project class
osama
T.6_WaterinSoil.pdf
Conducted by: Offered to :
Riyadh, Saudi Arabia, 2019-2020
Dr. Mohamed Ezzat Assistant professor of Civil Eng.
Department of Engineering Management
College of Engineering.
Prince Sultan University
Undergraduate Students –Senior Level.
Engineering Management Department.
College of Engineering.
Prince Sultan University
2nd semester- Year 2019-2020.
EM 306 : Soil Mechanics and Foundations
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TENTATIVE WEEKLY COURSE SCHEDULE WEEK UNIT/ TOPIC
Number of Contact
hours
1 Introduction 5
2 Soil Formation 5
3 Engineering Properties of Soil 5
4 Soil Exploration 5
5 Soil Compaction 5
6 Water in Soil 5
7 Stress in soils 5
8-9 Consolidation of soil 5
10-11 Shear Strength of soil 10
12-13 Bearing Capacity and Shallow Foundations 10
14 Deep Foundations 5
15 Lateral Earth Pressure & Retaining Structures As Scheduled
❑ Water in Soil Topic No. 6
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INTRODUCTION
❑ Water in Soil Topic No. 6
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TYPES OF WATER IN SOIL
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❑ Structural water
❑ Absorbed (Free) water
❑ Water in Soil Topic No. 6
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SOIL PERMEABILITY Permeability is defined as:
q = k . i . A Darcy’s Law
❑ Water in Soil Topic No. 6
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FLOW OF WATER IN SOILS
❑ Hydraulic gradient, i = h/L
❑ Water in Soil Topic No. 6
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FLOW OF WATER IN SOILS
q = k 𝒉
𝑳 A eqn 5.1
q = kiA eqn 5.2
❑ Water in Soil Topic No. 6
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SEEPAGE VELOCITY (𝒗)
𝒗 actual = 𝒗
𝒏 eqn 5.4
𝒗 = ki eqn 5.3
Where, n = porosity
𝒗 = q\A
𝒒 = A * 𝒗
𝒒 = K I A = A * 𝒗
❑ Water in Soil Topic No. 6
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vactual
vactual = 𝒗(𝟏+𝒆)
𝒏 eqn 5.5
𝐞
(𝟏+𝐞)
SEEPAGE VELOCITY (𝒗) AND VOID RATIO ❑ Water in Soil Topic No. 6
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= 0.160 m
❑ Water in Soil Topic No. 6
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Example 1
❑ Using Flow rate equation (q):
Solution:
q = k I A
i = 𝒉
𝑳
= 𝟎.𝟏𝟔𝟎 𝒎
𝟐.𝟎𝟎 𝒎 = 0.0800
q = (6.90 * 10-4 m/s) (0.0800) (0.250 m2)
= 1.38 * 10-5 m3/s Ans.
❑ Water in Soil Topic No. 6
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❑ Water in Soil Topic No. 6
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Example 2
Given data : V = 1508 cm3, t= 16.0 min
𝒗 = 1.874 cm/min = 0.0312 cm/s
𝒗 actual = 𝒗(𝟏+𝒆)
𝒏 𝒗actual =
𝟎.𝟎𝟑𝟏𝟐 𝒄𝒎/𝒔 (𝟏+𝟎.𝟔𝟖)
𝟎.𝟔𝟖 = 0.0771 cm/s
𝒒 = 𝑽
𝒕 Where, q = flow rate
V= Volume (m3)
t = Time (sec)
𝒒 = 𝑽
𝒕 =
𝟏𝟓𝟎𝟖
𝟏𝟔 ∗𝟔𝟎
Step (1) : Find the Flow rate :
= 94.25 cm3/min = 1.57 cm3/sec
Step (2) : Find the average Velocity (v):
𝒒 = 𝑽
𝒕 = A* 𝒗
1.57 cm3/sec = 50.3 * 𝒗
Given data : A = 50.3 cm2
Step (3) : Find the Actual Velocity (𝐯 actual): Given data : e = 0.68
❑ Water in Soil Topic No. 6
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Solution:
DETERMINATION OF COEFFICIENT OF PERMEABILITY K
❑ Water in Soil Topic No. 6
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FLOW OF WATER IN SOILS
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▪
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▪ Falling-head Test ▪ Constant-head Test
❑ Water in Soil Topic No. 6
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Constant-head method
❑ Water in Soil Topic No. 6
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Solving for k gives
q = k . i . A
𝐐
𝐭 = k .
Δ𝒉
𝐋 . A
K = 𝐐 .𝐋
𝐭 .𝚫𝐡 .𝐀 eqn 5.8
Constant-head method
❑ Water in Soil Topic No. 6
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❑ Water in Soil Topic No. 6
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Example 3
❑ Constant head test formula:
A = 𝝅 (𝟏𝟎.𝟏𝟔 𝒄𝒎)𝟐
𝟒 = 81.07 cm2
k = 𝟐𝟓𝟎 𝒄𝒎𝟑 (𝟏𝟏.𝟒𝟑 𝒄𝒎)
𝟖𝟏.𝟎𝟕 𝒄𝒎𝟐 𝟔𝟓.𝟎 𝒔 (𝟓.𝟓 𝒄𝒎) = 0.0986 cm/s
K = 𝐐 .𝐋
𝐭 .𝚫𝐡 .𝐀 eqn 5.8
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❑ Water in Soil Topic No. 6
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Solution:
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Falling-head method ❑
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❑ Water in Soil Topic No. 6
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➢ −
➢
➢
q = −𝐝𝐡
𝐝𝐭 . a
K = 2.3 𝐚 .𝐋
𝐀 .𝐭 log10
𝐡𝟏
𝐡𝟐
Falling-head method
❑ Water in Soil Topic No. 6
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❑ Water in Soil Topic No. 6
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Example 4
k = 𝟐.𝟑 𝒂𝑳
𝑨𝒕 log
𝒉𝟏
𝒉𝟐
A = 𝝅 (𝟏𝟎.𝟏𝟔 𝒄𝒎)𝟐
𝟒 = 81.07 cm2
Using Falling head test formula :
k = (𝟐.𝟑) 𝟏.𝟖𝟑 𝒄𝒎𝟐 (𝟏𝟓.𝟖𝟎 𝒄𝒎)
𝟖𝟏.𝟎𝟕 𝒄𝒎𝟐 𝟐𝟎∗𝟔𝟎𝒔 log
𝟏𝟐𝟎.𝟎 𝒄𝒎
𝟏𝟏𝟎.𝟎 𝒄𝒎 = 2.58 * 10-5 cm/s
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❑ Water in Soil Topic No. 6
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Solution:
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COEFFICIENT OF PERMEABILITY (K)
k = C1 D10 2 eqn 5.26
k = 0.35 D10 2 eqn 5.27
❑ Water in Soil Topic No. 6
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Degree of permeability Value of k (m/s)
High Over 10-3
Medium 10-3 to 10-5
Low 10-5 to 10-7
Very low 10-7 to 10-9
Practically impermeable Less than 10-9
COEFFICIENT OF PERMEABILITY (K)
❑ Water in Soil Topic No. 6
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PERMEABILITY OF STRATIFIED SOIL
❑ Water in Soil Topic No. 6
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PERMEABILITY OF STRATIFIED SOIL ▪
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❑ Water in Soil Topic No. 6
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Horizontal flow of water in stratified soil.kHZ = 𝒌𝟏 𝑯𝟏+𝒌𝟐 𝑯𝟐+𝒌𝟑 𝑯𝟑+ ….
𝑯𝟏+𝑯𝟐+𝑯𝟑 =
𝜮𝒌 .𝑯
𝜮 𝑯
q = q1 + q2 + q3 + ……
= k1 . i . H1 + k2 . i . H2 + k3 . i . H3 + ……
q = kHZ . i . H
AVERAGE PERMEABILITY IN THE HORIZONTAL DIRECTION:
❑ Water in Soil Topic No. 6
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Vertical flow of water in stratified soil.
Δh = Δh1 + Δh2 + Δh3 + ……
𝐪 .𝚺𝐇
𝐊𝐕𝐋 . 𝐀 =
𝐪 .𝐇𝟏
𝐤𝟏 . 𝐀 +
𝐪 .𝐇𝟐
𝐤𝟐 . 𝐀 +
𝐪 .𝐇𝟑
𝐤𝟑 . 𝐀 + ……
kVL = 𝚺𝐇
𝐇𝟏
𝐤𝟏 +
𝐇𝟐
𝐤𝟐 +
𝐇𝟑
𝐤𝟑 + ……
= 𝚺𝐇
σ 𝐇
𝐤
AVERAGE PERMEABILITY IN THE VERTICAL DIRECTION:
❑ Water in Soil Topic No. 6
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❑ Water in Soil Topic No. 6
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Example 5
Kx = 𝟏.𝟐 ∗ 𝟏𝟎−𝟑 𝒄𝒎/𝒔 𝟏.𝟓 𝒎 + 𝟐.𝟖 ∗ 𝟏𝟎−𝟒 𝒄𝒎/𝒔 𝟐.𝟎 𝒎 + 𝟓.𝟓 ∗ 𝟏𝟎−𝟓 𝒄𝒎/𝒔 (𝟐.𝟓 𝒎)
𝟏.𝟓+𝟐.𝟎+𝟐.𝟓 𝒎
Kx = 4.16 * 10 -4 cm/s
Step (2) : average permeability in the Ver tical direction:
kHZ = 𝒌𝟏 𝑯𝟏+𝒌𝟐 𝑯𝟐+𝒌𝟑 𝑯𝟑+ ….
𝑯𝟏+𝑯𝟐+𝑯𝟑 =
𝜮𝒌 .𝑯
𝜮 𝑯
Ky = 𝟏.𝟓+𝟐.𝟎+𝟐.𝟓 𝒎
𝟏.𝟓 𝒎 / 𝟐.𝟒 ∗ 𝟏𝟎−𝟒 𝒄𝒎/𝒔 + 𝟐.𝟎 𝒎 / 𝟑.𝟏 ∗ 𝟏𝟎−𝟓 𝒄𝒎/𝒔 + 𝟐.𝟓 𝒎 / 𝟒.𝟕 ∗ 𝟏𝟎−𝟓𝒄𝒎/𝒔
Ky = 9.96 * 10 -6 cm/s
Step (1) : average permeability in the
horizontal direction:
kVL = 𝚺𝐇
𝐇𝟏
𝐤𝟏 +
𝐇𝟐
𝐤𝟐 +
𝐇𝟑
𝐤𝟑 + ……
= 𝚺𝐇
σ 𝐇
𝐤
❑ Water in Soil Topic No. 6
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Solution:
❑
❑
CAPILLARY RISE IN SOILS
h = 𝟒𝑻
𝒅γ eqn 5-39
h = 𝟎.𝟎𝟑𝟎
𝒅 eqn 5-40
❑ Water in Soil Topic No. 6
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Solution
h = 𝟒𝑻
𝒅γ
h = 𝟒(𝟎.𝟎𝟕𝟑 𝑵/𝒎)
[ 𝟎.𝟓 𝒎𝒎 𝟏 𝒎 /𝟏𝟎𝟎𝟎 𝒎𝒎 (𝟗𝟕𝟗𝟎 𝑵/𝒎𝟑)
h = 0.060 m
❑ the height of capillary rise in the tube.
❑ Water in Soil Topic No. 6
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Example 6
❑
CAPILLARY RISE IN SOILS
h = 𝑪
𝒆𝑫𝟏𝟎 eqn 5-41
❑ Water in Soil Topic No. 6
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FLOW NETS & SEEPAGE
❑ Water in Soil Topic No. 6
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FLOW NETS & SEEPAGE
q = 𝒌∗𝒉∗𝑵𝒇
𝑵𝒅
❑ Water in Soil Topic No. 6
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❑ Water in Soil Topic No. 6
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Example 7
q = 𝒌𝒉𝑵𝒇
𝑵𝒅
K = (4.80 * 10-3 cm/s)
= 4.80 * 10-5 m/s
Nf = 5 Nd = 9
h = 4m – 1m = 3 m
q = (𝟒.𝟖𝟎 ∗ 𝟏𝟎−𝟓𝒎/𝒔)(𝟑 𝒎)(𝟓)
𝟗 = 0.0008 m3/s per m of sheet-pile
1
2 3
45 6
7 8
9 1 2 3
5
❑ Water in Soil Topic No. 6
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Solution:
❑ Steps of Construction of flow netFLOW NETS & SEEPAGE
1. Draw the section and boundaries 2. Draw the Flow Lines “Should be parallel ”
3. Draw equipotential lines “ should be perpendicular on flow lines and almost equal” 4. Count Nf and Nd
❑ Water in Soil Topic No. 6
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o
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o 𝐤𝐲 ∗ 𝐤𝐱
o
FLOW NETS & SEEPAGE
q = 𝒌𝒚𝒌𝒙 𝒉𝑵𝒇
𝑵𝒅 eqn 5-47
❑ Water in Soil Topic No. 6
❑ Page :39 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
RECIPE FOR SUCCESS,
As long as you live, Just Keep
L e a r n i n g …
References
❑ Page :40 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
• Das, B., M. (2014), “ Principles of geotechnical Engineering ” Eighth Edition, CENGAGE Learning, ISBN-
13: 978-1-133-10867-2.
• Knappett, J. A. and Craig R. F. (2012), “ Craig’s Soil Mechanics” Eighth Edition, Spon Press, ISBN: 978-0-
415-56125-9.
• Orabi, A. (2015),Soil Mechanics, “Introduction &Properties of Soil lecture notes”, International university of
sciences and technology.
• Terzaghi, K. (1936) "Stress Distribution in Dry and in Saturated Sand Above a Yielding Trap-Door",
Proceedings. First International Conference on Soil Mechanics and Foundation Engineering, Cambridge,
Massachusetts, pp. 307-311.
• Terzaghi, K. (1943). “Theoretical Soil Mechanics”. John Wiley & Sons, New York.
• Meyerhof, G. G. (1951). “The Bearing Capacity of Foundations”. In Géotechnique, vol. 2, no. 4, pp. 301-
332.
• Radwan, A. (2013), “fundamentals of Soil Mechanics”. Helwan university, Faculty of engineering. Civil
Department library.
• El-Kadi, F. (2002), “Principles of Soil Mechanics”. Ain shams university, Faculty of engineering. Civil
Department library.
• Vesic, A. S. (1975). Principle of pile foundation design. Soil Mechanics Series No 38, School of
Engineering, Duke University.
• Joseph E. Bowels, (1999), "Physical and Geotechnical Properties of Soils"; McGraw Hill Book.
❑ Water in Soil Topic No. 6
• Presentation of the theories and principles of soil mechanics
and foundation engineering.
• Explore the equipment's and instrumentations used for in-situ
and laboratory testing of soil.
• Outline the design standards of different types of foundation,
soil support systems according to several international codes.
• Provide sufficient field case studies and solved examples so that
students can make judgements as to the credibility of results
that they may obtain, or review, in the future.
Soil is a complex multiphase material. A sound understanding of
the fundamental principles and design applications of soil
mechanics is needed to predict the behavior and performance of
soil as a construction material or as a supporting medium for
engineering structures.
The main objective of this course is to provide the undergraduate
student with an insight into the theories and principles of soil
mechanics and foundation engineering, and its applications in
practical problems. The methodology that will be followed in this
course to achieve its objectives are directed towards the following
points:
Preface
Course Instructor
Dr. Mohamed Ezzat Al-Atroush
Dr. Mohamed Ezzat obtained his Ph.D. Degree from Ain Shams University, Egypt, in 2018. He joined the Prince Sultan University (PSU) in 2019 as an Assistant Professor in the area of Civil Engineering. He has broad experience in the field of geotechnical engineering on academic and professional works. Also, he has published many international journal and conference publications in the area of Geotechnical Engineering. He is a member of several international technical committees, such as the American society of civil engineers (ASCE).
On the other hand, Dr. Ezzat participated in many consultancy projects involving site investigations, problematic soils, evaluation of stability of slopes and escarpments, construction and permanent dewatering, design of deep excavation support, traditional and specialized lab testing, field monitoring, geophysical studies, foundation and bridge design, effect of tunnel induced ground deformations on adjacent surface and underground structures. His main research interests are in the Large Diameter bored piles, tunneling and deep excavations, Dynamic soil-structure interaction, Ground Improvement, and Energy and Sustainable Geotechnics.
