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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

inuence 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 inuence 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 signicant. 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 classied as follows: “local scour” that occurs around pile

foundation forming a scour hole; “contraction scour” that 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 simplied 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 simplied 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 inuence 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 simplied 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 Mindlin’s 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 congurations is of interest.

For this, the p-multipliers method is the widely adopted that quanties

the relationship between p-y curves of single piles and pile rows, where p

is the local soil resistance (dened 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 inuence 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 prole, 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 Modied Cam Clay constitutive model is adopted to describe the

stress–strain 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-

ding–reloading lineκ=Cs/2.3=0.061, a slope of the critical state

lineM=6sinφ′/(3−sinφ′) = 1.07, while φ′=26.9◦is the critical

friction angle. According to the Modied Cam Clay model, the variation

of the initial void ratio with depth is:

e0=e1−λln(q2

M2p′+p′)+κln(q2

M2p′2+1)(1)

where p′is 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 Coefcient of permeability

Su Undrained shear strength

D Pile diameter

K

0

Coefcient 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 unloading–reloading line

M Slope of the critical state line

φ′Critical friction angle of soil

p′Mean 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

Coefcient 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, Young’s modulus E =20.9 GPa, and a

Poisson’s 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 load–displacement 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-place” method, 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 coefcient 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 step” imposing 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

load–displacement 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)

0◦13◦19◦22◦25◦

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

load–displacement 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

conguration 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. Simplied 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 simplied 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 proles 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 inuence 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 dened as the “scour ratio” R=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 load–displacement curves at

the pile heads, bending moment proles 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 =L−Sgdecreases. 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=0−2.8) with a xed

slopeβ=25◦, which are labelled as Case A.

For this group of analysis cases, Fig. 3 (a) compares the

load–displacement 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 load–displacement 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

Output” of 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 proles 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=0.7−2.8) 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 prole 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 prole 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 =0.7–2.8,

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 load–displacement curves of the cap from Group B

analyses, with scour-hole slope angle β from 0 up to 25◦and a xed R=

2.1 while Fig. 8 (b) shows the corresponding tangent stiffness curves. As

previously pointed out, the scour-hole angle β=0◦simplies 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 load–displacement

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 simplied 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 load–displacement curves, when the scour hole slope

angle varies from β=13◦toβ=25◦, differences between bending mo-

ments are minor; therefore, preliminary assessment of the role of

scouring on the lateral behavior are well quantied 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 simplied 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.

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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 load–displacement curves for pile group with different

pile spacing.

Z. Wang et al.

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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 load–displacement

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 inuencing 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 coefcient of deter-

mination greater than 96.9%. Front row:

p= (2.92 +1.87 ×R−0.36 ×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.

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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.

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Computers and Geotechnics 150 (2022) 104913

13

p= (2.383 +0.927 ×R−0.172 ×R2) × (0.307 −0.00215 × (− 1)β)

× (0.839 +1.208 ×0.626S/D)(4)

Rear row:

p= (2.177 +0.33 ×R−0.061 ×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 inuence of scouring

on the lateral bearing capacity of large pile diameter pile groups, the

follow-up research needs to further consider the inuence 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 inuence of the shape of the scour hole and the spacing of the

piles is considered. The inuence 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 inuence of local

scouring on laterally loaded pile groups. A parametric study investigates

the inuence of varying normalized scour depth, scour hole slope angle,

and pile spacing for single piles and pile groups with comparable

effective scouring. Results quantied 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 conrmed 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 26–46% 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 load–displacement

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 inuence 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 inuence

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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