Optimization Design of Sand and Loess High Slope Based on Combination of Wide and Narrow Platfom——A Case Study of a High Slope in Yulin City

Abstract

Due to the limited land resources available for engineering construction in Northern Shaanxi, engineering activities such as mineral resources development, basic engineering construction, slope reduction and building houses, and farming are often accompanied by the formation of a large number of Manually Excavated high slopes. Effective high slope design can reduce the waste of land resources, mitigate the damage to the natural environment, and reduce the project cost to a certain extent. Therefore, this paper takes a high sand loess slope in Yulin City, Shaanxi Province as an example, through field investigation, system theoretical analysis and numerical simulation calculation, comprehensively considering the anti scouring property, overall stability and excavation volume of the slope, the design scheme that meets the requirements and consumes the least capital is compared and selected, so as to obtain the optimal slope shape. The conclusion shows that the optimal single slope height of sand loess high slope in Northern Shaanxi is 7–8 m, and the slope ratio is 1:0.75. The setting of wide platform can change the stress distribution of high slope and weaken the continuity of effective plastic strain. The optimal slope shape of the high side slope includes the single slope of 8 m, the slope ratio of 1:0.75, the narrow platform of 3 m wide, 3 wide platforms are arranged, the location of ③④⑤, the width of 10 m, and the excavation volume of 696 m³ (per linear meter).

1 Introduction

With the development of the national economy and the continuous promotion of the western development strategy, engineering construction projects in the western loess region have been increasing, and the limited available land resources have been unable to meet the current demand. Therefore, people try to solve this problem by changing the topography and landscape, but with this comes the formation of more and more artificial excavation of high slopes during the construction of engineering projects [1, 2]. According to research, the number of slope damages in China has accounted for more than half of the number of geological disasters since the twentieth century, and the problem of high slopes has become increasingly prominent [3]. It is generally considered that rocky slopes with a height greater than 30 m and soil slopes with a height greater than 20 m are high slopes, and their stability is mainly determined by the basic characteristics of the geotechnical body itself and the degree of human modification [4, 5]. In recent years, railroad, water conservancy and hydropower and highway construction industries have conducted more systematic research on loess slopes below 30 m, and achieved good results [6,7,8]. And at present, the slope height is no longer satisfied with 30 m, and the figure keeps breaking new records. Although in the process of engineering construction, emphasis has been placed on avoiding engineering construction in adverse geological locations, but high filling and deep excavation of roadbed, artificial slope reduction to build houses and other acts are inevitable, especially in some areas where available land is scarce is difficult to avoid. Northern Shaanxi is a typical loess area, and due to its special physical and mechanical properties, the loess structure is easily damaged when encountering precipitation or earthquake effects, resulting in serious geological disasters such as collapse, landslide, and slope scour [9, 10]. During September–November last year alone, 11 geological disasters occurred in northern Shaanxi under the action of heavy precipitation, resulting in 8 deaths, hundreds of people affected, and direct economic losses of more than 6 million yuan. It can be seen that it is necessary to conduct an in-depth study of certain areas, especially in such areas with special geological and environmental conditions, and the study of slope stability is particularly important.

The current analysis methods for slope stability research can be broadly divided into two types of analysis methods: deterministic and uncertainty [11]. Among them, the deterministic analysis methods mainly include limit theory equilibrium method, plastic limit analysis method, finite element method, Monte Carlo method, etc.; the uncertainty analysis methods mainly include fuzzy comprehensive evaluation method, gray analysis method, information quantity simulation method; besides, there are some other uncertainty analysis methods, such as quantitative theory method, quantitative table method, etc.

With the continuous improvement and development of slope prevention technology, nowadays there are more and more kinds of slope management methods, among which, the common form of high slope protection is slope reduction + interception and drainage + greening, among which the slope shape of slope reduction mainly includes “equidistant step slope” and “wide and narrow platform slope The shape of slope reduction mainly includes “equidistant step slope” and “wide and narrow platform slope”. According to the survey, the protection effect of “wide and narrow platform slope” is better in terms of overall stability of slope. However, whether it is “equidistant stepped slope” or “wide and narrow platform slope”, the problems of slope scour and overall stability are still significant and there are large safety hazards, and the unreasonable setting of slope reduction platform will lead to the increase of excavation volume, thus destroying the original terrain and wasting cost. Therefore, on the basis of slope stability research, it is a new issue worth thinking about how to optimize the design of slopes for different engineering fields.

Currently, many scholars have achieved good results in slope optimization design. Qian Gao, Wanjun Ye, Yanan Zheng et al. optimized the design of high slopes based on reliability theory analysis and proposed an effective and reliable design scheme [12,13,14]; Xinli Hu et al. designed the optimal slope angle so as to establish a slope optimization model [15]; Linhai Wan et al. proposed an open-air slope design scheme by establishing a radial basis function (RBF) neural network model, which solved the actual slope of the iron ore mine of water plant problem [16]; Yuming Xu used FLAC3D for slope stability evaluation so as to optimize the design of slopes [17]; Xuan Zhou proposed an optimal design scheme suitable for slopes based on sensitivity analysis [18]; Hongwei Fang et al. proposed a new slope optimization design method based on the limit curve method, giving objective quantitative indicators of slope instability [19]; Nengpan Ju et al. relied on a highway, put forward a set of operational highway slope optimization design research program [4].

In the existing slope research, most of the slopes with the same width platform are used as the research object to carry out the slope optimization design, but little research has been done on the “wide and narrow platform slope”.The current research on this type of slope is mainly based on engineering experience and engineering analogy, and lacks practical basis and theory, in which the safety and stability of slopes still threaten people's life and property safety and social development to a certain extent. Therefore, based on a sandy loess high slope in Fugu County, Yulin City, Shaanxi Province, this paper analyzes the single-stage slope scour resistance and overall stability of the slope based on the idea of combining wide and narrow platforms, so as to propose a feasible slope optimization design scheme and provide some ideas for the optimization design of sandy loess high slope.

2 Profiles

2.1 Study Area Profile

The study area belongs to Fugu County, Yulin City, Shaanxi Province, and is located in the northernmost part of Shaanxi Province. It has a temperate continental monsoon climate, with cold and long winters and hot and short summers, low precipitation in spring and winter, high precipitation in summer and autumn, mostly heavy rainfall or continuous rains, low rainfall and high evaporation, severe spring droughts, frequent sand and wind, cold and dry sandy areas and mainly concentrated in the northwest, large temperature differences between day and night, and many early frosts and hail. The surface rivers in Fugu County are relatively dense, with dense gullies, of which there is only the Shagoucha Gully on the east side of the study area site, which belongs to the Yellow River water system, with heavy rise and sediment content in the rainy season and broken flow in the dry season. The study area is located in the border area between Inner Mongolia Plateau and the northeastern part of the Loess Plateau in northern Shaanxi Province, which is a loess gully landscape with micro-geomorphology divided into loess residual beams and river valleys. The overall topography shows a trend of high in the south west and low in the north east.Loess is widely distributed in the region, and its strong wet-sink nature, loose soil, porosity, and vertical fissure development make it prone to slope scouring and slope destabilization under heavy or persistent rainfall, and in severe cases, it will trigger geological disasters such as landslides [20,21,22,23].

Due to the constraints of the topography, a large number of artificially excavated high slopes have been formed in the study area due to engineering activities such as mineral resources development, infrastructure construction, slope reduction for housing and farming, as shown in Fig. 1. and Fig. 2.

Fig. 1

Photo of Shagoucha sandy loess high slope

Fig. 2

Photo of High slope of Shenghai coal mine

All the high slopes seen in this survey have been graded, and the overall stability is better with “wide and narrow platform slope”. However, when the slope surface is not protected, the slope surface is prone to serious scouring damage under rainfall conditions, especially heavy or continuous rainfall. In addition, the wide platform will lead to an increase in excavation volume, thus increasing the investment of project funds. Therefore, it is especially important to optimize the factors affecting the scouring and stability of high slopes.

2.2 Side Slope Profile

The slope studied in this paper is the high slope of Shagoucha coal mine located in the west of Fugu County, Yulin City, Shaanxi Province. The maximum slope height of this slope is about 50 m, the longitudinal length is about 220 m, the slope gradient is 35–60°, the slope surface generally tends to the north-east, grass and other plants are planted on the slope surface, the slope is relatively intact, and no water fall hole is developed.

The slope is mainly composed of Quaternary Upper Pleistocene loess (Q³_eol), and its physical and mechanical indexes are determined by indoor geotechnical tests. The basic physical and mechanical indexes are shown in Table 1, and the cumulative gradation curve of grain size is shown in Fig. 3. Among them, the mass fractions of clay particles (particle size < 0.005 mm), powder particles (particle size 0.005–0.075 mm) and sand particles (particle size > 0.075 mm) are 8.20, 71.80 and 20.00%, respectively.

Table 1 Basic physical properties of the soil bodies in the study area

Fig. 3

Accumulated cascade curve of powdered loess particle size

Loess slope, due to the special nature of its material composition, is prone to deformation and damage under the action of rainfall, and the main form of damage is slope scouring, which will affect the stability of the slope and thus make the slope destabilized and damaged, therefore, it is necessary to carry out the research of slope scouring resistance of the slope.

3 Optimal Design of Scour Resistance Based on Single-stage Slope

The process of scour damage of loess slopes is more complex, and scour damage is one of the most harmful and common phenomena in slope design [20, 24]. Tests have shown that there are many factors affecting the scouring of loess slopes [25, 26], and in addition to natural factors such as precipitation and earthquakes, the morphological characteristics of the slope are also important influencing factors. In order to investigate the influence of slope morphology such as slope length, slope height and slope rate on scour resistance, the limit equilibrium method is used to obtain the optimal single-stage slope rate by considering changing the slope length of the single-stage slope under the most unfavorable precipitation working conditions with the help of field investigation and previous research results.

4 Slope Water Infiltration Analysis

The slope water infiltration problem has been developed and studied for a long time, and numerous empirical and theoretical formulations have been formed. In this paper, the Green-Ampt model is selected, which has low requirements for parameters, clear physical meaning, strong applicability, fast and simple calculation and meets the accuracy requirements [20, 27, 28]. The model formulation is:

$$i = k_{s1} [1 + (h_{0} + h_{f} )\frac{1}{{z_{f} }}]$$

(1)

Among them:

$i$—— Infiltration rate cm/min;

$k_{s1}$——Saturated hydraulic conductivity, cm/min;

$h_{0}$——Soil surface water accumulation depth, cm;

$h_{f}$——Wet front suction, cm;

$z_{f}$——Generalized wetting front depth, cm;

Since the infiltration time is relatively short, Eq. 1 can be simplified as:

$$i = k_{s1} \left( {\frac{{h_{f} }}{{z_{f} }}} \right)$$

(2)

The rainfall lasted for 12 h, and the parameters were obtained by indoor infiltration test $k_{s1}$, taking 3.32 × 10^–6 m/s, $h_{f}$ and $z_{f}$ the field experiment results with reference to similar soil properties, of which $z_{f}$ 236.6 cm was taken and $h_{f}$ 150 cm was taken.

4.1 Slope Soil Force Analysis

According to the principle of dynamics, the stability of the soil unit on the slope is analyzed as the object of study, so as to ensure the stability of the slope as a whole. The force analysis of the soil unit is shown in Fig. 4:

Fig. 4

Schematic diagram of soil elements on slope

According to the conditions of equilibrium of forces, parallel to the direction of the slope:

$$F_{{_{D} }} + G\sin \theta = \mu (F_{s} + G\cos \theta - F_{L} )$$

(3)

Among them:

$$F_{{_{D} }} = 1.9\pi \rho C_{D} D^{2} \mu^{1/9} \left[ {\left( {p - i} \right)L} \right]^{2/9} \sin^{ - 1/9} \theta \cos^{1/3} \theta d^{2/3}$$

(4)

$$F_{L} = 1.9\pi \rho C_{L} D^{2} \mu^{1/9} \left[ {\left( {p - i} \right)L} \right]^{2/9} \sin^{ - 1/9} \theta \cos^{1/3} \theta d^{2/3}$$

(5)

$$G{ = (}\gamma_{{\text{s}}} - \gamma_{w} )\pi D^{3} /6$$

(6)

$$F_{S} = \gamma_{S} J_{S} \pi D^{3} /6$$

(7)

G——Gravity; d——Sharmov's formula particle diameter; Same value as $D$;

$\rho$——Density; $C_{D}$, $C_{L}$——Resistance coefficient, Lifting force coefficient;

p——Rainfall intensity; $\theta$——Slope angle;

I——Infiltration rate; L——Slope length;

$\gamma_{s}$, $\gamma_{w}$——Saturated capacity, Watercapacity;$\mu$——Roughness coefficient;

$D$——Diameter; $J_{s}$——Hydraulic gradient

4.2 Parameter Selection

The physical and mechanical parameters of the soil required for the model were obtained from indoor tests of soil samples in the study area; the single-width rainfall intensity was obtained from the statistics of annual rainfall in the study area; the infiltration rate of the slope surface was calculated from the infiltration analysis.CD and CL were calculated by referring to the research results of Jemenyev Idgiazarov [26], and the values of the calculated parameters of the final force analysis are shown in Table 2.

Table 2 Table of slope design parameters

4.3 Single-stage Slope Scour Analysis

In measuring the limit equilibrium state of the slope soil against scouring, the slope soil is exactly in the limit state when the difference between the slip resistance and the decline force is 0, i.e.

$$F_{{_{D} }} + G\sin \theta - \mu (F_{s} + G\cos \theta - F_{L} ) = 0$$

(8)

According to the calculation combined with the field survey results, the single slope height of the slope in the study area is mainly 7–8 m, and 1:0.75 is selected as the optimal anti-scouring slope rate for the single slope height.

5 Optimized Slope Design Based on Overall Stability

When discussing the scour resistance of slopes, slope morphology is one of the decisive factors, and reasonable slope morphology plays an important role in reducing scour damage. However, in the actual slope design, the overall stability of the slope is another key indicator.

For artificial excavation of loess high slope, the most common method is slope rate method, which involves many factors, not only affects the overall stability of slope, but also affects construction period, engineering capital investment, environmental protection, etc. Therefore, it is crucial to design a safe, effective and economical slope reduction optimization plan. According to the field survey, the loess high slopes in northern Shaanxi can be mainly divided into two categories: one is slow slope and narrow platform, and the other is wide platform and narrow slope. Among them, the single slope height and slope rate of slow slope and narrow slope are small, with poor anti-scouring performance and large volume of works, and serious damage to the environment; while the volume of works of wide platform and narrow slope is relatively small, and it has great advantages in resistance to slope damage and overall slope damage. Since the design is only based on practical experience, the optimization design theory is lacking. Therefore, in this paper, considering the anti-scouring performance of the slope and taking the overall stability of the slope as the premise, the width, location and quantity of the wide platform of the slope are studied with the help of MIDAS numerical simulation software.

According to GB 50,330–2013 Technical Specification for Construction Slope Engineering, the high slope of coal mine industry belongs to Grade III slope, and the safety factor is required to be greater than 1.25, therefore, 1.25 is used as the stability evaluation index in the numerical simulation analysis.

5.1 Geometric Models

The basic assumptions for establishing the model are: firstly, the geotechnical body is regarded as a uniform isotropic elastic body; secondly, the plane strain state is considered; thirdly, the geotechnical body obeys the Moore-Coulomb damage criterion.

The total slope height of the high side slope in this study is 48 m. According to the actual survey and previous engineering experience, the single slope rate of this model is designed to be 1:0.75; the slope height is 8 m; the width of the narrow platform is 3 m; the wide platform is taken to be 6–16 m, and the interval is 2 m in turn; the number of wide platforms is 1–4, and the position is freely combined. The following is an example of two 10-m wide platforms, modeled as shown in the Fig. 5.

Fig. 5

Schematic diagram of two wide platform high slope models

5.2 Boundary Model

The simulation parameters are selected in Table 2.

The strength discounting method is used in the calculation, and the convergence condition in the analytical control is set to the displacement standard 0.001 m. The boundary conditions are horizontal and vertical constraints at the lower boundary and horizontal constraints at the left and right boundaries. Quadrilateral cells are used to divide the mesh. The specific model is generalized in the calculation, and each layer of the geotechnical body is considered as an isotropic material. The analysis considers the influence range of the model, the model extension dimension is 50 m from the top of the slope to the X axis, 40 m from the foot of the slope to the left, and 30 m from the foot of the slope to the Y axis.and the actual distance of the slope height above the foot of the slope to the top of the slope.

5.3 Analysis of Results

Stress-strain Analysis.

Due to space limitation, the simulation results for one and two wide platforms are listed here. Simulation results for three and four wide platforms are similar to them and are not shown separately here.

• (1) One wide platform

Take the 10 m wide platform as an example, the wide platform is set at ①, ③ and ⑤ respectively. When the wide platform is located at ①, the maximum effective plastic strain is located at the toe of the slope above the wide platform(Fig. 6(a)); when the wide platform is located at ③(Fig. 6(b)), the effective plastic strain is distributed in the whole slope, and the maximum value is located at the foot of the slope; when the wide platform is located at ⑤(Fig. 6(c)), the effective plastic strain is only distributed in the slope below the wide platform.

Fig. 6

Plastic strain zone of one wide platform

Take the location of wide platform ③ as an example, the width of wide platform is 8, 12 and 16 m respectively, with the increase of wide platform width, the maximum effective plastic strain decreases and the strain concentration area is all located at the foot of the slope, but the distribution of effective plastic strain area in the slope is gradually discontinuous, which indicates that the overall stability of the slope has improved (Fig. 6(d-e)).

It can be concluded from this that when there is only one wide platform, the width of the wide platform is large enough and the location is close to the foot or the top of the slope, the whole slope can be analyzed as two independent slopes above and below with the wide platform as the boundary.

• (1) Two wide platforms

Take the 10 m wide platform as an example, the wide platform is set at ①②, ②④ and ④⑤ respectively.When the wide platform is located in ①②, the maximum effective plastic strain is located at the foot of the slope above the wide platform (Fig. 7(a));when the wide platform is located at ②④, the effective plastic strain is distributed throughout the slope, and the maximum value is located at the foot of the slope (Fig. 7(b)); when the wide platform is located at ④⑤, the effective plastic strain is concentrated only in the slope below the wide platform (Fig. 7(c)).

Fig. 7

Plastic strain zone of two wide platforms

Take the location of wide platform ②④ as an example, the width of wide platform is 8, 12 and 16 m respectively, with the increase of platform width, the maximum effective plastic strain decreases first and then increases (Fig. 7(d-e)).

It can be concluded from this that when there are two wide platforms, the changes of effective plastic strain zone, maximum stress strain and stability are similar to one wide platform, and the strain zone has been obviously divided by the wide platform. The maximum effective plastic strain at the lower side of the wide platform position is greater than that at the upper side of the wide platform position, and the strain concentration phenomenon gradually appears at the slope corner of the upper slope, and the overall stability of the slope improves and basically meets the requirements after the width is greater than 14 m.

Analysis of Stability Simulation Results.

The simulation results of the wide platform model with different widths are shown in Fig. 8.

Fig. 8

Relationship between wide platform position and stability coefficient Optimized slope design combining excavation volume and stability

For the 48 m high slope in this study, when there is only one wide platform (Fig. 8(a)), as the wide platform gradually moves from the foot of the slope to the top, the stability coefficient shows an overall trend of first increasing and then decreasing, and the stability coefficient is the largest when the wide platform is at position ③. However, no matter changing the position of wide platform or the width of wide platform (6–16 m), it cannot meet the stability requirement. When there are two wide platforms, the stability of high side slope meets the requirements when the width of wide platform is 16 m and the location of wide platform is ①③, ①④, ②③, ②④, ②⑤, ③④, ③⑤; the width of wide platform is 14 m and the location of wide platform is ①③, ②③, ②④, ②⑤, ③④, ③⑤; the width of wide platform is 12 m and the location of wide platform is ②③, ②④, ③④. Among them, the stability coefficient is the highest when the location of wide platform of the same width is ②④. When there are three wide platforms, except for the 6 and 8 m wide platforms, most of the other wide platforms can meet the stability requirements. Among them, the stability coefficient is the highest when the position of wide platform of the same width is ②③④. When there are four wide platforms, only the 6 m wide platform does not meet the stability requirements, and the rest all meet. Among them, the stability factor is the highest when the position of the wide platform of the same width is ②③④⑤.

As the excavated wide platform gradually moves from the foot of the slope to the top of the slope, the stability coefficient changes obviously. When there is only one wide platform, the stability of the middle position is often the highest; when there are multiple wide platforms, the stability coefficient increases when the wide platform positions are adjacent to each other, especially the stability of the wide platform position located in the middle adjacent to each other is the highest.

As can be seen from Fig. 9, the stability coefficient changes with the excavation volume, and the width, location and number of wide platforms change. Under the premise of satisfying the overall stability requirement of the slope, the smaller the excavation volume, the less the corresponding project economic consumption and the less damage to the original ecological environment. In this simulation, there are 67 slopes that meet the overall stability of slopes.

Fig. 9

Relation diagram between excavation amount and stability coefficient

Through comprehensive consideration and analysis, 3 wide platforms with 10 m width and location ③④⑤ are the optimal slope design for the 48 m high slope in this study.

6 Conclusions

• (1) The optimal single slope height of 7–8 m and slope rate of 1:0.75 for sandy loess high slopes in northern Shaanxi Province are studied on the artificial excavation slope of Shagoucha coal mine in western Fugue County, Yulin City, Shaanxi Province.

• (2) The setting of wide platform can change the stress distribution of high slope and weaken the continuity of effective plastic strain: when it is located at the foot and top of the slope, the distribution of potential slip surface is bounded by the location of wide platform and distributed on the slope above and below the wide platform; when it is located in the middle of the slope, the distribution of potential slip surface is discontinuous at the wide platform, and when the wide platform is continuously distributed and the width is large, the high slope can be considered as two independent slopes for analysis Calculation.

• (3) Considering only the overall stability of the slope, setting 1 wide platform cannot meet the slope stability requirements; setting 2 wide platforms, when the size of wide platform is larger than 12 m, only a few slope shapes meet the requirements; setting 3 wide platforms, when the size of wide platform is larger than 10 m, the number of slope shapes that meet the stability requirements is larger; setting 4 wide platforms, except when the size of wide platform is 6 m, all other slope shapes meet the stability requirements.

• (4) Combining the scour resistance and excavation volume, considering the overall stability of the slope, the optimal slope shape of this artificial excavation slope is: single slope height of 8 m, slope rate of 1:0.75, narrow platform width of 3 m, arrangement of 3 wide platforms, position ③④⑤, width of 10 m.

The research results can compensate to a certain extent the defects of the traditional loess high slope stability analysis and evaluation in which the potential slip surface is assumed to run through the whole slope, and also solve to a certain extent the difficulties of high slope shape selection mainly by experience, and provide guidance basis for future slope management projects in the area, which has important practical significance.