distance between each pixel and the nearest point on the fault trace
using the GRID function EUCDISTANCE. This approach does not
explicity yield the epicentral distance, rather the distance to
fault-rupture, because the epicenter is not known for the scenario
earthquake. PGA was calculated for a scenario M=7 earthquake.
Because of the near-field limitations of the attenuation
relationship, the minimum epicentral distance was set to 1 kilometer.
Attenuation of PGA is shown in Figure
9. With PGA calculated, it was then a simple matter to calculate
Newmark displacements from the critical acceleration maps created for
dry and saturated conditions. The seismic slope-performance maps
created are shown for dry and saturated conditions in Figures 10
and 11.

## Yegian and others (1991)

To
address the inability of PGA as the sole descriptor of seismic
shaking to explicitly consider frequency content and duration, Yegian
and others (1991) developed an expression for calculating median
normalized Newmark displacement (DN*).
Newmark displacements were calculated for the regression analysis by
double-integrating 348 time histories of actual earthquakes, which
were compiled by Franklin and Chang (1977).

(5)



In
the equation, Neqis an equivalent number of cycles and T is the predominant
period of the input motion. To employ this model, values for these
two parameters needed to be selected. The mean number of equivalent
cycles for an M=7 earthquake is approximately 8 according to
Seed and others (1975). Based on Seed and others (1969), the
predominant period at rock outcrops for distances less then 40
kilometers is approximately 0.30 seconds. Maps depicting Newmark
displacements for dry (Figure
12) and saturated (Figure
13) conditions were then produced using the PGA map described
above.

## Jibson and others (1998)

Recognizing
that PGA tends to correlate poorly with earthquake damage, Jibson
(1993) developed an equation based on Arias intensity (Ia)
to better characterize the damaging effects of ground-motion. Jibson
(1993) also noted the general lack of agreement among simplified
approaches which are based on critical acceleration ratio. The
regression equation was calibrated by double-integrating eleven
acceleration time histories, including ten from California, with
Arias intensities less than 10m/sover a range of critical acceleration
values (0.02 - 0.40g). The equation was later updated using 555
records from 13 earthquakes (Jibson and others, 1998). The form of
the equation was also altered to make the critical acceleration term
logarithmic, thus reducing the sensitivity to critical acceleration
noted by Miles and Ho (1999). The equation takes the form:

(6)



To
forecast the areal distribution of Arias intensity for a M=7
earthquake on the Hayward fault, the attenuation relationship of
Wilson and Keefer (1985) was used as suggested by Jibson (1993). The
following equation yields Arias intensity in meters per second.

(7)



The
parameter R is as defined previously and his the focal
depth in kilometers. A representative value for San Francisco Bay
area earthquakes of 10 kilometers was chosen for calculating the map
of Arias intensity shown in Figure
14. Newmark displacements were calculated based on the areal
distribution of Arias intensities for dry and saturated conditions.
The respective maps are shown in Figures 15
and 16.

## Miles and Ho (1999)

As
mentioned above, the simplified approaches to Newmark's analysis were
created from the motivation to reduce the numerical complexity
associated with the double-integration algorithm. This motivation
seems doubly important in the case of spatial hazard analysis.
However, the ever increasing power of computer processors, the advent
of parallel processing, and the speed of low-level programming
languages in fact makes the simplification of numerics less of a
priority. In addition, the tendency to use a single ground-motion
predictor rather than acceleration time histories reduces much of the
advantage of a permanent-displacement analysis over the pseudo-static
approach. Considering this, Miles and Ho (1999) applied the
double-integration algorithm of Wilson and Keefer (1983) for
calculating Newmark displacements to a 30 km2area of the East Bay Hills, which lie within the Oakland East
quadrangle.

In the
study of Miles and Ho (1999), input time histories were generated
using the stochastic simulation developed by Boore (1983). Artificial
accelerograms were used in lieu of actual records from the Hayward
fault of adequate size and because of the short-comings associated
with scaling earthquake records from other seismic zones. The first
step of the simulation involves windowing Gaussian white noise having
zero mean. The transient noise is then transformed to the frequency
domain and multiplied by a theoretical amplitude spectrum (Hanks and
McGuire 1981). The simulated Fourier spectrum is then transformed
back to the time domain. Because of the stochastic nature of the
simulation, several realizations of the simulation must be run in
order to obtain a stable prediction.

For this
report, a C program called NMGRID was written for conducting spatial
seismic landslide hazard analysis using the double-integration
approach. The program requires ASCII formatted grid files that can be
output by most commercial GIS. The program cycles through the pixels
of the supplied critical acceleration grid, double-integrating the
appropriate time history at each step. The time history is
programmatically selected from a set of time histories3⁄4supplied as ASCII text files3⁄4based on the source to site distance value of the current pixel3⁄4supplied as part of an ASCII grid. An
ASCII grid of Newmark displacements is output for importing into any
GIS for map production or further hazard or risk analysis.

To
avoid the time-consuming task of performing the double-integration
analysis a number of times as suggested by Boore (1983), the set of
random numbers that yielded mean displacements for the test area of
Miles and Ho (1999) was used for this report. Thus, a single suite of
acceleration time histories for an M=7 earthquake occurring at
a 10 kilometer pseudo-depth were generated for every 500 meter
interval away from the Hayward fault. The simulation parameters used
are listed in Table
1 and reflect parameters suggested for Northern California
earthquakes (Boore, 1996). Application of the double-integration
method to the 10-meter resolution quadrangle took about eight hours
to complete each analysis on a Sun Microsystems Ultra 1 170MHz. In
contrast, the simplified methods required only a few minutes. The
seismic slope-performance forecasted using the double-integration
approach is shown in the maps of Figures 17
and 18 for
dry and saturated conditions, respectively.

DISCUSSION

With
seismic slope-performance maps created using the three simplified
approaches and the double-integration approach of Miles and Ho
(1999), it is possible to compare potential discrepancies among the
approaches. The objective of this report is to reveal any differences
between the four approaches and assess the potential effects of using
a particular approach over another. Thus, the maps created using each
approach are visually compared. Such qualitative comparison will
assist in determining the effects of using such maps as a visual tool
in a decision-making process. The approaches are then compared using
a statistical analysis to better quantify the discrepancies among
them.

Beginning
by comparing the two simplified approaches that are calibrated using
PGA, it is apparent that the two models predict similar distributions
but notably different levels of Newmark displacement for both dry and
saturated conditions. Even more notable is that the maps created
using Yegian and others (1991) have a visibly greater amount of
orange to red pixels, that is, pixels having greater than ten
centimeters of Newmark displacement. The difference is most obvious
for the maps depicting saturated conditions. The difference in
slope-performance is also effectively illustrated by the total mean
displacement for each model and respective condition (Table
2). The mean resulting from the method of Ambraseys and Menu
(1988) is 2.22 and 13.17 centimeters, respectively, for dry and
saturated conditions. The corresponding values for Yegian and others
(1991) are 6.89 and 44.74 centimeters. Both approaches were performed
using the same PGA maps. The only difference in parameterization is
that of the predominant period and equivalent cycles used with Yegian
and others (1991). The values used were admittedly conservative. An
observation regarding the Ambraseys and Menu approach that is not
visibly discernible is that it does not result in any pixels having
zero displacement. This is an obvious side-effect of the log-linear
form of the regression equation.

Based on
a different ground-motion descriptor, it would be logical to expect a
difference between the Jibson and others (1998) approach and the
previous two PGA-based approaches. This expectation is born out for
both dry and saturated conditions. Whereas between the PGA based
approaches the distribution of Newmark displacements are only subtly
different, the maps produced using the Jibson and others (1998)
approach show noticeably different distributions. The average Newmark
displacements for the Jibson and others (1998) maps, both dry and
saturated, are 1.42 and 10.72 centimeters. Thus, the approach appears
to forecast lower Newmark displacements on average even though it
predicts greater areal extent. Similar to the Ambraseys and Menu
(1988) model, the Jibson and others (1998) model takes on a
logarithmic form. This may explain the large areas having Newmark
displacement less than 2 centimeters. Also noteworthy of the Jibson
and others (1998) maps is the slightly greater increase in Newmark
displacements on average from dry to saturated conditions when
compared to the PGA-based maps.

The
final comparison is that between the double-integration approach
using simulated accelerograms (Miles and Ho, 1999) and the simplified
approaches. It would be expected that maps created using the
simplified approaches bear a resemblance to those from the
double-integration approach. This is because each simplified approach
was, in some way, developed by double-integrating earthquake
accelerograms. Note, however, that actual earthquake records were
used in these instances. There is a general similarity between the
double-integration and simplified maps. Yet, markedly different
distributions and magnitudes of Newmark displacement are evident.
Having average Newmark displacements of 1.03 and 9.34 centimeters for
dry and saturated conditions, the Miles and Ho (1999) approach
results in the lowest average predicted Newmark displacements (Table
2). Interesting however, is the magnitude increase of Newmark
displacement, on average, from dry to saturated conditions. This is
the greatest increase of any of the approaches and suggests a
significant dependency on critical acceleration as that is the only
parameter that varies with ground water conditions. The approach of
Jibson and others (1998) exhibits the second largest increase.
Examination of the two PGA-based approaches reveals obvious bands of
hazard in the respective maps (Figures 10,
11, 12,
13) that
parallel the Hayward fault. This may indicate an unrealistic
influence by PGA attenuation. The fact that the Jibson and others
(1998) and Miles and Ho (1999) approaches do not exhibit pronounced
banding supports the conclusion that Arias intensity correlates
better with Newmark displacement (Jibson, 1993).

To
provide an easier and quantitative means of comparing the four
approaches, cumulative distribution functions for each Newmark
displacement map were calculated and plotted in Figures 19
and 20.
The plots show the probability of exceedance for a given value of
Newmark displacement, as predicted by each Newmark analysis. Tables 3
and 4
list the exceedance probabilities for Newmark displacements of 2, 5,
and 10 centimeters to assist in the interpretation of the cumulative
distribution plots. For dry conditions (Figure 19), each approach
exhibits distributions of similar shape. The approach of Jibson and
others (1998) predicts the greatest probability for values of Newmark
displacement less than 1.5 centimeters and the least probability for
displacements greater than 5 centimeters (Table 3). However, the
approach does not yield the lowest maximum predicted displacement
(Table 2). The approach of Miles and Ho (1999) predicts the lowest
probabilities for displacements less than 5 centimeters. The two
PGA-based approaches yield significantly greater probabilities for
Newmark displacements greater than 5 centimeters, with the approach
of Yegian and others (1991) predicting the higher probabilities. For
saturated conditions (Figure 20), the relative differences between
the distributions are similar to those for dry conditions. Notice
however, that the distributions do not exhibit as pronounced a
reduction in probability for higher values of displacement. This
reflects the increase in overall Newmark displacements for saturated
conditions as observed with the slope-performance maps.

The
cumulative distribution plots show that the magnitude of Newmark
displacements predicted by each approach differ significantly. And
although the shape of the distributions are similar, there is still
discernible distinction between them. This discrepancy seems to be a
function of the ground-motion model used. Three different
ground-motions models were employed and there are correspondingly
three distinct distributions. This observation can be most readily
made using the cumulative distribution plot for dry conditions
(Figure
19). Thus, the means of modeling the particular ground-motion
parameter used by each approach is likely to have a significant
effect on predicted regional Newmark displacements. The cumulative
distribution plots also illustrate the difficulty in interpreting
analysis results in map form. It appears that the maps produced using
the approach of Jibson and others (1998) is more conservative than
those produced using the Miles and Ho (1999) approach. And in fact,
the average Newmark displacements are higher. However, the cumulative
distribution plots show that the Jibson and others (1998) approach
predicts lower probabilities for Newmark displacement values greater
than 5 centimeters. To make an assessment of which approach predicts
greater hazard, the associated probability of failure must be
evaluated.

The
comparison of the four approaches is based on the use of three
different ground-motion models. Thus, a true comparison of the
approaches can only be accomplished by using a single model of
ground-motion. This of course is not possible with simple attenuation
relationships. However, by calculating the Arias intensity of each
simulated time history generated for use with the double-integration
approach, Miles and Ho (1999) were able to make a true comparison
between the Jibson (1993) model and the double-integration approach.
The results showed an even larger discrepancy, with the Jibson model
forecasting larger magnitudes of Newmark displacement. It is
reasonable to expect that the results corresponding to the models of
Ambraseys and Menu (1988) and Yegian and others (1991) follow these
findings.

The
disagreement among the approaches that was observed in the discussion
above has the potential to greatly effect any decision-making
process. For example, a pipeline manager may want to locate areas of
poor seismic slope-performance in order to identify pipes to be
retrofitted against earthquake-triggered landslides. Taking the two
approaches that exhibited the most extreme difference3⁄4the Miles and Ho (1999) approach and the approach of Yegian and
others (1991)3⁄4it is apparent that use of one approach over another can have
significant economic effects. If for instance, only the Yegian and
others (1991) approach was employed to map seismic slope-performance,
a potentially larger number of pipes would be slated for
modification.

With the
increasing popularity of GIS and spatial-analysis, it is equally
likely that results of a regional Newmark analysis be used as a
component in other GIS-based models, for example, probability of
slope failure (i.e. hazard) or infrastructure damage (i.e. risk). In
applications such as these, the effects of using a particular seismic
slope-performance model are more uncertain. The effects would depend
on the hazard or risk model used and the spatial-analysis technique
employed to implement the model (e.g. focal or local analysis). What
is certain is that whatever the difference may be, it will be carried
through each subsequent analysis. Thus, if spatial coverages of
Newmark displacements are passed on to outside parties for further
spatial-analysis, it is important that quality metadata (information
about data and analysis) is not only maintained but transferred and
exploited (Miles and Ho, 1999b).

# Summary
& Conclusion

Several
permanent-displacement approaches to seismic slope-performance
analysis were presented. These approaches were applied through
spatial-analysis to produce Newmark displacement maps for both dry
and saturated conditions. The maps resulting from each approach were
compared to reveal the discrepancies and assess the potential effects
of using one approach in place of another in a decision-making
context. Although the comparisons indicated significant differences
between the approaches, no effort was made to identify the "correct"
approach. Of course, the double-integration algorithm of Wilson and
Keefer (1983) forms the basis from which all the approaches compared
in this report were derived. The approach of Miles and Ho (1999)
directly implements the double integration algorithm. However, the
validity of their particular implementation is no more certain than
the other approaches because the ground motion time histories used
were artificial and may not accurately depict actual ground motions
in all instances. Of course, it would be a simple matter to use
actual earthquake time histories if available. Further, the
double-integration algorithm is quite costly with respect to
processing time, and so the approach may not be practical for
application to large areas. Rather, as suggested in Miles and Ho
(1999), a progressive analysis technique should be employed. This
consists of using simplified approaches to identify areas of moderate
to poor slope-performance, which are then more thoroughly
investigated using the double-integration approach using actual or
artificial accelerograms.

This
report only considered Newmark displacement approaches to seismic
slope-performance zonation. It is also possible that a statistical or
pseudo-static approach be used. Although these approaches were not
considered, it is reasonable to conclude that the results will be
different from the approaches presented here. This widespread
disagreement is understandable since it is unlikely that any
universal seismic slope-performance analysis exists for all seismic
zones and input conditions. A significant reason for this is the
difficulty in accurately characterizing potential seismic shaking.
Another important issue, although not directly related to the
specific approach, is the quality of the material property data used
to conduct a hazard analysis. The cost of performing material testing
on a regional scale can be prohibitive, and test data compiled from
many disparate sources may not provide any significant improvement
over simpler estimates (Keefer and Miles, unpub. data, 1999).

Considering
the variety of approaches to assessing seismic slope-performance and
the effect of basing a decision on single one of them, it seems that
the solution is to move away from reliance on the medium of static
maps. Instead, multiple models can be used to investigate many
scenario earthquakes under a variety of conditions in a
computer-based spatial decision support system (SDSS). In this way, a
decision-maker can quickly and conveniently determine the different
levels of seismic slope-performance as forecasted by any number of
zonation approaches. Alternatively, a single approach can be employed
with a variety of ground motion models. Results of such
investigations can then be extended to assess related hazard and
risk. Currently, work is being done to develop a standalone SDSS that
is able to implement any seismic slope-performance, landslide hazard,
or landslide risk model to investigate multiple scenarios and
conditions (Miles and others, 1999). With this tool, the differences
that exist between approaches can be exploited to make better and
more educated decisions.

# References

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N. A. and Silva, W. J., 1997, Equations for estimating horizontal
response spectra and peak acceleration from Western North America
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Ambraseys,
N.N. and Menu, J.M., 1988, Earthquake-Induced Ground Displacements:
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Bell,
Frederic G., 1981, Engineering properties of Soils and Rocks: Boston:
Butterworths.

Boore,
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Franklin,
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Embankments by Newmark's Sliding Block Analysis: Report 5,
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Vicksburg, MI.

Hanks,
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Ground Motion, Seismological Society of America Bulletin: v. 71, no.
6, p. 2071-2095.

Harp,
E.L. and Jibson, R.W. , 1995, Inventory of landslides triggered by
the 1994 Northridge, California earthquake: U.S. Geological Survey
Open-File Report 95-213, 17 p, 2 pl.

Herbel,
W.A., 1994, Development of a GIS Based Landslide Hazard Map:
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Ho, C.L.,
and Miles, S.B., 1997, Deterministic Zonation of Seismic Slope
Instability: An Application of GIS: ASCE Geotechnical Special
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Engineering, p. 87-102.

Jibson,
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Jibson,
R.W., 1993, Predicting Earthquake-Induced Landslide Displacements
Using Newmark's Sliding Block Analysis: Transportation Research
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Keefer,
David K. ed., 1997, The Loma Prieta, California, earthquake of
October 17, 19893⁄4landslides: U.S. Geological Survey Professional Paper 1551-C, 183 p.

Keefer,
David K., 1984, Landslides Caused by Earthquakes: Geological Society
of America Bulletin, 95, p. 406-421.

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Steven L., 1996, Geotechnical Earthquake Engineering: New Jersey:
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F.I. and Seed, H.B. (1978) "Simplified procedure for estimating
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Geotechnical Engineering Division, ASCE, v. 104, no. GT3, p. 299-321.

McCrink,
T.P., and Real, C.R., 1996,Evaluation of the Newmark method for mapping earthquake-induced
landslide hazards in the Laurel 7.5' quadrangle, Santa Cruz County,
California: Final Technical Report for U.S. Geological
Survey Contract 143-93-G-2334, 47 p.

Miles,
S.B. and Ho, C.L., 1999, Rigorous Landslide Hazard Zonation using
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Dynamics and Earthquake Engineering (in press).

3⁄41999b, Applications and issues of GIS in civil engineering modeling:
Journal of Computing in Civil Engineering, ASCE (in press).

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S.B., Keefer, D.K., and Ho, C.L., 1999, Seismic Landslide Hazard
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the U.S. Conference on Lifeline Earthquake Engineering: Seattle, WA,
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Miles,
S.B., 1997, Rigorous Landslide Hazard Zonation using Newmark's Method
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D.H., 1969, Areal Engineering Geology of the Oakland East quadrangle,
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H.B., Mori, K., and Chan, C.K., 1975, Influence of seismic history on
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Table
1.Parameters
used to conduct Boore (1983) simulation.





|Ds,
                                        stress drop            | 70
                                        bars   
|------------------------------------------------------------------ | --------------------------------------------------
|fmax,
                                        cutoff frequency     | 15.9
                                        Hz   
|b,
                                        shear wave velocity     | 3.8
                                        km/sec
|r,
                                        density                 | 2.8
                                        g/cm3 
|F,
                                        free surface factor     | 2                                                 
|Rqf,radiation pattern                                              | 0.55                                              
|V,
                                        energy partition factor | 0.71                                              
|B*,
                                        near-surface factor    | 2.3                                               



Table
2.Summary
statistics of Newmark displacement maps for dry and saturated
conditions.



|Approach                       | Mean (cm) | s(cm)  | Min. (cm) | Max. (cm)
|------------------------------ | --------- | ------ | --------- | ---------
|Ambraseys and Menu (1988): Dry | 2.22      | 8.66   | 0.08      | 308.35   
|Ambraseys and Menu (1988): Wet | 13.17     | 45.15  | 0.10      | 520.97   
|Yegian and others (1991): Dry  | 6.89      | 34.72  | 0.00      | 1250.25  
|Yegian and others (1991): Wet  | 44.74     | 170.63 | 0.00      | 1607.57  
|Jibson and others (1998): Dry  | 1.42      | 5.59   | 0.09      | 311.35   
|Jibson and others (1998): Wet  | 10.72     | 44.35  | 0.12      | 598.93   
|Miles and Ho (1999): Dry       | 1.03      | 6.14   | 0.00      | 129.60   
|Miles and Ho (1999): Wet       | 9.34      | 32.64  | 0.00      | 268.00   



Table
3.Dry
conditions: Probability of exceeding three different Newmark
displacements as predicted by the four permanent displacement
approaches.

|Dry                                   | Miles and Ho (1999) | Jibson and others (1998) | Ambraseys and Menu (1988) | Yegian and others (1991)
|------------------------------------- | ------------------- | ------------------------ | ------------------------- | ------------------------
|2
                                cm  | 10%                 | 16%                      | 21%                       | 29%                     
|5
                                cm  | 4%                  | 3%                       | 13%                       | 19%                     
|10
                                cm | 2%                  | 1%                       | 5%                        | 14%                     



Table
4.Saturated
conditions: Probability of exceeding three different Newmark
displacements as predicted by the four permanent displacement
approaches.

|Saturated                             | Miles and Ho (1999) | Jibson and others (1998) | Ambraseys and Menu (1988) | Yegian and others (1991)
|------------------------------------- | ------------------- | ------------------------ | ------------------------- | ------------------------
|2
                                cm  | 28%                 | 40%                      | 36%                       | 41%                     
|5
                                cm  | 20%                 | 18%                      | 27%                       | 33%                     
|10
                                cm | 14%                 | 11%                      | 21%                       | 25%