D209

A Simplified Method to Estimate the Nonlinear Distribution of Lateral Forces Acting on Stabilizing
Piles in Soil Slopes〇Ning BAO, Jianfeng CHEN, Gonghui WANG

Abstract: Precise prediction of the lateral force acting

Fig. 1(a) shows the profile of sliding wedge. The

on the piles is of significance to assess the stability ofdirection of slip plane at the ith sublayer can be

pile-reinforced soil slopes. A simplified pressure-based

represented as the line PC based on the theory of polemethod is presented for estimating the lateral force

point (Fig.1b), and the inclination angle i isdistribution on the piles embedded in a semi-infinite

determined as:

inclined soil slope. The soil arching theory was i = CPF +  = ( CIE + EIF ) /2 + (1)EIF = arccos ( lIE / lIF ) . According

incorporated to calculate the driving forces transferred

where CIE =  − 

onto piles after determining the active lateral earth

to the geometric relationship of the triangle ΔOIE andpressure between adjacent piles through the horizontal

ΔMIC, lIE = lOI sin  , lIF = lIC = ( lOI + c cot  ) sin  . E.. (1)slice method. The published numerical study wasis then rewritten as:

selected to examine the applicability of the proposed
method. It is demonstrated that the predicted result is in1
lOI sin 
i =  +  + arccos 
2  c cos  + lOI sin   (2)good agreement with the observed data in terms of boththe shape and magnitude of the distribution of lateralforces.
1 Introduction
For the past decades, the pile stabilization method
has come into widespread use to reinforce the slopes
which are identified to be potentially unstable. The
piles work passively to resist the driving forces ofsliding soils and transfer them downward to theunderlying stable stratum subjected to the flowing soils.
Bearing on sufficient lateral forces, the piles may
produce significant internal forces even to failure. In
this context, an appropriate estimation of the
distribution of lateral forces acting on the piles arisingfrom the sliding mass is therefore necessary forFig. 1 (a) Profile of cross section UU′ with multiple

improving the design of piles and slope stabilization.

sublayers (b) the Mohr’s circle representation of theHowever, limited closed-form analytical solutions havestress state on soil element I

been presented to date regarding the nonlinear

To get lOI , it is found lIF2 = lID2 + lDF2 in the triangle

distribution of lateral forces resting on the piles.

ΔFID. And lID =  v' i − lOI , lDF =  v' i tan  . Substituting them

2 Theoretical analysis

into E.. (2) and simplifying, it then follows that:

2.1 Profile of sliding wedge

()lOI = Ai − Bi + Ci / cos 2(3) Ai =  H i cos 2  + c sin  cos where  Bi =  2 H i2 cos 2  ( cos 2  − cos 2  ) .
222
Ci = c cos  + c H i cos  sin ( 2 )2.2 Calculation of lateral earth pressure
Fig. 2 shows the force on the ith sublayer. To

Fig. 3 (a) Schematic representation of the soil arch

determine the active earth pressure p . The succeeding(b) Uniform stress distribution in zone Ⅱ'iformulations follow the horizontal and vertical force

3 Method verificatione.uilibrium re.uirements and the moment-balance

Fig. 4 compared the predicted results using there.uirement to the midpoint of the plane gh with anproposed method with the field test data and numerical

inclination angle of  i , and can be expressed as:

results obtained from Lier (2012). It can be seen thatpi H cos  + cli cosi − Ri cos ( /2 −  + i ) = 0

wi + qi Li − cH − Ri sin ( /2 −  + i ) − cli sin i−qi −1Li −1 − pi H sin  = 0(4)(5)

qi −1Li −1 ( Li −1 cos  + li cosi ) / 2 + cH cos  lmi +pi Hlmi sin ( −  ) −  Silmi cos  / 2 −The prediction using the proposed method had asatisfactory agreement with the numerical results interms of the shape and magnitude of distribution oflateral forces. The difference in the predicted maximum(6)

qi Li ( Li cos  − li cosi ) / 2 = 0

lateral forces to the field data was as small as 2.1 kN/m.
While the other methods overestimated the lateralforces to different extents.

Fig. 2 Force components acting on the ith sublayer
2.3 Soil arching effect behind piles
The stress distribution in the arch zone is shown in
Fig. 3. The e.uation of the radial e.uilibrium is:d r / dr + ( r −   ) / r = 0(7)The boundary conditions at the inner and outerboundaries are computed as:

Fig. 4 Comparison of the numerical and calculated

 in =  r = D / 2 = C ( D2 / 2 ) ^ ( K p − 1) + 2c K p / (1 − K p )(8-a)

 out =  r = R = CRout ^ ( K p − 1) + 2c K p / (1 − K p )(8-b)

2outresults
4 Conclusions

As a result, the lateral force per unit depth pai

A simplified pressure-based method is presented

transferred onto the piles because of arching, can befor estimating the lateral force distribution on piles. The

calculated by subtracting the lateral force on the soil

predicted results from the proposed method were inmass between adjacent piles from the driving force on

good agreement with the observed data in terms of boththe outer arch boundary.

the shape and magnitude of the distribution of lateralpai =  out D1 − p D2'i(9)forces.