In the study of unsaturated soil slope stability under rainfall infiltration, it is worth continuing to explore how much rainfall infiltrates into the slope in a rain process, and the amount of rainfall infiltrating into slope is the important factor influencing the stability. Therefore, rainfall infiltration capacity is an important issue of unsaturated seepage analysis for slope. On the basis of previous studies, rainfall infiltration law of unsaturated soil slope is analyzed. Considering the characteristics of slope and rainfall, the key factors affecting rainfall infiltration of slope, including hydraulic properties, water storage capacity
In the stability analysis of landslide, rainfall is a very important factor. A large amount of statistical data shows that most of landslides occur after a rainfall or during a rainfall. There exists a law that landslides increase with increased rainfall in a region. Such rain-induced landslide and slope failure are the most common ones in many countries such as Japan, Hong Kong, and Southeast Asia.
With the development of percolation theory of saturated and unsaturated soil, both at home and abroad, researchers have been increasingly aware that the occurrences of soil slopes have close relationship with soil unsaturated seepage in rainy season. The physical process of rainfall infiltration into ground and its seepage through unsaturated-saturated soils has been studied by hydrogeologists, soil scientists, and geotechnical researchers. Landslides of Three Gorges Reservoir are mainly clay fragments with gravel, and slide belts are mainly soft clay, silty clay with gravel, or the clasts of sandstone or mudstone. As to this type of landslide, main influence of the rainfall is rainfall infiltration changes seepage field of sliding body.
In order to analyze a rainfall infiltration process on slide, some factors can be considered, such as slope’s characteristics, precipitation, evaporation, and other aspects. From the slope, the main factors include permeability of slope soil, slope, vegetation coverage, fissure distribution, and initial soil moisture content. To the rainfall, rainfall intensity, rainfall type, and rainfall duration have important influences on rainfall infiltration process. For the evaporation, evaporation intensity and duration can be considered as the crucial factors [
Effect of rainfall intensity and duration on slope stability [
In the relevant studies on rainfall infiltration, especially in landslide research field, rainfall seepage is simplified in many articles, which is assumed to be a constant. For example, Fredlund [
Ding and Liu [
Xie et al. [
According to the force and motion characteristics of water, a seepage process can be divided into three stages:
Rainfall infiltration is controlled by the infiltration rate of a landslide, which is defined as the actual water amount in a rainfall process through the unit area of surface in per unit time, and with speed dimension typically is expressed in
The governing equation for 1D vertical infiltration in unsaturated soils is given by the following equation [
Srivastava and Yeh [
Homogeneous soil profile for calculation (based on [
The upper boundary at the ground surface is subjected to a rainfall infiltration (
Main factors, influencing rainfall infiltration of an unsaturated slope, include slope characteristics, precipitation, and evaporation. From the slope aspect, the main factors are slope seepage properties, slope gradient, vegetation coverage on slope surface, fissure distribution, and soil capillary water. From precipitation, rainfall intensities, rainfall types, and rainfall duration are the primary elements. To evaporation, the key factors are surface evaporation intensities and duration.
To precipitation and evaporation, they affect slope stability by mainly changing water distribution in slope, and they are external factors. The properties of slope itself are the internal factors, and the key is permeability of rock and soil.
Similar to the flow through a saturated soil, water flow through an unsaturated soil is generally governed by Darcy’s law. However, comparing the water flow in an unsaturated soil with the saturated flow, two major differences stand out:
Two extreme cases of the infiltration problem can be first considered: water coefficient permeability tending to zero and that tending to infinity. At the former extreme there will be no infiltration of water into the soil stratum. At the latter extreme, water will infiltrate into the soil stratum easily but will immediately drain away through the boundaries. However, at intermediate values of water coefficient of permeability rainwater will infiltrate to a certain degree and will not entirely drain away. This implies that there exists a critical saturated permeability that may result in the greatest rainfall infiltration.
In general, mass landslides occur with large rainfall intensity. From preceding analysis, in this case, the amount of water infiltrating into slope mainly depends on soil infiltration capacity, that is to say, permeability coefficient. For saturated soil, its permeability coefficient can be considered as a constant generally, and for unsaturated soil, its permeability coefficient changes with a large range; there are usually 3 to 5 orders of magnitude. Permeability coefficient of unsaturated soils is a function of volumetric water content (
Curve of matric suction and permeability coefficient of cohesive soil.
Soil water characteristic curve of cohesive soil.
From the graphs, with increase of volumetric water content, matric suction decreases rapidly. At the same time, permeability coefficient increases rapidly. When volumetric water content increases to saturation, matric suction decreases to zero; then permeability coefficient is equal to permeability coefficient of saturated soil.
Water storage capacity of a soil,
Figure
Soil water characteristic curves for different soils.
According to much research on this respect, the continuous rainfall, whose intensity does not exceed the infiltration rate, is the most favorable for rainfall infiltration. The input-regulating element calculates the actual infiltration rate into the slope considering the rainfall intensity and infiltration capacity, according to the following equations:
Rainfall infiltration rate depends on rainfall intensity as well as the water permeability coefficient and the hydraulic gradient of topsoil. Both the water permeability coefficient and hydraulic gradient vary throughout the infiltration process due to the variations of negative pore-water pressure in the soil. The initial pore-water distribution is an essential input for transient flow analyses in unsaturated soils. Previous studies indicate that the antecedent infiltration rate not only has a significant influence on the initial pore-water distribution and hence on the pore-water pressure redistribution as a result of subsequent rainfall infiltration, but also indirectly results in a change of the water permeability coefficient of the soil [
Variations in subsequent rainfall infiltration rate are often restricted by the hydraulic properties of the soil and ground conditions, and rainfall infiltration in initially unsaturated soils results in an increase in the water permeability coefficient due to an increase of water content, and it simultaneously leads to a decrease of hydraulic gradient due to a decrease of negative pore-water pressure. If both the antecedent and subsequent rainfall infiltration rates are highest, the change in negative pore-water pressure after the rainfall will be the lowest. Therefore, it can be imagined that the negative pore-water pressure in the soil may be greatly reduced if a prolonged antecedent rainfall is combined with a heavy subsequent rainstorm.
An infiltration model is used to estimate the rainfall excess in runoff analysis and is important for accurate simulation of a runoff hydrograph. Many infiltration models must accommodate rainfall intensities that are sometimes higher and sometimes lower than the infiltration capacity. The infiltration capacity depends on the moisture content in the upper soft layer which in turn depends on the rainfall intensity. Therefore, the infiltration capacity varies when the rainfall intensity varies.
Only a few infiltration models take rainfall intensities into consideration; however, most of them are described using equations with a physical basis. The physical model is a theoretical one for unsaturated soil moisture movement, but the model treatment in terms of computation and modeling of the rainfall-runoff process may be more complex than the conceptual model when considering the rainfall intensity. The infiltration model proposed recently by Fujimura and Ando is a fairly simple conceptual model [
Relationship between infiltration capacity and soil moisture.
Rainfall-induced landslides are the results of coworks of three basic rain variables (rainfall, rain intensity, and rain duration). Rain, inducing the occurrence or landslides reactivity, is generally the some rain with the maximum characteristic parameter, such as the greatest continuous rain, the longest continuous rain, the most strength continuous rain, or the greatest combination rain. In order to decide which rainfall has the closest correlation with landslide occurrence, that is to say, how to decide critical rainfall by using variables, Zhang et al. [
Considering that one rain process not always induce landslide occurrences and only part rainfall of one rain process influences landslide, cumulative rainfall cannot be deemed as critical rainfall obviously. Hence, effective rainfall is recognized, which could be obtained by using this day’s rainfall in some time multiplying effective rainfall coefficient. While deciding effective rainfall coefficient, it intends to adopt power exponent form in the following:
The rainfall seepage is not only related with precipitation, characteristic of rock and soil, but related with groundwater level, preceding moisture content of slope, vegetation, and so on. Therefore, the crucial factors can be divided into external factors and intrinsic factors:
During the rainfall infiltration of landslide, the rainfall seepages to the slope surface firstly, then it is gradually infiltrates into deep slope with rainfall duration, and the excess water recharges the groundwater finally. Initial water distribution in slope soil directly determines rainfall infiltration rate and soil water capacity, thus affecting final infiltration amount. According to the principle of soil water balance, soil moisture in the slope depends mainly on rainfall, evaporation, and infiltration, and soil initial moisture content is mainly controlled by the antecedent rainfall and evaporation before the calculation period. That is to say, rainfall infiltration is a function of the current and antecedent rainfall, evaporation, soil initial water content, and other factors. The regression model of rainfall infiltration can be expressed as follows:
It is essential to obtain the appropriate values for the above constants by trial and error methods, according to observation data of long time series, and combined with test methods.
This paper presents a simplified approach for the analysis of landslides triggered by rainfalls. Some conclusions can be attained. In order to analyze the rainfall infiltration process on landslide, some factors can be considered. Considering the characteristics of slope and rainfall, the key factors are divided into external factors and intrinsic factors. The influences of hydraulic properties, water storage capacity Based on external factors changing, this paper presents three calculation models of rainfall infiltrability for unsaturated slope, including In order to determine the amount of rain penetration during a rainfall process, the relationship of rainfall and infiltration is described by the system response analysis, and the prototype of regression model of rainfall infiltration is given.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This study is supported by the National Natural Science Foundation of China (no. 51009097), Public Non-profit Welfare Project from China Ministry of Water Resources (no. 201301022 and 201201037), and Jiangsu Province Waterway Communication and Transportation Project (no. 2011Z01-1).