gradient, interior connecting details, door opening ratio of the wall, as well as the strength and elastic modulus of the masonry, the following conclusions can be drawn: (1) The wooden and tile tower eaves have lesser sensitivity to the dynamic modification, their architectural details can be simplified as the battens with the same mass and elastic modulus. In the case of Huqiu pagoda, the most of eaves were destroyed by environment erosion long ago, and the influence of the remnant brick braces to the dynamic behavior can be ignored. (2) Because the strengthened foundation can be regarded as the fixed bearing of the analysis model, the sensitivity of the leaning gradient of Huqiu pagoda is rather low and can be ignored; (3) The door opening ratio of the wall and elastic modulus of the masonry have evidence influence to the dynamic behavior, so the great attention should be paid. To simplify the updating process further, the masonry's modulus is only selected as the structural modification parameter on the basis that the accurate dimensions of doors on the wall have been measured.

The elastic modulus is depended mostly on the damage condition and material property of the brick and mortar. In this investigation, based on the field test data of the materials and observation on the damage condition, the elementary elastic modulus of each storey and their estimated adjusting range and positions were determined. To convenient for modeling and analysis of the computer, by adjusting the elementary elastic modulus to simulate synthesis influence on the material, damage, and repaired conditions of the masonry to the structural stiffness parameter. Thus, the adjusted modulus can be called as the synthesis modulus or composite modulus.

More than 40 elementary models that reflecting the possible combination with various material properties and damage conditions were selected for the model updating. When the model is updated, the reference updating criterion (1), that is, [&>2] = \a)2T] and [0] = [0t], is adopted. The modification to the synthesis modulus follows the rule: Predicted mode shapes are in general agreement with the measurements while the errors in natural frequencies are within allowable limit.

The updating objective limit in this investigation is that: (1) The displacement of mode shape at every storey is the same sign as the measured displacement, (2) The allowable error for natural frequencies is ±10%.

The model updating was carried out by analysis program ANSYS. And an Errors Evaluation Program has been compiled for the error evaluation and the new parameter selection. A refined model for the dynamic behavior of the Huqiu Pagoda was obtained from the 40 elementary models. The results show that when the synthesis modulus of the wall is 2029 MPa for the first story and seventh story, and 1552 MPa for the second to sixth story, respectively, the errors in the first four order natural frequencies are within ±7%, and predicted mode shapes agree generally with the measured ones. The comparison of natural frequencies between the analysis model and test result is listed in Table 7. The corresponding mode shapes are showed in Figure 9.

a) The mode shapes from the test
b) The mode shapes from F.E.A. Figure 9. Comparison of the first four order mode shapes.

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