Influence of Soft Surface Soil on Site Seismic Response in Tianjin Area

Influence of Soft Surface Soil on Site Seismic Response in Tianjin Area | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Influence of Soft Surface Soil on Site Seismic Response in Tianjin Area Ying Cao, Wuping Gao, Zhisheng Wang, Chengguo Yan, Fei Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4677183/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Soft soil is a prevalent type of special soil, boasting mechanical characteristics like low strength, significant deformation, and heightened sensitivity. Engineering-wise, it often poses hazards such as settlement and uneven subsidence when subjected to seismic forces. Moreover, the substantial impact of soft soil on seismic events has been widely recognized. Investigations into the seismic response characteristics of soft soil primarily concentrate on two key aspects: the presence of soft soil in the form of interlayers and soft soil sites. By conducting a statistical analysis of dynamic parameters pertaining to soft soil in the Tianjin area, this study provides recommended values for such parameters in the area. Subsequently, ten distinct models of soft soil strata with varying layer thickness are established to examine the influence of soft surface soil’s thickness on characteristic parameters of site ground response spectra. This research furnishes valuable insights for seismic design within the study area. Earth and environmental sciences/Natural hazards Earth and environmental sciences/Solid earth sciences/Seismology Soft soil site Input ground motion Soil stratum structure Influence analysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Soft soil, a type of loosely consolidated fine-grained soil, falls under the category of special soils. Typically characterized by a moisture content surpassing the liquid limit, a natural void ratio exceeding 1.0, low strength, significant deformation, and heightened sensitivity, it arises from Quaternary fluvial deposition, commonly near bodies of water such as rivers, lakes, and seas. Its composition primarily encompasses silt, silty soil, peat, and peaty soil, often resulting in substantial or irregular settlement of structures. When subjected to seismic forces, it can induce engineering hazards like soft soil liquefaction. As outlined in the Specification for Geotechnical Investigation in Soft Clay Area (JGJ83—2011) [ 1 ] , when seismic fortification intensity in a specific region reaches 7 degrees or higher, evaluating the potential for soft soil liquefaction becomes imperative in areas with thick soft soil layer. Consequently, soft soil generally proves unsuitable for serving as foundation soil for buildings. Nonetheless, in light of rapid urban development and diminishing available land for construction in coastal areas, a magnitude of buildings have been erected atop soft soil layers in recent years. The dynamic shear modulus ratio and damping ratio are critical parameters in the dynamic analysis of soft soil. Typically, these parameters are derived from indoor triaxial tests or resonant column tests. However, the high sensitivity and poor disturbance resistance inherent in soft soil often led to significant errors throughout the entire process, from sample preparation to testing in indoor experiments, resulting in biased test results. Soft soil presents distinctive seismic response characteristics when juxtaposed with typical soils, primarily manifested in soft soil sites and interlayers. Huang et al. [ 2 ] scrutinized the impact of soft soil interlayers on ground acceleration across various regions, revealing that when soft soil interlayers are positioned at the base of bedrock, the amplitude of the peak point of the ground acceleration response spectrum is minimal. Meanwhile, Peng and Lv [ 3 ] elaborated on the seismic response of typical soft soil sites in Binhai New Area, Tianjin, as well as Yantai, Shandong, uncovering a notable amplification effect of ground motion within such sites, with peak acceleration amplification factors reaching up to 1.9 times. Moreover, scholars [ 4 – 11 ] have conducted seismic response analyses on typical soft soil sites in diverse regions, indicating that the positioning of soft soil layers yields varying effects on seismic responses. Generally, soft soil layers demonstrate considerable amplification effects when positioned atop the ground surface, whereas some isolation effects may be observed when they are situated near the bedrock at the base. Expanding upon prior research, this study plunges into the dynamic characteristics of soft soil in the Tianjin area. Its primary emphasis lies in examining how the thickness of soft surface soil affects seismic effects within the region. Additionally, the study offers recommended values for the dynamic shear modulus ratio and damping ratio of soft soil through statistical analysis. 1 Overview of the study area In China, based on the engineering properties and distribution areas of soft soil, it is roughly divided into three regions [ 12 ] : Zone I, Zone II, and Zone III. The boundary between Zone I and Zone II soft soil extends from the eastern Qinling Mountains to the northern coastline of Lianyungang. The boundary between Zone II and Zone III soft soil runs from the Miaoling Mountains, eastward along the Nanling Mountains, to the coastline near Putian. Situated on the western fringe of Bohai Bay, Tianjin boasts a silty coastline stretching over 150 kilometers, shaped by Late Pleistocene marine transgression deposits, presenting a quintessential example of soft soil in Zone I [ 1 ] . In recent years, urban expansion has led to a proliferation of public and civil structures erected on soft soil foundations. Hence, this study shifts its focus to Tianjin’s soft soil as its research subject. Here are the principal physical and mechanical properties of the soft soil in the study area: Natural moisture content varies between 53.20% and 97.20%, with an average of 63.95%. Porosity ranges from 1.46 to 2.63, averaging at 1.77. Density spans from 1.48 g/cm 3 to 1.73 g/cm 3 , with an average of 1.62 g/cm 3 . Liquid limit ranges from 33.60–55.60%, averaging at 50.41%. Plastic limit varies between 19.10% and 27.90%, with an average of 25.80%. Liquidity index varies between 1.27 and 3.29, with an average of 1.57. Plasticity index ranges from 14.50 to 27.70, averaging at 24.40. Compression modulus ranges from 1.46 MPa to 3.96 MPa, with an average of 2.05 MPa. Cohesion spans from 2.70 kPa to 8.25 kPa, averaging at 5.17 kPa. Internal friction angle varies from 0.00° to 4.84°, with an average of 0.90°. 2 Data sources and analysis methods This study compiled and analyzed data from 134 boreholes within the Tianjin area, bolstered by three additional boreholes featuring direct measurements. The primary objective was to gather and systematize information pertaining to the dynamic shear modulus ratio and damping ratio in soft soil. Leveraging this foundational data, the study proceeded to conduct an analysis aimed at delineating the range and average values of the dynamic shear modulus ratio and damping ratio in the study area, as detailed in Table 1 . The supplementary borehole experimental data were acquired by the Institute of Disaster Prevention, capitalizing on a dual-directional dynamic triaxial testing apparatus manufactured by GCTS, USA, with the model STX-200. Table 1 List of Range Values of Dynamic Shear Modulus Ratio and Damping Ratio for Typical Soft Soil in Tianjin Area Parameter Shear Strain (×10 − 4 ) 0.05 0.1 0.5 1 5 10 50 100 Maximum G/G max 0.9995 0.9990 0.9950 0.9901 0.9522 0.9088 0.6659 0.5210 λ(%) 6.58 7.42 9.96 11.36 16.72 19.53 32.32 32.85 Minimum G/G max 0.9849 0.9703 0.8673 0.7656 0.3952 0.2462 0.0613 0.0316 λ(%) 0.55 0.76 1.61 2.23 4.64 6.27 11.50 13.90 Average G/G max 0.9957 0.9915 0.9591 0.9223 0.7146 0.5643 0.2204 0.1309 λ(%) 3.47 4.30 7.02 8.63 13.18 15.19 18.65 19.48 3 Establishment of on-site geological profiles 3.1 Actual on-site soil profiles To adequately factor in the nonlinear characteristics of site soils and their influence on seismic response calculations, this study selected seismic borehole data from engineering investigations in Tianjin. The borehole information is listed in Tables 2 and 3 . Table 2 List of soft soil layers Number Soil Buried depth (m) Shear wave velocity (m/s) Density (g/cm 3 ) T1 Silty Clay 3.9 134.0 1.81 T2 Clay 16.8 139.0 1.74 T3 Clay 22.3 204.0 1.99 T4 Silt 32.4 293.0 2.08 T5 Clay 36.7 285.0 1.99 T6 Silt 49.0 373.0 2.09 T7 Clay 53.4 365.0 1.98 T8 Sand-Silt 63.3 492.0 2.07 T9 Clay 69.5 442.0 1.98 Bedrock Sand-Silt 72.1 526.0 2.07 Table 3 The list of dynamic shear modulus ratio and damping ratio of each soil layer in the seismic response analysis model Soil Number Parameter Shear Strain(×10 − 4 ) 0.05 0.1 0.5 1 5 10 50 100 T1 G/G max 0.9963 0.9926 0.9639 0.9303 0.7275 0.5717 0.2107 0.1178 λ 0.0226 0.0313 0.0544 0.0685 0.1104 0.1293 0.1602 0.1665 T2 G/G max 0.9966 0.9933 0.9674 0.9368 0.7477 0.5971 0.2286 0.1291 λ 0.0436 0.0534 0.0848 0.1028 0.1541 0.1767 0.2136 0.2214 T3 G/G max 0.9955 0.9911 0.9569 0.9174 0.6896 0.5263 0.1818 0.1000 λ 0.0273 0.0351 0.0623 0.0790 0.1281 0.1495 0.1825 0.1890 T4 G/G max 0.9968 0.9936 0.9688 0.9394 0.7562 0.6079 0.2367 0.1342 λ 0.0436 0.0534 0.0848 0.1028 0.1541 0.1767 0.2136 0.2214 T5 G/G max 0.9969 0.9937 0.9695 0.9407 0.7604 0.6135 0.2409 0.1370 λ 0.0258 0.0323 0.0543 0.0674 0.1063 0.1243 0.1550 0.1616 T6 G/G max 0.9960 0.9920 0.9611 0.9251 0.7118 0.5526 0.1981 0.1099 λ 0.0194 0.0253 0.0464 0.0597 0.1002 0.1187 0.1486 0.1547 T7 G/G max 0.9982 0.9965 0.9826 0.9658 0.8495 0.7383 0.3607 0.2201 λ 0.0265 0.0332 0.0560 0.0699 0.1135 0.1360 0.1822 0.1944 T8 G/G max 0.9962 0.9924 0.9633 0.9293 0.7243 0.5678 0.2081 0.1161 λ 0.0156 0.0265 0.0475 0.0606 0.1001 0.1182 0.1479 0.1540 T9 G/G max 0.9966 0.9932 0.9670 0.9061 0.7256 0.5344 0.2266 0.1278 λ 0.0246 0.0314 0.0550 0.0674 0.1131 0.1334 0.1676 0.1748 Bedrock G/G max 0.9961 0.9923 0.9628 0.9282 0.6813 0.5085 0.2055 0.1145 λ 0.0187 0.0247 0.0470 0.0613 0.1064 0.1276 0.1628 0.1750 3.2 Profiles with different thicknesses of soft surface soil To elucidate the influence of varying thicknesses of soft surface soil on ground response spectra, this study established profiles comprising ten different thicknesses of soft soil layers. The thicknesses of the soft soil layers were 2 m, 4 m, 6 m, 8 m, 10 m, 12 m, 14 m, 16 m, 18 m, and 20 m. For ease of comparison, the thickness of these ten sets of soil layer profiles was standardized to 40 m. Beneath the soft soil layer lay a silty layer, with the bottom layer consisting of bedrock. The parameters for each profile are presented in Tables 4 and 5 , where the dynamic shear modulus ratio and damping ratio for soft soil are derived from recommended values obtained through actual soil layer calculations in this study, while other parameters are referenced from actual site data. Table 4 Dynamic shear modulus ratio and damping ratio of bedrock and silt layer profiles Parameter Shear Strain(×10 − 4 ) 0.05 0.1 0.5 1 5 10 50 100 Bedrock G/G max 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 λ(%) 0.40 0.80 1.00 5.10 2.10 3.00 3.60 4.60 Silt G/G max 0.9968 0.9936 0.9688 0.9394 0.7562 0.6079 0.2367 0.1342 λ(%) 2.25 2.89 5.14 6.55 10.87 12.92 16.47 17.25 Table 5 Physical and Mechanical Parameters of Soil Layer in Profile Density(g/cm 3 ) Shear wave velocity(m/s) Soft Soil 1.74 128 Silt 2.08 270 Bedrock 2.20 500 4 Selection of input ground motion In 1940, the Empire Valley earthquake, with a magnitude of 7.1, struck the United States, yielding the El Centro waves, which marked the inaugural instance of humans obtaining records of high peak acceleration. Since then, numerous scholars have conducted extensive dynamic response analyses of structures and sites, utilizing this robust earthquake record as input ground motion time history. This dataset has been widely embraced by the seismic community, facing little dispute. As per the Codes for Seismic Design of Buildings (GB50011-2010), the seismic fortification intensity in the Tianjin area falls within the 7-degree and 8-degree zones. Therefore, for this study, the amplitude of the El Centro waves was adjusted, setting the seismic wave amplitudes to 0.1 g and 0.2 g (designated seismic waves A and B), as depicted in Fig. 1. These corresponded to the acceleration time histories for seismic intensities of VII and VIII, respectively. The analysis duration encompassed the first 15 seconds, capturing the stronger ground motion, with baseline correction applied. For the issue concerning elastic homogeneous media in semi-infinite space, the ground motion field’s value at the free surface was twice that of the incident wave field. Based on this theoretical finding, this study progressed to a practical approximation, specifying that the seismic waves at the seismic input interface should be inputted at half the value of the ground motion time history at the free bedrock. 5 Determination of calculation methods Presently, notwithstanding a variety of calculation methods available for analyzing the seismic response of engineering site soil layers [ 13 – 19 ] , the frequency domain equivalent linearization method remains the predominant approach in engineering practice, serving as an approximation for managing soil nonlinearity. In 2016, researcher Yuan and Dr. Li, alongside others [ 20 ] introduced the SOILQUAKE program, a novel method for soil layer seismic response analysis based on the equivalent linearization method. This program adeptly tackled the issue of “short, stout, and fat” results frequently encountered in the analysis of seismic response in weak soil layers. Given the focus of this study on the seismic response characteristics of soft soil, the SOILQUAKE program has been chosen as the method for analyzing the seismic response of soft soil layers. 6 Calculation results and analysis 6.1 Analysis of calculation results of actual site soil profile This study employed the actual soil profiles established in Section 3.1 as the calculation model. The seismic wave A, scaled to a magnitude of 0.1 g via the El Centro wave, served as the input ground motion. It progressed to a comparative analysis between the maximum, minimum, and average values of the dynamic shear modulus ratio and damping ratio of soft soil in the Tianjin area from Table 1 and the measured values of silty clay in Table 3 . Furthermore, a comprehensive comparative analysis was undertaken, encompassing aspects such as the shape of the response spectra and characteristic parameters of the design response spectrum. Ultimately, this article furnished recommended values for the dynamic shear modulus ratio and damping ratio for soft soil based on the analysis. Table 6 Deviation between characteristic parameters obtained from different dynamic parameters and those obtained from measured values（%） Average Maximum Minimum Characteristic period 0.99 0.99 16.83 Platform values 6.98 7.30 14.61 Analysis of Fig. 2 and Table 6 reveals the following observations: (1) The deviation in the characteristic period remained consistent at 0.99% when considering the maximum and average values of various dynamic parameters. However, the deviation markedly escalated to 16.83% when factoring in the minimum value. Consequently, the minimum value was disregarded for determining the characteristic period. (2) Upon examination of platform values, it is evident that the deviation progressively increased from the smallest to the largest values when accounting for the average, maximum, and minimum values. In summary, it is noteworthy that the response spectrum characteristic parameters derived from the minimum values significantly diverged from the actual measured values, whereas those derived from the average values exhibited the least deviation. Therefore, the average values were selected as the recommended values for the dynamic shear modulus ratio and damping ratio for soft soil in the Tianjin area in this study, as evidenced by Table 7 . Table 7 List of Recommended Values in this article Parameter Shear Strain(×10 − 4 ) 0.05 0.1 0.5 1 5 10 50 100 G/G max 0.9957 0.9915 0.9591 0.9223 0.7146 0.5643 0.2204 0.1309 λ(%) 3.47 4.30 7.02 8.63 13.18 15.19 18.65 19.48 6.2 Analysis of results for uniform single soil layer profiles based on varying thicknesses of soft surface soil In this study, we utilized ideal soil layer profiles consisting of 10 different thicknesses of soft surface soil layers, ranging from 2 m to 20 m, as established in section 3.2 , to serve as calculation models. The seismic response analysis of soil layers was conducted using the one-dimensional equivalent linearization software SOILQUAKE. For this analysis, seismic waves A and B, adjusted to intensities of 0.1 g and 0.2 g, respectively, following modulation by the El Centro waves, were employed as input ground motions to shed light on the influence of soft surface soil’s thickness on ground response spectra. Tables 4 and 5 list the parameters of soil density, shear wave velocity, dynamic shear modulus ratio, and damping ratio. The recommended values for the dynamic shear modulus ratio and damping ratio of soft soil were determined based on this study. Analyzing Figs. 3 and 4, the following observations can be made: (1) The thickness of the soft surface soil wielded a dramatic impact on the characteristic period. Under the same input ground motion, the characteristic period initially diminished with escalating layer thickness. Nevertheless, upon reaching an 8 m layer thickness, the characteristic period commenced to ascend with further increments in layer thickness. In conditions of identical layer thickness, the numerical value of the characteristic period rose with the heightened intensities of input ground motion. (2) Regarding platform values, when subjected to the same input ground motion, the platform values initially increased temporarily with increasing layer thickness. However, once the layer thickness hit 6 m, a gradual descent trend emerged. Under the same layer thickness conditions, the platform values exhibited a more complex behavior. For larger layer thicknesses (16 m, 18 m, 20 m), the platform values of seismic wave B (0.2 g) were lower than those of seismic wave A (0.1 g). Conversely, for smaller layer thicknesses (2 m, 4 m, 6 m, 8 m, 10 m, 12 m, 14 m), the platform values of seismic wave B (0.2 g) and seismic wave A (0.1 g) alternated in an increasing trend. 6.3 Validation of experimental results To address the abrupt changes in response spectrum characteristic parameters when the thickness of the soft surface soil is small (0–6 m), this study progressed to an experimental analysis using a shaking table. The shaking table featured a platform size of 1.5 m × 1.5 m, a maximum load capacity of 2000 kg, an operating frequency range of 0–60 Hz, a maximum overturning moment of 20 kN·m, a maximum eccentricity of 0.3 m, and a maximum horizontal acceleration of 2.0 g when unloaded. The input ground motions are the ones listed in Fig. 1. The dimensions of the test model box were 0.5 m × 0.5 m × 0.5 m. The model consisted of a soft soil layer atop a silty soil layer, with varying soft soil layer thicknesses for different test conditions. Detailed experimental conditions are enumerated in Table 8 , with varying combinations of the test model. The experimental results are presented in Figs. 5 and 6. Table 8 List of experimental conditions Soil layer thickness(m) Soft soilSilt Soft soilSilt Working condition one 0.05 0.45 Working condition two 0.10 0.40 Working condition three 0.15 0.35 Figure 5 and 6 suggest that the experimental results demonstrate a slight elevation compared to the calculated soil layer counterparts, albeit maintaining a consistent curve trend. Integrating both datasets, the analysis of the amplification effect of the soft surface soil on seismic motion unravels an initial rise in amplification effect with increasing thickness, followed by stabilization after reaching a certain threshold. 7 Conclusion This study pooled and systematized measured data on the dynamic shear modulus ratio and damping ratio for soft soil in the Tianjin area, laying the groundwork for an initial database. From this database, both range values and average values were calculated. Subsequently, using measured boreholes as exemplars, models were devised to discern the distinctions among response spectrum characteristic parameters acquired under various conditions of the dynamic shear modulus ratio and damping ratio, in comparison with the measured values. The analysis revealed that when averaging the dynamic shear modulus ratio and damping ratio, the resultant outcomes exhibited the least deviation from the measured values. Consequently, these average values are opted for the recommended values within this study. To investigate the influence of different soft soil layer thicknesses on the response spectrum characteristic parameters, this study established ten sets of soil layer profile models with varying thicknesses of soft surface soil. The input ground motions consisted of two adjusted El Centro waves (0.1 g and 0.2 g). The findings are as follows: (1) Under identical input ground motion, the characteristic period initially decreased with increasing layer thickness but started to rise again once the layer thickness exceeded 8 m. The overall trend indicated an augmentation in the characteristic period with layer thickness, although a short-period oscillation occurred before reaching 8 m, likely causing the temporary reduction. The platform value experienced a sharp increase with growing layer thickness until it reached 6 m, after which it stabilized within a certain range. This sharp increase was attributed to the significant amplification effect when the soft soil layer was positioned atop the ground surface. (2) For the same layer thickness conditions, the characteristic period increased as the intensity of the input ground motion rose. The behavior of the platform value was more complex: for larger layer thicknesses (16 m, 18 m, 20 m), the platform value for seismic wave B (0.2 g) was lower than that for seismic wave A (0.1 g). For smaller layer thicknesses (2 m, 4 m, 6 m, 8 m, 10 m, 12 m, 14 m), the platform values for seismic wave B (0.2 g) and seismic wave A (0.1 g) fluctuated within a certain range. To verify the accuracy of calculation results for the soil layer, experimental validation was conducted. Although the experimental results were slightly higher than the calculated results, the trends were consistent. Declarations Author Contribution Y.C. Conceptualization and wrote the main manuscript text ; Z.S.W. Formal analysis;C.G.Y.project administration;F.Y.prepared figures .All authors reviewed the manuscript. Data Availability The datasets generated and/or analysed during the current study are not publicly available due [REASON WHY DATA ARE NOT PUBLIC] but are available from the corresponding author on reasonable request. References Ministry of Housing and Urban-Rural Development of the People's Republic of China, Specification for geotechnical investigation in soft clay area(JGJ83-2011)[S].Beijing: China Architecture and Building Press,2011. Tianjin Earthquake Office, Earthquake damage caused by the Tangshan earthquake in Tianjin[M].Tianjin: Tianjin Science and Technology Press,1984. Peng Juyan, Tang Rongyu, Lv Yueju, et al. Tianjin seashore site classification and its effect on ground motion[J]. Earthquake Engineering and Engineering Vibration,2004,24(2):46–52.. Yuan Xiaoming, Sun Rui, Sun Jing, et al. Laboratory experimental study on dynamic shear modulus ratio and damping ratio of soils[J]. 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Study on the dynamic characteristics of soft soil[J]. RSC Advance,2020,10(08): 4630–4639. Feng Qiao, Jingshan Bo, Chaoyu Chang, Liang Wang, Chao Shen. Comparative Study of the Seismic Response Characteristics of Three Special Soils[J]. Applied Sciences, 2023, 13(20): 11375. People's Republic of China earthquake industry standard, Evaluation of seismic safety for engineering sites(DB001-94)[S].Beijing: Seismological Press,1994 Liao Zhengpeng. Seismic District Planning: Theory and Practice[M]. Beijing:Beijing Publishing House.1989. Liao Zhenpeng, Li Xiaojun. Equivalent Linearization Method for Seismic Response of Surface Soil[A]. Seismic District Planning(Theory and Practice). Beijing: Seismological Press, 1989,141–153. Liao Zhenpeng, Li Xiaojun. Equivalent Linearization Method for Seismic Response of Surface Soil[A]. Seismic District Planning(Theory and Practice). Beijing: Seismological Press, 198,141–153. Li Xiaojun. One-dimensional soil layer seismic response linearization calculation program[A]. Seismic District Planning(Theory and Practice). Beijing: Seismological Press, 1989.,350 – 265. Idriss I M, Son J. User’s manual for SHAKE91–A computer program for conducting equivalent linear seismic response analyses of horizontally layered soil deposits center for geotechnical modeling[R]. Department of Civil and Environmental Engineering, University of California.Davis, California, August.1992. Qi Wenhao. Study on the Comparison of Soil Layers Seismic Response Analysis Methods[D]. Harbin.Institute of Engineering Mechanics, China EarthquakeAdministration.2004. Hashash Y.M.A. DEEPSOIL V3.7 User Manual and Tutorial [M]. USA: [s.n.]. 2009. Yuan Xiaoming, Li Ruishan, Sun Rui. A new generation method for earthquake response analysis of soil layers[J].CHINA CIVIL ENGINEERING JOURNAL,2016,49(10):95–105 + 122. Additional Declarations No competing interests reported. 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Gao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuUlEQVRIiWNgGAWjYLCChIoaOTb25gMkaHlw5pgxH8+xBOJ1MD5sY06cJ5GjQJxy+YjcYw8S2NjS2xhyGBh+VGwjrMXwRl66QQKPTG4bw9kDjD1nbhOhZXaOmUSCBFtuG2NfAjNjG9FaDJjT2Zh5DIjTIi8N0pLADPQOsVoM5N8B/XLgmGEbD1vCQaL8It9z9tjDn/9q5OXnPz744EcFMbYc4GGDcw4QVg+ypQFJyygYBaNgFIwCrAAA++I6NqbBKxYAAAAASUVORK5CYII=","orcid":"","institution":"Tianjin Earthquake Agency","correspondingAuthor":true,"prefix":"","firstName":"Wuping","middleName":"","lastName":"Gao","suffix":""},{"id":333021228,"identity":"b05cea6b-9bf5-4529-9d5a-eb610dbcf608","order_by":2,"name":"Zhisheng Wang","email":"","orcid":"","institution":"Tianjin Earthquake Agency","correspondingAuthor":false,"prefix":"","firstName":"Zhisheng","middleName":"","lastName":"Wang","suffix":""},{"id":333021229,"identity":"efbea992-7106-4a78-b933-c7f6d9d48974","order_by":3,"name":"Chengguo Yan","email":"","orcid":"","institution":"Tianjin Earthquake Agency","correspondingAuthor":false,"prefix":"","firstName":"Chengguo","middleName":"","lastName":"Yan","suffix":""},{"id":333021230,"identity":"5f8d6e80-c0ae-4a67-a3d8-ffd08f59a54c","order_by":4,"name":"Fei Yang","email":"","orcid":"","institution":"Tianjin Earthquake Agency","correspondingAuthor":false,"prefix":"","firstName":"Fei","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2024-07-03 02:55:58","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4677183/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4677183/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":61520113,"identity":"50624f38-92ad-4048-8d1b-ba21744e7a35","added_by":"auto","created_at":"2024-07-31 17:10:05","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":114902,"visible":true,"origin":"","legend":"\u003cp\u003eTime history curve of El Centro wave after amplitude modulation\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4677183/v1/1d304f5af10d05039f295a4b.png"},{"id":61520116,"identity":"1f332b1c-d855-423d-b182-4de2581b58e1","added_by":"auto","created_at":"2024-07-31 17:10:05","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":59095,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of design response spectra\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4677183/v1/7e864cef059596097ecdd338.png"},{"id":61520526,"identity":"0a888172-0f62-45c3-a9fa-21da0b91c318","added_by":"auto","created_at":"2024-07-31 17:18:05","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":36414,"visible":true,"origin":"","legend":"\u003cp\u003eCharacteristic period under different surface thickness conditions of soft soil\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4677183/v1/825fa6cfa5a6875259b53929.png"},{"id":61520114,"identity":"96f135ce-1638-422f-b8a2-1b381e001eea","added_by":"auto","created_at":"2024-07-31 17:10:05","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":47772,"visible":true,"origin":"","legend":"\u003cp\u003ePlatform values under different soft soil surface thickness conditions\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4677183/v1/f78a2fabe9ec4925b306d807.png"},{"id":61520117,"identity":"1a9900db-71ad-40cc-80e4-e05d03d27f1d","added_by":"auto","created_at":"2024-07-31 17:10:05","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":32288,"visible":true,"origin":"","legend":"\u003cp\u003eCharacteristic period under different surface thickness conditions of soft soil\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4677183/v1/90ddf35737858e937f2cd03e.png"},{"id":61520527,"identity":"39b69807-79a3-4d55-b336-7716e2a74585","added_by":"auto","created_at":"2024-07-31 17:18:05","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":37253,"visible":true,"origin":"","legend":"\u003cp\u003ePlatform values under different soft soil surface thickness conditions\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4677183/v1/16cb20ef40dcec86e9aeb9f6.png"},{"id":101835680,"identity":"aa433701-52dc-4da6-9fcc-df0b46b7dd43","added_by":"auto","created_at":"2026-02-04 07:25:58","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1213892,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4677183/v1/a1bc3c79-73cc-45ec-a3bb-dead9d11e8c0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Influence of Soft Surface Soil on Site Seismic Response in Tianjin Area","fulltext":[{"header":"Introduction","content":"\u003cp\u003eSoft soil, a type of loosely consolidated fine-grained soil, falls under the category of special soils. Typically characterized by a moisture content surpassing the liquid limit, a natural void ratio exceeding 1.0, low strength, significant deformation, and heightened sensitivity, it arises from Quaternary fluvial deposition, commonly near bodies of water such as rivers, lakes, and seas. Its composition primarily encompasses silt, silty soil, peat, and peaty soil, often resulting in substantial or irregular settlement of structures. When subjected to seismic forces, it can induce engineering hazards like soft soil liquefaction. As outlined in the \u003cem\u003eSpecification for Geotechnical Investigation in Soft Clay Area\u003c/em\u003e (JGJ83\u0026mdash;2011) \u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e, when seismic fortification intensity in a specific region reaches 7 degrees or higher, evaluating the potential for soft soil liquefaction becomes imperative in areas with thick soft soil layer. Consequently, soft soil generally proves unsuitable for serving as foundation soil for buildings. Nonetheless, in light of rapid urban development and diminishing available land for construction in coastal areas, a magnitude of buildings have been erected atop soft soil layers in recent years.\u003c/p\u003e \u003cp\u003eThe dynamic shear modulus ratio and damping ratio are critical parameters in the dynamic analysis of soft soil. Typically, these parameters are derived from indoor triaxial tests or resonant column tests. However, the high sensitivity and poor disturbance resistance inherent in soft soil often led to significant errors throughout the entire process, from sample preparation to testing in indoor experiments, resulting in biased test results.\u003c/p\u003e \u003cp\u003eSoft soil presents distinctive seismic response characteristics when juxtaposed with typical soils, primarily manifested in soft soil sites and interlayers. Huang et al. \u003csup\u003e[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/sup\u003e scrutinized the impact of soft soil interlayers on ground acceleration across various regions, revealing that when soft soil interlayers are positioned at the base of bedrock, the amplitude of the peak point of the ground acceleration response spectrum is minimal. Meanwhile, Peng and Lv \u003csup\u003e[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/sup\u003e elaborated on the seismic response of typical soft soil sites in Binhai New Area, Tianjin, as well as Yantai, Shandong, uncovering a notable amplification effect of ground motion within such sites, with peak acceleration amplification factors reaching up to 1.9 times. Moreover, scholars \u003csup\u003e[\u003cspan additionalcitationids=\"CR5 CR6 CR7 CR8 CR9 CR10\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/sup\u003e have conducted seismic response analyses on typical soft soil sites in diverse regions, indicating that the positioning of soft soil layers yields varying effects on seismic responses. Generally, soft soil layers demonstrate considerable amplification effects when positioned atop the ground surface, whereas some isolation effects may be observed when they are situated near the bedrock at the base.\u003c/p\u003e \u003cp\u003eExpanding upon prior research, this study plunges into the dynamic characteristics of soft soil in the Tianjin area. Its primary emphasis lies in examining how the thickness of soft surface soil affects seismic effects within the region. Additionally, the study offers recommended values for the dynamic shear modulus ratio and damping ratio of soft soil through statistical analysis.\u003c/p\u003e "},{"header":"1 Overview of the study area","content":"\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e \u003cp\u003eIn China, based on the engineering properties and distribution areas of soft soil, it is roughly divided into three regions \u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e: Zone I, Zone II, and Zone III. The boundary between Zone I and Zone II soft soil extends from the eastern Qinling Mountains to the northern coastline of Lianyungang. The boundary between Zone II and Zone III soft soil runs from the Miaoling Mountains, eastward along the Nanling Mountains, to the coastline near Putian.\u003c/p\u003e \u003cp\u003eSituated on the western fringe of Bohai Bay, Tianjin boasts a silty coastline stretching over 150 kilometers, shaped by Late Pleistocene marine transgression deposits, presenting a quintessential example of soft soil in Zone I \u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e. In recent years, urban expansion has led to a proliferation of public and civil structures erected on soft soil foundations. Hence, this study shifts its focus to Tianjin\u0026rsquo;s soft soil as its research subject. Here are the principal physical and mechanical properties of the soft soil in the study area:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eNatural moisture content varies between 53.20% and 97.20%, with an average of 63.95%.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePorosity ranges from 1.46 to 2.63, averaging at 1.77.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eDensity spans from 1.48 g/cm\u003csup\u003e3\u003c/sup\u003e to 1.73 g/cm\u003csup\u003e3\u003c/sup\u003e, with an average of 1.62 g/cm\u003csup\u003e3\u003c/sup\u003e.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eLiquid limit ranges from 33.60\u0026ndash;55.60%, averaging at 50.41%.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePlastic limit varies between 19.10% and 27.90%, with an average of 25.80%.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eLiquidity index varies between 1.27 and 3.29, with an average of 1.57.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePlasticity index ranges from 14.50 to 27.70, averaging at 24.40.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eCompression modulus ranges from 1.46 MPa to 3.96 MPa, with an average of 2.05 MPa.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eCohesion spans from 2.70 kPa to 8.25 kPa, averaging at 5.17 kPa.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eInternal friction angle varies from 0.00\u0026deg; to 4.84\u0026deg;, with an average of 0.90\u0026deg;.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"2 Data sources and analysis methods","content":"\u003cp\u003eThis study compiled and analyzed data from 134 boreholes within the Tianjin area, bolstered by three additional boreholes featuring direct measurements. The primary objective was to gather and systematize information pertaining to the dynamic shear modulus ratio and damping ratio in soft soil. Leveraging this foundational data, the study proceeded to conduct an analysis aimed at delineating the range and average values of the dynamic shear modulus ratio and damping ratio in the study area, as detailed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The supplementary borehole experimental data were acquired by the Institute of Disaster Prevention, capitalizing on a dual-directional dynamic triaxial testing apparatus manufactured by GCTS, USA, with the model STX-200.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eList of Range Values of Dynamic Shear Modulus Ratio and Damping Ratio for Typical Soft Soil in Tianjin Area\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"17\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c16\" colnum=\"16\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c17\" colnum=\"17\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"15\" nameend=\"c17\" namest=\"c3\"\u003e \u003cp\u003eShear Strain (\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c17\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMaximum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG/G\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9995\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003e0.9990\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e0.9950\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.9901\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e0.9522\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c13\" namest=\"c12\"\u003e \u003cp\u003e0.9088\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c15\" namest=\"c14\"\u003e \u003cp\u003e0.6659\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e \u003cp\u003e0.5210\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eλ(%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003e7.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e9.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e11.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e16.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c13\" namest=\"c12\"\u003e \u003cp\u003e19.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c15\" namest=\"c14\"\u003e \u003cp\u003e32.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e \u003cp\u003e32.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMinimum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG/G\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9849\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003e0.9703\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e0.8673\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.7656\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e0.3952\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c13\" namest=\"c12\"\u003e \u003cp\u003e0.2462\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c15\" namest=\"c14\"\u003e \u003cp\u003e0.0613\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e \u003cp\u003e0.0316\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eλ(%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003e0.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e1.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e4.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c13\" namest=\"c12\"\u003e \u003cp\u003e6.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c15\" namest=\"c14\"\u003e \u003cp\u003e11.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e \u003cp\u003e13.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG/G\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9957\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003e0.9915\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e0.9591\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.9223\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e0.7146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c13\" namest=\"c12\"\u003e \u003cp\u003e0.5643\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c15\" namest=\"c14\"\u003e \u003cp\u003e0.2204\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e \u003cp\u003e0.1309\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eλ(%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003e4.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e7.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e8.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e13.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c13\" namest=\"c12\"\u003e \u003cp\u003e15.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c15\" namest=\"c14\"\u003e \u003cp\u003e18.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e \u003cp\u003e19.48\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e "},{"header":"3 Establishment of on-site geological profiles","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e3.1 Actual on-site soil profiles\u003c/h2\u003e \u003cp\u003eTo adequately factor in the nonlinear characteristics of site soils and their influence on seismic response calculations, this study selected seismic borehole data from engineering investigations in Tianjin. The borehole information is listed in Tables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eList of soft soil layers\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSoil\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBuried depth\u003c/p\u003e \u003cp\u003e(m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eShear wave velocity\u003c/p\u003e \u003cp\u003e(m/s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDensity\u003c/p\u003e \u003cp\u003e(g/cm\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSilty Clay\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e134.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eClay\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e16.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e139.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eClay\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e22.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e204.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSilt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e32.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e293.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eClay\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e36.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e285.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSilt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e49.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e373.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.09\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eClay\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e53.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e365.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSand-Silt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e63.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e492.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eT9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eClay\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e69.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e442.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBedrock\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSand-Silt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e72.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e526.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe list of dynamic shear modulus ratio and damping ratio of each soil layer in the seismic response analysis model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSoil\u003c/p\u003e \u003cp\u003eNumber\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"8\" nameend=\"c10\" namest=\"c3\"\u003e \u003cp\u003eShear Strain(\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eT1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG/G\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9963\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9926\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9639\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9303\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.7275\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.5717\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.2107\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.1178\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eλ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0226\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0313\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e 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\u003cp\u003e0.7383\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.3607\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.2201\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eλ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0265\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0332\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0560\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0699\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.1135\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.1360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.1822\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.1944\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eT8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG/G\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9962\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9924\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9633\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9293\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.7243\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.5678\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.2081\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.1161\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eλ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0265\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0475\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0606\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.1001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.1182\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.1479\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.1540\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eT9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG/G\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9966\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9932\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9670\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9061\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.7256\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.5344\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.2266\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.1278\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eλ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0314\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0550\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0674\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.1131\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.1334\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.1676\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.1748\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eBedrock\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG/G\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9961\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9923\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9628\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.6813\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.5085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.2055\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.1145\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eλ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0187\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0247\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0470\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0613\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.1064\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.1276\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.1628\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.1750\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e3.2 Profiles with different thicknesses of soft surface soil\u003c/h2\u003e \u003cp\u003eTo elucidate the influence of varying thicknesses of soft surface soil on ground response spectra, this study established profiles comprising ten different thicknesses of soft soil layers. The thicknesses of the soft soil layers were 2 m, 4 m, 6 m, 8 m, 10 m, 12 m, 14 m, 16 m, 18 m, and 20 m. For ease of comparison, the thickness of these ten sets of soil layer profiles was standardized to 40 m. Beneath the soft soil layer lay a silty layer, with the bottom layer consisting of bedrock. The parameters for each profile are presented in Tables\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, where the dynamic shear modulus ratio and damping ratio for soft soil are derived from recommended values obtained through actual soil layer calculations in this study, while other parameters are referenced from actual site data.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDynamic shear modulus ratio and damping ratio of bedrock and silt layer profiles\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" morerows=\"1\" nameend=\"c2\" namest=\"c1\" rowspan=\"2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"8\" nameend=\"c10\" namest=\"c3\"\u003e \u003cp\u003eShear Strain(\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eBedrock\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG/G\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.0000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.0000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eλ(%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e3.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e4.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSilt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eG/G\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9968\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9936\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9688\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.9394\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.7562\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.6079\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.2367\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.1342\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eλ(%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e10.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e12.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e16.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e17.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePhysical and Mechanical Parameters of Soil Layer in Profile\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDensity(g/cm\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eShear wave velocity(m/s)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoft Soil\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e128\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSilt\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e270\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBedrock\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e "},{"header":"4 Selection of input ground motion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003cp\u003eIn 1940, the Empire Valley earthquake, with a magnitude of 7.1, struck the United States, yielding the El Centro waves, which marked the inaugural instance of humans obtaining records of high peak acceleration. Since then, numerous scholars have conducted extensive dynamic response analyses of structures and sites, utilizing this robust earthquake record as input ground motion time history. This dataset has been widely embraced by the seismic community, facing little dispute. As per the \u003cem\u003eCodes for Seismic Design of Buildings\u003c/em\u003e (GB50011-2010), the seismic fortification intensity in the Tianjin area falls within the 7-degree and 8-degree zones. Therefore, for this study, the amplitude of the El Centro waves was adjusted, setting the seismic wave amplitudes to 0.1 g and 0.2 g (designated seismic waves A and B), as depicted in Fig.\u0026nbsp;1. These corresponded to the acceleration time histories for seismic intensities of VII and VIII, respectively. The analysis duration encompassed the first 15 seconds, capturing the stronger ground motion, with baseline correction applied.\u003c/p\u003e \u003cp\u003eFor the issue concerning elastic homogeneous media in semi-infinite space, the ground motion field\u0026rsquo;s value at the free surface was twice that of the incident wave field. Based on this theoretical finding, this study progressed to a practical approximation, specifying that the seismic waves at the seismic input interface should be inputted at half the value of the ground motion time history at the free bedrock.\u003c/p\u003e "},{"header":"5 Determination of calculation methods","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n\u003cp\u003ePresently, notwithstanding a variety of calculation methods available for analyzing the seismic response of engineering site soil layers \u003csup\u003e[\u003cspan additionalcitationids=\"CR14 CR15 CR16 CR17 CR18\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e, the frequency domain equivalent linearization method remains the predominant approach in engineering practice, serving as an approximation for managing soil nonlinearity. In 2016, researcher Yuan and Dr. Li, alongside others \u003csup\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e introduced the SOILQUAKE program, a novel method for soil layer seismic response analysis based on the equivalent linearization method. This program adeptly tackled the issue of \u0026ldquo;short, stout, and fat\u0026rdquo; results frequently encountered in the analysis of seismic response in weak soil layers. Given the focus of this study on the seismic response characteristics of soft soil, the SOILQUAKE program has been chosen as the method for analyzing the seismic response of soft soil layers.\u003c/p\u003e \u003c/div\u003e "},{"header":"6 Calculation results and analysis","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e6.1 Analysis of calculation results of actual site soil profile\u003c/h2\u003e \u003cp\u003eThis study employed the actual soil profiles established in Section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e as the calculation model. The seismic wave A, scaled to a magnitude of 0.1 g via the El Centro wave, served as the input ground motion. It progressed to a comparative analysis between the maximum, minimum, and average values of the dynamic shear modulus ratio and damping ratio of soft soil in the Tianjin area from Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and the measured values of silty clay in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Furthermore, a comprehensive comparative analysis was undertaken, encompassing aspects such as the shape of the response spectra and characteristic parameters of the design response spectrum. Ultimately, this article furnished recommended values for the dynamic shear modulus ratio and damping ratio for soft soil based on the analysis.\u003c/p\u003e \u003cp\u003eTable 6 Deviation between characteristic parameters obtained from different dynamic parameters and those obtained from measured values（%）\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"553\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"25%\" valign=\"top\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003eAverage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003eMaximum\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003eMinimum\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25%\" valign=\"top\"\u003e\n \u003cp\u003eCharacteristic period\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\" valign=\"top\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\" valign=\"top\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\" valign=\"top\"\u003e\n \u003cp\u003e16.83\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25%\" valign=\"top\"\u003e\n \u003cp\u003ePlatform values\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\" valign=\"top\"\u003e\n \u003cp\u003e6.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\" valign=\"top\"\u003e\n \u003cp\u003e7.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\" valign=\"top\"\u003e\n \u003cp\u003e14.61\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e \u003cp\u003eAnalysis of Fig.\u0026nbsp;2 and Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e reveals the following observations:\u003c/p\u003e \u003cp\u003e(1) The deviation in the characteristic period remained consistent at 0.99% when considering the maximum and average values of various dynamic parameters. However, the deviation markedly escalated to 16.83% when factoring in the minimum value. Consequently, the minimum value was disregarded for determining the characteristic period.\u003c/p\u003e \u003cp\u003e(2) Upon examination of platform values, it is evident that the deviation progressively increased from the smallest to the largest values when accounting for the average, maximum, and minimum values.\u003c/p\u003e \u003cp\u003eIn summary, it is noteworthy that the response spectrum characteristic parameters derived from the minimum values significantly diverged from the actual measured values, whereas those derived from the average values exhibited the least deviation. Therefore, the average values were selected as the recommended values for the dynamic shear modulus ratio and damping ratio for soft soil in the Tianjin area in this study, as evidenced by Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eList of Recommended Values in this article\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"16\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c16\" colnum=\"16\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"15\" nameend=\"c16\" namest=\"c2\"\u003e \u003cp\u003eShear Strain(\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c11\" namest=\"c9\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c13\" namest=\"c12\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c15\" namest=\"c14\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c16\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eG/G\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e0.9957\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0.9915\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e0.9591\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e0.9223\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.7146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e0.5643\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e0.2204\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e0.1309\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eλ(%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e3.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e4.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e7.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e8.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e13.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003e15.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c14\" namest=\"c13\"\u003e \u003cp\u003e18.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c16\" namest=\"c15\"\u003e \u003cp\u003e19.48\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e6.2 Analysis of results for uniform single soil layer profiles based on varying thicknesses of soft surface soil\u003c/b\u003e \u003c/p\u003e \u003cp\u003eIn this study, we utilized ideal soil layer profiles consisting of 10 different thicknesses of soft surface soil layers, ranging from 2 m to 20 m, as established in section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e, to serve as calculation models. The seismic response analysis of soil layers was conducted using the one-dimensional equivalent linearization software SOILQUAKE. For this analysis, seismic waves A and B, adjusted to intensities of 0.1 g and 0.2 g, respectively, following modulation by the El Centro waves, were employed as input ground motions to shed light on the influence of soft surface soil\u0026rsquo;s thickness on ground response spectra. Tables\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e list the parameters of soil density, shear wave velocity, dynamic shear modulus ratio, and damping ratio. The recommended values for the dynamic shear modulus ratio and damping ratio of soft soil were determined based on this study.\u003c/p\u003e \u003cp\u003eAnalyzing Figs.\u0026nbsp;3 and 4, the following observations can be made:\u003c/p\u003e \u003cp\u003e(1) The thickness of the soft surface soil wielded a dramatic impact on the characteristic period. Under the same input ground motion, the characteristic period initially diminished with escalating layer thickness. Nevertheless, upon reaching an 8 m layer thickness, the characteristic period commenced to ascend with further increments in layer thickness. In conditions of identical layer thickness, the numerical value of the characteristic period rose with the heightened intensities of input ground motion.\u003c/p\u003e \u003cp\u003e(2) Regarding platform values, when subjected to the same input ground motion, the platform values initially increased temporarily with increasing layer thickness. However, once the layer thickness hit 6 m, a gradual descent trend emerged. Under the same layer thickness conditions, the platform values exhibited a more complex behavior. For larger layer thicknesses (16 m, 18 m, 20 m), the platform values of seismic wave B (0.2 g) were lower than those of seismic wave A (0.1 g). Conversely, for smaller layer thicknesses (2 m, 4 m, 6 m, 8 m, 10 m, 12 m, 14 m), the platform values of seismic wave B (0.2 g) and seismic wave A (0.1 g) alternated in an increasing trend.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e6.3 Validation of experimental results\u003c/h2\u003e \u003cp\u003eTo address the abrupt changes in response spectrum characteristic parameters when the thickness of the soft surface soil is small (0\u0026ndash;6 m), this study progressed to an experimental analysis using a shaking table. The shaking table featured a platform size of 1.5 m \u0026times; 1.5 m, a maximum load capacity of 2000 kg, an operating frequency range of 0\u0026ndash;60 Hz, a maximum overturning moment of 20 kN\u0026middot;m, a maximum eccentricity of 0.3 m, and a maximum horizontal acceleration of 2.0 g when unloaded. The input ground motions are the ones listed in Fig.\u0026nbsp;1. The dimensions of the test model box were 0.5 m \u0026times; 0.5 m \u0026times; 0.5 m. The model consisted of a soft soil layer atop a silty soil layer, with varying soft soil layer thicknesses for different test conditions. Detailed experimental conditions are enumerated in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, with varying combinations of the test model. The experimental results are presented in Figs.\u0026nbsp;5 and 6.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eList of experimental conditions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eSoil layer thickness(m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSoft soilSilt\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSoft soilSilt\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWorking condition one\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWorking condition two\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWorking condition three\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFigure 5 and 6 suggest that the experimental results demonstrate a slight elevation compared to the calculated soil layer counterparts, albeit maintaining a consistent curve trend. Integrating both datasets, the analysis of the amplification effect of the soft surface soil on seismic motion unravels an initial rise in amplification effect with increasing thickness, followed by stabilization after reaching a certain threshold.\u003c/p\u003e \u003c/div\u003e "},{"header":"7 Conclusion","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003cp\u003eThis study pooled and systematized measured data on the dynamic shear modulus ratio and damping ratio for soft soil in the Tianjin area, laying the groundwork for an initial database. From this database, both range values and average values were calculated. Subsequently, using measured boreholes as exemplars, models were devised to discern the distinctions among response spectrum characteristic parameters acquired under various conditions of the dynamic shear modulus ratio and damping ratio, in comparison with the measured values. The analysis revealed that when averaging the dynamic shear modulus ratio and damping ratio, the resultant outcomes exhibited the least deviation from the measured values. Consequently, these average values are opted for the recommended values within this study.\u003c/p\u003e \u003cp\u003eTo investigate the influence of different soft soil layer thicknesses on the response spectrum characteristic parameters, this study established ten sets of soil layer profile models with varying thicknesses of soft surface soil. The input ground motions consisted of two adjusted El Centro waves (0.1 g and 0.2 g). The findings are as follows:\u003c/p\u003e \u003cp\u003e(1) Under identical input ground motion, the characteristic period initially decreased with increasing layer thickness but started to rise again once the layer thickness exceeded 8 m. The overall trend indicated an augmentation in the characteristic period with layer thickness, although a short-period oscillation occurred before reaching 8 m, likely causing the temporary reduction. The platform value experienced a sharp increase with growing layer thickness until it reached 6 m, after which it stabilized within a certain range. This sharp increase was attributed to the significant amplification effect when the soft soil layer was positioned atop the ground surface.\u003c/p\u003e \u003cp\u003e(2) For the same layer thickness conditions, the characteristic period increased as the intensity of the input ground motion rose. The behavior of the platform value was more complex: for larger layer thicknesses (16 m, 18 m, 20 m), the platform value for seismic wave B (0.2 g) was lower than that for seismic wave A (0.1 g). For smaller layer thicknesses (2 m, 4 m, 6 m, 8 m, 10 m, 12 m, 14 m), the platform values for seismic wave B (0.2 g) and seismic wave A (0.1 g) fluctuated within a certain range.\u003c/p\u003e \u003cp\u003eTo verify the accuracy of calculation results for the soil layer, experimental validation was conducted. Although the experimental results were slightly higher than the calculated results, the trends were consistent.\u003c/p\u003e \u003c/div\u003e "},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eY.C. Conceptualization and wrote the main manuscript text ; Z.S.W. Formal analysis;C.G.Y.project administration;F.Y.prepared figures .All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated and/or analysed during the current study are not publicly available due [REASON WHY DATA ARE NOT PUBLIC] but are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMinistry of Housing and Urban-Rural Development of the People's Republic of China, Specification for geotechnical investigation in soft clay area(JGJ83-2011)[S].Beijing: China Architecture and Building Press,2011.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTianjin Earthquake Office, Earthquake damage caused by the Tangshan earthquake in Tianjin[M].Tianjin: Tianjin Science and Technology Press,1984.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePeng Juyan, Tang Rongyu, Lv Yueju, et al. Tianjin seashore site classification and its effect on ground motion[J]. Earthquake Engineering and Engineering Vibration,2004,24(2):46\u0026ndash;52..\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYuan Xiaoming, Sun Rui, Sun Jing, et al. Laboratory experimental study on dynamic shear modulus ratio and damping ratio of soils[J]. Earthquake Engineering and Engineering Vibration,2000,(04)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMiu Linchang, Soft Soil Mechanical Properties and Engineering Practice[M].Beijing: Science Press,2012.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBo Jingshan, Li Xiuling, Liu Hongshuai. Effects of soil layer construction on peak accelerations of ground motions[J].Earthquake Engineering and Engineering Vibration,2003(03):35\u0026ndash;40.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBo Jingshan, Li Xiuling, Liu Dedong, et al. Effects of soil layer construction on platform value of response spectra[J].Earthquake Engineering and Engineering Vibration,2003(04):29\u0026ndash;33.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBo Jingshan, Li Xiuling, Liu Dedong, et al. Effects of soil layer construction on characteristic periods of response spectra[J].Earthquake Engineering and Engineering Vibration,2003(05):42\u0026ndash;45.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLAN Jing-yan, BO Jing-shan, LV Yue-jun. Study on the Effect of Shear Wave Velocity on the Design Spectrum[J]. Technology for Earthquake Disaster Prevention, 2007, (01):19\u0026ndash;24.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFeng Qiao, Jingshan Bo, Wenhao Qi, Liang Wang, Chaoyu Chang, Zhaopeng Zhang and Jing Wang. Study on the dynamic characteristics of soft soil[J]. RSC Advance,2020,10(08): 4630\u0026ndash;4639.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFeng Qiao, Jingshan Bo, Chaoyu Chang, Liang Wang, Chao Shen. Comparative Study of the Seismic Response Characteristics of Three Special Soils[J]. Applied Sciences, 2023, 13(20): 11375.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePeople's Republic of China earthquake industry standard, Evaluation of seismic safety for engineering sites(DB001-94)[S].Beijing: Seismological Press,1994\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiao Zhengpeng. Seismic District Planning: Theory and Practice[M]. Beijing:Beijing Publishing House.1989.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiao Zhenpeng, Li Xiaojun. Equivalent Linearization Method for Seismic Response of Surface Soil[A]. Seismic District Planning(Theory and Practice). Beijing: Seismological Press, 1989,141\u0026ndash;153.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiao Zhenpeng, Li Xiaojun. Equivalent Linearization Method for Seismic Response of Surface Soil[A]. Seismic District Planning(Theory and Practice). Beijing: Seismological Press, 198,141\u0026ndash;153.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi Xiaojun. One-dimensional soil layer seismic response linearization calculation program[A]. Seismic District Planning(Theory and Practice). Beijing: Seismological Press, 1989.,350\u0026thinsp;\u0026ndash;\u0026thinsp;265.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIdriss I M, Son J. User\u0026rsquo;s manual for SHAKE91\u0026ndash;A computer program for conducting equivalent linear seismic response analyses of horizontally layered soil deposits center for geotechnical modeling[R]. Department of Civil and Environmental Engineering, University of California.Davis, California, August.1992.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQi Wenhao. Study on the Comparison of Soil Layers Seismic Response Analysis Methods[D]. Harbin.Institute of Engineering Mechanics, China EarthquakeAdministration.2004.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHashash Y.M.A. DEEPSOIL V3.7 User Manual and Tutorial [M]. USA: [s.n.]. 2009.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYuan Xiaoming, Li Ruishan, Sun Rui. A new generation method for earthquake response analysis of soil layers[J].CHINA CIVIL ENGINEERING JOURNAL,2016,49(10):95\u0026ndash;105\u0026thinsp;+\u0026thinsp;122.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Soft soil site, Input ground motion, Soil stratum structure, Influence analysis","lastPublishedDoi":"10.21203/rs.3.rs-4677183/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4677183/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSoft soil is a prevalent type of special soil, boasting mechanical characteristics like low strength, significant deformation, and heightened sensitivity. Engineering-wise, it often poses hazards such as settlement and uneven subsidence when subjected to seismic forces. Moreover, the substantial impact of soft soil on seismic events has been widely recognized. Investigations into the seismic response characteristics of soft soil primarily concentrate on two key aspects: the presence of soft soil in the form of interlayers and soft soil sites. By conducting a statistical analysis of dynamic parameters pertaining to soft soil in the Tianjin area, this study provides recommended values for such parameters in the area. Subsequently, ten distinct models of soft soil strata with varying layer thickness are established to examine the influence of soft surface soil\u0026rsquo;s thickness on characteristic parameters of site ground response spectra. This research furnishes valuable insights for seismic design within the study area.\u003c/p\u003e","manuscriptTitle":"Influence of Soft Surface Soil on Site Seismic Response in Tianjin Area","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-31 17:10:00","doi":"10.21203/rs.3.rs-4677183/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"48bbf2dc-4ea2-48f7-ae29-289abebbac15","owner":[],"postedDate":"July 31st, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":35257552,"name":"Earth and environmental sciences/Natural hazards"},{"id":35257553,"name":"Earth and environmental sciences/Solid earth sciences/Seismology"}],"tags":[],"updatedAt":"2026-02-04T07:25:33+00:00","versionOfRecord":[],"versionCreatedAt":"2024-07-31 17:10:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4677183","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4677183","identity":"rs-4677183","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}