EngineeringManagement Department
Riyadh, Saudi Arabia, 2019-2020
CLASS PROJECT
EM 306: Soil Mechanics and Foundations
2nd semester (192) – Year 2019-2020.
1 | P a g e Soil Mechanics and Foundations
Prince Sultan University
College of engineering
Engineering Management Department.
Academic Year 2019-2020 – Semester (192)
EM 306: Soil Mechanics and Foundations
Class Project 2019/2020
Soil Testing Technical Report
Introduction
The geotechnical report is a tool used to communicate the site conditions and design and
construction recommendations to the site design, building design, and construction personnel.
Site investigations for building design projects have the purpose of providing specific information
on subsurface soil, rock, and water conditions. Interpretation of the site investigation information,
by a geotechnical engineer, results in design and construction recommendations that should be
presented in a project geotechnical report.
Geotechnical investigation reports present site-specific data and have three major components:
1. Background Information: The initial sections of the report summarize the geotechnical
engineer’s understanding of the facility for which the report is being prepared and the purposes
of the geotechnical investigation. This section would include information on loads, deformations
and additional performance requirements. This section also presents a general description of site
conditions, geology and geologic features, drainage, ground cover and accessibility, and any
peculiarities of the site that may affect the design.
2. Work Scope: The second part of the investigation report documents the scope of the
investigation program and the specific procedures used to perform this work. These sections will
identify the types of investigation methods used; the number, location and depths of borings,
exploration pits and in situ tests; the types and frequency of samples obtained; the dates when
the field investigation was performed; the subcontractors used to perform the work; the types and
number of laboratory tests performed; the testing standards used; and any variations from
conventional procedures.
3. Data Presentation: This portion of the report, generally contained in appendices, presents
the data obtained from the field investigation and laboratory testing program, and typically
includes final logs of all borings, exploration pits, and piezometer or well installations, water level
readings, data plots from each in-situ test hole, summary tables and individual data sheets for all
laboratory tests performed, rock core photographs, geologic mapping data sheets and summary
plots, subsurface profiles developed from the field and laboratory test data, as well as statistical
summaries. Often, the investigation report will also include copies of existing information such as
boring logs or laboratory test data from previous investigations at the project site. The intent of a
geotechnical investigation report should be to document the investigation performed and present
the data obtained. The report should include a summary of the subsurface and lab data.
4. Conclusion and recommendations: this is the most important part conclusions should be
drawn based on the results of both in-situ and laboratory soil testing. These conclusions are used
to come out with the foundation design and construction recommendations.
2 | P a g e Soil Mechanics and Foundations
Prince Sultan University
College of engineering
Engineering Management Department.
Academic Year 2019-2020 – Semester (192)
EM 306: Soil Mechanics and Foundations
The Project Statement:
The residential villa shown in the Figure below, will be constructed in Jeddah city (KSA), in front of
the sea beach. This building consists of only two floors. According to the architectural design, the
ground floor will be used as a reception area, and the second floor will be used as bedrooms and living
space.
Figure (1): Architectural Design fo the residential villa
The structural system is shown in drawings below, and the columns and beams distribution on both
first and second slabs of the two floors are presented. As shown in Figures (2 and 3), The structural
system mainly depends on the Solid Slab system, and the load will be transferred from slabs to beams
and then to columns.
Based on the initial calculations performed by the structural consultant, it was found that the load
transferred from each of the columns A,D,F, and K (Corner columns) is 1000 kN, and for the interior
columns B,C,G, and H each of them transfer 2500 kN to the foundations, as shown in Figure 4.
3 | P a g e Soil Mechanics and Foundations
Prince Sultan University
College of engineering
Engineering Management Department.
Academic Year 2019-2020 – Semester (192)
EM 306: Soil Mechanics and Foundations
Figure (2): Structural system of The First Floor
Figure (3): Structural system of The Second Floor.
4 | P a g e Soil Mechanics and Foundations
Prince Sultan University
College of engineering
Engineering Management Department.
Academic Year 2019-2020 – Semester (192)
EM 306: Soil Mechanics and Foundations
Figure (4): Cross Section.
Geotechnical consultant have performed site investigation works at the construction site, and the
following section presents the results of field and laboratory tests conducted using both disturbance
and un-disturbance soil samples
1. The Soil profile shown in Figure (5) organizes the results obtained for soil samples taken
along the borehole depth. The profile shows the results of the in-situ standard penetration test
SPT and atterberg limit test for soil samples at each 1m depth.
2. Sieve analysis test results for three disturbance samples obtained from boreholes (Layer 1
and 2) at depths of 1.0, 3.0, and 5.0 m below the ground surface are shown in Figure (6). Also,
results of the Sieve analysis test for another three disturbance samples obtained from
boreholes at depths 7.0 and 8.50 m below ground surface (Layer3 and 4) are shown in Figure
(7).
3. Permeability test has performed for a soil sample taken from layer (1), the sample length and
diameter were 15.80 cm and 10.16 cm, respectively. Also cross-section area of the test
equipment tube was 1.83 cm2. After 5.0 days, the water head was changed from 120 cm to
110 cm.
4. Consolidation Test has also been performed for un-distrubance sample taken from layer (1),
and mv was obtained with 4.2 * 10-4 m2/kN. Besides, the unconfined test that shown the
unconfined strength of this soil sample equals 150 kN\m2.
5 | P a g e Soil Mechanics and Foundations
Prince Sultan University
College of engineering
Engineering Management Department.
Academic Year 2019-2020 – Semester (192)
EM 306: Soil Mechanics and Foundations
Figure (5): Borehole Profile with atterberg limit and SPT test results
Figure (6): Sieve analysis test results of three samples extracted at depths 1.0, 3.0, and 5.0 m
below ground surface.
6 | P a g e Soil Mechanics and Foundations
Prince Sultan University
College of engineering
Engineering Management Department.
Academic Year 2019-2020 – Semester (192)
EM 306: Soil Mechanics and Foundations
Figure (7): Sieve analysis test results of three samples extracted at depths 1.0, 3.0, and 5.0 m
below ground surface.
Based upon, if you are the geotechnical consultant, it is required to:
1. Use the given data of field and laboratory tests to classify and describe the four soil
layers and complete the soil profile (Layer 1,2,3 and 4).
2. Correct N-SPT values and calculate bearing capacity for the first and second soil layers
only.
3. Choose the suitable foundation level.
4. Based on the given columns loads, Choose the suitable foundation system to support
this column load. Consider the factor of safety of 3.0.
5. Calculate the predicted immediate settlement under this footing (1) and (2); if the soil
passion’s ratio is 0.30.
6. Recalculate the settlement after 5 Years.
7. If the allowable settlement is 15 cm, and the allowable differential settlement is 1:300.
Check the safety of this building.
8. Write down a geotechnical report summarizing all your performed works and give your
fundamental recommendations for foundation design and construction.
Deadline: Monday, 20th April 2020
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
Construction Management Program (CMP)
Soil Shear Strength
Topic No. 9
Topic (9)
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Soil Shear Strength Topic No. 9
SHEAR STRENGTH OF SOIL
❑ Soil Shear Strength Topic No. 9
❑ Page :2 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
1. DEFINITION:
When a soil is subjected to vertical and lateral
stresses, deformations in different directions
may occur. The pore water pressure and water
content of the soil may also change. When the
stress exceeds a certain limit, accompanied by a
certain strain, failure of the soil occurs. This
failure is usually characterized by movement of
the affected soil mass by slip along a certain
plane, which is called the shear plane.
❑ Soil Shear Strength Topic No. 9
❑ Page :3 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
2. THE MOHR-COULOMB FAILURE CRITERION
τf = c + σ tan ɸ
Where
τf : Shear strength of the soil
σ: Normal stress acting on the plane of failure
c, ɸ: Shear strength parameters
c: Apparent cohesion
ɸ: Angle of shear resistance (internal friction)
As a function of effective normal stress:
τf = c’ + σ tan ɸ’
c’, ɸ’: Effective shear strength parameters.
Where
❑ Soil Shear Strength Topic No. 9
❑ Page :4 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Soil Shear Strength Topic No. 9
❑ Page :5 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
4. DETERMINATION OF SHEAR STRENGTH PARAMETERS
(a) Direct shear test
❑ Soil Shear Strength Topic No. 9
❑ Page :6 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
4. DETERMINATION OF SHEAR STRENGTH PARAMETERS
(a) Direct shear test
Three types of the test can be carried out:
1. Slow test: Pore water pressure will not developed during test.
2. Consolidated–quick test: Sample is allowed to consolidate under the vertical load,
followed by quick shear.
3. Quick test: Water content of the sample remains unchanged during test.
Disadvantages of shear box:
❑ Shear stresses are unequally distributed over the shear surface.
❑ Area of shear surface changes as test progresses.
❑ Water content of saturated samples of many types of soil may be changed.
❑ Soil Shear Strength Topic No. 9
❑ Page :7 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
For loose sand and gravel, the cohesion (c) is equal to zero.
τ = σ tan ɸd
Angle of repose
❑ Soil Shear Strength Topic No. 9
❑ Page :8 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
1. The soil at a site is formed of sand. The groundwater is 2 m below ground
surface. The angle of internal friction of the sand is 35o, its dry density is 1.
8
t/m3 and specific gravity 2.65. Find the shear resistance of the soil at a depth
of 5 m.
Example 1
❑ Soil Shear Strength Topic No. 9
❑ Page :9 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
γd =
𝑮𝒔
𝟏+𝒆
. γw 1.80 =
2.65
1+𝑒
* 1.00
e = 0.47
2
γsat =
𝑮𝒔+𝒆
𝟏+𝒆
. γw =
2.65+0.472
1+0.472
= 2.12 t/m3
σ = γd . H1 + γsat . H2 = 1.80 * 2.00 + 2.12 * 3.00 = 9.96 t/m2
u = γw . Hw = 1.00 * 3.00 = 3.00 t/m
2
σ’ = σ – u = 9.96 – 3.00 = 6.96 t/m2
τf = c + σ tan f = zero + 6.96 tan 35 = 4.88 t/m
2
Solution:
❑ Soil Shear Strength Topic No. 9
❑ Page :10 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
2. A direct shear box test was carried out on dry coarse sand. The box is 6 x 6
cm. When a normal load of 28.8 kg was applied, the shear load at failure was
17.3 kg. find the angle of internal friction of the sand. Find the magnitude and
direction of the principal stresses.
Example 2
❑ Soil Shear Strength Topic No. 9
❑ Page :11 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
σ =
𝑵𝒐𝒓𝒎𝒂𝒍 𝒍𝒐𝒂𝒅
𝑨𝒓𝒆𝒂
=
28.80
6 ∗6
= 0.80 kg/cm2
τ =
𝑺𝒉𝒆𝒂𝒓 𝒍𝒐𝒂𝒅
𝑨𝒓𝒆𝒂
=
17.30
6 ∗6
= 0.48 kg/cm2
Draw σ – τ Plot point A (0.80 , 0.48)
Plot OA, this is the rupture line ϕ = 31o
Draw AM ┴ OA, M is the center of Mohr circle
σ3 = OB = 0.528 kg/cm
2 & σ1 = OC = 1.648
Solution:
❑ Soil Shear Strength Topic No. 9
❑ Page :12 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
3. Quick shear box tests were carried out on three specimens of partially saturated
clay. Results are as follows:
Find the apparent cohesion and angle of internal friction. Determine the unconfined
compressive strength of a specimen of the same soil.
Example 3
❑ Soil Shear Strength Topic No. 9
❑ Page :13 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Draw AM ┴ rupter line, M is the center of Mohr circle
Draw σ – τ , Draw rupture line
Measure ϕ = 8.60o & cu = 0.8 kg/cm
2
To draw Mohr circle with σ3 = zero
Calculate α = 45 +
ϕ
𝟐
= 45 +
8.60
2
= 49.3o
Draw OA making an angle α to the horizontal
qun = σ1 = 1.88 kg/cm
2
Solution:
❑ Soil Shear Strength Topic No. 9
❑ Page :14 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
4. Quick shear box tests were carried out on three specimens of sandy clay. The cross section of
the shear box was 6 x 6 cm. Results are as follows:
If a specimen of the same soil is tested in triaxial compression with cell pressure of σ3 = 1 kg/cm
2,
find the total axial stress at which failure will be expected to occur.
Example 4
❑ Soil Shear Strength Topic No. 9
❑ Page :15 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
divide results by the area of the shear box (6 * 6 cm)
Plot the results, Measure ϕu = 14
o & cu = 0.44 kg/cm
2
To draw Mohr circle with σ3 = 1.00
From A, Draw AM ┴ rupture line
M is the center of Mohr circle, σ1 = 2.77 kg/cm
2
Calculate α = 45 +
ϕ
𝟐
= 45 +
𝟏𝟒
2
= 52o
Draw BA making an angle α to the horizontal
Solution:
❑ Soil Shear Strength Topic No. 9
❑ Page :16 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
4. DETERMINATION OF SHEAR STRENGTH PARAMETERS
(b) Triaxial compression test
❑ Soil Shear Strength Topic No. 9
❑ Page :17 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
4. DETERMINATION OF SHEAR STRENGTH PARAMETERS
Three types of the test can be carried out:
1. 1. Quick (unconsolidated–undrained) UU-test: No drainage is allowed.
2. Consolidated–quick (consolidated–undrained) CU-test: Drainage is allowed in the
consolidation stage only.
3. Slow (consolidated–drained) CD-test: Drainage is allowed in all stage of the test.
❑ Soil Shear Strength Topic No. 9
❑ Page :18 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
5. The results of consolidated undrained triaxial tests with pore water pressure
measurement on a compacted soil at failure are as follows:
Determine the apparent cohesion and angle of internal friction referred to total
and effective stresses.
Example 5
❑ Soil Shear Strength Topic No. 9
❑ Page :19 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
For total stress analysis
For effective stress analysis
Solution:
❑ Soil Shear Strength Topic No. 9
❑ Page :20 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
4. DETERMINATION OF SHEAR STRENGTH PARAMETERS
(c) Unconfined compressive strength test
❑ Soil Shear Strength Topic No. 9
❑ Page :21 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
(d) Pocket penetrometer test
4. DETERMINATION OF SHEAR STRENGTH PARAMETERS
It can be used for ordinary works, the
unconfined compressive strength can be
measured directly
❑ Soil Shear Strength Topic No. 9
❑ Page :22 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
(e) Vane shear test
4. DETERMINATION OF SHEAR STRENGTH PARAMETERS
❑ The test is suitable for saturated clays of
very soft to firm consistency.
❑ Field vane tests are typically 50–75 mm
diameter and 100 –150 mm long.
❑ Laboratory vanes, 13 mm diameter and 50
mm long.
Torque = D2 cu (
𝑯
𝟐
+
𝐷
6
)
cu (field) = . cu
❑ Soil Shear Strength Topic No. 9
❑ Page :23 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
6. A vane 10 cm long and 8 cm diameter was used to measure the shear
strength of a soft clay. The torque at failure was 450 kg.cm. Calculate the
undrained cohesion.
Torque = D2 cu (
𝑯
𝟐
+
𝐷
6
)
450 = (8)2 cu (
𝟏𝟎
𝟐
+
8
6
)
cu = 0.35 kg/cm
2
Solution:
Example 6
❑ Soil Shear Strength Topic No. 9
❑ Page :24 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 :25 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.
❑ Soil Shear Strength Topic No. 9
• 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 ofcivil 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.
Prince Sultan University, Riyadh, Saudi Arabia, 2019-2020
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
Construction Management Program (CMP)
Consolidation Rate
Topic No. 8.2
Topic (8)
Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
Consolidation Rate Topic No. 8
CONSOLIDATION RATE
Page :2 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
ONE-DIMENSIONAL CONSOLIDATION
Drainage and Deformations
occur in Vertical direction only.
(none laterally)
A reasonable simplification for
solving consolidation problems
Page :3 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
TERZAGHI SPRING ANALOGY
When water drains from the soil pores, the load is gradually shifted from water to soil particles. For
fully saturated soils, the load transfer is accompanied by a volume change equal to the volume of
drained water. This process is known as CONSOLIDATION.
Page :4 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
Page :5 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
• Magnitude of settlement → compression index (Cc)
• Rate of consolidation → co-efficient of consolidation (Cv)
CONSOLIDATION TEST
INTERPRETATION OF TEST RESULTS
1. Time ~ Deformation curve
i. Cv (Coefficient of
consolidation)
2. Pressure ~ Deformation curves
i. Cc (Compression index)
ii. Cr (Recompression index)
iii. aV (Coefficient of compressibility)
iv. mV (Coefficient of volume change)
Page :6 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
USEFUL DEFINITIONS
Degree of consolidation (U):
It’s the ratio of the vertical settlement of the clay layer at time t to its final settlement.
FACTORS AFFECTING THE DEGREE OF CONSOLIDATION:
1- Time.
2- Drainage path.
3- Soil permeability.
4- Soil compressibility.
Page :7 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
Coefficient of consolidation (Cv):
USEFUL DEFINITIONS
It’s a coefficient that depends on soil compressibility and permeability
FACTORS AFFECTING COEFFICIENT OF CONSOLIDATION:
1- Soil permeability.
2- Soil compressibility.
Drainage path (HD):
It’s the longest distance
that water will path
through to leave the clay
layer.
Page :8 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
Time factor (Tv):
USEFUL DEFINITIONS
U 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Tv 0.008 0.031 0.071 0.126 0.197 0.287 0.403 0.567 0.848
For U = 50% Tv = 0.197
For U = 90% Tv = 0.848
Page :9 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
DEFORMATION – TIME PLOT
Used to determine Cv (coefficient of
consolidation)
Rate of consolidation (U)
Consolidation Time (t)
Time-Deformation relationship
Methods of Determining Cv :
1. Casagrande’s log-time method (1938)
2. Taylor’s Square root of time method (1948)
Page :10 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
Example 2
For the soil stratification shown in figure and considering the illustrated
loading condition, determine the following:
i. Final settlement under the footing.
ii. The settlement after 5 years.
iii. The time for 80% consolidation.
G.W.T
1.5 m
1150 kN
SAND
γd = 18.9 kN/m
3
3 * 4 m
CLAY
γsat = 20 kN/m
3 mv = 6.2 * 10
-4 m2/kN k = 8.9 * 10-9 cm/sec
Consolidation Rate Topic No. 8
Page :11 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Solution:
i- Final settlement of the footing:
∆σ =
𝟏𝟏𝟓𝟎
𝟔∗𝟕
= 27.4 kN/2
∆H = mv . ∆σ . H
= 6.2 * 10-4 * 27.4 * 6 = 0.102 m
= 10.2 cm (Final settlement)
G.W.T
1.5 m
1150 kN
SAND
γd = 18.9 kN/m
3
3 * 4 m
CLAY
γsat = 20 kN/m
3 mv = 6.2 * 10
-4 m2/kN k = 8.9 * 10-9 cm/sec
Consolidation Rate Topic No. 8
Page :12 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
ii- The settlement after 5 years:
cv =
𝒌
𝒎𝒗 . γ𝒘
=
𝟖.𝟗 ∗ 𝟏𝟎−𝟏𝟏
𝟔.𝟐 ∗ 𝟏𝟎−𝟒 ∗𝟏𝟎
= 1.44 * 10-8 m2/sec
T =
𝒄𝒗.𝒕
(𝑯𝒅)
𝟐 =
𝟏.𝟒𝟒 ∗ 𝟏𝟎−𝟖 ∗𝟓 ∗𝟐𝟒 ∗𝟔𝟎 ∗𝟔𝟎 ∗𝟑𝟔𝟓
(𝟔)𝟐
= 0.063
A. Determine Consolidation Coefficient (cv):
b. Time Factor (T):
→ U = 0.28 from chart
∆H5 years = U * ∆Hf = 0.28 * 10.2 = 2.9 cm
c. Settlement after 5 years :
Consolidation Rate Topic No. 8
Page :13 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Solution:
iii- Time for 80% settlement:
For 80% cons. T 0.567 (from table)
→ 0.567 =
𝟏.𝟒𝟒 ∗ 𝟏𝟎−𝟖 ∗ 𝒕𝟖𝟎%
(𝟔)𝟐
→ t80% = 1.42 * 10
9 sec = 45 years
U 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Tv 0.008 0.031 0.071 0.126 0.197 0.287 0.403 0.567 0.848
Consolidation Rate Topic No. 8
Page :14 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Secondary compression settlement can be computed from
SETTLEMENT OF LOADS ON CLAY DUE TO SECONDARY COMPRESSION
Ss = Cα H log
𝒕𝒔
𝒕𝒑
eqn 7.25
Ss = secondary compression settlement
Cα = coefficient of secondary compression
H = initial thickness of clay layer
ts = life of the structure (or time for which
settlement is required)
tp = time to completion of primary consolidation
Page :15 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
A foundation is built on a sand deposit underlain by a highly compressible
clay layer 5.0 m thick. The clay layer’s natural water content is 80%. Primary
consolidation is estimated to be complete in 10 years. Determine the
secondary compression settlement expected to occur from 10 to 50 years
after construction of the foundation
Example 7
Page :16 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
From eqn 7.25,
Ss = Cα H log
𝒕𝒔
𝒕𝒑
From Fig 7.22, with w = 80%
Cα = 0.015
H = 5.0 m
ts = 50 years
tp = 10 years
Ss = (0.015) (5.0 m) (log
𝟓𝟎 𝒚𝒆𝒂𝒓𝒔
𝟏𝟎 𝒚𝒆𝒂𝒓𝒔
)
Ss = 0.052 m
Solution:
Page :17 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation Rate Topic No. 8
RECIPE FOR SUCCESS,
As long as you live, Just Keep
L e a r n i n g …
References
Page :18 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.
Consolidation Rate Topic No. 8
• 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 ofcivil 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.
Prince Sultan University, Riyadh, Saudi Arabia, 2019-2020
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
Construction Management Program (CMP)
Bearing Capacity and Shallow Foundations
Topic No. 10
Topic (10)
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Bearing Capacity and Shallow Foundations Topic No. 10
The Design of foundations have to satisfy Two fundamental
requirements, respectively;
Fig (2), Relative and total settlement of pisa tower.
1. Complete failure of the foundation must be
prevented with an sufficient margin of safety.
2. The relative and total settlements of the
foundation must be kept within limits that can be
tolerated by the superstructure.
Fig (1), Foundation Failure of the condo building in
China
PRINCIPLE OF FOUNDATION DESIGN
(Meyerhof, 1951)
❑ Page :2 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
1. Safety factor of two is generally used in
practice to obtain the maximum safe
foundation load (Load Control Criteria).
2. The settlement of the foundation under
working load has to be estimated
independently to ascertain its effect on the
superstructure (Settlement Control Criteria).
PRINCIPLE OF FOUNDATION DESIGN
❑ Page :3 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
INTRODUCTION
❑ Foundations may be classified as
o Shallow (e.g. isolated footing, raft foundation) Df≤ 4.0 m
o Deep (pier, drilled shaft, or pile group) Df 4.0 m
❑ Page :4 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Footing may be classified in several ways
o Individual footing
o Combined footing
o Wall footing
o Strap footing
o Mat or raft foundation
TYPES OF SHALLOW FOUNDATIONS
❑ Page :5 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Foundations must be designed to satisfy Three general criteria
1. They must be located properly so as not to be adversely affected by outside
influence
2. They must be safe from bearing capacity failure
3. They must be safe from excessive settlement
FOUNDATION DESIGN
❑ Page :6 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ In general the typical load/pressure types includes:
o Dead load
o Live load
o Wind load
o Snow load
o Earth pressure
o Water pressure
o Earthquake forces
LOADS ON FOUNDATIONS
❑ Page :7 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ The depth & location of foundations are dependent on :
o Significant soil volume change
o Adjacent structures & property lines
o Groundwater
o Underground defects
o Building codes
DEPTH & LOCATION OF FOUNDATIONS
❑ Page :8 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Bearing capacity: refers to the ability of the soil to support a foundation & structure.
❑ Ultimate bearing capacity (qult): refers to the loading per unit area (Stress) that will
just cause shear failure in the soil.
❑ Allowable bearing capacity (qa): refers to the loading per unit area that the soil is
able to support without unsafe movement
BEARING CAPACITY ANALYSIS
qa =
𝒒𝒖𝒍𝒕
𝒇𝒂𝒄𝒕𝒐𝒓 𝒐𝒇 𝒔𝒂𝒇𝒆𝒕𝒚 (𝑭𝑶𝑺)
❑ A factor of safety (FOS) of 2.5 to 3.0 is commonly applied
❑ Page :9 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
THEORY OF BEARING CAPACITY
❑ The set of slip surface giving the least value of Q is the most critical
❑ As load (Q) is applied, the footing undergoes a certain amount of settlement as it is pushed downward
❑ A wedge of soil directly below the footing’s base move downward with the footing
❑ This is resisted by shear resistance of the soil along the slip surfaces cde & cfg (see Fig. 9.6) & weight of the soil in sliding
wedge acfg & bcde
❑ Page :10 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ The following equations for calculating qult were developed by Terzaghi (Terzaghi and Peck,
1967)
BEARING CAPACITY ANALYSIS
❑ Continuous footing (width B)
qult = cNc + γ1 Df Nq + 0.5 γ2 BNγ eqn 9.1
Where,
qult = ultimate bearing capacity
c = cohesion
Nc , Nq , Nγ = Terzaghi’s bearing capacity factors
γ1 = effective unit weight of soil above base of foundation
γ2 = effective unit weight of soil below foundation
Df = depth of footing or distance from ground surface to base of footing
B = width of continuous or square footing
R = radius of circular footing
for both cohesive & cohesionless soils
❑ Page :11 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Circular footing (radius R)
qult = 1.2 cNc + γ1 Df Nq + 0.6 γ2 RNγ eqn 9.2
❑ Square footing (Width B)
qult = 1.2 cNc + γ1 Df Nq + 0.4 γ2 BNγ eqn 9.3
BEARING CAPACITY ANALYSIS
for both cohesive & cohesionless soils
❑ Page :12 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Values of Terzaghi’s dimensionless bearing capacity factors for
different values of can be obtained from Fig. 9.7 or Table 9.1 or
equations below:
BEARING CAPACITY ANALYSIS
Nq = e
tanϕ tan2 𝟒𝟓𝒐 +
ϕ
𝟐
eqn 9.4
Nc = cot ϕ (Nq – 1) eqn 9.5
Nγ = (Nq – 1) tan (1.4 ϕ) eqn 9.6
❑ Page :13 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Dense sand & stiff clay produce what is called
general shear
❑ Loose sand & soft clay produce local shear
❑ For the latter, Nc, Nq & N are replaced by N’c, N’q
& N’
TYPES OF FAILURE
c’ =
𝟐
𝟑
c eqn 9.7
ϕ’ = arctan (
𝟐
𝟑
tan ϕ) eqn 9.8
❑ Page :14 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ In the case of cohesionless soils,
c = 0
❑ Value of may be determined using corrected SPT values
as covered in Chapter 3 or using this figure.
BEARING CAPACITY ANALYSIS
❑ For cohesive soils, shear strength is most critical just after
construction when shear strength is assumed to consist
only of c
qult = cNc + γ1 Df Nq + 0.5 γ2 BNγ eqn 9.1
❑ Page :15 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
o qu = 134 kN/m2
o = 20.40 kN/m3
o Groundwater was not encountered during
subsurface exploration
o Df = 0.6m
❑ Determine the qult & allowable wall load using a FOS of
3
A strip of footing 1 m wide is supported in a uniform deposit of stiff clay. Given the
following:
Example 1
❑ Page :16 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ As the supporting stratum is stiff clay, a general shear condition is evident.
For a continuous wall footing
qult = cNc + γ1 Df Nq + 0.5 γ2 BNγ
=
134
2
= 67 kN/m2c =
𝒒𝒖
𝟐
γ1 = γ2 = 20.40 kN/m
3
Df = 0.6 m
B = 1 m
If we use c > 0 , ϕ = 0 analysis for cohesive soil, using the
table, bearing capacity values are :
Nc = 5.14, Nq = 1.0 , Nγ = 0
Solution:
❑ Page :17 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
(cont’d)
qult = (67) (5.14) + (20.40) (0.6) (1.0) + (20.40) (1) (0)
= 357 kN/m2
qa = (357)/3 = 119 kN/m
2
Allowable wall loading = qa * B
= (119) (1) = 119 kN/m of wall length
qult = cNc + γ1 Df Nq + 0.5 γ2 BNγ
qa =
𝒒𝒖𝒍𝒕
𝒇𝒂𝒄𝒕𝒐𝒓 𝒐𝒇 𝒔𝒂𝒇𝒆𝒕𝒚 (𝑭𝑶𝑺)
Solution:
❑ Page :18 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
A column footing 2 m x 2 m is buried 1.5 m below
the ground surface in a dense cohesionless soil. The
footing is to carry a total load of 1500 kN .The
results of lab & field tests are as follows:
o = 20.10 kN/m3
o Average corrected SPT N-value = 30
o Groundwater was not encountered during
subsurface exploration
❑ Determine the
FOS against bearing capacity failure
Example 2
❑ Page :19 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
Because the supporting stratum is dense cohesionless soil, a general shear condition is evident.
qult = 1.2 cNc + γ1 Df Nq + 0.4 γ2 BNγ
c = 0
γ1 = γ2 = 20.10 kN/m
3
Df = 1.5 m
B = 2 m
From the chart, with Ncorrected = 30, ϕ = 36
o
the following bearing capacity factors are obtained:
Nq = 37.75 , Nγ = 44.43
Square Footing
Step (1): Find soil bearing capacity:
Solution:
❑ Page :20 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
qult = (1.2) (0) (Nc) + (20.10) (1.5) (37.75) + (0.4) (20.10) (2) (44.43)
qult = 1852.6 kN/m
2
qult = 1.2 cNc + γ1 Df Nq + 0.4 γ2 BNγ
qactual =
𝑸
𝑨
=
1500
2 ∗2
= 375 kN/m2
FOS against bearing capacity failure
FOS=
𝒒𝒖𝒍𝒕
𝒒𝒂𝒄𝒕𝒖𝒂𝒍
=
1852.6
375
= 4.9 > 3.0
Step (1): Find soil bearing capacity:
Step (2): Find Actual stress on the footing :
Step (3): Find FOS:
SAFE
Solution:
❑ Page :21 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
RECIPE FOR SUCCESS,
As long as you live, Just Keep
L e a r n i n g …
References
• 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.
❑ Page :59 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
• 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.
Prince Sultan University, Riyadh, Saudi Arabia, 2019-2020
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
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Stresses in Soil Topic No. 7
EFFECTIVE, NEUTRAL AND TOTAL STRESSES IN SOIL
❑ Page :2 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
EFFECTIVE, NEUTRAL AND TOTAL STRESSES IN SOIL
A. Total stress (σ):
σ = σ eff + u
❑ Page :3 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
EFFECTIVE, NEUTRAL AND TOTAL STRESSES IN SOIL
B. Effective stress (σ‘):
σeff = σ t – u
C. Neutral stress (pore pressure u):
u = γw . hw
❑ Page :4 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
CASES TO BE CONSIDERED
(A) Case of submerged soil
σ = γsat . h + γw . h1
u = γw . h1
σ’ = γsub . h
Calculation of effective stress in submerged soil
❑ Page :5 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
(B) Case of soil with surcharge
σ = q + γb . h1 + γsat . h
Calculation of effective stress in loaded soil
u = γw . hw
σ’ = q + γb . h1 + γsub . h
❑ Page :6 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
Example 1
❑ Page :7 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
Solution:
❑ Page :8 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
STRESSES IN SOIL DUE TO EXTERNAL LOADS
❑ Page :9 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
INTRODUCTION
❑
❑ Page :10 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
❑
INTRODUCTION
❑ Page :11 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
▪
▪
▪
▪
ELASTIC THEORY
❑ Page :12 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
o Boussinesq equation:
1. STRESSES DUE TO CONCENTRATED LOAD
Pz =
𝟑𝐐
𝟐𝛑 𝐳
𝟐
𝟏
𝟏+
𝐫
𝐳
𝟐
𝟓
𝟐
𝐩𝐳 =
𝐐 =
𝐳 =
=
Zone of influence for concentrated Load
❑ Page :13 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
o Boussinesq equation:
1. STRESSES DUE TO CONCENTRATED LOAD
❑
𝒑𝒛 =
𝟑
𝑷
𝟐𝝅𝒛𝟐 𝟏 + (𝒓/𝒛)𝟐 𝟓/𝟐
=
𝑷
𝒛𝟐
𝑰𝑩
𝐖𝐡𝐞𝐫𝐞,
𝐈𝐁
❑
❑ Page :14 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
𝒑𝒛 =
𝟑𝑷
𝟐𝝅𝒛𝟐 𝟏 + (𝒓/𝒛)𝟐 𝟓/𝟐
=
𝑷
𝒛𝟐
𝑰𝑩
Example 2
❑ Page :15 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
Given Data :
𝒛 = 6m, 𝒓 = 0, 𝑷 = 2500kN
From eqn,
𝒑 =
(𝟑)(𝟐𝟓𝟎𝟎kN)
(𝟐)𝝅(𝟔𝐦)𝟐[𝟏 + (𝟎/𝟔𝐦)𝟐]𝟓/𝟐
= 𝟑𝟑.𝟐kN/m𝟐
𝒑 =
𝟑𝑷
𝟐𝝅𝒛𝟐 𝟏+(𝒓/𝒛)𝟐
𝟓/𝟐
Solution:
❑ Page :16 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
❑
(cont’d)
pz =
𝑷
𝒛𝟐
IB
pz =
𝟐𝟓𝟎𝟎
(𝟔 𝒎)𝟐
* 0.48 = 33.3 kN/m
Solution:
❑ Page :17 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
2. STRESSES DUE TO A LINE LOAD
Pz =
𝐪
𝐳
. NL
Where:
𝐱
𝐳
𝐲
𝐳
Figure 6.3: Stresses due to line load
Pz
❑ Page :18 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
❑
❑
❑
3. STRESSES DUE TO A LOADED SURFACE AREA
❑ Page :19 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
𝒑𝒛
𝑷/A
𝑳 + 𝒛
o
3.A Approximate method
o
𝒑𝒛 =
𝑷
(𝑩 + 𝒛)(𝑳 + 𝒛)
eqn 6−6
𝐩𝐳 =
𝐏 =
𝐁 =
𝐋 =
𝐳 =
𝒑𝒛
𝒁
❑ Page :20 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
o
3.A Approximate method
❑ Page :21 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
❑
Example 3
❑ Page :22 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
p =
𝑷
(𝑩+𝒛)(𝑳+𝒛)
P =
𝟑𝟔𝟎𝟎 𝒌𝑵
(𝟑 𝒎+𝟔 𝒎)(𝟓 𝒎+𝟔 𝒎)
= 36.4 kN/m2
Solution:
❑ Page :23 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
1. Uniform load on a circular area
▪
▪
▪
▪
▪
3.B Method based on Elastic Theory
𝒑𝒛 = 𝑷 ∗ 𝑰
❑ Page :24 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
❑ Page :25 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
❑
Example 4
❑ Page :26 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
𝑟
𝑎
0 𝑚
2 𝑚
𝑧
𝑎
5 𝑚
2 𝑚
𝒑𝒛 = 𝑷 ∗ 𝑰
Solution:
❑ Page :27 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
(cont’d)
Total vertical pressure = overburden pressure (po)
+ vertical increment (p)
po = γz = 16.97 kN/m
3 (5 m) = 84.8 kN/m2
Total vertical pressure = 84.8 + 60.0 = 144.8 kN/m2
Solution:
❑ Page :28 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Stresses in Soil Topic No. 7
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
Construction Management Program (CMP)
Consolidation in Soil
Topic No. 8
Topic (8)
Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
Consolidation in Soil Topic No. 8
CONSOLIDATION OF THE SOIL
Consolidation in Soil Topic No. 8
Page :2 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
CONSOLIDATION OF THE SOIL
The volume of a soil mass is decreased under stress. This decrease is known
as compression, and the capacity of soil to decrease in volume under stress is
know as compressibility.
If voids are filled with air, compression will occur rapidly,
since air is compressible and can escape easily from the
voids (called Elastic settlement). On the other hand, if
the voids are filled with water, decrease in volume can
only take place when the water is expelled out of the
voids (called Primary settlement). In partially saturated
soils, compression is accompanied by compression of
air and
expulsion of water.
Consolidation in Soil Topic No. 8
Page :3 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Total compression = Elastic settlement + Primary settlement +
Secondary settlement.
Where:
Elastic (Immediate) settlement: Occurs due to
compression of air.
Primary (Consolidation) settlement: Occurs due to
expulsion of water.
Secondary (Creep) settlement: Occurs due to
rearrangement of soil particles.
Consolidation in Soil Topic No. 8
Page :4 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
IMMEDIATE (ELASTIC) SETTLEMENT
7.1eqn
1
2
u
si
E
qBCS
Si = immediate settlement
Cs = shape & foundation rigidity factor (Table 7.1 &
7.2)
q = acting load on the foundation area (Stress)
B = width or diameter of foundation
=Poisson’s ratio for the applied stress range
Eu = undrained elastic modulus of clay
• Eu may be evaluated using the results of
undrained triaxial compression tests
• Eu = 500 Cu ~ 1500 Cu (Empirical Range)
• Cu = soil cohesion shear strength as
determined from the undrained tests
Consolidation in Soil Topic No. 8
Page :5 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
A square 3m x 3m rigid footing is resting on a deep clay deposit. The
footing is to carry a concentrated load of 1800 kN. The undrained elastic
modulus of clay Eu is estimated to be 40MPa, and the Poisson’s ratio of the
clay is 0.5. Determine the expected immediate settlement beneath the
centre of the footing.
3.0 x3.0
m
Clay Deposit
µ = 0.5
E = 40000 kN/m2
P = 1800 kN
Example 1
Consolidation in Soil Topic No. 8
Page :6 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
From eqn 7.1
Si = Cs q B (
𝟏−𝝁𝟐
𝑬𝒖
)
From Table 7.1, Cs = 0.82
Si = (0.82) (
𝟏𝟖𝟎𝟎 𝒌𝑵
𝟑 𝒎 (𝟑 𝒎)
) (3 m) (
𝟏−𝟎.𝟓𝟐
𝟒𝟎∗𝟏𝟎𝟑 𝒌𝑵/𝒎𝟐
)
Si = 0.0092 m = 9.2 mm
Solution:
Consolidation in Soil Topic No. 8
Page :7 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Typical values of modulus of elasticity Typical values of poisson ratio
Consolidation in Soil Topic No. 8
Page :8 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
PRIMARY (CONSOLIDATION) SETTLEMENT
It is a gradual compression due to expulsion of water from soil voids accompanied
by transfer of stress from pore water to soil particles caused by application of
sustained external stress is known as
consolidation.
The rate of consolidation is governed by the rate at which pore water escapes, and
hence it is directly related to soil permeability.
Consolidation in Soil Topic No. 8
Page :9 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
PRIMARY (CONSOLIDATION) SETTLEMENT
(a) Consolidation test using Odometer:
In order to determine the compression
characteristics of a soil, a consolidation
test is carried out in an apparatus called
oedometer
Consolidation in Soil Topic No. 8
Page :10 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
CONSOLIDATION TEST
Consolidation in Soil Topic No. 8
Page :11 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
o Diameter of test specimen = 6.35 cm
o Initial height of specimen = 1.98 cm
o Specific gravity of solids = 2.72
o Dry mass of specimen = 75.91 g
o Pressure versus deformation dial
readings are as given in the following
table
Pressure,
p
(kPa)
Initial
deformation
dial reading at
beginning of first
loading
(mm)
Deformation dial
reading
representing
100% primary
consolidation (mm)
0 0 0
25 0 0.401
50 0 0.721
100 0 1.244
200 0 1.933
400 0 2.908
800 0 4.013
A clayey soil obtained from the field was subjected to a laboratory consolidation test. The
test results are as follows:
Determine initial void ratio & e-log p curve
Example 2
Consolidation in Soil Topic No. 8
Page :12 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Volume of solid in specimen (Vs)
=
𝑫𝒓𝒚 𝒎𝒂𝒔𝒔 𝒐𝒇 𝒔𝒐𝒍𝒊𝒅
𝑼𝒏𝒊𝒕 𝒎𝒂𝒔𝒔 𝒐𝒇 𝒔𝒐𝒍𝒊𝒅
=
𝑫𝒓𝒚 𝒎𝒂𝒔𝒔 𝒐𝒇 𝒔𝒐𝒍𝒊𝒅
𝒔𝒆𝒄𝒊𝒇𝒊𝒄 𝒈𝒓𝒂𝒗𝒊𝒕𝒚 𝒐𝒇 𝒔𝒐𝒍𝒊𝒅𝒔 (𝒖𝒏𝒊𝒕 𝒎𝒂𝒔𝒔 𝒐𝒇 𝒘𝒂𝒕𝒆𝒓)
Vs =
𝟕𝟓.𝟗𝟏 𝒈
𝟐.𝟕𝟐 (𝟏.𝟎 𝒈 /𝒄𝒎𝟑)
= 27.91 cm3
Initial volume of specimen (Vt) =
𝟏.𝟗𝟖 𝝅(𝟔.𝟑𝟓 𝒄𝒎)𝟐
𝟒
Vt = 62.74 cm3
Step (1): Determine The initial Void ratio:
Initial volume of voids in specimen (Vv) = (62.74 – 27.91) cm
3
Vv = 34.83 cm
3
=
𝟑𝟒.𝟖𝟑
𝟐𝟕.𝟗𝟏
= 1.248Initial void ratio (eo) =
𝑽𝒗
𝑽𝒔
GS =
γ𝒔
γ𝒘
γd =
𝑾𝒔
𝑽𝒕
Reminder
Step (1)
Solution:
Consolidation in Soil Topic No. 8
Page :13 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Step (2) develop the e-log p curve:
1. one must determine the height of solids in the specimen
height of solid in specimen (Hs) =
𝑽𝒔
𝒂𝒓𝒆𝒂 𝒐𝒇 𝒔𝒑𝒆𝒄𝒊𝒎𝒆𝒏
Hs =
𝟐𝟕.𝟗𝟏
𝝅(𝟔.𝟑𝟓 𝒄𝒎)𝟐 /𝟒
Hs = 0.881 cm
Pressure,
p
(kPa)
Initial deformation
dial reading at
beginning of first
loading (mm)
Deformation dial
reading representing
100% primary
consolidation (mm)
0 0 0
25 0 0.401
50 0 0.721
100 0 1.244
200 0 1.933
400 0 2.908
800 0 4.013
2. The change in thickness of the specimen (∆H)
can be found by subtracting the initial
deformation dial reading from the deformation
dial reading representing 100% primary
consolidation.
For the 25 kPa pressure,
∆H = (0.401 – 0) = 0.0401 cm
Step (2)
Solution:
Consolidation in Soil Topic No. 8
Page :14 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
dividing ∆H by Hs
Ex:
For the 25 kPa pressure,
∆e =
𝟎.𝟎𝟒𝟎𝟏 𝐜𝐦
𝟎.𝟖𝟖𝟏 𝐜𝐦
= 0.046
4.Finally, e can be computed
by subtracting ∆e from eo
Ex:
For the 25 kPa pressure,
e = 1.248 – 0.046 = 1.202
Pressure
p (kPa)
Initial
deformation
dial reading at
beginning of
first loading
(mm)
Deformation
dial reading
representing
100% primary
consolidation
(mm)
H
(cm)
e Void
ratio
(e)
0 0 0 0 0 1.248
25 0 0.401 0.0401 0.046 1.202
50 0 0.721 0.0721 0.082 1.166
100 0 1.244 0.1245 0.141 1.107
200 0 1.933 0.1933 0.219 1.029
400 0 2.908 0.2908 0.330 0.918
800 0 4.013 0.4013 0.456 0.792
3. Change in void ratio (∆e) can be determined by:
∆H =Rn- R0
∆e = ∆H/ Hs
e = eo –
∆
e
Solution:
Consolidation in Soil Topic No. 8
Page :15 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Hs = 0.881 cm
Step (5): Plot The e-log p curve is prepared by plotting void ratio e and
pressure, with the latter on a log scale
Solution:
Consolidation in Soil Topic No. 8
Page :16 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
1. Stress – Strain curve 3.(e – log P) curve2. Void Ratio–Pressure Plots
CONSOLIDATION TEST OUTCOMES
∆e
P
Used to Obtain mv
e
P
Used to Obtain av
Log P
av =
∆𝒆
∆𝝈
mv =
𝒂𝒗
𝟏+𝒆𝒐
cc =
𝒆𝟏 − 𝒆𝟐
𝒍𝒐𝒈 (𝒑𝟐/𝒑𝟏)mv =
𝑺𝒕𝒓𝒂𝒊𝒏
𝑺𝒕𝒓𝒆𝒔𝒔
=
∆𝑯𝒇
𝑯𝒐
∆𝝈𝒇
Used to Obtain CC
aV (Coefficient of compressibility)mV (Coefficient of volume change)
Cc (Compression index)
Consolidation in Soil Topic No. 8
Page :17 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
To determine if the clay is
normally consolidated (NC),
it is necessary to know the
present effective overburden
pressure (po = γ*h):
This pressure is the
result of the effective
weight of soil above mid-
height of the
consolidating clay layer
NORMALLY CONSOLIDATED CLAY
o With the e-log p curve developed from laboratory test, the point corresponding
to 0.4 eo is determined
Consolidation in Soil Topic No. 8
Page :18 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
(a) Normally consolidation clay
σ‘c = σ‘o & Over consolidation (OCR) =
𝝈′𝒄
𝝈′𝒐
= 1
(b) Over consolidation clay
σ‘c > σ‘0
OCR > 1
(c) Under consolidation clay
σ‘c < σ‘o Where:
Overburden stress (σ’o) = Σγ.H
TYPE OF CLAY
σ
‘ c
Consolidation in Soil Topic No. 8
Page :19 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
SETTLEMENT OF LOADS ON CLAY DUE TO
PRIMARY CONSOLIDATION
Consolidation in Soil Topic No. 8
Page :20 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
a. For Normally Consolidated Clay
(a) Normally consolidation clay
σ‘c = σ‘o & Over consolidation (OCR) =
𝝈′𝒄
𝝈′𝒐
= 1
cc =
𝒆𝟏 − 𝒆𝟐
𝒍𝒐𝒈 (𝒑𝟐/𝒑𝟏)
eqn 7.4
Sc = Cc
𝑯
𝟏+𝒆𝒐
(log
𝒑
𝒑𝒐
) eqn 7.18
SETTLEMENT OF LOADS ON CLAY DUE TO PRIMARY CONSOLIDATION
Sett. (∆Hf) = mv . ∆σ . H
Sett. = Σ
𝟏
𝑬
. ∆σ . H
Consolidation in Soil Topic No. 8
Page :21 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
cc = 0.009 (L.L.
– 10)
b. For Over Consolidated Clay
Overconsolidated clay is generally less
compressible
The analysis of clay for consolidation
settlement differs whether the clay is
normally consolidated or overconsolidated
(b) Over consolidation clay
σ‘c > σ‘0 OCR > 1
Consolidation in Soil Topic No. 8
Page :22 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Example 3
For the shown footing in figure, it is
required to calculate the expected
compression of the clay layer due
to the shown loading
condition.
1600 kN
1.5 m
1.5 m
4.5 m
3.0 * 3.0 m
G.W.T
Dry Sand
Gs = 2.65
e = 0.52
Clay
Gs = 2.75, e = 0.52
mv = 1.85 * 10
-4 m2/kN
Page :23 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation in Soil Topic No. 8
Solution:
∆σ =
𝟏𝟔𝟎𝟎
𝟔.𝟕𝟓 ∗𝟔.𝟕𝟓
= 35.1 kN/m2
∆H = mv . ∆σ . H
∆H = 1.85 * 10-4 * 35.1 * 4.5
→ ∆H = 0.029 m = 2.9 cm
1600 kN
1.5 m
1.5 m
4.5 m
3.0 * 3.0 m
G.W.T
Dry Sand
3.75
Clay
mv = 1.85 * 10
-4 m2/kN
6.75 * 6.75 m
Sandstone
∆σ
Step (1): Determine the external stress
Step (2): Determine the Settlement
Page :24 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation in Soil Topic No. 8
Example 4
For the shown footing in figure, it
is required to calculate the
expected compression of the clay
layer due to the shown loading
condition.
4.0 * 6.0 m
G.W.T
N.L. Clay
γsat = 18.7 kN/m
2
e = 1.1 L.L. = 60%
1.0
5.0
100 kN/m2
Sandstone
Page :25 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Consolidation in Soil Topic No. 8
Solution:
4.0 * 6.0 m
G.W.T
N.L. Clay
γsat = 18.7 kN/m
2, e = 1.1 , L.L. = 60%
1.0
5
.0
m
100 kN/m2
Sandstone
z
=
2
.5
6.5 * 8.5m
∆σ
σo = 1 * 18.7 + 2.5 * 8 = 40.5 kPa
∆σ =
𝟏𝟎𝟎 ∗ 𝟒 ∗ 𝟔
𝟔.𝟓 ∗𝟖.𝟓
= 43.4 kPa
cc = 0.009 (L.L. – 10)
→ cc = 0.009 (60 – 10) = 0.45
∆H =
𝒄𝒄
𝟏+𝒆
. H . Log
𝝈𝒐+∆𝝈
𝝈𝒐
Step (1): Determine the external stress
Step (2): Determine the Settlement
Page :26 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
∆H =
𝟎.𝟒𝟓
𝟏+𝟏.𝟏
* 500 * log
𝟒𝟎.𝟓+𝟒𝟑.𝟒
𝟒𝟎.𝟓
= 20 cm
Consolidation in Soil Topic No. 8
RECIPE FOR SUCCESS,
As long as you live, Just Keep
L e a r n i n g …
References
Page :27 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.
Consolidation in Soil Topic No. 8
• 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 ofcivil 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.
Prince Sultan University, Riyadh, Saudi Arabia, 2019-2020
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
Construction Management Program (CMP)
Bearing Capacity and Shallow Foundations
Topic No. 10
Topic (10)
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
SPECIAL CASES FOR BEARING CAPACITY
❑ Bearing Capacity and Shallow Foundations Topic No. 10
1.
EFFECT OF GWT ON THE BEARING CAPACITY
Level of GWT affect the soil bearing capacity as follow:
❑ Case 1: If dw > B G.W.T has No effect.
γ1 = γ2 = γb
❑ Case 2 If dw < B G.W.T has effect.
γ1 = γb
γ2 = γsub + Fw (γb – γsub)
Fw : Obtained from Figure 3.7
[Case 1]
[Case 2]
[Case 3]
[Case 4]
[Case 5]
❑ Page :22 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
EFFECT OF GWT ON THE BEARING CAPACITY
Level of GWT affect the soil bearing capacity as follow:
❑ Case 3: If dw = Df G.W.T has effect.
γ1 = γb γ2 = γsub
❑ Case 4 If dw < Df G.W.T has effect.
γ1 . Df = γb . dw + γsub . (Df – dw)
❑ Case 5 If G.W.T at surface G.W.T has effect.
γ1 = γ2 = γsub
[Case 1]
[Case 2]
[Case 3]
[Case 4]
[Case 5]
❑ Page :23 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
A 2.5 m x 2.5 m square footing is located 2 m below the ground surface . The GWT is located at
the ground surface. The subsoil consists of a uniform deposit of soft, loose soil. The lab test
results are
o = 20o
o c = 15 kN/m2
o = 16.5 kN/m3
❑ Determine the allowable load that can be imposed on this square footing using a FOS of 3
Example 3
❑ Page :24 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
Because the footing is resting on soft, loose soil, eqn 9.3 must
be modified to reflect a local shear condition:
c’ =
𝟐
𝟑
c
qult = 1.2 c’N’c + γ1 Df N’q + 0.4 γ2 BN’γ
=
2
3
* 15 = 10 kN/m2
ϕ’ = arctan (
𝟐
𝟑
tan ϕ)
ϕ’ = arctan (
2
3
tan 20o) = 13.6o
Step (1): Find soil bearing capacity:
With ϕ’ = 13.6o , Using the chart
N’c = 10 , N’q = 3 , N’γ = 1
Solution:
❑ Page :25 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
Qallowable = qa * area of footing
Qallowable = (55.63) (2.5) (2.5) = 34.77 kN
B = 2.5 m, Df = 2 m
γ1 = γ2 = 16.5 – 9.81 = 6.7 kN/m
3 Case 5
qult = (1.2) (10) (10) + (6.7) (2) (3) + (0.4) (6.7) (2.5) (1)
qult = 166.9 kN/m
2
qa =
𝟏𝟔𝟔.𝟗
𝟑
= 55.63 kN/m2
Step (1): Find soil bearing capacity:
qult = 1.2 c’N’c + γ1 Df N’q + 0.4 γ2 BN’γ
qa =
𝒒𝒖𝒍𝒕
𝒇𝒂𝒄𝒕𝒐𝒓 𝒐𝒇 𝒔𝒂𝒇𝒆𝒕𝒚 (𝑭𝑶𝑺)
The Max Load the footing can carry
Solution:
❑ Page :26 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
1. If a footing is subjected to a inclined load, the inclined load can be resolved into
vertical & horizontal components
2. The vertical component can then be used for bearing capacity analysis.
3. the bearing capacity must be corrected by an Ri factor which can be obtained from
Fig. 9.18
2.
FOOTING IS SUBJECTED TO A INCLINED LOAD
Corrected qult for inclined load = qult * Ri
❑ Page :27 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ The footing’s stability with
regard to the horizontal
component must be checked
against sliding
FOOTING IS SUBJECTED TO A INCLINED LOAD
❑ Page :28 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ A square footing (1.5 m by 1.5 m) is subjected to an inclined load as shown
❑ Determine the FOS against bearing capacity failure
Example 4
❑ Page :29 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
For a square footing, Qult can be calculated as follow:
Qult = 1.2 cNc + γ1 Df Nq + 0.4 γ2 BNγ
c =
𝒒𝒖
𝟐
=
180
2
= 90 kN/m2
γ1 = γ2 = 20.40 kN/m
3
Df = 1.5 m, B = 1.5 m
If we use > 0, ϕ = 0 analysis for cohesive soil,
Fig 9.7 gives
Nc = 5.14, Nq = 1.0, Nγ = 0
Qult = 1.2 (90) (5.14) + (20.40) (1.5) (1.0) + 0.4 (20.40) (1.5) (0)
Qult = 585.72 kN/m
2
Solution:
❑ Page :30 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
(cont’d)
From Fig 9.18, α = 30o & cohesive soil,
Ri = 0.42
Corrected qult for inclined load
= (0.42) (585.72) = 246 kN/m2
Qv = Q cos 30
o = 200 (cos 30o) = 173 kN
FOS =
𝑸𝒖𝒍𝒕
𝑸𝒗
=
246 (1.5 ∗1.5)
173
= 3.2
Correct the obtained Qult due to the inclined load:
Find FOS:
Solution:
❑ Page :31 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Eccentric loads result from loads
applied somewhere other than the
footing’s centroid or from applied
moments
❑ Footings with eccentric loads may be
analyzed for bearing capacity using
o The concept of useful width
o Application of reduction factors
3.
FOOTING IS SUBJECTED TO ECCENTRIC LOAD
o This means that bearing capacity as eccentricity
o This linear relationship has been confirmed in cohesive soil
❑ Page :32 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Useful Width method
❑ Reduction factor method
B’ = B – 2 (e)
FOOTING IS SUBJECTED TO ECCENTRIC LOAD
Qult = Qult * Re
❑ Page :33 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
A 1.5 m x 1.5 m footing is located 1.2 m below the ground surface. The footing is subjected to an
eccentric load of 350 kN. The subsoil consists of a thick deposit of cohesive soil with:
o qu = 200 kN/m
2
o = 20.40 kN/m3
❑ GWT is at a great depth, & its effect can be ignored
❑ Determine the FOS against bearing capacity failure by:
o concept of useful width
o using reduction factor
Example 5
❑ Page :34 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
1. Using The concept of useful width
Solution
the useful width = 1.1 m
qult = 1.2 cNc + γ1 Df Nq + 0.4 γ2 BNγ
c =
𝒒𝒖
𝟐
=
200
2
= 100 kN/m2
B’ = B – 2 (e)
the useful width = 1.5- 2*0.2 = 1.1 m
If we use c > 0, ϕ = 0 analysis for cohesive soil, Fig 9.7 gives
Nc = 5.14 , Nq = 1.0 , Nγ = 0
γ1 = 50 , γ2 = 20.40 kN/m
3 , B = 1.1 m
qult = 1.2 (100) (5.14) + (20.40) (1.2) (1.0) + 0.4 (20.40) (1.1) (0) =
qult = 641.3 kN/m
2
FOS =
641.3
350
1.1∗1.5
= 3.02
B’
❑ Page :35 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
For cohesive soil, Fig 9.22 gives Re = 0.76
In this case, qult is computed based on actual width.
Eccentricity ratio =
𝒆𝒙
𝑩
=
0.2
1.5
= 0.13
qult = 1.2 cNc + γ Df Nq + 0.4 γ BNγ
qult = 1.2 (100) (5.14) + (20.40) (1.2) (1.0) + (0.4) (20.40) (1.5) (0)
qult = 641.3 kN/m
2
2. Using The Reduction factor method
Solution
= 641.3 * 0.76 = 487.4 kN/m2qult corrected for eccentricity = qult * Re
FOS =
𝟒𝟖𝟕.𝟒
𝟑𝟓𝟎
𝟏.𝟓∗𝟏.𝟓
= 3.13
B
❑ Page :36 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ If footing are on slopes, their bearing capacities are less
than if the footings were on level ground
❑ Ultimate bearing capacity for continuous footing on
slope is given by:
4. FOOTING ARE ON SLOPES
qult = cNcq +
𝟏
𝟐
γ2 BNγq eqn 9.9
❑ Page :37 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Page :38 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
A bearing wall for a building is to be located close to a slope. The GWT is located at a
great depth. Determine the allowable bearing capacity using a FOS of 3
Example 6
❑ Page :39 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
β = 30o ,
𝒃
𝑩
=
𝟏.𝟓 𝒎
𝟏.𝟎 𝒎
=1.5, Chart
qult = cNcq +
𝟏
𝟐
γ2 BNγq
From Fig 9.25b with ϕ = 30o,
c = 0 , γ2 = 19.50 kN/m
3 ,
B = 1.0 m
𝑫𝒇
𝑩
=
𝟏.𝟎 𝒎
𝟏.𝟎 𝒎
= 1.0 (use dashed line)
Nγq = 40
qult = (0) (Nγq ) + (1/2) (19.50) (1.0) (40)
qult =390 kN/m
2
qa =
𝟑𝟗𝟎
𝟑
= 130 kN/m2
Solution:
❑ Page :40 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
DEIGN OF SHALLOW FOUNDATION
❑ Bearing Capacity and Shallow Foundations Topic No. 10
DEIGN OF FOOTINGS (SIZE)
❑ After the soil’s allowable bearing capacity has been determined, the footing’s required
area can be determined by dividing the footing load by the allowable bearing capacity
❑ The following example illustrates how it’s computed
qnet = qult – γ1 Df
Qnet, all =
𝒒𝒖𝒍𝒕
𝑭𝑶𝑺=𝟑
qult = 1.2 cNc + γ1 Df Nq + 0.4 γ2 BNγ
❑Net Ultimate Bearing Capacity
❑Ultimate Bearing Capacity
❑Net allowable Bearing Capacity (Net Safe)
To be USED IN FOOTING DESIGN
❑ Page :41 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
TERZAGHI’S GENERAL EQUATION:
qult = c . Nc . λc + γ1*Df . Nq . γ λ q + γ2 . B . Nγ . λγ
Where
qu : Effective pressure at founding level = γ1 . Df
c2 : Cohesion below founding level.
qo : Effective stress above founding level = γ1 . Df
γ1 : Unit weight of soil above founding level.
Df : Depth of founding level.
γ2 : Unit weight of soil below founding level.
B : width of the footing.
Nc , Nq and Nγ : Terzaghi’s bearing capacity factors, Table 3.1.
λc , λq and λγ : Terzaghi’s bearing capacity factors shape factors, Table 3.2.
❑ Page :44 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
Code’s shape factors
Footing Shape λc λq λγ
Strip 1.0 1.0 1.0
Rectangular 1 + 0.30 *
B
L
1 + 0.30 *
B
L
1 – 0.30 *
B
L
Square & Circular 1.3 1.3 0.7
Terzaghi’s shape factors
Footing Shape λc λq λγ
Strip 1.0 1.0 0.5
Square 1.3 1.0 0.4
Circular 1.3 1.0 0.3
❑ Page :45 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
A square footing rests on a uniform thick deposit of stiff clay
with qu = 115 kN/m
2. The footing is located 1.2m below the
gound surface & is to carry a total load of 1250 kN.
❑ = 19.60 kN/m3
❑ GWT is at great depth
❑ Determine the necessary square footing dimensions using
a FOS of 3
Example 7
❑ Page :42 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
γ1 = γ2 = 19.6 kN/m
3
From Fig 9.7,
Nc = 5.14 , Nq = 1.0 , Nγ = 0
qult = 1.2 (62) (5.14) + (19.6) (1.5) (1.0)
qult = 411.816 kN/m
2
qnetall =
𝒒𝒖𝒍𝒕
𝟑
= 129.4 kN/m2
qult = 1.2 cNc + γ1 Df Nq + 0.4 γ2 BNγ
c =
𝒒𝒖
𝟐
=
124
2
= 62 kN/m2
Required footing area =
𝟏𝟐𝟓𝟎
𝟏𝟐𝟗.𝟒
= 9.65 km2
B2 = 9.65 m2 , B = 3.10 m
Use B = 3.10 mqnet = qult – γ1 Df = 411.816 -19.6*1.2 =388.3
Solution:
❑ Page :43 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
Find out the allowable bearing capacity of a clayey soil supporting a square
footing 2.20 * 2.20 m2. The footing is founded at a depth 2.0 m below the
ground level. The bulk unit weight of the soil is 2.0 t/m3. An undisturbed
sample of the clay was tested and the unconfined compressive strength was
found to be 8.0 t/m2.
Example 8
❑ Page :46 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
= 4.0 * 5 * 1.30 + 2.0 * 2.0 * 1 * 1.30 + 2.0 * 2.20 * zero * 0.70 = 31.20 t/m2
Using Code
qu = c2 . Nc . λc + γ1 . Df . Nq . λq + γ2 . B . Nγ . λγ
Where:
Soil is clay
φ = zero & c =
𝐪𝐮𝐧
𝟐
=
8.0
2
= 4.0 t/m2
Solution:
❑ Page :47 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
Φ = zero
Nc = 5, Nq = 1 and Nγ = zero
Square footing
λc = λq = 1.30 and λγ = 0.70
qnu = qu – γ1 . Df
= 31.20 – 2.0 * 2.0 = 27.20 t/m2
qna =
𝐪𝐧𝐚
𝐅 .𝐒
=
27.20
3
= 9.67 t/m2
Solution:
❑ Page :48 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Contact pressure refers to the pressure acting between a footing’s base & the soil below.
❑ The pressure distribution beneath a footing varies depending on the footing
❑ shape,
❑ rigidity
❑ depth
❑ type of soil
CONTACT PRESSURE [Rigid footing & Uniform stress]
❑ Page :49 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Footing may also fail as a result of excessive settlement
❑ Thus, after the size of the footing has been determined by bearing
capacity analysis, footing settlement should be calculated & the design
revised if calculated settlement is excessive
❑ Calculation of settlement has been covered in chapter 7
TOTAL & DIFFERENTIAL SETTLEMENT
❑ Page :56 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ The required base of the footing may be determined by dividing the column
load by the allowable bearing capacity
❑ Determining the thickness and shape of the footing and amount & location
of reinforcement are ultimately the responsibility of a structural engineer
❑ In general, the geotechnical engineer furnishes the contact pressure diagram
& the shear & moment at section at the face of column, pedestal or wall
STRUCTURAL DESIGN OF FOOTINGS
❑ From this information, the structural engineer can do the actual
structural design of the footing
❑ Page :57 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
❑ Page :58 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
STRUCTURAL DESIGN OF FOOTINGS
RECIPE FOR SUCCESS,
As long as you live, Just Keep
L e a r n i n g …
References
• 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.
❑ Page :59 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Bearing Capacity and Shallow Foundations Topic No. 10
• 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.
Prince Sultan University, Riyadh, Saudi Arabia, 2019-2020
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
Construction Management Program (CMP)
Lateral Earth Pressure & Retaining Structures
Topic No. 12
Topic (12)
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
LATERAL EARTH PRESSURE
❑ Lateral Earth Pressure & Retaining Structures Topic No. 1
2
❑ Page :2 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
LATERAL EARTH PRESSURE
1.1 Introduction
Many theories are developed to
estimate the acting lateral earth
pressure, each theory has its own
assumptions. So during application, it
should be considered the compatibility
between the theory and the retaining
structure conditions.
RANKINE’S THEORY (1857)
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :3 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
A retaining wall 6.00 m high has a smooth vertical back. The backfill is sand
with a horizontal surface at the top of the wall. The density of the backfill is
1.80 t/m3 , its angle of shearing resistance (angle of internal friction) is 30o.
There is a ground water table located at depth 2.00 m below ground surface.
Draw active pressure distribution diagram, and find its magnitude and point of
application per unit length of the wall.
Example
1
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :4 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Since the wall with smooth back
Rankine theory can be used
Soil is sand
ϕ = 30 & c = zero
=
1 −sin 30
1+sin 30
= 0.3
3
Pa1 = (1.80 * 0) * 0.33 = Zero
Pa = (q + Σγ . H) . Ka – 2c √Ka
Ka =
𝟏−𝐬𝐢𝐧 𝝓
𝟏+𝐬𝐢𝐧 𝝓
Pressure distribution:
Pa2 = (1.80 * 2.0) * 0.33 = 1.19 t/m
2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :5 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Pw = γw . hw
Pa3 = (1.80 * 2.0 + 0.80 * 4.0) * 0.33 = 2.24 t/m
2
= 1.00 * 4.0 = 4.00 t/m2
Magnitude of the pressure & and point of application:
Force Value Location Value
Pa1 0.50 . Pa2 . H1 = 0.50 * 1.19 * 2.0 = 1.19 y1
H1
3
+ 4.00 =
2
3
+ 4.00
= 4.67
Pa2
0.50 . (Pa2 – pa1) . H
0.50 * (6.89 – 0.82) * 8.0 = 24.28
y2
H
3
=
8.00
3
= 2.67
Pa3
0.50 . (pa3 – pa2) .
H2
0.50 * (2.24 – 1.19) * 4.0 = 2.10
y3
H2
3
=
4.00
3
= 1.33
Pw 0.50 . pw . Hw = 0.50 * 4.0 * 4.0 = 8.00 yw
H𝑤
3
=
4.00
3
= 1.33
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :6 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Pa = Pa1 + Pa2 + pa3 + pw = 1.19 + 4.76 + 2.10 + 8.00 = 16.05 t/m’
Pa . Y = Pa1 . y1 + Pa2 . y2 + pa3 . y3 + pw . yw
16.05 * Y = 1.19 * 4.67 + 4.76 * 2.00 + 2.10 * 1.33 + 8.00 * 1.33
Y = 1.78 m
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :7 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
A retaining wall 8.00 m high has a smooth vertical back, the wall supports a
cohesive backfill with a horizontal surface at the top of the wall. The density of
the backfill is 1.80 t/m3 , its cohesion 0.25 kg/cm2. Calculate the depth of tension
cracks behind the wall, draw active pressure distribution diagram, and find its
magnitude and point of application per unit length of the wall.
Example 2
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :8 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Since the wall with smooth back
Rankine theory can be used
Soil is clay
ϕ = zero & c = 2.50 t/m2
=
1 −sin(𝑧𝑒𝑟𝑜)
1+sin(𝑧𝑒𝑟𝑜)
= 1.00
Pa = (q + Σγ . H) . Ka – 2c √Ka
Ka =
𝟏−𝐬𝐢𝐧 𝝓
𝟏+𝐬𝐢𝐧 𝝓
Pressure distribution:
Pa1 = (1.80 * 0) * 1.00 – 2 * 2.50 * √1.00 = 5.00 t/m
2
Pa2 = (1.80 * 8) * 1.00 – 2 * 2.50 * √1.00 = 9.40 t/m
2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :9 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Pa = (q + Σγ . H) . Ka – 2c √Ka
0.0 = (1.80 * Zcr) * 1.00 – 2 * 2.50 * √1.00
Depth of tension Cracks (at pa = 0.0):
Zcr = 2.78 m
Magnitude of the pressure & and point of application:
Force Value Location Value
Pa
0.50 . Pa2 . (H – Zcr)
0.5 * 9.40 * (8 – 2.78) = 24.53 t/m’
y
H−Zcr
3
=
8.00 −2.78
3
= 1.74 m
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :10 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
A retaining wall 7.00 m high has a smooth vertical back, the wall supports a
cohesive backfill with a horizontal surface at the top of the wall. The backfill has
the following properties:
for the top 3.00 m , γ = 1.75 t/m3 , ϕ = 15o and c = 0.15 kg/cm2 ,
and for the lower 4.00 m , γ = 1.85 t/m3 , γsub = 0.95 t/m
3 , ϕ = 20o and c = 0.10
kg/cm2 .
A ground water table is located at depth 5.00 m. Determine the depth of tension
cracks behind the wall, draw active pressure distribution diagram, and find its
magnitude and point of application per unit length of the wall.
Example 3
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :11 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Since the wall with smooth back
Rankine theory can be used
=
1 −sin 15
1+sin 15
= 0.59Ka1 =
𝟏−𝐬𝐢𝐧 𝝓𝟏
𝟏+𝐬𝐢𝐧 𝝓𝟏
Pressure distribution:
=
1 −sin 20
1+sin 20
= 0.49Ka2 =
𝟏−𝐬𝐢𝐧 𝝓𝟐
𝟏+𝐬𝐢𝐧 𝝓𝟐
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :12 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Pa = (q + Σγ . H) . Ka – 2c √Ka
Pa1 = (1.75 * 0) * 0.59 – 2 * 1.50 * √0.59 = 2.30 t/m
2
Pa2 = (1.75 * 3) * 0.59 – 2 * 1.50 * √0.59 = 0.79 t/m
2
Pa3 = (1.75 * 3) * 0.49 – 2 * 1.00 * √0.49 = 1.17 t/m
2
Pa4 = (1.75 * 3 + 1.85 * 2) * 0.49 – 2 * 1.00 * √0.49 = 2.99 t/m
2
Pa5 = (1.75 * 3 + 1.85 * 2 + 0.95 * 2) * 0.49 – 2 * 1.00 * √0.49 = 3.92 t/m
2
Pw = γw . hw = 1.00 * 2 = 2.00 t/m
2
Pa = (q + Σγ . H) . Ka – 2c √Ka
0.0 = (1.75 * Zcr) * 0.59 – 2 * 1.50 * √0.59
Depth of tension Cracks (at pa = 0.0):
Zcr = 2.23 m
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :13 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Magnitude of the pressure & and point of application:
Force Value Location Value
Pa1
0.50 . Pa2 . (3 – Zcr)
0.50 * 0.79 * (3 – 2.23) = 0.30
y1
3 −Zcr
3
+ 4.00 =
3 −2.23
3
+
4.00 = 4.26
Pa2 Pa3 * 2 = 1.17 * 2.0 = 2.34 y2
2
2
+ 2 = 3.00
Pa3
0.50 . (pa4 – pa3) . 2
0.50 * (2.99 – 1.17) * 2 = 1.82
y3
2
3
+ 2 = 2.67
Pa4 Pa4 * 2 = 2.99 * 2.0 = 5.98 y4
2
2
= 1.00
Pa5
0.50 . (pa5 – pa4) * 2
0.50 * (3.92 – 2.99) * 2 = 0.93
y5
2
3
= 0.67
Pw 0.50 . pw . Hw = 0.50 * 2.0 * 2 = 2.00 yw
H𝑤
3
=
2.00
3
= 0.67
Pa = Pa1 + Pa2 + pa3 + pa4 + pa5 + pw = 13.37 t/m’
Pa . Y = Pa1 . y1 + Pa2 . y2 + pa3 . y3 + pa4 . y4 + pa5 . y5 + pw . yw
Y = 1.58 m
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :14 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
A retaining wall 4.00 m high has a smooth vertical back. The backfill
is sand with an inclined surface to horizontal with 15o . The density
of the backfill is 1.90 t/m3 , its angle of shearing resistance (angle of
internal friction) is 30o. Calculate the acting earth pressure in case of
active and passive conditions.
Example 4
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :15 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Since the wall with smooth back
Rankine theory can be used
In case of active condition:
Where:
β = 15 & ϕ = 30
Ka = Cos β
𝐂𝐨𝐬 𝜷 − 𝐂𝐨𝐬𝟐𝜷 − 𝐂𝐨𝐬𝟐𝜷
𝐂𝐨𝐬 𝜷+ 𝑪𝒐𝒔𝟐𝜷 − 𝑪𝒐𝒔𝟐𝜷
= 0.373
Pa = γ . H . Ka
Pa = 1.9 * 4 * 0.373 = 2.83 t/m
2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :16 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Pa = 0.50 . pa . H
Pa = 0.5 * 2.834 * 4 = 5.67 t/m’
Resultant of the pressure:
In case of passive condition:
Kp = Cos β
𝐂𝐨𝐬 𝜷+ 𝐂𝐨𝐬𝟐𝜷 − 𝐂𝐨𝐬𝟐𝜷
𝐂𝐨𝐬 𝜷− 𝑪𝒐𝒔𝟐𝜷 − 𝑪𝒐𝒔𝟐𝜷
= 2.502
Pp = γ . H . Kp
Pp = 1.9 * 4 * 2.502 = 19.01 t/m
2
Pp = 0.50 . pp . H
Pp = 0.5 * 19.01 * 4 = 38.03 t/m’
Resultant of the pressure:
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :17 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
RETAINING WALLS
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :18 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
1.4 RETAINING WALLS
1.4.1 Introduction
Retaining wall are structures
used to support earth or other
materials, the most common
types may be classified into five
main types as shown in Figure
1.2 and Figure 1.3 ; Gravity
walls, Semigravity walls,
Cantliver walls, Counterfort
walls and Buttress walls. This
classification based on the
method of achieving stability.
Figure 1.2: Types of retaining walls (a) Gravity wall (b) Semigravity wall
(c) Cantliver wall (d) Counterfort wall (e) Buttress wall
Figure 1.3: (a) Gravity wall in site (b) Buttress wall in site
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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1.4.2 Types of retaining walls
Gravity wall: depends upon its ownweight to resist the earth pressure, it is made of masonry or concrete and so
is proportioned that no tension is developed any where and the resultant of forces fails within the
middle third of the base.
Semi gravity wall: is intermediate between gravity and cantliver wall, a small amount of reinforcing steel is used
to reduce the mass of concrete.
Cantliver wall: is a reinforced concrete wall in the form of an inverted T, each projection of the wall acts as a
cantliver. The stability of this wall is partially provided by the weight of the soil on the heel portion
of the base. It is economical for walls of heights up to 6.00 to 7.50 m.
Counterfort wall: is used when the soil be retained is of greater height. The vertical slab and the base slab tied
together by counterforts placed at suitable intervals along the wall to reduce the bending
moments and shears. The vertical slab and heel slab act as continuous slab. The counterfort is
subjected to tensile forces.
Buttressed wall: is similar to counterfort wall except that counterforts called buttresses are provided in front of
the wall and in compression instead of tension. The buttresses reduce the clearance in front of
the wall and therefore their use is limited.
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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1.4.3 The common uses of retaining walls
Figure 1.4 shows the most common uses for
retaining walls such as;
❖ Side hill way or rail way
❖ Elevated high way or rail way
❖ Depressed high way or rail way
❖ Canal sides
❖ Flood wall
❖ Bridge abutment
❖ Retain earth fill around a building
❖ Granular material storage
❖ Erosion protection
Figure 1.4: The common uses for retaining walls
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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1.4.4 Stability of retaining walls
Retaining walls must proved adequate stability against sliding and overturning and it should have sufficient
factor of safety against bearing capacity failure. Also the retaining wall must be checked for total settlement
and overall stability.
1.4.4.1 Stability against overturning
A retaining wall must be stable about the Centre of rotation (the toe) against overturning. The lateral pressure
due to backfill and surcharge tends to rotate the retaining wall about its toe. This overturning moments is
stabilized by the weight of the backfill above the inner base (the hell slab) plus the weight of the wall. The
factor of safety against overturning is usually Taken as 1.50 for Cohesionless soil and 2.00 for cohesive soil, and
calculated as;
F.S =
𝐒𝐭𝐚𝐛𝐢𝐥𝐢𝐳𝐢𝐧𝐠 𝐦𝐨𝐦𝐞𝐧𝐭
𝐨𝐯𝐞𝐫𝐭𝐮𝐫𝐧𝐢𝐧𝐠 𝐦𝐨𝐦𝐞𝐧𝐭
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
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1.4.4.2 Stability against sliding
The horizontal component of the lateral pressure tends to cause the wall to slide along its base. The resisting
force against sliding is the friction, adhesion or combination of both which act along the bottom of the wall. The
factor of safety against sliding is usually to be 1.50, and calculated as;
F.S =
𝐑𝐞𝐬𝐢𝐬𝐭𝐚𝐧𝐜𝐞 𝐟𝐨𝐫𝐜𝐞
𝐝𝐫𝐢𝐯𝐢𝐧𝐠 𝐟𝐨𝐫𝐜𝐞
When the factor of safety is difficult to be attain, a key may be constructed under the base. It is common practice
to neglect the passive pressure of the soil in front of the wall unless the designer is cerain that this soil will not
be removed during the service life of the wall.
1.4.4.3 Stability of the base against bearing capacity failure
The ultimate soil pressure can be computed by any theoretical method and then divided by a suitable factor of
safety to obtain the allowable pressure. The factor of safety may taken as 2.00 for granular soils and 3.00 for
cohesive soil. In general, the base is a footing subjected to a horizontal load from the earth pressure and
eccentric vertical load. The pressure distribution below the base is obtained from Navier equation. The
maximum pressure at the toe must not exceed the allowable pressure on the soil.
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :23 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
SOLVED EXAMPLES
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :24 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Check the stability of the given
retaining wall to retain earth
embedment of 5.50 m high above
ground level, the foundation is to be
1.00 m deep. The net safe bearing
capacity is 1.20 kg/cm2 , the retained
soil as shown in Figure 2.10. A ground
water table is located as indicated in
Figure 2.14.
Note: Neglect the passive resistance.
Example 5
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :25 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Ka1 =
1 −sin 15
1+sin 15
= 0.59
Pa1 = 1.70 * zero * 0.59 – 2 * 4 * 0.59 = 6.14 t/m
2
Pa = γ . h . Ka – 2c √Ka
(a) Horizontal loads:
Rankine theory can be used
Assume the wall with smooth back
Ka2 =
1 −sin 32
1+sin 32
= 0.31
Pa2 = 1.70 * 3.5 * 0.59 – 2 * 4 * 0.59 = 2.53 t/m
2
Pa3 = 1.70 * 3.5 * 0.31 = 1.85 t/m
2
Pa4 = (1.70 * 3.5 + 0.95 * 3.0) * 0.31 = 2.73 t/m
2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :26 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
= 1.85 * 3 = 5.55 t/m’
Pa1 = pa3 * 3
y1 =
1
2
* 3 = 1.50 m
= 0.5 * (2.73 – 1.85) * 3 = 1.32 t/m’
Pa2 = 0.5 * (pa4 – pa3) * 3
y2 =
1
3
* 3 = 1 m
= 1 * 3 = 3.00 t/m2
Pw1 = γw * hw1
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :27 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
= 0.5 * 3 * 3 = 4.50 t/m’
Pw1 = 0.5 * pw1 * hw1
yw1 =
1
3
* 3 = 1.00 m
= 1 * 2 = 2.00 t/m2
Pw2 = γw * hw2
= 0.5 * 2 * 2 = 2.00 t/m’
Pw2 = 0.5 * pw2 * hw2
yw2 =
1
3
* 2 = 0.67 m
u1 = pw1 = 3.00 t/m
2 u2 = pw2 = 2.00 t/m
2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :28 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
The weights from wall, soil, uplift and moments about the toe are calculated:
W Weight
Value
(ton)
Arm (m)
Moment
(m.t)
W1 2.5 * (0.5 * 1.50 * 5.50) 10.31 0.50 +
2
3
* 1.50 = 1.50 15.47
W2 2.5 * (1 * 5.50) 13.75 1.50 +
1
2
= 2.0 27.50
W3 2.5 * (6.50 * 1) 16.25 4 – (
1
2
* 2.30) = 2.85 52.81
W4 1.70 * (3.5 * 3.5) + 1.95 * (3.5 * 2) 34.48 6.50 –
3.5
2
= 4.75 163.78
U1 – 6.50 * 2 13.00
6.50
2
= 3.25 – 42.25
U2 – 0.50 * 6.50 * (3 – 2) 3.25
2
3
* 6.50 = 4.33 – 14.07
ΣW 58.54 203.24
(b) Vertical loads:
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :29 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
• Against overturning:
(c) Check stability:
Overturning moment = Pa1 . y1 + Pa2 . y2 + (Pw1 * yw1 – Pw2 * yw2)
O.T.M = 5.55 * 1.50 + 1.32 * 1 + (4.50 * 1 – 2 * 0.67) = 12.81 m.t.
Stability moment = Σmoment due to vl loads
S.M = 203.27 m.t.
F.S =
𝐒 .𝐌
𝐎.𝐓.𝐌
=
203.27
12.81
= 15.86 > 1.50 o.k.
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :30 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
• Against sliding:
Sliding force = Pa1 + Pa2 + (Pw1 – Pw2)
S.F = 5.55 + 1.32 + 4.50 – 2.00 = 9.37 t/m2
Resisting force = Resulting friction from vl loads
R.F = Σ(W – U) . tanδ
= 58.54 * tan
3
4
32 = 26.06 t/m’
F.S =
𝑹.𝑭
𝑺.𝑭
=
26.06
9.37
= 2.78 > 1.50 o.k.
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :31 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Eccentricity from base mid:
The total net moment = (S.M – O.T.M)
= 203.24 – 12.81= 190.43 m.t
The total vertical load = 58.54 ton
Distance of resultant ത𝐱 from toe is:
ത𝐱 =
𝟏𝟗𝟎.𝟒𝟑
𝟓𝟖.𝟓𝟒
= 3.24 m
e =
𝐁
𝟐
– ത𝐱
• Against bearing capacity failure:
=
6.5
2
– 3.24 = 0.01 < B/6 in the middle third
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :32 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
qtoe =
𝚺𝐰
𝐁𝐋
𝟏 +
𝟔 𝐞
𝐁
=
58.54
6.5 ∗1
1 +
6 ∗0.01
6.5
= 9.09 t/m2 < qall.
qheel =
𝚺𝐰
𝐁𝐋
𝟏 −
𝟔 𝐞
𝐁
=
58.54
6.5 ∗1
1 −
6 ∗0.01
6.5
= 8.92 t/m2 < qall.
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :33 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Design a cantilever wall to retain a bank of earth
4.8 m high above ground level. The bottom of
the base is 1.2 m below ground level. The soil
has a density of 1.8 t/m3 and angle of internal
friction of 30o. The surface of the bank is
horizontal and is subjected to surcharge of 1.5
t/m2. Check stability and calculate straining
actions only for concrete design.
Example 6
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :34 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
=
1 −sin 30
1+sin 30
= 0.33
(a) Horizontal loads:
Rankine theory can be used
Assume the wall with smooth back
Ka =
𝟏 −𝐬𝐢𝐧 𝝓
𝟏−𝐬𝐢𝐧 𝝓
Kp =
1
ka
= 3.00
Pa = (q + γ . h) Ka
Pa1 = (1.5 + 1.80 * 0) * 0.33 = 0.50 t/m
2
Pa2 = (1.5 + 1.80 * 6) * 0.33 = 4.10 t/m
2
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :35 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
= 0.50 * 6 = 3 t/m’
Pa1 = pa1 . H
y1 =
1
2
* 6 = 3 m
= 0.50 * (4.10 – 0.50) * 6 = 10.80 t/m’
Pa2 = 0.50 . (pa2 – pa1) . H
y2 =
1
3
* 6 = 2 m
Pp = γ . h . Kp
= 1.80 * 1.2 * 3 = 6.48 t/m2
Pp = 0.50 . pp . h
= 0.50 * 6.48 * 1.2 = 3.89 t/m’
yp =
1
3
* 1.2 = 0.40 m
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :36 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
The weights from wall, soil, surcharge and moments about the toe are calculated:
W Weight
Value
(ton)
Arm (m)
Moment
(m.t)
W1 2.5 * (0.5 * 0.25 * 5.5) 1.720 1.4 + (
2
3
* 0.25) = 1.57 2.70
W2 2.5 * (0.3 * 5.5) 4.125
1.4 + 0.25 + (
1
2
* 0.30)
= 1.80
7.43
W3 2.5 * (0.5 * 4) 5.000
1
2
* 4.00 = 2.00 10.0
W4 1.8 * (2.05 * 5.5) 20.440 4 – (
1
2
* 2.05) = 2.975 60.80
W5 1.5 * 2.05 3.075 2.975 9.15
ΣW 34.36 90.08
(b) Vertical loads:
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :37 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
• Against overturning:
(c) Check stability:
Overturning moment = Pa1 . y1 + Pa2 . y2
O.T.M = 3.00 * 3 + 10.8 * 2 = 30.6 m.t.
Stability moment = Σmoment due to vl loads + Σmoment due to passive (neglected)
S.M = 90.08 – 9.15 = 80.93 m.t.
F.S =
𝐒 .𝐌
𝐎.𝐓.𝐌
=
80.93
30.60
= 2.64 > 1.50 o.k.
Note:
the surcharge load must not considered in any stabilizing computations.
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :38 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
R.F = Σ(W – W5) . tanδ + Pp
= (34.36 – 3.075) * tan
2
3
30 + 3.888 = 15.28 t/m’
F.S =
𝑹.𝑭
𝑺.𝑭
=
15.28
13.80
= 1.11 > 1.50 Not satisfied
• Against sliding:
Sliding force = Pa1 + Pa2
S.F = 3.00 + 10.80 = 13.80 t/m’
Resisting force = Resulting friction from vl loads + Pp
Solution:
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ 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
• 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.
❑ Lateral Earth Pressure & Retaining Structures Topic No. 12
❑ Page :40 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
• 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.
Prince Sultan University, Riyadh, Saudi Arabia, 2019-2020
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
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑
o
o
❑
INTRODUCTION
❑ Water in Soil Topic No. 6
❑ Page :2 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
TYPES OF WATER IN SOIL
•
•
•
•
•
❑ Structural water
❑ Absorbed (Free) water
❑ Water in Soil Topic No. 6
❑ Page :3 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
SOIL PERMEABILITY
Permeability is defined as:
q = k . i . A Darcy’s Law
❑ Water in Soil Topic No. 6
❑ Page :4 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
o
o
FLOW OF WATER IN SOILS
❑ Hydraulic gradient, i = h/L
❑ Water in Soil Topic No. 6
❑ Page :5 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
❑
❑
FLOW OF WATER IN SOILS
q = k
𝒉
𝑳
A eqn 5.
1
q = kiA eqn 5.2
❑ Water in Soil Topic No. 6
❑ Page :6 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
❑
❑
❑
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
❑ Page :7 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
vactual
vactual =
𝒗(𝟏+𝒆)
𝒏
eqn 5.5
𝐞
(𝟏+𝐞)
SEEPAGE VELOCITY (𝒗) AND VOID RATIO
❑ Water in Soil Topic No. 6
❑ Page :8 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
= 0.160 m
❑ Water in Soil Topic No. 6
❑ Page :9 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Page :10 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
o
o
❑ Water in Soil Topic No. 6
❑ Page :11 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Page :12 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Solution:
DETERMINATION OF COEFFICIENT OF
PERMEABILITY K
❑ Water in Soil Topic No. 6
❑ Page :13 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
FLOW OF WATER IN SOILS
❑
▪
▪
▪ Falling-head Test ▪ Constant-head Test
❑ Water in Soil Topic No. 6
❑ Page :14 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
▪
▪
▪
▪
▪
▪
▪
▪
▪
Constant-head method
❑ Water in Soil Topic No. 6
❑ Page :15 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Page :16 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
o
o
o
o
o
o
❑
❑ Water in Soil Topic No. 6
❑ Page :17 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
o
o
o
o
o
o
❑ Water in Soil Topic No. 6
❑ Page :18 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Solution:
❑
❑
❑
Falling-head method
❑
▪
▪
▪
❑ Water in Soil Topic No. 6
❑ Page :19 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
➢ −
➢
➢
q =
−𝐝𝐡
𝐝𝐭
. a
K = 2.3
𝐚 .𝐋
𝐀 .𝐭
log10
𝐡𝟏
𝐡𝟐
Falling-head method
❑ Water in Soil Topic No. 6
❑ Page :20 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
o
o
o
o
o
o
❑
❑ Water in Soil Topic No. 6
❑ Page :21 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
o
o
o
o
o
o
❑ Water in Soil Topic No. 6
❑ Page :22 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Solution:
❑
o
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
❑ Page :23 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
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
❑ Page :24 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
PERMEABILITY OF STRATIFIED SOIL
❑ Water in Soil Topic No. 6
❑ Page :25 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
PERMEABILITY OF STRATIFIED SOIL
▪
▪
▪
➢
➢
o
o
❑ Water in Soil Topic No. 6
❑ Page :26 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Page :27 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Page :28 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑ Water in Soil Topic No. 6
❑ Page :29 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Page :30 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Solution:
❑
❑
CAPILLARY RISE IN SOILS
h =
𝟒𝑻
𝒅γ
eqn 5-39
h =
𝟎.𝟎𝟑𝟎
𝒅
eqn 5-40
❑ Water in Soil Topic No. 6
❑ Page :31 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Page :32 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Example 6
❑
CAPILLARY RISE IN SOILS
h =
𝑪
𝒆𝑫𝟏𝟎
eqn 5-41
❑ Water in Soil Topic No. 6
❑ Page :33 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
FLOW NETS & SEEPAGE
❑ Water in Soil Topic No. 6
❑ Page :34 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
❑
❑
FLOW NETS & SEEPAGE
q =
𝒌∗𝒉∗𝑵𝒇
𝑵𝒅
❑ Water in Soil Topic No. 6
❑ Page :35 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Water in Soil Topic No. 6
❑ Page :36 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Page :37 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Page :38 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
o
o
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.
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
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
TENTATIVE WEEKLY COURSE SCHEDULE
WEEK UNIT/ TOPIC
Number of Contact
hour
s
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
❑ Soil Compaction Topic No. 5
DEFINITION & PURPOSE OF COMPACTION
❑
❑
o
o
o
❑
❑ Soil Compaction Topic No. 5
❑ Page :2 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
DEFINITION & PURPOSE OF COMPACTION
𝛾𝑑
=
𝛾
1 + 𝑤𝑐
❑
❑
❑
❑ Soil Compaction Topic No. 5
❑ Page :3 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
LABORATORY COMPACTION TEST
❑
o
o
❑
o
❑ Soil Compaction Topic No. 5
❑ Page :4 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
LABORATORY COMPACTION TEST
o Proctor Test:
Video: Proctor Test.
❑ Soil Compaction Topic No. 5
❑ Page :5 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
•
LABORATORY COMPACTION TEST
o Proctor Test:
❑ Soil Compaction Topic No. 5
❑ Page :6 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
❑
LABORATORY COMPACTION TEST
o Proctor Test:
Lab. Test
❑ Soil Compaction Topic No. 5
❑ Page :7 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
LABORATORY COMPACTION TEST
❑
❑
o Proctor Test:
❑ Soil Compaction Topic No. 5
❑ Page :8 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
LABORATORY COMPACTION TEST
4.2eqn
1
s
ws
wG
G
ZAV +
=
o Proctor Test:
❑ Soil Compaction Topic No. 5
❑ Page :9 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
❑
❑
❑
o
o
Example 1
❑ Soil Compaction Topic No. 5
❑ Page :10 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
Solution:
γ =
𝑾
𝑽
γ =
𝟒𝟎𝟎𝟎 −𝟐𝟎𝟐𝟑
𝟗𝟒𝟒
= 2.09 g/cm3 = 20.9 kN/m3
γd =
𝜸
𝟏+𝒘
γd =
𝟐𝟎.𝟗 𝒌𝑵/𝒎𝟑
𝟏+𝟎.𝟏𝟎
= 19 kN/m3
❑ Soil Compaction Topic No. 5
❑ Page :11 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
❑
❑
Test No. 1 2 3 4 5
Dry unit weight (kN/m3) 17.61 18.32 18.57 18.09 17.11
Moisture content 7.1 10.0 13.4 16.7 20.1
Example 2
❑ Soil Compaction Topic No. 5
❑ Page :12 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
o
o
𝛾𝑑 =
𝛾
1 + 𝑤𝑐
Solution:
❑ Soil Compaction Topic No. 5
❑ Page :13 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
FACTORS AFFECTING COMPACTION OF SOIL
❑ Compaction of soil can be affected by:
❑ Soil Compaction Topic No. 5
❑ Page :14 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
o
•
•
•
•
o
B. COMPACTION EFFORT
❑
FACTORS AFFECTING COMPACTION OF SOIL
❑ Soil Compaction Topic No. 5
❑ Page :15 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
o Max dry unit weight & optimum moisture content can be affected by:
❖
•
•
FACTORS AFFECTING COMPACTION OF SOIL
C. TYPE OF SOILS
❑ Soil Compaction Topic No. 5
❑ Page :16 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
o
o
o
o
FACTORS AFFECTING COMPACTION OF SOIL
C. TYPE OF SOILS
❑ Soil Compaction Topic No. 5
❑ Page :17 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
o
o
C. TYPE OF SOILS
FACTORS AFFECTING COMPACTION OF SOIL
❑ Soil Compaction Topic No. 5
❑ Page :18 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
o
o
❑
FIELD COMPACTION
❑ Soil Compaction Topic No. 5
❑ Page :19 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
o
o
FIELD COMPACTION
❑ Tampers
o
o
o
❑ Soil Compaction Topic No. 5
❑ Page :20 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑Rollers
o
▪
▪
▪
▪
▪
FIELD COMPACTION
❑ Soil Compaction Topic No. 5
❑ Page :21 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
o
▪
▪
→
▪
FIELD COMPACTION
❑ Soil Compaction Topic No. 5
❑ Page :22 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
▪
▪
▪
▪
FIELD COMPACTION
❑ Soil Compaction Topic No. 5
❑ Page :23 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
✓
✓
FIELD COMPACTION
❑ Soil Compaction Topic No. 5
❑ Page :24 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
FIELD COMPACTION
❑ Soil Compaction Topic No. 5
❑ Page :25 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
DYNAMIC COMPACTION
❑
❑
❑
Ground improvement technique
❑ Soil Compaction Topic No. 5
❑ Page :26 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
EFFECT OF DYNAMIC COMPACTION ON SOIL
• In Cohesive soils:
❑ Soil Compaction Topic No. 5
❑ Page :27 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
❑
▪
▪
▪
DYNAMIC COMPACTION
• In Cohesionless soils:
❑ Soil Compaction Topic No. 5
❑ Page :28 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
1. Approximate depth of influence, (D):
o For cohesionless soils:
o For cohesive soils:
❑
CALCULATIONS OF DYNAMIC COMPACTION
4.3Eqn 5.0 WhD =
dropped dist ance
weight
4.4 Eqn.
=
=
=
h
W
WhD
❑ Soil Compaction Topic No. 5
❑ Page :29 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
DYNAMIC COMPACTION
❑
❑
❑ Soil Compaction Topic No. 5
❑ Page :30 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
FIELD CONTROL OF COMPACTION
❑ Soil Compaction Topic No. 5
❑ Page :31 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
❑
o
o
o
o
IN-PLACE SOIL UNIT WEIGHT TEST
❑ Soil Compaction Topic No. 5
❑ Page :32 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
SAND CONE TEST
Video: Sand Cone test.
https://www.youtube.com/watch?v=VxRQJ8s7
eK8
❑ Soil Compaction Topic No. 5
❑ Page :33 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
o
o
IN-PLACE SOIL UNIT WEIGHT TEST
❑ Soil Compaction Topic No. 5
❑ Page :34 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
o
o
o
o
o
❑
Example 3
❑ Soil Compaction Topic No. 5
❑ Page :35 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Weight of sand used in test hole
= Weight of sand to fill test hole & funnel – Weight of sand to fill funnel
= 867 g – 319 g = 548 g
Volume of test hole =
𝟓𝟒𝟖 𝒈
𝟏𝟓𝟑𝟖 𝒈 /𝒄𝒎𝟑
= 356 cm3
Wet unit weight of soil in – place =
𝟕𝟒𝟕 𝒈
𝟑𝟓𝟔 𝒄𝒎𝟑
= 2.1 g/cm3 = 21 kN/m3
From eqn 4.1,
γd =
𝜸
𝟏+𝒘
γd =
𝟐𝟏 𝒌𝑵/𝒎𝟑
𝟏+𝟎.𝟏𝟑𝟕
= 18.4 kN/m3
Solution:
❑ Soil Compaction Topic No. 5
❑ Page :36 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
o
o
FIELD CONTROL OF COMPACTION
❑
❑
o
o
o
o
❑ Soil Compaction Topic No. 5
❑ Page :37 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
o
o
❑
o
o
❑
Example 4
❑ Soil Compaction Topic No. 5
❑ Page :38 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
=
𝒊𝒏 −𝒑𝒍𝒂𝒄𝒆 𝒅𝒓𝒚 𝒖𝒏𝒊𝒕 𝒘𝒆𝒊𝒈𝒉𝒕
𝒎𝒂𝒙 𝒍𝒂𝒃 𝒅𝒓𝒚 𝒖𝒏𝒊𝒕 𝒘𝒆𝒊𝒈𝒉𝒕
* 100
=
𝟏𝟖.𝟓
𝟏𝟖.𝟔
* 100 = 98.9%
Solution:
❑ Soil Compaction Topic No. 5
❑ Page :39 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
❑
❑
❑
Example 5
❑ Soil Compaction Topic No. 5
❑ Page :40 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
= total dry weight of soil required to be excavated
from the borrow pit
= (18.90 kN/m3) (15.000 m3) = 283.500 kN
=
𝟐𝟖𝟑.𝟓𝟎𝟎
𝟏𝟕.𝟏𝟖
= 16.500 m3
Solution:
❑ Soil Compaction Topic No. 5
❑ Page :41 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
• 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.
❑ Soil Compaction Topic No. 5
❑ Page :42 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
• 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.
Conducted by: Offered to :
Riyadh, Saudi Arabia, 2019-202
0
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
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
mailto:mezzat@psu.edu.sa
❑ Page :2 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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
❑ Revision Extra Tutorial Class
SOIL CLASSIFICATION &
SOIL EXPLORATION
❑ Page :3 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
INTRODUCTION
•
•
•
❑ Page :4 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
GENERAL TYPES OF SOIL
❑ Page :5 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
• Soil Colour, and bulky shape.
• Soil Textural Class [Grain size].
• Density of Soil [bulk, dry, saturated,
Submerged].
• Pore Space [water content, void ratio,
degree of saturation, porosity].
• Soil Consistence [Atterberg Limits].
PROPERTIES OF SOIL
Physical properties Chemical
properties
Engineering properties
(Mechanical properties)
• Soil Strength (stresses at failure).
• Soil deformation (settlement).
• Soil water behavior and its effect
in soil mass.
• Soil Structure [Composition].
• Minerals
• chemical analysis
❑ Page :6 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
PHASES SYSTEM OF SOILS
•
•
Voids (air or
water)
Solid Particles
❑ Page :7 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
SOIL GRAIN SIZE DISTRIBUTION
❑ Page :8 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
Classification
Test
Soil
Type
Atterberg Limits
Hydrometer Analysis
Sieve Analysis
Classification of Soil
Non-Cohesive soil Cohesive soil
❑ Page :9 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
Example .1
Sieve number 4 10 20 40 60 100 200 Pan
Sieve diameter
(mm)
4.75 2.0 0.85 0.425 0.250 0.150 0.075 Pan
Weight retained
(gm)
28 42 48 128 221 86 40 24
❑ Page :10 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
Step (1): Determine finer percentage % :
Sieve
No.
Opening
mm
Mass
retained
gm
% Retained
on each sieve
(R%)
∑
%Retained
% Pass
F%
4 4.75 28 4.54 4.54 95.5
10 2.00 42 6.81 11.35 88.7
20 0.85 48 7.78 19.13
80.9
40 0.425 128 20.74 39.87
60.1
60 0.250 221 35.81 75.68
24.3
100 0.15 86 13.94 89.62 10.4
200 0.075 40 6.49 96.11 3.9
pan – 24 3.89 100 0
Total mass (m) = 617 gm 100%
Solution: 𝒎𝒂𝒔𝒔 𝒓𝒆𝒕𝒂𝒊𝒏𝒆𝒅 𝒐𝒏 𝒆𝒂𝒄𝒉 𝒔𝒊𝒆𝒗𝒆
𝒕𝒐𝒕𝒂𝒍 𝒎𝒂𝒔𝒔
∗ 𝟏𝟎𝟎
=
Check !
❑ Page :11 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
Step (2): Draw Grain Size Distribution Curve:
•
•
Solution:
Semi Log Scale Paper
95.5
88.7
80.9
60.1
24.3
10.4
3.9
0
10
20
30
40
50
60
70
80
90
100
0.01 0.1 1 10
P
a
s
s
P
e
r
c
e
n
ta
g
e
%
Particle Size (mm)
Grain Size Distribution
% Pass
❑ Page :12 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
0
10
20
30
40
50
60
70
80
90
100
0.01 0.1 1 10
P
a
s
s
P
e
rc
e
n
ta
g
e
%
Particle Size (mm)
% Pass
D10 = 0.16mm Ans.
Step (3): Obtain D10 , D30 , D60 :
Solution:
D30 = 0.28mm Ans.
D60 = 0.42mm Ans.
D10
D30
D60
❑ Page :13 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
Solution:
Step (4): Calculate Cu, and CC:
CU =
𝐃
𝟔𝟎
𝐃
𝟏𝟎
CC =
𝐃
𝟑𝟎
𝟐
𝐃
𝟔𝟎
. 𝐃𝟏𝟎
= 0.42/0.16 = 2.625
= 1.167
= 0.282/(0.42*0.16)
• Uniformity coefficient (Cu);
• Coefficient of gradation (CC );
Poorly Graded Course Grained Soil (GP or SP) ??
D10 = 0.16 mm
D30 = 0.28 mm
D60 = 0.42 mm
❑ Page :14 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
0
10
20
30
40
50
60
70
80
90
100
0.01 0.1 1 10
P
a
s
s
P
e
rc
e
n
ta
g
e
%
Particle Size (mm)
% Pass
Step (5): Percentages of different Components
Solution:
sand
Clay+ silt
– Form grading curve:-
• % Fines (% Clay + % Silt)
[0- 0.075 mm] = 3.9%
• % Sand
[0.075-4.75 mm] = 88.7 – 3.9
= 84.8%
• % Gravel
[4.75- 75 mm] = 100 – 88.7 = 11.3%
Gravel
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Step (5): Percentages of different Components
Solution:
– Form grading Table:-
• % Fines (% Clay + % Silt)
[0- 0.075 mm] = 3.9%
• % Sand
[0.075-4.75 mm] = 88.7 – 3.9
= 84.8%
• % Gravel
[4.75- 75 mm] = 100 – 84.8 – 3.9 = 11.3%
Sand
Clay
Gravel
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•
PARTICLE SIZE DISTRIBUTION CURVE:
•
•
❑ Page :18 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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CONSISTENCY LIMITS
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Test No. Tin weight (gm) Tin + wet soil (gm) Tin + dry soil (gm) No. of blows
1 23.68 40.86 34.68 13
2 22.93 42.62 35.78 20
3 26.27 38.02 34.27 47
• Plastic limit test:
Test No. Tin weight (gm) Tin + wet soil (gm) Tin + dry soil (gm)
1 25.34 32.17 31.01
2 24.83 30.48 29.51
• Liquid limit test (Casagrande Apparatus):
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Example .2
35
40
45
50
55
60
0 10 20 30 40 50
W
a
te
r
C
o
n
te
n
t
%
Number of Blow
Wc%
Test W1 W2 W3 Wc% No of blows Log N
1 23.68 40.86 34.68 56.18 13 1.11
2 22.93 42.62 35.78 53.22 20 1.30
3 26.27 38.02 34.27 46.88 47 1.67
Solution:
Step (1): Find Liquid limit (L.L):
You can draw on a semi log scale.
Or on a normal scale.
25 Below
Or, Log 25 = 1.4corresponding to N = 25 blows
Wc = LL = 51.60% Ans.
LL
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Test W1 W2 W3 Wc%
1 25.34 32.17 31.01 20.4
6
2 24.83 30.48 29.51 20.73
PL =
𝐖𝐜𝟏+𝐖𝐜𝟐
𝟐
Pl =
𝟐𝟎.𝟒𝟔+𝟐𝟎.𝟕𝟑
𝟐
= 20.60%
Step (2): Find Plastic limit (P.L):
Solution:
Step (3): Find Shrinkage limit (S.L):
SL =
γ𝒘
γ𝒅
−
𝟏
𝐆𝐬
=
𝐞
𝐆𝐬
Sl =
𝟎.𝟕𝟗
𝟐.𝟔𝟓
= 29.80%
❑ Page :22 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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Solution
PI = LL – PL
Ic =
𝐋𝐋 −𝐖𝐜
𝐋𝐋 −𝐏𝐋
IL =
𝐖𝐜 −𝐏𝐋
𝐋𝐋 −𝐏𝐋
In organic Clays of highly Plasticity (CH)
= 51.60 – 20.60 = 31% Ans.
=
𝟓𝟏.𝟔𝟎 −𝟑𝟓.𝟔𝟕
𝟓𝟏.𝟔𝟎 −𝟐𝟎.𝟔
= 0.5138 Ans.
=
𝟑𝟓.𝟔𝟕 −𝟐𝟎.𝟔𝟎
𝟓𝟏.𝟔𝟎 −𝟐𝟎.𝟔𝟎
= 0.486 Ans.
Step (4): Find consistency indices
Plasticity index:
Consistency index:
Liquidity index:
❑ Page :23 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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• Burmister (1949)
❑ Page :24 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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Summary of Soil Classification
❑ Page :25 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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Percentages of Components:
Classification using USCS
❑ Page :26 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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Example 3
Sieve opening (m) 5.0 2.0 1.0 0.5 0.2 0.1 0.075
Weight retained (gm) 11.8 9.43 103.62 42.05 66.33 8.56 8.3
Size (mm) 0.06 0.052 0.043 0.023 0.014 0.0064 0.0027
% Finer 99.0 93.7 91.0 89.5 80.6 55.4 24.33
❑ Revision Extra Tutorial Class
❑ Page :29 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Solution:
Sieve opening
(mm)
Weight Retained
(gm)
Total Weight
Retained (gm)
% Retained % Pass
5 11.8 11.8 1.3 98.7
2 9.43 21.23 2.4 97.6
1 103.62 124.85 13.9 86.1
0.5 42.05 166.9 18.5 81.5
0.2 66.33 233.23 25.9 74.1
0.1 8.56 241.79 26.9 73.1
0.075 8.3 250 27.8 72.
2
% Pcorr. = %P *
𝐖𝐟𝐢𝐧𝐞𝐬
𝐖𝐓𝐨𝐭𝐚𝐥
= %P *
𝟔𝟓𝟎
𝟗𝟎𝟎
Diam. (mm) 0.06 0.052 0.043 0.023 0.014 0.0064 0.0027 0.0013
% Pass 99.0 93.7 91.0 89.5 80.6 55.4 24.33 6.4
% Pcorr. 71.5 67.7 65.6 64.6 58.2 40.0 17.57 4.
62
❑ Revision Extra Tutorial Class
❑ Page :30 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Solution:
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❑ Page :31 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Solution:
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❑ Page :32 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Solution:
MIT Classification
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❑ Page :33 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
SOIL EXPLORATION
❑ Page :34 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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Example 4
❑ Page :35 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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❑
❑
o
o
o
Solution:
For square footing with a design
pressure between 50-450 kN/m2
Reminder
❑ Page :36 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
Number of Borings
❑ Approximate spacing
requirements of Boreholes
❑ Page :37 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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❑ Method 2:
𝑵 = 𝑵′ × ( Τ𝟏𝟎𝟎 𝒑𝟎)
Τ𝟏 𝟐
STANDARD PENETRATION TEST (S.P.T)
❑
❑
❑ Method 1:
𝑪𝑵 = 𝟎.𝟕𝟕𝐥𝐨𝐠𝟏𝟎
𝟏𝟗𝟏𝟓
𝒑𝟎
𝒑𝟎in kN/m
𝟐
❑ Page :38 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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Example 5
CN = 0.77 log10
𝟏𝟗𝟏𝟓
𝑷𝟎
N = N’ * (100/p0)
1/2
❑ Page :39 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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SOLUTION
❑Using Method (1):
𝟏𝟗𝟏𝟓
𝐏𝟎
❑
❑Using Method (2):
❑ Page :40 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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❑
RESULTS OF STANDARD PENETRATION TEST
❑ Page :41 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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❑
❑
❑
EXAMPLE 6
❑ Page :42 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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SOLUTION
( ) ( )
( ) ( ) ( )
2
32
32
N/m94.8233
6
0920
2
18400920
mN5023
62
=
+
=
+
=
c
…
π
.
c
/dh/dπ
T
c
Reminder
❑ Page :43 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
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❑
❑
SOLUTION
❑ Page :44 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
RECIPE FOR SUCCESS,
As long as you live, Just Keep
L e a r n i n g …
References
• 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.
• Cheng Liu and Jack B. Evett, Soils and Foundations, 8th Edition; 2013.
❑ Page :45 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Revision Extra Tutorial Class
• 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.
<
p
>Conducted by: Offered to :
Riyadh, Saudi Arabia, 2019-202
0
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
❑ OBJECTIVES OF THE LECTURE
■■ To give a brief explanation about evaluation of soil properties, including reconnaissance, steps of
soil exploration (boring, sampling, and testing), and the record of field exploration. Although different
types of soil tests are discussed.
2019-2020 (192)
❑ Page :1 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
TE
N
TATIVE 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
❑ Soil Exploration Topic No. 4
Soil Exploration
❑ Soil Exploration Topic No. 4
❑ Page :2 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
DEFINITIO
N
❑
❑
❑ Soil Exploration Topic No. 4
❑ Page :3 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
STAGES OF SOIL EXPLORATION
Stage (1):
Reconnaissance
Stage (2):
Preliminary Investigation
Stage (3):
Detailed investigation
Boring –Sampling – Testing
Stage (4):
Report Writing
❑ Soil Exploration Topic No. 4
❑ Page :4 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
RECONNAISSANCE
❑
❑
▪
▪
❑
▪
▪
❑
❑ Soil Exploration Topic No. 4
❑ Page :5 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
STEP(2) OF SOIL EXPLORATION
❑ Detailed Soil exploration consists of three steps:
o
o
o
❑ Soil Exploration Topic No. 4
❑ Page :6 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
1. BORING:
❑ Common types of borings are:
❑ Soil Exploration Topic No. 4
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A. AUGER BORING:
❑ Soil Exploration Topic No. 4
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A. AUGER BORING:
•
•
❑ Soil Exploration Topic No. 4
❑ Page :9 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
B. TEST PITS:
Shoring
❑ Soil Exploration Topic No. 4
❑ Page :10 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
•
❑ Soil Exploration Topic No. 4
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C. CORE BORINGS
❑ Soil Exploration Topic No. 4
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core barrel
Videos : Core Boring
C. CORE BORINGS
•
•
•
•
❑ Soil Exploration Topic No. 4
❑ Page :13 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
•
•
•
•
C. CORE BORINGS
❑ Soil Exploration Topic No. 4
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❑ Compression tests :
❑ Permeability tests:
Rock Compression tests
Rock Permeability Test
C. CORE BORINGS
❑ Soil Exploration Topic No. 4
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CORE RECOVERY
❑ Soil Exploration Topic No. 4
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ROCK QUALITY DESIGNATION (RQD)
❑ Soil Exploration Topic No. 4
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NUMBER OF BORINGS & DEPTH OF BORING
❑ Soil Exploration Topic No. 4
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❑ROUGH GUIDE FOR INITIAL SPACING OF BORINGS:
NUMBER OF BORINGS
o
o
o
•
•
❑
❑ Soil Exploration Topic No. 4
❑ Page :19 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
ROUGH GUIDE FOR INITIAL SPACING OF BORINGS :
❑ Soil Exploration Topic No. 4
❑ Page :20 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
In general, the depth of boring should:
▪
▪
▪
DEPTH OF BORINGS
Determination of the minimum
depth of boring
❑ Soil Exploration Topic No. 4
❑ Page :21 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
DEPTH OF BORINGS
❑ Soil Exploration Topic No. 4
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❑
❑
❑
❑
GROUNDWATER TABLE (GWT)
❑ Soil Exploration Topic No. 4
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DEPTH OF BORINGS
❑ GWT & Depth of boring:
o
o
o
❑ Soil Exploration Topic No. 4
❑ Page :24 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
DEPTH OF BORINGS
❑ Soil Exploration Topic No. 4
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Example 1
❑ Soil Exploration Topic No. 4
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❑
❑
o
o
o
Solution:
❑ Soil Exploration Topic No. 4
❑ Page :27 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Sampling
❑ Soil Exploration Topic No. 4
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STEPS OF SOIL EXPLORATION
2. SAMPLING:
•
•
❑ Soil Exploration Topic No. 4
❑ Page :29 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
2. SAMPLING:
❑ Soil Exploration Topic No. 4
❑ Page :30 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Disturbed Undisturbed
Boring Method
Auger boring o Carving a sample from test pits
o Pushing Shelby tube into soil to
extract sample
Characteristics
some of their characteristics are
changed due boring process.
exactly the same as it was when it
existed in place within the ground
Packaging and
Transportation
airtight container (plastic bag or
airtight jar)
coated with paraffin wax
Lab. Tests these
samples are used
for
• soil grain-size analysis, liquid
and plastic limits
• specific gravity
• the compaction
• CBR tests
• Strength,
• Compressibility,
• Permeability
❑ Soil Exploration Topic No. 4
❑ Page :31 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Testing
❑ Soil Exploration Topic No. 4
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❑ Laboratory Test
o
❑ Field Test
o
o
o
o
o
3.TESTING
STEPS OF SOIL EXPLORATION
❑ Soil Exploration Topic No. 4
❑ Page :33 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
GROUNDWATER TABLE (GWT)
❑
❑
❑
❑
❑ Soil Exploration Topic No. 4
❑ Page :34 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
STANDARD PENETRATION TEST (ASTM D 1586)
❑ Soil Exploration Topic No. 4
❑ Page :35 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
STANDARD PENETRATION TEST (S.P.T)
❑ Soil Exploration Topic No. 4
❑ Page :36 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
STANDARD PENETRATION TEST (S.P.T)
❑ Soil Exploration Topic No. 4
❑ Page :37 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
STANDARD PENETRATION TEST (S.P.T)
❑ Soil Exploration Topic No. 4
❑ Page :38 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Method 2:
𝑵 = 𝑵′ × ( Τ𝟏𝟎𝟎 𝒑𝟎)
Τ𝟏
𝟐
STANDARD PENETRATION TEST (S.P.T)
❑
❑
❑ Method 1:
𝑪𝑵 = 𝟎.𝟕𝟕𝐥𝐨𝐠𝟏𝟎
𝟏𝟗𝟏𝟓
𝒑𝟎
𝒑𝟎in kN/m
𝟐
❑ Soil Exploration Topic No. 4
❑ Page :39 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Example
2
❑ Soil Exploration Topic No. 4
❑ Page :40 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Using Method (1):
❑
Ans.
Solution:
❑ Soil Exploration Topic No. 4
❑ Page :41 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
36)907.0)(40( ==correctedN
907.0
1915
log77.0
kN/m2.127)kN/m0.21)(m6(
0
10
23
0
=
=
==
p
C
p
N
Using Method (2):
Solution:
❑ Soil Exploration Topic No. 4
❑ Page :42 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
46.35
)kN/m2.127100()40(
)100(
kN/m2.127
212
21
0
2
0
=
=
=
=
corrected
N
N
p’NN
p
❑
RESULTS OF STANDARD PENETRATION TEST
❑ Soil Exploration Topic No. 4
❑ Page :43 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
RESULTS OF STANDARD PENETRATION TEST
❑ Soil Exploration Topic No. 4
❑ Page :44 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
RESULTS OF STANDARD PENETRATION TEST
❑ Soil Exploration Topic No. 4
❑ Page :45 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
❑
❑
❑
❑
VANE TEST
❑ Soil Exploration Topic No. 4
❑ Page :46 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Soil Exploration Topic No. 4
❑ Page :47 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
VANE TEST
❑
❑ Soil Exploration Topic No. 4
❑ Page :48 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
( )3-3
)6/()2/(
32
dhd
T
c
+
=
❑
❑
VANE TEST
❑ Soil Exploration Topic No. 4
❑ Page :49 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
❑
❑
Example 3
❑ Soil Exploration Topic No. 4
❑ Page :50 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Solution:
❑ Soil Exploration Topic No. 4
❑ Page :51 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
( ) ( )
( ) ( ) ( )
2
32
32
N/m94.8233
6
0920
2
18400920
mN5023
62
=
+
=
+
=
c
…
π
.
c
/dh/dπ
T
c
❑
❑
Solution:
❑ Soil Exploration Topic No. 4
❑ Page :52 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
RECORD OF SOIL EXPLORATION
“REPORT WRITING”
❑ Soil Exploration Topic No. 4
❑ Page :53 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
RECORD OF SOIL EXPLORATION
❑
❑
❑
❑
❑ Soil Exploration Topic No. 4
❑ Page :54 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
RECORD OF SOIL EXPLORATION
❑ Soil Exploration Topic No. 4
❑ Page :55 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑
o
o
o
o
❑
RECORD OF SOIL EXPLORATION
geological profile
❑ Soil Exploration Topic No. 4
❑ Page :56 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
• 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.
• Cheng Liu and Jack B. Evett, Soils and Foundations, 8th Edition; 2013.
❑ Soil Exploration Topic No. 4
❑ Page :57 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
• 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.
Conducted by: Offered to :
Riyadh, Saudi Arabia, 2019-202
0
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
❑ OBJECTIVES OF THE LECTURE
■■ To illustrate the main characteristics and types of soil
■■ To give a brief explanation about Different Properties of Soil:
• Physical and Chemical Properties:
o To present the soil Composition and Weight Volume Relationships
o To Demonstrate grain size distribution and consistency of Soil.
o To Highlight different methods used for soil Classifications
• Mechanical and Engineering Properties.
2019-2020 (192)
SOIL
GRAIN SIZE DISTRIBUTION
❑ Engineering Properties of soils Topic No. 3
❑ Page :65 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
SOIL TEXTURAL CLASS
•
•
•
❑ Engineering Properties of soils Topic No. 3
❑ Page :66 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
•
SOIL TEXTURAL CLASS
USDA Soil Classification System
❑ Engineering Properties of soils Topic No. 3
❑ Page :67 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
SOIL – PARTICLE SIZE
Particle-Size Classifications
Name of
organization
Grain size
(mm)
Gravel Sand Silt
Clay
MIT >2 2 to 0.06 0.06 to 0.002 < 0.002
USDA >2 2 to 0.05 0.05 to 0.002 < 0.002
AASHTO 76.2 to 2 2 to 0.075 0.075 to 0.002 < 0.002
USCS 76.2 to 4.75 4.75 t0 0.075 < 0.075
❑ Engineering Properties of soils Topic No. 3
❑ Page :68 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
•
•
•
Clay Particles
Silt Particles
Sand Particles
Gravel
SOIL TEXTURAL CLASS
❑ Engineering Properties of soils Topic No. 3
❑ Page :69 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
❑
❑
•
•
•
SOIL TEXTURAL CLASS
❑ Engineering Properties of soils Topic No. 3
❑ Page :70 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
GRAIN SIZE DISTRIBUTION
➢
➢
➢
➢
❑ Engineering Properties of soils Topic No. 3
❑ Page :71 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Classification
Test
Soil
Type
Atterberg Limits
Hydrometer Analysis
Sieve Analysis
Classification of Soil
Non-Cohesive soil Cohesive soil
❑ Engineering Properties of soils Topic No. 3
❑ Page :72 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
A. Mechanical analysis (sieve analysis) B. Sedimentation analysis (Hydrometer )
❑ Engineering Properties of soils Topic No. 3
❑ Page :73 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
A. MECHANICAL ANALYSIS
(SIEVE ANALYSIS)
❑ Engineering Properties of soils Topic No. 3
❑ Page :74 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
SOIL GRAIN SIZE DISTRIBUTION
❑ Page :75 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
Classification
Test
Soil
Type
Atterberg Limits
Hydrometer Analysis
Sieve Analysis
Classification of Soil
Non-Cohesive soil Cohesive soil
❑ Page :76 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
Example .1
Sieve number 4 10 20 40 60 100 200 Pan
Sieve diameter
(mm)
4.75 2.0 0.85 0.425 0.250 0.150 0.075 Pan
Weight retained
(gm)
28 42 48 128 221 86 40 24
❑ Page :77 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
Step (1): Determine finer percentage % :
Sieve
No.
Opening
mm
Mass
retained
gm
% Retained
on each sieve
(R%)
∑
%Retained
% Pass
F%
4 4.75 28 4.54 4.54 95.5
10 2.00 42 6.81 11.35 88.7
20 0.85 48 7.78 19.13
80.9
40 0.425 128 20.74 39.87
60.1
60 0.250 221 35.81 75.68
24.3
100 0.15 86 13.94 89.62 10.4
200 0.075 40 6.49 96.11 3.9
pan – 24 3.89 100 0
Total mass (m) = 617 gm 100%
Solution: 𝒎𝒂𝒔𝒔 𝒓𝒆𝒕𝒂𝒊𝒏𝒆𝒅 𝒐𝒏 𝒆𝒂𝒄𝒉 𝒔𝒊𝒆𝒗𝒆
𝒕𝒐𝒕𝒂𝒍 𝒎𝒂𝒔𝒔
∗
𝟏𝟎𝟎
=
Check !
❑ Page :78 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
Step (2): Draw Grain Size Distribution Curve:
•
•
Solution:
Semi Log Scale Paper
95.5
88.7
80.9
60.1
24.3
10.4
3.9
0
10
20
30
40
50
60
70
80
90
100
0.01 0.1 1 10
P
a
s
s
P
e
rc
e
n
ta
g
e
%
Particle Size (mm)
Grain Size Distribution
% Pass
❑ Page :79 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
0
10
20
30
40
50
60
70
80
90
100
0.01 0.1 1 10
P
a
s
s
P
e
rc
e
n
ta
g
e
%
Particle Size (mm)
% Pass
D10 = 0.16mm Ans.
Step (3): Obtain D10 , D30 , D60 :
Solution:
D30 = 0.28mm Ans.
D60 = 0.42mm Ans.
D10
D30
D60
❑ Page :80 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
Solution:
Step (4): Calculate Cu, and CC:
CU =
𝐃
𝟔𝟎
𝐃
𝟏𝟎
CC =
𝐃
𝟑𝟎
𝟐
𝐃
𝟔𝟎
. 𝐃𝟏𝟎
= 0.42/0.16 = 2.625
= 1.167
= 0.282/(0.42*0.16)
• Uniformity coefficient (Cu);
• Coefficient of gradation (CC );
Poorly Graded Course Grained Soil (GP)
D10 = 0.16 mm
D30 = 0.28 mm
D60 = 0.42 mm
❑ Page :81 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
0
10
20
30
40
50
60
70
80
90
100
0.01 0.1 1 10
P
a
s
s
P
e
rc
e
n
ta
g
e
%
Particle Size (mm)
% Pass
Step (5): Percentages of different Components
Solution:
sand
Clay+ silt
– Form grading curve:-
• % Fines (% Clay + % Silt)
[0- 0.075 mm] = 3.9%
• % Sand
[0.075-4.75 mm] = 88.7 – 3.9
= 84.8%
• % Gravel
[4.75- 75 mm] = 100 – 88.7 = 11.3%
Gravel
❑ Page :83 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
Step (5): Percentages of different Components
Solution:
– Form grading Table:-
• % Fines (% Clay + % Silt)
[0- 0.075 mm] = 3.9%
• % Sand
[0.075-4.75 mm] = 88.7 – 3.9
= 84.8%
• % Gravel
[4.75- 75 mm] = 100 – 84.8 – 3.9 = 11.3%
Sand
Clay
Gravel
❑ Page :84 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
•
PARTICLE SIZE DISTRIBUTION CURVE:
•
•
❑ Page :85 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
B. SEDIMENTATION ANALYSIS
(HYDROMETER)
❑ Engineering Properties of soils Topic No. 3
❑ Page :86 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
SEDIMENTATION ANALYSIS (HYDROMETER)
•
•
❑ Engineering Properties of soils Topic No. 3
❑ Page :87 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Methodology:
•
•
•
SEDIMENTATION ANALYSIS (HYDROMETER)
❑ Engineering Properties of soils Topic No. 3
❑ Page :88 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
This method is based on Stoke’s law:
𝒗 =
(𝒑𝒔 − 𝒑𝒘)
𝟏𝟖 𝜼
D2
v
η
SEDIMENTATION ANALYSIS (HYDROMETER)
❑ Engineering Properties of soils Topic No. 3
❑ Page :89 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
PARTICLE SIZE DISTRIBUTION CURVE
❑ Engineering Properties of soils Topic No. 3
❑ Page :90 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
DATA OBTAINED FROM SIEVE ANALYSIS
•
❑ Engineering Properties of soils Topic No. 3
❑ Page :91 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
CONSISTENCY LIMITS
❑ Page :92 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
CONSISTENCY AND WATER CONTENT
•
•
❑ Engineering Properties of soils Topic No. 3
❑ Page :93 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
PORE SPACE EFFECT
❑ Engineering Properties of soils Topic No. 3
❑ Page :94 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
•
•
CONSISTENCY OF SOIL
❑ Engineering Properties of soils Topic No. 3
❑ Page :95 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
•
CONSISTENCY OF SOIL
•
❑ Engineering Properties of soils Topic No. 3
❑ Page :96 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
ATTERBURG LIMITS
•
Moisture content
•
DEFINITION :
❑ Engineering Properties of soils Topic No. 3
❑ Page :97 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
•
Moisture content
ATTERBURG LIMITS
•
❑ Engineering Properties of soils Topic No. 3
❑ Page :98 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
CONSISTENCY LIMITS
•
•
•
•
•
❑ Engineering Properties of soils Topic No. 3
❑ Page :99 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
•
•
ATTERBURG LIMITS
Moisture content
❑ Engineering Properties of soils Topic No. 3
❑ Page :100 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
IMPORTANCE OF ATTERBURG LIMITS
.
❑ Engineering Properties of soils Topic No. 3
❑ Page :101 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
CONSISTENCY INDICES
❑ Engineering Properties of soils Topic No. 3
❑ Page :102 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
PLASTICITY INDEX (PI)
PI = LL – PL
•
•
•
•
❑ Definition:
❑ Engineering Properties of soils Topic No. 3
❑ Page :103 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
NP:
•
•
•
PLASTICITY INDEX (PI)
PLASTICITY:
❑ Engineering Properties of soils Topic No. 3
❑ Page :104 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
PLASTICITY :
❑ Engineering Properties of soils Topic No. 3
❑ Page :105 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
LIQUIDITY INDEX (LI)
LI =
𝑾𝒄 −𝑷𝑳
𝑷𝑰
❑ Definition:
❑ Engineering Properties of soils Topic No. 3
❑ Page :106 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
•
•
•
LIQUIDITY:
In this case: LI < 1.
In this case: LI > 1.
❑ Engineering Properties of soils Topic No. 3
❑ Page :107 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
CONSISTENCY INDEX (CI)
CI =
𝑳𝑳 − 𝑾𝒄
𝑷𝑰
❑ Definition:
❑ Engineering Properties of soils Topic No. 3
❑ Page :108 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
ACTIVITY (A)
•
A =
𝑷𝑰
𝐏𝐞𝐫𝐜𝐞𝐧𝐭𝐚𝐠𝐞 𝐛𝐲 𝐰𝐞𝐢𝐠𝐡𝐭 𝐟𝐢𝐧𝐞𝐫 𝐭𝐡𝐚𝐧 𝟐μ𝒎
❑ Definition:
❑ Engineering Properties of soils Topic No. 3
❑ Page :109 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
ACTIVITY (A)
❑ Engineering Properties of soils Topic No. 3
❑ Page :110 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
SHRINKAGE RATIO (SR)
•
SR =
𝑴𝟐
𝑽𝟐 ∗ 𝒑𝒘
Gs =
𝟏
𝟏
𝑺𝑹
−
𝑺𝑳
𝟏𝟎𝟎
❑ Definition:
❑ Engineering Properties of soils Topic No. 3
❑ Page :111 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
Example 2
Test No. Tin weight (gm) Tin + wet soil (gm) Tin + dry soil (gm) No. of blows
1 23.68 40.86 34.68 13
2 22.93 42.62 35.78 20
3 26.27 38.02 34.27 47
• Plastic limit test:
Test No. Tin weight (gm) Tin + wet soil (gm) Tin + dry soil (gm)
1 25.34 32.17 31.01
2 24.83 30.48 29.51
• Liquid limit test (Casagrande Apparatus):
❑ Page :112 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
35
40
45
50
55
60
0 10 20 30 40 50
W
a
te
r
C
o
n
te
n
t
%
Number of Blow
Wc%
Test W1 W2 W3 Wc% No of blows Log N
1 23.68 40.86 34.68 56.18 13 1.11
2 22.93 42.62 35.78 53.22 20 1.30
3 26.27 38.02 34.27 46.88 47 1.67
Solution:
Step (1): Find Liquid limit (L.L):
You can draw on a semi log scale.
Or on a normal scale.
25 Below
Or, Log 25 = 1.4corresponding to N = 25 blows
Wc = LL = 51.60% Ans.
LL
❑ Page :113 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
Test W1 W2 W3 Wc%
1 25.34 32.17 31.01 20.46
2 24.83 30.48 29.51 20.73
PL =
𝐖𝐜𝟏+𝐖𝐜𝟐
𝟐
Pl =
𝟐𝟎.𝟒𝟔+𝟐𝟎.𝟕𝟑
𝟐
= 20.60%
Step (2): Find Plastic limit (P.L):
Solution:
Step (3): Find Shrinkage limit (S.L):
SL =
γ𝒘
γ𝒅
−
𝟏
𝐆𝐬
=
𝐞
𝐆𝐬
Sl =
𝟎.𝟕𝟗
𝟐.𝟔𝟓
= 29.80%
❑ Page :114 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
Solution
PI = LL – PL
Ic =
𝐋𝐋 −𝐖𝐜
𝐋𝐋 −𝐏𝐋
IL =
𝐖𝐜 −𝐏𝐋
𝐋𝐋 −𝐏𝐋
In organic Clays of highly Plasticity (CH)
= 51.60 – 20.60 = 31% Ans.
=
𝟓𝟏.𝟔𝟎 −𝟑𝟓.𝟔𝟕
𝟓𝟏.𝟔𝟎 −𝟐𝟎.𝟔
= 0.5138 Ans.
=
𝟑𝟓.𝟔𝟕 −𝟐𝟎.𝟔𝟎
𝟓𝟏.𝟔𝟎 −𝟐𝟎.𝟔𝟎
= 0.486 Ans.
Step (4): Find consistency indices
Plasticity index:
Consistency index:
Liquidity index:
❑ Page :115 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
• Burmister (1949)
❑ Page :116 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
Summary of Soil Classification
❑ Page :117 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
Percentages of Components:
Classification using USCS
❑ Page :118 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
❑ Page :119 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
❑ Page :120 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
MECHANICAL
PROPERTIES OF SOIL
❑ Engineering Properties of soils Topic No. 3
❑ Page :121 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
• Soil Colour, and bulky shape.
• Soil Textural Class [Grain size].
• Density of Soil [bulk, dry, saturated,
Submerged].
• Pore Space [water content, void ratio,
degree of saturation, porosity].
• Soil Consistence [Atterberg Limits].
PROPERTIES OF SOIL
Physical properties Chemical
properties
Engineering properties
(Mechanical properties)
• Soil Strength (stresses at failure).
• Soil deformation (settlement).
• Soil water behavior and its effect
in soil mass.
• Soil Structure [Composition].
• Minerals
• chemical analysis
❑ Page :122 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
❑ OBJECTIVES OF THE LECTURE
■■ To illustrate the main characteristics and types of soil
■■ To give a brief explanation about Different Properties of Soil:
• Physical and Chemical Properties:
o To present the soil Composition and Weight Volume Relationships
o To Demonstrate grain size distribution and consistency of Soil.
o To Highlight different methods used for soil Classifications
• Mechanical and Engineering Properties.
2019-2020 (192)
PERMEABILITY, CAPILLARITY & FROST HEAVE
❑
o
o
o
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PERMEABILITY
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CAPILLARITY
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FROST HEAVE
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FROST HEAVE
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COMPRESSIBILITY
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COMPRESSIBILITY
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COMPRESSIBILITY
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COMPRESSIBILITY
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SHEAR STRENGTH
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𝒔 = 𝒄 + 𝝈𝐭𝐚𝐧𝝋
friction oft coefficien tan
friction internal of angle
pressure normallar intergranu effective
cohesion c
strengthshear s where
=
=
=
=
=
SHEAR STRENGTH
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COMPACTNESS—RELATIVE DENSITY
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RECIPE FOR SUCCESS,
As long as you live, Just Keep
L e a r n i n g …
References
• 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.
• Cheng Liu and Jack B. Evett, Soils and Foundations, 8th Edition; 2013.
❑ Page :135 Dr. Eng. Mohamed Ezzat EM306: Soil Mechanics and Foundations
❑ Engineering Properties of soils Topic No. 3
• 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.