Simplified Analysis of a Pile due to Soil Movement. Figure 1 ..... IIA sheet pile wall having a stiffness EpIp of 2.40 Ã 107 kNm2/m and an embedment depth of 8 m.
Response of Free-Head Piles Due to Lateral Soil Movement Wei Dong Guo Ph.D, M.Eng, B.Eng, M.I.E.Aust Lecturer, Griffith University, Gold Coast, Australia
Eng How Ghee B.Eng (Hons) Ph.D student, Griffith University, Gold Coast, Australia
Summary: A number of numerical approaches have been developed to predict response of piles due to lateral soil movement. Recently a correlation between an ‘equivalent load’ and the magnitude of soil movement has been established by the first author, which allows the response of piles due to soil movement to be analysed readily using the solutions developed for laterally loaded piles. The accuracy of either prediction is dependent on ‘good’ selection of input parameters, such as the limiting force profile between the pile and soil mobilised that may vary from case to case. Therefore, it is necessary to investigate this profile before any reliable predictions can be made. This paper attempts to back-figure the profile using a closed-form solution against measured response of three piles. It was found that the back-figured profile for each pile is generally consistent with that suggested for laterally loaded piles.
INTRODUCTION Piles may be used to provide lateral resistance against soil movement. These piles are known as passive piles, and commonly found stabilizing a sliding slope, supporting bridge abutments, and providing a lateral pressure barrier adjacent to a pile driving or an excavation operation. Design of the passive piles often requires a limiting force profile between the pile and soil that is not yet available, but has been based on a certain proportion of the profile developed for a lateral loading pile. It is not clear how this usage affects the prediction, as the profile may vary with the amount of soil movement, and pile-soil relative stiffness etc. Such an effect may be examined by back estimation through comparison between measured and predicted response of piles using a closed form solution (Guo, 2003). The close-form solution was recently established for an elastic-plastic soil (Guo, 2002, 2003), by simulating the pile-soil interaction as a series of independent springs acting along the shaft and at the pile base. The coupled effect among the springs is also accounted for by introducing a membrane (Guo and Lee, 2001). The elasticplastic solution for the pile under lateral loading provides sufficiently accurate means in comparison with some existing numerical results, in terms of predicting the bending moment, shear force, deflection and rotation response of the pile. The major advantage of the closed-form solution is that it allows a unique limiting force profile (a key parameter) to be back-estimated, which has been conventionally determined using empirical or semi-empirical relationships derived from field or laboratory test results. For passive piles, the effect of soil movement of the unstable layer can be converted to an equivalent load on the piles (Guo, 2003), so that the response of the piles can be predicted using the closed form solution. However, no rigorous guidelines have yet been provided for determining the limiting force profile. This paper provides a preliminary investigation on such profiles based on three recorded cases of measured pile response.
RESPONSE OF PILES DUE TO LOAD Elastic-plastic solutions were developed previously for a free-head pile (Guo, 2002) and a fixed-head pile (Guo, 2003). Using these solutions together with relevant measured pile response, limiting force profiles were widely explored (Guo, 2003; Guo and Zhu 2003), which provided conditions and some justifications on using the existing force profiles. Generally, the net limiting force per unit length, pu around a laterally loaded pile may be expressed as p u = A L (α 0 + x ) n
(1)
where AL = gradient of the limiting force profile, α0 = a constant to include the force at x = 0, n = exponent of the limiting force profile, x = the depth below the location of the equivalent load. The values of ‘AL’, ‘α0’ and ‘n’ may be back-estimated through matching theoretically predicted values with the measured pile response of
displacement, and maximum bending moment to different load levels. The depth at which the interface force between the pile and soil just touches the pu, is the critical depth, xp. RESPONSE OF PILES DUE TO SOIL MOVEMENT A simplified approach for predicting pile response due to lateral soil movement was proposed previously by Guo (2003), using the above-mentioned closed form solution for a laterally loaded pile shown in Figure 1(a). The main idea for this simplified model is summarised in Figure 2. As shown in Figure 2(a), the response of the pile due to soil movement can be resolved into two portions in the sliding soil and in the stable soil, respectively. Response of the portion in the sliding soil can be predicted readily (Guo, 2003). The portion in the lower stable layer may be treated as an ‘imaginary’ free-head pile (Figure 2(b)) under an equivalent load P. The length of the imaginary pile is the difference between the pile length and the thickness of the upper sliding layer. As shown in Figure 2(b), the equivalent load exerted on the pile at the level of sliding interface may be calculated as: P=
(
AL (Ls + α o )n+1 − (x s + α o )n+1 1+ n
)
(2)
where Ls = thickness of the sliding soil layer; xs = thickness of the soil layer within which the soil displacement is less than the pile displacement. The xs is dependent of the load P, thus initially, the thickness xs may be taken as that of the sliding layer. The following procedure may be used for the calculation: ws
P Plastic zone, x p
Normalised force, p/pu
Plastic zone 1 Ls
θt Transition zone
0.5
Elastic zone
Spring, k
Membrane, Np
a) Coupled load transfer model
Remove this part
0
Elastic zone 0 2 Normalised deflection, w/d
b) Load transfer (p-y) curve
Figure 1. Coupled Load Transfer Analysis
Sliding soil
L L2
Equivalent P
L L2
wt
xs Ls-xs Ls
Stable Soil
Stable soil
a) The Problem
b) The imaginary pile
c) Soil and Pile parameters
Figure 2. Simplified Analysis of a Pile due to Soil Movement
(1) The estimated load in Eq. (2) is applied at the head of the imaginary free-head pile. For cases where a transition zone exists between the sliding and stable soil layer, the equivalent load may be applied at the top of the transition zone. (2) The displacement wt and rotation θt at the location of equivalent load on the imaginary pile may be calculated from the closed-form solutions for laterally loaded piles (Guo, 2003). Therefore, the uniform soil movement, ws may be assessed as: w s = w t + θ t (L s − x s )
(3)
The upper portion (above transition surface) of the pile in the sliding soil is assumed to move rigidly around the head of the ‘imaginary pile’. The estimated soil movement is acceptable only when the resistance on the portion is below that for a full slip developed around the portion in the sliding layer, as an excess movement would not increase the resistance of the pile. With the estimated head displacement and -rotation of the imaginary pile, the pile displacement profile in the upper sliding soil may be readily estimated. (3) With the estimated pile profile from step (2) and a given soil movement profile, a new thickness of xs may be estimated. If this new depth agrees with the assumed depth of xs within a desired accuracy, the xs is accepted as the real value; otherwise, a new depth, xs may be assumed, and steps (1)-(3) are repeated. Normally, only a few iterations are needed to obtain satisfactory results. The iteration procedure has been implemented into a spreadsheet program (Guo 2003), which was used in the following three cases of back-estimation of soil parameters against measured pile response.
CASE STUDIES Case 1 Piles Embedded in an Unstable Seafloor (McClelland and Cox, 1976) McClelland and Cox (1976) reported a field test on the failure of a flare pile in the Mississippi delta-front region. The flare pile was a steel tube, 0.76 m outer diameter, and was embedded to a depth of 45 m in the seafloor. The wall thickness of the pile was back-calculated to be about 7 mm (Lee et al., 1991), hence the computed flexural stiffness EpIp, was about 234.78 MNm2. The delta mainly consisted of soft unconsolidated marine clays with the presence of large gas porosities in the order of 15-20%. The biogenic gases and the active marine activities had a significant effect on the soil shear strength. Figure 3(a) shows a typical shear strength profile for the Mississippi River Delta Soil. A substantial submarine slide occurred during Hurricane Carla in 1961, and the pile had been sheared off at approximately 23.5 m below the mudline. The top 20 m of the pile had translated about 0.72 m within the sliding soil layer. This translation was sufficient to cause the pile to yield. However, no data on the amount of displacement within the sliding soil layer was reported. pu/c ud
0
0
10
20
4
6
8
10
12
Wo=86.99-(-0.0195)×23.5×1000=545.24 mm
30 32
23.5 m
Slide
θt ws=100.44 mm (Eq. (3))
Failure Zone
34 30 40
2
Crust Zone
10 20
0
30
xp=27.98 (m)
50
Transition Zone
Basement Zone
60
x p=27.98 (m)
L
z/d
Depth below mudline (m)
Soil shear strength (kPa)
wt=86.99 mm
36 38
Cur rent pr edict ion (Guo, 2003) Mat lock (1970)
Stable Soil
40 a) Soil shear strength profile (Bea and Audibert, 1980)
b) Limiting force profile
c) Pile and soil movement
Figure 3. Simulation of a Failed Pile in Mississippi River Delta Soil The following assumptions was made to analyse this case: 1) The average undrained shear strength of clay, cu was taken as 19 kPa for the stable layer. 2) The ultimate resistance between pile and soil for clay, pu was taken as that shown in Figure 3(b). 3) The average Young’s Modulus of soil Es was taken as 500cu (Lee et al., 1991), thus the average shear modulus was 3.4 MPa (νs = 0.4). 4) The equivalent Young’s modulus of 1.43×104 MPa was adopted for the pile, using a radius of 0.38 m and the above-mentioned flexural stiffness. Using the above-mentioned spreadsheet program, the resulting predictions are shown in Figure 4 (a), (b) and (c) for the pile below the slip depth Ls of 23.5 m using the parameters in Table 1. The equivalent load was applied at the surface of the stable soil layer (Figure 2(b)). Therefore, only the response of the pile below the stable soil layer was compared. The predicted bending moment and shear force profiles compare well with those obtained from boundary element method (BEM)(Lee et al., 1991), along the pile shaft below the stable layer. The locations of the maximum bending moment and shear force are also in very good agreement with the BEM predictions. The predicted displacement and rotation of the pile at the sliding surface were high (Table 1), indicating that the limiting force was reached, and the soil was in a plastic state. A hinge may have developed in the pile, as shown in Figure 4(c) where the deflection of the pile increased dramatically. The current method was not able to predict the deflection well, as it is only valid for piles behaving elastically. From the input parameters given in Table 1, the equivalent load acting on the pile at the surface of stable soil may be computed using Eq. (2): 36.1 (23.5 + 0.6)0.8+1 − (22.81 + 0.6)0.8+1 = 314.02 kN P= 1 + 0.8 The limiting force profile and the equivalent load P back-figured herein are indicative only, since the soil movement of 720 mm is far more than a limiting value required to fully mobilise pile resistance. Generally, when the soil movement is below the limit, the limiting force profile (Figure 3(b)) may be adjusted to match well the predicted response with the measured response of the pile and soil. Excess soil movement will not increase the equivalent load on the pile but drag the pile away, which is the current case. The xp was measured from the
(
)
ground level, therefore the actual slip depth below the location of the equivalent load is the difference between xp and the thickness of the upper sliding and/or transition layer. Table 1. Analysis of the Pile Reported by McClelland and Cox (1976) αo (m) 0.6
AL (kPa/m) 36.1
0.8
Gs (MPa) 3.4
Bending moment, (kNm) -900
-700
-500
-300
-100
100
-300
24
Depth (m)
Depth (m)
Current prediction
xp (m) 27.98
P (kN) 314.02
ws (mm) 100.44
Pile deflection (mm)
Shear force (kN) -100 100 300 24
-6
-2 24
2
6
10
28
32
36
θt (× 10-3) -19.49
wt (mm) 86.99
28
28
32
xs (m) 22.81
Depth (m)
n
32
36
36
BEM prediction
40 a) Bending moment profile
40 c) Pile deflection profile
40 b) Shear force profile
Figure 4. Comparisons Between the Current Prediction and that by Lee et al. (1991) Case 2 Piles Used to Stabilise Sliding Slope (Carrubba et al., 1989) A full scale reinforced concrete instrumental pile was tested to study the response of piles used to stabilize a sliding slope (Carrubba et al., 1989). The pile was 1.2 m in diameter, and 22 m in length. Pressure cells were installed along the pile shaft and an inclinometer was installed at the centre of the pile. The pile was bored into the sliding slope, which had a sliding surface at a depth of 6.2d (9.5 m) from the ground surface. This sliding surface was assumed to have a transition layer of approximately 2 m as estimated from the measured bending moment and shear force profile (Figure 5 (b) and (c)). The unconsolidated undrained strength cu for both the sliding layer and the stable layer was 30 kPa. The field data collected over duration of 5 months showed that a plastic hinge was developed in the pile at a depth of 12.5 m measured from the ground surface. No information was available regarding the soil movement that caused the pile to yield. Table 2. Analysis of the Pile Reported by Carrubba et al. (1989) n 0.5
AL (kPa/m) 90
αo (m) 1
Gs (MPa) 5.4
xs (m) 3.90
xp (m) 12.61
P (kN) 836.10
wt (mm) 58.11
θt (× 10-3) -9.66
ws (mm) 92.89
Similar parameters to those used by Chen and Poulos (1997) were adopted herein: 1) The Young’s modulus of soil, Es was taken as 15 MPa (=500cu), uniform with depth. Thus the average shear modulus, Gs was 5.4 MPa (νs = 0.4). 2) The flexural stiffness of the pile, EpIp was taken as 2,035.8 MNm2, with Ep being taken as 20,000 MPa. 3) The soil movement profile was assumed to vary uniformly from the ground surface down to the surface of the transition layer, with a value of 95 mm. The limiting force profile was obtained by trying different values of n (0.5-1.5) and AL (72-108 kN/m2) to match the predicted with the measured pile response. The parameters for the best match as shown in Figure 5(b) and (c) were summarised in Table 2, which offered a limiting force profile (Figure 5(a)) increasing with depth, and of slightly lower gradient with depth than that proposed for piles under a lateral loading (Matlock, 1970). The equivalent load was applied at the depth Ls of 7.5 m (rather than 9.5 m), which is just above the surface of the transition layer. The match between the measured and predicted is reasonably good, considering the effect of the transition zone.
2
pu/cud 4 6
Bending moment (kNm) 8
10
-2400
6
-1600
7 8 10
Depth (m)
z/d
9 xp=12.61 (m)
11 12
0
Current prediction (Guo, 2003)
Measured
-600
-200
200
6
6
10
10
14
600
14
18
18
Current prediction
13 14
Shear force (kN)
-800
Depth (m)
0
Matlock (1970)
a) Limiting force profile
22 b) Bending moment profile
22 c) Shear force profile
Figure 5. Comparisons Between the Predicted and Measured (Carruba et al., 1989) Pile Responses Case 3 Piles Behind Retaining Wall (Leung et al., 2000) Leung et al. (2000) conducted a centrifuge model test at 50g to study the behaviour of piles subjected to soil movement. The soil movement was caused by unstrutted deep excavation in dense sand. The response of a model single pile located at 3 m behind a retaining wall was tested at 50g, to simulate the performance of a typical bored pile, 0.63 m in diameter, 12.5 m in length and of a flexural stiffness EpIp of 2.20 × 105 kNm2. The model retaining wall supporting the excavation and made of aluminium alloy plate was used to simulate a KSPIIA sheet pile wall having a stiffness EpIp of 2.40 × 107 kNm2/m and an embedment depth of 8 m. The unit weight and relative density of the sand used in the test were 15.78 kN/m3 and 90%, respectively. Under a confining stress ranging from 50 to 100 kPa, the estimated friction angle of the sand was about 43°. The Young’s modulus of soil was assumed to increase linearly with depth z (Es = 6z MPa). Therefore, an average Es of 27 MPa corresponding to the modulus at a depth of 4.5 m (Gs = 9.6 MPa, νs = 0.4) was adopted in the current calculation. With the above-mentioned data and parameters given in Table 3, predictions were made for three different depths (2.5 m, 3.5 m and 4.5 m) of excavation. The ultimate limiting force was maintained identical for all the predictions. The slip surface was taken as 4.5 m below ground surface, above which a significant increase in soil movement was noted, at the maximum excavation depth of 4.5 m. Table 3. Analysis of the Pile Reported by Leung et al. (2000) Excavation Depth (m) N AL (kPa/m) αo (m) Gs (MPa) xs (m) xp (m) P (kN) w t (mm) θt (× 10-3) w s (mm)
2.5 1 278.12 0 9.6 4.44 4.75 74.59 2.39 -0.97 2.45
3.5 1 278.12 0 9.6 4.43 4.79 86.93 2.84 -1.16 2.92
4.5 1 278.12 0 9.6 4.42 4.83 99.23 3.31 -1.35 3.42
The limiting force profile was selected to match the value given by Fleming et al. (1992) for cohesionless soil as shown in Figure 6(a). Figures 7, 8 and 9 present the comparisons between the predicted and measured results, which offered results tabulated in Table 3. The measured bending moment profile and pile deflection profile were well predicted for all excavation depths. The slip depth xp (= 0.25~0.33 m) was rather low. Thus the limiting profile had little effect on the prediction. The current prediction yielded a uniform soil movement, ws, ranging from 2.45 to 3.42 mm (Table 3). Measured at the end of excavation of 4.5 m and 3 m away from the wall, the free-field soil movement was about 14 mm at the surface and decreased linearly to zero at a depth of 7.5 m. After the installation of the pile, the free-field movement at the location of the pile may be well below the measured movement profile, due to the restraining effect of the retaining wall in front of the pile. Therefore, the currently predicted soil movement may be reasonable.
pu/γd 0
20
40
Bending moment (kNm) 60
80
-100
-50
0
6
-2
50
0 Current prediction (Guo, 2003)
Pile deflection (mm) 0 2 4 0
6
xp=4.75 (m)
xp=4.75 (m)
4
4
Depth (m)
z/d 10
Depth (m)
Fleming et al. (1992)
8
8 12
8 12
Measured Current prediction
16
16
12 b) Bending moment profile
a) Limiting force profile
c) Pile deflection profile
Figure 6. Predicted vs Measured Pile Responses at 2.5 m Excavation Depth -80
Bending moment (kNm) -60 -40 -20 0 0
20
Pile deflection (mm) 0 5 0
-5
xp=4.79 (m)
4 Depth (m)
Depth (m)
Wo=2.84-(-0.00116)×4.5×1000=8.06 mm
xp=4.79 (m)
4 8 12 Measured
10
4.5 m
8 L 12
16
wt=2.84 mm
16
Stable Soil
Current prediction
c) Pile and soil movement
b) Pile deflection profile
a) Bending moment profile
θt w =2.92 mm (Eq. (3)) s
Figure 7. Predicted vs Measured Pile Responses at 3.5 m Excavation Depth
-90
Bending moment (kNm) -70 -50 -30 -10 0
Pile deflection (mm) 0 5 10
-5
10
15
Wo=3.31-(-0.00135)×4.5×1000=9.39 mm
0
xp=4.83 (m)
4
8 12 Measured
16
Depth (m)
Depth (m)
4
4.5 m
8 xp=4.83 (m)
12 16
Current prediction
a) Bending moment profile
θt ws=3.42 mm (Eq. (3))
b) Pile deflection profile
L wt=3.31 mm
Stable Soil
c) Pile and soil movement
Figure 8. Predicted vs Measured Pile Responses at 4.5 m Excavation Depth
CONCLUSIONS A satisfactory prediction of pile response due to soil movement can be made only when suitable soil parameters are adopted. The effect of the parameters on the prediction in turn depends whether there is a relative slip developed between the pile and soil. Where a slip is mobilised, the limiting force profile becomes dominant, otherwise soil modulus has significant effect on the prediction. The three case studies shown here are only a preliminary attempt to search for a rational profile for piles due to lateral soil movement. The closed form solutions were found to be very efficient in the investigation.
ACKNOWLEDGEMENTS The work reported herein is currently sponsored by Australian Research Council Discovery Grant (DP0209027). This financial assistance is gratefully acknowledged.
REFERENCES Bea, R.G. and Audibert, J.M.E. (1980). “Offshore platforms and pipelines in Mississippi River Delta,” Journal of Geotechnical Engineering Division, ASCE, Vol. 106, No. GT8, pp. 853-869. Chen, L.T., and Poulos, H.G. (1997). “Piles subjected to lateral soil movements,” Journal of Geotechnical and Geoenvironmental Engineering,ASCE, New York, Vol.123, No.9, pp. 802-811. Carrubba, P, Maugeri, M., and Motta, E. (1989). “Esperienze in vera grandezza sul comportamento di pali per la stabilizzaaione di un pendio,” Proceedings of XVII Convegno Nazionale di Geotechica, Assn. Geotec. Italiana, Vol. 1, pp. 81-90. Fleming, W.G.K., Weltman, A. J., Randolph, M. F. and Elson, W. K. (1992). Piling Engineering, 2nd Edition, Blackie A & P, an imprint of Chapman & Hall, Glasgow, U.K. Guo, W.D. (2004?). “On critical depth and lateral pile response,” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, (tentatively accepted, June 11, 2002) Guo, W. D. (2003). “A simplified approach for piles due to soil movement,” Proceedings of 12th Pan-American Conference on Soil Mechanics and Geotechnical engineering, Cambridge, MIT, U.S.A., Vol. 2, pp. 2215-2220. Guo, W. D. and Zhu, B. T. (2003). “Laterally loaded fixed-head piles in sand,” Proceedings of the 9th Australia New Zeland Conference on Geomechanics, Auckland, New Zeland. Guo, W.D. and Lee, F.H. (2001). “Theoretical load transfer approach for laterally loaded piles,” International Journal of Numerical & Analytical Methods in Geomechanics, Vol. 25, No.11, pp. 1101-1129. Leung, C.F., Chow, Y.K. and Shen, R.F. (2000). “Behaviour of pile subject to excavation-induced soil movement,” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, New York, Vol.126, No. 11, pp. 947-954. Lee, C.Y., Poulos, H.G. and Hull, T.S. (1991). “Effect of seafloor instability on offshore pile foundations,” Canadian Geotechnical Journal, Vol.28, pp. 729-737. Maugeri, M. and Motta, E. (1991). “Stresses on piles used to stabilize landslides,” Landslides, A.A. Balkema, Rotterdam, The Netherlands, pp. 785-790. Matlock, H. (1970). “Correlations for design of laterally loaded piles in soft clay,” Proceedings of the II Annual Offshore Technology Conference, Houston, Texas, (OTC 1204), pp. 577-594. McClelland, B. and Cox, W.R. (1976). “Performance of pile foundations for fixed offshore structures,” Proceedings, BOSS ’76, International Conference on Behaviour of Off-Shore Structures, Vol.2, University of Trondheim, Norway, pp. 528-544.
