Simplified Calculation Method of Wharf Bank Slope Stability Considering Old Piles
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IOP Conference Series: Earth and Environmental Science
PAPER • OPEN ACCESS
Simplified Calculation Method of Wharf Bank Slope Stability Considering
Old Piles
To cite this article: Tianyun Liu and Linbo Xie 2021 IOP Conf. Ser.: Earth Environ. Sci. 638 012105
View the article online for updates and enhancements.
This content was downloaded from IP address 46.4.80.155 on 07/09/2021 at 17:37ISTTCA 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 638 (2021) 012105 doi:10.1088/1755-1315/638/1/012105
Simplified Calculation Method of Wharf Bank Slope Stability
Considering Old Piles
Tianyun LIU*, Linbo XIE
Tianjin Port Engineering Institute Company LTD. Of CCCC,
CCCC First Harbour Engineering Company Ltd.,
Key Laboratory of Port Geotechnical Engineering of Ministry of Communications,
Key Laboratory of Port Geotechnical Engineering of Tianjin, Tianjin 300222, China.
*
Corresponding author’s e-mail: liutianyun@tpei.com.cn
Abstract. Based on the requirements of durability, a simplified calculation method of wharf
slope stability considering the anti-sliding effect of old piles is derived according to the
allowable cracks of old piles. Firstly, the acting force between the sliding soil and the pile is
assumed to be distributed in a triangle, and the position of the resultant force of each pile is
determined. According to the maximum crack width limit of the old pile, the maximum
bending moment that the old pile can bear is calculated. According to the maximum bending
moment, the maximum horizontal force at the mud surface, where is the slip arc position, can
be inversely calculated, then the maximum anti-sliding force provided by the old piles can be
obtained, and the stability of wharf bank slope considering the anti-sliding effect of the old
piles is checked. In the slope stability calculation of Beira fishing wharf reconstruction project
in Mozambique, the simplified calculation method considering the anti-sliding effect of old
piles is adopted. The stability coefficient of wharf bank slope meets the requirements, and the
extra treatment of bank slope is cancelled, which saves the project investment and construction
period.
1. Introduction
According to the requirements of Chinese standard: Code for Foundation Design on Port and
Waterway Engineering [1] for stability calculation of soil slope, it is generally considered as plane
problem, and circular sliding surface should be used for calculation. Moreover, for soil slope and
foundation with piles, the anti-sliding effect of engineering piles should not be included in the stability
checking calculation，because the partial factor of resistance to slope stability of most wharfs is
relatively low, which is also lower than the relevant provisions of other countries. Considering the
anti-sliding force of piles, the slope safety reserve with low reliability is actually used, which leads to
the slope approaching the limit critical state. In practical engineering, problems such as excessive
deformation of wharf often occur, even if the slope is stable, it also affects the normal use of the wharf.
Therefore, it is stipulated in the Chinese standard that “the anti-sliding effect of piles may not be
included” to increase the reliability of the wharf. However, the old piles left after the demolition of the
old wharf no longer belong to the new wharf structure, and its large deformation will not affect the
normal use of the new wharf. According to the research results of the literature [2-5], the anti-sliding
effect provided by the old piles can be considered in the slope stability calculation of the new wharf.
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Published under licence by IOP Publishing Ltd 1ISTTCA 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 638 (2021) 012105 doi:10.1088/1755-1315/638/1/012105
2. Calculation formula of the wharf slope stability considering anti-sliding effect of old piles
For the piles with spacing of Si, when considering the plane problem, the anti-sliding force provided at
the sliding surface can be calculated as follows:
F
fi i Si
(1)
Then the standard value of anti-sliding moment considering pile action can be calculated according to
the following formula.
In the case of fast shear index of consolidation:
c b q b W -u b tan φ
MRK R（ ∑ ki i ki i ki ki i 1 ki ∑ fi ） (2)
cos αi sin ai tan φki
γ R
In the case of the simple slice method:
MRK R ∑ cki Li ∑ qki bi Wki cos αi tan φi ∑ fi (3)
In the case of total strength index:
MRK R（ ∑ Suki Li ∑ fi ） (4)
3. Calculation of the anti-sliding force provided by old piles
In equation (1), It is the key to determine the anti-sliding force Fi provided by each row of old piles. Fi
is decomposed into horizontal force Hi and vertical force Ni, which is transformed into how much
horizontal force Hi can be provided by old piles.
According to the research results of reference [6], the force distribution between sliding soil and
pile is triangular.
The point of resultant force is located at two thirds of the length of the pile in the sliding soil, as
shown in Fig.1, then the mud surface is the sliding arc, where Hi =Fi cosθi ，Hi0=Hi，Mi0= Hi0×Zi=
Hi×Zi, and Zi can be obtained by drawing and measuring from the map.
2h /3i
Fi F i
h M 0i
i θ i
H
0i
h /3
i z i
(a) (b) (c)
Figure 1. Distribution of the anti-sliding force of old pile
For the permanent wharf slope, the old piles will be subjected to horizontal load for a long time.
The durability factor of pile foundation in water transportation engineering should be considered.
According to the Chinese standards: Design Code for Concrete Structure of Port and Waterway
Engineering [7], different types of components and working conditions have different requirements for
the maximum crack width, as shown in table 1.
Table 1. Maximum crack width limit of reinforced concrete structure [Wmax]（mm）
Freshwater port Sea port
zone of water zone of water
zone above zone below Atmospheric Splash zone below
level level
water water zone zone water
fluctuation fluctuation
0.25 0.25 0.40 0.20 0.20 0.25 0.30
According to the Chinese standards: Design Code for Concrete Structure of Port and Waterway
Engineering [7], the maximum crack width of reinforced concrete members under tension, bending
and eccentric compression with rectangular, T-shaped, inverted T-shaped, I-shaped and circular
sections can be calculated according to formula (5).
2ISTTCA 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 638 (2021) 012105 doi:10.1088/1755-1315/638/1/012105
σ c d
Wmax α1 α2 α3 Es 0.30 1.4ρte
(5)
s
Where:
Wmax —Maximum crack width, mm.
α1—Force characteristic coefficient of member; 0 for flexural members; 0.95 for large eccentric
compression members; 1.10 for eccentric tension members and 1.20 for axial tension members.
α2—Influence coefficient considering the shape of reinforcement surface; the smooth steel bar is
1.4, and the ribbed steel bar is 1.0.
α3—The coefficient considering the effect of quasi permanent combination or repeated load is 1.5;
for the normal service limit state under transient condition, the value of action combination is 1.0-1.2,
and 1.0 is taken for construction period.
σs—Stress of longitudinal tensile reinforcement in reinforced concrete members, N/mm2.
Es—Elastic modulus of reinforcement, N/mm2.
c — Cover thickness of the outermost row of longitudinal tensile reinforcement, mm; when c is
greater than 50 mm, take 50 mm.
d—Reinforcement diameter, mm; when different diameters are used, the converted diameter of
weighted average is taken.
ρte—Effective reinforcement ratio of longitudinal tensile reinforcement.
Among them, the effective reinforcement ratio of longitudinal tensile reinforcement of rectangular,
T-shaped, inverted T-shaped and I-shaped sections is calculated according to the following formula.
A
ρte sAte
(6)
Where:
As—Effective tensile concrete section area, mm2; for axial tension members, the cross-sectional
area of all longitudinal reinforcement is taken; for bending, eccentric tension and eccentric
compression members, 2asb is taken; as is the distance from the centre of gravity of tensile
reinforcement to the edge of tensile zone; for rectangular section, b is the section width; for inverted
T-type and I-type section with tension flange, b is the flange width of tension area.
Ate—Section area of longitudinal reinforcement in tensile zone , mm2; for axial tension members,
the cross-sectional area of all longitudinal reinforcement is taken; for bending, eccentric tension and
large eccentric compression members, the cross-sectional area of longitudinal reinforcement in the
tension area or the reinforcement section area of the larger side under tension is taken.
The effective reinforcement ratio of longitudinal tensile reinforcement of circular section is
calculated according to the following formula.
βAs
ρte 2 2
π r -rl
(7)
rl r-2as (8)
Where:
β—Coefficient of contribution of longitudinal reinforcement in tension to maximum crack
development.
As—Cross sectional area of all longitudinal reinforcement, mm2.
r—Radius of circular section, mm.
rl—The difference between the radius of circular section and twice the distance from the centre of
reinforcement to the edge of the member, mm.
as—Distance from reinforcement centre to component edge, mm.
According to the Chinese standards: Design Code for Concrete Structure of Port and Waterway
Engineering [7], when the effective reinforcement ratio is less than 0.01, it should be taken as 0.01;
when it is greater than 0.1, it should be taken as 0.1.
The longitudinal stress of steel bars in members can be calculated according to table 2.
3ISTTCA 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 638 (2021) 012105 doi:10.1088/1755-1315/638/1/012105
Table 2. stress calculation of longitudinal stressed reinforcement
Rectangular, T-shaped, inverted T- Mq
σs
shaped, I-shaped sections 0.87As h0
Bending
Mq
Circular section σs rs
0.45 0.26
r As r
Where:
As —Section area of longitudinal reinforcement in tensile zone, mm2; for axial tension members,
the cross-sectional area of all longitudinal reinforcement is taken; for eccentric tension members, the
cross-sectional area of longitudinal reinforcement on the larger side of tension is taken; for bending
and large eccentric compression members, the cross-sectional area of longitudinal reinforcement in
tension area is taken; for circular section, the cross-sectional area of all longitudinal reinforcement is
taken.
Mq—Bending moment value calculated according to quasi permanent combination of actions,
Nꞏmm.
h0—Effective height of section, mm.
In order to ensure that the old pile can meet the durability requirements in the case of permanent
slope, the cracks caused by the deformation old pile under horizontal load must meet the maximum
crack limit requirements of the Chinese standards: Design Code for Concrete Structure of Port and
Waterway Engineering [7]. The maximum crack limit can be used to calculate the maximum stress
that the existing pile foundation can bear according to formula (5), and the maximum stress of the
existing pile foundation can be calculated according to table 2. The maximum bending moment that
the pile can bear is calculated by inverse calculation of large stress.
4. Calculation of maximum horizontal force on pile
According to the appendix “D.3 m method” of the Chinese standards: Code for Pile Foundation of
Harbour Engineering [8], when the pile top can rotate freely, the pile deformation can be calculated
according to the following formula. When the foundation is layered, m method adopts the weighted
average value of each soil layer within the depth range of 1.8T below the ground.
Mmax M0 C2 (9)
Mmax H0 TD2 (10)
5 Ep Ip
T (11)
mb0
Where:
H0—Horizontal load acting on the mud surface, kN.
T—Characteristic value of the relative stiffness of pile, m.
Ep—Elastic modulus of the pile material, kN/m2.
Ip— Moment of inertia of the pile section, m4.
M0— Bending moment acting on the mud surface, kNꞏm.
m— The proportional coefficient of the horizontal resistance coefficient increasing with the depth
of the foundation soil on the pile side, kN/m4.
b0— Converted width of pile, m.
h— Conversion depth, m; it can be found from “table D.3.3” of the Chinese standards: Code for
M0 H T
Pile Foundation of Harbour Engineering [8] according to the formula C1 or D1 0 .
H0 T M0
Mmax— Maximum bending moment of pile shaft, kNꞏm.
C2、D2— Dimensionless coefficient, it can be found from “table D.3.3” of the Chinese standards:
Code for Pile Foundation of Harbour Engineering [8] according to the formula h Zm ⁄T.
4ISTTCA 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 638 (2021) 012105 doi:10.1088/1755-1315/638/1/012105
According to the Chinese standards, the proportional coefficient m of the horizontal resistance
coefficient of the soil around the pile should be determined by the horizontal static load test of the
single pile. When there is no static load test data, the value can be taken according to table 3.
Table 3. m value of the non-rock soil
Precast pile, steel pile Cast in place pile
Horizontal Horizontal
displacement of displacement of
Category of foundation soil m m
corresponding single corresponding
（kN/m4） pile at the ground （kN/m4） single pile at the
（mm） ground（mm）
Mucky soil 2000~4500 2500~5000
Flow plastic (IL > 1), soft plastic (0.75 <
IL ≤ 1) clay;
e > 0.9 silt; 4500~6000 3000~5000
loose silty fine sand;
loose fill
Plastic (0.25 < IL ≤ 0.75) clay; 10
e= 0.75 ~ 0.9 silt;
6000~10000 5000~10000 6
slightly dense or medium dense; slightly
dense fine sand
Hard plastic (0 < IL ≤ 0.25) hard (IL ≤ 0)
clayey soil;
e < 0.75 silt; 10000~22000 10000~30000
medium dense medium coarse sand; dense
old fill
Medium dense and dense gravel sand and
— — 30000~80000
gravel soil
Note: 1. When the horizontal displacement of the pile top is greater than the listed value, m value
should be appropriately reduced; when the horizontal displacement is less than 1, the m value can be
appropriately increased;
2. When the mud surface is inclined, m value can be reduced properly
3. When the horizontal force is a long-term load, the value of m can be appropriately reduced.
According to table 3, the maximum bending moment that the old pile can bear will be inversely
calculated. According to the formula (9)-(11), the maximum horizontal force that the old pile can bear
at the mud surface can be inversely calculated, which is the anti-sliding force provided by the old pile
in the stability checking calculation of the permanent wharf bank slope.
5. Checking calculation process of the wharf bank slope stability considering anti-sliding effect
of old piles
Firstly, the stability of the bank slope is calculated according to the state of no pile, and the position of
the most dangerous slip arc is determined;
Secondly, according to the position of the most dangerous slip arc, it is assumed that the force
between the sliding soil and the pile is distributed in a triangle, and the position of the joint force
acting on each pile is determined.
Thirdly, according to the type and working conditions of the old pile, the maximum crack width
limit is determined, and the maximum bending moment that the old pile can bear is inversely
calculated according to the limit value.
Fourthly, according to the maximum bending moment and m method, the maximum horizontal
force at the mud surface, i.e. the sliding arc position, can be inversely calculated, and then the
maximum anti sliding force provided by the old pile can be obtained.
5ISTTCA 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 638 (2021) 012105 doi:10.1088/1755-1315/638/1/012105
Fifthly, the maximum anti sliding force obtained from the inverse calculation of each pile in the
sliding body is substituted into the formula (1)-(5) to check the stability of the permanent bank slope
considering the anti-sliding effect of the old piles.
6. Engineering application
Beira port is the second largest port in Mozambique. The old piles of the former Beira port fishing
wharf are precast concrete square piles with the size of 380 mm and the row spacing of 2.2 m-2.4 m,
as shown in Fig.2. C20 concrete is used and the main reinforcement in the pile is four φ32 grade I
plain round steel bars [9].
The circular sliding method is used to calculate the stability of the existing bank slope, and the
calculation result shows that the stability coefficient of the bank slope is 0.93, less than 1.0. However,
according to the field monitoring results, the bank slope is stable and there is no potential trend of
sliding, which indicates that the calculation results of bank slope stability without considering the
effect of old piles are inconsistent with the actual situation.
Figure 2. Distribution of the piles in the wharf bank slope
The anti-sliding position of the old pile belongs to the water level fluctuation area, reinforced
concrete structure, and the maximum crack width limit is 0.25 mm.
The anti-sliding forces provided by each old pile are calculated one by one by formula (5)-(11), as
shown in table 4.
Table 4. Anti-sliding force provided by the old piles（kN）
No. 1 2 3 4 5 6 7 8
Mi0/Hi0 1.93 2.10 2.23 2.30 2.30 2.27 2.07 1.87
C1i 1.031 1.120 1.191 1.226 1.226 1.209 1.102 0.995
D2i 1.604 1.681 1.743 1.774 1.774 1.758 1.666 1.573
H0imax 36.5 34.8 33.6 33.0 33.0 33.3 35.1 37.2
θi 30.8 25.1 19.6 14.4 9.2 4.1 0.9 5.9
Fi 42.5 38.4 35.6 34.1 33.4 33.4 35.1 37.4
According to the formula (1) and (2), the stability coefficient of bank slope is 1.11, which is
consistent with the actual situation of the site.
6ISTTCA 2020 IOP Publishing
IOP Conf. Series: Earth and Environmental Science 638 (2021) 012105 doi:10.1088/1755-1315/638/1/012105
7. conclusion
The old piles left in place after the old wharf is demolished are no longer used as the new wharf
engineering piles. The anti-sliding effect of the old piles can be considered in the new wharf if they
have good mechanical properties and durability.
Based on the durability requirements, the maximum anti-sliding force provided by the old pile can
be obtained by inverse calculation according to the allowable crack width of the pile, and a simplified
calculation method of bank slope stability considering the anti-sliding effect of the old pile is derived.
The simplified calculation method considering the anti-sliding effect of old piles is applied to the
bank slope stability calculation of Beira fishing wharf reconstruction project in Mozambique. The
stability coefficient of bank slope meets the requirements, and the extra treatment of bank slope is
cancelled, which saves the project investment and construction period.
References
[1] Code for Foundation Design on Port and Waterway Engineering (JTS147-2017).
[2] Wei Ru-long, Wang Nian-xiang, Yang Shou-hua. Interaction Between Plie-Support Pier and Bank
Slope. Chinese Journal of Geotechnical Engineering. 1992, 14(6):38-49.
[3] Zhu Zhen-yu, Wang Yuan-zhan, Li Yue-song, Zhu Chong-cheng. Finite Element Analysis of
Interaction Between Piled-Wharf and Slope. China Harbour Engineering. 2016(2):1-4.
[4] Liao Xing-hua, Zhang Ke-xu. Numerical Analysis of Pile-soil Interaction in Long-Piled Wharf of
Tianjin Port. Journal of Hydraulic Engineering, 2002(4):81-87.
[5] Liu Tian-yun, Zhuge Ai-jun, Yu Zhi-fa. numerical simulation study on the influence of pile
parameters on bank slope stability. Port & Waterway Engineering. 2020(4):156-161.
[6] Zhou Xi-reng, Wang Le-qin, Wang hui, Zhu Fu-ming. Modifications to Global Stability Analysis
on Slope of Piled Foundation Wharf. Chinese Journal of Rock Mechanics and Engineering.
2005,24(2)： 681-686.
[7] Design Code for Concrete Structure of Port and Waterway Engineering (JTS151-2011) .
[8] Code for Pile Foundation of Harbour Engineering (JTS164-4-2012) .
[9] Feasibility Study for Beira fishing port rehabilitation project in Mozambique. China Harbour
Engineering Company Limited, 2013.
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