DESIGN OF STIFFENED SLABS-ON- GRADE ON … Slabs on Grade on... · DESIGN OF STIFFENED...

J.L. Briaud –Texas A&M University.

DESIGN OF STIFFENED SLABS-ON-

GRADE ON SHRINK-SWELL SOILS

Jean-Louis BriaudPresident of ISSMGE, Professor Texas A&M University, USA

Remon AbdelmalakGeo-Engineer, Dar Al-Handasah Group, Cairo, Egypt

Xiong ZhangAssistant Professor, University of Alaska, USA


Threshold of Optimum Simplicity


• SOME FUNDAMENTAL REMARKS

• THE PROBLEM

• THE SOLUTIONS (FOUNDATIONS, DESIGNS)

• DEVELOPMENT OF THE DESIGN METHOD– EQUATION FOR SHAPE OF SOIL SURFACE (FLEX COVER)

– MAXIMUM WATER TENSION RELATED TO WEATHER

– MAX MOMENT AND DEFLECTION WHEN SLAB ON SOIL

– PARAMETRIC STUDY

– DESIGN CHART DEVELOPMENT

• CASE HISTORY


Soil State Swell Shrink

Unsaturated Yes No

Saturated Yes Yes

Saturated No Yes

GWL

THE THREE ZONES


WATER NORMAL STRESS

TENSION COMPRESSION

0

(SUCTION)

(pF )

uw (kPa)

(PORE PRESSURE)


Water Tension 200kPa

Water Tension 100,000kPa

WaterContractile Skin

SmectiteAl2Si4O10(OH)2

Water

QuartzSiO2

QuartzSiO2


GARNER’S STUDY (2002)

3 samples at 3 water contents sent to 8 laboratories.

WATER CONTENT, %

Sample 1

Sample 2

Sample 3

WATER TENSION

log (uw in kPa)

Sample 1

Sample 2

Sample 3

WATER TENSION, kPa

Sample 1

Sample 2

Sample 3

0 5 10 15 20 25 30 %

0 1 2 3 4 5 log kPa

0 15000 30000 45000 60000 kPa


Saturated Soils = 1 stress controls the behavior, theeffective stress, σ - uw

Unsaturated Soils = 2 stress state variables needed, σ - ua and uw - ua


For Unsaturated Soils

The effective stress is

σ’ = σ – α uw – (1- α) ua

σ’ = σ – α uw

The effective stress controls the behavior of the soil skeleton for saturated soils and for unsaturated soils (in most cases)


w

wSW

DV/V

wSH

0

gw/gdShrink-Swell

Index1


CLASSIFICATION OF SHRINK-SWELL POTENTIAL

ACCORDING TO SHRINK-SWELL INDEX

Potential

Very High

High

Moderate

Low

Iss

> 60%

40 – 60

20 – 40

< 20%

J.L. Briaud –Texas A&M University.13

TYPICAL DAMAGE CAUSED

BY SHRINK-SWELL SOILS

SUMMER WINTER

SwellSwell

No changeNo Change

Shrink Shrink

18

FOUNDATION SOLUTIONS

air gap

• Stiffened Slab on Grade

• Elevated Structural Slab on Piers

• Stiffened Slab on Grade and on Piers

• Thin Post Tensioned Slab


SOME DESIGN METHODS FOR

SLAB-ON-GROUND ON

SHRINK-SWELL SOILS

• BRAB (1968)

• Lytton (1970, 1972, 1973)

• Walsh (1974, 1978)

• Swinburne (1980)

• PTI (1980, 1996, 2004)

• AS 2870 (1980, 1996)

• WRI (1981, 1996)


..

.

Tributary Load Area

..

.0

.

.0 0

.

.0 0

.

.

Leqv

Leqv


Q (kN/m)

Mmax

Leqv Δ = f ( Q, EI, L)

EI

Tolerable Distortion

Δ / L = 1/480 Edge drop

Δ / L = 1/960 Edge liftACI 302

Weather Model

Moisture Diffusion Model

Soil Volume change Model

Soil- Structure Interaction Model


1. Develop a realistic shape of the soil mound partially covered by a flexible cover, function of ΔlogUff

2. Simulate the effect of the weather for 6 cities over a 20 year period to get ΔlogUff.

3. Place the foundation on top of that mound, and obtain Mmax and Δmax

4. Perform an extensive parametric study to find the most important parameters

5. Develop simple design charts based on the results of tasks 1 through 4 to obtain the beam depth and the beam spacing without having to use a computer

DEVELOPMENT OF THE METHOD

VARARIATION OF WATER TENSION

WITH DEPTH

DU(zmax) = 0.1 2DU0

Tension, U

Dep

th, z

Ue0

zmax

U(z,t)

DU0DU0

After Mitchell (1979)

2

2

10log w

U U

t z

U u


Where

ρ(x) = vertical movement

x = horizontal distance

f = the ratio between vertical movement and

volume change

γh = slope of the suction vs. volume change curve

H = the depth of the active zone

ΔUedge = amplitude of water tension variation at the edge of

the flexible cover (U = log(u))

L = length of the flexible cover (slab)

ω = 2 π/T where T is the weather return period

αfield = field diffusivity of soil.

2 21

112 12

2 1221 21122

2 1 exp 2 cosh2 2 1

cosh22

n

nfield field

h edge

n

field

H H xn nH

x f H ULH n

nnH

g

D


Developed a procedure to include the influence of the cracks

in the field on the value of alpha in the lab.

β = ratio of crack depth over depth of active zone (Hact)

FCrkDif = ratio of field diffusivity over lab diffusivity (αlab)

To = weather return period

Cracked Soil Diffusion Factor

0

10

20

30

40

50

60

70

1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00

lab T0 / Hact2

FC

rkD

if

Beta = 0.6667

Beta= 0.80

Beta = 0.5

Influence of cracks is minimum

when diffusivity

is very largeor very small


Ran 18 simulations of weatherfor 6 cities and

for 20 years each to get the change in water tension Δuff and Δuedge

at the ground surfaceusing the FAO-56 methodology

m

y

y

x

1.5

L

L0.5L

40 Columns of equal

width elements20 Columns of elements with

bias 1.1

25 C

olum

ns o

f el

emen

ts w

ith

bias

1.1

Edge Drop Mound

Cen

ter

Lin

e (

Lin

e of

sym

met

ry)

Foundation slab

ΔuedgeΔuff


Osborne (1999)

29

Current available methods

Temperature (Thornthwaite, MBC) temp only

Radiation (MMBC, Harg, Turc) temp + radiation

Combination ( FAO 56 PM, ASCE2000 PM) many factors

FAO 56 Penman-Monteith method

International standard, globally valid

Can use daily or hourly weather data

EVAPOTRANSPIRATION METHODS


FAO 56 PENMAN-MONTIETH METHOD

Ra

Rs

Rs

Rns

Rnl

Rn =R

ns-R

nlEarth

G=0

ET=(Rn-G)

absorption

Reflection from

clouds

Wind

Mass Transfer Process Energy Balance

Atmosphere

ET=( es- e

d) f (u)

Rl, down

Rl, up

2

0

2

9000.408

273

1 0.34

n s aR G u e eTET

u

g

g

D

D

FPenman-Montieth Method

31

7

7 1

7 1

( / )8.64 10

/ / 8.64 10 ( )

( )/ / 8.64 10 ( )

(bare soils and grass root zone)

w

bare soil surfacew

grass NWL s grass

tree NWL s tree

C

uk NWLm s

g z

S V V NWL H s

S V tree V NWL H s

NWL ET P

(tree root zone) CNWL ET

DIFFERENT BOUNDARY CONDITIONS

Net water loss, source term

Bare soil:

Grass root zone:

Tree root zone:


Daily MeanTemperature

of Arlington, Texas

0

20

40

60

80

100

08

/01

/99

10

/01

/99

12

/01

/99

02

/01

/00

04

/01

/00

06

/01

/00

08

/01

/00

10

/01

/00

12

/01

/00

02

/01

/01

04

/01

/01

06

/01

/01

08

/01

/01

10

/01

/01

(oF

)

Daily Mean Relative Humidity

of Arlington, Texas

0

20

40

60

80

100

08

/01

/99

10

/01

/99

12

/01

/99

02

/01

/00

04

/01

/00

06

/01

/00

08

/01

/00

10

/01

/00

12

/01

/00

02

/01

/01

04

/01

/01

06

/01

/01

08

/01

/01

10

/01

/01

(%

)

Daily Mean Wind Speed

of Arlington, Texas

0

2

4

6

8

10

08

/01

/99

10

/01

/99

12

/01

/99

02

/01

/00

04

/01

/00

06

/01

/00

08

/01

/00

10

/01

/00

12

/01

/00

02

/01

/01

04

/01

/01

06

/01

/01

08

/01

/01

10

/01

/01

(m/s

)

Daily Acumulative Rainfall

of Arlington, Texas

0

20

40

60

80

100

08

/01

/99

10

/01

/99

12

/01

/99

02

/01

/00

04

/01

/00

06

/01

/00

08

/01

/00

10

/01

/00

12

/01

/00

02

/01

/01

04

/01

/01

06

/01

/01

08

/01

/01

10

/01

/01

(mm

/day

)

Input Weather Data (FAO 56)

../../Short Course Shrink-Swell 2005/My Documents/FondSup-Paris/FondSup2003/simulation_presentaion1.xls


Weather DlogUff(kPa) 1.392 0.788 1.283

Soil-weather

H (m) 3.3 2.4 1.8

Soil ISS (%) 60 45 30

StructuralDimensions

(m)12X12 24X24 24X12

College

Station

TX

San

Antonio

TX

Austin

TX

Dallas

TX

Houston

TX

Denver

CO

DlogUff(kPa) 0.788 1.392 0.866 1.295 1.283 1.374

DlogUedge(kPa) 0.394 0.696 0.433 0.648 0.642 0.687


CALIBRATIONS OF MODEL AGAINST LARGE SCALE LAB EXPERIMENT


CALIBRATIONS OF MODEL AGAINST LARGE SCALE LAB EXPERIMENT

44 rows of elements &

60 columns of elements

each element is 10 X 10 mm

Foundation cover, R=0.4 m

(phase II only)

zr

Ax

is o

f sy

mm

etry

Tank bottom base

Tan

k p

erim

eter

wal

l

Free surface

Measured and Predicted Average Movements at soil surface

-2

-1

0

1

2

3

4

5

6

7

0 30 60 90 120 150 180 210 240 270Time (day)

Mo

vem

ents

(m

m)

Predicted

Measured


m

y

y

x

1.5 L

L0.5L

40 Columns of equal


bias 1.1

25 C

olumn

s of e

lemen

ts wi

th

bias 1

.1

Edge Lift Mound

Cente

r Line

( Line

of sy

mmetr

y)

Foundation slab

Edge Lift Case

140 Abaqus simulations covering manyweather, soil, and structure parameters


Edge Drop Case

140 Abaqus simulations covering manyweather, soil, and structure parameters

m

y

y

x

1.5 L

L0.5L

40 Columns of equal


bias 1.1

25 C

olumn

s of e

lemen

ts wi

th

bias 1

.1

Edge Drop Mound

Cente

r Line

( Line

of sy

mmetr

y)

Foundation slab


Soil mound and foundation elevations

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 1 2 3 4 5 6 7 8

x- coordinate (m)

y-

co

ord

ina

te (

m)

Initial Mound Elev.

Final Mound Elev.

Final Found Elev

Edge Drop Case


Bending moments and shearing forces

-60

-40

-20

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7 8

x- coordinate (m)

V (

kN

) o

r M

(k

N.m

)

Shearing Force, V

Bending Moment, M

Edge Drop Case


Soil mound and foundation elevations

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 1 2 3 4 5 6 7 8

x- coordinate (m)

y- c

oord

inat

e (m

)

Initial Mound Elev.

Final Mound Elev.

Final Found Elev

Bending moments and shearing forces

-60

-40

-20

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7 8

x- coordinate (m)

V (

kN

) or

M (

kN

.m)

Shearing Force, V

Bending Moment, M


w

MLeqv

max2

Bending

Moment

Diagram

Shearing

Force

Diagram

Mmax

Vmax

Weightless Perfectly

Flexible Cover

Initial Soil

Mound

ym

em

Deflected

Foundation Slab Lgap

Leqv

Final Soil Mound

Dmax

DEFINITIONS


IS-W Comment Iss (%) H (m) DU0 (pF) D (m) L (m) wimposed (kPa)

0 No mound 45 3.5 0 0.9 16 3.5

2.0475 reference 45 3.5 1.3 0.9 16 3.5

3.4125 Iss- Very High 75 3.5 1.3 0.9 16 3.5

2.73 Iss- High 60 3.5 1.3 0.9 16 3.5

1.365 Iss- Moderate 30 3.5 1.3 0.9 16 3.5

0.6825 Iss- Low 15 3.5 1.3 0.9 16 3.5

3.2175 H- Very High 45 5.5 1.3 0.9 16 3.5

2.6325 H- High 45 4.5 1.3 0.9 16 3.5

1.4625 H- Moderate 45 2.5 1.3 0.9 16 3.5

0.8775 H- Low 45 1.5 1.3 0.9 16 3.5

2.52 DU-Very High 45 3.5 1.6 0.9 16 3.5

2.28375 DU-High 45 3.5 1.45 0.9 16 3.5

1.81125 DU-Moderate 45 3.5 1.15 0.9 16 3.5

1.575 DU-Low 45 3.5 1 0.9 16 3.5

2.0475 wimposed-Very High 45 3.5 1.3 0.9 16 5

2.0475 wimposed -High 45 3.5 1.3 0.9 16 4.25

2.0475 wimposed-Moderate 45 3.5 1.3 0.9 16 2.75

2.0475 wimposed-Low 45 3.5 1.3 0.9 16 2

6.6 All maximums 75 5.5 1.6 0.9 16 3.5

0.225 All minimums 15 1.5 1 0.9 16 3.5

DlogUff


Influence of soil shrink-swell potential on Leqv

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2

Normalized Iss ( Iss / Iss (reference case))

No

rmal

ized

Leq

v

(Leq

v/

Leq

v (

refe

ren

ce c

ase

))

Edge drop case

Edge lift case

Influence of soil surface suction change on Leqv

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Normalized DU0 ( DU0 / DU0 (reference case))

No

rmal

ized

Leq

v

(Leq

v/

Leq

v (

refe

ren

ce c

ase)

)

Edge drop case

Edge lift case

Influence of slab beam depth on Leqv

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2

Normalized D ( D / D (reference case))

No

rmal

ized

Leq

v

(Leq

v/

Leq

v (

refe

ren

ce c

ase

))

Edge drop case

Edge lift case

Influence of slab imposed loads on Leqv

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5

Normalized wimposed ( wimposed / wimposed (reference case))

No

rmal

ized

Leq

v

(Leq

v/

Leq

v (

refe

ren

ce c

ase

))Edge drop case

Edge lift case

Influence of slab length on Leqv

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4

Normalized L ( L / 2H (reference case))

No

rmal

ized

Leq

v

(Leq

v/

Leq

v (

refe

ren

ce c

ase

))

Edge drop case

Edge lift case

Influence of depth of active moisture zone on Leqv

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2

Normalized H ( H / H (reference case))

No

rmal

ized

Leq

v

(Leq

v/

Leq

v (

refe

ren

ce c

ase

))

Edge drop case

Edge lift case

Leqv

as a f()of

Iss

ΔlogUff

HDLw


SOIL WEATHER INDEX Isw

Isw = Iss H ΔlogUedge

ΔlogUedge = 0.5 ΔlogUff

Iss = shrink-swell index = wsw – wsh (e.g. 0.2)

H = depth of shrink-swell movement (e.g. 3m)

ΔlogUff = change in water tension in the free field due to

weather (e.g. 1.4)

ΔlogUedge = change in water tension at the edge of the

foundation and at the soil surface (e.g. 0.7)

Isw = 0.2 x 3 x 0.7 = 0.42


Soil-Weather Index versus Equivalent cantilever length.

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6 7

Iss H DU0 (m)

Leqv. (m

)

944.0

12

0

R

bI

aILL

WS

WSeqv

Isw = Iss H ΔlogUff (m)

Le

qv

(m)

Soil-Weather Index vs Equivalent Cantilever Length


Water Tension based design charts (Edge drop)

Leqv design chart (Edge drop)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0 0.2 0.4 0.6 0.8 1 1.2

Iss. H. DUedge (m)

Leq

v (

m)

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

2

2

max

eqvqLM

Iss H ΔlogUedge (m)


Lgap design chart (Edge drop)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0 0.2 0.4 0.6 0.8 1 1.2

Iss. H. DUedge (m)

Lg

ap (

m)

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m




FDmax design chart (Edge drop)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0 0.2 0.4 0.6 0.8 1 1.2

Iss. H. DUedge (m)

FD

max

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

EIF

qL eqv

max

4

max

D

D




FV design chart (Edge drop)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0 0.2 0.4 0.6 0.8 1 1.2

Iss. H. DUedge (m)

FV

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 meqvvqLFV max




Leqv design chart (Edge lift)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 0.2 0.4 0.6 0.8 1 1.2

Iss. H. DUedge (m)

Leq

v (

m)

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

2

2

max

eqvqLM

Water Tension based design charts (Edge lift)



FDmax design chart (Edge lift)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0 0.2 0.4 0.6 0.8 1 1.2

Iss. H. DUedge (m)

FD

max

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

EIF

qL eqv

max

4

max

D

D




FV design chart (Edge lift)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 0.2 0.4 0.6 0.8 1 1.2

Iss. H.DUedge (m)

FV

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 meqvvqLFV max




Developed a simple correlation between theSlope of the SWCC Cw and the shrink-swell index Iss.

CW = 0.51 ISS

R2 = 0.889

0

5

10

15

20

25

15 20 25 30 35 40 45

Iss (%)

Cw

(%

)

ThereforeΔwedge = Cw ΔlogUedge = 0.5 Iss ΔlogUedge

Then ISW (for water tension) = ISS H ΔlogUedge = 2 H Δwedge

ISW (for water content) = H Δwedge

ISW (for water tension) = 2 ISW (for water content)

ISS = 0.734 PI

R2 = 0.4965

15

20

25

30

35

40

45

20 25 30 35 40 45 50

PI (%)

I SS

(%)


Leqv design chart (Edge drop)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

0 0.1 0.2 0.3 0.4 0.5 0.6

H. Dwedge (m)

Leq

v (

m)

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

2

2

max

eqvqLM

Water content based design charts (Edge drop)


Lgap design chart (Edge drop)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0 0.1 0.2 0.3 0.4 0.5 0.6

H. Dwedge (m)

Lg

ap (

m)

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m




FDmax design chart (Edge drop)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0 0.1 0.2 0.3 0.4 0.5 0.6

H. Dwedge (m)

FD

max

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

EIF

qL eqv

max

4

max

D

D



FV design chart (Edge drop)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0 0.1 0.2 0.3 0.4 0.5 0.6

H. Dwedge (m)

FV

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

eqvvqLFV max


Water content based design charts (Edge lift)

Leqv design chart (Edge lift)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 0.1 0.2 0.3 0.4 0.5 0.6

H. Dwedge (m)

Leq

v (

m)

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

2

2

max

eqvqLM



FDmax design chart (Edge lift)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0 0.1 0.2 0.3 0.4 0.5 0.6

H. Dwedge (m)

FD

max

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 mEIF

qL eqv

max

4

max

D

D



FV design chart (Edge lift)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 0.1 0.2 0.3 0.4 0.5 0.6

H.Dwedge (m)

FV

deq=0.63 m

deq=0.51 m

deq=0.38 m

deq=0.25 m

deq=0.13 m

eqvvqLFV max


PROPOSED

DESIGN PROCEDURE

1.Water content version: one version of

the method uses the water content of the

soil.

2.Water tension version: one version of

the method uses the water tension in the

soil.


PROPOSED

DESIGN PROCEDURE

1.Gather site specific information on

active depth and amplitude of water

content or water tension variation at the

foundation level.

2.Use 3 charts to obtain maximum

bending moment, maximum shear force,

and maximum deflection (distortion)


Design example

Soil and weather data:

Depth of movement zone, H = 3.0 m

Soil surface water content change Δwff = 20%

Slab data:

Slab dimensions = 20 X 20 m

Beam spacing, s = 3.0 m (for both directions)

Beam depth, h = 1.2 m

Beam width, b = 0.3 m

Slab load, w = 10 kPa


Soil-Weather Index Is-w

Δwedge = 0.5 Δwff = 0.5 x 0.2 = 0.1 or 10%

Is-w = Δwedge x H = 0.1 x 3 = 0.3 m

Slab bending stiffness

EI = E bh3/12 = 2 x 107 x 0.3 x 1.23 / 12 = 8.64 x 105 kN.m2

Equivalent slab thickness

b h3/12 = s deq3/12

deq = h (b/s)1/3 = 1.2 (0.3/3)1/3 = 0.56 m

Values from charts

Leq = 5.3 m for maximum moment

Lgap = 3.6 m for information

FΔmax = 2.9 for maximum deflection

Fv = 0.8 for maximum shear


Maximum bending moment

q = 10 x 3 = 30 kN/m line load on element

Mmax = 0.5 q Leq2 = 0.5 x 30 x 5.32 = 421.3 kN.m

Maximum deflection

Δmax = q Leq4 / f Δmax EI = 30 x 5.34 / 2.9 x 8.64 x 105

Δmax = 9.5 x 10-3 m

Maximum shear

Vmax = Fv q Leq = 0.8 x 30 x 5.3 = 127.2 kN

Distortion

L / Δmax = 10 / 9.5 x 10-3 = 1050

Leq / Δmax = 5.3 / 9.5 x 10-3 = 558


ELLISON BUILDING CASE

STUDY


CROSS SECTION

PLAN VIEW


Boring


Soil properties- Soil type: CH- PL=30%,LL=80%,PI= 50%- Percent clay = 60%- Allowable bearing pres. = 75 kPa- Depth to constant suction = 2.1 m- Modulus of Elasticity = 7000 kPa- Total unit weight = 20 kN/m3

Loads- No interior load- Perimeter loading = 32 kN/m- Live load = 2 kPa

LocationCollege Station, TX, USA

Concrete Slab properties- Compressive Strength = 20 MPa- Creep Modulus = 10000 MPA- Unit Weight = 23 kN/m3

- Beam width = 0.3 m- Slab thickness = 100 mm- Allowable distortion Δ/L=1/500

CASE HISTORY DATA


#4@16" OCEW

0.1 m

1.05 m

3-#6

#3 TIES @ 24" C-C

2-#5

6 MIL POLY

0.3 m

3-#6

70


Site Preparation - 11 June 2004


Fill and Compaction - 14 July 2004


Excavation and steel - 16 July 2004


Installing Tell Tales – 13 Aug 2004


0.5m

V.E

1.0m

V.E

2.0m

V.E

3.0m

V.E

5.0m

V.E

Lubricant

Concrete

Half inch

rod

Sand

PVC

Sleeve

Half inch

rod

Lubricant

Sand

PVC

Sleeve

CROSS SECTION


Installing Benchmark - 13Aug 2004


Installing Slab Bolts – 13 Aug 2004


Steel Framing - 13-25 Aug 2004


Wall Construction - Sept 2004


Completed Building


0.0

4.4

8.9

13.3

17.7

22.2

26.6

31.0

35.4

18.314.2

10.26.1

2.0-0.005

0

0.005

0.01

0.015

0.02

0.025

Elevation (m)

Length (m)

Width (m)

Elevation is referenced to the lowest point on Sept 1, 2004

0.02-0.025

0.015-0.02

0.01-0.015

0.005-0.01

0-0.005

-0.01-0Entrance

INITIAL ELEVATIONS - 1 Sept 2004


Soil movement log

0

3

6

9

12

15

-0.005 0 0.005 0.01 0.015

Movements (m)D

epth

(ft)

Corner Ext movement ( Sept - Oct )

Center Ext movement ( Sept - Oct )

Corner Ext movement ( Sept - Dec )

Center Ext movement ( Sept - Dec )

Corner Ext movement ( Sept - Feb05 )

Center Ext movement ( Sept - Feb05 )

Corner Ext movement ( Sept 04 - Apr05 )

Center Ext movement ( Sept 04- Apr 05 )

MOVEMENT (m)

DE

PT

H (

0.3

m)


Perimeter average level vs. Interior average level

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 30 60 90 120 150 180 210 240 270

Time (days)

Re

lati

ve

ele

va

tio

ns

in

(m

)

Perimeter average level

Interior average level

Difference (per-int)

SLAB MOVEMENT over 1 YEAR


COST

Foundation with 1.05 m deep beams: 100 $/m2

Foundation with 0.52 m deep beams: 60 $/m2

Completed Building: 1600 $/m2

Increase in cost: 40 $/m2 or40/1600 = 2.5% of building cost

Slab stiffness increased 8 times (1.05/0.52)3


Weather ModelFAO 56

(simulation for different cities)

Soil-Water Diffusion

ModelISS,lab, field

Soil Volume Change DU & H

Suction Envelopes

Soil- Structure Model

New Design Charts

The proposed method

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