Summary of doctor thesis of engineerin: Research of earth embankment stability on natural ground

Nội dung Text: Summary of doctor thesis of engineerin: Research of earth embankment stability on natural ground MINISTRY OF EDUCATION TRAINING UNIVERSITY OF TRANSPORT AND COMMUNICATIONS Do Thang RESEARCH OF EARTH EMBANKMENT STABILITY ON NATURAL GROUND Major: Highway Engineering Code: 62.58.02.05.01 SUMMARY OF DOCTOR THESIS OF ENGINEERING Hanoi 2014WORK TO BE COMPLETED IN LIST OF PUBLISHED WORKS UNIVERSITY OF TRANSPORT AND COMMUNICATIONS 1. Do Thang (2013). “Stress field in soil is obtained by using the theory of elastic and the theory of min (max)”. Vietnam Bridge and Road Magazine. 102013. pp. 30 33. SUPERVISORS: 2. Do Thang (2013). “Research of stability for vertical slope by limit 1: Prof. Dr Ha Huy Cuong analysis method”. Review of Ministry of Construction of VietNam. (Military University of Science and Technology) 11 2013. pp. 103 104. 2: PhD Vu Duc Sy 3. Do Thang (2014). “New method research earth embankment stability (University of Transport and Communications) on natural ground”. Review of Ministry of Construction of VietNam. 62014. Reviewers 1: Prof. Dr Nguyen Xuan Truc (National University of Civil Engineering) Reviewers 2: Prof. Dr Nguyen Van Quang (Hanoi Architectural University) Reviewers 3: Prof. PhD Nguyen Truong Tien (Vietnam Society Soil Mechnical and Geotechnical Engineering) The thesis is defended to the Council assessing doctoral dissertation at the case level: University of Transport and Communications at ….h… ……, 2014. Thesis can be found in the library: 1. National Library VietNam 2. University Library of Transport and Communications

SUPERVISORS:

1: Prof Dr Ha Huy Cuong

(Military University of Science and Technology) 2: PhD Vu Duc Sy

(University of Transport and Communications)

Reviewers 1: Prof Dr Nguyen Xuan Truc

(National University of Civil Engineering) Reviewers 2: Prof Dr Nguyen Van Quang

(Hanoi Architectural University) Reviewers 3: Prof PhD Nguyen Truong Tien

(Vietnam Society Soil Mechnical and Geotechnical Engineering)

The thesis is defended to the Council assessing doctoral dissertation

at the case level: University of Transport and Communications

at ….h…' ……, 2014

Thesis can be found in the library:

1 National Library VietNam

2 University Library of Transport and Communications

1 Do Thang (2013) “Stress field in soil is obtained by using the theory

of elastic and the theory of min ( max)” Vietnam Bridge and

Road Magazine 10/2013 pp 30 - 33

2 Do Thang (2013) “Research of stability for vertical slope by limit

analysis method” Review of Ministry of Construction of VietNam

11/ 2013 pp 103 - 104

3 Do Thang (2014) “New method research earth embankment stability

on natural ground” Review of Ministry of Construction of VietNam 6/2014

INTRODUCTION

1 The reason of selecting project

Subgrade is an important part of highway To ensure the stability of subgrade is a prerequisite to ensure the stability of the pavement structure Research methodology stable subgrade is widely used in today's designs is limited equilibrium methods Basic equations of this method consists of two balance equations (plane stress problem) and Mohr-Coulomb yield condition

However, the limit equilibrium method is not consider the phenomenon volume change of soil when using the yield condition Mohr- Coulomb On the other hand, the basic equations above do not allow determining the stress state in the yield imperfections, ie not consider the stress state of the entire soil mass Therefore, in the thesis "research of earth embankment stability on natural ground" is presented below, using theoretical min (max), author can apply directly limit theorem to study the stability of the overall soil mass and stability of the embankment on natural ground

2 Purposes of the research

Building a new method (method directly applicable limit theorem) evaluate soil stabilization in accordance with the actual working of the soil environment, the study contributes to the development of stable subgrade Applying the above method to build a computer program, set the tables and nomogram helps engineers quickly determine the height and slope of embankment limited In addition, using the lower limit theorems

of the theory of limit analysis tells us that the stress distribution in the soil mass before ruin and slip surfaces occur in soil mass, freely given variables appropriate enhance soil stabilization when necessary

3 Subjects and scope of the research

Research subjects: The earth embankment on natural ground

Scope of the research: The research of the stability problem of earth

embankment on natural background consider in the case of plane problems

4 Scientific meanings and pratice of the project

Soil is not so elastic material in plane problems, two balance equations are not sufficient to determine the three components of stress Author used more conditions min (max) to have enough equations determine the stress state in the entire soil mass and directly applicable limit theorem for stability studies and natural embankment and foundation

In the thesis presents the various stability problems: limited intensity

of the ground under load horizontally forward hard (Prandtl problem), block slope of dry sand , steep tomorrow so natural on under Business Use

of the external ear and self-weight, trapezoidal embankment on so natural under the effect of self-weight Since the study was able to draw conclusions and explanations and quantitative following:

- The yield condition Mohr- Coulomb said materials with internal friction greater the bigger the load capacity However, for embankment construction materials such as soil, sand, shred lascivious the material has a large capacity unit new headquarters is the material guarantee a better slope stabilization Practices embankment construction in our country attest to that

- Slip surface appears on the sliding surface slope and embankment surface when external load effects

- When study the stability of embankment only consider self weight

of the soil does not appear on the slip surface on slope and embankment surface

- Depending on the intensity (c, ) patch material to natural ground which happens all cases Disruptive packing material intensity the greater the height of the dam increasingly limited so large, increasingly large talus slope When embankment intensity (c, ) equal to or less than the natural ground intensity it takes only appear at the foot sliding embankment slopes, embankments When intense than natural background is ingrained into the sliding surface nature

- The calculation and comparison shows embankment height limit under the author’s method approximates the heights rebate under sliding surface methods (using a safety factor greater than 1) This is explained by the method of sliding surface gives the upper limit of the height of the embankment

Author has developed a computer program, set the tables and nomogram helps engineers quickly determine the height and slope of embankment limited Also, from the graph contours plastic flow rate will determine the net slip surfaces should be able to come up with measures for reinforcing appropriate place to raise the roadbed stability when needed

- Chapter 2: Facility theory to research stabilize earth embankment

stability on natural ground

- Chapter 3: Fundamental problem about limit load and slope

stability

- Chapter 4: Research of stability of soil mass with vertical slope

- Chapter 5: New method to research stability problem of the earth

embankment on natural ground

- Conclusions and Recommendations

- The appendix

6 New contributions of the thesis

1- Different from traditional methods of soil mechanics, author uses theory min (max) to be able to directly apply the method limit analysis to research earth embankment stability on natural ground (not given stress state or shape of slip line) Use the lower bound theorem of the theory of limit analysis gives us the stress distribution in the soil before failure and found slip line field, that we can take appropriate measures to improve

stability when needed

2- Different from traditional methods is research methods separate slope and bearing capacity of the natural, author built overall stability problem of the embankment so natural to be able to study the impact between them

3- The soil stability problems presented in the thesis is correct on mechanics, mathematics and strict new In terms of mathematical is that the non-linear programming problem because constraining is the yield

condition Mohr- Coulomb The solution method is a method of finite difference and to optimize the use of available content, author programmed

on Matlab's software to solve Difference schemes for the solution of the thesis results with high accuracy, such as Flamant problem with some, limited slope angle of internal friction materials that do not intend to use ice internal friction angle of the material, load within the limits of medium

to steep tomorrow theoretical formula (this result is also new), etc

4- Research methods stability problem of the earth embankment on natural ground is presented in the thesis in a new method Author has developed a computer program, set the tables and nomogram helps engineers quickly determine the height and slope of embankment limited Also, from the diagram contours plastic flow capabilities will determine the slip line field should be given the appropriate measures for reinforcing the right position to raise the embankment stability when required

Chapter 1 OVERVIEW OF RESEARCH OF EARTH EMBANKMENT

STABILITY ON NATURAL GROUND

This chapter presents the research of earth embankment stability on natural ground has been applied in Vietnam and countries around the world Next, the authors analyze strengths and weaknesses and the existence of that approach Finally presentation objectives and content of the research thesis

1.1 Analysis of related research in the country and abroad

1.1.1 The unstable form embankment on natural ground

According roads design standards TCVN 4054-2005 [7] and its foundation to ensure stability, maintaining the geometric size, have sufficient strength to withstand the impact of vehicle and load factors nature during use Therefore, the embankment must not be phenomena such as slope sliding, sliding part up on the slopes, slip surfacing, embankment subsidence on soft soil

1.1.2 Research methodology stable subgrade

Soil material is complicated, we do not know the full range of mechanical and physical characteristics of it However, soil samples studied in the laboratory experiments and pressure plate at the scene

showed that the land can be considered as ideal materials comply wizened the yield condition Mohr- Coulomb [34] to be able to use limit equilibrium method or the more general theorem of limit analysis to study the stability

of the soil mass So, in this section, before the introduction of the research methodology stable ground, the author presents the basic contact ideal plastic materials

1.1.2.1 The basic contact of elastic perfectly plastic material

There are many different mathematical models to establish the relationship between stress and deformation of plastic material So far, the researchers have agreed to use the model determines the speed plastic deformation according to the following equation [35], [36],[40], [41]:

(1.9)

where: is a scalar proportionality factor;

≥ 0 if f = k and f'= 0 (k is a yield limit);

= 0 if f < k or f = k and f' < 0

Relation (1.9) shows the dimensions of the plastic deformation of the surface normals coincide with the construction of flexible plastic surface in stress coordinates

So the formula (1.9) is called the normal rules, also known as

associated flow rule, regarded dimensional plastic deformation rate

coincides with the gradient of the plastic flow function

It is possible that the plastic problem is complex because flexible nonlinear properties However, designers are often interested in power limit, or limit load of the structure, ie the capacity to cause structural

damage In that case use "limit analysis" is a simple method that designers

are interested in [25], [33], [34], [48] The foundation of this approach are two definitions and the following theorem:

Definition 1: An equilibrium system, or a statically admissible field

of stresses is a distribution of stresses that satisfies the following conditions:

a It satisfies the conditions of equilibrium in each point of the body,

b It satisfies the boundary conditions for the stresses,

c The yield condition is not exceeded in any point of the body

ij

ij p

ij

)(f

Lower bound theorem: The true failure load is larger than the load

corresponding to an equilibrium system

Definition 2: A mechanism, or a kinematically admissible field of

displacements is a distribution of displacements and deformations that satisfies the following conditions:

a The displacement field is compatible, i.e no gaps or overlaps are produced in the body (sliding of one part along another part is allowed),

b It satisfies the boundary conditions for the displacements,

c Wherever deformations occur the stresses satisfy the yield condition

Remark: From the definition 2 we can see the structure or hard state,

or plastic (hard plastic systems)

Upper bound theorem: The true failure load is smaller than the load

corresponding to a mechanism, if that load is determined using the virtual work principle

From the definitions and theorem of limit analysis we see: lower bound - the stress balance; upper bound - only determine the stresses in the yield point The upper bound indicates the same flow as ranges or chute should be to determine the load limit, the upper bound can not be used separately but must use the lower bound Correct answers when the upper bound equal the lower bound

1.1.2.2 Method of subgrade stability research

Method of subgrade stability research (Bearing capacity of natural ground and slope stability) in plane stress problem is the method to solution following system of equations:

(1.14)

where: x, y, xy,yx is the stress state at a point in the soil;

 is the angle of internal friction;

0x

y

0yx

y x max

xy y

yx x

Third equation of the system (1.14) is the yield condition Coulomb written as stress component

Mohr-1.1.2.3 Bearing capacity of natural ground

Prandtl (1920) was the first to solve the equations analytically for the case of problem on the ice when the foundation could not land at the weight The load limit is determined from the lower limit theorems and limit theorems on the results can be considered equal to the Prandtl solution is the correct solution of the limit analysis method

Novotortsev (1938 ) address the general problem when the work load versus vertical oblique angle

In addition, there are several methods of calculating load limits other sliding surface is determined from the limit equilibrium methods such as Terzaghi method, Berezansev, Vesic, Ebdokimov, Meyerhof, Hansen,… Exact mathematical solution to the problem is an important consideration volumetric weight of the ground is very complex Therefore , many methods approximate solutions have been developed Sokolovski (1965 ) provide numerical solution methods based on approximation by finite difference

Actual construction and experimental models have shown that the soil mass destruction , the soil mass of the state of damage at the same time that place is still in stable equilibrium [24]

1.1.2.4 Research methodology slope stability

a Method assumes the slip surface

Actually common method used classic W.Fellenius fragmentation and auditing methods to Bishop slope stability assumption soil on the slope instability will slip round cylindrical slip surface Bishop method takes into account the effect of horizontal thrust from both sides of the sliding slice (not to the point of interest of the two horizontal forces put it)

In addition to the above two methods is very much the way fragmentation methods such as: Janbu method, Morgenstern-Price, Spencer, American engineers association, or methods based on general limit equilibrium theory GLE, the method takes into account the forces between the pieces to reflect most closely the actual interaction between the slice

b Method assumed stress field

To determine the height limit of a vertical slope according to the lower bound theorem, WF Chen [33], [34] has assumed stress field in three regions correspond to two equilibrium equations

Conduct Mohr circle for each area and get points to reach the foot of the steep yield limit first plastic (Mohr circle tangent to the Coulomb) when increment height of the vertical slope H

1.2 Shortcoming issues in the research of earth embankment stability

on natural ground

Research methodology stable roadbed is widely used in today's designs is limit equilibrium method or methods of solving equations (1.14) includes two balance equations and yield condition Mohr-Coulomb (plane stress problem) Solve the system under stress on users to limit theorem under the assumption of stress states in each region soil mass balance equation satisfied and Mohr - Coulomb condition, so here 's how indirect Solve the system used on the skating track on the limit theorem by writing equations in polar coordinates

However, the slope of the applied solution is very difficult to have assumed before sliding surface Methods commonly used method today is fragmented classical and Bishop method assuming circular slip surface is cylindrical W F Chen used a logarithmic spiral slip surface to calculate Limit equilibrium method with the above two solutions , as WF Chen commented [34], is not a proper application of limit analysis method of the above theory - ideal plasticity by for not considering the volume of soil mass phenomenon altered flow situations using the yield condition Mohr-Coulomb On the other hand, the basic equations above do not allow determining the stress state in the plastic flow imperfections, which is not considered a state of stress of the whole block of land because land is not

so elastic material with two balance equation which has three hidden, so can not determine the state of stress in the soil

1.3 Objectives and contents of the thesis research

Ngo Thi Thanh Huong when researchers calculated stresses in the ground transportation works [19], under the guidance of Prof Dr Ha Huy Cuong combined max shearing stress conditions to achieve the greatest

minimum value (min (max)) with two balance equations in plane stress problem to be system of equations:

y

0yx

0

xy y

yx x

y x 2

with 2 denotes the Laplace operator

System ( 1.47 ) has three equations to find three hidden is unknown

x, y and xy so the problem is defined Therefore, using this system of equations we can determine the stress state in the entire soil mass

PhD Ngo Thi Thanh Huong in his thesis on applied theory to solve the following problem :

- Status subcritical stress natural soil under the effect of self-weight

- Angle of slope of the critical mass of dry sand

- Load capacity of the ground under the foundation tape not consider myself weight

PhD Nguyen Minh Khoa in his thesis was developed to solve theoretical limit stress in the natural ground under the weight of the embankment effects and counter pressure pad

However, load embankment and breaks the rules applied load is distributed, ie not research of the simultaneous embankment and natural ground

Therefore, the author based on theoretical min (max) can be directly applied to limit theorem subgrade stability (research of the simultaneous stability of embankment and natural ground) Author should use the lower bound theorem without upper bound theorem by assuming that all points are capable of plastic flow For plane problems, we have:

V

x(

G is the shear modulus of soil;

In brackets [ ] is the yield condition Mohr-Coulomb written as stress component

Chapter 2 FACILITY THEORY TO RESEARCH STABILIZE

EARTH EMBANKMENT STABILITY ON NATURAL GROUND

This chapter presents the theoretical min (max) and differentiate with elastic theory, followed by presenting the problem constructively determine stress field in the earth Finally, the method presented in accordance finite difference solution and some results to show properties can use this theory to research of earth embankment stability on natural

ground

2.1 Theory min ( max )

Soil is the product of weathering processes on the same layer of the earth's crust, which formed the sediments In natural conditions, soil is multi-phase materials: solid phase (particles), liquid and gas phases The mechanical properties of the soil are complex, depend directly on the three phases interact with each other However, in the process of sediment due to self weight over time more and more land is "stable"

To distinguish theory min (max) with elastic theory, author study stress field in the soil based on two theories

2.1.1 Elastic stress field in soil

If soil is considered elastic material, the elastic stress field in the earth can be determined through displacement field, its deformation In the plane problem, using stress is unknown, the stress field can be determined

by the minimum potential energy problem (2.1)

0yx

mindV

2)1( 2

E

1Z

xy y

yx x

2 yx

2 xy y

x

2 y

2 x

V

where: Z is the elastic strain potential energy in the plane stress problem [1];

x, y, xy,yx is the stress state at a point in the soil;

E,  is the elastic modulus and Poisson's ratio of soil;

By variational calculus problem leads to extreme on the basic equations of the elastic theory

The plane stress problem to determining stress field in soil based on theory min (max) as follows:

y

0yx

min2

xy y

yx x

2 xy

2 y x max

(2.10)

where:  is the volume weight of the soil

The problem gives enough the equation to determine the stress state

in the soil In addition, we also received a volumetric strain of 0 This is an important factor to be applied strictly limited analytical methods for soil that yield condition Mohr-Coulomb

Now, we have the stress field in the soil is static determinacy field enough equation to solve the equation Therefore, the problem is soil mechanics problems identified, we can use to solve the problem of different stress states (such as external load)

2.2 Establish problem to identify stress field in soil

After obtaining these results, the problem identified stress field in the soil of roads, houses, dikes, dams entirely possible In the need to further examine the problem of constraint conditions For clearer presentation, we consider the problem to the stress state of embankment on natural ground due to self weight and external load (Figure 2.4)

O xy

 1

c ,00

 0m'1

y = 0; xy = 0 while only consider self weight (2.16)

y≠ 0; xy = 0 within the sphere of external load (2.17)

+ On inclined surface (slope):

)n,ycos(

)

n,xcos(

2)n,y(cos)

n,x(

(

min)

(

2 ) m , 2 ( xy ) m , 1 ( xy

2 ) m , 2 ( x ) m , 1 ( x

(

min)

y.(

2 ) n , 1 2 m ( xy ) n , 2 m ( xy

2 )

n , 1 2 m ( y ) n , 2 m ( y

(2.21)

Soil conditions inability tensile

The compressive stress satisfies the following conditions:

0

Yield condition Mohr-Coulomb

Stress state in soil must satisfy the yield condition Mohr-Coulomb follows:

0cos.csin2

y x

Condition every node is likely to yield

mindxdy

)cos.csin2

(G

V

y x



where: G is the shear modulus of soil

2.3 Finite difference method to solve the problem

Direct solution problem is very difficult, especially when considering the volumetric weight of the soil Therefore, the authors solve the problem

by finite difference method [15], [22]

Divide the soil mass into square blocks, each node has three unknown stresses, except for the nodes on the boundary mentioned above

In general there are 3 hidden in each node is x,y,xy

Balance equations and the objective function is written for center points of the finite difference grid

Problem has form squares objective function, constraints are linear and nonlinear There are many methods of solving nonlinear programming problem [29], but to take advantage of the extreme function is available [37], author programmed on Matlab's software to solve

2.4 Flamant problem solution by numerical method

To verify the correctness of the solution method and computer program, author solve Flamant problem by finite difference method, then compared with analytical solutions

Author writes program Dothang1 and Dothang1a to solve the problem

Results calculated vertical normal stress y at the position between the strip load by the finite difference method for results approximation with analytical solutions (less than 5% difference) The difference is due to the number of mesh elements difference is not large enough