A simple method to analyze infiltration into unsaturated soil slopes
Introduction
In tropical and sub-tropical areas, the water table is at great depth and the near surface soils experience negative pore-water pressure (suction). Similar conditions exist in embankments and other engineered fills placed above the water table level even in temperate climates. Experience has shown that many slope failures occur during or shortly after rainfall, as water infiltrates into the slope reducing near surface suction. Given changing climatic conditions (increasing and more intense rainfall events) and deforestation which removes the natural suction effects provided by tree roots, landslides are becoming much more prevalent throughout the world. In addition to the risk posed to life by rapid landslide events, additional problems are caused by the interruption of transport routes and contamination of water supplies.
Careful field measurements [1] have identified the key role of suction in maintaining the stability of steep slopes, and in providing a rational failure mechanism for rainfall induced landslides. Failure generally takes the form of shallow (typically <2 m deep), translational slides, which form parallel to the original slope surface. The mechanism of slope failure described by Fourie et al. [1], Lumb [2] and others comprises the downward migration of a wetting front from the surface of the slope. The advance of water causes a reduction of near surface soil suction, reducing the soil strength and leading to failure. Fredlund and Rahardjo [3] noted that traditional saturated soil mechanics approaches cannot model the problem successfully as the soil is unsaturated before and in many cases after failure.
Fredlund et al. [4] expanded the Mohr–Coulomb model to incorporate negative pore-water pressure (matric suction):where τ is the shear strength of unsaturated soils, c′ is the “effective cohesion”, σn is the total normal strength on the failure plane, ua is the pore-air pressure on the failure plane, ϕ′ is the angle of internal friction associated with the net normal stress state variable σn − ua, uw is the pore-water pressure on the failure plane, ua − uw is the matric suction on the failure plane, ϕb is the angle indicating the rate of increase in shear strength relative to the matric suction and C is the total cohesion of the soil.
It is common to consider the total cohesion (C) of unsaturated soil as been composed of two parts, the first of which is the effective cohesion and the second represents the contribution of suction to strength. Water flow through soil generates seepage (drag) forces, which change the effective stress. The effect is considered to be relatively minor and is ignored in the following.
Fourie et al. [1] and Pradel and Raad [5] show that when slope failure is caused by infiltration, the failure plane forms parallel to the existing slope surface. The authors suggest using an infinite slope model in which the soil strength is described by an expression of the form given in Eq. (1). The factor of safety (F) is given by:in which C is the total cohesion (incorporating the effect of suction and cementation), γ is the unit weight of the soil, α is the angle of the slope and h is the depth of slip surface, which is normally related to the depth of wetting front depth Zf.
The second part of Eq. (2) remains constant during rainfall, therefore failure of an unsaturated soil slope is caused by the total cohesion reducing as infiltration reduces the in situ suction and increases the wetting front depth. This results in an increase in the disturbing forces and a decrease in the resisting force. Eventually the soil strength will reduce sufficiently that in combination with the increasing load (weight of soil), failure will occur.
The loss of matric suction and the advance of the wetting front are controlled by the infiltration characteristics of the slope. An ability to model this process is critical to an accurate assessment of slope stability problems. Because of the importance of suction in maintaining the stability of slopes, the variation of the strength of unsaturated soil as a consequence of changes in water content is the topic of intensive research [4]. Estimating the change of water content that will occur during a given rainfall event is an extremely complex problem. It is usually solved by either:
- (i)
Simple physical models such as Green–Ampt [6] and Horton [7] equations.
- (ii)
Finite element analysis (FEA), which usually employ Richards’ equation [8] and incorporate input data from the soil water characteristic curve (SWCC) which accounts for the variation in soil permeability as the matric suction (or water content) varies.
Although the FEA approach is theoretically rigorous, unsaturated soil permeability is highly variable during infiltration and a rigorous analytical technique may still not yield correct results if the input parameters are uncertain. For this reason models such as Green–Ampt remain in widespread use due to their relative simplicity. This paper reviews several of the issues involved in analysing infiltration into unsaturated soil slopes using the Green–Ampt model. Some of the well-known limitations of the model are examined and a simple alternative approach which overcomes some of these limitations is proposed. The new model should be used for preliminary design and to identify critical slopes where FEA analyses are required. In the final section predictions of the infiltration response of slopes made with the new model are compared to both the Green–Ampt model and numerical analyses using FEA.
Section snippets
Infiltration analysis
During rainfall water infiltrates the soil from the surface and redistributes in the unsaturated zone. The distribution process depends upon the soil moisture conditions, water pressure, and unsaturated permeability. The infiltration capacity (i), which is a measure of the maximum rate at which water can enter the soil, varies throughout a rainfall event. It is controlled mainly by the permeability and water content of the soil and the topography of the slope. Generally in unsaturated slopes
New model considering suction variation
In this section a simple method (based on the Green–Ampt model) is developed to allow the assessment of infiltration into unsaturated soil slopes using basic soil properties.
Comparison with finite element method
Tami et al. [18] reported numerical simulations using SEEP/W (Geoslope Int.) performed to investigate boundary effects in their 2.45 m long, 2 m high and 0.4 m wide laboratory based slope experiment. They modelled a 400 mm deep fine sand layer overlying a 200 mm thick gravely sand at a slope angle of 30°. The fine sand had a saturated permeability (Ks) of 2.4 × 10−4 m/s, and the variation of suction with water content is shown Fig. 6. In order to study the effect of rainfall duration on the
Case study
Li et al. [13] describe a case study of a recently constructed instrumented slope cut through weathered Granite in Hong Kong. The slope which formed part of a highway project was 17.5 m high with a slope angle of 30° and had a 1m wide berm at mid-height. The instrumentation included moisture probes and tensiometers, which allowed the collection of moisture content and suction measurements through a wet and dry season.
The response of the slope to a single rainfall event is considered here. The
Conclusion
An understanding of the wetting front development is crucial to stability analysis of partially saturated soil slopes. Although rigorous results can be obtained using FEA analyses, soil permeability is a highly variable characteristic and FEA analysis will give inaccurate results if the permeability measurements are not representative of the in-situ conditions. This is one of the reasons why simple infiltration models remain in widespread use. The Green–Ampt model was seen to significantly
Acknowledgements
This project is funded by Iarnród Éireann. The authors thank Mr. Brian Garvey, Chief Civil Engineer with Iarnród Éireann for financial assistance received. The second author was the recipient of a Geotechnical Trust Fund award from the Geotechnical Society of Ireland. The authors acknowledge the useful comments of the reviewers.
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