This document presents an updated version of the Hoek-Brown failure criterion for rock masses. It resolves issues with applying the original criterion and sets out a recommended sequence of calculations. Guidelines are provided for determining equivalent Mohr-Coulomb parameters, rock mass strength, the disturbance factor, and the maximum minor principal stress value for relating Hoek-Brown and Mohr-Coulomb criteria. An associated software program called RocLab has also been developed.
This document discusses the Hoek-Brown failure criterion for estimating the strength and deformation properties of rock masses. It provides details on:
1) Estimating the intact rock strength (ciσ) and Hoek-Brown constant (mi) from triaxial test data on rock cores.
2) Methods for estimating ciσ and mi when direct testing is not possible.
3) Factors that influence rock mass strength estimates such as rock type, discontinuity spacing, and scale of the structure being analyzed.
The document discusses rock mass properties and the Hoek-Brown failure criterion for estimating the strength of jointed rock masses. It presents the generalized Hoek-Brown criterion equation and describes how to determine the intact rock properties of uniaxial compressive strength (σci) and the Hoek-Brown constant (mi) from triaxial test data or estimates. It also discusses estimating the Geological Strength Index (GSI) of the rock mass.
This document presents revisions to the Hoek-Brown failure criterion for rock masses. It resolves uncertainties in applying the criterion and incorporating it into numerical models. The revised criterion sets out a recommended calculation sequence and defines equations to determine rock mass strength parameters like cohesive strength and friction angle from the Geological Strength Index rating of rock mass quality. It also distinguishes between undisturbed and disturbed rock masses using a new disturbance factor.
This document discusses the key characteristics of soil strength and deformation behavior. It introduces the Mohr-Coulomb failure criterion and explains that soil strength depends on factors like effective stress, void ratio, composition, and stress history. It describes the different failure envelopes for peak, critical, and residual strength. It also discusses concepts like dilatancy, anisotropy, and how strength is influenced by factors like density, drainage conditions, overconsolidation ratio, and temperature. The document emphasizes the fundamental factors controlling soil strength and stress-deformation behavior.
This document discusses strength parameters for clays, including:
- The peak friction angle for clays decreases with increasing plasticity index and activity. Critical state friction angles range from 20-25° for kaolin clays and 20° for montmorillonite clays.
- The Hvorslev failure envelope models the strength of overconsolidated clays using equivalent friction angle and cohesion parameters.
- Undrained shear strength of clays decreases with increasing liquidity index and increases with overconsolidation ratio. Empirical equations relate strength to plasticity index and preconsolidation stress.
- Shear bands form after peak strength due to strain localization. Their thickness is 7-10 particle diameters
The document compares the direct displacement-based design (DDBD) method to the force-based design (FBD) method for reinforced concrete framed structures. It analyzes six moment-resisting frame buildings of varying heights using three computer programs. The results show that for buildings over 8 stories with ground accelerations over 0.5g, the DDBD method provides a more suitable approach by calculating more conservative and accurate base shear forces, as it considers the structure's inelastic behavior. Specifically, the DDBD method gives lower displacement values compared to other analysis methods, resulting in higher calculated base shear forces.
10 simple mathematical approach for granular fill Ahmed Ebid
This document presents a proposed mathematical approach to simulate ground deformation and soil parameter improvement from dynamic compaction. The approach uses two equations: 1) calculates ground settlement from a single tamper drop based on soil properties and compaction energy. 2) Calculates updated soil parameters based on settlement from the previous drop, allowing simulation of the compaction process. The approach is applied to four case studies and shows close agreement with measured results. It provides a simple way to design and test dynamic compaction procedures and monitor quality by comparing measured and calculated settlements.
Bearing capacity estimation rocks for foundationFajruSied
This document discusses methods for estimating the bearing capacity of rocks for foundations. It begins with definitions of ultimate and allowable bearing capacity. It then presents several equations that can be used to estimate ultimate bearing capacity based on factors like rock strength, joint spacing, and rock type. Correction factors for different foundation shapes are also provided. The document concludes by discussing approaches for determining an allowable bearing capacity value from the ultimate capacity using a factor of safety. It presents empirical correlations and guidelines from building codes for estimating allowable bearing values based on factors like rock quality designation (RQD) and rock mass rating (RMR).
This document discusses the Hoek-Brown failure criterion for estimating the strength and deformation properties of rock masses. It provides details on:
1) Estimating the intact rock strength (ciσ) and Hoek-Brown constant (mi) from triaxial test data on rock cores.
2) Methods for estimating ciσ and mi when direct testing is not possible.
3) Factors that influence rock mass strength estimates such as rock type, discontinuity spacing, and scale of the structure being analyzed.
The document discusses rock mass properties and the Hoek-Brown failure criterion for estimating the strength of jointed rock masses. It presents the generalized Hoek-Brown criterion equation and describes how to determine the intact rock properties of uniaxial compressive strength (σci) and the Hoek-Brown constant (mi) from triaxial test data or estimates. It also discusses estimating the Geological Strength Index (GSI) of the rock mass.
This document presents revisions to the Hoek-Brown failure criterion for rock masses. It resolves uncertainties in applying the criterion and incorporating it into numerical models. The revised criterion sets out a recommended calculation sequence and defines equations to determine rock mass strength parameters like cohesive strength and friction angle from the Geological Strength Index rating of rock mass quality. It also distinguishes between undisturbed and disturbed rock masses using a new disturbance factor.
This document discusses the key characteristics of soil strength and deformation behavior. It introduces the Mohr-Coulomb failure criterion and explains that soil strength depends on factors like effective stress, void ratio, composition, and stress history. It describes the different failure envelopes for peak, critical, and residual strength. It also discusses concepts like dilatancy, anisotropy, and how strength is influenced by factors like density, drainage conditions, overconsolidation ratio, and temperature. The document emphasizes the fundamental factors controlling soil strength and stress-deformation behavior.
This document discusses strength parameters for clays, including:
- The peak friction angle for clays decreases with increasing plasticity index and activity. Critical state friction angles range from 20-25° for kaolin clays and 20° for montmorillonite clays.
- The Hvorslev failure envelope models the strength of overconsolidated clays using equivalent friction angle and cohesion parameters.
- Undrained shear strength of clays decreases with increasing liquidity index and increases with overconsolidation ratio. Empirical equations relate strength to plasticity index and preconsolidation stress.
- Shear bands form after peak strength due to strain localization. Their thickness is 7-10 particle diameters
The document compares the direct displacement-based design (DDBD) method to the force-based design (FBD) method for reinforced concrete framed structures. It analyzes six moment-resisting frame buildings of varying heights using three computer programs. The results show that for buildings over 8 stories with ground accelerations over 0.5g, the DDBD method provides a more suitable approach by calculating more conservative and accurate base shear forces, as it considers the structure's inelastic behavior. Specifically, the DDBD method gives lower displacement values compared to other analysis methods, resulting in higher calculated base shear forces.
10 simple mathematical approach for granular fill Ahmed Ebid
This document presents a proposed mathematical approach to simulate ground deformation and soil parameter improvement from dynamic compaction. The approach uses two equations: 1) calculates ground settlement from a single tamper drop based on soil properties and compaction energy. 2) Calculates updated soil parameters based on settlement from the previous drop, allowing simulation of the compaction process. The approach is applied to four case studies and shows close agreement with measured results. It provides a simple way to design and test dynamic compaction procedures and monitor quality by comparing measured and calculated settlements.
Bearing capacity estimation rocks for foundationFajruSied
This document discusses methods for estimating the bearing capacity of rocks for foundations. It begins with definitions of ultimate and allowable bearing capacity. It then presents several equations that can be used to estimate ultimate bearing capacity based on factors like rock strength, joint spacing, and rock type. Correction factors for different foundation shapes are also provided. The document concludes by discussing approaches for determining an allowable bearing capacity value from the ultimate capacity using a factor of safety. It presents empirical correlations and guidelines from building codes for estimating allowable bearing values based on factors like rock quality designation (RQD) and rock mass rating (RMR).
1. The document presents an overview of fracture mechanics, including an atomic view of fracture, stress concentration effects of flaws, the Griffith energy balance approach, and the energy release rate.
2. It discusses how cracks propagate when sufficient stress is applied at the atomic level to break atomic bonds, and how flaws concentrate stress which can cause fracture at lower overall stresses than theoretical strength estimates.
3. The Griffith energy balance approach is summarized, showing how the energy required to create new crack surfaces must be balanced by the strain energy released from the material as the crack extends.
This document presents a study on modeling and analyzing the time-dependent settlement of soil foundations under vertical loading using a fractional Kelvin-Voigt viscoelastic model. The study derives an analytical solution for the settlement of a half-space foundation using Laplace transforms. Results show that the fractional model can more accurately predict long-term settlements compared to the classical Kelvin-Voigt model by varying the fractional order and viscosity coefficient. The determined influential distance of the load also affects settlement calculations.
A fully integrated discrete fracture model (DFM) is presented for coupled geomechanics and single-phase fluid flow in fractured porous media. The model discretizes the poroelasticity equations using finite elements on an unstructured grid, with special treatment for fractures. The flow equations are discretized using finite volumes. A sequential implicit solution strategy is employed to solve the coupled nonlinear equations. Changes in porosity and fracture permeability due to mechanical deformation are accounted for. The model aims to explicitly represent fracture geometry and its impact on stress/strain fields, unlike dual-continuum approaches. It is implemented within a general-purpose research simulator.
This document discusses stress distribution in soil due to various types of loading. It begins by introducing key concepts like how applied loads are transferred through the soil mass, creating stresses that decrease in magnitude but increase in area with depth. The factors that affect stress distribution, like loading size/shape, soil type, and footing rigidity are also covered. The document then examines specific load types - point loads, line loads, rectangular/triangular strip loads, and circular loads - providing the equations to calculate vertical stress increases below each. Several examples demonstrate calculating stress increases below compound load arrangements. The summary provides an overview of the key topics and calculations presented in the document.
This document summarizes a research paper that develops a mathematical model for analyzing the three-dimensional shape of a long twisted rod hanging under gravity, such as a pipeline being laid from a barge. The model uses the geometrically exact theory of linear elastic rods and formulates the problem as a boundary value problem that is solved using matched asymptotic expansions. The truncated analytical solution is compared to results from a numerical scheme and shows good agreement. The method is then applied to consider the near-catenary shape of a clamped pipeline during the laying process.
This document presents a method for calculating the energy release rate (ERR) in Mode I delamination of angle ply laminated composites using a double cantilever beam (DCB) test specimen. The compliance equation is used to calculate the ERR based on a second order shear deformation beam theory (SSTDBT) model of the DCB specimen. Numerical examples show good agreement between the ERR calculated from the compliance equation and those obtained using J-integral calculations for glass/polyester DCB specimens with [±30°]5 and [±45°]5 layups.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
This document discusses soil phase relationships and classification. It defines key terms like void ratio, porosity, degree of saturation, density, specific gravity, water content and unit weight. It explains the relationships between these parameters and provides typical values for various soil types. For example, it states that the void ratios of natural sand deposits range from 0.51 to 0.85 and dry unit weights of granular soils range from 14 to 18 kN/m3. The document also includes two examples problems demonstrating calculations using the defined relationships.
This document discusses stress distribution in soils due to surface loads. It introduces Boussinesq's formula and Westergaard's formula for calculating vertical stress at a point in soil from a surface point load, based on elastic theory. Boussinesq's formula assumes the soil is elastic, isotropic, and homogeneous, while Westergaard's formula accounts for soil anisotropy. Formulas are also provided for calculating stress from line loads, strip loads, and loads beneath the corner of a rectangular foundation. Examples are given to demonstrate calculating stress at different points using the formulas.
Chapter 2 free vibration of single degree of freedomRafi sulaiman
1) Using the BS 8002 method, the minimum depth of embedment (d) is calculated by determining the disturbing and restoring moments acting on the sheet pile wall and solving the equations iteratively.
2) Applying the CP2 (gross pressure) method, the depth of penetration (od) is found by taking moments of the lateral earth pressures, od is then increased by 30% to obtain the required depth of embedment (d).
3) Both methods simplify the actual pressure distribution to a concentrated force (R) and use factors of safety on the available passive resistance to determine a stable depth of embedment for the cantilever sheet pile wall.
The document presents a general analytical solution for determining the required anchor force to stabilize rock slopes undergoing toppling failure. It extends previous solutions by considering blocks of infinitesimal thickness, leading to ordinary differential equations that can be integrated for simple slope geometries. For a uniform slope, two failure modes are possible - sliding toe (ST) and tension toe (TT) - depending on the dip, cut slope angle, and friction angle. The solution provides an upper bound for the required anchor force for slopes higher than 20-30 times the average block thickness.
This document describes 9 numerical calculation methods for analyzing piled rafts, ranging from simple to more complex models. The simplest is the linear contact pressure method (Method 1), which assumes a linear distribution of contact pressures without interaction between the foundation and soil. Winkler's model (Methods 2-3) represents the soil as elastic springs, with pile reactions proportional to settlement. The continuum model (Methods 4-9) considers interaction between all foundation elements and layered soil, represented as a continuum. The most complex method is the modulus of compressibility method for layered soil (Methods 6-9). Finite element analysis is used except for one rigid raft method. The key equations for each method are presented.
Numerical and Analytical Solutions for Ovaling Deformation in Circular Tunnel...IDES Editor
Ovaling deformations develop when waves propagate
perpendicular to the tunnel axis. Two analytical solutions are
used for estimating the ovaling deformations and forces in
circular tunnels due to soil–structure interaction under
seismic loading. In this paper, these two closed form solutions
will be described briefly, and then a comparison between these
methods will be made by changing the ground parameters.
Differences between the results of these two methods in
calculating the magnitudes of thrust on tunnel lining are
significant. For verifying the results of these two closed form
solutions, numerical analyses were performed using finite
element code (ABAQUS program). These analyses show that
the two closed form solutions provide the same results only
for full-slip condition.
1) The bearing capacity of intact rock is higher than jointed rock mass. Failure modes include local shear, general shear, compressive, splitting, and brittle vs ductile behavior.
2) Allowable bearing stress on rock masses is estimated based on rock quality designation (RQD) and empirical relationships. Higher RQD corresponds to higher allowable stress.
3) For jointed rock, net allowable bearing pressure considers discontinuity spacing and thickness, footing width, rock strength, and depth factors. Pile foundations also include depth of socket factors. Pressuremeter tests can also estimate allowable pressure.
This document contains a multiple choice quiz on concepts related to stress and strain in materials. There are 40 questions covering topics like:
- The relationships between elastic modulus, shear modulus, and Poisson's ratio for materials
- Calculating stresses and strains in loaded structures
- Principal stresses and maximum shear stress
- Mohr's circle representation of stresses
- Elastic properties like modulus of elasticity, modulus of resilience
- Stresses in loaded bars, beams, and other basic structural elements
The questions require applying stress/strain and material property equations to calculate values or identify correct statements regarding stresses and deformations in loaded materials and structures.
This document presents an empirical formulation for determining the allowable bearing capacity of shallow foundations based on in situ measured shear wave velocity. It summarizes the classical theory for ultimate bearing capacity which has various uncertainties. An expression is proposed that relates allowable bearing capacity to only two soil parameters: unit weight and shear wave velocity. Case histories from 14 sites show this expression provides reliable and safe estimates of allowable bearing capacity while being more efficient than the classical theory which requires laboratory testing. The shear wave velocity represents real soil conditions and allows convenient single-step determination of allowable bearing capacity from geophysical surveys.
Ring or circular rafts can be used for cylindrical structures such as chimneys, silos, storage tanks, TV-towers and other structures. In this case, ring or circular raft is the best suitable foundation to the natural geometry of such structures. The design of circular rafts is quite similar to that of other rafts.
This document presents an alternative closed-form solution for calculating seismic earth pressures on retaining walls. The proposed solution is based on the theory of discontinuous stress fields and considers parameters like soil weight, friction angle, wall and backfill inclination, wall roughness, surface surcharge, and horizontal and vertical seismic acceleration. It aims to provide a simpler, more accurate, and conservative solution compared to existing methods like Coulomb and Mononobe-Okabe equations. The solution is presented through dimensionless graphs and is verified through comparison to established numerical solutions, showing maximum errors of around 10% for active pressures.
This document discusses ground reinforcement in seismic areas to improve the bearing capacity of shallow foundations. It presents the yield design theory framework for evaluating seismic bearing capacity, which defines a bounding surface delimiting allowable load combinations. This framework has been extended to a new design concept using soil reinforcement with inclusions to significantly improve foundation seismic bearing capacity. Numerical studies and experiments have validated this concept and the theoretical tools.
Slope Stability Evaluation for the New Railway Embankment using Stochastic & ...Dr.Costas Sachpazis
Evaluation of Slope stability is one of the day-to-day practices of geotechnical engineers. Nowadays, different methods are available to evaluate the stability of a particular slope. Despite the advances that have been made in site exploration, evaluating the stability of slopes remains a challenge. Recently, Ethiopia has been trying to construct a newly planned railway routes to connect the country’s development centers and link with ports of neighboring countries. However, this newly planned railway routes will pass in the heart of highly fragile mountainous terrains and earthquake prone regions. Therefore, the prime objective of this paper is to investigate the stability of the railway embankment by using three different stochastic approaches (First Order Reliability Method, Point Estimate Method and Monte Carlo Simulation) with commercially available finite element programs. Moreover, the seismic response of the railway embankment was studied by using a nonlinear analysis (FLAC2D v 7.0) program. The first order reliability method (FORM), Monte Carlo Simulation (MCS) and Point-estimate method (PEM) gave 3.2%, 4.14% and 1.5% of probability of failure respectively. In the mean time, there was no any indication of liquefaction observed due to stiff foundation clay soils and deep groundwater table.
1. The document presents an overview of fracture mechanics, including an atomic view of fracture, stress concentration effects of flaws, the Griffith energy balance approach, and the energy release rate.
2. It discusses how cracks propagate when sufficient stress is applied at the atomic level to break atomic bonds, and how flaws concentrate stress which can cause fracture at lower overall stresses than theoretical strength estimates.
3. The Griffith energy balance approach is summarized, showing how the energy required to create new crack surfaces must be balanced by the strain energy released from the material as the crack extends.
This document presents a study on modeling and analyzing the time-dependent settlement of soil foundations under vertical loading using a fractional Kelvin-Voigt viscoelastic model. The study derives an analytical solution for the settlement of a half-space foundation using Laplace transforms. Results show that the fractional model can more accurately predict long-term settlements compared to the classical Kelvin-Voigt model by varying the fractional order and viscosity coefficient. The determined influential distance of the load also affects settlement calculations.
A fully integrated discrete fracture model (DFM) is presented for coupled geomechanics and single-phase fluid flow in fractured porous media. The model discretizes the poroelasticity equations using finite elements on an unstructured grid, with special treatment for fractures. The flow equations are discretized using finite volumes. A sequential implicit solution strategy is employed to solve the coupled nonlinear equations. Changes in porosity and fracture permeability due to mechanical deformation are accounted for. The model aims to explicitly represent fracture geometry and its impact on stress/strain fields, unlike dual-continuum approaches. It is implemented within a general-purpose research simulator.
This document discusses stress distribution in soil due to various types of loading. It begins by introducing key concepts like how applied loads are transferred through the soil mass, creating stresses that decrease in magnitude but increase in area with depth. The factors that affect stress distribution, like loading size/shape, soil type, and footing rigidity are also covered. The document then examines specific load types - point loads, line loads, rectangular/triangular strip loads, and circular loads - providing the equations to calculate vertical stress increases below each. Several examples demonstrate calculating stress increases below compound load arrangements. The summary provides an overview of the key topics and calculations presented in the document.
This document summarizes a research paper that develops a mathematical model for analyzing the three-dimensional shape of a long twisted rod hanging under gravity, such as a pipeline being laid from a barge. The model uses the geometrically exact theory of linear elastic rods and formulates the problem as a boundary value problem that is solved using matched asymptotic expansions. The truncated analytical solution is compared to results from a numerical scheme and shows good agreement. The method is then applied to consider the near-catenary shape of a clamped pipeline during the laying process.
This document presents a method for calculating the energy release rate (ERR) in Mode I delamination of angle ply laminated composites using a double cantilever beam (DCB) test specimen. The compliance equation is used to calculate the ERR based on a second order shear deformation beam theory (SSTDBT) model of the DCB specimen. Numerical examples show good agreement between the ERR calculated from the compliance equation and those obtained using J-integral calculations for glass/polyester DCB specimens with [±30°]5 and [±45°]5 layups.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
This document discusses soil phase relationships and classification. It defines key terms like void ratio, porosity, degree of saturation, density, specific gravity, water content and unit weight. It explains the relationships between these parameters and provides typical values for various soil types. For example, it states that the void ratios of natural sand deposits range from 0.51 to 0.85 and dry unit weights of granular soils range from 14 to 18 kN/m3. The document also includes two examples problems demonstrating calculations using the defined relationships.
This document discusses stress distribution in soils due to surface loads. It introduces Boussinesq's formula and Westergaard's formula for calculating vertical stress at a point in soil from a surface point load, based on elastic theory. Boussinesq's formula assumes the soil is elastic, isotropic, and homogeneous, while Westergaard's formula accounts for soil anisotropy. Formulas are also provided for calculating stress from line loads, strip loads, and loads beneath the corner of a rectangular foundation. Examples are given to demonstrate calculating stress at different points using the formulas.
Chapter 2 free vibration of single degree of freedomRafi sulaiman
1) Using the BS 8002 method, the minimum depth of embedment (d) is calculated by determining the disturbing and restoring moments acting on the sheet pile wall and solving the equations iteratively.
2) Applying the CP2 (gross pressure) method, the depth of penetration (od) is found by taking moments of the lateral earth pressures, od is then increased by 30% to obtain the required depth of embedment (d).
3) Both methods simplify the actual pressure distribution to a concentrated force (R) and use factors of safety on the available passive resistance to determine a stable depth of embedment for the cantilever sheet pile wall.
The document presents a general analytical solution for determining the required anchor force to stabilize rock slopes undergoing toppling failure. It extends previous solutions by considering blocks of infinitesimal thickness, leading to ordinary differential equations that can be integrated for simple slope geometries. For a uniform slope, two failure modes are possible - sliding toe (ST) and tension toe (TT) - depending on the dip, cut slope angle, and friction angle. The solution provides an upper bound for the required anchor force for slopes higher than 20-30 times the average block thickness.
This document describes 9 numerical calculation methods for analyzing piled rafts, ranging from simple to more complex models. The simplest is the linear contact pressure method (Method 1), which assumes a linear distribution of contact pressures without interaction between the foundation and soil. Winkler's model (Methods 2-3) represents the soil as elastic springs, with pile reactions proportional to settlement. The continuum model (Methods 4-9) considers interaction between all foundation elements and layered soil, represented as a continuum. The most complex method is the modulus of compressibility method for layered soil (Methods 6-9). Finite element analysis is used except for one rigid raft method. The key equations for each method are presented.
Numerical and Analytical Solutions for Ovaling Deformation in Circular Tunnel...IDES Editor
Ovaling deformations develop when waves propagate
perpendicular to the tunnel axis. Two analytical solutions are
used for estimating the ovaling deformations and forces in
circular tunnels due to soil–structure interaction under
seismic loading. In this paper, these two closed form solutions
will be described briefly, and then a comparison between these
methods will be made by changing the ground parameters.
Differences between the results of these two methods in
calculating the magnitudes of thrust on tunnel lining are
significant. For verifying the results of these two closed form
solutions, numerical analyses were performed using finite
element code (ABAQUS program). These analyses show that
the two closed form solutions provide the same results only
for full-slip condition.
1) The bearing capacity of intact rock is higher than jointed rock mass. Failure modes include local shear, general shear, compressive, splitting, and brittle vs ductile behavior.
2) Allowable bearing stress on rock masses is estimated based on rock quality designation (RQD) and empirical relationships. Higher RQD corresponds to higher allowable stress.
3) For jointed rock, net allowable bearing pressure considers discontinuity spacing and thickness, footing width, rock strength, and depth factors. Pile foundations also include depth of socket factors. Pressuremeter tests can also estimate allowable pressure.
This document contains a multiple choice quiz on concepts related to stress and strain in materials. There are 40 questions covering topics like:
- The relationships between elastic modulus, shear modulus, and Poisson's ratio for materials
- Calculating stresses and strains in loaded structures
- Principal stresses and maximum shear stress
- Mohr's circle representation of stresses
- Elastic properties like modulus of elasticity, modulus of resilience
- Stresses in loaded bars, beams, and other basic structural elements
The questions require applying stress/strain and material property equations to calculate values or identify correct statements regarding stresses and deformations in loaded materials and structures.
This document presents an empirical formulation for determining the allowable bearing capacity of shallow foundations based on in situ measured shear wave velocity. It summarizes the classical theory for ultimate bearing capacity which has various uncertainties. An expression is proposed that relates allowable bearing capacity to only two soil parameters: unit weight and shear wave velocity. Case histories from 14 sites show this expression provides reliable and safe estimates of allowable bearing capacity while being more efficient than the classical theory which requires laboratory testing. The shear wave velocity represents real soil conditions and allows convenient single-step determination of allowable bearing capacity from geophysical surveys.
Ring or circular rafts can be used for cylindrical structures such as chimneys, silos, storage tanks, TV-towers and other structures. In this case, ring or circular raft is the best suitable foundation to the natural geometry of such structures. The design of circular rafts is quite similar to that of other rafts.
This document presents an alternative closed-form solution for calculating seismic earth pressures on retaining walls. The proposed solution is based on the theory of discontinuous stress fields and considers parameters like soil weight, friction angle, wall and backfill inclination, wall roughness, surface surcharge, and horizontal and vertical seismic acceleration. It aims to provide a simpler, more accurate, and conservative solution compared to existing methods like Coulomb and Mononobe-Okabe equations. The solution is presented through dimensionless graphs and is verified through comparison to established numerical solutions, showing maximum errors of around 10% for active pressures.
This document discusses ground reinforcement in seismic areas to improve the bearing capacity of shallow foundations. It presents the yield design theory framework for evaluating seismic bearing capacity, which defines a bounding surface delimiting allowable load combinations. This framework has been extended to a new design concept using soil reinforcement with inclusions to significantly improve foundation seismic bearing capacity. Numerical studies and experiments have validated this concept and the theoretical tools.
Slope Stability Evaluation for the New Railway Embankment using Stochastic & ...Dr.Costas Sachpazis
Evaluation of Slope stability is one of the day-to-day practices of geotechnical engineers. Nowadays, different methods are available to evaluate the stability of a particular slope. Despite the advances that have been made in site exploration, evaluating the stability of slopes remains a challenge. Recently, Ethiopia has been trying to construct a newly planned railway routes to connect the country’s development centers and link with ports of neighboring countries. However, this newly planned railway routes will pass in the heart of highly fragile mountainous terrains and earthquake prone regions. Therefore, the prime objective of this paper is to investigate the stability of the railway embankment by using three different stochastic approaches (First Order Reliability Method, Point Estimate Method and Monte Carlo Simulation) with commercially available finite element programs. Moreover, the seismic response of the railway embankment was studied by using a nonlinear analysis (FLAC2D v 7.0) program. The first order reliability method (FORM), Monte Carlo Simulation (MCS) and Point-estimate method (PEM) gave 3.2%, 4.14% and 1.5% of probability of failure respectively. In the mean time, there was no any indication of liquefaction observed due to stiff foundation clay soils and deep groundwater table.
This paper analyzes geomechanical data from three offshore wells in Brazil to characterize in-situ stress and identify critically stressed fractures. The stress tensor was determined to be normal stress regime. Fracture modeling found no critically stressed fractures for two wells and one fracture plane for the third, requiring an unrealistically low friction coefficient. The study concludes fractures likely do not play a significant role in reservoir dynamics and more detailed analysis is needed.
This document discusses the seismic safety assessment of rockfill dams. It presents an alternative approach to assessing slope stability under earthquake loading that is based on full dynamic time domain analysis, rather than the standard quasi-static method. The document describes the finite element model of a rockfill dam case study, including geometry, material properties, and applied static and earthquake loading. It notes that full dynamic analysis can better account for dynamic effects on slope stability compared to the quasi-static method.
This document discusses the modulus of subgrade reaction (Ks), which represents the relationship between applied stress and associated soil settlement beneath foundations. It defines Ks and describes several analytical models and methods for calculating Ks values, including plate loading tests, correlations with soil properties, and pseudo-coupled approaches that assign different Ks values depending on location beneath the foundation. Factors that influence Ks include soil type, moisture content, and foundation geometry.
Applying Geo-mechanics to Well Modelling and Inflow Performance RelationshipsDaniel Chia
1) The document describes applying geo-mechanics principles to model sand production and inflow performance in wells. It presents an equation that projects the "sanding line" which indicates when sand will be produced onto the flow rate vs bottom hole pressure graph.
2) Key concepts discussed include the Mohr-Coulomb failure criterion for predicting rock failure, concepts of total, effective and minimum/maximum horizontal stresses, and how stresses change around deviated or perforated wellbores.
3) Two example applications are presented to illustrate using geo-mechanics to model inflow relationships and sand production for a well, though actual formation measurements are preferable to the assumed values used in the examples.
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.
D2 (A6) Mikael Hallgren - Shear Design of Reinforced Concrete Beams Subjected...Svenska Betongföreningen
This document proposes updates to design rules for reinforced concrete beams subjected to air blast loads. It suggests new dynamic shear design models based on the dynamic shear span, including adopting and amending provisions from the draft Eurocode for flexural shear when the shear span is greater than the effective depth, and using strut-and-tie models with possible strength increases for shear compression failure when the shear span is less than or equal to the effective depth. The models are calibrated to test results but more studies are still needed. The dynamic shear span depends on peak pressure from explosion loading but may also be affected by pressure duration, requiring further investigation.
This document describes CUMBIA, a set of Matlab codes for analyzing reinforced concrete members. CUMBIA can perform monotonic moment-curvature analysis, force-displacement analysis, and axial load-moment interaction analysis. It uses material models for concrete and steel, including default Mander models for confined and unconfined concrete and King/Raynor models for steel. The section analysis iterates to find the neutral axis position for increasing concrete strains. Member response is obtained using a plastic hinge model, calculating displacements from equivalent plastic hinge length and moment-area relationships.
This document discusses foundation design and soil-structure interaction. It begins by introducing elastic foundation theory and its applications. It then discusses the governing equations for beams and plates on elastic foundations, including the Winkler and two-parameter elastic foundation models. It evaluates the spring constant in Winkler's soil model using plate load tests and discusses Poisson's ratio of soil.
This document discusses foundation design and soil-structure interaction. It begins by introducing elastic foundation models, which represent the soil as springs or elastic layers. These include the Winkler, Filonenko-Borodich, Hetenyi, and Pasternak models. The document then presents the governing equations for beams and plates on elastic foundations. It discusses determining soil reaction and evaluating the spring constant using plate load tests. The spring constant, or modulus of subgrade reaction, represents the soil's elastic properties.
This document summarizes numerical simulations of concrete elements using two approaches to model cracks: smeared cracking models and discrete cracking with cohesive elements. Smeared cracking models included elasto-plasticity with Rankine criterion, continuum damage mechanics, and smeared crack models. Cohesive elements were used to model discrete cracks. Both approaches were implemented in ABAQUS and used to simulate two benchmark problems: a Nooru-Mohamed mixed-mode fracture test and a Schlangen mixed-mode fracture test. The results from the different models were compared to experimental data.
CROSS-CORRELATION OF STRESSES IN THE TRAN REINFORCEMENT UNDER SHEAR LOAD AND ...IAEME Publication
The main aim of the present study is to give an answer to the question whether the transverse reinforcement, which is required for the shear resistance of columns, must be added to the one required for the cross section confinement, or it is possible for one to substitute the other. The superposition of these reinforcements is defended by the fact that the shear reinforcement results from the shear action, while the transverse reinforcement, required by the confinement, results from the axial compression of the section. The present study is experimental and uses strain gauges, in order to check the stresses of the transverse reinforcement. Useful conclusions are drawn.
Numerical modeling of the welding defect influence on fatigue life of the wel...inventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Diseno en ingenieria mecanica de Shigley - 8th ---HDes
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This document discusses design considerations for large underground caverns excavated in weak rock at depths of 100-300m below the surface for hydroelectric projects. It addresses the stability of caverns and surrounding rock mass given in situ stress conditions, effects of nearby slopes, and determining appropriate pillar sizes between excavations. The key design factors are the strength of the rock mass, influence of structural features like joints and bedding planes, sequence of excavation and support, and stress changes induced by nearby slopes and excavations. Pillar size between caverns must consider stresses imposed and stability of the rock mass.
This study used finite element modeling to analyze swelling behavior in a tunnel excavated through marl rock. Laboratory tests on marl rock samples were used to calibrate two finite element programs, FISS and Nisa-II. FISS modeled the tunnel using the laboratory swelling test results. Nisa-II modeled time-dependent creep behavior by defining a creep function relating stress, strain, and time. Both programs analyzed stresses around the tunnel and indicated higher stresses in the sidewalls compared to the roof and floor. The study demonstrated a method to numerically model swelling behavior in tunnels using laboratory test data.
1. HOEK-BROWN FAILURE CRITERION – 2002 EDITION
Evert Hoek
Consulting Engineer, Vancouver, Canada
Carlos Carranza-Torres
Itasca Consulting Group Inc., Minneapolis, USA
Brent Corkum
Rocscience Inc., Toronto, Canada
ABSTRACT: The Hoek-Brown failure criterion for rock masses is widely accepted and has been
applied in a large number of projects around the world. While, in general, it has been found to be
satisfactory, there are some uncertainties and inaccuracies that have made the criterion inconvenient
to apply and to incorporate into numerical models and limit equilibrium programs. In particular, the
difficulty of finding an acceptable equivalent friction angle and cohesive strength for a given rock
mass has been a problem since the publication of the criterion in 1980. This paper resolves all these
issues and sets out a recommended sequence of calculations for applying the criterion. An
associated Windows program called “RocLab” has been developed to provide a convenient means
of solving and plotting the equations presented in this paper.
1. INTRODUCTION
Hoek and Brown [1, 2] introduced their failure criterion in an attempt to provide input data for the
analyses required for the design of underground excavations in hard rock. The criterion was derived
from the results of research into the brittle failure of intact rock by Hoek [3] and on model studies
of jointed rock mass behaviour by Brown [4]. The criterion started from the properties of intact rock
and then introduced factors to reduce these properties on the basis of the characteristics of joints in
a rock mass. The authors sought to link the empirical criterion to geological observations by means
of one of the available rock mass classification schemes and, for this purpose, they chose the Rock
Mass Rating proposed by Bieniawski [5].
Because of the lack of suitable alternatives, the criterion was soon adopted by the rock mechanics
community and its use quickly spread beyond the original limits used in deriving the strength
reduction relationships. Consequently, it became necessary to re-examine these relationships and to
introduce new elements from time to time to account for the wide range of practical problems to
which the criterion was being applied. Typical of these enhancements were the introduction of the
idea of “undisturbed” and “disturbed” rock masses Hoek and Brown [6], and the introduction of a
modified criterion to force the rock mass tensile strength to zero for very poor quality rock masses
(Hoek, Wood and Shah, [7]).
One of the early difficulties arose because many geotechnical problems, particularly slope stability
issues, are more conveniently dealt with in terms of shear and normal stresses rather than the
principal stress relationships of the original Hoek-Brown riterion, defined by the equation:
c 5.0'3'3'1
'3
0
.
5 + +=smciciσσσσσ (1)
where '1σand '
3σ are the major and minor effective principal stresses at failure ciσis the uniaxial compressive
strength of the intact rock material and
m and s are material constants, where s = 1 for intact rock.
An exact relationship between equation 1 and the normal and shear stresses at failure was derived
by J. W. Bray (reported by Hoek [8]) and later by Ucar [9] and Londe1 [10].
Hoek [12] discussed the derivation of equivalent friction angles and cohesive strengths for various
practical situations. These derivations were based
1 Londe’sequations were later found to contain errors although the concepts introduced by Londe were extremely
important in the application of the Hoek-Brown criterion to tunnelling problems (Carranza-Torres and Fairhurst, [11])
upon tangents to the Mohr envelope derived by Bray. Hoek [13] suggested that the cohesive
strength determined by fitting a tangent to the curvilinear Mohr envelope is an upper bound value
and may give optimistic results in stability calculations. Consequently, an average value,
determined by fitting a linear Mohr-Coulomb relationship by least squares methods, may be more
2. appropriate. In this paper Hoek also introduced the concept of the Generalized Hoek-Brown
criterion in which the shape of the principal stress plot or the Mohr envelope could be adjusted by
means of a variable coefficient a in place of the square root term in equation 1. i −
−=DGSIs39100exp (4)
() (5) 3/2015/6121−−−+=eeaGSI
D is a factor which depends upon the degree of disturbance to which the rock mass has been
subjected by blast damage and stress relaxation. It varies from 0 for undisturbed in situ rock masses
to 1 for very disturbed rock masses. Guidelines for the selection of D are discussed in a later
section.
The uniaxial compressive strength is obtained by setting in equation 2, giving: 0'3=σ
acics.σσ= (6)
Hoek and Brown [14] attempted to consolidate all the previous enhancements into a comprehensive
presentation of the failure criterion and they gave a number of worked examples to illustrate its
practical application.
and, the tensile strength is: bcitmsσσ−= (7)
Equation 7 is obtained by setting in equation 2. This represents a condition of biaxial tension. Hoek
[8] showed that, for brittle materials, the uniaxial tensile strength is equal to the biaxial tensile
strength. tσσσ=='3'1
In addition to the changes in the equations, it was also recognised that the Rock Mass Rating of
Bieniawski was no longer adequate as a vehicle for relating the failure criterion to geological
observations in the field, particularly for very weak rock masses. This resulted in the introduction of
the Geological Strength Index (GSI) by Hoek, Wood and Shah [7], Hoek [13] and Hoek, Kaiser and
Bawden [15]. This index was subsequently extended for weak rock masses in a series of papers by
Hoek, Marinos and Benissi [16], Hoek and Marinos [17, 18] and Marinos and Hoek [19].
Note that the “switch” at GSI = 25 for the coefficients s and a (Hoek and Brown, [14]) has been
eliminated in equations 4 and 5 which give smooth continuous transitions for the entire range of
GSI values. The numerical values of a and s, given by these equations, are very close to those given
by the previous equations and it is not necessary for readers to revisit and make corrections to old
calculations.
The Geological Strength Index will not be discussed in the following text, which will concentrate
on the sequence of calculations now proposed for the application of the Generalized Hoek Brown
criterion to jointed rock masses.
Normal and shear stresses are related to principal stresses by the equations published by Balmer
[20].
1122''''''''1'3131313+−⋅−−+=σσσσσσσσσddddn (8)
2. GENERALIZED HOEK-BROWN CRITERION
This is expressed as ()1''''''131313+−=σσσσσστdddd (9) acibcisms
s
c
b
i
m
s + += σσσσσ'3'3'1 (2)
where
() 1'''3311−++=acibbsmamddσσσσ(10)
where mb is a reduced value of the material constant mi and is given by
a − − = DGSImmib1428100exp (3)
3. MODULUS OF DEFORMATION
The rock mass modulus of deformation is given by:
s and a are constants for the rock mass given by the following relationships: )40/)10((1010021)(−−
⋅
⋅
⋅ − = GSIcimDGPaEσ (11a)
The equivalent plot, in terms of the major and minor principal stresses, is defined by:
Equation 11a applies for ≤ciσ 100 MPa. For >ciσ 100 MPa, use equation 11b.
3. (15) )40/)10((1021)(−−
'''''''31sin1sin1sin1cos2σφφφφσ−++−=c ⋅
⋅
⋅ − = GSImDGPaE (11b)
Note that the original equation proposed by Hoek and Brown [14] has been modified, by the
inclusion of the factor D, to allow for the effects of blast damage and stress relaxation.
4. MOHR-COULOMB CRITERION
Since most geotechnical software is still written in terms of the Mohr-Coulomb failure criterion, it
is necessary to determine equivalent angles of friction and cohesive strengths for each rock mass
and stress range. This is done by fitting an average linear relationship to the curve generated by
solving equation 2 for a range of minor principal stress values defined by '3max3σσσ<<t, as illustrated
in Figure 1. The fitting process involves balancing the areas above and below the Mohr-Coulomb
plot. This results in the following equations for the angle of friction and cohesive strength : '
φ'c
h
T
.
t
o
l
c + ++++=−−−1'1'1')(6)2)(1(2)(6sin33abbabbnnmsamaamsamσσφ (12)
[]()())2)(1()(61)2)(1()()1()21( 1'1'''333aamsamaamsmasacabbabbcinnn+++++++−++=−−σσσσ (13)
Figure 1: Relationships between major and minor principal stresses for Hoek-Brown and equivalent
Mohr-Coulomb criteria.
5. ROCK MASS STRENGTH
The uniaxial compressive strength of the rock mass cσ is given by equation 6. Failure initiates at the
boundary of an excavation when cσ is exceeded by the stress induced on that boundary. The failure
propagates from this initiation point into a biaxial stress field and it eventually stabilizes when the
local strength, defined by equation 2, is higher than the induced stresses and . Most numerical
models can follow this process of fracture propagation and this level of detailed analysis is very
important when considering the stability of excavations in rock and when designing support
systems. '1σ'3σ
where cinσσσ'max33=
Note that the value of 'max3σ, the upper limit of confining stress over which the relationship between
the Hoek-Brown and the Mohr-Coulomb criteria is considered, has to be determined for each
individual case. Guidelines for selecting these values for slopes as well as shallow and deep tunnels
are presented later.
The Mohr-Coulomb shear strength τ, for a given normal stress σ, is found by substitution of these
values of and 'c'φ in to the equation:
''tanφστ+=c (14)
However, there are times when it is useful to consider the overall behaviour of a rock mass rather
than the detailed failure propagation process described above. For example, when considering the
strength of a pillar, it is useful to have an estimate of the overall strength of the pillar rather
than a detailed knowledge of the extent of fracture propagation in the pillar. This leads to the
concept of a global “rock mass strength” and Hoek and Brown [14] proposed that this could be
estimated from the Mohr-Coulomb relationship: ''''sin1cos2φφσ−=ccm (16)
with and determined for the stress range 'c'φ4/citσσσ<'3< giving
())2)(1(24))8(4(1'aasmsmasmabbbcicm+++−−+⋅=−σσ (17)
6. DETERMINATION OF σ′3MAX
The issue of determining the appropriate value of for use in equations 12 and 13 depends upon the
specific application. Two cases will be investigated: 'max3σ
1. Tunnels − where the value of is that which gives equivalent characteristic curves for the two
failure criteria for deep tunnels or equivalent subsidence profiles for shallow tunnels. 'max3σ
2. Slopes – here the calculated factor of safety and the shape and location of the failure surface have
to be equivalent.
For the case of deep tunnels, closed form solutions for both the Generalized Hoek-Brown and the
Mohr-Coulomb criteria have been used to generate hundreds of solutions and to find the value of
that gives equivalent characteristic curves. 'max3σ
4. For shallow tunnels, where the depth below surface is less than 3 tunnel diameters, comparative
numerical studies of the extent of failure and the magnitude of surface subsidence gave an identical
relationship to that obtained for deep tunnels, provided that caving to surface is avoided.
The results of the studies for deep tunnels are plotted in Figure 2 and the fitted equation for both
cases is:
94.0'''max347.0−− 'm
0
.
7 = Hcmcmγσσσ (18)
where is the rock mass strength, defined by equation 17, 'cmσγis the unit weight of the rock mass and
H is the depth of the tunnel below surface. In cases where the horizontal stress is higher than the
vertical stress, the horizontal stress value should be used in place of Hγ. ''3σσ
Figure 2: Relationship for the calculation of σ′3max for equivalent Mohr-Coulomb and Hoek-Brown
parameters for tunnels.
Equation 18 applies to all underground excavations, which are surrounded by a zone of failure that
does not extend to surface. For studies of problems such as block caving in mines it is
recommended that no attempt should be made to relate the Hoek-Brown and Mohr-Coulomb
parameters and that the determination of material properties and subsequent analysis should be
based on only one of these criteria.
Similar studies for slopes, using Bishop’s circular failure analysis for a wide range of slope
geometries and rock mass properties, gave:
91.0'max72.0−x a−
'm
0
.
2 = Hcmcmγσ (19)
where H is the height of the slope.
7. ESTIMATION OF DISTURBANCE FACTOR D
Experience in the design of slopes in very large open pit mines has shown that the Hoek-Brown
criterion for undisturbed in situ rock masses (D = 0) results in rock mass properties that are too
optimistic [21, 22]. The effects of heavy blast
damage as well as stress relief due to removal of the overburden result in disturbance of the rock
mass. It is considered that the “disturbed” rock mass properties [6], D = 1 in equations 3 and 4, are
more appropriate for these rock masses.
Lorig and Varona [23] showed that factors such as the lateral confinement produced by different
radii of curvature of slopes (in plan) as compared with their height also have an influence on the
degree of disturbance.
Sonmez and Ulusay [24] back-analysed five slope failures in open pit coal mines in Turkey and
attempted to assign disturbance factors to each rock mass based upon their assessment of the rock
mass properties predicted by the Hoek-Brown criterion. Unfortunately, one of the slope failures
appears to be structurally controlled while another consists of a transported waste pile. The authors
consider that the Hoek-Brown criterion is not applicable to these two cases.
Cheng and Liu [25] report the results of very careful back analysis of deformation measurements,
from extensometers placed before the commencement of excavation, in the Mingtan power cavern
in Taiwan. It was found that a zone of blast damage extended for a distance of approximately 2 m
around all large excavations. The back-calculated strength and deformation properties of the
damaged rock mass give an equivalent disturbance factor D = 0.7.
From these references it is clear that a large number of factors can influence the degree of
disturbance in the rock mass surrounding an excavation and that it may never be possible to
quantify these factors precisely. However, based on their experience and on an analysis of all the
details contained in these papers, the authors have attempted to draw up a set of guidelines for
estimating the factor D and these are summarised in Table 1.
The influence of this disturbance factor can be large. This is illustrated by a typical example in
which ciσ = 50 MPa, mi = 10 and GSI = 45. For an undisturbed in situ rock mass surrounding a
tunnel at a depth of 100 m, with a disturbance factor D = 0, the equivalent friction angle is 47.16°
while the cohesive strength is c 0.58 MPa. A rock mass with the same basic parameters but in highly
disturbed slope of 100 m height, with a disturbance factor of D = 1, has an equivalent friction angle
of 27.61° and a cohesive strength of 0.35 MPa. ='φ='='φ='c
Note that these are guidelines only and the reader would be well advised to apply the values given
5. with caution. However, they can be used to provide a realistic starting point for any design and, if
the observed or measured performance of the excavation turns out to be better than predicted, the
disturbance factors can be adjusted downwards.
8. CONCLUSION
A number of uncertainties and practical problems in using the Hoek-Brown failure criterion have
been addressed in this paper. Wherever possible, an attempt has been made to provide a rigorous
and unambiguous method for calculating or estimating the input parameters required for the
analysis. These methods have all been implemented in a Windows program called “RocLab” that
can be downloaded (free) from www.rocscience.com. This program includes tables and charts for
estimating the uniaxial compressive strength of the intact rock elements (ciσ), the material constant
mi and the Geological Strength Index (GSI).
9. ACKNOWLEDGEMENTS
The authors wish to acknowledge the contributions of Professor E.T. Brown in reviewing a draft of
this paper and in participating in the development of the Hoek-Brown criterion for the past 25 years.
able 1: Guidelines for estimating disturbance factor D
T
Appearance of rock mass
Description of rock mass
Suggested value of D
Excellent quality controlled blasting or excavation by Tunnel Boring Machine results in minimal
disturbance to the confined rock mass surrounding a tunnel.
D=0
Mechanical or hand excavation in poor quality rock masses (no blasting) results in minimal
disturbance to he surrounding rock mass.
t
Where squeezing problems result in significant floor heave, disturbance can be severe unless a
temporary invert, as shown in the photograph, is placed.
D=0
D = 0.5
No invert
Very poor quality blasting in a hard rock tunnel results in severe local damage, extending 2 or 3 m,
in the surrounding rock mass.
D = 0.8
Small scale blasting in civil engineering slopes results in modest rock mass damage, particularly if
controlled blasting is used as shown on the left hand side of the photograph. However, stress relief
results in some disturbance.
D = 0.7
Good blasting
D = 1.0
Poor blasting
Very large open pit mine slopes suffer significant disturbance due to heavy production blasting and
also due to stress relief from overburden removal.
In some softer rocks excavation can be carried out by ripping and dozing and the degree of damage
to the slopes is less.
D = 1.0
Production blasting
D = 0.7
Mechanical excavation
10. REFERENCES
1. Hoek, E. and Brown, E.T. 1980. Empirical strength criterion for rock masses. J. Geotech. Engng Div., ASCE 106
(GT9), 1013-1035.
2. Hoek, E. and Brown, E.T. 1980. Underground Excavations in Rock, London, Instn Min. Metall.
3. Hoek, E. 1968. Brittle failure of rock. In Rock Mechanics in Engineering Practice . (eds K.G. Stagg and O.C.
6. Zienkiewicz), 99-124. London: Wiley
4. Brown, E.T. 1970. Strength of models of rock with intermittent joints. J. Soil Mech. Foundn Div., ASCE 96, SM6,
1935-1949.
5. Bieniawski Z.T. 1976. Rock mass classification in rock engineering. In Exploration for Rock Engineering, Proc. of
the Symp., (ed. Z.T. Bieniawski) 1, 97-106. Cape Town, Balkema.
6. Hoek, E. and Brown, E.T. 1988. The Hoek-Brown failure criterion - a 1988 update. Proc. 15th Canadian Rock Mech.
Symp. (ed. J.C. Curran), 31-38. Toronto, Dept. Civil Engineering, University of Toronto.
7. Hoek, E., Wood D. and Shah S. 1992. A modified Hoek-Brown criterion for jointed rock masses. Proc. Rock
Characterization, Symp. Int. Soc. Rock Mech.: Eurock ‘92, (ed. J.A. Hudson), 209-214. London, Brit. Geotech. Soc.
8. Hoek, E. 1983. Strength of jointed rock masses, 23rd. Rankine Lecture. Géotechnique 33 (3), 187-223.
9. Ucar, R. (1986) Determination of shear failure envelope in rock masses. J. Geotech. Engg. Div. ASCE. 112, (3),
303-315.
10. Londe, P. 1988. Discussion on the determination of the shear stress failure in rock masses. ASCE J Geotech Eng
Div, 14, (3), 374-6.
11. Carranza-Torres, C., and Fairhurst, C. 1999. General formulation of the elasto-plastic response of openings in rock
using the Hoek-Brown failure criterion. Int. J. Rock Mech. Min. Sci., 36 (6), 777-809.
12. Hoek, E. 1990. Estimating Mohr-Coulomb friction and cohesion values from the Hoek-Brown failure criterion.
Intnl. J. Rock Mech. & Mining Sci. & Geomechanics Abstracts. 12 (3), 227-229.
13. Hoek, E. 1994. Strength of rock and rock masses, ISRM News Journal, 2 (2), 4-16.
14. Hoek, E. and Brown, E.T. 1997. Practical estimates of rock mass strength. Intnl. J. Rock Mech. & Mining Sci. &
Geomechanics Abstracts. 34 (8), 1165-1186.
15. Hoek, E., Kaiser P.K. and Bawden W.F. 1995. Support of underground excavations in hard rock. Rotterdam,
Balkema.
16. Hoek, E., Marinos, P. and Benissi, M. 1998. Applicability of the Geological Strength Index (GSI) classification for
very weak and sheared rock masses. The case of the Athens Schist Formation. Bull. Engg. Geol. Env. 57(2), 151-160.
17. Marinos, P and Hoek, E. 2000. GSI – A geologically friendly tool for rock mass strength estimation. Proc.
GeoEng2000 Conference, Melbourne.
18. Hoek, E. and Marinos, P. 2000. Predicting Tunnel Squeezing. Tunnels and Tunnelling International. Part 1 –
November 2000, Part 2 – December, 2000
19. Marinos. P, and Hoek, E. 2001. – Estimating the geotechnical properties of heterogeneous rock masses such as
flysch. Accepted for publication in the Bulletin of the International Association of Engineering Geologists
20. Balmer, G. 1952. A general analytical solution for Mohr's envelope. Am. Soc. Test. Mat. 52, 1260-1271.
21. Sjöberg, J., Sharp, J.C., and Malorey, D.J. 2001 Slope stability at Aznalcóllar. In Slope stability in surface mining.
(eds. W.A. Hustrulid, M.J. McCarter and D.J.A. Van Zyl). Littleton: Society for Mining, Metallurgy and Exploration,
Inc., 183-202.
22. Pierce, M., Brandshaug, T., and Ward, M. 2001 Slope stability assessment at the Main Cresson Mine. In Slope
stability in surface mining. (eds. W.A. Hustrulid, M.J. McCarter and D.J.A. Van Zyl). Littleton: Society for Mining,
Metallurgy and Exploration, Inc., 239-250.
23. Lorig, L., and Varona, P. 2001 Practical slope-stability analysis using finite-difference codes. In Slope stability in
surface mining. (eds. W.A. Hustrulid, M.J. McCarter and D.J.A. Van Zyl). Littleton: Society for Mining, Metallurgy and
Exploration, Inc., 115-124.
24. Sonmez, H., and Ulusay, R. 1999. Modifications to the geological strength index (GSI) and their applicability to the
stability of slopes. Int. J. Rock Mech. Min. Sci., 36 (6), 743-760.
25. Cheng, Y., and Liu, S. 1990. Power caverns of the Mingtan Pumped Storage Project, Taiwan. In Comprehensive
Rock Engineering. (ed. J.A. Hudson), Oxford: Pergamon, 5, 111-132.