Seismic Design of a Railway Viaduct in High Seismic Zone€¦ · The following paper outlines a...

9h Australian Small Bridges Conference 2019

Seismic Design of a Railway Viaduct in High Seismic Zone

Vishnu Balakrishnan, Chief Technical Principal, SMEC International, Australia

Ricardo Vitaliano Acosta Jr., Structures Design Manager, SMEC Philippines

Dr Nobuyuki Matsumoto, Civil Team Leader, Pacific Consultants Co. Ltd, Japan

Takayuki Omori, Dep. Civil Team Leader, Oriental Consultants Global Co., Ltd, Japan

Kaname Mizuno, Structures Team Leader, Pacific Consultants Co. Ltd, Japan

Onek Denis Obedi, Dep. Structures Team Leader, Pacific Consultants Co. Ltd, Japan

ABSTRACT

The design and detailing of rail viaducts for high seismic loads presents several unique challenges

that are often not covered adequately by codes of practice. For instance, designers must consider the

impact of the natural frequency of the structure on the safety of the train itself.

The following paper outlines a practical design approach for designing typical long, multiple span,

simply supported concrete viaducts for seismic events. It considers a staged design approach where

the safety of the train can be guaranteed under a so-called Level 1 earthquake and the safety of the

viaduct structure is checked under a higher Level 2 earthquake. The paper provides a detailed insight

into the benefits of using a push over method that accounts for the ductility of the viaduct piers over a

more standard force-based approach.

1 INTRODUCTION

The project will provide a high standard suburban commuter rail in the island of Luzon Philippines.

The project comprises the following components:

• Viaduct/ bridges over 35 km;

• Elevated embankment over 2 km;

• 9 bridges at river crossings and 3 highway/road bridge crossing;

• Depot, workshops and Operations Control Center (OCC); and

• 10 Stations.

The elevation along the alignment ranges from RL. 3.0 m to RL. 15.0 m above mean sea level

(AMSL). In general, the alignment is characterized by relatively flat terrain with an elevation

difference of less than 12.0m, and consists mostly of swampy areas and cultivated land.

SMEC International are the design sub-consultants and are responsible to carry out the Architectural,

Civil and Structural aspects of the project, for the Main Consultants, a joint venture of Japanese

Consultants.

The design and detailing of railway viaducts for high seismic loads presents several unique

challenges that are often not covered adequately by AASHTO, AustRoads or the Eurocode. For

instance, designers must consider the impact of the natural frequency of the structure on the safety of

the train itself under seismic conditions.

The following paper outlines a practical design approach for designing typical long, multiple span,

simply supported concrete viaducts for seismic events. It considers a staged design approach where

the safety of the train can be guaranteed under a so-called Level 1 earthquake and the safety of the

viaduct structure is checked under a higher Level 2 earthquake.

The paper provides a detailed insight into the benefits of using a push over method that accounts for

the ductility of the viaduct piers over a more standard force-based approach.


2 DESCRIPTION OF THE VIADUCTS

The viaducts are designed to be constructed as match cast precast segmental post-tensioned

concrete box girders. The simply supported spans are to be built span by span using over-slung

gantries due to:

• the length of the viaduct being sufficiently long enough to justify the capital and operating costs of the casting yard, molds equipment and gantries;

• the difficulty of access to transport segments along the crowded streets of Manila; and • the speed of construction required to meet the construction timeframe.

The typical span was determined to be 40 m based on:

• minimizing the construction depth of the box; • carrying out an economic analysis of spans versus foundation costs; and • the size of launching girders available in Asia.

The superstructure comprises a precast segmental box girder. The typical section of the box girder is

shown below in Figure 1.

Figure 1 Cross Section of Precast Segmental Box Girder Deck.

The section overall depth was determined to be 2.4m deep and an overall width of 10.3m to provide

for:

• Two standard gauge tracks (1435 mm) at 4m centers; and • 950 mm wide maintenance walkways with service troughs below each side.

Sloping webs were provided to improve the aesthetics of the viaduct.

The width of the base slab was determined from the following considerations:

• Sufficient distance between bearings to prevent uplift under torsional live load; • Sufficient distance between bearings to prevent uplift under seismic loads; and • Sufficient distance to provide for the post tensioning tendons in the base slab.

Each typical simply supported span consists of an abutment segment at each end and 12 typical

segments. Simply supported spans are typically 40 m long (centerline to centerline of piers) but may

vary in length between 24 m and 39 m to fit around existing constraints on the alignment. Constant

width webs are proposed to ease constructability and to maintain the number of typical segments.

The box was provided with internally post tensioned tendons. The tendons are galvanised steel duct

encased and are best suited for this form of construction as they have the largest eccentricity for

prestressing moments and hence, minimize the quantity of prestressing required. The tendons are


encased in concrete and are therefore less likely to suffer from vibration fatigue as compared to

external tendons.

The superstructure is supported on laminated elastomeric rubber bearings (two at each end) with a

steel seismic restraint pin at each end of each span into the pier head to transfer the large seismic

restraint forces to the substructure and to ensure that the superstructures at any pier do not displace

relative to each other and thereby are able to maintain the regularity of the track alignment. At one

end, the steel pins are provided with sufficient clearance to allow movement of the superstructure

under normal loading conditions (braking, temperature, creep and shrinkage).

The typical substructure comprises a reinforced concrete rectangular pier (2.5m wide (transverse to

bridge) x 3.5m long) with a pier head of 4.5 m wide x 3.0 m long to support the two adjacent spans. A

typical view of the substructure is shown in Fig. 2.

The typical pier is supported on 4 x 1500 mm diameter reinforced concrete bored piles socketed into

the founding material.

The minimum height of the pier above the pile-cap is 6m to provide for 5.4 m traffic clearance below

the superstructure and for minimum 0.6 m soil cover to the pile-cap. The maximum height of the pier

is approximately 20m.

The typical pile-cap was determined to be 7.2 m x 7.2 m x 2.5m deep with pile spacing of 4.5 m (3 x

pile diameter) in each direction.

Figure 2 Isometric View of Typical Pier.

Drainage pipes are located within the box girder and drain to a sump-pit in the top of the pier and

down the inside of the pier to connect to the longitudinal drains which outfall to the nearest river.

300Ø DRAINAGE

PIPE

4x1500Ø BORED

PILES

ELASTOMERIC

BEARINGS

HOLE FOR SEISMIC

RESTRAINT (EACH


3 DESIGN REQUIREMENTS

The project is designed in accordance with the following design codes:

• Department of Public Works and Highways, Philippines - Bridge Seismic Design Specifications 1st Edition 2013 (DPWH-BSDS) Ref.1;

• Department of Public Works and Highways, Philippines - Design Guidelines, Criteria and Standards; Volumes 1 to 6, 2015 (DPWH-DGCS) Ref.2;

• American Association of State Highway and Transportation Officials Guide Specifications for Load Resistance Factor Design Bridge Design 7th Edition (2012) including amendments up to 2016 (AASHTO-LRFD) Ref.3; and

• American Association of State Highway and Transportation Officials Guide Specifications for Load Resistance Factor Design Seismic Bridge Design 2nd Edition (2011) including amendments up to 2016 (AASHTO-LRFD-S) Ref. 4.

• Japanese Design Standards for Railway Structures and Commentary (Seismic Design) (2012) (JDSRS) Ref 5.

• Japanese Road Association Standard (JRA) (2012) Ref.6

It should be noted that the DPWH-BSDS and DPWH-DGCS refer to AASHTO LRFD-S for further reference and guidance.

3.1 Seismic Design Requirements

The seismic design criteria was adopted from the DPWH-BSDS. This code requires 2 earthquake

events to be considered:

• Level 1 Earthquake Event being a 1:100 year event with an associated Peak Ground

Acceleration = 0.12g; and

• Level 2 Earthquake Event being a 1:1000 year event with an associated Peak Ground

Acceleration = 0.60g.

Based on the Spectral Acceleration Maps for Level 1 and Level 2 Earthquake Ground Motion for the

bridge location from the DPWH-BSDS, the seismic response spectrum curves determined for the

various soil models are shown in Figure 3 below.

The following criteria was adopted from DPWH-BSDS (Volume 5 Cl 10.3):

• Ductility factor = 1.0; • Redundancy Factor = 1.0; • Operational Classification for viaduct = OC-II (Essential Bridges); • Resistance Factor (for all load effects) = 1.0 (AASHTO LRFD-S Clause 3.7); • Seismic Performance Zone = Zone 4

The Seismic Performance Level for OC-1 bridges is:

• Level 1 Event – Service Performance Level 1 (SPL-1) • Level 2 Event – Service Performance Level 2 (SPL-2) • Unseating of superstructures shall be prevented.

The limit state of the bridge for Seismic Performance Level 1 shall ensure that the mechanical

properties of the substructure and superstructure members and components are maintained within

the elastic range and that these members will perform without or with minimal damage.

The limit state of the bridge for Seismic Performance Level 2 shall ensure that:

• only the structural member where formation of plastic behavior (plastic hinging) is expected shall be allowed to deform plastically within the range of easy recovery of bridge function;

• Plastic hinges are allowed to form at the bottom of the pier columns for single column piers and at the top and bottom for rigid frame piers or piers rigidly connected with the superstructure; and

• No hinges are allowed in the piles or below ground elements in this case.

The AASHTO-LRFD traditional procedure to seismic design of bridges, which is adopted in DPWH-

BSDS, utilizes the force-based approach where structural damage is controlled by an assignment of a

certain level of strength derived by application of the response modification (R-factor).


Figure 3a DPWH Response Spectrums Used on the Project for the Various Soil Models.

Figure 3b Japanese Response Spectrums Used on the Project for the Various Soil Models (Refer Table 1 and Figure 7 for co-relationship of Japanese Soil Classes and DPWH Soil Classes).

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.00 1.00 2.00 3.00 4.00

Seis

mic

Co

effi

cien

t

Period of Structure

Seismic Coefficient Comparision - DPWH Response Spectrum Curves

Soil Models 1,2,4,7,8and 9 (Class D) L1

Soil Models 1,2,4,7,8and 9 (Class D) L2

Soil Model 3 and 6 (ClassE) L1

Soil Models 3 and 6(Class E) L2

Soil Model 5 (Class C) L1

Soil Model 5 (Class C) L2

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00000 1.00000 2.00000 3.00000 4.00000

Seis

mic

Co

effi

cien

t

Period of Structure

Seismic Coefficient Comparision - Japanese DSRS Response Spectrum Curves

DSRS L1 - G2

DSRS L2 - G2

DSRS L1 - G3

DSRS L2 - G3

DSRS L1 - G4

DSRS L2 - G4

DSRS L1 - G5

DSRS L2 - G5


For a major railway viaduct in a high seismic zone, it was considered that this approach had to be

strengthened to take account of a rigorous pushover assessment of displacement capacity as well as

a displacement check on the safety of operating trains during the earthquake event.

The AASHTO LRFD-S does not specifically address critical and essential bridges and does not

address railway bridges in particular, and therefore, additional reference was made to the JDSRS to

address the specific design requirements for displacement of the structure during railway operations

under seismic events.

The JDSRS considers that train has a natural transverse rocking response as it travels along the

railway. When the Level 1 seismic event occurs, the JDSRS requires that the transverse natural

period of the structure is limited such that the safety of the train from overturning due to the combined

response of the train and the substructure to the transverse seismic response is ensured. To simplify

this determination, the JDSRS has provided a graph of the range of natural period of the structure

versus the soil type versus the seismic intensity level (refer Figure 4).

The soil type classifications are based on the JDSRS classification system and are equated to the

DPWH soil classification types (refer Section 4).

The seismic intensity level shown in Figure 4, is determined from a study of Japanese Level 1

earthquake events and from comparison of the response spectrums (DPWH versus JDSRS), it can be

seen that the Level 1 response spectrums are similar – hence, the adoption of the JDSRS seismic

intensity level for Level 1 seismic events, for the purpose of ensuring the train safety during the Level

1 earthquake event (by preventing overturning of the train due to resonance of the train suspension

rocking and the frequency of the structural response), is considered to be acceptable.

Figure 4 Graph of Seismic Intensity vs Natural period of Structure for Operational Safety of Trains During the Level 1 Earthquake Event.

Hence, once the soil class is known and the transverse natural period of the structure is determined, it

can be quickly determined by reference to Figure 5, the structure is deemed to be compliant if the

intersection of soil class and transverse natural period is below the bold line.

Additionally, the Japanese Railway Design Team were of the opinion that the natural period of the

structure has to be less than or equal to 2.0 seconds. The principle of this requirement is to ensure

robustness of the system and to limit deflections during the seismic event. This requirement had no


real effect on the design except for piers which were taller than 16m. It should be noted that

deflections of the top of the pier at the Level 2 earthquake event for the 16m high piers is

approximately 350mm and hence, the need to impose a limit on the period of the structures to limit

the deflection.

A Type 1 Earthquake Resisting System was adopted – Ductile substructure with essentially elastic

superstructure (Figure 5). This category includes conventional plastic hinging in columns and walls

and abutments that limits inertial forces by full mobilization of passive soil resistance. A conventional

ductile response is required to be met (AASHTO LRFD-S Cl 4.7).

Figure 5 Type 1 Earthquake Resisting System Adopted for the Project.

A site specific ground shaking hazard assessment was not deemed to be required given the length of

the viaduct and the consistency of the geology.

The viaduct is classified as being in Seismic Design Category (SDC) D which requires that:

• Pushover analysis required; • Capacity design required; • SDC D level of detailing; and • Liquefaction assessment required.

Load factors and resistance factors are specified in AASHTO-LRFD-S (Clause 3.7) as 1.0 for all

permanent loads and as 1.0 for all factors respectively.

As the viaduct is defined as a Non-Regular Bridge (more than 6 spans), the elastic dynamic analysis

procedure is required. 5% damping was adopted to the response spectrum.

The elastic deflection demand calculated from the elastic dynamic analysis (Response Spectrum

Analysis) is required to be multiplied by the displacement magnification factor, Rd (AASHTO LRFD-S

Cl 4.3.3) to obtain the design demand displacement. This factor is a method of correcting for the

displacement determined from the elastic analysis for short period structures.

The demand capacity was then determined using a non-linear static analysis procedure (NSP or

pushover analysis).

Pushover analysis is an incremental linear analysis that captures the overall nonlinear behaviour of

the elements, including soil effects, by pushing them laterally to initiate plastic action. Each increment

of loading pushes the frame laterally, through all possible stages, until the potential collapse

mechanism is achieved. Because the analytical model used in the pushover analysis accounts for the

redistribution of internal actions as components respond in-elastically, NSP is expected to provide a

more realistic measure of behaviour than may be obtained from elastic analysis procedures.

The member ductility demand (µd) is defined as < 5 (AASHTO LRDF-S Cl.4.9) for single column

piers.

Column shear requirements to AASHTO LRFD-S (Cl. 4.10) and member capacity requirements to

AASHTO LRFD-S (Cl. 4.11) are also provided. Sections of members above and below the plastic

hinge have to meet the requirements of the overstrength factor x plastic moment of the hinge

(AASHTO LRFD-S Cl. 4.11.2 and 11.4.3).


P-delta effects were calculated and provided for in accordance with AASHTO LRFD-S (Cl. 4.11.5).

Capacity design was carried out to the requirements of AASHTO LRFD-S Section 8.

4 GEOTECHNICAL INFORMATION

A total of 485 boreholes up to 40 m depth were carried out over the length of the project –

approximately 1 borehole every 80 m length of project. There are approximately 997 piers on the

project.

Ideally, all piers should be designed using the geotechnical conditions obtained through field and

laboratory tests of the nearest borehole to the said pier. However, in large projects such as this

project where cost and project time become critical, it is general practice to group the boreholes into a

manageable set of representative cases that are used in the design of substructures.

4.1 Classification of Soil Models

A combination of probabilistic (using statistical parameters such as mean standard deviations and

correlation of borehole data) and deterministic (use of professional engineering experience and

judgement) approaches were used to develop the geotechnical models based on Standard

Penetration Test (N value) data. This methodology is shown in Figure 6.

To this end, 6 soil models were identified based on the boreholes available.:

• Model 1 – Average SPT N = 2 for the top 15m, then SPT N =50;

• Model 2 – Average SPT N = 6 for the top 15m, then SPT N =50;

• Model 3 – Average SPT N = 2 for the top 15m, then SPT N =10 for 15m then SPT N = 50;

• Model 4 - Average SPT N = 6 for the top 15m, then SPT N =15 for 15m then SPT N = 50.

• Model 5 – Average SPT N = 15 for first 3m; then N = 20 for next 4m and then SPT N = 50 for the rest of the depth; and

• Model 6 – Similar to Model 3 but top 6m is considered to be subject to a reduction factor for liquefaction

Refer to Figure 7 overleaf.

These soil models were related to the Japanese Soil Classes based on the estimated shear wave

velocities and are shown in the Table 1 below.

Figure 6 Methodology to Classify Boreholes into Soil Models.


Table 1: Geotechnical Soil Models

Project Soil

Models

DWPH (AASHTO) Soil Class

JDSRS Soil

Class

Typical Period of ground (to

JDSRS) (sec)

1 D G4 0.508

2 D G3 0.330

3 E G5 0.755

4 E G4 0.572

5 C G2 0.108

6 E G4 0.683

A total of 78 models were created to cater for the different pier heights in each soil model.

4.2 Determination of Linear and Non-Linear Soil Springs

4.2.1 Introduction

The horizontal, vertical, and vertical shear spring constants that were adopted for the project were

calculated from the equations presented in the DPWH BSDS (2013), which were in turn based on the

procedures outlined in the Japanese Road Association Standard (JRA) (2012).

4.2.2 Horizontal Spring Calculation

The calculation of the horizontal spring begins with calculating the horizontal subgrade modulus for a

rigid disc of 0.3-m diameter (kho), which is also referred to as the reference horizontal subgrade

modulus. This value is taken from the results of the standard plate load test, which measures the

load-deformation behaviour of a 0.3-m diameter disc. The subgrade modulus is measured as the

ratio of the load to the measured deflection. However, as it is not practical to perform plate load tests

along the length of the pile, the DPWH BSDS (2013) provides a correlation between the horizontal

subgrade modulus and the elastic modulus.

kho = 1/0.3 α Eo

Where:

Eo is the modulus of elasticity (kPa); α is the subgrade reaction coefficient (Table C.4.4.2-1, DPWH BSDS 2013) The reference horizontal subgrade modulus has to then be scaled up to the equivalent loading width

of the foundation (BH) to give the horizontal subgrade modulus (kh) for the given soil-pile

combination.

kh = kho (BH/0.3) (-0.75)

The equivalent loading width, BH, is a function of the characteristic depth of the pile.

BH =√(D/β)

Β = ∜((kh D)/4EI)

Where:

D is the pile diameter (m)

E is the pile modulus of elasticity (kPa)

I is the pile moment of inertia (m4)


Figure 7 Soil Class Summary showing Variation of SPT Count versus Depth from Ground Level.

The linear horizontal springs (Service Limit State and Extreme Limit State) are then calculated by

multiplying the horizontal subgrade modulus, kh, to the longitudinal cross-sectional area of the pile.

These spring constants may be used when analyzing piles that will remain within the linear range of

behaviour, i.e., deflections are small.

When considering the case wherein the pile deflections are large and are expected to behave in a

non-linear fashion, the non-linear horizontal springs (Extreme Limit State) are similarly calculated by

multiplying the horizontal subgrade modulus, kh, to the cross-sectional area of the pile. The difference

in the analysis between the linear and non-linear case is that the non-linear case assumes an

elastoplastic model load-deflection model for the pile.


Figure 8 Definition of Non Linear Horizontal Spring.

Transition from the elastic to the plastic state is defined as the point wherein the elastic curve reaches

the horizontal subgrade reaction upper limit (Phu). The horizontal subgrade reaction upper limit is

calculated as the passive earth pressure of the surrounding soil. For a multilayer soil, the passive

earth pressure is calculated as follows:

pP(n) =KP(n) γ(n) h(n) + 2C(n) √(KP(n) ) + KP(n) ∑[(γ(n-k) h(n-k) ]

Where:

Kp is the Rankine Passive Earth Pressure coefficient;

(n) is the nth layer of soil;

γ is the unit weight of the soil (kN/m3);

C is the cohesion (kPa);

h is the height of the soil (m) from ground surface;

n is the current segment number being analysed; and

k is the number of segments above the current segment.

Given the value of PHU and Kh, (Refer Figure 8), the displacement at which the ground will transition

from the elastic to the plastic state is defined as:

δHL = PHU / KH

4.2.3 Vertical Spring Calculation

The calculation of the vertical spring is similar to the procedure with the horizontal spring calculation in

that it begins with calculating the vertical subgrade reaction for a rigid disc of 0.3-m diameter (Kvo)

using the correlation to the elastic modulus given in JRA (2012). The vertical subgrade reaction (Kv)

is then calculated by scaling up the reference vertical subgrade modulus by the equivalent loading

width of the foundation (BV). The equations are as follows:

Kvo =1/0.3 α Eo

Kv = Kvo (BH/0.3)-0.75

BV =√(Av)

Where:

Eo is the modulus of elasticity (kPa);


α is the subgrade reaction coefficient (Table C.4.4.2-1, DPWH BSDS 2013);

Av is the cross sectional area of the pile (m2)

The linear vertical springs (Service Limit State and Extreme Limit) are then calculated by multiplying

the vertical subgrade modulus, KV, to the cross-sectional area of the pile. Once again, these spring

constants may be used when analyzing the piles whose vertical deflections are small.

For large pile deflections, the non-linear case has to be considered. The non-linear vertical springs

(Extreme Limit State) are also calculated by multiplying the vertical subgrade modulus, KV, to the

cross-sectional area of the pile. Once again, the difference in the analysis between the linear and

non-linear case is that the non-linear case assumes an elastoplastic model load-deflection model for

the pile.


the upper limit of the pile end bearing capacity (PNU). This upper limit is calculated as the end bearing

capacity of the pile.

Given the value of PNU and KV, the displacement at which the plastic will be reached is defined as:

δVL = PNU /KV

Figure 9 Definition of Non Linear Vertical Spring.

4.2.4 Vertical Shear Spring Calculation

The calculation of the vertical shear spring begins by multiplying the horizontal subgrade modulus, kH,

by 0.3 to give the vertical shear subgrade modulus (KSVB).

The linear vertical shear springs (Service Limit State and Extreme Limit State) are then calculated by

multiplying the vertical shear subgrade modulus, KSVB, to the surface area of the pile segment. Once

again, these spring constants may be used when analyzing the piles whose vertical deflections are

small.

For large pile deflections, the non-linear case has to be considered. The non-linear vertical springs

(ELS) are calculated by multiplying the vertical shear subgrade modulus, KSVB, to the surface area of

the pile segment. Once again, the difference in the analysis between the linear and non-linear case is

that the non-linear case assumes an elastoplastic model load-deflection model for the pile.



the upper limit of the pile shear capacity (PSV). This upper limit is calculated as the ultimate skin

friction of the pile.

Given the value of PSVB and KSVB, the displacement at which the ground will transition from the elastic

to the plastic state is defined as:

δSVL = PSVB / KSVB

5 STRUCTURAL MODEL FOR ELASTIC DYNAMIC ANALYSIS AND

PUSHOVER

5.1 General Model Definition

A spine model of each pier was created in the finite element program MIDAS Civil. Line elements can

behave three-dimensionally in the form of beam, beam-column elements and springs. A view of the

model is shown in Figure 10.

The hinge length was estimated using the recommendations of AASHTO-LRFD-S (Cl 4.11.6) as

typically 1.5m. The pier stem is modelled as 3m long elements to reflect the possibility of hinges at

the top and/or bottom of element. The pile cap is modelled as a rigid link from the underside of the

pier to the top of piles. Similarly, the piles are modelled as beam elements with nodes at 3m

vertically.

Actual section properties were modelled based on the shape and size of the elements. For the pier

and top of pile elements, the cracked inertias of the elements, based on the actual reinforcement

arrangement and material properties, was input.

Material properties were applied based on the nominal characteristic values specified.

Figure 10 3D view of Structural MIDAS Civil Model.

5.2 Loadings

The dead and superimposed dead load and 0.5 live load reactions from the superstructure were

modelled at the centroid of the deck as point loads.

The self-weight of the pier and piles were calculated automatically based on the cross-sectional areas

defined and the density of the material.

The weight of the pile cap was defined at the bottom of the pier as a point load.

All loads were specified to be converted into lumped masses during the analysis.

5.3 Boundary Conditions


Pile springs were applied to the piles at each node level to model the horizontal restraint and vertical

skin friction of the soil. These soil springs were modelled as horizontal and vertical bi-linear springs.

Bi-linear vertical springs were also applied to the pile toes and pile shaft to model the vertical support

of the ground.

5.4 Definition of Non-Linear Properties of Piles and Piers

The non-linear properties of the pier and piles were modelled using MIDAS General Section Designer

(GSD) in the form of Moment Curvature models for each element where plastic hinges are allowed to

form (at the bottom of pier columns and piles). Hinges are not allowed to form in the piles and the

hinge properties are defined to the piles to ensure that we can check to ensure that this is the case.

The concrete sections and arrangements of reinforcement was modelled in GSD.

The Mander Concrete model was adopted for the non-linear concrete stress strain model while the

Park Strain Hardening Model was adopted for steel reinforcement (Refer Figures 11 and 12). For the

purpose of the concrete and steel non-linear properties, the expected material properties (instead of

the characteristic material properties) was adopted as recommended in AASHTO LRFD-S.

Figure 11 Grade 40 Mpa Concrete – Mander Concrete Model for Stress-Strain.

The idealized moment curvature curves, (as stipulated in Figure 8.5.1 of AASHTO-LRFD-S) for the

pier and piles were then output for the applied axial loads. Iteration of the analysis was required to

determine the applied axial load for the Level 2 event. For the piles, two moment curvature profiles

were required – for the compression piles and for the tension piles.


Figure 12 Park Strain Hardening Steel Reinforcement Stress Strain Input – ASTM Grade 60 (420 Mpa) Reinforcement Shown.

6 ANALYSIS PROCEDURE

The analysis procedure adopted is described below:

1. Carry out the elastic response spectrum analysis;

2. Plot the transverse natural period of the model against the soil class on Figure 4 and ensure that

it is below or on the bold line;

3. Ensure the longitudinal natural period is less than or equal to 2.0 seconds. If either of this step or

step 2 are not met, the structure has to be stiffened by either adding more piles or increasing the

column size and/or reinforcement, in the required direction. If this is done, then step 1 above has

to be repeated. Note that this was merely an additional requirement which the Design Team felt

was prudent – the Japanese DSRS does not have such a limitation but where the period exceeds

2, requires more detailed investigation into the behavior of hinge formation;

4. Tabulate the pier axial load and moments under the L1 seismic event. The pier shear design and

pile design will be governed by the L2 seismic event and will be determined during the pushover

analysis later;

5. Plot the pier Level 1 axial load and pier moments on the column interaction diagram (P-M

interaction curve using a resistance factor of 1.0 (Φ=1.0) to ensure that the pier is elastic under

the Level 1 event. The P-M interaction curve is generated assuming characteristic material

strengths using the SMEC internal spreadsheets. If this step is not satisfied, then additional

reinforcement has to be provided to the structure and the process repeated from Step 1 (adding

more reinforcement will change the cracked section property and hence, increase the cracked

stiffness of the pier);

6. For the Level 2 event, tabulate the deflections of the top of the pier in the longitudinal and

transverse directions, from the response spectrum analysis. Determine the displacement

magnification factor, Rd to be applied to these deflections to account for short period soils. This

magnified displacement is the displacement demand required of the structure under the Level 2

seismic event;

7. Carry out the pushover analysis;


8. A typical pushover curve based on the idealised moment curvature of the elements is shown in

Figure 13 below. This shows a plot of the displacement of the top of pier against the applied load

at the top of the column.

9. The detailed hinge status at each step of the pushover analysis should be inspected to determine

the load step at which the pier hinges and to ensure that the pier hinges before the piles. At the

point that the pier hinges, we need to determine the corresponding deflection (deflection at yield).

We then need to review the remaining load steps to determine when the displacement demand

deflection is met. Obviously, this must occur before the pier hinge reaches it maximum rotation

capacity and fails. The Japanese DSRS recommends that the pushover curve be examined till

failure to demonstrate the extent of additional capacity left in the element;

10. The ductility factor of the pier is then calculated (AASHTO-LRFD-S Cl 4.9). It is recommended

that the rotational capacity of the hinge also be determined and compared to the rotation at failure.

AASHTO-LRFD does not provide clear guidance on this but reference was made to Eurocode 2 –

Design of Concrete Structures (BS EN1992-1-1:2004) Clause 5.6.3.

Figure 13 Typical Pushover Diagram (MIDAS Civil).

11. At the moment that the pier hinges, the column base and foundation experiences the maximum

moment possible. The pier moment is caused by the seismic inertial force (F) applied at the deck

centroid. In the longitudinal direction, this equates to a moment of FxH where H is the distance

from top of the pier to the base of the column because the deck is free to rotate about the

transverse axis, hence, transferring the force to the top of the pier without inducing an additional

moment due to the offset of the centroid of the deck from the top of the pier. In the transverse

direction, this inertial force sets up a couple in the bearings of the deck and the pier moment is =

Fx(d+H) where d is the offset from the deck centroid to the top of the pier;

12. Based on the above, the shear force to be resisted by the pier in the longitudinal and transverse

direction can be determined and the shear capacity of the section determined. The shear

reinforcement to be provided is to resist this applied shear force as well as to meet the minimum

detailing requirements of AASHTO-LRFD-S (Cl. 8.6);

13. Hence, the design of the column to resist the L2 seismic event is complete and the detailing of

reinforcement can be completed based on the detailing requirements of AASHTO-LRFD-S Cl. 8.6

to 8.9 inclusive;

14. Design of piles. As stated earlier, the pier hinging moment and the corresponding axial load and

pier column shear force are the maximum loads acting on the foundation. These loads are acting

at the load step when the pier hinge forms – refer Step 9 above. The pile forces (axial load,

moment and shear) determined from this load step are extracted and the piles designed to resist

these loads. Note that the resistance factor (Φ) = 1.0 for all elements for the seismic events.


15. The pile-cap can then be designed based on these pile loads using either a strut and tie approach

for non-flexural pile caps or a beam analogy for flexural pile-caps.

7 CONCLUSIONS

7.1 Differences in Outcomes Compared to the Force Based Approach

When using the traditional force based approach, the design for the Level 1 seismic event is the same

as the current applied approach.

For the design of the Level 2 seismic event, in the force based approach, the response modification

factor for single columns (R=1.5 for critical bridges, and 2.0 for essential bridges) is applied and

hence the elastic Level 2 Response Spectrum pier design moments are divided by R. In the

pushover method, the design is governed by the reinforcement required to meet the Level 1 design

event and is the plastic hinging moment of the column provided by the defined section and the

reinforcement arrangement.

In the force based approach, the foundation design moments are not reduced from the linear elastic

response spectrum analysis for Level 2 Earthquake, as the Response Modification factor for

foundations = 1.0. Table 2 below shows the difference in load effects on a pilecap for a typical pier

10m high in various soil classes on the project, for the two methods.

Important Note: In DPWH BSDS and AASHTO-LRFD, the required load combinations for Level 2

earthquake are:

• Longitudinal = 1.25 x Dead and Superimposed Dead loads + 0.5 Live Load + 100%

Longitudinal Earthquake + 30% Transverse Earthquake

• Transverse = 1.25 x Dead and Superimposed Dead loads + 0.5 Live Load + 100%

Transverse Earthquake + 30% Longitudinal Earthquake

For the purpose of the presentation of the table 2 below, while the loads have been factored as

required, the 30% earthquake in the relevant orthogonal direction has NOT been added to allow

clarity for comparison with the pushover method, which is uni-directional.

The final pier size and pile arrangement is shown in Table 3 below.

The following is to be noted before reading the conclusions:

• The Force Based Method does not include the 30% earthquake component in the summary to

be able to directly compare forces against the pushover method – but in complying with the

code, the forces listed in the force based need to be increased.

• The Response modification Factor for these piers is either 1.5 (critical bridges) or 2.0

(essential bridges). In this project, the bridges are classified as critical bridges and therefore,

a response modification factor of 1.5 is appropriate.


Table 2: Comparison of Foundation Loads for a 10m high Pier – Force Based Method vs

Pushover Method for a 10m High Pier for Level 2 Earthquake

Method Soil Class Direction of Earthquake

Vertical Force (kN)

Fy – Transverse Shear (kN)

Fz – Longitudinal Shear (kN)

My – Moment

about transverse

axis of pier

(kNm)

Mz – Moment

about Longitudinal

axis of bridge (kNm)

Force Based

Method –

but 30%

earthquake in

orthogonal

direction not

included and

No Response

Factor

Modification

1 Longitudinal 16,733 0 8,630 87,222 0

Transverse 16,733 11,882 0 0 120,723

2 Longitudinal 16,732 0 8910 87,974 0

Transverse 16,732 11,979 0 0 121,809

3 Longitudinal 17,142 0 15,923 155,889 0

Transverse 17,142 15,673 0 0 158,324

4 Longitudinal 16, 852 0 8,471 83,347 0

Transverse 16,852 10,220 0 0 103,480

5 Longitudinal 16,643 0 8,454 83,409 0

Transverse 16,643 11,305 0 0 114,191

6 Longitudinal 17,222 0 17,069 166,907 0

Transverse 17,222 16,904 0 0 170,202

Pushover Method

1 Longitudinal 13,779 0 4,374 43,748 0

Transverse 13,779 5,219 0 0 61,972

2 Longitudinal 13,779 0 4,374 43,748 0

Transverse 13,779 5,219 0 0 61,972

3 Longitudinal 13,779 0 4,374 43,748 0

Transverse 13,779 5,219 0 0 61,972

4 Longitudinal 13,779 0 4,374 43,748 0

Transverse 13,779 5,219 0 0 61,972

5 Longitudinal 13,779 0 4,374 43,748 0

Transverse 13,779 5,219 0 0 61,972

6 Longitudinal 14,170 0 7,568 75,684 0

Transverse 14,170 7,378 0 0 87,560

Hence, it can be immediately seen that for the force based approach (assuming a Response

Modification Factor of 1.5) and again, noting that the 30% orthogonal earthquake has not been

included, that:

a) The pier column (about longitudinal axis of the bridge – transverse axis similar) moments are

typically approximately 80,472 to 105, 549 kNm which are approximately 30 to 70% more

than the corresponding values for the pushover method. This would mean that a larger

column size and more rebar than 108 x 40mm bars would be required because as stiffness

increases, the applied earthquake force effect increases;

b) The design of the foundations would need to be carried for the un-reduced elastic moments

tabulated for the force based method where, we can clearly see that the applied axial load is

21% more than the pushover method (due to the load factors applied in the force based

method) while the applied moment and shears are approximately 100% more than that

required by the pushover method. This would result in more piles and increased pile lengths;

c) has no limit on the natural period of the structure in transverse or longitudinal direction which

may govern the safety of the train in operation – this issue is not addressed in the DPWH or

AASHTO codes as they are intended for highway bridges;


d) has no check for the deflection capacity of the pier nor the rotational capacity of the hinge in

the pier.

Table 3: Pier Size and Pile Arrangement Provided for 10m high Pier – Pushover Method for a

for Level 2 Earthquake

Soil Class Pier Size (Trans. Direction x Long.

Direction) (mm x mm)

No. Of 1500mm Dia. Piles

Remarks

1

3000 x 2000 with 54 x 40mm vertical bars

4 Piles adequate for pushover but 6 piles

provided to reduce pile load and shorten overall

pile length

2

3

4

5

6 3000 x 2500 with 108 x

40mm vertical bars

9 piles required to limit the transverse natural period to less than 1.4 seconds to meet the displacement limit requirements for

railways

Column size and pile numbers increased to limit transverse natural period to less than 1.4 seconds to meet the displacement limit requirements for railways. Soil Class 6 is the weakest soil class in the project.

7.2 Design Criteria for Train Operational Safety during Earthquakes

Earthquakes can occur at any time and it is indeed conceivable that trains may be operating during

the earthquake event. Current codes (DPWH, AASHTO-LRFD and AASHTO-LRFD-S) are intended

for highway bridges and do not specify special requirements for trains.

The Japanese code for railway structures (JDSRS) (available only in Japanese) has extensive

discussion on this issue and the key criteria has been described earlier in this paper. The JDSRS

requires the operational safety of the train to be checked for the Level 1 earthquake event only and

limits the natural period of the structure to be less than 2.0 seconds in both the longitudinal and

transverse directions. This has been found to only affect piers taller than 16m on this project or in the

weakest soil class (Class 6). Typically, this has been addressed by providing additional piles (2 to 5

additional piles depending on the soil condition and pier height).

7.3 Overall Conclusions

From the above discussion, it is hoped that :

• a clear process has been set out to explain the seismic design of this railway viaduct in a high

seismic region;

• it has been demonstrated that the pushover method is a relatively simple procedure which

results in significant economy over the traditional force based approach whilst providing a

more rational method to design structures in a high seismic zone;

• it has highlighted the issue of additional checks to ensure the operational safety of the train

during the Level 1 earthquake which is only explained in the Japanese Codes.

8 REFERENCES

• Ref 1 - Department of Public Works and Highways, Philippines - Bridge Seismic Design

Specifications 1st Edition 2013 (DPWH-BSDS);


• Ref 2 - Department of Public Works and Highways, Philippines - Design Guidelines, Criteria and

Standards; Volumes 1 to 6, 2015 (DPWH-DGCS);

• Ref 3 - American Association of State Highway and Transportation Officials Guide Specifications

for Load Resistance Factor Design Bridge Design 7th Edition (2012) including amendments up to

2016 (AASHTO-LRFD);

• Ref 4 - American Association of State Highway and Transportation Officials Guide Specifications

for Load Resistance Factor Design Seismic Bridge Design 2nd Edition (2011) including

amendments up to 2016 (AASHTO-LRFD-S);

• Ref 5 – Japanese Design Standards for Railway Structures and Commentary (Seismic Design)

(2012) (JDSRS)

• Ref 6 – Japanese Road Association Standard (2012) (JRA)

• Ref 7 - LRFD Seismic Analysis and Design of Bridges Reference Manual - U.S. Department of

Transportation Publication No. FHWA-NHI-15-004 Federal Highway Administration October 2014;

• Ref 8 – Applied Technology Council - Seismic evaluation and retrofit of concrete buildings Volume

1 and 2;

• Ref 9 - Eurocode 2 – Design of Concrete Structures (BS EN1992-1-1:2004).

9 ACKNOWLEDGEMENTS

The authors wish to thank the Main Consultants and SMEC International for permission to present this

paper. The views expressed in this paper are those of the authors.

The authors also wish to thank other members of the Japanese Design Team, in particular Sugihara

San and Osaka San who spent a lot of their time explaining the pushover method and the Japanese

methods and codes to the SMEC design team.

10 AUTHOR BIOGRAPHIES

Vishnu Balakrishnan, MICE, MIStruct E, MIEAust, CEng, Chief Technical Principal (Structures),

SMEC International.

With over 31 years experience in the design of bridges in Australia and internationally, Vishnu was the

Design Lead (Structures) on this project. He has been involved, in the capacity of senior bridge

engineer or team leader, in the detailed design of approximately 600,000 square meters of segmental

bridge deck and in the tender design of another 450,000 square meters of segmental bridge deck

alone. These segmental bridge projects include the tender design of the Melbourne City Link, detail

design of the Western Sydney Orbital, Brunswick River and Gunghalin Drive projects in Australia.

Internationally, Vishnu has been involved in the segmental detailed design of the Malaysia Singapore

Second Crossing Bridge and Ipoh Viaduct in Malaysia, bridges in Iraq and the tender design of the

Boubyan Viaduct in Kuwait.

Nobuyuki Matsumoto, Dr.Eng., MSc., BSc. Fellow of JSCE and JCI, PE Japan (Civil Eng.),

Advisory Executive, Pacific Consultant Co., Ltd (PCKK) Japan

Nobuyuki has 40 years experience as a structural engineer after joining the Japanese National

Railways (JNR) in 1979. He worked as a senior researcher of concrete structure laboratory and head

researcher of structural mechanics laboratory in the Railway Technical Research Institute (RTRI)

more than 30 years and stipulated the Japanese Design Standards for Railway Structures (Concrete

Structures and Deflection Limits). He joined PCKK in 2015 and worked as the team leader for civil

structures in this project. He was a member of UIC Panel of Structural Experts and ERRI D183/D216

committees, the chairman of mirror committee of ISO TC269 in Japan, and the secretary general of

Asian Concrete Federation.

Takayuki Omori, Manager, PE Japan(Industrial, Civil), Oriental Consultants Global.

With over 20 years experience in the design/construction field of the bridges and civil structures, in

Japan and internationally, Takayuki was the one of design manager (Civil structures) on this project.

He has been involved, the project manager or chief designer in the planning/preliminary


study/detailed design/construction/maintenance of 100 or more bridge or viaduct projects. Also he

had awarded on some of these projects by related mayor or ministry. Additionally, he was active as a

committee member in the field of infrastructure in Japan.

Kaname Mizuno, Technical Manager, PE Japan (Civil Eng), Pacific Consultants.

Who has over 20 years experience in the design/construction supervision of the rail way structures in

Japan and internationally, Kaname was the Viaduct and Bridge design manager on this project. He

has been involved, the project manager or chief designer in the planning/preliminary study/detailed

design/construction supervision/maintenance for railway structure projects. As a designer, he has

tackled complicated problems, such as adjacent structure to other structures, and structure and

railway system in cold regions. Internationally, he has been involved to Jakarta MRT project as RC

structure supervisor.

Onek Denis Obedi, BEng CEng,, Technical Consultant (Structures), Transportation & Railways,

Pacific Consultant Co., Ltd (PCKK) Japan

Since joining PCKK as a freshman in 2011, Mr Obedi has worked extensively in the planning, design,

and construction supervision of highway and railway viaducts & bridges in Japan and parts of South

East Asia. Since the revision of the seismic design code for bridges in Japan in 2012, Mr. Obedi has

been involved in seismic performance evaluation and retrofitting design of numerous bridges in

Japan. As one of the key members of the design team on this project, Mr. Obedi was responsible for

structural planning and preparation of design conditions including; optimization of span layouts for

viaducts and bridges; idealization of the geotechnical properties for over 480 boreholes, and

comparison of Japanese seismic design code with the AASHTO LRFD-S.

Ricardo Vitaliano Acosta Jr., Structures Design Manager, SMEC Philippines Inc.

Ricardo has a total of 17 years of experience in the design of bridges in the Philippines and other parts of Southeast Asia. He has been involved with the design of major Infrastructure Projects in the Philippines. His key projects include roles as the Structural Team Lead for the Metro Manila Skyway Stage 3 Project (17.6km long elevated expressway) SLEX Harbor Link Segment 10 (5.3km elevated expressway) and the NLEX-SLEX Connector Road (8km elevated expressway). On this project, Ricardo is the SMEC Philippines Design Lead (Structures) and responsible for the technical delivery of the project.

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