Available via license: CC BY 3.0
Content may be subject to copyright.
IOP Conference Series: Earth and Environmental Science
PAPER • OPEN ACCESS
Finite Element Analysis on Earth-rock Cofferdam Behavior during
Pumping and Drainage of Foundation Pit
To cite this article: Yang Deng et al 2019 IOP Conf. Ser.: Earth Environ. Sci. 376 012022
View the article online for updates and enhancements.
This content was downloaded from IP address 158.46.144.31 on 17/12/2019 at 17:10
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Published under licence by IOP Publishing Ltd
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
1
Finite Element Analysis on Earth-rock Cofferdam Behavior
during Pumping and Drainage of Foundation Pit
Yang Deng1, Changhai He1*, Shaojun Fu2, Jianwei Hui3
1State Key Laboratory of Water Resources and Hydropower Engineering Science,
Wuhan University, Wuhan, Hubei, 430072, China
2Xijing University, Xi’an, Shanxi 710123, China
3No. 6 Engineering Corporation Limited of CR20G, Xi’an, Shanxi 710016, China
*Corresponding author’s e-mail: hch_2003@163.com
Abstract. The drawdown velocity of foundation pit water level in existing projects is mostly
determined empirically, and the influence of water level drawdown velocity on the seepage
field and stress field in the weir body is not fully considered. The water level change of the
foundation pit is an important factor affecting the stability of the cofferdam. Therefore, it is of
great practical significance to study the variation law of seepage field and stress-strain field of
cofferdam during the pumping process of foundation pit, to accurately judge the stability of
cofferdam slope and to formulate reasonable pumping and drainage scheme. Based on the 1th
temporary earth-rock cofferdam of Yongning Water Conservancy Project, the nonlinear finite
element method is used to calculate the spatial-temporal evolution of seepage field and stress-
strain field of earth-rock cofferdam under different drawdown velocity of water level. The
overall deformation of the cofferdam, the shear failure and instability characteristics of the
slope, and the influence of water level changes on the stability of the cofferdam slope are
analysed. The results show that the distribution of unsaturated zone and negative pore pressure
zone is basically the same. The excessive water level drawdown velocity is easy to break the
balance between the seepage field and the water level fall time, resulting in the rise of
saturation line height and the increase of the upper bending rate. The effect of seepage control
is weakened, and the stability of the slope is poor. The shear deformation of the cofferdam
slope develops from the foot of the slope and extends to the crest of the cofferdam until it runs
through. At the same time, local plastic deformation occurs at the foot of the outer stone slag
berm, and the maximum deformation transits to the foot of the inner slope. Under the action of
seepage force, the stability of the inner slope is always smaller than that of the outer one; the
change of water level drawdown velocity is very sensitive to the stability of the slope, when the
drawdown velocity is greater than the critical velocity, the stability of the slope decreases
sharply. Combined with the characteristics of earth-rock cofferdam, on the basis of satisfying
the stability of cofferdam, the drawdown velocity of water level should be controlled within
1.28m/d. The research results of the thesis have reference significance for the selection of
pumping speed of foundation pit similar to earth-rock cofferdam.
1. Introduction
In the construction period of water conservancy and hydropower project, in order to carry out
foundation pit construction work in time, rationally formulate the foundation pit water level drawdown
velocity to coordinate the construction period and the slope anti-sliding stability relationship, and the
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
2
domestic combined engineering practice experience has established the allowable control range of the
water level drawdown velocity of the earth and rock cofferdam foundation pit. However, due to the
lack of theoretical basis, the engineering experience tends to be conservative, the structure and type of
cofferdam are diverse, the design data is rough and the experimental conditions are complex. The anti-
sliding safety evaluation of earth-rock cofferdam has not yet formed a unified standard [1-2]. The
domestic scholars represented by Ren Dachun et al [3-10] compiled a three-dimensional finite element
calculation program, and applied the saturated-unsaturated conditional seepage model to the stability
analysis of the impervious core wall with defects for the first time. The earth-rock cofferdam has
preliminarily explored the characteristics of the seepage field and the stability mechanism of the
seepage field under the effect of stable seepage and fluid-solid coupling. The factors such as the form
and depth of the cut-off wall and the change of nonlinear materials have been considered. The
characteristics of pore water pressure, saturation line height and osmotic slope during operation are
combined with the rigid body limit equilibrium method to evaluate the stability of the slope under the
seepage, and the optimization scheme of the seepage control system is provided. The theory of
unsteady seepage is applied. The influence law of the water level change of the foundation pit on the
seepage field and stability of the cofferdam during construction period is further analysed, which lays
a foundation for the research and application of the foundation pit pumping speed during the
construction process.
Although the numerical method has been widely used in the analysis of solving the problem of
seepage stability of complex geotechnical slopes [11-17], the problem of the influence of the water
level change of the foundation pit on the stability of the slope has not been studied in depth. The
stability analysis of the earth-rock slope with coupling effect considering the unsteady seepage-stress
is very little. The limit equilibrium method can’t reflect the overall deformation and plastic penetration
process of the slope. Under the condition of satisfying the stability of the slope and the construction
period, there is no exact method for the critical speed of the foundation pit to do precise prediction.
In order to ensure the safety and stability of the slope during the pumping of the foundation pit and
meet the minimum construction period, this paper considers the influence of heterogeneous soil
permeability anisotropy and matrix suction on permeability based on the unsteady seepage-stress field
coupling theory. The finite element method is used to study the seepage characteristics of cofferdam
under different pumping speed conditions. The overall strength reduction method based on field
variables is used to solve the stability coefficient of the temporary earth-rock cofferdam in the first
stage of Yongning Water Conservancy Project to determine the maximum deformation position and
potential sliding surface, objective stability analysis and evaluation of the slope, in order to provide
theoretical guidance and reference for the reasonable selection of actual engineering foundation
pumping speed.
2. Basic equations and fluid-solid coupling theory
2.1. Basic equations
For the unsteady seepage with free surface, the volume of soil compression or elastic release caused
by the decrease is much smaller than that of the free surface drop and the compressibility of soil and
water body can be neglected [18]. For unsaturated soils, the permeability coefficient is a function of
volumetric water content or matrix suction. That is,
( )
i r j
k k k
=
when Darcy's law is generalized to
anisotropic permeation, the basic equation for saturated-unsaturated seepage can be obtained:
( ) ( ) ( )
w
r x r y r z
S
h h h
k k k k k k n
x x y y z z t
+ + =
(1)
x
k
,
y
k
,
z
k
is saturated permeability coefficient(m/s) in direction
x
,
y
,
z
;
r
k
is the ratio of the
unsaturated permeability coefficient to the saturated permeability coefficient. For the unsaturated zone,
there are
0 1.0
r
k
;
n
is porosity;
w
S
is saturation;
is volumetric water content.
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
3
Considering the mathematical model describing the flow, the boundary conditions of the solution
include the head boundary, the flow boundary and the mixed boundary, which can be expressed as
( )
( )
( )
11
2
21
| , , ,
| , , ,
| , , , 0, | 0
n
h h x y z t
hvf x y z t
k
n
hf x y z t h
n
=
−
= =
= =
(2)
h
and
1
h
are known heads (m) of seepage field and similar boundary conditions respectively,
where
1
h
is a function of spatial coordinates and time.
2.2. Coupled mechanical mechanism of seepage-stress field
When there is seepage potential or head difference in porous geotechnical medium, the seepage force
along the flow direction is generated in the rock soil, and the stress field and displacement field are
changed. The effect of the penetrating force on the geotechnical medium can be calculated according
to the volumetric force of the continuous medium and the penetrating force and the hydraulic gradient.
The permeation volume force of the unit is converted into the external load of the equivalent node by
the formula (3) [19].
e
e
x
T
sy
z
x
T
sy
z
f
F N f dxdydz
f
f
F N f dxdydz
f
=
=
(3)
s
F
is the equivalent nodal force (N),
s
F
is the equivalent nodal force increment (N),
N
is
the unit function,
x
f
,
y
f
and
z
f
are the components of seepage force in the direction of
x
,
y
and
z
,
respectively.
According to the principle of effective stress of porous media, the change of stress state of
geometrical will change its pore ratio and porosity, causing the permeability of soil, ie the change of
permeability coefficient, further affecting the flow and pressure distribution of pore fluid, so the
infiltration of soil The coefficient can be expressed as a function of the stress state, ie:
( )
ij
kk
=
2.3. Stress-seepage coupling control equation
2.3.1. The equilibrium equation. Assuming that the saturated-unsaturated rock mass is a continuous
medium, and the soil particles and water are incompressible. At a certain moment, the virtual work of
the rock and soil and the forces acting on the rock and soil (physical and lateral forces) the virtual
work produced is the same. According to the potential energy variation theory and the Biot effective
stress principle, the equivalent integral form of the unsaturated soil stress balance equation can be
obtained [14, 20].
( )
T T T T
w
ep s w
V V V S
ufp
dV s C u dV u dV u dS
t t t t
− + = +
DM
(4)
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
4
ep
D
is an elastic-plastic matrix;
M
is a unit array in normal stress;
and
u
are virtual
displacement and strain;
t
is surface force,
f
is physical force;
s
is saturation;
w
u
is pore water
pressure;
s
w
s
Cu
=
is the change rate of unsaturated soil saturation to matric suction, which can be
obtained from the soil-water characteristic curve.
2.3.2. The continuous equation. Considering a non-saturated soil unit. According to the conservation
of mass, the amount of water flowing into the volume during the time should be equal to the increase
of the internal water storage. The fluid seepage is described by Darcy's law and introduced into the
hole. The pressure boundary condition is directly introduced into the finite element equation as a
forced boundary condition. Combined with the seepage head, the divergence theorem can be used to
obtain the equivalent integral form of the saturated-unsaturated seepage control equation.
( )
ww
u u n 0
w v w
sw
S
w
VV
uu
k z dV s C dV u qd
tt
+ + + + =
(5)
A is Hamiltonian operator,
x y x
= +
i j k
;
w
u
is variation of pore pressure function;
w
is water gravity;
z
is position head in gravity direction;
n
is porosity;
q
is water flow through
boundary in unit time.
2.4. Finite element solution format of governing equations
For a saturated-unsaturated porous continuum, the finite element is discrete with a certain type of
element, with the displacement, strain and pore pressure as unknowns, the structural unit node variable
interpolation function, simultaneous (4), (5) Establish a coupled mathematical model, and the finite
element format of the stress-seepage coupling control equation is
00
0
+=
••
-•W
W
KL aa
F
P
H
K S P
P
(6)
Tep
V
= dV
K B D B
,
( )
Tsw
Vs C u dV
−
= − +
L B M N
,
TT
VS
fp
dV dS
tt
=+
•
F N N
,
T
V
= s dV
−
−T
K N M B
,
T
s
VnC dV
−−
=
S N N
,
1T
V
w
k dV
−−
=
H N N
,
TT
VS
k dV qdS
z
−−
= − −
N
PN
3. Project Overview
The Yongning Water Conservancy Project is located at the Niuwan Peninsula in the lower reaches of
the Yongjiang River in Nanning. It is a large (2) type water conservancy project, including a barrage, a
13-hole dam, a power house and an access road, with a total installed capacity of 57.6 MW and normal
water storage at 67m, the barrage project spans the Yongjiang River. From the right bank to the left
bank, the joint project of earth dam, joint gravity dam and main plant is arranged in sequence. Two
sections of three-stage diversion are adopted. The first phase requires rapid construction and
temporary water retention during dry season. The cofferdam uses a widened narrow river bed for
diversion and navigation, and builds a first-stage cofferdam on its backwater side to provide dryland
construction conditions throughout the year (Figure 1). In the second and third phases, the main
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
5
construction of the 9-hole overflow weir, using the completed 4-hole overflow dam diversion and ship
lock navigation (Figure 2).
Figure 1. Temporary cofferdam
design floor plan
Figure 2. Plan layout of the second stage
cofferdam construction
The first-stage temporary earth-rock cofferdam is a key project to ensure the foundation excavation
of the first-stage construction, four-hole overflow dam and main building. The axis is from about
350m on the right bank upstream of the dam axis to the dam axis. The downstream right bank is about
320m away from the dam line, and the water depth is about 14m~18m. The sand gravel layer of the
alluvial deposit at the bottom of the riverbed is about 1.5m thick, and the riverbed is relatively flat.
The underlying bedrock is dominated by limestone and dolomitic limestone, with thick layered
structure, uniform lithology and good integrity.
Under the unfavourable conditions that the material source does not fully meet the underwater
filling requirements, the construction period is not enough to find the source of materials, and there is
no precedent for the construction of similar projects at home and abroad, considering the safety of
navigation on the water side of the river, after research and analysis, the Yongning Water Conservancy
The first phase of the temporary cofferdam structure of the hub has undergone major adjustments,
using the surrounding stone slag berm, the additional sub-berm of the crest, the central jet grouting
anti-seepage wall and the cofferdam structure of the backwater-filled clay combined with anti-seepage
(Figure 3). The maximum height of the cofferdam is 18.12m, the elevation is 66.40m, and the design
water level is 64.62m. The cofferdam is filled with the construction technology of the non-rolling
earth and stone mixture.
Figure 3. Schematic diagram of typical section material of temporary cofferdam
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
6
4. Model generalization and finite element analysis model
4.1. Grid model
Calculation range: For the first-stage temporary cofferdam geometric model, the intersection of the
dam axis and the axis of the crest of cofferdam is taken as the coordinate origin, the longitudinal
cofferdam is on the water-facing side as the X-axis positive direction, and the vertical upward is the Z-
axis positive direction. The Y axis is determined by the right hand rule. In order to reduce the
boundary effect and improve the accuracy of the calculation results, the calculation is carried out from
the upstream to the downstream along the Y-axis direction, with a total length of 896.0 m (Figure 4);
along the X-axis from the backwater side of the foundation pit to the water surface of the berm is
nearly 4 times wide and covers the entire riverbed and the bank slopes on both sides, totaling 396.0m.
The depth of the rock is 101.3m below the surface of the foundation along the Z axis. The top and
bottom elevations of the model are respectively 73.0m and -50.0m.
Figure 4. Model calculation area
map
Figure 5. finite element mesh model
Grid model: In the process of foundation pit pumping, the stability of the slope structure under the
coupling of unsteady seepage-stress field is mainly investigated. For the temporary cofferdam,
riverbed and slope soil, the displacement/pore pressure coupling element with linear pore pressure
distribution and first or second order displacement distribution function is adopted to simulate the
transient flow of saturated-unsaturated fluid in porous media.[20]. In addition to the 4-node tetrahedral
coupling element (C3D4P) at the upstream diaphragm and the longitudinal joint, the 8-node
hexahedron coupling element (C3D8P) is used. The finite element model is shown in Figure 5. The
total number of cells is 282,319 and the total number of nodes is 280,664.
Boundary conditions: The initial saturation of the model is set to 1.0, and different pore ratio
parameters are assigned as initial conditions according to different materials. The bottom and
surrounding of the model are the normal constraints of the surface of the vertical bedrock in the same
direction (X, Y, Z) with the origin coordinates. By default, it is impervious boundary; the inner side of
the cofferdam, the slope of the water-facing side and the surface of the riverbed are the boundary of
the head and the pressure of the pores. The boundary of the free slope is added to the inner slope, and
the height of the inner head and the pore pressure are function of coordinates and time.
4.2. Material parameters
4.2.1 Mechanical Models and Parameters. The Mohr-Coulomb constitutive model (referred to as the
M-C model) can better describe the mechanical behaviour of soil and other discrete materials.
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
7
According to the deformation of the carcass during the pumping period and the instability of the slope,
the soil can be approximated as an ideal elastoplastic material. In order to avoid the cumbersome
calculation and slow convergence caused by the sharp angle of the MC yield surface, the extended
classic MC model is used to simulate the deformation behaviour under hydrostatic load and seepage-
stress coupling.
The cofferdam materials mainly include clay, pebbly clay and berm filled with block stones. The
river bed is thinner and mainly composed of limestone. The physical and mechanical parameters of the
soil layer in the site are shown in Table 1.
Table 1 Recommended values of main indicators for soil layers in the site area
4.2.2 Permeability parameters of unsaturated soil. The pore water of the soil seeps continuously as the
water level of the foundation pit decreases, and the weir body transitions from saturated to unsaturated,
forming a saturated-unsaturated region on the slope of the clay. The saturated soil permeability
coefficient can be regarded as a constant (Table 2). For the unsaturated medium, the liquid medium-
gas two-phase coexist, the ability of the porous medium to transport fluid is weakened, and the
permeability coefficient is not constant, but a function of saturation [21]. According to the cumulative
distribution of soil particles (Table 3), considering the orthotropic anisotropy of clay seepage, the
empirical model [22] is used to estimate the soil water characteristic curve (Figure 6), and the
relationship between permeability coefficient and pore water pressure of unsaturated clay are
calculated. (Figure 7).
Table 2 Material permeability coefficient of the site
Parameter
Pebbly clay
Berm Block Stone
Concrete
Limestone
Permeability
coefficient
k/（ m/s ）
horizontal
5.0x10-6
1.0x10-5
1.22x10-10
1.2x10-9
vertical
4.6x10-7
Table 3 Test soil particle size distribution
Particle size /mm
60~2
2~0.075
0.075~0.005
<0.005
Component
Gravel
Sand
Silt
Clay particle
Proportion /%
7.15
15.1
49.2
28.55
4.3. Calculation of working conditions and water level changes Simulation of cofferdam
Foundation pit pumping is a complex unsteady seepage process. Considering the construction
schedule control, the initial drawdown velocity range and the maximum specified in [2] are not more
than 1.5m/d. According to the 0.5m/d gradient, the gradient is increased and decreased, and there are 6
kinds of calculation conditions (Table 4). Due to the large height of the longitudinal weir and the deep
water level of the foundation pit, the risk of collapse of the longitudinal slope during pumping is
relatively higher, and the riverbed in the longitudinal section is relatively flat. In order to facilitate the
Parameter
Dry unit
weight /
（kN·m-3）
Porosity/n
Compressive
modulus /
MPa
Internal
friction angle
/°
Cohesion
/kPa
Pebbly clay
17.4
0.374
6.9
25
22.0
Berm Block
Stone
22.5
0.500
400.0
30
0
Concrete
24.5
0.015
20000.0
40
1200.0
Limestone
27.0
0.048
17200.0
46
2720.0
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
8
analysis of the deformation of the earth-rock cofferdam and the development of the slope, the section
of weir body and river bed at dam axis site is selected as typical seepage section, and the position of
inner weir top and slope foot is selected as displacement characteristic point (Figure 8).
Figure 6. Clay moisture characteristic curve
Figure 7. Permeability coefficient versus pore
water pressure curve
Firstly, the gravity, static water load and pore water pressure are applied to the cofferdam and the
foundation soil respectively. The initial stress level and the stress coupling field of the foundation pit
with no displacement are generated by the automatic stress balance method. The static water load and
the pore water pressure are respectively reduced with time. The linear function relationship from small
to zero simulates the seepage change and the state of force deformation of the cofferdam in the process
of water level drop in the foundation pit.
Table 4 Calculation conditions
Working
condition
Drawdown
velocity/
（m/d）
Drainage time/d
Water level /m
Initial
End
1
0.5
30.0
63.50
48.50
2
1.0
15.0
3
1.5
10.0
4
2.0
7.5
5
2.5
6.0
6
3.0
5.0
Figure 8. Seepage-stress coupling analysis surface
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 200 400 600 800 1000 1200 1400 1600
Saturation
Matrix suction/kPa
saturation
0.0E+00
2.0E-07
4.0E-07
6.0E-07
8.0E-07
1.0E-06
0 200 400 600 800 1000 1200 1400 1600
horizontal
vertical
Pore water presurre/kPa
Permeability coefficient/(m.s-1)
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
9
4.4. Finite element strength reduction method
When using the finite element strength reduction method to analyse the slope stability, it is not
necessary to assume the slope sliding form and position, and use the field variable to establish the
function relationship between the incremental step and the material parameter. The shear strength of
soil can automatically be reduced to the ultimate failure of slope, and the position of sliding surface
and the reserve safety factor of slope strength can be obtained directly. The expression is:
'
t
c
cF
=
(7)
tan
' arctan
t
F
=
(8)
and are the shear strength that the soil can provide; and are the shear strength needed to
maintain equilibrium or the actual exertion of the soil; is the strength reduction factor.
The key to the analysis of slope stability by strength reduction method is the correct judgment of
the calculation results, and then whether the slope body reaches the critical failure state, and the
selection of the reduction range and the criterion is very important [16]. Since the cofferdam is
composed of heterogeneous soil materials, the reduction range has a great influence on the safety
factor of the slope. According to the concept of “cohesion ratio” proposed in [17], the cohesive soil
and the bedrock are sticky. The ratio of the bunching force is much less than 1, and it is more
reasonable to reduce the overall strength of the cofferdam. Considering the applicability and simplicity,
combined with the literature [18], the jointability of the characteristic part displacement abrupt
combined with the plastic zone is used as the slope instability criterion to analyse the cofferdam
deformation law and the plastic zone distribution, and then the minimum slope safety factor is
obtained.
5. Characteristics of seepage field in foundation pit dewatering
During the process of the water level drop of the foundation pit, the seepage field in the earth-rock
cofferdam is non-constant, and the carcass is mostly filled with clay, and the permeability is poor.
Over-pumping speed makes it difficult to dissipate excess pore water pressure in the cofferdam and
aggravates the seepage stability of the cofferdam. Therefore, it is particularly important to analyse the
effects of different pumping speed conditions on saturation, pore water pressure and saturation line
distribution of the cofferdam in different periods.
5.1. Saturation distribution
Due to the suction of the soil matrix, the unsaturated zone is mainly distributed near the crest of weir.
The saturation of the soil changes from top to bottom, and increases with the height, forming a clear
boundary with the saturated zone. With the seepage prevention wall as the centre of the cofferdam,
when the drawdown velocity is less than 1.0m/d, there is a local unsaturated zone at the top of the
outer clay, and the saturated boundary line of the inner clay is relatively low, and the change from the
inside to the outside is approximate flat (Figure 9(a) to (b)). When the drawdown velocity is greater
than 1.5m/d, the pore water can’t be discharged in time, the unsaturated area on the top of the outer
clay gradually disappears, the saturation gradient is dense and gradually increases, and the position of
the inner saturated boundary slightly increases with the increase of the speed and the degree of upward
bending increases, and the change approximates the inclined curve. (Figure 9(c) to (f)).
5.2. Pore water pressure
It can be seen from Figure 10, consistent with the distribution of unsaturated zone, the negative pore
pressure is mainly concentrated near the crest near the inner clay, the pore pressure increases with the
height and increases with a certain gradient, due to the anti-seepage wall resistance effect in the
seepage, the gradient of the pore pressure difference on both sides is larger, and the drop is particularly
c
'c
'
t
F
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
10
significant. The contour of the pore pressure below the bedrock tends to be gentle. The zero pore
pressure contour is used as the saturation line. When the drawdown velocity is less than 1.0m/d, the
seepage field change is consistent with the water level fall time. The saturation line height is low and
the change is very slow (Figure 10(a)~(b)). When the drawdown velocity is greater than 1.5m/d, the
seepage field changes behind the water level drop time, and the water retention of the clay, as the
water level drawdown, the lag time will prolong, causing the highest point of the saturation line to fall
behind the water level decline rate, infiltration The line rises slowly with the increase of pumping
speed, and the curvature of the free surface of the seepage increases gradually, and the hysteresis
effect is more significant (Figure 10(c)~(f)).
5.3. Total head distribution and osmotic slope
The analysis can be obtained from Figure 11. The total head value of the stone berm in the water
surface is constant. Under different pumping speed conditions, the total head change of the weir body
(a) v=0.5m/d
(b) v=1.0m/d
(c) v=1.5m/d
(d) v=2.0m/d
(e) v=2.5m/d
(f) v=3.0m/d
Figure 9. Distribution of saturation of earth and rock cofferdam
At the end of the foundation pit drainage, the water level elevation is reduced from 63.5m to
48.5m.
(a) v=0.5m/d
(b) v=1.0m/d
(c) v=1.5m/d
(d) v=2.0m/d
(e) v=2.5m/d
(f) v=3.0m/d
Figure 10. Pore water pressure distribution of earth and rock cofferdam (unit: Pa)
At the end of the foundation pit drainage, the water level elevation is reduced from 63.5m to
48.5m.
1.00
0.98
0.94
0.90
0.86
0.82
0.78
0.74
0.70
0.67
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
11
is mainly concentrated near the seepage prevention wall. With the increase of the depth of the seepage
wall, the osmosis slope gradually increases, and the penetration slope of the wall deep into the bedrock
is the largest, and the effect of seepage control is more obvious. However, as the water level slows
down, the hysteresis effect increases, and the seepage slope at the same position of the seepage
prevention wall decreases continuously, and the effect of seepage control is weakened, which is not
conducive to giving full play to the barrier effect of the seepage wall.
6. Stability analysis of cofferdam slope
At the same time as the water level of the foundation pit decreases, the hydrostatic pressure acting on
the slope of the cofferdam also decreases. If the pumping speed is too high, the pore water pressure in
the weir body cannot be dissipated with the decrease of hydrostatic pressure. The resulting penetration
will increase the risk of slope instability. Through the strength reduction method, the overall
deformation of the cofferdam and the plastic development law and the minimum safety factor of the
slope under different pumping speed reduction conditions are important, which is of great significance
for evaluating the safety of the cofferdam.
6.1. Deformation of the slope and plastic zone
The influence of the typical reduction factor on the deformation and plasticity distribution of the
cofferdam is shown in Figure 12. The position of the potential sliding surface of the slope and the
shape of the sliding surface can be obtained intuitively. Under different pumping speed conditions,
with the increase of the reduction factor, the shear strength of the soil material decreases, the anti-
sliding resistance of the slope foot decreases, the contour of the slope foot displacement is relatively
dense, and the plastic zone begins to appear from the inner slope bottom. Then, the curved plastic
surface is gradually extended to the crest, and the maximum deformation is concentrated on the inner
shallow slope. At the same time, local plastic deformation occurs at the foot of the outer stone slag
berm, and the seepage force in the slope increases with the increase of pumping speed, which leads to
the early penetration of the plastic zone of the inner weir slope and the transition of the maximum
deformation to the inner slope foot, thus forming the most dangerous sliding surface. The stability of
the outer weir slope is greater than that of the inner slope. If the shear strength of soil continues to be
reduced, the numerical calculation is still stable, the outer slope is basically connected, and finally a
double sliding surface trend is formed. However, the displacement and deformation of the slope have
been seriously distorted, and the deformation has exceeded its configuration. It is not reasonable to
take the convergence of numerical calculation as the criterion of slope instability.
(a) v=0.5m/d
(b) v=1.0m/d
(c) v=1.5m/d
(d) v=2.0m/d
(e) v=2.5m/d
(f) v=3.0m/d
Figure 11. Distribution of total head and seepage slope of cofferdam
At the end of the foundation pit drainage, the water level elevation is reduced from 63.5m to
48.5m.
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
12
Drawdown
velocity
Reduction coefficient
1.50
1.54
1.58
v=0.5m/d
v=1.0m/d
v=1.5m/d
v=2.0m/d
v=2.5m/d
v=3.0m/d
Figure 12. Cofferdam deformation and plastic zone
At the end of the foundation pit drainage, the water level elevation is reduced
from 63.5m to 48.5m.
6.2. Safety factor and critical water level drawdown velocity of slopes
Failure of slopes can be regarded as the process of gradual development of the plastic zone, expanding
into the state of complete plastic flow and unable to continue to bear the load. In order to further
explore the influence of pumping speed on the safety and stability of the cofferdam slope, the feature
point A, the slope foot characteristic point B displacement abruptness, and the connectivity of the
slope plastic zone are used as the slope instability criterion to estimate the overall stability of the slope.
As shown in Figure 13, the displacement of the characteristic point shows a similar law with the
change of the reduction factor. Under different pumping speed conditions, the displacement curve
decreases gently with the decrease of the reduction coefficient. After a certain time, the displacement
decreases slightly. When the plastic zone of the medial slope is basically penetrated or is about to
penetrate, the displacement of the characteristic point suddenly increases, and the curve drops sharply.
The reduction factor that satisfies the criterion of slope instability is the minimum safety factor, and
the safety of the slope is measured. When the drawdown velocity is 0.5m/d, the seepage field and the
water level fall time are more consistent. The instability of the slope is the double-slope sliding form,
the stability of the slope is the best, and the safety factor Ft is 1.58 (Figure 13(a)). With the increase of
the speed drop, the hysteresis effect is obvious, the permeability of the inner slope is increased, and the
slope stability is reduced. When the drawdown velocity is increased to 3.0m/d, the safety factor Ft is at
least 1.50. It is now a single-slope sliding trend, and the risk of collapse of the slope is the highest
(Figure 13(f)).
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
13
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70
0.5m/d（Top）
0.5m/d（Bottom）
Reduction coefficient/Ft
Deformation/mm
Ft=1.58
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70
2.0m/d（Top）
2.0m/d（Bottom）
Deformation/mm
Reduction coefficient/Ft
Ft=1.52
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70
3.0m/d（Top）
3.0m/d（Bottom）
Deformation/mm
Reduction coefficient/Ft
Ft=1.50
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70
1.0m/d（Top）
1.0m/d（Bottom）
Deformation/mm
Reduction coefficient/Ft
Ft=1.55
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70
1.5m/d（Top）
1.5m/d（Bottom）
Deformation/mm
Reduction coefficient/Ft
Ft=1.53
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70
2.5m/d（Top）
2.5m/d（Bottom）
Deformation/mm
Reduction coefficient/Ft
Ft=1.51
(a) v=0.5m/d
(b) v=1.0m/d
(c) v=1.5m/d
(d) v=2.0m/d
(e) v=2.5m/d
(f) v=3.0m/d
Figure 13. Curve of feature point displacement and reduction factor
The safety factor and the pumping speed reduction curve are shown in Figure 14. The cofferdam
safety factor has a multi-stage linear decreasing trend. The linear descending rate varies greatly in
different stages, and the turning inflection point appears at the intersection of the two straight lines. As
the pumping speed decreases, the safety factor decreases sharply with the decreasing rate of the slope
k1=0.1. When the drawdown velocity decreases to 1.28m/d, it decreases slowly with the decreasing
rate of the slope k2=0.02. Because there is a concrete anti-seepage wall in the middle of the corpus
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
14
callosum, which blocks most of the seepage replenishment, and the inner side slope is filled with clay,
the permeability is poor, and the stability of the slope is very sensitive to the change of the water level.
When the pumping speed is greater than the critical when the speed is reduced, the height of the
saturation line and the curvature of the free surface change little with the increase of the water level.
The safety sensitivity of the slope is reduced, and the slope is likely to be unstable due to excessive
seepage force. For soil cofferdams, the norm [12] believes that the base water level drawdown velocity
is controlled within 1.5m/d, combined with the particularity of the clay cofferdam project, in order to
avoid the slope of the foundation pit due to excessive osmotic pressure, resulting in slope If the
instability causes a collapse accident, the drawdown velocity should be controlled at 1.28m/d to ensure
the safety and stability of the slope during the pumping process.
Figure 14. Relationship between safety factor and
pumping rate
7. Conclusion
Taking the temporary cofferdam project of the first phase of Yongning Water Conservancy Project as
the background, considering the fluid-solid coupling theory, consider the unsaturated and seepage of
clay.
Based on the conditions, the finite element method was used to accurately simulate the earth-rock
cofferdam with significant adjustment of the structural form. The characteristics of the seepage field
inside the cofferdam under different pumping speeds were studied. The strength of the pumping was
analysed by the strength reduction method. The stability and the deformation characteristics of the key
parts and the influence of the development law of plastic deformation can provide a reference for the
reasonable selection of the pumping speed reduction of the temporary cofferdam foundation pit.
(1) During the pumping process of the foundation pit, the distribution of the unsaturated zone and
the negative pore pressure in the crucible body are basically the same, and the total head change is
mainly concentrated near the seepage prevention wall. The excessive water level slowdown easily
destroys the balance between the seepage field and the water level fall time, causing the height of the
saturation line and the saturation boundary line to rise synchronously and the degree of upward
bending is increasing, the hysteresis effect is obvious, and the anti-seepage wall eliminates the water
head and reduces the seepage. The ability to control is weakened and the problem of stable penetration
is outstanding.
(2) The shear deformation of the slope begins to develop at the inner bottom of the slope, and then
gradually forms a curved plastic surface to the dome. At the same time, local plastic deformation
occurs at the foot of the outer gravel bank. The seepage force in the slope decreases with the pumping
speed. Increased and strengthened, the plastic zone of the medial slope is penetrated in advance, and
the maximum deformation transitions to the inner slope foot to form the most dangerous sliding
1.48
1.5
1.52
1.54
1.56
1.58
1.6
0 0.5 1 1.5 2 2.5 3 3.5
Safety factor
Drawdown velocity/(m/d)
k1=0.1
k2=0.02
v=1.28m/d
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
15
surface. The stability of the outer slope is greater than that of the inner slope.
(3) The safety factor of cofferdam decreases with the increase of water level drawdown velocity.
When the pumping speed is greater than the critical speed, the height of the saturation line and the
curvature of the free surface of the seepage change little with the increase of the water level. The
safety sensitivity of cofferdam slope decreases, and the slope is likely to lose stability due to excessive
seepage force. In combination with the particularity of the clay cofferdam project, in order to ensure
the safety and stability of the slope during the pumping process, the drawdown velocity should be
controlled within 1.28m/d.
Acknowledgment
The fund: The General Program of National Natural Science Foundation of China (51879207)
The Author
Deng Yang, Male, 1994.8, Postgraduate, Research direction is hydropower construction and structural
stability analysis.
Correspondent Author
He Changhai, Male, 1966.9, Professor, Mainly engaged in hydropower project construction and other
aspects of research.
References
[1] DL/T 5397—2007 Specification for construction planning of hydropower engineering. Beijing:
China Electric Power Press, 2007.
[2] Water Resources and Hydropower Construction Bureau of the Ministry of Water Resources and
Electric Power. Handbook of construction planning of hydraulic and hydroelectric projects
（Vol. I）[M]. Beijing: China Water & Power Press, 1996.
[3] Ren, D.C., Wu, C.Y., Zhu, G.S. (1997) Saturated and unsaturated seepage analyses on Three
Gorges Project’s second stage cofferdam. Journal of Yangtze River Scientific Research
Institute, 14(2): 44-47.
[4] Li, S.C., Li, S.C., Zhu, W.S., et al. (2004) Hydro-mechanical coupling analysis on stability of
cofferdam of Tai’an pumped-storage station. Chinese Journal of Rock Mechanics and
Engineering, 23(8): 1275-1279.
[5] Wang, X.W., Dang, F.N., Jiang, L., et al. (2010) Three-dimensional seepage stability analysis of
high earth-rock cofferdam built on complex layer of deep coverage. Journal of Hydraulic
Engineering, 41(9): 1074-1078.
[6] Fan, Y.Y., Tang, C., Wang, E.Z. (2012) Seepage calculation and analysis of the upstream earth-
rock cofferdam of the Pinecone Hydropower Station. Applied Mechanics & Materials, 170-
173: 2017-2022.
[7] Yuan, S., He, Y.L., Cao, X.X. (2012) Influence of unsteady seepage on upstream slope stability
of Tuoba earth-rock cofferdam. Engineering Journal of Wuhan University, 45(2): 193-199.
[8] Luo, L.Z., Hu, Z.G., Liu, Q., et al. (2013) Slope stability analysis of high earth-rock cofferdam
considering construction and working processing. Engineering Journal of Wuhan University,
46(1): 84-88.
[9] Yin, P.B., He, W., Zhang, J.R., et al. (2016) Stability of soil cofferdam for anchorage foundation
of the Dongting Lake bridge considering unsaturated soil characteristics. Hydrogeology &
Engineering Geology, 43(2): 62-68.
[10] Zhao, H., Zhang, F., Chen, B., et al. (2016) Influence of pumping speed in foundation pit on
seepage and slope stability of cofferdam. Pearl River, 37(4): 55-58.
[11] Jia, C.Q., Huang, M.S., Wang, G.H. (2006) Strength reduction FEM in stability analysis of soil
slopes subjected to transient unsaturated seepage. Chinese Journal of Rock Mechanics and
Engineering, 26(06): 1290-1296.
WCHBE 2019
IOP Conf. Series: Earth and Environmental Science 376 (2019) 012022
IOP Publishing
doi:10.1088/1755-1315/376/1/012022
16
[12] Liao, H.J., Ji, J., Zeng, J. (2008) Stability analysis of soil slopes considering saturated and
unsaturated seepage effect. Rock and Soil Mechanics, 29(12): 3229-3234.
[13] Nian, T.K., Wan, S.S., Jiang, J.C., et al. (2010) Finite element analysis of slope stability under
drawdown conditions by strength reduction technique. Rock and Soil Mechanics, 31(7):
2264-2270
[14] Zhang, X.G., Xu, S.C., Yi, N.P. (2016) Stability analysis of slopes excavated in saturated and
unsaturated soils based on coupled consolidation theories. Hydro-science and Engineering,
(3): 10-19.
[15] Hu, S.S., Tong, S.J., Liu, B.Q., et al. (2014) Stability analysis of three-dimensional bridge
abutment slope based on strength reduction method for inhomogeneous slope. Rock and Soil
Mechanics, 35(Supp.2): 653-661.
[16] Liu, J.L., Luan, M.T., Zhao, S.F., et al. (2005) Discussion on criteria for evaluating stability of
slope in elastoplastic FEM based on shear strength reduction technique. Rock and Soil
Mechanics, 26(8): 1345-1348.
[17] Xue, L., Sun, Q., Qin, S.Q., et al. (2011) Scope of strength reduction for inhomogeneous slopes.
Chinese Journal of Geotechnical Engineering, 33(2): 275-280.
[18] Mao, C.X. (2003) Seepage computation analysis & control. Beijing: China Water & Power Press.
[19] Zhang, W. (2004) A study on seepage field and the coupling of stress field and seepage field and
its application. Wuhan University, Wuhan.
[20] Chen, W.Z., Wu, G.J., Jia, S.P. (2010) Application of ABAQUS in Tunnel and Underground
Engineering. Beijing: China Water & Power Press.
[21] Fei, K., Zhang, J.W. (2017) Detailed Explanation of ABAQUS Geotechnical Engineering
Example. Beijing: the Posts and Telecommunications Press.
[22] Xia, W.S., Lei, T.W., Liu, X.Z., et al. (2003) Deduction of characteristic curves of soil moisture
detention. Acta Pedologica Sinica, 40(2): 311-315.
