Study of Ground Vibration Site Effects on Substation in Inhomogeneous Strata

Abstract

A large substation confronts the risk of frequent tectonic earthquakes with a relatively high magnitude, thus it is necessary to analyze the seismic response of the site. To provide a reference for the seismic analysis of this substation, the seismic response of the substation site was investigated. Based on the Mohr–Coulomb elastic-plastic constitutive model, the finite element models of the soft soil site and engineering site were established, and the seismic responses of the soft soil site with and without backfill were analyzed. Subsequently, the effect of layered soil site on the acceleration amplification of various ground shocks was further studied, yielding the seismic acceleration amplification coefficients for soft soil site and engineering site. The results of the finite element model show that the seismic amplification factor of the soft soil site is 1.292. The seismic amplification factor of the engineering site varies under the action of simple harmonic wave, El Centro wave, and Kobe wave, with the amplification factors ranging from 1.092 to 1.405. Therefore, considering the effects of the spectral properties of seismic waves is essential for the seismic design.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

The substation is the core of the power system [1, 2], but its large substation equipment is vulnerable to seismic activities. Intense earthquakes can lead to extensive equipment destruction, resulting in significant economic losses [3–5]. Therefore, the seismic performance of large substations is of significant concern [6–8]. The results of numerous seismic investigations indicate that the site conditions significantly affect the ground motion under seismic actions, especially the amplification effect of the soil layers on the ground shaking [9–11]. Therefore, studying the seismic response of site soils and further grasping its laws are crucial for the seismic design and seismic damage analysis of substations. Since there are differences in the mechanical properties of layered site soils, the major challenges of this study are how to accurately simulate the response of layered site soils under various shocks and how to calculate the surface acceleration amplification factor for different sites.

An essential aspect in studying the seismic performance of large substations lies in the diversity of mechanical properties among different strata at various sites, which have a distinct amplifying effect on seismic events [12]. Investigating the dynamic properties and seismic responses of varied site soils is of utmost importance, particularly as the dynamic characteristics of these site soils significantly influence their seismic behavior. Considering the complexity of ground vibration and soil nonlinearity, the site with different soil layers is a complex system. To address this challenge, Idriss and Seed [13] proposed a one-way equivalent linearized fluctuation method to study the response of the site soil layer under transverse vibration. However, this method is inapplicable to soil, which is a very strong nonlinear material. Therefore, simplifying the complex nonlinear problem as a linear issue for resolution in soil engineering is not feasible. In instances where the strain on the soil layer is substantial, or ground shaking is intense, the high-frequency response amplification calculated by Yoshida et al. [14] using the equivalent linearization method is typically low, markedly differing from measured results. Consequently, the ground response is overestimated. The uncertainty of the seismic ground response is quantified by the analysis using the equivalent linear site response by Eddy et al. [15]. Zhao [16] delved into the soft soil layer on an elastic half-space and analyzed the lateral vibration of a free field. Liu et al. [17] expounded on the stress-strain relationship of the soil based on the one-dimensional fluctuation model and the fractional derivative viscoelastic Kelvin model, investigating the lateral vibration of the soil under shear seismic waves. Chen et al. [9] utilized an elastic-plastic boundary surface model to explore the three-dimensional seismic response of the soft soil site. However, the model parameters are cumbersome when the nonlinear characteristics of soil dynamics are considered. Due to the advancements in computer capabilities to handle nonlinear issues [18], the finite element method is employed in this study to compute the seismic amplification factor for layered soil sites.

A large substation poses challenges due to its intricate stratigraphy and tectonic activity, coupled with relatively poor regional geological stability and frequent high-magnitude tectonic earthquakes. To provide a reference for further research on the seismic response of the site, it is necessary to analyze the seismic response of the site and obtain the site amplification factor. Considering the natural stratification of the site and the nonhomogeneity of the soil layer, studying the seismic response, and analyzing the vibration characteristics are the basic issues for assessing the seismic hazard of engineering sites, evaluating the site effects, and dividing the seismic plots. The abovementioned research points are of practical significance and necessity.

In this paper, the data of soil information are obtained from the field address survey, and the finite element model of layered soil is reconstructed according to the drawings. A method based on commercial finite element software to calculate the site amplification factor is proposed, which can provide an important reference for the calculation of the amplification factor in the preliminary design stage of the project. To enhance the precision in the simulation of the seismic response at the soft soil site and engineering site, this study integrates the reconstruction of the backfill model with the excavation and filling diagrams of the site. Furthermore, a three-dimensional (3D) finite element model of the soft soil site without backfill soil and a finite element model of the engineering site with backfill were established, The ground vibration responses of the soft soil site and the engineering site under the action of different seismic waves were investigated to obtain the seismic amplification factor more accurately, thus laying the foundation for the seismic performance analysis of the soft soil site and the engineering site. The remainder of this paper proceeds as follows. Section 2 describes the structural model of the foundation soil. In Section 3, the geologic overview of the project is presented. In Section 4, the finite element model is developed and the amplification factor of seismic acceleration is calculated for the soft soil site without considering backfill. In Section 5, the amplification factor of seismic acceleration is calculated for the project site considering backfill. Finally, some conclusions are given in Section 6.

2. Structural Model of the Foundation Soil

Reasonable simulation of soil deformation is essential to simulate the ground vibration characteristics of the site, and the Mohr–Coulomb elastic-plastic model [19] is employed to analyze the ground vibration response of the site. The yield surface equation [19] is represented as follows:$$\begin{array}{}\text{(1)}& F=R_{mc}q-p\tan \phi -c=0,\end{array}$$where φ is the friction angle, $0^{\circ }\le \phi \le {90}^{\circ }$; c is the cohesion of the material; Θ is the polar deflection angle; r is the third invariant of the stress deflection tensor; and $R_{mc}$ (Θ, φ) is calculated according to [19].

A continuous smooth elliptic function of the plastic potential surface [19] in commercial finite element software is expressed as follows:$$\begin{array}{}\text{(2)}& G=\sqrt{{\epsilon c{|}_0\tan \psi }^2+{R_{mw}q}^2}-p\tan \psi ,\end{array}$$where ψ is the shear expansion angle; $c_0$ is the initial cohesion; ε = 0.1 is the eccentricity on the meridian plane; and $R_{mw}$ (Θ, e, φ) controls the function shape [19] on the π-plane with the following expression:$$\begin{array}{}\text{(3)}& R_{mw}=\frac{41-e^2{\cos }^2\Theta +{2e-1}^2}{21-e^2\cos \Theta +2e-1\sqrt{41-e^2{\cos \Theta }^2+5e^2-4e}}{R}_{mc}\frac{\pi }{3},\phi ,\end{array}$$where $e=3-\sin \phi /3+\sin \phi$ is the eccentricity on the π-plane.

In the commercial finite element software simulation process, centralized viscoelastic artificial boundary conditions are utilized, and the acceleration boundary is imposed by boundary conditions. The specific operation is as follows: in the commercial finite element software simulation process, we input the seismic wave data first, and then apply the acceleration boundary conditions around the perimeter and the bottom of the model.

3. Engineering Geology Overview

The Shajing site of the 500 kV Baiyi substation is located in the east-central region of the Yunnan-Guizhou Plateau, positioned within the upstream area of the Dianchi Basin, a subcatchment of the Jinsha River. The terrain in the northeast is elevated, gradually sloping towards the southwest, forming a terraced incline. The area of the proposed station is dominated by plateau-type denuded and dissolved remnant hills and sloping landforms, with microgeomorphic features of gently sloping east-west slopes. The general natural slope of the terrain ranges from 5 to 10 degrees, with localized slopes exceeding 10 degrees. The natural ground level within the exploration range spans approximately from 2255.00 m to 2290.00 m, with a maximum relative elevation difference of around 35.00 m. Positioned in the heart of the Yunnan-Guizhou Plateau, the site lies in the upper reaches of the Pudu River, a tributary of the Jinsha River.

According to the collected regional geological data, drilling exposures, and geological investigations around the station site, the proposed site and the surrounding overburden are mainly quaternary Holocene slope residual (Q4sl + el) clay ①, with hard-plasticized clay ①-1, clay ①-2, and soft-plasticized clay ①-3. The overlying bedrock is the Lower Permian Maokou Formation and Qixia Formation (P1m + q), with moderately weathered chert ②-1, strongly weathered chert ②-2, strongly weathered dolomite ③-1, fully weathered dolomite ③-2, and fully weathered marl ④-1. The tuff, dolomite, and marl present at the site are classified as harder rock, thereby falling under the geotechnical category V according to the regulations and norms. The physical and mechanical properties of each soil layer are detailed in Table 1.

Table 1

Physical and mechanical parameters of each soil layer.

	Number	γ	ω	$e_p$	$a_{\mathrm{v}1-2}$	$E_{\mathrm{s}1-2}$	CFSN		CFS		FSN		FS		$f_{\text{ak}}$	$C_Z$
							$c_q$	${\psi }_q$	$c_q$	${\psi }_q$	$c_q$	${\psi }_q$	$c_q$	${\psi }_q$
		(KN/m3)	(%)	—	(MPa)	(MPa)	(kPa)		(kPa)	(°)	(kPa)		(kPa)	(°)	(kPa)	(KN/m3)
1	①-1	18.5	40.0	1.20	0.30	7.50	40	22	35	17	31	17.8	26.56	13.87	180	42000
2	①-2	17.5	45.0	1.10	0.40	5.00	30	22	23	9	23	17.2	18.00	7.30	160	36000
3	①-3	17.0	55.0	1.35	0.80	3.00	18	11	12	7	14	9	9.0	5.9	80	16000
4	②-1	24.0	—	—	—	800 (ME)	260	—	—	—	200	—	—	—	1000	155000
5	②-2	22.0	—	—	—	80 (MD)	130	34	—	—	100	27	—	—	350	68000
6	③-1	21.5	—	—	—	75 (MD)	104	35	117	38	80	28	90	30	300	65000
7	③-2	20.5	—	—	—	75 (MD)	49	25	47	23	38	20	36	18	200	43000

CFSN, consolidation fast shear (not immersed in water); CFS, consolidation fast shear (immersed in water); FSN, fast shear (not immersed in water); FS, fast shear (immersed in water); ME, modulus of elasticity; MD, modulus of deformation; ① clayey soil; ② limestone; ③ dolomite; γ, the natural gravitational density; ω, the moisture content; $e_p$, the porosity ratio; $a_{\mathrm{v}1-2}$, the compression factor; $E_{\mathrm{s}1-2}$, the modulus of compression; $c_q,$the cohesive force; ${\psi }_q$, the angle of internal friction; $f_{\text{ak}}$, the eigenvalue of load-bearing capacity; $C_Z$, the compressive stiffness factor.

In terms of seismic zoning, the location of the Baiyi substation belongs to the class II site. For the class II site, the peak acceleration of basic ground shaking is 0.30 g, the characteristic period of the basic ground shaking acceleration response spectrum is 0.45 s, the corresponding basic seismic intensity is 8 degrees, and the design seismic grouping is the third group. The geological and tectonic movement in this area is more intense, the regional geological stability is relatively poor, and tectonic earthquakes occur frequently with a relatively high magnitude. Therefore, it is very necessary to analyze the seismic response of this site.

4. Amplification Effect Analysis of Seismic Acceleration in Soft Soil Sites

In the actual project, the soil conditions of the site are not entirely consistent with the results of the geological survey. To facilitate the construction of subsequent buildings, the original site is treated to a certain extent. The site is mainly covered with backfill. Changes in the geological conditions inevitably affect the ground vibration response of the site. Therefore, it is necessary to model and analyze the ground vibration response of the site from bedrock to backfill for understanding the acceleration amplification of the layered soil site containing backfill under various vibrations. This study provides a reference for seismic analysis of buildings on it.

In this section, a 3D finite element modeling based on commercial finite element software is employed to reconstruct the layered soil according to the commercial software drawings. In addition, the backfill is reconstructed in combination with the excavation and filling drawings of the site. Based on this 3D model, the acceleration amplification factor of the engineering site is investigated under different seismic wave effects. The differences in ground vibration characteristics of the site under different seismic wave input conditions are analyzed. The layered soil model with backfill conveniently reflects the acceleration distribution of each part of the site.

4.1. The Three-Dimensional Modeling of the Soft Soil Site

In this section, a 3D finite element model of the layered soil site is established by a commercial finite element software. Due to the complexity of the geometric model of the site and the irregularity of the demarcation line between multiple soil layers, the commercial software model is imported into commercial finite element software for reconstruction to obtain the 3D model. The borehole section with a large undulation of slope and more complicated soil layer distribution is selected as the representative site, and the soil layer distribution is shown in Figure 1.

[figure(s) omitted; refer to PDF]

From this drawing, it can be noticed that the soil stratification line of the commercial software drawing consists of polylines, which cannot be recognized and modeled directly in commercial finite element software. Therefore, the model is simplified by turning polylines into straight lines. The simplified plan is imported into commercial finite element software and the reconstruction of this 3D model is completed. The 3D model of the soil layer is created in commercial finite element software through the commercial software-finite element software interface using the abovementioned method. The illustrations of soil delineation and mesh delineation are presented in Figures 2(a) and 2(b), respectively. From Figure 2(a), we can see that there are four different soil layer divisions, which are clayey soil ①-1, clayey soil ①-2, clayey soil ①-3, and bedrock ②-1. Figure 2(b) corresponds to the finite element mesh divisions of these four soil layers, respectively.

[figure(s) omitted; refer to PDF]

The specific modeling information is as follows: the length of the site is 1,367 m, the width is 500 m, and the height of the highest point is 270 m. The grid adopts the C3D8RH elements. The approximate global size of the grid is 14 m, and the maximum deviation factor in the curvature control is 0.1. The meshing is tetrahedral-based. The reduced integration is used, and the hourglass control is set to augment to prevent the phenomenon of computational nonconvergence. The element number of the whole model is 71136.

4.2. Ground Stress Equilibrium

In the analysis of geotechnical engineering, accurate simulation of the initial stress field is crucial for the correctness of the subsequent computational analysis due to the special characteristics of the soil. In the process of establishing the equilibrium of the initial ground stress field, it is necessary to balance the initial stress in the soil so that the initial displacement of the soil is zero. The initial stress field cannot affect the results of subsequent dynamic analysis. The results of stress balancing in the finite element model of the soft soil site are shown in Figure 3. Soft soil site finite element model’s stress balance results are shown in Figure 3. Figures 3(a) and 3(b) show the stress distribution and displacement distribution, respectively. From Figure 3(a), it can be seen that the stress at the bottom of the model is −2 × 10⁷ Pa and the maximum stress at the surface is 3.46 × 10⁶ Pa. The displacement distribution in Figure 3(b) shows that the displacement at the bottom of the model is 0 and the maximum value is 1.849 × 10⁻¹² m. In conclusion, the initial displacement of the model is nearly zero, and the effect of ground stress equilibrium is effective [20]. This initial condition does not affect the subsequent seismic response analysis.

[figure(s) omitted; refer to PDF]

4.3. Seismic Wave Input

According to the principle of seismic wave selection, the classical El Centro wave is selected as the seismic wave input in this part. Based on the basic ground shaking peak acceleration of the site, the peak acceleration is adjusted to 0.3 g, and the duration of the seismic wave action is 20 s without losing the main information of the seismic wave. The acceleration time curve of the El Centro seismic wave is shown in Figure 4.

[figure(s) omitted; refer to PDF]

4.4. Seismic Response Analysis of Soft Soil Sites

The El Centro wave with a peak acceleration of 0.3 g is input into the finite element model to simulate the seismic response of the soft soil site. From the acceleration response result in Figure 5, the acceleration at the bottom of the model is 9.429 × 10⁻⁷ m/s², and the acceleration at the surface is 7.099 × 10⁻³ m/s². The larger acceleration is basically concentrated at the top of the slope. The acceleration time course curve of a point at the top of the slope is extracted in Figure 6. The maximum seismic acceleration on the surface of the soft soil site is 3.876 m/s², and the corresponding seismic amplification factor of the soft soil site is 1.292.

[figure(s) omitted; refer to PDF]

5. Amplification Effect Analysis of Seismic Acceleration in Engineering Sites

5.1. Finite Element Modeling of the Engineering Site

Finite element analysis (FEA) is an important method to calculate the dynamic response of a site under seismic action, and the main processes are as follows: reconstruction of the 3D model, definition of materials and contacts, input of seismic waves, and postprocessing of the results. The acceleration of the surface nodes can be obtained from the finite element model, and the acceleration amplification factor of the site is available by comparing it with the input seismic wave.

5.1.1. 3D Modeling of the Engineering Site

The distribution of layered soil in the area is illustrated in Figure 7. There is still a thick layer of backfill on this 3D model as the site has been excavated and filled. The height of the fill in this area can be calculated from the ground stress equilibrium of the site and the backfill portion can be reconstructed in commercial finite element software. After the abovementioned steps, the 3D model of the engineering site with backfill can be obtained, as shown in Figure 8, which can better reflect the layering characteristics of the engineering site and backfill, and it is more reasonable for finite element calculation. Figure 8(a) shows the schematic diagram of the model. From Figure 8(a), five different soil layer divisions can be seen, which are backfilling soil, clayey soil ①-1, clayey soil ①-2, clayey soil ①-3, and bedrock ②-1. Figure 8(b) illustrates the finite element mesh division, and it corresponds with the finite element mesh divisions of the five soil layers, respectively.

[figure(s) omitted; refer to PDF]

The specific modeling information is as follows: the length of the field is 680 m, the width is 150 m, and the height is 157 m. It is divided into two analysis steps: frequency analysis and modal dynamics analysis, in which the modal dynamics analysis step is 15 s with a time increment of 0.003 s. The outputs of the field variables are as follows: stresses, acceleration, and displacement. The boundary conditions of the model are as follows: the bottom is constrained by U1 and U2, and the sides are constrained by U2, thus simulating the constraints when a piece of infinite field is removed. The C3D8RH element in the commercial finite element software is utilized for the mesh. The approximate global size of the mesh is 15 m, and the maximum deviation factor in the curvature control is 0.1. The meshing is tetrahedral-based. A reduced integration is applied, and the hourglass control is set to augment to prevent computational nonconvergence. The element number of the whole model is 6800.

5.1.2. Finite Element Model Setup

The mechanical parameters of each soil layer in the finite element model are shown in Table 2. The site model consists of multiple layers of soil with very complex shapes between them, so constraints are considered in the contact setup to combine the layers together to form a whole. This contact setup allows for easy convergence of results and faster calculations.

Table 2

Table of material parameters.

Name of the material	Densities ρ (kg/m3)	Modulus of elasticity E	Poisson’s ratio (μ)
		(MPa)
Clayey soil ①-1	1830	6.99	0.3
Clayey soil ①-2	2070	8.52	0.27
Clayey soil ①-3	1950	8.68	0.24
Backfilling soil	1800	7.68	0.2

5.1.3. Seismic Wave Input

To reflect the ground vibration response of the engineering site under each waveform, the model was first tested by inputting the simple harmonic waveform, and then the ground vibration response of the soil at the site was calculated under the El Centro waveform and Kobe waveform, respectively. The three waveforms and peak accelerations are shown in Figures 9–11.

[figure(s) omitted; refer to PDF]

5.2. Seismic Response Analysis of the Engineering Site

According to the calculation results of commercial finite element software, the response of the node with the largest ground acceleration response is extracted from the model and the maximum value of the acceleration response is determined. According to the peak value of the ground acceleration response and the peak value of the seismic wave, the acceleration amplification factor of the engineering site can be derived.

Figure 12 illustrates the acceleration response of the whole process when the simple harmonic wave is input. From the figure, it can be seen that there are obvious stratification characteristics from the bottom to the surface of the model, and there are also stratification phenomena between different soil layers, indicating that the seismic wave propagation velocity is different during the propagation process in different soil layers. When time t is equal to 0.3 s, the seismic wave propagates from the bottom of the seismic source to the surface, and the response of the surface is relatively small. At time t = 1.2 s, the ground surface has a larger seismic response, which is manifested as a larger acceleration, and the maximum value of the ground acceleration is 1.834 m/s², which appears in the red region of the surface. When time t is equal to 1.2 s, the surface has a large seismic response, which is characterized by large acceleration, and the maximum value of surface acceleration is 1.834 m/s2, which appears in the red region of the surface. At t = 3 s, the bottom of the model accelerates to 1.002 × 10⁻⁹ m/s², indicating that the seismic wave has been terminated at this time, but due to the delayed propagation of the seismic wave, there is still a large acceleration of the surface. A comparison of the acceleration results under the simple harmonic wave at three different times shows that the locations of the maximum are essentially the same, occurring in the surface layer.

[figure(s) omitted; refer to PDF]

Comparing Figures 12(a) and 13(a), it can be found that the distributions of acceleration A1 and total acceleration at 0.3 s under the action of the simple harmonic wave are different, indicating that the simple harmonic wave exists the acceleration in other directions at 0.3 s. The comparison also shows that the distributions of acceleration A1 and total acceleration under the simple harmonic wave at 1.2 s are the same, which indicates that there is no acceleration in other directions for a simple harmonic wave at 1.2 s. To summarize, it can be concluded that acceleration A1 is equal to the total acceleration A of the simple harmonic wave in some cases, but in other cases, there are accelerations in other directions. It is only reasonable to utilize the total acceleration A when calculating the amplification factor.

[figure(s) omitted; refer to PDF]

The acceleration time curve at the highest point of the surface under the simple harmonic wave action is extracted, as shown in Figure 14. From the results obtained from the finite element model in Figure 14, it is obvious that the acceleration changes under the action of simple harmonic waves, and the maximum value of acceleration under this condition is 2.8104 m/s². According to the calculation, the acceleration amplification factor of the site in this service condition is 1.405.

[figure(s) omitted; refer to PDF]

Figure 15 illustrates the acceleration response with time for the input El Centro wave. From Figure 15, it can be seen that the seismic wave propagates at different speeds in different soil layers, and the acceleration of the El Centro wave has an obvious acceleration stratification phenomenon from the bottom of the model to the surface and among the five soil layers. The acceleration response of the El Centro wave at t = 1.2 s is smaller at the surface because the seismic wave has just propagated from the bottom of the source to the surface at this time. At t = 1.68 s, the El Centro wave has a larger acceleration at the surface, indicating that there is a larger seismic response at the surface at this time. At t = 1.68 s, the acceleration of the El Centro wave at the surface is larger, which indicates that there is a larger seismic response at the surface at this time. The maximum value of surface acceleration is 2.473 m/s², which appears in the red area of the surface. At t = 12 s, the acceleration of the El Centro wave at the bottom of the model is zero, which indicates that the seismic wave has been terminated at this time. However, there is still a large acceleration on the surface due to the delayed propagation of seismic waves. Comparing the acceleration response of the El Centro wave at t = 1.2 s, 1.68 s, and 12 s, it is observed that the maximum acceleration occurs at the surface.

[figure(s) omitted; refer to PDF]

The acceleration time curve at the highest point of the surface for the input El Centro wave condition is shown in Figure 16. From the results obtained from the finite element model, it is obvious that the acceleration changes under the action of the El Centro wave, and the maximum value of acceleration under this condition is 3.2188 m/s². According to the calculation, the corresponding acceleration amplification factor of the site is 1.092.

[figure(s) omitted; refer to PDF]

Figure 17 presents the acceleration response with time for the input Kobe wave. The figure provides insight into the distribution of acceleration for the Kobe wave, illustrating how it propagates from the bottom to the surface through different soil layers. When time t is equal to 2 s, the surface experiences a relatively smaller acceleration response of 1.11 × 10⁻⁴ m/s². This can be attributed to the recent propagation of seismic waves from the bottom to the surface at this given time. At t = 7.35 s, the El Centro wave exhibits a larger acceleration response at the surface, indicating a heightened seismic impact. Notably, the maximum acceleration in the red area of the surface reaches 2.346 m/s². At t = 13.5 s, the acceleration of the Kobe wave at the bottom of the model is 7.256 × 10⁻¹² m/s², which is basically close to zero, indicating that the seismic wave has been terminated at this time. However, due to the delayed seismic wave propagation, the acceleration at the surface is 1.262 × 10⁻¹ m/s², which is still large. Comparing the acceleration response of the Kobe wave at t = 2 s, 7.35 s, and 13.5 s, it can be found that the locations where the maximum acceleration occurs are at the surface.

[figure(s) omitted; refer to PDF]

The acceleration time curve at the highest point of the surface under the Kobe wave is presented in Figure 18. According to the results obtained from the finite element model, the change of acceleration under the action of the Kobe wave can be clearly seen, and the maximum value of acceleration under this condition is 5.7261 m/s². In this case, the corresponding acceleration amplification factor of the site is 1.351.

[figure(s) omitted; refer to PDF]

The acceleration amplification factor at the surface of the engineering site varies under different waveforms. Under different working conditions, the maximum acceleration of the input, the maximum acceleration of the surface response, and the corresponding acceleration amplification factor of the engineering site are summarized as shown in Table 3.

Table 3

Acceleration amplification factor for the project site.

	Input maximum acceleration (m/s2)	Response to maximum acceleration (m/s2)	Magnification factor
Simple harmonic wave	2	2.810	1.405
El Centro wave	2.997	3.219	1.092
Kobe wave	4.237	5.726	1.351

According to the calculation results of the three waveforms, the following patterns can be concluded. First, in terms of the acceleration amplification effect of the engineering site, the acceleration response of each point on the surface of the model is extracted, and it is found that each point has an obvious amplification effect under the action of different vibrations. For different seismic waves, the locations of the maximum acceleration response points are close to each other.

Comparing the site acceleration amplification coefficients for each case, it is evident that the amplification coefficients for different waveforms are not the same, and the amplification coefficients range from 1.092 to 1.405 for the three cases. The specific reasons for the analysis are as follows: the maximum acceleration of the soil surface under the action of seismic waves is affected by the intrinsic frequency of the site and the main action band of the input seismic wave. When the two are close to each other, the amplification effect of the site is more obvious. The main action bands of the different seismic waves are different, and the corresponding acceleration amplification coefficients obtained are different. Therefore, when considering the amplification effect of ground vibration for seismic design, it is necessary to account for the spectral characteristics of seismic waves, selecting a reasonable seismic wave input.

Table 4 shows the velocities at the base of the bedrock and the velocities at the surface, and from Table 4, it can be seen that the ratio of the velocities at the bottom of the model and at the surface is large. It indicates that the surface velocity of the site is much larger than the velocity of the foundation under seismic action. However, most of the damages to engineering structures are caused by excessive acceleration, so in the calculation of the seismic amplification effect of the site, the focus is on the ratio of the peak acceleration, and the ratio of the velocity of the ground surface and the bottom of the bedrock has a little reference value.

Table 4

Velocity comparison between foundation and surface at the project site.

	Velocity of the bedrock floor (m/s)	Velocity of the surface (m/s)
Simple harmonic wave	0.23	0.71
El Centro wave	0.13	0.55
Kobe wave	0.31	0.54

6. Conclusion

In this paper, the effects of a soft soil site without backfill and an engineering site with backfill on the acceleration amplification of various vibrations are investigated, particularly focusing on the changes in surface acceleration amplification coefficients of the engineering site with backfill due to different waveforms. The effects of different waveforms on the ground vibration characteristics of the project site are discussed. Different seismic waveforms have different main frequency bands so the final acceleration amplification factors are different. This model calculates the seismic amplification factor for soft soil sites and engineering sites. From the presented work, the following conclusions can be drawn:

(1) The acceleration at the slope top of the soft soil site is larger, the maximum seismic acceleration is 3.876 m/s², and the seismic amplification factor is 1.292. Under the effect of different vibrations, the acceleration amplification effect at each point of the engineering site is significant. For different seismic waves, the location of the point of maximum acceleration response is basically consistent.

(2) The amplification coefficients of surface acceleration at the engineering site under different waveforms are not the same. For the simple harmonic wave, El Centro wave, and Kobe case, the acceleration amplification factors of the site are 1.405, 1.092, and 1.351, respectively.

(3) In the seismic design, the influence of the spectral properties of seismic waves requires attention when considering the ground vibration amplification effect of the site. Thus, the selection of a reasonable seismic wave input is important.

(4) The finite element model does not consider piled soils, and the simplification of the boundary conditions may not be representative of infinitely large soils.

Authors’ Contributions

Jingqiu Yang conceptualized and investigated the study, developed the methodology, performed the formal analysis, and wrote and prepared the original draft. Quanjun conceptualized, supervised, reviewed, and edited the study, developed the methodology, collected the resources, and wrote the manuscript. Xinming Li developed the methodology and the software and investigated the study. Jinrui Zhang conceptualized and investigated the study and collected the resources. Xiaolin Li investigated the study, collected the resources, and performed formal analysis.

Acknowledgments

The authors acknowledge the financial support of the Science and Technology Project of Yunnan Power Grid Corporation (KJBB2021121).

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