A study on the characteristics of bridge bearings behavior by finite element analysis and model test

2.1. Design of spherical elastomeric bearing

The required performance of laminated rubber bearings is generally divided into physical and environmental characteristics. Physical characteristics include compressive stiffness and repeated fatigue, while environmental characteristics include temperature change, long-term aging and ozone, factors related to rubber.

The basic shape of spherical elastomeric bearings should, in general, be designed to show an appropriate form of elastic complex, depending on applied load, installation position and upper structure behavior. The designed spherical elastomeric bearing is a spherical elastic body of laminated steel plates and viscoelastic material, such as rubber, as shown in Fig. 2. Spherical elastomeric bearing was designed under much severer conditions (500 kN in vertical capacity and 0.03 rad in allowable rotational angle) than those of actual bridges.

2.2. Finite element analysis

In this study, a finite element analysis was made using the universal software ANSYS ver. 12, and Fig. 3 shows one example of a finite element model.

A convergence test was performed for appropriate size of elements with the number of elements at approximately 78,000 and the number of panel points at approximately 352,207. Like in the analysis conducted in the verification phase, three-dimensional element Solid 185 supporting viscoelastic materials was used. Reinforced steel plate SS400 and rubber Neo-Hookean were applied. Fig. 3 shows modeling for the finite element analysis of spherical elastomeric bearing.

In the finite element analysis, constraint and load conditions had $x$, $y$ and $z$ axes applied to the bottom of the bearing so spherical elastomeric bearings act in the same way as actual, and coupling load applied to the upper part of the bearing. In the compression analysis, a vertical load of 500 kN was applied to find the compression behavior characteristics of the bearing, and the findings of design and analysis were compared to each other, as shown in Table 1 and Fig. 4.

Fig. 3FEM modeling

The finite element analysis showed that vertical displacement was 2.51 mm in design and 2.73 mm in analysis with an error of 0.22 mm, while compressive stress was 18.14 MPa in design and 21.07 MPa in analysis with an error of 2.93 MPa. As shown above, design and analysis values for the bearing were very similar to each other, but analysis value was slightly higher than design value because there was a difference between functional formulas used when applying the error in the finite element analysis modeling and viscoelastic material rubber to the analysis.

Fig. 4Von-Mises stress

3.1. Dimensions of specimen

For spherical elastomeric bearing, a specimen of 500 kN in vertical capacity was designed and prepared, as shown in Table 2 and Table 3. To estimate the effects of shape factor applied to the device, the specimen of 500 kN in capacity was designed and prepared to have around 20, 12 and 8 in shape factor, and then tested. 2nd shape factor of the specimen was designed to have a constant value to raise the accuracy of the estimation of effects of 1st shape factor. The laminated elastic layer had NR (natural rubber) applied as its material, while NR had a special rubber with shear moduli ($G$) of 0.9 MPa and 1.2 MPa in 100 % shearing displacement applied. Table 2 shows the physical properties of the materials used in the test.

Fig. 5Hysteric curve of compression test (BS EN1337-3)

Fig. 6Hysteric curve of compression test (ISO 22762)

3.2. Test conditions and method

For characteristic test, a compression-shear fatigue tester (Fig. 7) was used. Table 4 shows the specifications of the tester. Compression test should measure and analyze vertical strength and deformation except the viscoelastic characteristics of laminated rubber, and establish the relation between elastomeric bearing vertical strength and deflection rather than ISO seismic isolator vertical strength measuring method, while rotation test was performed with inclination plates of 0.03 rad and 0.05 rad applied to compression test (0.0 rad). Compressive stiffness was calculated obtaining the results of deformation for 30 % and 100 % of design load with BS EN 1337-3 and ISO 22762 standards applied, and obtaining a change in compression load against vertical unit deformation. It was calculated using:

where ${\sigma }_{c2}$ is stress at maximum load and ${\sigma }_{c1}$ stress at 1/3 of maximum load, and is ${ϵ}_2$ deformation rate at maximum load and ${ϵ}_2$ deformation rate at 1/3 of maximum load.

Fig. 72,000 kN fatigue test machine

3.3. Test results and analysis

3.3.1. Compression test

A total of 6 specimens of three different types in shape factor with rubber shear modulus at 0.9 MPa and 1.2 MPa each were prepared for the test.

Table 5Compression test data

Classification				0.0 rad
				ISO	BS
Vertical load (kN)	S.F	Rubber thickness	Shear modulus	$K_q$	$K_{q,1st}$	$K_{q,2nd}$	$K_{q,3rd}$
500	20.48	3	0.9	865.8	858.2	844.4	834.6
			1.2	1026.9	1039.4	1100.0	1033.3
	12.28	5	0.9	627.5	614.4	633.3	627.5
			1.2	855.0	885.7	865.8	901.3
	7.676	8	0.9	344.7	342.0	351.8	351.5
			1.2	442.6	441.6	428.8	435.2

The compression test showed that where 1st shape factor was the same, the higher shear factor was, the higher compressive elastic modulus was. It also showed that where shear factor was constant, the higher 1st shape factor was, the higher compressive elastic factor was. It means that as 1st shape factor increased, the thickness of each rubber layer decreased and the compressive elastic factor of each elastic layer increased. Fig. 8 and Table 5 show briefly the results of characteristic test for compressive stiffness.

Fig. 8Compressive stiffness according to shape factor (0.0 rad)

3.3.2. Compression-rotation test

As shown in Fig. 9, the compression-rotation test with inclination plates applied also showed that the higher shape factor was, the higher rotational stiffness was, similar to the results of the compression test. While the rotation test is underway, no damage to or no permanent deformation specimens in appearance was observed, but there was a temporary bending in the laminated depending on rotation level, and it restored after the removal of load. A complete rotation by the inclination plate is made at 50 % of design load, and it needs to reset load range to estimate the compressive stiffness of spherical elastomeric bearings. Fig. 10 shows the results of compressive stiffness depending on shape factor and rotation angle.

Fig. 9Compression-rotation test

Fig. 10Rotation stiffness according to shape factor

a) Rotation 0.03 rad

b) Rotation 0.05 rad

As shown in Fig. 11, where the rotation angle of inclination plates was applied, compressive stiffness decreased more than where rotation angle not applied, with a slight difference in strength between different rotation angles. Unlike the compression test, the compressive stiffness test showed that stiffness dispersion occurred by accommodating displacement with rotational distortion by inclination plates of vertical force. It also showed that the higher rubber shear modulus was, the higher compressive stiffness by rotation was.

Table 6Compression-rotation test data

Classification				0.03 rad				0.05 rad
				ISO	BS			ISO	BS
Vertical load (kN)	S.F	Rubber thickness	Shear modulus	$K_q$	$K_{q,1st}$	$K_{q,2nd}$	$K_{q,3rd}$	$K_q$	$K_{q,1st}$	$K_{q,2nd}$	$K_{q,3rd}$
500	20.48	3	0.9	451.3	547.2	556.9	555.3	497.8	494.93	530.0	523.7
			1.2	692.9	713.5	764.4	742.4	680.2	675.25	683.0	694.9
	12.28	5	0.9	456.3	470.5	467.3	464.4	432.9	439.35	445.8	445.8
			1.2	577.3	618.0	617.1	619.8	566.1	573.33	588.0	586.3
	7.676	8	0.9	264.4	254.1	268.0	271.1	262.6	251.47	259.1	255.1
			1.2	326.1	320.4	324.4	331.4	335.0	320.75	348.2	332.4

Fig. 11Rotation stiffness according to rotation

a)$G=$ 0.9 MPa

b)$G=$ 1.2 MPa

In addition, it turned out that as shape factor increased, deviation from the rotation test with inclination plates applied increased greatly. Since if the shape factor decreases, the vertical deformation that can be accommodated by one deviation from the results of compressive stiffness with inclination plates applied is small. Two specimens with laminated rubber at shear modulus 0.9 MPa and 1.2 MPa applied showed that a change in stiffness by shape factor depending on rotation was small with similar tendency to each other.

Fig. 12Rotation stiffness according to rotation and shape factor

a)$G=$ 0.9 MPa

b)$G=$ 1.2 MPa

The analysis of the effects of shape factors depending on inclination plate angle showed that like the results of the analysis above, the stress induced by the inclination plate’s rotation was low compared to the compression test as the laminated bearing turned horizontally with shear deformation and increased displacement, and there was no great difference in stiffness change depending on a change in rotation angle. Fig. 12 shows compression-rotation test results with rotation angle and shape factor.

4.1. Similitude of scaled-down model

Vibration effects by bridge bearing have largely been evaluated by analytical and experimental methods. However, a vibration test using actual vehicles involves constraints related to test preparation, and difficulties in applying various variables. To overcome such shortcomings, a scaled-down model was introduced. The test involves a review of vibrations from running trains and basic structures depending on bearing types, and to do this, theories of various similarity methods were reviewed. This study adopted Jaschinski’s similarity law [8] (Jaschinski, 1999), which does not consider gravity acceleration in experimental environments. The adopted Jaschinski’s similarity law is used as a method to verify the multi-body dynamic theory for railway vehicles and the feasibility of non-linear equations. Scale-down ratio is 1/50 scale (Table 7), and the following similitude rate was used.

4.2. Preparation and installation of the structure

A scaled-down model of concrete railway bridge was prepared with a review of scale-down ratio, and tested. The scaled-down bridge structure has an acceleration track section of 25 m and a deceleration track section of 25 m built, and the measurement section of the bridge is 30 m×2 spans depending on scale-down ratio, and if the bridge is 60 m long, it was scaled down to 1/50 at 600 mm×2 spans (1200 mm).

Bearings used in the scale-down model test are spherical steel type (stiff bearing) and spherical elastomeric type (elastomeric bearing), as shown in Table 8. The detailed description of how these bearings were applied is: they were created as a single unit of upper and lower plates with the base uneven, and they were designed and created in such a way that one could test variables individually depending on whether or not rubber sheets were applied to the uneven; and each post has two spherical bearings, and a total of six bearings for 2 spans were prepared and applied. Fig. 13 shows bearings installed between posts and the deck.

Fig. 13Scale-downed model

Table 8Application bearings

Classification		Rubber spec.	Hardness
Spherical bearing		Rubberless	–
Spherical elastomeric bearing		Natural rubber	55

4.3. Preparation and application of scaled-down bogies

Fig. 14 shows the full-scale specification of railway vehicles. The vehicles were scaled down to 1/50 of actual train model, and a head car and rail were provided.

The head car was designed to be driven by a separate speed controller, which was connected to vehicles by a steel wire of Ø1.0 mm. For accurate control, a connection control device was mounted on the outside of vehicles, as shown in Fig. 15. A total of 7 freight cars were added, and existing links given to the train can cause the risk of derail due to separation distance. Thus, a new connection device was made of MC nylon blocks, and then applied. To meet similitude rate load, the same weight was installed on each car.

Table 9 shows the similarity results of the scaled-down model in train velocity. Setpoint for the speed controller used in this study was established to be available for measurement at 70 km/h, the general running speed of freight train, and it implemented maximum 244.4 km/h at 1/50 scale.

Fig. 14Vehicle specification

Fig. 15Condition of the installation

Fig. 16Vibration response measurement

4.4. Evaluation of vibration of bridge with bearings

To find vibration and displacement of foundation structures depending on bearing types while the train runs on the scaled-down railway bridge model, vibration and displacement of the miniature bridge structure at various train speeds (7.1 km/h, 33.1 km/h, 70.8 km/h, 141.5 km/h, 212 km/h, and 244 km/h) were measured, as shown in Fig. 16. The measurement was performed using the three vibration sensors installed under the bridge.

An acceleration sensor was installed at the center of the bridge, and vibration acceleration was measured by material of bearings while the train ran, and the $L_{max}$lue of the observed values was measured three times to display average value in a graph. Fig. 17 shows the results, in which acceleration values at the center of the bridge while the train ran are lower overall than those at the entry section. When the train ran at low or high speed as well, stiff bearings produced greater vibration overall than elastomeric bearings. In particular, at the entry section ACC #01 where the train enters the bridge, steel bearings produced great vibration, while at the exit section ACC#03, acceleration change occurred with speed change. It was observed that acceleration for stiff bearings increased compared to that for elastomeric bearings when the train ran at high speed.

Fig. 17Vibration velocity response according to train speed and bearings

a) ACC #01-Entrance

b) ACC #02-Center

c) ACC #03-Exit

4.5. Measurement of vibration damping by distance

To confirm distance attenuation of vibration depending on bearing type when the train runs on the scaled-down railway bridge model, sensors were installed at specific intervals, as shown in Fig. 18, and vibration was measured by material of bearings and train speed. A total of 5 spots were selected for measurement, as shown in Fig. 18, and vibration was measured at 40 cm, 80 cm, 160 cm and 320 cm from the bridge respectively.

Fig. 18Sound attenuation in distance

Fig. 19Vibration result according to speed and distance

a)$V=$ 7.1 km/h

b)$V=$ 33.1 km/h

c)$V=$ 70.8 km/h

d)$V=$ 141.5 km/h

e)$V=$ 212 km/h

f)$V=$ 244 km/h

The measurement of distance attenuation using the scaled-down railway bridge model showed the results in Fig. 19 depending on bearing type. According to the results, as the train approached the bridge, vibration increased overall, and steel bearings produced more vibration than elastomeric bearings in all sections. At a distance of 40 cm, elastomeric bearings reduced vibration by around 6 dB on average from that of stress bearings, but as the distance increases, the difference of vibration between bearing types decreased overall.