# Research and Experiment on Optimal Separation Distance of Adjacent Buildings Based on Performance

Authors: Hexian Luo; Qiaoyun Wu; Weijie Pan
Journal: Mathematical Problems in Engineering
 (2018)

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## Abstract

Firstly, constitutive models of two unequal height adjacent ten-story and six-story reinforced concrete frame structures were established based on OpenSees software in which a series of separation distances are set for incremental dynamic analysis (IDA), respectively. Secondly, the seismic vulnerability curves by postprocessing programming in Matlab software were obtained based on IDA datum, and the optimal separation distances of adjacent buildings with and without connecting dampers were obtained by comparing the seismic vulnerability of adjacent building at different separation distance and the seismic hazard analysis. Finally, a scaled model shaking table test of adjacent steel frame structures was performed. The conclusions are obtained by comparing the measured results of the test with those obtained by the OpenSees analysis, such as acceleration and displacement. The conclusions show that when two adjacent buildings are not connected with a damper, the distance of adjacent structures is suggested to be 0.3 m under moderate and strong earthquakes and the distance of adjacent structures is suggested to be a specified value of 0.24 m under rare earthquakes. When two adjacent buildings are connected with dampers, the separation distance is suggested to be 0.1 m under various performance conditions.


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## Body

## 1. Introduction

In order to prevent adjacent buildings from colliding, the most direct and effective method is to increase the distance between adjacent buildings. At the same time, to completely avoid adjacent structures colliding, the distance between adjacent buildings may be relatively wide, which may increase the area of construction land and construction cost and cause inconvenience to construction. Therefore, it is necessary to further study whether it is economical to avoid collisions at the safety level specified in the structure. In recent years, there have been studies on the critical separation distance of adjacent buildings. Jeng et al. pointed out that the use of absolute sum (ABS) method to calculate the critical separation distance of adjacent structures tends to give a conservative estimate, and its degree of conservation increases as the period values of two adjacent structures approach [1]. Furthermore, Jeng et al. proposed a differential spectrum method, namely, the double difference method (DDC method), which was used to solve the minimum separation distance between adjacent linear single degree of freedom (SDOF) structures to avoid collision [1]. Lopez-Garcia and Soong examined the accuracy of the DDC method in predicting the critical distance between adjacent linear single-degree-of-freedom structures [2]. And Lopez-Garcia and Soong studied the accuracy of four methods of calculating the critical separation distance of adjacent buildings by using the nonlinear single-degree-of-freedom hysteresis structural model under non-stationary seismic excitation [3]. Filiatrault et al. [4, 5] and Kasai et al. [6] extended the DDC method to the calculation of the minimum separation distance of adjacent nonlinear single-degree-of-freedom structures to avoid collision. In the study of Lin and Weng [7], based on the stochastic vibration theory, the critical separation distance between adjacent buildings was analyzed theoretically by using the linear elastic multiple-degree-of-freedom (MDOF) model. Penzien gave an analytical method for calculating the minimum separation distance required to prevent two adjacent structures from colliding, based on the equivalent linearization method and the complete quadratic combination (CQC) method [8]. Hao and Liu used the random vibration method to analyze the influence of the spatial variability of ground motion on the relative displacement of the elastic structure of adjacent lines [9]. Based on the reliability method and random vibration theory, Hong et al. [10] gave a procedure for estimating the critical separation distance between adjacent structures against collisions. Shrestha gave an analytical solution of the critical separation distance between adjacent buildings to avoid collisions, proposed the influence of different normalized critical separation distances on the collision response of adjacent linear and nonlinear SDOF structures, and pointed out that the DDC method is more accurate in calculating the critical separation distance between adjacent linear structures to avoid collisions, but the critical separation distance between adjacent nonlinear structural systems cannot be accurately calculated [11]. Wu et al. derived the analytical formulas for the optimum parameters of viscoelastic damper (VED) represented by Kelvin model and viscous fluid damper (VFD) represented by Maxwell model, which are used to connect the towers and the sky-bridge. The optimum parametric analysis indicates that the control performance is not sensitive to damper damping ratio of VED and relaxation time of VFD [12]. In addition, the authors have achieved some results in the study of seismic resistance of adjacent structures connected to dampers [13–17].It can be seen that there are few studies on seismic performance assessment of adjacent buildings considering collisions, lacking of mature theoretical and systematic research. Seismic design specifications have evolved from the initial static theory and response spectrum theory to dynamic theory to performance-based design theory; new, advanced, accurate, and highly efficient reliability-based assessments are needed to reduce the risk of seismic collisions. Therefore, this paper will analyze the structural seismic vulnerability of controlled and uncontrolled adjacent buildings under distinction separation distance and then obtain the critical separation distance between adjacent structures based on the principle of minimum seismic vulnerability of adjacent structures.


## 2. Adjacent Structural Calculation Models and Selection of Seismic Records

### 2.1. Adjacent Structure Calculation Model

The models selected in this paper are shown in Figure1 (controlled and uncontrolled structures calculation diagram). Structure 1 is a 10-story reinforced concrete frame, structure 2 is a 6-story reinforced concrete frame, and the structure is evenly arranged. In order to simplify the calculation, each of the structures takes a two-dimensional model.Figure 1
Adjacent structure calculation diagram (a) uncontrolled and (b) controlled.
(a) (b)The main design parameters of the two structures are as follows: the basic wind pressure is0.35kN/m2, the basic snow pressure is 0.25kN/m2, the ground roughness is Class B, the earthquake fortification intensity is 8 degrees, the earthquake prevention group is the second group, the design site category is II class, the characteristic cycle is 0.35 s, the design basic earthquake acceleration value is 0.20 g, on the frame seismic grade structure 1 is grade one, and the structure 2 is grade two. The beam and column main reinforcement level is HRB335, the level of stirrups is HPB300, the strength grades of columns, and beams and floors are C35. The floor height is 3.6 m, the section size of structure 1 is that beam size of 300 mm × 800 mm and column size of 750 mm × 750 mm, the size of structure 2 is beam size of 300 mm × 800 mm and column size of 800 mm × 800 mm, and the thickness of each structure is 150 mm.Establish a two-dimensional model of the structure and performing incremental dynamic analysis using the OpenSees software. The uniaxialMaterial Maxwell damper material and displacement-based nonlinear fiber beam-column element are selected to simulate. By analyzing, the first-order natural vibration frequency of two structures isω1=8.418rad/s and ω1=17.5254rad/s, respectively. The total mass of structures 1 and 2 is 303.0705t and 203.8021t, respectively.


### 2.2. Selection of Seismic Records

Relevant scholars have studied the fact that, for medium-height buildings, selecting 10 to 20 seismic records for incremental dynamic analysis can obtain more accurate seismic demand estimates [18]. In this paper the site category is II class, so in the database of the Pacific Earthquake Engineering Research Center (PEER), 12 seismic waves of the far-field with magnitude of 6.5~6.9 are selected. The spatial differential effect of ground motion is not considered in the analysis and only horizontal ground motion is considered.


### 2.3. The Choice of Separation Distance

According to old and new version ofCode for Seismic Design of Buildingsin China (GB50011-2001; GB50011-2010), separation distances of adjacent structures were obtained. To adjacent structures that are not connected with a damper, the following series of separation distances is set: 0.21 (old specification value), 0.24 (new specification value), 0.30, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, and 0.70 (unit: m); to adjacent structures that are connected with a damper, another series of separation distance is set: 0.05, 0.10, 0.15, 0.21(old specification value), 0.24 (new specification value), 0.30, 0.35, 0.40, 0.45, and 0.50 (unit: m).


## 2.1. Adjacent Structure Calculation Model

The models selected in this paper are shown in Figure1 (controlled and uncontrolled structures calculation diagram). Structure 1 is a 10-story reinforced concrete frame, structure 2 is a 6-story reinforced concrete frame, and the structure is evenly arranged. In order to simplify the calculation, each of the structures takes a two-dimensional model.Figure 1
Adjacent structure calculation diagram (a) uncontrolled and (b) controlled.
(a) (b)The main design parameters of the two structures are as follows: the basic wind pressure is0.35kN/m2, the basic snow pressure is 0.25kN/m2, the ground roughness is Class B, the earthquake fortification intensity is 8 degrees, the earthquake prevention group is the second group, the design site category is II class, the characteristic cycle is 0.35 s, the design basic earthquake acceleration value is 0.20 g, on the frame seismic grade structure 1 is grade one, and the structure 2 is grade two. The beam and column main reinforcement level is HRB335, the level of stirrups is HPB300, the strength grades of columns, and beams and floors are C35. The floor height is 3.6 m, the section size of structure 1 is that beam size of 300 mm × 800 mm and column size of 750 mm × 750 mm, the size of structure 2 is beam size of 300 mm × 800 mm and column size of 800 mm × 800 mm, and the thickness of each structure is 150 mm.Establish a two-dimensional model of the structure and performing incremental dynamic analysis using the OpenSees software. The uniaxialMaterial Maxwell damper material and displacement-based nonlinear fiber beam-column element are selected to simulate. By analyzing, the first-order natural vibration frequency of two structures isω1=8.418rad/s and ω1=17.5254rad/s, respectively. The total mass of structures 1 and 2 is 303.0705t and 203.8021t, respectively.


## 2.2. Selection of Seismic Records

Relevant scholars have studied the fact that, for medium-height buildings, selecting 10 to 20 seismic records for incremental dynamic analysis can obtain more accurate seismic demand estimates [18]. In this paper the site category is II class, so in the database of the Pacific Earthquake Engineering Research Center (PEER), 12 seismic waves of the far-field with magnitude of 6.5~6.9 are selected. The spatial differential effect of ground motion is not considered in the analysis and only horizontal ground motion is considered.


## 2.3. The Choice of Separation Distance

According to old and new version ofCode for Seismic Design of Buildingsin China (GB50011-2001; GB50011-2010), separation distances of adjacent structures were obtained. To adjacent structures that are not connected with a damper, the following series of separation distances is set: 0.21 (old specification value), 0.24 (new specification value), 0.30, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, and 0.70 (unit: m); to adjacent structures that are connected with a damper, another series of separation distance is set: 0.05, 0.10, 0.15, 0.21(old specification value), 0.24 (new specification value), 0.30, 0.35, 0.40, 0.45, and 0.50 (unit: m).


## 3. Analysis of Examples

### 3.1. Determination of Structural Performance Levels

Maximum interlayer displacement angleθmax that characterizes the overall structural damage index is picked as Engineering Demand Parameter (EDP). This paper divides the performance level of the structure into 4 levels: Immediately Occupation (IO), Slightly Damage (SD), Life Safety (LS), and Collapse Prevention (CP). It shows the performance targets corresponding to each limit state in Table 1.Table 1
Performance targetsyin each limit state.
y IO SD LS CP θ m a x 0.005 0.01 0.02 0.04


### 3.2. Incremental Dynamic Analysis

Choose peak ground acceleration (PGA) as Intensity Measure (IM) and maximum interlayer displacement angleθmax as Demand Measure (DM). By incremental dynamic analysis of adjacent structures under the action of the aforementioned 12 ground motions, each one is amplitude-modulated 25 times and the IDA curves when the adjacent structures are uncontrolled and controlled under 0.24 m distance are shown in Figures 2 and 3.Figure 2
IDA curves of structure 1 (separation distance 0.24m). (a) Uncontrolled and (b) controlled.
(a) (b)Figure 3
IDA curves of structure 2 (separation distance 0.24m). (a) Uncontrolled and (b) controlled.
(a) (b)Analyzing the IDA curve in Figures2 and 3, two structures of adjacent structure have a good convergence at the beginning of the IDA curve, which increases linearly and the structure is in an elastic phase. With the increase of PGA, when the maximum interlayer displacement angle is greater than 0.01, the slope of the IDA curve shows a wave rising trend; it indicates that the structure enters the plastic stage, causing the curve to appear hysteresis. Then when the interlayer displacement angle tends to 0.04, the slope of the curve is significantly reduced and the structure is dynamically unstable and collapses.Figures2 and 3 show that structure 1 with no damper attached exhibits hysteresis when the PGA reaches 0.7 g and structure 2 exhibits hysteresis when the PGA reaches 0.9 g. Structures 1 and 2 connected with the damper exhibit hysteresis when the PGA reached 1.1 g. It can be concluded that the Maxwell damper has a better control effect on adjacent structures and increases the elastic stability of the structure.


### 3.3. Seismic Vulnerability Analysis

#### 3.3.1. Macro Vulnerability Analysis

In order to understand the seismic responses of adjacent structures under various performance targets and separation distances, Figure4 shows the exceeding probability curves of uncontrolled adjacent structures in the LS limit state (with maximum interlayer displacement angle as EDP) under different distances. Due to space limitations, this section only gives the exceeding probability curves of uncontrolled adjacent structures in the LS limit state.Figure 4
Exceeding probability curves of uncontrolled adjacent structures in the LS limit state. (a) Structure 1 and (b) Structure 2.
(a) (b)Just seeing the behaviors for distances 0.21, 0.24, and 0.30 in Figure6, the trends of them are the same and the exceeding probability increases with the increase in PGA, but the rate of change in Figure 4(a) is bigger than that in Figure 4(b). It shows that the optimal arrangement of the separation distance of uncontrolled adjacent structures mainly depends on the response of the structure 2 and the design of different separation distances has less influence on the exceeding probability of the structure 1.Figure5 plots the total exceeding probability curves of uncontrolled adjacent structures in the disparate limit states (with maximum interlayer displacement angle as EDP) under different distances.Figure 5
Total exceeding probability curves of uncontrolled adjacent structures in disparate limit states. (a) IO; (b) SD; (c) LS; (d) CP.
(a) (b) (c) (d)Figure 6
Exceeding probability curves of controlled adjacent structures in the LS limit state. (a) Structure 1 and (b) Structure 2.
(a) (b)Figure5 shows that the difference in the total exceeding probability of adjacent structures with different distances is smaller in the IO limit state; it is indicating that the separation distance has no obvious effect on the structure under this performance level; in the SD limit state, when the ground motion intensity is low (PGA <1.2 g), it can be clearly seen that when the separation distance is 0.30 m, the total exceeding probability of the adjacent structure is the smallest; in the LS limit state, when PGA<1.25 g, the difference of the total exceeding probability of adjacent structures under disparate separation distances is small, but it can be seen that 0.30 m is the best separation distance; there is a big distinction between the total exceeding probabilities of adjacent structures with different separation distances in the CP limit state; when the separation distance is 0.7 m, the total exceeding probability of the adjacent structures is the smallest; when separation distances is 0.24 m (the new specification), the exceeding probability of adjacent structures is also small.According to the analysis, it can be seen that the critical separation distance between adjacent structures is not as large as possible. For example, in the limit state of LS and CP, when the separation distance is 0.55m, the total exceeding probability of adjacent structures is the largest. In addition, for this structure, when the separation distance is set to 0.3 m (greater than the new specified 0.24 m), the exceeding probability of the adjacent structure at each performance level is small.Similar to the uncontrolled adjacent structures, Figure6 shows the exceeding probability curves of controlled adjacent structures in the LS limit state (with maximum interlayer displacement angle as EDP) under disparate distances. Due to space limitations, this section only gives the exceeding probability curves of controlled adjacent structures in the LS limit state.Just seeing the behaviors for distances 0.05, 0.10, and 0.40 in Figure6, the trends of them are the same; the exceeding probability increases with the increase in PGA, but the rate of change in Figure 6(a) is bigger than that in Figure 6(b). So it can be seen from Figure 6 that the optimal arrangement of the separation distance of controlled adjacent structures mainly depends on the response of the structure 2 and the design of different separation distances has less influence on the exceeding probability of the structure 1.The total exceeding probability of the controlled adjacent structure is obtained by the method similar to the total exceeding probability of uncontrolled adjacent structures, as shown in Figure7.Figure 7
Total exceeding probability curves of controlled adjacent structures in disparate limit states. (a) IO; (b) SD; (c) LS; (d) CP.
(a) (b) (c) (d)Figure7 shows that in the IO and SD limit state, the total exceeding probability of adjacent structures is affected little by the separation distance; in the LS limit state, when the separation distance is taken as 0.1 m, the total exceeding probability of the adjacent structure is minimal; in the CP limit state, the distinction of the total exceeding probability of adjacent structures with different critical separation distances is larger; when the adjacent distance is taken as 0.1m, the total exceeding probability of adjacent structures is the smallest. Therefore, for the controlled adjacent structures proposed in this paper, the critical separation distance between adjacent structures can be set to 0.1m. Under this critical separation distance values, adjacent structures have smaller exceeding probabilities at all performance levels.From the total exceeding probability curves of adjacent structures with different critical separation distances shown in Figures5 and 7, it can be seen that the adjacent structure connecting with dampers can greatly reduce the need for separation distance (less than the specified 0.24m).


#### 3.3.2. Micro Vulnerability Analysis

In order to further study the influence of the damper on the critical separation distance between adjacent structures, the damper output force is used to represent EDP in this section and the microscopic vulnerability of the controlled adjacent structure is analyzed. When the EDP is represented by the damper output force, the quantitative limit value of each limit state cannot be clearly obtained by the analytical method; therefore, the seismic vulnerability curves of adjacent structures with multipleF values are given here, shown in Figure 8. Since the best separation distance is 0.10 m obtained in the previous section when the interstory drift angle is EDP, this section selects the adjacent distances of 0.10 m, 0.21 m (old specification value), and 0.24 m (new specification value).Figure 8
Damper output force seismic vulnerability curves. (a) F=200 kN; (b) F=300 kN; (c) F=400 kN; (d) F=500 kN.
(a) (b) (c) (d)Figure8 shows that when F<300 kN, the vulnerability curves of adjacent structures under disparate separation distances are steeper and the shape of the curves is not much different; and when F≥300 kN, the vulnerability curves change to flatness and the difference between the curves increase as the F value increases. It is obvious that when the adjacent distance is 0.10 m, the exceeding probability of adjacent structures is greater than the exceeding probability of 0.21 m and 0.24 m separation distance. It can be seen that when the adjacent distance is smaller, the output force of the damper is greater, so when the adjacent distance is small, a damper with a large output force should be selected.


## 3.1. Determination of Structural Performance Levels

Maximum interlayer displacement angleθmax that characterizes the overall structural damage index is picked as Engineering Demand Parameter (EDP). This paper divides the performance level of the structure into 4 levels: Immediately Occupation (IO), Slightly Damage (SD), Life Safety (LS), and Collapse Prevention (CP). It shows the performance targets corresponding to each limit state in Table 1.Table 1
Performance targetsyin each limit state.
y IO SD LS CP θ m a x 0.005 0.01 0.02 0.04


## 3.2. Incremental Dynamic Analysis

Choose peak ground acceleration (PGA) as Intensity Measure (IM) and maximum interlayer displacement angleθmax as Demand Measure (DM). By incremental dynamic analysis of adjacent structures under the action of the aforementioned 12 ground motions, each one is amplitude-modulated 25 times and the IDA curves when the adjacent structures are uncontrolled and controlled under 0.24 m distance are shown in Figures 2 and 3.Figure 2
IDA curves of structure 1 (separation distance 0.24m). (a) Uncontrolled and (b) controlled.
(a) (b)Figure 3
IDA curves of structure 2 (separation distance 0.24m). (a) Uncontrolled and (b) controlled.
(a) (b)Analyzing the IDA curve in Figures2 and 3, two structures of adjacent structure have a good convergence at the beginning of the IDA curve, which increases linearly and the structure is in an elastic phase. With the increase of PGA, when the maximum interlayer displacement angle is greater than 0.01, the slope of the IDA curve shows a wave rising trend; it indicates that the structure enters the plastic stage, causing the curve to appear hysteresis. Then when the interlayer displacement angle tends to 0.04, the slope of the curve is significantly reduced and the structure is dynamically unstable and collapses.Figures2 and 3 show that structure 1 with no damper attached exhibits hysteresis when the PGA reaches 0.7 g and structure 2 exhibits hysteresis when the PGA reaches 0.9 g. Structures 1 and 2 connected with the damper exhibit hysteresis when the PGA reached 1.1 g. It can be concluded that the Maxwell damper has a better control effect on adjacent structures and increases the elastic stability of the structure.


## 3.3. Seismic Vulnerability Analysis

### 3.3.1. Macro Vulnerability Analysis

In order to understand the seismic responses of adjacent structures under various performance targets and separation distances, Figure4 shows the exceeding probability curves of uncontrolled adjacent structures in the LS limit state (with maximum interlayer displacement angle as EDP) under different distances. Due to space limitations, this section only gives the exceeding probability curves of uncontrolled adjacent structures in the LS limit state.Figure 4
Exceeding probability curves of uncontrolled adjacent structures in the LS limit state. (a) Structure 1 and (b) Structure 2.
(a) (b)Just seeing the behaviors for distances 0.21, 0.24, and 0.30 in Figure6, the trends of them are the same and the exceeding probability increases with the increase in PGA, but the rate of change in Figure 4(a) is bigger than that in Figure 4(b). It shows that the optimal arrangement of the separation distance of uncontrolled adjacent structures mainly depends on the response of the structure 2 and the design of different separation distances has less influence on the exceeding probability of the structure 1.Figure5 plots the total exceeding probability curves of uncontrolled adjacent structures in the disparate limit states (with maximum interlayer displacement angle as EDP) under different distances.Figure 5
Total exceeding probability curves of uncontrolled adjacent structures in disparate limit states. (a) IO; (b) SD; (c) LS; (d) CP.
(a) (b) (c) (d)Figure 6
Exceeding probability curves of controlled adjacent structures in the LS limit state. (a) Structure 1 and (b) Structure 2.
(a) (b)Figure5 shows that the difference in the total exceeding probability of adjacent structures with different distances is smaller in the IO limit state; it is indicating that the separation distance has no obvious effect on the structure under this performance level; in the SD limit state, when the ground motion intensity is low (PGA <1.2 g), it can be clearly seen that when the separation distance is 0.30 m, the total exceeding probability of the adjacent structure is the smallest; in the LS limit state, when PGA<1.25 g, the difference of the total exceeding probability of adjacent structures under disparate separation distances is small, but it can be seen that 0.30 m is the best separation distance; there is a big distinction between the total exceeding probabilities of adjacent structures with different separation distances in the CP limit state; when the separation distance is 0.7 m, the total exceeding probability of the adjacent structures is the smallest; when separation distances is 0.24 m (the new specification), the exceeding probability of adjacent structures is also small.According to the analysis, it can be seen that the critical separation distance between adjacent structures is not as large as possible. For example, in the limit state of LS and CP, when the separation distance is 0.55m, the total exceeding probability of adjacent structures is the largest. In addition, for this structure, when the separation distance is set to 0.3 m (greater than the new specified 0.24 m), the exceeding probability of the adjacent structure at each performance level is small.Similar to the uncontrolled adjacent structures, Figure6 shows the exceeding probability curves of controlled adjacent structures in the LS limit state (with maximum interlayer displacement angle as EDP) under disparate distances. Due to space limitations, this section only gives the exceeding probability curves of controlled adjacent structures in the LS limit state.Just seeing the behaviors for distances 0.05, 0.10, and 0.40 in Figure6, the trends of them are the same; the exceeding probability increases with the increase in PGA, but the rate of change in Figure 6(a) is bigger than that in Figure 6(b). So it can be seen from Figure 6 that the optimal arrangement of the separation distance of controlled adjacent structures mainly depends on the response of the structure 2 and the design of different separation distances has less influence on the exceeding probability of the structure 1.The total exceeding probability of the controlled adjacent structure is obtained by the method similar to the total exceeding probability of uncontrolled adjacent structures, as shown in Figure7.Figure 7
Total exceeding probability curves of controlled adjacent structures in disparate limit states. (a) IO; (b) SD; (c) LS; (d) CP.
(a) (b) (c) (d)Figure7 shows that in the IO and SD limit state, the total exceeding probability of adjacent structures is affected little by the separation distance; in the LS limit state, when the separation distance is taken as 0.1 m, the total exceeding probability of the adjacent structure is minimal; in the CP limit state, the distinction of the total exceeding probability of adjacent structures with different critical separation distances is larger; when the adjacent distance is taken as 0.1m, the total exceeding probability of adjacent structures is the smallest. Therefore, for the controlled adjacent structures proposed in this paper, the critical separation distance between adjacent structures can be set to 0.1m. Under this critical separation distance values, adjacent structures have smaller exceeding probabilities at all performance levels.From the total exceeding probability curves of adjacent structures with different critical separation distances shown in Figures5 and 7, it can be seen that the adjacent structure connecting with dampers can greatly reduce the need for separation distance (less than the specified 0.24m).


### 3.3.2. Micro Vulnerability Analysis

In order to further study the influence of the damper on the critical separation distance between adjacent structures, the damper output force is used to represent EDP in this section and the microscopic vulnerability of the controlled adjacent structure is analyzed. When the EDP is represented by the damper output force, the quantitative limit value of each limit state cannot be clearly obtained by the analytical method; therefore, the seismic vulnerability curves of adjacent structures with multipleF values are given here, shown in Figure 8. Since the best separation distance is 0.10 m obtained in the previous section when the interstory drift angle is EDP, this section selects the adjacent distances of 0.10 m, 0.21 m (old specification value), and 0.24 m (new specification value).Figure 8
Damper output force seismic vulnerability curves. (a) F=200 kN; (b) F=300 kN; (c) F=400 kN; (d) F=500 kN.
(a) (b) (c) (d)Figure8 shows that when F<300 kN, the vulnerability curves of adjacent structures under disparate separation distances are steeper and the shape of the curves is not much different; and when F≥300 kN, the vulnerability curves change to flatness and the difference between the curves increase as the F value increases. It is obvious that when the adjacent distance is 0.10 m, the exceeding probability of adjacent structures is greater than the exceeding probability of 0.21 m and 0.24 m separation distance. It can be seen that when the adjacent distance is smaller, the output force of the damper is greater, so when the adjacent distance is small, a damper with a large output force should be selected.


## 3.3.1. Macro Vulnerability Analysis

In order to understand the seismic responses of adjacent structures under various performance targets and separation distances, Figure4 shows the exceeding probability curves of uncontrolled adjacent structures in the LS limit state (with maximum interlayer displacement angle as EDP) under different distances. Due to space limitations, this section only gives the exceeding probability curves of uncontrolled adjacent structures in the LS limit state.Figure 4
Exceeding probability curves of uncontrolled adjacent structures in the LS limit state. (a) Structure 1 and (b) Structure 2.
(a) (b)Just seeing the behaviors for distances 0.21, 0.24, and 0.30 in Figure6, the trends of them are the same and the exceeding probability increases with the increase in PGA, but the rate of change in Figure 4(a) is bigger than that in Figure 4(b). It shows that the optimal arrangement of the separation distance of uncontrolled adjacent structures mainly depends on the response of the structure 2 and the design of different separation distances has less influence on the exceeding probability of the structure 1.Figure5 plots the total exceeding probability curves of uncontrolled adjacent structures in the disparate limit states (with maximum interlayer displacement angle as EDP) under different distances.Figure 5
Total exceeding probability curves of uncontrolled adjacent structures in disparate limit states. (a) IO; (b) SD; (c) LS; (d) CP.
(a) (b) (c) (d)Figure 6
Exceeding probability curves of controlled adjacent structures in the LS limit state. (a) Structure 1 and (b) Structure 2.
(a) (b)Figure5 shows that the difference in the total exceeding probability of adjacent structures with different distances is smaller in the IO limit state; it is indicating that the separation distance has no obvious effect on the structure under this performance level; in the SD limit state, when the ground motion intensity is low (PGA <1.2 g), it can be clearly seen that when the separation distance is 0.30 m, the total exceeding probability of the adjacent structure is the smallest; in the LS limit state, when PGA<1.25 g, the difference of the total exceeding probability of adjacent structures under disparate separation distances is small, but it can be seen that 0.30 m is the best separation distance; there is a big distinction between the total exceeding probabilities of adjacent structures with different separation distances in the CP limit state; when the separation distance is 0.7 m, the total exceeding probability of the adjacent structures is the smallest; when separation distances is 0.24 m (the new specification), the exceeding probability of adjacent structures is also small.According to the analysis, it can be seen that the critical separation distance between adjacent structures is not as large as possible. For example, in the limit state of LS and CP, when the separation distance is 0.55m, the total exceeding probability of adjacent structures is the largest. In addition, for this structure, when the separation distance is set to 0.3 m (greater than the new specified 0.24 m), the exceeding probability of the adjacent structure at each performance level is small.Similar to the uncontrolled adjacent structures, Figure6 shows the exceeding probability curves of controlled adjacent structures in the LS limit state (with maximum interlayer displacement angle as EDP) under disparate distances. Due to space limitations, this section only gives the exceeding probability curves of controlled adjacent structures in the LS limit state.Just seeing the behaviors for distances 0.05, 0.10, and 0.40 in Figure6, the trends of them are the same; the exceeding probability increases with the increase in PGA, but the rate of change in Figure 6(a) is bigger than that in Figure 6(b). So it can be seen from Figure 6 that the optimal arrangement of the separation distance of controlled adjacent structures mainly depends on the response of the structure 2 and the design of different separation distances has less influence on the exceeding probability of the structure 1.The total exceeding probability of the controlled adjacent structure is obtained by the method similar to the total exceeding probability of uncontrolled adjacent structures, as shown in Figure7.Figure 7
Total exceeding probability curves of controlled adjacent structures in disparate limit states. (a) IO; (b) SD; (c) LS; (d) CP.
(a) (b) (c) (d)Figure7 shows that in the IO and SD limit state, the total exceeding probability of adjacent structures is affected little by the separation distance; in the LS limit state, when the separation distance is taken as 0.1 m, the total exceeding probability of the adjacent structure is minimal; in the CP limit state, the distinction of the total exceeding probability of adjacent structures with different critical separation distances is larger; when the adjacent distance is taken as 0.1m, the total exceeding probability of adjacent structures is the smallest. Therefore, for the controlled adjacent structures proposed in this paper, the critical separation distance between adjacent structures can be set to 0.1m. Under this critical separation distance values, adjacent structures have smaller exceeding probabilities at all performance levels.From the total exceeding probability curves of adjacent structures with different critical separation distances shown in Figures5 and 7, it can be seen that the adjacent structure connecting with dampers can greatly reduce the need for separation distance (less than the specified 0.24m).


## 3.3.2. Micro Vulnerability Analysis

In order to further study the influence of the damper on the critical separation distance between adjacent structures, the damper output force is used to represent EDP in this section and the microscopic vulnerability of the controlled adjacent structure is analyzed. When the EDP is represented by the damper output force, the quantitative limit value of each limit state cannot be clearly obtained by the analytical method; therefore, the seismic vulnerability curves of adjacent structures with multipleF values are given here, shown in Figure 8. Since the best separation distance is 0.10 m obtained in the previous section when the interstory drift angle is EDP, this section selects the adjacent distances of 0.10 m, 0.21 m (old specification value), and 0.24 m (new specification value).Figure 8
Damper output force seismic vulnerability curves. (a) F=200 kN; (b) F=300 kN; (c) F=400 kN; (d) F=500 kN.
(a) (b) (c) (d)Figure8 shows that when F<300 kN, the vulnerability curves of adjacent structures under disparate separation distances are steeper and the shape of the curves is not much different; and when F≥300 kN, the vulnerability curves change to flatness and the difference between the curves increase as the F value increases. It is obvious that when the adjacent distance is 0.10 m, the exceeding probability of adjacent structures is greater than the exceeding probability of 0.21 m and 0.24 m separation distance. It can be seen that when the adjacent distance is smaller, the output force of the damper is greater, so when the adjacent distance is small, a damper with a large output force should be selected.


## 4. Shaking Table Test

### 4.1. Experimental Set-Up

In order to verify the correctness of the aforementioned critical separation distance between adjacent structures based on seismic vulnerability, this section uses tests to verify. The experiments are performed on MTS uniaxial seismic shaking table of size 4 m × 4 m at the Huazhong University of Science and Technology. The test requires the two scale structures to be placed on the shake table at the same time, so the geometric similarity ratio is chosen to be 1:3. According to the similarity theory and dimension analysis, the similarity coefficient of other parameters of the experimental model is listed in Table2.Table 2
Similarity coefficients of the model parameters.
Physical quantity Length Acceleration Elastic modulus Time Velocity Earthquake force Similarity ratio 1/3 1 1 1 / 3 1 / 3 1/9After determining the geometric similarity, the geometric dimensions of the scale model can be calculated. Building A is constructed as a symmetric single-bay three-story steel frame while Building B is made as a symmetric single-bay two-story steel frame. The overall dimensions of Building A are 1.2 m×1.4 m in plane and 3.0 m in elevation while Building B has a dimensions of 1.2 m×1.4 m in plane and 2.0 m in elevation. The story height for each building is 1.0 m. The steel type is Q235, consistent with the prototype frame structure, as shown in Figure9(a). Considering the weight of the floor structure itself (the thickness of the steel plate is 14 mm) and the constant load and live load acting on the floor board or the roof plate, the clump weight on the floor board and the roof plate are 1.24 tons and 0.768 tons, respectively, as shown in Figure 9(b). Because the bolt hole pitch on the vibration table top is fixed, different separation distances are required to be selected in this experiment. Therefore, in the actual processing, collisions elements are added at the top of the two-story structure and corresponding positions of the three-layer structure. The element controls the adjacent distance by bolt rotation. A total of four sets of collision elements are arranged. Each set of the collision elements contains an impact end and a receiving end. The impact end is a steel block with a plane size of 50 mm × 50 mm and a thickness of 10 mm and the receiving end is a steel block with a plane size of 20 mm × 20 mm and a thickness of 5 mm, as shown in Figure 9(c).Figure 9
Experimental model: (a) configurations of the test models; (b) the clump weight; (c) the layout of the collision elements model (from left to right).
(a) (b) (c)


### 4.2. Instrumentation

A total of 6 accelerometers are arranged in the two buildings to measure their absolute acceleration response in thex direction. The locations of the accelerometers are indicated in Figure 10. Each floor of either building has one accelerometer at the center of one girder in the x direction. Building B has also an additional accelerometer at the baseboard in the x direction to check if the building is rigidly connected to the shaking table.Figure 10
Instrumentation of adjacent buildings: (a) laser displacement sensor; (b) acceleration sensor; (c) strain gauge; (d) force sensor.
(a) (b) (c) (d)The dynamic displacement responses of both buildings are obtained from the 3 laser displacement transducers which are located at each floor.Moreover, to monitor whether or not the maximum stress in a building exceeds the yield stress, one stain gauge is stuck on the surface of each column at its low end for each building. For all the experimental results presented in this paper, the information from the strain gauges indicates that both building models are elastic and linear. A total of 2 force sensors are arranged on the receiving ends of the collision elements to measure the pounding force.


### 4.3. Ground Motions and Loading Conditions

A total of ten seismic waves are selected in the shaking table test. The order of the input ground motions and the seismic wave parameters are listed in Table3. The peak ground accelerations (PGAs) are amplitude-modulated according to the test requirements (i.e., incremental dynamic analysis) to simulate different intensity of ground motion input. The test models are swept with the white noise after each seismic loading is completed to inspect the changes of the dynamic characteristic of the structures.Table 3
The parameters of the input ground motions.
No. Earthquake Magnitude PGA(g) Length 1 Kobe 6.9 0.62 4096(0.01s) 2 Imperial Valley 6.5 0.31 7997(0.005s) 3 Northridge 6.7 0.59 1222(0.02s) 4 Erzican 6.9 0.52 4262(0.005s) 5 Whiter Narrowas 6.0 0.21 1715(0.02s) 6 Northridge 6.7 0.75 1220(0.02s) 7 Imperial Valley 6.5 0.22 7564(0.005s) 8 Northridge 6.7 0.84 2000(0.02s) 9 Imperial Valley 6.5 0.60 7512(0.005s) 10 Imperial Valley 6.5 0.48 7792(0.005s)Combined with the previous studies and the structural self-vibration characteristics, the separation distance is set to be 7 mm and 10 mm, respectively. Each seismic wave is loaded step by step from a peak ground acceleration of 0.1 g to 0.5 g, and each level is loaded twice. Then the test models are swept by the white noise with a peak shift of 20 mm to measure the self-oscillation frequency of the building models.


### 4.4. Experimental Results and Discussions

#### 4.4.1. The Vulnerability Curves Which Are Expressed by the Top-Level Acceleration

The acceleration vulnerability curve of the top layer of the two-layer structure under multiplea values is given to understand the trend of the acceleration of the top layer of the two-layer structure with the increase of ground motion intensity. Due to the change of the separation distance, the final result is consistent. Here only the vulnerability curves of the two-layer structure under different a values are given when the adjacent spacing is 7 mm, as shown in Figure 11.Figure 11
Top-level acceleration vulnerability curves (separation distance 7 mm). (a)a=1m/s2; (b) a=2m/s2.
(a) (b)The figure shows that the vulnerability curves of the actual test model and the OpenSees model are very close. Whena=1m/s2, with the increase of PGA, the difference of exceeding probability reaches maximum of 0.06; when a=2m/s2, the difference reaches maximum of 0.04.


#### 4.4.2. The Vulnerability Curves Which Are Expressed by the Relative Displacements

When the structural reaction is expressed by the relative displacement between adjacent structures, since the limits of the quantified indices of the limit states cannot be determined explicitly by the analytical method, this section gives the structural seismic vulnerability curves of second layer under several relative displacements (7 mm, 10 mm), as shown in Figure12.Figure 12
Relative displacements vulnerability curves (a) 7 mm and (b) 10 mm.
(a) (b)Figure12 shows that vulnerability curves of the actual test model and the OpenSees model are very close. When relative displacement is 10 mm, distinction between calculated value and experimental value is appearing until PGA reached 0.25g. With the further increase of PGA, the difference of exceeding probability reaches the maximum, about 0.025; when relative displacement is 10 mm the first difference between calculated value and experimental value appears at PGA reached 0.2g, and then they are growing in the same trend with maximum deviation about 0.005.


#### 4.4.3. The Vulnerability Curves Which Are Expressed by Column Base of Steel Stress

When the structural reaction is expressed by the stressfy of the column base of steel of the local failure parameter, the quantitative limit value of each limit state cannot be clearly obtained by the analytical method. In this section the vulnerability curves are under the stress values 150N/mm2 and 300N/mm2, as shown in Figure 13.Figure 13
Column base of steel stress vulnerability curves. (a)150N/mm2 and (b) 300N/mm2.
(a) (b)It is obvious that the vulnerability curves of the actual test model and the OpenSees model are very close, the distinction of exceeding probability is about 0.02.


## 4.1. Experimental Set-Up

In order to verify the correctness of the aforementioned critical separation distance between adjacent structures based on seismic vulnerability, this section uses tests to verify. The experiments are performed on MTS uniaxial seismic shaking table of size 4 m × 4 m at the Huazhong University of Science and Technology. The test requires the two scale structures to be placed on the shake table at the same time, so the geometric similarity ratio is chosen to be 1:3. According to the similarity theory and dimension analysis, the similarity coefficient of other parameters of the experimental model is listed in Table2.Table 2
Similarity coefficients of the model parameters.
Physical quantity Length Acceleration Elastic modulus Time Velocity Earthquake force Similarity ratio 1/3 1 1 1 / 3 1 / 3 1/9After determining the geometric similarity, the geometric dimensions of the scale model can be calculated. Building A is constructed as a symmetric single-bay three-story steel frame while Building B is made as a symmetric single-bay two-story steel frame. The overall dimensions of Building A are 1.2 m×1.4 m in plane and 3.0 m in elevation while Building B has a dimensions of 1.2 m×1.4 m in plane and 2.0 m in elevation. The story height for each building is 1.0 m. The steel type is Q235, consistent with the prototype frame structure, as shown in Figure9(a). Considering the weight of the floor structure itself (the thickness of the steel plate is 14 mm) and the constant load and live load acting on the floor board or the roof plate, the clump weight on the floor board and the roof plate are 1.24 tons and 0.768 tons, respectively, as shown in Figure 9(b). Because the bolt hole pitch on the vibration table top is fixed, different separation distances are required to be selected in this experiment. Therefore, in the actual processing, collisions elements are added at the top of the two-story structure and corresponding positions of the three-layer structure. The element controls the adjacent distance by bolt rotation. A total of four sets of collision elements are arranged. Each set of the collision elements contains an impact end and a receiving end. The impact end is a steel block with a plane size of 50 mm × 50 mm and a thickness of 10 mm and the receiving end is a steel block with a plane size of 20 mm × 20 mm and a thickness of 5 mm, as shown in Figure 9(c).Figure 9
Experimental model: (a) configurations of the test models; (b) the clump weight; (c) the layout of the collision elements model (from left to right).
(a) (b) (c)


## 4.2. Instrumentation

A total of 6 accelerometers are arranged in the two buildings to measure their absolute acceleration response in thex direction. The locations of the accelerometers are indicated in Figure 10. Each floor of either building has one accelerometer at the center of one girder in the x direction. Building B has also an additional accelerometer at the baseboard in the x direction to check if the building is rigidly connected to the shaking table.Figure 10
Instrumentation of adjacent buildings: (a) laser displacement sensor; (b) acceleration sensor; (c) strain gauge; (d) force sensor.
(a) (b) (c) (d)The dynamic displacement responses of both buildings are obtained from the 3 laser displacement transducers which are located at each floor.Moreover, to monitor whether or not the maximum stress in a building exceeds the yield stress, one stain gauge is stuck on the surface of each column at its low end for each building. For all the experimental results presented in this paper, the information from the strain gauges indicates that both building models are elastic and linear. A total of 2 force sensors are arranged on the receiving ends of the collision elements to measure the pounding force.


## 4.3. Ground Motions and Loading Conditions

A total of ten seismic waves are selected in the shaking table test. The order of the input ground motions and the seismic wave parameters are listed in Table3. The peak ground accelerations (PGAs) are amplitude-modulated according to the test requirements (i.e., incremental dynamic analysis) to simulate different intensity of ground motion input. The test models are swept with the white noise after each seismic loading is completed to inspect the changes of the dynamic characteristic of the structures.Table 3
The parameters of the input ground motions.
No. Earthquake Magnitude PGA(g) Length 1 Kobe 6.9 0.62 4096(0.01s) 2 Imperial Valley 6.5 0.31 7997(0.005s) 3 Northridge 6.7 0.59 1222(0.02s) 4 Erzican 6.9 0.52 4262(0.005s) 5 Whiter Narrowas 6.0 0.21 1715(0.02s) 6 Northridge 6.7 0.75 1220(0.02s) 7 Imperial Valley 6.5 0.22 7564(0.005s) 8 Northridge 6.7 0.84 2000(0.02s) 9 Imperial Valley 6.5 0.60 7512(0.005s) 10 Imperial Valley 6.5 0.48 7792(0.005s)Combined with the previous studies and the structural self-vibration characteristics, the separation distance is set to be 7 mm and 10 mm, respectively. Each seismic wave is loaded step by step from a peak ground acceleration of 0.1 g to 0.5 g, and each level is loaded twice. Then the test models are swept by the white noise with a peak shift of 20 mm to measure the self-oscillation frequency of the building models.


## 4.4. Experimental Results and Discussions

### 4.4.1. The Vulnerability Curves Which Are Expressed by the Top-Level Acceleration

The acceleration vulnerability curve of the top layer of the two-layer structure under multiplea values is given to understand the trend of the acceleration of the top layer of the two-layer structure with the increase of ground motion intensity. Due to the change of the separation distance, the final result is consistent. Here only the vulnerability curves of the two-layer structure under different a values are given when the adjacent spacing is 7 mm, as shown in Figure 11.Figure 11
Top-level acceleration vulnerability curves (separation distance 7 mm). (a)a=1m/s2; (b) a=2m/s2.
(a) (b)The figure shows that the vulnerability curves of the actual test model and the OpenSees model are very close. Whena=1m/s2, with the increase of PGA, the difference of exceeding probability reaches maximum of 0.06; when a=2m/s2, the difference reaches maximum of 0.04.


### 4.4.2. The Vulnerability Curves Which Are Expressed by the Relative Displacements

When the structural reaction is expressed by the relative displacement between adjacent structures, since the limits of the quantified indices of the limit states cannot be determined explicitly by the analytical method, this section gives the structural seismic vulnerability curves of second layer under several relative displacements (7 mm, 10 mm), as shown in Figure12.Figure 12
Relative displacements vulnerability curves (a) 7 mm and (b) 10 mm.
(a) (b)Figure12 shows that vulnerability curves of the actual test model and the OpenSees model are very close. When relative displacement is 10 mm, distinction between calculated value and experimental value is appearing until PGA reached 0.25g. With the further increase of PGA, the difference of exceeding probability reaches the maximum, about 0.025; when relative displacement is 10 mm the first difference between calculated value and experimental value appears at PGA reached 0.2g, and then they are growing in the same trend with maximum deviation about 0.005.


### 4.4.3. The Vulnerability Curves Which Are Expressed by Column Base of Steel Stress

When the structural reaction is expressed by the stressfy of the column base of steel of the local failure parameter, the quantitative limit value of each limit state cannot be clearly obtained by the analytical method. In this section the vulnerability curves are under the stress values 150N/mm2 and 300N/mm2, as shown in Figure 13.Figure 13
Column base of steel stress vulnerability curves. (a)150N/mm2 and (b) 300N/mm2.
(a) (b)It is obvious that the vulnerability curves of the actual test model and the OpenSees model are very close, the distinction of exceeding probability is about 0.02.


## 4.4.1. The Vulnerability Curves Which Are Expressed by the Top-Level Acceleration

The acceleration vulnerability curve of the top layer of the two-layer structure under multiplea values is given to understand the trend of the acceleration of the top layer of the two-layer structure with the increase of ground motion intensity. Due to the change of the separation distance, the final result is consistent. Here only the vulnerability curves of the two-layer structure under different a values are given when the adjacent spacing is 7 mm, as shown in Figure 11.Figure 11
Top-level acceleration vulnerability curves (separation distance 7 mm). (a)a=1m/s2; (b) a=2m/s2.
(a) (b)The figure shows that the vulnerability curves of the actual test model and the OpenSees model are very close. Whena=1m/s2, with the increase of PGA, the difference of exceeding probability reaches maximum of 0.06; when a=2m/s2, the difference reaches maximum of 0.04.


## 4.4.2. The Vulnerability Curves Which Are Expressed by the Relative Displacements

When the structural reaction is expressed by the relative displacement between adjacent structures, since the limits of the quantified indices of the limit states cannot be determined explicitly by the analytical method, this section gives the structural seismic vulnerability curves of second layer under several relative displacements (7 mm, 10 mm), as shown in Figure12.Figure 12
Relative displacements vulnerability curves (a) 7 mm and (b) 10 mm.
(a) (b)Figure12 shows that vulnerability curves of the actual test model and the OpenSees model are very close. When relative displacement is 10 mm, distinction between calculated value and experimental value is appearing until PGA reached 0.25g. With the further increase of PGA, the difference of exceeding probability reaches the maximum, about 0.025; when relative displacement is 10 mm the first difference between calculated value and experimental value appears at PGA reached 0.2g, and then they are growing in the same trend with maximum deviation about 0.005.


## 4.4.3. The Vulnerability Curves Which Are Expressed by Column Base of Steel Stress

When the structural reaction is expressed by the stressfy of the column base of steel of the local failure parameter, the quantitative limit value of each limit state cannot be clearly obtained by the analytical method. In this section the vulnerability curves are under the stress values 150N/mm2 and 300N/mm2, as shown in Figure 13.Figure 13
Column base of steel stress vulnerability curves. (a)150N/mm2 and (b) 300N/mm2.
(a) (b)It is obvious that the vulnerability curves of the actual test model and the OpenSees model are very close, the distinction of exceeding probability is about 0.02.


## 5. Conclusions

This paper simulates the 6-10 layers concrete frame structure, but in the experimental verification stage, it is limited to the site conditions, and only the 2-3 layers steel frame structure is simulated. This is the choice considering the reuse and difficulty of the structure. Although the structural similarity has been explained, there are still many differences between the concrete structure and the steel structure. For example, the steel structure material is more uniform and the ductility and seismic performance are better. The concrete structure is better in integrity but the force is complicated, so it is not easy to simulate. These factors have a certain impact on the experimental results.Based on previous studies, this paper uses the performance-based theoretical method to perform incremental dynamic analysis and vulnerability analysis of adjacent structures and got optimal separation distance of uncontrolled and controlled adjacent structures by comparing the total exceeding probability of uncontrolled and controlled adjacent structures at disparate separation distances; then comparing the shake table test with the OpenSees calculation results, the following conclusions are drawn:(1)
Using the performance-based seismic design concept to control the vibration of two adjacent structures, it is verified that the damper has a good control effect on the adjacent structure, so that the IDA curve of the adjacent structure appears hysteresis at a large PGA, and it can reduce the separation distance of adjacent structures and increases the elastic stability of the structure.(2)
Both uncontrolled and controlled adjacent structures, the optimal design of separation distance depends mainly on the response of slave structure, and the different separation distances settings have little influence on the exceeding probability of the main structure. When two adjacent structures are not connected with a damper, the separation distance of adjacent structures should be set to 0.3 m under moderate-strong earthquakes, and the distance between adjacent structures should be set to 0.24 m under the effect of rare earthquakes. When two adjacent structures are connected with damper, the separation distance can be set to 0.1 m in various performance states.(3)
The comparison between the shaking table test and the numerical simulation shows that the calculated results of OpenSees are in accordance with the vibration response of the actual structure under the action of earthquake. The authenticity and reliability of OpenSees numerical simulation are proved.



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*Source: 3483401-2018-09-06.xml*