This document discusses several applications of slope stability analysis using the finite element method. It begins by introducing slope stability analysis and some traditional limit equilibrium methods. It then discusses two main advantages of the finite element method: it does not require assumptions about the failure surface shape or location, and it can model complex geometries and soil properties. The document presents several examples of applying the finite element method to analyze slope stability under various conditions, including accounting for drainage, brittle soil behavior, and engineering interventions. It compares results to traditional methods and notes the additional data on stresses, strains, and progressive failure that finite element analysis can provide.
THE various rocks are classified as according to rock mass classification system as it is used for used for various engineering design and stability analysis of underground structures.
Rock Mass Classification and also a brief description of Rock Mass Rating (RMR), Rock Structure Rating (RSR), Q valves and New Austrian Tunneling method(NATM)
THE various rocks are classified as according to rock mass classification system as it is used for used for various engineering design and stability analysis of underground structures.
Rock Mass Classification and also a brief description of Rock Mass Rating (RMR), Rock Structure Rating (RSR), Q valves and New Austrian Tunneling method(NATM)
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
TERZAGHI’S BEARING CAPACITY THEORY
DERIVATION OF EQUATION TERZAGHI’S BEARING CAPACITY THEORY
TERZAGHI’S BEARING CAPACITY FACTORS
Download vedio link
https://youtu.be/imy61hU0_yo
Tunnelling is a serious engineering project.
In addition to large investment cost, the challenges related to long and deep tunnels are considerable.
Important aspects which needs to be considered are related to the construction works, geology, environment and operation. his module highlights all these aspects.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
openings design in underground mines, different approaches, kirscha formulae for circular opening, plastic xzone effect on stability of opening, radial and tangential stresses distribution
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
TERZAGHI’S BEARING CAPACITY THEORY
DERIVATION OF EQUATION TERZAGHI’S BEARING CAPACITY THEORY
TERZAGHI’S BEARING CAPACITY FACTORS
Download vedio link
https://youtu.be/imy61hU0_yo
Tunnelling is a serious engineering project.
In addition to large investment cost, the challenges related to long and deep tunnels are considerable.
Important aspects which needs to be considered are related to the construction works, geology, environment and operation. his module highlights all these aspects.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
openings design in underground mines, different approaches, kirscha formulae for circular opening, plastic xzone effect on stability of opening, radial and tangential stresses distribution
Optimization and improvement in stability of counterfort retaining wall with ...eSAT Journals
Abstract Reinforced concrete retaining walls are meant to support more height of earth mass. Cantilever retaining wall is constructed up to height of 6 m and above that it becomes uneconomical. To support more height of earth mass advancement is done in cantilever retaining wall by adding relief shelf in it. Due to provision of relief shelf the soil pressure on the retaining wall is reduced resulting in improvement in stability of retaining wall. Cantilever retaining wall with one relief shelf is economical up to height of 10 m above that counterfort retaining wall with relief shelf is useful. In this paper analysis and design of counterfort retaining wall with one relief shelf is done for various positions of relief shelf. These results are studied to get minimum earth pressure, more stability and minimum moment in each component of retaining wall. The optimization of counterfort retaining wall is done to get minimum size of retaining wall. Due to this optimization extra formation width is available in hilly areas and excessive cutting is avoided thereby construction cost reduces. Keywords: Counterfort Retaining wall, relief shelf, earth pressure, Factor of safety, overturning, sliding, optimization
6.0 pendirian dan dasar kerajaan malaysia berhubung isu antarabangsasejarahkkb
6.0 pendirian dan dasar kerajaan malaysia berhubung isu antarabangsa
Untuk maklumat yang lebih banyak kunjungi blog kami http://sjhk3023enzanpismpjun2016.blogspot.my/
“For civil engineering”Soil friction angle,stress,Advantages of using LRFD me...Tapon Chakrabarti
Soil friction angle,friction angle for different soils according to USCS,Correlation between SPT-N value, friction angle, and relative density,Number of Cement bags required for a specific cement concrete ratios,What is stress and how does it develop?Advantages of using LRFD method and Comparison of ASD and LRFD,Disadvantages of Using LRFD method.
Finite element method in solving civil engineering problemSaniul Mahi
The applications of Finite Element Method in solving Civil Engineering problem and the merits of using a finite element procedure over the other methods.
Model Study of Slope Stability in Open Pit by Numerical Modeling Using the Fi...CrimsonPublishersAMMS
Model Study of Slope Stability in Open Pit by Numerical Modeling Using the Finite Element Method by Saadoun Abderrazak in Aspects in Mining & Mineral Science
Fixity depth of offshore piles in elastoplastic soft clay under dynamic loadeSAT Journals
Abstract
This work represents study of dynamic behavior of offshore piles embedded in elastoplastic soft clay, and estimating the fixity depth of pile. ABAQUS finite element program which used to simulate the problem. The soil was modeled in two case elastic state model and elastoplastic state model represented by cam-clay model, three dimension element used to represent the interaction between pile and soil, and laboratory tests used to getting the real properties of clayey soil and to descried interface. The results obtained developed two empirical equations used to calculate depth of pile fixity for pile embedded in elastic and elastoplastic soil respectively. Also, show the depth of pile fixity is increase about (40 %) due to change soil model from elastic to plastic, when pile embedded in elastoplastic soil its dependent on soil strength, interface properties and pile rigidity. The pile head displacement is increase about 90 % while the bending moment is decease 10 % at pile head.
Fixity depth of offshore piles in elastoplastic soft clay under dynamic loadeSAT Journals
Abstract
This work represents study of dynamic behavior of offshore piles embedded in elastoplastic soft clay, and estimating the fixity depth of pile. ABAQUS finite element program which used to simulate the problem. The soil was modeled in two case elastic state model and elastoplastic state model represented by cam-clay model, three dimension element used to represent the interaction between pile and soil, and laboratory tests used to getting the real properties of clayey soil and to descried interface. The results obtained developed two empirical equations used to calculate depth of pile fixity for pile embedded in elastic and elastoplastic soil respectively. Also, show the depth of pile fixity is increase about (40 %) due to change soil model from elastic to plastic, when pile embedded in elastoplastic soil its dependent on soil strength, interface properties and pile rigidity. The pile head displacement is increase about 90 % while the bending moment is decease 10 % at pile head.
1Introduction
The purpose of this research work is to study the fatigue related behavior of weld toe
and weld root geometrical parameters in fillet welds based on the effective notch stress
approach.
The fatigue tests of welded structures under fluctuating loads shows that the crack
initiation and propagation until the final failure is carried out mostly on the weld toe and
weld root. Since the geometrical effect on stress distribution over a part plays a
meaningful role in respect to increasing the stress concentration factor value and
consequently the risk of failure, in this research the geometrical variables of welding
which can be recommended in some case of welding procedures such as weld toe
waving and weld root penetration percentage is studied. The fillet weld models under
special case of loading and constraint analyzed by three-dimensional linear static
analyses of finite element method to define the maximum principal stress distribution in
the modeled cases. The fatigue effect of analysis added to model by utilizing the
effective notch stress approach, which models the sharp lines in weld toe, and weld root
by determined rounded radius of 1 mm for steel material to avoid the geometrical
singularity of numerical analysis and take into consideration the fatigue notch factor.
The models of this study focus on the variation of stress concentration factor due to
weld toe waving geometrical effects defining by two variables of waving width and
waving radius in two separate set of models which the weld flank angle has been
changed. This leads an understanding to the benefit of varying stress concentration
factor on the weld toe between waving tips and waving depths so that the significant
decrease of this factor in waving depths can stop the rate of arbitrary initiated crack
propagation.
That is a crack, which initiated in a susceptible location such as wave tips could be
controlled by the waving depths, which have a significantly lower stress.
Meanwhile the study continued to analyze the distribution of stress in fillet weld root in
respect of the percentage of weld penetration into the base material by the same fatigue
9
method and numerical analyzing tools. The result of this part depicts the usability of
analyzing models type applying the effective notch stress approach and can be utilized
to define an optimized penetration percentage in the weld root of fillet-welded joints
2Fatiguebasefracture
Material properties, relate to the quality control of materials and initial material
selection by a designer and employing only a look at the stress-strain analysis will cause
the valuable information is lost. There are factors other than exceeding the yield stress
and causing plastic deformation, which will affect structures. Fracture is concerned with
the initiation and propagation of a crack until the load can no longer be held by the
structure. It is well known that most structures will c.
Experimental Determination of Fracture Energy by RILEM Methodtheijes
This paper deals with investigation of fracture energy (GF) of concrete. The study involves experimental determination of fracture energy (GF) by testing three point bend concrete beams of same size but varying notch to depth ratios. RILEM fracture energy (GF) and Stress Intensity factor values is determined
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...msejjournal
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...MSEJjournal1
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...msejjournal
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...msejjournal
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...msejjournal
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
Stability analysis of open pit slope by finite difference methodeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
To Experimental Study of Comparison and Development of Design for Rigid Pavem...Agriculture Journal IJOEAR
Abstract— The development of design have been discussed adopted various types methods use. The Hadi and Arfiadi Method presents a formulation for the optimum rigid road pavement design by genetic algorithm, a new method. The Westergaard’s Method determines the stresses in the rigid concrete slab and also the pressure-deformation curve which depend upon the relative stiffness of the slab and the subgrade. Razouki and Al-Muhana also developed stress charts similar to Westergaard’s method. The paper reveals that the effects on the maximum bending tensile stress are quite significant due to the modulus of subgrade reaction, modulus of elasticity of concrete and slab The Maharaj and Gill method have performed axisymmetric finite element analysis by varying parameters, the thickness of pavement, pressure and elastic modulus of subgrade. The advantage of this method is that four types of design charts have been presented which other methods have note done. First type of design chart has been plotted between thickness of pavement and nodal deflections for various pressures for a particular elastic modulus of soil. Second type of design chart has been plotted between thickness of pavement and element stress for various pressures for a particular elastic modulus of soil. The third type of design chart has been plotted between thickness of pavement and nodal deflections for various elastic moduli of subgrade for a particular pressure. Each of the design charts has three parameters. For two known parameters, the third parameter can be obtained.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Introduction to AI for Nonprofits with Tapp Network
Slope stability
1. 1
TITLE: SLOPE STABILITY (FINITE SLOPES)
1.0 INTRODUCTION
Slope stability analysis is an important area in geotechnical engineering. Most textbooks on soil mechanics include
several methods of slope stability analysis. Before the calculation of slope stability in these methods, some
assumptions, for example, the side forces and their directions, have to be given out artificially in order to build the
equations of equilibrium. With the development of cheaper personal computer, finite element method has been
increasingly used in slope stability analysis. The advantage of a finite element approach in the analysis of slope
stability problems over traditional limit equilibrium methods is that no assumption needs to be made in advance
about the shape or location of the failure surface, slice side forces and their directions. Various calculations carried
out illustrate perfectly benefits that can be gained from modeling the behavior by the finite elements method. The
method can be extended to account for seepage induced failures, brittle soil behaviors, random field soil properties,
and engineering interventions such as geo-textiles, soil nailing, drains and retaining walls. Generally, there are two
approaches to analyze slope stability using finite element method. One approach is to increase the gravity load and
the second approach is to reduce the strength characteristics of the soil mass.
2.0 APPLICATION SLOPE STABILITY EVALUATION FINITE ELEMENT
METHODS
The various limit equilibrium methods are based on the arbitrary choosing a series of slip surfaces and of defining
that which gives the minimal value of the safety factor. Nowadays, we attend an intensive use of numerical analysis
methods giving access to the constraints and deformations within the formations constituting the subsoil. For that
purpose, it is necessary to know the behavior law of the considered formations; then, the volume of ground is
divided into simple geometric elements, each element being subjected to the action of the close elements.
The calculation will consist in determining stress fields and displacements compatible with the mechanic equations
and the behavior law adopted.
Many works were done in the finite elements field and we could cite works of ZIENKIEWICZ [5] or DHATT [6].
The finite element method makes it possible to calculate stresses and deformations state in a rock mass, subjected to
its self weight with the assumption of the behavior law adopted. In our calculations, a model with internal friction
without work hardening (perfect elastoplastic Model: Mohr-Coulomb) is used, which corresponds to the basic
assumptions of the analytical methods. In our work, we will use the method of reduction of soil resistance
properties, known as the “c-φ reduction” method. The c-φ method is based on the reduction of the shear strength (c)
and the tangent of the friction angle (tanφ) of the soil. The parameters are reduced in steps until the soil mass fails.
Plaxis uses a factor to relate the reduction in the parameters during the calculation at any stage with the input
parameters according to the following equation:
Where Msf is the reduction factor at any stage during calculations, tanφinput and cinput are the input parameters of
the soil, tanφ reduced and creduced are the reduced parameters calculated during the analysis [9]. The characteristics
of the interfaces, if there is, are reduced in same time. On the other hand, the characteristics of the elements of
structure like the plates and the anchoring are not influenced by Phi-C reduction. The total multiplier Msf is used to
define the value of the soil strength parameters at a given stage in the analysis at the failure stage of the slope, the
total safety factor is given as follows:
2. 2
The safety factor found using the method of c-φ reduction according to the criterion of Mohr Coulomb remains
comparable with those found by the analytical methods in both cases with or without presence of water. The
difference noted is the fact that for the analytical methods ,safety factors are assumed constants along the failure
surface. Moreover, finite element methods that provide access to stresses and strains within the soil, offer the
possibility of a detailed operating calculations as curves: displacements, the evolution of the safety factor according
to displacement , the localization of deformations and plastic zones. The taking into account of the behavior law in
the codes with the finite elements makes it possible to better determine the stress and strain state in various points.
The total displacements figure highlights the limit between the zone where there is no displacement (zero value) and
the zones where displacements occur (non null values) We note the circular form of this limit which points out the
slip surface adopted by the analytical methods. These displacements are important at the slope and the highest value
is in mid-slope. The horizontal component of displacements exceeds the vertical’s. The rupture curve identification
in Plaxis is based on the localization of the deformations on the slope we once again, find the circular form of slip
surfaces.
3.0 APPLICATION BY 3D ELASTO-PLASTIC FINITE-ELEMENT METHOD
This application works for the stabilities of the abutments of Houhe gravity-arch dam using elasto-plastic finite
element analyses and block theory. The gravity-arch dam is constructed by expanding the existing gravity dam. Due
to the complex geologic conditions, the natural abutments do not meet the stability requirements. Engineering
measures including concrete plugs and concrete backfills are thus designed to increase the safety of both abutments.
The effectiveness of these measures is evaluated in this study. The paper performs three-dimensional elasto-plastic
finite element analyses to obtain the stress and deformation characteristics of the abutments and the dam. The
stabilities of sliding blocks on the abutments are then evaluated by incorporating the results of finite-element method
analyses. It is found that the use of concrete plugs significantly increases the factors of safety against sliding for both
abutments. Concrete backfills not only provide the sliding resistance, but also are effective in reducing the
deformation of the abutments and improve the stress conditions along the base of the dam. The dam works under
satisfactory conditions as the results of applying these engineering measures. It may work if it is applied in the slope
stability process. A major advantage of FEM lies in its flexibility in modeling complex geometries and geologic
conditions.
Current FEM codes can simulate a variety of material behaviors as well as incorporate the influence of construction
procedures. Construction of the global finite element model of abutments and dam can be performed with ease using
advanced preprocessing modules. The analyses provide more realistic distribution of thrust forces acting on the
abutments for analyses of their stability. For approaches such as the limit equilibrium analyses or block theory thrust
forces are generally assumed to be constant and are estimated by simplified beam or arch models. This can be quite
different from real situations. Analyses by FEM also provide comprehensive information on the stress and
deformation characteristics of both the dam and the abutments. By incorporating the appropriate plastic material
models, FEM is theoretically capable of automatically identifying the location and places of the failure surface and
indicating the extent of progressive failure. Griffiths and Lane, for example, applied iterative FEM for automatic
analyses of slope stability problems by assuming that failure occurs when the results are non-convergent after a
specific number of iterations. However, identifying failure planes by FEM alone is computational extensive,
especially when there involves complex materials behaviors and complex potential sliding wedges. Besides, there
are no universally accepted failure criteria to implement for the FEM analysis. FEM model and analyses are
performed to provide more accurate stress distributions acting on the surfaces of those blocks. This results in a more
accurate evaluation of the stability conditions of the abutments. In addition to this, FEM analyses also provide
important information such as stress and deformation characteristics.
3. 3
4.0 APLICATION FINITE ELEMNT ANALYSIS FOR EVALUATION OF SLOPE
STABILITYINDUCED BY CUTTING
This paper concerned an evaluation of stability condition of slope. A slope stability induced by cutting was
evaluated by a finite element analysis. The finite element analysis employed a constitutive model in which non-
associated strain hardening-softening elasto-plastic material was assumed. In-site investigation was done by an
inclinometer for the boreholes. For defining the soil stratum, a new data processing system was applied in this paper
to generate a soil ground model, using many boring data. Soil samples were taken and subjected to geotechnical
laboratory tests. A triaxial compression test (CU ) was performed to determine the shear strength. The numerical
analysis did not consider the pore pressure, because no ground water was appeared in that area. The deformation
obtained by the numerical analysis was close to the results of inclinometer of borehole observed by in-site
investigation. The finite element analysis was able to predict the estimation of the slope stability induced by cutting.
4.1 LABORATORY TEST
Undisturbed sample lay around the sliding surface was taken from the cutting slope surface. The physical properties
of the sample are summarized in Table 1. The grain size distribution curve is shown in Fig.8. In order to investigate
the relationship between peak strength of the material, triaxial compression test (CU ) was conducted. The internal
friction angle and cohesion were 25 degrees and 12.5kN/m2, respectively. Yatabe (2004) reported that a residual
friction angle of clay of crystalline schist of Sambagawa metamorphic belt was about 15 degrees.
5.0 APPLICATION OF THE FINITE ELEMENT METHOD TO SLOPE STABILITY
This document outlines the capabilities of the finite element method in the analysis of slope stability problems. The
manuscript describes the constitutive laws of material behaviour such as the Mohr-Coulomb failure criterion, and
material properties input parameters, required to adequately model slope failure. It also discusses advanced topics
such as strength reduction techniques and the definition of slope collapse. Several slopes are analyzed with the finite
element method, and the results compared with outcomes from various limit equilibrium methods. Conclusions for
the practical use of the finite element method are also given.
Slope stability analysis is an important area in geotechnical engineering. Most textbooks on soil mechanics include
several methods of slope stability analysis. A detailed review of equilibrium methods of slope stability analysis is
presented by Duncan (Duncan, 1996). These methods include the ordinary method of slices, Bishop’s modified
method, force equilibrium methods, Janbu’s generalized procedure of Slices, Morgenstern and Price’s method and
Spencer’s method. These methods, in general, require the soil mass to be divided into slices. The directions of the
forces acting on each slice in the slope are assumed. This assumption is a key role in distinguishing one limit
equilibrium method from another. Limit equilibrium methods require a continuous surface passes the soil mass. This
surface is essential in calculating the minimum factor of safety (FOS) against sliding or shear failure. Before the
calculation of slope stability in these methods, some assumptions, for example, the side forces and their directions,
have to be given out artificially in order to build the equations of equilibrium. With the development of cheaper
personal computer, finite element method has been increasingly used in slope stability analysis. The advantage of a
finite element approach in the analysis of slope stability problems over traditional limit equilibrium methods is that
no assumption needs to be made in advance about the shape or location of the failure surface, slice side forces and
their directions. The method can be applied with complex slope configurations and soil deposits in two or three
dimensions to model virtually all types of mechanisms. General soil material models that include Mohr-Coulomb
and numerous others can be employed. The equilibrium stresses, strains, and the associated shear strengths in the
soil mass can be computed very accurately. The critical failure mechanism developed can be extremely general and
need not be simple circular or logarithmic spiral arcs. The method can be extended to account for seepage induced
failures, brittle soil behaviors, random field soil properties, and engineering interventions such as geo-textiles, soil
nailing, drains and retaining walls (Swan et al, 1999). This method can give information about the deformations at
working stress levels and is able to monitor progressive failure including overall shear failure (Griffiths, 1999).
4. 4
6.0 APPLICATION FINITE ELEMENT REALIBALITY ANALYSIS OF SLOPE
STABILITY
The method of nonlinear finite element reliability analysis (FERA) of slope stability using the technique of slip
surface stress analysis (SSA) is studied. The limit state function that can consider the direction of slip surface is
given, and the formulations of FERA based on incremental tangent stiffness method and modified Aitken
accelerating algorithm are developed. The limited step length iteration method (LSLIM) is adopted to calculate the
reliability index. The nonlinear FERA code using the SSA technique is developed and the main flow chart is
illustrated. Numerical examples are used to demonstrate the efficiency and robustness of this method. It is found that
the accelerating convergence algorithm proposed in this study proves to be very efficient for it can reduce the
iteration number greatly, and LSLIM is also efficient for it can assure the convergence of the iteration of the
reliability index.
In structural reliability analysis using the FORM, the most popular iterative searching algorithm of the design point
is perhaps the so-called first order second moment method (FOSM), which was originally developed by Hasofer and
Lind (1974), and later extended to non-normal random variables by Rackwitz and Fiessler (1978). However, it has
been demonstrated that if the limit state function is highly nonlinear, the iterative computation of the design point
and reliability index will probably be divergent in the FOSM algorithm. Since limit state function of the FERA of
slope stability is usually a highly nonlinear implicit function of soil parameters, it is necessary to study some new
iterative algorithms to assure the successful running of the nonlinear FERA code. In this study, a new iterative
algorithm— LSLIM, is presented to carry out the reliability analysis. LSLIM is another searching algorithm of
FORM. The iterative procedure in standard normal space has been listed by Gong (2003). Since the FERA for the
calculation of stress increment is carried out in the original space, the iteration of design point and reliability index
should also be performed in the original space. When basic variables are independent normally distributed variables,
7.0 APPLICATION STRENGHT REDUCTION AND STEP-LOADING FINITE
ELEMENT APPROACHES IN GEOTECHNICAL ENGINEERING
The finite element limit analysis method has the advantages of both numerical and traditional limit equilibrium
techniques and it is particularly useful to geotechnical engineering. This method has been developed in China,
following well-accepted international procedures, to enhance understanding of stability issues in a number of
geotechnical settings. Great advancements have been made in basic theory, the improvement of computational
precision, and the broadening of practical applications. These applications are evidence of the design improvements
and benefits made possible in geotechnical engineering by finite element modeling. As the stability analysis is
related to the analysis of force and strength instead of displacement, a perfect elastorplastic constitutive model is
sufficient for accurate finite element calculations without the consideration of hardening and softening rocks or
soils. The yield criterion is very important in the finite element limit analysis method as it has great effects on the
computational results. When the unit weight of the soil γ = 0 , the ultimate bearing capacity of rigid and smooth
strip foundations has closed form solutions in Prandtl. A finite element limit analysis model can be used to analyze
rigid and smooth strip foundations. The finite element model The load-displacement curve of the central point of the
foundation obtained from the finite element limit analysis method . It can be interpreted that the displacement of the
central point of the foundation increases as the load increases, and increases suddenly and sharply when the
foundation fails.
8.0 APPLICATION OF SLOPE STABILITY ANALYSIS BY FINITE ELEMENTS
The majority of slope stability analyses performed in practice still use traditional limit equilibrium approaches
involving methods of slices that have remained essentially unchanged for decades. This was not the outcome
envisaged when Whitman and Bailey (1967) set criteria for the then emerging methods to become readily accessible
to all engineers. The finite element method represents a powerful alternative approach for slope stability analysis
which is accurate, versatile and requires fewer a priori assumptions, especially regarding the failure mechanism.
5. 5
Slope failure in the finite element model occurs “naturally” through the zones in which the shear strength of the soil
is insufficient to resist the shear stresses. This paper describes several examples of finite element slope stability
analysis with comparison against other solution methods, including the influence of layering and s free surface on
slope and dam stability. Graphical output is included to illustrate deformations and mechanisms of failure. It is
argued that the finite element method of slope stability analysis is more powerful alternative to traditional limit
equilibrium methods and its widespread use should now be standard in geotechnical practice. Slope stability
represents an area of geotechnical analysis in which a nonlinear finite element approach offers real benefits over
existing methods.
Duncan’s review of finite element analysis of slopes concentrated mainly on deformation rather than stability
analysis of slopes, however attention was drawn to some important early papers in which elasto-plastic soil models
were used to assess stability. Smith and Hobbs (19740) reported results and obtained reasonable agreement with
Taylor’s (1937) charts. Zienkiewicz et al (1975) considered a c’.ø’slope and obtained good agreement with slip
circle solutions. Subsequent use of the finite element method in slope stability analysis has added further confidence
in the method.
9.0 CASE STUDY: RAILWAY SLOPE
The case study relates to a railway slope in Moroccan Prérif, between Tangier city and Tangier-Med port. The
geological formations are consisted of sandstone and marls alternations (Figure 2). The important rains caused a
landslide on a ravine which damaged locally the railway.
Stratigraphic column of sedimentary formations constituting the embankment.
6. 6
Finite element mesh of slope profile.
10.0 CONCLUSION
The analysis and design of failing slopes and highways embankment requires an in-depth understanding of the
failure mechanism in order to choose the right slope stability analysis method. The present study made it possible to
compare on a real geometrical model the computation results of the safety factor (defining the state of the slope
stability compared to the limit equilibrium) by various methods: limit equi-librium and finite elements methods. The
behavior law stress-strain which is lacking to the limit equilibrium meth- ods is integrated into the finite elements
methods. The results obtained with slices methods and FEM are similar. However, the results obtained using the
finite ele- ments are nearest those obtained by Bishop’s method than Fellenius’ method. If we compare the sliding
surfaces obtained with the slices methods with representations of the total displace- ment increments obtained with
FEM, it is possible to see that the failure mechanism was very well simulated by FEM. In the analyzed case it is
possible to see the circu- lar shape of the sliding surfaces in the graphics of the total displacements increments.The
determination of the safety factor is insufficient to identify problems of slope stability, the various calcula- tions
performed illustrate perfectly the benefits that can be gained from modeling the behavior by FEM: 1) the calculation
of displacements obtained by FEM allows to estimate the actual settlement and optimize ways of re-inforcement; 2)
the prediction of failure mechanism; 3) the use of the results of field tests to better approximate the real behaviour of
structures.
7. 7
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