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Home , Slope stability analysis, Soil physics

Effects of Pore- Pressure Distribution on Slope Stability under Rainfall

Wang Ji-Chenga,b， Gong Xiao-Nan*a， Ma Shi-guoa

a. Research Center of Coastal and Urban Geotechnical , 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 slopes. Rainfall infiltration affects pore-water pressure distribution of slopes, especially the changes of characteristics and of 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 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- 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 field under rainfall infiltration. Han (2012) researched into rainfall infiltration and two-layer soil slope stability based on Moore’s water

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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 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, 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 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） KSwψ 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 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 intercept and angle internal 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 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 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 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.

Vol. 19 [2014], Bund. H 1682

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

(d) Figure 2: The sketch of shallow slope with different distribution of pore-water pressure Fig.2 shows slope analysis. L is depth of groundwater level, W is unit width soil slip’s weight of sliding mass, α is slope angle, γt is saturated soil weight of wetted zone, γ0 is initial weight of unsaturated soil. The following are analyses and discussions of pore-water pressure distribution of (a)-(d): (a) when rainfall intensity is very small and smaller than initial infiltration coefficient of unsaturated soil, the matrix suction of the soil at slope surface is the largest, and rainfall infiltration can not change soil water content of the slope soil, the assumed matrix suctions of the wetting front still exist, rainfall infiltrations have no substantial influence on the slope stability. Therefore, slope stability will not be discussed under this circumstance. (b) because of the formation and existence of the hard crusting of slope surface, or the slope surface is covered by vegetation, slope surface may become saturated at a short time under small rainfall. Soil water content decreases gradually down the wetting front and no hydrostatic pressure appears. At this moment, wetting front is still safe due to matrix suction, and slope stability is still not seriously influenced. (c) this form of pore-water pressure at this soil profile is commonly seen. Due to heavy rainfall, wetted zone above wetting front is nearly saturated. Due to the influence of weight and matrix suction at wetting front, the wetting front continuously moves downward and meanwhile no hydrostatic pressure at wetted zone occurs. Because wetted zone is approximately saturated, matrix suction at wetting front decreases significantly or even disappears. Therefore, the increase of soil weight at wetted zone and the decrease of matrix suction make this wetting front a potential sliding plane and hence slope stability is greatly influenced. (d) this form of pore-water pressure shows that the soil above wetting front produce hydrostatic pressure. When shallow waterproof rocks and shallow groundwater exist at the bottom, under heavy rainfall, air inside the soil can not be drained freely and will be continually compressed until producing great jacketing force at the wetting front. When the force reaches a certain value, bubbles begin to discharge continually. This compression and discharge process is repeated again and again. The pore-water pressure here can engender great danger. Hydrostatic pressures at the wetting front produce uplift at the wetted zone, where hydrostatic forces are the biggest and effective stresses are the smallest. Meanwhile, the matrix suction decreases. Therefore, under this circumstance, as a potential dangerous sliding plane, wetted zone deserves particular consideration and analysis when analyzing slope stability. Vol. 19 [2014], Bund. H 1683

Establishment of stability analysis model Pore-water pressure distribution as illustrated in Figs. 2(c) and (d) may make wetting front a potential dangerous sliding plane, so what we should do is to analyze it and establish different stability analysis models. (1) from pore-water pressure distribution Fig.2(c) we know that inside the soil above wetting front uw=0, where uw is pore-water pressure on a certain point inside wetted zone. From Equation (8) we know that when matrix suction of wetted zone disappears and there is no hydrostatic pressure in wetted zone, uw=0, and Equation (8) can be transformed into:

c′′+ σn tanφ FS = （9） τm

1 W=γt zw 2 σn =Wcos α W zw τ m =Wcosαsinα u w =0

τm σn Figure 3: The sketch of soil slice from wetted zone Fig.3 is soil strip stress obtained from the shadow part of Fig.2(c).

2 σn= γ tfz cos α （10）

τm= γ tfz cosα sin α （11） Substitute Equations (10) and (11) into Equation(9), we get:

2 cz′′+ γtfcos αφ tan FS = （12） γtfz cos αα sin (2) as for pore-water pressure distribution Fig. 2(d), for inside soil above wetting front, 2 uw=γwzcos α, where z is the depth of any point above wetting front, and γw is unit weight of water. With continuous rainfall infiltration, positive pore-water pressure will appear at wetted zone soil, soil matrix suction (ua-uw) above wetting front will be 0. The pore-water pressure above 2 wetting front, which is uw=γwzwcos α, will be the biggest.

1 W=γt zw 2 zw σn =Wcos α W τ m =Wcosαsinα 2 uw=γw zwcos α

τm σn Figure 4: The sketch of soil slice from wetted zone Fig. 4 is soil strip stress obtained from the shadow part of Fig. 2(d). When the soil above wetting front produces positive pore-water pressure, combining Fig.4 and Equation (8), we can get the following equation: c′′+−(σ u )tanφ nw （ ） FS = 13 τm Vol. 19 [2014], Bund. H 1684

2 Substitute pore-water pressure at wetting front uw=γwzwcos α and Equations (10) and (11) into the equation above, we can get safety coefficient of the slope at the wetting front, which is:

2 cz′′+−(γγt ww) cosα tan φ c′ 1 (γγtw− )tan φ′ FS = = ⋅+ （14） γ twz cosα sin α γγtcosα sin α z wttan α

EXAMPLE ANALYSIS AND DISCUSSION To better understand the influence of pore-water pressure distribution on slope stability solution, we assume there is an infinite shallow slope which is covered with 2.00m sandy soil. At its bottom is waterproof rock. Groundwater level is L=1.40m below and parallels slope surface. Slope angle is 33.7° (slope ratio is 1:1.5), as is illustrated in Fig.2(c-d). Here we analyze slope stability only. Infiltration analysis is not considered. Parameter values are in Table 1. Due to slope surface runoffs, we assume there is no ponding on slope surface during rainfall. Tab.1 Parameters of soil b ᵞ / c′/ φ′/ φ / Soil layer t (kN/m3) kPa ° ° Sandy soil 19 5 25 15 5

4 uw=0 γ 2 uw= w zcos α 3 S F 2

1 FS=1 zw=82cm 0 0 20 40 60 80 100 120 140 Depth of wetting front z /cm w Figure 5: The safety factor curve of slope at the wetting front For pore-water pressure distribution in soil above wetting front, Fig.5 presents two dangerous slope stability solutions. By comparing variation curves of slope’s safety factors at wetting front, we can see that these two results are significantly different. When pore-water pressure at wetted zone is 0, the smallest safety factor of slope is Fs=1.10, at which slope can barely retain its stability. The smallest safety factor calculated according to positive pore-water pressure distribution is Fs=0.74. When wetting front of the slope reaches zw=82cm, the slope will have the danger of stability failure. Therefore, pore-water pressure distribution in soil above wetting front has significant influence on slope stability. The results calculated by adopting positive pore-water pressure distribution are too safe, while traditional methods which do not consider hydrostatic pressure are too dangerous.

DISCUSSION (1) The paper discusses theories relating to slope infiltration and proposes a method for solving slope rainfall infiltration by using Green-Ampt infiltration model. Four pore-water pressure distributions at wetted zone above wetting front are analyzed. Stability analysis models are established regarding pore-water pressure is 0 and greater than 0. (2) By comparing variation curves of slope’s safety coefficient at wetting front, we find that the safety coefficients calculated by adopting pore-water pressure 0 are too dangerous, while the results calculated by adopting positive pore-water pressure distribution are too safe. Under special soil conditions, this finding is significant for slope safety prediction. Vol. 19 [2014], Bund. H 1685

(3) For rainfall infiltration of special soils and slopes, entrapped air pressure and impervious soil will engender hydrostatic pressure. Therefore, more experiments and theoretical researches are needed to perfect slope stability analysis models.

ACKNOWLEDGEMENTS The financial support received from the Natural Science of China [No. 51078377] , the Science and technology project of Zhejiang Province, China [No. 2013C33SA800035], the Science and Technology Project of the Ministry of Housing and Urban-Rural Development of China [K3201326] is acknowledged.

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