1. Introduction
Surface barrier covers are commonly used as the capping of mine tailings [
1,
2], solid waste landfills [
3,
4] and low-level radioactive waste repositories [
5,
6]. It has been over forty years since the emergence of surface covers and a number of changes have taken place in the materials used for the covers. Among them, the representative ones include Soil Covers [
7], Compacted Clay Covers [
8,
9], and Geosynthetic Clay Liners in covers [
10,
11]. The main purpose of these kinds of surface covers is to prevent the rainwater from entering into the toxic waste below. Due to the similarity of the working mechanism of these types of covers, they are generally referred as the traditional covers.
However, a great deal of engineering experiences has shown that the traditional covers have obvious drawbacks in long-term service [
12,
13]. Due to the complex and changeable atmospheric environment, the traditional covers are subjected to periodic cycles of wetting/drying and freezing/thawing, causing the soil cracking of the overlying clay layers. The cracks in the clay layers significantly increase the permeability of the surface covers, resulting in the failure of water resistance. Lu et al. [
14] investigated the anti-seepage performance of loess landfill covers and verified that the hydraulic conductivity of cracked soil was three orders of magnitude higher than non-cracked soil. Melchior et al. [
15] monitored the landfill cover systems in Hamburg for 18 years and found severe cracking of the clay layer. The annual leakage of the cracked clay layer was approximately 10 times greater than the non-cracked status and the leakage rate (ratio of leakage to rainfall) rises to 42%. Additionally, the function of the surface covers in gas emission controlling aroused more and more attention among the scholars [
16,
17]. The soil cracking of traditional covers allows toxic and harmful gases entering the atmosphere, posing a threat to ecosystem and human beings.
Considering the disadvantages of the traditional covers, some scholars proposed the idea of Alternative Earthen Final Covers (AEFCs) [
12,
18,
19]. The AEFCs is not exclusively based on the idea of ‘water retention’ but rather on the idea of ‘water storage’, which means that the infiltrated water is retained in the soil layer during rainfall and evaporates into the atmosphere during sunny days. Thus, the AEFCs allows for a dynamic cycle of water migration. In order to maximize the water storage capacity of soil covering, capillary barrier covers are proposed [
20,
21,
22]. The capillary barrier cover usually consists of a layer of fine-grained soil underlain by a layer of coarse-grained soil. When the infiltrated water reaches the interface of two layers, the water cannot seep downward due to the differences in hydraulic conductivity between fine-grained soil and coarse-grained soil. At that time, water migrates along the interface and re-infiltrates upwards. Only the suction of the coarse-grained soil decreases to the water-entry value (point A in
Figure 1.) does the water can penetrate the interface and infiltrate into the coarse-grained layer. Subsequently, the moisture content of the coarse-grained soil continuously increases. When the hydraulic conductivity of the fine-grained and coarse-grained soils are equal, the capillary barrier covers completely fails and water enters the coarse-grained layer rapidly. Former studies have verified that the fine-grained soil in capillary barrier covers is nearly saturated when the breakthrough happens [
23,
24]. The coarse-grained soil will increase the water storage capacity of the overlying fine-grained soil, contributing to the overall impermeability of the surface cover. Furthermore, the fine-grained soils of capillary barrier cover usually consist of non-clayed soils, which effectively avoids the system failure caused by cracking. Additionally, the fine/coarse-grained soils are cheap and easy-available materials, which effectively reduces the cost of engineering.
Previous studies have deeply investigated the water storage capacity and water migration process of the capillary barrier covers. Through the visible tracer test, Qian et al. [
26] studied the performance of the capillary barrier covers under different thicknesses, rainfall intensities and slope angles. Results showed that the efficiency of capillary barrier covers increases with coarse-grained soil layer thickness and slope angle while decreases with rainfall intensity. A large-scale indoor experiment was carried out by Kampf et al. [
27] to investigate the uncertainties about conceptualization and parameterization of capillary barriers design. The data revealed that infiltrated water in fine-grained soil mainly migrates laterally in the saturated zone and the performance of capillary barrier covers is highly sensitive to the hydraulic properties of both fine and coarse soil. Considering the limitations of indoor experiments, some scholars have conducted filed tests and monitored the performance of established capillary barrier covers for a long time. Rahardjo et al. [
25] studied the capillary barrier covers under tropical heavy rainfall and verified that the capillary barrier covers can effectively contain the negative pore-water pressure of the coarse- grained soil layer. Zhang [
28] collected the monitor data of the Prototype Hanford Barrier (PHB) in the U.S up to 19 years. The monitoring record showed that the capillary barrier covers performed well in the 19 years even under extreme weather conditions. However, most of the previous research focused on the water storage and drainage capacity of capillary barrier covers, ignoring the stability analysis of capillary barrier covers.
In many engineering projects, the capillary barrier covers are placed on the slopes. Due to the capillary barrier effect, the water cannot infiltrate downward but store in the fine-grained soil during the rainfall. As the rain goes on, the fine-grained soil layer approximately reaches saturated, which greatly reduces the shear strength of the fine-grained soil. Additionally, in fine-grained soil layer, the water diversion exposes the fine-grained soil skeleton to seepage forces, leading to the occurrence of fine-grained soil instability. As the capillary barrier cover consists of a fine/coarse-grained bilayer structure, a weak zone of shear strength will also be formed at the interface of the two layers. With the increases of water content, the fine-grained soil layer may slide along the interface. Juca et al. [
29] reported the excessive movement of the landfill covers in Brazil and pointed out that the instability is caused by the water storage. In Italy, the catastrophic landslides with fine/coarse-grained soil structures have occurred at Bracigliano, Quindici, Sarno and so on [
30], which caused serious damages and aroused huge discussion [
31,
32]. Due to the different mechanical properties and water contents of the upper/underlying layers, it is widely considered that the failures usually happened at the top fine-grained layer or the interface of the fine/coarse-grained layers [
33,
34].
Recently, the analysis of infiltration and stability of the multi-layer slopes has been studied by many scholars. Based on the one-dimensional infiltration model and infinite slope analysis, Cho [
35] studied the shallow failures of two-layer slopes and verified the influence of the infiltration to slope stability. Mancarella et al. [
30] conducted the infiltration tests and pointed out significant localized moisture accumulation leads to the slope instability. Xiong et al. [
36] analyzed the stability of multi-layer slopes by assuming that the sliding surface is located at the wetting front. Through limit equilibrium analysis, results showed the first layer is most susceptible to slide. However, in these studies, the difference in hydraulic conductivity between the upper and lower layers is not so significant that the infiltrated water can enter the underlying layer freely, which is different from the characteristics of capillary barrier covers mentioned above.
In this article, a stability analysis method for the capillary barrier covers was proposed. Firstly, the infiltration process of the capillary barrier covers was conducted by analyzing the Green-Ampt model and considering the capillary barrier effect at the interface of fine/coarse grained soil. Next, considering the water storage and diversion, the stability analysis of the capillary barrier was divided into three stages considering the influence of seepage force and the changes of the wetting front profiles. Finally, the proposed method was analyzed and verified by using the cases in the published article.
3. Stability Analysis of Capillary Barrier Covers
The limiting equilibrium method is the most classic and accepted method of slope stability analysis [
45,
46,
47]. Due to the clear physical meaning, well-defined mechanical relationships and simple calculations, the limit equilibrium method is widely used in the stability analysis of various slopes. Many methods have been proposed based on the principle of limit equilibrium analysis, including the Swedish slice method [
48], the simplified Bishop method [
49,
50], the Janbu method [
51], the Morgenstern-Price method [
52] and so on. Among these methods, the Janbu method can be used for arbitrarily shaped sliding surfaces. Additionally, the calculation process of the Janbu method is simpler than others. For the fine/coarse-grained soil slopes, many realistic accidents and experiments have confirmed that the failure is mainly caused by the top fine-grained soil [
30,
33,
53]. Therefore, the stability of the fine-grained soil layer in the capillary barrier cover is analyzed using the Janbu method in this paper.
3.1. Sliding Surface in the Fine-Grained Soil
Initially, the rainfall water infiltrated into the fine-grained soil vertically with no diversion and the wetting front could be assumed to be parallel to the slope surface. At that time, the downward infiltration dominates water migration. The factor of safety can be calculated as:
where,
Fs: the factor of safety;
W: the gravity of upper zone;
N: the stress at the interface (equal to
Wcos
α);
c: the effective cohesion of soil;
L: the length of the slope;
: the internal friction of the soil;
: the slope angle.
As the rain goes on, the infiltrated water started to divert along the interface and the wetting front profile was considered to be the parabolic function shape. Assuming the wetting front as the sliding surface, the upper saturated zone was split into individual vertical slices (
Figure 5). Considering the water diversion at that time, the seepage force parallel to the slope surface can be calculated as:
where,
Qs: the seepage force;
: the unit weight of water;
J: the hydraulic gradient;
Vus: the volume of upper saturated zone.
Based on the force balance of vertical and horizontal directions on slice
i:
According to the limiting equilibrium conditions:
where,
: the effective cohesion and effective angle of internal friction of the soil.
Associating the Equations (15)–(17):
When it comes to the last slice:
The Equation (19) can be written as:
Subsequently, the torque equilibrium equation of each slice is listed:
Equation (23) can be simplified as:
Finally, the factor of safety Fs can be calculated by iteration. The iteration steps are listed as followed:
- (1)
Assume , substitute it into the Equation (23) and acquire the approximate value of Fs1.
- (2)
Use Fs1, and Equation (20) to calculate , and acquire the value of Ei.
- (3)
Substitute Ei and into Equation (28), acquire the value of Xi and .
- (4)
Substitute the calculated above into the Equation (23) and acquire the new value of Fs2.
- (5)
Repeat the steps above until the error of two Fsi less than the threshold.
3.2. Sliding Surface at the Interface between the Fine/Coarse-Grained Soil Layers
When the breakthrough point moves to the crest of the slope, the interface between the fine/coarse-grained soil layers becomes nearly saturated and the shear strength decreases. Considering the water diversion at that time (
Figure 6), the factor of safety can be calculated as:
where,
Fs: the factor of safety;
W: the gravity of upper zone;
N: the stress at the interface (equal to
Wcos
α);
: the cohesion of the interface soil;
L: the length of the slope;
: the internal friction of the interface soil;
: the slope angle;
: the seepage force.
3.3. Sliding Surface in the Coarse-Grained Soil
For the underlying coarse-grained soil, which is unsaturated through the infiltration process, the safety factor can be calculated using the modified Mohr-coulomb failure criterion [
54].
where,
is the shear stress at the slip surface,
is the cohesion,
is the net normal stress,
is the matric suction,
is the effective angle of friction,
is the angle which defines how the shear strength increases with the increase of matric suction.
Due to the unsaturated condition of the coarse-grained soil, the calculated safety factor may be higher than before when the sliding surface is in the coarse-grained soil layer. Former studies have proven that the failure of the capillary barrier covers mainly happened at the fine-grained soil layer [
30,
33,
53]. Thus, the final safety factor of the capillary barrier covers is the lower one between these two values in this article.
5. Conclusions
In this study, a stability analysis method considering the water redistribution and seepage forces of the capillary barrier covers was established based on the Green-Ampt model and Janbu method. The proposed method was verified and analyzed by the examples in the published articles.
Different from the infiltration process of homogeneous soil slopes, the infiltrated water is stored and diverted laterally because of the differences in the hydraulic conductivity of fine/coarse grained soils. When the water reached the interface of fine/coarse grained soils, it didn’t infiltrate downwards continuously, but diverted laterally towards the toe of the slope. Based on the law of conservation of mass, the wetting front profile was depicted as parabolic function in the method proposed. Next, as the infiltration goes on, the wetting front moves towards the crest of the slope. Compared with the traditional Green-Ampt model, the proposed model in this article is more consistent with the experimental results of the capillary barrier covers. Additionally, the influence of the seepage force is considered in the proposed method, which makes the stability analysis more accurate.
Using the examples in the published articles, the availability of the proposed method was verified. By calculating the relationship between infiltration time and safety factor, the results of the proposed method were close to the existing method at the initial stage of water infiltration. Subsequently, the diversion and redistribution of the infiltrated water caused the decreasing of safety factor. The safety factor calculated by the proposed method is lower than the published one due to the influence of seepage force. Additionally, the safety factors under different thickness of fine-grained soil were calculated. Results showed that the stability of capillary barrier covers is closed related to local climate. When the rainfall duration is short, increasing the thickness of fine-grained soil layer reasonably can improve the stability. Otherwise, the final safety factor of capillary barrier covers decreases with the thickness of fine-grained soil increases under enough long duration of rainfall.
Although the proposed method shows satisfying results, there are some simplifications in it. The spatial distribution of water is simplified as linear distribution and the wetting front shape is depicted as the parabolic function in this study. In addition, the preferential seepage in the fine-grained soil is also needed further study.