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methods_for_assessing_the_stability_of_slopes_during_earthquakes_nees.pdf

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evaluation_of_earthquake_induced_landslides__chapter_2_.pdf.pdf

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1- Prof. Jonathon Bray – Simplified Seismic Slope Displacement Procedures

Empirical Predictive Models for Earthquake-Induced Sliding

Displacements of Slopes

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Gokhan Saygili1 and Ellen M. Rathje, M.ASCE2

Abstract: Earthquake-induced sliding displacement is the parameter most often used to assess the seismic stability of slopes. The

expected displacement can be predicted as a function of the characteristics of the slope 共yield acceleration兲 and the ground motion 共e.g.,

peak ground acceleration兲, yet there is significant aleatory variability associated with the displacement prediction. Using multiple ground

motion parameters to characterize the earthquake shaking can significantly reduce the variability in the prediction. Empirical predictive

models for rigid block sliding displacements are developed using displacements calculated from over 2,000 acceleration–time histories

and four values of yield acceleration. These empirical models consider various single ground motion parameters and vectors of ground

motion parameters to predict the sliding displacement, with the goal of minimizing the standard deviation of the displacement prediction.

The combination of peak ground acceleration and peak ground velocity is the two parameter vector that results in the smallest standard

deviation in the displacement prediction, whereas the three parameter combination of peak ground acceleration, peak ground velocity, and

Arias intensity further reduces the standard deviation. The developed displacement predictive models can be used in probabilistic seismic

hazard analysis for sliding displacement or used as predictive tools for deterministic earthquake scenarios.

DOI: 10.1061/共ASCE兲1090-0241共2008兲134:6共790兲

CE Database subject headings: Earthquakes; Landslide; Slope stability; Probability; Seismic effects.

Introduction

The seismic performance of slopes and earth structures is often

assessed by calculating the permanent, downslope sliding displacement expected during earthquake shaking. Newmark 共1965兲

first proposed a rigid sliding block procedure, and this procedure

is still the basis of many analytical techniques used to evaluate the

stability of slopes during earthquakes. Newmark 共1965兲 realized

that accelerations generated by earthquake shaking could impart a

destabilizing force sufficient to temporarily reduce the factor of

safety of a slope below 1, leading to sliding episodes and the

accumulation of permanent, downslope sliding displacement. The

original Newmark procedure models the sliding mass as a rigid

block and utilizes two parameters: the yield acceleration 共ky, the

acceleration in units of g that initiates sliding for the slope兲 and

the acceleration–time history of the rigid foundation beneath the

sliding mass. A sliding episode begins when the acceleration exceeds ky and continues until the velocity of the sliding block and

foundation again coincide. The relative velocity between the rigid

block and its foundation is integrated to calculate the relative

1

Graduate Research Assistant, Dept. of Civil, Architectural, and

Environmental Engineering, Univ. of Texas, Austin, TX 78712. E-mail:

gokhansaygili@mail.utexas.edu

2

J. Neils Thompson Associate Professor, Dept. of Civil, Architectural,

and Environmental Engineering, Univ. of Texas, Austin, TX 78712.

E-mail: e.rathje@mail.utexas.edu

Note. Discussion open until November 1, 2008. Separate discussions

must be submitted for individual papers. To extend the closing date by

one month, a written request must be filed with the ASCE Managing

Editor. The manuscript for this paper was submitted for review and possible publication on May 15, 2007; approved on October 4, 2007. This

paper is part of the Journal of Geotechnical and Geoenvironmental

Engineering, Vol. 134, No. 6, June 1, 2008. ©ASCE, ISSN 1090-0241/

2008/6-790–803/$25.00.

sliding displacement for each sliding episode and the sum of the

displacements for each sliding episode represents the cumulative

sliding displacement 共Fig. 1兲.

The original rigid sliding block procedure is applicable to thin,

veneer slope failures. This failure mode is common in natural

slopes 共Keefer 1984兲, whereas deeper sliding surfaces are more

common in engineered earth structures 共although shallow failure

surfaces can also occur in engineered slopes兲. The sliding block

displacement methodology has been extended to account for the

deformable response of deeper sliding masses in earth structures

共e.g., Seed and Martin 1966; Makdisi and Seed 1978; Bray and

Rathje 1998兲, and to account for the coupled interaction between

sliding and dynamic responses 共Rathje and Bray 1999, 2000兲.

Nonetheless, for natural slopes, rigid sliding block analysis is the

most common analytical procedure used to predict the potential

for earthquake-induced landslides and will be the focus of this

work.

In practice, the expected permanent displacement for a slope is

often assessed by either 共1兲 selecting a suite of earthquake ground

motions appropriate for the design event, computing the sliding

displacement for each motion using the yield acceleration of the

slope, and computing the median and standard deviation of the

computed displacements, or 共2兲 using design charts and equations

that predict sliding displacement based on various ground motion

parameters and the yield acceleration. Although these approaches

attempt to deal with the variabilities inherent in earthquake engineering, they do not rigorously account for the variability in

earthquake ground motions or the variability in the predicted sliding displacement.

Alternatively, following the context of performance-based

earthquake engineering, seismically induced permanent sliding

displacement can be considered an engineering demand parameter

that describes the performance of slopes. A probabilistic assessment of the sliding displacement 共D兲 can be computed, with the

790 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / JUNE 2008

J. Geotech. Geoenviron. Eng., 2008, 134(6): 790-803

parameters that includes multiple characteristics of the ground

motion 共Bazzurro and Cornell 2002; Baker and Cornell 2005兲

D共x兲 =

兺z 兺y

i

j

⫻P关兩D ⬎ x兩GM1 = zi,GM2 = y j兴P关GM1 = zi,GM2 = y j兴

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共2兲

Here, the sliding displacement is conditioned on two ground

motion parameters, GM1 and GM2, and the joint probability of

occurrence of the two ground motion levels GM1 = zi and

GM2 = y j, P关GM1 = zi , GM2 = y j兴. Similar to the scalar approach, a

predictive model for displacement as a function of GM1 and

GM2 is required, along with the standard deviation in the prediction. However, the joint occurrence of GM1 and GM2 cannot be

derived from traditional PSHA hazard curves, and thus a more

complex approach is required 共Bazzurro and Cornell 2002兲.

Toward the development of sliding displacement hazard

curves, this paper describes rigid block displacement models appropriate for scalar and vector PSHA. The implementation of

these models in scalar and vector PSHA is discussed in Rathje

and Saygili 共2008兲.

Previous Work

Fig. 1. Acceleration–time history, sliding velocity–time history, and

sliding displacement–time history for a rigid sliding block and

ky = 0.1

result being a displacement hazard curve that describes the annual

rate of exceedance 共兲 as a function of displacement levels. The

use of a displacement hazard curve allows for a more rational

assessment of the displacement hazard at a site because it considers the probability that different performance levels are exceeded.

The mean annual rate of exceedance of the sliding displacement conditioned on a single ground motion parameter 共GM兲 is

defined as

D共x兲 =

兺z P关兩D ⬎ x兩GM = zi兴P关GM = zi兴

共1兲

i

where D⫽mean annual rate of exceedance of a sliding displacement level of x, P关D ⬎ x 兩 GM= zi兴 represents the probability the

displacement level x is exceeded when the ground motion level is

equal to zi; and P关GM= zi兴⫽probability of occurrence of ground

motion level zi. The term P关D ⬎ x 兩 GM= zi兴 is computed from a

predictive model for displacement as a function of the GM and

slope parameters, along with the aleatory variability 共standard deviation兲 in the prediction. The probability of occurrence for the

ground motion is derived from the derivative of the ground motion hazard curve 共GM兲. This derivative is also known as the

mean rate density of the ground motion, MRDGM共z兲 共Bazzurro

and Cornell 2002兲. Essentially, Eq. 共1兲 calculates the annual frequency of exceeding a given value of displacement by combining

the evaluation of the seismic hazard in terms of the ground motion parameter with the evaluation of sliding displacement conditioned on the value of the ground motion parameter.

Eq. 共1兲 is only applicable for a single ground motion parameter

and thus is considered scalar probabilistic seismic hazard assessment 共PSHA兲, but it can be extended to a vector of ground motion

Many researchers have proposed models that predict rigid block

sliding displacement as a function of ground motion parameters

共e.g., peak ground acceleration, Arias intensity兲 and site/slope parameters 共ky, site period兲. Newmark 共1965兲 computed rigid block

displacements for four earthquake motions and showed that displacement was a function of ky, peak ground acceleration 共PGA兲,

and peak ground velocity 共PGV兲. Franklin and Chang 共1977兲,

Ambraseys and Menu 共1988兲, Yegian et al. 共1991兲, and Ambraseys and Srbulov 共1994兲 developed charts and/or predictive equations for rigid sliding block displacements using different ground

motion data sets. However, these models were developed based

on somewhat limited data sets and the resulting predictive equations displayed very large variability 共ln ⬎ 1.0兲.

Recent research has used larger ground motion data sets to

develop displacement predictive models and developed better estimates of the variability 共ln兲 in the predictions. WatsonLamprey and Abrahamson 共2006兲 developed a model for rigid

block displacement using a large data set consisting of 6,158 recordings scaled with seven different scale factors and computed

for three values of yield acceleration. Their displacement model is

a function of various parameters including PGA, spectral acceleration at a period of 1 s 共SaT=1 s兲, root mean square acceleration

共ARMS兲, ky, and the duration for which the acceleration–time history is greater than the yield acceleration 共Durky兲. However, a

standard deviation for the predictive model was not presented,

although this information was available for preliminary versions

of the model and ranged from 0.3 to 0.7 in natural log space 共N.

Abrahamson, personal communication, 2005兲.

Jibson 共2007兲 developed predictive models for rigid block displacements using 2,270 strong motion recordings from 30 earthquakes. A total of 875 values of calculated displacement, evenly

distributed between four values of ky, were used to develop the

predictive models. Models were developed as a function of

ky / PGA 共called the critical acceleration ratio兲, ky / PGA and earthquake magnitude 共M兲, ky and Arias intensity 共Ia兲, and ky / PGA

and Ia. The standard deviations 共ln兲 for each of their proposed

models is close to 1.0 关reported as log = 0.5 in Jibson 共2007兲兴.

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / JUNE 2008 / 791

J. Geotech. Geoenviron. Eng., 2008, 134(6): 790-803

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Bray and Travasarou 共2007兲 presented a predictive relationship

for earthquake-induced displacements of rigid and deformable

slopes. Displacements were calculated using the equivalent-linear,

fully coupled, stick-slip sliding model of Rathje and Bray 共1999,

2000兲. 688 earthquake records 共2 orthogonal components per

record兲 obtained from 41 earthquakes were used to compute displacements for ten values of ky and eight site geometries 共i.e.,

fundamental site periods, Ts兲. Displacements for the two components of orthogonal motion were averaged and values less than

1 cm were set equal to zero because they were assumed to be of

no engineering significance. The model input parameters include

ky, the initial fundamental period of the sliding mass 共Ts兲, the

magnitude of the earthquake 共M w兲, and the spectral acceleration

at a degraded period equal to 1.5Ts, called Sa共1.5Ts兲. When considering shallow, rigid sliding surfaces, Sa共1.5Ts兲 is taken as PGA

and Ts = 0. The standard deviation 共ln兲 for the predictive model is

0.66.

Fig. 2 presents a comparison of several current models

共Watson-Lamprey and Abrahamson 2006; Bray and Travasarou

2007, and the Jibson 2007 ky / PGA model兲 for a shallow, rigid

sliding mass, a deterministic earthquake scenario of M w = 7 and

R = 5 km, and rock site conditions 共Vs30 = 760 m / s兲. The predicted

ground motion parameters for this scenario are listed in Fig. 2.

The values of PGA and SaT=1 s are from Boore and Atkinson

共2007兲, Ia is from Travasarou et al. 共2003兲, and Tm is from Rathje

et al. 共2004兲. Note that Jibson 共2007兲 and Bray and Travasarou

共2007兲 each use only one ground motion parameter 共PGA兲,

whereas Watson-Lamprey and Abrahamson 共2006兲 use four

parameters 共PGA, ARMS, SaT=1 s, and Durky兲. The Bray and

Travasarou 共2007兲 model predicts the largest displacement, the

Watson-Lamprey and Abrahamson 共2006兲 model predicts the

smallest, and the Jibson 共2007兲 ky / PGA model falls in between.

The difference between the Bray and Travasarou 共2007兲 and Jibson 共2007兲 models can be attributed to the fact that the Jibson

共2007兲 ky / PGA model only uses the ky / PGA ratio 共without a term

representing the absolute value of PGA兲 and thus cannot distinguish the effect of large PGA intensities on displacements. The

Bray and Travasarou 共2007兲 model does not predict any displacement for ky ⬎ 0.17 because at these values of ky the median displacement is less than 1 cm and their model assumes that D

⬍ 1 cm can be considered equal to zero. The smaller values from

Watson-Lamprey and Abrahamson 共2006兲 are due to the supplementary information provided by the additional ground motion

parameters, particularly the parameter Durky. The ⫾1 standard

deviation displacements for the Jibson 共2007兲 and Bray and

Travasarou 共2007兲 models are shown in Fig. 2共b兲. Generally, the

Bray and Travasarou 共2007兲 model displays less variability.

Of the current models, the Jibson 共2007兲 and Bray and

Travasarou 共2007兲 models are the most appropriate for PSHA

because they were developed using large data sets and rigorous

regression techniques, and they provide estimates of the ln of the

displacement prediction. Yet, the Jibson 共2007兲 model has significant aleatory variability 共ln兲 such that a large range of displacements is predicted for the given ground motion and site/slope

parameters. The ln for the Bray and Travasarou 共2007兲 model is

smaller than for Jibson 共2007兲; however, it does not take advantage of multiple ground motion parameters to predict the displacement and further reduce ln. The goal of this study is to develop

rigid block displacement predictive equations that utilize multiple

ground motion parameters in an effort to reduce the aleatory variability 共ln兲. These displacement predictive equations can be used

to develop hazard curves for sliding displacement using either the

scalar or vector approach.

Fig. 2. Comparison of predictive models for sliding displacement for

a deterministic scenario of M w = 7 and R = 5 km: 共a兲 median

predictions; 共b兲 ⫾ predictions

Framework for Model Development

Rigid sliding block displacements were computed using the rigid

sliding block programs developed by Jibson and Jibson 共2003,

Personal communications 2006兲. The computed displacement values were then used to develop predictive relationships for displacement as a function of ky and different combinations of

ground motion parameters, with the goal of identifying the com-

792 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING © ASCE / JUNE 2008

J. Geotech. Geoenviron. Eng., 2008, 134(6): 790-803

bination共s兲 of ground motion parameters that produce the smallest

variability in the prediction of sliding displacement. The developed displacement models can be used to compute hazard curves

for earthquake-induced permanent displacement, can be used as

predictive tools for deterministic earthquake scenarios, or can be

used to rapidly predict the likelihood of earthquake-induced landslides after an earthquake using recorded ground motions.

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Ground Motion Database

Variability in the expected ground motion is the biggest contributor to the variability in the displacement prediction; thus, using a

large, high-quality data set of strong motion records is essential to

developing a robust displacement model. Currently the number of

available records is considerable and one significant data set is

readily available from the Next Generation Attenuation 共NGA兲

strong motion database of the Pacific Earthquake Engineering Research Center 具http://peer.berkeley.edu/nga典.

The initial data set included motions from earthquakes M w

ranging from 5 to 7.9 and distances from 0.1 to 100 km. Motions

recorded at soft soil sites, on the crest or abutments of dams,

underground, not at the ground floor of a building, or in buildings

larger than four stories were removed from the database. Additionally, motions with high-pass filter corner frequencies larger

than 0.25 Hz or low-pass filter corner frequencies less than 10 Hz

were removed. The resulting data set included 2,383 motions.

Rigid sliding block displacements were computed for ky values of

0.05, 0.1, 0.2, and 0.3 g, which encompasses typical values for

earth slopes. For each motion, displacements were calculated for

positive and negative polarities, with the largest displacement

used for the model development. Displacements computed from

orthogonal components recorded at the same station during the

same earthquake were treated as separate data points for the

model.

Approximately 25% of the initial ground motion data set had

PGA values of less than 0.05 g, and thus these motions do not

predict any displacement for the ky values used. To further populate the database at larger values of PGA, displacements were also

calculated for each motion scaled by factors of 2.0 and 3.0. To

ensure that unreasonable PGA values were not used when scaling

the motions, the motions were capped at PGA= 1.0 g. However,

regressions were also performed using motions up to PGA= 2.0 g,

and similar results were obtained. The final displacement data set

when capping PGA= 1.0 g included approximately 14,000 nonzero displacements. Only these nonzero displacements were used

in the regression analysis. The distribution of records in the final

ground motion data set in terms of earthquake magnitude, closest

distance, and various ground motion parameters is given in Fig. 3.

Ground Motion Parameter Selection

The sliding displacement of earth slopes is a function of various

features of the expected ground motion such as intensity, f …

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