: GEOTECHNICAL ENGINEERING (201003) Assistant Professor Rajiv Kumar VISHWAKARMA INSTITUTE OF INFORMATION TECHNOLOGY PUNE 1
GEOTECHNICAL ENGINEERING : GEOTECHNICAL ENGINEERING Geotechnical engineering is branch of civil engineering deals with the rock and soil. Knowledge from the fields of geology, material science and testing and mechanic are applied by geotechnical engineers to safely and economically design foundations, retaining walls, and similar structures. Or Geotechnical engineering is the sub-discipline of civil engineering that involves natural materials found close to the surface of the earth. It includes the application of the principles of soil mechanics and rock mechanics to the design of foundations, retaining structures, and earth structures. 2
GEOTECHNICAL ENGINEERING: GEOTECHNICAL ENGINEERING Soil property changes from place to place. Even in the same place it may not be uniform at various depths. The soil property may vary from season to season due to variation in moisture content. The load from the structure is to be safely transferred to soil. For this, safe bearing capacity of the soil is to be properly assessed. At one time, Terzaghi stated: “There will be no soil mechanics without water.” 3
APPLICATION OF GEOTECHNICAL ENGINEERING : APPLICATION OF GEOTECHNICAL ENGINEERING Apart from finding safe bearing capacity for foundation of buildings, geotechnical engineering involves various studies required for the design of pavements, tunnels, earthen dams, canals and earth retaining structures. It involves study of ground improvement techniques also. Safe bearing capacity of soil can be determined by geotechnical engineering Find out the index properties and classification of soil should be studies in this branch. To find out the capability of subgrade soil Geotechnical engineering or soil mechanics is the basic requirement for designing of different type of foundation and the structure. 4
UNIT -1 INTRODUCTION AND INDEX PROPERTIES : UNIT -1 INTRODUCTION AND INDEX PROPERTIES Introduction to Geotechnical Engineering and its applications to Civil Engineering Complexity of soil structure Major soil deposits of India Field identification of soils Introduction to soil exploration-objective and purpose. Three phase soil system, weight –volume relationships, Index properties of soil–methods of determination and their significance. IS and Unified Soil classification systems. 5
PowerPoint Presentation: 6
PowerPoint Presentation: The planning of the subsurface investigation for soft clay can be divided into four major sections as follows: Desk study Site reconnaissance Extent of subsurface investigation (Preliminary Explorations) Selection of type of field tests and sampling methods(Detailed Explorations) Methods of Investigation 7
UNIT -2 PERMEABILITY AND SEEPAGE : UNIT -2 PERMEABILITY AND SEEPAGE Soil water, permeability definition and necessity of its study, Darcy’s law, factors affecting permeability. Laboratory measurement of permeability – Constant head method and Falling head method as per IS 2720. Field test for determination of permeability- Pumping in test and Pumping out test as per IS 5529part-I. Permeability of stratified soil deposits. Seepage and Seepage Pressure, quick sand phenomenon, critical hydraulic gradient, General flow equation for 2-D flow (Laplace equation), Flow Net, properties and application, Flow Net construction for flow under sheet pile and earthen dam. 8
SOIL-WATER SYSTEM : SOIL-WATER SYSTEM Soil properties : Soil is a complex mass of mineral and organic particles. The important properties that classify soil according to its relevance to making crop production (which in turn affects the decision making process of irrigation engineering) are: • Soil texture • Soil structure 9
SOIL-WATER SYSTEM : SOIL-WATER SYSTEM Soil texture: This refers to the relative sizes of soil particles in a given soil. According to their sizes, soil particles are grouped into gravel, sand, silt and day. The relative proportions of sand, silt and clay is a soil mass determines the soil texture.Figure 1 presents the textural classification of 12 main classes as identified by the US department of agriculture, which is also followed by the soil survey organizations of India. 10
SOIL-WATER SYSTEM : Engineering soil properties and parameters describe the behavior of soil under induced stress and environmental changes. Of interest to most geotechnical applications are the strength, deformability, and permeability of in situ and compacted soils . SOIL-WATER SYSTEM 11
PERMEABILITY AND SEEPAGE: PERMEABILITY AND SEEPAGE The coefficient of permeability (or permeability) in soil mechanics is a measure of how easily a fluid (water) can flow through a porous medium (soil). The flow of water through soils, called seepage , occurs when there is a difference in the water level (energy) on the two sides of a structure such as a dam or a sheet pile. 12
SOIL PERMEABILITY: SOIL PERMEABILITY A measure of the capacity of a geosynthetic to allow a fluid to move through its voids or interstices, as represented by the amount of fluid that passes through the material in a unit time per unit surface area under a unit pressure gradient. Accordingly, permeability is directly proportional to thickness of the geosynthetic. The coefficient of permeability k is a measure of the rate of flow of water through saturated soil under a given hydraulic gradient i , cm/cm, and is defined in accordance with Darcy’s law as: 13
PowerPoint Presentation: Permittivity: Like permeability, a measure of the capacity of a geosynthetic to allow a fluid to move through its voids or interstices, as represented by the amount of fluid that passes through a unit surface area of the material in a unit time per unit thickness under a unit pressure gradient, with laminar flow in the direction of the thickness of the material. For evaluation of geotextiles, use of permittivity, being independent of thickness, is preferred to permeability. SOIL PERMEABILITY 14
PowerPoint Presentation: FACTORS AFFECTING PERMEABILITY: GRAIN SIZE PROPERTIES OF PORE FLUID TEMPERATURE VOID RATIO DEGREE OF SATURATION ABSORBED WATER SHAPE OF PARTICLES SOIL PERMEABILITY 15
PowerPoint Presentation: GRAIN SIZE Grain size of the soil , or the effective size D10 is one of the factors which affect permeability . Allen Hazen gave the relation K=100(D10)2 Where, k= coeff of permeability in cm/s and D10 is the effective grain size of the soil. The permeability of coarse grained soil is more than that of fine grained soil. 16
PowerPoint Presentation: Properties of pore fluid The permeability is directly proportional to the unit weight of water and inversely proportional to its viscosity. Though the unit weight of water does not change in temp , there is grate variation in viscosity with temp. 17
PowerPoint Presentation: temperature Since viscosity of pore fluid decreases with the temp , permeability increases with temp , as unit weight of the pore fluid does not change much with change in temp . Void ratio Increases in void ratio increase the area available for flow , hence the permeability increases with critical condition 18
PowerPoint Presentation: Void ratio 19
PowerPoint Presentation: Degree of saturation The permeability of partially saturated soil is less than that of fully saturated soil Absorbed water The absorbed water surrounding the fine- soil particles is not free to move , and reduces the effective pore space available for the passage of water . 20
PowerPoint Presentation: Shape of particles Permeability is inversely proportional to the specific surface e.g. the angular particles have more specific surface area as compare to rounded particles. 21
DARCY’S LAW:: DARCY’S LAW: When the flow through soil is laminar, Darcy’s law (Darcy, 1856) applies: The darcy’s law states that for laminar flow the velocity of flow, v is proportional to the hydraulic gradient i . Where q = rate of flow, cm 3 /s. A = cross-sectional area of soil conveying flow, cm 2 k is dependent on the grain-size distribution, void ratio, and soil fabric and typically may vary from as much as 10 cm/s for gravel to less than 10 -7 cm/s for clays. For typical soil deposits, k for horizontal flow is greater than k for vertical flow, often by an order of magnitude. V= Ki (k is constant of proportionality) q = v . A = k i A 22
DARCY’S LAW:: DARCY’S LAW: V= Ki (k is constant of proportionality) q = v . A = k i A The rate of flow under laminar flow conditions through a unit cross sectional are of porous medium under unit hydraulic gradient is defined as coefficient of permeability. Hydraulic gradient is the total head loss per unit length. 23
PowerPoint Presentation: 24
PowerPoint Presentation: 25
LABORATORY DETERMINATION OF PERMEABILITY: LABORATORY DETERMINATION OF PERMEABILITY Constant head permeability test Variable head permeability test Permeability range for this test – 10 -3 to 10 -7 cm/sec CONSTANT HEAD PERMEABILITY TEST : The coefficient of permeability of a coarse-grained soil can be determined in the laboratory using a constant-head permeability test. The test includes a cylindrical soil specimen that is subjected to a constant head as shown in Figure 9.6. 26
PowerPoint Presentation: 27
CONSTANT HEAD PERMEABILITY TEST: CONSTANT HEAD PERMEABILITY TEST The length of the soil specimen is L and its cross-sectional area is A. The total head loss ( h L ) along the soil specimen is equal to the constant head, which is the difference in elevation between the water levels in the upper and lower reservoirs as shown in the figure. A constant head implies that we have reached a steady-state condition in which the flow rate is constant (i.e., does not vary with time). Using a graduated flask, we can collect a volume of water (Q) in a period of time (t ). From this we can calculate the flow rate q(= Q/t). 28
LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) PREPARATION OF TEST SPECIMEN: (DSS,USS,SSS) A 2.5-kg sample shall be taken from a thoroughly mixed air-dried or oven-dried material. The moisture content of the 2.5-kg sample shall be determined. The sample shall be placed in an airtight container. The quantity of water to be added to the stored sample to give the desired moisture content shall be computed and spread evenly over the sample, and after thoroughly mixing, the material shall again be placed in the storage container. The moisture content of the sample shall again be determined and the entire process repeated until the actual moisture content is within 0.5 percent of that desired. 29
PowerPoint Presentation: 30
PowerPoint Presentation: 31
LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) PREPARATION OF TEST SPECIMEN: The permeameter mould shall be weighed empty to the nearest gram. After greasing lightly the inside of the mould it shall be clamped between the compaction base plate and the extension collar. The assembly shall be kept on a solid base. The mould with the specimen inside shall be assembled to the drainage base and cap having porous discs. The porous discs shall be saturated before assembling the mould. 32
LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) PROCEDURE : For a constant head test arrangement, the specimen shall be connected through the top inlet to the constant head water reservoir. The bottom outlet shall be opened and when the steady state of flow has been established, the quantity of flow for a convenient time interval shall be collected and weighed or measured. Alternatively, the inlet may be at the bottom and water may be collected from the outlet at the top. The collection of the quantity of flow for the same time interval shall be repeated thrice. 33
LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) PROCEDURE : The linearity ( of Darcy’s law ) between the hydraulic gradient and the average velocity of flow for the soil under test should be established by performing the test over a range of hydraulic gradients. The hydraulic gradients in the permeability test should preferably include the hydraulic gradient likely to occur in the field and any deviation from linearity observed should be noted. 34
LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) RECORD OF OBSERVATION: The inside diameter and the height of the permeameter are measured and recorded as diameter D and length L of the specimen loss h. The heights H 1 and H 2 are measured to determine the head The temperature of water T is also measured and recorded. During the test, observations are made of volume of water, Q collected in a graduated jar in time t and are recorded. 35
LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) RECORD OF OBSERVATION: For the purpose of getting a quantitative description of the state of the sample, after the test, the weight of wet soil specimen W, is measured and recorded. Its dry weight W, is measured after drying for 24 hours. The water content, w is computed and noted. From the knowledge of the specific gravity G, of specimen and water content W, void ratio e and degree of saturation S are determined. 36
LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY CONSTANT HEAD PERMEABILITY TEST (IS 2720 PART 17) CALCULATIONS: The permeability K T at temperature T is calculated as: K T = Q / AIt K 27 = K T Y r / Y 27 K 27 - permeability at 27ºC, Y r - coefficient of viscosity at T ºC, Y 27 - coefficient of viscosity at27ºC, Q -quantity in cm 3 , A- area of specimen in cm 2 I -hydraulic gradient, and t- time in seconds. 37
PowerPoint Presentation: 38
PowerPoint Presentation: DETERMINATION OF COEFF PERMEABILITY BY CONSTANT HEAD TEST APPARATUS Permeater mould with 100mm dia. 127.3 mm high. accessories of the permeater like cover, base, detachable collar , porous stones, dummy plate. compaction hammer 2.6kg constant head water tank . I.S. sieve 4.75mm 39
PowerPoint Presentation: 40
PowerPoint Presentation: procedure Take 2.5 kg of oven dried soil passing 10mm i.s . sieve and add water to bring the moisture content to the desired level. Apply grease inside the mould , base plate and collar. clamp the mould between compaction base plate extension collar. Prepare soil specimen by filling it in 3 layers , each layer rammed 25 times with a 2.6 kg rammer filling through 310 mm. Remove the collar and excess soil. Determine the dry density of the soil specimen those prepared . 41
PowerPoint Presentation: 7 ) Saturate the porous discs in boiling in water. 8) Covers the specimen by filling at both ends with filter paper and assemble the mould with soil specimen to the drainage base and cup having porous discs. Immerse the mould with the specimen in a water tank for saturation 12-24 hours. Connect the specimen through the top inlet to the constant head water tank. Open the outlet and allow de-aired water to flow till a steady flow is established. Measure the head causing flow ‘h’ Collect the quantity of water (Q) in a measuring cylinder for convenient time interval (t) for this head ‘h’. Calculate the coeff of permeability (k). Record the test temp. 42
PowerPoint Presentation: 43
PowerPoint Presentation: 44
PowerPoint Presentation: 45
Quiz: Quiz What is permeability? What is the unit of permeability ? Use of permeability in soil mechanics? What is Darcy’s law ? Darcy’s law is applicable for which kind of flow? Factor affecting on permeability? What is the different method to determine the permeability in laboratory? 46
QUIZ : QUIZ What is constant head method to find the permeability ? What is the variable head method to find the permeability? With the help Constant head method we determine the permeability of …………soil. With the help of variable head method we determine the permeability of …..soil. 47
PowerPoint Presentation: Temperature - t - ( o C ) Density - ρ - ( kg/m 3 ) Specific Weight - γ - ( kN /m 3 ) 0 999.8 9.806 4 1000 9.807 10 999.7 9.804 20 998.2 9.789 30 995.7 9.765 40 992.2 9.731 50 988.1 9.690 60 983.2 9.642 70 977.8 9.589 80 971.8 9.530 90 965.3 9.467 100 958.4 9.399 48
LABORATORY DETERMINATION OF PERMEABILITY BY FALLING HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY FALLING HEAD PERMEABILITY TEST (IS 2720 PART 17) PROCEDURE: For a falling head test arrangement the specimen shall be connected through the top inlet to selected stand-pipe. The bottom outlet shall be opened and the time interval required for the water level to fall from a known initial head to a known final head as measured above the centre of the outlet shall be recorded. The stand-pipe shall be refilled with water and the test repeated till three successive observations give nearly same time interval; the time intervals being recorded for the drop in head from the same initial to final values, as in the first determination. 49
PowerPoint Presentation: 50
LABORATORY DETERMINATION OF PERMEABILITY BY FALLING HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY FALLING HEAD PERMEABILITY TEST (IS 2720 PART 17) PROCEDURE: Alternatively, after selecting the suitable initial and final heads, h 1 and h 2 respectively, time intervals shall be noted for the head to fall from h 1 , to √h 1 h 2 , and similarly from √h 1 h 2 to h 2 . The time intervals should be the same; otherwise the observation shall be repeated after refilling the stand-pipe. 51
LABORATORY DETERMINATION OF PERMEABILITY BY FALLING HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY FALLING HEAD PERMEABILITY TEST (IS 2720 PART 17) RECORD OF OBSERVATION: The dimensions of specimen, length L and diameter D, are measured. Area a of stand-pipe is recorded. The temperature T, of water is also measured and recorded. During the test, observations are made of initial time t i , final time t f initial head h 1 final head h 2 in stand-pipe and are recorded. 52
LABORATORY DETERMINATION OF PERMEABILITY BY FALLING HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY FALLING HEAD PERMEABILITY TEST (IS 2720 PART 17) RECORD OF OBSERVATION: The permeability K T is calculated and recorded. At the end of the test, the weight of wet soil specimen Wt is measured and recorded. Then the sample is dried in the oven for 24 hours and the dry weight W s is measured and recorded. The water content, W is computed and noted. Void ratio, e, and degree of saturation S are calculated using specific gravity G s of the specimen and water content, W. 53
LABORATORY DETERMINATION OF PERMEABILITY BY FALLING HEAD PERMEABILITY TEST (IS 2720 PART 17) : LABORATORY DETERMINATION OF PERMEABILITY BY FALLING HEAD PERMEABILITY TEST (IS 2720 PART 17) CALCULATIONS : At temperature T of water, the permeability K T is calculated as: kT = 2.303 aL / A ( t f _-t i ) * log 10 (h 1 /h 2 ) 54
Flow of Water in Soils : In the FLOW of WATER in SOILS Flow of Water in Soils Where Q is the water flow rate h 1 is the inlet head h 2 is the outlet head A is the cross-section area k is the permeability is the path length 1) Mathematical solutions a) exact solutions for certain simple situations b) solutions by successive approximate - e.g. relaxation methods 2) Graphical solutions 3) Solutions using the electrical analogue 4) Solutions using models Only graphical methods will be used in this course 55
PowerPoint Presentation: MOST OF PEOPLE FAIL NOT BECAUSE OF LACK OF ABILITY OR INTELLIGENCE BUT BECAUSE OF LACK OF DESIRE, DIRECTION, DEDICATION, AND DISCIPLINE. 56
FIELD TEST FOR DETERMINATION OF PERMEABILITY(IS 5529 PART 1) : FIELD TEST FOR DETERMINATION OF PERMEABILITY(IS 5529 PART 1) The field permeability test carried out to determine the permeability of each surface strata encounter up to bed rock as well as to ascertain overall permeability of strata. This test are carried out in standard drill holes where subsurface exploration for foundation are carried out by drilling. The test also carried out in auger holes or bore holes of larger size for depth up to 30m. The test carried out are either pumping in or the pumping out type. 57
FIELD TEST FOR DETERMINATION OF PERMEABILITY(IS 5529 PART 1) : FIELD TEST FOR DETERMINATION OF PERMEABILITY(IS 5529 PART 1) PUMPING IN TEST (Gravity feed in drill holes or bore holes ) Constant head method (cased well , open end test) Falling head method (uncased well) Slug method PUMPING OUT TEST : Unsteady state Steady state Bailor method 58
FIELD TEST FOR DETERMINATION OF PERMEABILITY(IS 5529 PART 1) : FIELD TEST FOR DETERMINATION OF PERMEABILITY(IS 5529 PART 1) PUMPING OUT TEST : The pumping out test is an accurate method for finding out in-situ permeability of the strata below water table or below river sand. This method is best suited for all ground water problems where accurate values of permeability representative of the entire aquifer are required for designing cut off or planning excavation . 59
FIELD TEST FOR DETERMINATION OF PERMEABILITY(IS 5529 PART 1) : FIELD TEST FOR DETERMINATION OF PERMEABILITY(IS 5529 PART 1) PUMPING IN TEST: The pumping in test method is applicable for strata above water table. The test is especially performed in formation of low permeability and limited thickness where adequate in formation of low permeability and limited thickness where adequate yield is not available for pump out test. 60
Coefficient of Permeability: Coefficient of Permeability : _________________________ aquifer CONFINED FLOW PUMPING TEST 61
Coefficient of Permeability: Coefficient of Permeability : ____________________________ aquifer UNCONFINED FLOW PUMPING TEST 62
PERMEABILITY OF STRATIFIED SOILS: PERMEABILITY OF STRATIFIED SOILS Consider a stratified soil having horizontal layers of thickness H 1 ,H 2 ,H 3 , . . ., H n with coefficients of permeability k 1 , k 2 , k 3 , . . , k n , as shown in Figure . For flow perpendicular to soil stratification, as shown in the figure, the flow rate q through area A of each layer is the same. Therefore, the head loss across the n layers is given as 63
PowerPoint Presentation: 64
PERMEABILITY OF STRATIFIED SOILS: PERMEABILITY OF STRATIFIED SOILS For a flow that is parallel to soil stratification, such as the one shown in Figure , the head loss h L over the same flow path length L will be the same for each layer. Thus, i 1 = i 2 = i 3 = · · · = i n . The flow rate through a layered system (with width = 1 unit) is 65
PowerPoint Presentation: 66
An idealized soil profile: An idealized soil profile 67
Example: Example A nonhomogeneous soil consisting of layers of soil with different permeabilities . Average coefficient of permeability in the horizontal direction and vertical direction 1.5 m 2.0 m 2.5 m K x = 1.2 x 10 -3 cm/s K y = 2.4 x 10 -4 cm/s K x = 2.8 x 10 -4 cm/s K y = 3.1 x 10 -5 cm/s K x = 5.5 x 10 -5 cm/s K y = 4.7 x 10 -6 cm/s 68
Quiz : Quiz The permeability of soil varies …………… The maximum particle size for which Darcy’s law in applicable is ……….. The coefficient of permeability of clay is generally ………. Constant head method is used for ……….. A soil has discharge velocity of 6 x 10 -7 m/sec and void ratio of 0.5. it’s seepage velocity ………….. 69
Seepage and Seepage Pressure: Seepage and Seepage Pressure 70
Seepage and Seepage Pressure: Seepage and Seepage Pressure 71
PowerPoint Presentation: 72
PowerPoint Presentation: 73
PowerPoint Presentation: 74
PowerPoint Presentation: 75
Flow Net construction for flow under sheet pile and earthen dam. : Flow Net construction for flow under sheet pile and earthen dam. Flow-net is a graphical representation of two dimensional steady state groundwater flow through aquifers. 76
Flow Net Theory: 77 Flow Net Theory Streamlines ψ and Equip. lines are . Streamlines ψ are parallel to no flow boundaries. Grids are curvilinear squares, where diagonals cross at right angles. Each stream tube carries the same flow.
Flow Net Theory: 78 Flow Net Theory
Flow Net in Isotropic Soil: 79 Flow Net in Isotropic Soil Portion of a flow net is shown below F Y Stream tube
Flow Net in Isotropic Soil: 80 Flow Net in Isotropic Soil The equation for flow nets originates from Darcy’s Law. Flow Net solution is equivalent to solving the governing equations of flow for a uniform isotropic aquifer with well-defined boundary conditions.
Flow Net in Isotropic Soil: 81 Flow Net in Isotropic Soil Flow through a channel between equipotential lines 1 and 2 per unit width is: ∆ q = K ( d m x 1)( ∆ h 1 / dl ) d m D h 1 dl F 1 F 3 D q F 2 D h 2 D q n m
Flow Net in Isotropic Soil: 82 Flow Net in Isotropic Soil Flow through equipotential lines 2 and 3 is: ∆ q = K ( d m x 1)( ∆ h 2 / dl ) The flow net has square grids, so the head drop is the same in each potential drop: ∆ h 1 = ∆ h 2 If there are n d such drops, then: ∆ h = ( H / n ) where H is the total head loss between the first and last equipotential lines.
Flow Net in Isotropic Soil: 83 Flow Net in Isotropic Soil Substitution yields: ∆ q = K ( d m x dl )( H/n ) This equation is for one flow channel. If there are m such channels in the net, then total flow per unit width is: q = ( m / n ) K ( d m /dl ) H
Flow Net in Isotropic Soil: 84 Flow Net in Isotropic Soil Since the flow net is drawn with squares, then d m dl , and: q = ( m / n ) KH [ L 2 T -1 ] where: q = rate of flow or seepage per unit width m = number of flow channels n = number of equipotential drops h = total head loss in flow system K = hydraulic conductivity
Drawing Method:: 85 Drawing Method: 1. Draw to a convenient scale the cross sections of the structure, water elevations, and aquifer profiles. 2. Establish boundary conditions and draw one or two flow lines Y and equipotential lines F near the boundaries.
Method:: 86 Method: 3. Sketch intermediate flow lines and equipotential lines by smooth curves adhering to right-angle intersections and square grids. Where flow direction is a straight line, flow lines are an equal distance apart and parallel. 4. Continue sketching until a problem develops. Each problem will indicate changes to be made in the entire net. Successive trials will result in a reasonably consistent flow net.
Method:: 87 Method : In most cases, 5 to 10 flow lines are usually sufficient. Depending on the no. of flow lines selected, the number of equipotential lines will automatically be fixed by geometry and grid layout. 6. Equivalent to solving the governing equations of GW flow in 2-dimensions.
Seepage Under Dams: 88 Seepage Under Dams Flow nets for seepage through earthen dams Seepage under concrete dams Uses boundary conditions (L & R) Requires curvilinear square grids for solution
Two Layer Flow System with Sand Below: 89 Two Layer Flow System with Sand Below K u / K l = 1 / 50
Two Layer Flow System with Tight Silt Below: 90 Two Layer Flow System with Tight Silt Below Flow nets for seepage from one side of a channel through two different anisotropic two-layer systems. (a) K u / K l = 1/50 . (b) K u / K l = 50 . Source: Todd & Bear, 1961.
Effects of Boundary Condition on Shape of Flow Nets: 91 Effects of Boundary Condition on Shape of Flow Nets
Radial Flow:: 92 Radial Flow: Contour map of the piezometric surface near Savannah, Georgia, 1957, showing closed contours resulting from heavy local groundwater pumping (after USGS Water-Supply Paper 1611).
Flow Net in a Corner:: 93 Flow Net in a Corner: Streamlines Y are at right angles to equipotential F lines
Flow Nets: an example: 94 Flow Nets: an example A dam is constructed on a permeable stratum underlain by an impermeable rock. A row of sheet pile is installed at the upstream face. If the permeable soil has a hydraulic conductivity of 150 ft/day, determine the rate of flow or seepage under the dam.
Flow Nets: an example: 95 Flow Nets: an example The flow net is drawn with: m = 5 n = 17
Flow Nets: the solution: 96 Flow Nets: the solution Solve for the flow per unit width: q = ( m / n ) K h = (5/17)(150)(35) = 1544 ft 3 /day per ft
Flow Nets: An Example: 97 Flow Nets: An Example There is an earthen dam 13 meters across and 7.5 meters high.The Impounded water is 6.2 meters deep, while the tailwater is 2.2 meters deep. The dam is 72 meters long. If the hydraulic conductivity is 6.1 x 10 -4 centimeter per second, what is the seepage through the dam if n = 21 K = 6.1 x 10 -4 cm/sec = 0.527 m/day
Flow Nets: the solution: 98 Flow Nets: the solution From the flow net, the total head loss, H , is 6.2 -2.2 = 4.0 meters. There are 6 flow channels ( m ) and 21 head drops along each flow path ( n ): Q = ( KmH / n ) x dam length = (0.527 m/day x 6 x 4m / 21) x (dam length) = 0.60 m 3 /day per m of dam = 43.4 m 3 /day for the entire 72-meter length of the dam
PowerPoint Presentation: 99
PowerPoint Presentation: 100
PowerPoint Presentation: 101
PowerPoint Presentation: 102
PowerPoint Presentation: 103
PowerPoint Presentation: 104
PowerPoint Presentation: 105
PowerPoint Presentation: 106
QUICK SAND PHENOMENON: QUICK SAND PHENOMENON When upward flow takes place at the critical hydraulic gradient, a soil such as sand loses all its shearing strength and can’t support any load. The soil is said to have become quick or alive or boiling will occurs. The popular name for this phenomenon is quick sand. Quick sand is not a type of sand but only a hydraulic condition. 107
PowerPoint Presentation: 108
PowerPoint Presentation: 109
PowerPoint Presentation: 110
PowerPoint Presentation: 111
General flow equation for 2-D flow (Laplace equation): G eneral flow equation for 2-D flow (Laplace equation) 112
FLOW NET: FLOW NET 113
PowerPoint Presentation: 1) flow lines and equipotentials are at right angles to one another. 2) the cylinder walls are also flow lines. 3) distances between the equipotentials are equal head drops between the equipotentials are also equal. Graphical Solutions - Flow Nets Equi-potentials Flow Lines Water IN 114
PowerPoint Presentation: Asymetric Flow 115
PowerPoint Presentation: Asymetric Flow Intersections are at right angles approximate to curvilinear square A B C D 116
PowerPoint Presentation: Asymetric Flow Intersections are at right angles approximate to curvilinear square A B C D n d pressure drops a 117
PowerPoint Presentation: pressure drop between AB and CD is H and let there be n d pressure drops and n f flow lines. Asymetric Flow where q f is the flow per unit cross-section and a x 1 is the cross- section between flow lines. the total seepage = 118
Summary of Flow Nets : Summary of Flow Nets Solutions are relatively straightforward. 1) draw the appropriate flow net 2) count the number of pressure drops in the flow net (over the relevant distance) 3) count the number of flow lines 4) do a simple calculation work out total flow work out pressure at any given point etc. 119
PowerPoint Presentation: Seepage around an obstruction H A B 120
PowerPoint Presentation: upward seepage force = Seepage around an obstruction downward force of the soil = A quicksand will occur if but very approximately ' = w so actual downward force of the soil Factor of safety = ----------------------------------------------------------- downwards force required to resist seepage force In the above example, n d = 10 and N ab ~ 3.5 i.e. the distance must exceed 0.35 times the difference in head of water. 121
PowerPoint Presentation: Rules for drawing flow nets:- 1) All impervious boundaries are flow lines. 2) All permeable boundaries are equipotentials 3) Phreatic surface - pressure is atmospheric, i.e. excess pressure is zero. Flow nets Summary h h h h h h Water table Change in head between adjacent equipotentials equals the vertical distance between the points on the phreatic surface. 4) All equipotentials are at right angles to flow lines 5) All parts of the flow net must have the same geometric proportions (e.g. square or similarly shaped rectangles). 6) Good approximations can be obtained with 4 - 6 flow channels. More accurate results are possible with higher numbers of flow channels, but the time taken goes up in proportion to the number of channels. The extra precision is usually not worth the extra effort. 122
PowerPoint Presentation: Uplift arises the total water pressure exerted on the base. Static head (constant for flat based obstruction) excess head. Uplift on Obstructions 0 1 2 3 Distance under obstruction (m) 4 3 2 1 0 Head of Water (m) 6 m 3 m 4 m 2 123
PowerPoint Presentation: If total uplift force > the self weight downward object will be displaced downstream. Draw flow net Plot graph of uplift pressure (Y –axis) against distance along base (X-axis). Uplift pressure is estimate from flownet head at the upstream head is ~0.75 of total head head at the down stream end it is ~0.25 of the total head. Uplift on Obstructions 124
PowerPoint Presentation: Base of the obstruction is 2m below the surface uplift force from the static head is 2 w multiplied by width (i.e. 6 w kN per metre length). the upward force is the area under the curve multiplied by w . In this example upward force = 6 w kN per metre length, i.e. in this case it equals the static head uplift. total uplift = 12 w kN m-1. Uplift reduces ability of the obstruction to resist movement through the pressure of water potential boulder blockages in a river man-made drop structure built in river engineering works to dissipate energy (see RDH's part of the Course). quicksand might form at the down stream end of the obstruction. Uplift on Obstructions 125
Flow Nets and Seepage: Flow Nets and Seepage 126
Flow Nets: Flow Nets 127
Flow Nets: Flow Nets 128
Flow Nets: Flow Nets 129
Flow Nets: Flow Nets 130
Flow Nets: Flow Nets 131
Flow Nets: Flow Nets 132
Flow Nets: Flow Nets 133
Flow Nets and Seepage: Flow Nets and Seepage x y D h D q Flow Channel Flow Line Equipotential Lines Flow Line Flow Line 134
Example: Example 135