Upload
pablo-tpi
View
221
Download
0
Embed Size (px)
Citation preview
7/24/2019 Cm5 Unidimensional English
1/36
UNIVERSIDAD NACIONAL DE COLOMBIABOGOT
SOIL MECHANICS
FLOW IN POROUS MEDIA
JULIO ESTEBAN COLMENARES MONTAEZ TITULAR PROFFESOR
BOGOT D.C2015 - II
7/24/2019 Cm5 Unidimensional English
2/36
In the last session stress physical concepts were approached, also effective stress and interstitial prconcepts were introduced
Effective stress of a saturated soil is defined as:
Underground Water can be found in three states: Hygroscopic, capillary and free or gravity:
In the saturated zone, where is located gravity water, the interstitial pressure is equal hydrostatic pre
Only if water is static condition , otherwise interstitial pressure decrease or increase in funct
direction
REVIEW
7/24/2019 Cm5 Unidimensional English
3/36
1. INTRODUCTION
2. DARCYS LAW
3. HYDRAULIC CONDUCTIVITY
4. HYDRAULIC CONDUCTIVITY IN MULTILAYER MEDIA
5. EFFECTIVE STRESSES DUE TO FLOW
6. TEST TO DETERMINE HYDRAULIC CONDUCTIVITY
CONTENT
7/24/2019 Cm5 Unidimensional English
4/36
1 INTRODUCTION
In this session the basic concepts about Unidimensional flow are studied, the concept
about infiltration force and hydraulic conduc
tivity are defined and also the variaeffective stresses due to flow is evaluated.
In the professional job is necessary to know the flow principals in porous mediaunderstand and to solve problematic related to:
I. Caudal of infiltration (Leak in ground dam, diggings and tunnels)
II. Variation of fluid volume (Consolidation Abatement of water table)
III. Stability of structures (Embankments - slopes)
7/24/2019 Cm5 Unidimensional English
5/36
1 INTRODUCTIONBetween the particles which form the soil, due to its geometric features, there are aamount of holes which are releases. Even in the soils of the fine fraction and its lami
particles, pores are connected to form a ductwork where fluids can move.
Taken from Lambe (1991)
Taken from http://coleccion.educ.ar/coleccion/CD23/contenidos/familia/index
Micrograph of a sample of Sandstone in which the dispositionof rocks pores is shown.
7/24/2019 Cm5 Unidimensional English
6/36
1 INTRODUCTION
Due to complicated path across porous media, friction between fluids and rough surfacparticles lets the main energy loss in the flow.
Basic theory about soil mechanics study that phenomenon with the following assumptions
I. The flow can be considerate incompressible.
II. The flow across soil is laminar
III. Darcys Law is valid for all kind of soil
7/24/2019 Cm5 Unidimensional English
7/36
1 INTRODUCTION
When considering a permanent and incompressible flow, Bernoullis principle says the total energy peunit weight that has the flow is given by:
7/24/2019 Cm5 Unidimensional English
8/36
1 INTRODUCTION
Using the Bernoullis equation in the soil topic, the speed load term can be despised due tothe magnitude of speeds which are following.
Using this equation in a soil element, the following is obtained:
( )
Hydraulic Gradient i is defined as total energy loss per unit length:
7/24/2019 Cm5 Unidimensional English
9/36
2 DARCYS LAW
Henry Darcy did a study about water flow across a sand bed in 1850.
Varying the pressure and length of bed, Darcy found that caudal which passes through the soil isproportional to hydraulic gradient applied. In math terms:
The proportionality constant of Darcys Lawis known as:
Hydraulic Conductivi ty of soil
7/24/2019 Cm5 Unidimensional English
10/36
2 DARCYS LAW
Discharge Speed is the speed of moving of a raindrop from Position 1 to Position 2. (fig 1).
Infiltration Speed is the average flow speed through soil, it means, the raindrop speed from
Position 3 to Position 4. (fig 1).
Infiltration speed takes intoeffective area where the fluid mmeans, relates flow speematerials porosity.
Using the continuity equation:
A
L
7/24/2019 Cm5 Unidimensional English
11/36
3 HYDRAULIC CONDUCTIVITY
Kinematic Viscosity of fluid.
Is accepted to say that hydraulic conductivity has two components:
Hydraulic Conductivity or permeability coefficient k describes the ease of a fluid to move in a porous medand its units are
Hydraulic conductivity of soil depends on following factors
I. Fluid viscosityII. Void ratio and its distribution in the soil massIII. Rugosity of mineral particlesIV. Degree of saturation
Absolute Permeability depends on pores
structure and its geometric. .
7/24/2019 Cm5 Unidimensional English
12/36
3 HYDRAULIC CONDUCTIVITY
Hydraulic conductiv ity can be expressed as a function of soil moisture conditions.
Is important to say that hydraulic conductivity decreasesquickly with decrease of degree saturation of soil. Thefollowing are some reasons:
1. In the drying, liquid phase is not continuous.
2. Decrease the effective area such that exist flow.
Taken from: Analysis of underground water contaminatiosystemshttp://www.bvsde.ops-oms.org/eswww/fulltext/repind46
7/24/2019 Cm5 Unidimensional English
13/36
4 HYDRAULIC CONDUCTIVITY IN AN ANISOTROPIC MEDIA
Due to formation of soils, variation of its properties can be important in small distances(depth and area).
Model the soil as an unique layer with equivalent parameters can be advantageous, it meato suppose that the effects in a real soil can be represented by a fictitious soil with averageproperties.
In the case of moving of fluid in porous media, is possible to determinate:
I. Equivalent hydraulic conductivity for horizontal flow
II. Equivalent hydraulic conductivity for vertical flow
7/24/2019 Cm5 Unidimensional English
14/36
4.1 HORIZONTAL FLOW
Using the continuity equation:
=
( )(
( ) 1=( )
In this conditions the hydraulic conditio
the same in all layers:
4 HYDRAULIC CONDUCTIVITY IN AN ANISOTROPIC MEDIA
7/24/2019 Cm5 Unidimensional English
15/36
4.1 VERTICAL FLOW The condition of problem is:
= + (From continuity equation:
=
= +
From Darcys equation:
4 HYDRAULIC CONDUCTIVITY IN AN ANISOTROPIC MEDIA
7/24/2019 Cm5 Unidimensional English
16/36
5 EFFECTIVE STRESSES DUE TO FLOW
Method: Unit weight and peripheral forces of water Flow up
Lh Lh L z
wt
wt w
'
'
7/24/2019 Cm5 Unidimensional English
17/36
Method: Unit weight submerged and infiltration forces Flow up
Li L
h L
L z
wb
wb
t w
'
'
'
5 EFFECTIVE STRESSES DUE TO FLOW
7/24/2019 Cm5 Unidimensional English
18/36
5 1 EFFECTIVE STRESSES DUE TO FLOW UP
hw
LX
soil
z
A
BUsing the Bernoullis equation between point A and a point X inthe soil mass, the pressure in that point is given by:
( )
Hydraulic gradient allow to determine the energy loss in any pointof sample. Using the energy equation between the points A and B:
Reference plane: Plane 1
Reference plane: Plane 2
7/24/2019 Cm5 Unidimensional English
19/36
5 1 EFFECTIVE STRESSES DUE TO FLOW DOWN
hw
LX
soil
z
A
B
Supposing that the hydrostatic pressures law can be applied inthe model, is possible demonstrate that:
Effective stress in any point in the soil mass:
( ) = = ( )
7/24/2019 Cm5 Unidimensional English
20/36
flow
hw
Lz
( ) Reference plane: Plane 1
Z Z
5 2 EFFECTIVE STRESSES DUE TO FLOW UP
Hydraulic gradient allow to determine the energy loss in any pointof sample. Using the energy equation between the points A and B:
Using the Bernoullis equation between point B and a point X inthe soil mass, the pressure in that point is given by:
Reference plane: Plane 2
7/24/2019 Cm5 Unidimensional English
21/36
flow
hw
Lz
( ) = ( ) =
Effective stress in any point in the soil mass:
Supposing that the hydrostatic pressures law can be applied inthe model, is possible demonstrate that:
5 2 EFFECTIVE STRESSES DUE TO FLOW UP
7/24/2019 Cm5 Unidimensional English
22/36
5 3 COMPARISON BETWEEN FLOW CONDITIONS
D e p t h
( m )
Vertical effective stress 'z ( kPa)
Hidrosttica F.Descendente F.Ascendente
7/24/2019 Cm5 Unidimensional English
23/36
5 4 INFILTRATION FORCE
When water flows through soil, a friction force between soil particles and fluid particlesis produced. The magnitude of that force is related with fluid viscosity.
The infiltration force always acts in flow direction and is equal to:
ww i
LA
hA
suelodel Volumen
on Infiltraci Fuerza j
_ _
_
When the infiltration force is equal to weight of soil mass in flow up, the condition of siphoning or boiling is presented. In that condition, the matrix of soil dont suppallowing the mineral particles move in the flow direction.
7/24/2019 Cm5 Unidimensional English
24/36
5 4 INFILTRATION FORCE
In order with the last description, the siphoning condition is presented when effectivestress is null.
( )
0 ( )
Is necessary to assess this condition in the projects which involve flow in soils and toverify that the gradient found is the greatest critical gradient of soil. A recommendationfor this is:
23
7/24/2019 Cm5 Unidimensional English
25/36
7/24/2019 Cm5 Unidimensional English
26/36
7/24/2019 Cm5 Unidimensional English
27/36
7/24/2019 Cm5 Unidimensional English
28/36
In the test, water of burette flows through soil.The initial difference of head, Ho in the timet=to=0 is registered and the flow through soilsample is allowed such that final difference of head in the time t is H.
In the Burette: dt
dH sQ
Through soil: k L H
Q
Is known that the most soils IN SITU are anisotropic,In that order, the horizontal hydraulic conductivityand vertical hydraulic conductivity are different.
6 MEASUREMENT OF HYDRAULIC CONDUCTIVITY
TEST OF VARIABLE HEAD
7/24/2019 Cm5 Unidimensional English
29/36
PUMPING TEST
The test involves pumping water from aconstant rate (under steady state) recorddecrease in groundwater level.
Analysis of field test is related to the t(the permeable layer of soil)
1. Unconfined Aquifer2. Confined Aquifer
6 MEASUREMENT OF HYDRAULIC CONDUCTIVITY
7/24/2019 Cm5 Unidimensional English
30/36
The process of exploitation of an aquifer or a unconfinedmedium is a bidimentional flow problem, but is preferredin one direction.
For simplicity, assume that the flow is completelyhorizontal and evenly distributed in the medium,obviating the vertical component.
This condition is known as the supposition of Dupuit Forchheimer.
PUMPING TEST
6 MEASUREMENT OF HYDRAULIC CONDUCTIVITY
7/24/2019 Cm5 Unidimensional English
31/36
For simplicity the mathematicapossible to use cylindrical
analyze the problem:
Assuming that the medium iswe can say that abatement ofthe same in all directions.
It means that the abatement odepend only of radius:
0
PUMPING TEST
6 MEASUREMENT OF HYDRAULIC CONDUCTIVITY
7/24/2019 Cm5 Unidimensional English
32/36
From the above, is possible say
Using Darcys law:
Q Q
Q (2) Q
Q( )ln
PUMPING TEST
6 MEASUREMENT OF HYDRAULIC CONDUCTIVITY
6 MEASUREMENT OF HYDRAULIC CONDUCTIVITY
7/24/2019 Cm5 Unidimensional English
33/36
Flujo radial
Impermeable
Superficiepiezmetrica
Pozo
Impermeable
Acuferoh1
h2
r 1
r 2
D
qPozos de
observacin
H
ro
Ri
The analysis of problem is doway that the last problem, t
possible conditions of flowaquifer
In the case h1>D for any time t
Q Q
Q (2 )
Q(2 )(
Si h1>D
Q
PUMPING TEST
6 MEASUREMENT OF HYDRAULIC CONDUCTIVITY
7/24/2019 Cm5 Unidimensional English
34/36
1. Flow through soil also can be considered as laminar flow due to its small speed, in thatorder v=k*i in which is a expression of Darcys law.
2. Hydraulic conductivity or permeability coefficient k describes the ease of a flua porous media and is obtained in laboratory test . [L/T]
3. Hydraulic gradient i is the total energy loss h per unit length l l : i= h /l
4. Discharge speed v is the speed of moving of water.
5. Infiltration speed vs is the average speed of flow through soil and is expressed as vs =
REVIEW
7/24/2019 Cm5 Unidimensional English
35/36
6. There are three important heads in flow through porous media: Head of position, head of
pressure and the total head
7. The principal methods to analyze the stresses in flow condition are: total aforces method and Infiltration forces and weight submerged
8. Infiltration forces per unit volume are expressed as i* w and in isotropic soilflow direction.
9. Siphoning or boiling is a state in which a soil without cohesion losses its strength due toflow . It overrides the effective stress.
REVIEW
7/24/2019 Cm5 Unidimensional English
36/36
BIBLIOGRAPHY
Holtz, R. (1981). Introduction to Geotechnical Engineering. (2dn Edition)
Craig, R. F. (1997) Soil Mechanics. 6th Edition. Chapman & Hall.
Lambe, T. W., Whitman, R. V. (1979). Soil Mechanics. John Wiley & Sons.
James Cook University, Australia. Engineering and Physical Sciences Rhttp: //eng1.jcu.edu.au/research/compgeo/geores.html
University of Cantabria, Spain. Virtual course of Soil Mechanics.
National Technological University Regional Faculty Santa Fe - Course: Foundations- Verification of safety to siphoning
http://eng1.jcu.edu.au/research/compgeo/geores.htmlhttp://eng1.jcu.edu.au/research/compgeo/geores.htmlhttp://eng1.jcu.edu.au/research/compgeo/geores.html