Soil mech. lec. ppt

SOIL MECHANICS
ENGR. RICHARD T. BARNACHEA
CE Instructor

REFERENCES:
O Soil Mechanics Fundamentals
by: Isao Ishibashi
Hemanta Hazarika
O Soil Mechanics and Foundation
by: Muni Budhu
O Geotechnical Engineering 2nd Edition
by: Renato Lancellota

Soil Mechanics
O Soil mechanics is the branch of
science that deals with the study of
physical properties of soil and the
behavior of soil masses subjected to
various types of forces.

Soil Mechanics
O Soil mechanics is one of the
engineering disciplines that deals with
soils as an engineering material.
O Since ancient ages, engineers have
been handling soils as an engineering
material for various construction
projects.

DEFINITION OF SOIL
The term Soil has various meanings, depending
upon the general field in which it is being
considered.
O To a Pedologist ... Soil is the substance existing
on the earth's surface, which grows and develops
plant life.
O To a Geologist ..... Soil is the material in the
relative thin surface zone within which roots occur,
and all the rest of the crust is grouped under the
term ROCK irrespective of its hardness.

O To an Engineer .... Soil is the un-aggregated
or un-cemented deposits of mineral and/or
organic particles or fragments covering
large portion of the earth's crust.
DEFINITION OF SOIL

Soil is a natural body comprised of solids
(minerals and organic matter), liquid, and
gases that occurs on the land surface,
occupies space, and is characterized by one or
both of the following: horizons, or layers, that
are distinguishable from the initial material as
a result of additions, losses, transfers, and
transformations of energy and matter or the
ability to support rooted plants in a natural
environment.
Soil is the oldest and most complex
engineering material.

Soil Formation
Parent Rock
Residual Soil
(remain at the
original place)
Transported Soil
(moved and
deposited to other
places)
- weathering (by
physical & chemical
agents) of parent
rock
- weathered and
transported far away
by wind, water and
ice

Transported Soils
Glacial soils: formed by transportation and
deposition of glaciers.
Alluvial soils: transported by running water and
deposited along streams.
Lacustrine soils: formed by deposition in quiet
lakes (e.g. soils in Taipei basin).
Marine soils: formed by deposition in the seas
Aeolian soils: transported and deposited by the
wind (e.g. soils in the loess plateau, China).
Colluvial soils: formed by movement of soil from its
original place by gravity, such as during landslide

SOIL FORMATION
Weathering is the process of the breaking down
rocks.
There are two different types of weathering.
Physical weathering
Chemical weathering
In physical weathering it breaks down the rocks, but
what it's made of stays the same.
Physical weathering involves reduction of size without
any change in the original composition of the parent
rock.
The main agents responsible for this process are
exfoliation, unloading, erosion, freezing, and thawing.

O In chemical weathering it still breaks down
the rocks, but it may change what it's made
of.
O Chemical weathering causes both reductions
in size and chemical alteration of the original
parent rock.
For instance, a hard material may
change to a soft material after chemical
weathering.

CHAPTER TWO
PHYSICAL
PROPERTIES
OF SOIL

BASIC DEFINITION AND PHASE RELATIONS
O SOIL is composed of solids, liquids, and gases.
O The solid phase may be mineral, organic matter, or
both.
O The spaces between the solids (soil particles) are
called voids.
O If all the voids are filled with water, the soil is
saturated. Otherwise, the soil is unsaturated.
O If all the voids are filled with air, the soil is said to be
dry.
O Water is often the predominant liquid and air is the
predominant gas.

O VOID RATIO; e : The ratio of the volume of voids (Vv)
to soil volume (Vs).
Void ratios of real coarse-grained soils vary between
1 and 0.3. Greater than 1 for clay soils.
O POROSITY; n : The ratio of the volume of voids (Vv)
to total volume (V).
0  n  1
O RELATIONSHIP BETWEEN VOID RATIO AND
POROSITY
or
s
v
V
V
e 
V
V
n v

n
n
e


1 e
e
n


1

O WATER CONTENT; ω : The ratio of the amount of
water (Ww) in the soil (Ws) and expressed as a
percentage.
O DEGREE OF SATURATION; S : The ratio of the
volume water (Vw) to volume of voids (Vv) and
expressed as a percentage.
0%  S  100%
%100x
W
W
s
w

%100x
V
V
S
v
w


O Completely dry soil S = 0 %
Completely saturated soil S = 100% or 1
Unsaturated soil (partially saturated soil)
S = Vw/Vv = (ωGs)/e
or
Se = ωGs

O UNIT WEIGHT, Ɣ : The ratio of weight to volume
γt = (Gs + Se) γw
(1 + e)
O SPECIFIC GRAVITY; GS : The ratio of unit weight of
soil to unit weight of water
or
O RELATIVE DENSITY; Dr :
w
w
w
V
W

s
s
s
V
W

V
W

w
s
Gs



%100
minmax
max
x
ee
ee
Dr o



w
VsWs
Gs

/


Special Cases for Unit Weight
O Saturated unit weight (S=1):
γsat = [(Gs + e)/(1 + e)] γw
O Dry unit weight (S=0):
γd = Ws/V = [Gs /(1 + e)] γw
O Effective or Buoyant (submerged) unit weight
is the weight of a saturated soil, surrounded
by water per unit volume of soil.
γ’ = γsat – γw = [(Gs - 1)/(1 + e)] γw

Example #1:
O A soil sample has a void ratio of
0.8, degree of saturation of 0.9 and
Gs of 2.68. Using SI units compute,
total unit weight, dry unit weight,
water content, and saturated unit
weight.

O A saturated sample of soil in a water
content container weighed 60g. After
drying in air its weight was 50g. The
container weighed 10g. Specific gravity
of the soils was 2.7. Determine
O water content
O void ratio
O total unit weight
O dry unit weight
Example #2:

O PARTICLE SIZE DISTRIBUTION is a screening
process in which coarse fractions of soil are
separated by means of series of sieves.
O Particle sizes larger than 0.074 mm (U.S. No.
200 sieve) are usually analyzed by means of
sieving.
O Soil materials finer than 0.074 mm (#200
material) are analyzed by means of
sedimentation of soil particles by gravity
(hydrometer analysis).
Determination of Particle Size
Distribution

Mechanical analysis is used in the
determination of the size range of particles
present in a soil, expressed as a percentage
of the total dry weight.
There are two methods that generally
utilized to determine the particle size
distribution of soil:
1. Sieve Analysis (for particle sizes >
0.075mm in diameter)
2. Hydrometer Analysis ( for particle
sizes < 0.075mm in diameter )

O Particle size distribution curve is a
representation in graphical or tabular form
of the various (diameter) grain sizes in a
soil, determined through sieving and
sedimentation.
O The particle diameters are plotted in log
scale, and the corresponding percent finer
in arithmetic scale.

Particle Size Distribution Curve

Sieve Analysis
O It is performed
by shaking the
soil sample
through a set of
sieves having
progressively
smaller
openings.

Hydrometer Analysis
O It is based on the
principle of
sedimentation of
soil grains in water.
O Used to extend the
distribution curve of
particle shape and
to predict the
particle size less
than 200 sieve.

Some commonly used measures are:
O a) Effective size: (D10)
It is the diameter in the particle size
distribution curve corresponding to 10%
finer. (maximum size of the smallest 10% of
the soil)
O b) Uniformity Coefficient : Cu =D60/D10
It is the ratio of the maximum diameter of the
smallest 60% to the effective size.
A well graded soil will have
Cu > 4 for gravel
Cu > 6 for sand

O c) Coefficient of Curvature:
Cc = (D30)²/(D60*D10)
D30 is the diameter corresponding the 30%
finer
O d) Clay Fraction: (CF)
It is the percentage by dry mass of particles
smaller than 0.002mm (2μm), and is an
index property frequently quoted relation to
fine grained soils (soils with 50% or more
finer than 63μm). It has a strong influence
on the engineering properties of fine
grained soils.

O e) Well-Graded Material – Contains particles
of a wide range of sizes. The smaller
particles fill the spaces left between the
larger particles; therefore the soil has
greater strength than a poorly graded soil,
and lower permeability.
O f) Poorly – Graded Material – Contains a
large portion of uniformly sized particles.
This particular soil has larger voids in its
structure and poor strength along with high
permeability.

O Soil A: Well Graded
O Soil B: Poorly Graded
O Soil C: Uniform

SOIL CLASSIFICATION
CHAPTER THREE

O PURPOSE:
To classified the soil into a group according
to the soil behavior and physical shape.
O TYPE OF CLASSIFICATION:
CLASSIFICATION BY VISUAL
AASHTO
USCS (UNIFIED SOIL CLASSIFICATION SYSTEM)
O SOIL TESTS
ATTERBERG LIMIT
SIEVE ANALYSIS
HYDROMETER ANALYSIS

CLASSIFICATION BY VISUAL
Carried out by direct observation (visual
examination) to the sample and approximate
the type of soil by:
Color
Smell
Sense/Feeling
Endurance (strength, durability)
Swelling (enlarge or expand)
Sedimentation

AASHTO
American Association of State Highway and
Transportation Officials
O The soil classified into 7 major categories (A-
1 to A-7)
O Based on:
The result of Sieve Analysis
Atterberg Limits
O The soil quality based on Group Index
Calculation.

AASHTO
O GROUP INDEX
O F = The percentage of soil pass sieve no. 200
)10)(15(01.0)}40(005.02.0){35(  PIFLLFGI
Subgrade Group Index Value
Very good Soil Class A-1-a (0)
Good 0 – 1
Medium 2 – 4
Bad 5 – 9
Very Bad 10 - 20

GROUP INDEX
Rules:
O If GI < 0, GI = 0
O GI  Integer Number
O No upper limit of GI
O For coarse grained,
O GI = 0 for A-1-a, A-1-b, A-2-4, A-2-5 and A-3
O GI =0.01(F-15)(PI-10) for A-2-6 and A-2-7
AASHTO

AASHTO PROCEDURE
Make examination of soil to determine whether it
is granular or silt clay materials
Determine amount passing No. 200 sieve
Granular Materials
35% or less pass No. 200 sieve
Silt-Clay Materials
36% or more pass No. 200 sieve
Less than 25%
pass No. 200 sieve
Run sieve analysis, also LL
and PL on minus No. 40
sieve material
A-1
Less than 50%
pass No. 40 sieve
Less than 15%
pass No. 200 sieve
Less than 30%
pass No. 40 sieve
Less than 50%
pass No. 10 sieve
PI less than 6
Less than 25%
pass No. 200 sieve
Less than 50%
pass No. 40 sieve
PI less than 6
A-1-a A-1-b
Greater than 50%
pass No. 40 sieve
A-2
Less than 35%
pass No. 200 sieve
Less than 10%
pass No. 200 sieve
Nonplastic
A-3
Run LL and PL on minus No.
40 sieve material
Silty
PI less than 10
Clayey
PI greater than 11
LL less
than 40
LL greater
than 41
A-2-4 A-2-5
LL less
than 40
LL greater
than 41
A-2-6 A-2-7
Run LL and PL on minus No.
40 sieve material
Silt
PI less than 10
Clay
PI greater than 11
LL less
than 40
LL greater
than 41
LL less
than 40
A-7
LL greater
than 41
A-4 A-5 A-6
PI equal to or less
than LL minus 30
or
PL equal to or
greater than 30
PI greater than LL
minus 30
or
PL less than 30
A-7-5 A-7-6

USCS (UNIFIED SOIL
CLASSIFICATION SYSTEM)
O First, dveloped by Arthur Casagrande for
wartime airfields construction in 1943, the
system was modified and adopted for regular
use by Army Corps of Engineers and then by
Bureau of Reclamation in 1952 as the
Unified Soil Classification System
(Casagrande 1948).
O Currently, it is adapted in ASTM and
periodically updated.

O The system uses simple six major symbols and four
modifiers as in the following:
Major symbols:
G – Gravel S – Sand
M – Silt C – Clay
O – Organic Pt – Peat
Modifiers:
W – Well graded (for gravel and sand)
P – Poorly graded (for gravel and sand)
H – High plasticity (for silt, clay, & organic soils)
L – Low plasticity (for silt, clay, & organic soils)

O Soil classification determined base on the
soil parameter i.e.:
- Diameter of soil particle
Gravel : pass sieve no.3 but retained at
sieve no. 4
Sand : pass sieve no. 4 but retained at
sieve no. 200
Silt and Clay : pass sieve no. 200
- Coefficient of soil uniform
- Atterberg Limits

Soil Consistency
Soil consistence provides a means of describing
the degree and kind of cohesion and adhesion
between the soil particles as related to the
resistance of the soil to deform or rupture
Soil Behave Like:
SOILD at very low moisture content
LIQUID at very high moisture content

Soil Consistency - Atterberg Limits
Depending on Moisture Content soil can be divided
into:
Shrinkage
Limit (SL)
Plastic Limit (PL)
Liquid Limit (LL)
Plasticity Index
(PI) = PL - LL
MoistureContent(w)
+
-
Liquidity
Index (LI)
LI = 0
LI = 1
1. Solid
2. Plastic
3. Liquid

Liquid Limit
Liquid Limit (LL) is defined as the moisture
content at which soil begins to behave as a
liquid material and begins to flow.
(Liquid limit of a fine-grained soil gives the
moisture content at which the shear strength
of the soil is approximately 2.5kN/m2)

Liquid Limit - Measurement
First Method
Casagrande
Apparatus
ASTM D-4318

Liquid Limit (LL) at N = 25

Liquid Limit – Flow Index
Flow Index
IndexFlowCalculate
WorkGroup
N2=30N1=20
w1=44
w2=39

Second Method
Fall Cone Method BS1377

Liquid Limit (LL) at d = 20 mm

Plastic Limit - Definition
The moisture content (%) at which the soil
when rolled into threads of 3.2mm (1/8 in) in
diameter, will crumble.
Plasticity Index (PI): is a measure of the range
of the moisture contents over which a soil is
plastic.
PI=LL-PL

Plastic Limit - Measurement
First Method
ASTM D-4318
PL = w% at dia. 3.2 mm (1/8 in.)

Plastic Limit - Measurement
Second Method
Fall Cone
Method BS1377
Plastic Limit (PL) at d = 20 mm

Plasticity Index - Definition
Plasticity Index is the difference between
the liquid limit and plastic limit of a soil.
PI = LL – PL

Plasticity Index - Definition
PI (%) = 4.12 IF (%)
PI (%) = 0.74 IFC (%)

O Soil compaction is defined as the method of
mechanically increasing the density of soil.
O it is a physical process to decrease the voids of soil
by static or dynamic loading.
O In construction, this is a significant part of the
building process.
O If performed improperly, settlement of the soil could
occur and result in unnecessary maintenance costs
or structure failure.

O PURPOSE
O Improving the soil quality
by:
- Increasing the shear
strength of soil
- Improving the bearing
capacity of soil
O Reduces the settling of
soil
O Reduces the soil
permeability
O To control the relative
volume change

TYPES OF COMPACTION
4 types of compaction effort on soil:
* Vibration
* Impact
* Kneading
* Pressure

O BASIC THEORY
Developed by R.R. Proctor on 1920 with 4
variables :
# Compaction efforts (Compaction Energy)
# Soil types
# Water content
# Dry Unit Weight
O LABORATORY COMPACTION TEST
* Standard Proctor Test
* Modification Proctor Test

STANDARD PROCTOR TEST
O The soil is compacted at cylindrical tube.
O Specification of test and equipment:
Hammer weight = 2,5 kg (5,5 lb)
Falling height = 1 ft
Amount of layers = 3
No. of blows/layer = 25
Compaction effort = 595 kJ/m3
Soil type = pass sieve no. 4

O The test is carried out several time
with different water content.
O After compaction, the weight,
moisture content and unit weight of
samples are measured.
O Test Standard :
AASHTO T 99
ASTM D698

MODIFIED PROCTOR TEST
O The soil is compacted at cylindrical tube.
O Specification of test and equipment:
Hammer weight = 4.5 kg (10 lb)
Falling height = 1.5 ft
Amount of layers = 5
No. of blows/layer= 25, 56
Compaction effort= 2693 kJ/m3
Soil type = pass sieve no. 4

O The test is carried out several time with
different water content.
O After compaction, the weight, moisture
content and unit weight of samples are
measured.
O Test Standard :
AASHTO T 180
ASTM D1557

Type of Compaction
Equipment
O Rubber Tire Roller
O Smooth Wheel Roller
O Sheepsfoot Roller
O Grid Roller
O Baby Roller
O Vibrating Plate

Rubber Tire Roller
O A heavily loaded wagon
with several rows of three
to six closely spaced tires
with tire pressure may be
up to about 700 kPa and
has about 80% coverage
(80% of the total area is
covered by tires).
O This equipment may be
used for both granular
and cohesive highway
fills.

Smooth Wheel Roller
O Compaction equipment
which supplies 100%
coverage under the
wheel, with ground
contact pressures up to
400 kPa and may be
used on all soil types
except rocky soils.
O Mostly use for
proofrolling subgrades
and compacting asphalt
pavements.

Sheepsfoot Roller
O This roller has many round or rectangular
shaped protrusions or “feet” attached to a steel
drum.
O The area of these protusions ranges from 30 to
80 cm².
O Area coverage is about 8 – 12% with very high
contact pressures ranging from 1400 to 7000
kPa depending on the drum size and whether
the drum is filled with water.
O The sheepsfoot roller is best suited for cohesive
soils.

Grid Roller
O This roller has about
50% coverage and
pressures from 1400
to 6200 kPa, ideally
suited for compacting
rocky soils, gravels and
sand.
O With high towing
speed, the material is
vibrated, crushed, and
impacted.

Baby Roller
O Small type of
smooth wheel
roller yang, which
has pressure
ranges from 10 to
30 kPa.
O The performance
base on static
weight and
vibration effect.

Vibrating Plate
O Compaction equipment,
which has plate shape.
In Indonesia this
equipment sometimes
called as “stamper”.
O Usually used for narrow
area and high risk when
use large compaction
equipment like smooth
wheel roller etc.

Dynamic Compaction
O The dynamic compaction method involves
dropping a heavy weight repeatedly on the
ground at regularly spaced intervals.
O The weight is typically between 80 and 360
kN, and the height changes from 10 to 30m.
O The impact of the free drop of weight creates
stress waves that densify the soil to a
relatively large depth.
O The method is effectively used for sandy soils
but is also applied to silt and clay soils.

O In order to indicate the level of compaction relative
to the densest and the loosest compaction level for
a given specific soil, most for granular soils, relative
density (Dr) is introduced and is defined in the
following equation:
Dr = ( emax – e ) x 100%
emax - emin
O When the in-situ soil’s void ratio is in its loosest (e =
emax) state, then, Dr = 0%. If it is in its densest (e =
emin), Dr = 100%.

O Maximum void ratio:
emax = Gs γw - 1
γmin
O Minimum void ratio:
emin = Gs γw - 1
γmax

Compaction Curve
O After the experiment, a set of wet unit weight
and water content are measured.
O The compaction effectiveness, however, is
compared in terms of increased dry unit
weight of the specimen instead of total unit
weight.
γt = (1+w) Gs γw = (1+w) γd
1+e
γd = Gs γw = γw
1+e 1+w

Example #1:
O Computation of test data:
A B
Water Content Total Unit Wt.
2.3 15.80
4.5 17.18
6.7 18.83
8.5 19.72
10.8 20.04
13.1 19.34
15 18.45
C
Dry Unit Wt.
15.45
16.44
17.65
18.18
18.08
17.10
16.04

Compaction Curve
14
16
18
20
0 2 4 6 8 10 12 14 16
Dry Unit Wt.
2.3
4.5
6.7
8.5
10.8
13.1
15
γdmax
wopt

Specification of Compaction
in the Field
O After the compaction curve for a given soil is
obtained from laboratory tests, the
specification of compaction in the field is
made.
O Relative compaction (R.C.) is defined as
R.C. = γd,field (x 100%)
γd,max

Example #2:
O At a borrow site, sandy soil was excavated.
The soil had total unit weight of 19.3 kN/m³,
water content of 12.3%, and specific gravity
of 2.66. the soil was dried, the maximum
and minimum void ratio tests were
performed, and maximum void ratio is 0.564
and minimum void ratio is 0.497 were
obtained. Determine the relative density of
the soil at the borrow site.

Outline of this Lecture
1. Permeability in Soils
2. Bernoulli’s Equation
3. Darcy’s Law
4. Hydraulic Conductivity
5. Hydraulic Conductivity Tests

Due to the existence of the inter-connected voids,
soils are permeable.
The permeable soils will allow water flow from
points of high energy to points of low energy.
Permeability is the parameter to characterize
the ability of soil to transport water.

Permeability in Soils
• Permeability is the measure of the soil’s
ability to permit water to flow through its pores
or voids.
• It is one of the most important soil
properties of interest to geotechnical
engineers.

Soil Permeability
Soil Properties
Physical
(Soil Characteristics)
Mechanical
Specific
Gravity
Moisture Content
Unit Weight
Gradation
Atterberg
Limits
Compaction Permeability Compressibility
Strength
(Shear)
1 – Constant-Head Test
2 – Falling-Head Test

Importance of permeability
• The following applications illustrate the importance
of permeability in geotechnical design:
– Permeability influences the rate of settlement of a
saturated soil under load
– The design of earth dams is very much based upon
the permeability of the soils used.
– The stability of slopes and retaining structures can be
greatly affected by the permeability of the soils involved.
– Filters made of soils are designed based upon their
permeability.

Use of Permeability
• Knowledge of the permeability properties
of soil is necessary to:
– Estimating the quantity of underground seepage;
– Solving problems involving pumping seepage
water from construction excavation;
– Stability analyses of earth structures and
earth retaining walls subjected to seepage forces.

Bernoulli’s equation
The total pressure in terms of water head is
formed from 3 parts: 1), pressure head; 2),
dynamic head; and 3), elevation head. This is
known as the Bernoulli’s equation:
v
h = + + Z
γw 2 g
h: total head in m, or ft;
P: water pressure in Pa, or psi;
γw: unit weight of water, in kN/m³), or lb/(ft³);
v: velocity of water, in m/s, or ft/s;
g: gravity acceleration m/s2 or ft/s²;
Z: elevation head in m, or ft.
P 2

The dynamic head is usually negligible since
the water flow velocity is usually small.
The elevation head is accounted from the
datum to the elevation of the bottom of the well,
and the pressure head is the portion above the
well bottom to the water table.
Piezometric surface
Pressure head P/γw
Elevation head Z
datum

Again, since the seepage flow velocity in soil is small, the dynamic head
(velocity head) can be neglected, so that the total head at any points is
h =
P
γ w
+ Z
Hydraulic gradient:
∆h
i =
L

may exist in fractured rock, stones,
gravels, and very coarse sands
in most soil we found the
following relation, i.e., the water
flow velocity in the soil is proportional
to the hydraulic gradient
v ∝ i

Darcy’s Law
• The coefficient of permeability, or hydraulic
conductivity, k, is a product of Darcy’s Law.
• In 1856, Darcy established an empirical
relationship for the flow of water through porous
media known as Darcy’s Law, which states:
v = -ki or q = -kiA
q = flow rate (cm³/s)
k = coefficient of permeability (cm/s)
A = cross-sectional Area (cm²)
i = hydraulic gradient

The parameter q in Darcy’s law is called the
flow rate or simply the flow (flux).
It describes in a unit time, over a unit cross-section area,
how much water in terms of volume has been flowed
through.
v
q = vA,
volume length
( = ⋅ area)
time time
A
The flow rate q is in the unit of velocity (L/t).
Examination of the Darcy’s law make us be
aware that the permeability k is also in the unit
of velocity.

In the field, the gradient of the head is the head
difference over the distance separating the 2 wells.
H2 − H1dH
v = −k = −k
dx ∆x
Water flow
H1 H2
∆x
EGL
HGL

Darcy’s law states that how fast the groundwater
flow in the aquifer depends on two parameters:
1. how large is the hydraulic gradient of the water
head (i=dH/dx); and
2. the parameter describing how permeable the
aquifer porous medium – the coefficient of
permeability (hydraulic conductivity) k.
The minus sign in the equation denotes that the
direction of flow is opposite to the positive
direction of the gradient of the head.

The physical description of groundwater flow in
soil is the Darcy’s law.
The fundamental premise for Darcy’s law to work
are:
1. the flow is laminar, no turbulent flows;
2. fully saturated;
3. the flow is in steady state, no temporal
variation.

Hydraulic conductivity k and
absolute permeability K
The absolute permeability is in the unit of LL
(length square); and the expression for the
relation is
γw
k = K
η

Units of the coefficient of Permeability k
The permeability k is in the dimension of velocity.
However, in different field people prefer use different
units for permeability simply because different fields
deal different scales of subsurface fluid flow.
In hydrogeology a used to be popular unit is meinzer; in
geotechnical world is cm/sec; and in petroleum engineering
people just use the unit of Darcy. Here are the conversions:
1 cm/sec = 864 m/day
1 darcy = 1 cm³ of fluid with viscosity of 1 centipose
in 1 sec, under a pressure change of 1 atm. over a
length of 1 cm through a porous medium of 1 cm² in
cross-sectional area.
1 Meinzer = 1gal/day/ft2

Hydraulic Conductivity
• The coefficient or permeability is also
known as hydraulic conductivity;
• Hydraulic Conductivity, k, is a measure
of soil permeability;
• k is determined in the lab using two methods:
– Constant-Head Test
– Falling-Head Test

Hydraulic Conductivity
(Cont.)
• Hydraulic conductivity of soils depends on
several factors:
–
–
–
–
–
Fluid viscosity
Pore size distribution
Grain size distribution
Void ratio
Degree of soil saturation

Constant Head Test
• The constant head test is used primarily
for coarse-grained soils;
• This test is based on the assumption of
laminar flow where k is independent of i
(low values of i);
• ASTM D 2434;
• This test applies a constant head of water
to each end of a soil in a “permeameter”.

Constant-head hydraulic
conductivity test with permeameter

Procedure (Constant
head)
1. Setup screens on the permeameter
2. Measurements for permeameter, (D), (L), H1
3. Take 1000 g passing No.4 soil (M1)
4. Take a sample for M.C.
5. Assemble the permeameter – make sure seals are air-tight
6. Fill the mold in several layers and compact it as prescribed.
7. Put top porous stone and measure H2
8. Weigh remainder of soil (M2)
9. Complete assembling the permeameter. (keep outlet valve closed)
10.Connect Manometer tubes, but keep the valves closed.
11.Apply vacuum to remove air for 15 minutes (through inlet tube at
top)
12.Run the Test (follow instructions in the lab manual) …..
13.Take readings
– Manometer heads h1 & h2
– Collect water at the outlet, Q ml at time t ≈ 60 sec.

Calculation (Constant head)
• Determine the unit weight;
• Calculate the void ratio of the compacted
specimen;
h
from Q = Akit = A(k )t
• Calculate k as: L
QL
get k =
• Calculate Aht
k20 0 C = kT0C
η
η
T0 C
200C

 In a soil test, it took 16.0 min for 1,508cm3 of
water to flow through a sand sample, the cross-
sectional are of which was 50.3cm2. The void ratio
of the soil sample was 0.68.
 1. What is the velocity of water through the soil?
2. What is the actual (interstitial) velocity of water?
Assignment:

Falling Head Test
• The falling head test is used both for
coarse-grained soils as well as fine-
grained soils;
• Same procedure in constant head test
except:
– Record initial head difference, h1 at t = 0
– Allow water to flow through the soil specimen
– Record the final head difference, h2 at time
t = t2
– Collect water at the outlet, Q (in ml) at time t ≈
60 sec

Calculation (Falling head)
• Calculate k as
• Where:
aL h1
k = ln
At h2
A = inside cross sectional area of the water tank
a = inside cross sectional area of the standing pipe
h1 = distance to bottom of the beaker before the test
h2 = distance to bottom of the beaker after the test
• Calculate k 20 0 C = kT 0C
η
η
T 0 C
200 C

Example:
O Figure shows water flow through soil the specimen in
a cylinder. The specimen’s k value is 3.4 x 10 cm/s.
-4
Datum
280mm
50mm
125mm
100mm
75mm
200mm80mm
A
B
C
D

O a.) Calculate pressure heads at pts. A,B,C
and D and draw the levels of water height
in standpipes.
O b.) Compute the amount of water flow q
through the specimen.

Example #2:
O A 900 mm long cylindrical soil sample, contained as shown in
the figure, is subjected to a steady state flow under constant
head. Find the pore water pressure at a point X.
300 mm
900 mm
400 mm
A
B
X
300 mm

FLOW NETS
Flow Net - graphical construction used to calculate
groundwater flow through soil.
Comprised of Flow Lines and Equipotential Lines.
Flow Line - a line along which a water particle moves
through a permeable soil medium.
Flow Channel - strip between any two adjacent flow lines.
Equipotential Lines - a line along which the potential head
at all points is equal.
NOTE: Flow Lines and Equipotential Lines must meet at
right angles!

Δh
hL
Δh
impervious strata
Δq
Δq
Δq
datum
Streamlines and Equipotential Lines
Nf
Nd

Therefore, flow through one channel is:
q = khL(Nf/Nd)
where q = total amount of water flow
hL = total head loss
Nf = number of total equipotential line drops
Nd = number of flow channels
An equipotential line is a contour of constant total head.
The blue lines shown in the figure are all equipotential lines,
where the total head is constant along each of them.
In a flow net, such as the one shown in the figure, the
equipotential lines are drawn such that the total head
difference between two adjacent ones is the same (= Δh)
throughout the flow region.
If there are Nd equipotential drops in a flow net, Δh = hL/Nd.

Example #3:
O A long horizontal drain at 3 m depth collects the ground water in a low-lying
area. The free water table coincides with the ground level and the flownet for
the ground water flow is shown in Fig. 1. The 6 m thick sandy clay bed is
underlain by an impervious stratum. Permeability of the sandy clay is 6.2 × 10-5
cm/s.

(a) Find the discharge through the drain in m3/day,
per meter length of drain.
(b) Find the pore water pressure at X, 1.5 m into the
soil, directly above the drain.
(c) Estimate the velocity of flow at X.

Soil mech. lec. ppt

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