# Research on the Formation Mechanism of Loess Vertical Joints

Authors: Chenxing Wang; Ruijun Jiang; Hong Wang; Tonglu Li; Haiwei Kang; Xiaokun Hou
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

The popular occurrence of vertical joints in loess formation aggravates the anisotropism of loess and contributes to various geohazards (e.g., slope failures and soil erosion). To alleviate the geohazards caused by the vertical joints, researches need to be carried out to investigate the formation mechanism of these vertical joints. However, the theoretical analysis of the vertical joints’ formation mechanism is limited up to now. In this study, we conducted a laboratory column experiment to observe joint development. Furthermore, using the unsaturated soil theory, we proposed a theoretical model to investigate the tensile stress that contributes to the formation of the loess vertical joint. In the experiment, the air-dried and crushed soil was sifted into the column, which simulates the free fall deposition process of the natural loess in China and contributes to a uniform state. 2500 ml of water was added at the top of the column. The topsoil experienced a wetting-drying process. During desaturation, 9 similar vertical joints were developed with similar horizontal distance. A theoretical model that calculates the interparticle force or tensile force between two adjacent particles was proposed based on the force balance equations. The theoretical model elucidates the phenomena in a laboratory experiment well and provides an insight into the formation mechanism of vertical joints in a uniform soil. The results highlight the generation of vertical joints in the initial deposition stage of loess with a uniform particle arrangement. Besides, the tensile force that contributes to the joint formation arises from the matric suction and surface tension of the solid-water-air contractile film.


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## Body

## 1. Introduction

The loess plateau of China has the most widely distributed (6.4 × 104 km2) and thickest (e.g., 200 m) loess deposits in the world. The loess transported by wind from the Gobi desert deposits mainly in the north-west region (Figure 1). The aeolian depositing loess forms with a metastable structure that is sensitive to water. When the loess is subjected to water, the stiffness and strength markedly decrease, leading to various disasters (e.g., landslides, collapse deformation, and differential settlement) [1–6]. The most common geohazard is landslide [7]. Li et al. [8] proposed a unified landslide classification system for loess slopes based on the possible mechanisms underlying each class of failure. The failure of loess slopes is typically associated with the loess joint and water. It is well acknowledged that water is the dominant factor that induces various geological hazards in the loess plateau of China [2, 5, 9, 10]. Extensive studies have been carried out to investigate the hydromechanical properties of loess with various water contents [11–13] and water migration characteristics in the thick loess layer [2, 14–17]. However, the loess vertical joint has not received enough attention that it deserves [18].Figure 1
Loess area of China (adapted from Hou et al. [14]).Loess vertical joints are weak structural planes in the intact loess that developed during the loess formation [8, 18, 19]. Figure 2 illustrates a typical vertical joint developed in the late Pleistocene during loess deposition. The joint cuts the loess into columns that are prone to fail when the foot is wetted. Furthermore, the vertical joint is the preferential flow path of ground surface water (e.g., precipitation and irrigation water). The surface water contributes to the marked variation of the hydraulic condition of a hillslope and further failure of the slope [17, 20, 21]. Besides, during rainfall, extensive erosion occurs along the vertical joints [22]. Figure 3 shows typical erosive holes at the top of the loess highland.Figure 2
Typical vertical joints developed in late Pleistocene.Figure 3
Erosive holes on the top of the loess highland.Available studies attribute the formation of vertical joints to differential collapse deformation [23], tension force [23, 24], privilege pore characteristics (e.g., pore concentration zone and vertical tubular channel) [8], and biological activities [25]. Luo et al. [23] used remolded soils composed of several soil layers with different heights. After the inundation of the specimen, joints appeared at the points where the layer thickness was changeable and differential collapsibility happened. The joints expanded in the vertical direction. Therefore, Luo et al. [23] believe that uneven collapsibility is the reason for the development of vertical joints. However, field observation suggests that vertical joints also develop at the place where the loess beds are completely uniform without uneven collapsibility. Wang et al. [24] considered that horizontal tensile stress at the edge of the large pores in loess is the fundamental factor to generate vertical joints. The tensile stress is created by the overburden pressure. However, for the aeolian deposit, the horizontal stress caused by overburden is typically compression stress other than tension stress under the confined condition. Li et al. [8] believed that the privilege pore zone and vertical tubular channel in loess are the micromesoscopic structural basis for the development of vertical joints. However, the analysis in this study is descriptive without theoretical or quantitative investigation. Some other scholars [26] held the idea that structural characteristics, horizontal tension, and weathering were the major reasons for vertical joints’ formation in loess. However, most of these studies are qualitive analysis. Theoretical studies of vertical joints’ formation mechanism are rather limited in the literature.The objective of this study is to reveal the formation mechanism of the vertical joint. A column model experiment was conducted. Air-dried and crushed loess particles were sifted into the column, which simulated the natural deposition process of in situ loess. Afterward, the soil was subjected to water and vertical joints appeared at the top of the column. A theoretical model was established to quantitatively investigate the formation mechanism of the vertical joints. The experimental and theoretical investigation of this study reinforces our understanding of the formation mechanism of the loess vertical joint.


## 2. Materials and Methods

### 2.1. Soil Samples and Tests

The soil samples were collected from the southern edge of the Loess Plateau in Jingyang county near Xi’an city, China (Figure1). The basic physical properties of the sample are shown in Table 1. The soil grain size distribution curve and cumulative distribution curve obtained by a Bettersize 2000 laser grain size analyzer are presented in Figure 4. Based on the data in Table 1 and Figure 2, the soil can be classified as clay of low plasticity (CL) according to the Unified Soil Classification System (USCS : ASTM 2011). Parameter d50 is the particle diameter below which the mass of particles takes account of 50 %. d50 is regarded as a measurement of the intensity of winter monsoon winds that are responsible for dust transportation [27]. d50 of this tested soil is 15.1 μm.Table 1
Physical properties of soils used in this study.
ParameterValueSpecific gravityGs2.69Liquid limitwl (%)30.2Plastic limitwp (%)19.8Plastic indexIp10.4Initial water content (%)2.6Sand content (2–0.075 mm) (%)0.7Silt content (0.075–0.002 mm) (%)84.9Clay content (≤0.002 mm) (%)14.4Figure 4
Grain size distributions of the tested soil.


### 2.2. Laboratory Model Experiment

The laboratory model experiment was conducted in a plexiglass cylinder shown in Figure5(a). Its height was 200 cm. The inner and outer diameters were 23.6 cm and 25 cm, respectively. The soil prepared for the model experiment was air-dried and crushed into powder with grinding rubber. The water content of air-dried soil is 2.6%. The soil powder was sifted into the cylinder via a 0.5 mm sieve continuously to simulate the natural deposition process of loess. When the specimen achieved the required height (i.e., 180 cm height), the total mass was 91.1 kg. Under this self-weight compaction state (or initial state), the soil has a void ratio e0 of 1.650 and a dry density of 1.02 g/cm3. Then the static loading of 30 kg (i.e., 6.7 kPa) was loaded on the top to compact the soils. The soil height was stable at 1780 mm within 3 days. The density and dry density of soils after loading were 1.17 g/cm3 and 1.14 g/cm3, respectively. The void ratio e1 after loading was 1.360. This condition was defined as the weak compaction state. A layer of fine sand with a thickness of 100 mm that functions like a porous stone was evenly placed on the top of the column. This layer of sand was to prevent concentrated infiltration along the sidewall and to facilitate uniform infiltration at the top surface of the sample. The saturated permeability coefficient of the weak compaction state sample was 6.42 × 10−4 m/s, measured by TST-55 permeameter.Figure 5
(a) The model experiment and (b) fissure phenomena after water penetration.Water was added on top of the column by a spray, which simulates the natural rainfall. The spraying process lasted for 30 minutes and the total volume of water added was 2500 ml. The saturated zone appeared on the top for a short period. Then water moved downwards along with a decrease of the soil-water content for the top saturated soil. One hour later, nine vertical cracks with roughly equal distance formed, as shown in Figure3(b). The fact that the crack is the initial form of the loess joint should be noted. We measured the water content (i.e., 31.5 %) of soil where the crack developed. The total settlement of the soil column was 50 mm. This state was defined as the postinfiltration state. The soil void ratio e2 at this state reduced to 1.100. The vertical crack did not develop either horizontally or vertically in the following 24 hours during which the soil at the top underwent a drying process. The length and width of the cracks were listed in Table 2.Table 2
The vertical joints in the model experiment.
NumberLength (cm)Width (mm)110.33.2210.33.338.02.349.02.458.02.569.53.576.03.389.03.295.03.2


### 2.3. Theoretical Model

The laboratory model experiment showed that the formation of vertical joints in loess was highly related to water. To analyze the role of water in the vertical joints formation, an idealized model was proposed. In this model, the interparticle force is mainly composed of matric suction and surface tension, ignoring the change of internal force of soil particles caused by air pressure. Meanwhile, soil particles were considered as uniform spheres with the same diameters [28]. These soil grains were arranged evenly as shown in Figure 6, regardless of the fine particle clustering between the coarse grains. Using the average particle diameter of the sample d50 as the grain size, the average volume of a single soil particle is(1)VP=16πd503.Figure 6
The cross section of soil particles arrangement.For a cube model whose edge isl μm as a unit, the volume is(2)V=l3.The volume of the solid particles in the cube model is(3)VS=V1+e,where e is the void ratio of soil. The number of soil particles is(4)N=VSVP.Assuming that the center of soil particles arranged following the shape of the cube model, the grain number along the side of the cube model is(5)n=N3.The distanceac between the centers of two particles is(6)ac=ln.ac also can be derived by placing formula (1)–formula (5) into formula (6) as follows:(7)ac=d50π1+e63.The soil particle arrangement of the horizontal cross section at any void ratio is shown in Figure6. If ac is equal to d50, the distance between two particles will be 0, which means the soil particles contact each other. This state is defined as the dense arrangement state. In this state, the void ratio e3 is 0.91 theoretically [28].When the soil is partially saturated, the air-water-soil interface forms between the two particles. The geometric relationship is illustrated in Figure7:(8)r1=acosθ−R,(9)r2=atanθ−r1,where r1 is the radius of the contractile skin; r2 is the center radius of the capillary water column; R is the radius of the ideal soil particle; a is half of the center spacing between soil particles; θ is the filling angle.Figure 7
Toroidal geometry of the air-water-solid interface.For monosized particles, a free-body diagram for the relevant system forces that involves a contribution from air pressure, pore water pressure, surface tension, and applied external force or overburden pressure is shown in Figure8.Figure 8
Free-body diagram of inter-particle forces.The resultant interparticle force is(10)Ps=ua−uwπr22+Ts2πr2,where ua is air pressure; uw is pore water pressure; ua−uw is the matric suction and Ts is surface tension, which is 72.0 mN/m at 25°C.From equation (10), it can be seen that the interparticle force is related to the matric suction, surface tension, and soil-water content (i.e., r2). The relationship between matric suction and surface tension in unsaturated soil can be expressed using the Laplace [29](11)ua−uw=Ts1r1−1r2.Substituting equations (8) and (9) into (11), the matric suction is(12)ua−uw=TScosθasinθ+2Rcosθ−2aa−Rcosθasinθ+Rcosθ−a.Therefore, with a given particle spacing (i.e.,a), a specific filling angle θ corresponding to a certain value of matric suction can be calculated using equation (12). By substituting the filling angle into equations (8) and (9), r1 and r2 can be obtained. Eventually, the interparticle force can be calculated from equation (10).


## 2.1. Soil Samples and Tests

The soil samples were collected from the southern edge of the Loess Plateau in Jingyang county near Xi’an city, China (Figure1). The basic physical properties of the sample are shown in Table 1. The soil grain size distribution curve and cumulative distribution curve obtained by a Bettersize 2000 laser grain size analyzer are presented in Figure 4. Based on the data in Table 1 and Figure 2, the soil can be classified as clay of low plasticity (CL) according to the Unified Soil Classification System (USCS : ASTM 2011). Parameter d50 is the particle diameter below which the mass of particles takes account of 50 %. d50 is regarded as a measurement of the intensity of winter monsoon winds that are responsible for dust transportation [27]. d50 of this tested soil is 15.1 μm.Table 1
Physical properties of soils used in this study.
ParameterValueSpecific gravityGs2.69Liquid limitwl (%)30.2Plastic limitwp (%)19.8Plastic indexIp10.4Initial water content (%)2.6Sand content (2–0.075 mm) (%)0.7Silt content (0.075–0.002 mm) (%)84.9Clay content (≤0.002 mm) (%)14.4Figure 4
Grain size distributions of the tested soil.


## 2.2. Laboratory Model Experiment

The laboratory model experiment was conducted in a plexiglass cylinder shown in Figure5(a). Its height was 200 cm. The inner and outer diameters were 23.6 cm and 25 cm, respectively. The soil prepared for the model experiment was air-dried and crushed into powder with grinding rubber. The water content of air-dried soil is 2.6%. The soil powder was sifted into the cylinder via a 0.5 mm sieve continuously to simulate the natural deposition process of loess. When the specimen achieved the required height (i.e., 180 cm height), the total mass was 91.1 kg. Under this self-weight compaction state (or initial state), the soil has a void ratio e0 of 1.650 and a dry density of 1.02 g/cm3. Then the static loading of 30 kg (i.e., 6.7 kPa) was loaded on the top to compact the soils. The soil height was stable at 1780 mm within 3 days. The density and dry density of soils after loading were 1.17 g/cm3 and 1.14 g/cm3, respectively. The void ratio e1 after loading was 1.360. This condition was defined as the weak compaction state. A layer of fine sand with a thickness of 100 mm that functions like a porous stone was evenly placed on the top of the column. This layer of sand was to prevent concentrated infiltration along the sidewall and to facilitate uniform infiltration at the top surface of the sample. The saturated permeability coefficient of the weak compaction state sample was 6.42 × 10−4 m/s, measured by TST-55 permeameter.Figure 5
(a) The model experiment and (b) fissure phenomena after water penetration.Water was added on top of the column by a spray, which simulates the natural rainfall. The spraying process lasted for 30 minutes and the total volume of water added was 2500 ml. The saturated zone appeared on the top for a short period. Then water moved downwards along with a decrease of the soil-water content for the top saturated soil. One hour later, nine vertical cracks with roughly equal distance formed, as shown in Figure3(b). The fact that the crack is the initial form of the loess joint should be noted. We measured the water content (i.e., 31.5 %) of soil where the crack developed. The total settlement of the soil column was 50 mm. This state was defined as the postinfiltration state. The soil void ratio e2 at this state reduced to 1.100. The vertical crack did not develop either horizontally or vertically in the following 24 hours during which the soil at the top underwent a drying process. The length and width of the cracks were listed in Table 2.Table 2
The vertical joints in the model experiment.
NumberLength (cm)Width (mm)110.33.2210.33.338.02.349.02.458.02.569.53.576.03.389.03.295.03.2


## 2.3. Theoretical Model

The laboratory model experiment showed that the formation of vertical joints in loess was highly related to water. To analyze the role of water in the vertical joints formation, an idealized model was proposed. In this model, the interparticle force is mainly composed of matric suction and surface tension, ignoring the change of internal force of soil particles caused by air pressure. Meanwhile, soil particles were considered as uniform spheres with the same diameters [28]. These soil grains were arranged evenly as shown in Figure 6, regardless of the fine particle clustering between the coarse grains. Using the average particle diameter of the sample d50 as the grain size, the average volume of a single soil particle is(1)VP=16πd503.Figure 6
The cross section of soil particles arrangement.For a cube model whose edge isl μm as a unit, the volume is(2)V=l3.The volume of the solid particles in the cube model is(3)VS=V1+e,where e is the void ratio of soil. The number of soil particles is(4)N=VSVP.Assuming that the center of soil particles arranged following the shape of the cube model, the grain number along the side of the cube model is(5)n=N3.The distanceac between the centers of two particles is(6)ac=ln.ac also can be derived by placing formula (1)–formula (5) into formula (6) as follows:(7)ac=d50π1+e63.The soil particle arrangement of the horizontal cross section at any void ratio is shown in Figure6. If ac is equal to d50, the distance between two particles will be 0, which means the soil particles contact each other. This state is defined as the dense arrangement state. In this state, the void ratio e3 is 0.91 theoretically [28].When the soil is partially saturated, the air-water-soil interface forms between the two particles. The geometric relationship is illustrated in Figure7:(8)r1=acosθ−R,(9)r2=atanθ−r1,where r1 is the radius of the contractile skin; r2 is the center radius of the capillary water column; R is the radius of the ideal soil particle; a is half of the center spacing between soil particles; θ is the filling angle.Figure 7
Toroidal geometry of the air-water-solid interface.For monosized particles, a free-body diagram for the relevant system forces that involves a contribution from air pressure, pore water pressure, surface tension, and applied external force or overburden pressure is shown in Figure8.Figure 8
Free-body diagram of inter-particle forces.The resultant interparticle force is(10)Ps=ua−uwπr22+Ts2πr2,where ua is air pressure; uw is pore water pressure; ua−uw is the matric suction and Ts is surface tension, which is 72.0 mN/m at 25°C.From equation (10), it can be seen that the interparticle force is related to the matric suction, surface tension, and soil-water content (i.e., r2). The relationship between matric suction and surface tension in unsaturated soil can be expressed using the Laplace [29](11)ua−uw=Ts1r1−1r2.Substituting equations (8) and (9) into (11), the matric suction is(12)ua−uw=TScosθasinθ+2Rcosθ−2aa−Rcosθasinθ+Rcosθ−a.Therefore, with a given particle spacing (i.e.,a), a specific filling angle θ corresponding to a certain value of matric suction can be calculated using equation (12). By substituting the filling angle into equations (8) and (9), r1 and r2 can be obtained. Eventually, the interparticle force can be calculated from equation (10).


## 3. Analysis and Results

Theoretical analysis is conducted with three series of parameters using the theoretical model established above. The three series correspond to the three different states in the laboratory experiment, namely, the initial state, weak compaction state, and postinfiltration state. The physical parameters (i.e., water content, dry density, and void ratio) corresponding to the three states have been obtained during the experiment and are used in this section. The particle size is 15.1μm, which equals d50 of the tested soil in the laboratory experiment. In the experiment, the soil at the top of the soil column experiences a wetting-drying process following four stages that are shown in Figure 9. In the beginning, there is no water in the pores. The space among soil particles is filled with air (Figure 9(a)). In such a scenario, there are neither contractile films nor surface tension acting on the soil particles. After infiltration, the surface soil is saturated, and the pores between particles are filled with water (Figure 9(b)). In this state, matric suction is zero. In addition, there is no surface tension acting on the soil particles. When the water propagates downward after we stop adding water from the top, air enters the pore and is surrounded by free water (Figure 9(c)). In such a scenario, the air-water surface tension does not act on the soil particles. However, the matric suction is not zero and tends to pull the adjacent particles together. With downward propagation of the water, the water content of the soil at the top of the column decreases with the discharged water space occupied by the air. Then the water-air-solid interface develops (Figure 9(d)) and the contractile film plays an important role in pulling the adjacent soil particles together.Figure 9
The process development of water-air-solid phases in loess: (a) totally dry state; (b) saturated state; (c) isolated air pore state; (d) water-air-solid interaction state.
(a)(b)(c)(d)According to equation (7), interparticle space ac is only related to void ratio e as d50 is constant. The parameters of soil at different states (i.e., initial deposition state, weak compaction state, and postinfiltration state) in the laboratory experiment process are shown in Table 3. The parameters at the dense arrangement state, which assumes that ac equals d50, are also shown in Table 3.Table 3
The parameters in different experimental states.
NumberState of soilVoid ratioeDry densityρd (g/cm3)Interparticle spaceac (μm)Shrinkage spaces (μm)1Initial deposition1.6501.0216.841.742Weak compaction1.3601.1416.201.103Postinfiltration1.1001.2915.590.494Dense arrangement0.9101.4215.100.00Note: shrinkage spaces is the difference between the interparticle space and d50.The data in Table3 shows that the soil pores are continuously compressed and the void ratio reduces gradually as the soil state changes from the initial deposition state to the dense arrangement state. The position of soil particles changes and the shrinkable space between particles decreases. Based on equation (10), the relationship between matric suction and interparticle force at different states can be obtained (Figure 10).Figure 10
The change of interparticle force with matric suction in different states.If the soil is approximately saturated or matric suction is close to zero (i.e., 1 kPa in Figure10), the interparticle force increases with the decrease of the particle distance or void ratio. Along with the increase of matric suction, the interparticle force decreases gradually or keeps constant at the beginning and then drops down suddenly in the initial deposition, weak compaction, and postinfiltration states. This result suggests that, before it reaches a turning value, the matric suction has a limited effect on the interparticle force. However, the interparticle force reduces to zero when the matric suction is higher than this turning value. Here the turning values corresponding to the three states are 9.6 kPa, 32.7 kPa, and 128.1 kPa, respectively, which increase with the decrease of the particle distance. On the other hand, for the close arrangement state, the distance of the soil particles is the smallest among the four states. The interparticle forces at this state increase with the increase of matric suction continuously, which is significantly different from the former three states. In other words, the matric suction contributes significantly to the interparticle force for dense soil with a relatively low void ratio. However, regarding the loose state, the contribution of matric suction to the interparticle force is limited within a low suction range (e.g., 128.1 kPa for the postinfiltration state).During the drying process, the volume shrinkage occurs in both vertical and horizontal directions. The vertical shrinkage during drying induces subsidence that is different from the collapsibility, which occurs during wetting [14]. The interparticle force increases during the drying process. Therefore, it is the surface tension acting on the contractile skin and the matric suction that contribute to the interparticle force and further the formation of the vertical joints.Furthermore, the tensile stress (i.e., interparticle force in macroscopic scale) is calculated. At first, the soil-water characteristic curve (SWCC) in the postinfiltration state is obtained using the tensiometer method. Typical suction measurement methods in the laboratory include the pressure plate method [30, 31], filter paper method [32, 33], and tensiometer method [34]. In this study, the TEN-15 tensiometer, which measures matric suction in the range of 0 to approximately 90 kPa, was used herein to obtain the drying soil-water characteristic curve of the sample. The sampling process was the same as the laboratory model experiment process. The measured data points were fitted by equation (13) [35]. The results are shown in Figure 11.(13)wψ=wr+ws−wr1+aua−uwnm,where w is mass water content; wr and ws are residual water content and saturated water content, respectively; ua−uw is matrix suction; a, m, and n are fitting parameters.Figure 11
Soil-water characteristic curve.According to Figure6, assuming that the particle diameter is 15.1 μm and the total length l is 93.5 μm, there are 6 particles in both vertical and horizontal directions. The area of cross section is S = (15.59×6)2 = 8750 μm2. There are 36 connecting points, so the tensile stress σs is(14)σs=nPsS=36×10128750,Ps=4.11×109Ps.In the previous equations,n is the number of connecting points, Ps is the interparticle force in every connection point, and S is the area of the section. In this condition, parameters are calculated in the drying process. The data are presented in Table 4.Table 4
The parameters of interaction between soil particles at the 15.59μm interparticle spacing.
Water contentw (%)tua−uw (kPa)Filling angle Θ (°)Shrinkable film radiusr1 (μm)Capillary column radiusr2 (μm)Interparticle forcePs (106 N)Tensile stressσs (kPa)6.380.217.00.61.81.606.609.964.519.70.72.11.797.3618.052.622.10.92.31.927.8823.836.226.41.22.72.078.5229.124.031.01.53.12.168.8831.517.534.21.93.42.199.0233.911.538.12.43.82.219.0837.26.142.83.14.12.209.0639.03.046.33.74.42.199.0040.61.049.14.44.62.178.92From the laboratory experiment, the water content is 31.5 % when vertical joints appear. The tensile stress is 9.02 kPa when matric suction increases to 17.5 kPa. This tensile stress is close to the largest interparticle force condition (i.e., interparticle force is 9.06 kPa when matric suction is 11.5 kPa). But, with continuing desaturation, the interparticle force in the microscope and tension stress in the macroscope decrease and the shrinkage stops. During the laboratory experiment, it was observed that joints did not develop during further drying. This phenomenon coincides with the theoretical calculation. The total shrinkage (the sum width of 9 vertical joints in Table2) is 2.69 cm. The theoretical estimation in the perimeter is 2.90 cm from the initial deposition state to the postinfiltration state, which is also similar to the experimental results.


## 4. Discussion

The available formation mechanisms of the loess vertical joint, which include the differential collapse deformation mechanism [23], tension stress concentration mechanism [23, 24], privilege pore characteristics [8], and biological activities [25], are all based on the nonuniform initial state. In other words, the initial state of the soil is anisotropic with more connected pores in the vertical direction. However, we deem that the aeolian loess is originally uniform. It is the wetting-drying circles which the soil experiences in the following decades that contribute to the anisotropy concentrated pores and vertical joints. This vertical joint (open or closed) will be inherited and develop furthermore at gravity loading during its depositional period. It can evolve into the process of densification or reerosion [20]. Unloading at the edge of slopes is a typical process to make the original crack extend to vertical joints with a length of several meters. Vertical joints in loess are deemed to inherit from the original crack.This theoretical model is an ideal model without considering the fine clay particles clustering between the silt particles. In addition, this model attributes the deformation of the soil element to the variation of the distance between two soil particles without considering the rearrangement of the soil particles. Even though it simplifies the real condition of the soil, the theoretical model presented here provides an insight into the mechanical mechanism of vertical joints’ formation. Based on the theory of unsaturated soil, both the matric suction and surface tension contribute to the interparticle force of soil particles. Besides, the contributions of the matric suction and surface tension are both related to the soil-water content (i.e.,r2 in the theoretical model). This is closely related to the test results. We need to note that the contribution of surface tension, which is always neglected in the literature [36–39], is highlighted in this study. This study enriches and perfects the research of loess vertical joints and provides scientific basis for prevention and control of geological disasters caused by vertical joint of loess.


## 5. Conclusions

The following conclusions can be drawn from the results presented in this paper:(1)
A laboratory model experiment was carried out to simulate the initial aeolian deposition process of the loess and the subsequent wetting-drying process that natural loess experiences after deposition. The basic parameters in initial deposition state, weak compaction state, and postinfiltration state were obtained, respectively. The generation, evolution, and cessation processes of cracks were well recorded.(2)
A theoretical model with unsaturated soil theory was proposed to calculate interparticle force or tensile force. This model explained the experimental phenomena well.(3)
The joints in loess can form in the initial deposition stage with a uniform particle arrangement. They occur when air-water-solid menisci emerge in the drying process after infiltration and stop evolving when the soil dries to a certain matric suction. Vertical joints in loess can be regarded as an inheritance of original cracks.(4)
The matric suction and surface tension stress arising from the solid-water-air contractile skin contribute to the formation of the loess vertical joints.



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