Seismic Performance Analysis Of An Irregular Existing Building Using The Future Seismic Code RPA 2018 And Non Linear Dynamic Analysis

Abstract

After the El Asnam earthquake which struck Algeria in 1980, the first national Algerian Seismic Code for new buildings was adopted in 1981 and called RPA 1981. These regulations were the primary source of seismic design requirements for new buildings throughout the nation. The goal of these regulations is to assure that seismic performance will avoid serious injury and loss of life, loss of function in critical facilities and minimize structural and nonstructural repair costs. Since the creation of the National Earthquake Engineering Research Center (CGS) in 1985, a national earthquake hazard reduction program has been sponsored by the governmental authorities and the Algerian seismic regulations have known five developments and improvements (1981, 1983, 1988, 1999 and 2003). Because reinforced concrete is the most common building material in Algeria, this paper will deal with the main provisions of the new proposed code RPA 2018 which is in line with the current generation of seismic codes. A comparative study of an irregular strategic existing RC building is performed. Demand and capacity are compared in terms of base shear forces. A nonlinear dynamic analysis is performed to also compare the story displacements. Finally, the paper concludes with a discussion of the specific results.

Full text

10th International International Civil Engineering Conference (ICEC-2019)
“Technological Transformation of Civil Engineering”
February 23-24, 2019, Karachi, Pakistan.
Seismic Performance Analysis Of An Irregular Existing Building Using The
Future Seismic Code RPA 2018 And Non Linear Dynamic Analysis
Youcef Mehani, Abderrahmane Kibboua
National Earthquake Engineering Research Center, Hussein-Dey, Algiers, Algeria
ymehani@cgs-dz.org, akibboua@cgs-dz.org
Benazouz Chikh, Mustapha Remki
National Earthquake Engineering Research Center, Hussein-Dey, Algiers, Algeria
bchikh@cgs-dz.org, mremki@cgs-dz.org
Abstract
After the El Asnam earthquake which struck Algeria in 1980, the first national Algerian Seismic Code for
new buildings was adopted in 1981 and called RPA 1981. These regulations were the primary source of
seismic design requirements for new buildings throughout the nation. The goal of these regulations is to
assure that seismic performance will avoid serious injury and loss of life, loss of function in critical
facilities and minimize structural and nonstructural repair costs. Since the creation of the National
Earthquake Engineering Research Center (CGS) in 1985, a national earthquake hazard reduction program
has been sponsored by the governmental authorities and the Algerian seismic regulations have known five
developments and improvements (1981, 1983, 1988, 1999 and 2003).
Because reinforced concrete is the most common building material in Algeria, this paper will deal with
the main provisions of the new proposed code RPA 2018 which is in line with the current generation of
seismic codes. A comparative study of an irregular strategic existing RC building is performed. Demand
and capacity are compared in terms of base shear forces. A nonlinear dynamic analysis is performed to
also compare the story displacements. Finally, the paper concludes with a discussion of the specific
results.
Keywords
Base shear force, Inter story displacements, Seismic demand, Seismic capacity, Non linear dynamic
analysis.
1. Introduction
The northern region of Algeria lies in an active seismic zone (Messaoudi et al.,). Consequently, all
structures must designed to resist the earthquakes likely to occur in the future. Many colonial
nonconforming existing buildings are still in use, and some are considered as existing strategic buildings
(Mehani et al., 2013; Kibboua et al., 2011; Kibboua, 2012; Kibboua et al., 2017). Because of the
importance of changes in the new seismic code version, it is opportune to make a comparative study of a
strategic existing RC building according to the new proposed seismic code RPA 2018 (CGS, 2018) which
will be edited in the near future (Belazougui, 2017), and a nonlinear time history analysis. This paper is
aimed to compare some of the seismic design provisions in terms of shear base forces and inter story
displacements.

2. Design Base Shear Force
The horizontal seismic action is described by two orthogonal components considered as independent and
represented by the same response spectrum. According to the new proposed RPA 2018 the seismic base
shear forces obtained by the equivalent static analysis method is given by Eq. (1).
W
R
AISDQ
7.0V =
(1)
Where:
- V: seismic base shear force.
- A: peak ground acceleration estimated at the bedrock for the reference return period of 475 years,
expressed as a fraction of the gravity g = 9.81 m/s², and to be adopted in the different seismic zones.
- I: importance factor. Buildings are classified in four importance classes according to their functions.
- S: soil amplification factor independent of the vibration period.
- D: f (T), mean dynamic amplification factor, function of the fundamental period, taking into account
viscous damping ratio and damping correction factor.
- Q: quality factor depending on structural simplicity, uniformity, symmetry and redundancy.
- R: global behavior factor to take into account energy dissipation capacity.
- W: total seismic weight.
- T: fundamental natural period.
2.1 Vertical distribution of base shear force
The total base shear force distribution is linear to each story in proportion to the story mass with its height
from the base. The seismic horizontal force is given by Eq. (2).
∑
=
=
−
=
ni
1i ii
kkt
k
hW
hW)FV(
F
(2)
Where:
Fk: seismic horizontal force at the Kith level.
Ft: for long period buildings greater than 0.7 sec, an extra force is applied to the top in addition to Fn
equal to 0.07 TV and not exceed 0.25 V. Otherwise it is assumed to be zero.
Wk: seismic weight at level k.
hk: height of level k from the base.
2.2 Design spectrum for elastic analysis
To avoid explicit inelastic structural analysis in design, nonlinear behavior of structural elements is taken
into account by performing an elastic analysis based on a response spectrum reduced with respect to the
elastic one. This reduction is accomplished by introducing the behavior factor R which permits a design
for forces smaller than those corresponding to a linear elastic response.
According to new proposed seismic code RPA 2018, the horizontal components of the seismic action, the
design spectrum Sa/g (T), is defined by the following Eq. (3).


=









AIS 
+
.η

 0 < T

.η
 T
<T

.η

 T<T

.η

 T<4s
With 
0.2AI
 (3)
Where:
T1, T2 and T3: limit periods for each ground type.
3. Non Linear Dynamic Analysis
To emphasis our study, a nonlinear dynamic analysis has been performed. The nonlinear dynamic
analysis is used to compute deformations, stresses and section forces more accurately by considering the
time dependent nature of the dynamic response to earthquake ground motion. It is also conducted to avoid
many limitations of simplified response methods. The overall objective is to develop a set of time
histories that are representative of site ground motions that may be expected for the design earthquake and
that are appropriate for the types of analyses planned for specific structures. According to the new
concept in the Algerian seismic code, during major earthquakes, structures are allowed to undergo
deformations beyond the elastic limit state to absorb deformation energy (Chowdhury and Dasgupta,
2009). A nonlinear dynamic time history analysis using step by step integration method is a very useful
tool to determine the most appropriate realistic response of elements, and hence the performance of the
whole structure. Dynamic response analysis of structures represents a numerical computation of structural
systems with defined characteristics of masses, stiffness, damping, etc, and defined ranges of elastic
(linear) and plastic (non linear) behavior expressed via displacements, velocities, accelerations and forces
(Chopra, 2001). The most general approach for solving the nonlinear dynamic response of structural
system is the direct numerical integration of the dynamic equilibrium equations. This involves the attempt
to satisfy dynamic equilibrium at discrete equal time intervals after the solution has been defined at time
zero (Chowdhury and Dasgupta, 2009). The solution of the nonlinear dynamic equilibrium equations is
carried out in incremental form using the following Eq. (4).
[ ]
{ }
[ ]
{ }
[ ]
{ }
[ ]
{ }
g
UIMUKUCUM  −=∆+∆+∆
(4)
Where:
[ ]
M
: Mass matrix.
[ ]
C
: damping matrix.
[ ]
K
: Stiffness matrix.
{ }
U

∆
: Incremental acceleration vector.
{ }
U

∆
: Incremental velocity vector.
{ }
U∆
: Incremental displacement vector.
g
U

: Ground acceleration.
To determine the non-linear response of the structure, the D.R.A.B.S (Bozinovski and Gavrilovic, 1993)
program is used and the bilinear model is adopted. The figure (1) represents the relationship force-
displacement (F-δ).

Figure 1: Bilinear model
Where:
K1 = (Fu-Fy)/ (Xu-Xy) and Lp = K2/K=αK/K
Three real ground motion records are used in the nonlinear dynamic analysis taking into account the soil
conditions, frequency content and the aspect of near field and far field.
- Ulcinj (Albatros, Montenegro) N-S 1979.
- El Centro (California, USA) N-S May 8th, 1940.
- Cherchell (Algeria) N-S October 29th, 1989.
The figure (2) shows the selected recorded earthquakes.
Figure 2: Selected earthquake accelerograms
4. Limit State
There are numerous limit states that can be considered in seismic vulnerability studies. In the traditional
approaches, two limit states are considered. The elastic and the ultimate limit states (Bozinovski and
Gavrilovic, 1993). The first is defined in terms of strength and calculated using the building material
properties, whereas the second is estimated in terms of displacements using a given ductility factor,
eventually converted to forces using a reduction factor (Wagh et al., 2016). More recent approaches
consider multi-linear behavior relationships for the elements and define different damage states as break
points in the behavior curves either in displacement or rotation (drift). The structural performance level
considered for the system assessment carried out in the present study is for a major earthquake (475 years
D
A
I
J
G
–F
y
–X
y
X
F
B
X
y
F
y
K
H
K1
C
Accelerogram of ULCINJ ALBATROS
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 5 10 15 20 25 30 35 40
Time (s)
Acceleration (m/s²)
Accelerogram of EL CENTRO
-3
-2
-1
0
1
2
3
4
0 5 10 15 20 25 30 35 40
Time (s)
Acceleration (m/s²)
Accelerogram of CHERCHEL
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 5 10 15 20 25
Time (s)
Acceleration (m/s²)

return period). The limit inter story displacement for major earthquake is given by the following equation
(IZIIS and CGS, 1993).






=∆ 125
&
150 HH
M
(5)
5. Case study
To better show the differences between the analysis with the new proposed seismic code RPA 2018 and
the nonlinear time history analyses, a comparative study has been performed considering a strategic
existing reinforced concrete building.
5.1 Mechanical characteristics of the materials
Mechanical material characteristics were defined using a range of in-situ and laboratory testing and
inspection techniques to obtain the necessary information.
Concrete
- Characteristic compressive cylinder strength at 28 days: fc28 = 20 Mpa
- Design tensile strength: σt = 1.8 Mpa
- Yield strain: εe = 0.002
- Ultimate strain: εu = 0.0035
Steel
- Characteristic tensile yield strength of reinforcement: fe = 400 Mpa
- Characteristic tensile strength of shear reinforcement: ft = 235 Mpa
- Yield strain of reinforcement: εy = 0.002
- Yield strain of shear reinforcement: εe = 0.0018
- Ultimate strain: εu = 0.010
5.2 Description of the building
The analyzed building is the general surgery building belonging to the Beni Messous University Hospital
Complex, located in the Wilaya of Algiers and set up on a medium soil or ground type (S3). It was built
in the fifties. Our focus will be on the Bloc 02 of the building. It is a four (04) story irregular existing
reinforced concrete and a basement. The partition and exterior enveloping walls are made of hollow clay
bricks. The structural system is a reinforced concrete resisting moment frames, which consists of
reinforced concrete columns and beams. Floors are in reinforced concrete slabs. The figures 3 and 4 show
the different drawing in plans of the irregular existing building.

Figure 3: Plan view of the first floor
Figure 4: Plan view of current floors (2nd, 3rd and 4th)
5.3 Structural analysis
Considerable advances in computer technology and availability of increased computational resources
brought more detailed approach for modeling reinforced concrete structures using finite elements. For this
purpose and based on existing drawings and the site inspection, the structure was modeled in 3D space
frames with rigid diaphragms and a fixed base, using the nonlinear computer program (Wilson and
Habibullah, 2015). The figure 5 shows the structural system in plan and three dimensional view of the
existing structure.

Figure 5: 3D Model of the structure
6. Seismic assessment by the new code RPA 2018
The main change is the upgrade of the Wilayates from a low (IIa) to a high (III) seismicity zone.
Consequently, the peak ground acceleration becomes higher. Table (1) shows the different seismic
parameters taken into account for this study.
Table 1: Seismic parameters
Seismic parameters
RPA 2018
Zone
III
Group
1A
A (%g)
0.35
I
1.40
S
1.20
ξ
7
η
0.88
T(s)
0.49
D
2.20
Q
1.20
R
3.5
T1(s)
0.20
T2(s)
0.60
T3(s)
2.00
Table (2) shows the seismic demand in terms of shear forces for both main directions according to the
new proposed seismic code RPA 2018.

Table 2: Demand and capacity in terms of shear forces for RPA-2018
Level
RPA 2018
Fxi (KN)
Vxi (KN)
Quxi (KN)
Fyi (KN)
Vyi (KN)
Quyi (KN)
4
3056.381
3056.381
5525.133
3056.381
3056.381
4052.291
3
2342.544
5398.925
5861.935
2342.544
5398.925
4096.414
2
1561.696
6960.621
6112.881
1561.696
6960.621
4314.732
1
1785.723
8746.344
8283.338
1785.723
8746.344
7995.744
Figures (6) and (7) show the capacity and the demand in terms of shear forces in main longitudinal (XX)
and transversal (YY) directions according to the current RPA99/version 2003 [16] and the future RPA
2018.
Figure 6: Capacity and demand in terms of
shear forces in longitudinal (XX) direction
Figure 7: Capacity and demand in terms of
shear forces in transverse (YY) direction
Tables (3) and (4) resume the main results in terms of inter story displacements in main longitudinal (XX)
and transverse (YY) directions.
Table 3: Capacity and demands in terms of inter story displacements (cm) in the longitudinal
direction (XX)
Level Earthquake ∆x (cm) ∆xcap (cm)
1.5% h
i
(cm)
∆xmeth (cm)
4
Ulcinj
0.87
3.63
4.80
2.32
El Centro
0.78
Cherchell
0.84
3
Ulcinj
2.49
3.22
4.80
2.32
El Centro
2.20
Cherchell
1.70
2
Ulcinj
3.97
2.74
4.80
2.32
El Centro
3.37
Cherchell
2.32
1
Ulcinj
4.13
2.28
4.80
2.32
El Centro
3.17
Cherchell
2.08
0
1
2
3
4
02000 4000 6000 8000 10000
Level
Shea r f orce (KN)
DEMAND XX 2003
CAPAC ITY XX
DEMAND XX 2016
0
1
2
3
4
02000 4000 6000 8000 10000
Level
Shea r f orce (KN)
DEMAND YY 2003
CAPAC ITY YY
DEMAND YY 2016

Table 4: Capacity and demands in terms of inter story displacements (cm) in the transverse
direction (YY)
Level Earthquake ∆y (cm) ∆ycap (cm)
1.5% h
i
(cm)
∆ymeth (cm)
4
Ulcinj
1.50
5.46 4.80 2.32
El Centro
1.28
Cherchell
1.35
3
Ulcinj
4.53
4.23 4.80 2.32
El Centro
3.58
Cherchell
3.26
2
Ulcinj
5.82
2.63 4.80 2.32
El Centro
4.69
Cherchell
3.92
1
Ulcinj
2.92
2.27 4.80 2.32
El Centro
2.23
Cherchell
1.63
Figures (8) and (9) show the capacity and the demand in terms of inter story displacements in main
longitudinal (XX) and transverse (YY) directions, obtained through the nonlinear time history analysis for
a major earthquake.
Figure 8: Capacity and demand in terms of
inter story displacements in longitudinal
direction (XX)
Figure 9: Capacity and demand in terms of
inter story displacements in transverse
direction (YY)
Figures (10) and (11) show the capacity and the demand in terms of absolute displacements in main
longitudinal (XX) and transverse (YY) directions, obtained through the nonlinear time history analysis for
a major earthquake.
0
1
2
3
4
012345
Level
Inter story displacement (cm)
Capaci ty
Ulcinj
El Centro
cherchel
0
1
2
3
4
0123456
Level
Inter story displacement (cm)
Capaci ty
Ulcinj
El Centro
cherchel

Figure 10: Capacity and demand in terms of Figure 11: Capacity and demand in terms of
absolute displacements in longitudinal of absolute displacements in transverse
direction (XX) direction (YY)
7. Conclusion
This comparative study has concluded the following:
1. Considerable differences in parameters on determining shear forces in the new code.
2. Considerable differences are pronounced in design response spectrum and spectral accelerations
which leads to major differences in the assessment of base shear forces.
3. Base shear force with version 2018 > 2.89% than base shear force with the version 2003.
4. Inter story displacements demand exceed capacity at all levels in both main directions in case of a
strong earthquake motion.
5. Absolute displacements under considered earthquake motions exceed considerably the expansion
gap of 05 cm between blocs in the two main directions in case of a strong earthquake motion.
8. References
Belazougui, M. (2017). “Algerian seismic building code: main features of the new draft RPA 2015”, 16th
World Conference on Earthquake, 16WCEE 2017, Santiago Chile.
Bozinivski, Z., Gavrilovic, P. (1993). Computer program for dynamic response analysis of building
structures, DRABS, IZIIS, University of Skopje, Republic of Macedonia.
Bozinivski, Z., Gavrilovic, P. (1993). Computer program for ultimate analysis of rectangular reinforced
concrete sections of frames and walls systems, UARCS, IZIIS, University of Skopje, Republic of
Macedonia.
CGS. (2003). Seismic Code for Building Design and Construction, R.P.A 99/ Version 2003, National
Earthquake Engineering Research centre, Algiers, Algeria.
CGS. (2018). Seismic Code for Building Design and Construction, R.P.A 2018/ New version in Draft,
National Earthquake Engineering Research centre, Algiers, Algeria.
Chopra, A.K. (2001). Dynamics of structures. Theory and Applications to Earthquake Engineering,
Prince-Hall, Englewood Cliffs, NJ.
Chowdhury, I., Dasgupta, S.P. (2009). Dynamics of structures and foundation. A unified approach.1-
Fundamentals, CRC Press, Taylor and Francis Group, Balkema.
Chowdhury, I., Dasgupta, S.P. (2009). Dynamics of structures and foundation. A unified approach.2-
Applications, CRC Press, Taylor and Francis Group, Balkema.
IZIIS., CGS. (1993). Methodology and vulnerability study of strategic buildings in the city of Algiers,
National Earthquake Engineering Research Center, Algiers, Algeria.
0
1
2
3
4
012345678910 11 12
Level
Abso lute displacement (c m)
Capaci ty
Ulcinj
El Centro
cherchel
0
1
2
3
4
012345678910 11 12 13 14 15
Level
Abso lute displacement (c m)
Capaci ty
Ulcinj
El Centro
cherchel

Kibboua, A., Naili, M., Benouar, D., and Kehila, F. (2011), “Analytical Fragility Curves for Typical
Algerian Reinforced Concrete Bridge Piers”. Structural Engineering and Mechanics, Vol. 39, No.3, pp
411- 425.
Kibboua, A. (2012). “Développement d’une méthodologie d’analyse pour la vulnérabilité sismique des
piles de ponts algériens (Development of a methodology analysis for the seismic vulnerability of the
Algerian bridge piers)”. Ph.D. Thesis, University of Science and Technology Houari Boumediene, Bab
Ezzouar, Algiers, Algeria.
Kibboua, A., Hemaidi-Zourgui, N., Kehila, F. and Remki, M. (2017). “Comparison between fragility
curves of RC bridge piers designed by old and recent Algerian codes”. Eurasian Journal of Engineering
Sciences and Technology, Vol. 1, No. 2, pp 56- 67.
Mehani, Y., Bechtoula, H., Kibboua, A., and Naili, M. (2013). “Assessment of seismic fragility curves for
existing RC buildings in Algiers after the 2003 Boumerdes earthquake”. Struct. Eng. Mech, Vol. 46,
No.6, pp 791-808.
Messaoudi, A., Laouami, N., and Mezouar, N. (2017). “Slope topography-induced spatial variation
correlation with observed building damages in Corso during the May 21, 2003, Mw 6.8, Boumerdes
earthquake (Algeria)”. Journal of Seismology, Vol. 21, No. 4, pp 647-665.
Wagh, A.R., Salunke, P.J., Narkhede, T.N. (2016). “Review on seismic design and assessment of high-
rise structures using various international codes”. International Journal for Scientific Research and
Development, Vol. 4, No. 3, pp 1851-1855.
Wilson, E., Habibullah, A. (2015). Extended 3D Analysis of Building Systems Nonlinear Version 13,
Computer and Structures, Inc. Berkeley, California, 2015.