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Effects of Pore-Water Pressure Distribution on Slope Stability Under Rainfall Infiltration

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Effects of Pore-Water Pressure Distribution on Slope Stability Under Rainfall Infiltration Effects of Pore-water Pressure Distribution on Slope Stability under Rainfall Infiltration Wang Ji-Chenga,b， Gong Xiao-Nan*a， Ma Shi-guoa a. Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China; b. Taizhou Vocational and Technical College, Taizhou, Zhejiang 318000, China *Corresponding author, e-mail: [email protected] ABSTRACT Natural slopes are mostly unsaturated residual soil slopes. Rainfall infiltration affects pore-water pressure distribution of slopes, especially the changes of characteristics and water content of soils above wetting front. Theories concerning soil infiltration were discussed. A method using Green-Ampt infiltration model to resolve rainfall infiltration was proposed. Four pore-water pressure distribution types in wetted zone were analyzed. Stability analysis models corresponding to two forms of pore-water pressure, viz. greater than and equals to 0, were established. By comparing the variation curves of slope safety coefficients at wetting front, the article shows that safety coefficient is unsafe if pore- water pressure is 0, but safety coefficient is too safe if pore-water pressure is positive. This research is of great significance for slope rainfall safety prediction under special soil conditions. KEYWORDS: rainfall infiltration; infinite slope; slope stability; pore-water pressure INTRODUCTION Natural slopes are mostly covered by residual soils, which are usually unsaturated slopes and have a negative pore-water pressure (Fredlund & Rahardjo 1993), viz. matrix suction. Matrix suction is of great importance for slope stability. Rainfall infiltration is an important factor inducing landslide of unsaturated slopes(Chen 2003). Due to rainfall infiltration, residual soils’ self-weight increases while wetted zones’ matrix suction decreases or even disappears. Under different rainfall intensity and soil conditions, wetted zone has different pore-water pressure forms. Therefore, different stability analysis models should be established in accordance with the damages at slope’s wetting front. Scholars carried out profuse researches on rainfall infiltration of slopes (LIN 2009; HAN 2013). Lin Hongzhou et al. (2009) discussed rainfall influence on slope failure and the choice of proper early warning parameters of precipitation with a model experiment of slope failure caused by rainfall. Xu (2005) analyzed the stability of unsaturated slopes under rainfall infiltration and produced an unsaturated indirect fluid-solid coupling model considering infiltration coefficient curve, soil-water curve, and modified Mohr-Coulomb failure criterion, and carried out a coupling numeric simulation of ponding field and stress field under rainfall infiltration. Han (2012) researched into rainfall infiltration and two-layer soil slope stability based on Moore’s water - 1677 - Vol. 19 [2014], Bund. H 1678 quality model and illustrated the failure mechanism of rainfall infiltration of two-layer soil slopes. Based on traditional Green-Ampt infiltration model, Kenneth Gavin (2008) proposed a simple rainfall infiltration analysis approach for the evaluation of wetting front development and the calculation of unsaturated soil slope stability at different time. Rainfall infiltration led to the decrease or even disappearance of unsaturated soil’s matrix suction. In view of this, Sung (2008) researched into the failure process of infinite two-layer slopes under rainfall infiltration and established a two-layer slope rainfall infiltration model and used this model to analyze two-layer slope stability. However, these researches regarded wetted zone’s unit weight as saturated unit weight and pore-water pressure as zero. For rainfall infiltration under certain circumstances, these calculations were unsafe. In view of this, this research means to analyze infinite slope’s stability under rainfall infiltration through different pore-water pressure distribution of wetted zone. Two slope stability analysis models are established under unsafe wetted zone pore-water pressure distribution. Comparisons are made to these two models. INFILTRATION MODELS Darcy’s law can be used in solving ponding of saturated soils with no need of considering the influence of soil’s matrix suction. However, for unsaturated soils, ponding turns to be complex. There are many infiltration models concerning unsaturated soil theories, such as Green-Ampt infiltration model (Green and Ampt 1911), Kostiakov model, Horton model, Philip model, Richards equation(WANG and LAI 2002), etc. Horton and Kostiakov models are two empirical equations and their parameters have no substantial physical significance. Philip model is obtained by vertical infiltration and is not accurate for long duration calculation. Richards equation is more accurate but more complex. Moreover, it needs water movement parameters of soil and its calculation needs analytical method or numerical method. It is not suitable for practical infiltration process analysis. Green-Ampt infiltration model is a better choice to probe into infiltration of unsaturated soils. In 1911, Green and Ampt put forward their classical Green-Ampt infiltration model as illustrated in Fig.1. h0 θi θS θ Wet soil = θ θS zw zw t Ψ w Dry soil = θ θi z Figure 1: Green-Ampt infiltration model In Fig.1, zw is depth of wetting front at time t; h0 is ponding water head at soil surface; θS is saturated water content at wetted zone; θi is initial water content of soil; ψw is average matrix suction water head of wetting front. Green-Ampt infiltration model was initially used for the infiltration of thin ponding on homogeneous and dry soils. Generalization and assumption are made to the uniform infiltration process on the profile. The most basic assumption is that wetting front is always a distinct dry-wet profile in the infiltration process, viz. the saturated water content of the wetted zone is θS, initial water content of prior wetting front is θi, soil water profile displays a step-wise shape, hence it is also called piston model. The model is as the following: Vol. 19 [2014], Bund. H 1679 zhw0++ψ w iKwS= （1） zw In the equation, iw (the subscript “w” stands for wetting front point) is infiltration rate, KS is saturated infiltration coefficient. For infinite homogeneous soil, considering the influence of soil surface’s hard crust, soil surface becomes immediately saturated under intense rainfall. For slope surface, due to the existence of runoffs, the ponding is approximately zero, viz. h0=0. From the model and differential equation above, iwdt=∆θdzw. Slope infiltration can be learned from the following: Function relationship between the depth of the wetting front and the time is ∆θ zww+ ψ tz=ww − ψ ln （2） KSwψ where Δθ is the difference of water content before and after the wetted zone is wetted. Average matrix suction water head of wetting front ψw is a function of water content and can be obtained by experiments or the following equation: ψ ψ = i K (ψ)dψ （3） wr∫0 where ψi is matrix suction water head corresponding to initial water content, Kr is relative hydraulic penetrability, ψ (ψ≥0) is matrix suction water head corresponding to water content θ. SWCC curve and relative hydraulic penetrability of soils can be solved by the following equations: θ − θ = + Sr （ ） θ (ψ) θr m , ψ≥0 4 + n 1 (αψ) −m 2 −+nn−1 {11(αψ) (αψ) } = （ ） Kr (ψ) m/2 , ψ≥0 5 + n 1 (αψ) where θr is residual water content of soils, and α, n and m are constants. When values of the parameters are given, Equation (2) can be used to solve rainfall infiltration of slopes. STABILITY ANALYSIS OF INFINITE SLOPES Theories concerning unsaturated slopes Shear strength formula of unsaturated soils can be expressed by using independent stress constants (Fredlund and Raharajo 1993). Shear strength formula using positive stress and matrix suction can be expressed as the following: b τf=+−c′′(σ nau)tanφφ +− ( uuaw ) tan （6） where τf is unsaturated soil shear strength, σn is positive stress of unit width soil slips’ bottom, c' and ϕ' are soil’s effective cohesion intercept and angle internal friction respectively, ϕb is suction friction angle of shear strength and matrix suction changes, ua is air pressure, (ua-uw) is the value of matrix suction at wetting front. Safety coefficient of wetting front can be solved from the ratio between total anti-slip force and downslide force at wetted zone. Anti-slip force at the wetting front can be solved by using the formula of shear strength of unsaturated soils. Downslide force is the component of soil weight Vol. 19 [2014], Bund. H 1680 along the slope. According to non-saturated soil Mohr-Coulomb failure criterion and limit equilibrium method, slope stability safety factor can be solved as (Fredlund and Raharajo 1993): τf FS = （7） τm b c′′+−(σnau)tanφφ +− ( uuaw ) tan FS = （8） τm where τm is downslide force at the bottom of soil slip of unit width. Pore-water pressure distribution of infinite slopes Figs.2(a)-(d) illustrate pore-water pressure distribution of wetted zone in the slope infiltration process under conditions of different rainfall intensity and slope soil characteristics. Here we assume that the wetting front is a plane approximately paralleling the slope (HAN and HUANG 2012; Sung 2009), the potential slip surface approximately overlapped with the wetting front (HAN 2013). Under groundwater level is hydrostatic pressure, and pore-water pressure of the soil displays a linear decrease from the groundwater level to the wetting front. The internal pore-water pressure of the wetted zone is controlled by rainfall. α rain earth's surface 0 α (-) 1 potential slip surface wetting front α W groundwater table γt τm (+) L σn ua pore water table bed rock γ0 (a) Figure 2 continues on the next page. Vol. 19 [2014], Bund. H 1681 rain α earth's surface 0 α 1 (-) potential slip surface wetting front α W (-) groundwater table γt τm (+) L σn ua pore water table bed rock γ0 (b) rain α earth's surface 0 α 1 potential slip surface wetting front zw α W (-) groundwater table γt τm (+) L σn ua pore water table bed rock γ0 (c) Figure 2 continues on the next page.
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