Effect of Colluvial Soil Slope Fracture ’ s Anisotropy Characteristics on Rainwater Infiltration Process

Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province, Changsha University of Science & Technology, Changsha 410114, China School of Civil Engineering, Changsha University of Science & Technology, Changsha 410114, China School of Traffic and Transportation Engineering, Changsha University of Science & Technology, Changsha 410114, China National Engineering Laboratory of Highway Maintenance Technology, Changsha University of Science & Technology, Changsha 410114, China School of Civil Engineering, Nanjing Forestry University, Nanjing 210037, China


Introduction
Colluvial soil slope whose soil layer thickness is within 7 m is widely distributed in the southern part of China [1].Under the influence of rainfall, it can easily bring shallow landslide or debris flow which is the main geological hazard in southern China.A large number of engineering practices and tests have proved that the strength of slope soil has the characteristics of deterioration with increase of water content [2].erefore, mastering the occurrence state of rainwater in slope soil becomes the precondition for studying the stability of slope.Because the slope soil has the characteristics of low strength and strong evaporation, the peristalsis and uneven evaporation of the upper and lower layers occur after rainfall infiltration in the diluvial layer, thus causing a clear fracture.In addition, the fracture's permeability is obviously different from the surrounding soil, which induces water to infiltrate into the slope soil more quickly and expand the infiltration range.In particular, when the permeability of the undisturbed slope soil is low, the infiltrated water may change the whole seepage field of the slope above the bedrock.erefore, the process of rainwater anisotropic infiltration induced by fractures should be analyzed in the design of drainage measures for colluvial soil slope.e anisotropic seepage is mainly caused by the following aspects: (1) fracture depth, (2) ratio of the permeability coefficient along the fracture direction to vertical fracture direction (permeability ratio μ), (3) angle of fracture distribution (θ), and (4) fracture density.
At present, scholars worldwide have conducted a significant amount of research on fracture seepage.Ju et al. [3] and Qian et al. [4] studied the seepage properties of fractured rocks under different confining pressures.Chen et al. [5] and Huang et al. [6] studied the numerical calculation method of the discrete fracture model for twodimensional seepage in fractured rock.Yang et al. [7] and Chai and Xu [8] studied the composite element model of rock fracture seepage coupling with normal stress.Su et al. [9] and Zeng et al. [10] have carried out a rough single fracture percolation-dissolution coupling model controlled by the surface reaction and diffusion migration.Ju et al. analyzed the variation of seepage properties with fracture roughness and the influence of the rough structure on seepage mechanism through laboratory tests.
In addition, the fractal model of relationship between water flow resistance and fracture roughness was obtained [3].Liu et al. used the DFN-GEN program to generate the fracture-rock calculation model, studied the hydraulic characteristics of the fractured rock mass, and discussed the influence law of stress on the equivalent permeability coefficient of the fractured rock mass [11].Chen and Song carried out a numerical calculation method for the discrete fracture network model for flow and heat transfer in two-dimensional fractured rocks.
e model is used to simulate a randomly generated fracture network to study the characteristics of flow and heat transfer in fractured rock [12].Leung and Zimmerman studied the fluid flow in a random two-dimensional fracture network and established a macroscopic effective hydraulic conductivity estimation method based on the fracture network parameters [13].Xue and Chen established a composite element model considering the coupling of rock fracture seepage and normal stress.
e analysis shows that the normal stress causes the seepage uneven penetration of the fractured rocks; that is, the osmotic gradient, the uplift pressure, and seepage velocity of the local area increase significantly [14].Chen et al. discussed the seepage properties of the joint surface and derived the normal and tangential stiffness coefficient formulas of the joint plane and the equivalent permeability coefficient formula of the joint system [15].Huo et al. established a rough singlefracture seepage-dissolution coupling model controlled by the surface reaction and diffusion migration.e results show that the distribution of aperture, flow velocity, and concentration of Ca 2+ appeared as inhomogeneous wormholes.
e flow through the fracture increased during the whole period of simulation, and the factor controlling the chemical reaction varied during the dissolution [16].Su et al. believe that the overall permeability of the fracture increases slowly at the initial moment.As the aperture increases and penetrates, the dissolution rate will gradually increase, which is an accelerated process [9].
Song et al. studied the influence of fluid-solid coupling on shale mechanics and seepage laws.e shale seepage tests under different saturations show that, under fluid-solid coupling conditions, the higher the saturation, the higher the propagation and the seepage ability of microcracks under pressure [17].Huang et al. carried out numerical analysis on the hydrothermal coupling model of lowtemperature fractured rocks.It is believed that both the fracture width and delivery head of fracture water affect completed freezing time.
e completed freezing time increases with the increase of fracture width and delivery head of fracture water [6].Zeng et al. studied the seepage law considering the formation dip angle, established the modified radial flow formula of the inclination angle, and obtained the formation pressure distribution and the production formula of the inclined formation by the plane radial seepage theory [18].
From the above studies, we can see that the existing researches mainly focus on the fracture seepage test method, numerical calculation theory, and the establishment of the constitutive model, and the research object is mostly rock fissure seepage.However, the research on soil slope fracture seepage is seldom carried out.In the last two years, the frequency of soil slope instability caused by rainfall was increasing.erefore, the fracture causing the change of the seepage field of soil slope and leading to slope instability phenomenon ultimately cannot be ignored.is paper intends to study the influence of slope fracture anisotropy on the rainwater infiltration process in colluvial soil slope.What's more, the occurrence characteristics of rainwater under the influence of fracture anisotropy are obtained to provide a reference for slope stability analysis and design of drainage measures when fractures exist.

Numerical Realization of Fracture Anisotropy
In this paper, the SEEP/W module of finite element software GEO-slope is used to calculate the seepage process of rainwater [19].e fracture depth, fracture angle, permeability coefficient ratio, and fracture density are simulated by the following methods [20][21][22]: (1) a solid element is established equivalent to a fracture in the model, and a fracture is defined as another material different from the colluvial soil; (2) to simulate the distribution of fractures by changing the length, angle, and spacing of the established fracture solid element; (3) the anisotropy of the fracture unit is simulated by defining the ratio (μ) of the permeability coefficient (k ′ y ) along the direction of fracture and the permeability coefficient (k ′ x ) in the direction of vertical fracture.e angle of fractures distribution (θ) should also be taken into account here.e schematic diagram is shown in Figure 1.
In Figure 1, the fracture angle (θ), the fracture permeability coefficient (k x ′ and k y ′ ), and the actual set fracture permeability coefficient (k x and k y ) satisfy the following formula: 2 Advances in Civil Engineering where θ is the angle between the crack and the vertical direction, k x ′ and k y ′ are the permeability coe cients in the direction of vertical fracture and permeability coe cient along the direction of fracture, respectively, and k x and k y are the permeability coe cients along the X and Y directions in the global coordinate system, respectively.

Numerical Model and Boundary Conditions.
A simple slope with a height of 20 m and an angle of 30 °is used in the calculation.e fracture is considered within a depth of seven meters on the surface of the slope.
e fracture is designed at the middle and top of the slope.e length of fracture is 1 m, 3 m, and 5 m, and the angle of fracture is 0 °, 30 °, and 60 °.As shown in Figure 2, the in uence of the number of fractures on the seepage process is considered according to the uniform distribution of fractures in the middle and top of the slope.e numbers of fracture are 1, 2, 3, 4, and 5.In the calculation of rainfall in ltration, when the rainfall intensity is less than the saturation permeability coe cient of slope surface soil, the slope surface adopts the unit ow boundary, which is controlled by the rainfall intensity.When the rainfall intensity is greater than the permeability coe cient of slope surface soil, the slope surface is set as the head boundary.
e calculation of saturated-unsaturated seepage under rainfall condition requires an initial condition, and the in ltration of rainwater is transient seepage based on the initial condition.In the natural state, the area above the groundwater level is generally unsaturated.According to the Van Genuchten (VG) model, the natural state determines the distribution of the initial matrix suction eld in the slope.However, the permeability coe cient of the unsaturated region is much smaller than that of the saturated permeability coe cient because of the existence of matrix suction.
e continuous in ltration of rainwater in the slope is controlled by the permeability coe cient of the unsaturated region.erefore, the accurate determination of the initial state is the key to simulate the rainwater in ltration process.At present, there are two representative methods for the simulation of the unsaturated region in the initial state [23]: (1) the above area of the groundwater level shall be linearly assigned according to the hydrostatic pressure, which will result in a large di erence in the negative pore water pressure at di erent positions of the slope surface, and (2) the pore water pressure below the groundwater is calculated according to hydrostatic pressure.
e pore water pressure on the underground water level is 0 kPa.e pore water pressure in the area above the underground water level is tted by using the VG model.However, the negative pore water pressure on the slope in contact with the atmosphere should be the same.
As far as the literature is concerned, most scholars use the rst method to simulate the initial seepage eld.In fact, since the surface of slope is in contact with the atmosphere, the drought-wet degree of the slope surface is close, and the negative pore water pressure is basically the same.erefore, the second method is used to simulate the initial seepage eld of slope, as shown in Figure 3.

Calculation Parameters and Schemes.
e actual project supported in this paper is the slope of K107 + 670 of the Rucheng-Chenzhou expressway in Hunan Province, so the parameters used in the calculation are derived from the test of undisturbed soil [24].To obtain the permeability of weakly weathered limestone, the borehole water pressure test was carried out on the rock.According to the test results, k x k y 1.0 × 10 −9 m/s.e saturated permeability coe cient of homogeneous (gravel) silty clay was obtained by the laboratory test, and k x 1.0 × 10 −7 m/s, and k y 0.83 × 10 −7 m/s.e saturated water content is measured by the laboratory test of the original sample.e saturated water content of silty clay is 0.35, and that of weakly weathered limestone is 0.05.e residual water content (w r ) of silty clay which is acquired by the laboratory test is 0.02.e permeability coe cient in the direction of vertical fracture is k x ′ 2.83 × 10 −2 m/s.e permeability coe cients along the direction of fracture are k y ′ 1k x ′ , 10k x ′ , 100k x ′ , and 1000k x ′ , respectively, and μ are 1, 10, 100, and 1000 [25].
en, k x and k y in the global coordinate system with different permeability coe cient ratios (μ) and fracture angles (θ) are calculated according to Equations ( 1) and ( 2). e results are shown in Figure 4.
To simulate the most unfavorable rainfall conditions, the rainfall intensity value was calculated by using the maximum rainfall of 7 days in the last 20 years in the Rucheng-Chenzhou area, Hunan Province.e rainfall is 585 mm (9.67 × 10 −7 m/s) [26].To consider the in uence of fracture length, fracture angle, fracture permeability coe cient ratio, and fracture density on the rainwater seepage process, the designed calculation scheme is shown in Table 1. 4 Advances in Civil Engineering the fracture section is almost equal when rainfall is 1 d and 7 d, respectively.e infiltration depth at 7 days of rainfall is obviously greater than that at 1 day, which is 2.0 m and 1.7 m, respectively.e infiltration depths are greater than that of 1 m fracture.e results show that, after 1 day of rainfall, the fracture is almost filled with the infiltration rainwater.However, the rainwater infiltration depth is related to rainfall duration, soil permeability coefficient, and seepage boundary condition.By analyzing the reason, because of the large permeability coefficient of the fracture, the infiltration rainwater on the slope will enter into the fracture quickly.However, because of the small permeability coefficient of soil, the rainwater in the fracture is not easy to seep out the slope soil.Rainwater will converge inside the fracture until the fracture is completely filled with rainwater.
e pressure head is almost the same as the fracture depth in the fracture.When the fissure is filled with rainwater, the infiltration of fracture rainwater into the slope will be changed into pressure permeability.erefore, the greater the fracture depth, the greater the pore water pressure in the fracture, and the greater the infiltration depth at the time of rainfall stopping.
Figure 6 shows the distribution of the saturation line around fractures at different fracture depths (7 days of rainfall).e area around the fracture is saturated after seven days of rainfall.e size of the saturated region is positively correlated with the depth of the fracture.e continuous saturation zone is not formed in the slope except the fracture.In particular, when the fracture depth is 5 m, the saturation line down the fracture has merged with the underground water line.e saturated area increases rapidly and eventually leads to the rise of the groundwater level, which affects the seepage field of the slope to a greater extent.In conclusion, under the same conditions, the fracture depth determines the size of the saturated area around the fracture.
e formation of the rapid seepage path is the direct cause of the rise of the groundwater level in the fractured slope.

Influence of Fracture Permeability Coefficient Ratio.
Figure 7 shows the distribution curves of pore water pressure with buried depth of fracture at different fracture permeability ratios.As shown in Figure 7, after 7 days of rainfall, the pore water pressure of each scheme fracture section  Advances in Civil Engineering increases to a certain extent.When μ � 1, the pore water pressure decreases gradually with the increase of buried depth in the fracture range, and it is always in a negative pressure.When μ ≥ 10, the pore water pressure increases gradually with the increase of buried depth in the fracture range.eir pore water pressure distribution law is basically consistent, and the numerical difference is small.Figure 8 shows the distribution curve of the fracture permeability coefficient with buried depth when rainfall stops.When μ ≥ 10, the permeability coefficient is obviously larger than that of the initial state and μ � 1.
Combined with the analysis of Figures 7 and 8, it is not difficult to find the reasons for the above phenomenon.When μ � 1, the unsaturated state is always maintained in the fracture range.e maximum permeability coefficient in the fracture range is 1.51 × 10 −7 m/s, which is less than 9.67 × 10 −7 m/s of rainfall intensity.erefore, the infiltration process of rainfall is actually controlled by the soil permeability coefficient.However, when μ ≥ 10, the vertical permeability coefficient of fracture increases significantly relative to μ � 1. e fracture is saturated rapidly.e unsaturated permeability coefficient is changed to the saturation permeability coefficient.e permeation coefficient is much larger than the rainfall intensity, and the infiltration process of rainwater is controlled by the rainfall intensity.erefore, when μ ≥ 10, the distribution of pore water pressure is basically the same, and the numerical difference is small.
Figure 9 shows a cloud map of pore water pressure in the fracture area with different permeability coefficient ratios.For convenience of analysis, only the fracture area is displayed.It can be seen that when μ � 1, the whole fracture area  6 Advances in Civil Engineering is the negative pressure area after 7 days of rainfall.When μ ≥ 10, a certain range of the saturation zone appears along the fracture.e maximum pore water pressure in this area is above 20 kPa.e distribution of the saturated area is similar, which further shows that the distribution of pore water pressure in Figure 7 is objective.
In conclusion, the in uence of the fracture permeability coe cient on the rainfall in ltration process is mainly related to the relative magnitudes of the permeability coe cient and rainfall intensity.When the permeability coe cient of the fracture is less than the rainfall intensity, the permeability coe cient ratio has little e ect on the in ltration process.When the permeability coe cient is greater than the rainfall intensity, the permeability coe cient ratio has a great in uence on the in ltration process of rainwater.However, with the increasing of the permeability coe cient ratio, the in uence of rainwater on the seepage process is not obvious.

In uence of Anisotropic Direction of Fracture on the
Rainwater In ltration Process. Figure 10 shows the variation of pore water pressure along the fracture section with buried depth at di erent fracture angles after rainfall.e following can be seen from the graph: (1) the pore water pressure caused by rainfall in the range of fracture depth changes from the negative value of the initial state to the positive value.e value increases linearly with the increase of buried depth.e di erence of the pore water pressure distribution curve with di erent fracture angles is small.e pore water pressure distribution curve is parallel to that of the initial state.e results show that di erent fracture angles have little e ect on distribution of pore water pressure.(2) e smaller the fracture angle is, the greater the maximum pore water pressure in the fracture depth range is, and the greater the depth of the positive pore water pressure is. Figure 11 shows the distribution of pore water pressure in the top of the slope at di erent fracture angles.It can be seen that, with the increase of fracture angle, the depth of in ltration decreases, but the range of the surface saturation area of slope increases obviously.e results show that the in uence of fracture angle on the in ltration process of rainwater is mainly re ected on in ltration depth and the range of the surface saturation area.
From the above analysis, it can be seen that the in uence of di erent fracture angles on the seepage eld of the slope is mainly re ected in the in ltration depth, in uence range, and degree.When the fracture angle is small, the in uence depth of rainwater in ltration is greater, but it has little in uence on the surface seepage eld of the slope.However, when the fracture angle is large, the in uence depth of rainwater in ltration is relatively small, but the in uence on the surface seepage eld of the slope is greater.
e reasons for this can be summarized as follows: (1) after a long period of rainfall, the fractures gradually reached saturation.e saturation permeability coe cient is much larger than the rainfall intensity, and the in ltration process is controlled by the rainfall intensity.Under the same condition of rainfall, almost all of rainwater is in ltrated.erefore, the fracture angles have little e ect on the distribution of pore water pressure with buried depth.(2) e smaller the fracture angle is, the greater the vertical permeability coe cient is.As a result, rainwater is more likely to cause saturation in the deep fracture areas.Accordingly, the surface saturation area of slope is relatively small.When the fracture angle increases, the vertical permeability coe cient becomes smaller and the horizontal permeability coe cient becomes larger.e rainwater is easy to gather in the shallow layer of the slope and seepage along the horizontal direction, which causes the saturation region of the slope surface to increase obviously.

In uence of Fracture Density on the Rainwater In ltration
Process.
e size of fracture density often determines the stability of the slope.Especially, when the fracture depth is large, rainwater easily enters the deep slope directly, which has great in uence on slope stability.Hence, in the middle to the top of the model, a di erent number of fractures whose length is 5 m are set up.In each of the ve schemes, there are 1, 2, 3, 4, and 5 ssures, respectively.e ve schemes are used to analyze the in uence of fracture density on the rainwater in ltration process.Figure 12 shows the distribution of pore water pressure at di erent number of fractures.It can Advances in Civil Engineering be seen from Figure 12 that when there is no fracture, the slope still maintains the negative pressure state after rainfall, and there is no saturation zone.When there is a fracture, rainwater in ltrates along the fracture and forms a saturated positive pressure zone inside the slope.With the increase of fracture density, the saturated positive pressure region is connected to each other in the slope.e in uence range and the degree of the rainwater on the seepage eld are larger and larger.e range of the saturated zone formed by 1 to 5 fractures is 16.4 m 2 , 34.7 m 2 , 60.9 m 2 , 75.6 m 2 , and 110.7 m 2 , respectively.e area of the saturated area increases with the number of fractures in the form of the formula y 15.968x 1.2073 , as shown in Figure 13. Figure 14 shows the variation process of the saturation line in the fracture with rainfall time when 5 m long ssures are distributed in the middle and upper parts of the slope.
e saturation zone formed by each fracture exists independently during 2 days of rainfall.After 3 days of rainfall, the saturated area of the lower part of the single fracture began to merge and connect gradually.e saturation line increases obviously with the continuous rainfall.
In conclusion, the existence of long fractures as the dominant seepage path will help rainwater enter the slope quickly.Rainfall can directly recharge the slope groundwater and form a large area of the saturation area.e existence of the saturated zone increases the weight of soil and reduces the unsaturated strength of soil.Especially when there are many fractures in the slope at the same time, the in uence area of rainwater in ltration will be further enlarged, which will be unfavorable to the slope stability.

Analysis of In uence of Fracture on Slope Stability.
e formation of cracks in soil slopes, especially loose slopes, mainly comes from two aspects: (1) slip of slope soil; (2) when the upper soil evaporates and shrinks, the lower soil cannot synchronize, so the upper and lower soil shrinkage is  8 Advances in Civil Engineering uneven, resulting in cracks.e existence of a fracture causes it to lose its original strength on the surface of a fracture [27].
When the crack develops to a certain extent, it will inevitably affect the slope stability [28].Specifically, the most important causes of soil slope instability caused by fractures can be summarized in three aspects: (1) as far as the fracture itself is concerned, the degree of development of the fracture will determine the strength of the soil, which includes the density, depth, and width of the fracture.At present, there is not a criterion of how the degree of crack development affects the strength of soil, but some useful research has been carried out [29].(2) e pore water pressure and water content increase due to rainwater entering the fractures and slope soil.e unsaturated strength of the soil will be reduced.At the same time, the gravity of the soil will be increased, which will lead to the increase of the sliding force.
(3) For colluvial soil slope, the lower part of the slope is impervious bedrock.When rainwater enters the fracture and surrounding soil, the hydrodynamic pressure will be generated in the sliding body of the upper part of the bedrock, and the slope sliding moment will be significantly increased.
In view of the fact that fracture affects slope stability, the influences of the fracture depth, fracture angle, and fracture density on the rainwater infiltration process are analyzed.e results show that the pore water pressure of the soil around the fracture increases under the condition of rainfall.e soil reaches the saturation state (water content increases).When the fracture density is high, the continuous saturation zone is formed inside the slope.According to bivariate unsaturated shear strength formula put forward by Fredlund et al. [30], the strength of unsaturated soil is determined by several factors [31,32] such as effective shear strength parameters (c′ and φ′), matrix suction (u a −u w ), and φ b .When the soil is saturated, the effective shear strength parameters (c′ and φ′) decrease, the matrix suction almost disappears in the saturated region, and φ b decreases accordingly.As a result, the strength of unsaturated soil decreases significantly.Moreover, when rainwater enters the soil along the fractures, the weight of soil will increase, which leads to the increase of slope sliding force.Combining the calculation results with the theory of unsaturated shear strength shows that fracture can enhance the infiltration of rainwater in the slope soil and thus affects the slope stability significantly.e range of the saturated zone and variation law of the pore water pressure under fracture seepage are obtained, which provides a reference for the parameter partition assignment of slope stability analysis under fracture seepage.

Conclusions
e influence of anisotropy of slope fracture on the rainwater infiltration process of slope soil is simulated by the numerical method, and the following conclusions are obtained: (1) e fracture depth, permeability coefficient ratio, fracture angle, and fracture density all affect the infiltration of rainwater to a certain extent and mainly reflect in the influence on pore water pressure, infiltration rate of rainwater, infiltration depth, and infiltration range.It is worth considering in slope stability analysis and slope drainage design.(2) Under the same rainfall conditions, the greater the fracture depth, the greater the pore water pressure in the fissure, and the greater the influence range on the slope.e effect of the permeability coefficient ratio  on the in ltration process of rainwater is mainly related to the relative size of the permeability coe cient and rainfall intensity.When the permeability coe cient is less than the rainfall intensity, the in uence of μ on the in ltration process of rainwater is small.While the permeability coe cient is greater than the rainfall intensity, the in uence of μ on the in ltration process of rainwater becomes more and more signi cant.(3) Fracture angle has little e ect on the distribution law of pore water pressure.e in uence of rainwater on the surface layer of slope is big when the angle is large.For small fracture angle, rainwater has a greater in ltration depth.(4) Under the same rainfall condition, the area of the saturated zone increases exponentially with the number of fractures.e concentrated distribution of long fractures is the direct cause of the large-scale connected saturated zone in the slope and the rise of the groundwater level.Advances in Civil Engineering

Figure 4 :
Figure 4: Fracture permeability coefficient in the global coordinate system.

Figure 7 :Figure 5 :Figure 6 :
Figure 7: Distribution curves of pore water pressure with depth in different fracture permeability coefficient ratios (x � 15 m).

Figure 8 :
Figure 8: Distribution curve of the permeability coefficient with depth in different fracture permeability coefficient ratios (x � 15 m).

Figure 10 :
Figure 10: Distribution curves of pore water pressure with depth in di erent fracture angles (fracture depth 3 m).

Figure 12 :
Figure 12: Effect of fracture quantity on pore water pressure field (fracture depth 3 m, unit: kPa).

Figure 13 :
Figure 13: e relationship between the fracture numbers and the area of saturation.

Figure 14 :
Figure 14: e distribution of the phreatic line with the rainfall time when the fracture density is 5 (fracture depth 3 m).

Table 1 :
Schemes for numerical analysis.