Bearing Capacity of Shallow Foundations

Dr. Sayed Mohamed Elaraby

Ain Shams UniversityFaculty of Engineering

Structural Engineering Dept.Geotechnical Group

3rd Year Civil

1

Table of Contents• Part 1: Review of Soil Compressibility and Shear Strength

2Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th Ed.

• Part 2:

1. Introduction

2. Geotechnical Design Criteria for Foundations

3. Modes of Shear Failures

4. Bearing Capacity Equations

5. Effect of the Groundwater Table

6. Effect of the Load Eccentricity

7. Bearing Capacity of Multi-layers Soils

Code: Egyptian Code of Practice for Soil Mechanics and Foundations Part 3 : Shallow Foundations - 2001

3

Review of Soil Compressibility and Shear Strength

Part 1

4

CD or CID

CU or CIU

UU

Traxial Tests Other tests Unconfined + direct shear

CD/ Sand

UU/Clay

𝝉 = 𝝈′ 𝐭𝐚𝐧𝝓′

𝝉 = 𝒄𝒖 & 𝝓 𝒖 = 𝟎

CU/NC Clay 𝝉 = 𝝈′ 𝐭𝐚𝐧𝝓′

𝝉 = 𝝈 𝐭𝐚𝐧𝝓

CD/OC Clay

NC Clay𝝉 = 𝒄′ + 𝝈′ 𝐭𝐚𝐧𝝓′

Soil Shear Strength

5

ECP-Part 3

6

ECP-Part 3

7

Di

D

𝑆 = 𝛿𝑖

𝛿𝑖 =Δ𝑝

𝐸𝑠𝐷𝑖 = 𝑚𝑣 Δ𝑝 𝐷𝑖Sand & Clay :

Clay (NL): 𝛿𝑖 =𝐶𝑐 𝐷𝑖1 + 𝑒0

log 1 +Δ𝑝

𝑝0′

Clay (OC): 𝛿𝑖 =𝐶𝑟 𝐷𝑖1 + 𝑒0

log 1 +Δ𝑝

𝑝0′

Tests: Odometer & Triaxial

Soil Compressibility

8

ECP-Part 3

9

1. Introduction

Part 2

• Foundation Types:

Shallow foundations

a. Spread Isolated footings (square, circular,

rectangular, strip footings)

a. Combined Footings

b. Mat or Raft Foundations

Deep foundations

a. Bored piles (drilled piers)

b. Driven piles

c. Caissons10

11

Shallow Foundations

RaftsSpread/Isolated Footings

Combined Footings

Basics

• Depth of foundation ≤ twice the foundation width.

• Shear resistance of the soil above the foundation level is ignored.

Strip

12

Geotechnical engineers have two ways of defining bearing pressure: gross bearing pressure qgross and net bearing pressure qnet.

𝑞𝑔𝑟𝑜𝑠𝑠 =𝑊 +𝑄

𝐴=𝑊

𝐴+𝑄

𝐴Where

𝑞𝑛𝑒𝑡 =𝑄

𝐴

𝑞 = 𝛾1𝐷𝑓 ≅𝑊

𝐴𝑞𝑔𝑟𝑜𝑠𝑠 = 𝑞 + 𝑞𝑛𝑒𝑡

𝑂𝑟 𝒒𝒏𝒆𝒕 = 𝒒𝒈𝒓𝒐𝒔𝒔 − 𝒒

Ultimate gross bearing capacity qu,gross (or simply qu) is the maximum gross pressure between the foundation and the soil which will produce shear failure in the soil.

Ultimate net bearing capacity qu,net

𝒒𝒖,𝒏𝒆𝒕 = 𝒒𝒖 − 𝒒

q=g1 Df

Q

W

qgross

13

Allowable bearing capacity qall is what is used in geotechnical design, and is the ultimate bearing capacity divided by a factor of safety. It usually defined in terms of the net stress.

Factor of safety Fb. In order to determine the allowable bearing pressure qall , the ultimate bearing capacity qult is divided by a factor of safety.

𝒒𝒂𝒍𝒍 =𝒒𝒖,𝒏𝒆𝒕𝑭𝒃

=𝒒𝒖 − 𝒒

𝑭𝒃

For dense sands and stiff clays 𝑞𝑢 ≫ 𝑞

𝒒𝒂𝒍𝒍 ≈𝒒𝒖𝑭𝑺

14

ECP-Part 3

15

2. Geotechnical Design Criteria for Foundations

16

Foundation must be safe against shear failure.

Foundation must not settle excessively.

The differential settlement must not cause distress to the structure.

CostTimeOther considerations

Transcona grain elevator

failure (1913)

Pisa Tower, Italy

Silos, Winnipeg,

Canada

Farm Silo Foundation Failure (1976)

Footing Width 17

Co

nta

ct P

ress

ure

Allowable Pressure

18

ECP-Part 3

19

ECP-Part 3

20

3. Modes of Shear Failures

21

General Shear FailureThere is a continuous shear failure of the

soil (solid lines) from below the footing tothe ground surface.

When the load is plotted versussettlement of the footing, there is adistinct load at which the foundation fails(solid circle), and this is designated Qult.

The value of Qult divided by the footingarea is considered to be the ultimatebearing capacity qult of the footing.

A general shear failure ruptures and pushes up the soil onboth sides of the footing. For actual failures in the field, thesoil is often pushed up on only one side of the footing withsubsequent tilting of the structure.

A general shear failure occurs for soils that are in a dense orhard state.

Local Shear Failure

The failure pattern is observed only immediately below the footing (a wedge and slipsurfaces originating at the edges of the footing).

There is soil bulging on both sides of the footing, but the bulging is not as significantas in general shear.

The load-settlement curve does not show a clear peak as in the general shear failure. When the load per unit area equals qult, the movements are accompanied by jerks

(sudden movements). Local shear failure can be considered as a transitional phase between general shear

and punching shear. Because of the transitional nature of local shear failure, thebearing capacity could be defined as the first major nonlinearity in the load-settlement curve (open circle) or at the point where the settlement rapidly increases(solid circle).

The vertical compression under the footing is significant

22

Local Shear Failure

The failure pattern is not easy to observe (unlike in the failure modes discussedearlier). The soil outside the loaded area remains relatively uninvolved and there isminimal movement of soil on both sides of the footing.

The process of deformation of the footing involves compression of soil directly belowthe footing as well as the vertical shearing of soil around the footing perimeter.

the load settlement curve does not have a dramatic break and for punching shear,the bearing capacity is often defined as the first major nonlinearity in the load-settlement curve (open circle). A punching shear failure occurs for soils that are in aloose or soft state.

The vertical compression under the footing is significant.

23

24

Shal

low

fo

un

dat

ion

s

Deep foundations

25

4. Bearing Capacity Equations

26

Active wedge

Radial wedgePassive

wedge

1

Terzaghi’s Method

27

Local Shear Failure

𝑐𝑙𝑜𝑐𝑎𝑙 𝑠ℎ𝑒𝑎𝑟 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 = 0.67 𝑐

𝜙𝑙𝑜𝑐𝑎𝑙 𝑠ℎ𝑒𝑎𝑟 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 = tan−1 0.67 tan𝜙

28

Example 1: Strip footing on cohesionless soil

Friction Angle: 36 degree Unit weight of soil: 18 kN/m3

Footing dimension: B = 2 m Depth of foundation: Df = 1m Factor of safety: Fb = 3

f

q = 1 * 18 = 18 kPa Nq = 47 Ng = 54

qu = 18 * 47 + 0.5 * 18 * 2 * 54 = 1818

qu,net = 1818-18 = 1800 kPa

qall,net = 1800/3 = 600 kPa

qall,net = 600 + 18 = 618 kPa

29

Example 2: Strip footing on cohesive soil

Undrained shear strength : 75 kPa Unit weight of soil: 18 kN/m3

Footing dimension: B = 2 m Depth of foundation: Df = 1m Factor of safety: Fb = 3

Nq = 1 Ng = 0Nq = 5.7q = 1 * 18 = 18 kPa

qu = 75 * 5.7 + 18 * 1 = 446

qu,net = 446 - 18 = 428 kPa

qall,net = 428/3 = 143 kPa ≈ the unconfined strength (2*75 = 150 kPa)

qall,gross = 143 + 18 ≈ 160 kPa

30

ECP-Part 3

31

32

Inclination Factors

33

34

35

5. Effect of the Groundwater Table

36

Groundwater ConsiderationZone 2

Zone 3

Zone 4

Zone 1

Zone 1 g1= g1,sub

Zone 3 g1= g1,b

g1

g2

d

≈B

2

g2= g2,sub

q = Df g1,subZone 2

g2= g2,sub

q = d g1,b + (Df –d)g1,sub

q = Df g1,b

g2= g2,sub+ (g2,b- g2,sub ) (d-Df)/B

Zone 4 g1= g1,b q = Df g1,b

g2= g2,b

37

ECP-Part 3

38

6. Effect of Eccentricity

39

M1

M2

𝑒𝐵 =𝑀1𝑃

𝑒𝐿 =𝑀2𝑃

𝐵′ = 𝐵 − 2𝑒𝐵 𝐿′ = 𝐿 − 2𝑒𝐿

B B

B - eB

40

Example 3:

For the square footing shown in the figure, determine the ultimate load using the ECP and assuming a one-way eccentricity of 0.15 m and a local shear failure.

B’ = 1.5 – 2*0.15 = 1.2 mL = 1.5 m

lq = 1 + 0.3 * 1.2/1.5 = 1.24

lg = 1 - 0.3 * 1.2/1.5 = 0.76

flocal failure = tan-1 ( 0.67 * tan 30) = 21 deg.

Nq = 7 Ng = 2.5

qu = 0.7 * 18 * 7* 1.24 + 8 * 1.2 * 2.5 * 0.76 = 128 kPa

GWT

qu,net = 128 – 0.7 * 18 = 115 kPa

Qu = 115 * 1.2 * 1.5 ≈ 200 kN

41

7. Bearing Capacity of Multi-layers Soils

42

ECP-Part 3

43

Thank you

Questions ?