1 . Stability analysis results according to the finite element method by hnh_ress
V1.00 software (geotextile reinforced embankment stability analysis) case of:
different heights embankment , different slopes coefficients , good soil or soft
soil, dangerous sliding surface result is the ellipse -shaped face. The center of the
ellipse is determined slip in a position to face the same level of high embankment
. The software program set algorithm to draw lines passing through the point of
distortion has the largest shear strain in embankment (Display > Slip suface
stresses), then use the sliding surface approximation method to test ellipse
equation and copper pointed out countless times in circular slip surfaces assuming
a circular slip surfaces are approximate. In case of arc shape sliding surface is
considered as a special case of the ellipse shape .
The results of this study contribute to further clarify the previous study at home
and abroad [57] , [60] that the slip surface is not circular slip surfaces .
2 . Construction tension expressions (Tmax) - (4.36) of the geotextile layers in
reinforced embankment. Where Tmax is caculated according to form of ellipse
slip surface from the research results, stability analysis by finite element method.
And tension value (Tmax) of the geotextile layer also has built-in hnh-ress
software (Report > Geotextile Forces).

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angential bottom soil column
with the ith lateral Rd : radius circular slip ; fms : partial material factor applied to
tgφ'cv ; φ'cv : friction angle at the base construction material in large deformation
effective stress conditions ; ui : pore-water pressure effects on the ith sliding piece
Troj traction required for 1 meter long embankment at each point along the
bottom of the embankment j is defined as : (1.5)
Among them : YJ ¬ arm is in the vertical direction of the torque to the dangerous
sliding surface at the center point on the bottom of the embankment j ; MRRj :
largest holding torque by strengthening core at point j on the bottom of
embankment ; MDJ : maximum torque slip at the bottom of the embankment j
(human factor has been) ; MRSj : keeping the largest torque generated by the soil
at the bottom of the embankment point j (human factor has been) .
1.1.2.2 Method of computation analysis on reinforced soil embankment good
natural
1 . Where the external stability of one or more results to sabotage occurs,
treatment options may ways , such as reducing roof slope embankment ,
increasing the width column layout , using quality packing material good quality ,
enhanced by the foundation soil reinforcement measures , counter pressure pad ,
- 6 -
packing material used is lightweight , reinforced combinations in various high
level , more layout drainage system to reduce pressure pore water pressure , or
combined treatment options in [15] , [32] .
2 . Internal stability [ 15] , [32] , [33] , [35] , [57] , [53] , [63] The method of
calculating reinforced embankment on the basis of gender balance method and
use the term partial coefficients corresponding to limit state are calculated .
Includes :
a. Method two wedge blocks ( slip surfaces kinked shape ) [12] , [15]
Driving forces synthesis ( synthetic human disturbance ) in the case of a slope no
more subject to external load is calculated as :
( 1.7 )
Among them : the human Rh disturbing synthesis of 1m length along the slope ;
ffs is the partial factor applied to the unit weight of the soil , K is the ratio of
stress ( pressure ) horizontal and vertical stress ; ɣ is the unit weight of the soil ;
H is the height of embankment .
To pull off being reinforced , reinforced distance vertically is determined from the
expression:
(1.8)
Among them : Svj gap remains vertical in slope at j ; Tj is the greatest traction in
the 1 m core length in slope at j ; ffs the partial load factor applied to the weight
unit volume of soil , hj is the height of the embankment on the slope j ; fq is the
partial load factor applied to the external load , ws is the external load due to
static load ( evenly distributed on the surface at structure [ 15 , p . 10 ] ) .
Paragraph anchor Lej not happen to slip reinforcement is determined from the
limit state vandalism , anchor length remains satisfied [ 15 , p . 118 ] .
(1.9)
Among them : Lej is reinforced anchor length minimum calculated at j ; fp : partial
factor control remains pulled slip phenomenon , fn : partial coefficient control
works damaged due cause ; fms : partial factor applied to tgφ'p and c ' , ws :
external load , α ' : interaction coefficient indicates the relationship between
power and ground anchor reinforced with tgφ'p ; φ'p : corner resistance biggest
cut of fill materials ; αbc ' : stickiness factor denotes an anchor link between soil
health - reinforced with c ' c ' : effective cohesion of the packing material .
Comment crease sliding surface method
- The method of calculating " wedge block two " not consider the effects of
horizontal thrust due to the inclination of the upper surface created ( only
considering the vertical force is the weight soil ) . " Block wedge two part " is a
general form of the limit equilibrium method . This method has the advantage of
simplicity , the present destructive potential can determine the approximate
gradually in a wide range . In addition, this method is also easy to set up a loop
calculation program on your computer. Crease sliding surface method is used in
- 7 -
case of ground sandwiched between soft soil [12] , occurred sliding surface will
follow the crease sliding surface soft soil layer , this case Fsmin safety factor is
determined principle of sliding block fragmentation , applied to heterogeneous
soil types ( sandwiched weak soil layer ) .
b . The method for calculating fragmentation circular slip surfaces [12] , [15] ,
[32] , [33] , [35] , [49] , [65] , [63] The assumptions for the fragmented approach
to circular slip surface properties of the reinforced embankment interaction forces
between the fragments are ignored because of the complex remains influential to
the power and presence of sliding soil core makes little disturbed . In addition, the
method also assumes interaction force between the core is ignored and the core
layer are horizontal ; remains only to be considered at the position sliding surface
intersects with assumptions at each piece separately ; torque to keep the combined
effects of soil aggregate and not less than slipping torque caused by the weight of
soil ( with interest calculated torque rotary sliding blocks ) . Thus equilibrium
conditions need to satisfy to solve the problem : (1.10)
Where: MD sliding torque caused by the weight of the soil itself and external load
; MRS : torque due to a shear strength of the soil ; MRR : holding torque due to the
presence of aggregates in slope ( 1.11 )
Where: Tj is the greatest traction in core in slope at j ; yj : j distance to the center
core layer sliding Y axis ; ffs : partial factor applied to the unit weight of the soil ;
fq : partial factor applied to the external load , Wi : weight of the ith soil column ;
Wsi : external load acting on the piece i c ' : unit cohesion of fill materials
identified in effective stress conditions , ui : pore water pressure exerted on the
sliding surface in pieces i ; φ'p : maximum shear angle of fill materials ; fms : the
partial material factor applied to tgφ'p and c ' ; : adjust the torque coefficient (
limit state damage taken by 1.25 , limit state obtained by using 1.0 ) .
In length it remains to be determined not undermining slip occurs remains is :
(1.14)
Lej is reinforced anchor length at least j in slope ; fp : partial coefficient to control
the core is pulled slip phenomenon , fn : partial coefficient to control the
economic consequences caused by damaged buildings cause ; fms : partial factor
applied to tgφ'p and c ' , ws : external load ( due to static load ) , α ' : interaction
coefficients indicate the relationship between power and ground anchor reinforced
with tgφ ' p ; φ'p : maximum shear angle of fill materials ; αbc ' : stickiness
coefficient indicates the relationship between soil anchor strength - reinforced
with c ' c ' : effective cohesion of the packing material .
Slip circle method was developed by [48] : K. Terzaghi , AV Bishop ; G.B. Janbu
; A.A. Nichiprovich ; Theory Method humidity .
Comment circular slide fragmentation methods : Method assuming stable sliding
- 8 -
surface with a radius R , are commonly used calculations to figure out the most
dangerous slip with a safety factor Fsmin . Slip circle method can calculate the
slope stability is generally different shapes , suitable only for homogeneous soil .
Essence reinforcing factors to be considered tensile strength Tmax .
c . Some other computational methods for reinforced embankments based on
equilibrium torque or force .
i . The method combined stress calculations [15] , [32] , [33] The destructive
method combined stress calculations , is determined on the basis of combined
stress theory and the method of analysis according to Mohr interest . In the final
analysis , this method is somewhat more complex but potentially better analysis
can be reviewed by the local variation of stress .
ii . The method calculates the logarithmic spiral slip surface [15] This method ,
assuming slip surfaces logarithmic spiral has simplified the calculations , can be
directly determined torque causing imbalance . Holding torque ( due to the
presence of aggregates in slope MRR ) must be greater than the torque cause
imbalance (M0), ie, M ≥ M0 .
Among them : MRR is the torque due to a presence of aggregates in slope , Mo :
torque imbalance caused by slope (1.15)
Where: Tj is local tension of the fabric at j ; YJ : the core layer j distance to the
center of the Y -axis slide .
(1.16)
ffs is the partial factor for the unit weight of the soil ; fq : partial coefficients for
external load ; wi : ith soil column weight ; Wsi : external load acting on the piece
i ; ui : Pore water pressure effect on the ith sliding piece ; : torque correction
factor . The length of the anchor reinforcement is also determined by the formula
(1.14)
iii . Gravity method cohesion (Rankin) [15] , [35] , [63] This method of
calculation applied retaining wall is adjusted to calculate the slope remains the
case . In calculating principle applies two wedge blocks but adjusted to determine
how lateral pressure of the soil and the connecting points of greatest traction
corresponding to the tilt of the structure .
Comment analytic methods .
The analytical method based on limit equilibrium , embankment stability analysis
using assumed sliding surface : circular , with every crease ... assumed sliding
surface found a corresponding safety factor . So should identify numerous slip
surfaces with values different safety factor . Therefore, the ability to find the most
dangerous sliding surface with safety factor hardly accurate fit . Circular sliding
surface method is mainly applied to homogeneous background ; kinked slip
surface applied to multi-layered backgrounds , different physical properties . The
- 9 -
analytical method applied in the case of computational geometry embankment
sections normal , relatively simple . Not yet reviewed analytical methods to elastic
modulus ( E ) of land , land cover , and reinforcement material stiffness ( EA ) of
the reinforcement material in the background .
1.1.2.3 Numerical methods and computational software
1 . Method extreme Gauss principle and finite difference [8] extreme method
Gauss principle by GS . Prof. Ha Huy Cuong proposed , Hoang Dinh Dam
authors consider the problem in the absence of reinforcement layout and software
problems have reinforced horizontal . This problem is multi-layered elastic
system , relations between state suat_bien application form on the basis of elastic
theory for the case of plane strain problem . In the case of reinforced embankment
, to determine the state of stress - deformation of the embankment below the
horizontal reinforcing effects of vehicle weight ( distributed on a circle with a
radius defined ) is asymmetric problem axis , Hoang Dinh Dam authors have used
finite difference methods to calculate .
2 . Basis of a calculation software program .
a. Geo.Slope Software ( Canada ) [10] , [11] , [12] , [20] , [22]
Stability calculations : Theoretical Foundations of stability calculation in the
program Geo.Slope balance of power and torque to balance safety factor based on
the theory of general limit equilibrium ( General Limit Equilibrium - GLE ) .
As of stress , deformation : finite element method is applied in this problem based
on stability problems limit equilibrium . Variables , the factor of safety obtained
from using limit equilibrium methods . Thus , the factor of safety (Fs) is
calculated by finite element software is regarded as a stable factor in Slope / w , is
defined as the ratio of the total jet cutting along the sliding surface ( ΣSr ) to the
total shear stress along the slip surface that (ΣSm) :
b . Plaxis software (Netherlands) In the stability analysis and slope deformation
problem embankment using geotextile , see Plaxis model stress-strain relationship
of geotextile and contact elements between geotextiles for ground assuming ideal
elastic plastic Mohr - Coulomb as picture 1:27
Finite element method determines stability safety factor method decreased c - φ
read as follows : ,
,
u ii i
s
r r u r
stan c
F
tan c s
(1.19)
Among them : , and is the friction angle , unit cohesion and undrained cohesion of
the ground ; , and is the friction angle , cohesion and unit cohesion was not
impaired drainage of land background . The decline in value is calculated as
- 10 -
31
E
2sin
31-sin
2c cos
1-sin
1
follows arctan ir
s
tan
F
; i
r
s
c
c
F
and
,
,
u i
u r
s
s
s
F
(1.20)
c . Software phase2 ( Canada ) phase2
software calculates stability analysis and slope
excavation constructed by FEM method , find
the safety factor method decreased by c - φ .
Phase2 Plaxis see similar stress-strain relationship of geotextile and contact
elements with geotextile ground is linear Mohr - Coulomb model in Figure 1.27
Comments calculation methods : The software presented above are considered in
calculating the drag system behavior of geotextile and contact elements geotextile
with elastoplastic ground is ideal , the standard linear Mohr - Coulomb vandalism.
In fact , this relationship is complex includes several different stages according to
Robert M.Koerner model is presented in the next chapter . Therefore, in
calculating not realistically describe the material work .
Compared to other analytical methods mainly solved the problem of slope normal
shaped , circular slip surfaces , kinked hypothesis , based on the limit equilibrium
calculations taking into account the intensity geotextile ART but not considering
the elastic modulus (E) of land , the reinforcement material and stiffness (EA) of
the reinforcement material , the finite element method to calculate all kinds slope
different shapes , which consists of multiple layers embankment complex nature ,
the safety factor is defined as unique and single sliding surface based on the
consideration transferred in the element node . On the other hand , the finite
element method also include many factors affect the elastic modulus of the
ground , elastic modulus , hardness of structural reinforcement material in the soil
; Compared with organic difference method limit approximation problem by
differential equations , applicable only basic rectangular in shape with a simple
relationship , while finite element methods solve approximation results by word
solution of the problem , the background can be applied to any geometric shape
and have complex boundary problem in discrete relationships . From the
comparison presented above shows the finite element method has several
advantages compared to other methods .
1.2 These issues exist which thesis research will focus .
1 . The calculation methodology slope stability embankment with or without
reinforcement geotextile materials , commonly used analytical methods according
calculate equilibrium limit based on the assumption sliding circular , sliding
surface kinked hypothesis . However, numerous studies around the world show
that the slip surface is not sliding round and should be studied by the proposed
calculation methods [15] , [57] , [60] .
2 . Calculations embankment stabilization geotextile reinforcement method
- 11 -
analysis considering only the intensity of the geotextile (Tmax) without
considering the stiffness of geotextile (characterized by elastic modulus eg) .
3 . Relationship stress - deformation of the geotextile is a complex non-linear path
. Therefore need to develop computational models suitable for materials which
have ties pull this complex behavior .
4 . Tension Tmax values of geotextile -reinforced embankment should be studied
to determine the calculated value at each point (location) of the layer of geotextile
-reinforced embankment reaching the limit state intensity .
5 . The study determined the effect of hardness (EAg) geotextile to the safety
factor embankment stability .
6 . The study reinforced embankment geotextile on : the number of necessary
geotextile use , embankment slope coefficient , strength and stiffness of geotextile
reinforcement affect safety fine the embankment , should be studied computation .
From the experimental results calculated to draw the graph using geotextile ,
serving for quick reference in the preliminary design work embankment geotextile
reinforcement .
1.3 Objectives of the study : Select models and algorithms built computer
program problem embankment geotextile reinforcement by finite element method
. From this set , solve real-world problems in construction of reinforced
embankments and suggest that problems exist thesis focused research .
1.4 Contents of Applications Research geotextiles in the construction and
computational models embankment geotextile reinforcement in the world and
Vietnam . Computer model stability problem , embankment reinforcement
permeability of geotextiles by the finite element method . Compared with other
programs , other software in the world and Vietnam to establish algorithms and
computational software program for research .
1.5 Research Methodology : Based on the construction of computational models
using the finite element method , established algorithms and software programs
compare with the calculation methods and programs in and outside the country,
solving accounting and proposed outcomes achieved . Selection and calculation
model building problem embankment reinforcement geotextile material is
presented in the next chapter .
CHAPTER 2 COMPUTATIONAL MODELS OF GEOTEXTILE
REINFORCED EMBANKMENT PROBLEM .
2.1 Purpose and requirements .
2.1.1 Purpose : Selection , calculation model built using reinforced embankment
soft materials describes geotechnical realistic work of structural materials in the
system " soil - core " FEM method study the parameters affecting the stability
analysis and stress states - deformation of reinforced embankment
2.1.2 Requirement calculation model towards working closely with the actual
materials in structural system " + core land " was modeled and selection of
materials characteristic landforms, such that proper reinforcement case .
- 12 -
2.2 Properties of Geotextile [42] , [62] , [63] .
2.2.1 Some properties of the concept of geotextile [62] , [63]
Within the scope of this thesis , the hardness is not used in accordance with the
concept of bending stiffness hardness concept here is understood as : ( EA / L ) is
the stiffness of the unit element bearing axial bar , model chemical element
geotextile in finite element problems . And so EA is called the element stiffness
geotextile , unit is kN .
2.2.2 Road relations stress - deformation of the geotextile
According to the model of Robert M.Koerner in " Designing with Geosynthetics "
, 5th Edition, (USA, 2005) [63] , depending on the geotextile fabricating various
relationships that last curve behavior quite complex . Some types of geotextile
typical path ties stress - deformation characteristic is shown in figure 2.1 .
According to Robert M.Koerner , stress-strain relations of contact elements with
geotextile ground in a laboratory slide relations includes several phases : phase
nonlinear , 0 - 1 , increasing stress and deformation continued slow growth , the
period re- durable (hardened) - paragraphs 1-2 , to increased stress and
deformation increases , and the softening phase - paragraphs 2-3 , to reduce stress
and increase distortion. That relationship is shown in Figure 2.2
2.2.3 Some examples of determining mechanical properties of geotextiles [63]
2.3 Modeling the problem: FEM method in the Plaxis program , Pharse2 are
considered stress - related deformation of the geotextile pull is ideal elastoplastic
Mohr - Coulomb modeled (Figure 1.27) . That is the road slope - related stress as
linear distortion (this slope is characterized by elastic modulus geotextiles) . Then
, when the state of intensity , the geotextile will be destroyed immediately .
However, according to Robert M. Koerner model of the stress - deformation of
the geotextile is a non-linear path consists of several stages (Figure 2.1) . So
depending on the degree of deformation of the geotextile that the stress state will
be different . The following section will build computer model problem
embankment geotextile reinforcement by finite element method . In particular ,
the specific relationship stress - deformation of the geotextile is built in a
- 13 -
nonlinear model of Robert M. Koerner .
2.3.1 Some assumptions : Assumptions ground up n type, the background is one
or more natural soils , each soil layer uniformity . Soft geotextile reinforcement
placed in a soil layer or between two layers of soil . Minutes embankment slope
m1 , m2 , ... mn . View the soil is elastoplastic multi-layered system , each layer is
characterized by elastic modulus Es , Poisson's ratio ν and intensity characteristics
as unit cohesion c , friction angle . View reinforced elastic plastic material
resistant traction only , not pressurized , which is characterized by (Eg) elastic
modulus, hardness Eag and tensile strength Tmax.
2.3.2 Develop computational models stability problem of reinforcing soft
embankment according to the finite element method [23]
2.3.2.1 The basic equations of the theory of elasticity [1], [24]
According to Hooke's law , the relationship between the stress-strain response by
the formula:
1
1
1
2 1
2 1
2 1
x x y z
y y x z
z z x y
xy xy
yz yz
zx zx
E
E
E
E
E
E
(2.2)
2.3.2.3 The safety factor method decreased c - φ
The safety factor is calculated as the ratio of the actual resistance and the
minimum resistance as follows : (2.20) or
(2:21)
Among them : , and is the friction angle , unit cohesion and undrained cohesion of
the ground ; , and is the friction angle , cohesion and unit cohesion was not
impaired drainage of land background .
The decline in value is arctan ir
F
tan
S
: i
r
F
c
c
S
and ,,
u i
u r
F
s
s
S
(2.22)
Comment calculations by the finite element method taking into account many
factors characteristic of the ground and reinforcing materials such as elastic
modulus ground ; strength , elastic modulus , hardness reinforcement material .
Finite element method to find stability safety factor in the decline of the iterative
solution c - φ .
In the next chapter will focus on building research program algorithm and FEM
- 14 -
calculation method to calculate math embankment reinforced by geotextile . In
particular , the program will build computer algorithm analysis according to the
relational model stresses - deformation of the geotextile by Robert M.Koerner .
This model has not been built in algorithm programs around the world as :
Geo.Slope ; Plaxis or Pharse2 . This is close to the actual model of the kind of
work geotextile material which is related stress - deformation complex is given in
Robert M.Koerner Designing with Geosynthetics , 5th Edition [63] in 2005
previously in this document and in the 1986 version does not have version 1990
or have incomplete model stresses - deformation of materials geotextile.
CHAPTER 3 THE PROGRAM ALGORITHM AND SOFTWARE TO
ANALYSE GEOTEXTILE REINFORCEMENT EMBANKMENT BY FINITE
ELEMENT METHOD
3.1 Develop algorithms .
3.1.1 triangular plate element [18], [24] .
A flat block structure can be divided into three nodes triangular element . Each
displacement element has six degrees of freedom located at the nodes . The
buttons are numbered 1 , 2 , 3 in the opposite direction clockwise . The matrix
elements of the triangle is given by the general equation is rewritten as follows :
e
T T Tek B E B dV h B E B d Ah B E B
(3.2)
3.1.2 Element level parametric triangular plates [18] , [24] , [64] Coordinates any
point in the element coordinates interpolated from nodes: .
1
1
n
e
i
i
N
,
1
n
e
i i
i
x x N
, and
1
n
e
i i
i
y y N
( 3.4 ) displacements at any point in the
element displacements are interpolated according to the button :
1
n
e
x xi i
i
u u N
,
1
n
e
y yi i
i
u u N
(3.5)
The form function of triangular plate element 3 knots written as class parameter
1 1N ; 2 2N ; 3 3 1 21N (3.6)
The form function of triangular plate elements are nodes 6: 1 1 12 1N ;
2 2 22 1N ; 3 3 32 1N ; 4 1 24N ; 5 2 34N ; 6 3 14N
Stiffness matrix of triangular plate element written in the local coordinate system
is:
111
2 1
0 0
T TeK B E B dV h B E B J d d
( 3:13 )
The integral in Eq (3:13) can be done by using numerical integration are:
- 15 -
111
1 2 2 1 1 2
10 0
, 0.5 ,
n
i i i
i
f d d W f
(3:14)
3.1.3 Mohr - Coulomb model [ 33 ] , [ 54 ] , [ 59 ] , [ 64 ] Mohr - Coulomb model
is the first model included the effects of stress on the intensity of the ground . The
damage occurs when the stress states followed , normal stress on any plane of
material that satisfies the equation: tan c Mohr - Coulomb model can
be written as a function of stress components main (with the convention that
compressive stress is negative ) as follows (Chen and Mizuno, 1990) [54] :
1 3 1 3
1 1
sin cos
2 2
c (3:16)
3.1.4 Contact Element .
3.1.4.1 Contact element theory [26] , [48] Contact element is used to describe the
phenomenon of slip between two materials with large differences in hardness .
For example, the contact between geotextile and soil. Stress often limited slip
largest by plastic Mohr - Coulomb criteria. Contact elements is characterized by
normal stress and tangential stress, and these two components is related to the
normal deformation and shear strain as follows : .
0
0
n
s
k
k
(3:26) Where: 0
0
n
s
k
D
k
(327)
D is called the elastic matrix , and kn; ks is the normal stiffness and tangential
Stiffness matrix of contact elements :
1
1
T
K B D B t J d
(3.28)
Among them : [B] is a matrix relationship between deformation and displacement
; [D] is the elastic matrix as above , is the determinant of Jacobi matrix and t is the
thickness of the element .
Deformation of the element :
yt yb
xt xb
u u
t
u u
t
(3:33)
In that matrix deformation displacement relations in expression ( 3:28 ) takes the
following-form: 1 2 3 4
1 2 3 4
0 0 0 01
0 0 0 0
N N N N
B
N N N Nt
(3:35)
3.1.4.2 The nonlinear model of contact between the land and VDKT : stress-strain
relationship of the contact elements are often assumed to be ideal elastic plastic
Mohr - Coulomb . However, the actual behavior of the contact between the
geotextile and soil includes several stages as non-linear , re durable and soft goods
. Therefore , depending on the degree of contact between deformation and
geotextile - soil that stress exposure status is different in construction algorithm
- 16 -
calculates loop characteristic way relationship stress - deformation characterized
the relationship as shown in Figure 2.2 .
3.1.5 Geotextile Element .
3.1.5.1 Theory of Computation Element VDKT : VDKT element is modeled with
bar elements have the characteristic stiffness elastic is pulled .
FEM method , displacements at any point within the element can be approximated
by the first two buttons of the displacement element is :
1 1 2 2z x xu N u N u (3:36)
3.1.5.2 The nonlinear model of the geotextile element: Conduct of the nonlinear
geotextile element quite complex . Can model the nonlinear behavior of the line
segment , based on the degree of deformation geotextile that can determine the
corresponding stress . The relationship of this behavior is shown in Figure 2.1
3.1.6 Nonlinear Analysis [24] When analyzing structures under nonlinear material
models or nonlinear geometry , stiffness matrix or load vector depends on the
displacement . Typically , the problem is nonlinear solution based on the linear
approximation of . Currently, two methods are the most widely used Newton -
Raphson and Newton - Raphson improvement .
3.1.7 General block diagram program .
3.2 Construction program features :
3.2.1 Introduction to computer interface program hnh_ress V 1:00
Program Name : hnh_ress V 1:00 ( HNH_ Reinforced Embankment Stability
Software - Software calculates reinforced embankment stability ) .
Figure 3.12 Declaring relationship stress – Figure 3.13 Declare hardness (EAG) based
strain of the geotextile on stress-deformation path of geotextile
Fg 3.14 Trails approximately sliding surface Fg 3.15 Approximately the ellipse
running through the most extensive deformation and circle slide
3.2.2 Introduction hnh_ress V1.00 computer program
- 17 -
Hnh_ress program was built by the
finite element method calculation
problem geotextile reinforced
embankment . In this stress-strain
relationship of geotextile are Robert M
Koerner model - described working
closely with the local reality of the
ground fabric . Calculation of
geotextile jet curve behaves as follows :
Jet geotextile in the calculation of load
balancing at each step of the iterative
solution of finite element method is determined by the power curve behavior -
displacement . This curve is constructed from samples geotextile experimental
results ( as shown in the form 3.16 ) . In the first step to finding solutions is the
initial displacement of the system , the stiffness of geotextile to build the stiffness
matrix is the slope of the first straight line from the origin ( if the behavior is
approximately equal to the line segment ) or tangent of the curve ( if the road is
approximately equal to the curve behavior ) at the origin of Ki . After each step
solution , displacement of geotextile be determined Uj and thus determine the
actual jet geotextile was defined as Tj . Secant stiffness is also determined by the
expression : Ktj = Tj / Uj (3.43).
In addition, the program features hnh_ress V1.00 has also established algorithms
to draw lines connecting points shear strain has the largest shear strain in
embankment ( Display > Slip Surface stresses ) , and calculate the sliding surface
to approximately result in the most appropriate form of sliding surface ( Report >
slip line) . Methods and results slip surface approximation is presented in later
chapters . Details of the program are presented in appendix 3 .
Conclusion Chapter 3 : The program geotextile reinforced embankment
HNH_RESS V1.00 software programs are calculated by the finite element
method . This program calculates external functions , stability analysis problems ,
stress condition - deformation of the embankment with conventional finite
element as the other programs , there are also other functions using its specific
programs such as geotextile in reinforced embankment is declared and calculated
stress path relations - including multi-stage deformation of the model Robert M.
Koerner , so the hardness of geotextile also declared properties payment under
this model , the program also displays the results in graphical and text formats on
the dangerous sliding surface of the embankment , and shear strain draw lines
connecting points of maximum shear strain in the soil as well as the result of
calculating the approximate form of text sliding surface and concluded most
logical form of the slip surface . The program can also calculate any problems ,
not limited to changes in the input parameters ( geometrical shapes , materials ,
parameters ) and can edit , write additional computational needs , user research .
- 18 -
The content of research, empirical calculations using the computer program to the
problem of geotextile reinforced embankment load vehicles will be presented in
chapter 4 .
CHAPTER 4 EXPERIMENTAL CALCULATIONS FOR GEOTEXTILE
REINFORCED EMBANKMENT IN HIGHWAYS CONSTRUCTION
In this chapter, the case of soil embankment on soft soil and natural good, is
reinforced and non-reinforced geotextile is calculated according to the finite
element method which uses computer programs to hnh_ress V1.00 perform
analysis. Also some analysis, other studies are also presented in this chapter
contents.
4.1 The natural causeway on good ground
4.1.1 General Data calculated
Table 4.1 Characteristics of good soil embankment
Soil height up (m) ɣ (kN/m3) C (kN/m2) φ (0) E (kN/m2)
Embankment 6, 8, 10, 12 17.0 15 20 10000
Foudation - 17.0 20 25 50000
Table 4.2 Characteristics of geotextile under 1m width
Tmax (kN/m) E (kN/m
2
) Thickness (m) EA (kN)
24 486970 0,0033 1607
Table 4.3 Load vehicles
vehicles n G
(kN)
B
(m)
L
(m)
q
(kN/m
2
)
qv
(kN/m
2
)
1 2 130 10 4,2 6,2 15,5
2 2 300 10 6,6 14,3 35,7
3 2 800 10 4,5 35,5 88,75
4.1.2 Analysis of embankment stability: hardness and strength of geotextile
relations with each other through elastic deformation characteristic limits:
max
e
T
EA
(4.4)
4.1.2.1 High embankment 6m
Table 4.4 safety factor of slope
High embankment factor of slope Layer number Distance (m) Fs
6 1/1 0 0 1,20
So with 6m high embankment safety at a safety factor Fs = 1.2 so in this case
without geotextile reinforcement. In the case of larger embankment slope as 1/0,
75 and at ensuring the safety factor Fs = 1.2, the required geotextile
reinforcement.
4.1.2.2 High embankment 8m
1. The influence of the geotextile layer and the distance between the geotextile
- 19 -
layer to the safety factor of slope
Table 4.5 Effect of number of layers and the distance between the geotextile layer
High
embankment (m)
factor of slope
Layers
number
Distance (m) Fs
8 1/1 0 0 1,06
8 1/1 1 0 1,07
8 1/1 2 0,5 1,12
8 1/1 3 0,5 1,17
8 1/1 4 0,5 1,21
8 1/1 2 0,3 1,11
8 1/1 3 0,3 1,15
8 1/1 4 0,3 1,19
8 1/1 2 0,4 1,12
8 1/1 3 0,4 1,16
8 1/1 4 0,4 1,20
8 1/1 4 0,6 1,23
8 1/1 3 1,0 1,21
8 1/1 4 1,0 1,27
8 1/1 3 1,5 1,24
8 1/1 4 1,5 1,34
8 1/1 3 2,0 1,27
8 1/1 4 2,0 1,27
2. Determine the tension of geotextile work in embankment
Table 4.6 tension in the geotextile slope vandalized
3. Effect of slope coefficients to the safety factor of slope
Table 4.7 Effect of slope coefficients
High
embankment
(m)
factor of slope Layers number Distance (m) Fs
8 1/1 and 1/1,25 0 0 1,20
8 1/1 and 1/1,50 0 0 1,28
4. Effect of geotextile strength and number of geotextile layers to the safety factor
of slope
Table 4.8 Effect of strength and geotextile layers number
Tmax (kN/m) factor of slope Layers number Distance (m) Fs
12 1/1 7 0,4 1,20
14 1/1 7 0,4 1,22
16 1/1 6 0,4 1,21
- 20 -
18 1/1 5 0,4 1,19
20 1/1 5 0,4 1,20
22 1/1 5 0,4 1,22
24 1/1 4 0,4 1,20
26 1/1 4 0,4 1,20
28 1/1 4 0,4 1,21
5 . Where embankment roof TCVN 4054-05 [ 5 ] According to the standard
TCVN4054 - 05 8m embankment was covered with a slope coefficient of 1/1 , 75
kinds of land use and land cover as the background for the table 4.1 does not need
reinforced with geotextile .
4.1.2.3 The 10m and 12m high embankment : thesis in full for high embankment
10m , 12m with 5 cases affect the safety embankment stability as covered in
Section 8 meters high . The results of the calculations made in the table .
4.1.3 Building chart investigation geotextile used in high embankment
From the calculated results on high embankment 8m , 10m , 12m recorded in the
table 4.8 ; 4:12 ; 4:16 ; 4:17 table can construct the graph of the relationship
between the intensity and number of geotextile fabric geotechnical engineering .
The chart is used to lookup in the selection of geotextile preliminary design
calculations embankment height as follows :
Fg 4.9 The relationship between the
intensity and number of geotextile
layers slope coefficient of 1/1
Figure 4.10 The relationship between the
intensity and number of geotextile layers
slope coefficients 01/01/25
- 21 -
4.2 The embankment on soft soil
4.3 Identify types of slope slip under the sliding surface approximation method
4.3.1 Method approximately sliding surface (Figure 4.16)
4.3.2 Some examples of shear strain and route calculation is approximately
determined by the form of the slip surface hnh_ress program V1.00
Figure 4:23 approximated result slip surface 12m high embankment, slope 6m on
1/1, 5 and 6 m below the slope 1/1, 5, non-geotextile reinforcement
Some analytical results on record at 4:23 the following table:
Figure 4.11 The relationship between the intensity and number of geotextile
layers, the slope coefficient 1/1.5
Figure 4:15 Elipse shaped slip
embankment on soft soil
Figure 4.16 sliding surface approximation
method
- 22 -
Table 4:23 Some approximation results slip surfaces
Embankment type
Number,
distance
Fs
Approximately
sliding surface
ellipse Circle
Embankment 8m; 2m up and
6m down, slope 1/1
6 layer, d=0,4m;
T=16kN/m
1,21 39,628 47,128
Embankment 10m; 4m up 1/1
and 6m dowm, slope 1/1,5
3 layer, d=
0,4m;
T=16kN/m
1,22 86,758 120,602
Embankment 12m; 6m up 1/1
and 6m down slope 1/1,5
6 layer, d=
0,5m;
T=28kN/m
1,21 77,978 145,042
Embankment 12m; 6m up
1/1,25; 6m down slope 1/1,5
7 layer, d=
0,4m;
T=12kN/m
1,21 109,498 171,162
Embankment 8m; 2m up
1/1,75; 6m down slope 1/1,75
No geotextile
1,27 68,46 98,37
Embankment 10m; 4m up
1/1,25; 6m down slope 1/1,5
No geotextile
1,21 119,387 120,749
Embankment 12m; 6m up
1/1,5; 6m down slope 1/1,5
No geotextile
1,19 154,31 155,78
Commenting on the results embankment sliding surface slope :
The analytical results and calculate approximate sliding surface embankment
geotextile reinforcement according to the finite element method in the stability
program hnh_ress V1.00 ( Reinforced Embankment Stability Software ) in the
case of the earth embankment embankment on soft soil well and the results are
analyzed dangerous sliding surface slope embankment slip shaped ellipse , the
ellipse center is determined with the same high level causeway . These results
contribute to clarify the previous studies that slip is not circular slip [ 57 ] , [ 60 ] .
As a result of this ellipse shaped slip surfaces will contribute to the research in
order to improve stability calculation ground cover and ground cover
reinforcement .
In case of arc shape sliding surface is considered as a special case of the ellipse
shape sliding surface [ 25 ] .
4.4 Develop formulas tension ( Tmax ) of the geotextile layer in embankment
The analysis results show that all the geotextile layer will reach the tensile
strength of the geotextile . Thus the tension of geotextiles in ground cover was
- 23 -
determined from stable equilibrium .
4.4.1 geotextile tension in cylindrical sliding surface method
4.4.2 Develop a formula to calculate geotextile tension ( Tmax ) by finite element
method slip surface ellipse .
Because the results analyzed by finite element method can determine the slip
surface is unique . So after sliding surface ellipse results can be applied to
determine the tension in the geotextile layer from the stable equilibrium condition
2 2 2
1 1 1
1
,max
1
x x xn
i i t t n n x w
i x x x
i n
i
i
Px f r dx f r dx w r dx
T
y
(4.36)
4.5 Determining the influence of stiffness geotextile (EAg) to secure stability
coefficients embankment
4.5.1 Develop expressions identify stiffness geotextile (EAg) affect the safety
factor: the minimum value of the stiffness of the geotextile (EAg) as follows:
1 3
2
1 3
2
1 1
f RCf p p s
g
p f f
K c K SE
EA
K
(4.51)
The finite element analysis showed that the value taken by α = 0.024.
4.5.2 Influence of geotextile stiffness to stability safety factor
4.5.3 Relationship Chart influence of hardness (EAg), intensity (Tmax) geotextile
and soil Modulus background (Es) to secure stable
Figure 4:26 Map Tmax calculated tension
in the geotextile according slip ellipse
- 24 -
Figure 4:28 Relationship of stiffness geotextile (EAG) and embankment modulus (Es) to
secure stable (Fs = 1.2). Intensity Tmax = 12, 14, 16 kN / m
Figure 4.29 Relationships stiffness geotextile (EAG) and embankment modulus
(Es) to secure stable (Fs = 1.2). Intensity Tmax = 18, 20, 22 kN / m
Figure 4:30 Relationship of geotextile stiffness (EAg) and embankment modulus
(Es) to secure stable (Fs = 1.2). Intensity Tmax = 24, 26, 28 kN / m
4.6 Comparison of core capabilities and slid off the geotextile reinforcement
affect safety reinforced embankment stabilization: Total contact force between the
geotextile and great ground and compared with the intensity of large geotextile
most Tmax = 28 kN / m. Therefore geotextile intensity factors influencing new,
dominant factor of safety embankment stability. When the state of vandalism,
broken core capabilities far greater than the ability to slip reinforcement.
4.7 Comparison of results between hnh_ress and Plaxis: (Table 4.28); The results
of Plaxis don’t reflect the region's biggest shear strain as hnhress software.
- 25 -
4.8 Findings of chapter 4
1 . Stability analysis results according to the finite element method by hnh_ress
V1.00 software (geotextile reinforced embankment stability analysis) case of:
different heights embankment , different slopes coefficients , good soil or soft
soil, dangerous sliding surface result is the ellipse -shaped face. The center of the
ellipse is determined slip in a position to face the same level of high embankment
. The software program set algorithm to draw lines passing through the point of
distortion has the largest shear strain in embankment (Display > Slip suface
stresses), then use the sliding surface approximation method to test ellipse
equation and copper pointed out countless times in circular slip surfaces assuming
a circular slip surfaces are approximate. In case of arc shape sliding surface is
considered as a special case of the ellipse shape .
The results of this study contribute to further clarify the previous study at home
and abroad [57] , [60] that the slip surface is not circular slip surfaces .
2 . Construction tension expressions (Tmax) - (4.36) of the geotextile layers in
reinforced embankment. Where Tmax is caculated according to form of ellipse
slip surface from the research results, stability analysis by finite element method.
And tension value (Tmax) of the geotextile layer also has built-in hnh-ress
software (Report > Geotextile Forces). .
3 . The analytical results on the software, influence to safety factor of geotextile
reinforcement high embankment stabilization, include :
a. Effect of layers number and the distance between the geotextile layers to the
safety factor of slope embankment, height 6m , 8m , 10m , 12m . Table 4-4 ,
Table 4-5 , Table 4-9 , Table 4-13 .
b . Determine the tension Tmax geotextile layers in the embankment vandalized ,
high embankment 8m , 10m , 12m . Table 4-6 , Table 4-10 , Table 4-14 .
c . Effect of embankment slope coefficient (slope coefficients and standard TCVN
4054-05) safety factor to stabilize embankments 8m , 10m , 12m . Table 4-7 ,
Table 4-11 , Table 4-15 .
d . Effect of geotextile strength and geotextile layers to the safety factor 8m high
embankment stability, 10m, 12m. Table 4-8, Table 4-12, Table 4-16, Table 4-17
e . Effect of geotextile stiffness to stability safety factor 12m high embankment .
Table 4-24, Table 4-25, Table 4-26, Table 4-27 .
f . When the roadbed fill with soil types typically have physical properties to the
table as 4.1 or better and cover the Vietnam standard TCVN 4054-05 slope
coefficient of 1/1.75 achieved stable safety Fs > 1.2 should not need to use
geotextile reinforcement. Geotextile is used to fill the reinforced soil slope
coefficient over land or weaker .
g . Building the relationship charts between the intensity of geotextiles and
geotextile layers used to lookup the preliminary design embankment height 8m ,
10m , 12m, according to the different slope coefficients. Figure 4-9 , Figure 4-10 ,
- 26 -
Figure 4-11 .
4 . Building the stiffness of geotextile expressions EAg (4.51) affect the safety
factor of slope geotextile embankment reinforced. Draw the graph of the
relationship stiffness geotextile (EAg) , intensity (Tmax) and embankment
modulus (Es) to secure stable (Fs = 1.2) . Figure 4-28, Figure 4-29, Figure 4-30
5 . Comparison of core capabilities and slipped off the safety impact remains
stable geotextile reinforcement embankment .
6 . Comparison of analytical results on the computer program Plaxis and hnh_ress
CONCLUSIONS AND RECOMMENDATIONS
1.Conclusion
1 - Building a calculation model of the embankment reinforced by geotextile
based on stress - deformability relation of a nonlinear with multiple stages of
geotextile (Robert M Koener) is described closely to working reality of this
material.
2 - The program “hnh_ress V1.00” ( Reinforced Embankment Stability Software )
is built using FEM consistent with calculation standards in the world and Vietnam
. The feature of pull - behavior relationship of geotextile under a elastic and
plastic curve is fully described in the program (Define > Stress - Strain Curve >
Geotextile). Hence, the stiffness of geotextile (EAg), characterized by elastic
modulus (E), is also the slope of this curve.
3 – In the thesis, the author proposes the dangerous sliding surface of reinforced
embankment slope which is in the shape of ellipse. The center of the ellipse is
determined at the position that is as high as embankment surface. By using error
approximation method of sliding surface, testing results of sliding surface in
ellipse shape are the most reasonable. The sliding surface in an arc shape is
considered as a special case of the sliding surface ellipse shape.
4 - From the ellipse shape sliding surface results, analytical expressions and
computer program software (hnh_ress V1.00), (Report > Geotextile Forces) are
developed to calculate the tension Tmax of geotextile layers in reinforced
embankment.
5 – The stiffness of geotextile has affected reinforced embankment stability
safety. The thesis formed the expressions to determine the minimum stiffness of
geotextile (EAg) and charts of the relationship between stiffness of geotextile
(EAg) and elastic mudulus of soil and other factors that affect the embankment
stability safety.
6 - The results were analyzed by the hnh_ress V1.00 software. The safety effects
of high embankment stabilization reinforced by geotextile include:
i . The number of layers and the distance between the geotextile layers can affect
the embankment stability safety factor. With the same number of geotextile layers
, if we increase the distance between the layers to lay the layers of geotextile
along the depth of embankment (from the embankment surface down), the factor
of safety will increase significantly.
- 27 -
ii . Tension values Tmax at every point of the geotextile layers in embankment
(the slope reaches the state of vandalism) are always identified.
iii . The factor of slope influences the safety factor of embankment stability . The
soil selected by table 4.1 and slope factor by Vietnam standard at TCVN 4054-05
does not require the reinforcement of geotextile . Geotextile is used for
strengthening the embankment that is weaker or has greater slope coefficients.
iv . Geotextile intensity (Tmax) and the number of geotextile layers affect the
stability safety factor . The greater geotextile intensity is, the higher the stability
safety factor becomes. The diagrams showing the relations between intensity and
number of geotextile layers that affect the stability safety factor can be used in the
preliminary design of reinforced high embankment.
v . The stiffness of geotextile (EAg) affects the safety factor of embankment
slope. When geotextile is reinforced in the embankment, and the soil has the
elastic modulus Es, we should choose geotextile type with (EAg) minimum
stiffness defined in expression (4.51) to achieve the safety, stability and saving of
material.
2.Recommendations
The author proposes the research findings and proposals to be considered using in
calculation and study about the embankment reinforced by geotextile. The
author’s calculation method should be futher researched and compared to other
calculation methods to find out errors and draw out rules . The method of
calculation may continue to be studied in case of building the embankment
reinforced by geogrids.

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