SITE EFFECTS MODELING BY
HYBRID TECHNIQUE:
THE CASE STUDY OF SOFIA, BULGARIA
IVANKA PASKALEVA
PETIA DINEVA
CRISTINA LA MURA
GIULIANO F. PANZA
BULGARIAN ACADEMY OF SCIENCE
CENTRAL LABORATORY FOR SEISMIC MECHANICS
AND EARTHQUAKE ENGINEERING
BULGARIAN ACADEMY OF SCIENCE
UNIVERSITA’ DEGLI STUDI DI TRIESTE
DIPARTIMENTO DI SCIENZE DELLA TERRA
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
Main Topics
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HYBRID TOOL: a brief introduction;
the viscoelastic isomorphism of Bardet
model: advantages and implementation in
the hybrid technique;
simulation study: effect of the Bardet
model, application to Sofia, Bulgaria;
conclusions
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
Review….Hybrid Tools
Site Effect: difference in earthquake ground motion
between two nearby sites!
Lateral heterogeneities may give rise to complex wave patterns,
so high performance methods have to be developed for
simulating seismic wave propagation in complex media.
In hybrid computational schemes the numerical method is applied
in the laterally inhomogeneous part of the medium,whereas
the laterally homogeneous part is treated with analytical method.
Combination of MSM and BIEM
is the hybrid technique
used in this work.
27o CONVEGNO GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
Review…..MSM - BIEM…
It has the potential to investigate the combined effects
of different physical phenomena, like
• lateral inhomogeneity
• surface topography
• water saturation in soils
• seismic source properties
MSM is applied for numerical simulation from the source
position to the local region of interest, while the BIEM is
used inside the local multilayered geological region.
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
VISCOELASTIC ISOMORPHISM…
In order to describe the poroelastic properties of the layers,
the viscoelastic isomorphism of Bardet is used.
A two phase solid - fluid system (saturated system) is used
its main components are:
• dry rock (dry soil)
n = Vp/V is the porosity
V is the total volume of the solid
Vp is the pore volume
• solid grain
• fluid
bulk modulus and density
Kg
g
Kf
f
Kdry
dry =(1 - n)g
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
VISCOELASTIC ISOMORPHISM…
Elastic properties of the saturated system
density
shear modulus
sat = dry + nf = (1-n)g + n f
 = dry = sat =
governing equation of motion in the frequency domain are
describing the wave propagation in fluid saturated soils
Biot (1956)
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
VISCOELASTIC ISOMORPHISM…
Q and R are the Biot’s elastic constants for saturated soils
….BIEM has a limited usage in dynamic poroelasticity due
to the multiphase nature of the model……
an equivalent viscoelastic model is proposed (Bardet 1992)
saturated soil is considered
as a viscoelastic material
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
VISCOELASTIC ISOMORPHISM…
Bardet introduced the viscoelastic isomorphism by equating
Wave numbers in Biot’s
poroelastic model

Wave numbers in
viscoelastic model
from this operation an equivalence between the poroelastic
material and the linear Kelvin - Voigt viscoelastic material
is established
so a two phase poroelastic dynamic behavior is
approximated by the dynamic response of one-phase
viscoelastic material
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
SIMULATION STUDY…..
FORMULATION OF THE PROBLEM
Let us consider a finite local saturated geological region
imbedded in a vertical inhomogeneous half space where
a seismic source is buried
the non-parallel
layers in Ω are
water saturated
all soil layers in
Ωo are isotropic,
anelastic and
homogeneous
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
SIMULATION STUDY…..
The main aim is to obtain synthetic seismograms at sites
along the free surface of the region Ω.
TWO SUB-PROBLEMS
• external sub-problem: wave propagation from seismic
source to the boundary 
• internal sub-problem: wave propagation in the finite
local geological region Ω
The two problems are combined through the fulfillment of the
compatibility and equilibrium conditions at the boundary 
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
SIMULATION STUDY…..
2 and 3 are water saturated, 1 is not saturated,
points S’s are the sites where solutions are computed
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
SIMULATION STUDY…..
EARTHQUAKE SCENARIO
two earthquake scenarios have been used, they do differ
for the value of the magnitude M
for both
Scenario a) M= 3.7
strike angle 21o
dip angle
44o
rake angle 309o
source depth 12km
src/rec dist 20km
Scenario b) M= 6.5
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
SIMULATION STUDY…..
EFFECT OF THE BARDET MODEL
earthquake scenario a)
main peak decreases for
saturated soils
peaks are shifted to
lower frequencies
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
SIMULATION STUDY…..
EFFECT OF THE BARDET MODEL
earthquake scenario a)
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
SIMULATION STUDY…..
EFFECT OF THE BARDET MODEL
earthquake scenario a)
main peak decreases for
saturated soils
duration of the signal is
reduced in saturated soils
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
CASE STUDY: SOFIA
one station called
REDUTA from the
residential district
it is located in;
here there is the
Geo Milev Park
together with a
medical center, a
library and
one of the most
prestigious schools
of Sofia.
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
CASE STUDY: SOFIA
another called
MLADOST4 for
the same reason as
the former;
in this district the
Business Park
Sofia
has been
constructed and the
airport is not so far
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
CASE STUDY: SOFIA
The parametric study of site effects in two different water
saturated geological profiles, corresponding to two
different zones of the city, is made in
terms of acceleration response spectral ratio, i.e.
RSR =
RS from signals along the laterally varying section
RS from signals for the bedrock
the single - degree - of - freedom damped oscillator used
for the computation of the response spectra is with
5% damping
the earthquake scenario is b), so M = 6.5
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
CASE STUDY: SOFIA
REDUTA
dry soil
horizontal component
saturated soil
20
20
15
15
R
S 10
R
R
S 10
R
5
5
0
0
0
0.2
0.4
0.6
0.8
1
0
0.2
Period (sec)
Site S 1
S2
0.4
0.6
0.8
1
Period (sec)
S4
Site S1
S2
S4
vertical component
27
27
18
18
R
S
R
R
S
R
9
9
0
0
0 .2
0 .4
0 .6
Period (sec)
Site S1
S2
0 .8
1
0
0
S4
0.2
0.4
0.6
Period (sec)
Site S1
S2
S4
0.8
1
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
CASE STUDY: SOFIA
MLADOST4
dry soil
horizontal component
saturated soil
vertical component
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
CASE STUDY: SOFIA
different response for different sites: there are site effects
due to the mixed influence of lateral inhomogeneity and
saturation of soil
there is a shift of the peaks toward the higher periods for
saturated soils
the main peaks of saturated soils decreases with respect
to dry soils
the fluid acts as stiffener of the material: the pore pressure
induced by the seismic load resists the compression and
stiffens the rock
fluid acts as a viscous damping element: a diffusion process
dominated by viscous effects
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY
CONCLUSIONS
The simulation has been performed for the city of Sofia;
Soil mechanical properties and geotechnical parameters
are those more common in the central part of the city.
The hybrid MSM - BIEM technique, combined with the
viscoelastic isomorphism of Bardet, is applied for the
investigation of the site effects phenomena
due to several different physical properties like lateral
inhomogeneity and water saturation in soil.
The hybrid technique allows to study simultaneously
the combined effects, hence a better
estimation of the seismic risk is provided.
THANKS for the ATTENTION!!!
27o CONVEGNO NAZIONALE GRUPPO NAZIONALE di GEOFISICA della TERRA SOLIDA October 8, 2008 TRIESTE - ITALY