# Study on the Seismic Effect of the Interbedded Soil Layer in the Yinchuan Alluvial Plain

Authors: Shun Yang; Xin Han; Qiyun Lei; Sihan Yu; Chao Liu
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

This paper presents a numerical analysis of two types of representative site profiles in the Yinchuan Plain under earthquake loading. The analyzed soil profiles, based on borehole investigations performed over the years, are used to explore the seismic response of the sites in this area. In total, eleven stratified soil models are used in this study, which can be grouped into two categories: a single interbedded soil model and multiple interbedded soil model. A one-dimensional equivalent linearization method is applied to evaluate the seismic response of different soil models under four exceeding probabilities in terms of peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), and spectral acceleration (Sa). The results show that the significant amplification effect of PGA occurs in rare and extremely rare earthquakes, with an amplification ratio of 1.4∼1.7 when the single silty clay layer is located at the model ground. In this scenario, the spectral acceleration is amplified at a period of approximately 1.0 s. For the multilayered soil cases, the amplification effect tends to decrease, whereas the characteristic periods increase with increasing numbers of soil layers and the ground acceleration is deamplified under a high motion intensity when the number of soil layers is ≥ 5. This study, to a certain degree, has reference value for seismic microzonation in this area.


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## Body

## 1. Introduction

The Yinchuan alluvial plain is located in the middle part of the Yellow River Basin. The thickness of the Quaternary sediments in the plain can reach thousands of meters. The interbedded stratigraphic structure is widely developed within 100 meters in the near surface and is mainly interbedded with silty clay and fine sand. On the other hand, active faults have developed in this plain area, and strong earthquakes have occurred throughout history, such as the 1709 PingluoM 8 earthquake. Recently, with the policy that supports Ningxia in building a pilot zone for ecological protection and high-quality development of the Yellow River Basin, large numbers of infrastructures, industrial parks, and other projects have been built on the Yinchuan Plain. One of the important steps is thus to evaluate the seismic risk of this area and to estimate the amplitude of ground motions to reduce earthquake-induced disasters. Therefore, research on seismic effects on the interbedded soil layer in the Yinchuan alluvial plain can provide a reference value for engineering seismic design and disaster prevention in the Yinchuan Plain.In 1928, Bo et al. [1] realized the importance of site conditions on the site seismic response when analyzing the seismic damage to buildings during the 1906 San Francisco earthquake. This finding has been shown by the following earthquakes: the 1923 Kanto earthquake in Japan, 1967 Venezuela earthquake, 1968 and 1970 Manila earthquakes in the Philippines, 1975 Haicheng earthquake in China, 1976 Tangshan earthquake, 1985 Mexico earthquake, and 2008 Wenchuan earthquake. In general, site conditions refer to local geological conditions, such as the overlying soil layer, landforms, and fracture zone near the surface of the site. With the development of strong earthquake observations and theoretical studies, numerous studies have shown that the seismic effect at the site is closely related to the soil properties, soil structures, overburden thickness, motion intensities, and other parameters. Essentially, the effect of site conditions on earthquake damage is the result of significant amplification or attenuation of the ground motion that comes from the bedrock. In recent years, the effect of near-surface soil conditions on ground motions has received increasing attention, and strong-motion observations demonstrate that the amplification effect of the surface ground motion is more evident in soft to medium-hard clay and sandy soil grounds than in hard soil conditions. In addition, the amplification effect has a large range of periods for soft to medium-hard grounds, generally in the range of 0.3∼1.1 s [1]. In contrast, the surface spectral acceleration for the hard soil site shows a significant amplification in the higher frequency range. Using a one-dimensional equivalent linearization method, Bo et al. [2] investigated the influence of local site conditions on the peak values and the spectral characteristics of ground motion. Bo et al. [2] summarized some recent advances in seismic site effects and further analyzed the influence of different soil structures on the characteristic period of the surface acceleration response spectrum based on several typical site profiles. Chen and Chen [3] conducted a numerical analysis on the influence of the burial depth and thickness of a soft soil layer on the ground motion at a deep site. The analysis showed that, with a special sediment thickness or input ground motion, the amplification effect decreases as the softness of the surface soil layer increases, and the variations in the peak ground accelerations and amplification ratios are not evident when a limit thickness is reached. Interestingly, the deamplification effect of ground motions can be observed when a very thick soft soil layer is located at the ground, acting as a natural damper. Zhou et al. [4] demonstrated that the thickness of a hard interlayer also has an obvious influence on the peak ground acceleration and spectral acceleration, and the presence of a hard interlayer can reduce the soil nonlinearity. Although some research on seismic site effects has been carried out from various aspects (e.g., [5–20]), few reports on the effect of interbedded stratigraphic structure on seismic responses at sites in alluvial plains are available.


## 2. Soil Model

Soil is a strongly nonlinear material, and the greater the ground motion is, the stronger the nonlinearity. The equivalent linearization method is one of the main methods to estimate the nonlinear characteristics of a site under seismic action. The basic idea is to treat the soil as a viscoelastic material; the overall dynamics have approximately the same effect, with an equivalent shear modulus and equivalent damping ratio under different strain amplitudes; the shear moduli and damping ratios are replaced, and the nonlinear problem becomes a linear problem, usually by analyzing the fluctuation in the frequency domain or when time domain iterations are complete. In essence, the equivalent linearization method is still a linear method that simulates the nonlinear constitutive history of soil with only the “equivalent linear” mechanism. However, the equivalent linearization method is still the mainstream current dynamic analysis. This method has many experimental results, its form is relatively intuitive and simple, and it has accumulated much engineering experience [21]. Considering the above reasons and its consistency with existing codes and engineering applications, this method is still used to calculate the seismic response of the soil layer in this paper. This method is physically meaningful and requires fewer soil parameters. It requires only the soil density, shear wave velocity, and the curves of shear stiffness degradation and damping build-up with increasing shear strains. These parameters are determined through laboratory tests and field investigation, as listed in Tables 1 and 2.Table 1
Models and soil mechanical parameters.
ModelSoil nameLayer depth (m)Soil thickness (m)Vs/m⋅s−1ρ/t⋅m−3Soil type numberModel 1-1Silty clay10102651.951Fine sand20102931.926Fine sand30103591.926Fine sand40104261.926Fine sand50105001.926Model 1-2Fine sand10102261.906Silty clay20103371.972Fine sand30103691.926Fine sand40104331.926Fine sand50105001.926Model 1-3Fine sand10102761.906Fine sand20102871.916Silty clay30103722.003Fine sand40104331.926Fine sand50105001.926Model 1-4Fine sand10102361.906Fine sand20103111.876Fine sand30103881.926Silty clay40104412.054Fine sand50105001.926Model 1-5Fine sand10102221.906Fine sand20103071.916Fine sand30103891.926Fine sand40104531.966Silty clay50105002.15Model 2-1Fine sand772071.896Fine sand1472711.906Fine sand2173291.916Fine sand2873731.926Fine sand3574191.936Fine sand4274631.946Silty clay5085002.15Model 2-2Fine sand772001.896Fine sand1472811.906Fine sand2173231.916Silty clay2883991.963Fine sand3574081.936Fine sand4274431.946Fine sand5075001.966Model 2-3Fine sand772181.896Fine sand1472791.906Fine sand2173191.916Silty clay2873881.963Fine sand3574121.936Fine sand4274511.946Silty clay5085002.15Model 2-4Silty clay772691.921Fine sand1472791.906Fine sand2173221.916Silty clay2873931.963Fine sand3574101.936Fine sand4274481.946Silty clay5085002.15Model 2-5Silty clay772691.921Fine sand1472721.906Silty clay2173721.963Fine sand2873901.963Silty clay3574312.04Fine sand4274481.946Fine sand5085001.966Model 2-6Silty clay772691.921Fine sand1472721.906Silty clay2173721.963Fine sand2873901.963Silty clay3574312.04Fine sand4274481.946Silty clay5085002.105Table 2
Dynamic nonlinear parameters for different soil types.
Soil type numberSoil nameParameterγd (10−4)0.050.10.51510501001Silty clayGd/Gdmax0.97970.96030.82850.70730.32580.19460.04610.0236λ0.00540.00950.03250.05100.10320.11990.13830.14112Silty clayGd/Gdmax0.99030.98090.91120.83690.50650.33910.09310.0488λ0.00600.00850.01880.02580.04590.05350.06300.06463Silty clayGd/Gdmax0.98660.97360.88060.78670.42450.26940.06870.0356λ0.00710.01110.02960.04310.08220.09600.11240.11504Silty clayGd/Gdmax0.98450.96960.86430.76100.38910.24150.05990.0309λ0.00750.01120.02670.03710.06400.07260.08230.08375Silty clayGd/Gdmax0.98360.96780.85720.75010.37520.23090.05660.0291λ0.01190.01760.04200.05820.09940.11220.12640.12856Fine sandGd/Gdmax0.99030.98090.91120.83690.50640.33910.09310.0488λ0.00860.01180.02450.03270.05520.06340.07360.07537Bed rockGd/Gdmax1.0001.0001.0001.0001.0001.0001.0001.000λ0.50.50.50.50.50.50.50.5In the study area, a number of borehole investigations have been performed for different purposes; thus, the soil profiles are collected from the literature and reports. Based on the available soil profiles, it is possible to group these profiles into two categories: a single interbedded soil model and multiple interbedded soil model. Considering different positions and numbers of silty clay layers, eleven stratified soil models are used in this study, as shown in Figure1.Figure 1
Schematic diagram of soil models.


## 3. Input Seismic Load

Because of the shortage of strong earthquake data in this area, the synthesis method is used in this calculation. This project adopts the probabilistic seismic hazard analysis method stipulated in the national standard “Evaluation of Seismic Safety for Engineering Sites” (GB 17741-2005). The specific steps are as follows:(1)
On the basis of regional and near-field regional seismicity, regional and near-field regional seismotectonic backgrounds, and the seismic zones and the estimation of the seismic trend of each seismic zone over the next hundred years, the potential source areas of each seismic zone are delineated.(2)
The seismicity parameters of the seismic zone and potential source area are determined.(3)
The seismic hazard analysis for each site is carried out one by one using the selected attenuation relation of ground motion and the probability analysis method of seismic hazards.(4)
The acceleration response spectra on bedrock with different risk levels are evaluated for each of the sites.On the basis of each acceleration response spectra on bedrock, the corresponding ground motion input is synthesized according to the method stipulated in the “Evaluation of Seismic Safety for Engineering Sites” (GB 17741-2005). The specific steps are as follows:(1)
The target response spectrum is converted to the corresponding power spectrum by(1)Sω=ε/πωSa2ω−Ln−π/ωTLn1−r,whereSω is the power spectrum; εis the damping ratio; Sa2ωis the target response spectrum; T is duration; and r is the exceeding probability of the target reaction spectrum.(2)
Stable Gaussian processes with zero mean values are generated by the trigonometric series superposition method:(2)Xt=∑i=0nAicosωit+φi,whereAi=4SωiΔω0.5 and the initial phase φi is a uniformly distributed random variable during 0−2π.(3)
The stationary time history is multiplied by the nonstationary strength envelope to obtain the nonstationary acceleration time history:(3)at=Ψt⋅Xt.The nonstationary envelope function is of the following form:(4)Ψt=tt120<t≤t11t1<t≤t2e−ct−t2t2<t≤T,where t1 is the rising part of the peak, t1−t2 is the stationary segment of the peak, T is the duration, and c is the attenuation coefficient of the peak.Eighty-five control points of the target response spectrum were selected within 0.04∼6 seconds to ensure the precision of the target response spectrum fitting during the synthetic ground motion. In the process of synthesis, the time history of the synthesized acceleration accurately meets the peak acceleration of the target and approximates the response spectrum of the target acceleration by approximating the target spectrum step by step.To maximize the reflection of the actual structure subjected to seismic action, site-specific ground motions are necessary. In this paper, artificial ground motions are generated by gradually approaching the target design spectrum in this area. Four ground motions with different amplitudes are generated based on the return period of this area, as shown in Figure2. They correspond to exceeding probabilities of 63% (frequently occurring earthquakes), 10% (normally occurring earthquakes), and 2% (rarely occurring earthquakes) in 50 years and 1% in 100 years (extremely rarely occurring earthquakes).Figure 2
Ground motions under different probabilities.


## 4. Results

### 4.1. Model 1: Single Interbedded Soil Model

Five typical profiles with a single silty clay layer at different depths are built, as shown in Figure1 (Model 1). The site profiles and corresponding soil parameters are input into the one-dimensional analysis model and then analyzed under different earthquake loadings. The results of peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), and spectral acceleration (Sa) are presented. As shown in Figure 3 and Table 3, silty clay with burial depths of 0–10 m (Model 1-1) and 41–50 m (Model 1-5) have a more evident amplification effect on the PGA response than the other models, with a maximum amplification ratio of approximately 1.7. The amplification ratios increase with increasing motion intensity, and the maximum ratio is observed for the case of exceeding probabilities of 2% in 50 years. A further increase in motion intensity leads to a decrease in the amplification ratio due to the increase in the burial depth of silty clay. In addition, it is possible to see that the location of the silty clay layer significantly affects the calculated PGA response for strong ground motion. Under the action of normally occurring earthquakes, the amplification ratios range from 1.29 to 1.32, showing a minor effect on the acceleration response. With regard to the PGV and PGD responses, amplification effects are also observed. However, these two parameters are less sensitive to the burial depth of the silty clay due to the small difference in amplification ratios. The fundamental site frequencies of Model 1-1 and Model 1-5 are close to a certain period of seismic waves of rarely occurring earthquakes (extremely rarely occurring earthquakes), so resonance is generated, resulting in the intensification of ground vibration and a significant amplification effect.Figure 3
Amplification ratios of ground motion for the five single interbedded models under four seismic inputs.
(a)(b)(c)Table 3
Ground motion amplification ratios for the five single interbedded models under four seismic inputs.
Bedrock inputModel 1-1Model 1-2Model 1-3Model 1-4Model 1-5PGA (gal)1 (60)1.35 (81.00)1.25 (75.00)1.42 (85.20)1.37 (82.40)1.37 (82.40)1 (202)1.32 (266.6)1.26 (254.6)1.30 (262.4)1.27 (256.8)1.29 (261.3)1 (395)1.69 (699.4)1.31 (516.8)1.39 (547.4)1.39 (548.4)1.66 (654.0)1 (680)1.47 (998.0)1.03 (698.2)1.16 (786.0)1.13 (770.4)1.42 (963.8)PGV (cm/s)1 (4)1.18 (4.70)1.05 (4.20)1.20 (4.80)1.20 (4.80)1.10 (4.40)1 (19)1.02 (19.4)1.01 (19.2)1.06 (20.2)1.02 (19.4)1.04 (19.7)1 (35)1.69 (59.2)1.58 (55.4)1.54 (53.8)1.58 (55.2)1.55 (54.1)1 (65)1.94 (126.0)1.90 (123.4)1.86 (121.0)2.00 (130.1)1.98 (128.7)PGD (cm)1 (2)1.00 (2.0)1.00 (2.0)1.00 (2.0)1.00 (2.0)1.00 (2.0)1 (5)1.24 (6.2)1.24 (6.2)1.28 (6.4)1.16 (5.8)1.22 (6.1)1 (14)1.23 (17.2)1.27 (17.8)1.30 (18.2)1.29 (18.1)1.24 (17.3)1 (24)1.50 (36.0)1.58 (36.0)1.49 (35.8)1.45 (34.9)1.48 (35.6)Note. The values in the parentheses show the amplitudes of the PGA, PGV, and PGD.Figure4 compares the spectral acceleration in the five cases. Under the action of frequently occurring earthquakes and normally occurring earthquakes, the burial depth of silty clay has little influence on the spectrum amplitudes and shapes, leading to similar spectrum curves. With the increase in motion intensities, a significant divergence in the spectral accelerations occurs in the short period range. Under rarely occurring earthquakes, the maximum spectral acceleration appears at a period of 0.4 s for Model 1-1, while the response spectrum reaches its peak value at a period of 0.2 s for other burial depths. This means that the ground soft soil layer amplifies the acceleration over a longer range of periods, and such an influence is increased for extremely rarely occurring earthquakes. Under this earthquake type, the maximum value for the ground clay appears at a period of approximately 1.0 s, and “twin peaks” occur. This is caused by the resonance of the soft surface layer. In general, the amplitude of the first peak (approximately 0.3 s) increases as the burial depth of the silty clay layer increases. It can be speculated that the bottom clay layer suppresses the wave propagation at high frequencies, but the high-frequency component is amplified to some extent as it propagates from the bottom clay layer to the ground surface.Figure 4
Spectral accelerations for the five single interbedded models under four seismic inputs.
(a)(b)(c)(d)


### 4.2. Model 2: Multiple Interbedded Soil Models

Considering different depths of the silty clay layer and relative locations with respect to the sand layer, six typical profiles are built, as shown in Figure1 (Model 2). The results of the peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), and spectral acceleration (Sa) are presented in Figures 5 and 6 and Table 4.Figure 5
Amplification ratios of ground motion for the six multiple interbedded models under four seismic inputs.
(a)(b)(c)Figure 6
Spectral accelerations for the six multiple interbedded models under four seismic inputs.
(a)(b)(c)(d)Table 4
Ground motion amplification ratios for the six multiple interbedded models under four seismic inputs.
Bedrock inputModel 2-1Model 2-2Model 2-3Model 2-4Model 2-5Model 2-6PGA (gal)1 (60)1.37 (82.40)1.34 (80.1)1.31 (78.6)1.32 (79.2)1.33 (79.8)1.39 (83.2)1 (202)1.29 (261.3)1.26 (254.6)1.25 (252.2)1.24 (250.5)1.23 (249.0)1.25 (252.0)1 (395)1.66 (654.0)1.45 (573.5)1.35 (534.2)1.27 (501.7)1.18 (467.6)1.08 (427.4)1 (680)1.42 (963.8)1.17 (798.3)1.01 (689.2)0.9 (612.0)0.77 (525.2)0.72 (489.0)PGV (cm/s)1 (4)1.10 (4.40)1.05 (4.20)1.10 (4.40)1.15 (4.6)1.05 (4.2)1.05 (4.2)1 (19)1.04 (19.7)1.01 (19.2)1.02 (19.4)1.05 (20.0)1.06 (20.2)1.07 (20.3)1 (35)1.55 (54.1)1.58 (55.4)1.61 (56.4)1.49 (52.1)1.42 (49.6)1.40 (49.0)1 (65)1.98 (128.7)1.9 (123.4)1.96 (127.4)1.83 (119.2)1.64 (106.3)1.75 (113.8)PGD (cm)1 (2)1.00 (2.0)1.00 (2)1.00 (2)1.00 (2.0)1.00 (2.0)1.00 (2.0)1 (5)1.22 (6.1)1.24 (6.2)1.28 (6.4)1.4 (7.0)1.42 (7.10)1.46 (7.30)1 (14)1.24 (17.3)1.27 (17.8)1.32 (18.5)1.34 (18.3)1.38 (19.3)1.41 (19.8)1 (24)1.48 (35.6)1.58 (36.0)1.63 (39.2)1.69 (37.1)1.71 (41.0)1.78 (42.8)As shown in Figure5, under the action of frequently occurring earthquakes and normally occurring earthquakes, the difference in PGA amplification ratios for different soil models is small. Table 4 shows that the amplification coefficients are generally between 1.25 and 1.35. With increasing motion intensity, the amplification ratios show an increased divergence for different soil models. More specifically, for the same seismic inputs, the amplification ratios generally decrease with an increasing number of soil layers, particularly for high motion intensities. For extremely rarely occurring earthquakes, when the number of soil layers is greater than 3, the PGA amplification ratio is less than 1.0, which demonstrates that a larger number of soft clay layers isolate the propagation of ground motions to some degree. Compared to the results of Model 1, the larger number of soil layers increases the variation in the PGV and PGD responses but is still relatively small compared to the PGA response. Interestingly, the PGD response increases as the number of soil layers increases. This can be attributed to the large deformation in each clay layer because of the low stiffness.The predominant period of ground motions is related to the thickness of the soil and the shear wave velocity of the soil. The increased number of interlayers will lead to stronger reflection and refraction of seismic waves. As a consequence, the high-frequency components are filtered out while the abundant long-period components are retained. As a result, the seismic waves differ greatly from the natural vibration period of the site, making the amplification ratio of the peak acceleration of the ground surface appear to be less than 1.0.Figure6 presents the corresponding spectral accelerations. Similarly, the difference in the spectral accelerations is minor for low motion intensity (i.e., frequently occurring earthquakes and normally occurring earthquakes), meaning that the soil structure has little influence. As motion intensities increase, a significant divergence in the spectral accelerations occurs in the low period range. The increased number of soil layers tends to decrease the acceleration response in the low period range, and the predominant period increases to a long period due to the significant stiffness degradation. This is more evident for extremely rarely occurring earthquakes. For instance, the amplitude of spectral acceleration decreases from 1300 gal in Model 2-1 to approximately 800 gal in Model 2-6 at a period of 0.3 s, and the corresponding predominant period increases from 0.3 s to approximately 1.1 s. This can be explained by the strong reflection and refraction of seismic waves in multilayered grounds, resulting in the filtering out of the high-frequency components of ground motion while amplifying the long-period components. The results of Model 1 and Model 2 both highlight that the presence of a certain number of soil layers can effectively reduce the acceleration response spectrum at high frequencies.


## 4.1. Model 1: Single Interbedded Soil Model

Five typical profiles with a single silty clay layer at different depths are built, as shown in Figure1 (Model 1). The site profiles and corresponding soil parameters are input into the one-dimensional analysis model and then analyzed under different earthquake loadings. The results of peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), and spectral acceleration (Sa) are presented. As shown in Figure 3 and Table 3, silty clay with burial depths of 0–10 m (Model 1-1) and 41–50 m (Model 1-5) have a more evident amplification effect on the PGA response than the other models, with a maximum amplification ratio of approximately 1.7. The amplification ratios increase with increasing motion intensity, and the maximum ratio is observed for the case of exceeding probabilities of 2% in 50 years. A further increase in motion intensity leads to a decrease in the amplification ratio due to the increase in the burial depth of silty clay. In addition, it is possible to see that the location of the silty clay layer significantly affects the calculated PGA response for strong ground motion. Under the action of normally occurring earthquakes, the amplification ratios range from 1.29 to 1.32, showing a minor effect on the acceleration response. With regard to the PGV and PGD responses, amplification effects are also observed. However, these two parameters are less sensitive to the burial depth of the silty clay due to the small difference in amplification ratios. The fundamental site frequencies of Model 1-1 and Model 1-5 are close to a certain period of seismic waves of rarely occurring earthquakes (extremely rarely occurring earthquakes), so resonance is generated, resulting in the intensification of ground vibration and a significant amplification effect.Figure 3
Amplification ratios of ground motion for the five single interbedded models under four seismic inputs.
(a)(b)(c)Table 3
Ground motion amplification ratios for the five single interbedded models under four seismic inputs.
Bedrock inputModel 1-1Model 1-2Model 1-3Model 1-4Model 1-5PGA (gal)1 (60)1.35 (81.00)1.25 (75.00)1.42 (85.20)1.37 (82.40)1.37 (82.40)1 (202)1.32 (266.6)1.26 (254.6)1.30 (262.4)1.27 (256.8)1.29 (261.3)1 (395)1.69 (699.4)1.31 (516.8)1.39 (547.4)1.39 (548.4)1.66 (654.0)1 (680)1.47 (998.0)1.03 (698.2)1.16 (786.0)1.13 (770.4)1.42 (963.8)PGV (cm/s)1 (4)1.18 (4.70)1.05 (4.20)1.20 (4.80)1.20 (4.80)1.10 (4.40)1 (19)1.02 (19.4)1.01 (19.2)1.06 (20.2)1.02 (19.4)1.04 (19.7)1 (35)1.69 (59.2)1.58 (55.4)1.54 (53.8)1.58 (55.2)1.55 (54.1)1 (65)1.94 (126.0)1.90 (123.4)1.86 (121.0)2.00 (130.1)1.98 (128.7)PGD (cm)1 (2)1.00 (2.0)1.00 (2.0)1.00 (2.0)1.00 (2.0)1.00 (2.0)1 (5)1.24 (6.2)1.24 (6.2)1.28 (6.4)1.16 (5.8)1.22 (6.1)1 (14)1.23 (17.2)1.27 (17.8)1.30 (18.2)1.29 (18.1)1.24 (17.3)1 (24)1.50 (36.0)1.58 (36.0)1.49 (35.8)1.45 (34.9)1.48 (35.6)Note. The values in the parentheses show the amplitudes of the PGA, PGV, and PGD.Figure4 compares the spectral acceleration in the five cases. Under the action of frequently occurring earthquakes and normally occurring earthquakes, the burial depth of silty clay has little influence on the spectrum amplitudes and shapes, leading to similar spectrum curves. With the increase in motion intensities, a significant divergence in the spectral accelerations occurs in the short period range. Under rarely occurring earthquakes, the maximum spectral acceleration appears at a period of 0.4 s for Model 1-1, while the response spectrum reaches its peak value at a period of 0.2 s for other burial depths. This means that the ground soft soil layer amplifies the acceleration over a longer range of periods, and such an influence is increased for extremely rarely occurring earthquakes. Under this earthquake type, the maximum value for the ground clay appears at a period of approximately 1.0 s, and “twin peaks” occur. This is caused by the resonance of the soft surface layer. In general, the amplitude of the first peak (approximately 0.3 s) increases as the burial depth of the silty clay layer increases. It can be speculated that the bottom clay layer suppresses the wave propagation at high frequencies, but the high-frequency component is amplified to some extent as it propagates from the bottom clay layer to the ground surface.Figure 4
Spectral accelerations for the five single interbedded models under four seismic inputs.
(a)(b)(c)(d)


## 4.2. Model 2: Multiple Interbedded Soil Models

Considering different depths of the silty clay layer and relative locations with respect to the sand layer, six typical profiles are built, as shown in Figure1 (Model 2). The results of the peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), and spectral acceleration (Sa) are presented in Figures 5 and 6 and Table 4.Figure 5
Amplification ratios of ground motion for the six multiple interbedded models under four seismic inputs.
(a)(b)(c)Figure 6
Spectral accelerations for the six multiple interbedded models under four seismic inputs.
(a)(b)(c)(d)Table 4
Ground motion amplification ratios for the six multiple interbedded models under four seismic inputs.
Bedrock inputModel 2-1Model 2-2Model 2-3Model 2-4Model 2-5Model 2-6PGA (gal)1 (60)1.37 (82.40)1.34 (80.1)1.31 (78.6)1.32 (79.2)1.33 (79.8)1.39 (83.2)1 (202)1.29 (261.3)1.26 (254.6)1.25 (252.2)1.24 (250.5)1.23 (249.0)1.25 (252.0)1 (395)1.66 (654.0)1.45 (573.5)1.35 (534.2)1.27 (501.7)1.18 (467.6)1.08 (427.4)1 (680)1.42 (963.8)1.17 (798.3)1.01 (689.2)0.9 (612.0)0.77 (525.2)0.72 (489.0)PGV (cm/s)1 (4)1.10 (4.40)1.05 (4.20)1.10 (4.40)1.15 (4.6)1.05 (4.2)1.05 (4.2)1 (19)1.04 (19.7)1.01 (19.2)1.02 (19.4)1.05 (20.0)1.06 (20.2)1.07 (20.3)1 (35)1.55 (54.1)1.58 (55.4)1.61 (56.4)1.49 (52.1)1.42 (49.6)1.40 (49.0)1 (65)1.98 (128.7)1.9 (123.4)1.96 (127.4)1.83 (119.2)1.64 (106.3)1.75 (113.8)PGD (cm)1 (2)1.00 (2.0)1.00 (2)1.00 (2)1.00 (2.0)1.00 (2.0)1.00 (2.0)1 (5)1.22 (6.1)1.24 (6.2)1.28 (6.4)1.4 (7.0)1.42 (7.10)1.46 (7.30)1 (14)1.24 (17.3)1.27 (17.8)1.32 (18.5)1.34 (18.3)1.38 (19.3)1.41 (19.8)1 (24)1.48 (35.6)1.58 (36.0)1.63 (39.2)1.69 (37.1)1.71 (41.0)1.78 (42.8)As shown in Figure5, under the action of frequently occurring earthquakes and normally occurring earthquakes, the difference in PGA amplification ratios for different soil models is small. Table 4 shows that the amplification coefficients are generally between 1.25 and 1.35. With increasing motion intensity, the amplification ratios show an increased divergence for different soil models. More specifically, for the same seismic inputs, the amplification ratios generally decrease with an increasing number of soil layers, particularly for high motion intensities. For extremely rarely occurring earthquakes, when the number of soil layers is greater than 3, the PGA amplification ratio is less than 1.0, which demonstrates that a larger number of soft clay layers isolate the propagation of ground motions to some degree. Compared to the results of Model 1, the larger number of soil layers increases the variation in the PGV and PGD responses but is still relatively small compared to the PGA response. Interestingly, the PGD response increases as the number of soil layers increases. This can be attributed to the large deformation in each clay layer because of the low stiffness.The predominant period of ground motions is related to the thickness of the soil and the shear wave velocity of the soil. The increased number of interlayers will lead to stronger reflection and refraction of seismic waves. As a consequence, the high-frequency components are filtered out while the abundant long-period components are retained. As a result, the seismic waves differ greatly from the natural vibration period of the site, making the amplification ratio of the peak acceleration of the ground surface appear to be less than 1.0.Figure6 presents the corresponding spectral accelerations. Similarly, the difference in the spectral accelerations is minor for low motion intensity (i.e., frequently occurring earthquakes and normally occurring earthquakes), meaning that the soil structure has little influence. As motion intensities increase, a significant divergence in the spectral accelerations occurs in the low period range. The increased number of soil layers tends to decrease the acceleration response in the low period range, and the predominant period increases to a long period due to the significant stiffness degradation. This is more evident for extremely rarely occurring earthquakes. For instance, the amplitude of spectral acceleration decreases from 1300 gal in Model 2-1 to approximately 800 gal in Model 2-6 at a period of 0.3 s, and the corresponding predominant period increases from 0.3 s to approximately 1.1 s. This can be explained by the strong reflection and refraction of seismic waves in multilayered grounds, resulting in the filtering out of the high-frequency components of ground motion while amplifying the long-period components. The results of Model 1 and Model 2 both highlight that the presence of a certain number of soil layers can effectively reduce the acceleration response spectrum at high frequencies.


## 5. Conclusions

This paper analyzes the seismic response of different soil models that include different numbers and locations of silty clay layers. Based on the parametric analysis performed herein, the following conclusions can be drawn:(1)
When the silty clay is at the soil ground and bottom, significant amplification effects of the PGA for high motion intensity appear. Additionally, the predominant period is increased due to the presence of the ground clay layer. Important engineering facilities should avoid sites with silty clay at the top of the soil layer or treat the silty clay layer.(2)
As the numbers of soil layers and motion intensities increase, the amplification coefficient of the PGA gradually decreases to less than 1.0 for extremely rarely occurring earthquakes. The deamplification effect is observed for soil layer numbers greater than 3 in this study, thereby acting as a natural damper. However, the PGD shows the opposite trend due to the large deformation caused by the soft clay layers.(3)
The spectral accelerations are less affected by the presence of the soil layer for weak motion intensities. As motion intensities and the number of soil layers increase, the amplitude at high frequencies is generally deamplified, and the predominant period of the response spectrum becomes larger. In other words, in the case of large earthquakes, the greater the number of interlayered soil layers, the more obvious the amplification effect of the long-period ground motion.



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*Source: 1519750-2021-09-08.xml*