Study on the distribution characteristics and seismic hazard evaluation of loess seismic landslides in the southern Ningxia area

Abstract

The unique topographical and geomorphological characteristics of the southern Ningxia area, coupled with the active seismic activity background, have led to loess earthquake-induced landslides becoming the predominant type of seismic geological disaster in this region. Among them, the landslides triggered by the 1920 Haiyuan M8.5 great earthquake are particularly typical and severe. This study is based on the detailed data of 600 loess earthquake-induced landslides within the study area obtained from field investigations, and provides a detailed and in-depth summary of the distribution characteristics of loess earthquake-induced landslides in the Ningnan area. The results show that the landslides in this area have typical characteristics such as gentle slope gradient of the developed slope, large scale of landslides, long sliding distance, wide disaster impact range, and strong group occurrence. Further analysis reveals that the spatial distribution of landslides is mainly influenced by the comprehensive effects of seismic motion intensity, loess cover thickness, type of fault rupture, and hydrological conditions. Based on the loess landslide geometric parameter database in southern Ningxia, this study applies a binary logistic regression model to successfully establish a rapid evaluation formula for the seismic stability of loess slopes in the study area. The discriminant accuracy of this formula can reach more than 95%, providing an efficient and accurate method for the seismic stability evaluation of loess slopes. On this basis, in combination with the geological model database of loess slopes in the study area, the rapid evaluation formula for the seismic stability of loess slopes is used to systematically evaluate the seismic stability of loess slopes in the study area under different seismic motion intensities, and finally six loess earthquake-induced landslide hazard zoning maps of the Ningnan area under different estimated seismic motion intensities are compiled. The research results of this paper not only enrich the theoretical system of seismic geological disaster research in the Ningnan area, but also provide a strong decision-making reference for the prevention and response strategy formulation of earthquake-induced landslide disasters in practical applications.

Introduction

Co-seismic landslides are a significant secondary hazard associated with earthquakes, often causing widespread damage and loss of life. Maintaining a comprehensive inventory of co-seismic landslides is crucial, as it aids in understanding the spatial and temporal distribution of landslides triggered by seismic events. This information is essential for disaster risk reduction, emergency response planning, and the development of effective mitigation strategies.

For instance, the database compiled by Keefer (1999) for earthquake-induced landslides from 1980 to 1997 provides a detailed account of landslides triggered by 36 earthquakes worldwide. This dataset highlights the correlation between earthquake magnitude and landslide distribution, emphasizing the need for region-specific hazard assessments¹. Similarly, the 2023 Kahramanmaraş earthquakes in Türkiye triggered thousands of landslides, demonstrating the devastating impact of seismic activity on slope stability². The use of aerial photogrammetry in the 2020 Elazig earthquake in Türkiye further illustrates the importance of modern techniques in accurately mapping and analyzing co-seismic landslides³.

In 1949, the M7.4 Khait earthquake in Tajikistan triggered numerous landslides, including a massive loess flow in the Yasman valley (estimated volume 245 Mm³) and the Khait landslide (volume 75 Mm³). These landslides caused widespread destruction and significant casualties, with approximately 7200 deaths in the epicentral region. The Yasman valley loess flow alone killed around 4000 people, making it one of the deadliest landslides in recent history⁴.

Central America, a region of high seismic activity, frequently experiences landslides that exacerbate earthquake damage. Regional data show that landslide areas are comparable to global trends, but the number of slides can be disproportionately high for the magnitude of earthquakes in some areas. Landslide characteristics vary across the isthmus: soil falls and slides in volcanic soils are common in Guatemala and El Salvador, while extensive translational slides in lateritic soils are prevalent in Costa Rica and Panama. Hazard assessment methods developed in Costa Rica need modification for application in northern countries⁵.

These studies underscore the necessity of maintaining and updating co-seismic landslide inventories to enhance our understanding of earthquake-induced hazards and to improve preparedness and response capabilities.

Loess is a special type of soil. Compared with other soil types, its unique suspended pores and weak cementation structure endow it with strong dynamic and hydrosensitive catastrophic characteristics, exhibiting extremely high dynamic vulnerability. It is highly susceptible to inducing large-scale loess landslides under moderate to strong seismic activities, and thus has a strong potential for causing disasters.

The southern Ningxia area is characterized by thick loess cover, fragmented topography, undulating ridges and gullies. The Late Pleistocene Malan loess, which overlies the Tertiary mudstone, is prone to joint development, is loose and porous, and has poor stability. It is highly susceptible to slope instability under seismic action. The 1219 Guyuan M6½ earthquake, the 1306 southern Guyuan M6½ earthquake, the 1622 Guyuan M7 earthquake, and the 1920 Haiyuan M8.5 great earthquake all induced large-scale loess landslides. The losses caused by earthquake-induced loess landslides often exceed those directly caused by earthquakes. For example, the loess landslide induced by the 1975 Xiji M5.5 earthquake at Luzihetan Village buried the village, causing heavy casualties. The most typical earthquake is the 1920 Haiyuan M8.5 great earthquake that occurred 100 years ago. This earthquake induced a large number of loess seismic landslides in the southern Ningxia and neighboring areas, the boundaries of which are still basically well-preserved to this day. While causing heavy casualties, economic losses, and ecological destruction, it also provided a natural laboratory for seismological researchers to study the distribution characteristics, occurrence mechanisms, disaster modes, seismic hazards, and risk prevention of loess seismic landslides.

Since the 1990s, scholars both domestically and internationally have begun to pay extensive attention to loess landslide disasters induced by earthquakes, and have conducted field investigations and in-depth studies on the distribution patterns, basic characteristics, and formation mechanisms of loess landslides from multiple perspectives. Bai Mingxue (1990), Zou Jinchang (1996), Yuan Li Xia (2005), Chen Yongming (2006), Deng Longsheng (2013), Ye Ling (2013), Yang Shun (2017), Wang Lanning (2020), and Duan Yushi (2023) have successively summarized the characteristics of loess seismic landslides in the southern Ningxia area based on multiple batches of field investigation work, indicating that they are widely distributed, occur in groups, and form belts^{6,7,8,9,10,11,12,13,14}. There are three areas with a high incidence of landslides (southwest of Xiji County, west of Pengyang County in Guyuan, and southeast of Haiyuan County), which are mainly influenced by regional tectonics, topographic features, hydrological distribution, and the dynamic characteristics of loess. The loess seismic landslides in the study area often exhibit the following characteristics: (1) The slopes in landslide-prone areas are gentle, and their stability before the earthquake is high; (2) The scale of the sliding soil mass is large, the sliding distance is long, and the disaster impact range is wide; (3) Landslides occur in groups and form a string of bead-like dams; (4) The sliding surfaces are mostly located in the Malan loess layer or at the contact surface between loess and bedrock; (5) Loess liquefaction can trigger large-scale loess landslides.

Zhang (2007), Wang (2014), Zhang Xiaochao (2015), Wang (2018), Chang (2021), Wang (2023), Tian (2024), and Peng (2024) conducted in-depth research on the development mechanisms of loess earthquake-induced landslides in the study area through methods such as field investigations, in-situ tests, laboratory tests, and numerical analyses^{15,16,17,18,19,20,21,22,23}. They concluded that the development mechanisms of loess earthquake-induced landslides in the study area can be mainly divided into three types: shear-type landslides, liquefaction-type landslides, and collapse-type landslides. Shear-type landslides can be further classified according to the lithology of the sliding surface into landslides within the loess layer, landslides at the contact surface between loess and mudstone, and landslides cutting into the bedrock. Liquefaction-type landslides can be categorized based on the location of the liquefied layer into bottom liquefaction sliding type, surface liquefaction mudflow type, and combined bottom-surface liquefaction sliding-flow type. Collapse-type landslides can be subdivided according to the failure form of the slope body into subsidence-sliding type and collapse-sliding type.

Landslide hazard evaluation can provide probability prediction, spatial prediction, and intensity prediction of landslide disasters, which is one of the main methods for prevention and control of landslide disasters and also one of the effective approaches advocated and promoted internationally. In recent years, machine learning models based on artificial intelligence theory have developed rapidly, among which logistic regression models and neural network models are the most widely used. Xu et al. (2018) compared and analyzed six GIS-based landslide susceptibility evaluation models and found that the logistic regression model yielded the best results^23,24. Bragagnolo et al. (2019) proposed a novel approach for landslide susceptibility mapping based on an artificial neural network ensemble (ANNE), incorporating seven parameters from geomorphological, geological, and environmental factors. Their study, conducted in Porto Alegre and Rio de Janeiro, Brazil, demonstrated that the susceptibility maps generated by ANNE were more accurate than those published by official agencies, highlighting the efficiency and reliability of this method in developing robust landslide susceptibility maps²⁵. Rastkhadiv et al. (2023) employed machine learning algorithms based on statistical models to delineate landslide hazard zones in the Sarvabad region. They utilized a combination of statistical-based models, including frequency ratio–random forest (FR-RF), frequency ratio–support vector machine (FR-SVM), weights of evidence–random forest (WoE-RF), and weights of evidence–support vector machine (WoE-SVM), to identify key factors contributing to landslide susceptibility²⁶.Ma et al. (2025) investigated the mechanisms and influencing factors of landslides triggered by the 2013 extreme rainfall event in Tianshui using a logistic regression (LR) model. By integrating rainfall and landslide data, their study provided valuable insights into the formation processes and critical factors associated with rainfall-induced landslides in the region²⁷.

Neural network models, as a classic machine learning method, have been successfully applied in many fields. Yang (2020, 2022) successively used logistic regression, RBF neural network, and MLP neural network to evaluate the seismic hazard of loess landslides in the study area. A comprehensive analysis concluded that the logistic regression evaluation model has the advantages of high evaluation accuracy, fast evaluation speed, and simple and applicable operation^28,29.

This study aims to systematically investigate the distribution characteristics and seismic hazard potential of loess landslides in southern Ningxia, providing a scientific basis for seismic disaster prevention and mitigation in the region. Southern Ningxia is characterized by the presence of two major active Quaternary faults, the eastern Liupan Mountain Fault and the Haiyuan Fault. These faults have historically been the source of numerous moderate-to-strong earthquakes. Since the 1970 Xiji M5.5 earthquake, no earthquakes above M5.0 have occurred in the region over the past 50 years, suggesting a heightened hazard of future moderate-to-strong seismic events. The region is also marked by thick loess cover with relatively poor stability, making it highly susceptible to landslides triggered by seismic activity. To mitigate seismic disaster hazard in southern Ningxia, this study focuses on the following four research components: (1) Analysis of the spatial distribution characteristics of 600 loess landslides triggered by the 1920 Haiyuan M8.5 earthquake, exploring the relationships between landslides and factors such as seismic intensity, faulting, and topography; (2) Development of a rapid assessment formula for the seismic stability of loess slopes using a binary logistic regression model, based on geometric parameters of loess slopes and seismic intensity data; (3) Calculation of peak ground acceleration (PGA) at different probability levels in the study area using probabilistic seismic hazard analysis (PSHA); (4) Systematic evaluation of the seismic stability of loess slopes under various seismic motion intensities, combining the rapid assessment formula and seismic hazard analysis results, and the creation of six loess landslide hazard zoning maps under different estimated seismic motion intensities.

These research findings can serve as an important reference for seismic disaster hazard prevention, earthquake disaster prevention and mitigation planning, and risk assessment of related engineering construction projects within the study area.

Regional seismic tectonic background

The study area is located in the northeastern margin of the Tibetan Plateau, a special tectonic region with dense distribution of active faults and strong seismic activity. Since the Quaternary period, with the continuous uplift of the Tibetan Plateau and the northward thrust of the Indian plate, the main characteristic of tectonic activity has been vertical differential movement with overall compressional uplift as the background, accompanied by left-lateral strike-slip movement, such as the Haiyuan fault zone and the eastern piedmont fault zone of Liupan Mountain. Both historically and in modern times, the study area and its surroundings have been regions with frequent earthquakes, making it one of the most severely earthquake-affected areas in China(as shown in Fig. 1). A total of 33 moderate to strong earthquakes have occurred in the area, including 1 earthquake of M8.5, 5 earthquakes of M7-7.9, 8 earthquakes of M6-6.9, and 19 earthquakes of M4.7-5.9. These frequent moderate to strong earthquakes have caused severe disaster losses and ecological destruction in the study area. However, since the 1970 Xiji M5.5 earthquake, no earthquakes above magnitude 5.0 have occurred in the southern Ningxia and neighboring areas within the past 50 years, indicating a high potential seismic risk in the region. The topography in the area is diverse, which can be roughly divided into bedrock mountainous areas, loess ridge hilly areas, loess knolls, and river valley terraces, with clear layers and orderly distribution. The advantageous natural topographic and geomorphological conditions, combined with the frequent moderate to strong seismic activities, make loess landslides in the study area prone and frequent, such as the large-scale, dense, and cluster loess landslides induced by the 1920 Haiyuan great earthquake, resulting in heavy economic losses and casualties.

Fig. 1

Geological strata and seismic tectonic distribution map of the study area. The map was created with the legitimate software ArcGIS (Esri, version 10.8- https://www.esri.com/).

Distribution characteristics of loess seismic landslides

Spatial distribution characteristics

This paper takes the loess seismic landslides induced by the 1920 Haiyuan M8.5 great earthquake as the main research object to analyze the distribution characteristics of loess seismic landslides in the southern Ningxia area. Based on the basic data of more than 600 coseismic landslides of the Haiyuan great earthquake obtained through field investigations, a landslide database was established, and the spatial distribution relationship between landslide distribution and seismic intensity as well as the distance to the fault rupture was obtained (see Figs. 2 and 3).The seismic intensity data for the 1920 Haiyuan M8.5 earthquake (Fig. 2) were obtained from the China Earthquake Networks Center (CENC) database, which provides detailed records of historical earthquake impacts. For more detailed intensity maps, we also referred to the studies by Zhang et al. (2007) and Wang et al. (2014), which provide comprehensive analyses of the earthquake-induced landslides and their spatial distribution^30,31. As shown in Figs. 2 and 3, the landslides in the study area exhibit a clustered and densely developed characteristic, and can be mainly divided into three distribution areas in space, namely Zone A, B, and C in Fig. 3.

Fig. 2

Seismic intensity and landslide distribution of the 1920 Haiyuan M8.5 great earthquake. The map was created with the legitimate software ArcGIS (Esri, version 10.8- https://www.esri.com/).

Fig. 3

Distance to the fault rupture of the 1920 Haiyuan M8.5 great earthquake and landslide distribution. The map was created with the legitimate software ArcGIS (Esri, version 10.8-https://www.esri.com/).

The landslides in Zone A are mainly distributed within a 10-kilometer range on the north side of the Haiyuan fault zone, in the Jiucai Township of Haiyuan County. The Malan loess in this area is carpet-like in coverage over the Tertiary mudstone. However, due to the influence of eolian deposition and the relatively steep original topographic slopes, the loess cover is relatively thin, with a general thickness of about 5–10 m, leading to poor overall stability of the slopes. Additionally, this region is located in the extreme epicentral area (intensity XI) of the 1920 Haiyuan great earthquake. The ground motion was intense, causing the Malan loess to slide along the original topography of the underlying bedrock, resulting in irregularly shaped “peeling-style collapse” phenomena (as shown in Fig. 4).

Fig. 4

“Peeling-type collapse” landslide in the extreme seismic area (zone A).

The landslides in Zone B are primarily distributed in the southwestern part of Xiji County, within a 30–60 km range south of the Haiyuan fault zone. The loess cover in this region is relatively thick, with a general thickness ranging from 10 to 50 m, and an optimal thickness of approximately 25 m. The Malan loess overlies the Tertiary mudstone, forming a typical bimodal stratigraphic structure. During the 1920 Haiyuan great earthquake, this area was located within the IX intensity zone, where the ground motion was intense, leading to the development of large-scale, cluster loess seismic landslides. Due to the thick loess cover, the boundaries of the developed loess seismic landslides are relatively regular, specifically manifesting as “armchair-shaped,” “elongated,” and “horseshoe-shaped” forms (as shown in Fig. 5).

Fig. 5

Well-defined loess seismic landslides with regular boundary morphologies in zone B.

The landslides in Zone C are predominantly located within a 20–60 km range southeast of the Haiyuan fault zone, in the eastern Guyuan and western Pengyang regions. The loess cover in this area is relatively thick, with a general thickness ranging from 20 to 50 m and an optimal thickness of approximately 30 m. The Malan loess overlies the Tertiary mudstone, and the slopes are relatively steep with well-developed incised valleys. During the 1920 Haiyuan great earthquake, this region was situated within the IX and VIII intensity zones and was at the terminal end of the fault rupture direction. The combined effects of seismic motion intensity and the propagation direction of seismic waves resulted in the development of a large number of large-scale and morphologically intact loess seismic landslides in this area, compared to the VIII intensity zone south of Zone B (as shown in Fig. 6).

Fig. 6

Loess seismic landslides with regular boundary morphologies in zone C.

Based on the spatial distribution characteristics of landslides, the landslides in the study area are primarily concentrated in the three Zone A, B, and C shown in Fig. 3. The specific reasons are as follows: within the same seismic intensity range, the loess cover on the north side of the fault zone is thinner, and the eolian loess contains a higher proportion of large-grained sand and gravel, with relatively low original slope angles. Moreover, the north side is located on the hanging wall of the fault rupture, where seismic motion attenuates more rapidly. Therefore, apart from the landslides developed in the extreme epicentral area (Zone A), there are fewer landslides in other regions. In contrast, the densely developed landslide Zone B and C are mainly characterized by loess ridges and gullies, with thicker loess cover, and deeply incised valleys. These conditions are conducive to the formation of loess seismic landslides. As shown in Fig. 2, there are very few landslides distributed in the areas south of the fault zone with intensity X and above. Figure 1 indicates that this region is predominantly composed of bedrock mountainous areas with sporadic loess cover, lacking the stratigraphic conditions necessary for the development of loess landslides, thus resulting in sparse landslide distribution. In areas below the VIII intensity zone, the seismic energy is relatively low, and the high-frequency components in the seismic motion are insufficient to trigger loess seismic landslides. In summary, the development of seismic landslides in the area is the result of the combined effects of topography, lithology, and seismic motion characteristics. Earthquakes not only provide the external triggering conditions for landslide occurrence but also cause soil loosening through vibration, leading to fatigue, softening, or liquefaction of the soil, thereby reducing the shear strength of the soil and rock mass and significantly increasing the probability of seismic landslide occurrence.

Distribution characteristics in topography and geomorphology

Distribution characteristics in the valley geomorphic region

The loess landslides induced by the Haiyuan great earthquake formed a large number of dams in the upper reaches of the Lan Ni River in Xiji County, among which the largest, the Dangjiacha dam, was 5 km long and about 300 m wide. Field investigation results show that the landslides along the Lan Ni River are mainly concentrated on the south bank of the river, while there are almost no landslide phenomena on the north bank. Specifically, a series of dam-forming landslides such as Dangjiacha landslide, Dagenzi landslide, Zhenhu Township landslide, Huierchakou landslide, and Maoping Village landslide are all located on the south bank of the river and slide towards the northwest and northeast directions (see Fig. 7). The reasons for this distribution characteristic are mainly as follows: First, the loess in the northwest region is mainly formed by the deposition of dust particles from the northwest and northeast desert areas, which are transported by monsoons from the northwest to the southeast, resulting in a thicker loess cover on the northwest slopes and a relatively thinner loess cover on the southeast slopes. The thicker loess cover provides a favorable material basis for landslide development. Second, the water flow in the upper reaches of the Lan Ni River moves from the southwest to the northeast, and under the influence of the Coriolis force, the erosion of the south bank by the water flow is more significant, thus providing good free-face conditions for landslide development. Finally, a comparative analysis of the vegetation cover on the north and south banks of the slope found that the vegetation cover on the south side is significantly higher than that on the north side, which makes the groundwater conditions of the south side slope strata relatively higher, providing sufficient groundwater conditions for landslide development.

Fig. 7

Landslide distribution on the north and south banks of the Lan Ni river.

Distribution characteristics in the loess ridge geomorphic region

Loess ridges are the principal geomorphic units where loess seismic landslides develop in the study area, with landslides occurring on the ridge slopes accounting for over 90% of the total. Statistical analysis of the distribution of landslides and the extension directions of the loess ridges within the study area reveals that landslides are predominantly concentrated on both sides of loess ridges extending in the 180°±50° direction. The reason for this is that the windward slopes of loess ridges extending in the 180°±50° direction are subjected to strong loess eolian deposition from the northern desert areas, resulting in thicker loess deposits, with a general thickness of approximately 20 m. Moreover, the fluvial erosion and downcutting in the gullies are intense, leading to a high incidence of loess seismic landslides on one or both slopes of such gullies.

According to field investigation and remote sensing interpretation results, as shown in Figs. 8 and 9, landslides on loess ridges extending in the NW direction are mainly concentrated on the eastern slopes of the ridges, while landslides on loess ridges extending in the SE direction predominantly occur on the western slopes. The primary reason for this difference is the varying thickness of loess cover on the two slopes. The study area is overall influenced by loess eolian deposition from the NE direction (Mu Us Desert) and the NW direction (Tengger Desert). Specifically, the eastern slopes (windward slopes) of loess ridges extending in the NW direction are subjected to strong NE-directed loess eolian deposition, leading to thicker loess deposits. In contrast, the western slopes (windward slopes) of loess ridges extending in the SE direction are subjected to strong NW-directed loess eolian deposition, also resulting in a thick loess layer. In comparison, the loess cover on the leeward slopes is relatively thinner, hence landslides are more densely distributed on the windward slopes.

Fig. 8

Distribution of landslides on both sides of loess ridges extending in the NW direction.

Fig. 9

Distribution of landslides on both sides of loess ridges extending in the SE direction.

Distribution characteristics in the loess knoll geomorphic region

Loess knolls and loess micro-basins are unique geomorphic units in loess hilly areas and are also high-incidence areas for loess seismic landslides. According to field investigations, convergent failure slides have occurred on the surrounding slopes within the knolls and micro-basins in locations such as Hanjia Knoll, Zhangwan Village, Xiajiawan, and Tai zi Knoll (as shown in Fig. 10). Field investigation studies have shown that the loess structure in these areas is loose and the cover is relatively thick, with good water convergence conditions, leading to a higher water content in the internal soil mass, thereby resulting in the internal wall soil strength being lower than that of the external wall. During an earthquake, loess knolls and loess micro-basins are prone to amplify seismic motion, exacerbating the seismic damage to the internal wall soil mass, and thus triggering convergent failure slide phenomena.

Fig. 10

Convergent development of loess seismic landslides within loess knolls.

Development characteristics of loess seismic landslides

The original topography is one of the key factors controlling landslide development and is also an important indicator for macro-prediction of loess seismic landslides. As shown in Fig. 11, statistical analysis of the original slope height and angle of landslides within the study area reveals that the original slope height is mainly distributed between 40 and 140 m, involving 292 landslides, accounting for 84% of the total number of landslides counted; the original slope angle is mainly concentrated between 10° and 22°, accounting for 79% of the total number of landslides counted.

Fig. 11

Distribution of original topographic slope height and angle of landslides.

Loess seismic landslides in the study area are primarily developed in the widely distributed low and gentle loess hilly regions. According to field investigations, the original slope shapes of the loess ridge slopes in the area are generally straight and the slope surfaces are relatively gentle. However, due to fluvial downcutting and incision, a significant free-face angle is formed at the slope front, generally ranging from 50° to 70°, which provides favorable free-face conditions for the development of loess seismic landslides (as shown in Fig. 12).

Fig. 12

Original topography and geomorphology of loess ridge slopes in the study area.

As shown in Fig. 13 and 82.9% of the landslide slopes are distributed between 4° and 12°, with 68.7% of the landslide slopes concentrated in the range of 4° to 10°. Field investigations indicate that the slopes of the vast majority of loess-mudstone contact surface landslides fall within this range. These landslide bodies are generally flat, with clear landslide traces, steep rear walls, and thin rear edges. In some landslides, the exposed slip surface can be seen between the rear wall and the rear edge, and small bulges are locally developed at the front edge of some landslides. Particularly for such landslides developed on both sides of deep and long gullies, the landslide mass often accumulates to the opposite slope, forming local uplifts, which are mostly cut through by later-developed “V”-shaped gullies. In addition, landslides with slopes less than 4° account for 10.6% of the total number counted. Except for a few individual loess liquefaction landslides, the majority of these low-angle landslides are cluster loess landslides within loess knolls. These landslides are large in scale and have long sliding distances, with the maximum reaching 1 to 2 km. The landslide bodies are generally flat, with local undulations. Due to severe human modifications in later periods, the current topographic undulations are no longer obvious.

Fig. 13

Histogram of landslide slope angle distribution.

As illustrated in Fig. 14, statistical analysis of the measured sliding distances of 320 loess seismic landslides within the study area reveals that 77% of these landslides have sliding distances less than 400 m. This characteristic is predominantly influenced by the geomorphological features where the landslides develop. The majority of loess seismic landslides in the study area occur within the gullies on both sides of loess ridges. The sliding distances of these landslides are largely constrained by the width of the gullies in the sliding direction and the obstruction posed by the opposing slopes. Consequently, the sliding distances of landslides occurring on both sides of loess ridge gullies are mostly less than 400 m, typically around 1.5 times the width of the gullies. However, approximately 10% of the landslides exhibit sliding distances greater than 600 m. These landslides are predominantly group-occurrence loess landslides within loess knolls, characterized by their large scale, gentle sliding mass, and long sliding distance. As shown in Fig. 15 and 80% of the landslides have areas less than 0.4 square kilometers. The reasons for this are consistent with those for the sliding distances, as the original geomorphological conditions where the landslides develop not only control the sliding distances of the landslide bodies but also their scales.

Fig. 14

Histogram of sliding distances of loess seismic landslides in the study area.

Fig. 15

Histogram of landslide area of loess seismic landslides in the study area.

According to the aforementioned analysis, loess seismic landslides in the southern Ningxia area are densely distributed in the loess ridge regions with greater topographic undulations. The distribution of landslides is not only directly affected by the intensity of seismic motion but also has a close spatial association with the Haiyuan fault zone. Furthermore, by analyzing the development characteristics of landslides, it can be concluded that the landslides in the area have typical characteristics such as gentle development slopes, large landslide scales, long sliding distances, wide disaster impact ranges, and strong cluster occurrence.

Seismic hazard evaluation of loess slopes in the study area

This study, based on an in-depth analysis of the topography, geomorphology, and lithological parameters of loess slopes within the study area, utilizes the proposed rapid evaluation formula for the seismic stability of loess slopes to systematically assess and calculate the seismic stability of original landslide slopes and user-defined computational points under various seismic motion intensities(as shown in Fig. 16). The seismic motion intensities employed are derived from probabilistic seismic hazard calculations, covering a range of probability levels to ensure the comprehensiveness and accuracy of the evaluation results. Through detailed seismic hazard evaluations of the computational results, this study ultimately produced a hazard zoning map of loess seismic landslides in the southern Ningxia area under different estimated seismic motion intensities. This zoning map intuitively displays the potential risk distribution of loess seismic landslides in the southern Ningxia area under various seismic motion intensities, providing important scientific evidence and technical support for seismic disaster risk prevention, earthquake disaster mitigation planning, and risk evaluation of related engineering construction projects in the region.

Fig. 16

Flowchart of seismic hazard evaluation for loess landslides in the study area.

Construction of the foundation database of loess slopes

The foundation database for rapid evaluation of seismic stability of loess slopes is constructed based on detailed investigation data from 600 landslides. By combining remote sensing interpretation with field verification, an additional 500 sets of slope basic data were supplemented, resulting in a total of 1100 sets of basic slope data determined in the ArcGIS database as the foundational model data for rapid evaluation (as shown in Fig. 17). The model data mainly include slope height H, slope angle A, slope type B, intensity I, and intensity index K. These data have the primary advantage of being easily obtainable, which can meet the basic requirements for rapid evaluation.

Fig. 17

Spatial distribution map of loess slopes in the study area. The map was created with the legitimate software ArcGIS (Esri, version 10.8- https://www.esri.com/).

Rapid evaluation formula for seismic stability of loess slopes

Integrating the results of three rapid evaluation models for the seismic stability of loess slopes proposed by Yang (2021, 2022), this study selects the binary logistic regression analysis model with the highest discriminative accuracy and the most convenient discriminative operation as the final calculation formula^20,21. Logistic regression analysis is a multivariate statistical analysis method for handling complex variables with multiple factors and has been widely applied in research fields such as medicine, biology, and sociology. The limit state of slope stability is divided into two conditions: “sliding” and “non-sliding.” Assuming that “sliding” is denoted as 1 and “non-sliding” as 0 in the determination results, the stability evaluation of landslides then becomes a binary variable problem. When evaluating the seismic stability of slopes, due to the coupled influence of affected factors, there is no clear distinction between sliding and non-sliding. Logistic regression analysis can effectively handle complex, non-continuous problems and is suitable for predicting binary classification variable problems of whether landslides will occur or not. Moreover, logistic regression analysis has relatively flexible requirements for independent variables, which can be continuous variables, ordinal variables, and nominal variables, etc., and can effectively eliminate the impact of excessive discrete degree of single factors on the prediction results.

The logistic regression model can be expressed as follows: Let P be the probability of a landslide occurring, with a value range of [0,1]. Consequently, $\left( {1 - p} \right)$represents the probability of no landslide occurring. Taking the natural logarithm of the ratio of these probabilities yields $\ln \left[ {\frac{p}{{\left( {1 - p} \right)}}} \right]$. Let $Z = \ln \left[ {\frac{p}{{\left( {1 - p} \right)}}} \right]$and consider it as the dependent variable^35,36. The influencing factor indicators $x_{i}$ (where$i$ = 1,2,…,n) are taken as the independent variables to establish a linear regression Equation^35,36:

$$Z = \ln \left( {\frac{p}{{1 - p}}} \right) = \mathop B\nolimits_{0} + \mathop B\nolimits_{1} \mathop x\nolimits_{1} + \mathop B\nolimits_{2} \mathop x\nolimits_{2} + \cdot \cdot \cdot \cdot \cdot + \mathop B\nolimits_{n} \mathop x\nolimits_{n}$$

(1)

This can be transformed into:

$$P = \frac{{\exp \left( Z \right)}}{{1 + \exp \left( Z \right)}} = \frac{{\exp \left( {\mathop B\nolimits_{0} + \mathop B\nolimits_{1} \mathop x\nolimits_{1} + \cdot \cdot \cdot + \mathop B\nolimits_{n} \mathop x\nolimits_{n} } \right)}}{{1 + \exp \left( {\mathop B\nolimits_{0} + \mathop B\nolimits_{1} \mathop x\nolimits_{1} + \cdot \cdot \cdot + \mathop B\nolimits_{n} \mathop x\nolimits_{n} } \right)}}$$

(2)

In Eqs. (1) and (2), $B_{i}$ (where $i$= 1,2,…,n) are the regression constants.

The fundamental principle of logistic regression is to utilize known statistical data to establish a logistic regression model, thereby transforming the nonlinear relationship between independent variables and the dependent variable into a relationship between independent variables and the phenomenon of logic, and subsequently obtaining the coefficients of the independent variables through parameter estimation. The method of loess slope seismic stability based on logistic regression analysis reveals the corresponding relationship between slope height, slope angle, site intensity, and sliding probability. When the independent variables change, they do not directly affect the probability results but rather indicate the degree of change in the logical calculation results, eliminating the misjudgment impact caused by singular values of single factors on the results^35,36.

The evaluation method of loess slope seismic stability based on logistic regression model analysis is directly determined by the measured data of loess slopes in the study area, considering the uncertainty of earthquakes and the interactions between various influencing factors as implicit quantities. During the process of regional slope stability prediction or earthquake disaster relief emergency in the study area, the seismic stability of loess slopes in the area can be quickly evaluated by directly measuring slope height, slope angle, and estimating seismic motion intensity.

This study employs the regression analysis module in the statistical analysis software SPSS (Statistical Product and Service Solutions) to calculate the coefficients of independent variables in the logistic regression model. Through regression analysis of 700 sets of slope survey data, Eqs. (3 and 4) are derived, which use five conventional parameters—slope height, slope angle, intensity, slope type index, and calculated intensity index—as evaluation indicators for the seismic stability evaluation formula of loess slopes.In the formula, slope height, slope angle, and intensity are the independent variables involved in the logistic regression analysis. The slope type index and calculated intensity index are model optimization factors derived based on the distribution and development characteristics of loess earthquake-induced landslides in the study area. The consideration of model optimization factors is aimed at evaluating whether the formula can be more reasonably and accurately applied to the rapid assessment of the seismic stability of loess slopes in the study area, compared with the basic logistic regression model.

$$P = \frac{1}{{1 + \mathop e\nolimits^{{ - z}} }} * B * \eta$$

(3)

In the equations, P represents the probability of slope failure, with P ≥ 0.5 indicating failure and P<0.5 indicating stability^35,36; B is the slope type index, taking a value of 1 when the loess cover thickness on the loess slope is ≥ 5 m, and 0 when it is < 5 m; η is the calculated intensity index, taking a value of 1 when the intensity is ≥VII+, and 0 when the intensity is <VII+; z is the stability evaluation index, as shown in Eq. (2).

$$z = - 22.8805 + 0.003858 * H + 1.31932 * A + 0.875739 * I$$

(4)

In the equation, z is the stability evaluation index; H is the slope height (in meters); A is the slope angle (in degrees); I is the estimated intensity value of the site where the slope is located. During calculation, the intensity (such as VIII, IX, X) is converted to numerical values (8, 9, 10) and substituted into Eq. (4) for computation.

In the aforementioned equation, the determination criterion for the slope type index B is primarily based on the height difference of the rear wall of loess seismic landslides within the study area. The rear wall area of a landslide marks the posterior boundary of the landslide mass, and its height and morphology can reflect the scale and sliding depth of the landslide. Field investigations have revealed that the majority of the landslide beds in the area are exposed, thus the height difference of the landslide rear wall can, to a certain extent, reflect the thickness of the loess cover on the loess slope. As shown in Fig. 18, the minimum height difference of the landslide rear wall in the area is 5 m, hence 5 m is established as the threshold for determining the slope type index B.

Fig. 18

Histogram of rear wall height differences of loess seismic landslides in the study area.

Qi (1998) summarized the investigation of landslides triggered by the 5.8 magnitude earthquake in Yongden, Gansu on July 22, 1995. The landslides were mainly distributed in areas with an intensity of VII+ and VIII degrees, with virtually no landslides occurring in areas of VI degree and below³². The landslides were predominantly aligned along faults and river terraces, with gullies often developing at the foot of slopes, especially at the bends of these gullies, where larger-scale landslides were more likely to occur. According to the seismic disaster investigation data from the Ningxia Seismological Bureau, a 5.5 magnitude earthquake occurred in Subao (now Xiji County’s Zhenhu Township) on December 3, 1970, with the epicentral area located in Subao Commune and an intensity of VII+ degrees. A major landslide occurred on both banks of a water dam located 1 km northwest of Luzicha in Subao Commune, with the east slope experiencing a vertical displacement of 50 m over a 300-meter terrain, and the west slope a vertical displacement of 80 m over a 400-meter terrain. Based on the aforementioned investigation results of landslide disasters in loess areas from these two earthquakes, the minimum seismic motion intensity to induce loess earthquake landslides is VII+ degrees, and thus this is used as the threshold for determining the intensity index η in calculations.

This study validates the rationality and applicability of the seismic stability evaluation formula for loess slopes derived from logistic regression analysis by verifying 700 sets of regression analysis data and 91 sets of non-regression analysis data. As shown in Table 1, the average success rate of back-validation using 700 sets of regression analysis data reaches 96.3%, with excellent results. As shown in Table 2, the success rate of discriminant validation using 91 sets of slope data not involved in regression analysis reaches 98.3%, with excellent results. Therefore, it can be concluded that, under the conditions that meet the applicability criteria, this formula is suitable for the rapid evaluation of seismic stability of loess slopes in the area.

Table 1 Result table for back-prediction validation of data in logistic regression analysis.

Table 2 Verification and discriminant result table of the discriminant formula.

The input seismic motion for seismic hazard evaluation

This study employs the Conditional Probabilistic Seismic Hazard Analysis (CPSHA) method to determine the input seismic motion for the rapid evaluation of seismic stability of loess slopes. The CPSHA method is an extension of the Probabilistic Seismic Hazard Analysis (PSHA) theory, which accounts for the spatiotemporal inhomogeneity of seismic activity. This approach reflects the temporal inhomogeneity of seismic activity through seismic activity parameters and spatial inhomogeneity through the division of seismic belts and potential seismic source zones, as well as differences in their seismic activities. Additionally, the CPSHA method proposes a multi-factor comprehensive evaluation method for the spatial distribution function of potential seismic source zones and the idea of segmental statistical seismic activity parameters to reflect the temporal inhomogeneity of seismic activity. In conjunction with the characteristics of seismic motion attenuation in China, this method applies an elliptical attenuation relationship and uses specific tectonic scales and more detailed tectonic markers to delineate potential seismic source zones, thereby reducing the scale of potential seismic source zones and more accurately reflecting the spatial distribution inhomogeneity of seismic activity.

The basic approach and computational methods of the CPSHA method include the following steps: First, the study area is divided into potential seismic source zones to clarify the seismic activity characteristics of different regions. Second, recurrence models for each potential seismic source zone are established to quantitatively describe the frequency and intensity of seismic activity. Third, seismic motion prediction models are constructed to predict the impact of earthquakes from different source zones on the target site. Finally, the seismic hazard at the site is calculated by integrating the above information, providing scientific and reliable seismic motion input parameters for the evaluation of seismic stability of loess slopes.

This study takes the study area as the computational region and employs a refined grid division strategy. Within the computational region, calculation control points are precisely divided at intervals of 6″×6″ (longitude and latitude), totaling 852,145 calculation points. Based on the probabilistic seismic hazard analysis method (CPSHA method), this study calculates the peak ground acceleration (PGA) of the bedrock at each control point under different time scales and exceedance probability conditions, including PGA values for 50-year exceedance probabilities of 10% and 2%, as well as 100-year exceedance probabilities of 63%, 10%, 2%, and 1%. By establishing the conversion relationship between PGA and seismic intensity, this study ultimately produces seismic intensity distribution maps for the study area under six probability levels. These seismic intensity distribution maps intuitively display the seismic hazard levels of the study area under different probability conditions, providing precise and reliable input seismic motion data for the rapid evaluation of seismic stability of loess slopes (as shown in Fig. 19).

Fig. 19

Seismic intensity distribution maps of the study area under six probability levels. The map was created with the legitimate software ArcGIS (Esri, version 10.8- https://www.esri.com/).

Seismic hazard evaluation of loess slopes in the study area

This study, based on the topographic and geomorphological parameters of loess slopes obtained within the study area, constructed a foundational model database and utilized the proposed rapid evaluation formula for the seismic stability of loess slopes to systematically evaluate the seismic stability of 1,100 loess slopes under different seismic motion intensities. Specifically, this study conducted precise evaluations of the seismic stability of each loess slope according to the different seismic motion intensity levels detailed in Sect. “The input seismic motion for seismic hazard evaluation”, and subsequently produced hazard zoning maps of loess seismic landslides in the southern Ningxia area under various estimated seismic motion intensities, as shown in Fig. 20.

Regarding the hazard zoning criteria, this study established that when the evaluation result P ≥ 0.5, the area is classified as a high-risk zone, indicating a higher probability of loess seismic landslides occurring under the corresponding seismic motion intensity, requiring focused attention and prevention measures. Conversely, when the evaluation result P < 0.5, the area is classified as a low-risk zone, suggesting a relatively lower risk of loess seismic landslides under the given seismic motion intensity conditions. Through this scientific and clear evaluation standard, this study provides a clear and reliable basis for the hazard zoning of loess seismic landslides in the southern Ningxia area, offering strong support for earthquake disaster risk prevention, land use planning, and risk evaluation of related engineering construction projects in the region, and holds significant practical application value.

Fig. 20

Seismic landslide susceptibility zonation map of the study area under six probability levels. The map was created with the legitimate software ArcGIS (Esri, version 10.8- https://www.esri.com/).

According to the evaluation results shown in Fig. 18, under the condition of a 100-year exceedance probability of 63%, the study area is identified as a low-risk stable zone. This is primarily due to the low seismic motion intensity in the area, which results in a lower risk of loess seismic landslides. Under other exceedance probability conditions, as the seismic motion intensity increases, the scope of high-risk instability areas also expands accordingly, particularly from a 50-year exceedance probability of 10–2%, where this change is particularly significant. When the exceedance probability is reduced to 2% and 1% for 100 years, the difference in the scope of high-risk instability areas is minimal. The main reason is that once the local seismic motion intensity reaches a certain threshold, the stability of the slope depends on its soil and rock structure, rather than the seismic motion intensity. Therefore, slopes with thin or no loess cover exhibit higher stability.

By analyzing the expansion of high-risk instability areas, it can be observed that most areas in the western and southwestern parts of Xiji County, 90% of the area in Pengyang County, the northeastern part of Yuanzhou District, and the areas around Jiucai Township and Lijun Township in Haiyuan County are at extremely high risk of landslides when the seismic motion intensity increases. This can be verified by the distribution of landslides triggered by the 1920 Haiyuan great earthquake. Additionally, certain areas in the eastern part of Haiyuan County, such as Shidian Township, the northern part of Xian Town, and parts of Gancheng Township, also have a certain risk of landslides. Although the loess slopes in these areas have a low angle and thick cover, the 1920 Haiyuan 8.5 magnitude great earthquake triggered sporadic loess seismic landslides in these regions. However, the risk of inducing loess seismic landslides during moderate to strong earthquakes in these areas cannot be ignored.

In recent years, significant progress has been made in landslide hazard assessment research in Western China, a region highly susceptible to landslide disasters. Wang et al. (2021) employed a SCM-ANFIS hybrid machine learning model to evaluate seismic landslide hazards in Sichuan, China. Their study revealed that high-risk areas are predominantly located near active faults, with risk diminishing as distance from the fault increases. The model results closely matched the actual distribution of seismic landslides, demonstrating its applicability for long-term landslide risk assessment over large areas³³. Qian et al. (2023) conducted research in the intersection area of Min County and Zhang County in Dingxi City, Gansu Province, China. By statistically analyzing historical earthquake-induced landslide data, they established an evaluation index system comprising eight influencing factors: earthquakes, slope gradient, slope height, slope aspect, lithology, average annual rainfall, river basins, and geomorphological types. Using the information value model, logistic regression model, and a coupled information value-logistic regression model, they analyzed the susceptibility of loess landslides in the region. The results indicated that earthquakes, rivers, and rainfall are the primary factors triggering loess landslide disasters, with the earthquake factor having the highest contribution rate. The precision of the three models was tested using the receiver operating characteristic (ROC) curve, with AUC values of 0.889, 0.617, and 0.898, respectively. The coupled information value-logistic regression model exhibited the highest precision³⁴. Ma et al. (2025) utilized a data-driven logistic regression (LR) model to construct a landslide probability assessment model, incorporating total rainfall and landslide data. The model’s uncertainty was quantified through 20 runs, and the probability of landslides under various rainfall scenarios was analyzed. The results showed that the predicted landslide probability distribution was consistent with the actual distribution, with high probability areas mainly located on valley sides. As rainfall accumulates, areas with low probability (< 0.005) decrease, while those with moderate probability (0.01–0.02) increase²⁷.

The hazard assessment methodology employed in this study integrates the research findings of Wang et al. (2021) and Qian et al. (2023), incorporating factors such as seismic intensity, topography, and geological conditions to establish a landslide susceptibility model tailored for the southern Ningxia region. Wang et al. (2021) demonstrated the application of hybrid machine learning models in seismic landslide risk assessment, providing a significant reference for our study. Qian et al. (2023) validated the superiority of the information value-logistic regression coupled model in loess landslide hazard assessment through comparative analysis of multiple models. Ma et al. (2025) further confirmed the applicability and reliability of the data-driven logistic regression model under various rainfall scenarios. By comparing our results with those of Ma et al. (2025), we verified the accuracy and applicability of our model. Compared with Wang et al. (2021), our study identified similar patterns in landslide distribution but observed significant differences in the relationship between landslide frequency and earthquake magnitude in certain areas, likely attributable to the unique geological and topographical characteristics of southern Ningxia. Building on existing literature, our study provides a detailed distribution and hazard assessment of loess landslides in southern Ningxia through extensive field surveys and data analysis, offering new insights and methodologies for hazard assessment in the region.

Conclusions

This study, based on extensive collection and organization of previous research results and in-depth field investigations, conducted a systematic study on the distribution characteristics and seismic hazard assessment of loess landslides in the southern Ningxia area. The study results reveal the following key findings:

Firstly, loess seismic landslides in the southern Ningxia area exhibit a distinct pattern of dense spatial distribution, primarily concentrated in the loess ridge regions with significant topographic undulations. The distribution of landslides is not only directly affected by the intensity of seismic motion but also closely related to factors such as fault rupture, groundwater, and micro-geomorphology. Additionally, the landslides in the study area display a series of typical characteristics, including gentle development slopes, large landslide scales, long sliding distances, wide disaster impact ranges, and strong cluster occurrence.

Secondly, based on the geometric parameter database of loess landslides in the southern Ningxia area, this study carefully selected key indicator parameters such as slope height, slope angle, seismic motion intensity, slope type index, calculated intensity index, and slope stability status. By applying the binary logistic regression model, these parameters were analyzed in depth, and a rapid assessment formula for the seismic stability of loess slopes was successfully proposed, providing an efficient and practical method for the seismic stability assessment of loess slopes.

Thirdly, using the foundational model database established based on the topographic and geomorphological parameters of loess slopes in the study area, this study applied the proposed rapid assessment formula for the seismic stability of loess slopes to comprehensively evaluate the seismic stability of loess slopes under different seismic motion intensities. Ultimately, six hazard zoning maps of loess seismic landslides in the southern Ningxia area under different estimated seismic motion intensities were drawn, providing an intuitive and scientific visualization tool for seismic landslide risk assessment in the region.

In summary, the results of this study not only provide a macro-level basis for seismic emergency response and seismic disaster loss assessment but also enable quantitative assessment of loess seismic landslides in seismic emergency, seismic disaster loss assessment, and seismic safety evaluation. Furthermore, the hazard zoning maps of loess seismic landslides in the southern Ningxia area under different seismic motion intensities can serve as important references for future seismic disaster prevention and mitigation planning, land use planning, and risk assessment of related engineering construction projects in the region, holding significant theoretical and practical value.

This study systematically summarized the distribution characteristics of loess seismic landslides in the southern Ningxia area and conducted hazard zoning research on loess seismic landslides within the study area. However, the study still has the following limitations: First, the loess seismic landslide samples in this study all originated from the 1920 Haiyuan 8.5 magnitude great earthquake and are mainly distributed in the southern Ningxia area, which limits the applicability of the project results geographically; second, the rapid assessment method for the seismic stability of loess slopes used in this study is relatively conservative; third, the number of loess slope samples used for assessment calculations is relatively low, which somewhat restricts the accuracy of the rapid assessment zoning results.

In view of the above issues and the new demands for loess seismic landslide research, future work should focus on the following aspects: First, comprehensively consider the interactive effects of multiple factors to optimize and propose a more accurate and efficient assessment method for the seismic stability of loess slopes; second, expand the collection range and number of loess slope samples to improve the accuracy and reliability of the rapid assessment zoning results; third, initiate the construction of a two-dimensional loess slope database to further enhance the sample accuracy and scientific nature of the rapid assessment of the seismic stability of loess slopes; fourth, deeply explore the regional disaster-causing nature of loess seismic landslides, achieving a shift in research focus from “whether landslides will occur” to “the potential disaster range and loss caused by landslides after they occur,” providing more scientific and systematic theoretical support and technical guidance for the comprehensive prevention and control of loess seismic landslides.