國立交通大學土木工程系黃安斌老師 1

An-Bin Huang

Chapter 6Mat Foundations

6.1 Introduction When a line of multiple columns are supported by a single

footing – combined footing

When more than one line of columns are supported by aconcrete slab, includes: Rectangular footing Trapezoidal footing Strap footing

Generally used with soil that has a low bearing capacity

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6.2 Combined footings

•Find resultant Q1+Q2

•The resultant should pass through the centroid

•Determine the dimensions of the footing

Rectangular combined footing

Trapezoidal combined footing

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Strap combined (cantilever) footing

6.3 Common types of mat foundations aka raft foundation

High column load on soft soils

Spread footings cover more than half the building area

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Common types of mat foundations

(a) Flat plate(b)Flat plate thickened under

column(c)Beams and slab(d)Flat plate w/ pedestals(e)Slab w/ basement walls

Effective embedment for mats

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6.4 Bearing capacity of mat foundations

idsqiqdqsqcicdcscu FFFBNFFFqNFFFNcq 2

1

fuunet Dqq )(

B = smaller dimension of the mat

Minimum FS = 1.75 – 2 but mostly larger than 3

The general bearing capacity equation

國立交通大學土木工程系黃安斌老師 6

qnet(all) in clays

B

D

L

Bsq f

uallnet 4.01195.0

1713.1)(

qFFNsq cdcscuu = 0Nc = 5.14Consider Fcs & Fcd

FS = 3

qnet(all) in granular soil

22

60)( /

25

3.0

08.0mkN

mmSF

B

BNq e

dallnet

260

60)( /

25

)(63.16

2533.01

08.0mkN

mmSN

mmS

B

DNq eef

allnet

When B is large:

Fd = 1 + 0.33(Df/B) ≤ 1.33

Equation (6.12)

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Raft versus isolated footings

Mat foundationsTotal settlement of 50mm and differential

settlement 19mm Isolated footingsTotal settlement of 25mm and differential

settlement 19mm Rigidity helps Consider Fd = 1, allowable settlement = 50mm,

Eq. 6.12 can be approximated as:

260)( /25 mkNNq allnet

Net bearing pressure

)(allnetf qDA

Q

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6.5 Differential settlement of mats American Concrete Institute Committee, 1988

Based on rigidity factor, Kr

∑ ∑

flexural rigidity of the superstructure and foundation perunit length at right angle to B

∑ = flexural rigidity of the framed members at right anglesto B

∑ = flexural rigidity of the shear walls (a = thickness, h = height of shear wall)

3BE

IEK

s

br

The ratio of differential/total settlement

= elastic modulus of the material of the structure

= moment of inertia per unit length of the structure atright angle to B

= elastic modulus of the soil

B = width of the mat foundation

= 0 if Kr > 0.5

= 0.1 if Kr = 0.5

= 0.35 (square mat) to 0.5 (long mat) if Kr = 0

3BE

IEK

s

br

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6.6 Field settlement observations for mat foundations

Table 6.1

Based on Equation 6.12 (when B is large)

60

)(2

N

qmmS allnet

e

(Meyerhof, 1965)

260

60)( /

25

)(63.16

2533.01

08.0mkN

mmSN

mmS

B

DNq eef

allnet

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6.7 Compensated foundations

For structures on very soft clays….

For compensated foundations

fDA

Qq

For fully compensated foundations (q = 0)

A

QDf

f

unetunet

DAQ

q

q

qFS

)()(

f

fu

DAQ

B

D

LB

c

FS

4.01

195.0114.5

For saturated clays

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6.8 Structural design of mat foundations

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Emirate towers on raft-pile foundation

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Burj Dubai, >800 m

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Proposed Nakheel tower in Dubai > 1000m

Homework

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End of Chapter 6