# Analysis of Influencing Parameters of the Improved Model for Rainfall Infiltration in Unsaturated Tailings Soil

Authors: Qingchao Yang; Zhe Hao; Wenjing Cheng; Shengyou Lei; Da Teng; Ying Zhang; Xiaoming Wang; Qian Zhang
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

The rainfall infiltration analysis method is an important method for slope stability forecast and prevention. Slope angle and unsaturated soil layers are not shown in the conventional Green-Ampt (GA) infiltration model. In this paper, based on the GA model of rainfall infiltration in tailings slopes, two aspects of slope angle and the proportion of the transition layer of the wet layer are modified. The rainfall infiltration test of unsaturated tailing soil was conducted using a self-developed large-size tailing slope model test device. The results of GA model, improved GA model, and Richards’ equation calculation model are compared. The results show that the difference between the three models is small in the free infiltration stage, but the infiltration rate is lower than that of the GA model. With the gradual increase of rainfall time into the ponding infiltration stage, the expansion depth and infiltration rate of the wetting front of the improved GA model and Richards’ equation are greater than those of the GA model. The difference between the GA model and the improved GA model and Richards’ equation for the extended depth of wetting front increases with the increase of rainfall duration, while the difference of infiltration rate changes in the opposite trend. The results of the improved GA model and Richards’ equation to calculate the expansion depth and infiltration rate of wetting fronts are consistent, and the difference basically tends to stabilize with the increase of rainfall ephemeris. The results of the improved GA model are closer to the measured data, which can provide a reference for analyzing the rainfall infiltration pattern of open pit tailing dams and slope stability research. On the basis of the improved GA model, the influence of slope angle, rain intensity, initial water content, and saturation infiltration coefficient on rainfall infiltration was analyzed, and the analysis of parameter sensitivity indexes showed that slope inclination and initial water content had a greater influence on the model.


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## Body

## 1. Introduction

Tailings storage facility is an important integrated structure for storing tailings [1] and a major source of danger with high potential energy [2]. Due to a large number of unsaturated tailings with loose structures [2, 3], it is easy to cause dam failures under continuous rainfall [4, 5]. Therefore, studying rainfall infiltration law of unsaturated tailings soil and establishing an accurate prediction model is of great theoretical significance and practical value for improving the safe and stable operation of the tailings pond under the condition of rainfall [6] and tailings pond accident prediction [3, 7, 8]. For rainfall infiltration on slopes, many scholars have used simplified rainfall infiltration models to predict the infiltration characteristics of slopes [9]. Green-Ampt (GA) infiltration model [10, 11] is widely used in the study of rainfall infiltration problems on slopes by intuitively solving the advancement of wetting fronts [12]. Jahanshir and Manouchehr [13] and Deng and Zhu [14] further extended the applicability of the GA model by considering vertically stratified soil parameters and effective suction values. Yao et al. [15] explored the effect of the extended model on the shallow stability of slopes under rainfall conditions. Richa et al. [16] found an analytical expression for the effective saturated hydraulic conductivity and analyzed the infiltration rate of unsaturated soils and the evolutionary characteristics of soil surface moisture under rainfall conditions. Wang et al. [17] established a numerical model of flow-solid coupling on the slope of foundation pits with soil-rock composite strata to analyze the change law of hydraulic coupling caused by rainfall. Guo et al. [18] analyzed the effect of inhomogeneous initial water content on the improved GA model in conjunction with the field monitoring results. Sanghyun et al. [19] investigated a simplified model applying the GA method to a two-layer soil body. Fernández et al. [20] proposed a modified GA model of rainfall and runoff to estimate infiltration rates and cumulative infiltration. Sung [21] and Pan et al. [22] modified the GA model by considering an initial inhomogeneous water content distribution and a constant rainfall intensity. Wen et al. [23] and Peng et al. [24] discussed the stratification characteristics of the GA infiltration model under ponding conditions, but none of them discussed the scaling of the actual stratification thickness and the slope environment under the stratification assumption.At present, the calculation of rainfall infiltration depth has a certain theoretical basis, but the GA model applied to unsaturated tailings soil has more deficiencies, and the improvement of the accuracy of the model also needs further exploration. Therefore, the slope angle of the tailings slope and the ratio of the transition layer to the wetted layer on the slope were modified on the basis of the GA model. The effects of slope angle, rain intensity, initial water content, and saturation infiltration coefficient on the depth of rainfall infiltration were analyzed according to the modified model, and the sensitivity of relevant parameters of the model was analyzed to provide a reference for studying the tailings dams’ stability under the action of rainfall.


## 2. Study Method

### 2.1. Classical GA Infiltration Model

During continuous rainfall, the rainfall infiltration process of slopes is influenced by the slope water content and slope volume water [25] and the traditional GA model was initially used to analyze the saturated infiltration of slopes under rainfall conditions. The schematic diagram of GA infiltration model is shown in Figure 1, according to [26] with some modifications. θs is the saturated water content of unsaturated slope soils; θi is the initial water content of unsaturated slope soil; h0is the depth of water accumulation on the horizontal surface of the unsaturated soil; hdis the depth of the wetting front in the vertical direction.Figure 1
The schematic diagram of GA infiltration model.The soil is assumed as a homogeneous mass in the model. The wetting front formed by the rainfall infiltration serves as the partition interface between the wetted layer’s saturated water content and the unwetted layer’s initial water content. The matrix suction of the soil below the wetting front is considered to be constant.According to the characteristics of rainfall infiltration, it is divided into two stages [19, 26–28]: Stage I is defined as the free infiltration stage, which is characterized by the soil infiltration coefficient greater than the rainfall intensity, so the soil rainfall infiltration boundary is controlled by the rainfall intensity to reflect. Stage II is defined as the ponding infiltration stage, which is characterized by the rainfall intensity greater than the soil infiltration coefficient, so the soil rainfall infiltration boundary is controlled by the soil infiltration capacity to reflect.It is assumed thattp is the time elapsed in the transition from stage I to stage II. Zfp is the depth of the wetting front at the moment of tp.The relationship between the depth of the wetting front and the infiltration time in the free infiltration stage I of rainfall is shown in the following equation:(1)hd=qθs−θit,0≤t≤tp,where q is the magnitude of rainfall intensity; tp=θs−θiSf/qq/ks−1; ks is the saturated permeability coefficient of unsaturated slope soils; and Sf is the substrate potential head of the unwetted layer relative to the saturated layer. The substrate potential head is taken as half of the water potential corresponding to the inlet pressure value of the soil [17, 20, 29].When the infiltration surface is inclined, the accumulation of water is difficult to happen. The effect of water accumulationh0 is negligible. The depth of the wetting front as a function of rainfall time is given in the following equation:(2)t−tp=θs−θikszf−zp−sfInzs+sfzfp+sf,t>tp,where Zfp=Sf/q/ks−1.Equations (1) and (2) are the control equations of the traditional GA infiltration model, which are simple in structure and convenient to solve. However, the influence of slope angle and unsaturated zone on rainfall infiltration was not considered in the equations, which deviates greatly from the actual situation.


### 2.2. Improved Infiltration Model

According to seepage characteristics of unsaturated tailings soil air in the pore space prevents the wetted zone from being fully saturated [3, 30]. Based on the assumption of saturated-unsaturated stratification of rainfall infiltration in tailings slope, the schematic diagram of improved GA infiltration model is shown in Figure 2.Figure 2
The schematic diagram of improved GA infiltration model.The basic assumptions of the improved GA infiltration model are as follows:(1)
Following the GA model, a well-defined wetting front exists, and the water content of the soil before the wetting front is the initial water content.(2)
The tailing soil slope is divided into wetted and unwetted layers, and the infiltration process adopts the layering assumption, and the wetted layer is divided into the saturated and transition layers.(3)
To improve the accuracy of calculating the moisture content of the wetted layer during rainfall, a 1/4 elliptical curve representation is used.Assumptions (1) and (2) have been used extensively in the published literature [23, 24, 28, 31–34] which have been shown to be reasonable, where the intersection of the transition region with the natural region is referred to as the wetted peak surface.The experimental results of hypothesis (3) in the published literature [23, 24, 33, 34] have verified the reasonableness of hypothesis (3).Saturation layer is as follows:(3)θh=θs,0≤h≤hp.Transition layer is as follows:(4)θh=θd+θs−θd1−h−hs/hw2hs≤h≤hd.Unwetted layer is as follows:(5)θh=θd,h≥hd.In published literatures [15, 23, 24, 33, 34], experimental results have verified the validity and correctness of the equations for the volumetric water content (3)–(5) of the soil profile.(6)hs=hd−hw=1−λhd,where hs is the saturation layer depth; hw is the transition layer depth; hd is the unwetted layer depth; and λ=hw/hd.Cumulative measurement of rainwater infiltration into unsaturated tailings soil is as follows:(7)I=∫0hθh−θddh.Saturation layer is as follows:(8)Is=θs−θdhs.Transition layer is as follows:(9)Iw=π4θs−θdhw,I=Is+Iw=θs−θdhs+π4θs−θdhw.It is assumed that, in the initial stage of slope rainfall, rainfall can completely penetrate into tailings soil.(10)i=qcosβ,where β is the slope angle and i is the infiltration rate.According to Darcy’s law, the infiltration rate during the infiltration stage of ponded water can be expressed as follows:(11)i=kshscosβ+Sf′+h0hs,where Sf′ is the matrix potential head applied to the saturated layer by the transition layer.It is obtained according to the studies of Peng et al. [24] and Zhu and Duan [27].(12)Sf′=k¯ksSf=1−ki/kslnks/kiSf,where k¯ is the equivalent value of permeability coefficient of transition layer soil and ki is the equivalent values of permeability coefficients for unsaturated soils in the unwetted layer.It is assumed thattp is the time elapsed in transition from stage I to stage II. The wetting front depth and infiltration rate of unsaturated slope vertical slope at the moment of tp are Zp and ip, respectively.(13)qcosβdt=4+π−4λ4θs−θidhd,qcosβ=ip=ks1−λhdcosβ+Sf′+h01−λhd.When the infiltration surface is inclined, water accumulation can hardly occur. The accumulation of waterh0 can be ignored. It can be simplified to the following equation:(14)hd=4qcosβ4+π−4λθs−θit0≤t≤tp.The depth of rainfall infiltration when ponding infiltration first begins to occur ishp.(15)hp=Sf′1−λcosβq/ks−1.The time required for infiltration of accumulated water to occur istp.(16)tp=4+π−4λθs−θiSf′41−λqcos2βq/ks−1.After entering stage II,(17)ksλhdcosβ+Sf′+h0λhddt=4+π−4λ4θs−θidhd,t>tp,note the boundary conditions t=tp and hd=hp, while ignoring h, the differential equation is solved.(18)t−tp=4+π−4λ4kscosβθs−θihd−hp−Sf′λcosβΙnSf′+λcosβhdSf′+λcosβhp,t>tp,In summary, the effects of slope angle and unsaturated zone layer conditions were considered in equations (14) and (18) for the rainfall infiltration model.


## 2.1. Classical GA Infiltration Model

During continuous rainfall, the rainfall infiltration process of slopes is influenced by the slope water content and slope volume water [25] and the traditional GA model was initially used to analyze the saturated infiltration of slopes under rainfall conditions. The schematic diagram of GA infiltration model is shown in Figure 1, according to [26] with some modifications. θs is the saturated water content of unsaturated slope soils; θi is the initial water content of unsaturated slope soil; h0is the depth of water accumulation on the horizontal surface of the unsaturated soil; hdis the depth of the wetting front in the vertical direction.Figure 1
The schematic diagram of GA infiltration model.The soil is assumed as a homogeneous mass in the model. The wetting front formed by the rainfall infiltration serves as the partition interface between the wetted layer’s saturated water content and the unwetted layer’s initial water content. The matrix suction of the soil below the wetting front is considered to be constant.According to the characteristics of rainfall infiltration, it is divided into two stages [19, 26–28]: Stage I is defined as the free infiltration stage, which is characterized by the soil infiltration coefficient greater than the rainfall intensity, so the soil rainfall infiltration boundary is controlled by the rainfall intensity to reflect. Stage II is defined as the ponding infiltration stage, which is characterized by the rainfall intensity greater than the soil infiltration coefficient, so the soil rainfall infiltration boundary is controlled by the soil infiltration capacity to reflect.It is assumed thattp is the time elapsed in the transition from stage I to stage II. Zfp is the depth of the wetting front at the moment of tp.The relationship between the depth of the wetting front and the infiltration time in the free infiltration stage I of rainfall is shown in the following equation:(1)hd=qθs−θit,0≤t≤tp,where q is the magnitude of rainfall intensity; tp=θs−θiSf/qq/ks−1; ks is the saturated permeability coefficient of unsaturated slope soils; and Sf is the substrate potential head of the unwetted layer relative to the saturated layer. The substrate potential head is taken as half of the water potential corresponding to the inlet pressure value of the soil [17, 20, 29].When the infiltration surface is inclined, the accumulation of water is difficult to happen. The effect of water accumulationh0 is negligible. The depth of the wetting front as a function of rainfall time is given in the following equation:(2)t−tp=θs−θikszf−zp−sfInzs+sfzfp+sf,t>tp,where Zfp=Sf/q/ks−1.Equations (1) and (2) are the control equations of the traditional GA infiltration model, which are simple in structure and convenient to solve. However, the influence of slope angle and unsaturated zone on rainfall infiltration was not considered in the equations, which deviates greatly from the actual situation.


## 2.2. Improved Infiltration Model

According to seepage characteristics of unsaturated tailings soil air in the pore space prevents the wetted zone from being fully saturated [3, 30]. Based on the assumption of saturated-unsaturated stratification of rainfall infiltration in tailings slope, the schematic diagram of improved GA infiltration model is shown in Figure 2.Figure 2
The schematic diagram of improved GA infiltration model.The basic assumptions of the improved GA infiltration model are as follows:(1)
Following the GA model, a well-defined wetting front exists, and the water content of the soil before the wetting front is the initial water content.(2)
The tailing soil slope is divided into wetted and unwetted layers, and the infiltration process adopts the layering assumption, and the wetted layer is divided into the saturated and transition layers.(3)
To improve the accuracy of calculating the moisture content of the wetted layer during rainfall, a 1/4 elliptical curve representation is used.Assumptions (1) and (2) have been used extensively in the published literature [23, 24, 28, 31–34] which have been shown to be reasonable, where the intersection of the transition region with the natural region is referred to as the wetted peak surface.The experimental results of hypothesis (3) in the published literature [23, 24, 33, 34] have verified the reasonableness of hypothesis (3).Saturation layer is as follows:(3)θh=θs,0≤h≤hp.Transition layer is as follows:(4)θh=θd+θs−θd1−h−hs/hw2hs≤h≤hd.Unwetted layer is as follows:(5)θh=θd,h≥hd.In published literatures [15, 23, 24, 33, 34], experimental results have verified the validity and correctness of the equations for the volumetric water content (3)–(5) of the soil profile.(6)hs=hd−hw=1−λhd,where hs is the saturation layer depth; hw is the transition layer depth; hd is the unwetted layer depth; and λ=hw/hd.Cumulative measurement of rainwater infiltration into unsaturated tailings soil is as follows:(7)I=∫0hθh−θddh.Saturation layer is as follows:(8)Is=θs−θdhs.Transition layer is as follows:(9)Iw=π4θs−θdhw,I=Is+Iw=θs−θdhs+π4θs−θdhw.It is assumed that, in the initial stage of slope rainfall, rainfall can completely penetrate into tailings soil.(10)i=qcosβ,where β is the slope angle and i is the infiltration rate.According to Darcy’s law, the infiltration rate during the infiltration stage of ponded water can be expressed as follows:(11)i=kshscosβ+Sf′+h0hs,where Sf′ is the matrix potential head applied to the saturated layer by the transition layer.It is obtained according to the studies of Peng et al. [24] and Zhu and Duan [27].(12)Sf′=k¯ksSf=1−ki/kslnks/kiSf,where k¯ is the equivalent value of permeability coefficient of transition layer soil and ki is the equivalent values of permeability coefficients for unsaturated soils in the unwetted layer.It is assumed thattp is the time elapsed in transition from stage I to stage II. The wetting front depth and infiltration rate of unsaturated slope vertical slope at the moment of tp are Zp and ip, respectively.(13)qcosβdt=4+π−4λ4θs−θidhd,qcosβ=ip=ks1−λhdcosβ+Sf′+h01−λhd.When the infiltration surface is inclined, water accumulation can hardly occur. The accumulation of waterh0 can be ignored. It can be simplified to the following equation:(14)hd=4qcosβ4+π−4λθs−θit0≤t≤tp.The depth of rainfall infiltration when ponding infiltration first begins to occur ishp.(15)hp=Sf′1−λcosβq/ks−1.The time required for infiltration of accumulated water to occur istp.(16)tp=4+π−4λθs−θiSf′41−λqcos2βq/ks−1.After entering stage II,(17)ksλhdcosβ+Sf′+h0λhddt=4+π−4λ4θs−θidhd,t>tp,note the boundary conditions t=tp and hd=hp, while ignoring h, the differential equation is solved.(18)t−tp=4+π−4λ4kscosβθs−θihd−hp−Sf′λcosβΙnSf′+λcosβhdSf′+λcosβhp,t>tp,In summary, the effects of slope angle and unsaturated zone layer conditions were considered in equations (14) and (18) for the rainfall infiltration model.


## 3. Experimental Validation of Rainfall Model for Tailings Slope

### 3.1. Experimental Model

The self-developed test device for tailings rainfall infiltration model includes a model box and rainfall device, as shown in Figure3. The test model’s length, width, and height are 7 m, 1.2 m, and 1.8 m, respectively, forming a five-sided closed rectangular body. One side is a 7 m long transparent plexiglass board with the thickness of 1 cm, the other three sides are made of cement brick, the top is open, the bottom is evenly paved with a 10 cm thick gravel layer, and the permeable geotextile is laid above to form the tailing slope drainage channel. The rainfall system of rainfall infiltration model test device is mainly composed of automatic water make-up ball valve water tank, automatic frequency conversion constant pressure water pump, plastic water pipe, stainless steel vacuum water pressure gauge, high-precision electronic turbine flowmeter, rainfall device, electric elevator, and water retaining curtain. Rainfall device uses 20 mm diameter PVC pipe with 50 mm hole spacing and 1 mm diameter of the hole. The elbow is connected by right-angle tees. The rainfall intensity is controlled by a flow meter and copper valve, and the range of rainfall intensity is 10∼280 mm/h to follow the test setting requirements. The elevator is adopted in the model system to adjust the height of the rainfall device, and the maximum height above the ground can reach 4.5 m. The water retaining curtain is set around the rainfall device to prevent the rainfall splashing.Figure 3
Rainfall test model for tailings slope.


### 3.2. Model Filling

To better match the actual operating conditions of tailings dams, tailings sands were excavated using the profile method to locate within 2 m of the burial depth in front of a tailings pond site [25]. The slope in the tailing model tank is 4.48 m long, 1.2 mm wide, 1.2 m high. The layered compaction method is used to establish the model of dam construction, as shown in Figure 4.Figure 4
Schematic diagram of model filling (distance measured in mm).


### 3.3. Monitoring Equipment and Programs

In the rainfall model, the nozzles of the simulated rainfall device were evenly distributed at a 4.5 m vertical distance of rainfall device from the horizontal surface of the bottom of the slope, and the rainfall intensity was set at 20 mm/h for this test. The rainfall intensity test was completed before the test. Firstly, the rain cloth was used to cover the test model. After the rainfall intensity reached 20 mm/h and the monitoring values were stable, the rain cloth was removed to start the formal experiment, and the rainfall lasted for 5 hours. Because the groundwater depth of the large- and medium-sized tailings pond slope is more than 4 m in practical, far lower than the rainfall infiltration area, this paper ignores the influence of groundwater on slope infiltration. The water content and pore water pressure sensors were arranged at the toe, middle, and shoulder of the tailings dam, and the vertical distance from the slope surface was 10, 20, and 30 cm, respectively, represented byT and U. In order to avoid mutual interference between T and U sensors in the same layer, they were arranged with a horizontal interval of 60 cm. The sensor number and position are represented by Txy and Uxy, where x indicates the sensor position number and y indicates the sensor’s vertical depth from the slope.For example, T110 is a soil volumetric moisture sensor with a vertical depth of 10 cm in the middle of the slope. The sensor in the model is linked with the data acquisition instrument, and the data is automatically recorded every 1 min. The tensiometer is 10 cm away from the boundary of the model and 56 cm away from the toe and shoulder of the slope, and the horizontal distance between each tensiometer is 112 cm. S represents tensiometer, the meanings ofx and y are the same as mentioned above, and the data is recorded every 10 min. The specific burial location of the monitoring equipment is shown in Figure 5.Figure 5
Detection equipment installation location map (distance measured in mm): (a) sensor burial location map; (b) sensor location plan.
(a)(b)


## 3.1. Experimental Model

The self-developed test device for tailings rainfall infiltration model includes a model box and rainfall device, as shown in Figure3. The test model’s length, width, and height are 7 m, 1.2 m, and 1.8 m, respectively, forming a five-sided closed rectangular body. One side is a 7 m long transparent plexiglass board with the thickness of 1 cm, the other three sides are made of cement brick, the top is open, the bottom is evenly paved with a 10 cm thick gravel layer, and the permeable geotextile is laid above to form the tailing slope drainage channel. The rainfall system of rainfall infiltration model test device is mainly composed of automatic water make-up ball valve water tank, automatic frequency conversion constant pressure water pump, plastic water pipe, stainless steel vacuum water pressure gauge, high-precision electronic turbine flowmeter, rainfall device, electric elevator, and water retaining curtain. Rainfall device uses 20 mm diameter PVC pipe with 50 mm hole spacing and 1 mm diameter of the hole. The elbow is connected by right-angle tees. The rainfall intensity is controlled by a flow meter and copper valve, and the range of rainfall intensity is 10∼280 mm/h to follow the test setting requirements. The elevator is adopted in the model system to adjust the height of the rainfall device, and the maximum height above the ground can reach 4.5 m. The water retaining curtain is set around the rainfall device to prevent the rainfall splashing.Figure 3
Rainfall test model for tailings slope.


## 3.2. Model Filling

To better match the actual operating conditions of tailings dams, tailings sands were excavated using the profile method to locate within 2 m of the burial depth in front of a tailings pond site [25]. The slope in the tailing model tank is 4.48 m long, 1.2 mm wide, 1.2 m high. The layered compaction method is used to establish the model of dam construction, as shown in Figure 4.Figure 4
Schematic diagram of model filling (distance measured in mm).


## 3.3. Monitoring Equipment and Programs

In the rainfall model, the nozzles of the simulated rainfall device were evenly distributed at a 4.5 m vertical distance of rainfall device from the horizontal surface of the bottom of the slope, and the rainfall intensity was set at 20 mm/h for this test. The rainfall intensity test was completed before the test. Firstly, the rain cloth was used to cover the test model. After the rainfall intensity reached 20 mm/h and the monitoring values were stable, the rain cloth was removed to start the formal experiment, and the rainfall lasted for 5 hours. Because the groundwater depth of the large- and medium-sized tailings pond slope is more than 4 m in practical, far lower than the rainfall infiltration area, this paper ignores the influence of groundwater on slope infiltration. The water content and pore water pressure sensors were arranged at the toe, middle, and shoulder of the tailings dam, and the vertical distance from the slope surface was 10, 20, and 30 cm, respectively, represented byT and U. In order to avoid mutual interference between T and U sensors in the same layer, they were arranged with a horizontal interval of 60 cm. The sensor number and position are represented by Txy and Uxy, where x indicates the sensor position number and y indicates the sensor’s vertical depth from the slope.For example, T110 is a soil volumetric moisture sensor with a vertical depth of 10 cm in the middle of the slope. The sensor in the model is linked with the data acquisition instrument, and the data is automatically recorded every 1 min. The tensiometer is 10 cm away from the boundary of the model and 56 cm away from the toe and shoulder of the slope, and the horizontal distance between each tensiometer is 112 cm. S represents tensiometer, the meanings ofx and y are the same as mentioned above, and the data is recorded every 10 min. The specific burial location of the monitoring equipment is shown in Figure 5.Figure 5
Detection equipment installation location map (distance measured in mm): (a) sensor burial location map; (b) sensor location plan.
(a)(b)


## 4. Model Validation and Analysis

### 4.1. Model Validation

The basic physical and mechanical parameters of the tailing soil at a depth of 5 cm from the slope surface in the model trough were precisely measured, as shown in Table1. The soil and water characteristic curve and permeability coefficient curve of the tailing soil are shown in Figure 6 and Figure 7.Table 1
Properties of tailing soil at 5 cm depth.
PropertyValueNatural moisture content,ω (%)12.3Natural density,ρ (g/cm3)1.84Granule density,Gs (g/m3)2.71Saturated permeability coefficient (cm/s)4.15 × 10−4Poisson’s ratio,e0.33Liquid limit,WL (%)26.7Plastic limit,Wp (%)16.1Sf (m)1.0Sf′ (m)0.8Figure 6
Soil and water characteristic curve.Figure 7
Permeability coefficient curve.The positions T110, T120, and T130 were selected, and the moisture sensor data were collated when the wetting front arrived at different depths; the variation curves of volumetric moisture content with rainfall duration at different depths are shown in Figure8.Figure 8
Variation curve of water content with rainfall calendar time.Figure8 shows that once the moisture sensor in the model soil responds, the volumetric water content gradually increases from the initial 12% to 30% in a saturated state with the increase of rainfall duration. It indicates that the layers transit from the initial state to the saturated state with the moisture content in the soil at each depth under the rainfall conditions.Figure9 shows the variation of pore water pressure and wetting front depth with different rainfall durations. The curves U120, U220, and U320 in the figure are the measurement data of each measuring point, and the wetting layer front depth of the curve is calculated using the improved GA model. When the rainfall duration is less than 114 min (t < 114 min), the pore water pressure at each measurement point did not change significantly. When t = 114 min, the pore water pressure at measurement point U220 began to increase, indicating that the wetting front has reached 20 cm depth at this time. The pore water pressure at U120 and U320 measurement points only started to increase when t = 114 min, mainly because the rainfall intensity at U120 and U320 measurement points was less than 20 mm/h due to the distance from the rainfall point. After the wetting front reached each measurement point, the pore water pressure continued to increase until t = 182 min, and the saturated layer reached 20 cm, which further confirmed the obvious stratification phenomenon in the wetting layer. According to the response time of pore water pressure and water content sensor, the average depth ratio of transition layer to wetted layer is 0.43 when the depth of the wetted layer reaches 20 cm, t = 117 min, which is basically consistent with the model test results and verifies the correctness of the improved GA model.Figure 9
Pore water pressure and calculated depth in different locations at the same depth.


### 4.2. Comparative Analysis of Infiltration Models

To further validate the method proposed in this paper, the GA model, the improved GA model, and Richards’ equation [35] were compared with the dynamic change law of wetting front and infiltration rate of unsaturated tailings soil slopes under rainfall conditions. In this paper, Geo-studio is used to establish the numerical model and Seep/W module to solve Richards’ equation [36, 37]. The computational model is built with the 2.2 model, and the full mechanics parameters and seepage characteristics parameters are shown in 3.1. Richards’ equation model is shown in Figure 10, with 591 cells and 645 nodes of the grid. The slope surface of the slope is set as the rainfall boundary, and the bottom and both sides of the slope are set as the impermeable boundary. Monitoring lines of rainfall intensity and infiltration depth are shown in 2.3.Figure 10
Calculation model.The relationship between wetting front depth and time in the GA model, the improved GA model, and Richards’ equation calculation model is shown in Figure11. It can be seen from Figure 11 that the depths of the wetting fronts of the three models match well at the beginning (t < 30 min), and the differences are small. With the increase of rainfall time, the difference of wet front depth of the three models starts to increase. When rainfall time is 152 min, the depth of the wet front obtained by Richards’ equation calculation model is about 0.47 m larger than that of the improved GA model. When rainfall time increases to 722 min, the difference increases to 0.60 m, and then the difference basically stabilizes. The difference between the wet front depth calculated by the GA model and that obtained by the improved GA model and Richards’ equation calculation model keeps increasing.Figure 11
Depth change curve of wetting front.Select T110, T120, and T130 positions, according to the time when the wetting front reaches the depth, compare the calculated values of the three models with the measured values of the infiltration test, as shown in Table2. It can be seen that the calculated values of layered assumption model are in good agreement with the measured data. The improved GA model is only slightly higher than the measured value, with a maximum deviation of about 27 min. However, the GA model deviates from the measured values, and the deviation increases with increasing depth.Table 2
Statistical table of measured data and model calculated parameters.
TypeArrival time of wetting front/minPonding infiltrationduration/minInfiltration depth at thebeginning of ponding infiltration/cm10 cm20 cm30 cmGA model55153302307.8Richards’ equation calculation model52135266——Improved GA model431232294612.9Measurement3311420252—Figure12 shows the rainfall infiltration rate curve of tailings slope with rainfall duration. The infiltration rate of the improved GA model in rainfall infiltration stage I is slower than that of the GA model, and the difference between the two is less than 1 mm/h. After reaching the rainfall infiltration stage II, the infiltration rate of the improved GA model gradually exceeds that of the GA model. The gap between the two models reaches the maximum of 4 mm/h at 70 min, then gradually decreases with the continuous infiltration, and remains at 2 mm/h. The rainfall duration for ponding infiltration calculated by the modified GA model and GA model is 30 min and 46 min, respectively. The GA model is 22 min slower than the measured value, while the modified GA model is 6 min slower than the measured value. The infiltration depth calculated by the GA model at the beginning of ponding infiltration is 5.1 cm less than the results of the modified GA model.Figure 12
Infiltration rate of the slope with rainfall duration.The GA model and the improved GA model predict slightly different results compared to Richards’ equation. Here the GA model predicts smaller ponding time, smaller vertical infiltration depth in early time and higher infiltration depth in later time, and higher infiltration rates for most of the time. Since the infiltration rate is related to the infiltration coefficient and the hydraulic gradient, the numerical simulation of the improved GA model and Richards’ equation calculation model takes into account the effects of the dip angle on the hydraulic gradient and the unsaturated zone on the infiltration coefficient. For the sloping surface case, the improved GA model performs well, capturing both the trend of enhanced infiltration on the slope and the trend of changes in the calculated results of Richards’ equation. With the increase of rainfall time, the difference of infiltration rate finally remained basically around 1.52 mm/h. There is a great deviation from the infiltration rate obtained by GA model.There are two main model differences reasons: (1) The stratification assumption model corrects for the cumulative infiltration of rainfall infiltration processes. (2) The average matrix suction head of the unsaturated layer is regarded as the matrix potential on the saturated layer, and the effects of slope angle and the ratio of the transition layer to the wetted layer are taken into account, thus correcting the conventional GA model.


### 4.3. Influence Factors of Rainfall Infiltration

#### 4.3.1. Tailings Pond Slope Angle

Figure13 shows the variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and slope angles when the initial water content is 12%, the rainfall intensity is 20 mm/h, and the saturation infiltration coefficient is 4.15 × 10−4 cm/s. The rainfall time required for rainfall to infiltrate to the same depth of the slope body increases with increasing slope angle, and this phenomenon is more significant when the slope angle is greater than 60°. The reason is that when the slope angle exceeds 60°, the gradient of rainfall and infiltration potential energy per unit area of slope surface decreases greatly, which causes more difficulty in the infiltration of rainfall in the soil of the slope.Figure 13
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and slope angles.


#### 4.3.2. Rainfall Intensity

When the slope angle is 30°, the initial water content is 12%, the saturation infiltration coefficient is 4.15 × 10−4 cm/s, the variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and rainfall intensity is shown in Figure 14. It can be seen that the rainfall ephemeris required for rainfall infiltration to the same depth of the slope decreases with the increase of rainfall intensity, and this phenomenon is more obvious when the rainfall intensity is less than 20 mm/h. From 1.2 above, it can be seen that, in stage I of rainfall infiltration, rainfall intensity affects the amount of rainfall received on the slope unit area, thus affecting the infiltration of slope soil, and the rate of rainfall infiltration is determined by rainfall intensity; however, when rainfall infiltration reaches stage II, it can be seen from Figure 4 that rainfall intensity exceeding 20 mm/h has less influence on rainfall infiltration, which is because the rate of rainfall infiltration in this stage is controlled by the infiltration capacity of slope soil and is not related to rainfall intensity. Therefore, rainfall intensity mainly affects the relationship between infiltration depth and rainfall duration with the slope ponding infiltration time changes.Figure 14
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and rainfall intensity.


#### 4.3.3. Initial Water Content

When the slope angle is 30°, the rainfall intensity is 20 mm/h, and the saturation infiltration coefficient is 4.15 × 10−4 cm/s. The variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and initial water content is shown in Figure 15. The rainfall duration required for rainfall infiltration to the same depth in the slope decreases gradually with increasing initial water content, and this phenomenon is more obvious at an initial water content of 25%. This is caused by the increase of rainfall infiltration depth in the tailings soil with the increase of initial water content. The effect of initial water content on the depth of infiltration of the model response deepens with time for a constant infiltration time.Figure 15
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and initial water content.


#### 4.3.4. Saturation Permeability Coefficient

When the slope angle is 30°, the rainfall intensity is 20 mm/h, and the initial moisture content is 12%, the variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and infiltration coefficient is shown in Figure16. The rainfall duration required for rainfall infiltration at the same depth gradually increases with the decrease of permeability coefficient, which is more obvious when the saturated infiltration coefficient is 2 × 10−4 cm/s. The influence of soil permeability coefficient on rainfall infiltration becomes more significant with the increase of depth. The reason is that the infiltration rate of rainfall is controlled by the infiltration capacity of slope soil in stage II of water infiltration.Figure 16
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and infiltration coefficient.


### 4.4. Sensitivity Analysis of Influencing Parameters of Rainfall Infiltration

In this paper, the rainfall infiltration impact parameters are normalized (Table3) [38, 39] and sensitivity analysis is conducted according to the sensitivity classification [40].Table 3
Parameter sensitivity classification.
ClassificationIndexSusceptibilityI0 ≤ |I| ≤ 0.05InsensitiveII0.05 ≤ |I| ≤ 0.2Commonly sensitiveIII0.2 ≤ |I| ≤ 1Highly sensitiveIV|I| ≥ 1Overwhelming sensitiveThe amplitude of variation of the key model parametersβ, q, θi, and ks is uniformly set to 20% [23, 40], and the sensitivity index is calculated as follows:(19)I=ΔOΔFiFiO,where O is the model output; Fi is the parameters that affect the model output results; ΔO is the change value of the model output result; and ΔFi is the amount of parameter change that affects the model output results.The results of the sensitivity index calculations for the key parameters affecting the depth of rainfall infiltration are shown in Table4. The positive and negative signs in the table indicate that the parameter changes are positively or negatively correlated with the model calculated values [40].Table 4
Sensitivity analysis of rainfall infiltration depth.
NumberInput parametersValue rangeOutput objective function (depth of infiltration at different times) corresponding to sensitivity indexSensitivity levelh30h60h90h120h180h2401β200.17−1.06−3.99−6.13−7.51−8.79IV−200.170.574.235.425.975.91IV2q200.32−0.05−0.16−0.26−0.34−0.38III−20−0.04−0.16−0.22−0.26−0.29−0.3III3θi200.080.070.230.310.390.42III−200.32−0.05−0.16−0.26−0.34−0.38III4ks20<0.05<0.050.10.090.080.08II−20<0.05−0.11−0.1−0.09−0.08−0.08IIFrom Table4, it can be seen that the four model parameters ranked by the sensitivity are β ≥ θi≥ q ≥ ks. When the angle of tailings slope increases by 20%, the sensitivity index belongs to grade IV, and the maximum sensitivity index attains 8.79. However, when it goes down by 20%, the sensitivity index belongs to class IV. When the model parameter saturation permeability coefficient is floated up by 20%, its maximum sensitivity coefficient is 0.1. When it goes down by 20%, its maximum sensitivity index is 0.11, and its sensitivity index belongs to class II. At the same time, when the two model parameters of rainfall intensity and initial water content float up and down by 20%, the sensitivity indices are relatively the same, both of which belong to class III. Therefore, when applying this model for tailings dam slope design and stability evaluation, the parameters β and θi should be considered first.


## 4.1. Model Validation

The basic physical and mechanical parameters of the tailing soil at a depth of 5 cm from the slope surface in the model trough were precisely measured, as shown in Table1. The soil and water characteristic curve and permeability coefficient curve of the tailing soil are shown in Figure 6 and Figure 7.Table 1
Properties of tailing soil at 5 cm depth.
PropertyValueNatural moisture content,ω (%)12.3Natural density,ρ (g/cm3)1.84Granule density,Gs (g/m3)2.71Saturated permeability coefficient (cm/s)4.15 × 10−4Poisson’s ratio,e0.33Liquid limit,WL (%)26.7Plastic limit,Wp (%)16.1Sf (m)1.0Sf′ (m)0.8Figure 6
Soil and water characteristic curve.Figure 7
Permeability coefficient curve.The positions T110, T120, and T130 were selected, and the moisture sensor data were collated when the wetting front arrived at different depths; the variation curves of volumetric moisture content with rainfall duration at different depths are shown in Figure8.Figure 8
Variation curve of water content with rainfall calendar time.Figure8 shows that once the moisture sensor in the model soil responds, the volumetric water content gradually increases from the initial 12% to 30% in a saturated state with the increase of rainfall duration. It indicates that the layers transit from the initial state to the saturated state with the moisture content in the soil at each depth under the rainfall conditions.Figure9 shows the variation of pore water pressure and wetting front depth with different rainfall durations. The curves U120, U220, and U320 in the figure are the measurement data of each measuring point, and the wetting layer front depth of the curve is calculated using the improved GA model. When the rainfall duration is less than 114 min (t < 114 min), the pore water pressure at each measurement point did not change significantly. When t = 114 min, the pore water pressure at measurement point U220 began to increase, indicating that the wetting front has reached 20 cm depth at this time. The pore water pressure at U120 and U320 measurement points only started to increase when t = 114 min, mainly because the rainfall intensity at U120 and U320 measurement points was less than 20 mm/h due to the distance from the rainfall point. After the wetting front reached each measurement point, the pore water pressure continued to increase until t = 182 min, and the saturated layer reached 20 cm, which further confirmed the obvious stratification phenomenon in the wetting layer. According to the response time of pore water pressure and water content sensor, the average depth ratio of transition layer to wetted layer is 0.43 when the depth of the wetted layer reaches 20 cm, t = 117 min, which is basically consistent with the model test results and verifies the correctness of the improved GA model.Figure 9
Pore water pressure and calculated depth in different locations at the same depth.


## 4.2. Comparative Analysis of Infiltration Models

To further validate the method proposed in this paper, the GA model, the improved GA model, and Richards’ equation [35] were compared with the dynamic change law of wetting front and infiltration rate of unsaturated tailings soil slopes under rainfall conditions. In this paper, Geo-studio is used to establish the numerical model and Seep/W module to solve Richards’ equation [36, 37]. The computational model is built with the 2.2 model, and the full mechanics parameters and seepage characteristics parameters are shown in 3.1. Richards’ equation model is shown in Figure 10, with 591 cells and 645 nodes of the grid. The slope surface of the slope is set as the rainfall boundary, and the bottom and both sides of the slope are set as the impermeable boundary. Monitoring lines of rainfall intensity and infiltration depth are shown in 2.3.Figure 10
Calculation model.The relationship between wetting front depth and time in the GA model, the improved GA model, and Richards’ equation calculation model is shown in Figure11. It can be seen from Figure 11 that the depths of the wetting fronts of the three models match well at the beginning (t < 30 min), and the differences are small. With the increase of rainfall time, the difference of wet front depth of the three models starts to increase. When rainfall time is 152 min, the depth of the wet front obtained by Richards’ equation calculation model is about 0.47 m larger than that of the improved GA model. When rainfall time increases to 722 min, the difference increases to 0.60 m, and then the difference basically stabilizes. The difference between the wet front depth calculated by the GA model and that obtained by the improved GA model and Richards’ equation calculation model keeps increasing.Figure 11
Depth change curve of wetting front.Select T110, T120, and T130 positions, according to the time when the wetting front reaches the depth, compare the calculated values of the three models with the measured values of the infiltration test, as shown in Table2. It can be seen that the calculated values of layered assumption model are in good agreement with the measured data. The improved GA model is only slightly higher than the measured value, with a maximum deviation of about 27 min. However, the GA model deviates from the measured values, and the deviation increases with increasing depth.Table 2
Statistical table of measured data and model calculated parameters.
TypeArrival time of wetting front/minPonding infiltrationduration/minInfiltration depth at thebeginning of ponding infiltration/cm10 cm20 cm30 cmGA model55153302307.8Richards’ equation calculation model52135266——Improved GA model431232294612.9Measurement3311420252—Figure12 shows the rainfall infiltration rate curve of tailings slope with rainfall duration. The infiltration rate of the improved GA model in rainfall infiltration stage I is slower than that of the GA model, and the difference between the two is less than 1 mm/h. After reaching the rainfall infiltration stage II, the infiltration rate of the improved GA model gradually exceeds that of the GA model. The gap between the two models reaches the maximum of 4 mm/h at 70 min, then gradually decreases with the continuous infiltration, and remains at 2 mm/h. The rainfall duration for ponding infiltration calculated by the modified GA model and GA model is 30 min and 46 min, respectively. The GA model is 22 min slower than the measured value, while the modified GA model is 6 min slower than the measured value. The infiltration depth calculated by the GA model at the beginning of ponding infiltration is 5.1 cm less than the results of the modified GA model.Figure 12
Infiltration rate of the slope with rainfall duration.The GA model and the improved GA model predict slightly different results compared to Richards’ equation. Here the GA model predicts smaller ponding time, smaller vertical infiltration depth in early time and higher infiltration depth in later time, and higher infiltration rates for most of the time. Since the infiltration rate is related to the infiltration coefficient and the hydraulic gradient, the numerical simulation of the improved GA model and Richards’ equation calculation model takes into account the effects of the dip angle on the hydraulic gradient and the unsaturated zone on the infiltration coefficient. For the sloping surface case, the improved GA model performs well, capturing both the trend of enhanced infiltration on the slope and the trend of changes in the calculated results of Richards’ equation. With the increase of rainfall time, the difference of infiltration rate finally remained basically around 1.52 mm/h. There is a great deviation from the infiltration rate obtained by GA model.There are two main model differences reasons: (1) The stratification assumption model corrects for the cumulative infiltration of rainfall infiltration processes. (2) The average matrix suction head of the unsaturated layer is regarded as the matrix potential on the saturated layer, and the effects of slope angle and the ratio of the transition layer to the wetted layer are taken into account, thus correcting the conventional GA model.


## 4.3. Influence Factors of Rainfall Infiltration

### 4.3.1. Tailings Pond Slope Angle

Figure13 shows the variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and slope angles when the initial water content is 12%, the rainfall intensity is 20 mm/h, and the saturation infiltration coefficient is 4.15 × 10−4 cm/s. The rainfall time required for rainfall to infiltrate to the same depth of the slope body increases with increasing slope angle, and this phenomenon is more significant when the slope angle is greater than 60°. The reason is that when the slope angle exceeds 60°, the gradient of rainfall and infiltration potential energy per unit area of slope surface decreases greatly, which causes more difficulty in the infiltration of rainfall in the soil of the slope.Figure 13
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and slope angles.


### 4.3.2. Rainfall Intensity

When the slope angle is 30°, the initial water content is 12%, the saturation infiltration coefficient is 4.15 × 10−4 cm/s, the variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and rainfall intensity is shown in Figure 14. It can be seen that the rainfall ephemeris required for rainfall infiltration to the same depth of the slope decreases with the increase of rainfall intensity, and this phenomenon is more obvious when the rainfall intensity is less than 20 mm/h. From 1.2 above, it can be seen that, in stage I of rainfall infiltration, rainfall intensity affects the amount of rainfall received on the slope unit area, thus affecting the infiltration of slope soil, and the rate of rainfall infiltration is determined by rainfall intensity; however, when rainfall infiltration reaches stage II, it can be seen from Figure 4 that rainfall intensity exceeding 20 mm/h has less influence on rainfall infiltration, which is because the rate of rainfall infiltration in this stage is controlled by the infiltration capacity of slope soil and is not related to rainfall intensity. Therefore, rainfall intensity mainly affects the relationship between infiltration depth and rainfall duration with the slope ponding infiltration time changes.Figure 14
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and rainfall intensity.


### 4.3.3. Initial Water Content

When the slope angle is 30°, the rainfall intensity is 20 mm/h, and the saturation infiltration coefficient is 4.15 × 10−4 cm/s. The variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and initial water content is shown in Figure 15. The rainfall duration required for rainfall infiltration to the same depth in the slope decreases gradually with increasing initial water content, and this phenomenon is more obvious at an initial water content of 25%. This is caused by the increase of rainfall infiltration depth in the tailings soil with the increase of initial water content. The effect of initial water content on the depth of infiltration of the model response deepens with time for a constant infiltration time.Figure 15
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and initial water content.


### 4.3.4. Saturation Permeability Coefficient

When the slope angle is 30°, the rainfall intensity is 20 mm/h, and the initial moisture content is 12%, the variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and infiltration coefficient is shown in Figure16. The rainfall duration required for rainfall infiltration at the same depth gradually increases with the decrease of permeability coefficient, which is more obvious when the saturated infiltration coefficient is 2 × 10−4 cm/s. The influence of soil permeability coefficient on rainfall infiltration becomes more significant with the increase of depth. The reason is that the infiltration rate of rainfall is controlled by the infiltration capacity of slope soil in stage II of water infiltration.Figure 16
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and infiltration coefficient.


## 4.3.1. Tailings Pond Slope Angle

Figure13 shows the variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and slope angles when the initial water content is 12%, the rainfall intensity is 20 mm/h, and the saturation infiltration coefficient is 4.15 × 10−4 cm/s. The rainfall time required for rainfall to infiltrate to the same depth of the slope body increases with increasing slope angle, and this phenomenon is more significant when the slope angle is greater than 60°. The reason is that when the slope angle exceeds 60°, the gradient of rainfall and infiltration potential energy per unit area of slope surface decreases greatly, which causes more difficulty in the infiltration of rainfall in the soil of the slope.Figure 13
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and slope angles.


## 4.3.2. Rainfall Intensity

When the slope angle is 30°, the initial water content is 12%, the saturation infiltration coefficient is 4.15 × 10−4 cm/s, the variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and rainfall intensity is shown in Figure 14. It can be seen that the rainfall ephemeris required for rainfall infiltration to the same depth of the slope decreases with the increase of rainfall intensity, and this phenomenon is more obvious when the rainfall intensity is less than 20 mm/h. From 1.2 above, it can be seen that, in stage I of rainfall infiltration, rainfall intensity affects the amount of rainfall received on the slope unit area, thus affecting the infiltration of slope soil, and the rate of rainfall infiltration is determined by rainfall intensity; however, when rainfall infiltration reaches stage II, it can be seen from Figure 4 that rainfall intensity exceeding 20 mm/h has less influence on rainfall infiltration, which is because the rate of rainfall infiltration in this stage is controlled by the infiltration capacity of slope soil and is not related to rainfall intensity. Therefore, rainfall intensity mainly affects the relationship between infiltration depth and rainfall duration with the slope ponding infiltration time changes.Figure 14
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and rainfall intensity.


## 4.3.3. Initial Water Content

When the slope angle is 30°, the rainfall intensity is 20 mm/h, and the saturation infiltration coefficient is 4.15 × 10−4 cm/s. The variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and initial water content is shown in Figure 15. The rainfall duration required for rainfall infiltration to the same depth in the slope decreases gradually with increasing initial water content, and this phenomenon is more obvious at an initial water content of 25%. This is caused by the increase of rainfall infiltration depth in the tailings soil with the increase of initial water content. The effect of initial water content on the depth of infiltration of the model response deepens with time for a constant infiltration time.Figure 15
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and initial water content.


## 4.3.4. Saturation Permeability Coefficient

When the slope angle is 30°, the rainfall intensity is 20 mm/h, and the initial moisture content is 12%, the variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and infiltration coefficient is shown in Figure16. The rainfall duration required for rainfall infiltration at the same depth gradually increases with the decrease of permeability coefficient, which is more obvious when the saturated infiltration coefficient is 2 × 10−4 cm/s. The influence of soil permeability coefficient on rainfall infiltration becomes more significant with the increase of depth. The reason is that the infiltration rate of rainfall is controlled by the infiltration capacity of slope soil in stage II of water infiltration.Figure 16
Variation of rainfall infiltration depth in the tailing slope with the changes of rainfall duration and infiltration coefficient.


## 4.4. Sensitivity Analysis of Influencing Parameters of Rainfall Infiltration

In this paper, the rainfall infiltration impact parameters are normalized (Table3) [38, 39] and sensitivity analysis is conducted according to the sensitivity classification [40].Table 3
Parameter sensitivity classification.
ClassificationIndexSusceptibilityI0 ≤ |I| ≤ 0.05InsensitiveII0.05 ≤ |I| ≤ 0.2Commonly sensitiveIII0.2 ≤ |I| ≤ 1Highly sensitiveIV|I| ≥ 1Overwhelming sensitiveThe amplitude of variation of the key model parametersβ, q, θi, and ks is uniformly set to 20% [23, 40], and the sensitivity index is calculated as follows:(19)I=ΔOΔFiFiO,where O is the model output; Fi is the parameters that affect the model output results; ΔO is the change value of the model output result; and ΔFi is the amount of parameter change that affects the model output results.The results of the sensitivity index calculations for the key parameters affecting the depth of rainfall infiltration are shown in Table4. The positive and negative signs in the table indicate that the parameter changes are positively or negatively correlated with the model calculated values [40].Table 4
Sensitivity analysis of rainfall infiltration depth.
NumberInput parametersValue rangeOutput objective function (depth of infiltration at different times) corresponding to sensitivity indexSensitivity levelh30h60h90h120h180h2401β200.17−1.06−3.99−6.13−7.51−8.79IV−200.170.574.235.425.975.91IV2q200.32−0.05−0.16−0.26−0.34−0.38III−20−0.04−0.16−0.22−0.26−0.29−0.3III3θi200.080.070.230.310.390.42III−200.32−0.05−0.16−0.26−0.34−0.38III4ks20<0.05<0.050.10.090.080.08II−20<0.05−0.11−0.1−0.09−0.08−0.08IIFrom Table4, it can be seen that the four model parameters ranked by the sensitivity are β ≥ θi≥ q ≥ ks. When the angle of tailings slope increases by 20%, the sensitivity index belongs to grade IV, and the maximum sensitivity index attains 8.79. However, when it goes down by 20%, the sensitivity index belongs to class IV. When the model parameter saturation permeability coefficient is floated up by 20%, its maximum sensitivity coefficient is 0.1. When it goes down by 20%, its maximum sensitivity index is 0.11, and its sensitivity index belongs to class II. At the same time, when the two model parameters of rainfall intensity and initial water content float up and down by 20%, the sensitivity indices are relatively the same, both of which belong to class III. Therefore, when applying this model for tailings dam slope design and stability evaluation, the parameters β and θi should be considered first.


## 5. Conclusions

The existing infiltration depth prediction model only includes a single factor; thus the GA model is modified to enhance its applicability.(1)
The relationship between wet front depth and rainfall time predicted by the improved GA model is closer to the actual value of the infiltration test than that calculated by the GA model and Richards’ equation and has higher accuracy. In the time period of free infiltration, the difference between the wetting front extensions of the three models is small. With the increase of rainfall duration, the infiltration depths obtained from the improved GA model and Richards’ equation are consistent with each other. The difference between the two infiltration depths tends to be stable, but the difference with the GA model infiltration depth becomes larger.(2)
At the initial stage of infiltration, the expansion rate of the wetting front of the three models is faster, and the infiltration rates of the improved GA model and Richards’ equation are smaller than those of the GA model. After reaching the stage of water infiltration, the transport speed of the wetting front tends to decrease, and the infiltration rates of the three models decrease rapidly. The change of infiltration rate calculated by the improved GA model and Richards’ equation tends to be consistent, and the results are larger than those of the GA model. This difference becomes smaller with the continuation of infiltration.(3)
The effect of slope angle, rainfall intensity, initial water content, and saturated permeability coefficient and other parameters on slope rainfall infiltration is analyzed by using the improved GA model. The influence parameters have a critical value, and the influential effect on the infiltration of rainfall on the slope will change abruptly when the critical value is exceeded.(4)
When applying this model to the rainfall infiltration in tailings slopes, the influence of slope angle and initial water content should be focused on to provide the theoretical basis for the construction and stability research of tailings dams in the future.



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*Source: 7401917-2022-07-16.xml*