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Updated CPT-based p – y formulation for laterally loaded piles in cohesionless soil under static loading

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The p–y method is currently the most popular design method to predict the response of piles to lateral load. The authors had previously used numerical methods to develop a cone penetration test (CPT)-based p–y formulation for piles in sand and this has subsequently been shown by independent verification to show considerable promise. This paper addresses some of the uncertainties associated with the original p–y formulation by examining the influence of pile bending stiffness, the presence of a water table, the cross-sectional shape of the pile and soil non-homogeneities. Numerical experiments are presented examining these four effects and lead to an updated proposal for a CPT-based p–y formulation. This formulation, which is consistent with the original proposal, is validated against three-dimensional finite-element calculations and data obtained from a full-scale offshore monopile foundation supporting a wind turbine.
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1
Updated CPT-based p-y formulation for laterally loaded piles in
cohesionless soil under static loading
S.K. Suryasentana1 BEng
B.M. Lehane2 BE, MAI, DIC, PhD, FIEAust, CPEng
1 PhD Student
Oxford University, Dept. of Engineering Science
(Formerly the University of Western Australia)
2 Corresponding Author
Professor, School of Civil & Resource Engineering
The University of Western Australia.
35 Stirling Highway, Crawley WA 6009, Australia
Phone +61 8 6488 2417
Fax +61 8 6488 1044
E-mail: Barry.Lehane@uwa.edu.au
2
Abstract
The p-y method is currently the most popular design method to predict the response of piles to
lateral load. The authors had previously used numerical methods to develop a CPT-based p-y
formulation for piles in sand and this has subsequently been shown by independent verification
to show considerable promise. This paper addresses some of the uncertainties associated with
the original p-y formulation by examining the influence of pile bending stiffness, the presence
of a water table, the cross-sectional shape of the pile and soil non-homogeneities. Numerical
experiments are presented examining these four effects and lead to an updated proposal for a
CPT-based p-y formulation. This formulation, which is consistent with the original proposal,
is validated against 3D Finite Element calculations and data obtained from a full scale offshore
monopile foundation supporting a wind turbine.
3
Introduction
The p-y method is the de facto standard for the analysis of laterally loaded piles due to its
simplicity and long, proven record in Industry. This method uses p-y curves to represent the
non-linear relationship between the net soil resistance at any depth per unit length of soil
adjacent to a pile (p) and the lateral deflection of the pile at that depth (y).
There are a number of formulations to derive these p-y curves but all use some measure of soil
strength to determine the relationship between p and y. Currently, the most popular formulation
to derive these p-y curves is that recommended by the American Petroleum Institute (API) and
(Det Norske Veritas) DNV design standards (API 2011; DNV 2013); this formulation is
referred to, in the following, as the API method. The API method for piles in sand is derived
empirically using data from full-scale tests on free-headed piles and it uses the soil friction
angle, ϕ', as the primary measure of soil strength to determine the relationship between p and
y.
Although the API method has been used in Industry with reasonable success, it has a number
of acknowledged limitations and uncertainties. Firstly, the API method was derived based on
the test results from small diameter piles and its applicability to large diameter piles is
uncertain. Doubts about the applicability of the API method to large diameter piles have been
expressed previously (Murchison & O’Neill 1983) but the increasing popularity of large
diameter monopiles as the foundation of choice for onshore and offshore wind turbines has
intensified interest in the method’s reliability. Secondly, the API method is highly sensitive to
the choice of the sand friction angle ϕ' and such sensitivity is exacerbated by the need to employ
empirical correlations with in-situ test results to assess ϕ' .
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To address these limitations, some researchers (Novello 1999, Dyson & Randolph 2001 and
Suryasentana & Lehane 2014a) proposed using the cone penetration test (CPT) end resistance
(qc) as the measure of soil strength to determine the relationship between p and y. The primary
advantage of this approach is that it is a direct method and not susceptible to the subjectivity
associated with inference of ϕ' values.
The p-y formulation proposed by Suryasentana & Lehane (2014a), which was derived for a
wished-in-place circular pile in dry sand, was obtained via a regression analysis on a large
series of 3D Finite Element (FE) computations that predicted the lateral pile response in a
variety of different sands and a cavity expansion approximation using Finite Elements to
predict corresponding CPT qc profiles in each sand deposit. The sand was modelled in Plaxis
2D and 3D analyses using a non-linear elasto-plastic constitutive model, referred to as the
Hardening Soil (HS) model (Schanz et. al. 1999). The regression analysis led to the following
equation, which was based on results obtained for a large range of soil parameters typical of
loose to dense sands for pile diameters ranging from 0.5m to 5m and for normalised lateral
deflection values (y/D) in the range 0.01 and 0.2.


 (1a)


 (1b)
Where pu is the ultimate lateral resistance (per unit length), is the soil unit weight, z is the
depth below ground level, D is the pile diameter and qc is the CPT end resistance.
Equation (1) has subsequently been assessed against several published cases studies by
Suryasentana & Lehane (2014b) and Li et al. (2014) and shown to provide consistently good
5
predictions. Equation (1) was, however, derived for flexible circular piles under fully dry and
homogeneous soil conditions. Therefore, its applicability to rigid or non-circular piles under
fully saturated or non-homogeneous conditions is uncertain. This paper does not deal with the
dynamic response of piles to lateral loading; this subject is discussed by Dobry et al. (1982)
and many others.
a) Influence of pile bending stiffness on p-y curves
Although the p-y relationship is understood to be a soil-pile interaction response, rather than
solely a soil response, all existing p-y formulations are independent of the pile’s flexural
rigidity (EpIp). Previous investigations on the dependency of the p-y response on EpIp have been
conflicting. Ashour & Norris (2000), for example, investigated the effect of EpIp on p-y curves
using the Strain Wedge analysis technique and deduced that the stiffness and ultimate
resistance of the p-y response generally increased with EpIp. In contrast, Fan & Long (2005)
used 3D Finite Element (3D FE) analyses and deduced that the p-y response is generally
independent of EpIp. The type of response of a laterally loaded pile depends primarily on the
soil stiffness, pile length (L) and EpIp value. Poulos & Hull (1989) postulated that, under lateral
loading, a pile essentially rotates as a rigid body if L is less than 1.48R or behaves flexibly (i.e.
bending is significant) if L exceeds 4.44R, where R = (EpIp/Es)0.25 and Es is an equivalent linear
Youngs modulus for the soil. A rigid response results in a shearing force at the pile toe, which
can be a significant portion of the total lateral soil resistance for a large diameter pile.
Moreover, the rotational behaviour may induce a different p-y response to that of a flexing
behaviour. Therefore, given that Equation (1) was derived for statically loaded flexible piles,
its suitability for the design of rigid piles is examined in the following.
6
b) Influence of the presence of a water table on p-y curves
The API method relates p to the vertical effective stress (σ'v) and hence assumes implicitly that
the p-y response at any given depth in unsaturated soil is stiffer and reaches a higher ultimate
resistance than that in saturated soil. Although Equation (1) was derived for fully dry
conditions, Suryasentana & Lehane (2014b) substituted the γz term with the vertical effective
stress (σ'v) in this equation and obtained reasonable predictions for fully saturated conditions.
A specific examination of the suitability of this substitution is made in this paper.
c) Influence of pile cross-sectional shape on p-y curves
Equation (1) was derived for a pile with a circular cross-sectional shape and hence the
applicability of the equation to non-circular cross-sections is uncertain. Murchison and O’Neill
(1983) proposed applying a shape factor to their p-y formulation of 1.5 for uniformly tapered
piles or H piles but suggested that a square pile of width, B, would generate the same lateral
soil response as a circular pile with a diameter of B. However, Ashour & Norris (2000) and
Reese & Van Impe (2001) argue that a square pile mobilizes a higher net lateral soil resistance
than a circular pile with the same width. Additionally, Gleser (1984) contended that a square
pile mobilizes less lateral soil resistance than a circular pile with the same second moment of
area; this contention implies that a square pile of width B mobilizes less lateral soil resistance
than a circular pile of diameter 1.14B. Based on the foregoing, it would appear that there is
consensus that a square pile of width B can mobilize the same or more lateral soil resistance
than a circular pile of diameter B but not more than a circular pile of diameter 1.14B. Given
the widespread use of square precast concrete piles, modifications required to Equation (1) to
allow predictions of the lateral response of such piles are investigated in the following.
7
d) Effect of soil non-homogeneity on p-y curves
It is recognised that p-y springs do not directly allow for the transfer of shearing forces between
soil layers. The development of Equation (1) indirectly allows for such transfer as the pressure
and displacement values calculated at any given soil layer incorporate interaction with adjacent
soil layers. Equation (1) was, however, derived assuming a homogeneous sand layer for which
the stiffness at a given strain level varied only with the stress level. The applicability of
Equation (1) to lateral pile analysis in situations where there are appreciable differences in soil
properties is investigated in this paper.
Analysis and results
The suitability of Equation (1) to cater for issues (a) - (d) is investigated here by comparing the
p-y curves obtained from a variety of 3D Finite Elements simulations of lateral pile tests. As
was the case for the derivation of Equation (1) in Suryasentana & Lehane (2014a), the Plaxis
2D program was used to derive CPT qc profiles from cavity expansion analyses and the Plaxis
3D FE program was used to simulate lateral pile tests (with the load applied at ground level)
under a free head condition; the Hardening Soil (HS) constitutive model and fully drained
conditions were assumed throughout. The mesh set-up details, mesh calibration, CPT qc
derivation and p-y curves extraction process are described in Suryasentana & Lehane (2014a).
A loose and a dense sand with the HS parameters provided in Table 2 were employed to
represent a typical range of sands encountered in-situ. The HS parameters are described in
Suryasentana & Lehane (2014a) and Schanz et. al. (1999).
a) Influence of pile bending stiffness on p-y curves
To evaluate the dependency of the p-y response on EpIp and to investigate if the response for
rigid piles is different from that of flexible piles, lateral pile test FE simulations were carried
out using four different sets of pile properties, as shown in Table 1. The first three of these
8
employed EpIp values of 1.0, 0.1 and 10 times that of a solid concrete pile. The EpIp value
adopted for the fourth analysis assumed a solid steel pile with a length 4 times less than that of
the other 3 piles; this pile is classified as rigid according to the Poulos & Hull (1989) criterion.
The FE simulations were carried out for the loose and dense sands (with properties given in
Table 2) under fully unsaturated conditions with two different pile diameters (2m and 0.5m),
whilst maintaining similar L/D ratios.
For clarity purposes, only the results of the 2m diameter piles are presented in the figures
(although the results of the 0.5m diameter piles provide closely comparable trends). Figure 1
shows the effect of different EpIp values on the p-y curves in the loose and dense sand at z/D=1
and 2. It is evident that the p-y response is independent of EpIp for both the flexible and rigid
piles in the loose and dense sand. This finding supports that of Fan & Long (2005) that p-y
curves are not a function of the flexural rigidity.
b) Influence of the presence of a water table on p-y curves
Lateral pile test FE simulations were carried out using 2m and 0.5m diameter flexible piles
(Case F1 as shown in Table 1) for two typical cases involving a water table at (i) z/D = 1.5,
which is typical of many onshore sites and (ii) ground level, which is representative of offshore
environments. The FE simulations were carried out for the loose and dense sand (with
properties given in Table 2).
The net pressures calculated at z/D=1 and z/D=2 for the 2m diameter pile are normalised by
the vertical effective stress, p/(σ'vD), and plotted against normalised displacement (y/D) in
Figure 2. It is seen that, when plotted in this normalised form, the curves tend to reach the same
ultimate value for each depth. The p-y curves at depths below the water table are, however, a
little stiffer than their fully unsaturated counterparts and mobilize their normalized ultimate
9
resistances at a lower displacement. Further analysis indicated that p-y curves above and below
the water table could be unified approximately by factoring the normalised displacement (y/D)
by the following function of the vertical total and effective stresses at any given depth:

(2)
where is the water pressure at ground level (). The modification of the y/D values
according to equation (1) for the analyses summarised in Figure 2 is shown on Figure 3 and is
seen to provide a relatively unique normalised pressure-displacement response at each depth.
The maximum effect of this factor arises for full saturated conditions and leads to an initial
stiffness about 35% stiffer than that predicted by Equation (1).
(c) Square vs. circular piles
The lateral pile test FE simulations summarised in Table 3 were carried out to examine
differences between fully rough piles with square and circular cross-sectional areas. Three
different widths were selected for the square piles: the first was set equal to the diameter of the
circular pile (B=D), the second had a width that gave the same second moment of area as the
circular pile (B=D/1.14) and the width of the third was so that its perimeter was the same as
the circular pile (B=D/1.27). The Ep value for each pile was assigned such that EpIp was
identical for all piles. The FE simulations were carried out in fully unsaturated loose and dense
sand (with the properties given in Table 2).
The calculated normalised pressure-displacement curves at z/D=1 for the 0.5m diameter pile
are plotted on Figure 4. It is evident that the normalised p-y curves for the square piles with
widths of B=D and B=D/1.14 are generally stiffer than that of the circular pile. The best match
in response between a circular and square pile emerged when the square pile had approximately
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the same perimeter as the circular pile. Further evidence supporting this observation is provided
in Figure 5, which shows that the pile head load-displacement behaviour of a circular pile and
a square pile of equivalent perimeter are virtually identical for a number of pile diameters;
which indicates that this trend is not diameter specific. Square piles per unit volume of concrete
are therefore about 27% more efficient than circular piles in resisting lateral load (if structural
moment capacities are not controlling).
(d) Effect of soil non-homogeneity on p-y curves
The effects of non-homogeneity were examined in lateral pile test FE simulations involving
2m and 0.5m diameter flexible piles (F1 as shown in Table 1) installed in an unsaturated,
layered stratigraphy comprising an upper layer with a thickness of 1.5 D overlying a deep
uniform layer. The first set of analyses was performed with the upper layer having the
properties of dense sand and the lower comprising loose sand (with the properties given in
Table 2). The second set of analyses examined the pile response with the loose sand overlying
the dense sand.
The calculated results for the 2m diameter pile are plotted on Figure 6. It is evident that the p-
y responses at z/D=1 and z/D=2 are not dependent on the nature of the sand at a distance of 1
D above or below these two depths. These analyses therefore support the general validity of
the use of p-y springs (and Equation 1) for laterally loaded pile analysis. p-y curves were also
extracted for the transition depth at 3m below ground level. These curves indicate that the
response at this depth is not equal to the average values for a loose or dense sand but is weighted
towards the p-y response of the underlying soil.
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Updated Formulation
Rationale for updating
The analyses described above suggest that Equation (1) can be updated with the inclusion of
two factors, ηw and De:


 (3)
where pu is given in equation 1a, the saturation factor (ηw) is given in equation (2) and the
effective diameter, De is the actual diameter, D, of a circular pile and 1.27B for a square pile
of width B. Equation (3) is identical to Equation (1) for circular piles in dry sand conditions.
Equation (1a) indicates that the ultimate lateral resistance (pu) continues to increase both with
z/D and y/D. The numerical analyses only examined p-y curves at z/D 4 as the sand properties
in upper 4 diameters of a laterally loaded pile dominate its performance and very often the
pile’s finite moment capacity restricts the development of high lateral stresses at deeper levels.
The calculations indicated that, at these deeper levels, the ultimate net lateral pressure value
does not exceed the CPT qc value; this limit is considered a sensible upperbound for lateral
resistance at depth.
The initial stiffness of the p-y curve, which is found by differentiating Equation (3) with respect
to y, tends to an infinite value as y approaches zero. It can be shown that that this differentiation
can only yield a finite value at y=0 when the exponent of y is unity (noting that differential is
zero if this exponent is greater than 1). The regression analysis of the FE computations was
12
therefore repeated by increasing the exponent of 0.89 to a fixed value of unity. This analysis
gave the updated p-y formulation provided in Equation (5).
The initial stiffness, dp/dy at y=0, determined using Equation (5), gives a much lower value
than the true initial stiffness (k0). This occurs as the FE analyses were not conducted using a
constitutive model that incorporated the high stiffness of sand at very small (elastic) strain
levels (note that the regression of the FE analyses was performed for 0.01 y/D 0.1). If
required, k0 can be assessed directly from in-situ measurements of small strain shear moduli
(Gmax) and using the following approximation based on recent analyses given in Di Laora &
Rovithis (2014):

  (4)
where ν0 is the small strain Poissons ratio (typically 0.1 to 0.2). The now common use of the
seismic cone allows measurement of Gmax as well as qc. Fully elastic conditions in sand can be
assumed when the elemental strain is less than about 0·003% (Tatsuoka et al., 1997). Using
this strain limit and the approximate transformation based on cavity expansion proposed by
Jardine (1992), the y/D value at which conditions in the sand mass become essentially non-
elastic is about 0·01%.
The updated CPT-based formulation may therefore be written as:
 y/De <0.0001 (5a)



 y/De 0.01 (5b)


 (5c)
Equation (5) requires interpolation between equations (5a) and (5b) for 0.0001< y/De <0.01.
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Formulation check
To check the validity of Equation (5), the predictions for p/(σ'vD) obtained using this equation
for y/D ratios up to 0.1 are compared in Figure 7 with values calculated from the current series
of FE analyses (comprising pile diameters of 0.5m and 2.0m in loose and dense sand with
various water table locations) and the analyses reported in Suryasentana & Lehane (2014a),
which involved 10 different sand types and 10 pile diameters. It is evident that a very good fit
is obtained to all the data, apart from the predictions from Equation (5) for the smaller diameter
pile (D=0.5m), which tend to be lower than the FE calculations for large p/(σ'vD) ratios. Closer
examination of all the analyses indicated that Equation (5) provides conservative estimates of
the lateral stiffness at vertical effective stress levels less than about 10 kPa.
Verification of proposed p-y formulation
A standard p-y load transfer program, Oasys ALP (Oasys 2015), was used to conduct laterally
loaded pile analyses using p-y curves predicted by Equation (5). This program, which is similar
in form to many commercially available laterally loaded pile programs, represents the pile as a
series of beam elements and the soil as a series of non-linear, non-interacting springs located
between each beam element. The predicted pile responses are compared here against the
responses calculated using 3D FE analyses and also against data from an offshore wind farm.
Verification against 3D FE calculations
Although the finite element (FE) method is generally considered the best means for analysing
laterally loaded piles, the high computational resources and modelling complexity required by
the FE method limits its widespread adoption by practitioners. One of the main advantages of
the p-y method compared to FE method is its ease in providing reasonably accurate predictions
very quickly. Comparisons are made in the following between the pile head load-displacement
14
response predicted using the p-y approach with Equation (5) and the FE method. The following
cases are examined for a 2m diameter, 40m long pile (as per Case F1 in Table 1):
Uniform loose sand in dry conditions and with water at z =0 and z =3m (1.5D)
A 3m dense sand layer overlying a deep uniform loose sand layer in dry conditions and
with water at z=0 and z=3m (1.5D)
The CPT qc profiles for each case (allowing for the different assumed locations of the water
table) are provided in Figure 8. As for other qc predictions in this paper, these profiles were
derived using the spherical cavity expansion procedure described in Suryasentana & Lehane
(2014a) for the HS soil parameters listed in Table 2.
Figure 9 compares the pile head load-displacement predictions obtained using Equation (5) and
the p-y method with the FE calculations. It is seen that, despite the considerable added
complexity associated with performing 3D FE analyses, Equation (5) leads to predictions that
differ by less than 10% from the FE calculations for the cases analysed. Such small differences
are consistent with those obtained in separate analyses (e.g. those analyses reported in
Suryasentana & Lehane 2014b).
Verification against offshore wind farm field study
Hald et al. (2009) reported full scale load measurements on an instrumented wind turbine in
the Horns Rev Offshore Wind Farm, which is approximately 30 km west of Esbjerg in the
North Sea. A steel 4m diameter monopile was used as the foundation for the instrumented
turbine. This pile was driven to an embedment of 21.9 m (or 31.8m below the mean sea level);
the pile wall thickness and EpIp varied along the pile as indicated in Table 4. Bending moments
obtained at various elevations on the tower indicated that a lateral load of 240 kN and
15
corresponding bending moment of 18,700kNm at ground level occurred during the peak wind
speed event.
The measured CPT profile at the site is shown on Fig 14. In keeping with the reported soils
data, a unit weight of 20 kN/m3 was adopted for all the sand except in the very loose layer
between 14.9m and 19.9m depth where a value of 17 kN/m3 was assumed. The CPT data
combined with these unit weights were sufficient to allow generation of the p-y curves using
Equation (4). Subsequent predictions of pile bending moments during the peak wind event
(using OASYS ALP) are shown on Figure 10 and are seen to only slightly over-estimate the
measured bending moments. Such good agreement is encouraging given the high vertical
variability of the in-situ qc values and supports the contention that Equation (4) can be used for
the analysis of large diameter offshore piles.
Conclusions
The paper builds on previous research to develop an updated, numerically derived, CPT based
formulation for the estimation of p-y springs for the analysis of laterally loaded piles in sand
under static loading. This formulation, which is shown to be applicable to the practical range
of flexural rigidities encountered in practice, was modified to allow for higher normalised
lateral stiffness of sand in saturated conditions and for the higher resistances shown by square
piles. It is shown that 3D FE predictions of pile response are well matched using a standard
load transfer program coupled with the proposed p-y formulation. This approach is also shown
to provide very good predictions for the bending moments measured on a large diameter
offshore monopile.
16
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Notation
cohesion
cone penetration test
pile diameter
relative density
initial void ratio
minimum void ratio
maximum void ratio
drained secant Young’s modulus determined at 50% mobilised strength
when the lateral consolidation stress equal pref
pile Young’s modulus
second moment of area
pile length
lateral soil resistance per unit pile length
steady state penetration resistance
local pile displacement
depth below groundline
bulk unit weight
peak friction angle
dilation angle
Poissons ratio
effective vertical stress
total vertical stress
saturation factor
shape factor
19
Flexible Pile
(F1)
Flexible Pile
(F2)
Flexible Pile
(F3)
Rigid Pile
Cross-section
Circular
Circular
Circular
Circular
Material type
Linear Elastic
Linear Elastic
Linear Elastic
Linear Elastic
Drainage type
Non-porous
Non-porous
Non-porous
Non-porous
Ep (kPa)
30 x 106
30 x 105
30 x 107
200 x 106
γpile (kN/m3)
24
24
24
77
υ
0.2
0.2
0.2
0.2
D (m)
2 and 0.5
2 and 0.5
2 and 0.5
2 and 0.5
L (m)
40 and 10
40 and 10
40 and 10
10 and 2.5
Table 1: Pile properties used for Case (a), (b) and (d)
20
Loose Sand
Dense Sand
einit
0.7
0.55
emax
0.78
0.78
emin
0.49
0.49
Dr
0.28
0.79
Ko
0.45
0.45
γunsaturated (kN/m3)
18
18
γsaturated (kN/m3)
21
21
υ
0.2
0.2
E50 ref (kPa)
20000
60000
Eoed ref (kPa)
20000
60000
Eur ref (kPa)
60000
180000
c (kPa)
0
0
ϕ (degrees)
36.1
45.2
ψ (degrees)
5
12
Table 2: Soil properties used for Cases (a) to Case (d)
21
Circular Pile
(F1)
Square Pile
(S1)
Square Pile
(S2)
Square Pile
(S3)
Cross-section
Circular
Square
Square
Square
Material type
Linear Elastic
Linear Elastic
Linear Elastic
Linear Elastic
Drainage type
Non-porous
Non-porous
Non-porous
Non-porous
Ep (kPa)
30 x 106
17.7 x 106
30 x 106
46.5 x 106
γpile (kN/m3)
24
24
24
24
υ
0.2
0.2
0.2
0.2
Width (m)
2 and 0.5
2 and 0.5
1.75 and 0.438
1.57 and 0.393
L (m)
40 and 10
40 and 10
40 and 10
40 and 10
Table 3: Pile properties used to compare square and circular piles
22
Depth below pile head (m)
Wall thickness (mm)
EpIp (x108 kNm2)
0 11.8
50
2.54
11.8 19.6
52
2.64
19.6 23.6
50
2.54
23.6 27.6
40
2.05
27.6 31.6
40
2.05
Table 4: Properties of steel monopile foundation for Horns Rev wind turbine, assuming
Ep=210GPa (Hald et al. 2009)
23
Figure 1: Comparison of p-y curves of flexible piles with varying EpIp
0
5
10
15
20
25
0 0.05 0.1 0.15 0.2
p/s'vD
y/D
z/D=1 (F1) z/D=2 (F1)
z/D=1 (F2) z/D=2 (F2)
z/D=1 (F3) z/D=2 (F3)
z/D=1 (Rigid) z/D=2 (Rigid)
Loose Sand (D=2m)
0
10
20
30
40
50
60
0 0.05 0.1 0.15 0.2
p/s'vD
y/D
z/D=1 (F1) z/D=2 (F1)
z/D=1 (F2) z/D=2 (F2)
z/D=1 (F3) z/D=2 (F3)
z/D=1 (Rigid) z/D=2 (Rigid)
Dense Sand (D=2m)
24
Figure 2: Comparison of p-y curves of a flexible pile (F1) obtained under various saturation
conditions
0
5
10
15
20
25
0 0.05 0.1 0.15 0.2
p/s'vD
y/D
z/D=1 (Dry)
z/D=1 (Water table at z/D=0)
z/D=1 (Water table at z/D=1.5)
z/D=2 (Dry)
z/D=2 (Water table at z/D=0)
z/D=2 (Water table at z/D=1.5)
Loose Sand (D=2m)
0
10
20
30
40
50
60
70
0 0.05 0.1 0.15 0.2
p/s'vD
y/D
z/D=1 (Dry)
z/D=1 (Water table at z/D=0)
z/D=1 (Water table at z/D=1.5)
z/D=2 (Dry)
z/D=2 (Water table at z/D=0)
z/D=2 (Water table at z/D=1.5)
Dense Sand (D=2m)
25
Figure 3: Incorporation of saturation factor to p-y curves shown in Figure 2
0
5
10
15
20
25
0 0.05 0.1 0.15 0.2
p/s'vD
wy/D
z/D=1 (Dry)
z/D=1 (Water table at z/D=0)
z/D=1 (Water table at z/D=1.5)
z/D=2 (Dry)
z/D=2 (Water table at z/D=0)
z/D=2 (Water table at z/D=1.5)
Loose Sand (D=2m)
0
10
20
30
40
50
60
70
0 0.05 0.1 0.15 0.2
p/s'vD
wy/D
z/D=1 (Dry)
z/D=1 (Water table at z/D=0)
z/D=1 (Water table at z/D=1.5)
z/D=2 (Dry)
z/D=2 (Water table at z/D=0)
z/D=2 (Water table at z/D=1.5)
Dense Sand (D=2m)
26
Figure 4: Comparison of p-y curves of square and circular piles (only the curves at z/D=1 are
shown for clarity purposes)
0
5
10
15
20
25
30
35
0 0.05 0.1 0.15 0.2
p/s'vD
y/D
Circular (D = 0.5m)
Square, S1 (B = D)
Square, S2 (B = D/1.14)
Square, S3 (B = D/1.27)
Loose Sand (z/D=1)
0
10
20
30
40
50
60
70
80
90
100
0 0.05 0.1 0.15 0.2
p/s'vD
y/D
Circular (D = 0.5m)
Square, S1 (B = D)
Square, S2 (B = D/1.14)
Square, S3 (B = D/1.27)
Dense Sand (z/D=1)
27
Figure 5: Predictions for pile head load displacement for circular piles of different diameters
and their corresponding square piles with B = D/1.27.
0
100
200
300
400
500
600
700
800
900
1,000
0 10 20 30 40 50 60 70
Lateral load, F (kN)
y (mm)
Circular (D = 2m)
Circular (D = 1m)
Circular (D = 0.5m)
Circular (D = 0.2m)
Square (B = 1.57m)
Square (B = 0.79m)
Square (B = 0.393m)
Square (B = 0.157m)
Loose Sand
0
100
200
300
400
500
600
700
800
900
1,000
0 5 10 15 20 25 30
Lateral load, F (kN)
y (mm)
Circular (D = 2m)
Circular (D = 1m)
Circular (D = 0.5m)
Circular (D = 0.2m)
Square (B = 1.57m)
Square (B = 0.79m)
Square (B = 0.393m)
Square (B = 0.157m)
Dense Sand
28
Figure 6: Comparison of p-y curves obtained from a two-layer soil configuration against that
obtained from a homogeneous soil configuration
0
10
20
30
40
50
60
70
0 0.05 0.1 0.15 0.2
p/s'vD
y/D
z/D=1 (Uniform Loose Sand)
z/D=1 (Layered Loose Sand)
z/D=2 (Uniform Dense Sand)
z/D=2 (Layered Dense Sand)
Loose Sand Overlying Dense Sand (D=2m)
3m
Loose
Dense
0
10
20
30
40
50
60
70
0 0.05 0.1 0.15 0.2
p/s'vD
y/D
z/D=1 (Uniform Dense Sand)
z/D=1 (Layered Dense Sand)
z/D=2 (Uniform Loose Sand)
z/D=2 (Layered Loose Sand)
Dense Sand Overlying Loose Sand (D=2m)
3m
Dense
Loose
29
Figure 7: Comparison of p/σ'vD predicted by Equation 5 vs measured p/σ'vD.
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100
Predicted p/s'vD
Measured p/s'vD
Suryasentana & Lehane
(2014a)
D=2m
30
Figure 8: Predicted CPT profiles of numerical test cases using the cavity expansion method
0
5
10
15
20
25
30
35
40
45
0 2 4 6 8 10 12 14 16
z (m)
qc(MPa)
Dry
Water table at z/D=0
Water table at z/D=1.5
Uniform Loose Sand (D=2m)
Loose
F
0
5
10
15
20
25
30
35
40
45
0 2 4 6 8 10 12 14 16
z (m)
qc(MPa)
Dry
Water table at z/D=0
Water table at z/D=1.5
Dense Sand Overlying Loose Sand (D=2m)
3m
Dense
Loose
F
31
Figure 9: Comparison of pile head load-displacement predictions using Equation 5 with the
FE method.
0
1
2
3
4
5
6
7
8
9
0 50 100 150 200 250 300 350
Lateral load, F (MN)
y (mm)
FE (Dry)
FE (Water table at z/D=0)
FE (Water table at z/D=1.5)
Eq 5 (Dry)
Eq 5 (Water table at z/D=0)
Eq 5 (Water table at z/D=1.5)
Uniform Loose Sand (D=2m)
Loose
F
0
1
2
3
4
5
6
7
8
9
0 20 40 60 80 100 120 140 160 180
Lateral load, F (MN)
y (mm)
FE (Dry)
FE (Water table at z/D=0)
FE (Water table at z/D=1.5)
Eq 5 (Dry)
Eq 5 (Water table at z/D=0)
Eq 5 (Water table at z/D=1.5)
Dense Sand overlying Loose Sand (D=2m)
3m
Dense
Loose
F
32
Figure 10: Measured CPT profile at the Horns Rev wind turbine site (Hald et al. 2009) and
the comparison of measured peak bending moments and bending moments predicted using
Equation 5.
0
5
10
15
20
25
0 10 20 30 40 50
Depth below ground level (m)
qc(MPa)
-80
-60
-40
-20
0
20
40
0 5 10 15 20
Depth below ground level (m)
Bending Moment (MNm)
Peak measured moment
(at peak wind speed)
Equation 3
Ground level
... In the − framework, such soil reactions emerge from the constitutive behaviour of deformable soil spring elements, which yields a relationship between the lateral soil reaction ( ) and corresponding pile deflection ( ) at a given location (fully local approach). − modelling approaches have significantly evolved in time with regard to mathematical formulation and calibration procedures, so as to accommodate a variety of geotechnical, geometrical, and loading conditions (API (American Petroleum Institute), 2011; DNV, 2014; Suryasentana and Lehane, 2016;Byrne et al., 2019). * Corresponding author. ...
... However, there is still a substantial demand for enhanced cyclic − models, since the majority of the existing cyclic formulations are typically unable to reproduce soil ratcheting effects and, therefore, the cyclic accumulation of pile deflection. This is the case, for example, of well-known − formulations for monotonic loading (Matlock, 1970;DNV, 2014;Suryasentana and Lehane, 2016;Byrne et al., 2019), even when their cyclic versions are obtained based on the well-known Masing rules (Pyke, 1979); on the other hand, existing − models for seismic applications (Boulanger et al., 1998;Choi et al., 2015) will often tend to over-predict the accumulated displacement when used to tackle cyclic loading conditions that are commonly experienced by offshore (mono)piles. ...
... Further, the modelling of pilesoil gapping is inspired by the approach of Boulanger et al. (1998), who introduced a set of parallel springs to represent the physical mechanisms of 'frictional drag' and 'gap closure'. The model builds directly on the work of Suryasentana and Lehane (2016), in that their original CPT-based philosophy is extended to tackle cyclic loading conditions and pile-soil gapping effects. After a detailed description of the mathematical formulation and its modelling implications, the suitability of the new − model is finally assessed against original field data from recent mediumscale pile loading tests. ...
Article
The analysis of cyclically loaded piles is acquiring ever greater relevance in the field of geotechnical engineering, most recently in relation to the design of offshore monopiles. In this area, predicting the gradual accumulation of pile deflection under prolonged cycling is key to performing relevant serviceability assessments, for which simplified pile–soil interaction models that can be calibrated against common geotechnical data are strongly needed. This study proposes a new cyclic p−y model for piles in sand that takes a step further towards meeting the mentioned requirements. The model is formulated in the framework of memory-enhanced bounding surface plasticity, and extends to cyclic loading conditions the previous monotonic, CPT-based p−y formulation by Suryasentana and Lehane (2016); additionally, detailed modelling of pile–soil gapping is introduced to cope with the presence of unsaturated sand layers or, more generally, of cohesive soil behaviour. After detailed description of all model capabilities, field data from an onshore cyclic pile loading test are simulated using the proposed p−y model, with the most relevant parameters calibrated against available CPT data. Satisfactory agreement is shown between experimental and numerical results, which supports the practical applicability of the model and the need for further studies on a fully CPT-based calibration.
... A function developed by Suryasentana and Lehane [61] using 3D finite element analyses of monopiles (diameters up to 5 m) describes the nonlinear relationship between p and y as a function of CPT tip resistance (qc), to directly incorporate measured soil strength. This addresses the drawbacks associated with the use of ′ values, which incur parameter transformation errors, and additionally has been shown to be accurate for large-diameter offshore monopiles [62]. ...
... The numerical monopile model was developed in MATLAB employing Euler-Bernoulli beams supported on nonlinear Winkler springs, where the properties of the springs were derived using the CPT-based p-y model from Suryasentana and Lehane [61,62]. Figure 6 shows the configuration of the monopile model and demonstrates how a discretised CPT profile is used to characterise each discrete p-y spring. ...
... the soil reaction at a given spring depth (kN/m), is the bulk unit weight of the soil (kN/m 3 ), is the spring depth (m), is the pile diameter (m), is the lateral deflection of the spring (m) and , is the CPT end resistance value averaged over the discretised spring length (kPa). The initial stiffness modulus of each spring is specified in Equation 10[62]. is the initial (maximum) shear modulus of the soil and 0 is the Poisson ratio(typically 0.1 to 0.2). The initial shear modulus can be readily extracted from values through the simple expression 0 ≈ 6 [44]. ...
Article
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The growing demand for clean renewable energy sources and the lack of suitable nearshore sites is moving the offshore wind industry toward developing larger wind turbines in deeper water locations further offshore. This is adding significant uncertainty to the geotechnical design of monopiles used as foundations for these systems. Soil testing becomes more challenging, rigid monopile behaviour is less certain, and design methods are being applied outside the bounds of the datasets from which they were originally derived. This paper examines the potential impact of certain elements of geotechnical uncertainty on monotonic load-displacement behaviour and design system natural frequency of an example monopile-supported offshore wind turbine (OWT). Geotechnical uncertainty is considered in terms of spatial variability in soil properties derived from Cone Penetration Tests (CPT), parameter transformation uncertainty using the rigidity index, and design choice for subgrade reaction modelling. Results suggest that spatial variability in CPT properties exhibits limited impact on design load-displacement characteristics of monopiles as vertical spatial variability tends to be averaged out in the process to develop discrete soil reaction-lateral displacement (p-y) models. This highlights a potential issue whereby localised variations in soil properties may not be captured in certain models. Spatial variability in CPT data has a noticeable effect on predicted system frequency responses of OWTs employing a subgrade reaction model approach, and the influence of subgrade reaction model choice is significant. The purpose of this paper is to investigate the effect of uncertainty in soil data, model transformation, and design model choice on resulting structural behaviour for a subset of available design approaches. It should be noted that significant further uncertainty exists and a wide variety of alternative models can be used by designers, so the results should be interpreted qualitatively.
... Solid lines represent the results of the pile load tests (after Taborda et al., 2020), dashed lines represent the results of the 3D FE calculations. where Equation 1 is by Novello (1999), Equation 2 is by Dyson & Randolph (2001), Equation 3 is by Li et al. (2014), Equation 4 is by Suryasentana & Lehane (2016), D = pile diameter, γ 0 = effective unit weight of soil, z = depth, G max = small strain shear modulus, p u = ultimate lateral soil resistance (for more details refer to Suryasentana & Lehane, 2016) and f(y) = exponential function that depends on lat eral displacement (for more details refer to Surya sentana & Lehane, 2016). Equations 1 to 4 were used to derive p-y curves which were then inserted in a 1D Timoshenko beam model for modelling of the pile-soil lateral behaviour. ...
... Solid lines represent the results of the pile load tests (after Taborda et al., 2020), dashed lines represent the results of the 3D FE calculations. where Equation 1 is by Novello (1999), Equation 2 is by Dyson & Randolph (2001), Equation 3 is by Li et al. (2014), Equation 4 is by Suryasentana & Lehane (2016), D = pile diameter, γ 0 = effective unit weight of soil, z = depth, G max = small strain shear modulus, p u = ultimate lateral soil resistance (for more details refer to Suryasentana & Lehane, 2016) and f(y) = exponential function that depends on lat eral displacement (for more details refer to Surya sentana & Lehane, 2016). Equations 1 to 4 were used to derive p-y curves which were then inserted in a 1D Timoshenko beam model for modelling of the pile-soil lateral behaviour. ...
Conference Paper
Full-text available
A joint academia-industry project, the Pile Soil Analysis (PISA) project, resulted in an empir ical method for assessing the monotonic lateral loading response of large diameter monopiles. The method predicts four soil reactions, namely the distributed load and the distributed moment along the pile shaft, the pile base shear and the pile base moment. The method considers pile load test data and 3D numerical modelling. A 1D framework allows prediction of the four soil reactions. In this paper, a CPT-based approach is proposed to derive the four soil reaction components for use in a 1D model for conceptual design of mono-piles in sand subject to monotonic lateral loading. The approach relies on results from 3D finite element ana lyses that were performed considering soil conditions for a sand site used in the PISA project (Dunkirk site). The results are compared to pile load test data from the PISA project, showing good agreement, particularly for load levels related to the serviceability limit state.
... where γ is the unit weight of the soil (assumed 20 kN/m 3 for dense sand applications), z is the spring depth and D in the diameter of the monopile. The initial stiffness of the p-y spring is determined based on a correlation to small-strain shear modulus, see Suryasentana and Lehane (2016). ...
... where γ is the unit weight of the soil (assumed 20 kN/m 3 for dense sand applications), z is the spring depth and D in the diameter of the monopile. The initial stiffness of the p-y spring is determined based on a correlation to small-strain shear modulus, see Suryasentana and Lehane (2016). ...
Conference Paper
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Offshore Wind Turbines (OWT) are a successful renewable energy solution; however, emerging turbine sizes require pile geometries beyond the calibration range of existing design standards. This necessitates soil sampling and rigorous finite element modelling, which is problematic for quick design estimates. Cone Penetration Test (CPT)-based p-y methods can provide preliminary deflection estimates, although their applicability becomes increasingly uncertain as pile slenderness ratios, length normalized by diameter (L/D), reduce. This is due to the increase in diameter incurring additional resistances that p-y models alone cannot account for. To incorporate the additional resistance, this paper defines a CPT-based moment-rotation (m-θ) model by rescaling empirically derived axial capacity functions (known as τ-w curves). Various monopile dimensions are simulated and pile-head displacements are compared for CPT-based p-y models with and without m-θ springs. The net effect of incorporating m-θ springs increases as monopile diameters (and rigidity) increase and diminishes as piles increase in slenderness,
... For sandy soil, the p-y model proposed by Suryasentana and Lehane (2016) was adopted: ...
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Excavation causes disturbance to the surrounding soil, affecting the soil's mechanical properties. This study presents a case study to investigate the effect of excavation disturbance on soil properties and pile capacity via in situ tests. A series of multifunctional piezocone tests, multichannel analysis of surface wave tests, and electrical resistivity tomography tests were conducted at three sites of the Taihu tunnel region before and after excavation with different depths. The changes in soil mechanical properties and the pile capacity loss were evaluated using the test results. The results indicated that excavation disturbance decreased the cone tip resistance, sleeve friction, soil resistivity, shear wave velocity, and undrained shear strength. In contrast, the friction ratio and the effective friction angle were not affected. The average cone tip resistance of soils in the excavation disturbance zone was approximately 51%, 46%, and 62% of its initial value at Sites A, B, and C, respectively. The variation in soil properties was only observed within a limited depth below the excavation surface, which is defined as the excavation disturbance zone. The piezocone test successfully identified the depth of the excavation disturbance zone, and the disturbance zone height was approximately 0.42 times the excavation depth. In the disturbance zone, the cone tip resistance and the undrained shear strength of the soil decreased linearly from approximately 90%-0% with increasing depth. Because of excavation disturbance, the axial and lateral capacities of a pile beneath the Taihu tunnel were reduced by about 9% and 50%, respectively.
... Because the p-y curves are mostly empirically developed based on results of specific field pile load tests, the predictions using the p-y method is not always accurate (Anderson et al. 2003;Choi et al. 2014;Han et al. 2015Han et al. , 2017a. In addition, because the p-y method was originally developed for long, slender piles, questions have been raised regarding the applicability of the p-y method to the analysis of large-diameter monopiles (Doherty and Gavin 2012;Suryasentana and Lehane 2016). Significant discrepancies have been observed between the lateral load response of monopiles obtained from the p-y method and those obtained from three-dimensional (3D) finite-element (FE) analyses (Achmus et al. 2005;Hearn and Edgers 2010;Wiemann 2005, 2006), centrifuge model tests (Choo and Kim 2016;Hearn and Edgers 2010;, and field load tests (Hu and Yang 2018;Li et al. 2017). ...
Chapter
This research uses a numerical model for waves in porous media to evaluate the damped wave effectiveness of bamboo breakwater built in the coastal zone in Mekong delta. The extended Boussinesq model for waves in porous media used in this research was developed by Vu et al. (2018). Internal wave generation technique using a source term addition method is applied to generate waves. The porosity characteristics of the model are matched with the bamboo breakwater from Mai et al. (2019). The numerical results show a very good agreement with the results of Mai et al. (2019) and imply that the effectiveness of the wooden breakwater in dissipating waves is affected by the width and the porosity of the bamboo breakwater and the nonlinearity of the incoming waves.
Chapter
Pile foundations are often used to resist lateral loads to support offshore structures, transmission towers, and high-rise buildings. For the design of laterally loaded piles, the p-y method is widely adopted. Extensive research efforts have been paid on the development of p-y curves for circular piles. However, p-y curves for piles with other cross-section shapes have received limited attention. This paper presents a comprehensive numerical study to investigate the pile shape effects on p-y curves of laterally loaded piles in soft clay. Based on the numerical results, the p-y curves of piles with different pile shapes (i.e., circular, square, and H pile sections) are proposed. The proposed p-y curves are fundamentally linked to soil stress-strain response, providing engineers a simple approach to construct p-y curves for pile design based on soil stress-strain response measured in the laboratory, without the need for time-consuming numerical analyses.
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In this study, the suitability of the pseudostatic approach for the seismic analysis of pile foundations in layered soils is explored by means of experimental data from centrifuge tests performed at 60g. A free-head single pile and a capped (1 × 3) pile group, embedded in a two-layered soil comprising a soft clay layer underlain by dense sand, are tested in the centrifuge under sinusoidal and earthquake excitations. For the pseudostatic analysis, a one-dimensional Winkler model is developed using hyperbolic p-y curves from design codes. The kinematic and inertial loads on the pile foundations are derived using the experimentally measured free-field soil displacements and accelerations, respectively. Different approaches of modifying the p-y relationship to account for soil layering are compared. The importance of considering peak spectral acceleration in lieu of peak ground acceleration at the soil surface to compute the inertial force for the pseudostatic analysis is highlighted. Pile group effects are investigated by considering p-multipliers from literature to account for pile-soil-pile interaction. Results reveal that: (i) for low-intensity seismic motions, the pseudostatic approach with inertial pile-head loading stemming from peak ground acceleration (PGA) at soil surface led to a reasonable agreement of the maximum bending moment with experimental data for both single pile and pile group, (ii) for high-intensity base excitations, the use of the peak spectral acceleration, instead of PGA, at soil surface with suitable damping considerations to derive the inertial load in the pseudostatic model provided a maximum bending moment prediction that was acceptable for the single pile but conservative for the piles in the group compared to the centrifuge records.
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Simple expressions are developed for the equivalent horizontal spring and damping coefficients at the top of an end-bearing pile embedded in a uniform linear soil. Beam on elastic foundation and dynamic finite element analyses are used. It is demonstrated that, for long end-bearing piles, the top displacement response at high frequencies is independent of the pile length, and the pile behaves identically to a long floating pile in a half-space. A numerical criterion is presented to decide when a pile is long or short.
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Lateral force-displacement (P-y)-based Winkler spring models are commonly applied for the design of piles, P being the soil lateral reaction and y the lateral displacement. Despite their relative simplicity, P-y models can capture important aspects of pile behaviour including non-linear soil stiffness. Several P-y models based on cone penetration tests (CPTs) have been proposed over the last two decades, developed largely using empirical curve fitting to results of field tests, centrifuge modelling and finite-element analyses on relatively flexible piles installed in calcareous sand. However, major uncertainties exist when attempting to extrapolate empirical models for use with soil types and pile geometries outside the database on which they were formulated. There is an urgent need for a reliable P-y method for application to the design of rigid monopiles used extensively for offshore wind projects. A series of field lateral load tests performed on open-ended steel pipe piles driven in dense siliceous sand is reported here. The pile embedment length and load eccentricity were varied to investigate the behaviour of rigid and flexible monopiles. The measured pile response was used to evaluate the performance of a number of recent CPT-based P-y models and an update to an existing power-law model is suggested for rigid monopiles in siliceous sand.
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Kinematic bending of elastic single fixed-head piles in continuously inhomogeneous soil is explored in both static and dynamic regime. A generalized parabolic function is employed to describe the variable shear modulus in the inhomogeneous stratum, which can simulate both cohesive and cohesionless soil deposits. The problem is treated numerically by means of rigorous elastodynamic finite-element analyses and simplified beam-on-dynamic-Winkler-foundation (BDWF) formulations. A novel expression is proposed for the active length of a pile in inhomogeneous soil, by means of kinematic interaction considerations. This allows an alternative interpretation of kinematic soil-pile interaction along an effective depth, contrary to existing definitions in which soil response is evaluated at a specific location. Following this interpretation, a design formula for kinematic pile-head moments is derived for both static and dynamic loading. A new dimensionless parameter is identified to govern dynamic pile bending, which allows a straightforward assessment of frequency effects in pile design.
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The formulations for the lateral load-displacement (p-y) springs conventionally used for the analysis of laterally loaded piles have been based largely on the back-analysis of the performance of small-scale instrumented piles subjected to lateral load. Although such formulations have been employed with much success in industry, their applicability to large-diameter piles, such as those used to support offshore wind turbines, is uncertain and has necessitated further research in this area. Moreover, with the growth in popularity of in-situ cone penetration tests (CPTs), there are demands for a theoretically supported direct method that can enable the derivation of p-y curves from the CPT end resistance (q c). In this paper, a numerical derivation of CPT-based p-y curves applicable to both small- and large-diameter laterally loaded single piles in sand is presented. Three-dimensional finite-element analyses are performed using a non-linear elasto-plastic soil model to predict the response of single piles in sand subjected to lateral loads. The corresponding CPT q c profile is derived using the same soil constitutive model by way of the cavity expansion analogue. An extensive series of computations of the lateral pile response and CPT q c values is then employed to formulate a direct method of constructing p-y curves from CPT q c values. The proposed method is shown to be generally consistent with existing empirical correlations and to provide good predictions in relation to the measurements obtained during lateral load tests on instrumented piles in an independent case study.
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This paper describes the results of a centrifuge modeling study of the response of piles embedded in calcareous sand under monotonic lateral loading. A number of features have been explored, including method of installation, rate of loading, and pile head restraint. The study has led to recommendations for load-transfer curves with the magnitude of lateral resistance linked to the soil strength through the cone resistance. Modification factors have been developed to allow for different methods of installation and for different rates of loading. The proposed load-transfer curves and resulting pile response are shown to provide an excellent match with the experimental data, and are compared with results derived using existing guidelines for terrigenous sands. Significant differences are demonstrated, confirming the need to treat calcareous sediments separately from other soil types with respect to lateral pile response.