Soil System Identification Using Earthquake Records
and Experimental Data
Mourad Zeghal
Department of Civil and Environmental Engineering
Rensselaer Polytechnic Institute
Troy, NY, 12180
Abstract
Strong-motion earthquake records constitute an invaluable source of knowledge on the actual dynamic behavior of geotechnical-systems. Centrifuge model tests provide meritorious
complementary information in view of the relative scarcity of case history records. This paper presents an overview of soil-system identification techniques used in constitutive model
development and calibration. Local shear stress-strain histories of sites, infinite slopes, and
simple embankments may be directly evaluated from downhole (vertical) array accelerations
using simple nonparametric identification techniques. A conceptually similar point-wise technique may be used to identify the local constitutive response of distributed multidimensional
soil-systems using the accelerations recorded by clusters (2-D or 3-D arrays) of closely spaced
instruments. Global system identification techniques are warranted for full-scale geotechnicalsystems equipped with sparse distributions of instruments installed along the boundaries. Soilsystem identification analyses are destined to experience significant developments over the
next few years in view of the drastic and continuous improvements in sensors, instrumentation, and computer technologies.
Introduction
Soil models have reached high levels of refinement and sophistication induced by drastic improvements in computer and testing technologies over the last decades (e.g., Prevost and Popescu 1996,
Zienkiewicz et al.1998). These models may not be fully calibrated solely on the basis of soilsample tests. Because of limitations in reproducing in-situ state of stress and boundary conditions,
there is consensus that these tests do not completely reflect the actual response of complex soilsystems, especially at large deformation and failure conditions. The predictive capabilities of soil
models under severe excitations remain limited as long as they have not been verified and calibrated
using realistic loading conditions. Earthquake case histories and centrifuge physical model tests
are invaluable sources of information about the actual behavior and mechanisms of soil-systems.
System identification and inverse problem techniques provide adequate tools for computer-aided
model development and calibration based on case history records and experimental data (Tarantola
1987, Woodbury 1999).
Historically, soil-systems were at first instrumented with accelerometers installed along their
surface and boundaries. Thereafter, vertical (downhole) seismic arrays have been used to monitor
1
the dynamic response of level sites with large lateral extent, infinite slopes, and some earth dams
(Elgamal et al.2001). These arrays provided valuable direct information on the local mechanisms
of one-dimensional vertical seismic wave propagation (e.g., Zeghal et al.1995). Identification and
modeling of complex full-scale soil-systems subjected to multidimensional dynamic excitations is
a significantly more difficult task, especially when the behavior of these systems is marked by the
development of localized response mechanisms (e.g., formation of shear bands). Normally, a measured or recorded response using surface and simple vertical instrument arrays provides enough
information to identify only global models that capture the main features of the dynamic response
of earth dams, soil-quay walls, and other complex geotechnical systems. The multidimensional response of a massive soil-system may be assessed locally using point-wise identification techniques
and accelerations recorded by clusters of closely spaced instruments. This paper presents a brief
overview of local and global identification techniques used in analyses of the constitutive behavior
of soil-systems.
Local Identifications
Vertical (downhole) accelerometer arrays are used to monitor the dynamic response of full-scale
sites, infinite slopes and embankments as well their centrifuge model counterparts. Non-parametric
local estimates of lateral shear and vertical normal strains and associated stresses may be directly
evaluated anywhere within the instrumented zone if the installed array of accelerometers extends
to the ground surface (Zeghal et al.1995). Local identification analyses of the constitutive behavior of multidimensional soil-systems may be conducted using dense instrument configurations, as
discussed below.
One-dimensional wave propagation conditions
A simple identification procedure was developed by Zeghal, Elgamal and co-workers (Zeghal and
Elgamal 1993, Zeghal et al.1995) to estimate local shear stress and strain histories of level sites and
infinite slopes directly from vertical (downhole) array accelerations. Using a shear beam model
to describe lateral site response, seismic shear stress may be evaluated at a number of locations
within instrumented soil layers as follows (Zeghal and Elgamal 1993, Zeghal et al.1995):
τi (t) = τi−1 (t) + ρi
üi−1 + üi
∆zi , τo = 0, i = 1, 2, 3, · · ·
2
(1)
in which subscript i refers to the ith accelerometer at level zi , üi = ü(zi ,t) is acceleration at level
zi , ρi is average mass density between levels zi−1 and zi , and ∆zi is spacing interval between accelerometers. The corresponding shear strains are given by:
µ
¶
∆zi
∆zi+1
1
(ui+1 − ui )
+ (ui − ui−1 )
, i = 1, 2, 3, ..
(2)
γi (t) =
∆zi + ∆zi+1
∆zi+1
∆zi
in which ui = u(zi ,t) is absolute displacement (evaluated through double time-integration of the
recorded acceleration history ü(zi ,t)). This technique was employed to evaluate seismic shear
stress-strain histories of Wildlife Refuge (Zeghal and Elgamal 1994), Lotung (Zeghal and Elgamal
1993, Zeghal et al. 1995), and Port Island (Elgamal et al.1996a) sites, as well as a number of soilsystem centrifuge models (Zeghal 1999). A shear-wedge idealization was employed by Zeghal and
2
End
Start
Nonparametric
Stress Estimates
Optimization
and
Model Update
Nonparametric
Strain Estimates
Constitutive
Model
Computed
Stresses
Recorded
Accelerations
Figure 1: Algorithm of local system identification analyses using vertical downhole array instruments
Abdel-ghaffar (2001) to identify the stress-strain histories of earth dams using the same technique.
These analyses revealed valuable information on the complex mechanisms of soil-system motion
amplification, liquefaction, and lateral spreading.
The evaluated non-parametric estimates of stresses and strains (Eqs. 1 and 2) may then be
used to locally calibrate models of the constitutive behavior of soil-systems using the algorithm
shown in Fig. 1. Fig. 2 shows a good agreement between the recorded accelerations at Lotung
and the prediction of a computational model that was calibrated using this algorithm (Elgamal et
al.1996b). This approach is obviously not feasible in analyses of a multidimensional response. A
more general local identification algorithm is presented below.
Multidimensional conditions
A new system identification technique was developed recently by Zeghal and Oskay (2001) to
analyze the local mechanisms of multidimensional soil-systems using the motion recorded by a
cluster of closely spaced accelerometers appropriately arranged in 2-D or 3-D configurations (depending on the dimensionality of the system response). The developed algorithm (Fig. 3) consists
of: (1) evaluation of strain tensor time histories using the recorded accelerations, (2) estimation of
the corresponding stress tensor utilizing a pre-selected class of constitutive models of soil response,
(3) computation of the accelerations associated with the estimated stress tensors using the equilibrium equations, and (4) evaluation and calibration of an optimal model of soil response based on a
minimization of the discrepancies between recorded and computed accelerations. This identification approach does not require solution of the associated boundary value problem or the availability
of recordings of boundary conditions. The proposed algorithm requires specific local instrument
array configurations which are expected to become widely used in centrifuge and 1-g shake table
model tests (and eventually in full-scale system instrumentation). Fig. 4 exhibits schematically
a range of quay wall-soil system conditions that may advantageously be analyzed using local arrays. A subset of these conditions was investigated at Rensselaer Polytechnic Institute based on
centrifuge model experimentation. Fig. 5 shows a close agreement between recorded accelerations
3
Lotung site, LSST 16
200
100
0
−100
(Surface, N10W)
(cm/sec/sec)
−200
200
100
0
−100
(6 m, N10W)
Acceleration
−200
200
100
0
−100
(11 m, N10W)
−200
200
100
0
−100
Computed
−200
0
10
(17 m, N10W)
Recorded
20
30
Time (sec)
40
50
60
Figure 2: Lotung site computational model predictions calibrated using non-parametric estimates
of shear stress and strain histories (Elgamal et al.1996b).
and computed model response at the central location of a cluster of 9 (3-by-3) 2-D accelerometers
installed behind the quay-wall structure of a centrifuge soil-system. The employed computational
model was calibrated using the accelerations recorded by this cluster of 9 instruments.
Global Identifications
Model identification and calibration for a full-scale distributed-parameter geotechnical system with
extended boundaries, such as an earth dam, is a complex enterprise. Local identification analyses
are commonly precluded for existing systems. Installing a multidimensional cluster of instruments
within the bulk of a massive soil-system represents a significant technical challenge and may compromise the system structural integrity. Sparse instrument configurations along the system surface
and boundary commonly do not provide enough information to fully develop a global model and
determine the mechanisms controlling the whole system response and associated parameters. Thus,
the corresponding identification problems are commonly indeterminate.
A priori information may be introduced to reduce or potentially remove this indeterminacy.
Zeghal and Abdel-Ghaffar (2001) advantageously formulated the system identification problem of
Long Valley earth dam using earthquake case history records as a Bayesian combination of a priori
and experimental information with theoretical knowledge (Fig. 6). The a posteriori measure of
4
Start
End
Recorded
Accelerations
Optimization
and
Model Update
Computed
Accelerations
Strains
Constitutive
Model
Computed
Stresses
Figure 3: Algorithm of local identification analyses of multidimensional soil-systems.
Quay wall
Compacted Soil
Stiff Cohesive Non−liquefiable Soil
Water interlayer
Loose Liquefied Sand
Very Stiff Non−liquefiable Soil
Acceleration [m/s2]
Acceleration [m/s2]
Figure 4: Schematic of a quay wall-soil system showing a range of local conditions that may
advantageously be analyzed using the developed local identification technique.
2
1
0
−1
−2 Lateral
2
Measured Accelerations
Computed Accelerations
1
0
−1
−2 Vertical
0
1
2
3
4
5
Time [sec]
6
7
8
9
10
Figure 5: Local identification of a soil-quay wall centrifuge model: acceleration time histories at
the central location of a 9 (3-by-3) cluster of 2-D instruments (Zeghal and Oskay 2001).
5
Joint MDFs
Marginal MDFs
A Priori-experimental Information
A Priori-experimental Information
d
d
f a (d,p)
f a (d)
f a (p)
p
Theoretical Information
d
Theoretical Information
d
f m (d,p)
f m (d,p)
p
p
A Posteriori Information
d
p
A Posteriori Information
d
f p (d,p)
f p (d)
f p (p)
p
p
Figure 6: Schematic description of the solution of a system identification problem as a combination
of information (Zeghal and Abdel-Ghaffar 2001).
density function ( f p (p) in Fig. 6) provides an updated state of knowledge on model parameters
that reflects all available information, and theoretically solves the problem. For complex soilsystems, the solution commonly reduces to evaluating a central estimator of the model parameters
(e.g., maximum likelihood) and an approximation to the covariance. Fig. 7 exhibits the recorded
and computed (a priori and optimal) accelerations for the center crest station of the Long Valley
dam (Zeghal 2001). The predictions of an optimal visco-elastoplastic model were found to be in
relative good agreements with the recorded upstream-downstream response.
Conclusions
This paper presented a overview of local and global soil-system identification analyses. For multidimensional system conditions, local identification techniques necessitate clusters (2-D or 3-D
arrays) of closely spaced instruments. Such techniques do not require the availability of recordings or measurements of boundary conditions, or?? the solution of the boundary value problem
associated with an observed system. Global identification analyses are warranted for full-scale
soil-systems equipped sparsely with instruments installed along their free surface and boundaries.
The fields of local and global geotechnical system identifications are destined to experience significant developments over the next few years in view of the drastic and continuous improvements in
6
Long Valley Earth Dam. Center Crest Station, UD Motion (Chan. 20). EQ. 6, May 27, 1980, 7:51 PDT
120
600 A priori EP model
A priori EP model
100
200
80
0
60
Fourier amplitude spectrum (cm/s)
400
Acceleration (cm/s2)
−200
−400
−600
600 Optimal VEP model
400
200
40
20
1200
Optimal VEP model
100
80
0
60
−200
40
−400
20
−600
0
2
4
6
8
10
Time (s)
EP:
VEP:
Recorded
Computed
Elasto−Plastic
Visco−Elasto−Plastic
0
0
2
4
6
Frequency (Hz)
8
10
Figure 7: Long Valley earth dam a priori and optimal (visco-elastoplastic) model predictions along
with the recorded response: upstream-downstream motions and Fourier transforms at the crest
center during a strong motion earthquake (Zeghal and Abdel-Ghaffar 2001).
sensor, instrumentation, and computer technologies.
Acknowledgements
This research was supported by the National Science Foundation, Grant No. CMS-9984754. This
support is gratefully acknowledged.
References
Arulanandan, K. and Scott, R. F., Eds. (1993). “Verification of Numerical Procedures for the
Analysis of Soil Liquefaction Problems,” Vol. 1, Balkema.
Elgamal, A.-W., Zeghal, M. and Parra, E. (1996a). “Liquefaction of an Artificial Island in Kobe,
Japan,” Journal of Geotechnical Engineering, ASCE, Vol. 122, No. 1.
Elgamal, A.-W., Zeghal, M., Parra, E., Gunturi, R., Tang, H.T., and Stepp, C.J. (1996b). “Identification and Modeling of Earthquake Ground Response I: Site Amplification,” Soil dynamics
and Earthquake Engineering, Vol. 15, No. 8, 499-522.
7
Elgamal, A.-W., Lai, T., Yang, Z., and He, L. (2001). “Dynamic Soil Properties, Seismic Downhole Arrays and Applications in Practice,” 4th International Conference on Recent Advances
in Geotechnical Earthquake Engineering and Soil Dynamics, S. Prakash, Ed., San Diego
California.
Prevost, J. H. and Popescu, R. (1996). “Constitutive Relations for Soil Materials,” Electronic
Journal of Geotechnical Engineering, Vol. 1.
Tarantola, A. (1987). Inverse Problem Theory: Methods for Data Fitting and Model Parameter
Estimation, Elsevier.
Woodbury, K. A., Ed. (1999). “Inverse Problems in Engineering: Theory and Practice,” Third
International Conference on Inverse Problems in Engineering, June 13-18, Port Ludlow,
Washington, The American Society of Mechanical Engineers, New York.
Zeghal, M. and Elgamal, A.-W. (1993). “Lotung Site: Downhole Seismic Data Analysis,” Report,
Department of Civil Engineering, Rensselaer Polytechnic Institute, Troy, New York.
Zeghal, M. and Elgamal, A.-W. (1994). “Analysis of Site Liquefaction Using Earthquake Records,”
Journal of Geotechnical Engineering, ASCE, Vol. 120, No. 6, 996-1017.
Zeghal, M., Elgamal, A.-W., Tang, H. T. and Stepp, J. C. (1995). “Lotung Downhole Seismic Array: Evaluation of Soil Nonlinear Properties,” Journal of Geotechnical Engineering, ASCE,
Vol. 121, No. 4, pp. 363-378.
Zeghal, M., Elgamal, A.-W. Zeng, X., and Arulmoli, K. (1999). “Mechanisms of Liquefaction
Response in Sand-Silt Dynamic Centrifuge Tests,” Soil Dynamics and Earthquake Engineering, Vol. 18, No. 1, 71-85.
Zeghal, M., and Abdel-Ghaffar, A. M. (2001). “Evaluation of the Nonlinear Seismic Response of
Earth Dams: I. Pattern Recognition,” submitted for Journal publication.
Zeghal, M., and Oskay, C. (2001). “Local System Identification Analyses of the Dynamic Response of Soil Systems,” submitted for Journal publication.
Zienkiewicz, O. C., Chan, A. H. C., Pastor, M., Schrefler, B. A., and Shiomi, T. (1998). Computational Geomechanics with Special Reference to Earthquake Engineering, John Wiley and
Sons, England.
8