project class

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