# Analysis of Factors Influencing Stability of Overlying Soil Layer on Thin Bedrock Based on Crack Development-Closure Test

Authors: Guangming Wu; Haibo Bai; Luyuan Wu; Shixin He; Bin Du
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

The water-blocking properties of the clay layer at the bottom of the Cenozoic overburden in China are an important factor influencing the safety of thin bedrock coal seam mining. Clay has remolding properties that are unlike the nonreversible characteristics of cracks in brittle rock, and failure cracks in clay can reclose or continue to expand under the influence of different external factors. In this work, the soil layer on top of thin bedrock is the research object, and the influences of the particle composition, water content, soil layer thickness, and crack width on the crack development-closure state of soil layer are analyzed by the orthogonal test method. Visual analysis shows that the order of influence of each factor on the stability of soil layer is the crack width, particle composition, soil layer thickness, and water content. The stability of soil layer decreases with increasing crack width and sand content and decreasing soil layer thickness; in addition, soil layer stability decreases first and then increases with increasing water content. Further variance analysis shows that the crack width and particle composition are key factors that impact the stability of soil layer and that the soil layer thickness has some influence, while the water content has little effect on the stability of soil layer. In addition, the crack will reclose when the sand content in soil is less than 50% and the crack width is less than or equal to 1.0 mm, and the soil layer is prone to further failure when the sand content in soil is more than 50% and the crack width is greater than or equal to 3.0 mm; when the soil layer thickness is 15.0 cm, its stability is better than when the soil layer thickness is 10.0 cm or 5.0 cm.


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## Body

## 1. Introduction

Environmental problems, such as water resource shortages and surface degradation caused by coal mining, are becoming increasingly prominent as the intensity of coal mining in China increases. The aforementioned is especially true in midwestern areas, where underground latent water resources are widely distributed in the Cenozoic overburden. The damage to underground latent water resources is particularly evident in the coal seam mining process [1–4]. Therefore, ideas and methods, such as “green coal mining [5–7]” and the “coexistence of coal and water [8–11],” have been proposed. These ideas and methods have provided new ways of protecting underground latent water resources.To find solutions to specific problems, such as maintaining the safety of coal seam mining and researching the water-blocking mechanisms of clay, scholars in China and abroad have carried out useful studies by establishing safety assessment methods, conducting field measurements, and running numerical simulations. For example, the concept of the risk coefficient of water inrush in loose porous aquifers and the clay at the bottom of the Quaternary system that has been put forward can be used as part of the mining protection layer [12–15]. These studies provide guidance to improve the extent of coal seam mining under thin bedrock.Simultaneously, much research has also been conducted on the protection of water resources in the process of mining coal resources. The influence of coal mining on underground latent water resources were divided into four categories, namely, serious, moderate, slight, and no water loss, and an aquifer-protection mining technique can be successfully applied by modifying a few mining parameters, such as the mining height or advance rate. Moreover, the key factor in protecting underground latent water resources is the thickness of the weathered bedrock located immediately below the aquifer [16–20]. Mining activities can cause not only surface and subsurface water loss but also chemical, trace metal, and microbiological pollution of surface and subsurface water [21–25].The water flowing fractured zone usually penetrates through thin bedrock while mining coal seams under thin bedrock. At this time, the clay layer at the bottom of the Cenozoic overburden becomes an important water-blocking structure and plays an important role in preventing the water in porous aquifers and phreatic aquifers from flowing to the working face [26]. In addition, the properties, distribution characteristics, and mining failure characteristics of clay have important influences on its water-blocking performance [27–30]. Unlike the development of dry crack or the development of crack in slopes, retaining walls, and other soil engineering structures [31–35], the direction of mining-induced shear/tension crack in the overlying soil layer during thin bedrock coal seam mining is generally nearly vertical and the crack is subject to erosion and scouring by upper phreatic aquifer water [36]. In addition, clay has remolding properties, which are unlike the nonreversible crack in brittle rock [37–40]. The crack in soil will reclose under the action of stress and water swelling property and other factors. For example, Huang et al. [41] found that the crack in the soil swelled with water and the crack reclosed when the amount of expansion exceeded the width of the crack. Zhang et al. [42, 43] studied the functional relationship between the soil suction and resilient modulus by repeated load triaxial test and considered that the resilient modulus increases with the increase in the minimum bulk stress, soil suction, and degree of compaction and decreases with increasing octahedral shear stress.The characteristics of crack development-closure in soil layer are of great significance to the stability of the overlying soil and its water-blocking effect in thin bedrock coal seam mining. In this paper, four factors that affect the development-closure state of crack, namely, particle composition, soil layer thickness, crack width, and water content, are examined. The crack development-closure characteristics of soil layer are analyzed by the orthogonal test method. The aim of the work is to provide a reference for the stability analysis of overlying soil and the protection of underground latent water resources in thin bedrock geological regions during thin bedrock coal seam mining.


## 2. Hydrogeological Conditions of Thin Bedrock Coal Seam Mining

### 2.1. Thin Bedrock Definition

At present, there is no clear standard for the definition of thin bedrock, and researchers have different definitions of thin bedrock according to their own research purposes. For instance, thin bedrock can be defined according to the height of three zones based on the view of water prevention [44]. Similarly, researchers define thin bedrock according to whether there exists a key stratum based on the view of mine pressure control [15]. This article defines thin bedrock (as shown in Figure 1) in terms of the water prevention view [44], and (1) if the bedrock thickness Hb is smaller than the height of the caving zone Hc, it is called ultrathin bedrock; (2) if the bedrock thickness Hb is larger than the height of the caving zone Hc but smaller than the height of the water flowing fractured zone Hc + Hf, it is called thin bedrock; and moreover, (3) if the bedrock thickness Hb is larger than the height of the water flowing fractured zone Hc + Hf, it is called normal thickness bedrock. Ultrathin bedrock and thin bedrock are commonly referred to as thin bedrock.Figure 1
Classification diagram of bedrock: (a) ultrathin bedrock,Hb < Hc; (b) thin bedrock, Hb < Hc + Hf; (c) normal thickness bedrock, Hb > Hc + Hf.
(a)
(b)
(c)


### 2.2. Hydrogeological Conditions of Thin Bedrock

The Carboniferous and Permian (C3-P1) and Jurassic (J1-J2) are the main coal forming periods in China (as shown in Figure 2). Tectonism leads to interruption or denudation in the strata deposit after the deposition of coal measure strata has been completed. As a result, some of the strata between the coal measure strata and the Cenozoic overburden are missing, and the Cenozoic overburden is directly deposited on the coal measure strata (as shown in Figure 3).Figure 2
Distribution diagram of the major coal resources in China.Figure 3
Hydrogeological profile of thin bedrock.The water flowing fractured zone generally penetrates through thin bedrock and into the Cenozoic overburden with the progression of coal mining under such geological conditions. Accordingly, the failure state and water-blocking properties of soil in the Cenozoic overburden are key factors in determining whether a hydraulic connection between the Cenozoic porous aquifers and the working face will occur. Typical hydrogeological conditions of thin bedrock are shown in Figure3.


### 2.3. Failure Process of the Overlying Soil of Thin Bedrock

The overlying soil layer of thin bedrock will deform or even fail with the deformation and caving of the bedrock as the coal seam is continuously exploited, and the process of deformation and failure of the overlying soil layer can be divided into three stages, as shown in Figure4. First, the coal seam is mined out. Second, the bedrock collapses or fractures. Third, the collapse or fracture of the thin bedrock leads to a reduction in the supporting space of the overlying soil layers, and the overlying soil layers will subside due to the self-weight load. Then, the overlying soil layers undergo deformation and failure. Consequently, the essential cause of deformation or failure of the soil is the reduction in the supporting space in its lower part.Figure 4
Failure process of the overlying soil layers of thin bedrock: (a) natural state; (b) coal seam mining out ⟹ thin bedrock collapses or fractures ⟹ supporting space decreases and soil layer subside; (c) overlying soil layers recompact on the collapsed thin bedrock.
(a)
(b)
(c)The overlying soil will deform and produce cracks under the influence of coal seam mining. The cracks may reclose or continue to broaden by scouring and finally lead to further soil destruction under the action of water flow scouring in loose porous aquifer and other conditions. The key factors affecting the development-closure state of the cracks in soil layer are particle composition, dry-wet state (which can be expressed by the saturation or water content), crack dimension (crack length and width), and soil stress state.The main external forces are the self-weight stress and phreatic aquifer hydrostatic pressure in the overlying soil of thin bedrock, and their influence mode is long-term slow action. Therefore, the influence of the dynamic change in external forces can be temporarily neglected. Then, four factors can be selected, namely, the soil particle composition, water content, crack length, and crack width, and influence analysis of these factors on the development-closure state of the cracks in soil layer can be performed through orthogonal experimental methods.


## 2.1. Thin Bedrock Definition

At present, there is no clear standard for the definition of thin bedrock, and researchers have different definitions of thin bedrock according to their own research purposes. For instance, thin bedrock can be defined according to the height of three zones based on the view of water prevention [44]. Similarly, researchers define thin bedrock according to whether there exists a key stratum based on the view of mine pressure control [15]. This article defines thin bedrock (as shown in Figure 1) in terms of the water prevention view [44], and (1) if the bedrock thickness Hb is smaller than the height of the caving zone Hc, it is called ultrathin bedrock; (2) if the bedrock thickness Hb is larger than the height of the caving zone Hc but smaller than the height of the water flowing fractured zone Hc + Hf, it is called thin bedrock; and moreover, (3) if the bedrock thickness Hb is larger than the height of the water flowing fractured zone Hc + Hf, it is called normal thickness bedrock. Ultrathin bedrock and thin bedrock are commonly referred to as thin bedrock.Figure 1
Classification diagram of bedrock: (a) ultrathin bedrock,Hb < Hc; (b) thin bedrock, Hb < Hc + Hf; (c) normal thickness bedrock, Hb > Hc + Hf.
(a)
(b)
(c)


## 2.2. Hydrogeological Conditions of Thin Bedrock

The Carboniferous and Permian (C3-P1) and Jurassic (J1-J2) are the main coal forming periods in China (as shown in Figure 2). Tectonism leads to interruption or denudation in the strata deposit after the deposition of coal measure strata has been completed. As a result, some of the strata between the coal measure strata and the Cenozoic overburden are missing, and the Cenozoic overburden is directly deposited on the coal measure strata (as shown in Figure 3).Figure 2
Distribution diagram of the major coal resources in China.Figure 3
Hydrogeological profile of thin bedrock.The water flowing fractured zone generally penetrates through thin bedrock and into the Cenozoic overburden with the progression of coal mining under such geological conditions. Accordingly, the failure state and water-blocking properties of soil in the Cenozoic overburden are key factors in determining whether a hydraulic connection between the Cenozoic porous aquifers and the working face will occur. Typical hydrogeological conditions of thin bedrock are shown in Figure3.


## 2.3. Failure Process of the Overlying Soil of Thin Bedrock

The overlying soil layer of thin bedrock will deform or even fail with the deformation and caving of the bedrock as the coal seam is continuously exploited, and the process of deformation and failure of the overlying soil layer can be divided into three stages, as shown in Figure4. First, the coal seam is mined out. Second, the bedrock collapses or fractures. Third, the collapse or fracture of the thin bedrock leads to a reduction in the supporting space of the overlying soil layers, and the overlying soil layers will subside due to the self-weight load. Then, the overlying soil layers undergo deformation and failure. Consequently, the essential cause of deformation or failure of the soil is the reduction in the supporting space in its lower part.Figure 4
Failure process of the overlying soil layers of thin bedrock: (a) natural state; (b) coal seam mining out ⟹ thin bedrock collapses or fractures ⟹ supporting space decreases and soil layer subside; (c) overlying soil layers recompact on the collapsed thin bedrock.
(a)
(b)
(c)The overlying soil will deform and produce cracks under the influence of coal seam mining. The cracks may reclose or continue to broaden by scouring and finally lead to further soil destruction under the action of water flow scouring in loose porous aquifer and other conditions. The key factors affecting the development-closure state of the cracks in soil layer are particle composition, dry-wet state (which can be expressed by the saturation or water content), crack dimension (crack length and width), and soil stress state.The main external forces are the self-weight stress and phreatic aquifer hydrostatic pressure in the overlying soil of thin bedrock, and their influence mode is long-term slow action. Therefore, the influence of the dynamic change in external forces can be temporarily neglected. Then, four factors can be selected, namely, the soil particle composition, water content, crack length, and crack width, and influence analysis of these factors on the development-closure state of the cracks in soil layer can be performed through orthogonal experimental methods.


## 3. Experimental Device and Scheme

### 3.1. Experimental Device and Specimen Preparation

The crack development-closure experimental device for soil layer is shown in Figure5.Figure 5
Experimental device for crack development-closure in soil layer: (a) schematic diagram of the experimental device; (b) experimental device.
(a)
(b)The main functions of the experimental device are as follows: (1) the water tanks I and II, the water inlet pipe, and the overflow pipe keep the water level above the soil layer constant; that is, a constant hydrostatic pressure is maintained and (2) the volume of outflow water from the cracks is measured by using a measuring cylinder, and the flow volume can be calculated in terms of the volume of outflow water.The change in soil particle composition is simulated by changing the ratio of bentonite clay to fine sand (0.075 mm < particle diameter ≤ 0.25 mm), which is shown in Figure6. The higher the sand content is, the lower the content of hydrophilic minerals in the soil is, and the worse the hydrophilicity and water swelling properties of the soil are.Figure 6
Soil composition: (a) bentonite clay; (b) fine sand.
(a)
(b)The water content is realized by adding water. First, the dry weight of the soil layer is calculated in terms of the soil density (1.884 g/cm3). Then, the quality of water needed to added can be calculated according to the water content. The crack length means the length of the crack in the vertical direction, and the cracks in the soil layer are actually not straight. The cracks made in experiments are straight cracks because it is difficult to make bending cracks in specimens; therefore, the thickness of the soil layer is equal to the crack length. A crack is formed when the iron wire penetrates the soil layer after the soil layer was compacted and formed according to the design thickness (as shown in Figure 7).Figure 7
Production drawing of cracks in soil: (a) iron wires of different diameters; (b) crack fabrication process; (c) crack formation.
(a)
(b)
(c)


### 3.2. Experimental Scheme

The symbols of each factor in the experiments and their level values are shown in Table1.Table 1
Experimental factors and their level values.
Level
Factor
Particle composition
Water content
Soil layer thickness
Crack width
Symbol
Cc
ω
Cl
Cw
1
Cc10 (soil-sand ratio 1 : 0)
ω
15 (15%)
Cw1 (1.0 mm)
2
Cc11 (soil-sand ratio 1 : 1)
ω
20 (20%)
Cl10 (10.0 cm)
Cw2 (2.0 mm)
3
Cc13 (soil-sand ratio 1 : 3)
ω
25 (25%)
Cl15 (15.0 cm)
Cw3 (3.0 mm)There are four factors in the experiments, and each factor has three levels. The purpose of the experiments is to analyze the influence of four factors on the development-closure state of the cracks in soil layer. Simultaneously, the effect of the interaction between the particle composition and the other factors on the crack development-closure state is emphatically investigated. The free degree of four experimental factors (each of which has three levels) and four sets of interactions is4×3−1+4×3−1×3−1=24; therefore, the L27(313) orthogonal table can be used to design the experimental scheme, which is shown in Table 2.Table 2
Experimental schemes for the crack development-closure state of soil layer.
Experiment number
Column
1
2
3
4
5
6
7
8
9
10
11
12
13
Scheme number
Factor
Cc
Cl
Cc × Cl
Cw
Cc × Cw
Cl × Cw
ω
Cc ×Cω
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Cc10 Cl5 Cw1 ω15
2
1
1
1
1
2
2
2
2
2
2
2
2
2
Cc10 Cl5 Cw2 ω20
3
1
1
1
1
3
3
3
3
3
3
3
3
3
Cc10 Cl5 Cw3 ω25
4
1
2
2
2
1
1
1
2
2
2
3
3
3
Cc10 Cl10 Cw1 ω20
5
1
2
2
2
2
2
2
3
3
3
1
1
1
Cc10 Cl10 Cw2 ω25
6
1
2
2
2
3
3
3
1
1
1
2
2
2
Cc10 Cl10 Cw3 ω15
7
1
3
3
3
1
1
1
3
3
3
2
2
2
Cc10 Cl15 Cw1 ω25
8
1
3
3
3
2
2
2
1
1
1
3
3
3
Cc10 Cl15 Cw2 ω15
9
1
3
3
3
3
3
3
2
2
2
1
1
1
Cc10 Cl15 Cw3 ω20
10
2
1
2
3
1
2
3
1
2
3
1
2
3
Cc11 Cl5 Cw1 ω25
11
2
1
2
3
2
3
1
2
3
1
2
3
1
Cc11 Cl5 Cw2 ω15
12
2
1
2
3
3
1
2
3
1
2
3
1
2
Cc11 Cl5 Cw3 ω20
13
2
2
3
1
1
2
3
2
3
1
3
1
2
Cc11 Cl10 Cw1 ω15
14
2
2
3
1
2
3
1
3
1
2
1
2
3
Cc11 Cl10 Cw2 ω20
15
2
2
3
1
3
1
2
1
2
3
2
3
1
Cc11 Cl10 Cw3 ω25
16
2
3
1
2
1
2
3
3
1
2
2
3
1
Cc11 Cl15 Cw1 ω20
17
2
3
1
2
2
3
1
1
2
3
3
1
2
Cc11 Cl15 Cw2 ω25
18
2
3
1
2
3
1
2
2
3
1
1
2
3
Cc11 Cl15 Cw3 ω15
19
3
1
3
2
1
3
2
1
3
2
1
3
2
Cc13 Cl5 Cw1 ω20
20
3
1
3
2
2
1
3
2
1
3
2
1
3
Cc13 Cl5 Cw2 ω25
21
3
1
3
2
3
2
1
3
2
1
3
2
1
Cc13 Cl5 Cw3 ω15
22
3
2
1
3
1
3
2
2
1
3
3
2
1
Cc13 Cl10 Cw1 ω25
23
3
2
1
3
2
1
3
3
2
1
1
3
2
Cc13 Cl10 Cw2 ω15
24
3
2
1
3
3
2
1
1
3
2
2
1
3
Cc13 Cl10 Cw3 ω20
25
3
3
2
1
1
3
2
3
2
1
2
1
3
Cc13 Cl15 Cw1 ω15
26
3
3
2
1
2
1
3
1
3
2
3
2
1
Cc13 Cl15 Cw2 ω20
27
3
3
2
1
3
2
1
2
1
3
1
3
2
Cc13 Cl15 Cw3 ω25The dependent variable of the experiments is the development-closure state of the cracks in soil layer, that is, the change in crack dimension, and the water rate of flowQ can be used to indicate the change in soil crack dimension (the water rate of flow is defined as the volume of fluid flow through cracks per unit time, and the unit is m3/s). Then, the development-closure state of the cracks in soil layer can be determined according to the change trend of Q. (1) The water rate of flow Q decreases gradually to 0 m3/s, which indicates that the crack dimension gradually decreases to closure. (2) The water rate of flow Q gradually increases to ∞ m3/s, which means that the crack gradually broadens due to water flow scouring and finally leads to soil further destruction. (3) The water rate of flow Q is between 0 m3/s and ∞ m3/s, which indicates that the crack is ultimately neither reclosed nor broadened by water flow scouring.


## 3.1. Experimental Device and Specimen Preparation

The crack development-closure experimental device for soil layer is shown in Figure5.Figure 5
Experimental device for crack development-closure in soil layer: (a) schematic diagram of the experimental device; (b) experimental device.
(a)
(b)The main functions of the experimental device are as follows: (1) the water tanks I and II, the water inlet pipe, and the overflow pipe keep the water level above the soil layer constant; that is, a constant hydrostatic pressure is maintained and (2) the volume of outflow water from the cracks is measured by using a measuring cylinder, and the flow volume can be calculated in terms of the volume of outflow water.The change in soil particle composition is simulated by changing the ratio of bentonite clay to fine sand (0.075 mm < particle diameter ≤ 0.25 mm), which is shown in Figure6. The higher the sand content is, the lower the content of hydrophilic minerals in the soil is, and the worse the hydrophilicity and water swelling properties of the soil are.Figure 6
Soil composition: (a) bentonite clay; (b) fine sand.
(a)
(b)The water content is realized by adding water. First, the dry weight of the soil layer is calculated in terms of the soil density (1.884 g/cm3). Then, the quality of water needed to added can be calculated according to the water content. The crack length means the length of the crack in the vertical direction, and the cracks in the soil layer are actually not straight. The cracks made in experiments are straight cracks because it is difficult to make bending cracks in specimens; therefore, the thickness of the soil layer is equal to the crack length. A crack is formed when the iron wire penetrates the soil layer after the soil layer was compacted and formed according to the design thickness (as shown in Figure 7).Figure 7
Production drawing of cracks in soil: (a) iron wires of different diameters; (b) crack fabrication process; (c) crack formation.
(a)
(b)
(c)


## 3.2. Experimental Scheme

The symbols of each factor in the experiments and their level values are shown in Table1.Table 1
Experimental factors and their level values.
Level
Factor
Particle composition
Water content
Soil layer thickness
Crack width
Symbol
Cc
ω
Cl
Cw
1
Cc10 (soil-sand ratio 1 : 0)
ω
15 (15%)
Cw1 (1.0 mm)
2
Cc11 (soil-sand ratio 1 : 1)
ω
20 (20%)
Cl10 (10.0 cm)
Cw2 (2.0 mm)
3
Cc13 (soil-sand ratio 1 : 3)
ω
25 (25%)
Cl15 (15.0 cm)
Cw3 (3.0 mm)There are four factors in the experiments, and each factor has three levels. The purpose of the experiments is to analyze the influence of four factors on the development-closure state of the cracks in soil layer. Simultaneously, the effect of the interaction between the particle composition and the other factors on the crack development-closure state is emphatically investigated. The free degree of four experimental factors (each of which has three levels) and four sets of interactions is4×3−1+4×3−1×3−1=24; therefore, the L27(313) orthogonal table can be used to design the experimental scheme, which is shown in Table 2.Table 2
Experimental schemes for the crack development-closure state of soil layer.
Experiment number
Column
1
2
3
4
5
6
7
8
9
10
11
12
13
Scheme number
Factor
Cc
Cl
Cc × Cl
Cw
Cc × Cw
Cl × Cw
ω
Cc ×Cω
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Cc10 Cl5 Cw1 ω15
2
1
1
1
1
2
2
2
2
2
2
2
2
2
Cc10 Cl5 Cw2 ω20
3
1
1
1
1
3
3
3
3
3
3
3
3
3
Cc10 Cl5 Cw3 ω25
4
1
2
2
2
1
1
1
2
2
2
3
3
3
Cc10 Cl10 Cw1 ω20
5
1
2
2
2
2
2
2
3
3
3
1
1
1
Cc10 Cl10 Cw2 ω25
6
1
2
2
2
3
3
3
1
1
1
2
2
2
Cc10 Cl10 Cw3 ω15
7
1
3
3
3
1
1
1
3
3
3
2
2
2
Cc10 Cl15 Cw1 ω25
8
1
3
3
3
2
2
2
1
1
1
3
3
3
Cc10 Cl15 Cw2 ω15
9
1
3
3
3
3
3
3
2
2
2
1
1
1
Cc10 Cl15 Cw3 ω20
10
2
1
2
3
1
2
3
1
2
3
1
2
3
Cc11 Cl5 Cw1 ω25
11
2
1
2
3
2
3
1
2
3
1
2
3
1
Cc11 Cl5 Cw2 ω15
12
2
1
2
3
3
1
2
3
1
2
3
1
2
Cc11 Cl5 Cw3 ω20
13
2
2
3
1
1
2
3
2
3
1
3
1
2
Cc11 Cl10 Cw1 ω15
14
2
2
3
1
2
3
1
3
1
2
1
2
3
Cc11 Cl10 Cw2 ω20
15
2
2
3
1
3
1
2
1
2
3
2
3
1
Cc11 Cl10 Cw3 ω25
16
2
3
1
2
1
2
3
3
1
2
2
3
1
Cc11 Cl15 Cw1 ω20
17
2
3
1
2
2
3
1
1
2
3
3
1
2
Cc11 Cl15 Cw2 ω25
18
2
3
1
2
3
1
2
2
3
1
1
2
3
Cc11 Cl15 Cw3 ω15
19
3
1
3
2
1
3
2
1
3
2
1
3
2
Cc13 Cl5 Cw1 ω20
20
3
1
3
2
2
1
3
2
1
3
2
1
3
Cc13 Cl5 Cw2 ω25
21
3
1
3
2
3
2
1
3
2
1
3
2
1
Cc13 Cl5 Cw3 ω15
22
3
2
1
3
1
3
2
2
1
3
3
2
1
Cc13 Cl10 Cw1 ω25
23
3
2
1
3
2
1
3
3
2
1
1
3
2
Cc13 Cl10 Cw2 ω15
24
3
2
1
3
3
2
1
1
3
2
2
1
3
Cc13 Cl10 Cw3 ω20
25
3
3
2
1
1
3
2
3
2
1
2
1
3
Cc13 Cl15 Cw1 ω15
26
3
3
2
1
2
1
3
1
3
2
3
2
1
Cc13 Cl15 Cw2 ω20
27
3
3
2
1
3
2
1
2
1
3
1
3
2
Cc13 Cl15 Cw3 ω25The dependent variable of the experiments is the development-closure state of the cracks in soil layer, that is, the change in crack dimension, and the water rate of flowQ can be used to indicate the change in soil crack dimension (the water rate of flow is defined as the volume of fluid flow through cracks per unit time, and the unit is m3/s). Then, the development-closure state of the cracks in soil layer can be determined according to the change trend of Q. (1) The water rate of flow Q decreases gradually to 0 m3/s, which indicates that the crack dimension gradually decreases to closure. (2) The water rate of flow Q gradually increases to ∞ m3/s, which means that the crack gradually broadens due to water flow scouring and finally leads to soil further destruction. (3) The water rate of flow Q is between 0 m3/s and ∞ m3/s, which indicates that the crack is ultimately neither reclosed nor broadened by water flow scouring.


## 4. Experimental Results and Discussion

### 4.1. Direct Analysis of the Experimental Results

#### 4.1.1. Experimental Results

The water rate of flow results at 6 h for each experiment is shown in Table3.Table 3
Experimental results of crack development-closure in soil layer.
Experiment number
Column
1
2
3
4
5
6
7
8
9
10
11
12
13
Experimental results:Qi (10−6 m3/s)
Factor
Cc
Cl
Cc × Cl
Cw
Cc × Cw
Cl × Cw
ω
Cc ×ω
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.000
2
1
1
1
1
2
2
2
2
2
2
2
2
2
1.517
3
1
1
1
1
3
3
3
3
3
3
3
3
3
9.758
4
1
2
2
2
1
1
1
2
2
2
3
3
3
0.000
5
1
2
2
2
2
2
2
3
3
3
1
1
1
1.442
6
1
2
2
2
3
3
3
1
1
1
2
2
2
3.667
7
1
3
3
3
1
1
1
3
3
3
2
2
2
0.000
8
1
3
3
3
2
2
2
1
1
1
3
3
3
0.650
9
1
3
3
3
3
3
3
2
2
2
1
1
1
5.375
10
2
1
2
3
1
2
3
1
2
3
1
2
3
0.000
11
2
1
2
3
2
3
1
2
3
1
2
3
1
2.433
12
2
1
2
3
3
1
2
3
1
2
3
1
2
11.183
13
2
2
3
1
1
2
3
2
3
1
3
1
2
0.000
14
2
2
3
1
2
3
1
3
1
2
1
2
3
2.050
15
2
2
3
1
3
1
2
1
2
3
2
3
1
10.325
16
2
3
1
2
1
2
3
3
1
2
2
3
1
0.000
17
2
3
1
2
2
3
1
1
2
3
3
1
2
1.800
18
2
3
1
2
3
1
2
2
3
1
1
2
3
6.033
19
3
1
3
2
1
3
2
1
3
2
1
3
2
0.483
20
3
1
3
2
2
1
3
2
1
3
2
1
3
6.508
21
3
1
3
2
3
2
1
3
2
1
3
2
1
∞
22
3
2
1
3
1
3
2
2
1
3
3
2
1
0.783
23
3
2
1
3
2
1
3
3
2
1
1
3
2
4.583
24
3
2
1
3
3
2
1
1
3
2
2
1
3
∞
25
3
3
2
1
1
3
2
3
2
1
2
1
3
0.008
26
3
3
2
1
2
1
3
1
3
2
3
2
1
0.975
27
3
3
2
1
3
2
1
2
1
3
1
3
2
12.167Table3 shows that the water rate of flow for 6 of the 27 experiments (experiments 1, 4, 7, 10, 13, and 16) gradually decreases to 0 m3/s, which indicates that the cracks in the soil finally reclose under the experimental conditions of these 6 experiments. There are 19 experiments (experiments 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 19, 20, 22, 23, 25, 26, and 27) whose water rate of flow is between 0 m3/s and ∞ m3/s, which indicates that the cracks are ultimately neither reclosed nor broadened by water flow scouring under these 19 experimental conditions. The water rate of flow for 2 of the 27 experiments (experiments 21 and 24) gradually increases to ∞ m3/s, which indicates that the cracks gradually broaden due to water flow scouring and finally lead to soil destruction under the experimental conditions of these 2 experiments.


#### 4.1.2. Analysis of Experiments That the Water Rate of Flow Decreases Gradually to 0 m3/s

One comparison of the initial cracks and reclosed cracks in the experiments in which the water rate of flow decreases gradually to 0 m3/s is shown in Figure 8.Figure 8
One comparison of the initial cracks and reclosed cracks: (a) initial cracks of experiment No. 10; (b) cracks reclosed of experiment No. 10.
(a)
(b)The water rate of flow curves changes with time in the experiments in which the water rate of flow gradually decreases to 0 m3/s is shown in Figure 9.Figure 9
Change curve of the crack rate of flow that decreases to 0 m3/s.As shown in Figure9, the water rate of flow of the 6 groups gradually decreases to 0 m3/s (that is, the cracks reclosed in these experiments) under the same experimental conditions of Cc10∩Cw1 or Cc11∩Cw1, which indicates that when the ratio of soil to sand is greater than or equal to 1 : 1 and the crack width is less than or equal to 1.0 mm, the cracks are reclosed regardless of the thickness and water content of the soil. At the same time, the period with a sharp decrease in the water rate of flow in the 6 experiments is less than 20 minutes, which shows that the duration of the main change in the soil swelling increment Δs (or water swelling velocity rate vst) and soil compaction amount Δc (or compression velocity rate vct) is less than 20 minutes, namely, the sum of the swelling increment Δs and compaction amount Δc is larger than the sum of the broadening amount Δb and original crack width Cwo, which results in the cracks reclosed.


#### 4.1.3. Analysis of Experiments That the Water Rate of Flow between 0 m3/s and ∞ m3/s

A comparison of the initial and stable cracks in the experiments in which the water rate of flow is between 0 m3/s and ∞ m3/s is shown in Figure 10.Figure 10
One comparison of the initial cracks and stable cracks: (a) initial cracks of experiment No. 12; (b) cracks steady of experiment No. 12.
(a)
(b)The water rate of flow curves changes with time in the experiments in which the water rate of flow is between 0 m3/s and ∞ m3/s is shown in Figure 11.Figure 11
Change curve of the crack rate of flow between 0 m3/s and ∞ m3/s.As shown in Figure11, the water rate of flow of experiment 27 is the largest and is 12.167 (10−6 m3/s), while that of experiment 25 is the smallest and is 0.008 (10−6 m3/s). Intuitively, it cannot be determined which factor is the main factor and which factor is the secondary factor leading to the difference in the rate of flow results. Thus, further analysis of the experimental results is needed to determine the order of influence of each experimental factor on the water rate of flow.


#### 4.1.4. Analysis of Experiments That the Soil Layer Destroyed

One comparison of the initial cracks and destroyed soil in the experiments in which the water rate of flow increases gradually to∞ m3/s is shown in Figure 12.Figure 12
One comparison of the initial cracks and destroyed soil layer: (a) initial cracks of experiment No. 21; (b) cracks broaden lead to soil destruction of experiment No. 21.
(a)
(b)The water rate of flow curves changes with time in the experiments in which the water rate of flow increases to∞ m3/s is shown in Figure 13.Figure 13
Change curve of the crack rate of flow that increases to∞ m3/s.As shown in Figure13, the condition for cracks to be broadened by scouring causing further soil destruction is Cc13∩Cw3, and experiment 21 shows that the time from broadening of the crack by scouring to soil destruction is 25 minutes, while that in experiment 24, it is 310 minutes, which indicates that increasing the soil layer thickness or increasing the water content or both together can effectively increase the antidestructive capacity of the soil layer. Further analysis is needed to determine which conditions change to improve the antidestructive capacity of soil layer.


#### 4.1.5. Analysis of Experimental Results

The experimental results show that the crack will close when the sand content in soil is less than 50% and the crack width is less than or equal to 1.0 mm and the soil layer is prone to further failure when the sand content in soil is more than 50% and the crack width is greater than or equal to 3.0 mm. The experimental results preliminarily reveal that the greater the sand content and the wider the crack width and the smaller the thickness of the soil layer, the worse the stability of the soil layer, because the orthogonal test method is adopted instead of the comprehensive test method, and visual analysis and variance analysis are needed to get more accurate conclusions.


### 4.2. Visual Analysis of the Experimental Results

There are 27 groups of experimental results in Table3, and no two experiments among the 27 groups have identical experimental conditions; thus, it is not feasible to compare any of the 27 groups of experimental results directly. However, if these 27 sets of experimental results are combined, comparability of the orthogonal test results will be achieved.Taking Cc as an example and level 1 (Cc10) of experimental factor Cc appeared in experiment Nos. 1–9 in Table 3, the average of the rate of flow of these nine experiments is(1)QCc10¯=19Q1+Q2+Q3+Q4+Q5+Q6+Q7+Q8+Q9=190+1.517+9.758+0+1.442+3.667+0+0.650+5.375=2.49010−6m3/s,level 2 (Cc11) of experimental factor Cc appeared in experiment Nos. 10–18 in Table 3, the average of the rate of flow of these nine experiments is(2)QCc11¯=19Q10+Q11+Q12+Q13+Q14+Q15+Q16+Q17+Q18=190+2.433+11.183+0+2.050+10.325+0+1.800+6.033=3.75810−6m3/s,and level 3 (Cc13) of experimental factor Cc appeared in experiment Nos. 19–27 in Table 3, the average of the rate of flow of these nine experiments is(3)QCc13¯=19Q19+Q20+Q21+Q22+Q23+Q24+Q25+Q26+Q27=190.483+6.508+100+0.783+4.583+100+0.008+0.975+12.167=25.05610−6m3/s.The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results are∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).Q
Cc
10
¯
<
Q
Cc
11
¯
<
Q
Cc
13
¯, namely, the rate of flow is the largest when the particle composition is Cc13, and the rate of flow is the smallest when the particle composition is Cc10. This shows that the soil layer is prone to further failure when the particle composition is Cc13, and the soil layer is prone to maintain stability when the particle composition is Cc10.The above calculations can also be performed in the orthogonal table, as shown in Table4. Ij represents the sum of the experimental rate of flow results corresponding to level 1 of column j, and Ij¯ is the average of Ij; IIj represents the sum of the experimental rate of flow results corresponding to level 2 of column j, and IIj¯ is the average of IIj; IIIj represents the sum of the experimental rate of flow results corresponding to level 3 of column j, and IIIj¯ is the average of IIIj.Table 4
Visual analysis of the experimental results of crack development-closure in soil layer.
Experiment number
Column
1
2
5
10
Experimental results:Qi (10−6 m3/s)
Factor
Cc
Cl
Cw
ω
1
1
1
1
1
0.000
2
1
1
2
2
1.517
⋮
⋮
⋮
⋮
⋮
⋮
⋮
26
3
3
2
2
0.975
27
3
3
3
3
12.167
Ij
22.409
131.882
1.274
117.374
IIj
33.824
122.850
21.958
121.583
IIIj
225.507
27.008
258.508
42.783
I
j
¯
=
I
j
/
9
2.490
14.654
0.142
13.042
II
j
¯
=
II
j
/
9
3.758
13.650
2.440
13.509
III
j
¯
=
III
j
/
9
25.056
3.001
28.723
4.754
I
j
¯
−
II
j
¯
−1.268
1.004
−2.298
−0.467
I
j
¯
−
III
j
¯
−22.566
11.653
−28.581
8.288
II
j
¯
−
III
j
¯
−21.298
10.649
−26.283
8.755
The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results tend to∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).The experimental factor Cc is in the first column; therefore,I1¯ is QCc10¯, II1¯ is QCc11¯, and III1¯ is QCc13¯. Similarly, Cl, Cw, and ω are in the second, fifth, and tenth columns, respectively. Hence, I2¯ is QCl5¯, II2¯ is QCl10¯, and III2¯ is QCl15¯, while I5¯ is QCw1¯, II5¯ is QCw2¯, and III5¯ is QCw3¯; in addition, I10¯ is Qω15¯, II10¯ is Qω20¯, and III10¯ is Qω25¯.TheI¯, II¯, and III¯ values of each experimental factor in Table 4 are plotted using the longitudinal coordinate system, as shown in Figure 14.Figure 14
Relationship between the experimental factors and the rate of flow.
(a)
(b)
(c)
(d)It is easy to intuitively observe that if one experimental factor has a great influence on the experimental result, then this experimental factor is the main factor. Namely, the difference between the average rate of flow corresponding to different levels of the experimental factors is large, which is reflected in Figure14, and the points corresponding to the three levels of the experimental factors differ greatly in the longitudinal coordinates. In contrast, if one experimental factor has little influence on the experimental result, then this experimental factor is the secondary factor. That is, the difference between the average rate of flow corresponding to different levels of the experimental factors is small, which is reflect in Figure 14, and the points corresponding to the three levels of the experimental factors differ little in the longitudinal coordinates.The absolute average values of the difference betweenIj¯, IIj¯, and IIIj¯ in Table 4 are(4)I1¯−II1¯+I1¯−III1¯+II1¯−III1¯3=15.04410−6m3/s,I2¯−II2¯+I2¯−III2¯+II2¯−III2¯3=7.76910−6m3/s,I5¯−II5¯+I5¯−III5¯+II5¯−III5¯3=19.05410−6m3/s,I10¯−II10¯+I10¯−III10¯+II10¯−III10¯3=5.83710−6m3/s.The maximum absolute average value of the difference between the three levels of each experimental factor is factor Cw, followed by factors Cc and Cl and factorω. In addition, the influences of Cw and Cc on the experimental results are more notable than those of Cl and ω. The result indicates that the order of influence of each factor on the stability of soil layer is the crack width, particle composition, soil layer thickness, and water content and also indicates that the influence of crack width and particle composition on the failure of soil layer is greater than that of the soil layer thickness and water content.As seen from Figure14, the order of influence of the particle composition on the rate of flow is Cc13>Cc11>Cc10, which shows that the higher the sand content in the soil is, the worse the stability of the soil layer is. The order of influence of the soil layer thickness on the rate of flow is Cl5>Cl10>Cl15; that is, the smaller the soil layer thickness is, the more likely it is that the soil layer will fail. The order of influence of the crack width on the rate of flow is Cw3>Cw2>Cw1, which indicates that the larger the crack width is, the worse the stability of the soil layer is. The order of influence of the water content on the rate of flow is ω20>ω15>ω25, which indicates that the stability of the soil layer decreases first and then increases with increasing water content and that soil layer is prone to further failure when the water content is 20%.In addition, Table4 also shows that QCc13 (III1) is significantly larger than QCc10 (I1) and QCc11 (II1), and QCw3 (III5) is significantly larger than QCw1 (I5) and QCw2 (II5), while QCl15 (III2) is significantly smaller than QCl5 (I2) and QCl10 (II2). These observations indicate that when the sand content in the soil is higher than 50% and the crack width is larger than 2.0 mm, the soil layer is prone to further failure. When the soil layer thickness is 15.0 cm, the stability of the soil layer is better than those of the 10.0 cm or 5.0 cm; that is, increasing the thickness of the soil layer can increase the ability of soil layer to resist further failure.


### 4.3. Variance Analysis of the Experimental Results

#### 4.3.1. Sum of Squares of Deviations of Experimental Factors

Taking Cc as an example, the calculation method of the sum of squares of deviations of experimental factor is illustrated. Level 1 (Cc10) of experimental factor Cc appeared in experiment Nos. 1–9 in Table 3, and the sum of the rate of flow of the nine groups of experimental results is(5)QCc10=Q1+Q2+Q3+Q4+Q5+Q6+Q7+Q8+Q9,level 2 (Cc11) of experimental factor Cc appeared in experiment Nos. 10–18 in Table 3, and the sum of the rate of flow of the nine groups of experimental results is(6)QCc11=Q10+Q11+Q12+Q13+Q14+Q15+Q16+Q17+Q18,level 3 (Cc13) of experimental factor Cc appeared in experiment Nos. 19–27 in Table 3, and the sum of the rate of flow of the nine groups of experimental results is(7)QCc13=Q19+Q20+Q21+Q22+Q23+Q24+Q25+Q26+Q27.The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results are∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).Hence, the sum of squares of deviations of experimental factor Cc is(8)SCc=9QCc109−Q¯2+9QCc119−Q¯2+9QCc139−Q¯2,where Q¯ is the average rate of flow of the 27 groups of experimental results and Q¯=1/27∑i=127Qi.Expansion of formula (8) results in(9)SCc=QCc102+QCc112+QCc1329+27Q¯2−2Q¯QCc10+QCc11+QCc13=QCc102+QCc112+QCc1329+Q¯⋅∑i=127Qi−2Q¯⋅∑i=127Qi=QCc102+QCc112+QCc1329−127∑i=127Qi2.Let∑i=127Qi be factor G and G2/27 be factor CT; then, formula (9) can be simplified as follows:(10)SCc=QCc102+QCc112+QCc1329−CT.The data in Table3 are substituted into formula (10) to obtain SCc=2893.388.In the same way, the sum of squares of deviations of experimental factors Cl, Cw, andω can be calculated as(11)SCl=QCl52+QCl102+QCl1529−CT=750.586,SCw=QCw12+QCw22+QCw329−CT=4539.002,Sω=Qω152+Qω202+Qω2529−CT=436.702.The sum of squares of deviations of the above experimental factors can also be calculated on the orthogonal table, which is shown in Table5.Table 5
Calculating table of the sum of squares of deviations of experimental factors.
Experiment number
Column
1
2
5
10
13
Experimental results:Qi (10−6 m3/s)
Factor
Cc
Cl
Cw
ω
1
1
1
1
1
1
0.000
2
1
1
2
2
2
1.517
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
26
3
3
2
2
2
0.975
27
3
3
3
3
3
12.167
Ij
22.409
131.882
1.274
117.374
121.333
IIj
33.824
122.850
21.958
121.583
35.400
IIIj
225.507
27.008
258.508
42.783
125.007
I
j
2
502.163
17392.862
1.623
13776.656
14721.697
II
j
2
1144.063
15092.123
482.154
14782.426
1253.160
III
j
3
50853.407
729.432
66826.386
1830.385
15626.750
S
j
=
I
j
2
+
II
j
2
+
III
j
2
/
9
−
CT
2893.388
750.586
4539.002
436.702
571.385
The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results tend to∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).As shown in Table5, Ij represents the sum of the experimental results corresponding to level 1 of column j, and IIj represents the sum of the experimental results corresponding to level 2 of column j, while IIIj represents the sum of the experimental results corresponding to level 3 of column j. Therefore, I1 is QCc10, II1 is QCc11, and III1 is QCc13. Sj represents the sum of squares of deviations of the experimental results in column j; hence, S1 is SCc, S2 is SCl, S5 is SCw, and S10 is Sω.


#### 4.3.2. Sum of Squares of Deviations of the Interaction between the Experimental Factors

The interaction between two experimental factors accounts for two columns in the orthogonal table; therefore, the sum of squares of deviations of the interaction between two factors is the sum of the sum of squares of deviations of the two columns. Therefore, the sum of squares of deviations ofSCc×Cl is(12)SCc×Cl=S3+S4=I32+II32+III329−CT+I42+II42+III429−CT=641.506+545.085=1186.591.Similarly,SCc×Cw, SCc×ω, and SCl×Cw can be obtained:(13)SCc×Cw=S6+S7=I62+II62+III629−CT+I72+II72+III729−CT=2484.838+2585.032=5069.870,SCc×ω=S11+S12=I112+II112+III1129−CT+I122+II122+III1229−CT=636.161+484.380=1120.541,SCl×Cw=S8+S9=I82+II82+III829−CT+I92+II92+III929−CT=588.957+540.045=1129.002.The sum of squares of deviations of the interaction between experimental factors can also be calculated on the orthogonal table, which is shown in Table6.Table 6
Calculating table of the sum of squares of deviations of interaction between experimental factors.
Experiment number
Column
3
4
6
7
8
9
11
12
Experimental results:Qi (10−6 m3/s)
Factor
Cc × Cl
Cc × Cw
Cl × Cw
Cc ×ω
1
1
1
1
1
1
1
1
1
0.000
2
1
1
2
2
2
2
2
2
1.517
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
26
2
1
1
3
1
3
3
2
0.975
27
2
1
2
1
2
1
1
3
12.167
Ij
124.474
36.800
39.607
218.450
117.900
37.008
32.133
126.316
IIj
31.875
119.933
215.776
32.424
34.816
123.608
124.458
115.025
IIIj
125.391
125.007
26.357
30.866
129.024
121.124
125.149
40.399
I
j
2
15493.777
1354.240
1568.714
47720.403
13900.410
1369.592
1032.530
15955.732
II
j
2
1016.016
14383.924
46559.282
1051.316
1212.154
15278.938
15489.794
13230.751
III
j
2
15722.903
15626.750
694.691
952.710
16647.193
14671.023
15662.272
1632.079
S
j
=
I
j
2
+
II
j
2
+
III
j
2
/
9
−
CT
641.506
545.085
2484.838
2585.032
588.957
540.045
636.161
484.380
The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results tend to∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).


#### 4.3.3. Sum of Squares of Deviations of the Experimental Error

The sum of squares of deviations of the experimental error can be calculated by the sum of squares of deviations of the blank columns without experimental factors arranged in the orthogonal table. In this experiment, the error can be estimated by the sum of squares of deviations in column 13 of Table3 because column 13 does not arrange the experimental factor, and the sum of squares of deviations of column 13 does not include the difference between the levels of experimental factors but only reflects the magnitude of experimental errors.In addition, if the sum of squares of deviations of the other columns is close to the sum of squares of deviations of the blank column (column 13); then, the sum of squares of deviations of this column can be combined with the sum of squares of deviations of the blank column as an error estimate, which can make the error estimate more accurate.According to Tables5 and 6, the sum of squares of deviations of columns 4, 8, and 9 in this experiment is close to the sum of squares of deviations of the blank column (column 13). Therefore, S4, S8, and S9 can also be classified as errors as follows:(14)Se=S13+S4+S8+S9.The data in Tables5 and 6 are substituted into formula (14) to obtain Se=2245.472.


#### 4.3.4. Saliency Detection of Experimental Factors and Their Interactions

According to formula (8) for the calculation the sum of squares of deviations, it can be seen that the sum of squares of deviations may be large if the amount of data is large. That is, the sum of squares of deviations is related not only to the change in data itself but also to the amount of data. Therefore, the influence of the amount of data on the sum of squares of deviations is eliminated by introducing the free degree in orthogonal experiment, namely, comparing the average sum of squares of deviations SA/fA with Se/fe, where fA is the free degree of the sum of squares of deviations of experimental factor A and fe is the free degree of the sum of squares of deviations of experimental error.For orthogonal experiments, there are(15)ftotal=ntotal−1,fA=nA−1,fA×B=fA×fB,where ntotal is the total number of experiments and nA is the level amount of experimental factor A.Therefore, for this experiment,ftotal=27−1=26, fCc=3−1=2, fCl=3−1=2, fCw=3−1=2, fω=3−1=2, fCc×Cl=2×2=4, fCc×Cw=2×2=4, fCc×ω=2×2=4, and fCl×Cw=2×2=4.According to formula (14),(16)fe=ftotal−f13−f4−f8−f9=26−2−2−2−2=18.The ratio of the average sum of squares of deviations of the experimental factors (Sfactor/ffactor) to the average sum of squares of deviations of the errors (Se/fe) is called the F ratio, that is,(17)F=SA/fASe/fe.TheF ratio of the experimental factors and the interaction between the experimental factors is calculated in terms of formula (17) as follows(18)FCc=SCc/fCcSe/fe=2893.388/22245.472/18=11.597,FCl=SCl/fClSe/fe=750.586/22245.472/18=3.008,FCw=SCw/fCwSe/fe=4539.002/22245.472/18=18.193,Fω=Sω/fωSe/fe=436.702/22245.472/18=1.750,FCc×Cl=SCc×Cl/fCc×ClSe/fe=1186.591/42245.472/18=2.378,FCc×Cw=SCc×Cw/fCc×CwSe/fe=5069.870/42245.472/18=10.160,FCc×ω=SCc×ω/fCc×ωSe/fe=1120.541/42245.472/18=2.246,FCl×Cw=SCl×Cw/fCl×CwSe/fe=1129.002/42245.472/18=2.263.Look up theF ratio table, and it shows the following: F0.012,18=6.01, F0.052,18=3.55, F0.12,18=2.62, F0.014,18=4.58, F0.054,18=2.93, and F0.14,18=2.29. Thus, the following conclusions can be drawn:①
FCc>F0.012,18, which indicates that the change in the experimental factor of soil particle composition Cc has a highly salient influence on the experimental results, which is recorded as ∗∗∗.②
F0.052,18>FCl>F0.12,18, which indicates that the change in the experimental factor of soil layer thickness Cl has some influence on the experimental results, which is recorded as ∗.③
FCw>F0.012,18, which indicates that the change in the experimental factor of crack width Cw has a highly salient influence on the experimental results, which is recorded as ∗∗∗.④
Fω<F0.12,18, which indicates that the change in the experimental factor of soil water content ω has a nonsalient influence on the experimental results, which is recorded as ⊗.⑤
F0.054,18>FCc×Cl>F0.14,18, which indicates that the interaction between soil particle composition Cc and soil layer thickness Cl has some influence on the experimental results, which is recorded as ∗.⑥
FCc×Cw>F0.014,18, which indicates that the interaction between soil particle composition Cc and crack width Cw has a highly salient influence on the experimental results, which is recorded as ∗∗∗.⑦
FCc×ω<F0.14,18, which indicates that the interaction between soil particle composition Cc and soil water content ω has a nonsalient influence on the experimental results, which is recorded as ⊗.⑧
FCl×Cw<F0.14,18, which indicates that the interaction between soil layer thickness Cl and crack width Cw has a nonsalient influence on the experimental results, which is recorded as ⊗.The saliency detection of the above experimental factors and their interactions can be summarized as an analysis of variance table, as shown in Table7.Table 7
Saliency detection of experimental factors and their interactions.
Factor
Sum of squares of deviations
Free degree
Average sum of squares of deviations
F Ratio
Saliency grade
Cc
S
Cc = 2893.388
f
Cc = 2
S
Cc/fCc = 1446.694
11.597
∗∗∗Highly salient influence
Cl
S
Cl = 750.586
f
Cl = 2
S
Cl/fCl = 375.293
3.008
∗Some influence
Cw
S
Cw = 4539.002
f
Cw = 2
S
Cw/fCw = 2269.501
18.193
∗∗∗Highly salient influence
ω
S
ω = 436.702
f
ω = 2
S
ω/fω = 218.351
1.750
⊗Nonsalient influence
Cc × Cl
S
Cc×Cl = 1186.591
f
Cc×Cl = 4
S
Cc×Cl/fCc×Cl = 296.648
2.378
∗Some influence
Cc × Cw
S
Cc×Cw = 5069.870
f
Cc×Cw = 4
S
Cc×Cw/fCc×Cw = 1267.468
10.160
∗∗∗Highly salient influence
Cc ×ω
S
Cc×ω = 1120.541
f
Cc×ω = 4
S
Cc×ω/fCc×ω = 280.135
2.246
⊗Nonsalient influence
Cl × Cw
S
Cl×Cw = 1129.002
f
Cl×Cw = 4
S
Cl×Cw/fCl×Cw = 282.251
2.263
⊗Nonsalient influence
e
S
e = S13 + S4 + S8 + S9 = 2245.472
f
e = 18
S
e/fe = 124.748


## 4.1. Direct Analysis of the Experimental Results

### 4.1.1. Experimental Results

The water rate of flow results at 6 h for each experiment is shown in Table3.Table 3
Experimental results of crack development-closure in soil layer.
Experiment number
Column
1
2
3
4
5
6
7
8
9
10
11
12
13
Experimental results:Qi (10−6 m3/s)
Factor
Cc
Cl
Cc × Cl
Cw
Cc × Cw
Cl × Cw
ω
Cc ×ω
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.000
2
1
1
1
1
2
2
2
2
2
2
2
2
2
1.517
3
1
1
1
1
3
3
3
3
3
3
3
3
3
9.758
4
1
2
2
2
1
1
1
2
2
2
3
3
3
0.000
5
1
2
2
2
2
2
2
3
3
3
1
1
1
1.442
6
1
2
2
2
3
3
3
1
1
1
2
2
2
3.667
7
1
3
3
3
1
1
1
3
3
3
2
2
2
0.000
8
1
3
3
3
2
2
2
1
1
1
3
3
3
0.650
9
1
3
3
3
3
3
3
2
2
2
1
1
1
5.375
10
2
1
2
3
1
2
3
1
2
3
1
2
3
0.000
11
2
1
2
3
2
3
1
2
3
1
2
3
1
2.433
12
2
1
2
3
3
1
2
3
1
2
3
1
2
11.183
13
2
2
3
1
1
2
3
2
3
1
3
1
2
0.000
14
2
2
3
1
2
3
1
3
1
2
1
2
3
2.050
15
2
2
3
1
3
1
2
1
2
3
2
3
1
10.325
16
2
3
1
2
1
2
3
3
1
2
2
3
1
0.000
17
2
3
1
2
2
3
1
1
2
3
3
1
2
1.800
18
2
3
1
2
3
1
2
2
3
1
1
2
3
6.033
19
3
1
3
2
1
3
2
1
3
2
1
3
2
0.483
20
3
1
3
2
2
1
3
2
1
3
2
1
3
6.508
21
3
1
3
2
3
2
1
3
2
1
3
2
1
∞
22
3
2
1
3
1
3
2
2
1
3
3
2
1
0.783
23
3
2
1
3
2
1
3
3
2
1
1
3
2
4.583
24
3
2
1
3
3
2
1
1
3
2
2
1
3
∞
25
3
3
2
1
1
3
2
3
2
1
2
1
3
0.008
26
3
3
2
1
2
1
3
1
3
2
3
2
1
0.975
27
3
3
2
1
3
2
1
2
1
3
1
3
2
12.167Table3 shows that the water rate of flow for 6 of the 27 experiments (experiments 1, 4, 7, 10, 13, and 16) gradually decreases to 0 m3/s, which indicates that the cracks in the soil finally reclose under the experimental conditions of these 6 experiments. There are 19 experiments (experiments 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 19, 20, 22, 23, 25, 26, and 27) whose water rate of flow is between 0 m3/s and ∞ m3/s, which indicates that the cracks are ultimately neither reclosed nor broadened by water flow scouring under these 19 experimental conditions. The water rate of flow for 2 of the 27 experiments (experiments 21 and 24) gradually increases to ∞ m3/s, which indicates that the cracks gradually broaden due to water flow scouring and finally lead to soil destruction under the experimental conditions of these 2 experiments.


### 4.1.2. Analysis of Experiments That the Water Rate of Flow Decreases Gradually to 0 m3/s

One comparison of the initial cracks and reclosed cracks in the experiments in which the water rate of flow decreases gradually to 0 m3/s is shown in Figure 8.Figure 8
One comparison of the initial cracks and reclosed cracks: (a) initial cracks of experiment No. 10; (b) cracks reclosed of experiment No. 10.
(a)
(b)The water rate of flow curves changes with time in the experiments in which the water rate of flow gradually decreases to 0 m3/s is shown in Figure 9.Figure 9
Change curve of the crack rate of flow that decreases to 0 m3/s.As shown in Figure9, the water rate of flow of the 6 groups gradually decreases to 0 m3/s (that is, the cracks reclosed in these experiments) under the same experimental conditions of Cc10∩Cw1 or Cc11∩Cw1, which indicates that when the ratio of soil to sand is greater than or equal to 1 : 1 and the crack width is less than or equal to 1.0 mm, the cracks are reclosed regardless of the thickness and water content of the soil. At the same time, the period with a sharp decrease in the water rate of flow in the 6 experiments is less than 20 minutes, which shows that the duration of the main change in the soil swelling increment Δs (or water swelling velocity rate vst) and soil compaction amount Δc (or compression velocity rate vct) is less than 20 minutes, namely, the sum of the swelling increment Δs and compaction amount Δc is larger than the sum of the broadening amount Δb and original crack width Cwo, which results in the cracks reclosed.


### 4.1.3. Analysis of Experiments That the Water Rate of Flow between 0 m3/s and ∞ m3/s

A comparison of the initial and stable cracks in the experiments in which the water rate of flow is between 0 m3/s and ∞ m3/s is shown in Figure 10.Figure 10
One comparison of the initial cracks and stable cracks: (a) initial cracks of experiment No. 12; (b) cracks steady of experiment No. 12.
(a)
(b)The water rate of flow curves changes with time in the experiments in which the water rate of flow is between 0 m3/s and ∞ m3/s is shown in Figure 11.Figure 11
Change curve of the crack rate of flow between 0 m3/s and ∞ m3/s.As shown in Figure11, the water rate of flow of experiment 27 is the largest and is 12.167 (10−6 m3/s), while that of experiment 25 is the smallest and is 0.008 (10−6 m3/s). Intuitively, it cannot be determined which factor is the main factor and which factor is the secondary factor leading to the difference in the rate of flow results. Thus, further analysis of the experimental results is needed to determine the order of influence of each experimental factor on the water rate of flow.


### 4.1.4. Analysis of Experiments That the Soil Layer Destroyed

One comparison of the initial cracks and destroyed soil in the experiments in which the water rate of flow increases gradually to∞ m3/s is shown in Figure 12.Figure 12
One comparison of the initial cracks and destroyed soil layer: (a) initial cracks of experiment No. 21; (b) cracks broaden lead to soil destruction of experiment No. 21.
(a)
(b)The water rate of flow curves changes with time in the experiments in which the water rate of flow increases to∞ m3/s is shown in Figure 13.Figure 13
Change curve of the crack rate of flow that increases to∞ m3/s.As shown in Figure13, the condition for cracks to be broadened by scouring causing further soil destruction is Cc13∩Cw3, and experiment 21 shows that the time from broadening of the crack by scouring to soil destruction is 25 minutes, while that in experiment 24, it is 310 minutes, which indicates that increasing the soil layer thickness or increasing the water content or both together can effectively increase the antidestructive capacity of the soil layer. Further analysis is needed to determine which conditions change to improve the antidestructive capacity of soil layer.


### 4.1.5. Analysis of Experimental Results

The experimental results show that the crack will close when the sand content in soil is less than 50% and the crack width is less than or equal to 1.0 mm and the soil layer is prone to further failure when the sand content in soil is more than 50% and the crack width is greater than or equal to 3.0 mm. The experimental results preliminarily reveal that the greater the sand content and the wider the crack width and the smaller the thickness of the soil layer, the worse the stability of the soil layer, because the orthogonal test method is adopted instead of the comprehensive test method, and visual analysis and variance analysis are needed to get more accurate conclusions.


## 4.1.1. Experimental Results

The water rate of flow results at 6 h for each experiment is shown in Table3.Table 3
Experimental results of crack development-closure in soil layer.
Experiment number
Column
1
2
3
4
5
6
7
8
9
10
11
12
13
Experimental results:Qi (10−6 m3/s)
Factor
Cc
Cl
Cc × Cl
Cw
Cc × Cw
Cl × Cw
ω
Cc ×ω
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.000
2
1
1
1
1
2
2
2
2
2
2
2
2
2
1.517
3
1
1
1
1
3
3
3
3
3
3
3
3
3
9.758
4
1
2
2
2
1
1
1
2
2
2
3
3
3
0.000
5
1
2
2
2
2
2
2
3
3
3
1
1
1
1.442
6
1
2
2
2
3
3
3
1
1
1
2
2
2
3.667
7
1
3
3
3
1
1
1
3
3
3
2
2
2
0.000
8
1
3
3
3
2
2
2
1
1
1
3
3
3
0.650
9
1
3
3
3
3
3
3
2
2
2
1
1
1
5.375
10
2
1
2
3
1
2
3
1
2
3
1
2
3
0.000
11
2
1
2
3
2
3
1
2
3
1
2
3
1
2.433
12
2
1
2
3
3
1
2
3
1
2
3
1
2
11.183
13
2
2
3
1
1
2
3
2
3
1
3
1
2
0.000
14
2
2
3
1
2
3
1
3
1
2
1
2
3
2.050
15
2
2
3
1
3
1
2
1
2
3
2
3
1
10.325
16
2
3
1
2
1
2
3
3
1
2
2
3
1
0.000
17
2
3
1
2
2
3
1
1
2
3
3
1
2
1.800
18
2
3
1
2
3
1
2
2
3
1
1
2
3
6.033
19
3
1
3
2
1
3
2
1
3
2
1
3
2
0.483
20
3
1
3
2
2
1
3
2
1
3
2
1
3
6.508
21
3
1
3
2
3
2
1
3
2
1
3
2
1
∞
22
3
2
1
3
1
3
2
2
1
3
3
2
1
0.783
23
3
2
1
3
2
1
3
3
2
1
1
3
2
4.583
24
3
2
1
3
3
2
1
1
3
2
2
1
3
∞
25
3
3
2
1
1
3
2
3
2
1
2
1
3
0.008
26
3
3
2
1
2
1
3
1
3
2
3
2
1
0.975
27
3
3
2
1
3
2
1
2
1
3
1
3
2
12.167Table3 shows that the water rate of flow for 6 of the 27 experiments (experiments 1, 4, 7, 10, 13, and 16) gradually decreases to 0 m3/s, which indicates that the cracks in the soil finally reclose under the experimental conditions of these 6 experiments. There are 19 experiments (experiments 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 19, 20, 22, 23, 25, 26, and 27) whose water rate of flow is between 0 m3/s and ∞ m3/s, which indicates that the cracks are ultimately neither reclosed nor broadened by water flow scouring under these 19 experimental conditions. The water rate of flow for 2 of the 27 experiments (experiments 21 and 24) gradually increases to ∞ m3/s, which indicates that the cracks gradually broaden due to water flow scouring and finally lead to soil destruction under the experimental conditions of these 2 experiments.


## 4.1.2. Analysis of Experiments That the Water Rate of Flow Decreases Gradually to 0 m3/s

One comparison of the initial cracks and reclosed cracks in the experiments in which the water rate of flow decreases gradually to 0 m3/s is shown in Figure 8.Figure 8
One comparison of the initial cracks and reclosed cracks: (a) initial cracks of experiment No. 10; (b) cracks reclosed of experiment No. 10.
(a)
(b)The water rate of flow curves changes with time in the experiments in which the water rate of flow gradually decreases to 0 m3/s is shown in Figure 9.Figure 9
Change curve of the crack rate of flow that decreases to 0 m3/s.As shown in Figure9, the water rate of flow of the 6 groups gradually decreases to 0 m3/s (that is, the cracks reclosed in these experiments) under the same experimental conditions of Cc10∩Cw1 or Cc11∩Cw1, which indicates that when the ratio of soil to sand is greater than or equal to 1 : 1 and the crack width is less than or equal to 1.0 mm, the cracks are reclosed regardless of the thickness and water content of the soil. At the same time, the period with a sharp decrease in the water rate of flow in the 6 experiments is less than 20 minutes, which shows that the duration of the main change in the soil swelling increment Δs (or water swelling velocity rate vst) and soil compaction amount Δc (or compression velocity rate vct) is less than 20 minutes, namely, the sum of the swelling increment Δs and compaction amount Δc is larger than the sum of the broadening amount Δb and original crack width Cwo, which results in the cracks reclosed.


## 4.1.3. Analysis of Experiments That the Water Rate of Flow between 0 m3/s and ∞ m3/s

A comparison of the initial and stable cracks in the experiments in which the water rate of flow is between 0 m3/s and ∞ m3/s is shown in Figure 10.Figure 10
One comparison of the initial cracks and stable cracks: (a) initial cracks of experiment No. 12; (b) cracks steady of experiment No. 12.
(a)
(b)The water rate of flow curves changes with time in the experiments in which the water rate of flow is between 0 m3/s and ∞ m3/s is shown in Figure 11.Figure 11
Change curve of the crack rate of flow between 0 m3/s and ∞ m3/s.As shown in Figure11, the water rate of flow of experiment 27 is the largest and is 12.167 (10−6 m3/s), while that of experiment 25 is the smallest and is 0.008 (10−6 m3/s). Intuitively, it cannot be determined which factor is the main factor and which factor is the secondary factor leading to the difference in the rate of flow results. Thus, further analysis of the experimental results is needed to determine the order of influence of each experimental factor on the water rate of flow.


## 4.1.4. Analysis of Experiments That the Soil Layer Destroyed

One comparison of the initial cracks and destroyed soil in the experiments in which the water rate of flow increases gradually to∞ m3/s is shown in Figure 12.Figure 12
One comparison of the initial cracks and destroyed soil layer: (a) initial cracks of experiment No. 21; (b) cracks broaden lead to soil destruction of experiment No. 21.
(a)
(b)The water rate of flow curves changes with time in the experiments in which the water rate of flow increases to∞ m3/s is shown in Figure 13.Figure 13
Change curve of the crack rate of flow that increases to∞ m3/s.As shown in Figure13, the condition for cracks to be broadened by scouring causing further soil destruction is Cc13∩Cw3, and experiment 21 shows that the time from broadening of the crack by scouring to soil destruction is 25 minutes, while that in experiment 24, it is 310 minutes, which indicates that increasing the soil layer thickness or increasing the water content or both together can effectively increase the antidestructive capacity of the soil layer. Further analysis is needed to determine which conditions change to improve the antidestructive capacity of soil layer.


## 4.1.5. Analysis of Experimental Results

The experimental results show that the crack will close when the sand content in soil is less than 50% and the crack width is less than or equal to 1.0 mm and the soil layer is prone to further failure when the sand content in soil is more than 50% and the crack width is greater than or equal to 3.0 mm. The experimental results preliminarily reveal that the greater the sand content and the wider the crack width and the smaller the thickness of the soil layer, the worse the stability of the soil layer, because the orthogonal test method is adopted instead of the comprehensive test method, and visual analysis and variance analysis are needed to get more accurate conclusions.


## 4.2. Visual Analysis of the Experimental Results

There are 27 groups of experimental results in Table3, and no two experiments among the 27 groups have identical experimental conditions; thus, it is not feasible to compare any of the 27 groups of experimental results directly. However, if these 27 sets of experimental results are combined, comparability of the orthogonal test results will be achieved.Taking Cc as an example and level 1 (Cc10) of experimental factor Cc appeared in experiment Nos. 1–9 in Table 3, the average of the rate of flow of these nine experiments is(1)QCc10¯=19Q1+Q2+Q3+Q4+Q5+Q6+Q7+Q8+Q9=190+1.517+9.758+0+1.442+3.667+0+0.650+5.375=2.49010−6m3/s,level 2 (Cc11) of experimental factor Cc appeared in experiment Nos. 10–18 in Table 3, the average of the rate of flow of these nine experiments is(2)QCc11¯=19Q10+Q11+Q12+Q13+Q14+Q15+Q16+Q17+Q18=190+2.433+11.183+0+2.050+10.325+0+1.800+6.033=3.75810−6m3/s,and level 3 (Cc13) of experimental factor Cc appeared in experiment Nos. 19–27 in Table 3, the average of the rate of flow of these nine experiments is(3)QCc13¯=19Q19+Q20+Q21+Q22+Q23+Q24+Q25+Q26+Q27=190.483+6.508+100+0.783+4.583+100+0.008+0.975+12.167=25.05610−6m3/s.The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results are∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).Q
Cc
10
¯
<
Q
Cc
11
¯
<
Q
Cc
13
¯, namely, the rate of flow is the largest when the particle composition is Cc13, and the rate of flow is the smallest when the particle composition is Cc10. This shows that the soil layer is prone to further failure when the particle composition is Cc13, and the soil layer is prone to maintain stability when the particle composition is Cc10.The above calculations can also be performed in the orthogonal table, as shown in Table4. Ij represents the sum of the experimental rate of flow results corresponding to level 1 of column j, and Ij¯ is the average of Ij; IIj represents the sum of the experimental rate of flow results corresponding to level 2 of column j, and IIj¯ is the average of IIj; IIIj represents the sum of the experimental rate of flow results corresponding to level 3 of column j, and IIIj¯ is the average of IIIj.Table 4
Visual analysis of the experimental results of crack development-closure in soil layer.
Experiment number
Column
1
2
5
10
Experimental results:Qi (10−6 m3/s)
Factor
Cc
Cl
Cw
ω
1
1
1
1
1
0.000
2
1
1
2
2
1.517
⋮
⋮
⋮
⋮
⋮
⋮
⋮
26
3
3
2
2
0.975
27
3
3
3
3
12.167
Ij
22.409
131.882
1.274
117.374
IIj
33.824
122.850
21.958
121.583
IIIj
225.507
27.008
258.508
42.783
I
j
¯
=
I
j
/
9
2.490
14.654
0.142
13.042
II
j
¯
=
II
j
/
9
3.758
13.650
2.440
13.509
III
j
¯
=
III
j
/
9
25.056
3.001
28.723
4.754
I
j
¯
−
II
j
¯
−1.268
1.004
−2.298
−0.467
I
j
¯
−
III
j
¯
−22.566
11.653
−28.581
8.288
II
j
¯
−
III
j
¯
−21.298
10.649
−26.283
8.755
The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results tend to∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).The experimental factor Cc is in the first column; therefore,I1¯ is QCc10¯, II1¯ is QCc11¯, and III1¯ is QCc13¯. Similarly, Cl, Cw, and ω are in the second, fifth, and tenth columns, respectively. Hence, I2¯ is QCl5¯, II2¯ is QCl10¯, and III2¯ is QCl15¯, while I5¯ is QCw1¯, II5¯ is QCw2¯, and III5¯ is QCw3¯; in addition, I10¯ is Qω15¯, II10¯ is Qω20¯, and III10¯ is Qω25¯.TheI¯, II¯, and III¯ values of each experimental factor in Table 4 are plotted using the longitudinal coordinate system, as shown in Figure 14.Figure 14
Relationship between the experimental factors and the rate of flow.
(a)
(b)
(c)
(d)It is easy to intuitively observe that if one experimental factor has a great influence on the experimental result, then this experimental factor is the main factor. Namely, the difference between the average rate of flow corresponding to different levels of the experimental factors is large, which is reflected in Figure14, and the points corresponding to the three levels of the experimental factors differ greatly in the longitudinal coordinates. In contrast, if one experimental factor has little influence on the experimental result, then this experimental factor is the secondary factor. That is, the difference between the average rate of flow corresponding to different levels of the experimental factors is small, which is reflect in Figure 14, and the points corresponding to the three levels of the experimental factors differ little in the longitudinal coordinates.The absolute average values of the difference betweenIj¯, IIj¯, and IIIj¯ in Table 4 are(4)I1¯−II1¯+I1¯−III1¯+II1¯−III1¯3=15.04410−6m3/s,I2¯−II2¯+I2¯−III2¯+II2¯−III2¯3=7.76910−6m3/s,I5¯−II5¯+I5¯−III5¯+II5¯−III5¯3=19.05410−6m3/s,I10¯−II10¯+I10¯−III10¯+II10¯−III10¯3=5.83710−6m3/s.The maximum absolute average value of the difference between the three levels of each experimental factor is factor Cw, followed by factors Cc and Cl and factorω. In addition, the influences of Cw and Cc on the experimental results are more notable than those of Cl and ω. The result indicates that the order of influence of each factor on the stability of soil layer is the crack width, particle composition, soil layer thickness, and water content and also indicates that the influence of crack width and particle composition on the failure of soil layer is greater than that of the soil layer thickness and water content.As seen from Figure14, the order of influence of the particle composition on the rate of flow is Cc13>Cc11>Cc10, which shows that the higher the sand content in the soil is, the worse the stability of the soil layer is. The order of influence of the soil layer thickness on the rate of flow is Cl5>Cl10>Cl15; that is, the smaller the soil layer thickness is, the more likely it is that the soil layer will fail. The order of influence of the crack width on the rate of flow is Cw3>Cw2>Cw1, which indicates that the larger the crack width is, the worse the stability of the soil layer is. The order of influence of the water content on the rate of flow is ω20>ω15>ω25, which indicates that the stability of the soil layer decreases first and then increases with increasing water content and that soil layer is prone to further failure when the water content is 20%.In addition, Table4 also shows that QCc13 (III1) is significantly larger than QCc10 (I1) and QCc11 (II1), and QCw3 (III5) is significantly larger than QCw1 (I5) and QCw2 (II5), while QCl15 (III2) is significantly smaller than QCl5 (I2) and QCl10 (II2). These observations indicate that when the sand content in the soil is higher than 50% and the crack width is larger than 2.0 mm, the soil layer is prone to further failure. When the soil layer thickness is 15.0 cm, the stability of the soil layer is better than those of the 10.0 cm or 5.0 cm; that is, increasing the thickness of the soil layer can increase the ability of soil layer to resist further failure.


## 4.3. Variance Analysis of the Experimental Results

### 4.3.1. Sum of Squares of Deviations of Experimental Factors

Taking Cc as an example, the calculation method of the sum of squares of deviations of experimental factor is illustrated. Level 1 (Cc10) of experimental factor Cc appeared in experiment Nos. 1–9 in Table 3, and the sum of the rate of flow of the nine groups of experimental results is(5)QCc10=Q1+Q2+Q3+Q4+Q5+Q6+Q7+Q8+Q9,level 2 (Cc11) of experimental factor Cc appeared in experiment Nos. 10–18 in Table 3, and the sum of the rate of flow of the nine groups of experimental results is(6)QCc11=Q10+Q11+Q12+Q13+Q14+Q15+Q16+Q17+Q18,level 3 (Cc13) of experimental factor Cc appeared in experiment Nos. 19–27 in Table 3, and the sum of the rate of flow of the nine groups of experimental results is(7)QCc13=Q19+Q20+Q21+Q22+Q23+Q24+Q25+Q26+Q27.The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results are∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).Hence, the sum of squares of deviations of experimental factor Cc is(8)SCc=9QCc109−Q¯2+9QCc119−Q¯2+9QCc139−Q¯2,where Q¯ is the average rate of flow of the 27 groups of experimental results and Q¯=1/27∑i=127Qi.Expansion of formula (8) results in(9)SCc=QCc102+QCc112+QCc1329+27Q¯2−2Q¯QCc10+QCc11+QCc13=QCc102+QCc112+QCc1329+Q¯⋅∑i=127Qi−2Q¯⋅∑i=127Qi=QCc102+QCc112+QCc1329−127∑i=127Qi2.Let∑i=127Qi be factor G and G2/27 be factor CT; then, formula (9) can be simplified as follows:(10)SCc=QCc102+QCc112+QCc1329−CT.The data in Table3 are substituted into formula (10) to obtain SCc=2893.388.In the same way, the sum of squares of deviations of experimental factors Cl, Cw, andω can be calculated as(11)SCl=QCl52+QCl102+QCl1529−CT=750.586,SCw=QCw12+QCw22+QCw329−CT=4539.002,Sω=Qω152+Qω202+Qω2529−CT=436.702.The sum of squares of deviations of the above experimental factors can also be calculated on the orthogonal table, which is shown in Table5.Table 5
Calculating table of the sum of squares of deviations of experimental factors.
Experiment number
Column
1
2
5
10
13
Experimental results:Qi (10−6 m3/s)
Factor
Cc
Cl
Cw
ω
1
1
1
1
1
1
0.000
2
1
1
2
2
2
1.517
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
26
3
3
2
2
2
0.975
27
3
3
3
3
3
12.167
Ij
22.409
131.882
1.274
117.374
121.333
IIj
33.824
122.850
21.958
121.583
35.400
IIIj
225.507
27.008
258.508
42.783
125.007
I
j
2
502.163
17392.862
1.623
13776.656
14721.697
II
j
2
1144.063
15092.123
482.154
14782.426
1253.160
III
j
3
50853.407
729.432
66826.386
1830.385
15626.750
S
j
=
I
j
2
+
II
j
2
+
III
j
2
/
9
−
CT
2893.388
750.586
4539.002
436.702
571.385
The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results tend to∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).As shown in Table5, Ij represents the sum of the experimental results corresponding to level 1 of column j, and IIj represents the sum of the experimental results corresponding to level 2 of column j, while IIIj represents the sum of the experimental results corresponding to level 3 of column j. Therefore, I1 is QCc10, II1 is QCc11, and III1 is QCc13. Sj represents the sum of squares of deviations of the experimental results in column j; hence, S1 is SCc, S2 is SCl, S5 is SCw, and S10 is Sω.


### 4.3.2. Sum of Squares of Deviations of the Interaction between the Experimental Factors

The interaction between two experimental factors accounts for two columns in the orthogonal table; therefore, the sum of squares of deviations of the interaction between two factors is the sum of the sum of squares of deviations of the two columns. Therefore, the sum of squares of deviations ofSCc×Cl is(12)SCc×Cl=S3+S4=I32+II32+III329−CT+I42+II42+III429−CT=641.506+545.085=1186.591.Similarly,SCc×Cw, SCc×ω, and SCl×Cw can be obtained:(13)SCc×Cw=S6+S7=I62+II62+III629−CT+I72+II72+III729−CT=2484.838+2585.032=5069.870,SCc×ω=S11+S12=I112+II112+III1129−CT+I122+II122+III1229−CT=636.161+484.380=1120.541,SCl×Cw=S8+S9=I82+II82+III829−CT+I92+II92+III929−CT=588.957+540.045=1129.002.The sum of squares of deviations of the interaction between experimental factors can also be calculated on the orthogonal table, which is shown in Table6.Table 6
Calculating table of the sum of squares of deviations of interaction between experimental factors.
Experiment number
Column
3
4
6
7
8
9
11
12
Experimental results:Qi (10−6 m3/s)
Factor
Cc × Cl
Cc × Cw
Cl × Cw
Cc ×ω
1
1
1
1
1
1
1
1
1
0.000
2
1
1
2
2
2
2
2
2
1.517
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
26
2
1
1
3
1
3
3
2
0.975
27
2
1
2
1
2
1
1
3
12.167
Ij
124.474
36.800
39.607
218.450
117.900
37.008
32.133
126.316
IIj
31.875
119.933
215.776
32.424
34.816
123.608
124.458
115.025
IIIj
125.391
125.007
26.357
30.866
129.024
121.124
125.149
40.399
I
j
2
15493.777
1354.240
1568.714
47720.403
13900.410
1369.592
1032.530
15955.732
II
j
2
1016.016
14383.924
46559.282
1051.316
1212.154
15278.938
15489.794
13230.751
III
j
2
15722.903
15626.750
694.691
952.710
16647.193
14671.023
15662.272
1632.079
S
j
=
I
j
2
+
II
j
2
+
III
j
2
/
9
−
CT
641.506
545.085
2484.838
2585.032
588.957
540.045
636.161
484.380
The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results tend to∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).


### 4.3.3. Sum of Squares of Deviations of the Experimental Error

The sum of squares of deviations of the experimental error can be calculated by the sum of squares of deviations of the blank columns without experimental factors arranged in the orthogonal table. In this experiment, the error can be estimated by the sum of squares of deviations in column 13 of Table3 because column 13 does not arrange the experimental factor, and the sum of squares of deviations of column 13 does not include the difference between the levels of experimental factors but only reflects the magnitude of experimental errors.In addition, if the sum of squares of deviations of the other columns is close to the sum of squares of deviations of the blank column (column 13); then, the sum of squares of deviations of this column can be combined with the sum of squares of deviations of the blank column as an error estimate, which can make the error estimate more accurate.According to Tables5 and 6, the sum of squares of deviations of columns 4, 8, and 9 in this experiment is close to the sum of squares of deviations of the blank column (column 13). Therefore, S4, S8, and S9 can also be classified as errors as follows:(14)Se=S13+S4+S8+S9.The data in Tables5 and 6 are substituted into formula (14) to obtain Se=2245.472.


### 4.3.4. Saliency Detection of Experimental Factors and Their Interactions

According to formula (8) for the calculation the sum of squares of deviations, it can be seen that the sum of squares of deviations may be large if the amount of data is large. That is, the sum of squares of deviations is related not only to the change in data itself but also to the amount of data. Therefore, the influence of the amount of data on the sum of squares of deviations is eliminated by introducing the free degree in orthogonal experiment, namely, comparing the average sum of squares of deviations SA/fA with Se/fe, where fA is the free degree of the sum of squares of deviations of experimental factor A and fe is the free degree of the sum of squares of deviations of experimental error.For orthogonal experiments, there are(15)ftotal=ntotal−1,fA=nA−1,fA×B=fA×fB,where ntotal is the total number of experiments and nA is the level amount of experimental factor A.Therefore, for this experiment,ftotal=27−1=26, fCc=3−1=2, fCl=3−1=2, fCw=3−1=2, fω=3−1=2, fCc×Cl=2×2=4, fCc×Cw=2×2=4, fCc×ω=2×2=4, and fCl×Cw=2×2=4.According to formula (14),(16)fe=ftotal−f13−f4−f8−f9=26−2−2−2−2=18.The ratio of the average sum of squares of deviations of the experimental factors (Sfactor/ffactor) to the average sum of squares of deviations of the errors (Se/fe) is called the F ratio, that is,(17)F=SA/fASe/fe.TheF ratio of the experimental factors and the interaction between the experimental factors is calculated in terms of formula (17) as follows(18)FCc=SCc/fCcSe/fe=2893.388/22245.472/18=11.597,FCl=SCl/fClSe/fe=750.586/22245.472/18=3.008,FCw=SCw/fCwSe/fe=4539.002/22245.472/18=18.193,Fω=Sω/fωSe/fe=436.702/22245.472/18=1.750,FCc×Cl=SCc×Cl/fCc×ClSe/fe=1186.591/42245.472/18=2.378,FCc×Cw=SCc×Cw/fCc×CwSe/fe=5069.870/42245.472/18=10.160,FCc×ω=SCc×ω/fCc×ωSe/fe=1120.541/42245.472/18=2.246,FCl×Cw=SCl×Cw/fCl×CwSe/fe=1129.002/42245.472/18=2.263.Look up theF ratio table, and it shows the following: F0.012,18=6.01, F0.052,18=3.55, F0.12,18=2.62, F0.014,18=4.58, F0.054,18=2.93, and F0.14,18=2.29. Thus, the following conclusions can be drawn:①
FCc>F0.012,18, which indicates that the change in the experimental factor of soil particle composition Cc has a highly salient influence on the experimental results, which is recorded as ∗∗∗.②
F0.052,18>FCl>F0.12,18, which indicates that the change in the experimental factor of soil layer thickness Cl has some influence on the experimental results, which is recorded as ∗.③
FCw>F0.012,18, which indicates that the change in the experimental factor of crack width Cw has a highly salient influence on the experimental results, which is recorded as ∗∗∗.④
Fω<F0.12,18, which indicates that the change in the experimental factor of soil water content ω has a nonsalient influence on the experimental results, which is recorded as ⊗.⑤
F0.054,18>FCc×Cl>F0.14,18, which indicates that the interaction between soil particle composition Cc and soil layer thickness Cl has some influence on the experimental results, which is recorded as ∗.⑥
FCc×Cw>F0.014,18, which indicates that the interaction between soil particle composition Cc and crack width Cw has a highly salient influence on the experimental results, which is recorded as ∗∗∗.⑦
FCc×ω<F0.14,18, which indicates that the interaction between soil particle composition Cc and soil water content ω has a nonsalient influence on the experimental results, which is recorded as ⊗.⑧
FCl×Cw<F0.14,18, which indicates that the interaction between soil layer thickness Cl and crack width Cw has a nonsalient influence on the experimental results, which is recorded as ⊗.The saliency detection of the above experimental factors and their interactions can be summarized as an analysis of variance table, as shown in Table7.Table 7
Saliency detection of experimental factors and their interactions.
Factor
Sum of squares of deviations
Free degree
Average sum of squares of deviations
F Ratio
Saliency grade
Cc
S
Cc = 2893.388
f
Cc = 2
S
Cc/fCc = 1446.694
11.597
∗∗∗Highly salient influence
Cl
S
Cl = 750.586
f
Cl = 2
S
Cl/fCl = 375.293
3.008
∗Some influence
Cw
S
Cw = 4539.002
f
Cw = 2
S
Cw/fCw = 2269.501
18.193
∗∗∗Highly salient influence
ω
S
ω = 436.702
f
ω = 2
S
ω/fω = 218.351
1.750
⊗Nonsalient influence
Cc × Cl
S
Cc×Cl = 1186.591
f
Cc×Cl = 4
S
Cc×Cl/fCc×Cl = 296.648
2.378
∗Some influence
Cc × Cw
S
Cc×Cw = 5069.870
f
Cc×Cw = 4
S
Cc×Cw/fCc×Cw = 1267.468
10.160
∗∗∗Highly salient influence
Cc ×ω
S
Cc×ω = 1120.541
f
Cc×ω = 4
S
Cc×ω/fCc×ω = 280.135
2.246
⊗Nonsalient influence
Cl × Cw
S
Cl×Cw = 1129.002
f
Cl×Cw = 4
S
Cl×Cw/fCl×Cw = 282.251
2.263
⊗Nonsalient influence
e
S
e = S13 + S4 + S8 + S9 = 2245.472
f
e = 18
S
e/fe = 124.748


## 4.3.1. Sum of Squares of Deviations of Experimental Factors

Taking Cc as an example, the calculation method of the sum of squares of deviations of experimental factor is illustrated. Level 1 (Cc10) of experimental factor Cc appeared in experiment Nos. 1–9 in Table 3, and the sum of the rate of flow of the nine groups of experimental results is(5)QCc10=Q1+Q2+Q3+Q4+Q5+Q6+Q7+Q8+Q9,level 2 (Cc11) of experimental factor Cc appeared in experiment Nos. 10–18 in Table 3, and the sum of the rate of flow of the nine groups of experimental results is(6)QCc11=Q10+Q11+Q12+Q13+Q14+Q15+Q16+Q17+Q18,level 3 (Cc13) of experimental factor Cc appeared in experiment Nos. 19–27 in Table 3, and the sum of the rate of flow of the nine groups of experimental results is(7)QCc13=Q19+Q20+Q21+Q22+Q23+Q24+Q25+Q26+Q27.The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results are∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).Hence, the sum of squares of deviations of experimental factor Cc is(8)SCc=9QCc109−Q¯2+9QCc119−Q¯2+9QCc139−Q¯2,where Q¯ is the average rate of flow of the 27 groups of experimental results and Q¯=1/27∑i=127Qi.Expansion of formula (8) results in(9)SCc=QCc102+QCc112+QCc1329+27Q¯2−2Q¯QCc10+QCc11+QCc13=QCc102+QCc112+QCc1329+Q¯⋅∑i=127Qi−2Q¯⋅∑i=127Qi=QCc102+QCc112+QCc1329−127∑i=127Qi2.Let∑i=127Qi be factor G and G2/27 be factor CT; then, formula (9) can be simplified as follows:(10)SCc=QCc102+QCc112+QCc1329−CT.The data in Table3 are substituted into formula (10) to obtain SCc=2893.388.In the same way, the sum of squares of deviations of experimental factors Cl, Cw, andω can be calculated as(11)SCl=QCl52+QCl102+QCl1529−CT=750.586,SCw=QCw12+QCw22+QCw329−CT=4539.002,Sω=Qω152+Qω202+Qω2529−CT=436.702.The sum of squares of deviations of the above experimental factors can also be calculated on the orthogonal table, which is shown in Table5.Table 5
Calculating table of the sum of squares of deviations of experimental factors.
Experiment number
Column
1
2
5
10
13
Experimental results:Qi (10−6 m3/s)
Factor
Cc
Cl
Cw
ω
1
1
1
1
1
1
0.000
2
1
1
2
2
2
1.517
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
26
3
3
2
2
2
0.975
27
3
3
3
3
3
12.167
Ij
22.409
131.882
1.274
117.374
121.333
IIj
33.824
122.850
21.958
121.583
35.400
IIIj
225.507
27.008
258.508
42.783
125.007
I
j
2
502.163
17392.862
1.623
13776.656
14721.697
II
j
2
1144.063
15092.123
482.154
14782.426
1253.160
III
j
3
50853.407
729.432
66826.386
1830.385
15626.750
S
j
=
I
j
2
+
II
j
2
+
III
j
2
/
9
−
CT
2893.388
750.586
4539.002
436.702
571.385
The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results tend to∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).As shown in Table5, Ij represents the sum of the experimental results corresponding to level 1 of column j, and IIj represents the sum of the experimental results corresponding to level 2 of column j, while IIIj represents the sum of the experimental results corresponding to level 3 of column j. Therefore, I1 is QCc10, II1 is QCc11, and III1 is QCc13. Sj represents the sum of squares of deviations of the experimental results in column j; hence, S1 is SCc, S2 is SCl, S5 is SCw, and S10 is Sω.


## 4.3.2. Sum of Squares of Deviations of the Interaction between the Experimental Factors

The interaction between two experimental factors accounts for two columns in the orthogonal table; therefore, the sum of squares of deviations of the interaction between two factors is the sum of the sum of squares of deviations of the two columns. Therefore, the sum of squares of deviations ofSCc×Cl is(12)SCc×Cl=S3+S4=I32+II32+III329−CT+I42+II42+III429−CT=641.506+545.085=1186.591.Similarly,SCc×Cw, SCc×ω, and SCl×Cw can be obtained:(13)SCc×Cw=S6+S7=I62+II62+III629−CT+I72+II72+III729−CT=2484.838+2585.032=5069.870,SCc×ω=S11+S12=I112+II112+III1129−CT+I122+II122+III1229−CT=636.161+484.380=1120.541,SCl×Cw=S8+S9=I82+II82+III829−CT+I92+II92+III929−CT=588.957+540.045=1129.002.The sum of squares of deviations of the interaction between experimental factors can also be calculated on the orthogonal table, which is shown in Table6.Table 6
Calculating table of the sum of squares of deviations of interaction between experimental factors.
Experiment number
Column
3
4
6
7
8
9
11
12
Experimental results:Qi (10−6 m3/s)
Factor
Cc × Cl
Cc × Cw
Cl × Cw
Cc ×ω
1
1
1
1
1
1
1
1
1
0.000
2
1
1
2
2
2
2
2
2
1.517
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
26
2
1
1
3
1
3
3
2
0.975
27
2
1
2
1
2
1
1
3
12.167
Ij
124.474
36.800
39.607
218.450
117.900
37.008
32.133
126.316
IIj
31.875
119.933
215.776
32.424
34.816
123.608
124.458
115.025
IIIj
125.391
125.007
26.357
30.866
129.024
121.124
125.149
40.399
I
j
2
15493.777
1354.240
1568.714
47720.403
13900.410
1369.592
1032.530
15955.732
II
j
2
1016.016
14383.924
46559.282
1051.316
1212.154
15278.938
15489.794
13230.751
III
j
2
15722.903
15626.750
694.691
952.710
16647.193
14671.023
15662.272
1632.079
S
j
=
I
j
2
+
II
j
2
+
III
j
2
/
9
−
CT
641.506
545.085
2484.838
2585.032
588.957
540.045
636.161
484.380
The soil layer in experiment No. 21 and No. 24 is destroyed, and their experimental results tend to∞ m3/s. Because the value ∞ cannot participate in the calculation, the rate of flow result in experiment No. 21 and No. 24 is calculated to be a larger value of 100 (10−6 m3/s).


## 4.3.3. Sum of Squares of Deviations of the Experimental Error

The sum of squares of deviations of the experimental error can be calculated by the sum of squares of deviations of the blank columns without experimental factors arranged in the orthogonal table. In this experiment, the error can be estimated by the sum of squares of deviations in column 13 of Table3 because column 13 does not arrange the experimental factor, and the sum of squares of deviations of column 13 does not include the difference between the levels of experimental factors but only reflects the magnitude of experimental errors.In addition, if the sum of squares of deviations of the other columns is close to the sum of squares of deviations of the blank column (column 13); then, the sum of squares of deviations of this column can be combined with the sum of squares of deviations of the blank column as an error estimate, which can make the error estimate more accurate.According to Tables5 and 6, the sum of squares of deviations of columns 4, 8, and 9 in this experiment is close to the sum of squares of deviations of the blank column (column 13). Therefore, S4, S8, and S9 can also be classified as errors as follows:(14)Se=S13+S4+S8+S9.The data in Tables5 and 6 are substituted into formula (14) to obtain Se=2245.472.


## 4.3.4. Saliency Detection of Experimental Factors and Their Interactions

According to formula (8) for the calculation the sum of squares of deviations, it can be seen that the sum of squares of deviations may be large if the amount of data is large. That is, the sum of squares of deviations is related not only to the change in data itself but also to the amount of data. Therefore, the influence of the amount of data on the sum of squares of deviations is eliminated by introducing the free degree in orthogonal experiment, namely, comparing the average sum of squares of deviations SA/fA with Se/fe, where fA is the free degree of the sum of squares of deviations of experimental factor A and fe is the free degree of the sum of squares of deviations of experimental error.For orthogonal experiments, there are(15)ftotal=ntotal−1,fA=nA−1,fA×B=fA×fB,where ntotal is the total number of experiments and nA is the level amount of experimental factor A.Therefore, for this experiment,ftotal=27−1=26, fCc=3−1=2, fCl=3−1=2, fCw=3−1=2, fω=3−1=2, fCc×Cl=2×2=4, fCc×Cw=2×2=4, fCc×ω=2×2=4, and fCl×Cw=2×2=4.According to formula (14),(16)fe=ftotal−f13−f4−f8−f9=26−2−2−2−2=18.The ratio of the average sum of squares of deviations of the experimental factors (Sfactor/ffactor) to the average sum of squares of deviations of the errors (Se/fe) is called the F ratio, that is,(17)F=SA/fASe/fe.TheF ratio of the experimental factors and the interaction between the experimental factors is calculated in terms of formula (17) as follows(18)FCc=SCc/fCcSe/fe=2893.388/22245.472/18=11.597,FCl=SCl/fClSe/fe=750.586/22245.472/18=3.008,FCw=SCw/fCwSe/fe=4539.002/22245.472/18=18.193,Fω=Sω/fωSe/fe=436.702/22245.472/18=1.750,FCc×Cl=SCc×Cl/fCc×ClSe/fe=1186.591/42245.472/18=2.378,FCc×Cw=SCc×Cw/fCc×CwSe/fe=5069.870/42245.472/18=10.160,FCc×ω=SCc×ω/fCc×ωSe/fe=1120.541/42245.472/18=2.246,FCl×Cw=SCl×Cw/fCl×CwSe/fe=1129.002/42245.472/18=2.263.Look up theF ratio table, and it shows the following: F0.012,18=6.01, F0.052,18=3.55, F0.12,18=2.62, F0.014,18=4.58, F0.054,18=2.93, and F0.14,18=2.29. Thus, the following conclusions can be drawn:①
FCc>F0.012,18, which indicates that the change in the experimental factor of soil particle composition Cc has a highly salient influence on the experimental results, which is recorded as ∗∗∗.②
F0.052,18>FCl>F0.12,18, which indicates that the change in the experimental factor of soil layer thickness Cl has some influence on the experimental results, which is recorded as ∗.③
FCw>F0.012,18, which indicates that the change in the experimental factor of crack width Cw has a highly salient influence on the experimental results, which is recorded as ∗∗∗.④
Fω<F0.12,18, which indicates that the change in the experimental factor of soil water content ω has a nonsalient influence on the experimental results, which is recorded as ⊗.⑤
F0.054,18>FCc×Cl>F0.14,18, which indicates that the interaction between soil particle composition Cc and soil layer thickness Cl has some influence on the experimental results, which is recorded as ∗.⑥
FCc×Cw>F0.014,18, which indicates that the interaction between soil particle composition Cc and crack width Cw has a highly salient influence on the experimental results, which is recorded as ∗∗∗.⑦
FCc×ω<F0.14,18, which indicates that the interaction between soil particle composition Cc and soil water content ω has a nonsalient influence on the experimental results, which is recorded as ⊗.⑧
FCl×Cw<F0.14,18, which indicates that the interaction between soil layer thickness Cl and crack width Cw has a nonsalient influence on the experimental results, which is recorded as ⊗.The saliency detection of the above experimental factors and their interactions can be summarized as an analysis of variance table, as shown in Table7.Table 7
Saliency detection of experimental factors and their interactions.
Factor
Sum of squares of deviations
Free degree
Average sum of squares of deviations
F Ratio
Saliency grade
Cc
S
Cc = 2893.388
f
Cc = 2
S
Cc/fCc = 1446.694
11.597
∗∗∗Highly salient influence
Cl
S
Cl = 750.586
f
Cl = 2
S
Cl/fCl = 375.293
3.008
∗Some influence
Cw
S
Cw = 4539.002
f
Cw = 2
S
Cw/fCw = 2269.501
18.193
∗∗∗Highly salient influence
ω
S
ω = 436.702
f
ω = 2
S
ω/fω = 218.351
1.750
⊗Nonsalient influence
Cc × Cl
S
Cc×Cl = 1186.591
f
Cc×Cl = 4
S
Cc×Cl/fCc×Cl = 296.648
2.378
∗Some influence
Cc × Cw
S
Cc×Cw = 5069.870
f
Cc×Cw = 4
S
Cc×Cw/fCc×Cw = 1267.468
10.160
∗∗∗Highly salient influence
Cc ×ω
S
Cc×ω = 1120.541
f
Cc×ω = 4
S
Cc×ω/fCc×ω = 280.135
2.246
⊗Nonsalient influence
Cl × Cw
S
Cl×Cw = 1129.002
f
Cl×Cw = 4
S
Cl×Cw/fCl×Cw = 282.251
2.263
⊗Nonsalient influence
e
S
e = S13 + S4 + S8 + S9 = 2245.472
f
e = 18
S
e/fe = 124.748


## 5. Conclusions

In this work, based on the crack development-closure experiments, the following conclusions are obtained.Firstly, soil particle composition and crack width have a highly salient influence on the stability of soil layer, and soil layer thickness has some influence on its stability, while water content has a nonsalient influence on the stability of soil layer. As the crack width and sand content increase and the soil layer thickness decreases, the stability of the soil layer decreases.Secondly, the crack will reclose when the sand content in soil is less than 50% and the crack width is less than or equal to 1.0 mm, and the soil layer is prone to further failure when the sand content in soil is more than 50% and the crack width is greater than or equal to 3.0 mm.Thirdly, the interaction of experimental factors Cc and Cw has a highly salient influence on the stability of soil layer, while interaction of Cc and Cl has some influence on the stability of soil layer, and interaction of Cc andω and interaction of Cl and Cw have nonsalient influence on the stability of soil layer.



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*Source: 3648650-2019-12-31.xml*