Gonzales, C. et al.

Paper:

Analysis of Topographic Effects in Dynamic Responseof a Typical Rocky Populated Slope in Lima, Peru
Carlos Gonzales∗ , Shoichi Nakai∗ , Toru Sekiguchi∗ , Diana Calderon∗∗ ,Zenon Aguilar∗∗ , and Fernando Lazares∗∗∗ Department of Urban Environment Systems, Chiba University

1-33 Yayoi-cho, Inage-ku, Chiba 268-8522, Japan
E-mail: gonzales@chiba-u.jp∗∗ Japan Peru Center for Earthquake Engineering and Disaster Mitigation (CISMID),
Faculty of Civil Engineering, National University of Engineering, Lima, Peru
[Received June 30, 2014; accepted September 22, 2014]

A currently populated slope in the northeast part ofthe city of Lima was selected as the target area of thisstudy, with the aim of analyzing the influence of topography on its seismic response. A finite element
model was constructed using soil information obtainedby microtremor array measurements conducted in flatand sloping areas, and solved for plain strain conditions in the time domain using an input motion developed for the most critical slip model of a simulation for
megathrust earthquakes. Results showed that for thistypical rocky slope, topographic effects do not have asignificant influence on its seismic response, except forareas close to the foot of the slope where, even if soil
vibration is restricted, an amplification of the seismic
motion is still expected for short period structures.
Keywords: populated slope, microtremor arrays, finite
element model, topographic effects

1. Introduction
In the last 50 years, Lima, the capital of Peru, has experienced a complex urbanization process in which people
from different provinces chose to migrate to the capital
looking for a better quality of life. Therefore, these populations relocated not only to areas in the valley of Lima,but also the deserted rocky foothills close to the historicalcenter, resulting in the establishment of new districts withno urban planning policy [1].
The main concern for these new districts is that, inmany cases, they are located on steep slopes where little is known about their seismic response to earthquakes.
The majority of these locations were populated in the late1970s, after the last big earthquake struck Lima (October 3, 1974, Mw = 8.1), so an analysis of their behavior
under strong seismic motions is critical.
To accomplish this objective, a rocky populated slope,
located in the northeast part of Lima, was analyzed. In
the first stage of this research [2], the dynamic propertiesof the soil along the slope were estimated, and three seis-946

mometers were installed to record seismic events simultaneously: two in the flat area and one about 25 m higher
up the slope. The comparison of their respective Fourier
spectra, recorded for low magnitude earthquakes, did notshow a significant change in the response. Therefore, inthe second stage of this study, the decision was made to
develop a finite element model of the slope for the caseof a megathrust earthquake in Lima. The methodology
and analysis considerations for the generated model are
discussed in detail in the following sections.

2. Area of Study
For the present work, a typical rocky populated slope
in the south of the district of Independencia was chosen
as the target area (Fig. 1a). In general, the city of Lima
is built on the alluvial fan formed by the Chillon, Rimac,
and Lurin rivers during the Quaternary [3] and the soil in
Independencia consists primarily of conglomerate. In addition, due to the proximity of the target slope to the Andean foothills, stiff materials are expected at low depths,
and rocky outcroppings, mainly consisting of sandstoneand quartzite from the Marcavilca and Herradura geological formations, are evident in upper areas [4].

3. Microtremor Campaign
In order to estimate the dynamic properties of the soil
substructure for the target slope, seven microtremor array measurements were conducted along a line [2] that
included both the flat and the sloping parts of the foothill(line A-A ), with P denoting arrays on the flat area, and S
those on the sloping area (Fig. 1b). For the computationof reliable dispersion curves, several surface wave methods were applied to the recorded data, and their inversion
was performed by the optimization method known as the
Genetic Algorithms [5]. Due to the non-uniqueness of thesolution, the inversion analysis was conducted five times
for each profile (black lines in Fig. 1c).
From the estimated shear-wave velocity profiles along

Journal of Disaster Research Vol.9 No.6, 2014

Analysis of Topographic Effects in Dynamic Response ofa Typical Rocky Populated Slope in Lima, Peru

Fig. 1. (a) Elevation map of the city of Lima and Independencia district (red line). (b) Location of the microtremor arrays.
(c) Calculated shear-wave velocity profiles along line A-A [2].

line A-A (Fig. 1c), it can be seen that, for P Array1, thedepth to the bedrock (VS equal to 3000 m/s on average)
is about 150 m, and it gradually decreases as the bottom of the slope is approached (P Array3). In addition,
there is a drastic reduction in the depth to the stiff layers
for S Array1, indicating that the outcrop of stiff materials
must follow a line with a slope of about 50%.
It is important to highlight that for the construction ofhouses and roads on the slope, the earthmoving techniqueknown as “cut and fill” is commonly adopted, in which therequired flat filled areas are generated by the use of landfill materials that have poor dynamic properties. This isevident for S Array2, S Array3 and S Array4, where the
top layer has a shear-wave velocity lower than 200 m/s,
and a thickness that ranges from two to four meters. The
same pattern can be found for the majority of houses androads on the slope, with some variations in the thicknessof this shallow layer.

4. Finite Element Analysis
4.1. Dynamic Properties
When developing a finite element model, continuity inthe stratification is required, meaning that, for a given
layer, the value of its shear-wave velocity (VS ) must be
kept constant throughout the model. For this purpose, apattern VS structure was calculated from the average ofthe obtained VS values for the flat areas (including CSM∗ ,which is a slight modification of the original CSM proJournal of Disaster Research Vol.9 No.6, 2014

file obtained in a previous study [6], and was also projected onto line A-A ). This structure was then used asa substructure for profiles in the sloping area, for greater
depths than those estimated from linear and small circular
microtremor arrays. Attention was paid to the variationof the computed dispersion curves for each profile after
changing the values of VS , so their thicknesses were adjusted in order to obtain minimum discrepancy from theoriginal results.
The thickness of the shallow layer, consisting of borrowed materials, was assumed to be 2 m for all arrays inthe sloping area and, since projections of S Array2 andS Array3 are almost located in the same position on line
A-A , the same VS substructure was adopted for these twopoints. Final values of VS and thickness are presented inTable 1 for the seven microtremor array measurements
conducted for this study, and for the CSM∗ profile.
In total, seven different types of soil were considered
for the finite element model, and their mechanical and dynamic properties are shown in Table 2.

4.2. Geometry of the Slope
In order to generate the finite element mesh of theslope for its subsequent analysis, satellite images taken
by ALOS (Advanced Land Observing Satellite) on October 15, 2008 were used [7]. Altitude information was
extracted from the DSM (Digital Surface Model) generated from the PRISM (Panchromatic Remote-sensing Instrument for Stereo Mapping) image of the ALOS data
947

Gonzales, C. et al.

Table 1. Final values of VS and thickness for conducted microtremor arrays and CSM∗ .
P Array1
P Array2
CSM∗
P Array3
Layer Thickness (m) V S (m/s) Thickness (m) V S (m/s) Thickness (m) V S (m/s) Thickness (m) V S (m/s)
1
2.0
212
2.0
212
6.5
384
8.0
384
2
5.4
384
7.5
384
15.8
733
26.3
733
3
43.0
733
16.6
733
25.5
1623
28.5
1623
4
59.5
1623
32.0
1623
51.6
2405
41.0
2405
5
55.0
2405
42.3
2405
—
3504
—
3504
6
—
3504
—
3504
S Array1
S Array2
S Array3
S Array4
Layer Thickness (m) V S (m/s) Thickness (m) V S (m/s) Thickness (m) V S (m/s) Thickness (m) V S (m/s)
1
2.0
176
2.0
176
2.0
176
2.0
176
2
5.5
384
41.0
2405
41.0
2405
37.0
2405
3
28.5
1623
—
3504
—
3504
—
3504
4
41.0
2405
5
—
3504

Table 2. Dynamic properties for the adopted stratification.
Damping
Ratio - ξ
368
0.030
664
0.020
1197
0.010
2508
0.004
3716
0.003
5556
0.002
367
0.040

ρ (kg/m3 ) V S (m/s) G (MPa) V P (m/s)
Stratum-1
Stratum-2
Stratum-3
Stratum-4
Stratum-5
Stratum-6
Filled Soil

1700
1800
1800
2200
2200
2600
1500

212
384
733
1623
2405
3504
176

77
265
967
5794
12720
31916
47

Fig. 2. Points along lines A-A and B-B over the Digital
Surface Model from the ALOS satellite image.

through a matching process [8]. The subsequent DSM
had a pixel resolution of 5 m, a height resolution of 1 m,
and was processed using the GIS (Geographical Information System) software ArcGIS, by drawing a line over the
DSM and dividing it into 20-m segments (Fig. 2). Points
were created at every vertex of the newly generated segments, and the altitude was estimated by the bilinear interpolation of the information stored in the four nearest
cell (pixel) centers to the required point. Finally, points
used for the construction of the geometry were carefully
selected, since DSM includes not just the ground height,
but also the height of features such as buildings and trees.

4.3. Input Motion
The simulation conducted by Pulido [9] of a slip scenario for megathrust earthquakes in Lima concluded that
there is the potential for generating an earthquake with amoment magnitude of 8.9 off the coast of the capital. As
a result of this estimation, synthetic accelerograms were
calculated up to the surficial soil for the 8 sites where onedimensional shear-wave velocity models were available
in the capital [6]. For this study, the simulated waveform
obtained at CSM for the most critical slip model was assumed to be the same as for CSM∗ , owing to its proximity to line A-A . This waveform was therefore deconvoluted in order to obtain the input motion at the bottom
948

layer of the model (VS = 3504 m/s). Fourier spectra andwaveforms for both surface and deconvoluted motions areshown in Fig. 3.
Equivalent linear analysis was performed in order toclarify if the nonlinear behavior of soils could affect theCSM profile when the deconvoluted input motion is applied. For this type of analysis, a set of G/Gmax and hysteretic damping curves, developed by EPRI [10] and usedby Walling [11] for cohesionless soils, were adopted dueto the lack of this type of information for Lima. Similarvalues for both PGA and PGV were obtained for linear
and equivalent linear cases, allowing us to conclude that
nonlinear behavior does not have a significant influenceon the variation of the response. Therefore, calculations
for the slope model were made considering a linear response. Fourier and response spectra for both cases, aswell as transfer functions, are shown in Fig. 4.

4.4. Analysis Considerations
4.4.1. Time Domain Analysis
In dynamic analysis, when including damping, theequation of motion is typically written in the form
Mü + Cu̇ + Ku = −MIüe , . . . . . . . . (1)Journal of Disaster Research Vol.9 No.6, 2014

Analysis of Topographic Effects in Dynamic Response ofa Typical Rocky Populated Slope in Lima, Peru

Fig. 4. (a) Fourier spectra, (b) acceleration response spectra and (c) transfer functions for linear and equivalent linear
cases.
Fig. 3. Fourier spectra and time-histories for (a) surface
motion and (b) deconvoluted input motion.

specified for the two modes. Then, after solving Eq. (3),4π f m f n ξ. . . . . . . . (4)( fm + fn )ξ, . . . . . . . (5)βR =π ( fm + fn )αR =where M is the mass matrix, C the viscous damping matrix, K the stiffness matrix, ü the acceleration vector, u̇
the velocity vector, u the displacement vector, üe the seismic acceleration, and MIüe the inertia vector. Eq. (1)was solved numerically by means of the Newmark-βmethod [12] in which Δt, the time interval, and the parameter β were assumed to be 0.002 s and 0.25, respectively.

4.4.2. Attenuation TypeIn the time domain analysis, the viscous damping matrix, C, is frequency dependent. In the original formulation proposed by Rayleigh and Lindsay [13], C is assumed to be proportional to mass and stiffness matrices
as follows:
C = αR M + βR K,. . . . . . . . . . . (2)The coefficients αR and βR can be computed using two
significant natural modes, m and n, by means of the following equation:
⎡
⎡
⎤
⎤
1
1
 
2π fm ⎥ αRωξmαR
1 ⎢ ωm m ⎥1⎢⎢ 2π f m
⎥
⎥
= ⎢
=
,
⎣ 1
⎣ 1
⎦
⎦
2
2
ξn
β
β
R
R
2
π
f
ωn
n
2π f nωn. . . . . . . . . . . . . . . . (3)where ξm , ξn and fm , fn are damping ratios and frequencies, respectively, for the two corresponding modes m andn. Since the damping ratio is known to be frequency independent, equal values for modal damping ratios, ξ , are
Journal of Disaster Research Vol.9 No.6, 2014

andThe analysis was performed for several trials of the setof frequencies fm and fn , in order to find the closest PGA
possible to that for the EW component (chosen due to theorientation of line A-A ) of the simulated accelerogramat CSM∗ (assumed to be the same as for CSM) developed for the most critical slip model, following the recommendations given in [14] and [15]. Also, comparisons ofboth Fourier and response spectra, for 5% damping of thesynthetic and output waveforms from the finite element
model at CSM∗ , were used for the selection purposes. After several assumptions, the most suitable fm and fn were
found at 3.33 Hz and 25 Hz, respectively (Fig. 5).
4.4.3. Finite Element Model
A commercial program known as Soil Plus was utilized for construction of the two-dimensional finite element model of the target populated slope and its subsequent dynamic analysis.
Boundaries and thicknesses of the seven strata wereclearly defined from the shear-wave velocity profiles in
the flat area. Transitions of materials in the sloping area
were modeled based on the fact that layers with a low
shear-wave velocity gradually disappear approaching thefoot of the slope, because of the outcropping of stiff rocky
materials. During the microtremor field work on theslope, it was evident that fresh rock appears just above thecurrently inhabited areas. An approximate location for949

Gonzales, C. et al.

damper is attached, and A its area of influence. Additionally, in order to develop a consistent model, free groundelements with large mass were placed on the opposite
sides of the model with a thickness equal to 100000 m.
A scheme of dampers and free ground elements is also
shown in Fig. 6.

5. Analysis Results

Fig. 5. (a) Fourier spectra, (b) acceleration response spectra,and (c) waveforms for the frequency domain and (d) the time
domain (FEM): results at CSM∗ ( fm = 3.33 Hz and fn =25 Hz).

this outcropping was chosen with the help of the ALOS
satellite and Google Earth images.
In order to generate the mesh for each stratum, theirrespective surrounding edges were divided into control
points with increased spacing at greater depths. In general, quadrilateral shapes were used, but in specific cases,
such as in the transition to outcropping materials, triangular elements were generated.
The problem was solved for plain strain conditions, inwhich the thickness perpendicular to the analysis plane
was equal to 1 m for all soil elements. In order to savecomputation time and avoid the generation of an unnecessarily large number of degrees of freedom, the slopemodel was reduced from the original drawn line (reddots in Fig. 2) to the central-third portion represented byline B-B . In total, 7996 planar elements were generated
for the two-dimensional model, and their distribution foreach assumed stratum, as well as their graphical representation, is shown in Fig. 6.
4.4.4. Boundary Conditions
Compression and shear dampers were placed at thesides and bottom of the model. Depending on the typeof force applied, damper constants (Cc and Cs ) were calculated from the following expressions:andCc = ρ VP A . . . . . . . . . . (6)Cs = ρ VS A, . . . . . . . . . . (7)where ρ is the density, VP the compressional-wave velocity, VS the shear-wave velocity of the layer to which the950

The distribution of absolute values of peak acceleration
for horizontal motion, for the entire slope model, is presented in Fig. 7a. This figure shows that amplification of
the response is evident for surface layers in the flat areas,
whereas no larger values are found for the sloping areasof the model. In addition, Fig. 7b shows a close-up viewthat includes the foot of the slope and regions assumed tobe covered by borrowed soil.
Waveforms were extracted for three points along theslope: point a, close to the foot of the slope; point b, in thecenter of the populated areas covered by borrowed soil;
and point c, in the region where full outcropping of freshrock is assumed to start. In addition, a one-dimensional
amplification analysis was conducted for each of thesethree points, in which a soil column with the same mechanical and dynamic properties was analyzed and additionally solved for the time domain.
Results (Fig. 8) show that the largest PGA occurs at
point a, with an acceleration value (602 cm/s2 ) which only
differs by approximately 100 cm/s2 from the one obtained
for CSM∗ (Fig. 3a). This contrasts with lower values
found by FEM analysis for the other two points. Moreover, in Fig. 8a it is evident that Fourier amplitudes for
the FEM case are lower than those obtained from onedimensional analysis for points a, b, and c. These results are a consequence of the apparent restricted vibrations close to the foot of the slope caused by the stiffrocky hill next to the flat area. On the other hand, recent studies [16] have concluded that PGA and response
acceleration are key factors in the estimation of structural
damage in Peru. Therefore, comparisons of acceleration
response spectra (Fig. 8b) are shown, and a peak can beobserved for points a and b for periods close to 0.07 s.
Since one-story masonry houses and other essential structures (schools, community centers, etc.) are extensive inthese areas, an increase in their seismic response is expected due to the similarity of their natural periods of vibration to the value given above [17].
Results at this stage also confirm the fact that nonlinear
behavior of soils does not affect the response of the target
slope, since PGV values (24 cm/s on average) for points
along the slope are fairly low to consider this effect.

6. Conclusions
This study aimed to analyze the dynamic response ofa typical rocky populated slope in the city of Lima, andthe possibility of finding amplification due to topographic
Journal of Disaster Research Vol.9 No.6, 2014

Analysis of Topographic Effects in Dynamic Response ofa Typical Rocky Populated Slope in Lima, Peru

Fig. 6. Two-dimensional finite element model of the target slope.

Fig. 7. Distribution of the peak acceleration in the horizontal direction for (a) the entire finite element modeland (b) the sloping areas.

effects. The following conclusions can be drawn from thisstudy.
1. An equivalent linear analysis, carried out for the soilcolumn corresponding to the CSM profile, demonstrated that the effect of nonlinearity does not produce a significant influence on the seismic response.
Therefore, analysis of the complex slope model was
performed for the linear case.
2. A mathematical model was developed by means of
the finite element method (FEM) and solved for thetime domain, allowing us to obtain time-histories forseveral points on the sloping area. Comparisons of
the results for the FEM and one-dimensional cases
have shown that soil vibration close to the foot of
Journal of Disaster Research Vol.9 No.6, 2014

the slope may be restricted when considering the effect of the stiff rocky hill. Results also indicated thata larger response is evident for regions close to thefoot of the slope, for periods in the vicinity of 0.07 s.
This period coincides with the expected natural period of one-story masonry buildings that are extensive in these areas, meaning that they may be significantly affected by strong motions of large magnitude. This difference in the response seems to be
influenced more by the shear-wave velocity substructure of the slope than by topography effects.
Further analyses of other populated slopes throughout
the city are recommended, in order to develop a general
understanding of their seismic response, since geomet951

Gonzales, C. et al.

Fig. 8. Comparison of the (a1–3) Fourier spectra, (b1–3) acceleration response spectra for one-dimensional
and FEM analyses. Acceleration time-histories for (c1–3) one-dimensional and (d1–3) FEM analyses.

ric and geotechnical conditions may differ from the target
slope considered for this study that can be assumed to be
typical only for the stiff rocky slopes in the north regionof Lima.

952

Acknowledgements
This work was developed within the framework of the SATREPS
project on “Enhancement of Earthquake and Tsunami Disaster
Mitigation Technology in Peru,” under the patronage of the Japan
Science and Technology Agency (JST) and the Japan International
Cooperation Agency (JICA).
The authors would like to express their gratitude to these agencies and to the research assistants in CISMID who helped in thecompletion of the study.

Journal of Disaster Research Vol.9 No.6, 2014

Analysis of Topographic Effects in Dynamic Response ofa Typical Rocky Populated Slope in Lima, Peru

References:[1] J. Matos, Las Migraciones Campesinas y el Proceso de Urbanizacion en el Peru, UNESCO, 1990 (in Spanish).
[2] C. Gonzales, S. Nakai, T. Sekiguchi, D. Calderon, Z. Aguilar, andF. Lazares, “Estimation of the Dynamic Properties and Seismic Response of a Populated Slope in Lima, Peru,” Journal of Disaster
Research, Vol.9, No.1, pp. 17-26, 2014.
[3] Z. Aguilar, “Seismic Microzonation of Lima,” Japan-Peru Workshop on Earthquake Disaster Mitigation, Japan-Peru Center for
Earthquake Engineering Research and Disaster Mitigation (CISMID), Faculty of Civil Engineering, National University of Engineering, Lima, Peru, 2005.
[4] O. Palacios, J. Caldas, and Ch. Vela, “Geologia de los Cuadrangulos
de Lima, Lurin, Chancay y Chosica,” The Geological, Mining andMetallurgical Institute of Peru, pp. 25-29, 1992 (in Spanish).
[5] H. Yamanaka and H. Ishida, “Application of the Genetic Algorithms
to an Inversion of Surface-Wave Dispersion Data,” Bulletin of Seismological Society of America, Vol.86, No.2, pp. 436-444.
[6] D. Calderon, “Dynamic characteristics of the soils in Lima, Peru, by
estimating shallow and deep shear-wave velocity profiles,” Graduate School of Engineering, Chiba University, Japan, 2012.
[7] M. Matsuoka, H. Miura, S. Midorikawa, and M. Estrada, “Extraction of Urban Information for Seismic Hazard and Risk Assesment
in Lima, Peru Using Satellite Imagery,” Journal of Disaster Research, Vol.8, No.2, pp. 328-345, 2013.
[8] J. Takaku and T. Tadano, “PRISM on-Orbit Geometric Calibration
and DSM Performance,” IEEE Transaction on Geoscience and Remote Sensing, Vol.47, No.12, pp. 4060-4073, 2009.
[9] N. Pulido, “Earthquake rupture and slip scenarios for Central Andes
Peru, and strong motion simulations for Lima,” National ResearchInstitute for Earth Science and Disaster Prevention (NIED), 2013.
[10] Electric Power Research Institute (EPRI), “Guidelines for Determining Design Basis Ground Motions. Volume 1: Method andGuidelines for Estimating Earthquake Ground Motion in Eastern
North America,” Technical Report, 1993.
[11] M. Walling, W. Silva, and N. Abrahamson, “Nonlinear Site Amplification Factors for Constraining the NGA Models,” Earthquake
Spectra, Vol.24, No.1, pp. 243-255, 2008.
[12] N. Newmark, “A Method of Computation for Structural Dynamics,”
Journal of the Engineering Mechanics Division, Vol.85, pp. 67-94,
1959.
[13] J. Rayleigh and R. Lindsay, The Theory of Sound, 1st American Ed.
New York, Dover Publications, 1945.
[14] Y. Hashash and D. Park, “Viscous damping formulation and highfrequency motion propagation in non-linear site response analysis,”
Soil Dynamics and Earthquake Engineering, Vol.22, pp. 611-624,
2002.
[15] D. Park and Y. Hashash, “Soil damping formulation in nonlinear
time domain site response analysis,” Journal of Earthquake Engineering, Vol.8, No.2, pp. 249-274, 2004.
[16] L. Quiroz, “Evaluation of Seismic Performance of Residential
Buildings in Lima, Peru: A Case Study of Buildings Constructedwith Thin RC Walls and Confined Masonry Walls,” Graduate
School of Engineering, Division of Arquitechture and Urban Science, Department of Urban Environment Systems, Chiba University, Doctoral Thesis, 2014.
[17] R. Proaño and C. Zavala, “Estimation of the seismic response ofstructures based on SDOF systems for calculation of Seismic Vulnerability,” Proceedings of the XIV National Conference of Civil
Engineering, Iquitos, Peru, Paper No.EM-38, p. 12, 2003 (in Spanish).

Journal of Disaster Research Vol.9 No.6, 2014

Name:
Carlos Gonzales Trujillo

Affiliation:
Ph.D. Student, Department of Urban Environment Systems, Chiba University

Address:
1-33, Yayoi-cho, Inage-ku, Chiba 268-8522, Japan

Brief Career:2009 B.Sc. Civil Engineer, Faculty of Civil Engineering, National
University of Engineering (UNI), Lima, Peru
2010-2011 Research Assistant, Japan-Peru Center for Earthquake
Engineering Research and Disaster Mitigation (CISMID)
2012-2014 Master of Engineering, Chiba University
2014- Ph.D. student, Chiba University

Selected Publications:• “Estimation of the Dynamic Properties and Seismic Response of a
Populated Slope in Lima, Peru,” Journal of Disaster Research, Vol.9, No.1,
pp. 17-26, Feb. 2014.

953