Early Warning and Risk Assessment for Rainfall-Induced Shallow Loess Landslides

Abstract

Rainfall-induced shallow loess landslides pose a significant threat to human life and property. Early warning and risk assessment of these landslides are critical prerequisites for engineering control and disaster loss reduction. The Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Model (TRIGRS)-Three-dimensional Slope Stability Analysis Tool (Scoops 3D) joint model can overcome the shortcomings of using a single TRIGRS model for hydrological analysis and a single Scoops 3D model for slope stability analysis. Landslide risk assessment based on expected economic loss, on the other hand, can overcome the issue of maintaining the risk level edge and sorting at the same level. In this paper, the TRIGRS model’s head pressures were put into the Scoops 3D model, with the southeast of Fangta, a town in Shaanxi province, China, as the study area. The relationship between the slope gradient and the number of grids in each stable grade was certified. The rainfall thresholds for landslides, based on both rainfall intensity and rainfall duration, were obtained by rerunning the TRIGRS-Scoops 3D joint model. The landslide range and land uses of each dangerous slope were determined by maximum likelihood classification, and then the expected economic loss was calculated. To verify the reliability of the TRIGRS-Scoops 3D joint model, the identified dangerous slopes were compared with the results from landslide susceptibility mapping. The results show that the unstable grids are concentrated within a slope gradient of 30° to 35°, and the landslide early warning levels are divided into Tier 3, Tier 2, and Tier 1 Warnings. The occurrence of shallow loess landslides is affected by both rainfall intensity and rainfall duration, and the combined effect should be considered in early warning. The distribution of both extreme susceptible grids and high susceptible grids across all 23 dangerous slopes demonstrates the reasonableness of the TRIGRS-Scoops 3D joint model. The landslide susceptible probability within some dangerous slopes exhibits spatial variability. The mapping relationship between the slope gradient and loess landslides is extremely complex. This paper can provide a theoretical basis for the early warning and risk management for rainfall-induced shallow loess landslides; the proposed method is also applicable to other regions with similar geological and meteorological conditions.

1. Introduction

Geological disasters are frequent, and ecological issues are prominent in loess areas [1,2]. The triggering factors for shallow loess landslides include rainfall [3], wildfires [4], earthquakes [5], and snowmelt [6], all of which are potential triggers for shallow loess landslides, with rainfall being the most significant. Extreme rainstorms have been occurring frequently in the Loess Plateau, China. Rainstorms in Shaanxi Province’s Suide, Zizhou, and Mizhi counties triggered many loess landslides in July 2021, causing silt dam damage, river blockages, serious soil erosion, and surface morphological damage [7]. In September 2024, persistent heavy rainfall that broke historical records triggered loess landslides and formed barrier lakes in Minhe County, Qinghai Province, resulting in three deaths and one injury [8]. Global warming has caused China’s precipitation line to move northward, and the changes in climate and underlying factors of the Loess Plateau are serious and are not slowing down. Rainfall-induced shallow loess landslides are becoming one of the most serious threats to human and property safety [9]. As a result, conducting their early warning and risk assessments can serve as a basis for disaster emergency response, as well as engineering mitigation, which is of great significance for enhancing regional disaster prevention capacity [10].

Landslide spatial prediction serves as the foundation for early warning, encompassing knowledge-driven qualitative analysis, math-driven quantitative analysis, and deterministic analysis based on physical and mechanical models [11]. Knowledge-driven qualitative analysis relies on expert experience. While it is relatively intuitive, the results are strongly influenced by subjectivity and exhibit low stability [12]. Math-driven quantitative analysis primarily involves landslide susceptibility mapping (LSM) [13]. It calculates the probability of landslide occurrence for each grid or slope unit within the study area based on data-driven models, considering factors such as topography, hydrology, geology, vegetation, meteorological, and human activity conditions. However, it struggles to account for the water infiltration process in rock and soil masses [14]. Deterministic analysis based on physical and mechanical models can fully consider the influence of the variabilities of the geotechnical parameters, rainfall processes, and moisture seepage on probability of landslide occurrence for individual slopes, usually use Shallow Landslide Stability Model (SHALSTAB), Stability Index MAPping Model (SINMAP), Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability Model (TRIGRS) and Three-dimensional Slope Stability Analysis Tool (Scoops 3D) [15,16]. The application of SHALSTAB and SINMAP models is limited due to their weaknesses in sensitivity to parameters and assumptions regarding the sliding surface [17]. The prediction accuracy of the single TRIGRS model is relatively low because the gravity component of the rock and soil along the slope direction cannot be transmitted into the downstream adjacent rock and soil [18,19]. The Scoops 3D model cannot perform hydrological analysis on its own, but it is compatible with a variety of rainfall infiltration and hydrological models, and can simultaneously account for the complex distribution of pore water pressure and three-dimensional topographic conditions [20,21]. Loess has a loose structure and well-developed vertical joints, making it prone to forming steep slopes. Upon water saturation, the bonding force between particles weakens, leading to rapid structural failure and significant additional subsidence [22,23]. In addition, the terrain in loess regions is fragmented, characterized by numerous gullies and ravines, where the effect of gravity is particularly pronounced [24,25]. Therefore, it is necessary to consider both the influence of rainfall and the loess characteristics in the loess landslide study. The TRIGRS-Scoops 3D joint model can account for both the “rainfall-water infiltration” process and the influence of loess parameters [26,27]. However, there have been few studies using the joint model in the loess area recently.

The disaster capability of unstable slopes and vulnerability of the disaster-bearing bodies are involved in landslide risk assessment [28]. Disaster capability is the natural attribute of a hazard-pregnant environment; probability of occurrence and influence range are involved in the assessment of disaster capability, and it is dependent on factors like landslide volume, slope aspect, and terrain [29]. The vulnerability is the social attribute of disaster-bearing bodies, and it is measured by the total economic value and is dependent on the number and unit price of the disaster-bearing bodies [30]. Qualitative risk assessment has trouble with keeping the risk level edge, while quantitative risk assessment takes the expected economic loss as the most important result [31], which provides a direct and quantitative basis for the specific risk management and mitigation.

To incorporate the influences of both “rainfall-water infiltration” process and loess parameters in the early warning of shallow loess landslides [32], this paper proposes the TRIGRS-Scoops 3D joint model, specifically by feeding the head pressures calculated by the TRIGRS model into the Scoops 3D model, thereby achieving simultaneous analysis of water infiltration under varying rainfall conditions and slope stability analysis based on three-dimensional topography. The proportion of the unstable grids in the study area that were more than 25% were defined as dangerous slopes, and the spatial distribution of any dangerous slopes under the condition of the once-in-a-century rainfall was studied. Rainfall threshold curves for the different landslide warning grades based on rainfall intensity and rainfall duration were obtained and compared by a rerunning of the TRIGRS-Scoops 3D joint model. The landslide range and land uses of each slope were determined by maximum likelihood classification, and then the expected economic loss was calculated. To verify the reliability of the TRIGRS-Scoops 3D joint model, the identified dangerous slopes were compared with the results from LSM. The results can provide a basis for disaster emergency response, engineering mitigation, and land-use planning, and the methodology employed is also widely applicable to other loess-covered regions in China. The study flowchart is shown in Figure 1.

2. Study Area and Data

2.1. Study Area Overview

The study area is in the southeast of Fangta town, Jia county, Yulin city, Shaanxi province, and is in the south of the Maowusu desert. It is between 110°05′58″ E to 110°08′21″ E, 38°10′33″ N to 38°13′30″ N, with an area of 17.3 km². The study area is in a temperate continental semi-arid monsoon climate, with an average precipitation of 405 mm over the 50 years, and is concentrated from June to September, with the highest values being in August. However, the average precipitation in the past 10 years has been more than 470 mm, and the pressure of an increasing trend of precipitation is obvious. The average annual temperature is 9.6 °C, with an average maximum of 16.6 °C and an average minimum of 3.8 °C. It features cold winters and hot summers, with a large diurnal temperature range. The frost-free period is approximately 150 days [33].

Tectonically, the study area is in the north-central part of the Shanbei Depression within the Ordos Platform of the North China Platform, adjacent to the Dongsheng Uplift to the northeast. Neotectonic movement is characterized by slow, large-scale uplift and subsidence. The stratigraphic sequence is dominated by thick Mesozoic and Paleozoic sedimentary rocks, overlain by extensive Cenozoic Quaternary loess. There is no record of magmatic rock formation. The terrain is highly dissected, featuring a crisscross network of gullies and alternating mounds and ridges, with elevations ranging from 1042 to 1259 m. No large-scale faults or folds have developed, and seismic activity is rare. The Jialu River flows through the study area. Influenced by the semi-arid climate, runoff exhibits significant seasonal and interannual variations, with water discharge highly concentrated during the flood season, leading to severe soil erosion [34]. The study area is shown in Figure 2.

2.2. Study Data

2.2.1. Slope Gradient

The slope gradient distribution of the study area was derived based on ArcGIS 10.2 by processing the Digital Elevation Model (DEM) provided by NASA, with the download link: https://www.nasa.gov/ (accessed on 16 October 2025). The study area was resampled to a resolution of 10 m × 10 m, yielding a total of 104,946 grids. The slope gradient distribution in the study area is shown in Figure 3.

2.2.2. Flow Direction

DEM was processed with depression detection based on ArcGIS 10.2, and the flow direction of each grid was extracted, combined with the TRIGRS model and the actual terrain. Compared with the multiple flow direction algorithm, the single flow direction algorithm is simple and suitable for steep terrain. It assumes that each grid cell has only one main flow direction, and the flow direction is usually determined from the lowest point of the DEM along the steepest downhill direction until it reaches the boundary of the basin [35]. The flow direction of each grid using the single flow direction algorithm is shown in Figure 4.

2.2.3. Slope Unit

The slope unit was formed by the closure of the ridge line and the valley line. It can be regarded as the basic unit for landslide early warning and risk assessment. The hydrological analysis module of ArcGIS 10.2 was employed to extract the catchment basin corresponding to the positive and negative terrains. The original slope unit distribution was then obtained by using the catchment basin boundary as the valley line and the ridge line. Compared with the slope aspect map and the actual topography, the final slope unit distribution was obtained by readjusting the valley line and ridge line [36]. The 96 slope units and their slope aspects in the study area are shown in Figure 5.

2.2.4. The Thickness of the Loess

The study area is characterized by a high density of shallow landslides, with slip surfaces typically buried within 5 m depth [37]. This shallow failure mechanism is governed by the combined effects of well-developed vertical joint systems in the loess and the limited infiltration depth of intense rainfall. Vertical joints and fissures facilitate rapid preferential water flow, forming potential weak planes, while infiltration reduces soil shear strength. However, the wetting front under heavy rainfall seldom exceeds a few meters. Consequently, failure surfaces predominantly occur within shallow strata where moisture fluctuations are most pronounced, and soil strength is markedly degraded [38]. In the TRIGRS-Scoops 3D joint model, the soil thickness was accordingly set to 5 m.

2.2.5. Soil Parameter

The loess exposed in the study area is the “Malan Loess”, which formed approximately 50,000 to 100,000 years ago. It is characterized by a loose structure and continuous depositions. Moreover, due to the relatively small extent of the study area, the variability of loess parameters is low. Thus, one representative slope was selected for parameter determination. This slope forms part of the 71# slope in Figure 5, with its central point located at coordinates 110°07′52.12″ E, 38°12′09.27″ N. It is approximately 550 m long and 120 m high, and experienced a shallow landslide triggered by heavy rainfall on 16 August 2024. The post-failure scene is shown in Figure 6.

The natural density (ρ), natural moisture content (ρ_sat), liquid limit (w_L), and plastic limit (w_p) were measured on-site. The loess was transported to the laboratories in Shandong University of Technology, and geotechnical tests were employed to determine other parameters such as saturated volumetric water content (θ_s), residual volumetric water content (θ_r), saturated vertical permeability coefficient (K_S), partial saturated soil unit weight (γ_ps), cohesion (c), internal friction angle (φ) and saturated soil unit weight (γ_s) [39]. All the parameters were determined in accordance with the “Standard for Geotechnical Testing Method” (GB/T 50123-2019) [40], which is the most fundamental and widely adopted national standard for test methods in the field of geotechnical engineering in China [41]. The on-site measurement and sampling were conducted on 13 October 2025; the sampling location is shown in Figure 7, the loess transportation is shown in Figure 8, and the loess parameters are shown in

Table 1. Loess parameters.

Parameter	ρ	ρsat	wL	wp
Value	1.45 g·cm−3	13.35%	27.53%	13.25%
Parameter	θs	θr	KS	γps
Value	0.42	0.13	1.16 e−5 m/s	17.8 kN/m3
Parameter	c	φ	γs
Value	3.25 kPa	27.8°	21.42 kN/m3

.

Through laser particle size analysis, the particle gradation and grain size of the loess were analyzed, as shown in Figure 9 and

Table 2. Grain size distribution of the loess.

Particle size (μm)	0.000–0.220	0.220–0.470	0.470–1.005	1.005–2.148	2.148–4.591
Content (%)	0.00	0.83	3.19	4.14	6.71
Particle size (μm)	4.591–9.813	9.813–20.97	20.97–44.83	44.83–95.81	95.81–204.8
Value (%)	10.02	17.88	30.36	22.33	4.54

.

2.2.6. Rainfall Parameters

According to Mao et al. [42], the rainstorm intensity formula of Yulin city, Shaanxi province, is shown in Formula (1).

$$I={\displaystyle \frac{1370.03(1+1.152\lg P)}{{(t+9.44)}^{0.746}}}$$

(1)

where I is the rainfall intensity (m/s), P is the rainfall return period (years), and t is the rainfall duration (min).

Based on Formula (1), the rainfall intensities with rainfall durations of 6 h, 12 h, 24 h, and 48 h under the once-in-a-century rainfall return period are 5.5 × 10⁻⁵ m/s, 3.3 × 10⁻⁶ m/s, 1.98 × 10⁻⁶ m/s, and 1.19 × 10⁻⁶ m/s, respectively.

3. Study Methodology

3.1. Early Warning for Shallow Loess Landslide

Head pressure at different depths calculated by the TRIGRS model was produced in the form of three-dimensional data represented by multiple vertical points [43]. The head pressure was led into the Scoops 3D model, and the Bishop rock-soil moment balance method was selected for stability prediction, as shown in Formula (2) [44].

$$F_s={\displaystyle \frac{\tan \phi }{\tan \delta }}+{\displaystyle \frac{c-\chi \psi \left(Z,t\right){\gamma }_w\tan \phi }{{\gamma }_{a}Z\sin \delta \cos \delta }}$$

(2)

where F_s is the safety factor, γ_w is the water unit weight (kN/m³), γ_a is the natural soil bulk density (kN/m³), δ is the slope gradient (°), and ψ is the head pressure. F_s ≤ 1 indicates unstable, 1 < F_s ≤ 1.25 indicates potentially unstable, 1.25 < F_s ≤ 1.5 indicates relatively stable, and F_s > 1.5 indicates stable.

The rainfall intensity and rainfall duration were used as the variables for the early warning for shallow loess landslides, and the proportions of unstable grids reaching 25%, 40%, and 55% were the triggering conditions for the Tier 3, 2, and 1 Warnings, respectively.

Rerunning the TRIGRS-Scoops 3D joint model for 690 times, the rainfall intensities and rainfall durations of each grid were counted and fitted into rainfall threshold curves. The fitting method is shown in Formulas (3) and (4).

$$\lg I=\beta \lg t+\lg \eta$$

(3)

$$I=\eta t^{\beta }$$

(4)

where η and β are the fitting parameters.

3.2. Risk Assessment for Shallow Loess Landslide

Land use of the Google Earth image in the study area was automatically divided into six types based on the maximum likelihood classifier of ArcGIS 10.2 [45]: barren, building, river, road, forest land, and farmland. According to the field survey, the automatic division results were manually adjusted.

Landslide hazard mapping refers to determining the landslide ranges after the instability of dangerous slopes, including the influence range on both sides and the front coverage area [46]. The influence range on both sides is determined according to the slope aspect, topography, and engineering experience, and the front coverage area is calculated by the empirical formula [47], as shown in Formula (5).

$$L_{\max }=2(H_1-H_2)$$

(5)

where L_max is the maximum slipping distance (m), H₁ is the posterior border elevation (m), and H₂ is the anterior border elevation (m).

With reference to the “Compensation Standard for Land Acquisition and Demolition of Key Construction Projects in Yulin City”, the unit price of each land use was assigned, as shown in

Table 3. Unit price of each land use.

Land Use	Barren	Building	River	Road	Forest Land	Farmland
Unit price (yuan/m2)	11	1100	10	270	23	54

.

The calculation method of the expected economic loss is shown in Formula (6).

$$S={\displaystyle \sum _{i=1}^{n}H{W}_i{A}_i}$$

(6)

where S is the expected economic loss (yuan), n is the number of land uses, and i is the i-th land use, W_i is the unit price (yuan/m²) of the i-th land use, and A_i is the area of the i-th land use. H is the early warning level coefficient; the Tier 3 Warning takes 25%, the Tier 2 Warning takes 40%, and the Tier 1 Warning takes 55%.

4. Study Results

4.1. Early Warning for Shallow Loess Landslide

After visualization by Cloud Compare, the head pressures with rainfall durations of 6 h, 12 h, 24 h, and 48 h under the once-in-a-century rainfall return period of the study area are shown in Figure 10.

In Figure 10, the largest head pressures recorded with the rainfall durations of 6 h, 12 h, 24 h, and 48 h are 1.49 m, 1.61 m, 2.06 m, and 2.73 m, respectively.

The slope stability prediction results of the study area are shown in Figure 11.

Under the once-in-a-century rainfall return period, the number for grids of each stable grade with rainfall durations of 6 h, 12 h, 24 h, and 48 h are shown in

Table 4. Number of grids of each stable grade with different rainfall durations under the once-in- a-century rainfall return period.

Rainfall Duration	6 h	12 h	24 h	48 h
Stable Grade
Unstable	14,047	15,086	19,954	14,043
Potentially unstable	16,930	17,028	17,624	16,917
Relatively stable	16,739	16,648	16,237	16,739
Stable	57,230	56,184	51,131	57,247

. The number of unstable grids is at its largest when the duration is 24 h, so a 24 h rainfall duration was defined as the extreme rainfall condition under the once-in-a-century rainfall return period.

The relationship between the slope gradient and the number of grids of each stable grade is shown in Figure 12.

As shown in Figure 12, the unstable grids are concentrated within a slope gradient of 30° to 35°, the potentially unstable grids are concentrated within a slope gradient of 25° to 30°, and the stable grids are concentrated in a slope gradient of under 15°. The 23 slopes that reach the Tier 3 Warning under the extreme rainfall condition (9#, 15#, 18#, 38#, 42#, 44#, 45#, 49#, 51#, 52#, 54#, 58#, 63#, 75#, 76#, 77#, 79#, 80#, 82#, 83#, 86#, 91# and 92#) were defined as dangerous slopes with landslides.

The rainfall threshold curves for the dangerous slopes are shown in Figure 13, and the fitting parameters η and β are shown in

Table 5. Parameters of rainfall threshold curves for landslides.

Tier 3 Warning			Tier 2 Warning			Tier 1 Warning
Slope	η	β	Slope	η	β	Slope	η	β
9#	915.71	−2.16	9#	786.68	−1.51	9#	628.77	−1.23
15#	--	--	15#	633.74	−1.40	15#	580.84	−1.18
18#	917.89	−2.24	18#	786.68	−1.51	18#	580.84	−1.18
38#	1075.45	−2.25	38#	786.68	−1.51	38#	639.26	−1.27
42#	681.95	−1.88	42#	832.57	−1.48	42#	639.26	−1.27
44#	769.22	−2.26	44#	583.26	−1.28	44#	524.17	−1.08
45#	951.35	−2.49	45#	713.25	−1.45	45#	580.84	−1.18
49#	917.89	−2.24	49#	583.26	−1.28	49#	537.64	−1.13
51#	716.09	−1.94	51#	812.03	−1.51	51#	560.47	−1.18
52#	987.92	−1.95	52#	672.11	−1.40	52#	556.90	−1.18
54#	--	--	54#	803.06	−1.72	54#	583.26	−1.28
58#	--	--	58#	602.34	−1.54	58#	628.20	−1.24
63#	954.71	−1.97	63#	713.25	−1.45	63#	580.84	−1.18
75#	915.71	−2.16	75#	713.25	−1.45	75#	628.20	−1.24
76#	1074.86	−2.18	76#	787.77	−1.42	76#	626.48	−1.21
77#	--	--	77#	677.42	−1.50	77#	639.26	−1.27
79#	1349.34	−2.19	79#	787.77	−1.42	79#	518.23	−1.05
80#	1290.95	−2.33	80#	598.49	−1.25	80#	524.17	−1.08
82#	769.22	−2.26	82#	666.25	−1.34	82#	580.84	−1.18
83#	1083.60	−2.25	83#	713.25	−1.45	83#	560.47	−1.18
86#	1355.84	−2.70	86#	833.24	−1.60	86#	628.20	−1.24
91#	951.35	−2.49	91#	837.68	−1.55	91#	622.56	−1.22
92#	--	--	92#	833.24	−1.60	92#	580.84	−1.18

.

In the traversed rainfall range, all 23 dangerous slopes have reached the Tier 3, 2, and 1 Warnings. The 15#, 54#, 58#, 77#, and 92# slopes have reached the Tier 3 Warning in the natural state (no rainfall). The rainfall threshold curves for the Tier 2 and Tier 1 Warnings tend to shift towards the upper right, which signifies that the demand for rainfall is markedly higher than that observed in the Tier 3 Warning. At the same time, the 83# and 86# slopes are more likely to reach the Tier 3 Warning, and the 54# and 58# slopes are more likely to reach the Tier 2 and Tier 1 Warnings.

4.2. Risk Assessment for Shallow Loess Landslide

The land use division results are shown in Figure 14.

The areas of barren, building, river, road, forest land, and farmland in the study area are 1.68 km², 1.02 km², 0.20 km², 0.84 km², 8.72 km^2, and 4.02 km², accounting for 10.2%, 6.2%, 1.2%, 5.1%, 52.9% and 24.4% of the total land area, respectively.

Based on the maximum slipping distance, slope aspect, topography, and engineering experience, the landslide hazard mapping of the 23 dangerous slopes was carried out. The landslide ranges were counted based on ArcGIS 10.2, as shown in Figure 15 and

Table 6. The areas of each landslide range.

Slope	Area/km2	Slope	Area/km2	Slope	Area/km2	Slope	Area/km2	Slope	Area/km2
9#	0.24	44#	0.09	54#	0.09	77#	0.12	86#	0.2
15#	0.21	45#	0.35	58#	0.13	79#	0.31	91#	0.34
18#	0.21	49#	0.06	63#	0.21	80#	0.24	92#	0.16
38#	0.16	51#	0.18	75#	0.38	82#	0.11
42#	0.06	52#	0.08	76#	0.51	83#	0.21

.

The land uses of each landslide range are shown in

Table 7. The land uses of each landslide range.

Slope	Barren/m2	Building/m2	River/m2	Road/m2	Forest Land/m2	Farmland/m2
9#	14,299	11,986	1600	2931	176,872	28,461
15#	31,200	14,552	576	6982	119,628	34,361
18#	9533	13,330	3993	18,920	111,061	52,607
38#	43,979	15,369	280	4490	64,399	30,060
42#	14,693	5057	65	3889	26,183	14,102
44#	12,202	4597	200	1472	50,376	16,968
45#	29,794	17,147	14,159	6185	230,939	46,780
49#	2810	3279	485	12,828	27,683	14,046
51#	12,838	11,850	249	5939	125,189	27,247
52#	14,335	7708	311	2290	38,834	12,657
54#	4512	4202	57	1915	63,623	10,997
58#	16,801	10,645	263	3408	76,801	21,490
63#	8555	3882	3274	651	185,199	7604
75#	54,908	24,497	1208	10,835	212,729	77,479
76#	49,836	28,117	3471	16,442	290,315	124,779
77#	5708	3592	2469	2376	83,921	23,171
79#	35,912	13,835	5492	7610	184,755	63,448
80#	22,163	13,227	2854	8658	135,874	53,682
82#	21,524	10,536	237	2588	59,519	15,517
83#	26,039	10,735	2556	8138	106,156	55,877
86#	30,463	13,092	324	19,114	61,032	75,173
91#	62,042	25,575	1263	7114	180,364	64,529
92#	18,021	11,988	368	3625	87,295	40,951

.

The calculation results of the expected economic loss are shown in

Table 8. Expected economic loss under each landslide warning grade.

Slope	Expected Economic Loss/Million Yuan
	Tier 3 Warning	Tier 2 Warning	Tier 1 Warning
9#	494	790	1086
15#	571	914	1257
18#	633	1012	1392
38#	543	868	1194
42#	203	326	448
44#	192	307	422
45#	721	1154	1586
49#	213	340	468
51#	478	765	1052
52#	271	433	596
54#	181	290	399
58#	394	630	866
63#	231	370	508
75#	989	1583	2176
76#	1234	1975	2715
77#	197	314	432
79#	635	1016	1397
80#	580	927	1275
82#	368	589	810
83#	494	791	1088
86#	634	1015	1395
91#	960	1535	2111
92#	465	743	1022

and Figure 16.

From Table 8 and Figure 16, the expected economic loss of the 76# slope is the highest, exceeding 20 million yuan under the Tier 1 Warning. The main reason is that the farmland and building areas within the landslide range are large, which are 124,779 m² and 28,117 m², respectively. The economic losses of the 75#, 91#, and 45# slopes are second, with more than 15 million yuan under the Tier 1 Warning. The 42#, 44#, 49#, 54#, and 77# slopes are smaller, less than 5 million yuan under the Tier 2 Warning. The main reason for this is that their landslide ranges are small, and most of these are barren.

5. Discussions

5.1. Comparison with Landslide Susceptibility Mapping Results

This paper identified 23 dangerous slopes based on the TRIGRS-Scoops 3D joint model. To verify its accuracy, LSM was also conducted, and the LSM results were compared with those obtained from the TRIGRS-Scoops 3D joint model. The study area in this paper and the study area of Ma et al. [48] are both covered by Quaternary loess, and the formation mechanisms and morphological characteristics of landslides are highly similar. Therefore, this paper adopts the LSM method like that of Ma et al. [48]. Due to space limitations, only the framework and results of LSM are presented here, as follows:

(1)

A total of 11 hazard factors were selected, including elevation, slope gradient, slope aspect, distance from roads, Sediment Transport Index (STI), stream power index (SPI), topographic wetness index (TWI), Normalized Difference Vegetation Index (NDVI), plane curvature, profile curvature, and land use. The classification of each hazard factor is shown in

Table 9. Classification of each hazard factor.

Hazard Factor	Classification
Elevation (m)	1042–1085, 1085–1109, 1109–1130, 1130–1149, 1149–1169, 1169–1190, 1190–1212, 1212–1259.
Gradient (°)	0–7.476, 7.476–12.781, 12.781–17.846, 17.846–22.669, 22.669–27.492, 27.492–32.798, 32.798–39.550, 39.550–61.495.
Slope aspect	Plane, North, Northeast, East, Southeast, South, Southwest, West, Northwest.
Distance from road (m)	0–764.517, 764.517–1425.720, 1425.720–2045.599, 2045.599–2624.152, 2624.152–3182.043, 3182.043–3719.271, 3719.271–4318.487, 4318.487–5268.967.
STI	0–0.232, 0.232–0.697, 0.697–1.161, 1.161–1.683, 1.683–2.322, 2.322–3.135, 3.135–4.276, 4.276–7.401.
SPI	−13.816–−8.114, −8.114–−6.235, −6.235–−3.255, −3.255–−1.441, −1.441–−0.534, −0.534–0.438, 0.438–2.706.
TWI	−6907.755–328.303, 328.303–1106.866, 1106.866–1977.025, 1977.025–2709.790, 2709.790–3396.758, 3396.758–4037.928, 4037.928–4770.693.
NDVI	−0.186–0.026, 0.026–0.129, 0.129–0.176, 0.176–0.214, 0.214–0.242, 0.242–0.271, 0.271–0.304, 0.304–0.464.
Profile curvature	−13.997–−4.762, −4.762–−2.510, −2.510–−0.934, −0.934–0.193, 0.193–1.431, 1.431–3.121, 3.121–5.936, 5.936–14.720.
Plane curvature	−13.380–−3.392, −3.392–−1.597, −1.597–−0.587, −0.587–0.199, 0.199–0.984, 0.984–2.106, 2.106–3.902, 3.902–15.236.
Land use	Barren, Building, River, Road, Forest land, Farmland.

. Based on ArcGIS 10.2, classification maps of hazard factors were generated, as shown in Figure 17 (slope aspect and land use are shown in Figure 5 and Figure 14b, respectively).

(2)

A total of 246 landslides on the Loess Plateau were used to construct the training and validation sets [48]. Using the resampling function of ArcGIS 10.2, 6160 landslide grids of 10 m × 10 m were obtained. Meanwhile, 6160 non-landslide grids were randomly selected from non-landslide areas. 70% landslide grids (4312) and 70% non-landslide grids (4312) were selected as training samples, while 30% landslide grids (1848) and 30% non-landslide grids (1848) were validation samples. The Blending-XGBoost-CNN model was selected for landslide susceptibility modeling, in which the Blending framework was used to connect the XGBoost model and CNN model [49].

(3)

The study area was divided into five susceptible levels based on the landslide susceptibility probability, as shown in Figure 18. Specifically, extreme susceptible areas account for 5.78% of the total study area, high susceptible areas account for 10.54%, moderate susceptible areas account for 18.36%, minor susceptible areas account for 27.15%, and minimal susceptible areas account for 38.17%, respectively.

A comparison between Figure 18 and the calculation results of the TRIGRS-Scoops 3D joint model reveals the following:

(1)

The distribution of both extreme susceptible grids and high susceptible grids across all 23 dangerous slopes demonstrates the reasonableness of the TRIGRS-Scoops 3D joint model. For instance, the proportions of extreme susceptible grids and high susceptible grids in the 38# slope reached 38.15% and 49.64%, while in the 51# slope reached 34.27% and 52.19%, respectively.

(2)

The landslide susceptible probability within some dangerous slopes exhibits spatial variability. For example, although the proportions of extremely susceptible grids and highly susceptible grids in the 54# and 58# slopes are not high, they are concentrated on the eastern and southern sides. This is attributed to the large spatial scale of the slopes and the resulting differences in the microscopic hazard-pregnant environment. However, this does not reduce the probability of landslide occurrence under extreme rainfall conditions.

5.2. The Influence of Slope Gradient on Shallow Loess Landslides

The mapping relationship between the slope gradient and shallow loess landslides is extremely comple. Firstly, the higher the slope gradient, the more complex the internal stress state of the slope, the stronger the surface cutting, and the greater the probability of landslide occurrence [50]. This paper statistically analyzed the relationship between the number of grids of each stable grade and the slope gradient. The results show that the unstable grids in the study area are concentrated within a slope gradient of 30° to 35°, the potentially unstable grids are concentrated within the slope gradient of 25° to 30°, and the stable grids are concentrated in a slope gradient of below 15°. This is basically consistent with the existing studies, revealing that shallow loess landslides mostly occur in slope gradients of 30° to 40° [51]. Secondly, the intensity of rainfall infiltration is inversely proportional to the slope gradient [52]. Under heavy rainfall conditions, the smaller the slope gradient, the larger the runoff range, the smaller the flow rate, and the greater the infiltration volume [53,54]. For example, the gradient of the 54# and 58# slopes in the study area is lower than that of the surrounding slopes, and the rainfall infiltration is strong, which is the reason for its being easier to achieve the Tier 2 and 1 Warnings. Thirdly, steeper loess slopes generally have lower vegetation coverage, which reduces rainwater interception and further decreases slope stability. In future research, the author will elucidate the disaster mechanisms of shallow loess landslides from the following aspects: the influence of vegetation root models, spatial variability of loess parameters, slope scale, and crack development on the probability and scale of landslide occurrence under different slope gradient conditions.

6. Conclusions

In this paper, the head pressures calculated using the TRIGRS model were put into the Scoops 3D model, and shallow loess landslide spatial prediction in the study area was carried out, and the relationship between the slope gradient and the number of grids for each stable grade was certified. The rainfall thresholds for landslides, based on both the rainfall intensity and the rainfall duration, were obtained by rerunning the TRIGRS- Scoops 3D joint model. The landslide range and land uses of each dangerous slope were determined by maximum likelihood classification, and then the expected economic loss was calculated. To verify the reliability of the TRIGRS-Scoops 3D joint model, the identified dangerous slopes were compared with the results from LSM.

(1)

The unstable grids are concentrated within a slope gradient of 30° to 35°, the potentially unstable grids are concentrated in the slope gradient of 25° to 30°, and the stable grids are concentrated in a slope gradient of under 15°.

(2)

The rainfall threshold curves for the dangerous slopes were drawn, including 18 Tier 3 Warning curves, 23 Tier 2 Warning curves, and 23 Tier 1 Warning curves. The 15#, 54#, 58#, 77#, and 92# slopes reach the Tier 3 Warning in the natural state (no rainfall), and the 54# and 58# slopes are more likely to reach the Tier 2 and Tier 1 Warnings.

(3)

The expected economic loss of the 76# slope is the highest, exceeding 20 million yuan under the Tier 1 Warning. The 42#, 44#, 49#, 54#, and 77# slopes are smaller, less than 5 million yuan under the Tier 2 Warning.

(4)

The distribution of both extreme susceptible grids and high susceptible grids across all 23 dangerous slopes demonstrates the reasonableness of the TRIGRS-Scoops 3D joint model. The landslide susceptible probability within some dangerous slopes exhibits spatial variability.

(5)

The mapping relationship between the slope gradient and loess landslides is extremely complex. In future research, the author will elucidate the disaster mechanisms of shallow loess landslides from the following aspects: the influence of vegetation root models, spatial variability of loess parameters, slope scale, and crack development on the probability and scale of landslide occurrence under different slope gradient conditions.