EDUCATION&TRAINING AND RURAL DEVELOPMENT THUYLOI UNIVERSITY PHAM VAN LAP STUDY THE FLOW VELOCITY DUE TO WAVES AT SHALLOW TOE IN THE DESIGN CALCULATION OF THE DIKE TOE BY FILL ROCKS, APP
Trang 1EDUCATION&TRAINING AND RURAL DEVELOPMENT
THUYLOI UNIVERSITY
PHAM VAN LAP
STUDY THE FLOW VELOCITY DUE TO WAVES AT SHALLOW TOE IN THE DESIGN CALCULATION OF THE DIKE TOE BY FILL ROCKS, APPLIED TO CATHAI SEA-DIKE-HAI PHONG
Specialization: Hydraulic Engineering Code No.: 9580202
SUMMARY OF DOCRORAL DESERTATION
HANOI, 2019
Trang 2Supervisors: 1: Assoc Prof PhD Le Xuan Roanh
2: Prof PhD Ngo Tri Vieng
Assoc.Prof Tran Thanh Tung
The thesis will be presented at the meeting of the University Doctoral Committee
in room No……….on…14:00, day 21st, June, 2019
The thesis can be found at:
- The National Library
- Thuyloi University
Trang 3INTRODUCTION
1 The rational of the thesis
Located in the tropical-monsoon climate, Vietnam has a long coastline and is often affected by many storms There are 6 to 10 storms occurred during the year with a high scale of wind speed and some time they occurred later or sooner of the year climate In fact, in the past years, sea dykes and revetments are affected seriously after the storm leading to a large amount of money to repair them The dike toe protecting the sea side has main forms such as high revetment toe, shallow revetment toe and deep revetment toe Based on materials, it can be classified as: stone carpet, cylinder hollow well inside inserting rocks, pile and reinforced concrete sheet, steel sheet and so on
Calculating the size of stone is advised the formula (1.37) of TCVN9901: 2014 that is proposed by Izobat This formula only mentioned three factors: wave height, water depth and wavelength On the other hand, this formula is used linear wave theory for calculation In fact, rocks laided on the sea bed closed to dike toe are always pushed to slope of the embankment or moved to sea side, or along shore In fact, the phenomenon of rock sliding on the roof, up and down, friction between the rock and the revetment has caused abrasion and damage to the roof protection structure
For the above reasons, the impact of abrasive rock embankment is very dangerous to the safety of the embankment, it is necessary to find the exact velocity at the foot of the embankment (dike toe) so as to determine the weight
of stones accordingly The topic "Study the flow velocity due to waves at shallow toe in design of dike toe by fill rocks; applied to Cathai sea-dike-Hai Phong” has been proposed for research
2 Research objectives
The thesis will solve the following two basic objectives:
- Clarifying the effect of hydrodynamic and geometric factors on the current velocity due to wave at the dike toe by using rocks;
- Determining the formula to calculate the maximum flow velocity at the foot of the embankment (dike toe), then select the solution to design the structure of the foot protection of the embankment in both with or without roughness structures
3 Subjects and scope of research
- Research object: flow due to wave at seadike toe;
- Scope of research: dyke toe in the North of Vietnam
4 Research content
- Overview of stabilizing the sea dike toe using filled rock;
- Study the flow velocity due to wave at shallow sea dike toe by physical model;
- Digital model to study flow at shallow seadike toe
5 Approach and research methodology
Trang 45.1 Approach
In order to solve the objective of the thesis, the author chooses the inheritance method which is both creative and suitable to the conditions of Vietnam 5.2 Research methods
- Methods of general research; Experimental method; Digital model method; and applied research methods
6 Scientific and practical significance
- Scientific significance:The thesis has proposed a new calculation formula as a scientific contribution
- Practical significance: Finding the maximum velocity at the foot of the
revestment by the wave, propose a procedure to check the stone stability at the foot of the embankment
CHAPTER 1: OVERVIEW OF SEA-DIKE TOE STABILITY BY FILL ROCKS
1.1 Structure of the sea dyke toe
1.1.1 General structure of sea dykes
The structure of normal sea dykes has the following main components [1], [2], [3], [4]:
Dyke body, dike base, protection layer of sea side slope, dike top parts: dike face and dike crest wall, protection structure for land side slope, drainage ditches 1.1.2 Overview of protection layer of sea-dike toe
The toe dike is kept the protechtion layers and the upper structures from moving down due to the impact of external forces such as waves, currents, floating objects and other impacts causing instability The toe dike also has the task of forming a composite structure to protect the dike body when the erosion pit appears at the base of the embankment
Materials for foot embankment and toe can be stone, hollow cilinder well, sheet, concrete pile or other material to protect the embankment According to the geometry of foot embankment can be classified into 2 types: shallow dike toe and deep dike toe
1.1.3 The shallow toe of sea dike
The standard of classifying sea dike toe according to hydraulic boundary is as follows:
shallow dike toe : 1.0 < ds / (Hm0,0) < 4
Very shallow dike toe: 0.3 <ds/(Hm0,0) <1.0 (1.1)
In which:
ds is the water depth at the foot of the embankment (m), Hm0 height of water wave in the deep water (m)
1.2 The flow of shallow foot embankment area
1.2.1 Formation of regional flow near the foot of the embankment
Trang 5Usually, the coastal area is usually divided into four regions based on the transformation of waves from deep water into shallow water: shoaling zone, breaker zone, surf zone and swash zone
The area of the dike foot of the embankment is swash zone , when the waves reach the slope of dike, it will climb and stop, flowing down which is called as going up anf fall down flows Those flows directly affects the material at the foot
of the embankment
1.2.3 Wave flow due to waves attacking the foot of the shallow toe
When waves coming up and fall down on the sloping roof, being affected by the terrain and wind direction, there are three main types of currents at this area: cross-shore, long-shore and Rip (concentrated currents forward to the sea side) The dike toe is influenced by two flows as horizontal and longshore bank flows, the Rip flow is less affected comparing with two athers
a) Cross-shore flow
When the mass of water due to the wave carries close to the shore it dissolves and this amount of water will have to return to the sea - that is the reverse flow
or undertow The bottom flow can be relatively strong, usually 8-10% of √𝑔𝑑𝑠
at the point of measurement near the bottom Research on bottom flow has been made by Longuet-Higgins (1953), Dyhr-Nielsen and Sorensen (1970), Dally and Dean (1984), Hansen and Svendsen (1984), Stive and Wind (1986), and Svendsen, Schäffer, Hansen (1987) (EM 2002) [7]
(b) Undertow on the beach
When the wave travels from the sea to the shore, the current velocity is divided into 3 parts: surface velocity (wave front), velocity of the sub-surface water mass and undertow flow velocity The direction of the velocity of these regions is opposite
Figure 1.8: Longuet-Higgins flow velocity diagram (1953)
The current velocity at the bottom is determined as follows:
𝑈̅.𝑢𝑛𝑑𝑒𝑟𝑡𝑜𝑤 = − 𝛾𝐿𝑛
𝑠𝑖𝑛𝛼[1−(4𝜛𝑜 ) 0.5 𝑒 −0.5 𝑘𝑡 cos(𝜛𝑜−𝐵)]/2𝜛𝑜 (1.20) Inside:
α- bottom slope; Ln- change of the water level; ϓ- Breaking wave standard; k - coefficient of bottom resistance; characteristic coefficient:
Trang 6(d) Flow in swash zone
Swash zone is the area of wave impacting on the shore area in the form of water level fluctuation between the run-up and down waves The swash zone is conected betwen land and sea The swash region is strongly related to the surges
in the slope and when the waves fall down the slope The run- up flows are usually much stronger than the down flows According to Ruessink and Van Rijn [16], the velocity of run-up wave can be approximated: ub = √ (gds) with ds in the range of 0.1m to 0.2m, it accelerates to reach ub from about 1m / s to 3 m/s According to the study of Van Rijn et al 2018 (linear wave theory) [17], [18], the maximum flow velocity at the bottom can be expressed as follows:
Umax= Hs(Tp)-1sinh-1 (2ds/Ls) (1.23) Inside: ds is the water depth (m); Hs is the wave height, Tp is the wave period, Ls
is the wavelength
1.3 Study of stability of fill rocks dike toe
1.3.1 Study the foot of embankment of stone in the world
a) Study of steady flow, horizontal direction and stabilize solid
Considering material particles in an environment with flow velocity, it is affected
by 5 force components as shown in Figure 1.12 [19] In which FD is the dragging component due to the impact flow, FS is the cutting force due to the bottom stress,
FL is the lift force caused by the flow curvature, FF is the friction force between the particles holding it when moving W is the weight of the particle itself Different forces of the effect flow on the particle are determined as follows [19] Relationship between the parameters proposed by Izatbat:
d g K
= u d
g
= d g -
w
w s 2
Trang 7Figure 1.12: Impacting force of flow on particles in horizontal direction When calculating with the rock at the foot of the embankment, the density of seawater is equal to γn = 1025 kg/m3, density of the quarry rocks γđ = 2400kg/m3, formula (1.26) can be rewritten:
+ The flow of water proceeds to the slope
Stability of the solid block under the impact of flow is shown by the following formula (Pilarczyk - 1990) [20], [21], [22]
DΔ = 0.035∗Φ∗𝐾𝑇 ∗𝐾ℎ
Inside:
Δ= ( 𝜌đ −𝜌𝑤)
𝜌𝑤 = Relative density of materials (-),
D - Thickness of protection layer (m),
g- Gravity acceleration (g = 9.81 m/s2),
ucr - Directional average flow velocity on slope (m/s),
Φ - Stability coefficient (-),
Ψ – Limited Shields Number (-),
KT - Coefficient of turbulent flow (-),
Kh - Flow depth coefficient (-)
Ks - Roof slope coefficient (-)
Replacment of the known coefficients, the formula (1.31) rewrites:
1.3.2 Study of stability of embankment foot in Vietnam
1.3.2.1 Experimental and theoretical research
Trang 8Research on erosion of sea embankment is also interested by many Vietnamese scientists According to the authors Nguyen Van Mao (1999) [23], Nguyen Hoang Ha et al (2003) [25], Vu Minh Cat et al (2008, 2013), Le Hai Trung & et al(2008), Thieu Quang Tuan et al(2008) [26], [27], [28], [29] conducted a physical model study at the General Hydraulic Laboratory - Thuyloi University and a mathematical model carried out at the Ministry-level research project in
2007 of Marine Engineering Faculty [4] In addition to research on physical models, many authors also have studied on mathematical models, using Wadibe-
CT program [25], [27] Wadibe-CT numerical model developed by the Faculty
of Marine and Coastal Engineering, Thuyloi University
1.3.2.2 Application research
The published scientific work of dike toe dike in Vietnam is still rare The types
of dike toe are mainly used for hollow wells (circular and regular polygon shapes), foot-lock beams, gabions, and matric of rock covering bed of floor, that depended on the geological conditions and the design boundary The research of Marine Engineering Faculty staff has contributed more theory to explain the scour at the foot of the embankment concerning to slope of bed and toe made by hollow well
1.3.3 The disadvantages of dike toe reserch at the momemt
At present, some stone works at the foot of the embankment are still unstable, sometime the stone moves away from the original position
- In the calculation according to rules, this does not to mention the solutions to limit solid materials runing up due to the waves pushing on the embankment and rubbing the roof (especially the wave reduction by roughtness colums )
- The dissipation of wave energy on the embankment roof is currently being designed by designers to create raised edges with the height of a few centimeters,
an area of roughness on the surface area of about (20 ÷ 40)% It is necessary to study the effect of roughtness colums height on energy reduction of flow
1.4 Orienting research issues of the thesis
Maximum velocity according to TCVN 9901: 2014 is defined as follows[4]:
Umax =
sp s sp
sp
L
d g
L
H
.4sinh
Umax is the maximum velocity of the flow at the foot of the embankment(m/s);
Lsp is the design wave length(m); Hsp is the design wave height(m); ds i the water depth at toe of the embankment(m); g is the gravitational acceleration(m/s2
).
Trang 9Comparing the formula (1.37) with the formula (1.23), the formula (1.23) has mentioned the wave period factor (Tp) considering the influence Tp to the maximum velocity at the foot of the embankment However, the velocity at the foot of the embankment is also influenced by other factors such as slope of the embankment (m), the roughness of the embankment (a), the slope of the beach (i), The breaking wave similar index of Igrabien ()
The thesis will focus on theoretical and empirical research to find the current velocity near the bottom of ground, thereby proposing the calculation formula and checking the stone stability at the foot of the embankment Content included:
- Clarifying the flow regime and affecting the stability of shallow toe of dike made of stone;
- Developing a calculation method and proposing a process to check the stability
of stone placed at shallow toe of seadike
1.5 Conclusion chapter 1
- Foot embankment as dike toe is an important part of the sea dike structure, it is the base of the revetmet, keeping the body and revetment of dike to be stable under the impact of waves and currents In general, stability of the embankment
in particular and the dike body is depended on the characteristics of the ground geology, the depth of the flow, the wave height and the direction of the flow At the moment, rubble stone embankment is popularly used in design of sea dike with suitable natural conditions
- The flow at the foot of the embankment is belong to the surf zone, the nearshore area exists the following flows: cross-shore current, longshore current and Rip current, in which the velocity at the foot of the embankment is directly affect by the cross-shore current and longshore current
- There have been many domestic and international studies on current velocity due to waves at shallow toe of seadike Factors affecting the flow velocity have been studied by Shield, Paintal, De Boer, Lammers, Simons and many other researchers and have many publishs
However, there are some factors that have not been mentioned about the height
of roughness, wave slope or similar index of breaking wave The thesis needs research to clarify the influencing factors that noted abave
CHAPTER 2: DIGITAL MODEL STUDYING FLOWS AT THE SHALOW TOE OF REVETMENT
2.1 Set the problem
To expand the scope of the study and the effect of geometric parameters on the velocity of the shallow toe of revestment, the thesis has used MSS-2D numerical modeling to describe the flow velocity vector made by wave, analyzed the influences of hydraulic parameters and construction parameters on flow regime
at the foot of embankment; supportted the content of studying physical models
which is limited due to experimental conditions
Trang 102.2 Research direction of mathematical model
2.2.1 Some common software in research of coastal wave
We can name here some mathematical models using the typical Boussinesq
equation system such as: MIKE 21-BW, FUNWAVE, COULWAVE Besides,
there are some studies of mathematical models such as common digital wave
flume; IH2 (Spain), SOLA-VOF & DELAWAVE (USA), CADMASURF
(Japan) and MSS-2D, WADIBE-CT (Vietnam) [4]
2.2.2 Digital wave flume
2.2.2.1 Basic equations used in digital wave flume theory
Navier-Stokes equations are known as the right equations for describing fluid
motion, including problems of wave motion But to facilitate the application of
simplified system of equations from Navier-Stokes equations that can be
represented as: Nonlinear shallow-water equation system (NSW), Boussinesq
equation system (BAE) and Equation system full nonlinear potential lines
(FNPF)
+ The model based on a direct solution of the Navier-Stokes equation system
in case of closed turbulent flow
The thesis will be interested in spatially filtered Navier-Stokes equation using
the Smagorinsky turbulent diagram (Smagorinsky, 1963) The turbulent
coefficient (t) is determined from the strain stress (Sx,z) of the flow field The
formulas for calculating turbulent coefficient in two-dimensional model are as
follows [42]:
(2.3)where Cs is the model parameter calculated in the range of:
The author of the thesis has used the theory of digital wave flume by authors
Hieu and Tamnimoto to perform calculations [33], [36], [37], [42]
2D equation system (vertical and horizontal directions), continuous equation is
written as follows:
q z
x and z directions):
u x e
x
w z
u z x
u x
x
p z
) 2 ( x z x z
) ( xz
2 0 1
.
0 Cs
Trang 11w z
e
z
w z
z
u x
w x z
p z
e is the kinematic viscosity coefficient (sum of viscous and turbulent viscous);
g is the gravitational acceleration; q is the volume; qu, qw is the momentum source
in the x and z directions Dx, Dz are the energy reduction coefficients in the x and
z directions
+ Based on the Navier-Stokes equation system, Sakakiyama and Kajima (1992) have developed an extended equation system for unstable flow in an porous environment, in which the drag force due to the porous environment is modeled through drag and inertial forces increasingly due to resistance in the porous layer The system of equations proposed by Sakakiyama and Kajima (1992) two direction 2D as follows:
Continuous equation
v z x
q z
w x
x and z directions):
u x x e
z e
x v
z x
x
w z
u z x
u x
x
p z
wu x
z e
x v
z x
z
w z
z
u x
w x
z
p z
ww x
z
M x x
x
M v v
v
C C C
2
1
w u u x
1
w u w z
Trang 12x, z are the horizontal and vertical distance of the net in a porous environment;
CD is the drag coefficient
2.2.2.2 Structure of digital wave flume
The digital wave flume structure is outlined in Figure 2.2 The boundary conditions for running include: liquid edges such as water level, wave height, wave cycle, waveform (regular or random); hard edges including bottom elevation, bottom slope, slope of embankment, roughness then run and will give preliminary results In order to obtain the reliability, it is necessary to have
a mathematical model test in which two coefficients CD and CM need to do by physical modeling to determine the value The output part will have supporting software
2.3 Selection of boundary conditions in running the math model
2.3.1 Bases for setting up calculation parameters and testing physical models
Figure 2.2: Diagram of digital wave flume structure [34]
The flow velocity at the foot of the embankment is depended on the water depth (ds), the wave height at the foot of the embankment (Hs), the wave period (Tp), the slope of sea floor (i), the slope of the embankment (m), rough degree (a) To
go to the experiment and run the math model, the computational margins are chosen as below
(a) Hydrology in design
Surveying the general shoreline, wave parameters at the design point: according
to the calculation design frequency the wave height from 0.2m to 3m and more, corresponding to the wave period of about 5 seconds to 7 seconds in the shallow water zone, the water depth at the foot of the embankment is from 0.5m to 3m and more Therefore, the thesis will base on this calculation to establish scenarios [4], [38], [39]
(b) Topographic boundary, structure of dike slopes
According to the results of the study of the sea dyke program in the first phase from Quang Ninh to Quang Nam (MARD), the average beach slope i = 1% to 2% [4], the common slope of sea dyke is m = 3.0 to m = 3 5 [4], [40], [43], [44], [45], [46]
Trang 132.3.2 Modifying MSS-2D digital wave flume model
The model uses wave data Hs = 0.8m and Tp = 5.06s (T = 5s) as a basis for modifying the model
The results of model correction show that with the scenario, porosity n = 0.3, Cm
= 0.25 and Cd = 1.5 for velocity UmaxTT = 1.26 m/s, the results are consistent with the results of the physical test with the same condition UmaxTN (m/s) = 1.24 m/s (see chapter 3) Therefore the MSS-2D digital wave flume model selects the porosity parameters n = 0.3, Cm = 0.5 and Cd = 1.5 as a basis for verifying subsequent scenarios [annex 2]
2.3.3 Verification of the model in case of without roughness
Table 2.4: Results of the largest horizontal velocity test (Umax) by digital wave flume models and physical models
(m)
T (s) Umax
2.3.4 Verification of the roughness case
Table 2.7: Results of testing the maximum velocity between digital wave flume models and physical models