2D site response in alluvial basins by finite
difference-based numerical method
Cite as: AIP Conference Proceedings 2574, 020001 (2022); https://doi.org/10.1063/5.0106512
Published Online: 15 November 2022
Bilal Özaslan, Merve Akbaş and Recep İyisan
AIP Conference Proceedings 2574, 020001 (2022); https://doi.org/10.1063/5.0106512
© 2022 Author(s).
2574, 020001
2D Site Response in Alluvial Basins by Finite DifferenceBased Numerical Method
Bilal Özaslan a), Merve Akbaş, Recep İyisan
Istanbul Technical University, Faculty of Civil Engineering, 34469, Istanbul, Turkey
a)
Corresponding author: ozaslanb@itu.edu.tr
Abstract. The lateral irregularity of the soil media is typically formed by fault ruptures or topographic depressions filled
with sediments and this highly present geological formation is identified as a basin. On this type of project site, the
estimation of the surface ground motion of an earthquake is a complex problem in geotechnical earthquake engineering.
Contrary to the soil column assumption of the semi-infinite 1D soil model, the soil layers have both horizontal and
vertical discontinuities and change topographically and stratigraphically. Therefore, the question of how the soil response
would be shaped as a result of combinations of the effects of principal wave phenomena in the sedimentary basins,
surrounded by roughly circular or elliptical harder layers or the bedrock outcrops, is still a leak in the seismic code
provisions. In this study, basin conditions considering soil classes as soft clay (E) which defined by NEHRP 2020
provisions was investigated with different levels of bedrock inclination. Fully nonlinear time-domain analyses were
carried out on both 1D and 2D models of created basins by the Finite Difference-based numerical method. The results of
the nonlinear time-domain analyses were compared to clarify the effects of the basin edge inclination on the resultant
ground motions on the points located with equal intervals on the model surface. The acceleration response spectra of 2D
and 1D models were illustrated across the basin, and it is aimed to explain the dependence on the motion frequency and
the effect of the inclination angle of the basin edges to site response.
INTRODUCTION
The determination of an earthquake induced surface motion at a particular construction site depend on many
factors such as tectonics of the region, rupture mechanism, source distance, geological formations, soil conditions,
local surface topography and subsurface stratigraphy. Thus, the estimation of surface ground motion during
earthquakes and serving earthquake-resistant design are challenging issue in points of geotechnical and structural
earthquake engineering view. The difference of strong ground motion, which is influenced by both the periods of
seismic waves in input motion and the fundamental period of the soil half-space, is defined as amplification. The
strong motion is mostly amplified in terms of the amplitudes and periods of the waves in softer sediments because of
the impedance contrast between sediments and the underlying bedrock. Soil amplification is also associated with
several parameters such as incoming wave properties, soil properties under dynamic conditions, stratigraphy of the
investigated site and seismic bedrock depth. In recent studies, the change of the motion characteristics from bedrock
to the surface has been widely investigated by idealized 1D soil column of the semi-infinite soil space. However,
different to the simple assumption of the semi-infinite 1D soil model, the soil space has discontinuities on horizontal
and vertical directions. The discontinuity of soil media is naturally formed by fault or surface depressions filled with
alluvial and this geological formation is recognized as sedimentary basins which usually observed as surrounded by
rock outcrops.
To study the effect of seismic wave in basins with soft soil condition, Aki and Larner (1970) assessed motion on
the valley surface for plane SH waves [1]. Finite difference and finite element techniques have been performed to
study the effects of irregular layer interface by Smith (1975) [2]. Bard and Bouchon (1980) examined the formation
of surface waves and edge effects [3]. King and Tucker (1984) noted significant differences in surface peak
horizontal accelerations at the center and near the edges of the valleys [4]. Yamanaka (1989) has been studied in situ
World Multidisciplinary Civil Engineering-Architecture-Urban Planning Symposium (WMCAUS) 2021
AIP Conf. Proc. 2574, 020001-1–020001-10; https://doi.org/10.1063/5.0106512
Published by AIP Publishing. 978-0-7354-4266-5/$30.00
020001-1
investigation and numerical analysis to determine the propagation of the seismic waves within the deep sedimentary
layers of southwestern Kanto district, Japan [5]. Papageorgiou and Kim (1991) investigated the effect of bedrock
slope in the Caracas basin and Zhang and Papageorgiou (1996) in Marina basin, California [6,7]. Kawase (1996)
used the 2D model to analyze the basin edge effect in the Kobe basin with the Hyogoken Nanbu Earthquake 1995
[8]. Kamalian et al. (2006) and Graves et al. (1998) have been proposed that amplification increase is directly caused
by surface waves formed on the basin edge [9,10]. Bielak et al. (1999) estimated soil amplification and structural
damage together in a small valley in Kirovakan basin [11]. In relevant studies, Heymsfield (2000), Alvarez (2004),
Semblat et al. (2005), Iyisan and Hasal (2011), Iyisan and Khanbabazadeh (2013), Khanbabazadeh et al. (2016),
Riga et al. (2016), Makra and Chávez-García (2016), Yniesta et al. (2017), Chávez-García FJ et al. (2018), Cipta et
al. (2018), Moczo et al. (2018), Zhu et al. (2018), Saenz et al. (2019) the results obtained in the two-dimensional
numerical analyses have contributed to the basin effect phenomena [12-25]. In the recent studies, Hasal et al. (2018),
Khanbabazadeh et al. (2019), Ozaslan et al. (2020), it has been investigated by nonlinear dynamic analyses in
idealized 2D models of Dinar and Düzce basins [26-28]. According to the studies carried out in the last decade, it
has been recognized that the inclined layer interfaces affect the Love surface waves formed by the SH waves and the
Rayleigh waves formed by P and SV waves on the surface. The results have demonstrated that the resulting soil
amplifications cause stronger surface waves and longer shakings in the field.
As a consequence, particularly in alluvial basins, the inclination of the rock outcrop on the edge of the basin has
a significant effect that cannot be ignored on the site response. In this study, the basin effect was investigated under
changing bedrock edge slope in site class E defined by National Earthquake Hazards Reduction Program (NEHRP)
seismic code. One and two-dimensional dynamic analysis for the basins given by comparing the response spectra
obtained according to the period (T) and the location relative to the dimensionless distance from the basin edge
(x/L).
THE METHODOLOGY OF THE NONLINEAR NUMERICAL ANALYSIS
There are more than a few numerical techniques but finite element method, finite difference method, boundary
element and hybrid methods are the most preferred analysis methods. The performed numeric method must provide
to research of the responses in time and space by using hysteretic type constitutive models for soils. Therefore, the
motion from the bedrock can be transferred to the surface accurately throughout the defined soil model by fully
nonlinear dynamic analysis considering geometrical differences and advanced dynamic boundary conditions. In the
site response analyses, Fast Lagrangian Analysis of Continua 3D (FLAC3D) software which gives results in a
shorter time by calculating with the explicit finite difference method, has been used for performed 2D and 1D
analysis. In this type of analysis, the minimum dimensions of the zone in the discriminated volume and the smallest
time steps for each calculation need to ensure propagation of the highest frequency wave transmitted in the model.
Thus, this type of analysis requires a comprehensive knowledge of numerical methods and the constitutive models
of soils under dynamic loadings.
SPECIFICATION OF THE BASIN MATERIALS, MODEL BOUNDARY CONDITION
AND INPUT MOTION
In models with complex site geometry, seismic wave refraction, reflection, focusing and shifting cause the
surface response change for each location. In 2D site response analysis, the slope of the interface between the
bedrock and the overlying soft soil layers were assumed to be tanα = 1/1, 1/2, and 1/4. Nonlinear analyses were
performed on hypothetical models defined as site class E with mean shear wave velocity values (Vs30) less than 180
m/s for surface layers up to 30 m depth. The width (2L) of the studied symmetric basins is 1000 m and the depth (H)
is 100 m. Fig. 1 dimensions of the models used in the study.
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0
α
Vs1
γ1
z
z/ 0.2
L
Site class E
L
Vs2
γ2
0.4
-1.0
H
Bedrock
0
x/L
x
1.0
FIGURE 1. The model dimensions of basins with different edge slopes.
The viscous boundaries were used at the bottom of the models and given in Fig. 2 (b). The
nonreflecting Free field boundaries were applied on the lateral boundaries of the model in
continuum finite difference scheme by coupling the main grid to the free-field grid with viscous
dashpots. The assigned dashpots produce viscous normal and shear stresses tractions on the
model boundaries. The equations of the produced tractions were given by Equation 1-4.
𝑡𝑡𝑛𝑛 = −𝜌𝜌 𝐶𝐶𝑝𝑝 𝑣𝑣𝑛𝑛
(1)
(2)
𝑡𝑡𝑠𝑠 = −𝜌𝜌 𝐶𝐶𝑠𝑠 𝑣𝑣𝑠𝑠
Where, tn, ts normal and shear stresses traction, ρ is the mass density, Cp and Cs are the pressure (P) and shear
(S) wave velocities, vn and vs are the normal and shear components of velocity at the quiet boundary.
(3)
𝐹𝐹𝑥𝑥 = −𝜌𝜌 𝐶𝐶𝑝𝑝 �𝑣𝑣𝑥𝑥𝑚𝑚 −𝑣𝑣𝑥𝑥𝑓𝑓𝑓𝑓 �𝐴𝐴 + 𝐹𝐹𝑥𝑥𝑓𝑓𝑓𝑓
(4)
𝐹𝐹𝑦𝑦 = −𝜌𝜌 𝐶𝐶𝑠𝑠 �𝑣𝑣𝑦𝑦𝑚𝑚 − 𝑣𝑣𝑦𝑦𝑓𝑓𝑓𝑓 � 𝐴𝐴 + 𝐹𝐹𝑦𝑦𝑓𝑓𝑓𝑓
Where, Fx, Fy, are tractions of the free-field boundary, vxm, vym are x, y velocity of gridpoint in main grid at side
boundary. vxff, vyff are x, y velocity of gridpoint in side free field, A is the area of influence of free-field gridpoint.
Fxff, Fyff are free-field gridpoint force with contributions from the xx, xy stresses of the free-field zones around a
gridpoint [29].
(a
)
(b)
FIGURE 2. Shear modulus properties of the soil and bedrock sublayers
The mechanic properties of the soil and bedrock materials have been defined for both small and large strain
conditions. When the dynamic loading is applied to the materials the defined Mohr-Coulomb model present the
plastic deformations at high strain levels, while the hysteretic Ishibashi and Zhang (1993) model generates the at
small strain levels. This method produces elastoplastic nonlinearity under shear and compressional wave
propagation by analyzing strain-dependent nonlinear constitutive rules and yielding criteria. The shear wave velocity
(Vs), dynamic shear modules (G), volumetric bulk modules (K), mean shear wave velocities of layers from surface
to 30 m depth (Vs30), poisson ratios (ν), unit weights (γ) and shear strength parameters of soil (c, φ) have been
presented in Tab. 1. The shear modulus properties of the soil and bedrock were defined incrementally by sublayers
in accordance with the geological load distribution in soil nature in Fig. 2 (a).
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TABLE 1. Material properties of the soil layers and bedrock
#
Vs (m/s)
G (MPa)
K (MPa)
Vs30 (m/s)
ν
γ (kN/m3)
c (kPa)
φ (°)
Site class
E
150-550
35-550
130-1180
170
0.320.38
16-18
60-80
5
Bedrock
750-1200
1200-3000
2000-4800
-
0.25
22
-
-
In site response analysis, it is aimed to determine a single design spectrum that gives the average of the response
spectra calculated by running a large number of earthquakes. On the other hand, in this study, the effect of bedrock
slope of the basin has been investigated by a single earthquake to illustrate the differences between 1D and 2D
models for concerned period on each surface point. The baseline corrected and 25 Hz low-pass filtered real
accelerogram recorded from rock outcrop have been used for earthquake excitation. The acceleration time-history
and spectrum of the input motion are given in Fig. 3.
FIGURE 3. The acceleration time-history and spectrum of the input motion
RESULTS AND DISCUSSIONS
The idealized 2D and 1D models of alluvial basins with different bedrock slope are subjected to a strong ground
motion. The earthquake is applied to the basins at the bottom of seismic bedrock as SV plane waves. The seismic
waves propagating from the bedrock to the surface are affected by the inclined transition region of soft soil and rigid
bedrock on basin edges. The diffracted and transformed waves regenerate the surface motions by focusing on the
center or the edge of the basin. In the result evaluation, in 2D models, artificial seismographs were located on the
basin surface with 50 m interval to record resultant time histories and the response data from 1D soil model were
collected for each point from the top of the defined columns. In the nonlinear site-specific numeric analyses, the
response spectra of basins in soil class E defined at different edge slopes were examined, and the differences in
spectral accelerations in each period depending on the considered location of 1D and 2D analysis results are
presented in Fig. 4 to Fig. 9.
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FIGURE 4. 2D and 1D spectral acceleration of the basin edge slope 1/1
FIGURE 5. The ratio of 2D and 1D response spectrums across the basin with 1/1 edge slope
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FIGURE 6. 2D and 1D spectral acceleration of the basin edge slope 1/2
FIGURE 7. The ratio of 2D and 1D response spectrums across the basin with 1/2 edge slope
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FIGURE 8. 2D and 1D spectral acceleration of the basin edge slope 1/4
FIGURE 9. The ratio of 2D and 1D response spectrums across the basin with 1/4 edge slope
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In Fig. 4, it is seen that 2D response spectra reach up to 5 g at different points on the basin surface in a period of
0.2 s under the effect of high edge slope, but in 1D analyses it reaches 4 g at the basin edge between -0.9 and -1.0
positions. The 2D behavior is similar with decreasing slope, in Fig. 5 and Fig. 6 for a period of 0.2 s. In the 0.4 s
period, it is clearly seen that the maximum value accumulates in a region at the position x/L = -0.6 at the basin edge,
and in the period of 0.6 s, this region approaches the center and decreases to 4.5 g.
In the model with 1/2 edge slope, the maximum response spectrum was 4.5 g in the 0.4 s period increased in 0.6
s period and reached 5.5 g, and shifted to the x/L = -0.2 region. It is clearly seen in Fig. 8 that the greatest spectral
acceleration occurs in the center in the period of 0.6 s in the basin with 1/4 edge slope. In higher periods, the
maximum spectral acceleration value was measured at the center of the basin with 1/1 edge slope and at the position
x/L = -0.6. At this point, when the analysis results are examined in the same period, it is seen that the ratio of 2D/1D
reaches to 1.5-1.8. In the 1 s period, it is observed that the maximum value approaches 6 g and in the 1D analysis,
the maximum acceleration reaches up to 4.3 g spectral acceleration in 1 s period. While the period is 1.2, 1D and 2D
analysis results are similar across the basin. It is given in Fig. 6 that in the basin with an edge slope of 1/2, the
maximum values that similar to the 1/1 type basin because of the edge effect in high periods shift towards the basin
center.
Finally, in the basin with 1/4 edge slope, 2D spectral accelerations with a value of 4.5 g at the point x/L=-0.4 on
the sloping region for a period of 0.8 s, do not exceed 4 g in 1D analysis. In Fig. 8, 1D and 2D spectral accelerations,
which take similar values in 1 s period, increase up to 4 g in 2D analyses in the period of 1.2 s, while 1D analyses
remain at 3 g. In addition, spectral accelerations measured at each point on the surface of basins with different edge
slopes in all periods were proportioned and their changes are given in Fig. 5, Fig. 7 and Fig. 9.
CONCLUSIONS
Building earthquake-resistant structures on the living areas are one of the main purposes of civil engineering.
The prediction of the hazards on all living facilities has always been crucial in terms of engineering to avoid loss of
lives by reducing the destructive effect of earthquakes. Assessment a response spectrum is the main phenomenon in
design process of new buildings. In this study, the effect of basin geometry and slope of the bedrock on the sitespecific spectral acceleration has been identified. The results of 1D dynamic analysis have been compared with the
2D dynamic analysis. Basin models with 1/1, 1/2, 1/4 outcrop inclinations have been investigated. As a result, in 2D
analyses, it is seen that the aggravation caused by the basin effect reaches up to 2 and the 1D analysis results are
smaller than 2D analyses in almost all periods. Further studies performing numerical methods to understand
changing soil amplification depending on the features of the basin, and to make identification of the regions where
the edge effects occur due to geometric properties, will contribute to the elimination of the uncertainties related to
the earthquake damages and subsequent research.
ACKNOWLEDGMENTS
The authors declare that they have no known competing financial interests or personal relationships
that could have appeared to influence the work reported in this paper.
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