A presentation Soumaya Addou a Master student in Tohoku University made about Risk Assessment in Geotechnical Engineering during meeting of Risk commission, that is part of the Japanese Geotechnical Society - Tohoku branch.
Rock mechanics for engineering geology part 3Jyoti Khatiwada
Hydraulic fracturing is a method to estimate initial stresses by pressurizing a sealed borehole section until it fractures. The fracture orientation indicates the minimum stress direction. This provides the orientation of the maximum horizontal stress for vertical boreholes. The breakdown pressure estimates the minimum principal stress, while the reopening pressure estimates the maximum principal stress. This allows estimating the 2D stress field in the horizontal plane, making it suitable for deep measurements where no underground access exists. However, it requires space for equipment and is best suited to vertical boreholes.
SHEAR STRENGTH THEORY
the shear strength of any material is the load per unit area or pressure that it can withstand before undergoing shearing failure.
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.
This document discusses correlations between various geotechnical properties and the void ratio of soils. It defines void ratio as the ratio of volume of voids to volume of solids. Typical void ratio ranges are provided for different soil types. Relationships are presented between void ratio and properties such as unit weight, moisture content, maximum and minimum void ratios, relative density, shear modulus, hydraulic conductivity, preconsolidation pressure, and compression index. Graphs illustrate how properties such as shear strength and hydraulic conductivity vary with changes in void ratio.
This contains methods of exploration in rock. How the rock samplers are taken. Quality of rock samples and its reporting. Along with the laboratory tests conducting on these rock samples.
This document provides a summary of Lecture 2 on the Mohr-Coulomb failure criteria in geotechnical engineering. It introduces the relationship between normal and shear stresses on a failure plane using the Mohr-Coulomb equation. It then discusses the graphical representation of this relationship using Mohr's circle, showing how the major and minor principal stresses and maximum shear stress can be determined. It demonstrates how the Mohr circle expands under increasing loads until it contacts the failure envelope, indicating failure. The criteria is shown for both total and effective stresses, accounting for pore water pressure. Steps to derive the failure condition directly from the geometry of the Mohr circle are also presented.
Risk Assessment in Geotechnical Engineering .pptxSamirsinh Parmar
Risk assessment in Geotechnical Engg., prediction of results and behavior, field testing, load test set-up, number of tests and observations, methods of design, prediction, and analysis, risk and reliability in geotechnical engg.
This slide will help you to determine the immediate settlement for flexible foundation i.e. isolate footing and rigid foundation i.e. matt or raft foundation. To be more clear about the topic a numerical problem with the solution is given.
Rock mechanics for engineering geology part 3Jyoti Khatiwada
Hydraulic fracturing is a method to estimate initial stresses by pressurizing a sealed borehole section until it fractures. The fracture orientation indicates the minimum stress direction. This provides the orientation of the maximum horizontal stress for vertical boreholes. The breakdown pressure estimates the minimum principal stress, while the reopening pressure estimates the maximum principal stress. This allows estimating the 2D stress field in the horizontal plane, making it suitable for deep measurements where no underground access exists. However, it requires space for equipment and is best suited to vertical boreholes.
SHEAR STRENGTH THEORY
the shear strength of any material is the load per unit area or pressure that it can withstand before undergoing shearing failure.
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.
This document discusses correlations between various geotechnical properties and the void ratio of soils. It defines void ratio as the ratio of volume of voids to volume of solids. Typical void ratio ranges are provided for different soil types. Relationships are presented between void ratio and properties such as unit weight, moisture content, maximum and minimum void ratios, relative density, shear modulus, hydraulic conductivity, preconsolidation pressure, and compression index. Graphs illustrate how properties such as shear strength and hydraulic conductivity vary with changes in void ratio.
This contains methods of exploration in rock. How the rock samplers are taken. Quality of rock samples and its reporting. Along with the laboratory tests conducting on these rock samples.
This document provides a summary of Lecture 2 on the Mohr-Coulomb failure criteria in geotechnical engineering. It introduces the relationship between normal and shear stresses on a failure plane using the Mohr-Coulomb equation. It then discusses the graphical representation of this relationship using Mohr's circle, showing how the major and minor principal stresses and maximum shear stress can be determined. It demonstrates how the Mohr circle expands under increasing loads until it contacts the failure envelope, indicating failure. The criteria is shown for both total and effective stresses, accounting for pore water pressure. Steps to derive the failure condition directly from the geometry of the Mohr circle are also presented.
Risk Assessment in Geotechnical Engineering .pptxSamirsinh Parmar
Risk assessment in Geotechnical Engg., prediction of results and behavior, field testing, load test set-up, number of tests and observations, methods of design, prediction, and analysis, risk and reliability in geotechnical engg.
This slide will help you to determine the immediate settlement for flexible foundation i.e. isolate footing and rigid foundation i.e. matt or raft foundation. To be more clear about the topic a numerical problem with the solution is given.
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)
This document defines various terms related to geotechnical engineering and soil mechanics. It defines porosity as the ratio of void volume to total volume of a soil sample. It defines density index as a ratio used to characterize the relative density of a soil deposit. It lists various types of transported soils such as aeolian, alluvial, glacial, lacustrine, and marine deposits. It also defines terms such as void ratio, specific gravity, dry mass density, saturated density, permeability, seepage velocity, discharge velocity, and capillary tension.
The document discusses shear strength of discontinuities in rock masses. It introduces concepts like shear strength of planar surfaces, shear strength of rough surfaces, Barton's estimate of shear strength which relates shear strength to joint roughness coefficient (JRC) and joint compressive strength (JCS). It discusses estimating JRC and JCS in the field and how these parameters are influenced by scale. It also summarizes the shear strength of filled discontinuities and the influence of water pressure on shear strength.
Use of DMT in Geotechnical Design with Emphasis on Liquefaction AssessmentAli Rehman
This Presentation consists of brief introduction about Dilatometer Test, and basic correlations of DMT with various soil properties. Also It covers the assessment of Liquefaction potential of soil by DMT, including a case history of Chi-Chi Earthquake, Taiwan 1999.
I Hope it will be beneficial.
Best Regards:
Engr. Muhammad Ali Rehman
This document discusses soil classification systems. It describes the purpose of classifying soils and two commonly used systems: the Unified Soil Classification System (USCS) and the American Association of State Highway and Transportation Officials System (AASHTO). The USCS divides soils into major groups based on grain size and plasticity characteristics. The AASHTO system focuses on classifying soils for road construction using groups determined by liquid limit, plasticity index, and grain size distribution. Procedures and examples are provided for classifying soils in both systems.
This document discusses the shear strength of soils. It begins with an abstract describing shear strength and factors that influence it, such as particle interactions and stresses. It then outlines different methods to measure shear strength in the laboratory and field, including direct shear tests, triaxial shear tests, and vane shear tests. The Mohr-Coulomb failure criteria is also explained as a way to analyze shear strength based on normal and shear stresses. Key parameters that govern shear strength are identified as cohesion and the friction angle.
This document provides an overview of the course "Foundation Engineering" including:
- The course contents which covers topics like shallow foundations, deep foundations, retaining structures, and soil improvements across 10 chapters.
- The examination and grading system with 80 marks for final exam, 20 marks for internal assessment, and 25 marks for practical.
- An introduction to foundation engineering including different types of foundations, factors influencing foundation choice, and the general requirements for shallow foundations.
The document discusses two common soil classification systems: the Unified Soil Classification System (USCS) and the American Association of State Highway and Transportation Officials system (AASHTO). The USCS classifies soils into four major categories based on grain size, plasticity, and compressibility. The AASHTO system classifies soils into eight groups based on particle size distribution, liquid limit, and plasticity index for use in road construction. Both systems provide a standardized way to categorize soils based on simple tests to understand their engineering properties and behavior.
Rock mass classification or rock mass rating of rock materials in civil and m...Ulimella Siva Sankar
1. Rock mass classification systems provide a methodology to characterize rock mass strength using simple measurements and allow geologic data to be converted into quantitative engineering parameters.
2. The most widely used systems are RQD, RMR, and Q-system which evaluate factors like rock quality, joint conditions, and groundwater to determine an overall classification.
3. Classification systems estimate the rock mass strength and deformability, which can then be input into numerical models to design underground mine openings and support requirements.
The document provides an overview of geotechnical engineering and the typical components and process involved in a geotechnical engineering report and project. It discusses the four main components of field exploration, laboratory testing, findings and recommendations, and additional studies. It then goes into more detail about specific sections that would be included in a geotechnical report such as site conditions, field exploration methods, laboratory testing, engineering recommendations, earthwork recommendations, and construction observation services.
This document discusses rock mechanics and provides information on key concepts such as the classification of rocks, stress, strain, factors affecting rock behavior like temperature and pressure, different rock textures, brittle behavior, shear failure, rock strength, challenges in rock mechanics like spalling and wedge failure, and causes of such challenges like insufficient knowledge. It covers topics like sedimentary, metamorphic and igneous rocks, definitions of stress and strain, relationships between pressure, depth and temperature, and how internal and external conditions influence rock properties.
The document discusses various rock mass classification systems used in rock engineering. It introduces Terzaghi, Stini, and Lauffer's early classification systems from the 1940s-1950s. It then focuses on more commonly used modern systems like the Rock Quality Designation (RQD) developed by Deere, the Rock Structure Rating (RSR) developed by Wickham et al, and the Rock Mass Rating (RMR) system. The document provides details on how to calculate and apply these different rock mass classification ratings which are used to evaluate rock mass quality and aid in rock engineering design.
In-situ testing methods like the Standard Penetration Test (SPT) are used when it is difficult to obtain undisturbed soil samples. The SPT involves driving a split spoon sampler into the soil using a hammer and measuring the blow count. Corrections are made to the blow count for factors like hammer efficiency, borehole diameter, and overburden pressure. Empirical correlations with soil properties like density, shear strength, and type are then used to inform foundation design.
1. The document provides an introduction to soil mechanics including definitions of soil, soil mechanics, and the three phases of soil - solids, water, and air.
2. Soil can be classified as residual soils which form in place from weathering or transported soils which are deposited by forces like water, wind, or glaciers.
3. Understanding the properties of soil is important for civil engineers to effectively use soil in construction projects and address problems related to shear failure, settlement, seepage, and dynamic loading.
Bearing capacity of shallow foundations by abhishek sharma ABHISHEK SHARMA
elements you should know about bearing capacity of shallow foundations are included in it. various indian standards are also used. Bearing capacity theories by various researchers are also included. numericals from GATE CE and ESE CE are also included.
The document discusses various methods for soil exploration including test trenches, auger borings, rotary drilling, and geophysical methods. It also discusses soil sampling techniques for obtaining both disturbed and undisturbed samples. Common stages in a site investigation are described including desk studies, field investigations, laboratory testing, and reporting. The purpose of soil investigations is to determine subsurface soil conditions to influence foundation design and construction.
This document presents information about static cone penetration tests. It discusses the principles and applications of cone penetration testing. The principles section explains that a metal cone is penetrated into the subsurface at a constant rate, and the cone tip resistance, sleeve friction, and friction ratio are recorded to determine soil stratigraphy and properties. The applications section notes that data is used to estimate parameters like undrained shear strength and stress history, and that results can be directly applied to soil profiling and engineering designs.
Stress distribution in soils can be caused by self-weight of soil layers and surface loads. Stresses increase with depth due to self-weight and decrease radially from applied surface loads. Boussinesq developed equations to determine stresses below concentrated, line, strip and rectangular loads by representing them as point loads and using influence factors. Newmark proposed charts to simplify determining stresses below uniformly loaded areas of different shapes. Approximate methods like the 2:1 method also exist but are less accurate.
Development, Optimization, and Analysis of Cellular Automaton Algorithms to S...IRJET Journal
This document summarizes research on using cellular automaton algorithms to solve stochastic partial differential equations (SPDEs). It proposes a finite-difference method to approximate an SPDE modeling a random walk with angular diffusion. A Monte Carlo algorithm is also developed for comparison. Analysis finds a moderate correlation between the two methods, suggesting the finite-difference approach is reasonably accurate. It also identifies an inverse-square relationship between variables, linking to a foundational stochastic analysis concept. The research concludes the finite-difference method shows promise for approximating SPDEs while considering boundary conditions.
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
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)
This document defines various terms related to geotechnical engineering and soil mechanics. It defines porosity as the ratio of void volume to total volume of a soil sample. It defines density index as a ratio used to characterize the relative density of a soil deposit. It lists various types of transported soils such as aeolian, alluvial, glacial, lacustrine, and marine deposits. It also defines terms such as void ratio, specific gravity, dry mass density, saturated density, permeability, seepage velocity, discharge velocity, and capillary tension.
The document discusses shear strength of discontinuities in rock masses. It introduces concepts like shear strength of planar surfaces, shear strength of rough surfaces, Barton's estimate of shear strength which relates shear strength to joint roughness coefficient (JRC) and joint compressive strength (JCS). It discusses estimating JRC and JCS in the field and how these parameters are influenced by scale. It also summarizes the shear strength of filled discontinuities and the influence of water pressure on shear strength.
Use of DMT in Geotechnical Design with Emphasis on Liquefaction AssessmentAli Rehman
This Presentation consists of brief introduction about Dilatometer Test, and basic correlations of DMT with various soil properties. Also It covers the assessment of Liquefaction potential of soil by DMT, including a case history of Chi-Chi Earthquake, Taiwan 1999.
I Hope it will be beneficial.
Best Regards:
Engr. Muhammad Ali Rehman
This document discusses soil classification systems. It describes the purpose of classifying soils and two commonly used systems: the Unified Soil Classification System (USCS) and the American Association of State Highway and Transportation Officials System (AASHTO). The USCS divides soils into major groups based on grain size and plasticity characteristics. The AASHTO system focuses on classifying soils for road construction using groups determined by liquid limit, plasticity index, and grain size distribution. Procedures and examples are provided for classifying soils in both systems.
This document discusses the shear strength of soils. It begins with an abstract describing shear strength and factors that influence it, such as particle interactions and stresses. It then outlines different methods to measure shear strength in the laboratory and field, including direct shear tests, triaxial shear tests, and vane shear tests. The Mohr-Coulomb failure criteria is also explained as a way to analyze shear strength based on normal and shear stresses. Key parameters that govern shear strength are identified as cohesion and the friction angle.
This document provides an overview of the course "Foundation Engineering" including:
- The course contents which covers topics like shallow foundations, deep foundations, retaining structures, and soil improvements across 10 chapters.
- The examination and grading system with 80 marks for final exam, 20 marks for internal assessment, and 25 marks for practical.
- An introduction to foundation engineering including different types of foundations, factors influencing foundation choice, and the general requirements for shallow foundations.
The document discusses two common soil classification systems: the Unified Soil Classification System (USCS) and the American Association of State Highway and Transportation Officials system (AASHTO). The USCS classifies soils into four major categories based on grain size, plasticity, and compressibility. The AASHTO system classifies soils into eight groups based on particle size distribution, liquid limit, and plasticity index for use in road construction. Both systems provide a standardized way to categorize soils based on simple tests to understand their engineering properties and behavior.
Rock mass classification or rock mass rating of rock materials in civil and m...Ulimella Siva Sankar
1. Rock mass classification systems provide a methodology to characterize rock mass strength using simple measurements and allow geologic data to be converted into quantitative engineering parameters.
2. The most widely used systems are RQD, RMR, and Q-system which evaluate factors like rock quality, joint conditions, and groundwater to determine an overall classification.
3. Classification systems estimate the rock mass strength and deformability, which can then be input into numerical models to design underground mine openings and support requirements.
The document provides an overview of geotechnical engineering and the typical components and process involved in a geotechnical engineering report and project. It discusses the four main components of field exploration, laboratory testing, findings and recommendations, and additional studies. It then goes into more detail about specific sections that would be included in a geotechnical report such as site conditions, field exploration methods, laboratory testing, engineering recommendations, earthwork recommendations, and construction observation services.
This document discusses rock mechanics and provides information on key concepts such as the classification of rocks, stress, strain, factors affecting rock behavior like temperature and pressure, different rock textures, brittle behavior, shear failure, rock strength, challenges in rock mechanics like spalling and wedge failure, and causes of such challenges like insufficient knowledge. It covers topics like sedimentary, metamorphic and igneous rocks, definitions of stress and strain, relationships between pressure, depth and temperature, and how internal and external conditions influence rock properties.
The document discusses various rock mass classification systems used in rock engineering. It introduces Terzaghi, Stini, and Lauffer's early classification systems from the 1940s-1950s. It then focuses on more commonly used modern systems like the Rock Quality Designation (RQD) developed by Deere, the Rock Structure Rating (RSR) developed by Wickham et al, and the Rock Mass Rating (RMR) system. The document provides details on how to calculate and apply these different rock mass classification ratings which are used to evaluate rock mass quality and aid in rock engineering design.
In-situ testing methods like the Standard Penetration Test (SPT) are used when it is difficult to obtain undisturbed soil samples. The SPT involves driving a split spoon sampler into the soil using a hammer and measuring the blow count. Corrections are made to the blow count for factors like hammer efficiency, borehole diameter, and overburden pressure. Empirical correlations with soil properties like density, shear strength, and type are then used to inform foundation design.
1. The document provides an introduction to soil mechanics including definitions of soil, soil mechanics, and the three phases of soil - solids, water, and air.
2. Soil can be classified as residual soils which form in place from weathering or transported soils which are deposited by forces like water, wind, or glaciers.
3. Understanding the properties of soil is important for civil engineers to effectively use soil in construction projects and address problems related to shear failure, settlement, seepage, and dynamic loading.
Bearing capacity of shallow foundations by abhishek sharma ABHISHEK SHARMA
elements you should know about bearing capacity of shallow foundations are included in it. various indian standards are also used. Bearing capacity theories by various researchers are also included. numericals from GATE CE and ESE CE are also included.
The document discusses various methods for soil exploration including test trenches, auger borings, rotary drilling, and geophysical methods. It also discusses soil sampling techniques for obtaining both disturbed and undisturbed samples. Common stages in a site investigation are described including desk studies, field investigations, laboratory testing, and reporting. The purpose of soil investigations is to determine subsurface soil conditions to influence foundation design and construction.
This document presents information about static cone penetration tests. It discusses the principles and applications of cone penetration testing. The principles section explains that a metal cone is penetrated into the subsurface at a constant rate, and the cone tip resistance, sleeve friction, and friction ratio are recorded to determine soil stratigraphy and properties. The applications section notes that data is used to estimate parameters like undrained shear strength and stress history, and that results can be directly applied to soil profiling and engineering designs.
Stress distribution in soils can be caused by self-weight of soil layers and surface loads. Stresses increase with depth due to self-weight and decrease radially from applied surface loads. Boussinesq developed equations to determine stresses below concentrated, line, strip and rectangular loads by representing them as point loads and using influence factors. Newmark proposed charts to simplify determining stresses below uniformly loaded areas of different shapes. Approximate methods like the 2:1 method also exist but are less accurate.
Development, Optimization, and Analysis of Cellular Automaton Algorithms to S...IRJET Journal
This document summarizes research on using cellular automaton algorithms to solve stochastic partial differential equations (SPDEs). It proposes a finite-difference method to approximate an SPDE modeling a random walk with angular diffusion. A Monte Carlo algorithm is also developed for comparison. Analysis finds a moderate correlation between the two methods, suggesting the finite-difference approach is reasonably accurate. It also identifies an inverse-square relationship between variables, linking to a foundational stochastic analysis concept. The research concludes the finite-difference method shows promise for approximating SPDEs while considering boundary conditions.
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
The document discusses an automated method for classifying earth surfaces to assess landslide susceptibility using topographic data. It examines different geomorphometric classification approaches and parameters to distinguish landscape types related to landslides. The study tests supervised and unsupervised classification methods, compares results, and develops an integrated method using slope gradient, convexity and texture that identifies terrain features correlated with past landslide events. The automated integrated classification approach provides a useful tool for landslide susceptibility analysis at a territorial scale.
Autocorrelation_kriging_techniques for Hydrologysmartwateriitrk
This document provides an introduction to spatial autocorrelation and kriging. It discusses Tobler's first law of geography, which states that nearby locations tend to be more related than distant locations. Spatial autocorrelation refers to the correlation of a variable with itself over space as a function of distance. The document outlines common tests for spatial autocorrelation like Moran's I and variograms. It explains how kriging uses a variogram model and nearest neighbor distances to interpolate values at unsampled locations. Kriging aims to provide the best linear unbiased predictions and estimates of uncertainty. The history of variograms, kriging, and their development by mathematicians like Matheron and geologist Krige are
Introduction to back analysis;
Definition- Back analysis;
Historical Review- back analysis;
Factors affecting back analysis;
Steps to perform back analysis;
Solved numerical for demonstration of back analysis;
Practical Problems and limitations of back analysis;
Advantages of back analysis
How to make back analysis accurate?;
Concluding remarks;
Selected References; back analysis procedure;
Back analysis in slope stability problems
The document discusses response surface methodology (RSM), which uses statistical and mathematical techniques to model and analyze problems with responses influenced by several variables. RSM is used to optimize responses by exploring the relationships between variables and responses through designed experiments and polynomial mathematical models. Key aspects covered include first and second-order polynomial models, experimental designs like factorial and central composite designs, and techniques like steepest ascent to navigate response surfaces. Examples demonstrate how RSM can be applied to optimize process variables and responses.
Decision analysis applied to rock tunnel exploration 1978 baecherJunaida Wally
This document discusses applying decision analysis to planning rock tunnel exploration. Decision analysis provides a framework for making decisions under uncertainty. It involves defining alternatives, outcomes, variables, and relationships between them. Probabilities are assigned to uncertain variables. Expected costs are calculated for different exploration and construction strategies to determine the optimal approach. A decision tree is used to relate variables like geology, exploration method/cost, construction method/cost, and outcomes like total expected cost. Sensitivity analysis varies the variables to evaluate how robust the optimal strategies are. The framework provides a systematic way to determine if and where exploration is beneficial for reducing uncertainty and expected construction costs for a rock tunnel project.
Probabilistic slope stability analysis as a tool to optimise a geotechnical s...Mahdi_zoorabadi
This paper was presented in APSSIM 2016 (First Asia Pacific Slope Stability in Mining Conference). Probabilistic slope stability can be used to optimise the geotechnical studies.
Reliability and Fuzzy Logic Concepts as Applied to Slope Stability Analysis –...IJERA Editor
Considerable uncertainty exist with regard to stability of slopes due to several factors and recognition of these uncertainties has made designees to introduce factor of safety. Several studies, during recent years on analytical methods using soil properties have improved understanding the several uncertainties. The reliability analysis of slopes can be used to represent uncertainty in mathematical models, which can be assumed to follow the characteristic of random uncertainty. The distribution uncertain variable, which is unknown, makes its estimation difficult. Hence, the concepts of fuzzy set theory appear to be quite reliable when limited information is available. This paper attempts to review the slope stability problem and deals with the intricacies of the concept of reliability and fuzzy logic as applied to stability analysis of slope. It has been suggested that the FOSM algorithm provides a general agreement among the different slope stability solutions.
Reliability and Fuzzy Logic Concepts as Applied to Slope Stability Analysis –...IJERA Editor
Considerable uncertainty exist with regard to stability of slopes due to several factors and recognition of these uncertainties has made designees to introduce factor of safety. Several studies, during recent years on analytical methods using soil properties have improved understanding the several uncertainties. The reliability analysis of slopes can be used to represent uncertainty in mathematical models, which can be assumed to follow the characteristic of random uncertainty. The distribution uncertain variable, which is unknown, makes its estimation difficult. Hence, the concepts of fuzzy set theory appear to be quite reliable when limited information is available. This paper attempts to review the slope stability problem and deals with the intricacies of the concept of reliability and fuzzy logic as applied to stability analysis of slope. It has been suggested that the FOSM algorithm provides a general agreement among the different slope stability solutions.
Uncertainty modelling and limit state reliability of tunnel supports under se...eSAT Journals
Abstract
Underground openings and excavations are increasingly being used for civilian and strategic purposes all over the world. Recent
earthquakes and resulting damage have brought into focus and raised the awareness for aseismic design and construction. In
addition, underground tunnels, particularly, have distinct seismic behaviour due to their complete enclosure in soil or rock and their
significant length. Therefore, seismic response of tunnel support systems warrant closer attention. The geological settings in which
they are placed are often difficult to describe due to limited site investigation data and vast spatial variability. Therefore, the
parameters which govern the design are many and their variabilities cannot be ignored. A solution to this issue is reliability based
analysis and design. These real conditions of variability can only be addressed through a reliability based design. The problem
addressed here is one of reliability-based analysis of the support system of an underground tunnel in soil. Issues like the description of
the interaction between the tunnel lining and the surrounding medium, the type of limit state that would be appropriate, the nonavailability
of a closed form performance function and the advantages of response surface method [RSM] are looked into. Both static
and seismic environment with random variability in the material properties are studied here. Support seismic response is studied in
terms of thrust, moment and shear forces in the lining. Interactive analysis using finite element method [FEM], combined with RSM
and Hasofer-Lind reliability concept to assess the performance of the tunnel support, has proven useful under real field situations.
Index Terms: Tunnel, Reliability, Random, Seismic
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.
BLASTING FRAGMENTATION MANAGEMENT USING COMPLEXITY ANALYSIS David Wilson
This document discusses using complexity analysis to manage rock blasting fragmentation. It analyzes complexity levels and robustness of three blasting models - the empirical model used by a mine, an analytical model from literature, and field data from the mine. The analytical model has higher complexity and lower robustness. Complexity analysis can identify critical variables, compare models, and help design more robust blasting with less uncertainty given geological conditions. Future work aims to select the most robust model and identify the most critical fragmentation parameters through further complexity analysis.
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.
Modeling of Granular Mixing using Markov Chains and the Discrete Element Methodjodoua
The document presents a method for modeling granular mixing using Markov chains and the discrete element method (DEM). It motivates the use of Markov chains to efficiently simulate granular mixing as an alternative to computationally expensive DEM simulations. The theory and definitions of Markov chains and operators are provided. The method is applied to simulate mixing in a cylindrical drum, and the effects of the number of states, time step, and learning time are investigated. Properties of the resulting operator like the invariant distribution and mixing rates are analyzed to characterize the mixing dynamics.
This document summarizes a new methodology for probabilistic seismic hazard analysis (PSHA) that addresses common problems in the field. The methodology incorporates paleoearthquake data, accounts for uncertainties in earthquake parameters, relaxes assumptions about seismicity models, and does not require delineating source zones. It estimates hazard through peak ground acceleration and spectral acceleration curves. The methodology was applied to produce seismic hazard maps for South and Sub-Saharan Africa showing 10% probabilities of exceedance in 50 years. Computer codes implementing the methodology are available from the author.
On Projected Newton Barrier Methods for Linear Programming and an Equivalence...SSA KPI
This document describes projected Newton barrier methods for solving linear programming problems. It begins by reviewing classical barrier function methods for nonlinear programming which apply a logarithmic transformation to inequality constraints. For linear programs, the transformed problem can be solved using a "projected Newton barrier" method. This method is shown to be equivalent to Karmarkar's projective method for a particular choice of the barrier parameter. Details are then given of a specific barrier algorithm and its implementation, along with numerical results on test problems. Implications for future developments in linear programming are discussed.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Applications of layered theory for the analysis of flexible pavementseSAT Journals
base layers, exhibit nonlinear behavior under repeated wheel loads. The
properties of the granular materials play a significant role in the performance of these pavements. Therefore, accurate modelling of
the granular layers is essential in the evaluation of critical pavement responses under the application of loads, these materials exhibit
stress dependent characteristics. Thus, consideration of non-linearity in these layers is necessary for accurate estimation of the
pavement responses of a flexible pavement structure. The pavement responses are computed using Kenlayer computer program
developed by Huang. Using the Kenlayer program, this paper examines the effect of nonlinearity in granular on critical pavement
responses by conducting parametric analysis. The results indicate that the consideration of nonlinearity yields 23.13% reduction in
tensile strains at the bottom of bituminous layers and 0.76% increase in compressive strains on the top of the sub grade layers and
same surface deflections compared to the value obtained using linear elastic analysis. This indicates that nonlinear analysis is more
realistic and accurate.
Keywords: Granular layers, Kenlayer, Nonlinearity, Pavement responses.
Similar to Risk Assessment in Geotechnical Engineering (20)
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
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International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
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CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
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The CBC machine is a common diagnostic tool used by doctors to measure a patient's red blood cell count, white blood cell count and platelet count. The machine uses a small sample of the patient's blood, which is then placed into special tubes and analyzed. The results of the analysis are then displayed on a screen for the doctor to review. The CBC machine is an important tool for diagnosing various conditions, such as anemia, infection and leukemia. It can also help to monitor a patient's response to treatment.
3. 3
Outline
I. Introduction of concepts
1) Uncertainty and risk in Geotechnical engineering
2) Probability Theory and Random Variables
3) Random Process Models
4) Definition of Risk
II. Uncertainty in Geotechnical Context
1) Site Characterization
2) Soil Variability
3) Spatial Variability within homogeneous Deposits
III.Reliability analysis Methods
1) Introduction: Steps and Approximations
2) Event Tree Analysis
3) First Order Second Moment Method (FOSM)
4) First Order Reliability Method (FORM)
5) Monte Carle Simulation
4. I. Introduction of concepts
Most of the early pioneers in Geotechnical Engineering were aware of the limitations of
purely rational, deductive approaches to the uncertain conditions that prevail in the
Geological world. Their later writings are full of warnings not to take the results of
laboratory tests and analytical calculations too literally
Recently, there has been a trend to apply the results of reliability theory to Geotechnical
engineering. The offshore and nuclear power are at the forefront for the use of these
approaches.
The variability inherent in soils and rocks suggests that geotechnical systems are highly
amenable to a statistical interpretation.
① Uncertainty and risk in Geotechnical engineering
4
6. I. Introduction of concepts
The mathematical theory of probability deals
with:
- Experiments “random process generating
specific and a priori unknown results”
- Their outcomes “sample space”
In Geotechnical Engineering, we mostly deal with probability as a density function and
Probability is found by integrating the probability mass over a finite region.
𝑃 𝐴 =
𝐴
𝑓𝑋 𝑥 𝑑𝑥
It is convenient sometimes to represent probability by their moments
𝐸 𝑥 𝑛
=
−∞
+∞
𝑥 𝑛
𝑓𝑋 𝑥 𝑑𝑥
The most common is the second central moment , called the variance
𝜎2
= 𝐸 𝑥 − 𝐸(𝑥) 2
𝐸 𝑥 is the arithmetic average called the mean.
② Probability Theory and Random Variables
6
7. I. Introduction of concepts
For an uncertain quantity , various forms for the Probability Functions have been suggested :
- Probability Mass Function (pmf) :
Binomial (success and failures) : 𝐹 𝑥 𝑛 = 𝑥
𝑛
𝑝 𝑥
(1 − 𝑝) 𝑛−𝑥
Poisson distribution : 𝑓 𝑥 λ =
λ 𝑥 𝑒−λ
𝑥!
….etc
- Probability Distribution Function (pdf):
Exponential distribution : 𝑓 𝑠 λ = λ𝑒−λ𝑠
The Normal Probability Distribution
….etc
http://slideplayer.com/slide/5710846/
③ Random Process Models
7
8. I. Introduction of concepts
The determinant of risk is the combination of uncertain event and the adverse
consequence
𝑅𝑖𝑠𝑘 = (𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦, 𝐶𝑜𝑛𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒)
④ Definition of Risk
Many approaches have been adopted to describe
risks.
They consist on plotting the exceedance
probability of risks against their associated
consequences.
Chart showing average annuals risks posed by a variety of
traditional civil facilities and other large structures .
8
9. II. Uncertainty in Geotechnical Context
① Site Characterization
Concerns information about the geometry and material properties of local geological formations,
mainly :
The geological nature of deposits and formations
Location, thickness and material composition
Engineering properties of formations
Ground water level and its fluctuations
The random process models
used are usually models of
“Spatial variation”
Probability is in the model not the ground 9
10. II. Uncertainty in Geotechnical Context
② Soil Variability
The variability of elementary soil properties concerns various categories of physical properties :
- Index and classification properties : bulk properties, classification properties, …etc
- Consolidation properties: 𝐶𝑐, 𝐶𝑟, 𝑐 𝑣…etc
- Permeability: hydraulic conductivity
- Strength Properties: CPT, SPT parameters, effective friction angle, …etc
Variability in soil properties is inextricably related to the particular site
and to a specific regional geology
Parameter Soil Recorded COV (%) Source
𝐶𝑐, 𝐶𝑟
𝑐 𝑣
Bangkok Clay
Various
Dredge Spoils
Gulf of Mexico Clay
Ariake Clay
Singapore Clay
Bangkok clay
20
25-50
35
25-28
10
17
16
Zhu et al. (2001)
Lumb (1974)
Thevanayagam et al (1996)
Baecher and Ladd (1997)
Tanaka et al. (2001)
Tanaka et al. (2001)
Tanaka et al. (2001)
Values of the variability in consolidation parameter, expressed as Coefficient of Variation
10
11. II. Uncertainty in Geotechnical Context
3) Spatial Variability within homogeneous Deposits
Describing the variation of soil properties in space requires additional tools
In order to characterize the spatial variation of a soil deposit, a large number of tests is required
Use of a model 𝑧(𝑥) = 𝑡 𝑥 + 𝑢(𝑥)
Soil property
at location x
Trend at x
deterministic
residual variation at x
“random variable”
Estimate the trend by fitting well-
defined mathematical functions to
data points
Use of methods like “Regression
analysis”
Fitting the same data with a line versus a curve changes the residual variance11
12. II. Uncertainty in Geotechnical Context
3) Spatial Variability within homogeneous Deposits
The spatial association of residuals off the trend is expressed by a mathematical function that
describes the correlation of two residuals separated by a distance 𝛿, this description is called the
autocorrelation function.
𝑅 𝑧(𝛿) =
𝐶𝑜𝑣(𝑢(𝑥𝑖), 𝑢(𝑥𝑗))
𝑉𝑎𝑟 𝑢(𝑥)
𝑉𝑎𝑟 𝑢(𝑥) : The variance of the residuals across the site
Autocorrelation of rock fracture density in a copper porphyry deposit
12
13. III. Reliability analysis Methods
① Introduction: Steps and Approximations
Reliability analysis deals with the relation between the loads “Q” a system carry, and its ability to
carry those loads “R”.
The goal of the analysis is to estimate the probability of failure 𝒑 𝒇, the steps are :
1. Establish an analytical model
2. Estimate statistical descriptions of the parameters
3. Calculate statistical moments of the performance function
4. Calculate the reliability index
5. Compute the probability of failure
I. First Order Second Moment Method (FOSM)
II. First Order Reliability Method (FORM)
III. Monte Carle Simulation
…..etc 13
14. III. Reliability analysis Methods
② Event Tree Analysis
A graphical representation of the many chains of events that might result from some initiating event.
Its objective is to provide the Probability of system failure.
Example of event tree of the probability of embankment breach of a dam due to liquefaction
The event tree
begins with an
accident initiating
event : Earthquake,
flood,….etc
A joint probability is obtained by multiplying the conditional event probabilities along the chain
14
15. III. Reliability analysis Methods
③ First Order Second Moment Method (FOSM)
It uses the first terms of a Taylor series expansion of the performance function “F” to estimate the
expected value and variance of the performance function. When the variables are uncorrelated
Example : The James Bay Dikes
“Reliability Applied to Slope Stability Analysis” John T. Christian; Charles C. Ladd, and Gregory B. Baecher, 1994.
Uncertainties
in soil
properties
Scatter
- Spatial Variability
- noise
𝛼𝑐 𝑢 𝐹𝑉 = 𝑐 𝑢 + 𝑐 𝑒
Systematic
error
- Limited number of tests
- Bias :
Ex : The factor α is a
function of the plasticity
index. It is taken 𝛼 = 1
𝑐 𝑒 is a random experimental error.
Should not be included in stability analysis
to be found by “Autocovariance function” 15
16. Identify all
the variables
Determine the best
estimate of each
variable (The mean)
and the best estimate
of the factor of Safety
Estimate the
uncertainty
(the
variance)
Calculate the
partial
derivatives
∆𝐹
∆𝑋𝑖
Obtain
𝑉𝑎𝑟 𝐹
Calculate 𝛽
then
Probability
of failure 𝑝 𝑓
III. Reliability analysis Methods
③ First Order Second Moment Method (FOSM)
FOSM Calculations
The variance 𝜎 𝐹
2
= 𝑖=1
𝑛
𝑗=1
𝑛 𝜕𝐹
𝜕𝑋 𝑖
𝜕𝐹
𝜕𝑋 𝑗
𝜌 𝑋 𝑖 𝑋 𝑗
𝜎 𝑋𝑖
𝜎 𝑋 𝑗
Reliability index 𝛽 =
𝐸 𝐹 −1
𝜎 𝐹
• Factor of Safety
• Soil Profile and fill Properties
• Shear strength of foundation
clay
𝑝 𝑓 were computed on the assumption that F is normally distributed
16
The selected 𝑝 𝑓 was selected smaller
for higher embankments
Based on the revised target probabilities,
one obtains the consistent, desired
factors of safety.
17. III. Reliability analysis Methods
④ First Order Reliability Method (FORM)
This method, developed by Hasofer and Lind (1974) addressed some concerns about some
assumptions involved in the FOSM method.
For each variable 𝑥𝑖, we define 𝑥′
𝑖 having a mean value of zero and unit standard deviation.
𝑥′
𝑖 =
𝑥𝑖 − 𝜇 𝑥𝑖
𝜎𝑥𝑖
17
Limit state function
𝑔 𝑥′
1, 𝑥′
2, … , 𝑥′
𝑛 = 0
Safe and unsafe regions (Du. 2005)
Reliability index is interpreted geometrically as
the distance between the point defined by the
expected values of the variables and the closest
point on the failure criterion.
The probability of failure is the volume of the
hill on the failure side.
18. III. Reliability analysis Methods
④ First Order Reliability Method (FORM)
Lagrange’s multipliers is used to
find the minimum distance as :
𝛽 = 𝑑 𝑚𝑖𝑛 = −
𝑥′∗
𝑖
𝜕𝑔
𝜕𝑥′ 𝑖 ∗
𝜕𝑔
𝜕𝑥′ 𝑖 ∗
2
The design point in the reduced
coordinate is :
𝑥′∗
𝑖 = −𝛼𝑖 𝛽
With 𝛼𝑖=
𝜕𝑔
𝜕𝑥′ 𝑖
𝜕𝑔
𝜕𝑥′ 𝑖 ∗
2
18
1. Define the limit state equation
2. Assume initial values of 𝑥′𝑖 and obtain reduced variables
𝑥′
𝑖 =
𝑥 𝑖−𝜇 𝑥 𝑖
𝜎 𝑥 𝑖
3.Evaluate 𝜕𝑔
𝜕𝑥′𝑖
and 𝛼𝑖 at 𝑥′
𝑖∗
4.Obtain the new design point 𝑥′
𝑖∗ in terms of 𝛽
5. Substitute the new 𝑥′
𝑖∗ in the limit state equation 𝑔(𝑥′
𝑖∗)=0
and solve for 𝛽
6. Using the 𝛽 value obtained in step 5, re-evaluate
𝑥′∗
𝑖 = −𝛼𝑖 𝛽
7.Repeat steps 3 through 6 until 𝛽 converges
Rackwitz algorithm
19. 19
III. Reliability analysis Methods
⑤ Monte Carlo Simulation Methods
Example :
A system has 2 random inputs 𝑍1 and 𝑍2, the response is a random function 𝑔(𝑍1, 𝑍2)
System failure occurs if 𝑔(𝑍1, 𝑍2) > 𝑔 𝑐𝑟𝑖𝑡
We want to find 𝑝 𝑓 = 𝑃 𝑔(𝑍1, 𝑍2) > 𝑔 𝑐𝑟𝑖𝑡
𝑍1 and 𝑍2 follow a certain probability distribution, so the 𝑝 𝑓 can be expressed in terms of the
joint probability density function
𝑝 𝑓 =
𝑧2∈𝐹 𝑧1∈𝐹
𝑓𝑧1 𝑧2
𝑧1, 𝑧2 𝑑𝑧1 𝑑𝑧
F: the failure region
This kind of integrals can be evaluated in most cases numerically
Monte Carlo Simulation
20. 20
III. Reliability analysis Methods
⑤ Monte Carlo Simulation Methods
After simulating the random realizations of 𝑍1 and 𝑍2, 𝑔(𝑍1, 𝑍2) is evaluated for each.
we check if 𝑔(𝑍1, 𝑍2) > 𝑔 𝑐𝑟𝑖𝑡
𝐼𝑖 =
1 if 𝑔(𝑧𝑖1, 𝑧𝑖2) > 𝑔 𝑐𝑟𝑖𝑡
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
The estimate of the probability is 𝑝 𝑓 =
1
𝑛 𝑖=1
𝑛
𝐼𝑖
Page 23 - 24
Natural : associated with inherent randomness of natural processes manifesting as variability over time and for phenomena that take time at a single location, or as variability over space for phenomena that take place at different locations but at single time or variability over both time and space
Knowledge : attributed to lack of data, lack of information about events and processes or lack of understanding of physical laws that limits our ability to model the real world.
- Site :subsurface geology resulting from data and exploration uncertainties
- Model: the degree to which a mathematical model accurately mimics reality
- Parameter: precision to which model parameters can be estimated
- Inability to know social objectives, values and time preferences.
Modeling site characterization involves the following steps:
-Develop hypotheses about site geology
Build a random process model based on the hypotheses
Make observations in the field or laboratory
Perform statistical analysis of the observations to draw inferences about the random process model
Apply des\cision analysis to optimize the type, number and location of observations
It is not wise to apply typical values of soil property variability from other sites in performing a reliability analysis.
Cc: compression index, Cr: recompression index, cv: coefficient of consolidation
So means and standard deviations are used to describe the variability in a set of soil property data. But they mask spatial information.
The trend is determined by an equation and the residuals are characterized statistically by a random variable.
Data are used to estimate a smooth trend, and remaining variations are described statistically, the variance of the residual reflects the uncertainty
Since changing the trend changes Rz, the autocorrelation function reflects a modelling decision too.
Both the loads and resistance may be uncertain.
It means finding a way to compute the margin of safety, factor of safety or other measure of performance like a simple equation or a computational procedure.
The parameters include the properties of geotechnical materials and also loads and geometry. Usually they are described by their means, variances and covariances.
This usually means calculating the mean and variance of the performance function.
Calculate
calculate
Provide insight into the functioning of a system and into the associated uncertainties about the way the system functions.
The analysis attempts to generate all the subsequent events. The event outcomes are represented as branches issuing from the chance node representing a particular event.
A conditional probability is associated with each event
𝜌 𝑋 𝑖 𝑋 𝑗 is the covariance between two variables
- The James Bay project required the construction of 50 Km of dikes on soft sensitive clays. The method was used to evaluate the single or multi-stage construction of a typical dike whose cross section is the following.
The goal of the analysis is to understand the relative safety of different designs, obtain insights about the influence of different parameters and establish consistent criteria for preliminary designs.
The random experimental variations represented by 𝑐 𝑒 due to error in measurements and small scale fluctuations in soil must be eliminated to find the shear strength. Only the spatial variance represent a real effect that occurs in the field and needs to be taken into account.
A limited number of tests is used and different set of measurements would yield a different estimate, the bias means that the experimental technique may not measure directly the quantity of interest
𝜎 𝐹 the variance. 𝐸 𝐹 the mean
The function can be differentiated formally or numerically by divided differences
Factor of safety : method of slices is used so numerical method is required to evaluate the variance
Soil profile and fill properties : thickness of the crust, the depth to the till, unit weight, friction angle
Shear strength : for single stage analyses, uncertainty in 𝑐 𝑢 is based on the field vane data. For multi stage case, shear strengths were established from a combination of undrained strength ratios and the in situ stress history
To extrapolate the results there are two way, one could assume that the variance of F is constant or assume that the coefficient of variation is constant
Conclusion : target probabilities are being selected based on reasons such as the relative contribution of different modes of failure. The target probability selection depends also on the costs of reconstruction ( The probability was reduced with the increase of the height of the embankment)
The FOSM method involve some approximations that may not be acceptable :
Suppose that the moments of the failure criterion can be estimated accurately enough by starting with the mean values of the variables and extrapolating linearly.
The from of the distribution of F is known and can be used to compute 𝑝 𝑓
The objective from transforming the variables 𝑥 𝑖 into 𝑥 ′ 𝑖 is to obtain a standardized space of Normal variables to aid in the computation of reliability Index.
Finally the reliability index is used to find the probability of failure