New structural seismic protection for high-rise building structures

1.1. Fundamentals and advantages of SSIM method

As mentioned, Structural Seismic Isolation Method (SSIM) aims to provide high safety for Highly Reliable Structures (HRS) against strong earthquakes including near-fault and long-period ground motions. On the bases of this method, the present structure is converted to a Structural Seismic Isolation System (SSIS) by the SSIM method, which exhibited inverse pendulum behaviour. For this purpose, structure foot base (Fig. 1(a), part 2) and foundation contact surfaces (Fig. 1(a), part 4) can be designed as any curved surfaces (spherical, elliptical, etc) depending on the earthquake-soil-superstructure parameters and this contact surfaces are separated by elastomeric (lead core rubber or laminated rubber bearings) seismic isolation devices (Fig. 1(a), part 3). It would allow the structure foot base to turn around gyration centre through rubber bearing contact and maintains similar behaviour to the superstructure (Fig. 1(a), part 1). SSIS system provides the possibility of keeping the natural-period of the structure in a larger interval, which is greater than the predominant-period of the majority of possible earthquakes (including near-fault pulse) using currently existing conventional elastomeric isolators with up to 4 second period. In the case of using the CAMSBID-Bg structure (Fig. 1(c)), superstructure’s vibration dominant period will be approximately equal to the elastomeric isolator’s dominant period (2-4 second). Therefore, CAMSBID-Bg structure is prone to resonant vibrations under long-period earthquakes related to the excessive deformation in the isolation layers. Consequently, CAMSBID-Bg structures are vulnerable under near-fault and long-period ground motions. Due to this problem, the conventional application of the currently available seismic base isolation elastomeric devices is limited. In addition, as the SSIS system provides the opportunity of controlled rotation to the superstructure, less bending moment and shear force will be formed in the superstructure base, in comparison with CAMSBID-Bg structures.

Major advantages of SSIS system obtained by the SSIM method over previously studied methods [12-16] and CAMSBID method [8, 9] can be noted as follows:

– SSIS system is applicable for highly reliable structures including high-rise buildings while the majority of mentioned studies are focused on low-rise or medium-rise structures.

– Some of the mentioned seismic isolation methods require extra energy to function which may be inconvenient in some cases. On the other hand, the SSIS system is a totally passive seismic isolation which does not require any extra energy for functioning.

– The usage of friction pendulum isolator for the purpose of seismic isolation could be problematic due to stick-slip and non-uniform pressure distribution of the pendulum on steel plate, while the SSIS system uses elastomeric isolators.

– SSIS system is more reliable than CAMSBID-Bg systems under the effect of long-period and near-fault earthquakes due to the fact that the period of seismic isolators used in CAMSBID-Bg structure is between 2-4 seconds. While SSIS system’s period is much higher thanks to turn-around gyration centre and it does not cause resonant vibrations.

Fig. 1Schematic illustration of a) the SSIS system obtained by SSIM method and b) completed SSIS-Bg structure and c) CAMSBID-Bg structure: 1 – superstructure, 2 – curved surface superstructure foot base, 3 – elastomeric seismic isolation devices, 4 – foundation contact curved surface, 2b – plane surface CAMSBID-Bg superstructure foot base, 4b – Foundation contact plane surface of CAMSBID-Bg structure [21]

The governing equation and the mathematical model of the SSIS system with the spherical structure foot base and foundation contact surfaces (Fig. 2) have been presented as following [19]:

With:

where $\left[m\right]$, $\left[c\right]$, $\left[k\right]$ are mass, Rayleigh damping and stiffness matrix of the superstructure respectively and it is composed by FEM [35], $u$ is the relative displacement vector of the deformed states of the superstructure. $\dot{u}$ and $\ddot{u}$ are the velocity and acceleration vector respectively. $F_{\ddot{u}g}$ stands for seismic force:

with:

where, $\phi$ represents the absolute rigid structure’s rotation angle around the gyration centre, ${\ddot{u}}_g$ is the ground motion excitation; $F_{c0}=c_b{\rho }_2\dot{\phi }$ is total damping and $F_{kb}$ total stiffness forces of seismic isolator deployed in SSIS system which possess $c_b$ (total damping-coefficient) and spherical radius (${\rho }_2$). $F_{c,eq}=c_d{\rho }_2\dot{\phi }$ represents the sum of external dampers’ equal damping force which contains the $c_d$ (damping coefficient). $\phi$ is the solution of the Eq. (2):

where $h_i$ ($i=1,\mathrm{}n$) is the $z$ distance of the superstructure’s $i$-th mass $m_i$ from the gyration centre, $m_{0j}$, $h_{0j}$, ($j=1,\mathrm{}m$) are similar parameters for the underground part of the SSIS system.

Fig. 2General working mechanism schema of the SSIS-Bg system

The lateral displacement of superstructure’s base is indicated by ($u_b$) which correlates to the contact surface of the foundation. $u_y$ (yield displacement), $k_b$ (total stiffness) of the isolators, $\alpha$ (post to pre-yielding stiffness ratio commonly taken as; $\alpha =$ 0.1). The rations $d_r=u_{yb2}/u_y=$ 9.98 and $f_r=F_{yb2}/F_y=$ 2.01 respectively as described in Fig. 3. The parameter $\dot{Z}$ refers to dimensionless hysteresis displacement component satisfies the nonlinear first-order [37, 38] differential Eq. (5), $F_y$ and $Q$ refer to yield and characteristic strengths of the seismic isolator respectively. By defining the $F_0$ parameter as presented in Eq. (12) with regard to the total weight of the structure $W$ the yield strength of the seismic isolator can be normalized:

In some references normalized stiffness has been expressed as follows:

where $m_i$, $m_b$, and $m_t$ are the mass of the storey, base slab and total mass of the building respectively.

Fig. 3Illustration of the hysteresis loop of the LCRB isolator and its geometric rations [19]

In Eq. (5) $\beta$, $\alpha$, $n$ and $\gamma$ are dimensionless parameters and affects the shape of the hysteresis loop, the value of these parameters are predicted through experiments. Here, the value of above mentioned parameters are taken as: $n=2$; $\alpha =1$ and $(\beta +\gamma )/a=1$. The model of Eq. (5) decreases to a viscoplasticity model, in Eq. (5) $u_y$ refers to yield displacement. The base and top absolute displacement $(u_{b,abs},u_{n,abs})$ and acceleration $({\ddot{u}}_{b,abs},{\ddot{u}}_{n,abs})$ behaviour of SSIS-Bg structure are described via Eq. (16):

were, $u_b$, $u_n$ and ${\ddot{u}}_b$, $u_{0n}$are the base and top relative displacement and acceleration; $u_{0n}$, ${\ddot{u}}_{0n}$ are the top relative displacement and acceleration of the SSIS-Bg structure as a rigid body.

Pre-sizing and assessment of SSIS-Bg structure have been conducted by MATLAB and Simulink programming tools using presented governing equations by Kasimzade et al. [19] in the following section.

1.2. Assessment of the SSIS-Bg structure according to the basic demands of the SSIM method

A numerical verification of the SSIS-Bg structure is presented with an example of 26 storey steel framed structure. For comparability of the SSIS-Bg, FB-Bg and CAMSBID-Bg structures, its storey height, column axes ranges were accepted same respectively with an equal total mass of 3.04894E+7 kg as presented in Table 3. Pre-sizing SSIS-Bg (26-storey, 104 m), CAMSBID-Bg (24-storey, 96 m) and FB-Bg (24-storey, 96 m) steel superstructures are designed so that the maximum story angle is lower than 1/200. The steel grade SN-490 (with 357.0 MPa yield strength) for superstructure and reinforced concrete for the base part is used as material for members (Table 1). Total floor load (per meter square) containing the dead load of the columns and beams is 7840.0 N/m². Storey height, column axes ranges are accepted 4 m, 8 m respectively. Pre-sizing results for beams and columns were presented in Table 2. The floor mass distribution for FB-Bg, CAMSBID-Bg and SSIS-Bg structures are presented in Table 3.

The total superstructure mass ($M_{totalsuperstore}$) of CAMSBID-Bg and FB-Bg is presented according to the total mass of SSIS-Bg as following:

Assuming that the predominant period of the earthquakes in the area where FB-Bg, CAMSBID-Bg and SSIS-Bg structures will be built is about 11 s. The required total elastomeric isolator horizontal stiffness for the first approximation for the SSIS system is described in accordance with Eq. (2), in case of free vibration as $k_b=$ 8.2455E+7 N/m. Other parameters of the elastomeric isolator such as period, damping coefficient and damping ratio were defined as $T_b=$ 4 s, $c_b=\mathrm{}$1.5182E+7 Ns/m², ${\xi }_b=$ 0.15 respectively.

Based on above SSIS-Bg structure’s parameters and using governing equations for SSIS system from the previous section, SSIS-Bg structure’s performance was preliminary assessed to Kobe 1995 Earthquake $X$-direction acceleration excitation and base acceleration response were presented in Fig. 4.

As seen, the acceleration in the SSIS-Bg structure’s base significantly (about four times) was reduced. Based on preliminary design parameters and assessments results presented in this section, detailed finite element modelling of the SSIS-Bg structure comparing with FB-Bg, CAMSBID-Bg structures were presented in the following section.

Fig. 4Base acceleration responses of SSIS-Bg structure (red) in X-direction under the effect of the Kobe earthquake (cyan)

2.1. Preliminary design of the seismic elastomeric isolators

The preliminary dimension and analytical parameters of the seismic isolators are calculated based on ASCE 7-16 [40] and ASCE 41-13 [41] codes. Yield force ($F_v$), yield displacement ($u_y$), damping ratio and the vertical stiffness ($K_v$) are the necessary analytical parameters for finite element modelling of the seismic isolators. Minimum horizontal stiffness and the design displacement of the isolator are calculated using Eq. (17) and (18) respectively:

where $W$ stands for the total weight on a single bearing, $T_D$ for design period (here $T_D=$ 4 s), $B_D$ for damping coefficient, $g$ for gravity, $S_{D1}$ for spectral coefficient. The cross-section area of rubber ($A_r$) and post-yielding stiffness are calculated using Eq. (19) and (20) respectively:

where yield displacement ($u_y$) is 0.05-0.1 times of total rubber thickness ($R_T$) based on experimental data; $f_L$ is a factor which commonly taken 1.5. The characteristic strength ($Q$) of the elastomeric can be calculated using Eq. (21). Then the yield force ($F_y$) of the bearing can be calculated by Eq. (22):

Fig. 5a) The position of deployed seismic isolator in SSIS-Bg structure, b) the overall view and illustration of the finite element model of 26 storey structure SSIS-Bg equipped with SSIS system, and c) the general floor plan including the position of isolators of the structure

a)

b)

c)

Finally, the vertical stiffness ($K_v$) of the elastomeric bearing is calculated via Eq. (23):

where $E_c$, $G$ and $K$ is the compression of rubber-steel composite, shear and bulk modulus of rubber respectively. The value of $K$ and $G$ differs based on the type of rubber, the value of $K$ can vary between (1000 to 2500 MPa) and $G$ between (0.45 to 1 MPa). $S$ represents the hysteresis loop shape factor of the seismic isolator and the value of $S$ should range between 12 and 20. Based on the presented equation the parameters of the LCRB for SSIS-Bg and CAMSBID-Bg structures are calculated and presented in Table 4.

The final design of the elastomeric isolators parameters is implemented based on the compering first iteration results $K_{h,total}=$ 53×1.56E+6 = 82.68E+6 N/m with the required total horizontal stiffness of the isolators $k_b=$ 82.455E+6 N/m obtained from Eq. (2). Then it can be confirmed in every iteration by the assessment of the hysteresis loop of the elastomeric isolator.

3.1. Results and discussion

As presented in Figs. 7-8 the base and top acceleration response SSIS-Bg is tangibly lower than CAMSBID-Bg and FB-Bg structure in both $X$ and $Y$ directions. On the other hand, the top storey displacements of SSIS-Bg and CAMSBID-Bg are lower than FB-Bg structure and similar to each other as shown in Fig. 9.

While the acceleration response of SSIS-Bg is considerably lower than the CAMSBID-Bg and FB-Bg structures, the reduction of the base shear and base moment response of SSIS-Bg is significantly lower than CAMSBID-Bg and FB-Bg structures as well. It is achieved due to turn around the gyration centre of the SSIS-Bg structure. The base shear and base moment responses of SSIS-Bg, CAMSBID-Bg and FB-Bg structures due to the effect of the 1995 Kobe earthquake are presented in Fig. 10 and Fig. 11.

Fig. 11Base moment response of SSIS-Bg, CAMSBID-Bg and FB-Bg structures in X and Y directions respectively

Fig. 12Comparison of the hysteresis loops of the central seismic isolator of a), b) SSIS-Bg, c) d) CAMSBID-Bg structures

a)

b)

c)

d)

All peak top acceleration, top displacement (Table 6), base shear and base moment responses (Table 7), base acceleration, base displacement (Table 8) of the SSIS-Bg, CAMSBID-Bg and FB-Bg structures are presented as follows.

The SSIS-Bg, CAMSBID-Bg and FB-Bg structures were analysed under the effect of strong and long-period earthquakes listed in Table 5. The base acceleration responses of the SSIS-Bg structure is 22.94 % and 24.47 % lower (on average) than the CAMSBID-Bg structure in $X$ and $Y$ directions respectively as shown in Fig 13. Similarly, there are 19.21 % and 26.22 % difference between the top storey acceleration response of SSIS-Bg and CAMSBID-Bg structures as presented in Fig. 14. The response of FB-Bg structure clearly indicates to extreme vulnerably of similar structures under effect of long-period earthquakes.

While the acceleration response of SSIS-Bg structure is considerably lower compared to CAMSBID-Bg and FB-Bg structures, there is a tremendous difference between base shear and base moment responses of the SSIS-Bg, CAMSBID-Bg and FB-Bg structures. As presented in Fig. 15 the base shear response of SSIS-Bg structure is 74.86 % and 76.08 % lower (on average) than CAMSBID-Bg structure in $X$ and $Y$ directions respectively. On the other hand, the even higher differences are observed between the base moment response of SSIS-Bg and CAMSBID-Bg structures which is 84.92 % and 86.55 % in $X$ and $Y$ directions respectively (Fig. 16).

Fig. 13Peak base acceleration response of SSIS-Bg, CAMSBID-Bg structures in X and Y directions

Fig. 14Peak top storey acceleration responses of the SSIS-Bg, CAMSBID-Bg and FB-Bg structures in X and Y directions

Fig. 15Peak base shear response of the SSIS-Bg, CAMSBID-Bg and FB-Bg structures in X and Y directions

Fig. 16Peak base moment responses of the SSIS-Bg, CAMSBID-Bg and FB-Bg structures in X and Y directions