Lecture 2 bearing capacity

Lecture

2

INTERNATIONAL UNIVERSITY FOR SCIENCE & TECHNOLOGY

�م وا�� ا�� ا��و�� ا��

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


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.


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.



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.


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



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


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.

��

8

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.




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.


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 EQUATIONSTerzaghi’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.

∅�




The ultimate bearing capacity, , of the foundation now can be obtained by considering the equilibrium of the triangular wedge ACD shown in Figure below

��



Terzaghi’s Bearing Capacity Equation

�� = 0.5�� + �� + ��

�� , �� , � !��"#�#�"$ %&�'�&$()*�&(+",

and depends on angle of shearing resistance (ø)(.�/. 4 − 1, ��,)

4ℎ#"#:

� = 4$!(ℎ+*(ℎ#*++($ %

� = 7 $(4#$%ℎ(+*(ℎ#,+$8/#8+4(ℎ#*+7 !�($+ 8#9#8

� = � ∗ ��

�� = 0, �� = 1� !�: = 1.5; + 1 = 5.71*+"∅ = 0Dr. Abdulmannan Orabi IUST 16


Terzaghi’s Bearing Capacity Equation

�� = 0.5�� + �� + ��

�� , �� , � !�� = �ℎ�'*�&(+",

Shape factors for the Terzaghi equations

Sγ 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



Terzaghi’s 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∅)



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.




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.




Vertical load:

�� = 0.5��!� + ��!� + ��!�

�� = 0.5��$�!� + ��$�!� + ��$�!�

Inclined load:




tan 2( ) tan (45 )2

qN e π φ φ= +

( 1) cotC qN N φ= −

( 1) tan(1.4 )qN Nγ φ= −

where�� , �� , � !�� "#�#�"$ %&�'�&$()*�&(+",

�� = 0, �� = 1� !�: = ; + 2 = 5.14*+"∅ = 0




where

�� , �� , � !�� = �ℎ�'#*�&(+",

1 0.1 .......... 10q p

BS S K for

Lγ φ= = + × ≥

1 0 .2c p

BS K

L= + ×

CD = (� E(45 +∅

2)

�� = �� = 1*+"∅ = 0

24Dr. Abdulmannan Orabi IUST

!� , !� , � !!� = �#'(ℎ*�&(+",



where

1 0 .2 fC p

Dd K

B= + ×

1 0 .1 .... 1 0fq p

Dd d K f o r

Bγ φ= = + × ≥

!� =!� = 1*+"∅ = 0


$� , $� , � !$� = F &8$ �($+ *�&(+",



where

$� = $� = 1 −G

90

E

� )∅

$� = 1 −G

∅

E

∅ > 0

$� = 0*+"G ≠ 0� !∅ = 0

G<∅

V

H

R



Hansen’s Bearing Capacity Equation ( General Equation )

Df

V

η

+β




'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 e π φ φ= +

( 1) cotC qN N φ= −

( 1) tan(1.4 )qN Nγ φ= −

where�� , �� , � !�� "#�#�"$ %&�'�&$()*�&(+",

�� = 0, �� = 1� !�: = ; + 2 = 5.14*+"∅ = 0





where

�� , �� , � !�� = �ℎ�'#*�&(+",

'

'1

q

C

C

N BS

N L= + ×

'

'1 sinq

BS

Lφ= +

'

'1 0.4

BS

Lγ = − �� ≥ 0.6


!� , !� , � !!� = �#'(ℎ*�&(+",

where




1 0 .4Cd K= +

21 2 ta n (1 s in )qd Kφ φ= + −

1

1

tan ( ) 1

f f

f f

D DK fo r

B B

D DK fo r

B B

−

= ≤

= f

!� = 1*+"�88∅

30




$� , $� , � !$� = F &8$ �($+ *�&(+",

where

1

1

q

C q

q

ii i

N

−= −

−1

0.5(1 )

cot

iq

f a

Hi

V A C

α

φ= −

+

20.7

(1 )cot

i

f a

Hi

V A C

αγ φ= −

+2

(0.7 / 450)(1 )

cot

o

i

f a

Hi

V A C

αγ

ηφ

−= −

+

2 ≤ OP� !OE ≤ 5





where

%� , %� , � !%� = Q"+7 !*�&(+",

%�� =

RS

147S%� = 1 −

RS

147S

%� = %� = 1 − 0.5(� R T





where

/� , /� , � !/� = ��,#*�&(+",

/�� =

US

147S*+"∅ = 0

/� = 1 −US

147S

/� = exp(−2U(� ∅) /� = exp(−2.7U(� ∅)

U$ "�!$� ,Dr. Abdulmannan Orabi IUST 33



�� = 5.14�� 1 +�� + !�

� − $�� − %�

� − /�� + �*+"∅ = 0

Where :

�� = 0.2

��

Y�!�� = 0.4Z

$�� = 0.5 − 1 −

[\

]��

/�� =

US

147S*+"∅ = 0

%�� =

RS

147S


The equation for ultimate bearing capacity by Terzaghihas 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.


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.




�� = 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+44�(#"(�/8#

When the water table lies within the wedge zone, can compute the average effective weight of the soil in the wedge zone as

��


When the water table is below the wedge zone [depth approximately ], the water table effects can be ignored for computing the bearing capacity.



[ = 0.5� tan( 45 + ∅/2)

Water table below the base of the footing

!^ > [

��

G.W.T.



Effect of Soil Compressibility

The change of failure mode is due to soil compressibility, to account for which Vesic (1973) proposed the followingmodification of bearing capacity equation :

�� = 0.5��!�� + ��!�� + ��!��

�� , �� !�� "#,+$8&+='"#,,$/$8$()*�&(+",

Where :




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

F̀ =Qa

�� +��(� ∅�4ℎ#"#

Qa = ,ℎ#�"=+!787,+*,+$8

�� = #**#&($9#+9#"/7"!# '"#,,7"#�(�!#'(ℎ(�� +b

E)




Step 2. The critical rigidity index, , can be expressed asF̀ (�`)

F̀ (�`) =1

2#c' 3.3 − 0.45

�

Y&+( 45 −

∅�

2

Step 3. If , thenF̀ ≥ F̀ (�`) �� =�� =�� = 1

However, if , thenF̀ < F̀ (�`)

�� = �� = #c' −4.4 + 0.6�

Y(� ∅� +

3.07,$ ∅� 8+%2F̀

1 + ,$ ∅�

�: = 0.32 + 0.12�

Y+ 0.68+%F̀ *+"∅ = 0

�: = �� − 1 − ��

��(� ∅�*+"∅ > 0


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

fa

N DBq

B B

+ = +

� > 1.2= � ≤ 1.2=d + e. ffgh

i≤ d. ff


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�) = �� − �



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


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

0.08ln

�k(==)

25

��(jk�) = 16.63�TT�k(==)

25

45

Lecture 2 bearing capacity

Engineering

Transcript of Lecture 2 bearing capacity