Bearing capacity of shallow foundations by abhishek sharma ABHISHEK SHARMA
elements you should know about bearing capacity of shallow foundations are included in it. various indian standards are also used. Bearing capacity theories by various researchers are also included. numericals from GATE CE and ESE CE are also included.
TERZAGHI’S BEARING CAPACITY THEORY
DERIVATION OF EQUATION TERZAGHI’S BEARING CAPACITY THEORY
TERZAGHI’S BEARING CAPACITY FACTORS
Download vedio link
https://youtu.be/imy61hU0_yo
Geotechnical Engineering-II [Lec #19: General Bearing Capacity Equation]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Bearing capacity of shallow foundations by abhishek sharma ABHISHEK SHARMA
elements you should know about bearing capacity of shallow foundations are included in it. various indian standards are also used. Bearing capacity theories by various researchers are also included. numericals from GATE CE and ESE CE are also included.
TERZAGHI’S BEARING CAPACITY THEORY
DERIVATION OF EQUATION TERZAGHI’S BEARING CAPACITY THEORY
TERZAGHI’S BEARING CAPACITY FACTORS
Download vedio link
https://youtu.be/imy61hU0_yo
Geotechnical Engineering-II [Lec #19: General Bearing Capacity Equation]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Introduction
Geostatic Stresses
Boussinesq’s Equation
Vertical Stresses Under A Circular Area
Vertical Stresses Under A Rectangular Area
Equation Point Load Method
Newmark’s Influence Chart
BOUSSINESQ THEORY
VERTICAL STRESS DUE TO POINT LOAD
TABLE FOR VALUES OF BOUSSINESQ’S COEFFICIENT (퐼_퐵)
SOME POINTS FOR USING THE BOUSSINESQ’S EQUATION.
LIMITATIONS OF BOUSSINESQ’S SOLUTION.
This slide will help you to determine the immediate settlement for flexible foundation i.e. isolate footing and rigid foundation i.e. matt or raft foundation. To be more clear about the topic a numerical problem with the solution is given.
Geotechnical Engineering-II [Lec #17: Bearing Capacity of Soil]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Introduction
Geostatic Stresses
Boussinesq’s Equation
Vertical Stresses Under A Circular Area
Vertical Stresses Under A Rectangular Area
Equation Point Load Method
Newmark’s Influence Chart
BOUSSINESQ THEORY
VERTICAL STRESS DUE TO POINT LOAD
TABLE FOR VALUES OF BOUSSINESQ’S COEFFICIENT (퐼_퐵)
SOME POINTS FOR USING THE BOUSSINESQ’S EQUATION.
LIMITATIONS OF BOUSSINESQ’S SOLUTION.
This slide will help you to determine the immediate settlement for flexible foundation i.e. isolate footing and rigid foundation i.e. matt or raft foundation. To be more clear about the topic a numerical problem with the solution is given.
Geotechnical Engineering-II [Lec #17: Bearing Capacity of Soil]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Diagrid structural systems
are emerging as structurally efficient as well as architecturally significant assemblies for tall buildings.
. The evolution of tall building structural systems based on new structural
concepts with newly adopted high strength materials and construction methods have been towards “stiffness” and “lightness”. Structural systems are become
“lighter” and “stiffer”.
It is common knowledge that rather than directly standing the forces,
it is better to reduce them and dissipate the magnitude of vibrations.
Structure design of high rise buildings is governed by lateral loads due to
wind or earthquake.
Lateral load resistance of structure is provided by interior structural system
or exterior structural system.
The selected structural system should be such that it should be effectively
utilized for structural requirements.
Recently diagrid structural system is adopted in tall buildings due to its
structural efficiency and flexibility in architectural planning.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Using Imperialist Competitive Algorithm to Find the Optimum Shape Design of I...CSCJournals
In this paper, Imperialist Competitive Algorithm (ICA) and Genetic Algorithm (GA) are used to find the optimal form for torispherical dome ends under internal pressure load. According to fabrication and strength of material requirements, a group of compromised counters are studied. According to ASME Section VIII and BS5500 pressure vessel codes, a reasonable buckling pressure limit is proposed. Four-centered ellipse method is used to describe the geometry of the torispherical dome end that this method is commonly used in engineering drawing. A minimum weight optimization problem based on buckling pressure is studied. Two different size torispherical dome end examples are selected and studied. Imperialist Competitive Algorithm is found to be very efficient and easy to use for the applications, such as torispherical dome end and subjected to internally pressurized loading.
A COMPARATIVE STUDY OF VARIOUS METHODS TO EVALUATE IMPEDANCE FUNCTION FOR SHA...Samirsinh Parmar
Impedance function, Foundation Vibration, dynamic soil-structure interaction, Barkan, Dominguez, Dobry and Gazetas for evaluation of impedance functions for various modes of vibration of shallow foundation
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Design and Analysis of Algorithms-DP,Backtracking,Graphs,B&B
Lecture 2 bearing capacity
1. Lecture
2
INTERNATIONAL UNIVERSITY
FOR SCIENCE & TECHNOLOGY
وا م ا و ا ا
Dr. Abdulmannan Orabi
Civil Engineering and Environmental
Department
303421: Foundation Engineering
Bearing Capacity of Foundation
2. References
ACI 318M-14 Building Code Requirements for Structural
Concrete ( ACI 318M -14) and Commentary, American
Concrete Institute, ISBN 978-0-87031-283-0.
Bowles , J.,E.,(1996) “Foundation Analysis and Design” -5th
ed. McGraw-Hill, ISBN 0-07-912247-7.
Das, B., M. (2012), “ Principles of Foundation Engineering ”
Eighth Edition, CENGAGE Learning,
ISBN-13: 978-1-305-08155-0.
Syrian Arab Code for Construction 2012
Dr. Abdulmannan Orabi IUST 2
3. Bearing Capacity of Foundation
The soil must be capable of carrying the loads from
any engineered structure placed upon it without a
shear failure and with the resulting settlements
being tolerable for that structure.
This lecture will be concerned with evaluation of
the limiting shear resistance, or ultimate bearing
capacity of the soil under a foundation load.
3Dr. Abdulmannan Orabi IUST
4. It is necessary to investigate both base shear
resistance and settlements for any structure.
Bearing Capacity of Foundation
In many cases settlement criteria will control
the allowable bearing capacity; however, there
are also a number of cases where base shear (in
which a base punches into the ground - usually
with a simultaneous rotation) dictates the
recommended bearing capacity.
Dr. Abdulmannan Orabi IUST 4
5. Bearing Capacity of Foundation
Structures such as liquid storage tanks and mats are
often founded on soft soils, which are usually more
susceptible to base shear failure than to settlement.
Base shear control, to avoid a combination base
punching with rotation into the soil, is often of more
concern than settlement for these foundation types.
Dr. Abdulmannan Orabi IUST 5
6. Allowable Bearing Capacity
The recommendation for the allowable bearing
capacity to be used for design is based on the
minimum of either :
1. Limiting the settlement to a tolerable amount
2. The ultimate bearing capacity, which considers soil
strength, as computed in the following sections
Dr. Abdulmannan Orabi IUST 6
7. Allowable Bearing Capacity
The allowable bearing capacity based on shear
control is obtained by reducing (or dividing)
the ultimate bearing capacity (based on soil
strength) by a safety factor SF that is deemed
adequate to avoid a base shear failure to obtain
=
.
(2-1)
The safety factor is based on the type of soil (cohesive or cohesionless),
reliability of the soil parameters, structural information (importance,
use, etc.), and consultant caution.
Dr. Abdulmannan Orabi IUST 7
8. Dr. Abdulmannan Orabi IUST
Allowable Bearing Capacity
Most building codes provide an allowable
settlement limit for a foundation, which
may be well below the settlement derived
corresponding to given by equations( 2-1).
Thus, the bearing capacity corresponding to the
allowable settlement must also be taken into
consideration.
8
9. BEARING-CAPACITY EQUATIONS
Terzaghi’s Bearing Capacity Theory
Terzaghi (1943) was the first to present a comprehensive
theory for the evaluation of the ultimate bearing capacity
of rough shallow foundations. According to this theory, a
foundation is shallow if its depth, Df (Figure slid 11), is
less than or equal to its width. Later investigators,
however, have suggested that foundations with Df equal
to 3 to 4 times their width may be defined as shallow
foundations.
Dr. Abdulmannan Orabi IUST 9
10. BEARING-CAPACITY EQUATIONS
Terzaghi’s Bearing Capacity Theory
The effect of soil above the bottom of the foundation may also
be assumed to be replaced by an equivalent surcharge,
(where is the unit weight of soil).
= ∗
Terzaghi suggested that for a continuous, or strip, foundation
(i.e., one whose width-to-length ratio approaches zero), the
failure surface in soil at ultimate load may be assumed to be
similar to that shown in Figure on Slide 11.
Dr. Abdulmannan Orabi IUST 10
11. The failure zone under the foundation can be
separated into three parts (see Figure 4.6):
1. The triangular zone ACD immediately under
the foundation
2. The radial shear zones ADF and CDE, with the
curves DE and DF being arcs of a logarithmic
spiral
3. Two triangular Rankine passive zones AFH
and CEG
BEARING-CAPACITY EQUATIONS
Terzaghi’s Bearing Capacity Theory
Dr. Abdulmannan Orabi IUST 11
12. BEARING-CAPACITY EQUATIONS
Terzaghi’s Bearing Capacity Theory
The angles CAD and ACD are assumed to be equal to the
soil friction angle .
Note that, with the replacement of the soil above the bottom
of the foundation by an equivalent surcharge q, the shear
resistance of the soil along the failure surfaces GI and HJ
was neglected.
∅
Dr. Abdulmannan Orabi IUST 12
15. BEARING-CAPACITY EQUATIONS
Terzaghi’s Bearing Capacity Theory
The ultimate bearing capacity, , of the foundation
now can be obtained by considering the equilibrium of the
triangular wedge ACD shown in Figure below
Dr. Abdulmannan Orabi IUST 15
18. BEARING-CAPACITY EQUATIONS
Terzaghi’s Bearing Capacity Theory
for Local Shear Failure
Terzaghi suggested the following relationships for
local shear failure in soil:
where
, , ! "# =+!$*$#! /# "$ % * &(+",
= 0.5 + +
=
2
3
tan ∅ = tan (
2
3
∅)
Dr. Abdulmannan Orabi IUST 18
19. BEARING-CAPACITY EQUATIONS
Meyerhof ’s Bearing Capacity Equation
In 1951, Meyerhof published a bearing capacity theory
that could be applied to rough, shallow, and deep
foundations. The failure surface at ultimate load under a
continuous shallow foundation assumed by Meyerhof is
shown in Figure below.
Dr. Abdulmannan Orabi IUST 19
21. BEARING-CAPACITY EQUATIONS
Meyerhof ’s Bearing Capacity Equation
In this figure abc is the elastic triangular, bcd is the
radial shear zone with cd being an arc of a log spiral,
and bde is a mixed shear zone in which the shear varies
between the limits of radial and plane shears depending
on the depth and roughness of the foundation.
The plane be is called an equivalent free surface.
Dr. Abdulmannan Orabi IUST 21
24. BEARING-CAPACITY EQUATIONS
Meyerhof ’s Bearing Capacity Equation
where
, , ! = ℎ '# * &(+",
1 0.1 .......... 10q p
B
S S K for
L
γ φ= = + × ≥
1 0.2c p
B
S K
L
= + ×
CD = ( E
(45 +
∅
2
)
= = 1 *+" ∅ = 0
24Dr. Abdulmannan Orabi IUST
25. ! , ! , ! ! = #'(ℎ * &(+",
BEARING-CAPACITY EQUATIONS
Meyerhof ’s Bearing Capacity Equation
where
1 0 .2 f
C p
D
d K
B
= + ×
1 0.1 .... 10f
q p
D
d d K for
B
γ φ= = + × ≥
! = ! = 1 *+" ∅ = 0
Dr. Abdulmannan Orabi IUST 25
26. $ , $ , ! $ = F &8$ ($+ * &(+",
BEARING-CAPACITY EQUATIONS
Meyerhof ’s Bearing Capacity Equation
where
$ = $ = 1 −
G
90
E
) ∅
$ = 1 −
G
∅
E
∅ > 0
$ = 0 *+" G ≠ 0 ! ∅ = 0
G<∅
V
H
R
Dr. Abdulmannan Orabi IUST 26
28. BEARING-CAPACITY EQUATIONS
Hansen’s Bearing Capacity Equation ( General Equation )
'
0.5ult q q q q q q C C C C C Cq B N S d i g b qN S d i g b CN S d i g bγ γ γ γ γ γγ= + +
tan 2
( ) tan (45 )
2
qN eπ φ φ
= +
( 1)cotC qN N φ= −
( 1) tan(1.4 )qN Nγ φ= −
where
, , ! "# # "$ % & ' &$() * &(+",
= 0 , = 1 ! : = ; + 2 = 5.14 *+" ∅ = 0
Dr. Abdulmannan Orabi IUST 28
29. BEARING-CAPACITY EQUATIONS
Hansen’s Bearing Capacity Equation ( General Equation )
'
0.5ult q q q q q q C C C C C Cq B N S d i g b qN S d i g b CN S d i g bγ γ γ γ γ γγ= + +
where
, , ! = ℎ '# * &(+",
'
'
1
q
C
C
N B
S
N L
= + ×
'
'
1 sinq
B
S
L
φ= +
'
'
1 0.4
B
S
L
γ = − ≥ 0.6
Dr. Abdulmannan Orabi IUST 29
30. ! , ! , ! ! = #'(ℎ * &(+",
where
BEARING-CAPACITY EQUATIONS
Hansen’s Bearing Capacity Equation ( General Equation )
'
0.5ult q q q q q q C C C C C Cq B N S d i g b qN S d i g b CN S d i g bγ γ γ γ γ γγ= + +
1 0 .4Cd K= +
2
1 2 ta n (1 s in )qd Kφ φ= + −
1
1
tan ( ) 1
f f
f f
D D
K for
B B
D D
K for
B B
−
= ≤
= f
! = 1 *+" 88 ∅
30
31. BEARING-CAPACITY EQUATIONS
Hansen’s Bearing Capacity Equation ( General Equation )
'
0.5ult q q q q q q C C C C C Cq B N S d i g b qN S d i g b CN S d i g bγ γ γ γ γ γγ= + +
$ , $ , ! $ = F &8$ ($+ * &(+",
where
1
1
q
C q
q
i
i i
N
−
= −
−
1
0.5
(1 )
cot
i
q
f a
H
i
V A C
α
φ
= −
+
2
0.7
(1 )
cot
i
f a
H
i
V A C
α
γ
φ
= −
+
2
(0.7 / 450)
(1 )
cot
o
i
f a
H
i
V A C
α
γ
η
φ
−
= −
+
2 ≤ OP ! OE ≤ 5
Dr. Abdulmannan Orabi IUST 31
32. BEARING-CAPACITY EQUATIONS
Hansen’s Bearing Capacity Equation ( General Equation )
'
0.5ult q q q q q q C C C C C Cq B N S d i g b qN S d i g b CN S d i g bγ γ γ γ γ γγ= + +
where
% , % , ! % = Q"+7 ! * &(+",
% =
RS
147S
% = 1 −
RS
147S
% = % = 1 − 0.5 ( R T
Dr. Abdulmannan Orabi IUST 32
33. BEARING-CAPACITY EQUATIONS
Hansen’s Bearing Capacity Equation ( General Equation )
'
0.5ult q q q q q q C C C C C Cq B N S d i g b qN S d i g b CN S d i g bγ γ γ γ γ γγ= + +
where
/ , / , ! / = ,# * &(+",
/ =
US
147S
*+" ∅ = 0
/ = 1 −
US
147S
/ = exp (−2U ( ∅) / = exp (−2.7 U ( ∅)
U $ " !$ ,
Dr. Abdulmannan Orabi IUST 33
35. The equation for ultimate bearing capacity by Terzaghi
has been developed based on assumption that water table
is located at a great depth .
If the water table is located close to foundation ; the
equation needs modification.
The effective unit weight of the soil is used in the
bearing-capacity equations for computing the ultimate
capacity.
BEARING-CAPACITY EQUATIONS
Effect of Water Table on Bearing Capacity
Dr. Abdulmannan Orabi IUST 35
36. BEARING-CAPACITY EQUATIONS
Effect of Water Table on Bearing Capacity
The water table is seldom above the base of the footing,
as this would, at the very least, cause construction
problems. If it is, however, the q term requires
adjusting so that the surcharge pressure is an effective
value and an effective unit weight must be used in the
0.5 ϒB Nϒ term.
Water table above the base of footing
Water table below the base of footing
!^
G.W.T.
G.W.T.
Dr. Abdulmannan Orabi IUST 36
37. BEARING-CAPACITY EQUATIONS
Effect of Water Table on Bearing Capacity
= 2 [ − !^
!^
[E
+
[E
[ − !^
E
4ℎ#"# [ = 0.5 tan ( 45 + ∅/2)
!^ = !#'(ℎ +* 4 (#" ( /8# /#8+4 / ,# +* *++($ %
= 7 $( 4#$%ℎ( +* ,+$8 $ !#'(ℎ !^
= ,7/=#"%#! 7 $( 4#$%ℎ( /#8+4 4 (#" ( /8#
When the water table lies within the wedge zone,
can compute the average effective weight of the
soil in the wedge zone as
Dr. Abdulmannan Orabi IUST 37
38. When the water table is below the wedge zone [depth
approximately ], the water table effects
can be ignored for computing the bearing capacity.
BEARING-CAPACITY EQUATIONS
Effect of Water Table on Bearing Capacity
[ = 0.5 tan ( 45 + ∅/2)
Water table below the
base of the footing
!^ > [
G.W.T.
Dr. Abdulmannan Orabi IUST 38
39. BEARING-CAPACITY EQUATIONS
Effect of Soil Compressibility
The change of failure mode is due to soil compressibility, to
account for which Vesic (1973) proposed the following
modification of bearing capacity equation :
= 0.5 ! + ! + !
, ! "# ,+$8 &+='"#,,$/$8$() * &(+",
Where :
Dr. Abdulmannan Orabi IUST 39
40. BEARING-CAPACITY EQUATIONS
Effect of Soil Compressibility
The soil compressibility factors were derived by Vesic
(1973) by analogy to the expansion of cavities.
According to that theory, in order to calculate
,the following steps should be taken:
, !
Step 1. Calculate the rigidity index, Ir, of the soil at a
depth approximately B/2 below the bottom of the
foundation, or
F` =
Qa
+ ( ∅4ℎ#"#
Qa = ,ℎ# " =+!787, +* ,+$8
= #**#&($9# +9#"/7"!# '"#,,7"# ( !#'(ℎ ( +
b
E
)
Dr. Abdulmannan Orabi IUST 40
41. BEARING-CAPACITY EQUATIONS
Effect of Soil Compressibility
Step 2. The critical rigidity index, , can be expressed asF`( `)
F`( `) =
1
2
#c' 3.3 − 0.45
Y
&+( 45 −
∅
2
Step 3. If , then F` ≥ F`( `) = = = 1
However, if , then F` < F`( `)
= = #c' −4.4 + 0.6
Y
( ∅ +
3.07,$ ∅ 8+%2F`
1 + ,$ ∅
: = 0.32 + 0.12
Y
+ 0.6 8+%F` *+" ∅ = 0
: = −
1 −
( ∅
*+" ∅ > 0
Dr. Abdulmannan Orabi IUST 41
42. BEARING-CAPACITY from SPT
Bearing Capacity from SPT
The SPT is widely used to obtain the bearing capacity of
soils directly.
Considering the accumulation of field observations and the
stated opinions of the authors and others, this author adjusted
the Meyerhof equations for an approximate 50 percent
increase in allowable bearing capacity to obtain the following:
2
55 0.3
(1 0.33 )
0.08
f
a
N DB
q
B B
+
= +
> 1.2 = ≤ 1.2 =d + e. ff
gh
i
≤ d. ff
Dr. Abdulmannan Orabi IUST 42
43. BEARING-CAPACITY of Mat Foundation
The gross ultimate bearing capacity of a mat
foundation can be determined by the same equation used
for shallow foundations, or
= 0.5 $ ! + $ ! + $ !
The term B in Eq. above is the smallest dimension of the mat.
The net ultimate capacity of a mat foundation is
(jk ) = −
Dr. Abdulmannan Orabi IUST 43
44. BEARING-CAPACITY of Mat Foundation
The net allowable soil bearing capacity
(jk ) =
(jk )
. l
For mats on clay, the factor of safety should not be less
than 3 under dead load or maximum live load.
Under most working conditions, the factor of safety
against bearing capacity failure of mats on sand is
very large.
Dr. Abdulmannan Orabi IUST 44
45. Dr. Abdulmannan Orabi IUST
BEARING-CAPACITY of Mat Foundation
Bearing Capacity from SPT
The net allowable bearing capacity for mats constructed over
granular soil deposits can be adequately determined from the
standard penetration resistance numbers
(jk ) =
TT
0.08
ln
k(==)
25
(jk ) = 16.63 TT
k(==)
25
45