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BEARING CAPACITY OF MOVABLE DAM FOUNDATION ON SOFT CLAY SOIL
SUBJECTED TO COMBINED LOADING IN MEKONG DELTA
Ha Hai. NGUYEN1, Thai Van. TRAN1, Dinh Hoa. TRAN2
ABSTRACT: Movable dam is one of river barriers that has been studied and applied effectively in the Mekong Delta.
The principle of increasing the stability of the dam by enlarging foundation width to reduce the normal pressure so that
the dam could be placed directly on soft clay soil without soil improvement. The characteristic of the movable dams is
low vertical loading, large horizontal loading and moment. Bearing capacity of strip footing under eccentric and
inclined loads subjected to combined loading V: H: M is extremely complicated. In the case of the movable dam, it is
difficult to evaluate bearing capacity on soft soil because of low vertical loading but high eccentric and inclined ones.
On the other hand, the soil-structure interaction is also difficult to analyze. This study presents the bearing capacity of
movable dam footing on clay subjected to combined load V:H:M that is based on failure envelope by numerical
analysis and compare the results with previous researches. The authors also present method to check the stability of
movable dams on soft clay soils subjected to combined load in Mekong Delta.
Keywords: Movable dam, soft clay, combined loading, failure envelope.
1 Hydraulic Construction Institute, Hanoi, Vietnam. Corresponding author, email: ha.cloud08@gmail.com
2 Vietnam Academy for Water Resources
1.INTRODUCTION
1.1.General information about movable dam
Movable dam is a new technology, which is used
widely and effectively in Vietnam for almost 20 years
(Tran, D.H, 2008, Tran, V.T, 2014). This technology
also has its advantages on constructability on soft clay
soil. There are two types of movable dam including
beam-slab type and box type. The optimum principle of
the structure depends on lightweight beam that the
pressure on the foundation is less than bearing capacity
as shown in Fig. 1, it is possible to place the dam on soil
without treatment. The stability of the movable dams is
based on the friction between the foundation and soil
under and on 2 sides of the dams.
Fig. 1 Model of movable dam.
1.2.Problem definition
Movable dam is usually subjected to vertical loading
V, horizontal loading H, and moment M, so the model
which is used to examine the problem is also subjected
to V:H:M (Fig. 1, Fig. 2). Soil is assumed to
homogenous in this study, as site-specify in Mekong
delta. Soil has undrained shear strength su. In addition,
most of constructed movable dam did not have bridge, so
actual vertical loading is low, the ratio between vertical
loading and ultimate vertical loading: V/Vo<0.5 (Tran,
V.T, 2014)
Fig. 2: Loading model.
Tran, V.T and Nguyen, H.H (2013) proposed to use
dimensionless failure envelope V-H-M according to Ngo
Tran (1996) to calculate stability for movable dam.
Proceedings of the 10 th International Conference on Asian and Pacific Coasts
(APAC 2019) Hanoi, Vietnam, September 25-28, 2019
869
Fig. 3 Model of the problem.
Martin (1994) did some experiments with spudcan
foundation subjected to V:H:M. According to the results
of the experiments, he claimed that when the foundation
is subjected to two types of loads which are vertical
loads and horizontal loads at the same time, the
horizontal bearing capacity do not remain a constant
number. This value varied from H/V0=0 and
corresponding to the vertical loads V/V0= 0. Martin also
synthesized some tests, in which the foundation is
subjected to vertical loading, horizontal loading and
moment to produce dimensionless failure surface.
Ngo Tran (1996) analyzed failure envelope of strip
footing on two-dimensional finite element analysis. He
presented strip footing contact with clay soil by the
interfacing elements according to Mohr-Coulomb rule.
He also proposed failure envelope for two cases
corresponding to V/V0< 0.5 and V/V0 ! 0.5. This process
based on interface friction angle that assumed to equal
300 without doing any experiment to determine.
This paper studies the spatial failure envelopes of the
vertical-horizontal load, vertical-moment load, vertical-
horizontal-moment load of movable dam on three-
dimension model with contact friction angle 24,30
according to the author’s experiment of identifying
friction angle of movable dam on soft clay, Nguyen
(2018).
2. FAILURE ENVELOPE OVERVIEW
2.1. Literature review
According to Tan (1990), Bransby and Randolph
(1998), when analyzing numerical models, composite
loads applying on structure are controlled by
displacement-controlled through vertical displacement
(W), horizontal displacement (u) and rotational
displacement ("). These loads are assigned to the
reference point (LRP). The reaction force which could
be obtained at the loading point include: vertical load
(V), horizontal load (H) and moment (M). To plot a
failure evelope in three dimensions, there are two
displacement controlled method that could be used: (1)
probe analysis, Bransby and Randolph (1998) and (2)
swipe analysis, Tan (1990).
a. Method 1: probe analysis is also known as fixed
displacement analysis. The principle is to control the
displacements in the foundation and analyze its
behaviour. The foundation is subjected to the
simultaneous impact of the displacements (VH), (VM) or
(HM) with displacement which is kept unchange until
failures. The ratio of displacements are specified from
correlation of the linear rigidity of the foundation and
soft clay soil. For each analysis, plastic point is
determined, the envelope which shows the correlation
between (V-H), (V-M) or (H-M) is established from a
orbit of plastic points. When the stress reaches the failure
load, the ratio decreases, the iteration curve until the load
stop increasing in each step. This method provides the
exact location of the plastic point, but it needs to be
analyzed at different ratios.
b. Method 2: swipe analysis was first presented by
Tan (1990) based on centrifuge experiments. This
method consists of two stages. Stage 1, assigning the
restrain displacements in the desired direction (w or u)
until the ultimate capacity is reached. Stage 2, increasing
displacement gradually from zero until instability occurs.
The most valuable benefit (or advantage) of this method
is that we can identify the plastic point in only one
analysis. However Bransby and Randolph [6] indicated
that in the finite element method, the envelope that is
determined by method 2, is usually the boundary plastic
point found in method 1.
2.2. Failure envelope V-H-M
The limit load survey of the foundation is
simultaneously subjected to vertical, horizontal and
moment loads by examining the H-M (flat plate) chart,
which demonstrates the difference between various
vertical loading levels. This is an extended fixed
displacement analysis method for evelope, as shown in
Fig. 5.
Vertical loading
Ccnstant V
V
M/B or H
Constant w
Radical displacement
Fig. 4 Load path for V-H or V-M
The analysis process is divided into two steps: Step 1,
assigning displacement causing the vertical load (Vi);
Step 2 set horizontal displacement (u) and the rotational
displacement with a certain ratio; inspect the H-M
contour by increasing gradually the proportion of u/B".
For each value, u/B" will be indicated by the arrow of
the load as shown in Fig. 5.
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Fig.5 Horizontal displacement and rotational
displacement for each level of vertical loading
With the envelope load analysis method, Gottardi
(1999) presented the experimental process of the
centrifugal model to complete the envelope (V-H) or (H-
M) as shown in Fig. 6.
Fig. 6 Schematic diagram of load paths followed in
swipe tests (Gottadi, 1999)
When analyzing the working process of strip footing
on soft clay soil, the accuracy of the contact between
foundation and soil will decide the accuracy of the
calculation results. In the case when there are slidings
between the structure and the soil, it is necessary to use
special elements, which are called contact elements or
sliding elements. This particular simulation element is
used to adjust the contact between the structures and the
soil and ensure the continuity of calculation model. The
sliding resistance follow Coulomb law
max
(1)
The ABAQUS (2013) guide on the contact element
with limited shear stress max indicated that the slip
between the structure and the soil on the contact surface
occurs when i= .i > max, where i is the normal stress
reaction at the contact surface. When the slip occurs at
the limit i = max, the value of shear stress i is not
allowed to be zero. Interface friction is one of vital
parameter for soil-structure to assist improvement on
bearing capacity, sliding failure and shear failure. In this
study, the dam is connected to the soil with special
contact surfaces (using master-slave surface), allowing
for realistic simulation of possible detachment and
sliding at the soil-dam interfaces.
Fig. 7 Friction model with a limit on the critical shear
stress
The slippage of the dam along the interfaces is
governed by Coulomb's friction law by appropriately
response for the interface, ABAQUS (2013).
3.ANALYSIS AND ASSESSMENTS
The modelling of strip footings in a two-dimensional
plane strain model applied to movable dam brings
limitations, because dam foundation-soil interaction is a
strongly three-dimensional phenomena. In this paper, the
finite element analysis is three-dimensional model is
shown as Fig. 8. Finite element mesh is divided into two
parts: soils locate just below the foundation and the
surrounding area. At the intersection surface between
these two sections through tie constraints in Abaqus to
maintain the continuity of the model, as shown in Fig. 9.
The square footing is modeled as a rigid body. Soil
model is Von-miser, undrained shear strength su=1(kPa),
Young module of soil is specified by ratio with
undrained shear strengh E/su= 50.
Fig. 8 Model analysis
Fig. 9 Finite element mesh
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3.1.Vertical-horizontal load space
Analyzing movable dam on soft clay subjected to
vertical loading and horizontal loading simultaneously.
Two methods have been used in this research are probe
analysis and swipe analysis, as shown in Fig. 10. In the
case of probe analysis, the principle require the proccess
of loading up the foundation with vertical load (w) and
horizontal load (u) at the same time, as well as keeping
the value of displacement ratio constant and varied (w / u
= 0.05, 0.1, 0.2, 0.4, 1, 2, 3). On the other hand, the
swipe analysis method contain two steps. First step is
assigning vertical load through vertical displacement (w)
gradually until the foundation reaches the failure state,
Second step is to assign horizontal load by horizontal
displacement (u) and the correlation between V and H
would be plotted by vertical load vs horizontal load. This
reference is also considered the failure evelope (V-H).
(a)Probe analysis (b)Swipe analysis
Fig. 10 Probe analysis and swipe analysis
Carrying out the calculations for 7 levels of different
displacement ratio according to the above principal and
analyze load capacities corresponding to the friction
angle with and 24.3
0
, we obtained the failure envelope
as shown in Fig. 11.
3.2.Vertical - moment load space
Analyzing movable dam on soft clay subjected to
vertical loading and moment simultaneously by two
methods: probe analysis and swipe analysis as shown in
Fig. 12. According to probe analysis, the experiment
strategy was to increase the foundation with vertical load
(w) and moment (B) simultanenously, as well as keep
the value of displacement ratio unchange and varied (w /
u = 0.1, 0.2, 0.4, 0.6, 1). The swipe analysis method
require two steps. First step is to increase vertical
loading through vertical displacement (w) until the
foundation reaches the failure state. Second step
continue to increase moment (B) and then obtain the
(V-H) correlation.
Fig. 11 Failure envelope with = 24.30
(c)Probe analysis (d)Swipe analysis
Fig. 12 Load path vertical displacement (w) and
moment (u)
Performing two steps and failure envelope (V-M)
would be plotted as shown in Fig. 13, vetical axis is
M/BVo, and horizontal axis is V/Vo.
Fig. 13 Failure envelope V-M
3.3.Vertical - horizontal moment load space
To establish the failure envelope (V-H-M), the
method of analyzing displacement ratio includes 2 steps.
First step is to increase vertical load to a certain vertical
load level (Vi) according to vertical displacement (wi) ;
Second step is increase horizotal load and moment by
controlling the horizontal displacement and rotation with
the ratio of u/B=0.1, 0.2, 0.4, 0.6, 1.0, as shown in Fig.
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14. After that we got the corelation between horizontal
load and moment for each Vi.
Fig. 14 Probe analysis
The method consists of three steps:
First step is to increase vertical load to vertical load
level (Vi) according to vertical displacement (wi)
respectively; Second step is to increase horizontal load
by controlling horizontal displacement until reaching the
extreme horizontal load; Third step is to increase
moment by controlling the rotational displacement until
the limit is reached, the sequence of analysis is shown in
Fig. 16. The results of this analysis is the failure
envelope (V-H-M) for each vertical load (Vi).
Comparison of the diagram (H / Vo) with (M / BVo) for
vertical load V/ Vo = 0.3, 0.045, has the same failure
envelope as shown in Fig. 15.
Fig. 15 Swipe analysis with ratio displacement u- B
corresponding to wi (Vi)
Results of probe analysis have a good agreement
with swipe analysis. The authors analyse failure
envelope with a certain value of displacement to
compare two methods and establish the most accurate
failure envelope (V-H-M). With V/Vo= 0.05, 0.1, 0.15,
0.2, 0.25, 0.30, 0.35, 0.40 and 0.50. For each value of
V/Vo, we can establish a failure envelope H/Vo -M/BVo
and then do the same steps as shown in Fig 16.
The probe analysis results are good agreement with
the swipe ones so the failure envelope VHM is plotted in
plan as Fig. 17 and 3D failure envelope as Fig. 18.
Fig. 16 Failure envelope for V/Vo=0.45
Fig. 17 Plan of failure envelope VHM
3.4.Establish formula for checking stability
Stability of movable dam subjected combined
loading will be checked by equation 1:
a. Formula for checking stability against sliding:
00
00
;
.
(2)
where:
00
0;
interpolated by
0
and
0
in the Fig. 18.
b.Formula for checking stability against overturning
00
00
;
.
(3)
where:
00
0;
interpolated by
0
and
0
in the Fig. 18.
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Kn: Reliability factor,
m: Mobilised condition coefficient,
nc: Coefficient of the load combination,
H: Horizontal load (kN),
V: Vertical load (kN),
V0: Ultimate vertical bearing capacity (kN),
M: Calculated moment (kNm),
A: Area of foundation (m2).
Fig. 18 3D Failure envelope VHM .
This papers demonstrate to check stability of three
movable dams with clearance width corresponding 5m,
8m and 10m. Resultant forces acting on the free body
diagram of a movable dam longitudinal section as shown
in Fig. 19, tranversal section as shown in Fig. 20.
W
H
O
#
R
11
P
21
P
12
P
12
P
21
H
11
t
N
2
G
CV
G
XL
G
T
Fig. 19 Water pressure on movable dam longitudinally
L
Z
ng
Z
d
a
E
a
p
a
E
a
p
Fig. 20 Soil pressure on movable dam tranversally
Soil pressure acting on both sides of dam is symmetric
so can be skipped. Resultance force acting on movable
dam as shown in Table 1. Equation (2) and (3) are used
to checking stability against sliding and overturning of
three movable dams. Result of calculation is shown in
Table 2.
Table 1 Resultance force acting on movable dam
No
Width*
(m)
Combination
su
V
Vo
V/Vo
M/BVo
H/Vo
(kPa)
(kN)
(kN)
(kN)
(kN)
(kN)
1
5.0
1
12
2256.32
6384
0.353
0.013
0.045
2
12
1976.35
6384
0.310
0.025
0.078
2
8.0
1
12
3208.40
9159
0.350
0.016
0.041
2
12
2926.27
9159
0.319
0.031
0.057
3
10.0
1
15
3439.05
14032
0.245
0.002
0.071
2
15
4412.99
14032
0.314
0.005
0.063
Table 2 Checking stability of movable dam
No
Width*
(m)
Combination
Kn.nc/m
*(H/Vo)
[H/Vo] Kn.nc/m
*(M/BVo)
[M/BVo]
Checking
stability
1 5.0
1
0.0580
0.1051
0.0172
0.0889
O.K
2
0.0907
0.0926
0.0319
0.0642
O.K
2 8.0
2
0.0522
0.1043
0.0204
0.0897
O.K
1
0.0735
0.0948
0.0401
0.0872
O.K
3 10.0
2
0.0779
0.0792
0.0023
0.0482
O.K
1
0.0800
0.0948
0.0060
0.0780
O.K
* Corresponding to the width of opening flow through the movable dam
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4. CONCLUSIONS
In this paper, the authors analyze movable dam in
three-dimensional modelling and plot dimensionless
failure envelope V/Vo, H/Vo, M/BVo with V/Vo$ 0.5.
The main purpose of presenting failure envelope is to
check the stability of movable dam on soft clay soil. The
authors also establish two formula to check stability of
movable dam against sliding and overturning adopted to
failure envelope VHM that is more convinient for users.
This paper also presents checking stability of three
typical movable dams on soft clay soil in Mekong Delta
respectively width of opening flow through the movable
dam is 5.0m, 8.0m, 10.0m, the result in Table 2
demonstates they’re also stabilised. .
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875
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