earthquake behavior of reinforced concrete framed...

Earthquake behavior of reinforced concrete framed buildings on hill

slopes

by

Ajay Kumar Sreerama, Pradeep Kumar Ramancharla

in

nternational Symposium on New Technologies for Urban Safety of Mega Cities in Asia(USMCA 2013)

Report No: IIIT/TR/2013/-1

Centre for Earthquake EngineeringInternational Institute of Information Technology

Hyderabad - 500 032, INDIAOctober 2013

Earthquake behavior of reinforced concrete framed buildings on hill slopes

Ajay K SREERAMA1 and Pradeep K RAMANCHARLA2 1Ph.D Student, Civil Engineering, IIIT Hyderabad,

Gachibowli, Hyderabad-500032, India [email protected]

2Professor of Civil Engineering, Earthquake Engineering Research Centre, IIIT Hyderabad, Gachibowli, Hyderabad-500032, India

[email protected]

ABSTRACT

Recent earthquakes, 18 Sep 2011, Sikkim earthquake, M6.9 and 1 May 2013 Doda earthquake, M5.8 produced two major effects, namely on buildings and on hill slopes. The maximum intensity of ground shaking experienced during these earthquakes was only about VI or less on the MSK scale. Considering the low intensity of ground shaking in the affected areas, the damage attributed was disproportionately higher. It is mainly due to high amplification in local site areas. In this regard, a research is carried out to understand the performance of buildings on hill slopes. In this paper, the study of the behavior of a G+3 building on varying slope angles i.e., 15°, 30°, 45° and 60° is studied and compared with the same on the flat ground. Building is designed as per IS 456 and later subjected to earthquake loads. It was observed that as the slope angle is increasing, building is becoming stiffer. Two types of analyses were conducted viz., lateral load analysis and incremental dynamic analysis. It was observed from the initial results that the columns on the higher side of the slope i.e., short columns were subjected to more shear force then longer columns on the lower side. Finite element method is used to study the static behavior where as Applied Element Method (AEM) is used to perform incremental dynamic analysis. Keywords: hill-slopes, incremental dynamic analysis 1. INTRODUCTION North and northeastern parts of India have large scales of hilly terrain, which are categorized under seismic zone IV and V. In this region the construction of multistory RC framed buildings on hill slopes has a popular and pressing demand, due to its economic growth and rapid urbanization. This growth in construction activity is adding to tremendous increase in population density. While construction, it must be noted that Hill buildings are different from those in plains i.e., they are very irregular and unsymmetrical in horizontal and vertical planes, and torsionally coupled. Since there is scarcity of plain ground in hilly areas, it obligates the construction of buildings on slopes.

0ctober 2013, Hanoi, Vietnam

New Technologies for Urban Safety of Mega Cities in Asia

Recent earthquakes i.e., 18 Sep 2011, Sikkim earthquake (M6.9) and 1 May 2013 Doda earthquake(M5.8) produced two major effects, namely on buildings and on hill slopes. To perform well in an earthquake, a building should possess four main attributes i.e. simple and regular configuration, adequate lateral strength, stiffness and ductility (as per clause 7.1 of IS 1893-2002). 1.1. SEISMIC BEHAVIOUR OF BUILDINGS ON SLOPES IN INDIA Shillong Plateau earthquake (M8.0) of 1897 and the Kangra earthquake (M7.8) of 1905, were the major of several devastating earthquakes to occur in northern India. An estimated of more than 375,000 population were killed in epicentral region, and over 100,000 buildings were destroyed by the earthquake. Similarly in recent earthquakes like Bihar-Nepal (1980), Uttarkashi (1991), Sikkim (2011), and Doda (2013) affected many buildings on hill slopes. India having a great arc of mountains consisting of the Himalayas defines the northern Indian subcontinent. These were formed by the ongoing tectonic collision of the Indian and Eurasian plates where housing densities of approximately 62159.2 per Sq Km are around as per 2011 Indian census. Hence there is a need to study on the seismic safety and design of these structures on slopes. Dynamic characteristics of hill buildings are significantly different from the buildings resting on flat topography, as these are irregular and unsymmetrical in both horizontal and vertical directions. The irregular variation of stiffness and mass in vertical as well as horizontal directions, results in centre of mass and centre of stiffness of a storey not coinciding with each other and not being on a vertical line for different floors. When subjected to lateral loads, these buildings are generally subjected to significant torsional response. Further, due to site conditions, buildings on hill slope are characterized by unequal column heights within a story, which results in drastic variation in stiffness of columns of the same storey. The short, stiff columns on uphill side attract much higher lateral forces and are prone to damage.

Figure 1: An aerial view of houses located on hill slopes in Sikkim


2. CASE STUDY AND ANALYSIS A five different cases of G+3 buildings on varying slope angles i.e., 0°,15°, 30°, 45° and 60° are designed and analyzed as per IS 456 in SAP2000 as shown in Figure 2 and 3. The properties of the considered building configuration in the present study are summarized below.

Structural element sizes Beams : 300 x 300 mm

Columns: 300 x 300 mm Slab : 120 mm thick

Material properties

Grade of concrete: M25 Grade of Steel reinforcement bars: Fe 415 Loading

Live load : 3 kN/m2 Floor finish load : 1kN/m2

Self-weight of slab : 3kN/m2

4 @ 3000 mm

Figure 2: G+3 RC framed structure (Reference building)

The building has been subjected and analyzed for earthquake load i.e., N90E component of Northridge ground motion with a PGA of 0.565g and magnitude M6.7.

4 @ 3000 mm

Col 1 Col 2 Col 3 Col5 Col 4



Table 1: Buildings considered for study: Details of 5 buildings

Building

Description

Number of bays (Both

directions)

Bottom column lengths (m)

Col 1

Col 2

Col 3

Col 4

Col 5

A G+3 Regular building (0°) 4 3 3 3 3 3

B G+3 building on 15° slope 4 6.2 5.4 4.6 3.8 3

C G+3 building on 30° slope 4 9.92 8.19 6.46 4.73 3

D G+3 building on 45° slope 4 15 12 9 6 3

E G+3 building on 60° slope 4 23.8 18.6 13.4 8.2 3

Two types of analyses were conducted viz., lateral load analysis and incremental dynamic analysis. It was observed from the initial results that the columns on the higher side of the slope i.e., short columns were subjected to more shear force then longer columns on the lower side. Finite element method is used to study the linear and non linear static and dynamic behavior of building on slopes, where as Applied element method is used for incremental dynamic analysis.

Figure 3: Model of Building on slope

30°30°


3. RESULTS AND DISCUSSION From the linear static analysis it is observed that the Shorter Columns is observed to take more loads since shorter columns are stiffer and hence has more stress carrying capacity. From Figure 4 column 1 is observed to have base reaction reduced to zero as slope angle increase because of long column effect.

Figure 4: Base reaction Vs Slope

3.1. DYNAMIC CHARACTERISTICS OF BUILDING An inertia force is caused due to the oscillation of building during an earthquake, where it is foremost for us to understand the mode of oscillation i.e., Natural period and deformed shape. Numerical results are used to study the dynamic behavior and the factors that influence it.

Table 2: Natural time period of Buildings on varied slope angles

0° 15° 30° 45° 60°

T1 0.724 0.881 0.994 1.0604 1.1545

T2 0.236 0.276 0.296 0.312 0.343

T3 0.1413 0.1544 0.159 0.162 0.1691

From table 2, time period of buildings on slopes increase with increase in the slope angle. Since there is an increase in column length of the building the stiffness and mass of it is varying which alters the natural time period. We know

Col 1

Col 2

Col 3

Col 4 Col 5



that time period of structure is directly proportional to both mass and stiffness as below ; ; Stiffness influencing natural period:

Increasing the length of column because of building position on slope decreases the stiffness and increases mass of the structure. A study has been carried out on buildings A, B, C, D and E; where the top three storey of the building has same mass and stiffness, only the bottom portion of the building varies. It has been observed that due to the increase of column length the building becomes more flexible with less stiffness. Figure 5 shows the Stiffness degradation of whole structure as well as the effective stiffness of bottom storey of the structure with respect to the increase of slope.

Figure 5: % Stiffness Vs Slope

Mass influencing Natural period: An increase in mass of a building increass its natural period. Buildings B, C, D and E are with same paln size, column sizes but with different columns length at bottom (Figureure 6). The total seismic mass of the reference building A is 1055.12 kN while that in other buildings there is an increase in mass.

2

Tm

k mT

kT

1


Figure 6: % Mass Vs Slope

3.2. TIME HISTORY ANALYSIS The building has been analyzed for Northridge ground motion with a PGA of 0.565g and magnitude M6.7.

Figure 7: Fourier amplitude of Northridge ground motion

Figure 9 shows the evaluation results of the linear time history responses of the five buildings. Since the natural frequency of structure is resonating with the predominant frequency from Figure 8 we can observe the response of building on 60° and 30° slope is observed to have maximum displacement when compared to that of others. When observed the mass participation of the five buildings we can say the every structure is predominant in its first mode of vibration. It is also observed from below plot the storey drift of the building on 45° slope is very less when compared to that of other slope angles.



Figure 8: Maximum time history response of each storey for five cases

Figure 9(a): Northridge ground motion

Figure 9 (b): Time history response of A, B, C, D and E buildings


3.3. PUSH OVER ANALYSIS

Figure 10: Pushover curves of A, B, C, D and E buildings

After designing and detailing the RC frame structure, a linear static pushover analysis is carried out for evaluating structurtal response.Figureure 10 shows the resulting capacity curves for the five cases. Initially they are linear where axial load is predominant but falls under inelastic range where the flexure and shear comes into picture. From Figure 10 the area under the pushover curve i.e. the capacity of building on flat surface is more than that of buildings on slopes. PLASTIC HINGES MECHANISM From Figure 11 we can easily observe the formation of hinge mechanism where as the slope increases the zone near the shoter coulmn is falling under E and D performance levels, which clearly indictaes the complete collapse of the structure. Comparision of Figureures b, c,d and e reveals that the pattern of forming hinges are quite similar. Plastic hinges formation starts with base columns of lower stories and end beams, then propagates to upper stories and continue with yielding of intermediate columns.



(a) Building A (b) Building B

(c) Building C (d) Building D

(e) Building E

Figure 11: Hinge mechanism of A, B, C, D and E buildings


FRAGILITY CURVES

To undertstand the expected damage of the structures of varying time periods, fragility curves are plotted. Equation used to calculate the damage of the structure as explained below

Emax = Area under the pushover curve with line dropped parallel to initial stiffness at the end point. Ei = Energy dissipated at every displacement (Area under the curve at every displacement with line dropped parallel to initial stiffness. Conversion from Roof Displacement to Spectral Acceleration:

Sdi: Spectral Displacement ∆roof: Roof displacement obtained from pushover curve PF1: Participation factors for the first natural mode of the structure Ø1, roof: Roof level amplitude of the first mode

T: Time Period of the structure g: Acceleration due to gravity

Figure 12: Fragility Curves



From Figure 12 we can observe that for a given ‘g’ value the expected damage is more in 15° and 30° slope buildings than building on falt surface. Whereas the damage of structure on 45° and 60° slope are less than 15° and 45° because of increase in column dimensions, but relatively the damage level is more in 60° than compared to that of 45° slope building.

3.4. INCREMENTAL DYNAMIC ANALYSIS To understand and to estimate the structural performance thoroughly under seismic loads a method so called as Incremental dynamic analysis is performed on to the structures. It involves subjecting a structure to one or more ground motions scaled to multiples levels of intensity. The main advantage of IDA is that it addresses both demand and capacity of structure. In the present study Applied element method (AEM) is used to perform IDA. Applied element method is a discrete method in which the elements are connected by pair of normal and shear springs which are distributed around the element edges. These springs represents the stresses and deformations of the studied element. The elements motion is rigid body motion and the internal deformations are taken by springs only. The general stiffness matrix components corresponding to each degree of freedom are determined by assuming unit displacement and the forces are at the centroid of each element. The element stiffness matrix size is 6x6.

Figure 13(a): IDA response of the Building on flat surface with spring failure

pattern In present study Northridge ground motion is scaled to 4 levels i.e. up to 1g and applied incrementally on to the structures. From Figure 13 we can observe the response of the structure increases as the ‘g’ value is amplified. At the end of each ground motion the damage of structure and the spring’s failure pattern can be observed at the top and bottom of the plot. For building on 45° and 60° slope the structure is unstable.


Figure 13(b): IDA response of the Building on 15° slope with spring failure pattern

Figure 13(c): IDA response of the Building on 30° slope with spring failure

pattern 4. CONCLUSIONS The study clearly helps us to understand the significant difference between the seismic behaviors of building on slopes to building on flat surface. In summary, the natural period of building depends on the distribution of mass and stiffness along the building. As the slope angle increases, it is observed that the short column resist almost all the storey shear since other columns are flexible and tend to oscillate. A hinge mechanism is formed near the shorter column zone and is damaged earlier as the slope angle increases. From the fragility curve we can



easily observe the damage of the structure is more when it is on steep angle. Major challenge which has to be focused further is considering together plan irregularity (i.e. Torsional effect) and vertical irregularity. It would be desirable to study more cases before reaching some definite conclusions about the behavior of reinforced concrete framed buildings on slopes. REFERENCES

1. A.R.Vijaya Narayanan, Rupen Goswami and C.V.R. Murty., 15WCEE 2012 Performance of RC Buildings along Hill Slopes of Himalayas during 2011 Sikkim Earthquake.

2. Pandey A.D, Prabhat Kumar, Sharad Sharma., International Journal of Civil and Structural Engineering Volume 2, No 2, 2011 Seismic soil-structure interaction of buildings on hill slopes.

3. B.G. Birajdar, S.S. Nalawade., 13WCEE 2004 Seismic analysis of buildings resting on sloping ground.

4. ATC 40, Seismic evaluation and Retrofit of Concrete Buildings, Volume 1. 5. Nicholas A, Roger B., Current science, Vol.79, No.1, 2000., A Note on the

Kangra Ms=7.8 Earthquake of 4 April 1905. 6. Dimitrios Vamvatsikos, C.Allin Cornell., Incremental Dynamic Analysis,

Earthquake Engineering & Structural Dynamics 2002 7. Tagel-Din Hatem, Kimiro Meguro., Applied Element Method for

simulation of Nonlinear materials: Theory and application for RC structures, Structural Eng./Earthquake Eng., JSCE, Vol 17,No.2,2000

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