To verify if the seismic capacity of the as-built bridge structures meets the current seismic demand, this study first identifies the differences between the previous seismic design specification and SDSHB 2000, and assess the impact of the previously designed bridges based on SDSHB 2000. Next, the design concepts and theories of SDSHB 2000 and other international seismic codes adopted worldwide are explored to justify the adequacy of the original design.
Finally, an approach for the re-evaluation of seismic capacity and performance of existing bridges is to be proposed.
2 SEISMIC DESIGN SPECIFICATION FOR HIGHWAY BRIDGES 2.1 The Previous Seismic Design Specification
In the early bridge design specifications of Taiwan, the seismic design guidelines for bridge structures were only presented briefly in conceptual statements. Not until 1995 did the MOTC publish the first Seismic Design Specifications for Highway Bridges after conducting a series of studies in reference to the development of Japanese and USA seismic codes. The basic design philosophy implied by the specification is to make sure the bridge structure kept in the elastic range during moderate earthquakes while allowing them to fail in a ductile pattern without collapse during severe earthquakes.
2.2 Static Analysis Method
For regular bridge structures, a static analysis approach can be used, while for irregular bridges, a dynamic analysis procedure of either spectrum analysis or time history analysis should be adopted. Regular bridges refer to those of six spans or less, no abrupt or unusual changes in mass, stiffness or geometry, and no significant variations in these parameters from span to span or pier to pier.
For regular bridges, the equivalent static analysis method can be applied to calculate the design seismic forces for structural analysis.
2.3 Static Seismic Design Forces
To determine member forces due to earthquakes, the minimum total design horizontal force, V, shall be calculated as the following:
u y
d F
CW ZICW Z
V 1.2 (2.1)
where
Z :d the design horizontal ground acceleration coefficient C: the normalized acceleration response spectrum coefficient
W : total dead weight of the bridge unit including the weight of the superstructure and pier
Z: the horizontal ground acceleration coefficient I: the important factor
: the ratio of the ground acceleration expected to initiate yielding in they
structure to the design ground acceleration
F :u the seismic force reduction factor for bridge system
Note that, in equation (2.1), the ratio Fu
C should be regulated by inequality (2.2) as
where R* is the property factor for structural system associated with types of substructure as shown in Table 2.3. For short-period bridge, the seismic force will be magnified due to smaller Fu associated with period. But consideration of soil-structure interaction effect for the short-period bridge, the soil spring has more deformation induces the higher damping ratio. Hence the limitation of inequality is adopted for actual calculation.
As a result, the design earthquake force is modified as
F W
is the modification of acceleration response spectrum
coefficient regulated by inequality (2.2).
2.3.1 Horizontal Ground Acceleration Coefficient
The horizontal ground acceleration coefficient, Z, is represented for the ratio of the seismic ground acceleration of 475-year return period of to the gravitational acceleration, g. Taiwan is categorized into 4 seismic zones respectively with coefficients 0.33, 0.28, 0.23 and 0.18. The seismic zoning map is illustrated in Figure 2-1.
2.3.2 Important Factor
For critical bridge structures that need to maintain their function immediately after an earthquake event, I of 1.2 should be applied. Otherwise I of 1.0 is suggested.
2.3.3 Normalized Acceleration Response Spectrum Coefficient
The normalized acceleration response spectrum coefficients are expressed in terms of fundamental period and soil profiles as tabulated in Table 2-1 while the normalized vertical acceleration response spectrum coefficients are tabulated in Table 2-2.
Soil profiles may be classified in accordance with the fundamental period of the site, TG, into three types:
Type I ... TG 0.2 sec Type II ... 0.2 sec < TG 0.6 sec Type III ... 0.6 sec < TG
The fundamental period of the site, TG, can in turn be estimated by the following equation:
n
i 1 si i
G V
4 H T where
Hi: the thickness (m) of the i-th subsoil layer
Vsi : the shear wave velocity (m/s) of the i-th subsoil layer at low strains n : the number of layers above the base layer
It is recommended that shear wave velocities be directly measured via site investigations. In the absence of measured values, shear wave velocities may be obtained by using empirical formulae based on the Standard Penetration Test N-value as the following,
For cohesive soils : Vsi = 100 Ni1/3 (1＜Ni＜25) (m/s) For sandy soils : Vsi= 80 Ni1/3 (1＜Ni＜50) (m/s)
The base layer is defined as the layer under which all lower layers have an N-value greater than 25 for cohesive soils, or 50 for sandy soils.
2.3.4 αyand Seismic Force Reduction Factor for Bridge System
The amplification factor of the design earthquake load, αy, takes into account the fact that initial yielding of the bridge structure commences as the actual seismic force reaches αytimes of the design earthquake load. The value of αyis dependent on the types of bridge structures as well as the design methods adopted. For steel bridges, αy of 1.7 is considered. For reinforced concrete bridges, αy of 1.65 is used as the USD approach adopted and 1.9 as the WSD approach adopted.
The seismic force reduction factor for a bridge system, Fu is related to the ductility capacity, R, of the structural system, the period of the structure, T, and the soil profiles. The relationships between the ductility capacity, R, the property factor, R* and the allowable ductility capacity,R , are as following:a
2 . 1
* RR
(2.4)
5 . 1
1 1 R
Ra
(2.5)
where R* is dependent on the type of substructure as tabulated in Table 2-3.
The values of F are dependent on the type of soil profile as shown in theu following:
(a) Soil Type I
0.242 secT0.333sec
F =u 2Ra1
0.03secT0.15 sec
F =1.0u
0.03secT0.15 sec
F =1.0u
(c) Soil Type III
a
F =u 2Ra1
(d) Taipei Basin
a
0.8secT1.4 sec
F =u 2Ra1
2.3.5 Distribution of Seismic Forces of the Bridges
The seismic force per unit length, pe
x , applied along the bridge is calculated as:w : weight per unit length
xU : displacement
Furthermore, it is to define a minimum horizontal seismic design force, V*, that is required to avoid early yielding of the bridge under moderate earthquakes. It is calculated as the following:
F W
2.3.6 Vertical Seismic Forces
No vertical seismic force is considered in the bridge design.
2.4 Modification of Seismic Design Specifications after Chi-Chi Earthquake In response to the disaster of Chi-Chi Earthquake, MOTC revised the Seismic Design Specifications for Highway Bridges in April 2000. Major changes in the specifications are modifications of horizontal ground acceleration coefficients and the consideration of vertical seismic force.
2.4.1 Horizontal Ground Acceleration Coefficient
In the previous design code, the horizontal ground horizontal acceleration coefficients are classified into 4 grades corresponding to the 4 seismic zones of Taiwan, as described in Section 2.3.1. Nevertheless, after Chi-Chi Earthquake it has been reduced to only two design levels with Z=0.23 and 0.33 respectively. See Figure 2-2 for the seismic zoning map. Furthermore, the maximum amplification factor of the normalized acceleration response spectrum for Taipei Basin is increased from 2 to 2.5.
2.4.2 Vertical Seismic Force
In the previous seismic design code, no vertical seismic force is considered for the bridge structure but only the bearing facility. In the revised version, the effect of vertical ground acceleration is taken into account [4]. The vertical seismic force, Vv, should be calculated as the following:
uv
Z :v the ground vertical acceleration coefficient which is 32Z in Zone A and
3
1Z in Zone B.
C :v the normalized vertical acceleration response spectrum coefficient
F :uv the vertical seismic force reduction factor for bridge system. The values of Fuv are shown in the following:
(a) Soil Type I
0.194 secT0.288sec
Fuv = 2Ra1
0.03secT0.1 sec
Fuv =1.0
0.03secT0.1 sec
Fuv =1.0
(c) Soil Type III
(d) Taipei Basin
F =uv Ra
0.71secT1.32 sec
Fuv = 2Ra 1
Fuv =1.0 T0.03sec
Definitions of other parameters are the same as in Section 2.3.
Note that, in equation (2.9), the ratio
uv v
F
C should be regulated by inequality (2.10) as：
As a result, the design earthquake force is modified as
is the modification of acceleration response spectrum
coefficient regulated by inequality (2.10).
2.4.3 Prevention of Loss of Span
To prevent loss-of-span, both seismic design specifications suggest applying anti-fall-off devices. In the previous seismic code, the device is identified as the second level protection after the bearings is damaged by horizontal shear force so the yielding design strength of the anti-fall-off devices is two times of the design capacity of bearing, where the horizontal design shear force associated with plastic moment is applied to design bearings. In SDSHB 2000, the yielding design strength of anti-fall-off devices is equal to the dead load applied to the bearing. It supposes that the superstructure can be hold by this device when loss of span occurring.
2.5 Influences of the Modified Specifications on Bridge Structure Design In accordance with the Design Specifications of Highway Bridges, the design loads of various combinations are to be considered. Among which, those related to the seismic force, EQ, are usually most dominant, especially for the design of substructure. As previously discussed, by the modified seismic specification, the design demands of bridges are increased.
2.5.1 The Demand on Pier Section
The difference on the design horizontal seismic forces between the original code and the revised one is mainly attributed to the change of the horizontal ground acceleration coefficient, Z. It could be increased by as much as 83%.
Take the sites in the Jiu-Ru, Ping-Dong County for example, the horizontal seismic force by Eq. (2.1) of the previous specification is:
Vprevious = 0.18
While by the revised version, it is:
Vrevised= 0.33
The design horizontal seismic force is drastically increased by the revised design specification.
Besides, in the previous version, the overall design seismic loads for the bridge structure are to be determined from the combinations of the two orthogonal horizontal seismic forces as:
y
where Sx, Sy are the horizontal seismic forces in the longitudinal and transverse directions of the bridge. Symbol | | denotes the absolute value or magnitude of the force or moment.
In the revised specification, an additional vertical seismic force is considered in the loading combination as the following:
Z
where Sz denotes the vertical seismic force. It is evident that an additional seismic force of 0.3 Sz is considered.
For the design of pier section, various loading combinations were employed as demands to check the pier’s section nominal capacity that is described as a axial force-moment interaction curve, as shown in Figure 2-3. The curve area shall cover the points of demands of axial forces and moments induced by
various loading combinations. The loading combination with earthquake force experientially is to be the main demand on the pier’ section design. When the increment of horizontal seismic force and additional axial force induced by he vertical seismic force are considered, the revised demands will affect the design of the pier section.
2.5.2 The Design of Superstructure
The various loading combinations are also employed to design the superstructure’s section. In accordance with the pervious design experiences, the loading combination with earthquake force is not the main controlling demand for the superstructure design. However, when a new seismic combination, Sz 0.3Sy 0.3Sx , is considered, it would impose a significant effect on the design of the superstructure, in particular the increase of the depth of bridge girders.
2.5.3 Plastic Moments
In accordance with the concept of ductility design, the bridge piers during severe earthquakes are to resist the seismic forces inelastically via a yielding process without collapse. To ensure forming of the plastic hinges in the piers prior to damage of other structural members or bearings, the design capacity of other bridge members should be larger than a certain values determined by the plastic moment strength, Mp, of the piers at the plastic hinge locations. In the seismic design specifications, plastic moment is associated with the cross sectional nominal moment strength of the pier with consideration of a certain safety factor, say 1.3, for reinforced concrete bridges.[3] When calculating the nominal moment strength associated withMp, the seismic design specification further demands that the designed axial load of the pier includes not only the dead load but also the axial load induced by earthquake. For piers in a single-column form, the earthquake-induced axial force is minor and can be neglected by the previous specification as it considers only the horizontal seismic force. However, with the design vertical seismic force required by the revised specification, additional axial load to the piers is introduced, which in turn affects the axial force–moment interactive behaviour of the reinforced concrete columns. As a result, the design capacity of the substructure may have to be enhanced upon increase of the axial forces.
2.6 Summary
The design of bridges is more demanding by SDSHB 2000, which emphasizes the ductility design with enhanced horizontal seismic force for most seismic zones as well as additional consideration of vertical seismic force, as compared with those by the earlier version. The increment of plastic moment demand due to consideration of vertical seismic load is acknowledged. To avoid an economically irrational design with the ductility-based design concept adopted, the following practical concerns need to be addressed:
(a) The requirement of vertical seismic force in bridge design regardless of seismic area is controversial and debatable. Why and specifically where consideration of vertical seismic force is necessary needs to be reasonably defined.
(b) The allowable ductility capacity is critical to seismic design of bridges.
The ductility capacity of bridge piers suggested by SDSHB 2000 is associated only with the types of substructures. However, consideration of types of substructure alone is too simple to reflect the actual ductile behavior of the bridge columns. As a result, either reliability or economy of the design is not warranted.
(c) The bearings, based on the ductility design concept, should be strong enough to transfer as much seismic forces as required to form plastic hinges in the piers. This, however, might not be always achievable and could lead to other unexpected failure modes.
3 DIFFERENT CONCEPTS IN SEISMIC BRIDGE DESIGN
The conventional seismic design approach of bridges is based on a capacity design concept with the capacity defined in terms of strength to ensure integrity of the bridges under design earthquakes, while reserving sufficient ductile capability of the piers to avoid collapse of the bridges in severe earthquakes.
The SDSHD2000 of Taiwan adopts such a force-based design approach that determines the seismic force levels from the acceleration spectra. This method is initially developed for building structures. The structural characteristics of bridges, however, are intrinsically different from bridges in a sense that buildings extend vertically in space while bridges extend horizontally. Whether or not the force-based approach for seismic design of buildings is adequate for bridges is questionable. Recently, a displacement-based seismic design approach of Caltrans Seismic Design Criteria (SDC) [5] is developed where the displacement levels are determined from the ductility capacity of the bridge piers. SDC is the currently-in-practice code of seismic design and analysis methodologies for the design of new bridges in California, USA. It adopts a performance-based approach specifying minimum levels of performance for structural system as well as components.
The background in the development of SDC in California is similar to that of SDSHD in Taiwan. It has shown from the past earthquakes of California that structures designed in accordance with non-ductile design standards are seismically vulnerable. As a result, Caltrans has embarked on an extensive seismic retrofit program to strengthen the existing bridges to ensure satisfactory performance of the bridges during anticipated future earthquakes.
The concept and methodology of the displacement-based approach of SDC will be reviewed and discussed herein.
3.1 Design Philosophy
The seismic design philosophy based on the ductility of flexible structural members has been accepted worldwide. Ductility is defined as the ratio of the ultimate deformation to the deformation at yield of the primary structural member. Ductile response of structural components is characterized by the hysteretic loops of forces with respect to inelastic deformations in cycles without significant degradation of strength or stiffness. The area enclosed by the hysteretic loops represents the energy dissipated during the inelastic deformation process of the member. Structures with sufficient ductility are
more earthquake-resistant and economic than non-ductile structures based on an elastic design approach.
Despite both SDSHD2000 and SDC follow the same design philosophy of ductility, the ductile components to be considered in the design are somewhat different. In SDSHD2000, the pier column is the only component allowed for ductile behaviour via formation of plastic hinges during extreme earthquakes.
But in SDC, the ductile behavior can be contributed internally within the structural members by the formation of plastic hinges in piers and/or externally by supplemental protective devices such as isolation bearings or seismic dampers. In this way, the deformation or displacement of the protective components is limited to prevent the bridge structure from exceeding its ductility capacity.
3.2 Design Methodology
As mentioned earlier, two alternative design methodologies are developed for bridge seismic design: (1) the force-based approach, where the design seismic force levels are the elastic forces deducted from the ultimate forces of otherwise non-ductile structures determined from the acceleration response spectra based on a ductility-related reduction factor, with additional detailing of the members to ensure that adequate displacement/deformation capacity of the earthquake-resisting members is preserved; and (2) the displacement-based approach, where the ultimate design displacement based on a specified performance level is first determined with the corresponding seismic force calculated accordingly.
By the displacement-based approach of Caltrans SDC [8], the designer needs to ensure sufficient displacement ductility capacity and strength of the primary structural components to withstand the demand displacements imposed by the design earthquake of a desired performance level while maintain a minimum level of inelastic capacity at all potential plastic hinge locations. The displacement capacity of the bridges can be assessed with an inelastic static pushover analysis that incorporates non-linear inelastic load/deformation behavior of selected components.
The demand of displacement is described in terms of the displacement ductility,
defined as:D
Y D
D
(3.1)
Where is the estimated global frame displacement demand；D
is the yield displacement of the subsystem from its initial positionY
to the formation of plastic hinge
The global displacement, , includes components attributed to foundationD flexibility, .(i.e. foundation rotation or translation), flexibility of capacityf protecting components such as bent caps, , and the flexibility attributed tob elastic and inelastic response of ductile members, , and ,Y respectively,P as shown in Figure 3-1a and 3-1b. In SDC, it is recognized that the global displacement can mostly be attributed to the flexibility of pier columns, therefore substituting column’s lateral displacement for global displacement is acceptable. The displacement ductility capacities in analysis for various types of substructures have been calibrated to laboratory test result of fix-based pier columns. The design limits for displacement ductility demand are suggested as below:
For single column bents supported on fixed foundation, D 4； For multi-column bents supported on fixed or pinned footings, D 5； For pier walls (weak direction) supported on fixed or pinned footings,
5
D ；
For pier walls (strong direction) supported on fixed or pinned footings,
For pier walls (strong direction) supported on fixed or pinned footings,