Chapter 5 Seismic Analysis of RC Integral Bridge
5.4 Complementary Investigation of Material Properties in Full SSI No BA Model
The response of bridge-foundation-soil system with linear and nonlinear behaviours of different components are discussed in this section, i.e., linear behaviour of bridge with nonlinear behaviour of soil (lin str+nl soil no BA) model and nonlinear behaviour of bridge with linear behaviour of soil (nl str+lin soil no BA) model. The intention of the study is to investigate the individual effect of material nonlinearity on the overall response of the bridge. Under low level of shaking, nl str+lin soil no BA model remains linear like linear full SSI no BA model. Lin str+nl soil no BA model can be taken as an example of very stiff structure with very flexible soil profile e.g., nuclear structure. Although the vice versa is not realistic physically, still to investigate the influence of nonlinear structure on linear soil domain this case has been considered for the study.
5.4.1 Linear structural behaviour
For linear behaviour of the superstructure and the substructure, the influence of soil nonlinearity is visible by comparing the response of the linear behaviour of full SSI no BA model with the response of lin str+nl soil no BA model. From the observed SFTHs shown in Figs. 5.16(a) and 5.16(b), the nonlinearity of soil dominates the response in high intensity of shaking under GM#1for the lin str+nl soil no BA model. The peak shear force at the top of 8th pier gets reduced by a factor of 2.9 from the linear behaviour of full SSI no BA model to the response of lin str+nl soil no BA model. Normalized Fourier spectra of SFTHs are shown in Figs.5.16(c) and 5.16(d) under GM#1 and GM#2, respectively.
From the Fig.5.16(c), it is observed that under GM#1, the shear force content is higher in frequency domain as compared to the content obtained under GM#2. Once the soil is nonlinear, the peaks of SFTHs occur at different frequencies in these two models. To study the shift in the frequency corresponding to the occurrence of peak Fourier amplitude, normalized FTs are studied. From the normalized response spectra plot in Fig.
5.16(c), it is visible that peaks of Fourier amplitudes are occurring at the frequency of 2.25Hz and 2.38Hz for the linear behaviour of full SSI no BA model and lin str+nl soil no BA model, respectively. Due to nonlinearity of soil domain, the latter model is more deformable and comparatively less seismic forces are imposed at the base of bridge substructure. Due to linear elastic material behaviour, the bridge structure is stiffer under this condition and leads to the mentioned shift in frequency. In Fig. 5.16(d), FTs of SFTHs of Fig. 5.16(b) are plotted and normalized by the peak amplitude value obtained from FT under GM#2 for the linear behaviour of full SSI no BA model to emphasize on the nonlinearity developed in lin str+nl soil no BA model under both the ground motions.
The overall response for both the models gets reduced due to low intensity of shaking under GM#2, thus, the difference in the FT curves is not that significant.
0 10 20 30 40 -4000
-2000 0 2000 4000
(b) Peak (1934, 9.34s)
Peak (3661, 6.44s)
Shear Force, kN
Time, s
(a) 0 10 20 30 40
Peak (15.995s, 1733) Peak (15.615s, 1219) Linear full SSI no BA lin str+nl soil no BA
0.1 1 10
0.0 0.2 0.4 0.6 0.8 1.0
0.1 1 10
Normalized Fourier Amplitude
Frequency, Hz (d) (c)
Fig.5.16 Comparison of SFTHs at the top of 8th pier of bridge for linear behaviour of full SSI no BA model and lin str+nl soil no BA model under (a) GM# 1, (b) GM#2 and
normalized FTs of (c) SFTHs shown in (a) and (d) SFTHs shown in (b).
The same trend, as noted for the SFTHs, is observed in the velocity time history at the deck level for the two models under GM#1 and GM#2 (Figs. 5.17(a) and 5.17(b)).
The observed peak velocities are 0.71 m/s and 0.40 m/s for the linear behaviour of full SSI no BA model and lin str+nl soil no BA model, respectively. Under GM#2, the overall response gets reduced which leads to very small difference in the VTHs of the two models. However, both the normalized FT plots show a significant frequency shift in the occurrence of peak Fourier amplitude of VTHs (Figs. 5.17(c) and 5.17(d)). Even for the VTH under GM#2, the difference in the distribution of deck velocity response in frequency domain is very obvious for the two models, unlike the FTs of SFTHs where the difference was very small.
0 10 20 30 40 -0.6
-0.3 0.0 0.3
0.6 Peak 0.71
Peak 0.40
Velocity, m/s
0 10 20 30 40
Peak 0.24 Peak 0.18 Linear full SSI no BA lin str+nl soil no BA
Time, s (b) (a)
0.1 1 10
0.0 0.2 0.4 0.6 0.8 1.0
Normalised Fourier Transform
0.1 1 10
Frequency, Hz (d) (c)
Fig. 5.17 Comparison of VTHs for linear behaviour of full SSI no BA model and lin str+nl soil no BA model at the 8th pier top under (a) GM#1and (b) GM#2; normalised
FTs of VTHs under (c) GM#1 and (d) GM#2.
5.4.2 Nonlinear structural behaviour
The nonlinear behaviour of full SSI no BA model and the response of nl str+lin soil no BA model are compared to investigate the effect of soil nonlinearity (when the pier behaviour can be nonlinear) on the bridge response. From the SFTHs at the top of 8th pier for the two models under GM#1, the shear force for the nonlinear behaviour of full SSI no BA model is atleast 20% lesser than the shear force obtained for nl str+lin soil no BA model (Fig. 5.18(a)). However, under GM#2 also, the shear force response of nl str+lin soil no BA model exceeds that obtained for nonlinear behaviour of full SSI no BA model (Fig. 5.18(b)). This is due to the fact that for low intensity of earthquake shaking under GM#2, linear elastic behaviour is mobilized for the piers. Even the residual response after the dynamic analysis are similar in both the models which eventually depicts the response
under the initial static gravity analysis. So, in the modelling of this specific soil- foundation-bridge system, under higher PGA (≥ 0.48g of base excitation) nonlinearity of structure is likely to govern the response.
As observed in the results of the previous section, the normalized FT plots of SFTHs for the models show the same trend in the shift of frequency for the occurrence of peak Fourier amplitude under GM#1 (Fig. 5.18(c)). The peaks of normalized Fourier amplitude occur at 1.2 Hz and 0.6 Hz for nl str+lin soil no BA and nonlinear behaviour of full SSI no BA model, respectively. Under GM#2, the peaks of the Fourier amplitudes occur at 2.27 Hz and 2.34 Hz, respectively, for the two models (Fig. 5.18(d)). Due to high energy content in linear soil domain, nl str+lin soil no BA model’s Fourier amplitude is significantly higher than the other one (Fig. 5.18(c)). For the nonlinear behaviour of full SSI no BA model, the input seismic energy gets reduced through soil damping around the bridge foundation; this further reduces the possibility of nonlinear behaviour in the bridge piers. Hence, for that model, the bridge behaviour is comparatively stiffer as compared to the behaviour obtained for nl str+linsoil no BA model. From the velocity time histories at right abutment-deck junction, the peak velocities occur at 8.885 s and 9.495s under GM#1 and at 17.065 s and 16.525 s under GM#2 for nl str+lin soil no BA model and for nonlinear behaviour of full SSI no BA model, respectively (Figs. 5.19(a) and 5.19(b)).
Due to nonlinearity of soil, the peak velocity response of bridge reduces significantly under both the ground motions for the nonlinear behaviour of full SSI no BA model. Under both the ground motions, the frequency for the occurrence of peak Fourier amplitude is observed to be higher for the nl str+lin soil no BA model as compared to the other model (Figs. 5.19(c) and 5.19(d)). The difference in the magnitude of the peak Fourier amplitudes for the models also reflects the higher velocity response of the nl str+lin soil no BA model as compared to the other model. From these type of comparisons, it is easy
to conclude that under low intensity of ground motion, nonlinearity of soil highly influences the nonlinear behaviour of structure.
0 10 20 30 40
-2000 -1000 0 1000 2000
(b) Peak (8.475, 1642.7)
Peak (9.405, 1300.4)
Shear Force, kN
Time, s (a)
0 10 20 30 40
Peak (1259, 16.96s) Peak (966, 16.43s) nl str+lin soil no BA
Nonlinear full SSI no BA
0.1 1 10
0.0 0.2 0.4 0.6 0.8 1.0
0.1 1
(d)10
Normalised Fourier Transform
(c) Frequency, Hz
Fig. 5.18 Comparison of SFTHs for the nonlinear behaviour of full SSI no BA model and the nl str+lin soil no BA model at the top of 8th pier of bridge under (a) GM# 1 and
(b) GM#2; normalized FTs of SFTHs under (c) GM#1and (d) GM#2.