Discussion on the Relationship between Debris Flow Provenance Particle Characteristics, Gully Slope, and Debris Flow Types along the Karakoram Highway

Abstract

Debris flow, the most extensive and most severe geological hazard along the Karakoram Highway, frequently blocks the Karakoram Highway. Based on the methods of field measurement, indoor statistical analysis and theoretical research, this paper discusses the relationship between the four types of debris flow along the Karakoram Highway. The four types are the rain type, the rain glacier type, the glacier ice lake break type and the freeze–thaw type, and their particle characteristics and gully slope are also considered in the discussion. The results are as follows: (1) The provenance particle size of debris flow is controlled by the type of debris flow. Generally, the provenance average particle equivalent diameter of the debris flow induced by the glacier ice lake type is relatively small, followed by the freeze–thaw type and glacier ice lake break type, and the equivalent diameter of the debris flow induced by the rain type is relatively large; (2) The gully slope coefficient of the debris flow $C$ along the Karakoram Highway is greater than 1, and it increases with the increase in gully slope $\alpha$, that is, the larger $C$ is, the steeper the gully slope will be; (3) The gully slope coefficient $C$ and the average particle equivalent diameter $D$ of the four types of debris flow are distributed in the ellipse with them as the axis. This ellipse quantitatively describes the relationship between the gully slope of the four types of debris flow and the corresponding provenance particle characteristics. This paper analyzes the formation and causes of debris flow along the Karakoram Highway. It accurately understands the scientific connotation of debris flow formation in the surface matrix layer and improves the diversity, stability, and sustainability of the ecosystem. The paper also proposes ideas and suggestions for promoting the ecological protection and restoration of the Karakoram Highway. Therefore, the research has a certain theoretical significance and practical application value for the appropriate selection and rational design of the debris flow prevention projects along the China–Pakistan Highway.

1. Introduction

The China–Pakistan Highway, also known as the Karakoram Highway (KKH), is a plateau highway connecting the western Xinjiang city of China, Kashgar, and the northern Pakistan city, Thakot, with a total length of 1038 km, including 420 km in China [1,2]. The Karakoram Highway is not only the transportation link of northern Pakistan and an important part of its road network, but also the main traffic route from the northern region to the capital Islamabad and the southern coastal areas; it is of great significance to the economic development of the northern region. Moreover, it is an integral part of the Asian Highway Network, and it is the only land route from China to Pakistan, the South Asian subcontinent and the Middle East. The Karakoram Highway has important strategic and military significance [3,4].

The Karakoram Highway is located in the Himalayas, the largest earthquake zone in the world. It is situated in the hinterland of the Pamirs, passing through the Karakoram Mountains, the Hindu Kush Mountains, the Pamirs, and the western end of the Himalayas. The Karakoram Highway has the title of the most beautiful and precipitous high-altitude highway in the world. For decades, road builders from China and Pakistan have sacrificed their blood and lives for the Karakoram Highway, so it is also called the “China-Pakistan Friendship Highway” [5].

The highway crosses a wide area with special geological, landform, climate, and hydrological conditions [6,7]. The geological conditions are very complicated and affected by strong seismic activities and tectonic movements since the Quaternary glaciation. This leads to the development of folds, joints, and rock mass fractures. The rock structure is damaged, loose and, weak, and at the same time, it is easy to weather. Hence, it is easy to produce a large amount of detrital solid matter in the area along the Karakoram Highway. Moreover, in this area, the topography is complex and changeable. The terrain is high in the north and low in the south, and the altitude difference between the north and south is large. The average altitude of the mountain is more than 3000 m, and the mountain is steep (the gully slopes are 35–50 degrees, and some even reach 70 degrees). At the same time, the vegetation is sparse. The valley is deep and steep, and the ravines are densely distributed. Therefore, we can also see that the ecological environment of the Karakoram Highway is extremely fragile. The area where the highway is located belongs to a typical continental subtropical arid, semi-arid, and inland plateau mountainous climate region. The climate is distributed in vertical bands, with low temperatures, thin air, and abundant sunshine. The temperature difference between high mountains and valleys is large. This complex and varied mountainous topography can easily lead to variable climatic conditions and even extreme rainfall. The highway circulates along the Khunjerab River, the Hunza River, the Gilgit River, and the Indus River from north to south. The tops of the mountains on both sides are covered by permanent snow and glaciers all year round, and there are many modern glaciers in the valleys, such as the Batura glacier, Passu glacier, Gulmit glacier, and so on.

The combination of complex and unique geology, topography, climate, and hydrological conditions in the crossing area of the Karakoram Highway has led to the extensive development of geological hazards along the route [8,9,10,11], such as debris flows, collapse, landslides, rock avalanches, avalanches, rock slides, etc. These disasters have caused road conditions to deteriorate year by year, seriously affecting the normal traffic operation of the friendship road between China and Pakistan. They also affect the important logistics channels of resources, such as mining and transportation, on the trunk line, which has brought great damage to the maintenance of the road, the sustainable development of the road economy and the safety of the road. At the same time, disasters also have a negative impact on social development and people’s safety. The monitoring, evaluation and management of geological disasters reflect the need to cope with the complexity of sustainable development. The first priority is to ensure safety and the second is to reduce the economic losses caused by geological disasters such as debris flows, landslides, and collapses. The exploration of geological disasters on the Karakoram Highway also responds to the emerging field of natural disaster risk prevention and control.

2. Materials and Methods

2.1. Overview of Debris Flows along the Karakoram Highway

Debris flow is a common natural disaster that occurs in mountainous areas. Except for Antarctica, debris flow disasters are widely developed in the mountainous areas of the other six continents, with typical characteristics such as sudden outbreaks, ferocious onsets, and strong hazards. It can cause heavy casualties and huge property losses to the disaster-affected areas [12,13,14]. Among the geological disasters developed along the Karakoram Highway, debris flow is the most common and most harmful type of geological disaster. The concept of sustainable development of debris flow requires long-term, comprehensive, and coordinated measures to balance the relationship between debris flow disaster prevention and social and economic development. It includes reducing the occurrence and impact of the debris flows while considering the needs and sustainability of social and economic development. Additionally, it involves addressing issues such as ecological environment protection and cultural heritage preservation. The research team organized four large-scale field investigations on the Karakoram Highway and found that there are more than 140 debris flows in the area from Raikot (K470+500) to Khunjerab (K811), causing serious damage to the road (Figure 1), such as blocking the flow of rivers into lakes, flooding roads, burying and destroying road surfaces, cutting embankments, silting bridges and culverts, and impacting bridge and culvert foundations [14,15].

According to the previous research results of the team, from south to north, there are four types of debris flow disasters on the Karakoram Highway: the rain type, the rain glacier type, the glacier ice lake break type, and the freeze–thaw type [9,16]. The specific distribution is shown in

Table 1. Distribution of four types of debris flow disasters along the Karakoram Highway [9,16].

Debris Flow Type	Distribution Interval
Rain type debris flow	Distributed between Raikot (K470+500) and Daynore (K538)
Rain glacier type debris flow	Located between Daynore (K538) and Hasnabard (K623)
Glacier ice lake break type debris flow	Distributed between Hasnabard (K623) and Gosghil (K796)
Freeze–thaw type debris flow	Located between Gosghil (K796) and Khongjirap (K811)

.

2.2. Obtaining the Basic Data of Debris Flow Gully Slope and Provenance Particle Characteristics

The basic data on the four types of debris flow gully slope and provenance particle characteristics that developed along the Karakoram Highway were obtained by combining field measurement and indoor statistical analysis. Combining field measurements provides support for the accuracy and reliability of the research, while indoor statistics provide reference and help for the debris flow provenance particle characteristics [17]. The slope of the debris flow gully is measured using Laser Craft, a laser rangefinder imported from the United States, with an accuracy of 0.1 degrees. For some segmented debris flow gully, the slope of each segment is measured first, and then, the slope of the whole gully is calculated by the weighted average method. From the field investigation of the Karakoram Highway, it can be seen that most of the source particles distributed in the debris flow gully are in the shape of a cuboid, with particle size parameters in three directions: length, width, and height. Therefore, firstly, the most distributed provenance particles in each debris flow gully are selected as the average particle sample in the gully, and their size is measured in the three directions of length, width, and height with a tape with an accuracy of millimeters, and the average particle size of the debris flow provenance is obtained. Then, the equivalent volume diameter method (defined as the diameter of the ball with the same volume as the actual particle) in the equivalent particle size theory is adopted. The purpose is to convert average particle size into average particle equivalent particle size parameter to express its provenance particle characteristics [18]. In this study, for the convenience of expression, the debris flow gully slope is expressed by $\alpha$, and the provenance average particle equivalent diameter is expressed by $D$.

The method for determining the provenance average particle equivalent diameter of the debris flow on the Karakoram Highway is as follows:

(1)

Assuming that the average particle size in the three directions of length, width, and height of the debris flow source are $a$, $b$, and $c$, respectively. The equivalent volume diameter method can be used to obtain:

$$abc=\frac{4}{3}\pi {\left(\frac{D}{2}\right)}^3,$$

(1)

(2)

The provenance average particle equivalent diameter of the debris flow along the Karakoram Highway can be obtained as $D$:

$$D=\sqrt[3]{\frac{6abc}{\pi }},$$

(2)

The basic data of gully slope and the provenance particle characteristics of four types of debris flow disasters developed along the Karakoram Highway obtained by the above method are shown in

Table 2. Basic data of four types of debris flow disasters developed along the Karakoram Highway.

Debris Flow Type	Channel Number	Highway Stake Number		Slope (α) (°)	Average Particle Size (cm × cm × cm)	Average Particle Equivalent Diameter ($\mathit{D}$) (cm)
Rain type debris flows	1	K471+860		18.6	12 × 10 × 5	10.5
	2	K473+521		21.6	5 × 8 × 2	5.3
	3	K475+270		27.7	16 × 10 × 7	12.9
	4	K475+950-K476+125.3		30	8 × 13 × 7	11.3
	5	k477+896		15.3	5 × 9 × 3	6.4
	6	K477+380		21.7	9 × 10 × 2	7.0
	7	K478+250		26.3	6 × 10 × 4	7.7
	8	K479+840		16.2	10 × 9 × 5	9.5
	9	K480+036.1		15.3	15 × 6 × 4	8.8
	10	K481+525-K481+550		8.4	13 × 14 × 7	13.5
	11	K483+41-K483+468		5.3	3 × 1.5 × 4	3.3
	12	K486+670		17.7	10 × 13 × 8	12.6
	13	K489+700-740		5	15 × 7 × 10	12.6
	14	K490+050		21	12 × 5 × 6	8.8
	15	K490+225		19	13 × 15 × 5	12.3
	16	K491+70-k491+900		10.8	16 × 7 × 7	11.4
	17	K493+692-710		13.4	13 × 17 × 11	16.7
	18	K494+15-K494+185		14.4	14 × 11 × 9	13.8
	19	K496+650		8.3	13 × 14 × 21	19.4
	20	K496+820		30	31 × 21 × 13	25.3
	21	K503+723.5		18.1	13 × 8 × 4	9.3
	22	K504+731-772		16.8	11 × 13 × 9	13.5
	23	K504+860-872		13.2	9 × 13 × 9	12.6
	24	K505+090		17.3	17 × 12 × 9	15.2
	25	K505+367		23.1	16 × 6 × 12	13.0
	26	K506+100		35.9	20 × 16 × 8	17.0
	27	K506+683		14.8	11 × 5 × 1	4.7
	28	K508+355		23.6	11 × 7 × 5	9.0
	29	K508+577		28.5	9 × 8 × 5	8.8
	30	K508+865.8		16.4	15 × 10 × 3	9.5
	31	K512+980		12.3	8 × 10 × 15	13.2
	32	K515+340		5.4	16 × 7 × 6	10.9
	33 34 35	K518+830- K519+000	No.1 ditch	8.2	14 × 7 × 12	13.1
			No.2 ditch	20	5 × 6 × 4	6.1
			No.3 ditch	21.6	11 × 6 × 3	7.27
	36	K519+244		7	6 × 6 × 13	9.6
	37	K519+380		7.1	13 × 8 × 10	12.6
	38	K519+651		25.6	3.5 × 7 × 5	6.2
	39	K519+860		18.1	12 × 11 × 8	12.6
	40	K520+200-220		26.4	11 × 12 × 7	12.1
	41	K520+520		18	11 × 13 × 7	12.4
	42	K521+950		39.6	19 × 7 × 3	9.1
	43	K524+100		13.4	13 × 10 × 4	10.0
	44	K524+960		7.4	11 × 14 × 9	13.8
	45	K525+860-875		30.6	13 × 9 × 2	7.6
	46	K524+103		14.4	13 × 20 × 6	14.4
	47	K526+940		13.7	12 × 10 × 9	12.7
	48	K527+300		29	15 × 11 × 6	12.4
	49	K528+740		24.8	8 × 14 × 6	10.9
	50	K529+670		14.3	12 × 15 × 5	12.0
	51	K530+535		10.1	9 × 10 × 3	8.0
	52	K530+660		11.2	14 × 17 × 5	13.1
	53	K531+900		11.3	11 × 6 × 4	8.0
	54	K535+650-K536+000		3.4	16 × 11 × 10	15.0
Rain glacier type debris flows	55	K543+210-280		4.2	18 × 4 × 6	9.4
	56	K547+300		22.4	11 × 10 × 5	10.2
	57	K547+524		18.6	17 × 18 × 5	14.3
	58	K548+000		12.2	13 × 13 × 4	10.9
	59	K549+000		23.9	15 × 13 × 10	15.5
	60	K549+300		10.3	9 × 14 × 4	9.9
	61	K549+420		19.7	7 × 8 × 3	6.8
	62	K549+605		30.1	9 × 10 × 7	10.6
	63	K549+805		14.5	11 × 12 × 11	14.0
	64	K550+198.5		16.3	10 × 10 × 6	10.5
	65	K550+891		23.1	18 × 10 × 4	11.1
	66	K551+327		11.9	13 × 10 × 4	10.0
	67	K551+671		17.6	12 × 10 × 5	10.5
	68	K551+862		22.3	20 × 15 × 10	17.9
	69	K556+100		6	6 × 9 × 3	6.8
	70	K555+868		5.4	7 × 8 × 3	6.8
	71	K557+540		8.2	6 × 13 × 3	7.6
	72	K559+400		5.9	15 × 9 × 10	13.7
	73	K560+900		31	11 × 9 × 8	11.5
	74	K562+500		30.8	5 × 8 × 3	6.1
	75	K566+860		6.2	4 × 7 × 8	7.5
	76	K569+570		9.4	6 × 11 × 8	10.0
	77	K570+940		16.2	9 × 9 × 5	9.2
	78	K576+300		16	7 × 18 × 5	10.6
	79	K578+839-852.6		32.2	4 × 6 × 1	3.6
	80	K579+874		16.7	10 × 20 × 7	13.9
	81	K581+600		27.9	1 × 3 × 4	2.8
	82	K586+300		28.3	4 × 7 × 2	4.7
	83	K592+920		22.9	18 × 10 × 3	10.1
	84	K593+465		16.3	15 × 17 × 2	9.9
	85	K594+400		7.6	5 × 7 × 2	5.1
	86	K597+879		7.8	8 × 6 × 3	6.5
	87	K599+585		8.9	5 × 7 × 4	6.4
	88	K604+060		18	15 × 10 × 7	12.6
	89	K607+960		11.5	6 × 3 × 8	6.5
	90	K614+921		33.5	5 × 5 × 3	5.2
	91	K615+509		34.9	6 × 5 × 2	4.9
	92	K615+835		33.1	2 × 5 × 3	3.9
	93	K615+930		34	5 × 3 × 2	3.9
Glacier ice lake break type debris flows	94	K628		14.6	5 × 6 × 4	6.1
	95	K653+965		27.2	2 × 3 × 4	3.6
	96	K687+440		6	7 × 6 × 5	7.4
	97	K705+680-720		15.1	8 × 8 × 3	7.2
	98	K709+180		5.5	4 × 3 × 2	3.6
	99	K711+700		10.3	3 × 2 × 2	2.8
	100	K715+654-674		10.2	5 × 8 × 4	6.7
	101	K716+290-320		13.4	2 × 3 × 5	3.9
	102	K717+408		3.4	3 × 7 × 3	4.9
	103	K723+915		12.4	8 × 9 × 2	6.5
	104	K732+200		17.9	9 × 12 × 4	9.4
	105	K744+200		36.4	3 × 1 × 4	2.8
	106	K747+170		28.7	15 × 4 × 6	8.8
	107	K741+755		23.1	10 × 12 × 2	7.7
	108	K756+100		21.7	8 × 6 × 3	6.5
	109	K763+750		16.7	5 × 8 × 2	5.3
	110	K766+600		18.5	4 × 6 × 1	3.6
	111	K771+725-900		13.8	11 × 1 × 2	3.5
	112	K773+500		11.8	10 × 7 × 2	6.4
	113	K776+388		2.0	7 × 2 × 4	4.7
	114	K784+900		11.7	10 × 10 × 2	7.3
	115	K785+760		13.7	12 × 6 × 4	8.2
Freeze–thaw type debris flows	116	K801+060		21	20 × 12 × 8	15.4
	117	K802+048		16.5	12 × 7 × 8	10.9
	118	K802+225		13.6	25 × 15 × 10	19.3
	119	K802+400		15.8	16 × 8 × 8	12.5
	120	K803+588		15.1	6 × 9 × 3	6.8
	121	K806+600		16.9	5 × 7 × 2	5.1
	122	K811		4.5	15 × 8 × 13	14.4

.

3. Results and Discussion

3.1. Variation Law of Debris Flow Provenance Particle Characteristics along the Karakoram Highway

Figure 2 displays the distribution law of the provenance average particle equivalent diameter of the four types of debris flows developed along the Karakoram Highway, as identified in Table 2. The analysis of these data can help us better understand the provenance characteristics of different types of debris flows.

According to the analysis in Figure 2, the provenance average particle equivalent diameter of the rain type debris flows developed along the Karakoram Highway is between 5 and 20 cm. The provenance average particle equivalent diameter of the rain glacier type debris flows mainly varies from 3 to 15 cm. The provenance average particle equivalent diameter of the glacier ice lake break type debris flows is mainly distributed in the range of 2 to 10 cm. The provenance average particle equivalent diameter of the freeze–thaw type debris flows fluctuates between 5 and 15 cm. It can be seen that the provenance average particle equivalent diameter causing debris flow disasters on the Karakoram Highway is controlled by the type of debris flow. Generally, the provenance average particle equivalent diameter of the glacier ice lake break type debris flow is relatively small, followed by the freeze–thaw type debris flow, the rain glacier type debris flow, and the rain type debris flow is relatively large.

The difference between the average particle equivalent diameters of the four types of debris flows along the Karakoram Highway is mainly determined by the basic environmental conditions of their respective regions, such as climate, physical weathering, and ice and snow freezing and thawing. The specific reasons are as follows:

(1)

The area where the rain type debris flow is developed is located in the subtropical climate zone, with high temperature but a small temperature difference, weak physical weathering, and ice and snow freezing and thawing, so the damaging effect on rock and soil particles is relatively small, and the provenance average particle equivalent diameter is relatively large;

(2)

The distribution area of the glacier ice lake break type debris flow belongs to the typical inland plateau mountain climate, with small precipitation, thin air, strong solar radiation, low temperature and very large temperature difference, and strong physical weathering, and ice and snow freezing and thawing. At the same time, they are mainly started by glaciers, and there is strong friction between glaciers and particles, which has a strong destructive effect on rock and soil particles, so the provenance average particle equivalent diameter is small;

(3)

The distribution area of the rain glacier type debris flow lies between the areas where rain type debris flow and glacier ice lake break type debris flow develop. The weather, physical weathering, and the ice and snow freezing and thawing effects of this type of debris flow are also intermediate between the two types. As a result, the provenance average particle equivalent diameter of this type of debris flow is between the other two types of debris flow. Analyzing these characteristics can help us better understand the differences and features of different types of debris flow, and develop effective prevention and response measures;

(4)

The freeze–thaw type debris flow is mainly distributed in the section of the Karakoram Highway at an altitude of more than 4000 m. On the one hand, this section belongs to a typical alpine permafrost area, with thick permafrost depth, low temperature and large temperature difference, strong physical weathering, and ice and snow freeze–thaw effect. On the other hand, its surface material is mainly fine sandy soil with rich clay particles, and the larger particles are almost completely wrapped by the surface fine sandy soil. It weakens the damage of physical weathering and ice and snow freezing and thawing on these rocks and soils, so the provenance average particle equivalent diameter of the freeze–thaw debris flow in this section is relatively large, which also explains why the variation trend of the average particle size of the freeze–thaw debris flow source developed on the Karakoram Highway is larger than that of the glacier ice lake break type debris flow.

3.2. Relationship between Particle Characteristics of Debris Flow Source, Gully Slope, and Debris Flow Type

To study the quantitative relationship between the slopes ($\alpha$) of four types of debris flow gully developed along the Karakoram Highway and their corresponding average particle equivalent diameters ($D$), the gully slope coefficient ($C$) is defined as follows:

$$C=\frac{1}{\cos \alpha -\sin a}$$

(3)

As seen in Table 2, the slope of debris flow gullies distributed along the Karakoram Highway is in the range of 0° to 45° (excluding 0° and 45°). According to the analysis of Equation (3), the slope coefficient ($C$) of these debris flows is greater than 1 and increases with the increase in the gully slope ($\alpha$), that is, the greater the slope coefficient ($C$), the steeper the slope.

3.2.1. Rain Type Debris Flow

The slope of the rain type debris flow gully developed along the Karakoram Highway is mainly distributed in the range of 5° to 30°, and the average particle equivalent diameter is between 5 and 20 cm. The relationship between the two is shown in Figure 3.

The relationship between the slope coefficient ($C$) of rain type debris flow gully and its corresponding average particle equivalent diameter ($D$) is shown in Figure 4.

According to the analysis in Figure 4, about 95% of the slope coefficient ($C$) and the average particle equivalent diameter ($D$) of the source of rain type debris flow are distributed in an ellipse with the two as the axis, which can be expressed as:

$$\frac{{\left(D-11\right)}^2}{9^2}+\frac{{\left(C-1\right)}^2}{2^2}\le 1$$

(4)

3.2.2. Rain Glacier Type Debris Flows

The slope of the rain glacier type debris flow gully is an important factor affecting its occurrence and development. Based on research, it has been found that the slope of this type of gully is mostly distributed in the range of 5°to 35°. Additionally, the average particle equivalent diameter of the debris flow’s provenance is another important characteristic, and it is mainly distributed in the range of 3 to 15 cm. The relationship between the slope and the average particle equivalent diameter of the gully is shown in Figure 5.

The relationship between the slope coefficient ($C$) and the average particle equivalent diameter ($D$) of the rain glacier type debris flow gully is a key factor in understanding the characteristics and behavior of this type of debris flow. The relationship between these two parameters is shown in Figure 6, where it can be observed that there is a correlation between the slope coefficient and the average particle equivalent diameter.

Similarly, it can be concluded that the gully slope coefficient ($C$) and the corresponding average particle equivalent diameter ($D$) of most rain glacier type debris flows are also distributed in an ellipse with the two as the axis, and the specific expression of the ellipse is

$$\frac{{\left(D-10\right)}^2}{9^2}+\frac{{\left(C-2\right)}^2}{1^2}\le 1$$

(5)

3.2.3. Glacier Ice Lake Break Type Debris Flows

The slope of the glacier ice lake break type debris flow gully and the average particle equivalent diameter of the debris flow are two important factors that influence the occurrence and development of this type of debris flow. The slope of the gully fluctuates mainly in the range of 5° to 30°, while the average particle equivalent diameter of the debris flow is mainly between 2 and 10 cm. The relationship between these two parameters is shown in Figure 7. This relationship can be used to predict the potential occurrence and severity of glacier ice lake break type debris flows in different gully slopes and particle sizes.

The relationship between the slope coefficient ($C$) of the glacier ice lake type debris flows gully and its corresponding average particle equivalent diameter ($D$) is shown in Figure 8.

Similarly, as seen in Figure 8, the relationship between the slope coefficient ($C$) and the corresponding average particle equivalent diameter ($D$) of more than 95% of the glacier ice lake break type debris flows gully is also elliptic, and its specific expression is

$$\frac{{\left(D-5.5\right)}^2}{{\left(4.5\right)}^2}+\frac{{\left(C-2\right)}^2}{1^2}\le 1$$

(6)

3.2.4. Freeze–Thaw Type Debris Flows

The slope of the freeze–thaw type debris flows gully is mainly distributed in the range of 5° to 20°, and the average particle equivalent diameter fluctuates between 5 and 15 cm. The relationship between them is shown in Figure 9.

The relationship between the slope coefficient ($C$) of freeze–thaw type debris flows gully and the average particle equivalent diameter ($D$) is shown in Figure 10.

It can also be seen in Figure 10 that most of the slope coefficient ($C$) of the freeze–thaw type debris flows and the provenance average particle equivalent diameter ($D$) are also distributed in the ellipse with the two as the axis, and the relationship is

$$\frac{{\left(D-12.5\right)}^2}{{\left(7.5\right)}^2}+\frac{{\left(C-1.5\right)}^2}{{\left(0.5\right)}^2}\le 1$$

(7)

To sum up, the relationship between the gully slope coefficient and the average particle equivalent diameter of the four types of debris flow disasters (rain, rain glacier, glacier ice lake break, and freeze–thaw) developed along the Karakoram Highway can be expressed as an ellipse with both parameters as the axis. The elliptic expressions provide a quantitative representation of the changing relationship between the gully slope and the corresponding source particle characteristics of these debris flow events. The analysis of this relationship can aid in predicting the occurrence and severity of these events and designing effective prevention and control measures. Understanding the interplay between the gully slope and source particle characteristics is crucial in mitigating the damage caused by debris flow disasters along the Karakoram Highway.

3.3. Thoughts and Suggestions on Debris Flow Disasters

Through the study of the gully slope coefficient and the equivalent particle size distribution of the source average particle size of the rain type, the rain glacier type, the glacier ice lake break type, and the freeze–thaw type, ecological engineering, and civil engineering measures are carried out to control debris flow in different sections of the Karakoram Highway.

The ecological engineering measures are mainly to close the mountains along the Karakoram Highway for afforestation and plant vegetation to weaken the physical weathering, ice and snow freeze–thaw damage to these rock and soil bodies, and at the same time, block the water flow to form channels.

Civil engineering prevention and control measures aim to build slope protection and retain the walls in accordance with to the equivalent particle size of the source average particles, thereby strengthening the rock mass and weakening the damage of the external environment to the rock mass particles. According to the relationship between the slope coefficient of the channel and the equivalent particle size of the source average particle, the drainage project is constructed, adjusting and diverting debris flow circulation paths and silting sites. Based on the principle that the source of matter dominates the formation of debris flow, the channel debris flow control technology of ‘mainly draining and blocking large and small ones’ is an effective scientific prevention and control method. The research on the types of debris flow and taking corresponding prevention and control measures provides theoretical support and suggestions for sustainable governance.

During the process of highway construction, monitoring points are constructed in each section to build a spatial-temporal data model of ground substrate. To carry out layer current situation, development and utilization degree and potential analysis, forecast changes and development trend, and comprehensively analyze the overall situation of high-quality development of natural resources, ecological environment and regions. Elevation models and digital surface models can be established as the basis, and the idea of establishing a 2D and 3D integrated database can be established as the goal, and the space–time model can be bound to the survey attributes so that all data can be merged in the form of a database. In the process of implementation, it is necessary to strengthen analysis and evaluation, collect statistics, summarize the survey, monitor the data of the surface matrix layer, establish scientific evaluation indicators, carry out comprehensive analysis and systematic evaluation to provide a basis for scientific decision-making and strict management, and improve the sustainable development of the surrounding ecological environment and the sustainable use of the Karakoram Highway.

4. Conclusions

This paper draws several important conclusions. The characteristics of debris flow disasters vary significantly depending on their source and origin. The relationship between the gully slope and average particle equivalent diameter of the debris flow can be represented by an ellipse. The specific conclusions are as follows:

• The provenance particle size induced by debris flow on the Karakoram Highway is controlled by the type of debris flow. Generally, the provenance average particle equivalent diameter of the glacier ice lake break debris flow is relatively small, followed by the freeze–thaw and rain glacier debris flow, and the rain type debris flow is relatively large;
• This analysis shows that the slope coefficient of debris flow gullies along the Karakoram Highway is greater than 1, and it increases as the gully slope becomes steeper. In other words, gullies with higher slope coefficients have steeper slopes;
• The majority of debris flows that occur along the Karakoram Highway can be categorized into four types: rain type debris flows, rain glacier type debris flows, glacier ice lake break type debris flows and freeze–thaw type debris flows. These types of debris flows are characterized by their gully slope coefficient $C$ and the provenance average particle equivalent diameter $D$, which are distributed in an elliptical patterns. By analyzing these ellipses, we can better understand the relationship between the gully slope of each type of debris flow and the corresponding provenance particle characteristics.