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Abstract

Scour can cause the water-induced failure of fluvial and marine bridges and structures. Previous studies have focused on the scour mechanisms and their effects on the load capacity of single piles, although deep foundations consist mostly in pile groups. In this paper, scouring on pile groups embedded in soft clay is studied when piles are laterally loaded and affected by the formation of scour holes. This boundary problem is simulated using the three-dimensional finite element method. The scour depth, slope angle, and pile spacing are analyzed as main influence factors. Summary charts quantify how the dimensions of scour holes affect the lateral load capacity of 3x3 pile groups for varying pile spacing and their corresponding p-multipliers. Importantly, results indicate that it is unreasonable to design pile foundations by ignoring the influence of scour holes or directly removing the soil layer above the scour depth, as frequently assumed in practice.
Computers and Geotechnics 150 (2022) 104913
0266-352X/© 2022 Elsevier Ltd. All rights reserved.
Numerical evaluation of scour effects on lateral behavior of pile groups
in clay
Zengliang Wang , Hang Zhou
*
, Andrea Franza, Hanlong Liu
Key Laboratory of New Technology for the Construction of Cities in Mountain Areas, College of Civil Engineering, Chongqing University, Chongqing 400045, China
ARTICLE INFO
Keywords:
Local scour
Pile groups
Lateral behavior
Group effect
Numerical analysis
ABSTRACT
Scour can cause the water-induced failure of uvial and marine bridges and structures. Previous studies have
focused on the scour mechanisms and their effects on the load capacity of single piles, although deep foundations
consist mostly in pile groups. In this paper, scouring on pile groups embedded in soft clay is studied when piles
are laterally loaded and affected by the formation of scour holes. This boundary problem is simulated using the
three-dimensional nite element method. The scour depth, slope angle, and pile spacing are analyzed as main
inuence factors. Summary charts quantify how the dimensions of scour holes affect the lateral load capacity of
3x3 pile groups for varying pile spacing and their corresponding p-multipliers. Importantly, results indicate that
it is unreasonable to design pile foundations by ignoring the inuence of scour holes or directly removing the soil
layer above the scour depth, as frequently assumed in practice.
1. Introduction
For bridges and structures in marine and uvial environments, pile
foundation is among the main foundation scheme, and the evaluation of
the load capacity of these foundations has received extensive attention
so far (Abdrabbo and Gaaver 2012; Brown D A 1988; Cao, Chen 2020;
Cao, Ding 2021; Christensen and Shaun 2006; Heidari, El Naggar 2014;
Peng, Ding 2020; Peng, Liu 2021; Wang, Liu 2021). In particular, the
geotechnical design has to consider that foundations in marine and
uvial environments must withstand both vertical loads transferred by
the superstructure and lateral actions due to currents and waves.
In these environments, scour is a frequent natural phenomenon,
occurring when the soil close to the foundation is eroded by owing
water and waves, which can threaten the serviceability and safety of pile
foundations. This erosion reduces the effective buried depth and load
capacity of the pile foundation, especially in the lateral direction; in fact,
the lateral capacity of piles relies on the strength of the soil at shallow
depths, which is rst removed by scouring. Scour is considered the main
cause of water-induced bridge failures (Zhang et al. 2017), with severe
detrimental effects in extreme weather conditions such as hurricanes
and oods. Economic and safety losses for the public are signicant. For
instance, scour and ood induced failures accounted for, respectively,
80% and 60% of the total number of bridge failures in China and the
United States (Lagasse 2007; Liang, Wang 2017; Lin and Lin 2020),
whereas earthquakes contribution is limited to 2% in the United States
(Shirole and Holt 1991). Therefore, it is crucial to consider the impact of
scour in the design of water-related infrastructures. As suggested by
Arneson (2012), considering economic and safety issues, a complete pile
foundation design under scouring conditions requires integrated hy-
draulic, geotechnical, and structural analysis (Arneson, Zevenbergen
2012).
The removal and excavation of materials due to the action of owing
water may be classied as follows: local scourthat occurs around pile
foundation forming a scour hole; contraction scourthat is the result of
the cross-sectional area of the channel being reduced due to the con-
struction of piers and abutments; and general scour that occurs
removing material across the entire river channel (Prendergast and
Gavin 2014). Considering that the depth of local scour (localized around
piles) can be ten times the one of general scour (Fischenich and Landers
1999), local scour has the largest detrimental impact on the load ca-
pacity of piles. For simplicity, in practical design and load capacity es-
timates, local scour is often simplied to a general scour type of analysis
(i.e. the entire soil layer above the depth of the local scour are removed)
making the foundation design too conservative with increase in costs
and materials (Lin, Han 2014); for instance, this simplied general scour
technique overestimates the lateral displacement of single piles in sands
under horizontal load by a factor of 1.5 (Lin, Han 2014). Furthermore,
recent studies have characterized the inuence of the scour hole di-
mensions on the lateral load capacity of single piles using centrifuge
* Corresponding author.
E-mail address: zh4412517@163.com (H. Zhou).
Contents lists available at ScienceDirect
Computers and Geotechnics
journal homepage: www.elsevier.com/locate/compgeo
https://doi.org/10.1016/j.compgeo.2022.104913
Received 23 February 2022; Received in revised form 5 July 2022; Accepted 6 July 2022
Computers and Geotechnics 150 (2022) 104913
2
tests, three-dimensional nite element method (FEM) simulations, and
analytical studies (Chortis, Askarinejad 2020; Liang, Zhang 2018; Lin
and Jiang 2019; Lin and Lin 2019; Qi, Gao 2016; Zhang, Chen 2017), in
which the scour hole is simplied as an inverted truncated cone. Lin
(2016) proposes a calculation method for laterally loaded single piles in
soft clay under scour conditions by modifying the p-y curve (Lin, Han
2016). Based on the Mindlins elastic solution, Liang (2018) deduces the
change of unscoured soil stress around a single pile in a clay and obtains
its effect on the lateral behavior of the pile (Liang, Zhang 2018). How-
ever, designers frequently adopt pile group foundations in marine and
uvial environments. To the best of the Authors knowledge, there is a
lack of studies on the impact of local scour on pile groups under lateral
load in soft clay. This should be addressed to increase the resilience of
deep foundations for critical structures and infrastructure.
In the absence of scour, when pile groups are subjected to a lateral
load, the piles-in-group mobilize the soil strength directly in front of the
piles. As the load increases, the zones of soil resistance between neigh-
boring piles gradually overlap. The group effect consists of both the
edge effect and the shadowing effect due to, respectively, the
interaction of resistance zones within a pile row and between different
pile rows (Brown D A 1988; Fayyazi, Taiebat 2014; Rollins, Peterson
1998), with the edge effect being less noticeable than the shadowing
effect (Watford, Templeman 2021).
To describe the group effects, the ratio between the lateral load
withstood by a pile in group and isolated congurations is of interest.
For this, the p-multipliers method is the widely adopted that quanties
the relationship between p-y curves of single piles and pile rows, where p
is the local soil resistance (dened as the horizontal load per meter shaft)
and y the corresponding horizontal displacement (Brown D A 1988;
Ilyas, Leung 2004; Rollins K M 2006; Rollins, Peterson 1998). In this
paper, the p-multipliers method is used to describe the inuence of the
scour depth on pile-pile interaction and ultimate loads. Furthermore,
additionally to group effects, the scour depth is affected by the presence
of multiple piles leading to a further decrease in the load capacity of the
group (Lin and Lin 2020).
2. Scope
This paper aims at investigating the effects of local scour on the
behavior of laterally loaded pile groups (i.e., lateral load capacity,
bending moments, soil resistance prole, and p-multipliers) based on a
series of three-dimensional nite element analyses considering varying
scour hole dimensions and pile group layouts.
3. Validation of the model
3.1. Considered scenario
In the literature, there is no experimental or eld data on laterally
loaded pile groups embedded in clay in the presence of scouring.
Therefore, in this study, the centrifuge results from Ilyas (2004) of a
single pile and a 3x3 pile group embedded in undisturbed clay (with no
scouring) are used for validation (Ilyas, Leung 2004). These tests were
performed at 70 g using the National University of Singapore Geotech-
nical Centrifuge. The soil model is normally consolidated kaolin clay,
whose material properties are calibrated by Ilyas (2004) and summa-
rized in Table.1. The model piles are a hollow aluminum square tubes
having a width of 12 mm (at prototype scale, 840 mm), total and
embedment length of 260 mm and 210 mm, respectively (equivalent to
18.2 m and 14.7 m at the prototype scale), bending stiffness EmIm of 384
kNcm
2
(at prototype scale, 922 MNm
2
), and cross-section area 1.44 cm
2
(at prototype scale, 0.706 m
2
). The thickness of the soil layer is 245 mm
(equivalent to 17.15 m thickness). For further details on the centrifuge
test refer to (Ilyas, Leung 2004).
3.2. Material parameters and constitutive model
The Modied Cam Clay constitutive model is adopted to describe the
stressstrain relationship of the kaolin clay. Soil parameters used in this
study (previously adopted by Ilyas (2004)) are: a slope of the normal
consolidation lineλ=Cc/2.3=0.239, a slope of the unloa-
dingreloading lineκ=Cs/2.3=0.061, a slope of the critical state
lineM=6sinφ/(3sinφ) = 1.07, while φ=26.9is the critical
friction angle. According to the Modied Cam Clay model, the variation
of the initial void ratio with depth is:
e0=e1λln(q2
M2p+p)+κln(q2
M2p2+1)(1)
where pis mean effective stress; q is the deviatoric stress;e1=2.
Nomenclature
EmIm Bending stiffness
γ Average bulk unit weight of soil
C
c
Compression index
C
s
Recompression index
k Coefcient of permeability
Su Undrained shear strength
D Pile diameter
K
0
Coefcient of earth pressure at rest
S
g
Scour depth
S Pile spacing
U
_h
Horizontal displacement
M Bending moment of pile
R Ratio of scour depth to pile diameter
λ Slope of the normal consolidation line
κ Slope of the unloadingreloading line
M Slope of the critical state line
φCritical friction angle of soil
pMean effective stress
q Deviatoric stress
e Void ratio of soil
Deff Effective pile diameter of pile group
β Scour hole angle
F
_h
Horizontal reaction head forces
p
_h
Soil resistance
z Depth of soil
Le Pile embedded depth
Table 1
The properties of kaolin clay used in the centrifuge test (Ilyas, Leung 2004).
Parameter Value
Average bulk unit weight γ 16 kN/m
3
Average water content 66%
Liquid limit 79.8%
Plastic limit 35.1%
Compression index C
c
0.55
Recompression index C
s
0.14
Coefcient of permeability k 2 ×10
-8
m/s
Undrained shear strength Su at the ground surface 0 kPa
Undrained shear strength Su at 15 m depth (prototype) 20 kPa
Z. Wang et al.
Computers and Geotechnics 150 (2022) 104913
3
The single pile and pile group are simulated as elastic materials in the
nite element model. In the validation section of this paper, square-
section piles are simulated as in the centrifuge tests. However, to focus
on the effects of scouring on piles with circular cross-sections, in sub-
sequent sections the nite element models adopt equivalent solid piles
with the diameter D =0.94 m, Youngs modulus E =20.9 GPa, and a
Poissons ratio of 0.2 (which match prototype cross-sectional area and
bending stiffness values from the experiment).
3.3. Model description
Half of the domain is simulated considering symmetry. A mesh
convergence analysis was conducted indicating the change in the
density of ne meshes varied the loaddisplacement curve by less than
2%. Representative meshes of the nite element models adopted for the
single pile and the pile group are presented in Fig. 1 (b). The soil model
was partitioned in two regions shown in this gure with different colors,
to allow considering the presence of the scour hole (later discussed).
Eight-node trilinear displacement and pore pressure elements C3D8P are
used for the soil, while linear brick elements with reduced integration
C3D8R are assigned to piles. To minimize boundary effects, the sizes of
the domain are set in the horizontal loading x-direction and the trans-
verse y-direction equal to 128D and 44D, respectively, while the dis-
tance between the bottom boundary of the soil region and the model pile
tip is set to 16D. Horizontal displacements are xed at the vertical
boundaries (U
x
=U
y
=0) and symmetry plane (U
y
=0), whereas the
Fig. 1. (b). Three-dimensional nite element model for single pile and pile group.
Z. Wang et al.
Computers and Geotechnics 150 (2022) 104913
4
bottom boundary is constrained in all directions (U
x
=U
y
=U
z
=0). For
the soil-pile interface, the Coulomb friction law with a friction coef-
cient of 0.32 is assumed and the hard contact are considered to allow for
gap formation (Randolph and Wroth 1981).
Piles are modelled with the so-called wish-in-placemethod, while
the presence of an elevated rigid cap xed to the piles is considered with
a multi-point-constraint connecting the pile heads to a master node. The
model consists of four analysis steps: (i) initial geostatic step, imposing
initial stresses from the unit weight and a coefcient of earth pressure at
rest K
0
=0.43; (ii) static analysis step, in which the pile mode is
activated, both in terms of self-weight and soil-pile contact interface;
(iii) scour activation, omitted in the validation analyses, simulating
the formation of the local scour around piles by deactivating the cor-
responding soil region (i.e. using the model change method) so that the
soil loss caused by scour and the stress redistribution within the
remaining soil are captured; (iv) lateral loading stepimposing a hor-
izontal displacement along the symmetry plane to the master node,
while its rotational and the vertical degrees of freedom are free.
Piles in the group are labeled as either front (F), middle (M) or rear
(R) in the load direction while the terms central (C) and outer (O) are
used in the transverse direction.
3.4. Single pile and pile group lateral responses under no scouring
First, nite element predictions are compared with centrifuge mea-
surements for the single pile case in the absence of the scour hole. Fig. 2
(a) shows a good agreement between numerical and centrifuge
loaddisplacement curves of the pile head. Similarly, numerical
Fig. 2. Validation of the pile group FEM model against the centrifuge test
conducted by IIyas et al. (2004):
Table 2
The parameters studied in this paper.
Case Parametric study Parameter value
Case A
(β=25,S/D=
3)
Scour depth
(R=Sg/Deff)
0.7 1.4 2.1 2.5 2.8
Case B
(R=2.1,S/D=
3)
Scour hole angle
(β)
013192225
Case C
(β=25,R=2.1)
Pile spacing
(S/D)
3 4 5 6 7
Fig. 3. (b). The reduction in the tangent stiffness of the group for different
scour depth.
Z. Wang et al.
Computers and Geotechnics 150 (2022) 104913
5
predictions compare well with experimental data of the 3x3 pile group
in Fig. 2 (b). These results prove the reliability of the developed FEM
model in describing the lateral behavior, when analyzing the
loaddisplacement curves at the head level, of both single and capped
piles embedded in undisturbed clay.
4. Pile group affected by scouring effects
4.1. Effective diameter of pile groups
When studying scouring effects, single pile analyses are frequently
adopted for which the local scour depth is normalized by the pile
Fig. 4. Vector elds and contours of soil displacement: (a) unscoured single pile; (b) unscoured pile group; (e) R=2.1 single pile; (f) R=2.1 pile group.
Z. Wang et al.
Computers and Geotechnics 150 (2022) 104913
6
diameter. However, Under the scouring action of pile foundation,
different from single pile, the scour depth of pile group depends on the
conguration of pile group and the skew angle of ow. Based on this,
Sheppard (2003) proposed a calculation method to describe the scour
depth of pile groups, that is, the ‘effective pile diameter (Deff ) for pile
groups, which depends on the number of piles and their arrangement
and the angle between the water ow direction and pile group (Shep-
pard 2003). Which is the diameter of an equivalent single pile that
would result in a scour depth identical to the one of the pile group under
identical riverbed and ow conditions. It is worth noting thatDeff D, in
other words the effective diameter of a pile group is larger than that of
the single pile diameter for identical ow conditions. According to the
ume test and eld survey of pile group scour, the maximum scour
depth of pile group is 2.63 D
eff
(Bayram and Larson 2000; Lança, Fael
2013). Thus, in this paper, the scour depth of a pile group normalized by
effective pile diameter (S
g
/Deff ). The geometrical method suggested by
Sheppard (Sheppard 2003) is used to estimate the effective pile
diameter.
4.2. Simplied scour hole models
The FEM model displayed in Fig. 1 (b) is used to investigate the ef-
fects of scour on laterally loaded single piles and 3x3 pile groups with a
rigid elevated cap, respectively. Thus, the baseline model validated for
piles embedded in undisturbed soil is adopted for all simulations
accounting for the scouring. Previous research simplied the shape of
scour hole around single piles and pile groups as an inverted truncated
cone and pyramid, respectively, with the latter geometry following
experimental test results (Amini, Melville 2012; Lin and Wu 2019).
Therefore, as shown in Fig. 1 (a), these simplifying assumptions are
adopted. The parameters describing these proles are: the depth of the
scour hole Sg(normalized by the effective diameter) and the angle of the
scour hole β (which cannot exceed the soil internal friction angle (Lin
and Lin 2019; Butch 1996)). The undrained analysis was used in this
study, therefore, the scour slope angle should depends on the dimen-
sionless group involving s
u
and γ. Note that forβ =0 the general scour
case is obtained.
4.3. Considered scenarios of the parametric study
To assess the inuence of scouring on the group effect, for each pile
group case a corresponding single pile model is simulated having
equivalent scouring conditions (i.e. identical top and bottom areas as
well as scour depth Sg). A parametric study was conducted by varying (i)
the normalized depth of scour dened as the scour ratioR=Sg/Deff
(Sg/Deff=0.7, 1.4, 2.1, 2.5, 2.8), (ii) the angle of scour hole (β=0, 13,
19, 22, 25), and (iii) the pile spacing (S/D=3, 4, 5, 6, 7). As shown in
Table. 2, Group A, B, and C are introduced as labels to distinguish be-
tween group of analyses. Results include loaddisplacement curves at
the pile heads, bending moment proles of piles, and the soil resistance
Fig. 5. The relationship between the bending moment along pile shaft of each pile in a pile group under different scour depths.
Z. Wang et al.
Computers and Geotechnics 150 (2022) 104913
7
per unit meter along the pile shaft. Note that, as the scour depth
increases, the pile embedded depth Le =LSgdecreases. To ensure a
fully mobilized soil resistance, the lateral displacement imposed to the
master node is set to 0.3D (Abu-Farsakh, Souri 2018; Chortis, Askar-
inejad 2020; RP 2011; Souri 2017). The corresponding lateral reaction
forces is to the ultimate load of the foundation.
4.4. Effects of the scour depth
First, the scour depth is investigated. Pile groups all having an
effective diameterDeff =2.44 m and spacing equal to three pile di-
ameters (S/D=3) are considered subjected to different scouring con-
ditions: namely, the full range of scour depths (R=02.8) with a xed
slopeβ=25, which are labelled as Case A.
For this group of analysis cases, Fig. 3 (a) compares the
loaddisplacement curves at the top surface of the pile groups; hori-
zontal reaction head forces (F
_h
) are normalized by the ultimate lateral
load of pile group (Funscoured, obtained for horizontal head displace-
ments of 0.3D under unscoured conditions) and the horizontal
displacement (U
_h
) axis is normalized by pile diameter (D). Results
illustrate how the increase in the scour ratio R reduces the lateral load of
the pile group mobilized at all displacement levels, as expected due to
the fact that the increase in scour depth reduces the embedment
lengthLe. In particular, the ultimate load of the group subjected to the
largest scour (R=2.8) is approximately half the value under unscoured
Fig. 6. Each pile in pile group soil resistance-depth relationship curves under different scour depth.
Fig. 7. The value of p-multipliers (with different scour depth).
Z. Wang et al.
Computers and Geotechnics 150 (2022) 104913
8
conditions (R=0). To evaluate if there is any trend in the reduction of
the group stiffness with scouring, Fig. 3 (b) plots the tangential stiffness
associated with the loaddisplacement curves in Fig. 3 (a). Interestingly,
the reduction in tangent stiffness with scouring ratio R is nearly constant
with the lateral displacement level (U
_h
/D); therefore, the use of a
reduction factor relating the group secant stiffness (i.e., ratio between
horizontal load and displacement) of scoured and unscoured pile groups
is viable.
To understand the soil-pile interaction, contours and vectors of the
total displacements of the soil at the ultimate state (induced by U
_h
/D =
0.3) are shown in Fig. 4 for both the single pile and pile group of Case A
under R=0 and 2.1. As shown in Fig. 4 (c)-(d) forR=0, the soil
deformation pattern of the unscoured cases consists in a wedge-type
ow at the upper part of the foundation, a full ow along mid-
embedment of the foundation, and a rotation zone around the pivot
point; this pivot is located close to the tip and at the shaft of the single
pile and the central pile within the group. For single pile and pile groups
in Fig. 4 (g)-(f) with a scour depthR=2.1, scouring impacts signi-
cantly the soil ow mechanism: namely, the single pile is characterized
by an upwards soil ow whereas the rotation center of the pile groups is
on the shaft of the front pile. Therefore, scouring impacted the soil ow
mechanism in the performed analyses.
In the ABAQUS software, the bending moment-depth relationship of
each pile in a pile group can be obtained by the following method: (i) In
the modeling process of the nite element model, the corresponding sets
are set for the piles in different positions, and in the Create Field
Outputof the nite element software, set the results to be output (e.g.,
bending moments) in the results le of the model; (ii) After the model
calculation is completed, in the ODB result le, the piles that need to
output the bending moment are displayed through the set of pre-set
piles; (iii) The model pile is divided into equal intervals along the pile
shaft through Activate View Cut, and the bending moment distribution
of the pile can be obtained by outputting the bending moment of each
section; (iv) Finally, store the bending moment data obtained in step (iii)
into txt format through the Report Free Body Cut function of the
nite element software to obtain the corresponding bending moment-
depth relationship. Fig. 5 displays the bending moment proles ob-
tained for all piles in the analysis Case A corresponding to the ultimate
lateral head displacement (U
_h
/D =0.3). Compared with the unscoured
condition, the loads borne by the piles at different positions in the
laterally loaded pile group under the scour condition have changed
greatly. Bending moments of the front row are larger than values of the
other rows due to the shadowing effect in the group while bending
moments at the center position (C) are smaller than that for the outer
piles (O) due to the edge effects. Therefore, shadowing and edge effects
are both present in the case of scoured pile foundations. Also, the
maximum bending moments of piles decrease with the increase of the
scour depth (i.e. scour ratio R) due to a lower embedment length. The
locations of the maximum bending moment along the embedded shaft is
moving upwards the pre-scour ground line; however, as the scour depth
increases, the difference in bending moments between each piles in the
pile group gradually decreases.
The soil resistance p
_h
per unit meter of pile shaft is estimated, as for
the Euler-Bernoulli beam theory, from the second derivative of the
computed bending moment distributions, which are tted by a fourth-
order piecewise polynomial (Truong and Lehane 2018).
ph= d2M
dz2(2)
In Fig. 6, the soil resistance p
_h
along the embedded pile length is
plotted for pile groups of Case A analyses, with subplots covering all
scouring scenarios (R=0.72.8) As for the unscoured cases, The soil
resistance-depth distribution changes more steeply for piles at different
locations with increasing scour depth. In addition, the increase of the
scour depth increases the maximum soil resistance of the pile, and the
position of the maximum soil resistance gradually approaches the pile
bottom, especially the front row piles. Due to group effects, soil resis-
tance of piles arranged in a group is lower than for an isolated pile for all
scouring scenarios, with the difference in p_h of front and rear rows
increasing withR. This indicates that the normalized scour depth in-
creases the impact of group effects (due to pile-soil-pile interactions) in
the performed simulations. Note that the positive soil resistance values
follow (qualitatively) a parabolic prole with depth; this also applies to
varying slope angle beta (discussed in the following).
Next, p-multipliers are considered. Among several approaches to
calculate the p-multipliers, in this paper the method proposed by Souri
(2017) is adopted that allows evaluating the p-multiplier also in the
presence of scouring: the p-multipliers is estimated normalizing from the
average soil resistance prole along the shaft of each pile in a pile group
(p_g) against corresponding average resistance values computed in single
pile (p_s), under equal lateral head displacement of 0.3D. This approach
leads to a ratio similar (but not identical) to the ratio between head
forces (Ilyas, Leung 2004). Fig. 7 displays an increase in the p-multipliers
with the scour ratio R in Case A analyses localized betweenR =0.72.8,
indicating that a scour depth lower than 0.7D
eff
would have a minor
impact on the later pile group behavior. This increase depends on the
row location, being greater for the front row (varying from 0.65 to 0.85)
than for the middle rows (increasing from 0.5 to 0.6), whereas the p-
multiplier of the rear row is nearly constant. The fact that front rows
underwent the largest increase in, at least partly, due to the distance
between the bottom boundary of the scour hole and the pile being
greater than zero (Swb = 0) for single piles while it is minimal
(Swb =0) for pile groups, as shown in Fig. 1 (a).
Fig. 8. (b). The reduction in the tangent stiffness of the group for different
scour hole slope angle.
Z. Wang et al.
Computers and Geotechnics 150 (2022) 104913
9
4.5. Effects of the slope angle of scour holes
Fig. 8 (a) presents loaddisplacement curves of the cap from Group B
analyses, with scour-hole slope angle β from 0 up to 25and a xed R=
2.1 while Fig. 8 (b) shows the corresponding tangent stiffness curves. As
previously pointed out, the scour-hole angle β=0simplies to a gen-
eral scour all other scenarios. Results from Group B prove that a general
scour type of approach would result in overconservative design when
the slope angle is at least 50% the value of the internal friction angle.
This is due to larger scour slope angles reducing the size of the scour
hole. Also, for these analyses, the sensitivity of the loaddisplacement
relationship of pile groups on the values of the scour slope is limited,
with slope angle values between 48% and nearly 93% of the friction
angle leading to similar results. From Fig. 8 (b) associated with a rela-
tively highR=2.1, the group stiffness reduction with displacement
level is limited for scour slope angle greater than 48% the soil friction
angle, leading to a nearly linear trend of force-displacements, whereas
the foundation response to loading is highly nonlinear for the general
scour case. Thus, local and general scours result in different soil-pile
interaction mechanisms.
The bending moment of piles-in-group along pile shaft under
different scour hole slope angles are presented in Fig. 9. When the slope
angle β is greater than zero, there are notable differences in bending
moments between piles; the front row piles (FC, FO pile) have larger
maximum bending moments than middle rows (MO, MC pile) and rear
rows (RC, RO pile), while the maximum bending moment at the center
of the trailing row (MC, RC pile) is the lowest because of the overlapped
soil reaction zone. Contrarily, when the local scour is simplied to a
general scour hole (i.e. β=0), the difference between the bending
moments of all piles in a group is small. Thus, also bending moment
results indicated that the unscoured soil above the scour depth in a local
scour contributes to the soil resistance for laterally loaded pile groups.
As for the cap loaddisplacement curves, when the scour hole slope
angle varies from β=13toβ=25, differences between bending mo-
ments are minor; therefore, preliminary assessment of the role of
scouring on the lateral behavior are well quantied by head measure-
ments and, consequently, p-multipliers. Finally, the depth of the
maximum bending moment of the pile group is close to the post-scour
ground line under local scour conditions.
The soil resistance against depth for different scour angles is shown
in Fig. 10. And the p-multipliers of pile groups under different scour
angles from Group B are shown in Fig. 11. As for Group A results, the p-
multipliers of the front row are the largest also for varying slope angleβ.
Interestingly, the change of β has a larger impact on the p-multipliers of
the front row than the middle and rear rows, with difference between
the p-multipliers of the front and trailing rows increasing withβ. In fact,
the increase in the scour angle increases the lateral soil resistance of the
front row and, at the same time, increases the active earth pressure of the
rear row.
When local scour is simplied as general scour, the difference of p-
Fig. 9. The relationship between the bending moment along pile shaft of each pile in a pile group under different scour hole angle.
Z. Wang et al.
Computers and Geotechnics 150 (2022) 104913
10
Fig. 10. Each pile in pile group soil resistance-depth relationship curves under different scour hole slope angle.
Fig. 11. The value of p-multipliers (with different scour hole slope angle). Fig. 12. Normalized loaddisplacement curves for pile group with different
pile spacing.
Z. Wang et al.
Computers and Geotechnics 150 (2022) 104913
11
multipliers between different rows is small, which could be explained
that the load eccentricity (the length of the pile above the mudline) of
the pile is increased, so that the soil resistance at the post-scour ground
line is not fully mobilized.
4.6. Effects of pile spacing
To examine the effect of pile spacing, analyses of Group C 3x3 were
carried out including pile groups with center-to-center pile spacing of
3D, 4D, 5D, 6D, 7D, scour depth ratioR=2.1, and scour hole slope
angleβ=25. It should be noted that the bottom area of the scour hole
increases with the pile spacing, and the distance from the bottom
boundary of the scour hole to the center pile isS+D/2. As expected, also
in the presence of scouring, Fig. 12 shows that the lateral load at the cap
of pile groups reduced for closer pile spacing due to the group effect
(Rollins K M 2006), and that the nonlinearity of the loaddisplacement
curve is slightly more pronounced for the largest spacing.
Fig. 13 and Fig. 14 show the relationship between the bending
moment and soil resistance along the depth of each pile in the pile group
at different pile spacing, respectively. And the p-multipliers of pile
groups for varying pile spacing is summarised in Fig. 15. The p-multi-
pliers for all rows gradually increase with S/D underR=2.1; the in-
crease rate between S/D =3 and 7 is greater for the middle rows
(increasing from 0.6 to 0.85) while it is marginal for the front rows with
the larges p-multipliers (increasing from 0.85 to 0.95 between S/D). This
is due to the scour hole inducing a higher passive earth pressure on the
front row piles and a higher active earth pressure on the rear row piles
along the load direction. As the distance between the middle row piles
and the boundary of the scour hole increases, the impact of the scour
hole on the middle row piles gradually decreases, while its impact on the
front row piles and rear row piles remains unchanged.
4.7. Regression of p-multiplier values
The p-multiplier value is related to the scour depth ratio (R), scour
slope angle (β) and pile spacing (S/D). For design guidance in risk as-
sessments, an empirical expression between the p-multiplier and the
three inuencing factors is tted to the numerically computed p-multi-
plier values for front, middle and rear row piles and, respectively,
Equations (3), (4), (5) are obtained. Fig. 16 plots against a 1:1 line the
relationship between empirically estimated and numerically computed
p-multipliers, proving a satisfactory accuracy with coefcient of deter-
mination greater than 96.9%. Front row:
p= (2.92 +1.87 ×R0.36 ×R2) × (1.019 0.1× (− 1)β) × (1.769
1.64 ×0.997S/D)(3)
Middle row:
Fig. 13. The relationship between the bending moment along pile shaft of each pile in a pile group under different pile spacing.
Z. Wang et al.
Computers and Geotechnics 150 (2022) 104913
12
Fig. 14. Each pile in pile group soil resistance-depth relationship curves under different pile spacing.
Fig. 15. The value of p-multipliers (with different pile spacing). Fig. 16. The error between the nite element calculation p-multiplier and the
tting expression p-multiplier.
Z. Wang et al.
Computers and Geotechnics 150 (2022) 104913
13
p= (2.383 +0.927 ×R0.172 ×R2) × (0.307 0.00215 × (− 1)β)
× (0.839 +1.208 ×0.626S/D)(4)
Rear row:
p= (2.177 +0.33 ×R0.061 ×R2) × (5.392 0.167 × (− 1)β)
× (1.202 +1.17 ×0.998S/D)(5)
5. Limitation
When the pile spacing is greater than 5D, in addition to the scour
hole around the pile group, an independent small scour pit will be
formed around each pile in the pile group. For the inuence of scouring
on the lateral bearing capacity of large pile diameter pile groups, the
follow-up research needs to further consider the inuence of small scour
pits around each pile in the pile group on the laterally loaded pile group.
Furthermore, the local scour hole around pile group is a process of
gradual formation until the shape of the scour hole is stable. The method
used in this study is to directly remove the soil within the local scour
hole to consider the change of the stress state for the unscoured soil.
Subsequent research needs to consider the effect of the gradual forma-
tion of scour holes on the stress state of unscoured soil. Apart from this,
only the inuence of the shape of the scour hole and the spacing of the
piles is considered. The inuence of soil parameters such as the un-
drained shear strength of the soil on the lateral bearing capacity of the
pile group needs further research under scour conditions.
6. Conclusions
Finite element analyses are performed to study the inuence of local
scouring on laterally loaded pile groups. A parametric study investigates
the inuence of varying normalized scour depth, scour hole slope angle,
and pile spacing for single piles and pile groups with comparable
effective scouring. Results quantied the impact of scouring on foun-
dation stiffness to horizontal loads, mobilized soil resistance (and cor-
responding of p-multipliers) and pile bending moments within the
group. Finally, empirical expressions for the obtained p-multipliers are
suggested. The following conclusions can be drawn.
(1). Under the same lateral displacement, the increase in the scour
depth and the scour slope angle reduced the lateral load of the
pile foundation. Ignoring the scour effects overestimates the ca-
pacity of the pile foundations, whereas simplifying the local scour
as general scouring (i.e. complete removal of soil layer above the
scour depth) is conservative (by a factor as large as 44%). Thus,
this work conrmed the needs to consider the local scour hole in
the design of the pile groups in clays. In particular, under the
scour condition, the load borne by the front row piles in the pile
group increases gradually with the increase of the scour depth
and scour slope angle, and the front row piles are more likely to
be damaged in the actual project.
(2). Load-displacement curves of pile groups with different scour
depths and scour hole slope angles indicated that the scour depth
is the most critical factor affecting the lateral behavior. In
particular variation of the slope angle between 50% and 90% the
soil friction angle had limited impact on the lateral load, whereas
the lateral load of the pile group reduced by 2646% for scour
depth from 0.7Deff to 2.8Deff (Deff is the effective diameter of a pile
group).
(3). Considering that the local scouring reduced nearly uniformly the
lateral load of the foundation for the entire loaddisplacement
curve, the p-multipliers can effectively consider both group ef-
fects as well as scouring. As the scour depth increases, the p-
multipliers value of each row of piles in the pile group gradually
increases. Among them, the p-multipliers value of the front row
piles changes most, and the p-multipliers value of the rear row
piles changes less. The increase of the pile spacing reduces the
overlapped soil reaction zone and, consequently, the p-multi-
pliers value of each row of piles increases. Under scour condi-
tions, the inuence of pile spacing on the p-multipliers of the
middle row piles is greater than that of other rows.
CRediT authorship contribution statement
Zengliang Wang: Writing original draft, Data curation. Hang
Zhou: Conceptualization, Investigation. Andrea Franza: Writing re-
view & editing. Hanlong Liu: Validation.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Acknowledgements
The work was supported by the National Natural Science Foundation
of China, China, Grant/Award Number 51978105 and 52027812; the
Chongqing Science Foundation for Distinguished Young Scholars,
Grant/Award Number: cstc2021jcyj-jqX0017 and the Chongqing Youth
Top Talent Plan, Grant/Award Number: cstc2021ycjh-bgzxm0132.
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