^{1}

^{2}

^{3}

^{2}

^{4}

^{1}

^{1}

^{2}

^{3}

^{4}

The Loess Plateau is one of the most tectonically and seismically active areas in the world. Observations from past strong earthquakes, particularly the Minxian–Zhangxian and Wenchuan earthquakes, have shown distinctive evidence of seismic site effects in the mountainous area of southeastern Gansu province. In this study, seismic damage in the loess areas of southeastern Gansu province induced by these earthquakes was investigated and briefly described. Different types of ground motion were selected, and the one-dimensional equivalent linear method was used for numerical analysis of the ground motion effects in the loess regions. Moreover, seismic response analysis of a typical loess tableland was conducted. The results showed that the seismic responses of a typical loess tableland under different seismic excitations have totally different dynamic characteristics. Moreover, the seismic damage in loess regions was more serious under far-field seismic excitation compared with near-field seismic excitation with the same peak acceleration. Through this study, the quantitative assessment of ground motion effects can be approximately estimated and the mechanism of site amplification effects on ground motion is further explained.

Loess and loessic deposits cover an area of 631,000 km^{2} of the mainland of China, which accounts for approximately 6.6% of the total area of the country. The Loess Plateau is located on the upper and middle stream of the Yellow River, covering an area of 440,000 km^{2} in the northwestern part of China. Loess thickness generally exceeds 100 m over large areas of the Loess Plateau, with a maximum recorded thickness of 335 m in eastern Gansu province near the city of Lanzhou [

The study of seismic site effects has been an issue of growing interest in recent years, and many resources have been devoted to explain the causes and impacts of these effects. The microtremor H/V spectral ratio method has been widely used for site effect studies. Authors such as Zaslavsky et al. [

Seismic site effects are an important aspect in seismic hazard analysis. Tsai [

However, there are not many related studies about seismic site effects in the loess regions of western China. Several researchers, such as Wang et al. [

The Wenchuan Ms8.0 earthquake in 2008 and the Minxian–Zhangxian Ms6.6 earthquake in 2013 caused enormous buildings and houses to collapse. They also caused serious damage in the Loess Plateau. Based on seismic damage investigation after these devastating earthquakes, the site amplification effects on ground motion were very obvious. The influence of the isolated topography and steep slopes on the seismic damage and seismic intensity was significant, which mainly manifested as more severe seismic damage and higher seismic intensities. After the Wenchuan earthquake, a temporary strong motion array of three stations was installed near Wenxian County in Gansu province. The aftershocks of the Wenchuan earthquake recorded by the temporary strong motion array showed that the peak ground acceleration (PGA) at the top station was nearly 1.5 times larger than that at the bottom station [

The seismic damage characteristics and the seismic intensities can be different in the same area due to differences in topography, geomorphology, soil thickness, and altitude. For example, Liujiapo village (E104.974, W33.453) and Haoping village (E104.983, W34.442) are located in Wudu district, Longnan city, Gansu province. The altitude of Haoping village, at the top of the mountain, is 1811 m and the altitude of the Liujiapo village on the mountainside is 1485 m. The dominant frequency of the Haoping site was 1.85 Hz, and the dominant frequency of the Liujiapo site was 3.85 Hz. As shown in Figure

Differences in earthquake damage in two typical villages. (a) Topography of the two typical villages, (b) house damage in Liujiapo village, and (c) house damage in Haoping village.

Differences in earthquake damage in two typical villages. (a) Topography of the two typical villages, (b) house damage in Majiagou village, and (c) house damage in Xinglin village.

Site response analysis is crucial for defining the seismic hazard and distribution of damage during earthquakes. In this paper, the one-dimensional equivalent linear method is used to perform seismic ground motion analysis. This method is implemented based on elastic wave propagation theory, which assumes that the response of soil deposits is predominantly caused by the vertical propagation of shear wave from the bedrock. Each layer is assumed homogenous and isotropic and is characterized by its shear modulus, soil density, damping ratio, and thickness. The vertical propagation of shear wave through the system can be calculated by using the solution of the wave equation. The characteristic of this method is that the definite calculating parameters (such as the equivalent shear modulus and damping ratios) are used to describe the complex changes of the soil. Then, an iterative method is applied for dynamic response calculations; hence, the problem is changed from nonlinear to linear.

The dynamic parameters of loess, including the shear modulus and damping ratios, change under different shear strain amplitudes. The shear modulus and damping ratios were determined by dynamic triaxial tests conducted by the Key Laboratory of Loess Earthquake Engineering, China Earthquake Administration. The dynamic parameters of typical loess are shown in Table

The dynamic parameters of typical loess.

Index | Shear strain (×10^{−4}) | |||||||
---|---|---|---|---|---|---|---|---|

0.05 | 0.1 | 0.5 | 1 | 5 | 10 | 50 | 100 | |

G/GO | 0.965 | 0.914 | 0.885 | 0.750 | 0.634 | 0.288 | 0.110 | 0.055 |

0.008 | 0.015 | 0.031 | 0.043 | 0.072 | 0.129 | 0.173 | 0.205 |

From a geological perspective, an earthquake’s near-field is defined as the area within 20–50 km from the epicenter. Near-field earthquakes consist of a major portion of the fault energy in the form of pulses. These pulses tend to have a maximum Fourier spectrum in limited periods, whereas far-field earthquakes have a maximum Fourier spectrum in a broad range of periods [

The horizontal earthquake accelerogram in the N–S direction, recorded at the Minxian seismostation during the 2013 Minxian–Zhangxian Ms6.6 earthquake, was selected as the near-field seismic motion (Minxian seismic motion). The epicenter of this earthquake was located at (W34.5°, E104.2°) and the seismostation was 18 km away from the epicenter. Figure ^{−2}, and the energy of the earthquake ground motion was concentrated in the range of 3–10 Hz.

Accelerogram recorded at Minxian seismostation during the Minxian–Zhangxian earthquake.

The other horizontal earthquake accelerogram in the E–W direction, recorded at Tianshui seismostation during the 2008 Wenchuan Ms8.0 earthquake, was selected as the far-field seismic motion (Tianshui seismic motion). The epicenter of this earthquake was located at (W31.01°, E103.42°) and the seismostation was 415 km away from the epicenter. Figure ^{−2}, and the energy of earthquake ground motion was concentrated in the range of 0.5–4 Hz.

Horizontal acceleration history recorded at Tianshui seismostation during the Wenchuan earthquake.

A numerical scheme is presented to compute the seismic response of the loess site. Figure

One-dimensional idealization calculation model.

It was assumed that the loess soils at various depths have the same values of shear modulus and damping ratios, but different densities and shear wave velocities. The relevant parameters of the one-dimensional model are illustrated in Table

Soil parameters of one-dimensional model.

Lithology | Thickness (m) | Depth (m) | Density (kN·m^{−3}) | _{s} (m·s^{−1}) |
---|---|---|---|---|

Loess | 5 | 5 | 15.5 | 180 |

5 | 10 | 16.0 | 200 | |

5 | 15 | 16.3 | 230 | |

5 | 20 | 16.5 | 280 | |

5 | 25 | 16.8 | 300 | |

5 | 30 | 17.0 | 340 | |

5 | 35 | 17.1 | 370 | |

5 | 40 | 17.3 | 420 | |

5 | 45 | 17.4 | 450 | |

5 | 50 | 17.6 | 480 | |

5 | 55 | 17.8 | 490 | |

5 | 60 | 18.0 | 510 | |

5 | 65 | 18.2 | 520 | |

5 | 70 | 18.4 | 530 | |

5 | 75 | 18.5 | 530 | |

5 | 80 | 18.7 | 540 | |

5 | 85 | 18.9 | 550 | |

5 | 90 | 19.1 | 560 | |

5 | 95 | 19.2 | 560 | |

5 | 100 | 19.5 | 570 | |

Bedrock | 22.0 | 800 |

Figure

Ground motion acceleration time history of the sites with different overburden thicknesses. (a) Minxian seismic motion. (b) Tianshui seismic motion.

The distribution curves of the PGA amplification coefficients are presented in Figure

The distribution of the PGA amplification coefficients.

The normalized acceleration response spectra of the loess site under different seismic waves are illustrated in Figure

Acceleration spectra under the earthquake excitations. (a) Minxian seismic motion. (b) Tianshui seismic motion.

To discuss the topographical effects on the dynamic behavior under earthquake excitation in the loess regions, dynamic analysis of the typical loess tableland was carried out by applying the nonlinear dynamic finite element analysis method.

According to the field investigation, the most common tableland in eastern Gansu province has a typical broken-line sloping surface, and the thickness of the loess layer is about 100 m. Figure

Models of finite element analysis. (a) Profile of the loess slope (unit: m) and (b) finite element model.

In this simulation, the numerical calculation was deduced based on the plane strain assumption. In order to reduce the effect of boundary conditions on energy reflection and transmission properties, the coupling method of finite and infinite elements is presented. The infinite elements were used to simulate the lateral boundary conditions, and the artificial boundary condition was used for the bottom boundary. The horizontal direction at the bottom was released, and the different seismic waves (Figures

Before carrying out the dynamic calculation, the dynamic response characteristics of free field soil were evaluated using an equivalent linear approach. Then, the soil values of the dynamic shear modulus and damping ratio were finally determined during maximum shear strain. In dynamic finite element analysis, the soil is regarded as an elastic-plastic material and the shear modulus

In (

Soil mechanics parameters of the finite element model.

Lithology | Thickness (m) | Density (kN·m^{−3}) | Shear modulus (Pa) | Poisson’s ratio | Cohesion (kPa) | Frictional angle |
---|---|---|---|---|---|---|

Loess ① | 15 | 16.3 | 8.62E + 07 | 0.3 | 32 | 18° |

Loess ② | 20 | 17.0 | 1.97E + 08 | 0.3 | 35 | 18° |

Loess ③ | 20 | 17.6 | 4.06E + 08 | 0.3 | 38 | 19° |

Loess ④ | 25 | 18.5 | 5.20E + 08 | 0.3 | 42 | 20° |

Loess ⑤ | 20 | 19.2 | 6.02E + 08 | 0.3 | 46 | 21° |

Bedrock | 15 | 22.0 | 1.41E + 09 | 0.2 | 120 | 34° |

The seismic acceleration distribution characteristics of the loess tableland are discussed through the numerical analysis. Figure

Horizontal acceleration contour map under different seismic excitations. (a) under Minxian seismic excitation. (b) under Tianshui seismic excitation.

Figure

Distribution of the amplification coefficient with the distance.

Figure

Distribution of the amplification coefficient with distance on the top of the loess tableland.

According to the relevant studies, the spectrum characteristics of the strong motion at different positions of the loess tableland varied. The acceleration time histories of the different observation points (Figure ^{−2} (point B), 3.14 m s^{−2} (point M), and 3.86 m s^{−2} (point T). The dominant frequencies of the different observations were 4.8 Hz (point B), 4.3 Hz (point M), and 4.0 Hz (point T). Figure ^{−2} (point B), 5.1 m s^{−2} (point M), and 10.0 m s^{−2} (point T). The dominant frequencies of the different observations were 4.3 Hz (point B), 2.5 Hz (point M), and 1.7 Hz (point T).

Ground motion characteristics under Minxian seismic excitation: (a) acceleration time histories and (b) spectrum characteristics.

Ground motion characteristics under Tianshui seismic excitation: (a) acceleration time histories and (b) spectrum characteristics.

In summary, there was a delay in the peak acceleration time with the seismic wave propagation along the slope of the loess tableland. The ground motion at the top of the slope had the amplified low-frequency component, and the high-frequency components were filtered out. Moreover, the dominant frequency of the ground motion was lower when the observation point was located in the upper part of the loess tableland. This variation was more obvious under Tianshui seismic excitation.

Figure

Displacement-time history curve under different seismic excitations: (a) under Minxian seismic excitation and (b) under Tianshui seismic excitation.

Given the analysis above, it can be concluded that the horizontal displacement increases with increasing height of the loess tableland. The horizontal displacement response of the loess tableland under far-field seismic excitation is significantly greater than that under near-field seismic excitation. The horizontal displacement of the upper part of the tableland under the Tianshui seismic excitation is about five times greater than that under the Minxian seismic excitation. The numerical results illustrate that the seismic damage in loess regions is more serious under far-field seismic excitation compared with that under near-field seismic excitation with the same peak acceleration.

From the above numerical analysis results, it can be clearly seen that the seismic motion has a decisive influence on the site seismic response, and the seismic response of a typical loess tableland under different seismic excitations has totally different dynamic characteristics. Consequently, seismic damage characteristics in loess areas under different seismic excitations are also different. The reason can be summarized as follows.

First, the seismic amplification and soil-filtering effects play a crucial role in determining the seismic site effect. Far-field seismic waves have abundant low-frequency components, whereas near-field seismic waves are characterized by abundant high-frequency components. The soil-filtering effect is correlated with the soil thickness of the sites, and the amplification effect for different frequency components is not the same. Hence, the seismic ground motion under different seismic excitations could have different amplitudes and different response spectra.

Furthermore, at different positions of the loess tableland, the strong ground motion has different frequency components under the action of earthquakes. The dominant frequency of the strong motion at the bottom of the tableland is greater than that on the top of the tableland. Moreover, the dominant frequency of the loess site is related to the topography, geomorphology, soil thickness, and altitude. The site-predominant frequencies of different observation points in the epicenter of the Minxian–Zhangxian Ms6.6 earthquake, determined from microtremor measurements, are illustrated in Table

The site-predominant frequencies of different observation points.

Observation point | Longitude and latitude | Altitude (m) | Dominant frequency (Hz) |
---|---|---|---|

Point 1 | N 34°30′45″; E 104°10′8″ | 2775 | 1.6 |

Point 2 | N 34°30′45″; E 104°9′41″ | 2626 | 1.5 |

Point 3 | N 34°30′33″; E 104°9′30″ | 2645 | 1.3 |

Point 4 | N 34°29′54″; E 104°8′00″ | 2375 | 5.6 |

Moreover, when the frequencies of far-field seismic motion are relatively low, then the structures in the loess area are prone to damage under this type of seismic motion because of the quasiresonance response. The dynamic magnification factors of the structures in loess regions are related to the loess thickness. The displacement response under the far-field seismic excitation is significantly greater than under the near-field seismic excitation. For these reasons, there are different seismic damage characteristics in the same area under different types of seismic motion.

Based on the seismic damage investigation, different types of ground motions were selected considering the different earthquake characteristics. Then, a seismic site response analysis was conducted; the seismic response of the loess tableland was also investigated. The numerical results indicated that the mechanism of seismic response is very complex and that seismic damage can vary in the same area. The main conclusions drawn from the computational analysis results are as follows:

The seismic motion itself had a dominant influence on the site seismic response. The distribution of seismic damage in the same area was significantly different under different seismic excitations.

The site amplification effect appears to have obvious nonlinear features under near-field earthquakes, whereas it shows an approximately linear trend under far-field earthquakes.

Under near-field seismic excitation, the strongest seismic response occurs at the bottom of the tableland, whereas the strongest seismic response occurs at the top of the tableland under far-field seismic excitation.

The seismic response is strongest when the dominant frequency of the site is close to the dominant frequency of the strong motion. The dominant frequency of the loess site should be assessed considering the influence of the topography, geomorphology, soil thickness, and altitude.

All data generated or analyzed during this study are included within this article.

The authors declare that there are no conflicts of interest regarding the work submitted.

This study was financially supported by the National Natural Science Foundation of China (nos. 41701058 and 41472297), the Open Fund of State Key Laboratory of Frozen Soil Engineering (Grant no. SKLFSE201606), and the China Postdoctoral Science Foundation (Grant no. 2015M570490).