chapter 1 flow in soil

8/11/2019 Chapter 1 flow in soil

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Chapter 1: Flow in SoilChapter 1: Flow in Soil

Table of ContentsTable of Contents

1.3 Seepage analyses (Text book 8.41.3 Seepage analyses (Text book 8.4 – – 8.10)8.10)

1.11.1 Capillary in soil, soil shrinkage & soil expansion(Text book 9.9 & 9.10)

1.2 Head and flow of one and two dimensional(Text book 8.2 & 8.3)

1.4 Filter design (Text book 8.11)1.4 Filter design (Text book 8.11)



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Adapted from Dr. Lulie’s presentation slide

Adapted from Dr. Lulie’s presentation slide



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1.1 Capillarity (continued1.1 Capillarity (continued ……))Groundwater table (orGroundwater table (or phreatic phreatic surface) surface) – – the level whichthe level whichunderground water will rise in an observation well, pit orunderground water will rise in an observation well, pit orother open excavation in the earthother open excavation in the earthSoil beneath groundwater tableSoil beneath groundwater table – – filled with waterfilled with waterSoil moisture Soil moisture – – any water in soil located above the waterany water in soil located above the watertabletableCapillary rise Capillary rise – – phenomenon which water rises above thephenomenon which water rises above thegroundwater table against the pull of gravity but is ingroundwater table against the pull of gravity but is in

contact with the water table as its sourcecontact with the water table as its sourceCapillary moisture Capillary moisture – – the water associated with capillary risethe water associated with capillary riseVadose Vadose zone zone – – the soil region directly above the waterthe soil region directly above the watertable and wetted by capillary moisturetable and wetted by capillary moisture

Water in Capillary TubesWater in Capillary Tubes

Basic principles of capillary rise in soils related to theBasic principles of capillary rise in soils related to therise of water in glass capillary tubesrise of water in glass capillary tubes

The riseThe rise – – attractionattractionbetween the water andbetween the water and

the glass and to athe glass and to asurface tension, whichsurface tension, whichdevelops at the airdevelops at the air --waterwaterinterface at the top ofinterface at the top ofthe water column in thethe water column in thecapillary tubecapillary tube



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Water in Capillary Tubes (continuedWater in Capillary Tubes (continued ……)) Value of T Value of T ss for water varies according tofor water varies according totemperaturetemperature

As temperature increases, the value of T As temperature increases, the value of T ssdecreases, indicating a lessening height of capillarydecreases, indicating a lessening height of capillaryrise under warm conditionsrise under warm conditions

At room temperature, T At room temperature, T ss for water = 0.064 N/mfor water = 0.064 N/m At freezing, T At freezing, T ss for water = 0.067 N/mfor water = 0.067 N/m

In applying the development of capillary rise inIn applying the development of capillary rise intubes to capillary rise in soils:tubes to capillary rise in soils:hh cc

≈≈ 31/d mm (McCarthy, D. F., 2002)31/d mm (McCarthy, D. F., 2002)(*provided that d is in(*provided that d is in millimetresmillimetres ))

Water in Capillary Tubes (continuedWater in Capillary Tubes (continued ……))

Question:Question:Compute the height of capillary rise for water in a tubeCompute the height of capillary rise for water in a tubehaving a diameter of 0.05 mm (in SI units)having a diameter of 0.05 mm (in SI units)

Solution:Solution:

mmkN m x

m N

d

T h

w

sc 52.0

)/81.9)(105()/064.0)(4(4

35 === −γ



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Water in Capillary Tubes (continuedWater in Capillary Tubes (continued ……))The height of capillary rise is not affected by a slope orThe height of capillary rise is not affected by a slope orinclination in the direction of the capillary tube, or byinclination in the direction of the capillary tube, or byvariations in the shape and size of the tube at level belowvariations in the shape and size of the tube at level belowthe meniscusthe meniscus

Water in Capillary Tubes (continuedWater in Capillary Tubes (continued ……))

Capillary rise is not limited to tube, or enclosed, shapes. IfCapillary rise is not limited to tube, or enclosed, shapes. Iftwo vertical glass plates are placed so that they touch alongtwo vertical glass plates are placed so that they touch alongone end and, form a V, a wedge of water will rise up in theone end and, form a V, a wedge of water will rise up in the

V because of the capillary phenomenon V because of the capillary phenomenon



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Capillary rise in soil (continuedCapillary rise in soil (continued …….).)

Capillaryfringe

Capillary rise in soil (continuedCapillary rise in soil (continued …….).)

10 to 3010 to 30ClayClay1 to 101 to 10SiltSilt0.3 to 10.3 to 1Fine sandFine sand

0.150.15Coarse sandCoarse sand0.020.02 --0.10.1Small gravelSmall gravel

Meter (m)Meter (m)Soil TypeSoil Type

Table : Representative heights of capillary rise:Table : Representative heights of capillary rise:water in soilwater in soil



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Soil shrinkage & soil swellingSoil shrinkage & soil swelling

1.21.2 Head and flow of one and twodimensional

OneOne -- dimensional flowdimensional flow – – the velocity at allthe velocity at allpoints has the same direction and (for anpoints has the same direction and (for anincompressible fluid) the same magnitudeincompressible fluid) the same magnitude

TwoTwo --dimensional flowdimensional flow – – all streamlines inall streamlines inthe flow are plane curves and are identicalthe flow are plane curves and are identicalin a series of parallel planesin a series of parallel planes



Lecture 3 Notes – Two Dimensional Flow

In the previous section the seepage problems discussed were all lab models consisting ofone-dimensional flow. In field construction, structures used for water barriers generallyinvolve two- or three-dimensional seepage flow, such as:

(1) Cofferdam cells (sheet pile wall) and Concrete dams are confined flow; all the boundary conditions are well defined before the construction of flow nets.

(2) Earth dams and levees are unconfined flow; the top flow line is not defined inadvance of constructing the flow nets.

The purposes of studying the seepage conditions under or within these structures are:

1. to estimate the rate of flow (reservoirs for keeping water cut-off ability2. seepage force ( γ wi) (uplift force) (erosion)

3. pore pressure distribution for effective stress analysis

In this section we will concentrate on studying two-dimensional steady flow through soilmedia since most three-dimensional cases can be treated as two–dimensional cases whenthe size-dimension in one of the dimensions is much greater than the other twodimensions.

The Laplace Equation, a second order partial differential equation, is the theory behindthe flow net. This equation is a common mathematical representation of the energy lossthrough any resistive media (See textbook for its derivation and details). Methodsgenerally used for solving the Laplace’s equation are:

1. Direct mathematical solution (different boundary condition for different answer)2. Numerical solution (approximation, finite difference method)3. Electrical analogy solution (build electric model)4. Graphical solution (flow nets, a trial-and-error method)

Flow Net Construction

Flow net consists of Flow Lines (velocity line) and Equal Head Lines (equal potential orequal total head) . The characteristics or rules to construct a flow net for isotropic

permeability are listed below,

1. satisfy the boundary conditions 2. make flow lines intersect constant head lines at 90 ° 3. draw curvilinear squares



Although Flow Net is a trial-and-error graphical method, an unique solution will always be achieved when all these three construction requirements are met. A detailedexplanation of these three characteristics is shown below:

1. Boundary conditions for two dimensional flow

a. Soil water interface = constant head line

b. Impermeable boundary = flow line

2. flow lines are perpendicular to constant head lines for isotropic permeability (k x =k z)

From Darcy’s law:

Vx= −k x ∂h

∂x

Vz= −k z∂h

∂z

V = (−k x∂h

∂x)2 + ( −k z∂h

∂z)2

For isotropic permeability, K z = K z = k, giving

V =

(

∂h

∂x)

2+ (

∂h

∂z)

2

But

( hx)2+ ( hz)2= hn= normal derivative or normal gradient



The direction of the normal derivative is normal to the constant headlines. Thevelocity, V is in the direction of this gradient and is therefore normal to theconstant headlines.

3. Consider the condition necessary to have Equal Quantities of Flow betweenFlow Lines, when the head drops between constant headlines are equal.

If q 1 = q 2 = ∆q; V 1A1 = V 2A2; ki 1A1 = ki 2A2;

k(∆ h/a)(b)(1) = k ( ∆ h/c)(d)(1)



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1.21.2 Head and flow of one and twodimensional (continued…)

(1) (2)

1.3 Seepage analyses1.3 Seepage analyses



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1.3 Analysis of flow nets and seepage1.3 Analysis of flow nets and seepage

Many catastrophic failures in geotechnicalMany catastrophic failures in geotechnicalengineering result fromengineering result from instabilityinstability of soilof soilmassesmasses due to ground water flowdue to ground water flowLives are lost, infrastructures are damagedLives are lost, infrastructures are damagedor destroyed, and major economic lossesor destroyed, and major economic lossesoccurredoccurred

In this subchapter, you will study theIn this subchapter, you will study the basicbasicprinciples of twoprinciples of two --dimensional flow ofdimensional flow ofwater through soilswater through soils

1.3 Analysis of flow nets and seepage1.3 Analysis of flow nets and seepage(continued(continued ……))

The topics that you will study would helpThe topics that you will study would helpyou toyou to avoid pitfallsavoid pitfalls in the analyses andin the analyses anddesign of geotechnical systems where flowdesign of geotechnical systems where flowof ground water can lead to instabilityof ground water can lead to instabilityThe emphasis of this chapter is on gainingThe emphasis of this chapter is on gaininganan understanding of the forcesunderstanding of the forces thatthatprovoke failures from flow of groundprovoke failures from flow of groundwaterwater



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1.3 Analysis of flow nets and seepage1.3 Analysis of flow nets and seepage(continued(continued ……))

Learning Objectives:Learning Objectives:Understand theUnderstand the basic principlesbasic principles of twoof two --dimensional flowdimensional flowBe able toBe able to calculatecalculate seepage stresses, poreseepage stresses, pore --water pressure distribution, uplift forces,water pressure distribution, uplift forces,hydraulic gradients, critical hydraulic gradient,hydraulic gradients, critical hydraulic gradient,flow under and within earth structuresflow under and within earth structures

Be able toBe able to determine the stabilitydetermine the stability of geotechnicalof geotechnicalsystems subjected to twosystems subjected to two --dimensional flow ofdimensional flow ofwaterwater

1.3.1 Basic Concepts1.3.1 Basic ConceptsThe twoThe two --dimensional flow of water through soils isdimensional flow of water through soils isgoverned by Laplacegoverned by Laplace ’ ’ s equation. The popular form ofs equation. The popular form ofLaplaceLaplace ’ ’ s equation for twos equation for two --dimensional flow of waterdimensional flow of waterthrough soils isthrough soils is

WhereWhere k k xx andand k k zz are the coefficient of permeability in theare the coefficient of permeability in thex and z directions and H is the headx and z directions and H is the headThe assumptions in LaplaceThe assumptions in Laplace ’ ’ s equation are:s equation are:(i) Darcy(i) Darcy ’ ’ s law is valids law is valid(ii) The soil is homogeneous and saturated(ii) The soil is homogeneous and saturated(iii) The soil and water are incompressible(iii) The soil and water are incompressible(iv) No volume change occurs(iv) No volume change occurs

02

2

2

2

=∂∂

+∂∂

z

H k

x

H k z x



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1.3.1 Basic Concepts (continued1.3.1 Basic Concepts (continued ……))If the soil were an isotropic material thenIf the soil were an isotropic material then k k xx == k k zz andandLaplaceLaplace ’ ’ s equation becomes:s equation becomes:

The solution of LaplaceThe solution of Laplace ’ ’ s equation requires knowledge ofs equation requires knowledge ofthe boundary conditions.the boundary conditions.Common geotechnical problems have complex boundaryCommon geotechnical problems have complex boundaryconditions from which it is difficult to obtain a closedconditions from which it is difficult to obtain a closedform solution.form solution.

Approximate methods such as graphical methods and Approximate methods such as graphical methods andnumerical methods are often employed.numerical methods are often employed.In this subchapter, graphical method, called the flow netIn this subchapter, graphical method, called the flow nettechnique or flow net sketching, that satisfies Laplacetechnique or flow net sketching, that satisfies Laplace ’ ’ ssequation is discussed.equation is discussed.

02

2

2

2

=∂∂

+∂∂

z

H

x

H



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3.56 x 10 -4



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No of equipotentialdrops at point a

Elevation loss

hpγw



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hpγw

hpγw



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Uplift forcesUplift forces

Static Liquefaction, Heaving, Boiling, & PipingStatic Liquefaction, Heaving, Boiling, & Piping

Static liquefaction Static liquefaction – – the state which the effective stress becomesthe state which the effective stress becomeszero, the soil loses its strength and behaves like a viscous fluzero, the soil loses its strength and behaves like a viscous flu ididBoiling, quicksand, piping and heaving are used to describeBoiling, quicksand, piping and heaving are used to describespecific events connected to the static liquefaction statespecific events connected to the static liquefaction stateBoiling Boiling – – the upward seepage force exceeds the download forcethe upward seepage force exceeds the download forceof the soilof the soil

Piping Piping – – the subsurfacethe subsurface “ “pipepipe --shapedshaped ” ” erosion that initiates nearerosion that initiates nearthe toe of dams and similar structures. High localized hydraulicthe toe of dams and similar structures. High localized hydraulicgradient statically liquefies the soil, which progresses to thegradient statically liquefies the soil, which progresses to thewater surface in the form of a pipe, and water then rusheswater surface in the form of a pipe, and water then rushesbeneath the structure through the pipe, leading to instability abeneath the structure through the pipe, leading to instability a ndndfailurefailureQuicksand Quicksand – – existence of a mass of sand in a state of staticexistence of a mass of sand in a state of staticliquefactionliquefactionLiquefactionLiquefaction – – can be produced by dynamic events such ascan be produced by dynamic events such asearthquakesearthquakes



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PipingPiping

Piping (continuedPiping (continued ……))

The risk of piping can occur in severalThe risk of piping can occur in severalcircumstances, such as a cofferdam (a) or thecircumstances, such as a cofferdam (a) or thedownstream end of a dam (b)downstream end of a dam (b)In order to increase the factor of safety againstIn order to increase the factor of safety againstpiping in these cases two methods can bepiping in these cases two methods can beadoptedadopted

(1) increase the depth of pile penetration in (a)(1) increase the depth of pile penetration in (a)and inserting a sheet pile at the heel of the damand inserting a sheet pile at the heel of the damin (b); in either case there is an increase in thein (b); in either case there is an increase in thelength of the flow path of the water with alength of the flow path of the water with aresulting drop in the excess pressure at theresulting drop in the excess pressure at thecritical section.critical section.



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Piping (continuedPiping (continued ……))

A similar effect is achieved by laying down A similar effect is achieved by laying downa blanket of impermeable material fora blanket of impermeable material forsome length along the upstream groundsome length along the upstream groundsurfacesurface

(2) To place a surcharge or filter apron on(2) To place a surcharge or filter apron ontop of the downstream side, the weight oftop of the downstream side, the weight of

which increases the downward forceswhich increases the downward forces

Example:Example: --



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Others phenomenon: Quick sand,Others phenomenon: Quick sand,Frost heave in soils,Frost heave in soils, liquefactionliquefaction

QuicksandQuicksand

Dreaded quicksand condition occurs where aDreaded quicksand condition occurs where asand orsand or cohesionlesscohesionless silt deposit is subjected tosilt deposit is subjected tothe seepage force caused by upward flow ofthe seepage force caused by upward flow ofgroundwatergroundwater

The upward gradient of the water is sufficient toThe upward gradient of the water is sufficient tohold the soil particles in suspension, in effecthold the soil particles in suspension, in effectcreating a material with the properties of acreating a material with the properties of aheavy liquidheavy liquidElimination of seepage pressure will return theElimination of seepage pressure will return thesoil to a normal condition capable of providingsoil to a normal condition capable of providingsupportsupport



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Frost heave in soilsFrost heave in soilsWhen freezing temperatures develop in a soil mass, most of theWhen freezing temperatures develop in a soil mass, most of thepore water in the soil is also subject to freezing. As waterpore water in the soil is also subject to freezing. As watercystallizescystallizes , its volume expands approximately 9 percent, its volume expands approximately 9 percentIn considering void ratios and the degree of saturation for soilIn considering void ratios and the degree of saturation for soil s,s,expansion of a soil material as a result of freezing might beexpansion of a soil material as a result of freezing might beexpected to be on the order of 3 or 4 percent of the originalexpected to be on the order of 3 or 4 percent of the originalvolumevolume

Frost heave in soils (continuedFrost heave in soils (continued …………))In the normal frost heave occurrence, the source of water is theIn the normal frost heave occurrence, the source of water is thegroundwater tablegroundwater tableUpward movement from a water table to the freezing zoneUpward movement from a water table to the freezing zonerelates to a potential for migration (capillary rise)relates to a potential for migration (capillary rise)Height of capillary rise is quite limited in clean, coarseHeight of capillary rise is quite limited in clean, coarse --grainedgrainedsoilsoil



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Soil liquefactionSoil liquefaction

1.4 Filter design1.4 Filter design

Text book sec: 8.11

chapter 1 flow in soil

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