Lecture
2
INTERNATIONAL UNIVERSITY FOR SCIENCE & TECHNOLOGY
Dr. Abdulmannan Orabi
Civil Engineering and Environmental Department
303421: Foundation Engineering
Bearing Capacity of Foundation
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
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
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
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
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
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
Dr. Abdulmannan Orabi IUST
Allowable Bearing Capacity
Most building codes provide an allowable settlement limit for a foundation, whichmay 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.
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BEARING-CAPACITY EQUATIONS
Terzaghis 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
BEARING-CAPACITY EQUATIONS
Terzaghis 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
The failure zone under the foundation can be separated into three parts (see Figure 4.6):1. The triangular zone ACD immediately under the foundation2. The radial shear zones ADF and CDE, with the curves DE and DF being arcs of a logarithmic spiral3. Two triangular Rankine passive zones AFH and CEG
BEARING-CAPACITY EQUATIONS
Terzaghis Bearing Capacity Theory
Dr. Abdulmannan Orabi IUST 11
BEARING-CAPACITY EQUATIONSTerzaghis 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
BEARING-CAPACITY EQUATIONS
Terzaghis Bearing Capacity Theory
Dr. Abdulmannan Orabi IUST 13
BEARING-CAPACITY EQUATIONS
Terzaghis Bearing Capacity Theory
Dr. Abdulmannan Orabi IUST 14
BEARING-CAPACITY EQUATIONS
Terzaghis 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
BEARING-CAPACITY EQUATIONS
Terzaghis Bearing Capacity Equation
= 0.5 + +
, , !"##"$ %&'&$()*&(+",
and depends on angle of shearing resistance ()(./. 4 1, ,)
4#"#:
= 4$!(+*(#*++($ %
= 7 $(4#$%(+*(#,+$8/#8+4(#*+7 !($+ 8#9#8
=
= 0, = 1 !: = 1.5; + 1 = 5.71*+" = 0Dr. Abdulmannan Orabi IUST 16
BEARING-CAPACITY EQUATIONS
Terzaghis Bearing Capacity Equation
= 0.5 + +
, , ! = '*&(+",
Shape factors for the Terzaghi equations
S Sq SC
Square 0.8 1 1.3
Circular 0.6 1 1.3
Rectangular 1-0.2 B/L 1 1+0.3 B/L
Dr. Abdulmannan Orabi IUST 17
BEARING-CAPACITY EQUATIONS
Terzaghis Bearing Capacity Theoryfor 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
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
BEARING-CAPACITY EQUATIONS
Meyerhof s Bearing Capacity Equation
Dr. Abdulmannan Orabi IUST 20
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
BEARING-CAPACITY EQUATIONS
Meyerhof s Bearing Capacity Equation
Vertical load:
= 0.5! + ! + !
= 0.5$! + $! + $!
Inclined load:
Dr. Abdulmannan Orabi IUST 22
BEARING-CAPACITY EQUATIONS
Meyerhof s Bearing Capacity Equation
tan 2( ) tan (45 )2
qN e = +
( 1) cotC qN N =
( 1) tan(1.4 )qN N =
where , , ! "##"$ %&'&$()*&(+",
= 0, = 1 !: = ; + 2 = 5.14*+" = 0
Dr. Abdulmannan Orabi IUST 23
BEARING-CAPACITY EQUATIONS
Meyerhof s Bearing Capacity Equation
where
, , ! = '#*&(+",
1 0.1 .......... 10q pB
S S K forL
= = +
1 0 .2c pB
S KL
= +
CD = ( E(45 +
2)
= = 1*+" = 0
24Dr. Abdulmannan Orabi IUST
! , ! , !! = #'(*&(+",
BEARING-CAPACITY EQUATIONS
Meyerhof s Bearing Capacity Equation
where
1 0 .2 fC pD
d KB
= +
1 0 .1 .... 1 0fq pD
d d K f o rB
= = +
! =! = 1*+" = 0
Dr. Abdulmannan Orabi IUST 25
$ , $ , !$ = F &8$ ($+
