Study on Shaking Table Test and Vulnerability Analysis of 220 kV Indoor Substation in High-Intensity Areas

Abstract

This study investigates the seismic performance of the V3.0 220 kV standard-designed substation of the Southern Power Grid, located in a high-intensity seismic zone, with a focus on the application of seismic isolation technology. Seismic isolation and structural analysis were conducted and shaking table tests were performed on both isolated and non-isolated structural models. A total of 40 tests were carried out using three levels of ground motion intensity (i.e., 140 gal, 400 gal, and 800 gal) and in three directions (unidirectional, bidirectional, and triaxial). The dynamic characteristics, seismic response, and isolation effectiveness were evaluated. Results indicate that the test models exhibit strong agreement with theoretical and numerical predictions, with an average frequency deviation of 10.98%. The fundamental period of the isolated structure was extended by a factor of 2.33 compared to the non-isolated configuration. As the peak ground acceleration increased, structural frequency decreased, and the period increased. The isolated structure showed a lower first-period growth rate (4.82%) than the non-isolated structure (15.38%). Even under 800 gal excitations, the isolated structure remained within the elastic range. Seismic isolation significantly reduced structural response, with a control effectiveness exceeding 50%, enabling a one-degree reduction in seismic design intensity. A vulnerability analysis based on 200 simulated earthquake cases revealed that the isolated structure exhibited lower failure probabilities across four performance states. At 600 gal PGA, the failure probability in the LS3 state was reduced by 27.8%. These findings confirm the effectiveness and reliability of seismic isolation design for substations in high seismic intensity regions.

1. Introduction

Earthquake disasters not only pose a threat to human life but can also cause severe damage to critical infrastructure, particularly power systems, thereby disrupting the normal operation of other lifeline services [1,2,3,4]. Within power systems, substations serve as key nodes for energy transmission and distribution. Their safety and reliability directly influence the stability of the power supply. Thus, enhancing the seismic performance of substation structures and minimizing earthquake-induced losses are pressing issues in this field. Indoor substations, commonly adopted due to their compact footprint, centralized equipment, and dense layout, are widely utilized in urban core areas and industrial zones. Compared to traditional outdoor substations, indoor substations exhibit pronounced horizontal and vertical irregularities, non-uniform mass distribution, and more stringent requirements for both structural and equipment seismic performance.

Conventional seismic design primarily relies on increasing structural stiffness and strength to enhance resistance against seismic forces [5,6,7]. While this approach may reduce earthquake damage under moderate conditions, it presents limitations under high-intensity seismic events. Highly stiff structures tend to absorb more seismic energy, leading to concentration of internal stress and a heightened risk of structural failure [8]. Moreover, traditional seismic design often overlooks the interaction between structural components and equipment, making it inadequate for preventing equipment damage during seismic events [9,10,11,12]. In this context, seismic isolation has emerged as a promising alternative. By introducing isolation bearings between a structure’s foundation and superstructure, seismic isolation extends the natural period of vibration and reduces seismic energy transmission [13,14]. In recent years, it has been effectively applied in buildings such as hospitals and schools, demonstrating substantial improvements in seismic resilience [15,16,17].

Due to the significant horizontal and vertical irregularities inherent in indoor substations, their structural design is highly complex. Such designs typically involve large structural columns and shear walls to meet performance requirements. Incorporating seismic isolation layers in these configurations can effectively reduce the seismic response of the superstructure, thereby simplifying the design and enhancing structural reliability. However, research and application of seismic isolation in substation buildings remain limited. In particular, there is a lack of studies evaluating its effectiveness in mitigating vibrations in vertically and horizontally irregular substation structures using shaking table tests.

To address this gap, the present study investigates the seismic and isolation performance of a 220 kV indoor substation structure, designed according to the V3.0 standard of the Southern Power Grid for high seismic intensity regions, through earthquake simulation shaking table experiments. The study evaluates the rationality and applicability of the isolation design under such conditions. Furthermore, seismic vulnerability analysis is employed to assess the probabilistic seismic performance of the substation structure, providing a more comprehensive understanding of its behavior under various earthquake intensities. Vulnerability analysis is a probability-based method that quantifies the likelihood of a structure reaching or exceeding specific damage states under different seismic intensities [18,19]. For instance, Fei Shi et al. [20] quantified the influence of different redundancies in hybrid self-resetting supports on the seismic vulnerability of steel frame structures using incremental dynamic analysis (IDA). Similarly, Weiyuan Huang et al. [19] demonstrated that the inclusion of lead viscoelastic dampers significantly enhanced the seismic performance of frame structures under both mainshock and aftershock conditions. These studies underscore the limited yet valuable application of seismic vulnerability analysis in isolation structures for indoor substations.

This study contributes to addressing the structural complexity of irregular indoor substations in high seismic zones. The findings demonstrate that the use of seismic isolation technology not only enhances seismic resistance but also significantly reduces the probability of structural failure during earthquakes. This provides essential technical support for the future design and development of indoor substations in high seismic risk areas.

2. Design of Indoor Substation Structure and Test Model

2.1. Structural Overview

The 220 kV indoor substation, designed in accordance with the V3.0 standard of the Southern Power Grid, is an eight-story reinforced concrete structure with a plan dimension of 77.30 m × 39.15 m and a total height of 29.5 m. The beams and columns are constructed using C40-grade concrete, reinforced with HRB335-grade steel for both stirrups and longitudinal bars. The floor slabs are also composed of C40 concrete and reinforced with HRB400-grade steel bars. Shear walls are constructed using C40 concrete and HRB335-grade steel reinforcement. The substation accommodates 110 kV GIS (Gas-Insulated Switchgear) equipment on the second floor and 220 kV GIS equipment on the fourth floor. The structure is designed for a seismic fortification intensity of 8 degrees (0.20 g), classified under the second seismic group. The site is designated as Category VI, with a characteristic site period of 0.75 s. Figure 1 presents a cross-sectional view of the substation structure, which displays pronounced horizontal and vertical irregularities. Furthermore, due to the integration of various categories of electrical equipment, the substation qualifies as a heavy-duty structure. The square columns on the first floor have cross-sectional dimensions of 1000 mm, and a limited number of shear walls have been incorporated into the structural design.

2.2. Scale Model Design

Using dynamic similarity theory, scaled shaking table models for control and design can be defined as follows [21,22]:

$$m(\ddot{x}(t)+{\ddot{x}}_g(t))+c\dot{x}(t)+kx(t)=0$$

(1)

$$S_{\rho }{S}_l^3(S_a+S_a)+S_E\sqrt{{\displaystyle \frac{S_l^3}{S_a}}}\sqrt{S_l{S}_a}+S_E{S}_l^2=0$$

(2)

$$S_E/\left(S_{\rho }{S}_a{S}_l\right)=1$$

(3)

where m, c, and l are the structural mass, damping, and stiffness, respectively. $x(t)$, $\dot{x}(t)$, and $\ddot{x}(t)$ are the displacement, velocity, and acceleration responses, respectively. ${\ddot{x}}_g(t)$ is the seismic acceleration. S_E, S_p, S_s, S_a, and S_l are the proportional factors of elastic modulus, density, acceleration, and length, respectively.

The experiment was conducted using the shaking table facility at the Structural Laboratory of South China University of Technology. The table has a planar dimension of 4 m × 4 m and a maximum load capacity of 30 t. Based on the limitations of the equipment, a geometric scale ratio of 1:20 was adopted. The scaled model measures 3.84 m in length, 1.93 m in width, and 1.63 m in height, with an approximate weight of 18.19 t. This scaling ratio ensures that the dimensions of the test model are compatible with the available shaking table capacity. Owing to the relatively small scale of the model, it was not feasible to construct it using conventional reinforced concrete. Instead, micro-particle concrete was used as a substitute. The selected micro-particle concrete has an elastic modulus approximately 40% that of ordinary concrete. The corresponding similarity constants used for the experiment are presented in

Table 1. Parameters of scale shaking table test model.

Similarity Coefficient	Symbol	Formula	Ratio (Model/Prototype)	Similarity Coefficient	Symbol	Formula	Ratio (Model/Prototype)
Size	SL	SL = model L/prototype L	0.0500	Stress	Sσ	$S_{\sigma }=S_E$	0.4000
Elastic modulus	SE	SE = model E/prototype E	0.4000	Bending stiffness ratio	EI		2.5 × 10−6
Acceleration	Sa	$S_a=S_E{S}_L^2/S_m$	2.0000	Axial stiffness ratio	EA	0.0010	0.0010
Quality	Sm	Sm = model m/prototype m	0.0005	Stiffness	SK	$S_K=S_m{S}_a/S_l$	0.0303
Time	St	$S_t=\sqrt{S_L/S_a}$	0.1581	Force	SF	$S_F=S_{\sigma }{S}_L^2$	0.0010
Frequency	Sf	$S_f=1/S_t$	6.3245	Strain	Sε	$S_{\epsilon }=1$	1.0000
Velocity	SV	$S_V=\sqrt{S_L{S}_a}$	0.3162	Damping ratio	$S_{\xi }$	$S_{\xi }$= 1	1.0000
Displacement	Su	$S_u=S_L$	0.0500	Density	Sρ	$S_{\rho }$= $S_m$/$S_L^3$	4.0000

. It is also important to note that the electrical equipment within the substation was represented by equivalent mass blocks and placed accordingly within the test model.

At the same time, the floor material weight of the vibration table model calculated based on the scaling theory does not meet the weight equivalence requirements. Before the vibration table test, corresponding counterweights need to be added to the model floors according to the principle of weight similarity. The error between the theoretical and experimental total weight of the model structure after adding counterweights is 2.38%. Among them, the weight error between the first layer theory and the experimental model is the largest, which is 7.52%. This is mainly due to the need to make the actual vibration table weights on each floor more evenly distributed, ensuring that there is enough space for the weights to be properly arranged on the model. In summary, the theoretical calculation of the weight distribution of this vibration table has a small error compared to the actual total weight of the cultivation, which can meet the requirements of the vibration table test. The scaled model can effectively reflect the dynamic response of the original structure.

2.3. Seismic Isolation Parameter Design

Layered lead-core rubber bearings were employed for the seismic isolation design. The primary objective of this experiment was to evaluate the horizontal seismic isolation performance of the structural model under horizontal seismic wave excitation. Accordingly, the isolation bearings were designed with a focus on minimizing the horizontal stiffness deviation to ensure consistency and reliability. In the scaled model, the 108 isolation bearings of the prototype structure were represented equivalently by eight isolation bearings. A comparison of the design parameters between the prototype and the scaled model for the lead-core rubber isolation bearings is presented in

Table 2. Parameters of layered lead rubber bearings with original and scaled models.

Lead rubber bearing (original structure)	Equivalent stiffness (kN/mm)	Elastic stiffness (kN/mm)	Yield force (kN)	Stiffness ratio after yielding
	1.55	14.04	59	0.077
Lead rubber support (vibration table)	Equivalent stiffness (kN/mm)	Elastic stiffness (kN/mm)	Stiffness ratio after yielding
	0.6	44.23	0.403

.

Table 3. Comparison of the theory and experimental parameters for the scaled model.

Parameter	Equivalent Stiffness (kN/mm)	Elastic Stiffness (kN/mm)	Stiffness Ratio After Yielding
Original structure	170.22	1554.28	119.56
Similarity constant	0.03	0.03	0.03
Theoretical scaled model	5.11	46.63	3.59
Actual scaled model	4.8	44.23	3.38
Error (%)	6.1	5.2	5.85

shows the comparison between the theoretical and actual parameters of the scaled model. The specific dimensions and the scaled lead-core rubber bearing used in the shaking table test are illustrated in Figure 2. The similarity constant of the scaled model is 0.03, and the discrepancy between the theoretical and measured stiffness parameters of the bearings remains within 10%, meeting the required accuracy for experimental validation.

2.4. Experimental Cases and Layout of Measuring Points

In accordance with the “Code for Seismic Design of Buildings” [23], the experiment utilized one artificially synthesized seismic wave and two real strong earthquake records, as shown in Figure 3. The three seismic waves, namely, the artificial wave (EW1), natural wave 1 (EW2), and natural wave 2 (EW3), were applied for unidirectional input in both the X and Y directions, followed by bidirectional and triaxial input. To assess the performance of the substation seismic isolation design under higher-intensity seismic conditions, the peak ground acceleration (PGA) values for the input seismic waves were set to 140 gal, 400 gal, and 800 gal. These values were used in the shaking table tests to verify the reliability of the seismic isolation design for substation structures in areas with seismic intensities of 8 and 9 degrees. Additionally, to examine the changes in the dynamic characteristics of the structure following earthquake-induced action, a three-way white noise excitation input, with a peak acceleration of 50 gal and a frequency range of 0.1–50 Hz, was applied to the model before and after exposure to various earthquake intensities. The details of the shaking table test conditions are provided in

Table 4. Testing cases.

Isolated Model				Non_Isolated Model
Case	Earthquake	Direction	PGA (gal)	Case	Earthquake	Direction	PGA (gal)
C1	WNW	X + Y + Z	50	C21	WNW	X + Y + Z	50
C2~C5	EW3	X/Y/X + Y/X + Y + Z	140	C22~C25	EW3	X/Y/X + Y/X + Y + Z	140
C6	WNW	X + Y + Z	50	C26	WNW	X + Y + Z	50
C7~9	EW1/EW2/EW3	X	400	C27~C29	EW1/EW2/EW3	X	400
C10~12	EW1/EW2/EW3	Y	400	C30~C32	EW1/EW2/EW3	Y	400
C13/C14	EW3	X + Y/X + Y + Z	400	C33/C34	EW3	X + Y/X + Y + Z	400
C15	WNW	X + Y + Z	50	C35	WNW	X + Y + Z	50
C16~C19	EW3	X/Y/X + Y/X + Y + Z	800	C36~C39	EW3	X/Y/X + Y/X + Y + Z	800
C20	WNW	X + Y + Z	50	C40	WNW	X + Y + Z	50

.

Accelerometers, displacement sensors, strain gauges, and other instruments were installed on the experimental model to measure the dynamic response of the structure under seismic excitation. Accelerometers were placed on the surface of the shaking table, the conversion layer, and each floor to record the actual input acceleration from the shaking table, as well as the horizontal acceleration response at each floor above the conversion layer. Displacement sensors were positioned on the top plate of the isolation layer and on each floor to measure the displacement response at the top of the conversion layer and at each floor. The layout of the measurement points for the two-story accelerometers and displacement sensors is illustrated in Figure 4.

3. Analysis of Test Results

3.1. Structural Dynamic Characteristics

Table 5. Model frequency comparison among theory, testing, and numerical calculation.

Model	Original Structure		Theoretical Calculation		Scaling Simulation	Scaling Test Model	Error (B-A)/A	Error (C-A)/A
	Mode	Frequency/Hz	Frequency Similarity Ratio	Frequency/Hz (A)	Frequency/Hz (B)	Frequency/Hz (C)
non_isolated model	1	1.27	5.47	6.94	7.62	5.92	9.80%	14.70%
	2	1.44		7.89	8.33	7.62	5.58%	3.42%
Isolated model	1	0.417	5.47	2.28	2.48	2.54	8.77%	11.40%
	2	0.419		2.29	2.49	2.62	8.73%	14.41%

presents a comparison of the first-order frequencies obtained from theoretical calculations, experimental measurements, and numerical simulations of the shaking table model, while

Table 6. The frequency variation of the models after experiencing different seismic intensities.

Case	Non_Isolated Model (First Order)		Non_Isolated Model (Second Order)		Case	Isolated Model (First Order)		Isolated Model (Second Order)
	Frequency (Hz)	Period (s)	Frequency (Hz)	Period (s)		Frequency (Hz)	Period (s)	Frequency (Hz)	Period (s)
C21	5.92	0.169	7.62	0.131	C1	2.54	0.394	2.62	0.382
C26	5.78	0.173	6.80	0.147	C6	2.42	0.413	2.56	0.391
C35	5.38	0.186	6.41	0.156	C15	2.39	0.419	2.53	0.395
C40	5.13	0.195	6.06	0.165	C20	2.35	0.426	2.45	0.408

shows the frequency variation data of the test model after being subjected to different seismic intensities. The results demonstrate good agreement among the theoretical, experimental, and numerical frequencies, confirming the feasibility of the test model’s design and fabrication, as well as its ability to replicate the dynamic characteristics of the original structure. For instance, the first-order frequencies of the non-isolated structure model are 6.94 Hz (theoretical), 7.62 Hz (numerical), and 5.92 Hz (experimental), with errors of 9.80% and 14.70% relative to the theoretical value. Similarly, for the isolated structure model, the first-order frequencies are 2.28 Hz (theoretical), 2.48 Hz (numerical), and 2.54 Hz (experimental), with respective errors of 8.77% and 11.40% compared to the theoretical value. The minimum discrepancy between experimental and theoretical frequencies is 3.42%, with an average deviation of 10.98%.

In comparison to the non-isolated model, the period of the isolated structure model is significantly increased. Specifically, the first-order period extends from 0.169 s to 0.394 s, and the second-order period extends from 0.131 s to 0.382 s, representing 2.33-fold and 2.92-fold increases, respectively. These values fall within the typical range of two to five times the period increase expected for seismically isolated structures, thereby confirming the effectiveness and feasibility of the isolation design.

After experiencing earthquakes of different intensities, the frequency of the experimental model continuously decreases and the period increases. For example, the period of the non_isolated model under operating conditions C21, C26, C35, and C40 is 0.169 s, 0.173 s, 0.186 s, and 0.195 s, respectively. The reason for this is that as the input intensity of seismic motion increases, microcracks appear in the model structure, and the structural stiffness decreases, leading to a trend of frequency decrease and period increase. In addition, it can also be seen that the period increase effect of the isolation model is lower than that of the non_isolated model. After experiencing a large earthquake of 800 gal, the first order period of the isolation model changes from the initial 0.394 s to 0.426 s (only an increase of 4.82%), while the first order period of the non_isolated model changes from the initial 0.169 s to 0.195 s (an increase of 15.38%). From this, it can be concluded that under an earthquake action of 800 gal, the upper model structure of the isolation layer of the isolation structure model did not show any damage and remained in an elastic working state. However, after a large earthquake, the isolation model experienced crack development, decreased stiffness, and entered a plastic damage working state, but the overall structure remained intact and no visible cracks were observed.

3.2. Structural Displacement Response

Figure 5 illustrates the comparison of displacement responses of the model structure under various operating conditions, while Figure 6 presents the representative time-history curves for selected scenarios. The results indicate that the displacement response of the structure increases with rising earthquake intensity and varies with input direction. However, the implementation of seismic isolation significantly reduces the displacement response under identical seismic excitations. Furthermore, the effectiveness of seismic isolation becomes more pronounced with increasing floor height. Under seismic excitation with a peak ground acceleration (PGA) of 140 gal, the displacement reduction in the X-direction ranges from 50.0% to 68.4%, while in the Y-direction, it ranges from 50.7% to 62.8%. When the PGA is increased to 800 gal, the displacement control in the X-direction ranges from 51.1% to 64.6%, and in the Y-direction, from 50.1% to 63.7%.

Across all seismic intensities and directions, the displacement control achieved by the isolation system consistently exceeds 50%. It is also observed that due to the slightly lower stiffness of the structure in the Y-direction compared to the X-direction, the isolation system exhibits marginally better control performance in the X-direction. Overall, the seismic isolation design proves to be highly effective in mitigating displacement responses across a range of earthquake intensities and directions. This enhancement in seismic performance contributes to a substantial increase in structural safety and supports the feasibility of achieving a one-degree reduction in the seismic design requirement.

3.3. Structural Acceleration Response

Figure 7 presents the comparison of acceleration responses of the model structure under various operating conditions. The results demonstrate that the acceleration response of the structure exhibits a trend like that of the displacement response—namely, it increases progressively with higher earthquake intensity across different directions of seismic excitation. The implementation of seismic isolation effectively reduces the acceleration response, with the reduction becoming more significant at higher structural elevations. Specifically, under a peak ground acceleration (PGA) of 140 gal, the isolation system achieves a maximum and minimum reduction in X-direction acceleration of 56.4% and 51.4%, respectively. In the Y-direction, the corresponding control effects are 59.1% and 52.8%. When the PGA increases to 800 gal, the X-direction acceleration ranges from 51.0% to 62.4%, while the Y-direction reduction ranges from 52.3% to 61.6%. These results confirm that seismic isolation not only mitigates displacement but also substantially reduces the acceleration response of the substation structure, thereby enhancing its overall seismic resilience under various levels of seismic loading.

4. Vulnerability Analysis of Substation Structure

Given the limited number of seismic waves employed in the shaking table tests, it is challenging to comprehensively evaluate the structural seismic performance under a wide range of earthquake scenarios. To address this limitation, finite element simulations combined with seismic vulnerability assessment methods are utilized to enhance the understanding of the structural response. This integrated approach not only compensates for the restricted seismic input in the experimental setup but also provides a more thorough verification of the seismic performance of isolation-designed indoor substation structures.

4.1. Analysis Method

Structural seismic vulnerability refers to the probability value of a structure reaching or exceeding a specific ultimate failure state under the action of earthquakes of different intensities:

$$P_R(x)=P[DM\ge C|IM=x]$$

(4)

where the seismic demand parameter (DM) refers to the response parameter of the structure under earthquake action, which is used to quantify the dynamic behavior of the structure under specific seismic motion, such as inter story displacement angle. Seismic resistance (C) refers to the ability of a structure to resist damage during an earthquake, determined by the structural materials, components, and overall design. The distribution of seismic demand parameters DM and seismic resistance capacity C is influenced by seismic motion x. Due to the uncertainty of earthquake demand and seismic resistance, both are usually assumed to follow a log normal distribution. Meanwhile, the seismic intensity parameter IM (such as ground peak acceleration PGA or first period spectral acceleration S_a (T₁, 5%)) and the seismic demand parameter DM of the structure usually satisfy a power exponential regression relationship, expressed as

$$DM=a\cdot I{M}^b$$

(5)

where a and b are regression parameters determined through nonlinear regression analysis. After taking the natural logarithm of both sides, the power–law relationship is transformed into a linear relationship, and the expression for the failure probability can be written as [24,25,26]

$$P(DM\ge C|IM)=\Phi \left[{\displaystyle \frac{\ln (IM)-\ln (C)}{\sqrt{{\beta }_{DM}^2+{\beta }_C^2}}}\right]$$

(6)

where Φ is the standard normal distribution function, and $\sqrt{{\beta }_{DM}^2+{\beta }_C^2}$ is the root mean square of the logarithmic standard deviation of the demand parameter and seismic capacity, taken as 0.5 [24]. Ln(IM) and ln(C) are the logarithmic mean values of seismic intensity and seismic resistance, respectively.

4.2. Finite Element Modeling and Verification

The finite element model was developed using SAUSAGE software, as illustrated in Figure 8. Shell elements were employed to model the floor slabs and shear walls, with nodes possessing six degrees of freedom to facilitate connection with beam and column elements. Beams and columns were modeled using beam elements, which also have six degrees of freedom and are capable of representing axial deformations.

To validate the accuracy of the developed model, the scaled model from the shaking table test was selected as a benchmark, with the comparison results presented in

Table 7. Period of scaled and numerical models.

Mode	Scaled Model	Numerical Model Based on SAUSAGE	Ratio (Scaled Model/Numerical Model)
1	0.121 × Sf = 0.663	0.646	0.97
2	0.108 × Sf = 0.592	0.604	1.02
3	0.097 × Sf = 0.531	0.575	1.08

Note: Frequency scaling parameter S_f = 1/S_t = 5.4772.

. By multiplying the period of the shaking table’s scaled model by the scaling ratio and comparing it with the period obtained from the finite element model, it was found that the discrepancies were within 10%. Additionally, comparisons of the total mass and natural periods of models developed using SAUSAGE 2023, MIDAS 2024, and ETABS V22.5.1 software were conducted to further assess model accuracy, as shown in

Table 8. Natural periods of the numerical models.

Mode	SAUSAGE Software	ETABS Software	Error	MIDAS Software	Error
1	0.646	0.666	3.10%	0.648	0.31%
2	0.604	0.629	4.14%	0.582	3.64%
3	0.575	0.589	2.43%	0.563	2.09%

. The total mass calculated by SAUSAGE was 23,960.7 t, while MIDAS produced total masses of 23,610.4 t, resulting in a maximum deviation of only 2.3%. The first three natural periods obtained from MIDAS and ETABS were also compared with those from the SAUSAGE model. The differences in structural periods across the three software platforms were all within 5%, with a maximum error of 3.9%, demonstrating that the established model is both reasonable and effective. These discrepancies primarily arise from differences in mass calculation methods among the software packages, particularly when converting surface loads on slabs and line loads on beams into equivalent structural mass. Despite these variations, the errors remain minimal and within acceptable limits, confirming the reliability and effectiveness of the established finite element model for subsequent vulnerability analysis.

4.3. Seismic Intensity Index and Damage Index

In selecting seismic intensity indicators, vulnerability analysis uses peak ground acceleration (PGA) as the primary indicator. PGA is suitable for comparing the vulnerability of different buildings, making it easier to evaluate the seismic isolation performance of indoor substation structures. The maximum inter-story displacement angle (θ) is chosen as the damage evaluation index, as it is strongly correlated with the structural dynamic stability and is computationally efficient. For the frame shear wall structure, the “Code for Seismic Design of Buildings” (GB50011-2022) [23] divides building failure states into five levels: intact, slightly damaged, moderately damaged, severely damaged, and collapse, as shown in

Table 9. Quantitative indicators of destruction status.

Damage Degree	Damage Description	Quantitative Indicator
Intact (DS1)	The main load-bearing components are intact, and a few load-bearing components are damaged and do not require repair.	<3/1100
Slightly damage (DS2)	Minor cracks in individual load-bearing components and damage to non-load-bearing components do not require repair or require minor repairs.	3/1100~3/550
Moderately damaged (DS3)	Most load-bearing components are slightly damaged, while a few non-load-bearing components are severely damaged and require repair.	3/550~4/550
Severely damage (DS4)	Most load-bearing components suffer severe damage or even collapse.	4/550~9/500
Collapse (DS5)	Most of the main load-bearing components have collapsed.	≥9/500

and

Table 10. Structural performance level.

Structural Performance Level	Minor Damage (LS1)	Moderate Damage (LS2)	Severe Damage (LS3)	Collapse (LS4)
Maximum story drift θmax (%)	0.5	0.7	1.5	2

. The maximum inter-story displacement angle limit and the performance level corresponding to each failure state are determined based on experimental data.

4.4. Selection of Seismic Waves

To thoroughly account for the uncertainty of earthquake motion, supplement the response of indoor substation structures under various earthquake motions, address the limited number of seismic waves in vibration table experiments, and improve the accuracy of vulnerability analysis, 20 seismic waves are selected for analysis [27]. Based on site characteristics and standard response spectra, natural seismic waves are chosen from the PEER Pacific Seismic Database. Figure 9 illustrates the comparison between the selected seismic waves and the standard response spectrum, where the black curve represents the time history of the standard response spectrum, and the bold red curve represents the mean of all-natural seismic wave time histories. As shown in Figure 9, the mean of the natural seismic wave time history curve aligns closely with the standard response spectrum time history curve, indicating that the selected seismic waves effectively capture the characteristics of the target site and provide reliable seismic input for subsequent vulnerability analysis.

4.5. Vulnerability Result Analysis

In accordance with the Incremental Dynamic Analysis (IDA) methodology, 20 selected natural ground motion records were subjected to uniform stepwise scaling at intervals of 0.2 g, with the peak ground acceleration (PGA) adjusted from 0 g to 2.0 g. This procedure yielded 200 seismic loading cases for dynamic time-history analyses of both the fixed-base (original) and seismically isolated structures. The resulting data from the IDA simulations were statistically analyzed. A linear regression was performed with the natural logarithm of PGA (ln(PGA)) on the x-axis and the natural logarithm of the engineering demand parameter (ln(θ)) on the y-axis to derive the seismic demand models for both structural configurations. As illustrated in Figure 10, the coefficient of determination (R²) for the regression models of the fixed-base and isolated structures exceeded 0.85, indicating a strong correlation between the regression lines and the observed data. This confirms the reliability of the fitted seismic demand models.

According to the probability demand model, the relationship between displacement angle θ and PGA can be given as follows:

$$\ln (\theta )=a\cdot \ln (\mathrm{PGA})+b$$

(7)

where a can be obtained by taking the derivative of the logarithm of earthquake intensity, i.e., ln (PGA), as follows:

$$a={\displaystyle \frac{\partial \ln (\theta )}{\partial \ln (\mathrm{PGA})}}$$

(8)

The slope a in Equation (7) represents the rate of change of ln(θ) with respect to ln(PGA), reflecting how strongly the displacement angle of the structure is affected by seismic intensity. A larger value of a indicates that ln(θ) is more sensitive to changes in ln(PGA), meaning that increases in earthquake intensity led to greater variations in displacement, resulting in a more scattered structural response. Conversely, a smaller value of a shows that the effect of earthquake intensity on displacement is weaker, and the structural response is more stable. According to Figure 10, the slope for the original structure is 1.29768, while for the isolated structure, it is 1.17972. This indicates that the original structure is more sensitive to changes in earthquake intensity, and its response is more variable. In contrast, the isolated structure exhibits improved seismic performance, with more stable behavior under earthquake loading, demonstrating the effectiveness of the isolation design.

The vulnerability analysis results for each performance state (LS1, LS2, LS3, and LS4) are presented in Figure 11. As shown, for the original structure, the peak ground acceleration (PGA) corresponding to a 50% probability of failure in the LS1 state is 0.26 g, while a 100% failure probability is reached at a PGA of 0.83 g. In the LS2 state, a 50% probability of failure occurs at a PGA of 0.33 g, and full failure (100%) occurs at 0.93 g. For LS3, the PGAs corresponding to 50% and 100% failure probabilities are 0.65 g and 1.60 g, respectively. In the LS4 state, the PGA at 50% failure probability is 0.83 g, but even at a PGA of 1.60 g, the failure probability does not reach 100%. In contrast, for the isolated structure, the PGAs corresponding to a 50% probability of failure in LS1, LS2, LS3, and LS4 are 0.35 g, 0.45 g, 0.89 g, and 1.15 g, respectively.

For the isolated structure, when the peak ground acceleration (PGA) reaches 0.2 g, the failure probability in the LS1 state decreases by 16.1% compared to the original structure, while in the LS2 state, the failure probability decreases by 4.2%. This is because at a PGA of 0.2 g, there is a high probability of slight damage (LS1 state) to both the original and isolated structures. The isolation design reduces the probability of slight damage by 16.1%, with the failure probability remaining below 10%, indicating effective control. For moderate damage (LS2 state), both structures have a low probability of failure, and the reduction in failure probability due to isolation is relatively small. Nevertheless, the failure probability of the isolated structure in the LS2 state is less than 5%.

When the PGA reaches 0.6 g, the failure probability in the four performance states (LS1, LS2, LS3, LS4) for the isolated structure decreases by 5.2%, 18.2%, 27.8%, and 13.4%, respectively, compared to the non-isolated structure. The decline initially increases and then decreases as the performance state progresses. The primary reason for this trend is that in the low-damage state (LS1), the structure remains in the elastic or slightly non-linear stage. Since the failure probability is low in this stage, the impact of seismic isolation design is relatively limited, resulting in a modest decrease of 5.2%. As seismic intensity increases, the structure enters the plastic damage stage, and the energy dissipation capacity of the seismic isolation system becomes more significant. Particularly in the LS3 state, the isolation system effectively delays the structure from reaching the ultimate failure stage, reducing the displacement angle and acceleration response under seismic action, leading to a maximum decrease of 27.8% in failure probability. Therefore, vulnerability analysis reveals that under an earthquake with a PGA of 0.6 g, the isolation design effectively reduces the failure probability across all four performance states, especially in the LS2 and LS3 states (18.2% and 27.8%, respectively). The isolation design not only delays the critical point at which the substation structure enters the failure state but also ensures good seismic performance under higher earthquake loads, further validating the effectiveness and reliability of the substation structure’s isolation design in high-intensity areas.

5. Conclusions

This study investigates the seismic and isolation performance of a 220 kV indoor substation structure, designed according to the V3.0 standard for high-intensity areas, based on shaking table tests. The failure probability characteristics of the substation structures are evaluated using vulnerability analysis. The key conclusions drawn from this research are as follows:

• The test frequencies of the shaking table model structure exhibit strong consistency with the frequencies obtained from theoretical calculations and numerical simulations. This consistency confirms that the model can accurately reflect the dynamic characteristics of the substation prototype. The maximum error between the test and theoretical frequencies is only 3.42%, with an average error of 10.98%.
• The first period of the isolated structure is 2.33 times longer than that of the non-isolated structure, showing a trend of frequency decrease and period increase with the rise in input PGA. Notably, the growth rate of the isolated structure’s first period (4.82%) is lower than that of the non-isolated structure (15.38%). After experiencing an earthquake with a PGA of 800 gal, the isolated structure remains in the elastic state without any damage to the upper structure.
• The isolation design demonstrates significant control over the seismic response, with substantial attenuation of both displacement and acceleration under varying earthquake intensities and directions. The isolation effect exceeds 50%, leading to a considerable improvement in seismic resistance. As a result, the seismic fortification level of the substation can be reduced from 8 degrees to 7 degrees.
• The failure probability of the isolated substation structure, across the four performance states (LS1, LS2, LS3, LS4), shows a clear reduction compared to the non-isolated structure. The most significant decrease, 27.8%, occurs in the LS3 state at a PGA of 600 gal. The isolation design successfully delays the critical failure point, verifying the effectiveness and reliability of isolation technology in high-intensity earthquake zones.
• This research focuses on the dynamic response and vulnerability of isolated and non-isolated substation structures under seismic action, using electrical equipment as equivalent mass blocks. Future studies will aim to further investigate the seismic impact on real electrical equipment, providing essential data for ensuring the comprehensive safety performance of electrical systems during earthquakes.