NZGS 2006 Symposium: Earthquakes and Urban Development. Nelson, Feb. 2006; 127-142.
M. Cubrinovski
Department of Civil Engineering, University of Canterbury, Private Bag 4800, Christchurch.
Soil liquefaction has been a major cause of damage to pile foundations in many of the past earthquakes. Particularly damaging for piles have been excessive ground displacements caused by spreading of liquefied soils in sloping ground and in waterfront areas.
The analysis of piles subjected to lateral spreading is burdened by the uncertainties associated with the spreading of liquefied soils. Namely, it is very difficult to reliably predict the magnitude and spatial distribution of post-liquefaction ground displacements as well as to estimate the stiffness and strength of the spreading soils. Thus, the key issue is how to deal with unknowns in the analysis while capturing the essential features of pile behaviour.
From a practical viewpoint, we need rational analysis methods that permit us to assess the pile response by considering various lateral displacements and stiffness properties of spreading soils. This paper discusses efforts towards developing such an analysis methodology and addresses, (a) field performance and damage features of piles in the 1995
Kobe earthquake, (b) key parameters controlling the pile response to lateral spreading and (c) experimental findings from benchmark tests on full-size piles.
Soil liquefaction during strong earthquakes significantly affects the performance of pile foundations leading to damage and even collapse of piles. In the 1995 Kobe earthquake, for example, massive liquefaction of reclaimed fills caused damage to numerous pile foundations of buildings, storage tanks and bridge piers. The unprecedented level of damage to foundations of modern structures instigated a great number of research studies in an effort to better understand soil-pile interaction in liquefied soils and to improve the seismic performance of pile foundations. In the initial stage of these studies, detailed field investigations on the damage to piles, in-situ soil conditions and features of permanent ground displacements were conducted. The field investigations were then followed by experimental studies aiming to clarify the mechanism of the damage by means of seismic centrifuge tests,
1-g shake table tests and benchmark experiments on full-size piles. Based on these studies, new concepts and analysis procedures have been proposed in an effort to explore design methodologies for piles in liquefied soils. This paper discusses these efforts based on recent studies conducted in Japan.
When analyzing the behaviour of piles in liquefied soils, it is useful to distinguish between two different phases in the soil-pile interaction: a cyclic phase in the course of the intense ground shaking and consequent development of liquefaction, and a lateral spreading phase following the liquefaction. During the cyclic phase, the piles are subjected to cyclic ground displacements (kinematic loads) and horizontal loads from the superstructure (inertial loads), and the combination of these oscillatory kinematic and inertial loads determines the critical load for the pile during the shaking. Lateral spreading, on the other hand, is primarily a postliquefaction phenomenon that occurs in sloping ground or in backfills behind quay walls thus leading to large down-slope or seaward permanent ground displacements. The spreading is therefore characterized by very large unilateral ground displacements and relatively small inertial effects. In the studies on the 1995 Kobe earthquake, the effects of ground displacements on the pile response received particular attention, for two reasons. One reason is because it was found that the excessive lateral movement of liquefied soils was a key factor in the damage to piles, and the other is the fact that, by and large, these effects had been either ignored or crudely approximated in the seismic design codes for piles.

Figure 1. Reclaimed lands in the port area of Kobe
During the 1995 Kobe earthquake, widespread liquefaction occurred over areas of reclaimed land in the port district of Kobe city (Fig. 1). Reclaimed fills with thicknesses of 10-20 m extensively liquefied, littering ejected water and sand over the surface of artificial islands. In the portions unaffected by lateral spreading, the liquefaction resulted in settlement of the ground of about 30-40 cm and equally large horizontal ground displacements. The ground distortion was particularly excessive in the waterfront area where many quay walls moved several meters towards the sea and lateral spreading occurred in the backfills that progressed inland as far as 200 m from the revetment line.
Cyclic ground displacements
The ground shaking during the earthquake was recorded by an array of accelerometers at Port
Island including two sets of acceleration records in the liquefied deposits, at the ground surface and at 16 m depth, respectively. Horizontal cyclic displacements of the ground, estimated through double integration of the acceleration records as well as from results of detailed effective stress analyses of the instrumented site, indicated that the peak amplitude of the cyclic ground displacements was about 40 cm. This magnitude of lateral displacement might be considered as representative of cyclic ground displacements in areas unaffected by lateral spreading. Figure 2 shows a more exact time history of the cyclic ground displacements as computed in an effective stress analysis of the vertical array site (Ishihara and Cubrinovski, 2005).
Displacements of lateral spreads
In the waterfront area, the quay walls moved several meters towards the sea and lateral spreading occurred in the backfills behind the walls. Ishihara et al. (1997) investigated the features of movements of the quay walls and ground distortion in the backfills by ground surveying measurements along alignments in the direction perpendicular to the revetment line. They summarized the measured displacements at nearly thirty locations in plots depicting the permanent ground displacement as a function of the distance inland from the waterfront, as shown in Figure 3. In this figure, the shaded area shows the range of measured displacements along different sections while the solid line is an approximation for the average displacement. The lateral ground displacement is largest at the quay walls and decreases rapidly with distance from the waterfront. This is a typical distribution of permanent ground displacement due to spreading in waterfront areas that has been observed in many earthquakes and adopted in several empirical models e.g. (Bartlett and Youd, 1995; Tokimatsu and Asaka,
1998).

60
30
0
Relative displacements between GL-0m and GL-16m
-30
VA-site
-60
0 5 10
Time (seconds)
15 20
Figure 2. Cyclic horizontal displacements of liquefied deposits in the 1995 Kobe earthquake
The cyclic ground displacements in the free field of liquefied deposits are superimposed in
Figure 3 thus indicating that in the zone within a distance of approximately 50 m from the quay walls, the permanent ground displacements due to lateral spreading were significantly greater than the cyclic displacements. Conversely, the cyclic displacements were dominant at distances greater than 100 m from the quay walls. Thus, with respect to the magnitude and nature of lateral ground displacements we can distinguish different zones in the waterfront area in which either the cyclic displacements or lateral spreading displacements are relevant for the design of piles.
A large number of pile foundations of buildings, storage tanks and bridge piers located in the waterfront area of Kobe were damaged in the earthquake e.g. (Ishihara and Cubrinovski,
1998; 2004; JGS, 1998; Tokimatsu and Asaka, 1998). In order to inspect the damage to piles, detailed field investigations have been conducted on selected piles by means of several inspection techniques. For example, features of the damage were investigated by lowering a
U
G
Sea
Lateral spreading
2
1.5
1
0.5
Measured (N-S)
Ishihara et al. (1997)
Uozakihama Pier 211
Mikagehama Tank 101
H-Building
Fukaehama Building
Mikagehama Tank TA-72
Higashi-Nada Building
U
CL-max
= 30-40 cm
0
0 50 100 150 200
Distance from the waterfront, L (m)
Figure 3. Permanent lateral ground displacements due to spreading of liquefied soils in the
1995 Kobe earthquake

borehole video camera down the hole of pre-cast hollow-cylindrical piles to examine the development of cracks around the pile-wall. In the case of cast-in-place reinforced concrete piles, a hole was first drilled into the piles and then a video camera was lowered into the hole to inspect the distribution of cracks. In addition, a survey of pile deformation was carried out by lowering an inclinometer down the hole; by integrating the measured data on tilts through the depth, the lateral displacement and hence deformation of the pile was obtained. In some cases, the top part of the pile foundation was exposed by excavating the surface soils and visual inspection of the damage to the pile head was then carried out. Characteristic damage features of piles located within the lateral spreading zone are briefly described below by using three representative case histories.
Mikagehama Tank TA72
The performance of the pile foundation of an oil-storage tank, with a diameter of approximately 15 m and capacity of 2450 kl, was investigated in detail by Ishihara and
Cubrinovski (2004). The tank, which was located about 25-40 m inland from the quay walls, was supported on 69 PHC (pre-stressed high-strength concrete) piles, 23 m long and 45 cm in outer diameter. A cross-sectional view of the tank and its foundation is shown in Figure 4a.
During the earthquake, extensive liquefaction developed in the reclaimed soils with a seaward movement of the quay wall of about 1 m and consequent lateral spreading in the backfills. It was estimated that the permanent lateral ground displacement, at a distance corresponding to the location of the tank, was about 30-60 cm. After the earthquake, two of the piles were investigated using the aforementioned inspection methods. The outcome of the borehole camera recordings is summarized in Figure 4b where the observed distribution of cracks is shown for the inspected piles. The piles developed multiple cracks and suffered largest damage at a depth of approximately 12 to 14 m, which corresponds to the depth at the interface between the liquefied layer and the underlying non-liquefied layer.
(a) Pile No.2
(b) Pile No.9
Pile top
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
19.2
20.0
8.0
10.0
12.0
14.0
16.0
16.8
18.0
2.0
4.0
6.0
45 cm
Cracks
Figure 4. Mikagehama Tank TA72: (a) Side view of the tank and its foundation;
(b) Observed damage to piles

Uozakihama Bridge Pier 211
Large-diameter piles supporting massive bridge structures and storage tanks in proximity to the revetment line also suffered serious damage due to liquefaction and spreading (Ishihara and Cubrinovski, 1998). A typical example of such damage was seen in Pier 211 of the
Hanshin Bay Route No. 5 which was located in the southernmost part of Uozakihama Island.
Side views of Pier 211 and a plan view of its foundation are shown in Figure 5 (HHA, 1996).
The pier was supported on 22 cast-in-place reinforced concrete piles, 1.5 m in diameter and
41.5 m long. The damage to the piles summarized from borehole camera recordings of two inspected piles is shown in Figure 5b. The damage at the pile head was supposedly caused both by spreading loads and by inertial loads from the superstructure during the intense ground shaking. By and large, however, the cracks were predominantly found at depths corresponding to the interface between the liquefied layer and the underlying non-liquefied layer. This type of damage was typically observed in piles located near the waterfront and it could be attributed solely to the excessive lateral ground movement due to spreading.
Higashi-Nada Building
The last case history to be introduced is that of a pile foundation of a 3-story building in
Higashi-Nada (Tokimatsu and Asaka, 1998). The building was located 6 m from the quay wall and was supported by 38 prestressed concrete piles, 40 cm in diameter and about 20 m long. A cross-sectional view of the building and its foundation is shown in Figure 6a while a plan view of the foundation is shown in Figure 6b. The permanent spreading displacements at the site of the building have been estimated at about 80-100 cm while detailed inspections of two of the piles revealed serious damage to the piles at the pile head and at a depth corresponding to the interface between the liquefied layer and the underlying non-liquefied layer. The largest damage was found for the pile in proximity to the quay wall, which suffered failure about three to four meters below the pile top, as indicated in Figure 6a. Tokimatsu and
Asaka (1998) have shown that this failure pattern could be induced by pile-group effects or cross-interaction of piles subjected to variable magnitudes of lateral ground displacement.
Pile
0
4.18 m
S
Pile 4
N S
Pile 10
S N S
10
20
30
Cracks
40
45.7 m
Figure 5. Uozakihama Bridge Pier 211: (a) Side view of the pier and plan view of its foundation; (b) Observed damage to piles (Hanshin Highway Authority, 1996)

Figure 6. Higashi-Nada building: (a) Side view of the building and its foundation;
(b) Plan view of the foundation (Tokimatsu and Asaka, 1998)
Summary of damage features
The damage to the piles can be briefly summarized as follows.
1.
Piles in the zone of large lateral spreading displacements were consistently damaged at depths corresponding to the interface between the liquefied layer and the underlying non-liquefied layer. Since this damage was at large depths where inertial effects from the superstructure are known to be less significant, this damage can be attributed to the lateral loads arising from the excessive ground movements due to spreading.
2.
Damage at the pile head was encountered both for piles in the free field and piles located within the lateral spreading zone, near the quay walls. Inertial loads from the superstructure and kinematic loads caused by lateral ground displacements contributed to the damage of piles at the pile head.
3.
The variation of lateral spreading displacements with the distance from the waterfront shown in Figure 3 may result in different lateral loads being applied to individual piles depending on their position within the pile-group. This in turn may lead to significant cross-interaction effects and consequent bending deformation and damage to piles in accordance with the interaction loads from the pile-cap-pile system.
In addition to the typical damage patterns described above, other but less significant damage was consistently found at most of the inspected piles thus reflecting the complex nature of loads and behaviour of piles in liquefied soils.
A rigorous analysis of the behaviour of piles in liquefied soils undergoing spreading would require use of sophisticated numerical methods such as those employed in the effective stress analysis of saturated soils (Finn and Tavaraj, 2001; Cubrinovski et al., 2005a). In the design

considerations and for preliminary assessment of piles, however, a simplified analysis could be more appropriate provided that such analysis can satisfy the following requirements:
1. The adopted model must capture the kinematic mechanism associated with the spreading of liquefied soils;
2. The analysis should allow us to estimate the inelastic response and damage to piles;
3. The method should allow for variations in key parameters and assessment of the uncertainties associated with lateral spreading.
Based on these premises, a simplified method of analysis was developed in a previous study (Cubrinovski and Ishihara, 2004), a brief summary of which is given below.
Three-Layer Model
The most frequently encountered soil profile for piles in liquefied deposits consists of three distinct layers, as illustrated in Figure 7 where the liquefied layer is sandwiched between a non-liquefied crust layer at the ground surface and non-liquefied base layer. Liquefaction during strong ground shaking results in almost a complete loss of strength and stiffness of the liquefied soil, and consequent large lateral ground displacements. As demonstrated in the previous section, particularly large and damaging for piles are post-liquefaction displacements due to lateral spreading. During spreading, the non-liquefied surface layer is carried along with the underlying spreading soil, and when driven against embedded piles, the crust layer is envisioned to exert large lateral loads on the piles, e.g. (Berrill et al., 2001). Thus, the excessive lateral movement of the liquefied soil, lateral loads from the surface layer and significant stiffness reduction in the liquefied layer are key features that need to be considered when evaluating the pile response to lateral spreading.
In light of the liquefaction characteristics and kinematic mechanism as above, a three-layer soil model was adopted for a simplified analysis of piles, as shown in Figure 8. In this model, the pile is represented by a continuous beam while the interaction between the liquefied soil and the pile is specified by an equivalent linear spring (

2 k
2
). Here, k
2 is the subgrade reaction coefficient while

2 is a scaling factor representing the degradation of stiffness due to liquefaction and nonlinear behaviour. In the adopted pseudo-static approach, the spreading is represented by a horizontal free-field displacement of the liquefied soil while effects of the surface layer are modelled by an earth pressure and lateral force at the pile head, as indicated
Non-liquefied surface layer
Earth pressure
Lateral force
U
G p u
Liquefied layer p  k

Pile
Non-liquefied base layer
Free field displacement of liquefied soil
Figure 7. Simplified kinematic mechanism of lateral spreading

H
1
L
H
2
H
3 z
1 z
2
1
P h
P q
F
Surface layer
Pile
U
G2
Lateral displacement
EI
D o k
2
,

2
Liquefied layer
U (z
2
) z
3 k
3
,

3
Base layer
Figure 8. Three-layer model for analysis of piles in liquefied soils undergoing spreading in Figure 8. Assuming that both the soil and the pile exhibit linear behaviour, a closed-form solution was derived for the adopted soil-pile model based on the classical differential equation for a beam on an elastic foundation. The solution is briefly introduced below whereas its details can be found in Cubrinovski and Ishihara, (2004).
Closed-Form Solution for Linear Behaviour
The governing differential equations for the soil-pile model shown in Figure 8 are
EI d
4 y
1 dz
1
4

P h z
1

P q
EI d
4 y
2 dz
2
4
 
2 k
2
D o

U g 2
( z
2
)
 y
2


0
 z
1

H
1


0
 z
2

H
2

(1a)
(1b)
EI d
4 y
3 dz
3
4
  
3 k
3
D o y
3

0
 z
3

H
3

(1c) where D o and EI are the diameter and bending stiffness of the pile, y i
( z i
) is the horizontal pile displacement, z i and H i denote, respectively, depth in local coordinates and thickness of layer,
P q and P h are earth pressure parameters of the surface layer, k
2
and k reaction coefficients and

2 and

3
are horizontal subgrade
3
are respective stiffness degradation coefficients for the liquefied layer and non-liquefied base layer. Note that the product
 i k i
specifies a degraded soil stiffness.
Assuming a cosine function for the distribution of lateral ground displacement throughout the depth of the liquefied layer as

U g 2
( z
2
)

U
G 2
 cos


2 z
2
H
2



0
 z
2 the general solution of the differential equations takes the following form y
1
( z
1
)

P h
120 EI z
1
5 
P q
24 EI z
1
4 
A
1 z
1
3 
B
1 z
1
2 
C
1 z
1

D
1

H
2

(2)
(3a) y
2
( z
2
)
 e

2 z
2
H
2

 A
2 sin

2 z
2
H
2


B
2 cos

2 z
2
H
2

  e
 
2 z
2
H 2

 C
2 sin

2 z
2
H
2

D
2 cos

2 z
2
H
2



G
2 cos



2 z
2
H
2


(3b) y
3
( z
3
)
 e

3
H z
3
3

 A
3 sin

3 z
3
H
3


B
3 cos

3 z
3
H
3

  e
 
3 z
3
H
3

 C
3 sin

3 z
3
H
3

D
3 cos

3 z
3
H
3


(3c)
Here, the parameter G
2 is defined as
G
2

U
G 2
1
 4
(4)
1

64

2
4 whereas
 i is a dimensionless parameter expressing the flexibility of the pile relative to the soil and is given by
 i

H i


 i k i
4 EI
D o


1 / 4
(5)
The twelve constants A i
, B i
, C i and D i
( i = 1,3) can be determined from continuity and boundary conditions, and upon introducing these constants into the general solution, pile displacements can be readily computed using Eqs. (3a)-(3c). Bending moments, shear forces and lateral loads along the length of the pile can be computed using respectively the second, third and fourth derivative of the pile displacement, y i
( z i
). In this way, the pile response can be evaluated for assumed linear behaviour of the soil and pile.
Characterization of Nonlinear Behaviour
In order to extend the applicability of the above solution over the range of nonlinear behaviour, an iterative analysis based on the equivalent linear approach was developed
(Cubrinovski and Ishihara, 2004). In the adopted approach, equivalent linear, bi-linear and trilinear load-deformation relationships were adopted to characterize the nonlinear behaviour of the soil and the pile, as shown in Figure 9. Note that an equivalent linear p-

relationship or secant stiffness

2 k
2
was adopted for the liquefied layer in order to simplify the modelling of the highly nonlinear and very complex behaviour of liquefied soils undergoing spreading. In the analysis of a given pile, it is envisioned that

2 will serve as a parameter that will be varied over a relevant range of values thus allowing us to evaluate the pile response by assuming different properties of the liquefied soil.
On the other hand, it was postulated that non-liquefied soils in the surface layer and base layer exhibit bilinear pressure-displacement relationships defined by a subgrade reaction

H f
H
1
H
2
M
C
Y

U
U
G2
p p k
1 p
1-max


2 k
2

H
3
D o p k
3 p
3-max

Figure 9. Characterization of nonlinear behaviour and input parameters in the analysis coefficient k i
and an ultimate lateral pressure p i-max
( z i
). Similarly, a tri-linear momentcurvature relationship was adopted for the pile, which is a typical M-

relation for reinforced concrete piles. For the nonlinear load-deformation relationships of the pile, crust layer and base layer, three-independent equivalent linear models were developed respectively, which through iterative procedures provided equivalent linear parameters that can be used in the closed-form solution.
Equivalent Linear Model for the Pile
In the closed-form solution, a linear moment-curvature relationship of the pile is assumed through the bending stiffness EI . Instead of using the initial stiffness, however, it is possible to employ in the solution an equivalent linear or secant stiffness ( EI eq
) so as to approximately model the nonlinear moment-curvature relationship of the pile.
The calculation consists of an iterative procedure in which a series of equivalent linear analyses are made using the closed-form solution, as follows. First, an elastic analysis is carried out using the initial bending stiffness of the pile. Suppose that using the initial bending stiffness in the closed-form solution, the maximum bending moment computed in the first linear analysis is M
1-max
, as shown in Figure 10. Here, M
1-max
is the largest absolute bending moment computed along the length of the pile. Next, a reference bending moment ( M
1
) is evaluated by the average value of two bending moments, that is, the computed maximum bending moment ( M
1-max
) and the cracking moment of the pile (C), as illustrated in Figure 10.
The curvature

1
 corresponding to the reference bending moment is then used to determine the point C
1 on the actual moment-curvature relation of the pile, as indicated in Figure 10. The bending stiffness defined by the line OC
1
is then used to represent the stiffness of the pile in the second-step linear analysis, and new linear analysis is thus executed with the closed-form solution. In this manner, the iterative stepwise calculation is continued until eventually convergence has been obtained for the reference bending moment of the pile. In the last iteration, the computed reference bending moment, M n
, has a curvature that is compatible with the actual M-
 relationship of the pile, as depicted in Figure 10.

C
M
1
1
M
1-max
2
M
2
C 
C 
M n n
1
EI eq
(a)
O

 Curvature,

Figure 10. Schematic illustration of the equivalent linear model for the pile
Strictly speaking, the bending stiffness renewed in this way is applicable only for the points of the pile at which the computed bending moment coincides with the value of the reference moment. By and large, however, the equivalent stiffness defined as above provides a very reasonable approximation of the nonlinear deformational behaviour of the pile as well as a good estimate for its maximum response (Cubrinovski and Ishihara, 2004).
Equivalent Linear Model for the Base Layer
In principle, the equivalent linear model for the base layer is analogous to that proposed for the pile. The iterative calculation for the base layer, in effect, serves to evaluate the appropriate value of the degradation factor

 or the secant stiffness of the base layer

3 k
3
(Fig. 11) which is used in the closed-form solution (Fig. 8).
Lateral Loads from Surface Layer
The magnitude and direction of lateral loads from the surface layer on the pile depend on the relative displacement between the crust soil and the pile. Hence, the interaction loads in the surface layer cannot be known in advance, i.e., before the pile deformation is estimated. For this reason, the values of the earth pressure parameters P q
and P h
, and lateral force, F , in the analytical model (Fig. 8) will have to be determined through an iterative procedure. The aim of this iterative calculation is to adjust the lateral load from the surface layer so that eventually the load, which is applied as an input in the analysis, is nearly equal to the load corresponding to the computed pile response.
(c)
 r
 y
1
 p max
Relative displacement,

Figure 11. Schematic illustration of the equivalent linear model for the base layer

Calculation Flow
The simplified models discussed above separately for the nonlinear behaviour of the pile, base layer and surface layer are eventually combined into an integral computational procedure. The calculation flow of the overall procedure is outlined in Figure 12. It should be emphasized that all calculations of the pile response are carried out using the closed-form solution and soil-pile model shown in Figure 8.
This computational scheme allows us to identify the appropriate values of the bending stiffness ( EI ), stiffness of the base layer (

3
) and lateral loads from the surface layer ( P q
, P h and F ) for the computational soil-pile model shown in Figure 8. Thus, throughout the iterative computation, the values of EI ,

3
, P q
, P h
and F are systematically modified until eventually they are consistent with the pile response and adopted characterization of nonlinear behaviour shown in Figure 9. The input parameters for the analysis are listed in Table 1.
Table 1. Input parameters for the analysis (depicted in Figure 9)
Parameter type Pile Surface layer Liquefied layer Base layer
Geometry D o
Stress-deformation M-
 
H f
, H
1 k
1
, p
1-max
H
2

2
, k
2
H
3 k
3
, p
3-max
Ground displacement U
G2
 
M
C
,

C
),

M
Y
,

Y
),

M
U
,

U
): input parameters for trilinear M-f relationship, as shown in Figure 9
Input: - Parameters of soil-pile model (Fig. 9; Table 1)
- Lateral ground displacement, U
G2
Set: P q
= 0 , P h
= 0, F = 0
Linear analysis
(closed-form solution)
Equivalent linear model for pile ( new EI )
Equivalent linear model for base layer ( new

No
Convergence
Yes
Load adjustment
( new P , P , F )
No
Compatibility of load with relative displacements in the surface layer
Yes
Pile response incorporating nonlinear behavior of soil and pile
Figure 12. Outline of overall computational procedure

Key parameters influencing the pile response and hence requiring special attention are the magnitude of ground displacement U
G2
, ultimate pressure from the crust layer p
1-max and stiffness degradation parameter

2
for the liquefied layer. The lateral ground movement is in effect the sole external agency to be specified in the analysis, and clearly the size of the pile response will directly depend on the magnitude of the lateral ground displacement. The lateral load from the surface layer, on the other hand, may often be the critical load for the integrity of the pile because of its large magnitude and unfavourable position as a top-heavy load acting above a laterally unsupported portion of the pile in the liquefied soil. Finally, the stiffness reduction factor

2
affects the relative flexibility of the pile as represented by the non-dimensional factor

in Eq. (5), and in the extreme case, this influence may result either in behaviour typical for a relatively flexible pile that moves together with the surrounding soil or a relatively stiff pile that does not follow the ground movement. For these reasons, great efforts have been made over the past decade either to back-calculate these parameters from well-documented case histories or to evaluate them using experiments on soil-pile models.
The lateral displacement of the spreading soil ( U
G2
) can be evaluated using empirical correlations for lateral ground displacements of lateral spreads, e.g. (Tokimatsu and Asaka,
1998; Hamada et al., 2001; Youd et al., 2002). It is important to recognize, however, that in most cases it would be very difficult to make a reliable prediction for the spreading displacements. This difficulty is well illustrated in Figure 3 where a large scatter in the ground displacements is seen even for a single earthquake event and generally similar ground conditions. In this context, Youd et al. (2001) suggested to use a factor of 2 for the displacements predicted with their empirical model, in order to cover the expected range of variation in the spreading displacements.
The ultimate soil pressure from the surface layer per unit width of the pile can be estimated using a simplified expression such as, p
1-max
= pressure while

 u p p , where p p
( z
1
) is the Rankine passive u is a scaling factor to account for the difference in the lateral pressure between a single pile and an equivalent wall. Figure 13 shows the values of
 u observed in a benchmark lateral spreading experiment on full-size piles (Cubrinovski et al., 2005b) with the maximum lateral pressure on the single pile being about 4.5 times the Rankine passive pressure. Data from other experimental studies (Fig. 14) also show large values for the parameter
 u
clearly indicating that very large lateral loads can be applied from the crust layer on the pile. What is less certain, however, is the maximum load that would be mobilized in the case of pile groups since the pile-group effects on this parameter are not yet clearly
6
5
4
3
2
 u
1
Steel pile
PHC pile
0
0 20 40 60 80
Relative displacement between soil and pile,

= U g
(z) - U p
(z) (cm)
Figure 13. Ratio of lateral pressure from the crust layer on a single pile and Rankine passive pressure, measured in full-size test using large-scale shake table

8
7
6
5
4
3
2
1
11
10
9
Single piles in sand
Passive piles
Active piles
Meyerhof (1981)
Prasad (1999)
Broms (1964)
Passive piles
Poulos (1995)
Large scale test
(this study)
30 35 40 45 50 55
Figure 14. Ratio of ultimate pressure from the crust layer on a single pile and Rankine passive pressure, obtained in experimental studies (Cubrinovski et al., 2005) understood and quantified. In addition, sand boils, fissuring of the surface layer and impediment of ground deformation by adjacent foundations may significantly affect the ultimate pressure that can be mobilized in the surface layer thus making the possible variation in this parameter quite significant.
The factor

2
, which specifies the reduction of stiffness due to liquefaction and nonlinear behaviour, is affected by a number of factors including the density of sand, excess pore pressures, magnitude and rate of ground displacements and drainage conditions. Thus, there is a great deal of uncertainty and hence difficulty in the selection of its most appropriate value.
Typically,

2
may take a value in the range between 1/50 and 1/10 for cyclic liquefaction
(Tokimatsu and Asaka, 1998) and a value between 1/1000 and 1/50 in the case of lateral spreading (Ishihara and Cubrinovski, 1998; Yasuda and Berrill, 2000). The values of

2
backcalculated from the observed behaviour in the full-size tests on piles (Cubrinovski et al.,
2005b) are shown in Figure 15 as a function of lateral ground displacement, illustrating that even for a given earthquake event and ground conditions,

2
is not a constant, but rather it varies in the course of the lateral spreading.
The above discussion clearly demonstrates that the intrinsic uncertainties associated with spreading of liquefied soils are directly reflected in the values of U
G2
, p
1-max
and

2
. Hence, these parameters cannot be uniquely determined, but rather a relatively wide range of values for these parameters needs to be considered in the analysis of piles. The simplified method of analysis presented herein is envisioned as a rational tool of practical use in addressing these uncertainties and needs for parametric studies.
Lateral ground displacements of liquefied soils can be quite significant both during the intense shaking and the post-liquefaction phase of lateral spreading. Since the loads and properties of liquefied soils can be remarkably different during the cyclic phase and spreading phase, it is first necessary to identify the ground displacements and lateral loads that are relevant for the assessment of piles.

0.1
0.05
Range of

 values
0.01
Best fit
value
Steel pile
0.001
0 20 40 60 80
Ground displacement at top of liquefied layer (cm)
Figure 15. Degradation of stiffness in the liquefied layer as a function of lateral ground displacement (full-size test on piles, Cubrinovski et al., 2005b)
Piles subjected to large lateral displacements of liquefied soils are typically damaged at the pile head and at depths corresponding to the interface between the liquefied layer and underlying non-liquefied layer. Both inertial loads and kinematic loads from the crust layer contribute to the damage at the pile head while the damage at larger depths is attributed to the kinematic loads caused by the excessive lateral ground displacements. Cross-interaction or pile-group effects may significantly influence the behaviour of pile foundations that are subjected to spatially varying ground movements.
A simplified method of analysis for piles subjected to spreading has been presented. A three-layer soil model was adopted to represent the characteristic loading mechanism for piles in laterally spreading soils incorporating the effects of large ground displacements, significant stiffness reduction in liquefied soils and lateral loads from a crust layer at the ground surface.
Particular attention has been given to the modelling of nonlinear behaviour and to the need to estimate the inelastic response and damage to piles.
Key parameters influencing the pile response are identified to be the magnitude of ground displacement, ultimate lateral pressure from the surface layer and stiffness degradation of the liquefied soil. These parameters are associated with intrinsic uncertainties, however, and therefore one encounters difficulties in selecting their most appropriate values. A key requirement in the preliminary analysis of piles subjected to spreading is to address these uncertainties by evaluating the pile response for various magnitudes of lateral ground displacements and stiffness properties of the liquefied soils.
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, Taipei, pp. 1-14.
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