Class 5 Permeability Test ( Geotechnical Engineering )Hossam Shafiq I
This document discusses permeability testing methods for geotechnical engineering laboratory class. It describes two common permeability test methods: the constant-head test and falling-head test. The constant-head test applies a constant head of water to a soil specimen in a permeameter to measure hydraulic conductivity. The falling-head test similarly uses a permeameter but measures the change in head over time. Both tests aim to determine the hydraulic conductivity value k, which indicates a soil's ability to transmit water and is important for analyzing seepage, settlement, and slope stability.
This document discusses permeability and seepage in soils. It begins with an overview of permeability, noting that it is a measure of how easily water can flow through soil. Darcy's law is then presented, which relates permeability to flow velocity. Several laboratory tests for measuring permeability are also described, including constant head, falling head, and determination from consolidation or capillary tests. Real-world applications where permeability is important are mentioned, such as seepage through dams or behind retaining walls.
This document provides information about soil compressibility and consolidation. It discusses the different types of soil settlement that can occur when stress is applied, including immediate elastic settlement, primary consolidation settlement, and secondary consolidation settlement. It describes how consolidation settlement occurs as water is expelled from saturated soils under increased stress levels. Graphs are presented showing typical relationships between void ratio, effective stress, and compression index that help explain consolidation concepts. The role of overconsolidation ratio and preconsolidation stress are defined in relation to soil compressibility. Methods for estimating settlement magnitudes, such as using Casagrande's approach, are also summarized.
This document contains lecture notes on soil compressibility and consolidation from Khalid R. Mahmood, Assistant Professor of Civil Engineering at the University of Anbar in Iraq. The notes cover topics such as immediate settlement, primary consolidation settlement, secondary compression settlement, consolidation testing methods, and void ratio-effective stress relationships for normally consolidated and overconsolidated soils. Laboratory consolidation tests on soil samples are discussed as a method to determine compression indices, coefficient of permeability, and void ratio-effective stress behavior. Disturbance effects on consolidation testing results are also summarized.
These slides describes the permeability of soil in a very lucid manner. This has been posted specially for the students of Diploma and Degree Engineering courses.
This document discusses soil mechanics concepts related to lateral earth pressure. It defines active and passive earth pressures and describes Rankine's theory and assumptions for calculating lateral pressures on retaining walls. Equations are provided for determining active and passive earth pressure coefficients and distributions for cohesionless and cohesive soils. The effects of groundwater, surcharges, and sloping backfills are also examined. Sample problems are included to calculate lateral earth pressures and forces on retaining walls for different soil and loading conditions.
This document discusses flow nets, which are used to analyze seepage problems in soil mechanics. It covers:
1. Common boundary conditions like impermeable boundaries which are modeled as flow lines and submerged boundaries which are equipotentials.
2. Procedures for drawing flow nets including satisfying boundary conditions and creating a square mesh.
3. Using flow nets to calculate quantities of interest like flow and pore water pressure by relating the number of flow tubes and equipotentials.
4. Examples of applying flow nets to problems like seepage under a dam or stranded vessel rescue.
This document discusses the index properties of soil, which can be divided into soil grain properties and soil aggregate properties. Soil grain properties depend on individual grains and are independent of formation, including mineral composition, specific gravity, grain size and shape. Soil aggregate properties depend on the soil mass as a whole and represent collective behavior, influenced by stress history, formation and structure. Common index properties discussed include grain size distribution, Atterberg limits which classify soil consistency, and plasticity index. Engineering applications of index properties include soil classification, permeability estimation, and criteria for materials selection.
Class 5 Permeability Test ( Geotechnical Engineering )Hossam Shafiq I
This document discusses permeability testing methods for geotechnical engineering laboratory class. It describes two common permeability test methods: the constant-head test and falling-head test. The constant-head test applies a constant head of water to a soil specimen in a permeameter to measure hydraulic conductivity. The falling-head test similarly uses a permeameter but measures the change in head over time. Both tests aim to determine the hydraulic conductivity value k, which indicates a soil's ability to transmit water and is important for analyzing seepage, settlement, and slope stability.
This document discusses permeability and seepage in soils. It begins with an overview of permeability, noting that it is a measure of how easily water can flow through soil. Darcy's law is then presented, which relates permeability to flow velocity. Several laboratory tests for measuring permeability are also described, including constant head, falling head, and determination from consolidation or capillary tests. Real-world applications where permeability is important are mentioned, such as seepage through dams or behind retaining walls.
This document provides information about soil compressibility and consolidation. It discusses the different types of soil settlement that can occur when stress is applied, including immediate elastic settlement, primary consolidation settlement, and secondary consolidation settlement. It describes how consolidation settlement occurs as water is expelled from saturated soils under increased stress levels. Graphs are presented showing typical relationships between void ratio, effective stress, and compression index that help explain consolidation concepts. The role of overconsolidation ratio and preconsolidation stress are defined in relation to soil compressibility. Methods for estimating settlement magnitudes, such as using Casagrande's approach, are also summarized.
This document contains lecture notes on soil compressibility and consolidation from Khalid R. Mahmood, Assistant Professor of Civil Engineering at the University of Anbar in Iraq. The notes cover topics such as immediate settlement, primary consolidation settlement, secondary compression settlement, consolidation testing methods, and void ratio-effective stress relationships for normally consolidated and overconsolidated soils. Laboratory consolidation tests on soil samples are discussed as a method to determine compression indices, coefficient of permeability, and void ratio-effective stress behavior. Disturbance effects on consolidation testing results are also summarized.
These slides describes the permeability of soil in a very lucid manner. This has been posted specially for the students of Diploma and Degree Engineering courses.
This document discusses soil mechanics concepts related to lateral earth pressure. It defines active and passive earth pressures and describes Rankine's theory and assumptions for calculating lateral pressures on retaining walls. Equations are provided for determining active and passive earth pressure coefficients and distributions for cohesionless and cohesive soils. The effects of groundwater, surcharges, and sloping backfills are also examined. Sample problems are included to calculate lateral earth pressures and forces on retaining walls for different soil and loading conditions.
This document discusses flow nets, which are used to analyze seepage problems in soil mechanics. It covers:
1. Common boundary conditions like impermeable boundaries which are modeled as flow lines and submerged boundaries which are equipotentials.
2. Procedures for drawing flow nets including satisfying boundary conditions and creating a square mesh.
3. Using flow nets to calculate quantities of interest like flow and pore water pressure by relating the number of flow tubes and equipotentials.
4. Examples of applying flow nets to problems like seepage under a dam or stranded vessel rescue.
This document discusses the index properties of soil, which can be divided into soil grain properties and soil aggregate properties. Soil grain properties depend on individual grains and are independent of formation, including mineral composition, specific gravity, grain size and shape. Soil aggregate properties depend on the soil mass as a whole and represent collective behavior, influenced by stress history, formation and structure. Common index properties discussed include grain size distribution, Atterberg limits which classify soil consistency, and plasticity index. Engineering applications of index properties include soil classification, permeability estimation, and criteria for materials selection.
The document provides an overview of permeability of soil and seepage analysis. It defines key concepts like hydraulic head, Darcy's law, permeability of different soil types, and methods to determine permeability in the lab and field. It also covers seepage, derivation of the Laplace equation to model two-dimensional flow, and representation of flow using flow nets and their characteristics. Numerical methods are also mentioned as alternatives to analytical solutions of the Laplace equation.
This document discusses the consolidation of soil. It defines important terms like compression, compressibility, and consolidation. It outlines the differences between compaction and consolidation. The importance of consolidation theory is that it provides information on total settlement, time for settlement, and types of settlement. Terzaghi's spring analogy is described to explain the consolidation process. A one-dimensional consolidation test procedure is outlined. Important definitions related to consolidation like compression index, swelling index, and coefficients are provided. The document also discusses normally, under, and over consolidated soils and how to determine preconsolidation pressure. Terzaghi's one-dimensional consolidation theory and solution are presented. Methods to determine degree of consolidation and coefficient of consolidation from laboratory test data are
Class 7 Consolidation Test ( Geotechnical Engineering )Hossam Shafiq I
This document provides an overview of a geotechnical engineering laboratory class on conducting a consolidation test on cohesive soil. The consolidation test is used to determine key soil properties like preconsolidation stress, compression index, recompression index, and coefficient of consolidation. The procedure involves placing a saturated soil sample in a consolidometer, applying incremental loads, and measuring the change in height over time to generate consolidation curves. Students will perform the test, calculate soil properties from the results, and include 10 plots and calculations in a laboratory report.
1. The document discusses consolidation in soils, including terminology, oedometer tests, preconsolidation pressure, and Terzaghi's theory of one-dimensional consolidation.
2. Key points include that consolidation is the decrease in soil volume due to increased loading, and includes primary consolidation through pore water expulsion and secondary consolidation via soil molecule rearrangement.
3. Oedometer tests are used to determine soil compressibility and preconsolidation pressure, the maximum past effective stress.
4. Terzaghi's theory assumes consolidation is one-dimensional, and that excess pore pressures dissipate over time according to a consolidation equation.
This document provides an overview of geotechnical engineering and soil mechanics concepts across 5 lectures. It discusses the origin and formation of soils, soil classification systems, phase relationships in soils, permeability, consolidation, shear strength, and soil stabilization techniques. Key topics covered include soil composition, index properties, stress conditions in soil, seepage analysis, compaction, shear strength determination methods, and mechanical and chemical stabilization methods. Real-world engineering applications of soil mechanics are also mentioned.
The document discusses soil permeability and seepage. It defines soil permeability as the ease with which water flows through permeable materials like soil. Darcy's law states that the rate of water flow through a soil is proportional to the hydraulic gradient and the soil's hydraulic conductivity. The hydraulic conductivity depends on factors like soil type, density, temperature, and viscosity of water. Laboratory tests like constant head and falling head permeability tests are used to measure a soil's hydraulic conductivity.
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.
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.
Lacey's regime theory states that the dimensions and slope of a channel are uniquely determined by the discharge, silt load, and erodibility of the soil material. A channel is in regime if there is no scouring or silting. Lacey proposed equations to calculate parameters like velocity, slope, and dimensions based on variables like discharge, silt factor, and side slopes. The theory has limitations as the conditions of true regime cannot be achieved and parameters like silt grade/load are not clearly defined. Lacey also developed shock theory accounting for form resistance due to bed irregularities.
The document discusses soil consolidation and laboratory consolidation testing. It begins with an introduction to consolidation and describes the three types of soil settlement: immediate elastic settlement, primary consolidation settlement, and secondary consolidation settlement. It then discusses consolidation in more detail, including the spring-cylinder model used to demonstrate consolidation principles. Finally, it describes the process and components of a laboratory oedometer consolidation test.
This document discusses seepage forces and their effect on soil stability. It defines seepage forces as the viscous drag of water flowing through soil pores, which increases intergranular pressure and reduces effective stresses. Seepage forces are higher in more permeable soils like sand versus less permeable soils like clay. Two case studies of dam failures are presented: Nanak Sagar Dam in 1962 failed due to internal erosion from seepage forces, while Fontenelle Dam in 1965 also failed due to piping caused by seepage. The conclusion is that seepage forces can be strong enough to cause liquefaction, erosion, and failures of dams and retaining walls if not properly addressed.
This presentation includes Definition of Permeability, measurement of Permeability, Validity of Darcy's law, Darcy's Law, Methods of Finding Permeability, factors affecting permeability, Permeability of Stratified Soil
1) Consolidation is the process where saturated clay soils expel pore water in response to increased loading, causing volume change. 2) During initial loading, pore water pressure increases and the soil skeleton does not feel the load. 3) Over time, pore water pressure dissipates and the load is transferred to the soil skeleton. 4) One-dimensional consolidation testing involves incrementally loading a saturated soil sample and measuring volume change and pore pressure dissipation over time.
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.
Okay, here are the steps to solve this:
1) Given:
Specific gravity (Gs) = 2.65
Void ratio (e) = 0.5
2) Critical hydraulic gradient (icr) is given by the equation:
icr = Gs - 1/(1+e)
3) Substitute the values:
icr = 2.65 - 1/(1+0.5)
= 2.65 - 1/1.5
= 2.65 - 0.667
= 1.983
So the critical hydraulic gradient for this sand deposit is 1.983.
The document discusses soil consistency and Atterberg limits. It defines consistency as the firmness of cohesive soils, which varies with water content. Atterberg limits - liquid limit, plastic limit, and shrinkage limit - define the boundaries between solid, semi-solid, plastic, and liquid states. Tests are described to determine these limits and classify soil consistency. The plasticity index is also discussed as it relates to soil classification.
This document discusses consolidation settlement, which occurs when saturated soil is loaded and squeezed, causing water to be expelled over time (years depending on soil permeability) and the soil volume to decrease. As water flows out, the soil settles vertically in direct proportion to the volume decrease. Two methods estimate consolidation settlement: using the coefficient of volume compressibility (mv) or the void ratio-effective stress (e-logσ'v) relationship. Practical applications include using prefabricated vertical drains to accelerate consolidation in clay soils.
This document discusses principles of effective stress, capillarity, and seepage through soil. It defines total stress as the stress acting at a point from the total weight of soil above it, and effective stress as the total stress minus the pore water pressure. Capillarity allows water to move upward through small soil pores due to adhesive and cohesive forces. Seepage is the flow of water through soil, which depends on factors like permeability. Flow nets can be used to model two-dimensional seepage by drawing curves representing flow lines and equipotential lines meeting at right angles.
Basics of groundwater hydrology in geotechnical engineering: Permeability - ...ohamza
This document provides an overview of permeability and Darcy's law. It discusses soils as porous media, defines concepts like hydraulic head and gradient. It explains Darcy's law and how permeability is affected by factors like temperature. It also describes methods to determine the coefficient of permeability in the laboratory, such as constant head and falling head permeability tests. Stratified soils are discussed and how permeability is calculated for layered soils with vertical or horizontal flow.
Okay, let me solve this step-by-step:
Given:
Discharge of canal (Q) = 50 cumec
Let's assume:
Bed width (B) = x meters
Depth of water (D) = y meters
Cross-sectional area (A) = B*D + 1.5D^2
Wetted perimeter (P) = B + 3.6D
Hydraulic mean depth (R) = A/P
From the economical section condition:
R = D/2
Equating the two expressions of R and solving:
(B*D + 1.5D^2) / (B + 3
This document discusses laminar and turbulent flow, boundary layer theory, and the Moody chart. It defines laminar and turbulent flow and describes Reynold's experiment. It introduces boundary layer theory, defining boundary layer thickness using nominal, displacement, momentum, and energy thicknesses. It describes how the boundary layer develops over a flat plate from laminar to turbulent. The Moody chart is introduced as relating friction factor, Reynolds number, and surface roughness to predict pressure drop in pipe flow.
This document provides information on the design of unlined canals in alluvial soil based on Kennedy's theory and Lacey's theory. Kennedy's theory relates the critical velocity to the full supply depth and introduces a critical velocity ratio to account for different silt grades. Lacey's theory is based on the concept of a regime channel where silt grade and charge remain constant. It provides equations to calculate velocity, hydraulic mean depth, area, and bed slope without relying on trial and error. Both theories have drawbacks as they do not fully consider variables like changing silt grade and concentration.
The document provides an overview of permeability of soil and seepage analysis. It defines key concepts like hydraulic head, Darcy's law, permeability of different soil types, and methods to determine permeability in the lab and field. It also covers seepage, derivation of the Laplace equation to model two-dimensional flow, and representation of flow using flow nets and their characteristics. Numerical methods are also mentioned as alternatives to analytical solutions of the Laplace equation.
This document discusses the consolidation of soil. It defines important terms like compression, compressibility, and consolidation. It outlines the differences between compaction and consolidation. The importance of consolidation theory is that it provides information on total settlement, time for settlement, and types of settlement. Terzaghi's spring analogy is described to explain the consolidation process. A one-dimensional consolidation test procedure is outlined. Important definitions related to consolidation like compression index, swelling index, and coefficients are provided. The document also discusses normally, under, and over consolidated soils and how to determine preconsolidation pressure. Terzaghi's one-dimensional consolidation theory and solution are presented. Methods to determine degree of consolidation and coefficient of consolidation from laboratory test data are
Class 7 Consolidation Test ( Geotechnical Engineering )Hossam Shafiq I
This document provides an overview of a geotechnical engineering laboratory class on conducting a consolidation test on cohesive soil. The consolidation test is used to determine key soil properties like preconsolidation stress, compression index, recompression index, and coefficient of consolidation. The procedure involves placing a saturated soil sample in a consolidometer, applying incremental loads, and measuring the change in height over time to generate consolidation curves. Students will perform the test, calculate soil properties from the results, and include 10 plots and calculations in a laboratory report.
1. The document discusses consolidation in soils, including terminology, oedometer tests, preconsolidation pressure, and Terzaghi's theory of one-dimensional consolidation.
2. Key points include that consolidation is the decrease in soil volume due to increased loading, and includes primary consolidation through pore water expulsion and secondary consolidation via soil molecule rearrangement.
3. Oedometer tests are used to determine soil compressibility and preconsolidation pressure, the maximum past effective stress.
4. Terzaghi's theory assumes consolidation is one-dimensional, and that excess pore pressures dissipate over time according to a consolidation equation.
This document provides an overview of geotechnical engineering and soil mechanics concepts across 5 lectures. It discusses the origin and formation of soils, soil classification systems, phase relationships in soils, permeability, consolidation, shear strength, and soil stabilization techniques. Key topics covered include soil composition, index properties, stress conditions in soil, seepage analysis, compaction, shear strength determination methods, and mechanical and chemical stabilization methods. Real-world engineering applications of soil mechanics are also mentioned.
The document discusses soil permeability and seepage. It defines soil permeability as the ease with which water flows through permeable materials like soil. Darcy's law states that the rate of water flow through a soil is proportional to the hydraulic gradient and the soil's hydraulic conductivity. The hydraulic conductivity depends on factors like soil type, density, temperature, and viscosity of water. Laboratory tests like constant head and falling head permeability tests are used to measure a soil's hydraulic conductivity.
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.
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.
Lacey's regime theory states that the dimensions and slope of a channel are uniquely determined by the discharge, silt load, and erodibility of the soil material. A channel is in regime if there is no scouring or silting. Lacey proposed equations to calculate parameters like velocity, slope, and dimensions based on variables like discharge, silt factor, and side slopes. The theory has limitations as the conditions of true regime cannot be achieved and parameters like silt grade/load are not clearly defined. Lacey also developed shock theory accounting for form resistance due to bed irregularities.
The document discusses soil consolidation and laboratory consolidation testing. It begins with an introduction to consolidation and describes the three types of soil settlement: immediate elastic settlement, primary consolidation settlement, and secondary consolidation settlement. It then discusses consolidation in more detail, including the spring-cylinder model used to demonstrate consolidation principles. Finally, it describes the process and components of a laboratory oedometer consolidation test.
This document discusses seepage forces and their effect on soil stability. It defines seepage forces as the viscous drag of water flowing through soil pores, which increases intergranular pressure and reduces effective stresses. Seepage forces are higher in more permeable soils like sand versus less permeable soils like clay. Two case studies of dam failures are presented: Nanak Sagar Dam in 1962 failed due to internal erosion from seepage forces, while Fontenelle Dam in 1965 also failed due to piping caused by seepage. The conclusion is that seepage forces can be strong enough to cause liquefaction, erosion, and failures of dams and retaining walls if not properly addressed.
This presentation includes Definition of Permeability, measurement of Permeability, Validity of Darcy's law, Darcy's Law, Methods of Finding Permeability, factors affecting permeability, Permeability of Stratified Soil
1) Consolidation is the process where saturated clay soils expel pore water in response to increased loading, causing volume change. 2) During initial loading, pore water pressure increases and the soil skeleton does not feel the load. 3) Over time, pore water pressure dissipates and the load is transferred to the soil skeleton. 4) One-dimensional consolidation testing involves incrementally loading a saturated soil sample and measuring volume change and pore pressure dissipation over time.
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.
Okay, here are the steps to solve this:
1) Given:
Specific gravity (Gs) = 2.65
Void ratio (e) = 0.5
2) Critical hydraulic gradient (icr) is given by the equation:
icr = Gs - 1/(1+e)
3) Substitute the values:
icr = 2.65 - 1/(1+0.5)
= 2.65 - 1/1.5
= 2.65 - 0.667
= 1.983
So the critical hydraulic gradient for this sand deposit is 1.983.
The document discusses soil consistency and Atterberg limits. It defines consistency as the firmness of cohesive soils, which varies with water content. Atterberg limits - liquid limit, plastic limit, and shrinkage limit - define the boundaries between solid, semi-solid, plastic, and liquid states. Tests are described to determine these limits and classify soil consistency. The plasticity index is also discussed as it relates to soil classification.
This document discusses consolidation settlement, which occurs when saturated soil is loaded and squeezed, causing water to be expelled over time (years depending on soil permeability) and the soil volume to decrease. As water flows out, the soil settles vertically in direct proportion to the volume decrease. Two methods estimate consolidation settlement: using the coefficient of volume compressibility (mv) or the void ratio-effective stress (e-logσ'v) relationship. Practical applications include using prefabricated vertical drains to accelerate consolidation in clay soils.
This document discusses principles of effective stress, capillarity, and seepage through soil. It defines total stress as the stress acting at a point from the total weight of soil above it, and effective stress as the total stress minus the pore water pressure. Capillarity allows water to move upward through small soil pores due to adhesive and cohesive forces. Seepage is the flow of water through soil, which depends on factors like permeability. Flow nets can be used to model two-dimensional seepage by drawing curves representing flow lines and equipotential lines meeting at right angles.
Basics of groundwater hydrology in geotechnical engineering: Permeability - ...ohamza
This document provides an overview of permeability and Darcy's law. It discusses soils as porous media, defines concepts like hydraulic head and gradient. It explains Darcy's law and how permeability is affected by factors like temperature. It also describes methods to determine the coefficient of permeability in the laboratory, such as constant head and falling head permeability tests. Stratified soils are discussed and how permeability is calculated for layered soils with vertical or horizontal flow.
Okay, let me solve this step-by-step:
Given:
Discharge of canal (Q) = 50 cumec
Let's assume:
Bed width (B) = x meters
Depth of water (D) = y meters
Cross-sectional area (A) = B*D + 1.5D^2
Wetted perimeter (P) = B + 3.6D
Hydraulic mean depth (R) = A/P
From the economical section condition:
R = D/2
Equating the two expressions of R and solving:
(B*D + 1.5D^2) / (B + 3
This document discusses laminar and turbulent flow, boundary layer theory, and the Moody chart. It defines laminar and turbulent flow and describes Reynold's experiment. It introduces boundary layer theory, defining boundary layer thickness using nominal, displacement, momentum, and energy thicknesses. It describes how the boundary layer develops over a flat plate from laminar to turbulent. The Moody chart is introduced as relating friction factor, Reynolds number, and surface roughness to predict pressure drop in pipe flow.
This document provides information on the design of unlined canals in alluvial soil based on Kennedy's theory and Lacey's theory. Kennedy's theory relates the critical velocity to the full supply depth and introduces a critical velocity ratio to account for different silt grades. Lacey's theory is based on the concept of a regime channel where silt grade and charge remain constant. It provides equations to calculate velocity, hydraulic mean depth, area, and bed slope without relying on trial and error. Both theories have drawbacks as they do not fully consider variables like changing silt grade and concentration.
This document provides an overview of a reservoir engineering course focused on Darcy's Law and permeability. It covers key topics like laboratory analysis of rock properties including porosity, saturation and permeability. It also discusses linear and radial flow models based on Darcy's Law and techniques for determining permeability in the laboratory and averaging permeabilities for heterogeneous reservoirs. The document emphasizes that permeability is an important property that controls fluid flow in reservoirs and was first mathematically defined by Henry Darcy. It provides the equations for linear and radial flow based on Darcy's Law.
This document provides an overview of Darcy's law and permeability concepts covered in a reservoir engineering course. It begins by defining permeability as a property that controls fluid flow in porous media. Darcy's law is then introduced, which relates fluid flow rate to pressure drop, permeability, fluid properties, and geometry. The document goes on to discuss permeability measurement techniques, effective and relative permeability, reservoir properties, heterogeneity, and applications of Darcy's law to linear and radial flow models.
This document discusses vertical drains, which are used to accelerate consolidation in saturated clays. It describes how vertical drains work by shortening drainage paths within clay. Common installation methods involve creating boreholes and placing vertical drains made of sand or prefabricated materials like sandwick or band drains. Design considerations for vertical drains include drain spacing, fill height, soil permeability, and achieving a desired consolidation level within a given time. Mathematical equations are provided for analyzing consolidation based on Terzaghi's theory involving factors like coefficient of consolidation and excess pore water pressure. An example problem demonstrates calculating degree of consolidation over time for a layered soil system using vertical drains.
This document discusses the engineering properties of soil, including permeability, shear strength, compressibility, and compaction. It defines permeability as the property that allows water to pass through a porous material. Several factors that affect permeability are described, including particle size, void ratio, properties of pore fluid, and soil structure. Methods for determining permeability in the lab and field are presented. The concepts of shear strength and shear failure based on the Mohr-Coulomb failure criterion are explained. Laboratory tests for measuring shear strength like direct shear tests and triaxial tests are outlined. The document also covers compressibility and consolidation of soils, including definitions, the spring analogy model, laboratory consolidation testing, and parameters like compression index. Finally, it discusses comp
This document discusses the design of canals. It provides key terms related to canal design such as alluvial soil, silt factor, mean velocity, critical velocity, and more. It summarizes Kennedy's theory and Lacey's theory for the design of unlined canals on alluvial soils. Kennedy's theory relates critical velocity to depth while Lacey's theory relates mean velocity to hydraulic mean depth. The document also compares the two theories and lists some drawbacks of each. It provides the design procedure for both theories and references several textbooks on irrigation engineering.
This chapter reviews concepts of 1D open channel hydraulics relevant to modeling sediment transport in rivers and turbidity currents. It discusses simplifying the cross-sectional shape of channels to rectangular, defines important parameters like flow depth and velocity, and reviews equations for normal flow, boundary shear stress, and resistance relations that are used to estimate properties of bankfull flow conditions based on the assumption of normal flow.
Open Channel Flow: fluid flow with a free surfaceIndrajeet sahu
Open Channel Flow: This topic focuses on fluid flow with a free surface, such as in rivers, canals, and drainage ditches. Key concepts include the classification of flow types (steady vs. unsteady, uniform vs. non-uniform), hydraulic radius, flow resistance, Manning's equation, critical flow conditions, and energy and momentum principles. It also covers flow measurement techniques, gradually varied flow analysis, and the design of open channels. Understanding these principles is vital for effective water resource management and engineering applications.
A Note on the Beavers and Joseph Condition for Flow over a Forchheimer Porous...IJRESJOURNAL
ABSTRACT : In thiswork, an attemptis made to relate the slip parameter in the Beavers and Joseph condtionat the interface between a Darcy layer and a Navier-Stokes channel, to the slip parameter to beusedwhen the porous layer is a Forchheimer layer.
1) Water flows through the pores in soil from areas of higher total head to lower total head, similar to flow in pipes. The rate and quantity of flow are important for problems like filtration, flow through dams, and piping failure.
2) Darcy's law states that the velocity of flow through soil is directly proportional to the hydraulic gradient. The coefficient of permeability depends on factors like pore size, grain size, void ratio, and degree of saturation. It varies widely between soil types from clean gravel to clay.
3) The coefficient of permeability can be determined through constant head or falling head permeability tests in the laboratory. These tests involve measuring the flow rate of water through a soil sample under a constant or falling
This document discusses various characteristics of catchments that affect surface runoff, including:
1. The area, shape, slope, and drainage patterns of a catchment determine the volume and timing of surface runoff from storms.
2. Important geometric parameters that represent catchment characteristics are the stream order, stream density, drainage density, relief, slope, length, shape, and hypsometric curve.
3. Drainage density indicates the level of drainage development and influences how quickly runoff moves from the catchment, with higher densities associated with steeper slopes and less permeable soils.
This document provides an overview of a reservoir engineering course focused on fundamental rock properties. It discusses key topics like porosity, saturation, wettability, capillary pressure, and how they are determined through laboratory core analysis. Porosity refers to the pore space available to hold fluids and is classified as absolute or effective porosity. Saturation represents the fraction of pore space occupied by a fluid. Capillary pressure describes the pressure differential between immiscible fluids based on interface curvature. Laboratory tests on core samples are used to characterize these important rock properties.
Lecture 07 permeability and seepage (11-dec-2021)HusiShah
This document discusses permeability and seepage in geotechnical engineering. It begins by defining permeability as a measure of a soil's ability to allow water to flow through its pores or voids. It then discusses Darcy's law, which describes water flow through porous media, and how permeability/hydraulic conductivity is measured in the laboratory. The document also covers the Laplace equation for two-dimensional water flow and flow nets, which can be used to model groundwater flow patterns. It provides examples of how flow nets are constructed and how they can be used to calculate water flow and seepage pressures.
Uniform Flow: Basic concepts of free surface flows,
velocity and pressure distribution,
Mass, energy and momentum principle for prismatic and non-prismatic channels,
Review of Uniform flow: Standard equations,
hydraulically efficient channel sections,
compound sections,
Energy-depth relations:
Concept of specific energy, specific force,
critical flow, critical depth,
hydraulic exponents, and
Channel transitions.
This document defines and compares three types of boundary layer thickness:
1. Boundary layer thickness is the distance from the surface where the flow velocity is 99% of the free-stream velocity.
2. Displacement thickness is a theoretical thickness where displacing the surface would result in equal flow rates across sections inside and outside the boundary layer.
3. Momentum thickness is a measure of boundary layer thickness defined as the distance the surface would need to be displaced to compensate for the reduction in momentum due to the boundary layer. It is often used to determine drag on an object.
Uniform flow occurs in open channels when the water depth and cross-sectional area remain constant. It can only exist in channels with constant cross-sectional shape, slope, and discharge. Two common formulas used to calculate uniform flow are the Chezy and Manning's equations. The Manning's formula uses a roughness coefficient to account for channel materials. Normal depth is the critical depth at which flow just becomes uniform. Compound channels have multiple flow depths and calculating discharge involves dividing the channel into subsections. Critical slope is the minimum slope required for uniform flow at critical depth. When designing irrigation canals, parameters like roughness, slope, section shape, and depth-width ratios must be considered.
This document contains lecture notes on open channel hydraulics. It discusses various topics including classifications of open channel flow, basic principles of hydraulics applied to open channels, flow computation formulas, gradually and rapidly varied flow, unsteady flow, sediment transport, and channel geometry. The objectives of the course are to present principles of hydraulics and apply them to problems in civil, hydraulic, and irrigation engineering. After completing the course, students should understand how to apply hydraulic principles and be able to perform uniform and non-uniform, steady and unsteady flow computations in engineering problems.
hydro chapter_7_groundwater_by louy Al hami Louy Alhamy
This document discusses groundwater hydraulics and provides definitions and concepts related to aquifers and groundwater flow. It includes:
1) Definitions of key groundwater terms including the water table, aquifers, porosity, permeability, and hydraulic conductivity.
2) Descriptions of confined and unconfined aquifers and the differences between them.
3) An overview of Darcy's Law and how it relates groundwater flow rate to hydraulic gradient and aquifer properties.
4) Explanations of steady radial flow to wells using the Theim equation for confined aquifers.
5) Examples demonstrating calculations of transmissivity from pumping well data using the The
Similar to Basics of groundwater hydrology in geotechnical engineering: Permeability - Part B (20)
Basics of groundwater hydrology in geotechnical engineering: Permeability - Part B
1. Basics of groundwater hydrology in geotechnical engineering
Part B
Prepared by Dr O. Hamza
o_hamza at hotmail dot com
Lecture reference: OH GA03 B
OH_GA03_B
Permeability – Part B Dr O.Hamza
2. Content
• Introduction
• Quasi-one-dimensional
Quasi one dimensional and radial flow
• Field determination of coefficient of permeability
• Summary
S mmar
• Example problems
Permeability – Part B Dr O.Hamza
3. Introduction
Darcy’s law
q = Aki
where
k i coefficient of permeability with
is ffi i t f bilit ith
(Ref. Geotechnical on the Web)
dimensions of velocity (length/time)
Q Quantity of water
q is flow rate = = -----------------------
t Time
In a saturated porous media, the rate of flow of water q (volume/time)
through cross-sectional area ‘A’ is found to be proportional to hydraulic
th h ti l i f dt b ti lt h d li
gradient ‘ i ’
Permeability – Part B Dr O.Hamza
4. Introduction
Aquifer and Darcy’s law
Aquifer is a term used to designate a porous geological formation that:
- contains water at full saturation
- permits water to move through it under ordinary field conditions
Permeability – Part B Dr O.Hamza
5. Introduction
Aquifer and Darcy’s law
The horizontal flow rate q is constant. For an
aquifer of width B and varying thickness tt,
Darcy's Law indicates that
q=Aki
=Btki
or
Hydraulic gradient varies inversely with aquifer
thickness
Where flow occu s in a co
e e o occurs confined aqu e whose t c ess varies ge t y with
ed aquifer ose thickness a es gently t
position the flow can be treated as being essentially one-dimensional.
Permeability – Part B Dr O.Hamza
6. Quasi-one-dimensional
Quasi one dimensional and radial flow
• Cylindrical flow: confined aquifer
• Cylindrical flow: groundwater lowering
• Spherical flow
Permeability – Part B Dr O.Hamza
7. Quasi-one-dimensional and radial flow
Cylindrical flow: confined aquifer
Pumping aquifer
Confined aquifer
Steady-state pumping from a well which extends the full thickness of a
confined aquifer is one of the one dimensional problem which can be
one-dimensional
analysed in cylindrical coordinates.
Permeability – Part B Dr O.Hamza
8. Quasi-one-dimensional and radial flow
Cylindrical flow: confined aquifer
Darcy's Law still applies, with hydraulic
gradient dh/dr and area A varying with radius:
A = 2πr.t
2 rt
In this case pore pressure or head varies only with radius r
r.
Permeability – Part B Dr O.Hamza
9. Quasi-one-dimensional and radial flow
Cylindrical flow: confined aquifer
Integrating between the
borehole and at variable
distance r:
di t
where ro is the radius of the borehole and h0
the constant head in the borehole.
Permeability – Part B Dr O.Hamza
10. Quasi-one-dimensional and radial flow
Cylindrical flow: groundwater lowering
Pumping from a borehole can be used for
deliberate groundwater lowering in order to
facilitate excavation.
Permeability – Part B Dr O.Hamza
12. Quasi-one-dimensional and radial flow
Cylindrical flow: groundwater lowering
This is an example of quasi-one-
dimensional radial flow with flow thickness
t=h Then A=2πr h and
t=h. A=2πr.h Groundwater lowering
Original level of
water table
Integrating between the borehole and
at variable distance r: Drawdown
The radius of influence
Permeability – Part B Dr O.Hamza
13. Quasi-one-dimensional and radial flow
Spherical flow
Darcy's Law still applies, with hydraulic gradient dh/dr
and area A varying with radius: A=4πr²
where r0 is the radius of the piezometer
and h0 the constant head in the piezometer head varies only
with radius r
r.
Variation of pore pressure around a point source or side (for example, a
piezometer being used for in situ determination of permeability) is a one
in-situ one-
dimensional problem which can be analysed in spherical coordinates.
Permeability – Part B Dr O.Hamza
14. Determination of coefficient of permeability
• Laboratory measurement of the coefficient of permeability
L b t t f th ffi i t f bilit
• Field measurement of the permeability
• Empirical relations for the coefficient of permeability
Permeability – Part B Dr O.Hamza
15. Determination of coefficient of permeability
Field measurement of the permeability
Field measurement Laboratory measurement
• Field or in-situ measurement of permeability avoids the difficulties involved
in obtaining and setting up undisturbed samples
• Field or in-situ measurement of permeability provides information about bulk
permeability, rather than merely the permeability of a small and possibly
unrepresentative sample.
Is field measurement of permeability better than the lab
y
measurement?
Permeability – Part B Dr O.Hamza
16. Determination of coefficient of permeability
Field measurement of the permeability
Well-Pumping test
Observational boreholes
In a well-pumping test, a number of observation boreholes at radii r1 and
r2 are monitored to measure the pressure heads.
Permeability – Part B Dr O.Hamza
17. Determination of coefficient of permeability
Field measurement of the permeability
If the pumping causes a drawdown in an
unconfined (i.e. open surface) soil stratum Well-Pumping test
then the quasi one dimensional flow equation
quasi-one
is applied.
Integrating between the two test limits
and rearranging the equation:
Impermeable
(Assuming the pumping causes a drawdown in an
unconfined (i.e. open surface) soil stratum then)
Observational b h l
Ob ti l boreholes
Permeability – Part B Dr O.Hamza
18. Determination of coefficient of permeability
Field measurement of the permeability
If the soil stratum is confined and of thickness t Well-Pumping test
and remains saturated th
d i t t d then
Confined stratum
Permeability – Part B Dr O.Hamza
19. Determination of coefficient of permeability
Empirical relations for the coefficient of permeability
Empirical relations
p
k = function of (other parameters)
Permeability of all soils is strongly influenced by the density of packing of
the soil particles which can be simply described through void ratio e.
Several empirical equations for estimation of the coefficient of permeability
have been proposed in the past.
Permeability – Part B Dr O.Hamza
20. Determination of coefficient of permeability
Empirical relations for the coefficient of permeability
Permeability of granular soils
P bilit f l il
For fairly uniform sand Hazen (1930)
proposed the following relation between the
coefficient of permeability k (m/s) and the
effective particle size D10 (in mm) (the
particle size than which 10% soil is finer):
k = C D10
C.D 2
where C is a constant approximately equal to
pp y q
0.01 (see the figure beside)
Hazzan equation and data relating coefficient of
permeability and effective grain size of granular soils
Permeability – Part B Dr O.Hamza
21. Determination of coefficient of permeability
Empirical relations for the coefficient of permeability
Permeability of soft clays
P bilit f ft l
Samarasinghe, H
S i h Huang and D d Drnevich (1982) h
i h have suggested th t th
t d that the
coefficient of permeability of clays can be given by the equation:
en
k=C
1+ e
where
h
e is void ratio
C and n are constant to be determined experimentally
Consolidation of soft clay may involve a significant decrease in void ratio
and therefore of permeability.
Permeability – Part B Dr O.Hamza
22. Summary
• All soils are permeable materials, water being free to flow through the
interconnected pores between the solid particles.
• Water in saturated soil will flow in response to hydraulic g
p y gradient and occurs
towards the lower total head.
• Flow rate is proportional to the hydraulic gradient and can be affected by the
geometry of the pores.
pores
• The hydraulic gradient may be associated with natural flow or induced by
loading the soil (i.e. due to excavation or construction).
• Coefficient of permeability may be determined from laboratory experiments or
from in situe measurements
• Pore water pressure u at any point of the soil is computed from the definition
of the hydraulic head, u = γw(h-hz) (where h is total head and hz is
elevation head).
Permeability – Part B Dr O.Hamza
23. Quizzes and example problems
Work on:
• Quizzes: quiz 3 to 6 *
• Example problems: *
problem 3 and problem 4
* Note. quiz 1 and problem 1 and 2 are covered in Part A of
Permeability lecture
Permeability – Part B Dr O.Hamza
24. Working on Quizzes and Example problems
Quiz 3
The sets of nested piezometers shown below penetrate a layered aquifer.
•For one of the piezometers, indicate graphically the elevation head, pressure
head, and total head.
• For both cases, indicate the direction of the vertical flow between the layers.
• F case 2, what is a realistic situation th t might result i a set of h d
For 2 h ti li ti it ti that i ht lt in t f heads
such as this?
Note: The wells are drawn with some separation between them to allow you room to
label the heads. Assume, however, that they are truly nested, i.e., that they penetrate
the surface of the aquifer at the same location.
datum
Case 1 Case 2
Permeability – Part B Dr O.Hamza
25. Working on Quizzes and Example problems
Quiz 3
Solution:
S l ti
hw
h Flow Flow
hz
datum
Case 1 Case 2
The situation in Case 2 might happen if the middle layer is being pumped
OR if the middle layer is a zone of incredibly high conductivity.
Permeability – Part B Dr O.Hamza
26. Working on Quizzes and Example problems
Quiz 4
An inclined permeameter tube is filled with three layer of soil of different
permeabilities as shown in the figure
figure.
(i) Formulate q in terms of the different dimensions and permeabilities for
each soil element
(ii) D t
Determine th h d l
i the head loss (Δh) b t
between each soil element assuming
h il l t i
k1=k2=k3
(iii) Re-determine the head loss (Δh) between each soil element assuming
3k1=k2=2k3
(iv) Express the head at
points A, B, C, and D
A B C
(with respect to the
datum)
(v) Plot the various
heads versus
horizontal distance.
Permeability – Part B Dr O.Hamza
27. Working on Quizzes and Example problems
Quiz 4
(i) Flow rate q in each soil element is equal:
Δh
q = Aki = Ak
L
Δh Δh 2
q1 = Ak1 1 q 2 = Ak 2 q 3 = ...
L1 L2
q = q1 = q 2 = q 3
Δh = Δh1 + Δh 2 + Δh 3
Permeability – Part B Dr O.Hamza
28. Working on Quizzes and Example problems
Quiz 4
(ii) Flow rate q in each soil element is equal:
q = q1 = q 2 = q 3
29. Working on Quizzes and Example problems
Quiz 4
(iii) Flow rate q in each soil element is equal:
q = q1 = q 2 = q 3
31. Working on Quizzes and Example problems
Quiz 4
(v) Plotting
NOTE: It is coincident
that ll heads
th t all h d appears
in a straight line.
32. Working on Quizzes and Example problems
Quiz 5
The site consists of an unconfined aquifer and a confined aquifer separated by a
5-m thick
5 thi k confining layer. Water in the unconfined aquifer i f h and water
fi i l W t i th fi d if is fresh, d t
in the confined aquifer is saline. Two nested piezometers have been drilled,
one penetrating the unconfined aquifer (P1), and one penetrating the confined
aquifer (P2)
).
Land surface elevation: 68.1 m Temperature of water in P1 and P2: 16° C
Depth to P1: 21.2 m Depth to P2: 38.6 m
Depth to water in the well at P1: 4.3 m Depth to water in the well at P2: 4.9 m
Unit weight of fresh water at 16° C: 9.99 kN/m3 Unit weight of water in P2: 10.21 kN/m3
• Sketch a diagram (doesn’t have to be to scale) showing the information
described above.
• What is the total head (h1) for P1?
• Determine the pressure head for P2 (hw2-saline), and the equivalent fresh-water
pressure head for P2 (hw2-frish)
w2 frish
• What is the total fresh-water head (h2-fresh) for P2?
• Will you issue a permit to inject hazardous waste into the deep aquifer ? Why
or why not?
Permeability – Part B Dr O.Hamza
33. Working on Quizzes and Example problems
Quiz 5
4.3t
4.9
21.2
38.6 m
68.1 m
Datum
Permeability – Part B Dr O.Hamza
34. Working on Quizzes and Example problems
Quiz 5
Fresh water total head for P1 is 68.1 – 4.3 = 63.8 m
Saline pressure head for P2 is 38.6 – 4.9 = 33.7 m
For the equivalent fresh-water pressure head, pressure must be equal:
fresh water head
uSaline = ufirsh
So γSaline x 33.7 = γfrish x hw2-frish
solve for hw2-frish: = γSaline x 33.7 / γfrish
= 10.21 x 33.7 /9.99 = 34.4 m
so,
so h2-fresh = hz2 + hw2-frish = (68 1 – 38 6 ) + 34.4 = 63 9 m
f f (68.1 38.6 34 4 63.9
Thus flow is in an UPWARD direction from the lower aquifer, and you should
not issue the permit (In addition if you inject waste into the lower aquifer
permit. addition,
it will further increase the pressure head and increase the upward
gradient.)
Permeability – Part B Dr O.Hamza
35. Working on Quizzes and Example problems
Quiz 6
A soil profile consists of th
il fil i t f three l
layers with properties shown i th t bl b l
ith ti h in the table below.
Calculate the equivalent coefficients of permeability parallel and normal
to the stratum.
Layer Thickness (m) kx (parallel, m/s) kz (normal, m/s)
1 3 2x10-6
6 1.0x10 6
1 0x10-6
2 4 5x10-8 2.5x10-8
3 3 3x10-5 1.5x10-5
Answers:
For the flow parallel to the layers: kx= 9.6x10^-6 m/s
For the flow normal to the layers: kz=6.1x10^-8 m/s
Permeability – Part B Dr O.Hamza
36. Working on Quizzes and Example problem
Problem 3 Field measurement of the coefficient of permeability
3.
A stratum of sandy soil overlies a horizontal bed of impermeable material;
the surface of which is also horizontal. In order to determine the in situ
permeability of the soil, a test well was driven to the bottom of the stratum.
Two observation boreholes were made at distances of 12.5m and 25m
respectively from the test well.
Water was pumped from the test well at the rate of 3x10-3 m3/s until the
water level became steady. The heights of the water in the two observation
boreholes were then found to be 4.25m and 6.5m above the impermeable
bed.
Find the value, expressed in m3/day, of the Impermeable
coefficient of permeability of the sandy soil
ffi i t f bilit f th d il
Permeability – Part B Dr O.Hamza
37. Working on Quizzes and Example problem
Problem 3 Field measurement of the coefficient of permeability
3.
Key solution
This is a quasi-one dimensional
flow, from which we found that:
where:
q (rate of flow) = 3x10-3 m3/s = 3x10-3 x 60 x
60 x 24 = 259 2 m3/day
259.2
Impermeable
r1= 12.5m and r2 = 25m
h1= 4.25m and h2= 6.5m
ln(r2/r1) = 0.693
Note ‘ln’ is the logarithm to base e, also called the natural logarithm.
Permeability – Part B Dr O.Hamza
38. Working on Quizzes and Example problems
Problem 4 E i i l relations of th coefficient of permeability
4. Empirical l ti f the ffi i t f bilit
For a clay soil, the following are given:
soil
Void ratio 1.1 0.9
k (cm/s)
( /) 0 302 x 10-7
0.302 7 0 12 x 10-7
0.12 7
en
Use the following empirical relation: k=C
1+ e
proposed by Samarasinghe, Huang and Drnevich (1982) to estimate the
coefficient of permeability of the clay at a void ratio of 1 2
1.2.
Hint: form two equations with two unknowns C and n by substituting the
experimental values given in the table in the equation.
Permeability – Part B Dr O.Hamza