ABSTRACT To make efficient use of land resources and minimize the seismic destruction of structures in the ground fissures zone, the shaking table tests and 3-dimensional numerical

calculation of the soil were completed, based on the ground fissures site in Xi’an (Class II, with the shear wave velocity Vs ranging from 250 m/s to 500 m/s). Influence laws of ground

motion characteristics and geological structure characteristics on seismic response spectra were revealed. Based on the statistics and analysis of seismic waves of the ground fissures site,

standardized design response spectra and mathematical formula of the ground fissures site were determined. The findings indicated that: the ground fissure exerted an amplifying influence on

Besides, the structural response was related to the spectral characteristics of seismic waves. Bedrock waves with rich high-frequency components were more likely to resonate with SDOF

systems with short period, while Jiangyou waves and El Centro waves with more low-frequency components had more intense resonance responses. With the increasing of fault distance, the

characteristic period _T_g increased, but platform value of response spectra _β_max decreased. The value of _β_max was between 2.52 and 3.62. The distributed patterns were respectively

∨-shaped and ∧-shaped. The research results of the design spectra can be used in the seismic design of the superstructure in the ground fissures site. SIMILAR CONTENT BEING VIEWED BY OTHERS

RESEARCH PROGRESS AND PROSPECTS OF SEISMIC PERFORMANCE ON UNDERGROUND STRUCTURE EMBEDDED IN SOFT SOIL FOUNDATION Article Open access 19 September 2024 STUDY ON SEISMIC RESPONSE

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WAVES Article Open access 21 April 2024 INTRODUCTION The ground fissure is a discontinuous weak structural plane, characterized by soil in the fracture zone exhibiting significantly distinct

physical and mechanical properties compared to the adjacent soil. The discontinuity of soil mass caused by geological structure will affect the propagation law of seismic waves in the soil

medium, change the vibration characteristics of the original site1, and accelerate the damage of frame structures in ground fissure sites. Finally, the building structures in these sites

cannot meet the seismic fortification goal2. Although the “Xi’an Ground Fissures Site Investigation and Engineering Design Specification”3 stipulates the minimum avoidance distance of

building structures to reduce ground fissure disasters, some structural projects still have to be built across the cracks, such as the subway tunnel and pipeline engineering4. In the

meantime, the development of ground fissures will also cause serious damage to many existing structures and ancient buildings, affecting the service life of buildings. To effectively utilize

urban land resources and reduce the impact of ground fissures, scholars have studied the seismic response mechanism of soil-structure systems at ground fissure sites. Fu et al.5 established

a model of the high-rise frame concrete structure, thereby conducting an analysis on the internal force performance of such structures within the ground fissure sites. Liu et al.6 held the

view that the employment of flexible connections could effectively diminish the seismic amplification impact of ground fissures on tunnels of metro. Liu et al.7. analyzed the seismic

response of the ground fissure site under the coupled action of earthquakes and ground fissure activities through numerical simulation. Xiong et al.8 explored the distribution of ground

motion parameters at sites with ground fissures subjected to strong seismic events. Xiong et al.9 put forward a novel method for disaster control and reinforcement of frame structures that

span ground fissures. Deng et al.10 analyzed the disaster characteristics, failure mechanisms, and impact range of ground fissures on surrounding buildings. Xiong et al.11 conducted a

dynamic time-history analysis on the soil-structure system at ground fissure sites, and obtained its seismic response pattern. Deng et al.12. studied the dynamic response characteristics of

the site with grouped ground fissures by arranging seismic measurement points along multiple ground fissures. Chang13 and Cao14 respectively disclosed the dynamic response law of some ground

fissures in Linfen basin and Yuncheng basin through experiments. Zhou et al.15 explored the seismic response and destruction mechanism of frame structures spanning ground fissures through

shaking table tests. Liu4 and Chen16,17 determined the variation law of acceleration, earth pressure, and strain in the subway tunnel and subway station passing through ground fissures via

model tests and numerical analysis. Chen et al.18 carried out a three-dimensional numerical research on the isolation of subway stations crossing ground fissures, putting forward and

verifying an effective isolation method. Xu et al.19 developed a physical model to investigate the stress and deformation behavior of prefabricated utility tunnels crossing active ground

fissures. Liu et al.20 examined the vibration response of subway trains running through segmented tunnels in ground fissure environments. Cao et al.21 revealed the dynamic effect of ground

fissure site by studying the buried-hill-type ground fissures. Wei et al.22 constructed an integrated soil-structure model to analyze the dynamic behavior of complex connected structures

under ground fissure conditions. Zhang et al.23 analyzed the mechanical response and deformation law of the utility tunnel in the ground fissure site. Gao et al.24 studied the distortion

rules and destructive features of shield tunnels obliquely crossing ground cracks during earthquakes through shaking table model tests. It is evident that the existing research merely

qualitatively reveals the mechanical response laws of soil or structures at ground fissure sites, and no investigations have been carried out regarding the seismic response spectra of such

sites. Additionally, there is a lack of seismic design methods for structural engineering in ground fissure environments, and the relevant theories significantly lag behind engineering

practices. Therefore, this study focuses on the Xi’an ground fissure site, investigating the impact of seismic wave properties and site tectonic features on seismic response spectra through

a combination of shaking table experiments and numerical simulations. By analyzing the response spectrum of more than 3600 selected seismic waves, the distribution of the characteristic

period _T__g_ and the acceleration response spectrum platform value _β__max_ of the ground fissure site is revealed. Finally, the least square piece-wise fitting method is used to calibrate

the standardized design response spectra suitable for the seismic design of ground fissure site structures, and a seismic design method for these structures is formed. SHAKING TABLE TEST

DESIGN SEISMIC ACTIVITY BACKGROUND OF THE GROUND FISSURE SITE IN XI’AN Xi’an is situated in the Fenwei Seismic Belt, where seismic activities are frequent. Since the 2nd century BC up to

now, a total of 128 earthquakes with a magnitude of 4 or above and 25 earthquakes with a magnitude of over 5 have taken place within its territory. According to the “Code for Seismic Design

of Buildings”, the seismic fortification intensity in some areas reaches 8 degrees, and the designed basic seismic acceleration value is 0.30 g. Ground fissures, as a unique geological

phenomenon in the Xi’an area, are closely related to seismic activities. The strata are mainly composed of loess, paleosol, and silty clay, which have a significant impact on the seismic

performance of building structures. Historically, for instance, the great earthquake in Huaxian County in the 34 th year of the Jiajing reign during the Ming Dynasty caused the damage of

numerous buildings in Xi’an, such as the Ci’en Temple. Buildings in the areas of ground fissures were especially bore the brunt. Modern research indicates that the seismic response at the

ground fissure sites is complex. The activities of ground fissures will change the dynamic characteristics of the sites and exacerbate the damage of earthquakes to structures. It is

necessary to comprehensively consider the dual factors of earthquakes and ground fissures. XI ‘AN F4 GROUND FISSURE At present, there are 14 primary ground fissures and 4 secondary ground

fissures in Xi’an. Among them, the f4 ground fissure (Zhangba Road-Happy North Road ground fissure) has a strike of NE70°, a tendency towards SE, an inclination angle of 80°, and a surface

development zone width of 22–55 m. The ground fissure is composed of three intermittently exposed segments. The length of a single ground fissure is 6.9 km, and the cumulative extension

length is 13.6 km. The ground fissure of Xi’an Tangyan Road underground civil air defense engineering office lies in the western section of the f4 ground fissure. It inclines towards the

south with a dip angle of 80°. The strata on the southern side (hanging wall) are declining, while the northern side (footwall) is relatively rising, and recent activity is relatively weak.

There are evident staggered layers between different soil layers, with a vertical separation of ancient soil reaching 3.29 m, and the site belongs to Class II site3. As shown in Fig. 1, (a)

and (b) are the geological structure maps of the ground fissure site and the free site respectively. The soil layer distribution of the free site is the same as that of the footwall of the

ground fissure site. The soil parameters are shown in Table 1. To investigate the vibration characteristics of soil in ground fissure sites under horizontal earthquakes, the research team

conducted shaking table tests on both ground fissure and free sites at the Key Laboratory of Structural Engineering at Xi’an University of Architecture and Technology. In the course of the

testing, a laminar shear box was employed to hold the model soil in order to mimic the boundary conditions of the real site and obtain more reliable results. The inner dimensions of the box

were 3.0 m×1.5 m×1.5 m. Additionally, reducing the boundary effect and the reflection of seismic waves of the soil box by bonding flexible materials such as rubber foam on the inner wall of

the soil box. The soil box was composed of 13 rectangular steel frames, each with a height of 100 mm. In order to ensure the coordinated movement of the soil box and the soil, six smooth

rollers, each with a height of 12 mm, were arranged between the steel frames in each layer along the vibration direction. Additionally, to restrict the rotation of the soil box, four columns

were welded along its length, and rollers were placed on the contact surfaces between the columns and the steel frame. Finally, the steel frame was welded around the soil box for convenient

hoisting and fixed attachment to the shaking table. The soil box is shown in Fig. 2. TEST SIMILARITY RATIO The main research object of this shaking table model test was the soil at the

ground fissure site. During the test, it was not feasible to fully satisfy the similarity ratio for all parameters of the model soil. Therefore, it is necessary to ensure that the similarity

ratio for the physical parameters, which has a decisive impact on this test, is completely consistent, while the similarity ratio for secondary parameters can be moderately relaxed. In

order to prevent model distortion due to an excessively small scale ratio of the structural model, the geometric similarity ratio _S__l_ of the test model was ultimately set at 1/15, taking

into account the constraints of the shaking table’s size, load-bearing capacity, model scale effects, and lifting capacity. Based on similarity theory, the similarity ratios for other

physical quantities were calculated and are presented in Table 2. The test soil used in this study was collected from the site near the f4 ground fissure in Xi’an. The on-site soil samples

were processed by removing impurities, drying, screening, and proportioning evenly. These samples were then filled and compacted in layers within the soil box. For each layer of the model

soil samples, comprehensive tests regarding density, water content, and compactness should be carried out. Subsequent layers of soil were added only after the test results met the specified

requirements. The width of the ground fissure was set at 2 cm, based on the structural characteristics and geometric similarity ratio of the fracture surface. To simulate the soil within the

fissure, a mixture of fine silt and hydrated lime was used to fill the reserved crack4. The soil within the ground fissures predominantly consists of silt or silty clay. To ensure that the

mechanical behavior of the ground fissure area in the tests closely approximates real-world conditions, a mixture of fine silt and hydrated lime, with physical properties similar to those of

the actual soil, was employed to fill the pre-reserved fissures. The test model is illustrated in Fig. 3. MEASURING POINT ARRANGEMENT In order to record the acceleration time history at

different positions within the soil of a ground fissure site, 36 accelerometers were embedded in the model soil. These accelerometers were specially modified for waterproofing to ensure

reliable measurements. As shown in Fig. 4, accelerometers are symmetrically arranged on both sides of the ground fissure, and the measuring points are encrypted in the area near the ground

fissure, and the ranging is gradually increased to both sides of the fissure. For comparison purposes, the free site test also had measurement points arranged at the same locations. LOADING

SYSTEM Based on the Xi’an site category, the El Centro wave, Jiangyou wave, and Cape Mendocino wave were chosen as input seismic waves to investigate how the characteristics of seismic waves

impact the seismic response spectra of ground fissure sites. These three types of seismic waves were all recorded during actual strong earthquakes. They respectively represent the

characteristics of ground motions under different magnitudes, focal mechanisms, and site conditions, enabling a more comprehensive study of the influence of the characteristics of seismic

waves on the seismic response spectrum of the ground fissure site. The characteristic curves are presented in Fig. 5. Among them, the Jiangyou wave had an intensity of 0.597 g, a duration of

101.995 s, and a predominant frequency of 2.50 Hz. The intensity of El Centro wave was 0.342 g, the duration was 53.73 s, and the predominant frequency was 3.85 Hz. The intensity of Cape

Mendocino wave was 0.165 g, the duration was 59.96 s, and the predominant frequency was 4.55 Hz. The input of the seismic wave’s peak was carried out and adjusted in line with the similarity

ratio and the seismic intensity stipulated in the “Code for Seismic Design of Buildings”25. The peak of the seismic wave, ranging from 0.05 g to 1.2 g, was segmented into 7 levels of

loading. Following each level of loading, a white noise signal of 0.05 g was input to conduct a frequency sweep test for observing and measuring the alterations in the dynamic

characteristics of the model. SEISMIC RESPONSE SPECTRA ANALYSIS OF GROUND FISSURE SITE INFLUENCE ANALYSIS OF GROUND FISSURE In this study, the ground fissure site in Xi’an is taken as the

research object. Considering that Xi’an has a seismic fortification intensity of Degree 8 in certain areas, with a designed basic seismic acceleration value of 0.30 g, the test records of

the ground fissure sites and free sites under the action of the Jiangyou wave with an acceleration of 0.30 g are selected for analysis, aiming to study the influence of ground fissures on

the response spectra of a Single Degree of Freedom (SDOF) system with a damping ratio of ζ = 0.05. The results are presented in Fig. 6. As can be seen from Fig. 6, the response spectra for

both ground fissure sites and free sites exhibit multi-peak curves with the same number of peaks, though their trends differ. At the free site, the maximum peak of the response spectra is

1.215 g, corresponding to an excellence period of 0.08 s. In contrast, at the ground fissure site, the maximum peak values of the response spectra at the hanging wall B30 and footwall A30

are 2.567 g and 2.160 g, respectively, with a dominant period of 0.14 s. The response spectra values at the ground fissure site are approximately twice those at the free site. This indicates

that ground fissures amplify the excitation of seismic waves, resulting in a larger response spectra for the SDOF system at the ground fissure site compared to the free site, thereby

causing more intense acceleration responses of structures located at the ground fissure site2. Furthermore, the presence of ground fissures alters the tectonic characteristics of the

original site, which in turn affects the spectral characteristics of the surface seismic waves. It is evidenced by the fact that the predominant period T = 0.08 s at the free site is shorter

than the 0.14 s at the ground fissure site. This suggests that seismic waves recorded at ground fissure sites have a greater impact on the seismic response of low-frequency structures.

INFLUENCE ANALYSIS OF THE DIP ANGLE OF GROUND FISSURE Figure 7 illustrates the acceleration response spectra at B30 on the hanging wall of the ground fissure site when the dip angles are

60°, 70°, and 80° (0.30 g-Jiangyou wave). As observed from Fig. 7, the dip angle significantly affects the acceleration response spectra at the site. The maximum peak value of the response

spectra occurs at an 80° dip angle (2.860 g), followed by a 70° dip angle (1.444 g), and the minimum value is at a 60° dip angle (1.095 g). This indicates that a larger dip angle of ground

fissure results in a greater seismic response of the SDOF system. INFLUENCE ANALYSIS OF CRACK DISTANCE * According to the analysis results of the influence of the dip angle of ground

fissures, it is found that the acceleration response of the ground fissure site with dip angle of 80° is the largest, and the “hanging-wall/footwall effect” is the most obvious. Therefore,

when studying the influence of the crack distance, this site is taken as the basic calculation model for all working conditions. Figure 8 illustrates the acceleration response spectra of the

SDOF system (ζ = 0.05) under the action of a 0.30 g Jiangyou wave at varying distances from the crack in the ground fissure site. The crack distance is defined as the shortest distance from

a specified point to the surface rupture trace of the ground fissure or the rupture surface extending to the surface position, synonymous with the fault distance. From Fig. 8, it can be

observed that the maximum peaks of the SDOF response spectra on the hanging wall from B30 to B34 are 2.567 g, 2.316 g, 1.734 g, 1.298 g, and 1.176 g respectively. At the same time, the

maximum peaks on the footwall from A30 to A34 are 2.160 g, 2.040 g, 1.617 g, 1.275 g, and 1.174 g respectively. These data indicate that the impact of crack distance on surface acceleration

response spectra primarily manifests as an attenuation relationship: the closer to the ground fissure, the higher the peak value of the response spectra. On the contrary, the further from

the fissure, the lower the peak value, gradually with the free site response spectra peak value tends to be consistent. Additionally, when the crack distance is the same, the peaks of the

response spectrum are larger in the hanging wall than in the footwall, showing the “hanging-wall and footwall effect” consistent with the conclusion of Reference2. Furthermore, the crack

distance has a significant influence on the dominant period of the surface acceleration response spectra, although this effect is limited in scope. The closer the proximity to the ground

fissure, the larger the dominant period, indicating a richer low-frequency component of the seismic wave near the fissure. As the distance from the fissure increases, the dominant period (T

= 0.08 s) at the fissure site aligns with that of a site without fissures. This further demonstrates that the farther one is from the ground fissure, the smaller the impact of the fissure on

the seismic response of the structure. INFLUENCE ANALYSIS OF GROUND MOTION CHARACTERISTICS To study the response spectra change law of SDOF (ζ = 0.05) of ground fissure site under different

seismic waves, the test records at the cracks on the hanging wall under the seismic action of 0.30 g are selected for analysis, as presented in Fig. 9. Figure 9 reveals that the maximum

peak and dominant period of the acceleration response spectra differ depending on the seismic wave type. The peak value of the Jiangyou wave is the highest, followed by the El Centro wave,

with the Cape Mendocino wave being the lowest, recorded at 2.567 g, 2.337 g, and 1.707 g, respectively. These results suggest that the seismic response of structures at ground fissure sites

is influenced by the spectral properties of the seismic waves. A larger peak value of the response spectrum indicates that the acceleration response of the structure under this seismic wave

is greater, reflecting a more intense resonance response. Bedrock waves with rich high-frequency components are more likely to resonate with low-period SDOF systems, and the resonance

response of the Jiangyou wave and El Centro wave, which contain more low-frequency components, is more pronounced. In terms of the shape of the response spectrum, the response spectrum

values of the Jiangyou wave and the El Centro wave are relatively high in the low-frequency band and the curves are relatively gentle, indicating that the influence of their low-frequency

components on the structure lasts for a long time. While the response spectrum of the bedrock wave, which contains abundant high-frequency components, fluctuates greatly in the

high-frequency band, suggesting that its high-frequency components have a more sudden impact on the structural response. DESIGN RESPONSE SPECTRA OF GROUND FISSURES SITE RESPONSE SPECTRA

CALIBRATION METHOD The calibration of the design response spectra i_s the process_ of statistical averaging and smoothing the elastic acceleration response spectra calculated from strong

earthquake record, and representing it into the seismic design response spectra in a simplified standardized form. The response spectra are calibrated by employing the least square

piece-wise fitting method put forward by Guo Xiaoyun26, which is based on coordinate transformation. Through this approach, the nonlinear fitting problem is transformed into a linear fitting

one. The specific mathematical expression is: $$\beta \left( T \right)=\left\{ {\begin{array}{*{20}{l}} {1.0+\left( {{\beta _{\hbox{max} }} - 1.0}

\right)\frac{T}{{{T_0}}}}&{}&{}&{0 \leqslant T \leqslant {T_0}}&{}&{} \\ {{\beta _{\hbox{max} }}}&{}&{}&{{T_0} \leqslant T \leqslant {T_g}}&{}&{} \\

{{\beta _{\hbox{max} }}{{\left( {\frac{{{T_g}}}{T}} \right)}^\gamma }}&{}&{}&{{T_g} \leqslant T \leqslant {T_m}}&{}&{} \end{array}} \right.$$ (1) In the formula, _β_max

represents the height of the platform segment, which is the maximum value of the dynamic amplification factor, typically ranging from 2 to 3. _T_0 denotes the first inflection point cycle.

_T_g is the period corresponding to the intersection of the platform section and the descending section, referred to as the second inflection point period or the characteristic period in

seismic design codes. _T_m is the cut-off period of the falling section of the calibration response spectra curve. _γ_ is the attenuation index of the descending section, with values varying

according to different specifications, generally between 0.5 and 1.0. STATISTICAL ANALYSIS OF THE CHARACTERISTIC PERIOD _T_ G OF THE RESPONSE SPECTRA The Class II ground fissure site is

taken as the research object in this study. Through numerical calculations, 3636 seismic waves recorded on the ground fissure site are obtained, and the corresponding response spectra are

calculated. The least square method is repeatedly used to assign the characteristic period _T_g of each response spectra, minimizing the residual standard deviation in the regression

analysis. The period corresponding to the minimum standard deviation is considered the characteristic period _T_g. Figure 10 presents the change law of _T_g, the average value of _T_g, the

standard difference, as well as the variation factor of the response spectra at different positions. As can be observed from Fig. 10, the ground fissure has a significant impact on the site

characteristic period _T_g. As the crack spacing increases, _T_g gradually increases, and the distribution pattern forms a ‘∨’ shape. The soil near the ground fissure is relatively soft1.

Reference27 suggests that the softer the site, the longer the predominant period of the response spectra. However, the results of this analysis contradict this view. This discrepancy arises

because the influence of the ground fissure on the characteristic period is much greater than the impact of the site hardness.This disparity comes about due to the fact that the impact

exerted by the ground fissure on the characteristic period is more significant than that of the site hardness. By analyzing the standard difference and variation factor of the characteristic

period, it is observed that the statistical characteristics of the characteristic period of the response spectra at different crack distances exhibit large discreteness. The coefficient of

variation and standard deviation are smallest near the ground fissure, indicating low discreteness. As the crack distance increases, the discreteness of the characteristic period also

increases. These conclusions reflect the uncertainty in the statistical characteristics of the characteristic period of the response spectra, primarily caused by the differences in the

dominant wavelength of the seismic wave. STATISTICAL ANALYSIS OF THE PLATFORM VALUE _Β_ MAX OF THE RESPONSE SPECTRA The response spectra platform value _β_max is a crucial characteristic

parameter of the seismic design response spectra. In most building seismic design codes, the amplification factor spectra platform value is generally assumed to be a fixed value,

disregarding the influence of site characteristics27. However, the conditions at ground fissure sites are significantly different from those at free site. Even at two positions with small

distances, their acceleration responses differ markedly. Therefore, when studying the acceleration response spectra of ground fissure sites, it is essential to take into account the impact

of crack distance on the platform value of the amplification factor spectra. Figure 11 illustrates the distribution law of platform value _β_max, standard difference, and variation factor of

the response spectra at different crack distances. From Fig. 11, it is evident that the platform value _β_max of the response spectra is significantly affected by the crack distance. As the

crack distance increases, _β_max gradually decreases and tends to stabilize, displaying a “∧” shaped distribution law. The _β_max of the upper disk is greater than that of the symmetrical

position on the lower disk, and the _β_max of the upper disk declines more, demonstrating the “hanging-wall/footwall effect.” From the standard difference and variation factor of the

response spectra platform value, it can be seen that the statistical characteristics of the acceleration response spectra platform value _β_max at different crack distances exhibit

relatively stable dispersion. This means the dispersion at each measuring point tends to be consistent and does not change significantly with the crack distance. Most research results show

that the platform value _β_max of the free site amplification coefficient spectra ranges between 2 and 3, while the platform value _β_max of the hanging wall and footwall of the ground

fissure ranges between 2.52 and 3.62 and 2.52 to 3.21, respectively. This indicates that the _β_max at ground fissure site is significantly larger than that at free site. Thus, for

structures at ground fissure sites, it is unreasonable to conduct seismic design according to the “Code for Seismic Design of Buildings”25. For the first inflection point period _T_0 of the

straight-line rise and the transition to the platform section, this paper adopts a value of 0.1 s in accordance with China’s “Code for Seismic Design of Buildings”25. In China, when it comes

to the seismic design of common building structures, the natural vibration period typically does not exceed 3 s. Moreover, considering that ground fissure sites are not suitable for

constructing high building, the termination period _T_m of the curve descending section is set to 3 s. With _T_0 and _T_m determined, the parameters _T_g, _β_max and _γ_ in Formula (1) are

calculated using the least squares method. The standardized response spectra for the hanging wall and footwall of the ground fissure site are shown in Fig. 12. As illustrated in Fig. 12, the

standardized response spectra at different locations of the sites containing ground fissures exhibit significant differences, making them unsuitable for direct use in the aseismic design of

architectural structure. For the sake of streamlining the design process and guaranteeing the seismic resistance safety of structures, the envelope diagram of the design response spectra at

various locations is taken, and the design response spectra curve for the standardized ground fissure site is ultimately proposed, as shown in Fig. 13. Figure 13 is divided into three

sections: (1) The linear rising section, _T_0 = 0.1 s; (2) The platform segment, _β_max = 3.7, _T_g=0.4 s; (3) The curve descending section, _γ_ = 0.9. The mathematical expression for the

corresponding standardized design response spectra for the ground fissures site is: $$\beta \left( T \right)=\left\{ {\begin{array}{*{20}{l}} {1.0+2.7

\:\frac{T}{{{0.1}}}}&{}&{}&{0 \leqslant T \leqslant {T_0}}&{}&{} \\ 3.7&{}&{}&{{T_0} \leqslant T \leqslant {T_g}}&{}&{} \\ {{3.7_{\hbox{} }}{{\left(

{\frac{{{0.4}}}{T}} \right)}^{0.9} }}&{}&{}&{{T_g} \leqslant T \leqslant {T_m}}&{}&{} \end{array}} \right.$$ (2) In the expression of the standardized design response

spectra, according to the “Code for Seismic Design of Buildings” in China, the linear rising section has _T_0 = 0.1 s, which is in line with the dynamic response law of general building

structures in the initial stage of an earthquake. The platform segment has _β_max = 3.7 and _T_g=0.4 s, which comprehensively considers the statistical characteristics of the seismic

response spectrum of the ground fissure site and the seismic safety requirements of the structure. The curve descending section has _γ_ = 0.9, which can reasonably reflect the attenuation

characteristics of the seismic wave energy in the long-period section, ensuring that the design response spectrum can reasonably reflect the seismic response of the structure within

different period ranges. CONCLUSION In this study, the Xi’an ground fissure site is taken as the research object. Through the shaking table physical model test and numerical simulation of

the ground fissure site, the influence of seismic wave characteristics, site structural characteristics, and crack spacing on the seismic response spectra is revealed, and the standardized

design spectra curve and mathematical expression of the ground fissures site are determined. The main conclusions are presented below: (1). The presence of ground fissures amplifies the

excitation effects of seismic waves. The peak values of the reaction spectra at ground fissure site are approximately twice those observed at ordinary site, resulting in a significantly more

intense seismic response for structures located within these fissured areas. Additionally, ground fissures alter the frequency spectrum of the seismic waves at the site. Near the ground

fissure, the dominant period of the seismic wave increases, making it more sensitive to low-frequency structures. (2). At the same distances from the ground fissure, the peak values of the

response spectra on the hanging wall are higher than those on the footwall. This implies that the earthquake responses of the hanging wall structure are stronger than that at the

corresponding position on the footwall, thus manifesting the “hanging-wall/footwall effect”. Moreover, as the dip angle of the fracture increases, the amplification of the seismic wave

becomes more significant, resulting in a more conspicuous seismic response of the SDOF system within the ground fissure environment. (3).The earthquake response behavior of structures in

site with ground fissures is closely linked to the frequency spectrum of the seismic waves. Bedrock waves containing abundant high-frequency components are more likely to resonate with

low-period SDOF. In contrast, the resonance response of Jiangyou wave and El Centro wave with more low-frequency components is more intense. (4). The impact of ground fissures on the

characteristic period _T_g significantly outweighs that of site hardness. With the increase of the crack distance, the characteristic period _T_g gradually rises, while the amplification

coefficient spectra platform value _β_max gradually decreases and approaches a stable value. The _β_max for the hanging wall ranges from 2.52 to 3.62, whereas the _β_max for the footwall

ranges from 2.52 to 3.21. (5). This study primarily focuses on the ground fissure site in Xi’an (Class II, which refers to a specific soil classification category with a shear wave velocity

Vs ranging from 250 m/s to 500 m/s), and there is only one main fissure. The “Y”-shaped, lateral feather-shaped, and concealed ground fissures have not been studied yet. In future research,

the scope of the site and the forms of fissures should be expanded, the study of complex seismic waves should be deepened, and the seismic design methods should be improved, so as to enhance

the application value of the seismic design methods for structures in ground fissure sites. DATA AVAILABILITY The datasets generated during and/or analysed during the current study are

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Eng. Vib._ 32 (004), 54–62 (2012). (in Chinese). Google Scholar  Download references ACKNOWLEDGEMENTS The authors are grateful for the funding support provided by the Natural Science

Foundation Project of Inner Mongolia (2021BS05013), the Fundamental Research Funds for Inner Mongolia University of Science &Technology) (2024QNJS013). AUTHOR INFORMATION AUTHORS AND

AFFILIATIONS * School of Civil Engineering, Inner Mongolia University of Science and Technology, Baotou, 014010, China Chao Zhang, Weining Zhong, Jiaojiao Chen, Xin Li, Yu Pu, Jianlong Yi 

& Youjun Xu * Academician Workstation of Mine Safety and Underground Engineering, Inner Mongolia University of Science and Technology, Baotou, 014010, China Chao Zhang & Youjun Xu *

Engineering Research Center of Urban Underground Engineering at Universities of Inner Mongolia Autonomous Region, Inner Mongolia University of Science and Technology, Baotou, 014010, China

Chao Zhang & Youjun Xu Authors * Chao Zhang View author publications You can also search for this author inPubMed Google Scholar * Weining Zhong View author publications You can also

search for this author inPubMed Google Scholar * Jiaojiao Chen View author publications You can also search for this author inPubMed Google Scholar * Xin Li View author publications You can

also search for this author inPubMed Google Scholar * Yu Pu View author publications You can also search for this author inPubMed Google Scholar * Jianlong Yi View author publications You

can also search for this author inPubMed Google Scholar * Youjun Xu View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS Z put forward the core

concepts and overall framework of the research, and determined the main directions and goals of the study. Based on this, Z designed the overall plan for this experiment, including the

experimental steps, methods, and the evaluation method for expected results. Z* took the lead in the actual operation of the experiment, carried out the experiment in strict accordance with

the established experimental plan, and wrote the manuscript. C and I assisted in the experimental operation, and preliminarily organized and checked the experimental data. Y and P processed

the experimental data and carried out relevant numerical calculations. X revised and polished the paper. All authors reviewed the manuscript. CORRESPONDING AUTHOR Correspondence to Weining

Zhong. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature remains neutral with regard to

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http://creativecommons.org/licenses/by-nc-nd/4.0/. Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Zhang, C., Zhong, W., Chen, J. _et al._ Response spectra and design spectrum

of ground fissures site under seismic action. _Sci Rep_ 15, 16120 (2025). https://doi.org/10.1038/s41598-025-01036-9 Download citation * Received: 18 January 2025 * Accepted: 02 May 2025 *

Published: 08 May 2025 * DOI: https://doi.org/10.1038/s41598-025-01036-9 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get shareable link

Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative KEYWORDS * Ground fissures site *

Shaking table test * Numerical calculation * Seismic response spectra * Design spectra