Innovative base-isolated building with large mass-ratio TMD at basement for greater earthquake resilience

Takuya Hashimoto; Kohei Fujita; Masaaki Tsuji; Izuru Takewaki

Introduction

There is an increasing need and interest of construction of high-rise buildings in urban areas. This trend will be accelerated in the future. High-rise buildings and super high-rise buildings are required to resist for various external loadings, e.g. wind and earthquake loadings. Enhancement of resilience of such high-rise and super high-rise buildings after intensive wind and earthquake loadings is a major concern from the viewpoint of the business continuity plan (BCP) which is the most controversial issue in the sound development of society (Takewaki et al. , ).

Tuned mass dampers (TMD) are useful for the reduction of building responses to wind loading and are installed in many high-rise buildings all over the world (Soong and Dargush ). However it is well known that TMD is not effective for earthquake responses because of its limitation on stroke and realization of large mass-ratio TMD.

Nevertheless, some attempts have been made on the introduction of large mass-ratio TMD mainly for earthquake loading (Chowdhury et al. ; Feng and Mita ; Villaverde ; Arfiadi ; Zhang and Iwan ; Villaverde et al. ; Mukai et al. ; Tiang et al. ; Matta and De Stefano ; Petti et al. ; Angelis et al. ; Nishii et al. ; Xiang and Nishitani ). Actually several projects are being planned in Japan, e.g. installation of large-mass pendulum system at roof and usage of upper stories as TMD masses.

Recently large mass-ratio TMDs are investigated for base-isolated buildings (Villaverde ; Villaverde et al. ; Angelis et al. ; Nishii et al. ; Xiang and Nishitani ). While usual high-rise buildings exhibit large displacement around the top story, base-isolated buildings show relatively large displacement around the base-isolation story near ground surface. This property is very advantageous from the view point of mitigation of effect of excessive vertical load due to large mass-ratio TMD (Kareem ; Zhang and Iwan ; Mukai et al. ; Petti et al. ; Nishii et al. ; Xiang and Nishitani ).

However there still exist several issues to be resolved, e.g. avoidance of excessive vertical load by large mass-ratio TMD, reduction of TMD stroke, reduction of TMD support reactions.

The purpose of this paper is to propose an innovative system of base-isolated buildings with a large mass-ratio TMD at basement. The most serious issue of effect of excessive vertical load due to large mass-ratio TMD on the main building is avoided by introducing the large mass-ratio TMD at basement which is made possible due to the large displacement of a floor in the base-isolation story near basement. Another issue of large stroke of TMD even in the large mass-ratio TMD is overcome by introducing inertial mass dampers in parallel to the spring-dashpot system in the TMD system.

Base-isolated building with large-mass ratio TMD at basement

Figure 1(a) shows a conventional system with small mass-ratio TMD on the roof which is effective only for wind loading. On the other hand, Fig. 1(b) presents a high-rise building with large mass-ratio TMD on the roof which is believed to be effective for long-period ground motion and to cause significant vertical load on the building. Consider next a base-isolated building system, as shown in Fig. 1(c), with large mass-ratio TMD on the roof which lengthens the fundamental natural period of the high-rise building and also causes large vertical load on the building. The models in Fig. 1(b) and (c) are thought to be unrealistic because of their excessive vertical load. Figure 2(a) indicates the proposed base-isolated building system with large mass-ratio TMD at basement using sliders and rails. This model shown in Fig. 2(a) is called the Proposed-1 model. In Fig. 2(a) the large mass-ratio TMD is located on the sliders and rails and in Fig. 2(b) the large mass-ratio TMD is set on the floor just above the base-isolation system.

Fig. 1

Conventional model and unrealistic model with excessive vertical load

Fig. 2

Proposed-1 model and Proposed-2 model

Base-isolated building without TMD

Consider a base-isolated building without TMD. This model is called a BI model (see Ariga et al. ). Let k_I, c_I, m_I denote the stiffness, damping coefficient and mass of the base-isolation story in the BI model. Furthermore let k₁, c₁, m₁ denote the stiffness, damping coefficient and mass of the superstructure. The displacements of masses m₁ and m_I relative ground are denoted by u₁ and u_I, respectively. This model is subjected to the base ground acceleration ü_g. The equations of motion for this model can be expressed by

(1)

mI00m1u¨Iu¨1+cI+c1−c1−c1c1u˙Iu˙1+kI+k1−k1−k1k1uIu1=−mIu¨g−m1u¨g

Equ1_TeX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} \[ \left(\begin{array}{cc}\hfill {m}_I\hfill \hfill 0\hfill \\ {}\hfill 0\hfill \hfill {m}_1\hfill \end{array}\right)\left(\begin{array}{c}\hfill {\ddot{u}}_I\hfill \\ {}\hfill {\ddot{u}}_1\hfill \end{array}\right)+\left(\begin{array}{cc}\hfill {c}_I+{c}_1\hfill \hfill -{c}_1\hfill \\ {}\hfill -{c}_1\hfill \hfill {c}_1\hfill \end{array}\right)\left(\begin{array}{c}\hfill {\dot{u}}_I\hfill \\ {}\hfill {\dot{u}}_1\hfill \end{array}\right)+\left(\begin{array}{cc}\hfill {k}_I+{k}_1\hfill \hfill -{k}_1\hfill \\ {}\hfill -{k}_1\hfill \hfill {k}_1\hfill \end{array}\right)\left(\begin{array}{c}\hfill {u}_I\hfill \\ {}\hfill {u}_1\hfill \end{array}\right)=\left(\begin{array}{c}\hfill -{m}_I{\ddot{u}}_g\hfill \\ {}\hfill -{m}_1{\ddot{u}}_g\hfill \end{array}\right) \] \end{document}

Conventional base-isolated building with large-mass ratio TMD

Recently some systems of a base-isolated building with large-mass ratio TMD have been proposed. Mukai et al. () proposed a new-type active response control system to improve the effectiveness of base-isolated buildings. In this system, the TMD mass is connected both to a superstructure and the basement (ground). A negative stiffness mechanism is used to amplify the response of the TMD mass which enables the avoidance of introduction of large mass-ratio TMD. Nishii et al. () revised the system due to Mukai et al. () by replacing the active damper with negative stiffness with a passive inertial mass damper system. This model is called the Imass TMD model in this paper. Although their system is demonstrated to be effective for the reduction of superstructure response, the performance check on the reaction of the TMD system is not conducted. Xiang and Nishitani () presented a system for a base-isolated building with a TMD mass which is located on the base-isolation story level and connected directly to the ground. This model is called the NewTMD model in this paper. They demonstrated that their system is effective for a broad range of excitation frequency and proposed an optimization method for determining the system parameters.

Consider an Imass TMD model and a NewTMD model as shown in Fig. 3. Let k₂, c₂, m₂ denote the stiffness, damping coefficient and mass of the TMD system. z₂ indicates the inertial mass capacity of the inertial mass damper installed between TMD mass and ground in the Imass TMD model.

Fig. 3

Base-isolated building models treated in this paper (a BI Model: Simple base-isolated building, b Imass TMD Model: Model proposed by Nishii et al. (Nishii et al. ), c NewTMD Model: Model proposed by Xiang and Nishitani (Xiang and Nishitani ), d Proposed-1 Model: Base-isolated building with large-mass ratio TMD at basement, e Proposed-2 Model: Base-isolated building with large-mass ratio TMD at basement using inertial mass damper for stroke reduction)

For later comparison, the Imass TMD model and the NewTMD model are explained in the following. The equations of motion for Imass TMD model may be expressed by

(2)

mI000m1000m2+z2u¨Iu¨1u¨2+cI+c1+c2−c1−c2−c1c10−c20c2u˙Iu˙1u˙2+kI+k1+k2−k1−k2−k1k10−k20k2uIu1u2=−mIu¨g−m1u¨g−m2u¨g

Equ2_TeX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} \[ \begin{array}{l}\left(\begin{array}{ccc}\hfill {m}_I\hfill \hfill 0\hfill \hfill 0\hfill \\ {}\hfill 0\hfill \hfill {m}_1\hfill \hfill 0\hfill \\ {}\hfill 0\hfill \hfill 0\hfill \hfill {m}_2+{z}_2\hfill \end{array}\right)\left(\begin{array}{c}\hfill {\ddot{u}}_I\hfill \\ {}\hfill {\ddot{u}}_1\hfill \\ {}\hfill {\ddot{u}}_2\hfill \end{array}\right)+\left(\begin{array}{ccc}\hfill {c}_I+{c}_1+{c}_2\hfill \hfill -{c}_1\hfill \hfill -{c}_2\hfill \\ {}\hfill -{c}_1\hfill \hfill {c}_1\hfill \hfill 0\hfill \\ {}\hfill -{c}_2\hfill \hfill 0\hfill \hfill {c}_2\hfill \end{array}\right)\left(\begin{array}{c}\hfill {\dot{u}}_I\hfill \\ {}\hfill {\dot{u}}_1\hfill \\ {}\hfill {\dot{u}}_2\hfill \end{array}\right)\\ {}\kern11.75em +\left(\begin{array}{ccc}\hfill {k}_I+{k}_1+{k}_2\hfill \hfill -{k}_1\hfill \hfill -{k}_2\hfill \\ {}\hfill -{k}_1\hfill \hfill {k}_1\hfill \hfill 0\hfill \\ {}\hfill -{k}_2\hfill \hfill 0\hfill \hfill {k}_2\hfill \end{array}\right)\left(\begin{array}{c}\hfill {u}_I\hfill \\ {}\hfill {u}_1\hfill \\ {}\hfill {u}_2\hfill \end{array}\right)=\left(\begin{array}{c}\hfill -{m}_I{\ddot{u}}_g\hfill \\ {}\hfill -{m}_1{\ddot{u}}_g\hfill \\ {}\hfill -{m}_2{\ddot{u}}_g\hfill \end{array}\right)\end{array} \] \end{document}

On the other hand, the equations of motion for NewTMD model may be presented by

(3)

mI000m1000m2u¨Iu¨1u¨2+cI+c1−c10−c1c1000c2u˙Iu˙1u˙2+kI+k1+k2−k1−k2−k1k10−k20k2uIu1u2=−mIu¨g−m1u¨g−m2u¨g

Equ3_TeX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} \[ \left(\begin{array}{ccc}\hfill {m}_I\hfill \hfill 0\hfill \hfill 0\hfill \\ {}\hfill 0\hfill \hfill {m}_1\hfill \hfill 0\hfill \\ {}\hfill 0\hfill \hfill 0\hfill \hfill {m}_2\hfill \end{array}\right)\left(\begin{array}{c}\hfill {\ddot{u}}_I\hfill \\ {}\hfill {\ddot{u}}_1\hfill \\ {}\hfill {\ddot{u}}_2\hfill \end{array}\right)+\left(\begin{array}{ccc}\hfill {c}_I+{c}_1\hfill \hfill -{c}_1\hfill \hfill 0\hfill \\ {}\hfill -{c}_1\hfill \hfill {c}_1\hfill \hfill 0\hfill \\ {}\hfill 0\hfill \hfill 0\hfill \hfill {c}_2\hfill \end{array}\right)\left(\begin{array}{c}\hfill {\dot{u}}_I\hfill \\ {}\hfill {\dot{u}}_1\hfill \\ {}\hfill {\dot{u}}_2\hfill \end{array}\right)+\left(\begin{array}{ccc}\hfill {k}_I+{k}_1+{k}_2\hfill \hfill -{k}_1\hfill \hfill -{k}_2\hfill \\ {}\hfill -{k}_1\hfill \hfill {k}_1\hfill \hfill 0\hfill \\ {}\hfill -{k}_2\hfill \hfill 0\hfill \hfill {k}_2\hfill \end{array}\right)\left(\begin{array}{c}\hfill {u}_I\hfill \\ {}\hfill {u}_1\hfill \\ {}\hfill {u}_2\hfill \end{array}\right)=\left(\begin{array}{c}\hfill -{m}_I{\ddot{u}}_g\hfill \\ {}\hfill -{m}_1{\ddot{u}}_g\hfill \\ {}\hfill -{m}_2{\ddot{u}}_g\hfill \end{array}\right) \] \end{document}

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Technical Articles

Innovative base-isolated building with large mass-ratio TMD at basement for greater earthquake resilience

Abstract

Introduction

Base-isolated building with large-mass ratio TMD at basement

Base-isolated building without TMD

Conventional base-isolated building with large-mass ratio TMD