SEISMIC MITIGATION PERFORMANCE ANALYSIS
STUDY OF IRREGULAR BRIDGES
GUIDED BY,SUBMITTED BY,
Mrs.Soni Syed Vinoob Ameer Ali
Assistant professor S4 CASE
Department of civil engineeringKME16CECS06
Bridges are lifeline structures and their performance is critical during and after the earthquake. A large number of bridges constructed around the world were designed during the period when bridge codes had no seismic design provisions, or when these provisions were insufficient according to the current standards. Also, due to aging and the growth of vehicular loads in magnitude and volume, many existing bridges in India are experiencing deterioration. As the construction of new bridges involves huge time and money, the repair and rehabilitation of old and damaged bridges are necessary, to preserve their load carrying capacity and service performance. The RC Bridge decks, supported on unanchored elastomeric pad bearings are free to move over substructure during an earthquake. Excessive deck displacement causes unseating and sometimes complete collapse of the deck leading to closure of the bridge for long periods. The problem worsens for irregular bridge with significant variations in the pier/pile heights. For example, decks of 268 m long Chengappa bridge across Austen Strait in Andaman islands was unseated during the 2004 Sumatra-Andaman earthquake, which had taller piers in the middle for navigational purposes. The bridge will be modelled in AutoCad and exported to CSI SAP2000 software to analytically investigate the Performance of the bridge using the finite element (FE) analysis. Nonlinear force–deformation behavior of elastomeric pad bearing will be modeled using Friction Isolator link element. The FE model should be able to predict the observed response in the 2004 Sumatra-Andaman earthquake for comparable ground motions. Under design level earthquake ground motions, the model will experience unseating of the decks and possible collapse indicating higher vulnerability of irregular bridges with unanchored elastomeric pad bearings. A suitable retrofitting technique will be proposed in order to arrest the displacement of deck slab and girders.
Bridges with elastomeric pad bearings have not performed well during past earthquakes. It is generally found that damage is limited to excessive displacement of bridge deck causing unseating and sometimes collapse of the superstructure. One such bridge, Chengappa Bridge, suffered from problem like unseating of the bridge deck from its bearings during 2004 Sumatra-Andaman earthquake. There was no noticeable damage to the substructure.
Chengappa Bridge is the longest bridge in the in the Andaman Archipelago, India. This is the only bridge which is constructed over Austen Strait at Mayabander that connects Middle Andaman Island to North Andaman Island along the Andaman Trunk Route (12°52’57″N and 92°52’28”) . The bridge is 268 m long RC bridge, simply supported over 12 cast-in-place piers. The length of pile varies along the length of the bridge (Fig. 1). The bridge deck is made of pre-cast girders and cast-in-situ slab. The superstructure merely rested on the pier caps with no fastening between any of them and bearings are simple unanchored neoprene pads.
Figure 1. Elevation of Chengappa Bridge
The intensity of ground shaking during the 2004 Sumatra-Andaman earthquake in Port Blair was VI–VII on the MSK intensity scale . Rai et al.reported that fifth, sixth, and seventh spans of Chengappa bridge were displaced by about 700 mm horizontally and 220 mm vertically from their original position and fell off the bearings (Figs. 2 and 3). Other spans, including the third, fourth, eighth, ninth, tenth, and eleventh spans moved by about 20–150 mm horizontally. The structural damage was mostly confined to the end beams and the expansion joints above the bearings, pedestals etc. As a result, the bridge was closed immediately after the earthquake and thus, hampered post-earthquake emergency services across the islands.
Fortunately, the shaking at the site was rather low (VI–VII on the MSK intensity scale), and girders did not fall off the piers. Due to the remote location of the bridge and the unavailability of required manpower and machinery in the islands, the bridge remained out of operation for about a year. Inadequate seating of bridge deck over pier and abutment is serious concern for safety during stronger earthquake in future. Fragility curves represent the probability of structural damage due to various ground shakings. and more so they describe a relationship between ground motion and level of damage.
Figure 2. Displacement of deck slab after Sumatra Earthquake
Figure 3. Lateral and vertical displacement of deck slab and girders after Sumatra-Andaman Earthquake
The seismic demand data were typically obtained from computationally intensive nonlinear time-history analyses and for most bridges, damage states were defined in terms of column or bearing Failures. The unsatisfactory seismic performance of Chengappa bridge during the 2004 Sumatra-Andaman earthquake was primarily due to uneven distribution of pier/pile stiffness and lack of restrainers to arrest excessive displacement of the bridge deck. Out-of-phase movement is observed due to irregularity which significantly increased the displacement demand on substructure as well as connections.
SEISMIC ANALYSIS METHODS
The responses of bridges when subjected to seismic excitation are evaluated by elastic and inelastic analytical methods. The methods include the linear static analysis, linear dynamic analysis, nonlinear static analysis and nonlinear dynamic analysis.
1.1.1 Elastic Analysis Methods
The assumption made in the elastic analysis is that, the structures respond elastically to earthquakes. The elastic analysis methods include the linear static analysis, linear dynamic analysis and elastic procedure using the capacity-demand ratios. These methods are also known as force-based methods, as the primary emphasis is on the forces within the structure.
18.104.22.168 Linear static analysis
The simplest procedure for the seismic analysis of bridges is the linear static analysis, which has the primary assumption that the structure remains elastic when subjected to a static force load distribution. The static force applied on the structure is equivalent to the inertial force distribution associated with the fundamental mode of vibration. The inertial forces are reduced by response modification factors in order to account for an inelastic
response. To ensure a ductile response under strong earthquake motions, a collapse mechanism is postulated, resulting in the identification of plastic hinge locations. Special ductile detailing is provided in the plastic hinge locations to ensure ductile flexural responses. In this procedure, it is assumed that the actual strength of the structure is higher than the design strength, and that the structure is able to dissipate energy through yielding.
22.214.171.124 Linear dynamic analysis
In the linear dynamic analysis, the force demands on various components are determined by elastic dynamic analysis. The dynamic analysis may either be a response spectrum analysis or an elastic time-history analysis. The application of the linear dynamic analysis is favoured, due to its ability to account for the effects of higher modes of vibration. The dynamic characteristics of the bridge can be explicitly understood.
126.96.36.199.1 Response spectrum analysis
The response spectrum analysis is used to obtain an approximate solution of the coupled, second-order, linear differential equations of motion under forced vibration. The dynamic characteristics of the structure, such as natural frequencies, mode shapes, modal mass participation etc., are determined by the initial eigen value analysis. The principle of the
orthogonality of the mode shapes with respect to the mass, stiffness and damping is applied, to uncouple the coupled equations through modal transformation. The uncoupled equation corresponds to the equation of motion of a single-degree-of-freedom (SDOF) system associated with the mode of vibration. Since the peak response of all the modes does not occur at the same time period, the application of the modal combination rules, such asSquare-Root-of-Sum-of-Squares (SRSS) and Complete Quadratic Combination
(CQC) methods which are based on the random vibration theory, are used to determine the peak response with contributions from all the modes.
188.8.131.52.2 Elastic time-history analysis
The elastic time-history analysis provides the exact response of a structure as a function of time, and is determined using a step-by-step numerical integration of the equation of motion. The peak response can be obtained from the maximum value of the response-history plot.
184.108.40.206 Capacity/demand (C/D) ratio method
In the C/D ratio procedure, the demand forces and displacements resulting from the elastic analysis actions are compared with the capacity of different members. The demands for C/D calculations include gravity effects. A C/D ratio less than one indicate that the member needs retrofitting.
Elastic methods (force-based methods) can predict the elastic capacity of a structure, and indicate where the first yielding will occur. The serviceability of the structural components is evaluated in the elastic range of strength and deformation. As the yielding progresses, the methods fail to predict the failure mechanisms, and do not account for the redistribution of forces. The post-elastic behaviour of the structures cannot be identified. But almost all structures are expected to behave inelastically during a strong earthquake. In order to account for the post-elastic behaviour, the seismicforce reduction factor or the response modification factor (q-factor or R-factor) which is a function of the period and ductility ratio of the structure, is utilised. Even then, the actual behaviour of the structure cannot be understood, which claims an in-depth knowledge about the inelastic performance of the structures. Thus, the linear analysis procedures fail to capture the essential response characteristics, and are not efficient for retrofitting strategies. The method is proven to be convenient for bridge design and assessment for minor earthquakes (Yu et al 1999).
The drawbacks of force-based methods have led researches to develop displacement-based procedures for seismic performance evaluation. Though the traditional approach focuses on force based analysis, Kawashima and others (Kawashima 2000; Symans et al 2003; Calvi 2004) suggested that deformations are more critical parameters for defining performance.
1.1.2 Inelastic Analysis Methods
When the structures are subjected to earthquakes of strong magnitude they undergo significant inelastic deformation, and their dynamic characteristics change with time. The inelastic response of the structure to seismic loading can be understood more explicitly through displacement-based seismic analysis; an analysis method in which the primary emphasis is on displacements rather than forces. Displacement-based methods of analysis are capable of realistically predicting the deformations imposed by earthquakes on structures and they emphasise a graphical evaluation of the seismic performance (Symans et al 2003). The damage potential and ultimate failure can usually be directed to the inelastic displacement. Inelastic analysis methods include nonlinear static analysis and
nonlinear dynamic time-history analysis.
220.127.116.11 Nonlinear static analysis
Nonlinear static analysis or pushover analysis is an inelastic analysis which gives a nonlinear response of the structure in a global force – displacement format. It is a static analysis that directly incorporates material and geometrical nonlinear characteristics as well as the redistribution of forces. This is a performance based design approach, which has three characteristics i.e., demand, capacity and performance. The demand represents earthquake ground motion, the capacity represents the structure’s ability, and the performance represents whether the structure is able to withstand the demand or not. The methods for nonlinear static procedure are the Capacity Spectrum Method, CSM (ATC-40 1996), the Displacement Coefficient Method, DCM (FEMA-273 1997), the secant method (COLA 1995), the N2 method (Fajfar 2000) and the Modal Pushover Analysis (MPA) (Chopra and Goel 2001).
18.104.22.168 Nonlinear dynamic time-history analysis
Nonlinear dynamic time-history analysis is often used if a high degree of accuracy is required. The basic analysis problem is posed by the requirement that the incremental dynamic forces acting on a structure during a small time step, be in equilibrium. The difference between an elastic and inelastic time-history analysis is often de ned by the characteristics of the displacement-dependent lateral resisting forces within the structure. For elastic systems, the lateral resisting forces are a single-valued function of the displacement, whereas for inelastic systems, the lateral resisting forces are dependent on the prior history of motion. To obtain the time-history of the response, a numerical integration method is used to solve the differential equations of motion. The advantages of the nonlinear dynamic time-history analysis include, the ability to describe nonlinear inelastic response, and to represent the time-history of the seismic response of the structure. Some disadvantages of the nonlinear dynamic time-history analysis are (a) the
structural elements of nonlinear models are considerably more complex than those of their linear elastic counterparts, (b) processing and evaluating the output often requires considerable effort and (c) the results can be extremely sensitive to the input time history and structural models.
Displacement-based procedures provide a more rational approach than force-based procedures, by considering inelastic deformations rather than elastic forces. The analysis procedure provides crucial information on the response parameters, which cannot be obtained with conventional elastic static or dynamic methods.
To study the seismic performance of an Irregular Bridge having variable pier length.
To develop a three-dimensional nonlinear finite-element model of the reinforced cement concrete bridge located in Andaman Islands.
To perform response spectrum analysis and nonlinear time-history analysis in the transverse and the longitudinal directions to determine the inelastic response in both the directions.
To compare the performance of the bridge using response spectrum and Non Linear Time History analysis
Propose a retrofitting method for the bridge to arrest displacement of deck slab and avoid future disasters.
Bridge collapses caused by earthquakes can be devastating. Study of super structure elements of irregular bridges was minimally done. So a detailed study was conducted.
In the present study, an existing reinforced cement concrete T-beam cum slab bridge located in Andaman Islands , was considered for its seismic behaviour.
The analysis of the bridge was carried out using SAP2000, a nonlinear software package.
The performance of the bridge components in transverse and Longitudnal direction was assessed.
The deck displacements of the structure when subjected to seven earthquake ground motions were evaluated.
Retrofitting of bridge was done using high tensile steel cables in order to increase seismic resistance/ increase overall stiffness of the structure.
2.1 THEORETICAL INVESTIGATIONS
Priestly et al 1996, reviewed the bridge damages caused by earthquakes, and identified basic design deficiencies which were the direct consequences of the elastic design philosophy. The design deficiencies identified were i) an underestimation of seismic displacements due to the usage of gross section member stiffness ii) wrong moment shape patterns under combined gravity and low seismic force levels iii) mislocation of the point of contra flexure and iv) negligence of the concepts of ductility and capacity design in the elastic design process.
Regarding the global geometric modeling of the bridge components, the geometric discretisation effort increases significantly from the lumped parameter models (LPM) to the structural component models (SCM) and on to the finite-element models (FEM).
In the LPM, the mass, stiffness and damping are conveniently lumped or concentrated at discrete locations. The elements are idealized to represent the prototype bridge behaviour. In the SCM, the idealized structural system is connected to resemble the geometry of the bridge prototype. The superstructure is represented by a single line of multiple three-dimensional frame elements (spine-type configuration) which passes through the centroid of the superstructure, and it remains elastic for lateral loadings. In the FEM, the actual geometry domain of the bridge is discretized with a large number of small elements.
Yu et al 1999 evaluated the seismic performance and survivability of two bridges, namely the Moses Lake bridge and Mercer Slough bridge in Washington, using the elastic analysis, inelastic pushover analysis, capacity spectrum method and nonlinear time-history analysis. The results of the analyses were used to evaluate the advantages, limitations, and ease of application of each approach, for the seismic analysis. The force and displacement demands of the Moses Lake bridge and Mercer Slough bridge for three different seismic ground motions from historical earthquake records, were determined. The earthquake records used were the 1940 El Centro Earthquake record, the 1949 Olympia Earthquake record and the 1995 Kobe Earthquake record. Under imposed ground motions the survivability of the bridge structures was checked. Regarding the survivability of the structure the pushover analysis and the nonlinear dynamic time-history analysis provided the same conclusion.
Abeysingye et al 2002 determined the inelastic response of the Greveniotikos bridge during a design-level earthquake using the nonlinear pushover analysis. A three dimensional finite element model of the bridge was used. Parametric studies on the foundation stiffness, P-? effect and plastic hinge properties were carried out to evaluate the effects of different assumptions made in structural modeling and analysis. Different foundation stiffness did not result in a significant variation in the expected inelastic displacement. The P-? effect during the structural deterioration was substantially negligible in the bridge. While various properties of plastic hinges and pier cross section were used, the difference in the global response was observed, but this difference was lesser than the result obtained by varying the foundation stiffness.
Symans et al 2003 evaluated the effectiveness of various commercially available computer programs namely, SAP2000, and GT-STRUDL, for performing practical displacement-based seismic analysis of highway bridges. A secondary objective was to identify the fundamental differences between force-based and displacement-based
methods of analysis, particularly as they apply to highway bridges. The experience gained by utilizing the computer software revealed that some programs are well suited
to displacement-based analysis, both from the point of view of being efficient and providing insight into the behavior of plastic hinges.
Kappos et al 2005 analyzed the Krystallopigi bridge – a twelve span structure of 638m total length that crosses a valley in northern Greece using the inelastic standard pushover analysis, the modal pushover analysis (MPA) as well as the nonlinear time-history analysis. In the MPA, pushover analysis was carried out separately for each significant mode, and the contributions from the individual modes to calculate the response quantities (displacements, drifts etc.) were combined, using an appropriate combination rule (SRSS or CQC). The MPA provides a significantly improved estimate with respect to the maximum displacement pattern, reasonably matching the
results of the more refined nonlinear time-history analysis, even for increasing levels of earthquake loading that trigger an increased contribution of the higher modes.
Lupoi et al 2007 studied the applicability of the MPA proposed by Chopra et al (2001) for the assessment of a highway viaduct built in the sixties, with a total length equal to 420m, having 11 spans each of 33m and a continuous reinforced concrete deck pinned over the piers. Differences between the nodal displacements estimated by the MPA, and those by the nonlinear time-history analysis were found to be in the order of 15%, independently of the intensity level of the ground motion.
Fu and AlAyed 2008 aimed at studying the applicability of a nonlinear static procedure, by implementing the displacement coefficient method (DCM) in bridges. The accuracy and reliability of the method was checked using the nonlinear time-history analysis. A three span continuous bridge was analyzed for two levels of seismic intensities (design level and maximum considered earthquake). The nonlinear static analysis gave conservative results when compared to the nonlinear time history
analysis at the design Level, while it provided more conservative results at the maximum considered earthquake level.
Paraskeva and Kappos 2009 suggested an improvement to the MPA procedure, that the deformed shape of the structure responding inelastically to the considered earthquake level is used in lieu of the elastic mode shape. The procedure is then verified by applying it to the bridge of 100m long three-span Overpass Bridge. The bridges were assessed using the response spectrum, the standard pushover analysis (SPA), the MPA and the nonlinear response history analysis for spectrum-compatible motions, and they concluded that the MPA provides a good estimate of the maximum
inelastic deck displacement for several earthquake intensities, while the SPA could not well predict the inelastic deck displacements of bridges, wherever the contribution of the first mode to the response of the bridge was relatively low.
Moni and Alam 2010 considered several retrofitting provisions on three column reinforced concrete bridge bent in Canada which was designed before 1965 with inadequate seismic detailing. As the bridge bent designed only for gravity load failed to meet the seismic standards, several retrofitting techniques such as steel jacketing, CFRP jacketing and steel bracing were considered to improve the seismic performance. The nonlinear pushover analysis was conducted for the original and retrofitted frames. An artificial ground motion record was used to evaluate the dynamic response of these structures. The seismic demand/capacity ratio, drift ratio,
ductility has been estimated. The best retrofitting technique has been proposed for such multi-column bridge bents designed only for gravity load.
Nirav Thakkar and Durgesh C. Rai 2014, Seismic vulnerability of an irregular bridge with elastomeric pads: a case study
Performance of the bridge was analytically investigated using the finite element (FE) analysis program SAP2000. Nonlinear force–deformation behavior of elastomeric pad bearing was modeled using Friction Isolator link element. The FE model was able to predict the observed response in the 2004 Sumatra-Andaman earthquake for comparable ground motions. Under design level earthquake ground motions, the model predicted that the bridge will experience unseating of the decks and possible collapse indicating higher vulnerability of irregular bridges with unanchored elastomeric pad bearings.
Literature survey/ review of past studies
Fixing the dimensions and material properties of various components of bridge
Modeling of irregular bridge with variable pier height using AutoCAD software
Analysis of structure: Response spectrum and Non linear Time History analysis is performed using SAP2000 software.
Propose retrofitting using retainers which could have resisted the failure of the bridge.
A conclusion has to be made to provide a suitable retrofitting technique for increasing the performance of the bridge performance under seismic loading.
4.1 SAP 2000
SAP2000 is a very sophisticated, intuitive and versatile user interface powered software From its 3D object based graphical modeling environment to the wide variety of analysis and design options completely integrated across one powerful user interface, This intuitive interface allows you to create structural models rapidly and intuitively without long learning curve delays. Complex Models can be generated and meshed with powerful built in templates. Integrated design code features can automatically generate wind, wave, bridge, and seismic loads with comprehensive automatic steel and concrete design code checks per US, Canadian and international design standards. Advanced analytical techniques allow for step-by-step large deformation analysis, Eigen and Ritz analyses based on stiffness of nonlinear cases, catenary cable analysis, material nonlinear analysis with fiber hinges, multi-layered nonlinear shell element, buckling analysis, progressive collapse analysis, energy methods for drift control, velocity-dependent dampers, base isolators, support plasticity and nonlinear segmental construction analysis. Nonlinear analyses can be static and/or time history, with options for FNA nonlinear time history dynamic analysis and direct integration. From a simple small 2D static frame analysis to a large complex 3D nonlinear dynamic analysis,
4.2 AutoCAD 3D
AutoCAD 3D is a drafting tool. Its tools help us to generate standard 2D and 3D drawings. The bridge was modelled in AutoCAD 3D since modelling of irregular pier height bridges are are difficult to model in SAP. The bridges that can be modelled using these softwares are regular, curved or uniformly varying types of bridges.
MODELLING AND VALIDATION
The bridge deck is 9.3 m wide and length of bridge is divided into 20.61 m individual spans with an expansion gap of 50 mm. It consists of 200 mm thick RC slab, supported on four 1.35 m deep RC precast I-girders at 2.3 m spacing. The diameter of piers is 1.5 m and they are connected at the top by 1.8 m wide & 0.8 m deep pier cap beam. The foundation consists of four piles of 0.8 m diameter, embedded at least 3.0 m inside the rock giving full fixity to the pile base. The elevation at top of pier cap and top of pile cap is 12.7 m and 3.0 m, respectively. The size of the elastomeric bearing pad used is 500 mm×320 mm and 52 mm thick. The shear modulus of elastomer used in the bearing pad is assumed as 1 MPa.
5.1.2 Section and Material Properties
Material and section properties of various components of bridge are provided in table 1 and table 2.
Table 1 : Material Properties and Sections
Sl.No. Element Dimensions Concrete Grade N/mm2 Reinforcement Grade (MPa)
Length(m) Depth(m) Width(m) 1. Longitudinal Girder 20.61 I section Depth-1.35m, Flange Width-0.8m, Web Thickness-0.6m, Flange Thickness-0.15+.155m 30 415
2 Cross Girder 2.3 1 0.25 30 415
3. Pier varies — 1.5 (dia.) 30 415
4. Pier Cap 7.9 0.8 1.8 30 415
5. Pile varies 0.8 (dia) 30 415
6 Pile Connecting Beam 6.9 0.8 1 30 415
7 Pile Cap —- 1 1.8 30 415
8 Deck Slab 20.61 0.2 9.3 30 415
Bent NO 2 3 4 5 6 7 8 9 10 11 12 13
Pile length(m) 7.5 9.5 9.5 11 11 12 12 11 9.5 8.5 8.5 7.5
Table 2 : Pile Length
5.1.3 Modelling of the bridge in AutoCAD 3D
The Chengappa Bridge was modelled in AutoCAD 3D using line elements. Elevation and 3D view of the model is given in figure 4 and 5.
Figure 4. Elevation of the Chengappa Bridge Model
Figure 5. 3D View of the Chengappa Bridge Model
5.1.4 Model Export/ Property Assignment to SAP 2000
The AutoCAD 3D model was exported to SAP 2000(figure 6). Properties mentioned in section 5.1.1 and 5.1.2 were assigned to the model. Neoprene Pad Bearings were assigned to the model as Friction Isolator link element. Supports were provided at ends of the Bridge as Rigid Links and intermediate supports were considered as simply supported.
Figure 6. 3D View of the Property assignments in SAP 2000
5.2.1 Modal Analysis
The fundamental time period of the bridge along transverse direction and longitudinal direction is 1.563s and 1.45 s as against 1.763s and 1.63s as per the reference paper and the mode shapes. The local movement of middle three spans is observed in the fundamental mode along the transverse direction.
Figure 7. Fundamental Mode Shape along Transverse and Longitudinal Direction
The study bridge results in the fundamental time period of the bridge along transverse direction and longitudinal direction is 1.563s and 1.45 s as against 1.763s and 1.63s as per the reference paper.
The Andaman Islands have been placed in most severe seismic zone V of the Indian Seismic
Zone map. Many large earthquakes have visited the region in the past. The most significant one in the recent times was M 8.1 event on 26 June 1941which caused extensive damage in the Andaman Islands, including Port Blair. The Andaman Islands is surrounded by thrust and strike slip faults. Since 1973 nearly a dozen earthquakes have occurred in the region with at least one event greater than M6 which suggests that the region is witnessing a new phase of seismic activity. Moreover, these islands can be affected by large earthquakes in the region occurring on the boundary between Indo-Australian and Eurasian plates, as it happened in the 2004 Great Sumatra-Andaman earthquake
6.1 Actual Scenario of the bridge during 2004 Sumatra-Andaman Earthquake
The intensity of ground shaking during the 2004 Sumatra-Andaman earthquake in Port Blair was VI–VII on the MSK intensity scale. It was reported that fifth, sixth, and seventh spans of Chengappa bridge were displaced by about 700 mm horizontally and 220 mm vertically from their original position and fell off the bearings (Figs. 3 and 4). Other spans, including the third, fourth, eighth, ninth, tenth, and eleventh spans moved by about 20–150 mm horizontally. Refer Figure 2 and 8.
Figure 8. Lateral and vertical displacement of deck slab and girders
6.2 Seismic Parameters for the bridge
The Bridge is located in Seismic Zone V. As per IRC 6 and IS 1893:2002 the seismic parameters considered , Zone Factor(Z) for Zone 5 as 0.36,Importance Factor(I) as 1.5 and Response Reduction Factor (R) as 5.
6.3 Indian Standard IS 1893:2002 Response Spectrum Curve
Indian seismic code IS 1893:2002 specifies a response spectrum curve based on fundamental time period of the structure and other seismic parameters as defined in section 6.2.Refer figure 9 which shows the response spectrum curve for 2% damping to be used in response spectrum analysis.
Figure 9. IS 1893:2002 Response Spectrum Curve
6.4 Response Spectrum Analysis
Response spectrum analysis (RSA) is a linear-dynamic statistical analysis method which measures the contribution from each natural mode of vibration to indicate the likely maximum seismic response of an essentially elastic structure. Response-spectrum analysis provides insight into dynamic behavior by measuring pseudo-spectral acceleration, velocity, or displacement as a function of structural period for a given time history and level
of damping. It is practical to envelope response spectra such that a smooth curve represents the peak response for each realization of structural period.
Scaling of the response spectra curve was done as per the Indian standard IS 1893:2002 recommendation i.e design base shear ( Vdb) shall be compared with a base shear ( Vb) calculated using a fundamental period T of the structure , Where Vdb is less than Vb all the response quantities is to be multiplied by Vdb / Vb.
Response spectrum analysis gives an insight into the elastic behavior of the bridge during a maximum considered earthquake i.e IS 1893:2002 target spectrum. The analysis was done in SAP 2000 and response of the bridge was analysed.
6.4.1 Performance in IS 1893:2002 Earthquake Spectrum (RSA)
The bearing displacement under IS 1893:2002 earthquake spectrum is found to be varying from 100 mm to 625 mm, with an average of 350 mm, along the transverse direction of the bridge. Fig. 10 shows the transverse displacement of the deck slab at each pier after response spectrum analysis. The average transverse displacement of deck over all the piers is more than the threshold limit of 250 mm, which indicates that if the bridge is subjected to earthquake spectrum, it will become unusable.
Figure 10. Transverse Displacement profile of Deck Slab
6.5 Non Linear Time History Analysis(NLTH)
Nonlinear dynamic time-history analysis is often used if a high degree of accuracy is required. Since the bridge has a high degree of structural irregularity due to variation in pier height therefore it is necessary to perform Non linear time history analysis. This results in a higher accuracy of displacements than what was obtained in linear response spectrum analysis.
ASCE 07-05 standard specifies a requirement of minimum three accelerogram for the analysis. For the present case seven earthquake accelerograms are used in the analysis.
The earthquake data is obtained from Peer Ground motion database. The target spectrum is the IS 1893:2002 spectra at soft rock(Site Class C). The earthquake data’s are then scaled with respect to the target spectrum. The scale factor is then applied for the relevant load case in SAP2000. The component considered is the maximum Horizontal component for defining the time history functions.
6.5.1 Selected Ground Motions
According to Global seismic hazard assessment program the maximum seismicity in the region of Andaman is of value greater than M8 with a PGA value between 0.25g to 0.35g. Refer figure 11 and 12.
According to National Disaster Management Authority of India the Maximum potential magnitude in Andaman region is M8.4. Refer figure 13.
Seismicity of the region indicates that the bridge site can experience earthquake from variety of sources with epicentral distance ranging from as near as 15 km to as far as 1200 km. Earthquake may occur in the region with thrust type or strike slip type fault mechanism. The bridge is founded on rock. The List of Ground motions selected are as listed in table 3.
Figure 11. Seismic Hazard Map of India(GSHAP)
Figure 12. Probabilistic Seismic Hazard Map of India
Figure 13. Seismicity Map of India(GSHAP)
The details of earthquake accelerograms are obtained from PEER Ground motion database. It was scaled to IS 1893:2002 spectra by using the online tool in PEER ground motion database.
ASCE 07-05 standard states that the accelerogram which is to be considered for analysis to be scaled between 0.2Tn to 1.5Tn, where Tn stands for fundamental time period of the structure.
Table 3 : List of Ground Motions for NLTH analysis
Sl.NoEvent Name Station Name Magnitude (M) Epicentral Distance(km)
ED1 Northridge-01, 1994 Pacific Palisades – Sunset 6.69 18.2
ED2 Tabas, Iran, 1978 Dayhook7.35 20.6
ED3 Kern County, 1952 Taft Lincoln School 7.36 43.5
ED4 Taiwan SMART1, 1986 SMART1 E02 7.30 71.4
ED5 Denali, Alaska, 2002 TAPS Pump Station #09 7.90 94.4
ED6 Kocaeli, Turkey, 1999 Manisa7.51 325
ED7 San Fernando, 1971 San Diego Gas ; Electric 6.61 224
Fig. 14 shows the response spectra of the selected motions after scaling in comparison with IS 1893 spectra for the bridge site. It can be seen that energy of the motions, recorded at an epicentral distance of more than 100 km (ED6 and ED7), is concentrated within range of 1 s to 2.5 s period, similar to the 2004 Sumatra-Andaman earthquake ground motion. Hence, a bridge having fundamental time period within the range of 1 s to 2.5 s will be severely affected if earthquake intensity is significant.
Figure 14. Comparison of Response Spectrum
6.5.2 Performance in Design earthquake scenario using NLTH analysis,
The maximum deck displacement under design earthquake is found to be varying from 74 mm to 1718 mm, with an average of 470 mm, along the transverse direction of the bridge.
Elastomeric pad was placed such that the 500 mm side was parallel to the transverse direction of the bridge due to which bearing instability will occur when the displacement exceeds half the size of pad, i.e., 250 mm.
Fig. 15 shows the transverse displacement of the deck slab for the selected seven ground motions. The average transverse displacement of deck over all pier is more than the threshold limit of 250 mm, which indicates that if the bridge is subjected to design level earthquakes, all decks will fall from bearings pads and due to impact there may be damage to the soffit of beams and pier caps.
These results of analysis match well with the observed displacement of the deck after the 2004 Sumatra-Andaman earthquake. Thus we can conclude that the structure will be damaged again once an earthquake of similar magnitude occurs in this region. Retrofitting of the bridge needs to be done in order to avoid future damage due to earthquakes.
Figure 15. Transverse Displacement Profile of Deck Slab
6.6 Comparison of Results (RSA vs NLTH Analysis)
Response spectrum analysis and Non Linear Time history analysis was done for the Bridge. The purpose of doing this is to suggest based on the criticality of the structure which type of analysis needs to be performed in order to get acceptable performance of the structure under seismic loading.
Fig 14 and Fig 15 shows the deck displacement using RSA and NLTH analysis. It was found that average displacement was around 350 mm for RSA and 500mm for NLTH. It was also observed that there was sufficient variation in individual values of deck displacement. Values obtained were greater for NLTH analysis than RSA.
Therefore it can be suggested that for a critical structure especially in a seismic zone area, NLTH analysis can provide greater and more accurate responses in comparison to Response Spectrum analysis.
In order to study the effect of restrainer on seismic performance of the study bridge, restrainers were provided in both transverse and longitudinal directions of the structure and its performance was analysed. Providing restrainers is one of the effective retrofitting techniques with respect to time and cost.
The displacement of the deck slab and girders are found to be very much greater than the threshold value of 250mm. Retrofitting of the bridge using new type of bearings is not a suitable option for the bridge under study, since the size of the bearing to be provided in order to minimize displacement is greater than what is provided i.e 52 mm thick. This will increase the cost substantially due to variation of vertical alignment of the bridge as well as cost associated with the retrofitting process.
One of the methods suggested by US Department of Transportation (Federal Highway Administration) for retrofitting is by providing restrainers using high tensile cables bolted to pier cap and longitudinal girder in transverse and longitudinal direction for minimizing the displacement in their respective directions. Refer Fig. 16 for details of the longitudinal restraints to be provided.
Figure 16. Cable Restraints for minimizing Longitudnal displacement
In case of the bridge under study both longitudinal and transverse restraints are provided. The material used is Grade 270 tendon confirming to ASTM A416 standard. The cable is having a axial stiffness of 2.58 x 108 kN/m which was selected using trial and error method and is modelled a plastic (wen) element. Diameter of the cable can found out using the equation 1.0
K=EAL1+w3L2EA12T3 ———-Eq 1.0
K-Stiffness of the Cable
E-Modulus of Elasticity
w –weight per unit length of the cable
L-Length of the cable
Refer Figure 17 and Figure 18 which shows the transverse(Res-T) and longitudinal(Res-L) restraint provided in the SAP2000 Model .
Slabs are assumed to be connected using shear rods of 25mm dia HYSD 500 grade so that the slabs do not get displaced individually when the bridge is subjected to seismic forces. This needs to provided since the slabs are simply supported and do not have any rigid connection with the longitudinal and cross girders. The shear rods are modelled as Plastic(wen) in SAP 2000.Refer Figure 19
Figure 17. Cable Restraints in Longitudinal and Transverse Direction in SAP Model
Figure 18. Cable Restraints in Longitudinal and Transverse Direction
in SAP Model (Elements Included)
Figure 19. Link Rod connection between deck slab in SAP2000 model
7.1 Effect of Restrainer on Seismic Response of the Bridge
Provision of restrainers in transverse and longitudinal direction adds to overall stiffness of the system and the fundamental period of structure along transverse direction and longitudinal direction decreased from 2.300s and 2.030s to 1.512s and 1.066 s, respectively.
Due to restrainers, the dynamic characteristics of the bridge improved significantly as first two modes contribute to most of the dynamic response as opposed to multiple modes in absence of restrainers.
The deck displacements with and without restrainers are compared in Table 4. For the seismic analysis without restrainer, the average of maximum displacement along transverse direction is found to be between 60 mm and 1174 mm and for analysis using restrainers, as expected showed a significant reduction in displacement along transverse direction. The average maximum displacement was observed between 2mm and 57mm.
Table 4 : Average Transverse Deck Displacement with and without Restrainer
Ground Motion No. Average Transverse Displacement(mm)
Without Restrainer With Restrainer
ED1 74 3
ED2 233 3
ED3 210 2
ED4 60 2
ED5 481 6
ED6 1084 57
ED7 1174 51
Shear rods did not have much effect in arresting the displacement and it was also found out that the variation in time period with and without shear rods was negligible. The advantage of providing shear connection between deck slab was that it avoided uneven displacement of deck slab at the expansion joints. Thus the slab expansion joints will not be damaged to a great extend in case the bridge is subjected to seismic forces/stresses.
The deck displacements in longitudinal directions were also reduced significantly due to the effect of restrainer. It can be seen in Table 5 that the average longitudinal displacement without restrainer varied between 50mm to 995mm. This will result in severe pounding between deck slab which will ultimately lead to damage of deck slab, bearing , expansion joint. It was observed that the deck displacements with restrainers varied between 0mm to 15mm
Table 5 : Average Longitudinal Deck Displacement with and without Restrainer
Ground Motion No. Average longitudinal Displacement(mm)
Without Restrainer With Restrainer
ED1 77 1
ED2 200 3
ED3 173 2
ED4 47 0
ED5 407 8
ED6 880 12
ED7 995 15
The results obtained in response spectrum analysis vs time history analysis shows greater variations which leads to a conclusion that based upon criticality of the structure, geometric irregularity and seismic zones, specific type of seismic analysis method should be adopted for the design.
Bridges with varying pier heights or having high degree of structural irregularity needs to analysed using non-linear dynamic analysis in order to get more accurate analysis results.
Simply supported Girder bridges needs to be properly restrained with help of cable restrainers or any another form of restrainers in order to minimise the deck and girder displacements and thus increasing the stiffness of the bridge as a whole.
Depending upon the analysis longitudinal, transverse or combination of both type cable (high tensile strength steel wire rope) restrainers can be provided in order arrest displacement and damage due to seismic effects on the structure.
Fundamental time period of the structure decreased from 2.30 s to 1.51 s as the restrainers were provided which increased the stability of structure in case of future earthquakes.
Replacing elastomeric bearing may not be a possible solution for retrofitting bridges in all cases. Bridges which use elastomeric bearings have a bearing thickness of 52 mm when compared to roller bearing or friction pendulum bearing which requires a minimum thickness of 250mm.
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2 Nirav Thakkar and Durgesh C. Rai, “Seismic Vulnerability of an Irregular Bridge with Elastomeric Pads: A Case Study” Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering
3 Sruthi Chandran and P R Sreemahadevan Pillai 2017, Seismic vulnerability assessment of RC bridge –A Review.
4 José M. Jara ,Dorian Villanueva , Manuel Jara and Bertha A. Olmos 2013, Isolation parameters for improving the seismic performance of irregular bridges.
5 M Shizokua and Swagata Banerjee 2013, statistical and mechanistic fragility analysis of concrete bridges.
6 Abder Rahmane and Fouad Kehila 2014, Development of fragility curves for seismic evaluation of a reinforced concrete bridge