SOIL MODEL

ww

wwSWSW

∆∆V/V V/V

wwSHSH

00

γγww/γ/γddShrinkShrink--SwellSwellIndexIndex 11

Free Swell TestFree Swell Test

Free Shrink TestFree Shrink Test

∆∆WW

max

max

UN

SAT

.U

NSA

T.

SATURATED

SATURATED

((∆∆V/V/V)V)maxmax

J.L. Briaud J.L. Briaud ––Texas A&M University.Texas A&M University.

BASIC MODEL FOR VARIOUS SOILS

ww

∆∆V/V V/V

Clay, Low PlasticityClay, Low PlasticityIIssss = 10 = 10 −− 30 %30 %

ww

∆∆V/V V/V

ww

∆∆V/V V/V

ww

∆∆V/V V/V

Dirty Sand, SiltDirty Sand, SiltIIssss = 0 = 0 −− 10 %10 %

Gravel, Clean SandGravel, Clean SandIIssss = 0= 0

Clay, High PlasticityClay, High PlasticityIIssss = 30 = 30 −− 70 %70 %

J.L. Briaud J.L. Briaud ––Texas A&M University.Texas A&M University.

CLASSIFICATIONCLASSIFICATIONOF SHRINKOF SHRINK--SWELL POTENTIAL SWELL POTENTIAL

ACCORDING TO SHRINKACCORDING TO SHRINK--SWELL INDEXSWELL INDEX

PotentialPotential

Very HighVery High

HighHigh

ModerateModerate

LowLow

IIssss

> 60%> 60%

40 40 –– 6060

20 20 –– 4040

< 20%< 20%

J.L. Briaud J.L. Briaud ––Texas A&M University.Texas A&M University.

WATER STRESS

TENSION COMPRESSION

0

(SUCTION)

(pF )

uw (kPa)

(PORE PRESSURE)

Water Water StateState ExamplesExamples

SuctionSuctionpFpF cm cm

kPakPa

Degree Degree of of

SaturatioSaturationn

Water Water ContentContent

SwellSwell ShrinkShrink

Oven DryOven Dry 7 7 --101077 --101066 00 00

SuctionSuctionAir DryAir Dry 6 6 --101066 --

101055

TensionTensionShrinkage LimitShrinkage Limit 4 4 --101044 --

101033Near 100 Near 100

%%8 to 15 8 to 15

%%

Field Capacity Field Capacity Swell LimitSwell Limit

2 2 --101022 --101011

25 to 50 25 to 50 %%

0 0 0 0 00 100 %100 %

Large RiverLarge River 101033

101022

CompressioCompressionn

Deepest Deepest Offshore Offshore PlatformsPlatforms

101055

101044

Bottom of Bottom of Deepest OceanDeepest Ocean

101099

101088

YESYES

NONO

NONO

YESYES

SOME DESIGN METHODS FORSOME DESIGN METHODS FORSLABSLAB--ONON--GROUND ON GROUND ON SHRINKSHRINK--SWELL SOILSSWELL SOILS

BRAB (1968)BRAB (1968)Lytton (1970, 1972, 1973)Lytton (1970, 1972, 1973)Walsh (1974, 1978)Walsh (1974, 1978)SwinburneSwinburne (1980)(1980)PTI (1980, 1996, 2004)PTI (1980, 1996, 2004)AS 2870 (1980, 1996)AS 2870 (1980, 1996)WRI (1981, 1996)WRI (1981, 1996)

J.L. Briaud J.L. Briaud ––Texas A&M University.Texas A&M University.

THE WIRE REINFORCEMENT THE WIRE REINFORCEMENT INSTITUTE INSTITUTE FOUNDATION FOUNDATION

DESIGN DESIGN METHODSMETHODS

Cw =45

Cw =40

Cw =35

Cw =30

Cw =25

Cw =20

Cw=15

10 20 30 40 50 60 70 80 90 P.I.

1.1 3.0 4.8 6.4 7.7 8.9 10.0 11.0 12.0 PVC

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 Swell Index (%)

Supp

ort I

ndex

, C0.

6

0.7

0.8

0

.9

1.

0

-- WRI (1981, WRI (1981, 19961996))The Wire Reinforcement Institute design procedures war developed by Walter L. Snowden, P.E., of Austin, Texas. It is empirically derived by observing slab performance and writing and modifying equations to give results approximating the foundations that had been found to give satisfactory results. WRI uses the same approach as the BRAB method, that it can be considered as a modified version of BRAB.The WRI design procedure can be summarized as follows:The WRI design procedure can be summarized as follows:

11-- Determine the effective plasticity index (Determine the effective plasticity index (EffEff. PI) of the underlying 15 feet using . PI) of the underlying 15 feet using weighting factors equal to 3, 2, and 1 for the first, second, anweighting factors equal to 3, 2, and 1 for the first, second, and third 5d third 5--feetfeet--layer layer respectively.respectively.

22-- Modify Modify EffEff. PI for any natural ground slope and . PI for any natural ground slope and overconsolidationoverconsolidation using the using the correction coefficients obtained from WRI (1996) charts.correction coefficients obtained from WRI (1996) charts.

33-- Divide slabs of irregular shape into overlapping rectangles of Divide slabs of irregular shape into overlapping rectangles of length (L) and length (L) and width (Lwidth (L’’).).

44-- Choose the climatic rating index (CChoose the climatic rating index (CWW) (same as BRAB) and then ) (same as BRAB) and then determine the soildetermine the soil--climate support index.climate support index.

55-- Determine the beam spacing (S) using WRI (1996) beam spacing Determine the beam spacing (S) using WRI (1996) beam spacing chart.chart.

66-- Determine the cantilever length (Determine the cantilever length (lclc) based on the soil) based on the soil--climate support climate support index using WRI (1996) cantilever length chart.index using WRI (1996) cantilever length chart.

77-- Determine the length modification factor for the long and shortDetermine the length modification factor for the long and shortdirections (directions (klkl & & ksks) respectively using the WRI (1996) slab length ) respectively using the WRI (1996) slab length modification factor chart.modification factor chart.

88-- The modified cantilever lengths (The modified cantilever lengths (LcLc) in both directions will be ) in both directions will be klkl lclc & & ksks lclc..

99-- Calculate the number of beams in both directions as follows: Calculate the number of beams in both directions as follows: NlNl = L= L’’/S + 1 /S + 1 & Ns = L/S + 1 & Ns = L/S + 1

1010-- Maximum bending moment, shearing force and differential deflectMaximum bending moment, shearing force and differential deflection ion can be calculated for each direction from:can be calculated for each direction from:

( )

( )( )

IELLw

LwLV

LwLM

c

c

c

c

4'

'2

'

4

2

=∆

=

= Where: M = Moment, positive or negative

∆ = Deflection in inches

Ec = Creep modulus of elasticity of concrete

I = Moment of inertia of section

12- Assume beam widths and calculate (B ), sum of all beam widths.

13- Calculate beam depth either for reinforced steel or prestressed using the corresponding equation:

3

3

553

664

BMLd

BMLd

c

c

=

= Where: M = Moment in KF

Lc = Cantilever length (k Ic )

Reinforced Steel

Prestresses

THE POSTTHE POST--TENSIONING INSTITUTETENSIONING INSTITUTEFOUNDATION DESIGN FOUNDATION DESIGN METHODSMETHODS

DAMAGE MODES FOR SLABSDAMAGE MODES FOR SLABSON SHRINKON SHRINK--SWELL SOILSSWELL SOILS

∆

∆

y m

y m

e m

e m

E d g e M o is tu r e D is ta n c e

P e r im e te r L o a d

P e r im e te r L o a d

U n ifo r m L o a d

P e r im e te r L o a d

P e r im e te r L o a d

U n ifo r m L o a d

S la b L e n g th

S la b L e n g t h

I n i t ia l G r o u n d S u r fa c e

I n it ia l G r o u n d S u r fa c e

( a ) C e n te r l i f t (o r E d g e d ro p ) c a s e

(b ) E d g e l i f t ( o r C e n te r d ro p ) c a s e

Ground Surface If Slab Has No

Weight

Ground Surface If Slab Has No Weight

Thornthwaite Moisture Index (TMI)

(Thornthwaite, 1948)

100 60S DTMITE−

=

Where,

S = Sum of monthly water surplus during year,

D = Sum of water deficiency during year,

TE = Total Evapotranspiration for the year

0

0.5

1

1.5

2

2.5

-40 -30 -20 -10 0 10 20 30 40

Thoronthwaite Moisture Index, TMI

Edge

Moi

stur

e Va

riatio

n D

ista

nce,

Em

(m)

0

0.5

1

1.5

2

2.5

-40 -30 -20 -10 0 10 20 30 40

Thoronthwaite Moisture Index, TMI

Edge

Moi

stur

e Va

riatio

n D

ista

nce,

Em

(m)

Edge Lift

Edge Drop

Edge Left

Edge drop

Edge lift

-- PTI (1980, 1996, PTI (1980, 1996, 20042004))The PTI (2004) design method is significantly different from theThe PTI (2004) design method is significantly different from the PTI (1996) PTI (1996) method with regard to the determination of method with regard to the determination of emem & & ymym . The 2004 procedure . The 2004 procedure is as follows:is as follows:

11-- Calculate the Plasticity Index (PI) = LL Calculate the Plasticity Index (PI) = LL –– PLPL

22-- Calculate % fine clay (%Calculate % fine clay (%fcfc) = (%) = (%--22µµ / % / % --#200)*100; where (%#200)*100; where (%--22µµ) is ) is the weight of soil passing No. 200 sieve expressed as a percentathe weight of soil passing No. 200 sieve expressed as a percentage of the ge of the total soil sample & (%total soil sample & (%--#200) is the weight of soil finer than 2 microns #200) is the weight of soil finer than 2 microns expressed as a percentage of the total soil sample.expressed as a percentage of the total soil sample.

33-- Determine the soil Zone based on LL and PI using the PTI (2004)Determine the soil Zone based on LL and PI using the PTI (2004) Mineral Mineral Classification Chart.Classification Chart.

44-- Calculate the Activity Ratio (PI / %Calculate the Activity Ratio (PI / %fcfc))

55-- Calculate LL / % Calculate LL / % fcfc

66-- Determine Determine γγ0 using the corresponding Zone Chart based on (LL / % 0 using the corresponding Zone Chart based on (LL / % fcfc) & ) & (PI / %(PI / %fcfc))

Zone I

Zone II

Zone IVZone III

Zone V Zone VI

77-- Calculate Suction Compression Index (Calculate Suction Compression Index (γγh); where h); where γγh swell = h swell = γγ0 e0 eγγ0 (% 0 (% fcfc/ / 100) and 100) and γγh shrink h shrink = = γγ0 e0 e--γγ0 (% 0 (% fcfc/ 100)./ 100). PTI 2004 also suggests three PTI 2004 also suggests three alternative ways to determine (alternative ways to determine (γγh swell) using the expansion index (ASTM D h swell) using the expansion index (ASTM D 4829) procedure, using the consolidation4829) procedure, using the consolidation--swell pressure test (ASTM d 4546 swell pressure test (ASTM d 4546 Method C) procedure, and using the overburden pressure swell tesMethod C) procedure, and using the overburden pressure swell test t procedure. PTI 2004 gives empirical equations correlating the procedure. PTI 2004 gives empirical equations correlating the γγh swell with h swell with indices resulting from these tests. In addition, PTI 2004 presenindices resulting from these tests. In addition, PTI 2004 presents empirical ts empirical correction equations to correct correction equations to correct γγh for soils containing coarse grains.h for soils containing coarse grains.

88-- Calculate Unsaturated Diffusion Coefficient (Calculate Unsaturated Diffusion Coefficient (αα):):αα= 0.0029 = 0.0029 -- 0.000162 (S)0.000162 (S)--0.0122 (0.0122 (γγh);h);

Where Where S = S = --20.29 + 0.1555 (LL) 20.29 + 0.1555 (LL) --0.117 (PI) + 0.0684 (% 0.117 (PI) + 0.0684 (% --#200),#200), S is the S is the slope of suctionslope of suction--gravimetric water content curve.gravimetric water content curve.

99-- Calculate the Modified Unsaturated Diffusion Coefficient (Calculate the Modified Unsaturated Diffusion Coefficient (αα’’): ): αα’’= = αα Ff ; Ff ; where Ff is the soil fabric factor that depends on soil profile where Ff is the soil fabric factor that depends on soil profile content of roots, content of roots, layers, fractures or joints: Ff = 1.0 for (no more than 1 per velayers, fractures or joints: Ff = 1.0 for (no more than 1 per vertical foot), Ff = rtical foot), Ff = 1.3 ( 2 to 4 per vertical foot), and Ff = 1.4 ( 5 or more per ve1.3 ( 2 to 4 per vertical foot), and Ff = 1.4 ( 5 or more per vertical foot).rtical foot).

1010-- Determine the Determine the ThornthwaiteThornthwaite Moisture index, Moisture index, ImIm, from the provided US , from the provided US map (same as PTI 1996).map (same as PTI 1996).

1111-- Determine Determine eemm based on based on ImIm for center and edge lift using PTI (2004) for center and edge lift using PTI (2004) eemm--IImm relationship chart.relationship chart.

1212-- Calculate the weighted (Calculate the weighted (αα’’): ): αα’’weighted = (weighted = (ΣΣ FiFi x x DiDi x x αα’’i ) / (i ) / (ΣΣFiFi x x DiDi ); ); where D is the layer thickness, and F is the layer weight factorwhere D is the layer thickness, and F is the layer weight factor (for example, (for example, F=3 for the top layer in a threeF=3 for the top layer in a three--layer active zone).layer active zone).

1313-- Determine Determine emem based on weighted (based on weighted (αα’’) for center and edge lift using PTI ) for center and edge lift using PTI (2004) (2004) emem--αα’’ relationship chart and use maximum values of relationship chart and use maximum values of emem obtained obtained from this step and step 11.from this step and step 11.

1414-- Determine the Equilibrium Suction based on Determine the Equilibrium Suction based on ImIm using PTI (2004) using PTI (2004) equilibrium suction chart.equilibrium suction chart.

1515-- Determine the wet and dry suction profiles at the surface with Determine the wet and dry suction profiles at the surface with the the guidance of the PTI recommended values (2.5 guidance of the PTI recommended values (2.5 pFpF for the wettest condition for the wettest condition as in the case of heavy rain and no drainage, 4.5 as in the case of heavy rain and no drainage, 4.5 pFpF for the driest condition for the driest condition if the surface suction is controlled by vegetation, or 6.0 if the surface suction is controlled by vegetation, or 6.0 pFpF for the driest for the driest condition if the surface suction is controlled by evaporation frcondition if the surface suction is controlled by evaporation from bare soil)om bare soil)

1616-- Determine the Stress Change Factors (SCF) for center and edge lDetermine the Stress Change Factors (SCF) for center and edge lift ift from PTI (2004) SCF tables.from PTI (2004) SCF tables.

1717-- Determine weighted Suction Compression Index (Determine weighted Suction Compression Index (γγh mod) with the h mod) with the same weighting technique as mentioned in step 12.same weighting technique as mentioned in step 12.

1818-- Calculate Calculate ymym for center and edge lift as follows;for center and edge lift as follows;yymm edgeedge = (= (SCFSCFedgeedge) () (γγh swell modh swell mod))

yymm centercenter = (= (SCFSCFcentercenter) () (γγh shrink modh shrink mod))

7- Divide the slab into overlapping rectangles.8- Assume beams width and spacing.9- Use PTI (1996) p.21 equations to estimate a trial beam depth.10-Determine the trial section properties including the moment of inertia, section modulus, and cross sectional area of the slab and beams.11-Calculate the maximum moments, maximum shears, and maximum differential deflections in both directions using em & ym in the design equations provided in PTI (1996) pp 22-24.12- If the applied stresses and differential deflections are larger than the permissible values, increase the beam section and redo steps 8 through 11 until the allowable stresses and differential deflections are within the tolerable limits