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Basic Soil Mechanics: Volume I ดร.สุรยะ ทองมุณ ภาควชาวศวกรรมโยธาคณะวศวกรรมศาสตร์ มหาวทยาลัยเชยงใหม่

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Page 1: Basic Soil Mechanics: Volume I mid material.pdf · Be used as Construction Materials ... “Soil Mechanics is the application of laws of mechanics and hydraulics to engineering problems

Basic Soil Mechanics: Volume I

ดร.สรยะ ทองมณ ภาควชาวศวกรรมโยธาคณะวศวกรรมศาสตร

มหาวทยาลยเชยงใหม

Page 2: Basic Soil Mechanics: Volume I mid material.pdf · Be used as Construction Materials ... “Soil Mechanics is the application of laws of mechanics and hydraulics to engineering problems

แผนการสอนของอาจารย คณะวศวกรรมศาสตร มหาวทยาลยเชยงใหม ประจาภาคเรยนท 1 ปการศกษา 2558

ระดบปรญญาตร ภาควชาวศวกรรมโยธา

1. ชอผสอน ดร. สรยะ ทองมณ

2. รายละเอยดกระบวนวชา รหสกระบวนวชา 251371

ชอกระบวนวชา กลศาสตรดน (Soil Mechanics) ลกษณะกระบวนวชา ( / ) บรรยาย ( ) ปฏบต ( ) ฝกปฏบต ( ) อนๆ ระบ

ลกษณะการสอน ( / ) สอนคนเดยว ( ) สอนเปนกลม 2 คน

จานวนชวโมงสอนตอสปดาห 3 ชวโมงตอสปดาห

3. วตถประสงคของกระบวนวชา เพอใหนกศกษาสามารถเขาใจในการกาเนดของดน เพอใหนกศกษาเรยนรนยามและสมบตของดนทางกายภาพเบองตน

เพอใหนกศกษาสามารถจาแนกชนดของดนได

เพอใหนกศกษามความรพนฐานเกยวกบคณสมบตทางวศวกรรมของดน และพฤตกรรมการรบแรง

ของดน สาหรบประยกตในงานวศวกรรมฐานราก

เพอใหนกศกษาวเคราะหและสามารถคานวณการทรดตวของชนดนได

เปนวชาบงคบของสภาวศวกร สาขาวศวกรรมโยธา

4. คาอธบายลกษณะกระบวนวชา กาเนดดน คณสมบตทางเคมและกายภาพ การจาแนกประเภทดนสาหรบงานทางวศวกรรม การไหล

ของนาในดน การกระจายหนวยแรงในดน ทฤษฎคอนโซลเดชนและการคานวณการทรดตว กาลงรบแรง

เฉอน ทฤษฎกาลงทฤษฎกาลงรบแรงแบกทาน การบดอดดน

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5. แผนการสอน

สปดาหท เนอหา แบบฝกหด หมายเหต

1 แนะนากระบวนวชา และความสาคญของรายวชา

2 วฏจกรการกาเนดของดน และ ขนาดของอนภาคดน

3 ความสมพนธระหวางนาหนกและปรมาตรของดน

4 พลาสตกซตและโครงสรางของดน

5 การจาแนกประเภทของดน ครงท 1

6 ความซมนาของมวลดน

7 การไหลของนาในมวลดน

8 แรงเคนในสนาม ครงท 2

9 ปดสอบกลางภาค

10 การยบตวของดน

11 การยบตวของดน

12 กาลงเฉอนของดน

13 กาลงเฉอนของดน ครงท 3

14 คารบนาหนกของชนดน

15 คารบนาหนกของชนดน

16 แรงดนดนดานขาง ณ ภาวะสมดล เชงรกและเชงรบ ครงท 4

17 การบดอดดน

18 ปดสอบปลายภาค

6. กจกรรมทเนนผเรยนเปนสาคญ การทาแบบฝกหดทงแบบเดยว และแบบกลม

ผเรยนจะตองเรยนกระบวนวชา 251372 ซงเปนภาคปฏบตของวชานดวย

7. สดสวนการใหคะแนน คะแนนเกบระหวางเรยน 10 %

คะแนนสอบระหวางภาค 40 %

คะแนนสอบปลายภาค 50 %

8. หนงสอ/วารสาร ประกอบการเรยนการสอน Das, B.M. (1998), Principle of Geotechnical Engineering, 7th edition, CENGAGE Learning, USA

Page 4: Basic Soil Mechanics: Volume I mid material.pdf · Be used as Construction Materials ... “Soil Mechanics is the application of laws of mechanics and hydraulics to engineering problems

9. หนงสอ/วารสาร อานประกอบ อนรทธ ธงไชย (2548), วศวกรรมปฐพเบองตน, เอกสารคาสอนกระบวนวชากลศาสตรดน,

ภาควชาวศวกรรมโยธา, คณะวศวกรรมศาสตร, มหาวทยาลยเชยงใหม

มณเฑยร กงศศเทยม (2531), กลศาสตรของดนดานวศวกรรม, สมาคมศษยเกาวศวกรรม

ชลประทานในพระบรมราชปถมภ, พมพครงท 2

ส เชษ ฐ ล ขต เลอสรวง (2557 ), ปฐพกลศาสตร :ห ลกการ พ นฐาน (SOIL MECHANICS:

FUNDAMENTALS) ปรบปรงครงท 2, สานกพมพจฬาลงกรณ

Bowles, J.E. (1996), Foundation Analysis and Designs, 5th edition, McGraw-Hill

V.N.S. Murthy, “Geotechnical Engineering: Principles and Practices of Soil Mechanics and

Foundation Engineering” CRC Press, 2002

Lambe, T.W. and Whitman, R.V. (1979), Soil Mechanics, SI version, John Wiley & Sons,

Singapore

Craig, R.F., Soil Mechanics , 6th Edition , E & Fw. Spon London, 1997

10. เกณฑการวดผลและประเมนผล (/) องเกณฑ

(/) องกลม

ลงชอ ................................................. ผสอน

( ดร.สรยะ ทองมณ )

ลงชอ ................................................. ประธานหลกสตรฯ

( )

ลงชอ ................................................. หวหนาภาคฯ

( )

Page 5: Basic Soil Mechanics: Volume I mid material.pdf · Be used as Construction Materials ... “Soil Mechanics is the application of laws of mechanics and hydraulics to engineering problems

กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 1

CE 371 Soil Mechanics

Suriyah Thongmunee, Ph.D.

Introduction to Soil Mechanics

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กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 2

Referenced textbook

Textbook: Braja M. Das"Principles of Geotechnical Engineering”

5th Edition

Introduction to Soil Mechanics

4

Lecture Outline:

1. Introduction

2. Role of soil

3. Soil mechanics

4. Geotechnical engineering

5. History of Geotechnical Engineering

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กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 3

Soil ??ในทางวศวกรรม ??

Soil (ดน) คอ การรวมตวกนของแรหนขนาดเลกและวสดทถกยอยสลายตามธรรมชาต (solid particles) กบของเหลวและอากาศซงอยระหวางชองวางของแรหนหรอวสดเหลานน

Why civil engineers must study?

เนองจากดนถกใชเปนวสดในการกอสรางในหลายงานทางดานวศวกรรม ยกตวอยางเชน งานฐานราก งานเจาะ งานขด งานเขอน มาตงแตสมยอดตจนถงปจจบน และตอไปในอนาคต

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กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 4

Role of Soil in Civil Work?

• Be used as Foundation

• Be used as Construction Materials

Be used as Foundation

ฐานแผ เขมตอก

เขมเจาะ

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ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 5

Be used as Construction Materials

ชนทางถนนคนดนอางเกบนา

ถมทบานจดสรร

Structural Damage Caused by Soil

• Failure caused by overload on soil

• Large settlement caused by soil compressibility

• Crack caused by swelling and shrinkage

การพองตว/หดตว

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กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 6

What is soil mechanics?

“Soil Mechanics is the application of laws of mechanics and hydraulics to engineering problems dealing with sediments and other unconsolidated accumulations of solid particles produced by the mechanical and chemical disintegration of rocks regardless of whether or not they contain an admixture of organic constituent”…………… Terzaghi (1948)

What is Geotechnical engineering?

สาขาหนงของวศวกรรมโยธาทศกษาเกยวกบวสดธรรมชาตทถกพบใกลกบผวโลก รวมถงการประยกตใชหลกการพนฐานของกลศาสตรของดนและหน เพอการออกแบบฐานราก(foundation) โครงสรางกนดน(retaining structure) และโครงสรางดน (earth structure)

Page 11: Basic Soil Mechanics: Volume I mid material.pdf · Be used as Construction Materials ... “Soil Mechanics is the application of laws of mechanics and hydraulics to engineering problems

กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 7

Difference between Geotech. and Structural Engineering

Material(properties)

Force(stress)

Displacement(strain)

What Geotechnical Engineering do?

• To investigate existing subsurface conditions and materials• To determine their physical/mechanical and chemical properties• To assess risks posed by site conditions• To design earthworks and structure foundations• To monitor site conditions.

Page 12: Basic Soil Mechanics: Volume I mid material.pdf · Be used as Construction Materials ... “Soil Mechanics is the application of laws of mechanics and hydraulics to engineering problems

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ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 8

What Geotechnical Engineering do?It includes:

• Soil Mechanics (Soil Properties and Behavior).• Rock Mechanics (Rock Stability and Tunneling).• Foundation Engineering (Shallow & Deep Foundations).• Soil Dynamics (Dynamic Properties of Soils, Earthquake Engineering).• Earthworks Engineering (Embankments, Slops Stability, Dams).• Earth Retaining Structures• Pavement Engineering (Flexible & Rigid Pavements).• Ground Improvement (Soil Reinforcement, Geosynthetics).• Coastal and Ocean Engineering

History of Geotechnical Engineering

16

Page 13: Basic Soil Mechanics: Volume I mid material.pdf · Be used as Construction Materials ... “Soil Mechanics is the application of laws of mechanics and hydraulics to engineering problems

กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 9

History of Geotechnical Engineering Prior to the 18th century

1800’s

1700’s

1900’s

Pre-classical period(1700-1776)

Classical soil mechanicsphase I (1776-1856)

Classical soil mechanicsphase II (1856-1910)

Modern soil mechanics (1910-1927)

• Prior to the 18th century No Geotechnical Engineering prior to the 18th century (Skempton, 1985) Based on past experiences without any scientific character

Colosseum

Tower of Pisa1173 A.D.

Huang Ho river

1800’s1700’s 1900’s

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กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 10

• Pre-classical period (1700-1776)

Studies focused on natural slope, retaining and unit weights of various types of soils and the semi-empirical earth pressure theories.

Henri Gautier (1660-1737) studied the natural slopes of soils when tipped in a heap for formulation the design procedures of retaining walls.

Bernard Forest de Belidor (1671–1761) proposed a theory for lateral earth pressure on retaining walls specified a soil classification system.

Francois Gadroy (1705–1759) observed the existence of slip planes in the soil at failure.

1800’s1700’s 1900’s

• Classical soil mechanics - phase I (1776-1856)

Using principles of calculus to solve mainly the problem of retaining wall and earth pressure

»Charles Coulumb (1736-1806) used the laws of friction and cohesion for solid bodies to propose Coulomb’s theory.

»Jean Victor Poncelet (1788-1867) the first to use the symbol φ for soil friction angle

»Alexandre Collin (1808-1890) deep slips in clay slopes, cutting and embankments

»Wiliam John Macquorn Rankine (1820-1872) : Rankine’s theory

1800’s1700’s 1900’s

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กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 11

• Classical soil mechanics - phase II (1856-1910)This period focused on the experimental results from laboratory

tests on sand.

»Henri Philibert Gaspard Darcy (1803-1858) defined the term coefficient of permeability of soil.

»Joseph Valentin Boussinesq (1842-1929) developed the theory of stress distribution under loaded bearing areas.

»Osborne Reynolds (1842-1912) demonstrated the phenomenon of dilatancy in sand.

21

1800’s1700’s 1900’s

• Modern soil mechanics (1910-1927)This period was marked by a series of important studies and publications related to the

mechanic behavior of clays:

» Albert Atterberg (1846–1916), a Swedish chemist and soil scientist, explained the consistency of cohesive soils by defining liquid, plastic, and shrinkage limits.

» Arthur Bell (1874–1956), from England, developed relationships for lateral pressure and resistance in clay as well as bearing capacity of shallow foundations in clay.

»Wolmar Fellenius (1876–1957), from Sweden, developed the stability analysis of saturated clay slopes.

» Karl Terzaghi (1883–1963), from Austria, developed the theory of consolidation for clays as we know today.

1800’s1700’s 1900’s

Page 16: Basic Soil Mechanics: Volume I mid material.pdf · Be used as Construction Materials ... “Soil Mechanics is the application of laws of mechanics and hydraulics to engineering problems

กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 12

Father of modern soil mechanics??The development of modern Geotechnical

Engineering as a branch of Civil Engineering is absolutely impacted by one single professional individual – Karl Terzaghi

He started modern soil mechanics with his theories of consolidation, lateral earth pressures, bearing capacity, and stability.

(1883 - 1963)

Most of the foundation failures that occurred were not longer “acts of God”……

Geotechnical EngineeringHall of Frame

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กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 13

Charles Augustin CoulombThe Grandfather of Soil Mechanics

(1736 - 1806)

William John Macquorn Rankine

(1820 - 1872)

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Arthur Casagrande

(1902 - 1981)

Ralph Brazelton Peck

(1912 - 2008)

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Others• Henry Philibert Gaspxard Darcy• Christian Otto Mohr• Valentin Joseph Boussinesq• Alec Westley Skempton• Nilmar Janbu• Laurits Bjerrum• Etc.

“Education is the best provision for the journey to old age.”

Aristotle

อางอง

• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition

• รปภาพจาก google images

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กลศาสตรของดน : Soil Mechanics 7/23/2015

ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 1

CE 371 Soil Mechanics

Suriyah Thongmunee, Ph.D.

Origin of Soil and Grain Size

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ดร.สรยะ ทองมณ : Suriyah THONGMUNEE 2

Origin of Soil

What is soil come from?Soil are generally formed by

weathering of rocks.

The physical properties of a soil are dictated primarily by the minerals that constitute the soil particles and the rock form which it is derived.

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Origin of Soil

So, to better understand the physical properties of soil, we must be familiar with the basic types of rock, the rock-forming minerals, and weathering

process.

What is a rock?

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What is Rock ??In geology, “rock” is naturally occurring solid aggregate of minerals and/or mineraloids. There are three major groups of rock:

5

• Igneous rocks are formed by solidification of molten magma ejected from deep within earth’s mantle.

• Sedimentary rocks are formed by the deposits of gravel, sand, silt and clay with cementing agents under overburden pressure.

• Metamorphic rocks are the rocks formed by the process of changing the composition and texture by hear and pressure

Rock cycle The final products due to weathering are soils

Where is Soil ??

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Weathering ?In geology, “weathering” is the process of breaking down the rock by mechanical and chemical process into smaller pieces

Mechanical Weathering Process• Frost action/ice wedging• Abrasion• Exfoliation

Weathering ?In geology, “weathering” is the process of breaking down the rock by mechanical and chemical process into smaller pieces

4FeSiO3 + O2 + H2O → 4FeO(OH) + 4SiO2(pyroxene)+(oxygen)+(water) → (limonite)+ (silica)

CaCO3 + H2CO3 → Ca2+ + 2HCO3-(calcite)+(carbonic acid) → (calcium ion) +(bicarbonate ion)

Chemical Weathering Process• Oxidize• Hydration• Carbonation

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Transportation of Weathering Products• The products of weathering may stay in the same place or may

be moved to other places by ice, water, wind, and gravity.

• Soils that remain at their places of formation are called residual soils and soils that moved and deposited to other places are called transported soils.

• An important characteristic of residual soils is the gradation of particle size. Fine grained soil is found at the surface, and the grain size increases with depth. At greater depths, angular rock fragments may also be found.

Transportation of Weathering ProductsThe transported soils may be classified into several groups, depending on their mode of transportation and deposition:

• 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

• Marine soils—formed by deposition in the seas

• Aeolian soils—transported and deposited by wind

• Colluvial soils—formed by movement of soil from its original place by gravity

(e.g. landslides)

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Grain Size

Based on the weathering process, the sizes of particles that make up soil vary over wide range.

Soils are generally called Gravel, Sand, silt or clay, depending on the predominant size of particles within the soil.

Types of soil by Grain Size

• To describe soils by their particle size, several organizations have developed particle-size classifications.

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• Soils can be divided into cohesive and non-cohesive soils.

– Cohesive soil contains clay minerals and posses plasticity.

– Non-cohesive means the soil has no shear strength if no confinement. Sand is non-cohesive and non- plastic.

• Soils can be divided into undisturbed soil and disturbed soil.

• Furthermore, gravel and sand can be roughly classified as coarsetexture soils, while silt and clay can be classified as fine texture soils.

Types of soil by other factor

• Gravels are pieces of rocks with occasional particles of quartz, feldspar,

and other minerals.

• Sand particles are made of mostly quartz and feldspar.

• Silts are the microscopic soil fractions that consist of very fine quartz

grains and some flake-shaped particles that are fragments of micaceousminerals.

• Clays are mostly flake-shaped microscopic and submicroscopic particles of

mica, clay minerals, and other minerals.

Main minerals

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Clay minerals= 10-10 m (angstrom)

Clay mineralsDiffuse double layer

Absorbedwater Absorbed water

High viscosity water Free flow

Free flow

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Specific Gravity (GS)• Specific Gravity is as the ratio of the unit weight of a given material to

the unit weight of water.

Apparent Specific Gravity and Absolute Specific Gravity

• The specific gravity of soil solids is often required for various calculations in soil mechanics.

w

s

s

s .

ws V

WG

GS of common minerals

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Mechanical analysis of soil• Mechanical analysis is the determination of the size range of particles

present in a soil, expressed as a percentage of the total dry weight. Two methods generally are used to find the particle-size distribution of soil:

1. Sieve analysis: for particle sizes larger than 0.075 mm in diameter, and

2. Hydrometer analysis: for particle sizes smaller than 0.075 mm in diameter.

Coarse grain

Gravel – SandSieve Analysis

Fine grain

Silt – ClayHydrometer Analysis

0.075 mm

Sieve Analysis: coarse grained soils

Sieve analysis is used to determine the distribution of the larger grain sizes. The soil is passed through a series of sieves with the mesh size reducing progressively, and the proportions by weight of the soil retained on each sieve are measured. There are a range of sieve sizes that can be used, and the finest is usually a 75 m sieve. Sieving can be performed either wet or dry. Because of the tendency for fine particles to clump together, wet sieving is often required with fine-grained soils.

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Sieve Analysis Procedure

• Determine the mass of soil retained on each sieve and the pan at last (i.e., M1, M2, M3, .... Mn, and Mp).

• The sum of soil mass retained on each sieve plus the mass in the pan should be equal to

the total mass (ΣM = M1 + M2 + M3 +...+Mn + Mp).

• Determine the cumulative mass of soil retained above each sieve, for the i th sieve we have M1 + M2 + M3+....+Mi .

• the mass of soil passing the i th sieve is ΣM – (M1 + M2 + M3 +... +Mi )

• the percent of soil passing the i th sieve (percent finer) is:

100)...( 21

M

MMMMF i

Results from Sieve AnalysisThe results are plotted on semi-logarithmic graph paper with percent finer as the

ordinate (arithmetic scale) and sieve opening size as the abscissa (logarithmic scale). This plot is referred to as the particle-size distribution curve.

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Hydrometer Analysis : fine grained soils

Hydrometer Analysis is used to determine the distribution of fine grainedsoils. The method is based on the principle of sedimentation of soil grains in thewater. When a soil specimen is dispersed in water, the particles settle at differentvelocities, depending on their shape, size and weight, and viscosity of the water.

For simplicity, it is assumed that all the soil particles are spheres and that thevelocity of soil particles can be expressed by Stokes’ law, according to which:

s w18

D2

t

L

GD

wsws

)1(

1818

t

LKD

Hydrometer Analysis : fine grained soils

With the use of the SI units

• Viscosity, η, uses “gsec/cm2”

• Density of water, ρw, uses “g/cm3” (= 1 g/cm3)

• Length, L, uses “cm”

• Time, t, uses “minute”

• Diameter, D, in “mm”, we can get diameter of soil particles:

t

L

GD

wsws

)1(

1818

(min)t

)cm(LK

t

L

)G(

ηD

s•=•

1

30=

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Hydrometer Analysis : fine grained soils

Percent finer by weight finer than a given diameter can be also calculated by knowing the amount of soil in suspension, L, and t.

Hydrometer Analysis : fine grained soils

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Particle-size distribution curve

What we can calculate ?

What we can calculate ?

After construction of particle-size distribution curve, four parameters can be calculated:

• Effective size (D10): This parameter is the diameter in the particle-size distribution curve corresponding to 10% finer.

• Uniformity coefficient (Cu ) defined as:

• Coefficient of gradation (Cz) defined as:

• Sorting coefficient (S0): This parameter is an another parameter for measuring uniformity, used mostly by geologists,. It can be defined as:

Cu D60

D10

S0 D75

D25

Cz D2

30

D60 D10X

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What we can calculate ?

After construction of particle-size distribution curve, four parameters can be calculated:

• Effective size (D10): This parameter is the diameter in the particle-size distribution curve corresponding to 10% finer.

• Uniformity coefficient (Cu ) defined as:

• Coefficient of gradation (Cz) defined as:

• Sorting coefficient (S0): This parameter is an another parameter for measuring uniformity, used mostly by geologists,. It can be defined as:

Cu D60

D10

S0 D75

D25

Cz D2

30

D60 D10X

Particle-size distribution curve

D60 D30D10

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What the particle-size distribution shows us?

Curve I represents a type of soil in which most of the soil grains are the same size. This is called poorly graded soil.

What the particle-size distribution shows us?

Curve II represents a soil in which the particle sizes are distributed over a wide range, termed well graded. Cu= 4 for gravels and 6 for sands

Cz = 1 to 3 (for gravels and sands)

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What the particle-size distribution shows us?

Curve III represents a soil in which the soil might have a combination of two or more uniformly graded fractions. This type of soil is termed gap graded.

Particle ShapeThe particle shape can generally be divided into 3 major categories:

• Bulky particles are formed by mechanical weathering of rock and mineral. The angularity, A, and sphericity, S, of bulky particles are used to describe their shapes.

A = Average radius of corners and edges/ Radius of the maximum inscribed shape

De= equivalent diameter of the particle

V = volume of particle

Lp= length of particle

• Flaky particles have very low sphericity – usually 0.01 or less. These particles are predominantly clay minerals

• Needle-shaped particles are much less common than the other two particle types

S DeLp

De 6V

3

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Particle Shape

• Bulky

• Flaky

• Needle-shaped

Example 1

36

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Example 2

37

Example 3

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Quiz

“Education is the best provision for the journey to old age.”

Aristotle

อางอง• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition• รปภาพจาก google images

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CE 371 Soil Mechanics

Suriyah Thongmunee, Ph.D.

Weight-Volume Relationships

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Weight-Volume Relationships

Lecture Outline:

1. Introduction

2. Unit weight

3. Weight ratio

4. Volume ratio

5. Weight-Volume Relationships

6. Relative density

3

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Introduction

4

Air

Water

Soil (Solid)

Gs

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Introduction

Ws = weight of soil solid

Ww = weight of water

Wa = weight of air ≈ 0

WT = total weight

5

Vs = volume of soil solid

Vv = volume of voids

Vw = volume of water

Va = volume of air

V = total volume

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Unit weight

6

Total Unit weight ( ), defined as the ratio of the weight of soil sample to the whole volume:

Dry Unit weight (d), defined as the ratio of the weight of dry soil to the whole volume:

Saturated Unit weight (sat), defined as the ratio of the weight of saturated soil to the whole volume:

Solid Unit weight (s), defined as the ratio of the weight of soil solid to its volume:

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Unit weight Density

7

Total density ( ), defined as the ratio of the mass of soil sample to the whole volume:

Dry density (d), defined as the ratio of the mass of dry soil to the whole volume:

Saturated density (sat), defined as the ratio of the mass of saturated soil to the whole volume:

Solid density (s), defined as the ratio of the mass of soil solid to its volume:

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Weight ratio

8

Moisture content (w), also referred to as water content, is defined as the ratio of the weight of water to the weight of solid in a given volume of soil:

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Relationship between , d and w

9

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Volumetric ratios

11

Void ratio (e), defined as the ratio of the volume of voids to the volume of solid:

Porosity (n), defined as the ratio of the volume of voids to the total volume:

Degree of saturation (S), defined as the ratio of the volume of water to the volume of voids:

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Relationship between n and e

12

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Weight-Volume relationships

What do we need to make Weight-Volume relationships?

14

Gs

is the ratio of the weight of a volume of the substance (Solids) to the weight of an equal volume of the reference substance (Water)

Definition ??

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Weight-Volume relationships

From Gs = Ws / wVs

So, Ws = wVs Gs

or

From Gs = ms / wVs

So, ms = wVs Gs

15

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Relationship among , e, w and Gs

16

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Example 1

The mass of moist soil sample having a volume of 0.0057 m3 is 10.5 kg. The water content and the specific gravity were determined to be 13% and 2.68. Determineda. Total densityb. Dry densityc. Void ratiod. Porositye. Degree of saturation

18

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Example 2

The mass of moist soil sample having a volume of 0.33 ft3 is 39.93 lb. The oven-dried weight of soil and the specific gravity were determined to be 34.54 lb and 2.68. Determineda. Moisture contentb. Total unit weightc. Dry unit weightd. Void ratioe. Porosityf. Degree of saturation

19

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Soil properties for typical soil

20

คณสมบต หนวย ทราย

หลวม-แนน ดนเหนยว

แขงเชยงใหม

ดนเหนยวออน

กรงเทพฯ

ดนลกรงบดอดแนนใน

โครงสรางทาง อตราสวนชองวาง, e - 0.25 - 1.25 0.59 - 0.66 1.70 – 2.70 0.33 อตราสวนความชน, s (%) 0 –1 00 100 100 90 ความถวงจาเพาะ, Gs - 2.6 - 2.65 2.69 - 2.81 2.62 – 2.70 2.65 ความชน, w % 5 - 30 18.0 - 23.0 65 – 100 11 หนวยนาหนกรวม, t kN/m3 15 – 21 18.0 – 21.0 14.0 – 16.5 22.5

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Relative Density

For cohesionless soil (sand), the shear strength of sand normally depends on the packing state of sand.

21

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Relative Density

The looseness and denseness of granular soil can be defined numerically by relative density as shown follows:

22

ASTM D4253 and D4254

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Typical In-place soil have relative density of 30%- 80%

Qualitative description of sand

23

0

15

50

70

85

Very loose

loose

Medium

Very dense

Dense

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Typical granular soil

24

Type of soilVoid ratio Unit weight (kN/m3)

emax emin Sr min max

Well grade sand 0.70 0.35 100% 0%

19.5 15

22 19

Uniform sand 0.85 0.50 100% 0%

19 14

20.5 17.5

Silty sand with gravel 0.80 0.25 100% 0%

18 14

22.5 17

Sand with mica mineral and silt 1.25 0.75 100% 0%

17 12

19.5 15

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Example 1

25

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Example 2

26

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Quiz

27

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“Education is the best provision for the journey to old age.”

Aristotle

อางอง

• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition

• รปภาพจาก google images

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CE 371 Soil Mechanics

Suriyah Thongmunee, Ph.D.

Plasticity and Soil mass structure

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Plasticity and Soil mass structure

Lecture Outline:

1. Consistency of soil

2. Atterberg limits

3. Discussion on limits and indices

4. Liquidity and consistency indices

5. Activity

6. Plasticity chart

7. Soil mass structure

3

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Consistency of clay soil

Consistency is a term to indicate the firmness of cohesive soil such as very soft, soft, stiff, very stiff and hard.

4

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Consistency of clay soil

Water content changes, the physical properties of clay changes.

5

Water content

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Consistency of clay soil

Consistency of clay soil can be expressed in term of:

• Atterberg limits

• Unconfined compressive strength of soil

6

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Atterberg limits

7

Atterberg, a Swedish scientist and agricultural scientist, considered the consistency of soils in 1911, and proposed a series of tests for defining the properties of cohesive soils. Strength decreases as water content increases.

March 19, 1846 – April 4, 1916

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Atterberg limits

8

At a very low moisture content, soil behaves more like a solid. When the moisture content is very high, the soil and water may flow like a liquid. Hence, the behavior of soil can be divided into 4 basic states: solid, semi-solid, plastic, and liquid.

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Atterberg limitsLiquid Limit (LL) is defined as the moisture content at which soil begins to behave as a liquid material and begins to flow.Plastic Limit (PL) is defined as the moisture content at which soil begins to behave as a plastic material.

Shrinkage Limit (SL) is defined as the moisture content at which no further volume change occurs with further reduction in moisture content.

Plastic Index (PI) is the difference of moisture content between the liquid limit and the plastic limit

9

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Atterberg limits

10

Transition stage from liquid to solid states

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Liquid Limit• 150 g air dry soil passing #40 sieve

• At least four tests

• Range of blow varies from 5 – 40 blows

• Water content at 25 blows is LL.

11

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Liquid Limit

12

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Plastic Limit

13

• 20 g air dry soil passing #40 sieve

• At least three tests

• Rolling the soil sample until reach 3.2 mm in diameter

• Water content when the soil crumbles is PL.• Taking at least 6 g of the crumbled soil to determine

moisture content

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Shrinkage Limit

14

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Degree of shrinkage

15

100×=i

fir V

VVS

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Different states and Consistency of soil

16

States Limits Consistency Volume Change

Liquid Very Soft

………………… LL Liquid Limit …………….. Soft

Plastic Stiff Decrease in Volume

………………… PL Plastic Limit……………… Very Stiff

Semi-solid

…………………. SL Shrinkage Limit……….. Extremely Stiff

Solid Hard Constant

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Liquid Limit

17

Plasticity Level WL

Low Plasticity < 35 %

Intermediate Plasticity 35 – 50 %

High Plasticity 50 – 70 %

Very High Plasticity 70 – 90 %

Extremely High Plasticity > 90%

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Plastic Index

18

PI Plasticity level Hardness Testing method

0 – 3 Non-plastic ตามาก แตกเปนกอนเลกลงไดงาย

3 – 15 Slightly plastic คอนขางตา ใชนวบใหแตกไดงาย

15 – 30 Medium plastic ปานกลาง ใชนวบใหแตกยาก

> 31 Highly plastic สง ไมสามารถใชนวบใหแตกได

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Degree of shrinkage

19

Quality of soil Sr

Good < 5 %

Medium good 5 – 10 %

Poor 10 – 15 %

Very poor > 15%

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Discussion on limits and indices

• At the same LL, strength of soil having high PI (low PL) is higher than that having low PI (high PL) .

20

LL

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Discussion on limits and indices

• At the same PL, soil with a lower flow index, IF, has cohesive strength larger than soil with a higher flow index

21

PL

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Liquidity index

22

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Consistency index

23

100×=PLLL

wLLCI

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

LI and CI according to Consistency of soil

24

Consistency LI CI

Semisolid or solid state < 0 > 1

Very stiff state 0 1

Very soft state 1 0

Liquid state > 1 < 0

100×=PLLL

wLLCI

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Activity

25

Activity, A, is used to indicate the swelling potential of clay soil.

Inactive(non-swelling type)

Active(swelling type) Normal soil

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Plasticity chart

26

Low Medium High

30% 50%

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Soil mass structure

Soil mass structure, or soil structure, is defined as the geometric arrangement of soil particles. The structure depends on many factors as follows:

• Shape

• Size

• Mineralogical composition of soil particles

• Nature

• Composition of soil-water

27

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Structure in Cohesionless Soil

The structures generally encountered in cohesionless soils can be divided into two major categories: single grained and honeycombed.

28

single grained structure Honeycombed structure

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Structure in Cohesionless Soil

• Mainly depending on size, shape and relative position• Larger grain size• Wide range of void ratio

29

single grained structure Honeycombed structure

• Fine sand and silt• Large void ratio• Easily break down of the structure• Larger settlement

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Structure in Cohesive SoilMost of structure in cohesive soil is flocculated structure. Thus, clay with flocculated structure is low density and high void ratio. Clay deposits forming in salt water are highly flocculent comparing with that forming in fresh water.

30

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Structure in Cohesive Soil

31

In some cases, the sediment formed by settling of the individual particles has a dispersed structure, and all particles are oriented more and less parallel to one another. These cases are called “Dispersed structure” (face to face contact)

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Structure in Cohesive Soil

32

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Structure in composite Soil

33

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Example 1

34

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Example 2

35

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Quiz

36

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“Education is the best provision for the journey to old age.”

Aristotle

อางอง

• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition

• V.N.S. Murthy : Geotechnical Engineering

• เอกสารการสอน อ.อนรทธ ธงไชย

• รปภาพจาก google images

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CE 371 Soil Mechanics

Suriyah Thongmunee, Ph.D.

Soil Classification

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Soil Classification

2

Lecture Outline:

1. Classification Systems

2. ASSHTO system

3. Unified Soil Classification System

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Classification systems

Why soil should be classified ?

Soils in nature rarely exist separately as gravel, sand, silt, clay or organic matter, but are usually found as mixtures with varying proportions of these components.

Classifying soils into groups with similar behavior, in terms of simple indices, can provide geotechnical engineers a general guidance about engineering properties of the soils through the accumulated experience.

3

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Classification systems

How many indices are usually used in classification systems of soil?

Particle distribution and Atterberg limits

4

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Classification systems

How many systems are commonly used by geotechnical Engineering ?

AASHTO System : American Association of State Highway and Transportation Officials.

USCS : Unified Soil Classification System.

5

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

AASHTO system

3 Keys1. Grain Size:

Gravel : Fraction passing 75mm sieve and retained on #10 (2mm) US sieve

Sand : Fraction passing #10 sieve and retained #200 sieve

Silt and Clay : Fraction passing #200 sieve

6

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AASHTO system

3 Keys2. Plasticity:

PI > 10 : Clay

PI < 10 : Silt

7

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

AASHTO system

3 Keys3. Cobbles and boulders:

If cobbles and boulders were encountered, they are excluded from

the portion of the soil sample from which classification is made. However, the percentage of such material is recorded.

8

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AASHTO system

soil is classified into seven major groups: A-1 through A-7. Soils classified under groups A-1, A-2, and A-3 are granular materials of which 35% or less of the particles pass through the No. 200 sieve. Soils of which more than 35% pass through the No. 200 sieve are classified under groups A-4, A-5, A-6, and A-7. These soils are silt-clay materials.

9

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AASHTO system

10

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AASHTO system

11

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

AASHTO system

Group Index (GI): To evaluate the quality of a soil as a highway subgrade material, one must incorporate a number called the Group Index (GI) with the groups and subgroups of the soil. This index is written in parentheses after the group or subgroup designation. The group index is given by the equation:

where:

F200: % passing #200 sieves expressed as whole number

LL: liquid limit of soil

PI: Plasticity Index of soil

12

High Value = Low quality

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Classification procedure

For granular

13

Calculate “GI”

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Classification procedure

For silt-clay

14

Calculate “GI”

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AASHTO system

15

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

AASHTO system

16

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AASHTO system

17

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Example 1

18

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Example 2

19

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

USCS

The original form of USCS, Unified Soil Classification, System was

purposed by Casagrande in 1942. The USCS was revised in 1952. At the present, the USCS method is widely used by engineer.

It divides soil into 3 majors divisions: coarse-grained soils, fine-grained soil and highly organic soils.

20

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USCS

In the laboratory, grain-size distribution curve and atterberg limits

are used to classify. the peaty soil are identified by color, odor, spongy feel and fibrous texture.

The points must be kept in mind are

– Only soil sample passing a 75 mm sieve is classified

– Coarse fraction = percent retained above # 200 sieve

– Gravel fraction = percent retained above # 4 sieve

21

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

USCS

22

First letter(Type of soil)

Latter(Soil properties)

G = Gravel W = Well Grade

S = Sand P = Poorly Grade

M = Silt M = Silty

C = Clay C = Clayey

O = Organic Soil L = Low Liquid Limit

P = Peat H = High Liquid Limit

Example GW = Well grade gravel SC = Clayey sand CH = High liquid limit clay OL = Organic silt, low plasticity

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USCS

• Checking passing #200 sieve

if passing #200 sieve < 5%, no need to do Atterberg limits

if passing #200 sieve > 5%, need to do Atterberg limits and use plasticity chart

• Checking passing #200 sieve again

if passing #200 sieve < 50%, Coarse-grained soil

if passing #200 sieve ≥ 50%, need to do Atterberg limits

23

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Plasticity chart

24

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Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Example 3

26

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Example 4

27

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Quiz 1

28

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Quiz 2

29

“Education is the best provision for the journey to old age.”

Aristotle

อางอง

• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition

• V.N.S. Murthy : Geotechnical Engineering

• เอกสารการสอน อ.อนรทธ ธงไชย

• รปภาพจาก google images

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CE 371 Soil Mechanics

Suriyah Thongmunee, Ph.D.

Permeability

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Permeability

Lecture Outline:1. Soil Permeability2. Bernoulli’s Equation3. Darcy’s Law4. Hydraulic Conductivity5. Permeability Test in the Field

2

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Soil Permeability

What is Permeability?Soils are assemblages of solid particles with interconnected voids where water can

flow from a point of high energy to a point of low energy.

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

3

Easy to flow – High permeability Hard to flow – Low permeability

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Soil Permeability

Importance of permeability• Permeability influences on the rate of settlement of a saturated soil under load.• The stability of slopes and retaining structures can be greatly affected by the

permeability of the soils involved.• The design of earth dams is very much based on the permeability of the soils used.• Filters made of soils are designed based upon their permeability.

4

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Soil Permeability

The study of permeability is important for: • Estimating the quantity of underground seepage.• Investigating problems involving pumping seepage of water for underground

constructions.• Analyzing the stability of earth dams and earth retaining walls subjected to seepage

forces.

5

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Bernoulli’s EquationAccording to Bernoulli’s equation, total head at a point in water under motion can be

calculated by below equation. The total head is sum of pressure head, velocity head and elevation head.

However, when water flows through soils, the seepage velocity is often very small. Therefore, the total head at any point can be adequately represented by :

6

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Bernoulli’s EquationThe heads of water at points A and B as the water flows from A to B are given as follows (with respect to a datum):

Total head at point A :

Total head at point B :

Head loss between A and B :

Head loss in dimensionless form :

7

i : hydraulic gradient

Aw

AA Z

γ

uh +=

Bw

BB Z

γ

uh +=

BA hhh =Δ

L

hi

Δ=

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Bernoulli’s EquationThe variation of the velocity, v, with hydraulic gradient, i, can be divided into 3 zone as shown in figure below.

8

In most soil, the flow of water through the void spaces can be considered as laminar flow.

So, ∝

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Darcy’s LawIn 1856, Darcy proposed a simple equation for the discharge velocity of

water, v, through saturated soils, which may be expressed as

where,• v : discharge velocity, which is the quantity of water flowing in unit time through a unit

gross cross-sectional area of soil (l/t)• k : coefficient of permeability or hydraulic conductivity (l/t)• i: hydraulic gradient

9

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Darcy’s LawFlow rate , q, can be determined by multiple the equation proposed by

Darcy with gross cross-section area as shown below;

where,• q: flow rate (l3/s)• A: gross cross-sectional area (l3)

Moreover, quantity of water, Q, can be calculated by multiple the flow rate by

time duration, t;

10

kiAvAq ==

kiAtvAtqtQ ===

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Darcy’s LawSeepage velocity , vs, is the actual velocity of water through the void spaces.

11

Derivation of seepage velocity

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Hydraulic Conductivity

Hydraulic conductivity, k, also known as coefficient of permeability,

is the property of soil that describes the ease with which the water can move through pore spaces. It is usually expressed in cm/sec or m/sec in SI units.

The hydraulic conductivity of soils depends on several factors:• Fluid viscosity• Pore size distribution• Grain size distribution• Grain shape• Porosity• Void ratio• Degree of soil saturation

12

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Hydraulic Conductivity

13

Typical values of hydraulic conductivity of saturated soil

** For unsaturated soil, the hydraulic conductivity is lower than saturated soil and increases rapidly with increase of degree of saturation.

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Determination of “k”

Hydraulic conductivity, k, can be determined by using indirect methods, laboratory methods and field methods.

1. Indirect methods

2. Laboratory methods

3. Field methods

14

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Indirect Methods

Empirical formulas using index properties of soil

15

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Empirical formula

granular soils

Ck = 8 – 12 สาหรบทรายทมขนาดคละสมาเสมอ= 5 – 8 ทรายทมขนาดคละด

(mm/sec) D C k 210k

Hazen’s approximation (1930s)

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Empirical formula

The Kozeny-Carman equation

granular soilsIn 2003, Carrier published a paper in Journal of Geotechnical and Environmental Engineering, entitled: “Good-bye Hazen; Hello, Kozeny-Carman”

where Cs : shape factorSs : specific surface areaT : tortuosity of flow channels

γw : unit weight of waterη : viscositye : void ratio

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Empirical formulagranular soilsCarrier (2003)

where SF : shape factorfi : fraction of particles between a pair of two sieve sizes li (larger) and si (smaller), in

percentDli : Aperture diameter of larger sieveDsi : Aperture diameter of smaller sievee : void ratio

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Empirical formula

Chapuis (2004) proposed an empirical relationship for the hydraulic conductivity in terms of D10 and the void ratio, e, in the following form

where D10 : diameter at 10% passinge : void ratio

granular soils

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Samarasinghe, Huang and Drnevich (1982) suggested that the hydraulic

conductivity of normally consolidated clays can be given by:

where C and n are constants to be determined experimentally

Empirical formulagranular soils

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Laboratory Methods

constant head and falling head

21

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Laboratory test : Constant head

22

Aht

Q.L k

AtL

hk

kiAt Q

=

Δ=

=

∆h

L

QDATUM

The constant head test is used primarily for coarse-grained soils.

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Laboratory test : Falling head

23

h1

h2

2

1

hh ln

AtaL k

dtdh a - A

Lhk q

=

==

Integration

DATUM

The falling head test is used primarily for fined-grained soils.

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Example 1

24

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Example 1

25

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Example 2

26

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Example 2

27

Field Methods

pumping field test and borehole permeability test

28

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Permeability Test in the Field

Pumping test:The average hydraulic conductivity of a soil deposit in the direction of flow

can be determined by performing pumping tests from wells.

29

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Permeability Test in the Field

Pumping test:During the test, water is pumped out at a constant rate from a test well

that has a perforated casing. Several observation wells at various radial distances are made around the test well.

Steady state: the equilibrium state when the drawdown keeps no change at one particular location to the well, no further drawdown develops as pumping continues.

30

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Equation for k an unconfined aquifer

31

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Equation for k an confined aquifer

32

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Permeability Test in the Field

Porous borehole:

33

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Permeability Test in the Field

Cased hole and soil flush with bottom :

34

In this test, auger holes are made in the field that extend below the water table level. Casing is provided down to the bottom of the hole. The casing is filled with water. The water level in the casing is observed by measuring the depth of the water surface below the top of casing.

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Equivalent hydraulic conductivity in stratified soil

35Horizontal Direction Vertical Direction

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Equivalent hydraulic conductivity in stratified soil

36

Horizontal Direction

Condition

q = q1 + q2 + q3 + … + qn

ieq= i1 = i2 = i3 = in

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Equivalent hydraulic conductivity in stratified soil

37

Vertical Direction

Condition

v = v1 = v2 = v3 = vn

h = h1 + h2 + h3 + … + hn

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Example 3

38

Layer 1

Layer 2

Layer 3

Estimate the ratio of equivalent permeability, kH(eq)/kV(eq)

Layer No. Thickness (m) Hydraulic conductivity

1 3 k1= 10-4 cm/sec

2 4 k2= 3.2×10-2 cm/sec

3 5 k3= 4.1×10-5 cm/sec

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Example 3

39

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Example 4

40

Determine the rate of water supply in cm3/hr

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Example 4

41

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th E.

Quiz 1

42

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Quiz 2

43

“Education is the best provision for the journey to old age.”

Aristotle

อางอง

• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition

• V.N.S. Murthy : Geotechnical Engineering

• เอกสารการสอน อ.อนรทธ ธงไชย

• รปภาพจาก google images

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CE 371 Soil Mechanics

Suriyah Thongmunee, Ph.D.

Seepage

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Seepage

2

Lecture Outline:1. Laplace’s equation for continuity

2. Flow net construction

3. Determination of quantity of seepage

4. Determination of uplift pressure

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Laplace’s equation

In reality, the flow of water through soil is not in one direction only, nor is it uniform over the entire area perpendicular to the flow.

3

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Laplace’s equation

In such cases, the ground water flow is generally calculated by the use of graphs referred to as flow nets. The concept of the flow net is based on Laplace’s equation of continuity, which governs the steady flow condition for a given point in the soil mass.

4

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Laplace’s equation

5

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Laplace’s equation

In considered element soil block, the rates of inflow and outflow(q=va) can be determined as follows

Rate of Inflow

Rate of outflow

6

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Laplace’s equation

In steady flow and no volume change of soil mass, the rate of inflow should equal the rate of outflow (qin = qout). Thus,

7

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Laplace’s equation

With Darcy’s law, the discharge velocity can be expressed as

8

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Laplace’s equation

If soil is isotropic with respect to the hydraulic conductivity, the equation can be simplified as

9

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Laplace’s equation

The equation shown below is Laplace’s equation which can solve the seepage problems with more than one direction. However, the solution of equation is complicated.

10

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Flow net

The Laplace’s equation in an isotropic soil represents two orthogonal families of curves—that is, the flow lines and the equipotential lines.

11

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Flow net

Flow line is a line along which a water particle will travel from upstream to the downstream side in the permeable soil.

12

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Flow net

Equipotential line is a line along which the total head at all points is equal.

13

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Flow net

A combination of flow lines and Equipotential lines is called flow net.

14

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Flow net

To complete flow net, one must draw flow lines and equipotential lines in such a way that;

15

1. The equipotential lines intersect the flow lines at right angles.

2. The flow line should be parallel to adjacent flow line.

3. The equipotential line. should be parallel to adjacent equipotential line.

4. The flow elements formed are approximate squares.

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Flow net

Condition 1: The upstream and downstream surfaces of the permeable layer (lines ab and de) are equipotential lines.

16

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Flow net

Condition 2: Because ab and de are equipotential lines, all the flow lines intersect ab and de at right angles.

17

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Flow net

Condition 3: The boundary of the impervious layer—that is, line fg—is a flow line, and so is the surface of the impervious sheet pile, line acd.

18

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Flow net

Condition 4: The equipotential lines intersect acd and fg at right angles.

19

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Some cases of flow net

20

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Some cases of flow net

21

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Quantity of seepage

22

Darcy’s law : q = kia

Consider one flow channel

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Quantity of seepage

23

For n flow channel, we can calculate the quantity of seepage by using below equation;

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Uplift pressure

Uplift pressures are pressures, due to the water that seeps below structures, that exerts pressures on the bases of the structures.

24

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Example 1

25

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Example 2

26

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Example 3

27

Calculate the seepage loss in m3/day and uplift pressure at point 1,4 and 7Assume; 9 m of dam length

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Quiz 1

28

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Quiz 1

29

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Quiz 2

30

Calculate the seepage loss in m3/day and uplift pressure at the base of weir

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“Education is the best provision for the journey to old age.”

Aristotle

อางอง• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition• V.N.S. Murthy : Geotechnical Engineering• เอกสารการสอน อ.อนรทธ ธงไชย• รปภาพจาก google images

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Soil Mechanics

Suriyah Thongmunee, Ph.D.

In situ stresses

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

In situ stresses

2

Lecture Outline:

1. Effective Stress and Pore Water Pressure

2. Stresses in Soil without Seepage

3. Stresses in Soil with Upward Seepage

4. Stresses in Soil with Downward Seepage

5. Seepage Force

6. Heaving in Soil

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Effective stress and Pore Water Pressure

When a saturated soil mass is subjected the pressures

or stress (σ) as a result of an external load and the volumetric weight of the material itself, the pressures will be carried by two pressures.

1. pore water pressure (u)

2. effective pressure (σ’)

3

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Effective stress and Pore Water Pressure

Pore water pressure (u) or neutral stress is pressure due to the water in continuous void spaces. This pressure will act with equal intensity in all directions. The pore water pressure can be induced in the pores of a soil mass by a head of water over it.

Effective pressure (σ’) or intergranular is pressure transmitted through soil particle to soil particle at the contact points.

4

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Effective stress and Pore Water Pressure

In summary, the total stress (σ) is the sum of the effective stress (σ’) and the pore water pressure (u)(neutral stress).

The effective stress in a soil mass controls its volume change and strength. Increasing the effective stress (equivalent to reduce the pore pressure if the total stress is constant)

induces soil to move into a denser state of packing.

5

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Stresses in Soil without Seepage

Figure shows a column of saturated soil mass with no seepage of water in any direction. The total stress at the elevation of point A can be obtained from the saturated unit weight of the soil and the unit weight of water above it. Thus,

6

Where equals the submerged unit weight of soil.

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Stresses in Soil without SeepagePlots of the variations of the total stress, pore water pressure, and effective stress,

respectively, with depth for a submerged layer of soil placed in a tank with no seepage:

7

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Example 1

8

Dry Zone (S = 0%)

Thickness of 3 m, γd = 16.5 kN/m3

Capillary Zone (S = 0 %)

Thickness of 1 m, , γ = 17.6 kN/m3

Saturated Zone (S = 100%)

Thickness of 3 m, , γsat = 18.9 kN/m3

G.W.

Calculate and plot the variation

of σ, σ’ and u with depth

Impermeable layer

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σ with depth

σ, kN/m2

z, m

Example 1

Dry Zone (S = 0%)

Thickness of 3 m, γd = 16.5 kN/m3

Capillary Zone (S = 0 %)

Thickness of 1 m, , γ = 17.6 kN/m3

Saturated Zone (S = 100%)

Thickness of 3 m, , γsat = 18.9 kN/m3

G.W.

Impermeable layer

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

σ with depth

σ, kN/m2

z, m

49.5

Example 1

Dry Zone (S = 0%)

Thickness of 3 m, γd = 16.5 kN/m3

Capillary Zone (S = 0 %)

Thickness of 1 m, , γ = 17.6 kN/m3

Saturated Zone (S = 100%)

Thickness of 3 m, , γsat = 18.9 kN/m3

G.W.

Impermeable layer

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σ with depth

σ, kN/m2

z, m

67.1

49.5

Example 1

Dry Zone (S = 0%)

Thickness of 3 m, γd = 16.5 kN/m3

Capillary Zone (S = 0 %)

Thickness of 1 m, , γ = 17.6 kN/m3

Saturated Zone (S = 100%)

Thickness of 3 m, , γsat = 18.9 kN/m3

G.W.

Impermeable layer

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

σ with depth

σ, kN/m2

z, m

67.1

49.5

123.8

Example 1

Dry Zone (S = 0%)

Thickness of 3 m, γd = 16.5 kN/m3

Capillary Zone (S = 0 %)

Thickness of 1 m, , γ = 17.6 kN/m3

Saturated Zone (S = 100%)

Thickness of 3 m, , γsat = 18.9 kN/m3

G.W.

Impermeable layer

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u with depth

u, kN/m2

z, m

Example 1

Dry Zone (S = 0%)

Thickness of 3 m, γd = 16.5 kN/m3

Capillary Zone (S = 0 %)

Thickness of 1 m, , γ = 17.6 kN/m3

Saturated Zone (S = 100%)

Thickness of 3 m, , γsat = 18.9 kN/m3

G.W.

Impermeable layer

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

u with depth

u, kN/m2

0

29.43

Example 1

Dry Zone (S = 0%)

Thickness of 3 m, γd = 16.5 kN/m3

Capillary Zone (S = 0 %)

Thickness of 1 m, , γ = 17.6 kN/m3

Saturated Zone (S = 100%)

Thickness of 3 m, , γsat = 18.9 kN/m3

G.W.

Impermeable layer

z, m

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u, kN/m2

z, m

σ, kN/m2

z, m

σ', kN/m2

z, m

0

29.4

67.1

49.5

123.8

Example 1

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

u, kN/m2

z, m

σ, kN/m2

z, m

σ', kN/m2

z, m

0

29.4

67.1

49.5

123.8

Example 1

49.5

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u, kN/m2

z, m

σ, kN/m2

z, m

σ', kN/m2

z, m

0

29.4

67.1

49.5

123.8

Example 1

67.1

49.5

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

u, kN/m2

z, m

σ, kN/m2

z, m

σ', kN/m2

z, m

0

29.4

67.1

49.5

123.8

Example 1

67.1

49.5

94.4

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Example 2

19

Layer 1

Layer 2

Layer 3

G.W.

Impermeable layer

Layer No.

Thickness (m)

Soil parameter

1 4 e = 0.40,Gs = 2.62

2 5 e = 0.60,Gs = 2.68

3 3 e = 0.81,Gs = 2.73

Calculate and plot the variation

of σ, σ’ and u with depth

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Example 3

20

Calculate and plot the variation

of σ, σ’ and u with depth

Layer No.

Thickness (m)

Soil parameter

1 4 e = 0.40,Gs = 2.62

2 5 e = 0.60,Gs = 2.68

3 3 e = 0.81,Gs = 2.73

Because hard rain, ground water level shifted to ground surface

Layer 1

Layer 2

Layer 3

Impermeable layer

G.W.

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Stresses in Soil with Upward Seepage

If water is seeping, the effective stress at any point in a soil mass will differ from that in the static case. It will increase or decrease, depending on the direction of seepage.

22

Upward Seepage Downward Seepage

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Stresses in Soil with Upward Seepage

23

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Stresses in Soil with Upward Seepage

24

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Stresses in Soil with Upward Seepage

25

Plots of the variations of the total stress, pore water pressure, and effective stress, respectively, with depth for a submerged layer of soil placed in a tank with upward seepage:

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Stresses in Soil with Upward Seepage

26

The effective stress at a point located at a depth z measured from the surface of a soil layer

is reduced by an amount izw because of upward seepage of water.

If the rate of seepage and thereby the hydraulic gradient gradually are increased until σ’c= 0, the

hydraulic conductivity at zero effective stress is termed as critical hydraulic conductivity.

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Stresses in Soil with Upward Seepage

This situation generally is referred to as boiling, or a quick condition.

27

For most soils, the value of icrvaries from 0.9 to 1.1, with an average of 1

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Example 1

28

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Example 1

29

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Stresses in Soil with Downward Seepage

30

Plots of the variations of the total stress, pore water pressure, and effective stress, respectively, with depth for a submerged layer of soil placed in a tank with downward seepage:

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Seepage Force

The previous topics showed that the effect of seepage is to increase or

decrease the effective stress at a point in a layer of soil. Often, expressing the seepage force per unit volume of soil is convenient.

In Figure, it was shown that, with no seepage, the effective stress at a

depth z measured from the surface of the soil layer in the tank is equal to z’. Thus, the effective force (P’1) or static effective force on an area A is

31

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Seepage Force

In case of upward seepage, the effective stress at a depth z measured

from the surface of the soil layer in the tank is equal to z’-ziw. Thus, the effective force (P’2) on an area A is

32

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Seepage Force

Hence, the decrease in the total force because of seepage is

The volume of the soil contributing to the effective force equals zA, so the seepage force per unit volume of soil is

33

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Seepage Force

Similarly, for downward seepage, it can be shown that the seepage

force in the downward direction per unit volume of soil is w, but direction is opposite.

34

So, it can be concluded that the direction of seepage force is the same as direction of flow in case of isotropic soils

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Example 2

35

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Example 2

36

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Heaving in Soil due to flow

Seepage force per unit volume of soil can be used for checking possible failure of sheet pile structures where underground seepage may cause heaving (piping) of soil on the downstream side.

37

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Heaving in Soil due to flow

Terzaghi (1922) concluded that heaving generally occurs within a distance of D/2 from the sheet piles (when D equals depth of embedment of sheet piles into the permeable layer).

38

FS : factor of safetyW’ : submerged weight of soil in the heave zone per unit length of sheet pile U :uplifting force caused by seepage on the same volume of soil

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Heaving in Soil due to flow

39

D : Depth of embedment of sheet pileD/2 : heave zone , distance from sheet pile

’ : submerged unit weightw : water unit weightiav : average hydraulic gradient at the bottom of the block of soil (hav/D) This term refer to average head loss

between bottom and top of the considered soil mass

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Example 3

40

Check heaving condition of the sheet pile as shown in the figure

H = 10Nf = 5Nd = 11

h = 10/11

2519= m/kN . γsat

Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 5th E.

Example 3

41

6 78

9

10

11

D/2

D

W

Seepage Force

( )

9322=819×33680

699===

33680=10

3683=

3683=552+732+643+554

=××=Δ=Δ

=×=Δ=Δ

=×=Δ=Δ

=×=Δ=Δ

...

.

γi

U

'WFS

..

i

m .4

.... h

m 2.55 11

10 2.8 h)2.8( h

m 2.73 11

10 3 h)3( h

m 3.64 11

10 4 h)4( h

m. 4.55 11

10 5 h)5( h

wav

av

av

4

3

2

1

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How to protect heaving (piping)

42

“Education is the best provision for the journey to old age.”

Aristotle

อางอง

• Braja M. Das :"Principles of Geotechnical Engineering 5th Edition

• V.N.S. Murthy : Geotechnical Engineering

• เอกสารการสอน อ.อนรทธ ธงไชย

• รปภาพจาก google images