Numerical Study on Un-reinforced Masonry Test Model Supported on FREI
7.1. Introduction
This chapter describes the numerical study of un-reinforced masonry test model supported on FREI for evaluation of dynamic response under four different prescribed earthquake motions. The feasibility of FREI as an alternate of SREI for seismic isolation of un-reinforced masonry building is already presented in previous chapters.
Experimental study as carried out on a 1/5th scaled two storey un-reinforced masonry building supported on four square U-FREI is presented in Chapter 6. Stiffness and damping values of square U-FREIs are estimated through FE analysis and these results are also verified comparing the same obtained from experimental investigation.
However, shake table testing of base isolated model building is not always feasible due to high cost and time required for the preparation of model and test setup. Thus, as an alternative, numerical simulation of the model building is carried out using SAP2000 Version 14 in order to know the dynamic response of the base isolated building. Results of shake table testing of model building supported on U-FREIs are compared with the numerical result to validate the adopted numerical modelling approach. Acceleration and displacement at various floor levels are evaluated while the analysis is carried out for different prescribed ground motion as input. Different response parameters as obtained from shake table testing are compared with those obtained from the numerical analysis.
7.2. Modelling of Test Structure
SAP2000 Version 14 developed by Computers and Structures, Inc, Berkeley, USA is used for modelling and analysis of the base isolated test structure. Modelling and analysis of un-reinforced masonry test model building and FREIs are described briefly as below.
Base level beams of the test model building are modelled as beam element. The test model building supported on isolator undergoes nearly rigid body motion as observed during shake table test. Inter-storey drift at different levels of the test model building is found to be insignificant. Thus, in order to simplify the modelling, the brick walls are modelled using plate element. Floor slabs are also modelled using plate elements.
Extruded view of the model building is shown in Fig. 7.1.
Fig. 7.1 SAP2000 model of test building
7.3. Modelling of FREI
Isolators are modelled as equivalent multi-linear spring. Back bone curve obtained from force displacement hysteresis loops recorded during testing of isolator is used to represent the properties of multi-linear spring. Multi-linear pivot hysteretic plasticity model is used to define the property of spring.
The experimentally obtained force displacement hysteresis loops of U-FREI under horizontal cyclic loading along X-axis (Fig. 7.2a) and along 450 to X-axis (Fig. 7.2b) are used to define the link/support properties as adopted for modelling of isolator.
(a) along X-axis (b) 450 to X-axis
Fig. 7.2 Lateral load vs displacement of U-FREI during cyclic loading test
7.4. Comparison of Numerical and Shake Table Test Results
Numerical analyses of isolated system is carried out using scaled earthquake motions, which are presented in Chapter 6. The analysis is repeated for different acceleration intensity level of four earthquakes. Comparison of time histories of acceleration obtained from shake table test and numerical analysis at different level of the test model building corresponding to Koyna earthquake (full intensity) applied along X-axis are shown in Fig. 7.3. It may be observed that the pattern of acceleration time histories at a floor level from experimental and numerical exercises are quite similar. It is further observed that the peak acceleration obtained from analysis at base beam level and roof level are 6.1% and 3.4% lesser than those of the experimental results for the same earthquake. Similarly, at first floor level, the peak acceleration recorded from the numerical analysis is 14.5% higher than the experimental result. Comparisons of RMS values of acceleration recorded at different levels are also shown in Fig. 7.3. RMS
-4000 -2000 0 2000 4000
-60 -40 -20 0 20 40 60
Shear Force (N)
Horizontal Displacement (mm)
-4000 -2000 0 2000 4000
-60 -40 -20 0 20 40 60
Shear Force (N)
Horizontal Displacement (mm)
values of acceleration obtained from the experimental investigations are observed to be 5.0-10.4% lower than those obtained from the numerically simulated model. Therefore, the numerical model of the base isolated building may be considered as acceptable for evaluation of dynamic response characteristics of such building.
(a) Experimental result at base beam level (b) Analytical result at base beam level
(c) Experimental result at first floor level (d) Analytical result at first floor level
(e) Experimental result at roof level (f) Analytical result at roof level Fig. 7.3 Comparison of experimental and analytical acceleration responses at different
levels of model subjected to Koyna earthquake (full intensity) applied along X-axis
Similar exercises are repeated by considering other earthquake motion with different
-0.1 -0.05 0 0.05 0.1
0 1 2 3 4 5
Acceleration (g)
Time (Sec)
RMS=0.024
-0.1 -0.05 0 0.05 0.1
0 1 2 3 4 5
Acceleration (g)
Time (Sec)
RMS=0.027
-0.1 -0.05 0 0.05 0.1
0 1 2 3 4 5
Acceleration (g)
Time (Sec)
RMS=0.025
-0.1 -0.05 0 0.05 0.1
0 1 2 3 4 5
Acceleration (g)
Time (Sec)
RMS=0.028
-0.1 -0.05 0 0.05 0.1
0 1 2 3 4 5
Acceleration (g)
Time (Sec)
RMS=0.027
-0.1 -0.05 0 0.05 0.1
0 1 2 3 4 5
Acceleration (g)
Time (Sec)
RMS=0.028
test and numerical analysis at different level of the test model corresponding to full intensity of scaled acceleration history of Parkfield earthquake applied along X-axis are shown in Fig. 7.4.
(a) Experimental result at base beam level (b) Analytical result at base beam level
(c) Experimental result at first floor level (d) Analytical result at first floor level
(e) Experimental result at roof level (f) Analytical result at roof level Fig. 7.4 Comparison of experimental and analytical acceleration responses at different levels of model subjected to Parkfield earthquake (full intensity) applied along X-axis
Peak accelerations as obtained from the numerical analysis are 7.8% and 13.1% higher than those obtained from the experiment at base level and first floor level respectively, whereas the roof acceleration obtained from experiment is 3.1% lesser than the
-0.3 -0.15 0 0.15 0.3
0 5 10 15 20
Acceleration (g)
Time (Sec)
RMS=0.033
-0.3 -0.15 0 0.15 0.3
0 5 10 15 20
Acceleration (g)
Time (Sec)
RMS=0.039
-0.3 -0.15 0 0.15 0.3
0 5 10 15 20
Acceleration (g)
Time (Sec)
RMS=0.036
-0.3 -0.15 0 0.15 0.3
0 5 10 15 20
Acceleration (g)
Time (Sec)
RMS=0.041
-0.3 -0.15 0 0.15 0.3
0 5 10 15 20
Acceleration (g)
Time (Sec)
RMS=0.038
-0.3 -0.15 0 0.15 0.3
0 5 10 15 20
Acceleration (g)
Time (Sec)
RMS=0.041