Port Buildings

Vulnerability Assessment of Port Buildings

by

Pradeep Kumar Ramancharla, Terala Srikanth, Chenna Rajaram, Bal Krishna Rastogi, Santhosh KumarSundriyal, Ajay Pratap Singh, Kapil Mohan

Report No: IIIT/TR/2014/-1

Centre for Earthquake EngineeringInternational Institute of Information Technology

Hyderabad - 500 032, INDIAMarch 2014

VACI/IIIT-H/Report: 01

Assessment of Vulnerability of Installation near Gujarat Coast Vis-à-vis Seismic Disturbances

Title: Final Report on Vulnerability Assessment of Port Buildings (VAPB)

International Institute of Information Technology Hyderabad

Institute of Seismological Research

Government of Gujarat, India

Ministry of Earth Sciences

Government of India

August 2013

Earthquake Engineering Research Centre International Institute of Information Technology Gachibowli, Hyderabad – 500 032, India


2

Participants

From

International Institute of Information Technology, Hyderabad

Ramancharla Pradeep Kumar

Terala Srikanth

Chenna Rajaram

From

Institute of Seismological Research, Govt. of Gujarat

Bal Krishna Rastogi

Santosh Kumar Sundriyal

Ajay Pratap Singh

Kapil Mohan


3



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Abstract

Ports are lifeline systems that function as a storage and maintenance facilities for the transport of cargos and people via water. The port structures are frequently exposed to failure under severe seismic loading. It was not only observed during 1995 Kobe earthquake but also during 1989 Loma Prieta and 1999 Kocaeli earthquakes. The scenario is more critical if the port sites are located within the seismically vulnerable area like Gujarat state of India. During 2001 Bhuj earthquake, Kandla port building was damaged. In this report, a study has been carried out to find out the damage of port buildings. For this purpose Kandla port building has been selected as a typical building and the same is analyzed and designed as per Indian standards. The port building is modeled using 2D Applied Element Method (AEM) to perform damage analysis typical port building. In addition to this other methods have been used to calculate the response of port building including soil-structure-interaction (Annexure of Port Building). These analyses gave good insights of structural behavior but their response values are low and hence not considered in calculating the damage. Method used to estimate the damage is presented in the main part of this report. Pushover analysis is done to get base shear vs roof displacement of building using displacement control method. Using energy dissipation approach, damage is quantified at every displacement level and normalized to 1. It means when D=0 then building will not experience any damage and if D=1 means it is complete collapse. The damage states of the structure were defined as no damage (D<0.2), slight damage (D<0.4), Moderate damage (D<0.6), severe damage (D<0.8) and complete collapse (D>0.8). A fragility curve has been developed to quantify the damage of building with respect to different peak ground accelerations. Based on the fragility analysis of port building the following recommendations are drawn. It is found that the damage to the typical port building is 0.16 when it is subjected to a peak ground acceleration of 0.218g from seismological studies as expected at KHF Mandvi. If the same building is located at Jodiya which experiences 0.377g the damage would be o.25 and in case of building located at Jhangi which experiences a peak ground acceleration of 0.396g from Katch Mainland fault the building would experience a damage of around 0.34 damage.


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Table of Contents

1. Introduction………………………………………...……………………………….….……1

2. Port buildings…………………………………………………………………….…….……1

3. Building details……………………………………………………………………….…..…2

3.1 Geometry…………………………………………………………………….…...2

3.2 Material……………………………………………..………………………….…4

3.3 Soil……..…………………………………………….……………………………5

4. Numerical modeling………………………………………………………………………...5

4.1 Finite Element Method……………………………………….…………………6

4.2 Applied Element Method…………………………………….………………...8

5. Pushover analysis………………………………………………………...………………..19

6. Fragility analysis for port building (calculation of damage)………………… ……..21

7. Conclusions…...…………………………………………………………………………….23

8. References…………………………………………………………………...……………...23

9. Annexures…………………………………………………………………………………..24


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List of figures

1. The actual Kandla port building……………………………………………………….3

2. (a) Elevation of port building and (b) column details of port building……………3

3. Reinforcement details for members (a) column-1 (b) column-2 and (c) beam…….4

4. Soil properties at different depths.....…………………………..……………………...5

5. Overview of numerical techniques………………………………..…………………..6

6. Modified Takeda model…………………………………………..……………………7

7. Modeling of structure in AEM and element shape, contact point and dof …….…8

8. Quarter portion of stiffness matrix……………………………………………….……9

9. Material models for concrete and steel………………………………………..………9

10. (a) Principal Stress determination and (b) Redistribution of spring forces at element edges…………………………………………………………………………..10

11. Modeling of the structure AEM …………………………………………......………19 12. Vulnerability assessment of structure (Amin Karbassi, 2010)…………………….20 13. Base shear vs Roof displacement for the port building………………………..…..21 14. Schematic diagram represents Base shear vs Roof displacement of port building

for calculating damage …………………………………………..……………………22 15. Spectral accelerations plotted at Mandvi, Jodiya and Jhangi………………...........22 16. Fragility curve of port building for different PGA values…………………............23


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List of tables

1. Port building details …………………………………………………………..……….3 2. Comparison of damage for spectral accelerations obtained from acceleration

response spectra of KHF Mandvi, NKF Jodiya and KMF Jhangi…………………35


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1. Introduction Ports are lifeline systems that function as storage and maintenance facilities for

the transport of cargos and people via water. The port structures are frequently exposed to failure under severe seismic loading, for example, the Hyogoken Nambu earthquake of January 17, 1995, had resulted in extended closure of the port of Kobe (Sixth largest container port in the world; Werner 1998) with extensive cost for repairs. The failure of particular port can be a major issue of national interest and huge economic loss. The failure of port facilities during earthquakes is observed during the Loma Prieta earthquake of 1989, the Kobe earthquake of 1995, and the Kocaeli earthquake of 1999 (Werner 1998; PIANC 2001; Takahashi and Takemura 2005 etc.). The scenario is more critical if the port sites are located within the seismically vulnerable area like Gujarat state of India. During the Bhuj Earthquake of 2001, the liquefaction failures are reported in nearby port facilities (Madabushi and Haigh 2005; Dash et al. 2008). Many pile supported buildings, warehouses and cargo berths in the Kandla port area were damaged during the same event. Dash et al. (2008) showed that during Bhuj earthquake of 2001, 10 m thick loose to medium dense fine saturated sand was liquefied at Kandla port site and resulted severe damage at the mat-pile foundation which was supporting customs office tower. During strong shaking under seismic conditions, liquefaction, lateral spreading, slope instability, soil structure interaction, and site-specific ground motions are of the major geotechnical concerns for port structures. India has 12 major ports & 187 (Gujarat-40, Maharashtra-53, Goa-5, Daman & Diu-2, Karnataka-10, Kerala-13, Lakshadweep Islands-10, Tamil Nadu-15, Pondicherry-1, Andhra Pradesh-12, Orissa-2, West Bengal-1, Andaman & Nicobar Islands-23) non-major ports across 7,517 km long coastline. Some of the port buildings (Jay Kumar and Deepankar, 2012) are described as follows:

2. Port buildings

Kandla port (latitude: 23.030N, longitude: 70.130E) is a protected natural harbor, situated in the Kandla Creek and is 90 kms from the mouth of the Gulf of Kachchh, India. Maharao Khengarji III of Kachchh built an RCC jetty in 1931 where ships with draft of 8.8 m could berth round the year. In 1955, Kandla was declared as a major port by the Transport Ministry of Independent India, and almost twelve states of India are dependent on the Kandla port for bulk cargo handling. Kandla port has 10 berths, 6 oil jetties, 1 maintenance jetty, 1 dry dock, and small jetties for small vessels with present cargo handling capacity around 40 million ton per annum (MTPA).

Mundra port (latitude: 22.740N; longitude: 69.710E) is located at 60 km west of

Gandhidham in Kachchh district of Gujarat, India. The port was initiated in 1998 by the


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Adani Group as logistics base for their international trade operations when the port sector in India was opened for private operators. It is an independent and commercial port with 8 multipurpose berths, 4 container berths, and a single point mooring (SPM), presently capable of handling of 30 MTPA cargo and has future plan to achieve 50 MTPA by the fast track developments.

Hazira (Surat) port (latitude: 21.130N, longitude: 72.640E) is situated on the west

side of the Hazira (District Surat) peninsula. The major development of the port in the form of liquefied natural gas (LNG) terminal was carried out by Royal Dutch Shell group. Further developments in the form of construction of private bulk handling facilities by various manufacturing groups are in progress and considerable amount of money is invested to accommodate further vessel handling capacity for the future growth of this port.

Dahej (District: Bharuch) Port (latitude: 21.690N, longitude: 72.5350E) is the most

modern commercial port and storage terminal in the Gulf of Khambhat (Cambay) on the west coast of India. The Port is capable of handling vessels of 6,000 DWT to 60,000 DWT, and the present Storage Terminal capacity is about 300,000 cubic meters of hazardous liquid and gaseous chemicals falling in ‘A’, ‘B’, and ‘General’ classes. The location also includes some private ports within the Dahej area including some future port facilities.

Among all the ports in Gujarat, Kandla port is one of the major ports. The ports

of Kandla, Mundra, Dahej and Hajira are considered in this analysis. The main objective of this project is to estimate the amount of damage to the port buildings subjected to various ground accelerations.

3. Building Details 3.1 Geometry of building

Kandla, located at the mouth of the Little Rann of Kachchh on the south eastern

coast of the Kachchh district, is one of the major seaport-city of Gujarat that got affected during 2001 Bhuj earthquake. This area is located about 50 km from the epicenter of the 2001 Bhuj earthquake. Many pile-supported buildings, warehouses and cargo berths in the Kandla port area were damaged during the earthquake. The present study analyses the failure of the 22m high six-floor building called the Port and Customs Office Tower located very close to the waterfront.

The building was founded on 32 short cast-in-place concrete piles and each pile

was 18m long. The piles were passing through 10m of clayey crust and then terminated in a sandy soil layer below.


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The Port of Kandla is built on natural ground comprising recent unconsolidated

deposits of inter bedded clays, silts and sands. The vertical prole of the region slopes downwards in the easterly direction towards the coast line at about 12.5m/km. The water table is about 1.230 m below the ground. Fig. 1 shows the view of the natural grounds on which the Port of Kandla was built. The tower of the Port and Customs office considered for the present case study is located very close to Berths IV of the Kandla Port. The complete building details are given in Table 1. Figure 1: The actual Kandla port building (Selected as a typical building for damage

estimation)

X

Y

Z


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Figure 2: (a) elevation of port building and (b) column details of port building.The plan and elevation details are shown in figure 2.

Table 1: Typical Port building details

Building Member Dimension

Building height 22 m Building plan at sill level 9.6 m x 9.8 m Foundation raft 11.45 m x 11.90 m x 0.50 m No. of columns 12 No. of piles 32 Length of pile 18 m Diameter of concrete pile 0.4 m Beam dimensions 0.25 m x 0.45 m Slab thickness 0.15 m Column-1 dimensions 0.45 m x 0.45 m Column-2 dimensions 0.25x0.25 m

3.2 Material properties Live load on floor = 2 kN/m2 Live load on roof = 0.75 kN/m2

Floor finishing = 1 kN/m2 Grade of concrete used = M25

Poisson’s ratio = 0.2 The reinforcement details for members column-1. Column-2 and beam are shown in figure 3.

(a) (b) (c)


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Figure 3: Reinforcement details for members (a) column-1 (b) column-2 and (c) beam

3.3 Soil properties

The properties of soil at a depth of 40 m are shown in figure 4. The water table is 5 m below the ground level. The Rayleigh α and β values are taken as 0.01.

Figure 4: Soil properties at different depths

4. Numerical Modeling The numerical techniques can be categorize in two ways. The first case assumes that the material as continnum like finite element method (FEM). The other category assumes that the material as discrete model like rigid body spring model (RBSM), extended distinct element method (EDEM) and applied element method (AEM) (Hatem, 1998). The brief overview of continuum modeling and discrete modeling are discussed in the subsequent sections.

0 m

10 m

14 m

22 m

32 m

42 m

Soft clay with traces of fine sand, LL=62-68%, PL=26-28%, Su=10 kPa and γ=16 kN/m3

Fine sand, N<15 and γ=17 kN/m3

Coarse sand, N<15 and γ=17 kN/m3

Brown hard clay, LL=54-77%, PL=36-64%, Su=100 kPa and γ=8 kN/m3

Clayey sand, N<50 and γ=18 kN/m3


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The RBSM performs only in small deformation range. EDEM overcomes all the difficulties in FEM, but the accuracy is less than FEM in small deformation range. Till now there is no method among all the available numerical techniques, in which the behaviour of the structure from zero loading to total complete collapse can be calculated with high accuracy. Figure 5 represents the overview of numerical techniques. The overview of FEM and AEM is as follows:

Figure 5: Overview of numerical techniques

4.1 Finite Element Method (FEM) Finite element method is one of the most important techniques used in the analysis. In this method, elements are connected by nodes where the degrees of freedom are defined. The displacement, stresses and strains inside the element are related to the nodal displacements. The accuracy of the element depends on the size of element. The analysis can be done in elastic and nonlinear materials, small and large deformations except collapse behavior. At failure, the location of cracks should be defined before analysis which is not possible in collapse analysis. The problem becomes much more complicated when the crack occurs in 3D problems. In this analysis Takeda model is used. This model has been widely used in the nonlinear earthquake response analysis of RC structures. The description of model is as follows:

1. The cracking load Pcr, has not been exceeded in one direction. The load is reversed from the load P in the other direction. The load P is smaller than the yield load Py. (Unloading follows a straight line from the position at load P to the point representing the cracking load in the other direction)

2. A load P1 is reached in one direction on the primary curve such that P1 is larger than Pcr but smaller the yield load Py. The load is then reversed to –P2 such that P2<P1. (Unload parallel to loading curve for that half cycle)

3. A load P1 is reached in one direction such that P1 is larger than Pcr, but not larger than the yield load Py. The load is then reversed to –P3 such that P3>P1.


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(Unloading follows a straight line joining the point of return and point representing cracking in the other direction)

4. One or more loading cycles have occurred. The load is zero. (To construct the loading curve, connect the point at zero load to the point reached in the previous cycle, if that point lies on the primary curve or on a line aimed at a point on the primary curve. If the previous loading cycle contains no such point, go to the previous cycle and continue the process until such a point is found. Then connect that point to the point at zero load. EXCEPTION: If the yield point has not been exceeded and if the point at zero load is not located within the horizontal projection of the primary curve for that direction of loading, connect the point at zero load to the yield point to obtain the loading slope)

5. The yield load Py is exceeded in one direction. (Unloading curve follows the

slope given by the following equation 4.0

y

yrD

DkK

= in which, kr = slope of

unloading curve, ky = slope of line joining the yield point in one direction to the cracking point in the other direction, D = maximum deflection attained in the direction of the loading and Dy = deflection at yield)

6. The yield load is exceeded in one direction but the cracking load is not exceeded in the opposite direction. (Unloading follows point 5. Loading in the other direction continues as an extension of the unloading line up to the cracking load. Then, the loading curve is aimed at the yield point)

7. One or more loading cycles have occurred. (If the immediately preceding quarter cycle remained on one side of zero load axis, unload at the rate based on point 2, 3 and 5 whichever governed in the previous loading history. If the immediately preceding quarter cycle crossed the zero load axis, unload at 70% of the rate based on point 2, 3 and 5, whichever governed in the previous loading history, but not at a slope flatter than the immediately preceding loading slope)

This model includes (a) stiffness changes at flexural cracking and yielding, (b) hysteresis points/rules for inner hysteresis loops inside the outer loop and (c) unloading stiffness degradation with deformation. The response point moves toward a peak of the one outer hysteresis loop.


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Figure 6: Modified Takeda model The ground motion characteristics and dynamic analysis of the structure will be discussed in the following sections. The same analysis is also done using Applied Element Method (AEM). The description of methodology and material modeling are described as follows:

4.2 Applied Element Method (AEM) Finite Element Method could not be able to simulate the complete collapse behavior of structure, whereas, EDEM method follows till structural collapse of the structure, but accuracy is lesser than FEM. The method which combines the advantages of both FEM and EDEM is AEM. This is the only method, which can be used for analysis from crack initiation, crack propagation to till the complete collapse of the structure. Failure of reinforcement can also be found out from this method, which is important in estimating damage. In this project, assessment of damage plays a vital role. Pushover analysis is one of the methods to estimate capacity of structure. To assess damage of port building, AEM method has chosen for further analysis. A brief overview of AEM is as follows: 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. The stiffness matrix components


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diagram is shown in figure 7. The first quarter portion of the stiffness matrix is shown in figure 8. However, the global stiffness matrix is generated by summing up all the local stiffness matrices for each element.

Figure 7: Modeling of structure in AEM and element shape, contact point and dof

Figure 8: Quarter portion of stiffness matrix The material model used in this analysis is Maekawa compression model (Tagel-Din Hatem, 1998). In this model, the tangent modulus is calculated according to the strain at the spring location. After peak stresses, spring stiffness is assumed as a minimum value to avoid having a singular matrix. The difference between spring stress and stress corresponding to strain at the spring location are redistributed in each increment in reverse direction. For concrete springs are subjected to tension, spring stiffness is assumed as the initial stiffness till it reaches crack point. After cracking, stiffness of the springs subjected to tension is assumed to be zero. For reinforcement, bi-linear stress strain relationship is assumed. After yield of reinforcement, steel spring stiffness is assumed as 0.01 of initial stiffness. After reaching 10% of strain, it is assumed that the reinforcement bar is cut. The force carried by the reinforcement bar is redistributed force to the corresponding elements in reverse direction. For cracking criteria (Hatem, 1998), principal stress based on failure criteria is adopted. The models for concrete, both


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in compression and tension and the reinforcement bi-linear model are shown in figure 9.

Figure 9: Material models for concrete and steel

To determine the principal stresses at each spring location, the following technique is used in this analysis. The shear and normal stress components at point A are determined from the normal and shear springs attached at the contact point location shown in figure 10. The secondary stress σ2 from normal stresses and at point B and C can be calculated by using the equation given below:

cB

a

xa

a

xσσσ

−+=2 (1)

The principal tension is calculated as:

2

2

2121

22τ

σσσσσ +

−+

+=

P (2)

The value of principal stress (σP) is compared with the tension resistance of the studied material. When σP exceeds the critical value of tension resistance, the normal and shear spring forces are redistributed in the next increment by applying the normal and shear spring forces in the reverse direction. These redistributed forces are transferred to the element center as a force and moment, and then these redistributed forces are applied to the structure in the next increment. It is assuming that failure inside the element is represented by failure of attached springs (Hatem et al., 2000). If the spring gets failed, then the force in the spring is redistributed. During this process, springs near the crack portion tend to fail easily. However, the main disadvantage of this technique is that the crack width cannot be calculated accurately. In each increment, stresses and strains are calculated for reinforcement and concrete springs. In case of springs subjected to tension, the failure criterion is checked.


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Figure 10: (a) Principal Stress determination and (b) Redistribution of spring forces at element edges

4.3 Response of structure

In order to begin any physical system, it is necessary to formulate it in a mathematical form. The general dynamic equation for a structure is as follows:

gUM)t(fKUUCUM &&&&& −∆=++ (4)

Where [M] is mass matrix; [C] is damping matrix; [K] is nonlinear stiffness matrix; ∆f(t) is incremental applied load vector ∆U and its derivatives are the incremental displacement, velocity and acceleration vectors respectively. The above equation is solved numerically using Newmark's beta (Chopra, 2001) method.

For mass matrix the elemental mass and mass moment of inertia are assumed lumped at the element centroid so that it will act as continuous system. The elemental mass matrix in case of square shaped elements is as follows:

=

0.6/4

2

2

3

2

1

ρρρ

tD

tD

tD

M

M

M

(5)

Where D is the element size; t is element thickness and ρ is the density of material. From the above equation it is noticed that [M1] and [M2] are the element masses and [M3] is the mass moment of inertia about centroid of the element. The mass matrix is a diagonal matrix. The response of the structure is very near to the continuous/distributed mass system if the element size becomes small. If the damping is present, the response of the


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structure will get reduced. The damping matrix is calculated from the first mode as follows:

nmC ωξ2= (6)

Where ξ is damping ratio and ωn is the first natural frequency of the structure. For finding out the dynamic properties such as natural frequencies of a structure requires eigen values. The general equation for free vibration without damping is: 0KUUM =+&& (7)

For a non trivial solution, the determinant of the above matrix must be equal to zero. The solution of determinant of matrix gives the natural frequencies of the structure. The displacement response of the structure is calculated using Newmark’s beta method. Initially the response is calculated with an element size of 0.25 m. As the size of the element decreases, the response level will get saturate. This means the response will be same with decreasing the element size further. The structure is modeled in FEM and AEM and the elevation views are shown in figure 11.


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Figure 11: Modeling of the structure in AEM

5. Pushover analysis About 130 RC buildings collapsed during 2001 Bhuj earthquake in Ahmadabad

alone. Nearly 25000 other buildings are designed and constructed in the same manner in these areas. Though these structures are still standing, serious concerns have been arisen on their safety during future earthquakes. There are many cities with these types of structures, their safety cannot be guaranteed, they may be seismically deficient. There is an urgent need to assess the seismic vulnerability of buildings in urban areas of India as an essential component of a comprehensive earthquake disaster risk management policy. Detailed seismic vulnerability evaluation is a technically complex and expensive procedure and can only be performed on a limited number of buildings. It is therefore very important to use simpler procedures that can help to rapidly evaluate the vulnerability profile of different types of buildings, so that the more complex evaluation procedures can be limited to the most critical buildings.

Pushover analysis is mainly to evaluate existing buildings and retrofit them. It can also be applied for new structures. RC framed buildings would become massive if they were to be designed to behave elastically during earthquakes without damage also they become uneconomical. Therefore the structures must undergo damage to dissipate seismic energy. To design such a structure, it is necessary to know its performance and collapse pattern. To know performance and collapse pattern non linear static procedures are helpful. It is an incremental static analysis used to determine the force-displacement relationship, or the capacity curve, for a structure. The analysis involves applying horizontal loads, in a prescribed pattern, onto the structure incrementally; pushing the structure and plotting the total applied lateral force and associated lateral displacement at each increment, until the structure achieve collapse condition. A plot of the total base shear versus roof displacement in a structure is obtained by this analysis that would indicate any premature failure or weakness.

Figure 12. Vulnerability assessment of structure (Amin Karbassi, 2010)


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Now to get the load vs displacement curve for a structure, the structure is

pushed using either load control or displacement control. In this analysis displacement control is used till complete collapse of the structure. The base shear vs roof displacement plot is shown in figure 13. In this analysis, no need to specify plastic hinges. All these effects are incorporated in the analysis. The failure locations, cracking in concrete and yield of steel are determined automatically. The procedure of failure pattern is already described in section 4.2. The stiffness of the structure getting reduced when the first crack starts or the first spring fails. The spring fails when the principle stress exceeds the limited value. Now the first spring fails at (4.75 m, 18.48 m) which causes crack in the structure. In this analysis, steel failure is also allowed. When the structure reaches the peak load value in the load vs displacement curve, it starts coming down for further increase in the displacement. Base shear of the structure is calculated w.r.t roof displacement. For each roof displacement, base shear is calculated as the summation of horizontal forces at the bottom of each column. If the analysis is in load control, it is necessary to calculate displacement and vice-versa.

Figure 13. Base shear vs Roof displacement for the port building


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6. Fragility analysis for port building

Now the area under the load vs displacement curve is the total energy dissipated in the structure. We calculated elastic and inelastic energy of the structure at each and every displacement. The schematic diagram represents calculation of damage from pushover curve shown in figure 14. The damage parameter (D) is denoted as the ratio of inelastic energy to the total energy of the structure. Damage parameter is a dimensional less quantity. The dissipated energy at point ‘i’ is inelastic energy in damage calculation. The dissipated energy till collapse gives rise to total energy in damage calculation. With these damage values, fragility curve has generated which is in terms of displacement. It is necessary to convert displacement into acceleration. Following is the procedure:

Step-1: Spectral accelerations (Sa) are calculated using 4̟(SD)/T2. Where SD=spectral displacement and T=time period. Step-2: The spectral displacement (SD) values are calculated from base shear relation

roof

roof

roofroof

a

.PFSD

;.SD.PF

;WS.V

φ

φ

α

∆=

=∆

=

(9)

Where, V-base shear, W-seismic weight of structure, PF-participation factor. Step-3: Fragility curve can be drawn with acceleration and corresponding damage.


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KHF Mandvi

PGA = 0.218 g

KMF Jhangi

PGA = 0.396 g

NKF Jodiya

PGA = 0.377 g

Figure 14. Schematic diagram represents Base shear vs Roof displacement of port building for calculating damage. For the point up to linear (elastic) there is no damage. At point i it may correspond to moderate (0.5), i+1 may correspond to severe damage (0.8) while the last point corresponds to total collapse. Total area under the envelope is Emax while Ei is the area fom origin to i.

Figure 15. Spectral accelerations from response spectra of KHF Mandvi, NKF Jodiya

and KMF Jhangi

Figure 16. Fragility curve of port building for different PGA values

The acceleration response spectrum is drawn at KHF Mandvi, NKF Jodiya and KMF Jhangi. The PGA values at these stations are 0.218g, 0.377 g and 0.396g respectively. Figure 16 gives the damage curve of port building for different PGA values of ground motion. For the structure like Kandla port building, the total damage of the structure like Kandla port building is at around 0.16, 0.25 and 0.34 for KHF Mandvi (0.218 g), NHF Jodiya (0.377 g) and KMF Jhangi (0.396 g) response spectra respectively.


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7. Conclusions The damage of the structure like Kandla port building is easily identified from fragility curves for different ground motions. Pushover analysis is done to get base shear vs roof displacement of building using displacement control method. Using energy dissipation approach, damage is quantified at every displacement level. A fragility curve has been developed to quantify the damage of building with respect to different peak ground accelerations. Based on the fragility analysis of port building the following recommendations are drawn. It is found that the total damage of the structure like Kandla port building is at around 0.16, 0.25 and 0.34 for KHF Mandvi (0.218 g), NKF Jodiya (0.377 g) and KMF Jhangi (0.396 g) response spectra, respectively.

8. References [1] Tagel-Din Hatem, "A New Efficient Method for Nonlinear, Large Deformation and Collapse Analysis of Structures", Ph.D Thesis, Civil Engg. Dept., University of Tokyo, September, 1998. [2] Anil K Chopra, "Dynamics of Structures-Theory and Applications to Earthquake Engineering ", Prentice Hall International Series, 1995. [3] Tagel-Din Hatem and 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. [4] Steven L.Kramer., "Geotechnical Earthquake Engineering", Pearson Publishers, 1996. [5] Dash SR, Govindraju L, Bhattacharya S, A case study of damages of the Kandla port and customs office tower supported on a mat-pile foundation in liquefied soils under the 2001 Bhuj earthquake. Soil Dyn Earthquake Eng 29: 333–346, 2008 [6] Madabushi SPG, Haigh SK, The Bhuj, India earthquake of 26th January 2001. A field report by EEFIT. Institution of Structural Engineers, London, 2005 [7] PIANC/MarCom WG34, Seismic design guidelines for port structures. International Navigation Association. A.A. Balkema, Lisse, 2001 [8] Takahashi A, Takemura J, Liquefaction induced large displacement of pile supported wharf. Soil Dyn Earthq Eng 25:811–825, 2005 [9] Werner SD (ed), Seismic guidelines for ports. Technical Council on Lifeline Earthquake Engineering Monograph No. 12, ASCE, 1998. [10] Amin Karbassi, Performance based seismic vulnerability evaluation of existing buildings in old sectors of Quebec, Ph.D Thesis, University of Quebec, 2010.


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Annexures of Vulnerability Assessment Port Buildings


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Annexure-I

Nonlinear Time History Analysis

A study has been conducted to study the dynamic nonlinear behavior of port building. The dynamic properties of the building are as follows: The fundamental period of structure is 0.77 sec and the period of structure from mode-2 to mode-7 are 0.225 s, 0.112 s, 0.072 s, 0.057 s, 0.049 s and 0.038 respectively. The procedure for finding out the response of the structure is already discussed in the earlier sections. Now the structure is subjected to several ground motions from different places of Bhuj namely, Kachchh Mainland Fault: Bharuch, Dholera, Lalpur and Mandvi; Katrol Hill Fault: Bharuch, Dholera, Lalpur and Mandvi. The geographical locations of Dholera, Bharuch, Lalpur and Mandvi are (22.25, 72.2), (21.74, 73.01), (22.35, 69.96) and (22.82, 69.35). The characteristics of ground motions are as follows:

Ground motion characteristics For engineering purposes, (1) amplitude (2) frequency and (3) duration of the motion are the important characteristics (Steven L Kramer, 1996). Horizontal accelerations have commonly been used to describe the ground motions. The peak horizontal acceleration for a given component of motion is simply the largest (absolute) value of horizontal acceleration obtained from the accelerogram of that component. The largest dynamic forces induced in a certain types of structures (very stiff) are closely related to the PHA. Earthquakes produce complicated loading with components of motion that span a broad range of frequencies. The frequency content describes how the amplitude of ground motion is distributed among different frequencies. The frequency content of an earthquake motion will strongly influence the motion of structure. The broad band width of the Fourier amplitude spectrum is the range of frequencies over which some level of Fourier amplitude is exceeded. Generally band width is measured at a level of 1/√2 times of maximum Fourier amplitude. The Fourier transform of an accelerogram (t) x&& is given by,

∫−∞

∞

= dte )t(x2

1)(X ti- ω

πω && (10)

Where, (t) x&& is the amplitude of the accelerogram. The duration of strong ground motion can have a strong influence on earthquake damage. It is related to the time required for accumulation of strain energy by rupture along the fault.


27

There are different procedures for calculating the duration of ground motion, Brackted Duration: It is the time between the first and last exceedances of a threshold acceleration (usually 0.05 g) Trifunac and Brady Duration: It is the time interval between the points at which 5% and 95% of the total energy has been recorded. In our analysis Bracketed duration is used for calculating the duration of ground motion. The details of the ground motions are listed in table 2 and the ground motion records and its Fourier amplitude spectrums are shown in fig 17-24.

Table 2: Details of ground motions

S.No Region Ground Motion

Amplitude (g)

Duration (sec)

Frequency (Hz)

1 Katrol Hill Fault (KHF)

Bharuch 0.012 - 7.0-9.0 (0.110-0.142 sec) 2 Mandvi 0.308 21.50 6.3-8.5 (0.110-0.158 sec) 3 Lalpur 0.091 8.48 6.2-9.5 (0.105-0.160 sec) 4 Dholera 0.013 - 5.8-7.1 (0.140-0.172 sec) 5

Kachchh Mainland Fault (KMF)

Bharuch 0.018 - 6.7-9.2 (0.108-0.150 sec) 6 Mandvi 0.122 14.80 5.5-8.5 (0.117-0.180 sec) 7 Lalpur 0.086 11.00 6.2-9.6 (0.104-0.161 sec) 8 Dholera 0.021 - 5.8-7.1 (0.140-0.172 sec)

(a) (b) Figure 17: Ground motion record of Bhuj earthquake at KHF Bharuch (a) Ground

motion record (b) Fourier amplitude spectrum


28

(a) (b) Figure 18: Ground motion record of Bhuj earthquake at KHF Mandvi (a) Ground


(a) (b) Figure 19: Ground motion record of Bhuj earthquake at KHF Lalpur (a) Ground motion

record (b) Fourier amplitude spectrum

(a) (b)


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Figure 20: Ground motion record of Bhuj earthquake at KHF Dholera (a) Ground motion record (b) Fourier amplitude spectrum

(a) (b) Figure 21: Ground motion record of Bhuj earthquake at KMF Bharuch (a) Ground


(a) (b) Figure 22: Ground motion record of Bhuj earthquake at KMF Mandvi (a) Ground



30

(a) (b)

Figure 23: Ground motion record of Bhuj earthquake at KMF Lalpur (a) Ground motion record (b) Fourier amplitude spectrum

(a) (b) Figure 24: Ground motion record of Bhuj earthquake at KMF Dholera (a) Ground


The characteristics of ground motion are given in table 2. Characteristics of ground motions considered in the study are amplitude, frequency content and strong ground motion duration. These characteristics play a major role in the calculation of nonlinear time history response of the structure. For high PGA, the damage to the structure is high. However, the same PGA if it is occurring at frequency much away from resonating of the structure, it may not yield significant damage. Also duration of strong motion plays a vital role. For the purpose of understanding the sensitivity of the structure’s response to the given ground motions, these addition work has been carried out. However, in the final calculation the damage parameter using fragility curve only PGA is used.

The displacement response of the structure is calculated using Newmark’s beta method. Initially the response is calculated with an element size of 0.25 m. As the size of the element decreases, the response level will get saturate. This means the response will be same with decreasing the element size further. The structure is modeled in FEM and AEM and the elevation views are shown in figure 25 and 26.


31

(a) (b) Figure 25: Modeling of the structure (a) AEM and (b) FEM


32

Figure 26: 3D Modeling of the structure in AEM

To find out the behavior of the port building, 8 different ground motions at Dholera, Bharuch, Lalpur and Mandvi on the faults Kachchh Mainland Fault (KMF) and Katrol Hill Fault (KHF) generated by Institute of Seismological Research (ISR) are applied to the structure. For all the ground motions, the response is calculated at the top of port building. The fundamental period of the structure in first mode is 0.77 sec. The second and third modes are 0.225 and 0.11 sec respectively. From table 2, the predominant frequencies range of ground motions is 0.11-0.18 sec which is far from the fundamental


33

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KHFBRCH

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KHFDHLRA

Displacement Response (m)

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KHFLAL

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KHFMAND

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KMFBRCH

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KMFDHLRA


0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KMFLAL

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KMFMAND

period of the ground motion. The third mode frequency of the structure is getting matched with predominant period of all the ground motions. It means that the structure is predominantly vibrated in third mode. The responses of the structure for all the ground motions are plotted in figure 27.

Figure 27: Displacement response of the port building at different places in Gujarat

Since the structure is modeled in 3D and with vertical irregularity, it has response in all three directions. The calculated responses are in flexible direction of the building. The displacement responses of the structure are 2.2E-5, 5.3E-5, 1.5E-4, 6.5E-4, 3.2E-5, 8.3E-5, 1.2E-4 and 2.4E-4 m. From the analysis, the maximum response obtained from KHF


34

Mandvi ground motion is 6.5E-4 m. This is because of high PGA value among all the ground motions. But, the response of the structure will effect because of frequency not from PGA. It would experience more response if the fundamental period falls in the range of predominant period of ground motion. But, in this case, the fundamental period of the structure is far from the predominant period of the ground motion. The frequency range of ground motions is 5-10 Hz and the fundamental frequency of the structure is 1.3 Hz which is far from the frequency range of ground motions. From the analysis, it is observed that the nonlinear response of the structure is similar to linear. It means that the structure has not yielded for the ground motions given. The maximum displacement responses for the ground motions are tabulated in table 3. Since the responses of structure are very low for given ground motions, it is difficult to determine damage.

Table 3: Maximum displacement responses for the ground motions


Max. Displacement Response (m)

1 Katrol Hill Fault

(KHF)

Bharuch 2.2x10-5 2 Mandvi 6.5x10-4 3 Lalpur 1.5x10-4 4 Dholera 5.3x10-5 5


Bharuch 3.2x10-5 6 Mandvi 2.4x10-4 7 Lalpur 1.2x10-4 8 Dholera 8.3x10-5

Annexure-II

Comparison of responses

The same structure is modeled in SAP 2000. The same dynamic equilibrium equation is used to obtain response of the structure using FEM also. In dynamic analysis, the mass of the structure is used to compute inertial forces and this mass is obtained from mass density of the material and volume of the element. The assigned masses to the elements are actually lumped and transferred at the joints. No mass moments of inertia are produced for the rotational degrees of freedom. For efficiency and accuracy point of view, SAP2000 always uses lumped masses. In a joint local co-ordinate system, the inertial forces and moments at a joint are given as,


35

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KMFBRCH

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KMFDHLRA


0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KMFLAL

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KMFMAND

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KHFBRCH

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KHFDHLRA


0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KHFLAL

0 5 10 15 20 25 30 35 40-1

0

1x 10

-3 KHFMAND

=

3

2

1

3

2

1

3

2

1

3

2

1

3

2

1

3

2

1

r

r

r

u

u

u

r

0rSym

00r

000u

0000u

00000u

M

M

M

F

F

F

&&

&&

&&

&&

&&

&&

(11)

Where second derivatives of ‘u’ and ‘r’ are translational and rotational degrees of freedom at the joints and u1, u2, u3, r1, r2 and r3 are the specified mass values. In this analysis, Fast Nonlinear Analysis (FNA) method is used, developed by Wilson 1989.


36

Figure 28: Comparison of displacement responses of the port building using FEM and AEM The displacement responses of the structure are 2.0E-5, 2.5E-5, 1.2E-4, 5.5E-4, 2.8E-5, 4.06E-5, 1.08E-4, and 1.78E-4 m. Figure 28 shows that the displacement response of port building using both FEM and AEM approaches and they represented with solid line (AEM) and dashed line (FEM) respectively. From the above approaches, the accuracy of responses is maintained between 85 to 95%. Table 4 shows the comparison of maximum displacement responses for different ground motions using above approaches. The nonlinear displacement response of structure for KHF Mandvi is higher among all the responses. It is because of higher PGA value. Since Gujarat is under highly seismic area, the structure is analyzed for zone IV & V.

Table 4: Comparison of maximum displacement responses for the ground motions using AEM & FEM


Max. Displacement Response (m) - AEM

Max. Displacement Response (m) - FEM

1 Katrol Hill Fault

(KHF)

Bharuch 2.2x10-5 2.0x10-5 2 Mandvi 6.5x10-4 5.54x10-4 3 Lalpur 1.5x10-4 1.2x10-4 4 Dholera 5.3x10-5 2.5x10-5 5


Bharuch 3.2x10-5 2.85x10-5 6 Mandvi 2.4x10-4 1.78x10-4 7 Lalpur 1.2x10-4 1.08x10-4 8 Dholera 8.3x10-5 4.06x10-5

Annexure-III

Response due to amplified ground motions Gujarat state is under seismic zone III, IV and V. The ground motions are generated at places along the coast line of Gujarat. The upper coastal line of Saurashtra region is under seismic zone IV and coastal line of Kachchh region is under seismic zone V. As per IS: 1893-2002, the seismic zone factor for IV and V are 0.24 g and 0.36 g respectively. To understand the behavior of the structure under these seismic zones, the ground motions are normalized to 0.24 g and 0.36 g. The normalized ground motions are applied to the structure. The displacement responses of the structure for 0.24 g and 0.36 g are tabulated in table 5.


37

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFBRCH - 0.24g

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFDHLRA - 0.24g


0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFLAL - 0.24g

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFMAND - 0.24g

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFBRCH - 0.24g

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFDHLRA - 0.24g


0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFLAL - 0.24g

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFMAND - 0.24g

Table 5: Maximum displacement responses for ground motions normalized to 0.24 and 0.36 g (AEM)


Max. Displacement Response (m) – 0.24g

Max. Displacement Response (m) – 0.36g

1 Katrol Hill Fault

(KHF)

Bharuch 5.4x10-4 8.0x10-4 2 Mandvi 6.4x10-4 9.6x10-4 3 Lalpur 4.4x10-4 6.5x10-4 4 Dholera 1.0x10-3 1.5x10-3 5


Bharuch 5.3x10-4 8.2x10-4 6 Mandvi 5.5x10-4 8.2x10-4 7 Lalpur 4.1x10-4 6.1x10-4 8 Dholera 1.0x10-3 1.5x10-3


38

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFBRCH - 0.36g

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFDHLRA - 0.36g


0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFLAL - 0.36g

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFMAND - 0.36g

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFBRCH - 0.36g

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFDHLRA - 0.36g


0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFLAL - 0.36g

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFMAND - 0.36g

Figure 29: Displacement responses of the port building for amplified ground motions Normalized to 0.24 g and 0.36 g

Since, all the ground motions are normalized to 0.24 g, the PGA value is 0.24 g. It means, the maximum lateral force applied onto the structure is same. Even though, the PGA value is same for all ground motions, the displacement responses are different. Structure effects only because of frequency and not of PGA. Significant structural damage would occur, if ground motion frequency comes closer to the structure’s


39

frequency. In this analysis, no structural damage is noticed during time history analysis after normalization. Because structure vibrates at much lower frequency and ground motions are at higher frequency. Since the responses of structure are very low for amplified ground motions, it is difficult to determine damage of structure through pushover analysis. However, these responses are not used in further analysis.

Annexure-IV

Comparison of amplified 2D & 3D responses In this section, comparison of FEM, AEM (3D) and AEM (2D) analyses are done. The responses of amplified ground motion (0.24g) are considered for the purpose of comparison. The 2D and 3D responses are not coinciding with each other because, structure has torsion. Torsion comes in the structure due to uneven distribution of mass at top floor level. The effect of torsion can be clearly seen from figure 30.

Annexure-V

Soil structure interaction analysis of port building Past earthquake history all over the world shows that the amplification of ground motion is highly dependent on the local geological, topography and geotechnical conditions. Many studies have been devoted for the estimation of local site effects. It is observed that large concentration of damage in specific areas during an earthquake is due to site dependent factors related to surface geological conditions and local soil. Generally, the soil layers over the firm bedrock may attenuate or amplify the bed rock earthquake motion depending upon geotechnical characteristics, their depth and arrangement of layers (Steven L Kramer, (2003)). Local amplification of the ground is often controlled by the soft surface layer, which leads to the trapping of the seismic energy, due to the impedance contrast between the soft surface soils and the underlying bedrock.

There are several problems in numerical modeling where media is either infinite or semi-infinite. One of them is modeling of soil underneath the footing. During past few decades, it is very well recognized that structure resting on soil interacts dynamically with soil during earthquakes. Modeling of this problem becomes difficult due to the reason that soil extends up to infinity. A wave that is radiated from the source travels up to infinity before its amplitude is reduced to insignificant value. One simple solution


40

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFBRCH

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFDHLRA


0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFLAL

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFMAND

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFBRCH

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFDHLRA


0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFLAL

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFMAND

to carry out the analysis is to model the boundary at infinitely large distance such that influence of the boundary is not affecting the results in the vicinity of the source. However, such a system takes huge amount of computation time and resources. For this reason, many researchers studied the problem by modeling the media incorporating absorbing boundary condition like viscous boundary condition.


41

Figure 30: Comparison of AEM-2D, AEM-3D & FEM responses for ground motions normalized to 0.24 g (solid line with blue-AEM-3D, solid line with black-AEM-2D, dotted line

with green-FEM)

When we deal with SSI, two types of mechanisms take place, those are, a) kinematic interaction and b) inertial interaction.

a) Inertial interaction: Inertia developed in the structure due to its own vibrations gives rise to base shear and moment, which in turn cause displacements of the foundation relative to the free-field.

b) Kinematic interaction: The presence of stiff foundation elements on or in soil cause foundation motions to deviate from free-field motions as a result of ground motion. Kinematic effects are described by a frequency dependent transfer function relating the free-field motion to the motion that would occur on the base slab if the slab and structure were mass less.

At low level of ground shaking, kinematic effect is more dominant causing increase of period. Observations from recent earthquakes have shown that the response of the foundation and soil can greatly influence the overall structural response. There are several cases of severe damages in structures due to SSI in the past earthquakes (1989 Loma Prieta Earthquake, 1995 Kobe Earthquake).

In this study, we are introducing the effect of soil structure interaction (SSI) for the port building structure. The length, width and depth of soil are 13.45, 14.0 and 1.0 m respectively. The young's modulus is taken as 0.21x109 kN/m2, Poisson’s ratio is taken as 0.2. Initially the response of the soil is calculated by fixing the viscous boundaries. In this analysis, all the ground motions normalized to 0.36 g are given to the structure. The responses are plotted at ground and top of the structure. The displacement responses for ground and structure due to SSI are shown in figure 31 and 32. By considering SSI, makes the structure more flexible, stiffness of the structure decreases, resulting into increase in the natural period of the structure. This increase in the natural period of structure leads to higher amplitudes in the response of structure. Due to SSI, the response of structure increases from 8.4E-4 m to 1.0E-3 m when subjected to KHF Bharuch ground motion. Since the responses of structure and soil are very low for given ground motions, it is difficult to determine damage of structure through pushover analysis. However, these responses are not used in further analysis.


42

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFBRCH - SSI

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFDHLRA - SSI


0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFLAL - SSI

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KHFMAND - SSI

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFBRCH - SSI

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFDHLRA - SSI


0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFLAL - SSI

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-3 KMFMAND - SSI

Figure 31: Responses of the structure due to soil-structure-interaction


43

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-7 KHFBRCH - SSI

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-7 KHFDHLRA - SSI


0 5 10 15 20 25 30 35 40

-1

0

1

x 10-7 KHFLAL - SSI

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-7 KHFMAND - SSI

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-7 KMFBRCH - SSI

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-7 KMFDHLRA - SSI


0 5 10 15 20 25 30 35 40

-1

0

1

x 10-7 KMFLAL - SSI

0 5 10 15 20 25 30 35 40

-1

0

1

x 10-7 KMFMAND - SSI

Figure 32: Responses of the soil due to soil-structure-interaction

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