bearing capacity based on settlement

8/12/2019 Bearing Capacity Based on Settlement

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CHAPTER 3S LLOWFOUNDATION I ISAFEBEARINGPRESSUREANDSETTLEMENT CALCULATION

1 3 1 INTRODUCTION llowableand Safe Bearing PressuresThe methods of calculating the ultimate bearing capacity of soil have been discussed at length inChapter 12. The theories used in that chapter are based on shear failure criteria. They do notindicate the settlemen t that a footin g may unde rgo under the ultimate loading conditions. From theknown ultimate bearing capacity obtained from any one of the theories the allow able bearingpressure can be obtained by applying a suitable factor of safety to the ultimate value.

Whenw edesignafoundation w emusts ee thatth e structureis safeon twocounts. They are1. The supporting soil shouldbe safe from shear failuredue to the loads imposedon it by thesuperstructure2. The settlement of the foun dation should be within permissible limits.

Hence we have to deal w ith two types of bearing pressures. They are1. A pressure thati s safe from shear failure criteria2. A pressure that is safefrom settlement criteria.

For the sake of convenience let us call thefirst th eallowable b earing pressureand the secondth e safe bearingpressureIn all our design we use only the net bearing pressure and as such we call qna th e ne tallowable bearing pressure an d q sthe net safe bearing pressure. In designing a foundation we use


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546 Chap te r 3the least of the two bearing pressu res. In Chapter 12 we learnt thatqna is obtained by applying asuitablefactorofsafety norm ally3) to the netultim ate bearing capacity of soil.Inthis chapter wewilllearn how to obtainqs.Even w ithou t know ing the values ofqnaa ndqs it is possible to say fromexperience which of the two values should e used in design based upon the composition anddensityo fsoiland thesizeof the footing.Th e compositionan ddensi tyof thesoiland thesizeof thefootingdecide the relative values ofqna andqs.

Theul t imate bearing capaci tyoffootingsonsand increases w ithanincreasein thewidth,an din th e same way theset t lementof thefooting increases w ith increases in the width.In other wordsfo r a given settlement pthe corresponding uni t soil pressure decreases w i than increase in thewidth of thefooting.It istherefore, essential toconsider that settlement w illbe thecriterion for thedesign of footings in sand beyond a particular size. Experimental evidence indicates that fo rfootings smaller than about1.20m ,the allowable bearing pressureq is the criterio n for the designof footings, whereas settlement is the criterion fo r footings greater than 1.2 mwidth.

The bearing capacity of footings on clay is indepe ndent of the size of the footings and as suchth e unit bearing pressure remains theoretically constant in aparticular environment. However, th esettlement of the footing increases with an increase in the size. It is essential to take intoconsideration both the shear failure and the settlement criteria together to decide the safe bearingpressure.

However, fo otings onstiff clay, hard clay, and other firm soils generally require no settleme ntanalysisif thedesign provides amin imu m factoro fsafetyof 3 on the netultimate bearing capacityof the soil. Soft clay, compressible silt, and other weak soils will settle even under moderatepressure and there fore settlement an alysis is necessary.Effec t of Sett lement on the StructureIf the structure as a wh ole settlesuni formly into the ground there w ill not be any detrimental effecton the structure as such. The only effect it can have is on the service lines, such as water andsanitary pipe connections, telephone and electric cables etc. which can break if the settlement isconsiderable. Such un iform settlement is possible onlyif the subsoil is homogeneous and the loaddistribution is uniform. Bu ildings in Mexico City have undergone settlements as large as 2 m.However, th e differential set t lement if it exceeds th e permissible limits will have a devastatingeffect on thes tructure.

According to experience the differential settlement between parts of a structure may notexceed 75 percent of the normal absolute settlement. The various ways by which differentialsettlements may occur in a structure ar e shown in Fig. 13.1. Table 13.1 gives th e absolute an dpermissible differe ntial settlemen tsf orvariou s types of structures.

Foundation settlements must be estimated with great care for buildings, bridges, towers,power plants an d similar high cost structures. The settlements fo r structures such as fills,earthdams, levees, etc. can be estimated w ith agreaterm argin of error. pproaches for Determining the Net Sa fe Bearing PressureThree approaches may be considered for determining the net safe bearing pressure of soil. Theyare, 1. Field plate load tests,

2. Charts,3 . Empirical equations.


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Shallow Foundation II: Safe Bearing PressureandSettlement Calculation 547

Original positionof column base

Differential settlement a)

T

c)

t Relative rotation,/?

-Wall or panel Tension cracks

Tension cracks Relative deflection, A ^ , ,. ,Relative sa g Deflection ratio=A/L Relative ho g b)

Relative rotation,

Figure13 1 Def ini t ions of di fferent ial set t lemen t for f ram ed and load-bea ring wa l lstructures after Burland andWroth 1974)

Table 13 1a Maximum sett lements and dif ferent ial set t lem ents of bui ldings in cm.A f te r McDonald and Skempton, 1 9 55 )SI. no. C rite rion Isolated foundations Ra f t1. Ang ular distortion 1/3002. Greatest differential sett lements

Clays 4- 5Sands 3-253 . Max imum Set t lementsClays 7.5Sands 5.0

1/300

4.5

3.2510.06.25


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548 Ch a p te r 13Table 13 1b Permiss ib le se t t leme nts 19 55 , U.S.S.R. Building C o d e )

Sl.no. Typeo f building Average se t t lement cm)1 . Bui ld ing w i t h p l a in b r i c k w a l l son

con t inuous and sepa ra te founda t ions wi thw a l l l ength L to wa l l h e i g h tH

2.3

L JH >2 5LIH 5 0 0005L 0.0007L

3. Water tow ers si los etc. 0 004L 0.004L4. Slope of crane way as w ell as track

fo r b r idge crane t rack 0.003L 0 003Lwh ere L = d is tance be tween two co lum ns o r pa r t s o f s truc ture tha t se t t ledi f ferent a mo u n t s H = Height o fw a l l .

3 2 F IELD PLATE LOAD TESTSThe plate load test is a semi-direct method to estimate th e al lowable bearing pressure o f soil toinduce a given amo unt of se t t lement . Plates round or square varying in s ize from 30 to 60 cm andthickness o fa b o u t 2.5 cm are employed for the test .

The load on the plate is app l ied by making use of a hy draul ic jack. The reaction of thej ackload is taken by a cross beam o r a steel truss anchored suitably a tboth th eends . The settlemento fthe plate is mea sured by a set of three dial gaug es of sensitivity 0.02 mm p laced 120 apart . The dialgauges a re f ixed to indepen dent suppo rts which remain u ndis turbed during the tes t.

Figure 13.2a s ho w st hea r rangementfor a plate load test . T heme thod o fperforming th etesti sessent ial ly as fol low s:

1. Excav ate a pit of size not less than 4 to 5 times the size of the plate. The bottom of the pitshould coincide wi th t h e levelof thefounda t ion .2. If the water table is above th e level of the f o u n d a t i o n p u m p out the water careful ly andkeep i t a t the level of the found at ion.3. A suitable size o f plate is selected for thetest Normally a plate o fsize30 cm is used insandy soils and a larger size in clay soils. The ground should be levelled and the plate

should be seated over th eground .


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Shallow Foundation I I Safe BearingPressure an dSettlement Calculat ion 549

rod-

|kk^

Channel ILSteel girders

5IC ^V X /\

Anchors ^1

r _Extension^pipe ^~^^rt

13

L_

uc =

3-1

^ _Hydraulic> jackpDialgau h4

;ea

i55^ ^ - ^ S ; ItaJ ]

^ 7 N / \S;

Testplate/ | _ p__ | > Testpite tion

^na

U1Ci

ii

2Girders

i i /

p

i . t i i i i

)Test plate

i

Support

n1

4

Top planigur 13 2a Plate loadtest arrangement

A seating load ofabout70gm/cm2 is first applied an dreleased after some time.Ahigherload is next placed on the plate and settlements are recorded by means of the dial gauges.Observations on every load incre ment shall be taken un til the rate of settlement is less than0.25 mm per hour. Load increments shall be approximately one-fifth of the estimated safebearing cap acity of the soil. The average of the settlementsrecordedby 2 or 3 dial gaugesshall be taken as the settlement of the plate for each of the load increments.5. The test should continu euntila total settlement of 2.5 cm o r the settlement at w hich the soil

fails, whichever is earlier, is obtained.After the load isreleased,theelastic rebound of thesoil should be recorded.From the test results, a load-settlement curve should be plotted as shown in Fig. 13.2b.T heallowable pressure on aprototype foundation for an assumed settlement may be found bymak inguse of the following equations suggested by Terzaghi an d Peck 1948) fo r square footings ingranularsoils.


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55 Chapter 13Plate bearing pressure inkg/cm 2o rT /m 2

\ qa=Neta l lowable pressure

igur 13 2b Load sett lement curve of a plate load test

BS f =S x -where 5 = permissible sett lemento f foundat ionin mm,

S set t lementofplatein mm

I S . l b )

B = size of foundation in meters,b = size of plate in m eters.

For a plate 1 ft square, Eq. 13 . l a ) may be expressed as

f p 13.2)in whichS and5 ar e expressed in inches andB in feet.

The permiss ib le set t lement 5, for a prototype foundat ion should be known. Normal ly asett lement of 2.5 cm is recommended. In Eqs 13 . l a ) or 13.2) th e valuesof 5, andb ar eknown .The unknowns are5 andB.The value of S for any assumed sizeBmay be found from theequation. Using the plate load sett lement curve Fig. 13.3 the value of the bearing pressurecorresponding to the com puted value of 5 is found . This bearing pressure is the safe bearingpressure for a given permissible sett lement 5~ The principal shortcoming of this approach is theunreliabil ity of the extrapolation of Eqs 13. la) or 13.2) .

Since aload test is of short duration, consolidation sett lements cannot be predicted.T he testgives the value of immediate sett lement only. If the underlying soil is sandy in nature immediatesett leme nt may be taken as the total sett lement. If the soil is a clayey type, the imm ediate sett lem entis only a fraction of the total sett lement. Load tests, therefore, do not have m uch sign ificance inclayey soils to determine allowable pressure on the basis of a sett lement criterion.


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Shallow Foundation II : Safe Bear ing Pressurea nd ettlement Calculation 551P i s t p i n a T Founda t ion o fFla te load Load qnp eru n i t areates t c bu i ld ingl LLy ^ ^ ^ ^

S t i f f c lay

S o f t c layPre s sure b u l b s

Figure 13.2c Plate loadtest on non homogeneous soi lP l a t e l o a d t e s t s s h o u l d b e u s e d w i t h c a u t i o n a n d t h e p r e s e n t p r a c t i c e i s n o t t o r e l y t o o m u c h o n

t h i s t e s t . I f t h e s o i l i s n o t h o mo g e n e o u s t o a g re a t d e p t h , p l a t e l o a d t e s t s g i v e v e ry mi s l e a d i n gr e s u l t s .

A s s u m e , a s s h o w n i n F i g . 13.2c, t w o l a y e r s o f s o i l . T h e t o p l a y e r i s s t i f f c l a y w h e re a s t h eb o t t o m l a y e r i s sof t c l a y . T h e lo a d t e s t c o n d u c t e d n e a r t h e s u r f a c e o f t h e g ro u n d me a s u re s t h ec h a ra c t e r i s t i c s of the s t i f f c l a yb u t d o e s n o t i n d i c a t e the n a t u r eof the sof t c l a y s o i l w h i c hi sb e lo w .T h e a c t u a l f o u n d a t i o n o f a b u i l d i n g h o w e ve r h a s a b u l b o f p r e s s u r e w h i c h e x t e n d s t o a g r e a t d e p t hi n t o t he p o o r s o i l w h i c h i s h i g h ly c o mpre s s i b l e . H e re the so i l t e s ted b y t h e p la t e l o a d t e s t g i v e sr e s u l t s w h i c h a re h i g h ly o n t h eu n s a f e s i d e .

A p la t e l o a d t e s t i s n o t r e c o m m e n d e d in s o i l s w h i c h a re n o th o m o g e n e o u s a t lea s t to ad e p t he q u a l to \l/2 to 2t i m e s thew i d t hof the p r o t o ty p e f o u n d a t i o n .P l a t e l o a d t e s t s s h o u l d n o t b e r e l ie d o n t o d e t e r m i n e t h e u l t i m a t e b e a r i n g c a p a c i t y o f s a n d y

s o i l s a s t h e s c a l e effec t g i v e s v e ry mi s l e a d i n g r e s u l t s . H o w e ve r , w h e n t h e t e s t s a re c a r r i e d o n c l a ys o i l s , t h e u l t i m a t e b e a r i n g c a p a c i t y a s d e t e r m i n e d b y t h e t e s t m a y b e t a k e n a s e q u a l t o t h a t o f t h ef o u n d a t i o n s i n c e t h e b e a r i n g c a p a c i t y o f c l a y i s e s s e n t i a ll y i n d e p e n d e n t o f t he f o o t i n g s i z e .Housel s (1929) Method of Determining Safe earing Pressu re fromSettlement ConsiderationT h e m e t h o d s u g g e s t e d b y H o u s e l f o r d e t e r m i n i n g t h e s a f e b e a r i n g p r e s s u r e o n s e t t l e m e n tc o n s i d e r a t i o n i s b a s e d o n t h e f o l l o w i n g f o r m u l a

O = A m P n C13 3)p p \ ~ > . ~ > jw h e r e Q=l o a d a p p l i e d o n a g i v e n p l a t e ,A =c o n t a c t a re a o f p l a t e , P =pe r i me t e r o f p l a t e , m =ac o n s t a n t c o r r e s p o n d i n g to th b e a r i n g p r e s s u r e , n a n o t h e r c o n s t a n t c o r r e s p o n d i n g to p e r i m e te rs h e a r .Object ive

To d e t e rm i n e t h e lo a d X a n d t h e s i z e o f a f o u n d a t i o n f o r a pe rmi s s i b l e s e t t l e me n t 5-..H o u s e l s u g g e s t s t w o p l a t e l o a d t e s t s w i t h p l a t e s o f d i f f e r e n t s izes , say Bl x B a n dB 2 x B2 fo r t h i s p u r p o s e .


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552 Chap te r 3rocedure

1. Twoplate load tests are to be conducted at thefoundation levelof the prototype as per theprocedure explained earlier.2. Draw th e load-set t lement curvesfor eachof the plate load tests.3 . Select th e permissible settlement S .for thefoundat ion.4. Determ ine the loads Q { an d Q 2from each of the curves for the given permissible settlement

Now we may wri teth e fol lowing equat ionsQ\mAP\npP\ 13.4a)

fo r plate load test 1.Q=mAp nPp 13.4b)

for plate load test 2 .The unknown valuesofm a nd n can befoundb y solving th eaboveEqs. 13.4a)and 13. 5b).The equat ionfor aprototype foundat ionmay bewrittena sQf=mAfnP f 13.5)

where A = areaof the foundat ion,/ > , =perimeter of the foundation.Whe nA ,andP,areknow n, the size of the founda tion can be determined.

xample 13 1A plate load test using a plate of size 30 x 30 cm was carried out at the level of a prototypefoundation. The soil at the site was cohesionless with the water table at great depth. The platesettled by 10 mm at a load intensity of 160kN / m2 . Determine the settlement of a square footing ofsize 2 x 2 m under the same load intensity.SolutionThe set t lement of the foundat ion5,may be determined from Eq. 13.la).

= a 4 m m

xample 13 2For Ex. 13.1estimate the load intensity if the perm issible settlement of the p rototype found ation isl imitedto 40 mm.SolutionInEx. 13 .1,aload intensityof 160kN /m2 inducesasettlemento f30.24mm. If we assume thattheload-sett lement islinearwithin asmall range,we maywrite


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Shallow Foundation II: Safe earing PressureandSettlement Calculation 55where ,q { =160 kN/m2,S ^ = 30.24 mm, S^ = 40 mm. Substituting the known values

40q2 =160x= 211.64k N/ m2

xample13 3Tw oplate load tests w ere conduc ted at the level of a prototype fo und ation in cohesionless soil closeto each other. The following data are given:

Size of plate0.3 x 0.3 m0.6 x 0.6 m

Load applied30 kN90 kN

Settlement recorded25 mm25 mm

Ifa footing is to carry a load of1000kN, de termine the required size of the footin g for thesame settlement of 25 mm.olutionUse Eq. 13.3). For the two plate load tests we may write:

PLTl: Apl =0.3 x 0.3 =0.09m2; Ppl =0.3 x 4 = 1.2m; Q l =30 kNPLT2: Ap2 =0.6x0.6=0.36m2; Pp2 =0.6 x 4 =2.4m; Q 2= 90 kN

Now we have30 = 0.09m +1.2n90 =0 36m+2.4nOnsolving the equations we havem =166.67,andn =12.5For prototype foundation, we may w riteQ f =1 66.67Af 12.5 Pf

Assumethe size of the footing asB x B we haveAf =B2, Pf =4B an d Q f =1000kNSubstitutingwehave1000 =166.67fl2 505or B2 0.35-6= 0The solution givesB =2.3 m.The size of the footing = 2.3 x 2.3 m.


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Chap te r 13 3 3 EFFECT O F S IZE O F F O O T IN G S O N S E T T L E ME N TFigure 13.3a g ives typica l load-set t lement rela t ionships for footings of d i f fe ren t widths on thesurface of a homogeneous sand deposit. It can be seen that the ultimate bearing capacities of thefoot ings perun i tarea increase w ith the increase in the wid ths of the footing s. However, for a givensett lement 5,suchas 25 mm, the soil pressure is greaterfor afootingo f in termedia te widthB bthanfo r alargef oo t ing wi th BC .The pressures corresponding to the three widths in termed ia te, la rge andnarrow, are indicated by points b c a nd a respectively .

Thesame datai susedt oplot Fig. 13.3bw h ich showsth epressure per un it a rea correspondingto a g iven set t lem ent5 j , as afunc t ion of thewid th of the footing. The soil pressure for settlementl increases for increasing width of the footing, if the footings are relatively small, reaches amaxim um a t an in termedia tewid th ,an dthendecreases gradually with increasing wid th .

Altho ugh the rela t ion show n in Fig. 13.3b is generally valid for the behavior of footings onsand, it is influen ced by sev eral factors in clu din g the relative density of sand, the depth at wh ich thefoundation is established, and the position of the water table. Furthermore, the shape of the curvesuggests tha t fo r narrow footings small var ia t ions in the actual pressure, Fig. 13.3a, m ay lead tolarge variation in settlement and in someins tances to set tlements solargetha t the movem ent wouldbeconsidered abear ing capacity failure. On theo ther hand, a small change in pressure on aw idefoot ing has l i t t le inf lue nce on set t lements as small asS { an d besides,the value ofql correspondingto S j is far below that which produces a bearing capacity failure of the wide footing.

For all practical purposes, th e actual curve given in Fig. 13.3b can be replaced by anequivalent curve om n where om is the incl ined par t an d mn th e horizontal part. The hor izonta lportion of the curve indicates thatth e soil pressure corresponding to aset t lement S { is independen tof the s ize of the footing . The inclined por t ion om indicates the pressure increasing with width forth esameg iven set tlemen tS { up to the poin tm on the cu rve which is the l im it for a bear ing capacity

Soil p ressure ,q

Given se t t lement , S \

Narrow foot ing

a)

b)

Width of foot ing, B

Figure 13 3 Load-se t t lemen t curves fo r f oo t ings o f d i f f e ren t s izesPeck e t a l . , 1974)


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Shallow oundation II : Safe Bearing Pressurea ndSettlement Calculationfa i lure . This means that the footings up to size Bl inFig. 13. 3b shou ld be checked for bearingcapacity failure also while selecting a safe bearing pressure by settlement consideration.

The position of the broken lineso mn differs fo r different sand densities or in other words fordif ferent SP T N values. The soi l pressure that produces a given set t lement Sl on loose sand isobviously smaller thanthe soil pressure that produces th esame set t lement on a dense sand. SinceN-valueincreases with densi tyo fsand,qs therefore increases witha nincrease in thev a l u eofN .

13 4 DESIGN CHARTS FROM SPT VALUES FOR FOOTINGS ON SANDThe methodssuggestedbyTerzaghie tal., 1996)forestimating settlements andbearingpressuresof footings founde d on sand from SPT value s are based on the f indings of Burland and Burbidge 1985).The SPTvalues useda recorrected to astandard energy ratio.T heusua l symbolN cor isusedin all thecases as the corrected value.Formulas for Settlement CalculationsThe fol low ing formu las were developed for computing set t lements for square footings.

Fo r normally consolidated soils andgravels

corFo r preconsolidated sand and gravels

13.6)

fo r qs>pc Sc=B."-(qs-0.67pc) 13.7a)co r

I3 .7b)NIAco rIfthe footing is established at a depth below the groun d surface, the removal of the soil above

th e base level makes th e sand below th e base preconsolidated by excavation. Recompression isassumed for bearing pressures u p to preconstruction effective vertical stressq oat the base of thefoundat ion . Thus, for sands normally consolidated with respect to the original ground surface andfo r valuesofqsgreater tha nq o,w ehave,

fo r qs>q 0 S c = B075-(qs-Q.61q 0) 13 8a) or

fo r qs


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556 Chapter 13

0.1 1 10Bre a d th ,B m) log scale

igur 13 4 Th ickness of granular soi l beneath foundat ion contributing tosettlement in terpreted from settlement prof i les after Burland and Burbidge 1 9 8 5 )

q - e ffect ive ver t ical pressureatbase levelN = average corrected N va l ue w i t h i n th e depth of i n f l uenc eZ; below th e base the offoot ingThe depth of i n f l uenc eZ;i sobtained f romZ^B0-15 13.9)Figure 13.4 gives th e variat ion of the depth of influence with depth based on Eq. 13.9)

after B u r l a n da nd Burbidge, 1985).T he set t lementof a r ec t ang ul ar f o o ti ngo f sizeB x L may be obtained f rom2

13.10)L 1.25 1/8)S L/B>l) = S = 1 - B LI5 +0.25w h e n t h e rat ioL IB isv er y h ig h for as t r ip foot ing ,w e m a y wri te

Sc strip)S r square) = 1.56 13.11)

It ma y be noted here that the ground water table at the s i te may l ie above or wi th in the depthof i n f l uenc e Zr Bu rland and Burbidge 1985) recommend no correction for the set tlementcalculat ion ev enif thewater table lies withinth edepth ofi n f l uenc eZ;.On theother hand,if for anyreason, the water table were to rise into or above the zone of influence Z7 after the penetrat ion testswere conducted, the actual set t lement could be as much as twice the v alue predicted wi thou t takingth ew ater table into acco unt .


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Shallow Foundation II : Safe Bear ing Pressurea ndSettlement Ca lcu la t ion 557Chart for Estimating AllowableSoil PressureFig.13 5 gives a chart for estimating allowable bearing pressureqs on settlement consideration)corresponding to asettlement of 16 mm for different valueso f V corrected). From Eq. 13 . 6 ) ,anexpression forq may be written as for normally consolidated sand)

N yyl .41.7fl-75

where Q 1.75 0.75

13.12a)

13,12b)For sand havingapreconsolidationpressurepc,E q. 13.7)may bew rittenas

for q s>pc qs=16Q+Q.61pc 13.13a)for q sq o, qs = 1 6 Q + Q . 6 1 q ofor qs


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558 Chap te r 3The chart m Fig. 13.5 gives the relationships between B an d Q. The value of qs may beobtained from Qfor anygiven widthB. The Q to beused mu st conformto Eqs 13.12) , 13.13)and 13.14).The chart isconstructedfo rsquare footingso fwid thB.F orrectangular footings,thevalueof

qs should be reduced in accordance wi th Eq. 13.10). The bearing pressures determined by thisprocedure correspond to am ax im um set tl emen tof 25 mm at the end ofconstruct ion.Itmay be noted here that the design chart Fig. 13.5b) has been developed by taking the SPT

values corrected for 60 percentofstand ard energy ratio.Example 13 4A square footing of size 4 x 4 m is founded at a depth of 2 m below the gro und surface in loose tome dium dense sand. The corrected stand ard penetration test valueNcor =11. Compute the safebearing pressure qs by using the chart in Fig. 13.5. The water table is at the base level of thefoundat ion.SolutionFrom Fig. 13.5 Q = 5 fo r B =4 m andNcor = 11 .

From Eq. 13.12a)q =160=16x5= 80kN/m 2

Example 13 5Refer toExample 13.4. If the soilat the sitei s dense sand withNcor =30 , estimateqsf or B =4 m .SolutionFrom Fig. 13.5 Q =24 fo r B=4m andN =30. ~ - cor

FromEq. 13.12a) s =16Q = 16 x 24 = 384 kN/m2

13 5 EM PIRICAL EQU TIONS BASED ON SPT V A L U E SFORFOOTINGS ON COHESIONLESS SOILSFootings on granular soils are sometimes proportioned using empirical relationships. Teng 1969)proposed an equation for a settlement of 25 mmbased on the curves developed by Terzaghi andPeck 1948).The modified form of the equation is

13.15a)where q - netallowable bearin g pressurefor asettlementof 25 mm inkN/m 2 ,

Ncor = corrected standard penetration valu eR =water table correction factor Refe r Section 12.7)WZF d =depth factor = +D f IB


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Shallow oundation II :Safe Bear ing Pressure andSettlement Calculation 55 9Meyerhof (1956) proposed the fo l lowing equations which are sl ightly different from that ofTengqs=\2NcorRw2Fd for 5L2m (13.15c)where F d = l+ 0.33 D f/B ) < 1.33.

Experimental results indicate that the equations presented by Teng and Meyerhof are tooconservative. Bowles ( 1996) proposes an app roxim ate increase of 50 percent over that of Meyerhofwhich ca n also be applied to Teng s eq uations. Modified equations of Teng and M eyerhof are,

Teng s equat ion (m odif ied) ,^=53(Af c o r-3) - Rw2F d (13.16a)

Meyerhof s equation (m odified)qs=20NcorRw2FdforBl2m 13.16c)If the tolerable settlement is greater than 25 mm , the safe bearing pressure computed by theabove equation s can be increased l in early as,

where q s = ne t safe bearing pressure for a settlement S mm,qs= net safe bearing pressure for ase t tlement of 25 mm .13 6 SAFE BE RING PRES SURE FROM EMPIRICAL EQUATIONSB SED ON CPT V L U E S FOR FOOTINGS ON COHES IONLESS SOILThe static conepenetration test in which a standard cone of 10 cm 2 sectional area is pushed in to thesoil withou t the necessity of boring provides a m uch m ore accurate and detailed variation in the soilas discussed in Chapter 9. Meyerhof (1956) suggested a set of empirical equations based on theTerzaghi and Peck curves (1948). As these equation s were also found to be conservative, modifiedforms wi th an increase of 50 percent over the original values are given below.

qs =3.6qcRw2 kPa for B < 1 .2 m (13.17a)

nqs=2.lqc 1+Rw2kPa for 5>1.2m (13.17b)V JA n approximate formula for all widthsqs=2.7qcRw2kPa (13.17c)

whereqcis the cone p oint resistance in kg/cm 2 an d qsi n kPa.The above equations have been developed for a settlement of 25 mm.


16/40

56 Chap te r 13Meyerhof (1956) developed his equat ions based on the re la t ionship qc =4 Nco r kg/cm2 fo rpenetra t ion res is tance in sand whereNco r is the corrected SPT value.

x mple 13 6Ref er to Exa m ple 13.4a n d c o m p u t eqsby mo dif ied (a ) Teng 's m ethod, and (b) Meyerhof'sme thod .Solution(a ) Teng 's equa t ion (modif ied)E q . (13 .16a )

i f D where Rw 2=1 - j = 0.5sinceDw2=0F,= \ - = 1 + - = 1 . 5 < 2d B 4

B ysubs t i t u t ing

qs -53(11-3)11 x 0.5 x 1.592k N / m2(b )M eyerhofs equat ion (modif ied)E q . (13.16c)

where R =0.5 F, = l +0 . 3 3 x = l +0.33x- =1.165


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Sha l low Foundat ion II : Safe Bear ing Pressure and Set t lemen t Calcu la t ion 56

Bwhereqc=20kg/cm2,B =3m,Rw2=0.5.

This equation is for 25 mmsettlement.By substituting wehave

qs =2.1x20 11 I x 0.5 =37.3kN/m2For 40 mmsettlement,the valueofq is

40q =37.3 =60 kN/m 2s 25

13 7 FOUNDATION SETTLEMENT omponen ts of Total Sett lementThetotal settlementof afoundation comprises three partsasfollows

S=Se+Sc+Ss 13.18)where S = total settlement

S elastic or immediate settlementSc = consolidation settlementS s = secondary settlement

Immediate settlement,Se, is thatpart of the total settlement, 51 which is supposed to takeplace duringtheapplicationofloading.Theconsolidation settlementisthat part whichis due to theexpulsionofpore water from the voids and is time-dependent settlement. Secondary settlementnormal ly starts with th e completion of the consolidation. It means, during th e stage of thissettlement theporewater pressureiszeroand thesettlementisonlydue to thedistortionof thesoilskeleton.

Footings founded in cohesionless soils reach almost the final settlement, 5, during theconstruction stage itself due to thehigh permeability of soil. The water in the voids is expelledsimul taneously with th e application of load and as such th e immediate an d consolidationsettlementsinsuch soilsarerolled into one.

Incohesivesoils under saturated conditions, thereis nochangein thewater content duringth estage of immediate settlement.Thesoil mass is deformed without an ychange in volume soonafter th e application of the load. This is due to the low permeability of the soil. With th eadvancementoftime there willbegradual expulsionofwater undertheimposedexcessload.Thetime required for thecomplete expulsiono fwaterand toreach zero water pressuremay beseveralyears depending upon th epermeabilityof the soil. Consolidation settlement m aytake many yearstoreach it sf inalstage. Secondary settlementissupposed to takeplace after th ecompletion of theconsolidation settlement, thoughinsome of theorganic soils therewi l lbeoverlapping of the twosettlementsto acertain extent.

Immediate settlementsofcohesive soilsand thetotal settlementofcohesionless soilsmay beestimated from elastic theory. The stresses and displacements depend on the stress-straincharacteristics of theunderlying soil.A realistic analysis is difficult because these characteristicsarenonlinear. Results from th e theoryof elasticityare generally used in practice, it being assumedthat th e soil is homogeneous an d isotropic and there is a linear relationship between stress an d


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19/40

Shallow Foundation II : Safe Bear ing Pressurea nd ettlement Calculation 561. Laboratory method ,2. Field me thod.

LaboratoryMethodFor set t lement analys is , the valuesofE s atdifferent depths below the found at ionbaseare required.One way of determining E s is to conduct triaxial tests on representative undisturbed samplesextracted from th edepths required.Forcohesive soils, und raine d triaxial testsand for cohesionlesssoils drained triax ial tests are required. Since it is prac tically impossible to ob tain un distu rbe dsample of cohesionless soils, the laboratory method of obtaining E s can be ruled out . Even withregards to cohesive soils, there willb edis turbanceto thesample at different stages of handl ingit,an d as such the values of E S obtained from u ndr aine d triaxial tests do not represent the actualcondi t ions and norm ally give very low v alues . A sug gest ion is to determine E s over the range ofstress relevant to the particular problem. Poulos et al . , 1980)suggest that the un dis turbed t r iaxialspecimen be given a prel iminary preconsol idat ion und er Q conditions with an axial stress equal toth e effective overburden pressure at the sampling depth. This procedure at tempts to return th especimen to itsorigin al stateo feffective stressin theground, as suming thatthehorizontaleffectivestressin thegroundwas thesameasthat producedby the laboratoryK Q condi t ion. Simonsand Som1970)have sho wn that t r iaxial tes ts on London clay in which specimens were brou ght back to theiroriginal in situ s t resses gave elas t ic moduli which were much higher than those obtained fromconvent ionalun drained t r iaxial tes ts. This has been conf irmed by Marsland 1971)who carried out865 mm diameter plate loading tes ts in 900 mm diameter bored holes in London clay. Mars landfound that the average moduli determined from the loading tests were between 1.8 to 4.8 timesthose obtained from undrained t r iaxial tes ts .A suggestion to obtain th e more realistic valuef or E sis,

1. Und is turbed samples obtained from th efield must be reconsolidated under a stress systemequal to that in thefield ^-condition),2. Sam ples mu st be reconsolidated isotrop ically to a stress equal to 1/2 to 2/3 of the in situvertical stress.

It may be noted here that reconsolidation of disturbed sensitive clays would lead tosignificantch ange in the water content and hence astiffer s t ructure wh ich wou ld lead to a very highE - Because of the many difficulties faced in selecting a modulus value from the results oflaboratory tests, it has been suggested that a correlation between the modulus of elasticity of soiland the und rained shear s t rength may provide a basis for set tlement calculat ion. The m odulus Emay beexpressed as

E s= Acu 13 . 19)where th e valueof A for inorganicstiff clay variesfromabout500 to 1500 Bjerrum, 1972) an dc uis the und rained cohesion. I t may general ly be assumed that highly plas t ic clays give lower valuesfo rA, and lowplasticity give higher valuesfor A. Fororganic or soft clays th e valueof A mayvaryfrom 100 to 500. The undrained cohesion cu ca n be obtained from any one of the field testsmentioned below an d also discussed inChapter 9. ield methodsField methods ar e increas ingly used to determine th e soil strength parameters. They have beenfound to be more reliable than the ones obtained from laboratory tests. The field tests that arenormal ly used forthis purpose ar e

1 . Plate load tests PL T)


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564 C h a p t e r 13Table 13 2 Equa t ions fo r computing s by m king use of SPT and C PTva lues inkPa)

Soil SPT CPTS and ( n o r m a l l y c o n s o l i d a t e d) 500 Nco r + 1 5 ) 2 t o 4qc

(35000 to 50000) log N co r \+Dr2)qc(U.S.S.R Pract ice)

Sand ( sa tu ra ted) 250 N + 1 5 )S and (ove rc onso l idate d) 6 to 30qcGrave l ly sand and gravel 1200 N +6 )C l a y e y sand 32 0 Nco r + 1 5 ) 3 t o 6 qcSil ty sand 300 Nco r + 6) 1 to 2 qcSoft c lay 3 to 8qc

2. S tandard pene t rat ion test (SPT)3. S tat ic cone pene t rat ion test (CPT)4. Pressurem ete r tes t (PMT)5. F lat d i latom ete r tes t (DMT)

Plate load tests, if conducted at levels at which Es i s r equi red , g ive qu i te re l iab le values ascompared to laboratory tests . Since these tests are too expensive to car ry ou t , they are rare ly usedexcept in m a jo r p r o je c ts .

M a n y invest igators have obtained cor re lat ions be tween Eg and f ie ld tests such as SPT, CPTand PMT. The cor re lat ions be tween ES and SPT or CP T are applicable m ost ly to cohesionless so i lsan d i n so mecases cohesive so i ls under undr ained condi t ions. PMT can be used for cohesive so i ls tod e t e r mi n e b o t h th e i m m e d i a t e an d consol idat ion se t t lements toge ther .

Some of the cor re lat ions ofyw i t h N and qc are given in Table 13.2. These cor re lations havebeen co l lec ted f r o m va r i o u s so u r c e s .

13 9 METHODS OF COMPUTING SETTLEMENTSM a n y m e t h o d s a r e ava i lab le fo r c o m p u t i n g e las t i c (i mm e d i a te ) an d c o n so l i d a t i o n se t t l e me n t s . On lythose m ethods that are of prac t ical in te rest are d iscussed here . The var io us m ethods d iscussed inthis chapte r are the f o l l o w in g : omputationof ElasticSettlements

1. E last ic se tt lement based on the theory of e last ic i ty2 . Janbu e t al ., (1956) method of de te rmining se t t lement under an undrained condi t ion .3. Sc h m e r t m an n s me t h o d o f c a lc u la t i n g se t tl e me n t i n g r an u la r so i ls b y u s i n g CPT values.

Computation of Consolidation Settlement1. e-\ogp me thod by making use of oedomete r tes t data.2 . Sk e m p t o n -B je rr u m m e t h o d .


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Shallow Foundation II: Safe Bearing Pressure an d Sett lement Calculat ion 56513 10 ELASTIC SETTLEMENT BENEATH TH E C O R N E R O F AUNIF ORM L Y L OADE D F L E X IBL E ARE A BAS E D O N T H E T H E O R Y O FELASTICITYThe net elastic settlement equation for a flexible surface footing may be written as,

P a - > 2 ) ,S B If (13.20a)swhere Se = elastic settlementB = width of foundat ion ,

E s = mo dulus of elasticity of soil, j = Poisson s ratio,

qn = ne t foundat ion pressure ,7, = inf luen ce factor .In Eq. (13.20a), for saturated clays, \ L - 0.5,a nd Es is to be obtained under undrained

condit ions as discussed earlier. For soils other than clays, t he v a lue o f has to be ch osen sui tablyand the corresponding value ofEs has to be determined. Table 13.3gives typic al v alues for/i assuggested by Bowles (1996).7, is a function of the LIB ratio of the foundat ion, and the thickness H of the compressiblelayer. Terzaghi has a given a method of ca lculating 7,from curves derived by Steinbrenner (1934),for Poisson s ratio of 0.5, 7 ,= F 1?for Poisson s ratio of zero, 7 ,= F7+ F2.

where F{ an d F2 are factors w hich depend upon the ratios ofH /B an d LIB.For intermediate values of// , the value of I fcan be computed by mean s of interpolation or bythe equation

l-f,-2f,2)F 2 (13.20b)The values of F j an d F2 are given in Fig. 13.7a. The elastic settlement at any point N(Fig. 13.7b) is given by

I-//2)S e atpointN=-S-_ [ I f2 B 2 +7 /37?3+7 /4 7 ?4] 1320c)

Table13 3 Typ ical range of values fo r Poisson s rat io (Bowles , 1996)Type of soil yClay, saturated 0.4-0.5Clay, unsaturated 0.1-0.3Sandy clay 0.2-0.3Silt 0.3-0.35Sand (dense) 0.2-0.4Coarse (void rat io 0.4 to 0.7) 0.15Fine grained (void rat io = 0.4 to 0.7) 0.25Rock 0.1-0.4


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566 Chapter 13Values o f F _ ) a n d F 2 (

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Figure 13 7 Sett lement due to load on sur face o f elastic layer a)F andF versusH/B b)Method o f es t imat ings e t tlement A f ter Steinbrenner, 1934)

To ob ta in th e se t t lement at the center of the loaded a r ea , th e principle of superposi t ion isfol lowed. In such a case Ni n Fig. 13.7b w i l l be at the center of the area when B{ =B4= L =B3 andB = LrThen t he sett lement a t the center is equa l to four t imes th e se t t lement a t any one corner. T hecurves in Fig . 13.7a a re based on the assum pt ion tha t the modulu s of deforma t ion is constant wi thdep th .

In th e case of a r ig id founda t io n, the imme dia te se t t lemen t a t the cente r i s approximate ly 0 .8t imes tha t obta ined for a f l ex ib l e founda t ion at the center. A correction factor is appl ied to theimm edia te se t t lement to a l low for the depth of found a t ion by means of the depth fac tor ~ Fig. 13.8givesF o x s (1948) correction curve for depth factor. The final elastic settlement is

(13.21)where ,

s =f ina l e last ic se t t lemen tr igidi ty fac tor taken as equa l to 0.8 for a h ighly r ig id founda t iondepth fac tor from F ig . 13.8se t t l emen t for a surface f lex ib le foot ing

Bowles (1996) has g iven the inf lu ence fac tor for var ious shapes of r ig id and f lex ib le foot ingsas show n in Table 13.4.


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Shallow Foundation II: Safe Bearing Pressure and Settlement CalculationTable 13 4 Influence factorl Bowles, 1988)

567

ShapeCircleSquareRectangleL/B= 1.5

2.05.0

10.0100.0

Flexible0.850.951.201.201.311.832.252.96

average va lues)footing Rigidfooting

0.880.821.061.061.201.702.103.40

Corrected settlementforfoundationofdepthDT~lr ritli fnr^tnr Calculated settlementforfoundationatsurfaceQ.50 0.60 0.70 0.80 0.90 1.0

Df/^BL

V

0 .10.20.30.40.50.60.70.80.9 n0.90.80.70.60.50.40.30.20 .1

n

19Lr

D,ri

m//

7TT

y^r

11

j\ l l >//

Ik1I

10025

I// 10, the ma ximu m strainis found to occur at a depth equal to the wid th and reaches zero at a depth equal to 4B.The modifiedtriangular vertical strain influence factor distribution diagram asproposedby Schmertmann 1978)is shown inFig. 13.10.The area of this diagram is related to the settlement. The equation forsquare as well as circular footings) is

-jj-te 13.23)

^ swhere, S = total settleme nt,

qn = netfoundation base pressure = q - q Q),q = total foun dation pressure,

q 0 = effective overburden pressure atfoun dation level,A z = thickness ofelemental layer,lz = vertical strain influenc e factor,

C j = depth correction factor,C 2 = creep factor.

The equations fo rCl an d C 2ar e =1 ~0-5 -7- 13.24)

C2 =l +0.21og10 13>25)where tis time in years for w hich period settlement is required.

Equation 13.25) isalso applicable fo rLIB > 1 0except thatthesumm at ioni s from 0 to 4B.The modulus of elasticity to be used in Eq. 13.25)depends upon the type of foundation asfollows:For a square footing,E s = 2.5qc 13.26)For a strip footing, L IB >1 0,E = 3 . 5 f l 1 3 . 2 7 )


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570 Chapter 13Rigid foundat ion vert ica l s t ra inin f luence factor z0 0.1 0.2 0.3 0.4 0.5 0.6

t

> 3BC*

4 B L

L/B > 10

>Peak/=0.5+0.1.

D ;

>I H

1mB/2 for LIB = 1B fo r L IB >1 0

ill I

Depth topeak/,

igur 13 10 Ve rtical strain Influence fact or diagrams af ter Schmertmann etal. 1978)Fig . 13.10 g i v e s t h e v e r t i c a l s t r a i n i n f l u e n c e f a c t o r/z d i s t r i b u t i o n f o r b o t h s q u a r e a n d s t r i pf o u n d a t i o n s i f t he r a t i oL I B > 1 0.V a l u e sfo r r e c t a n g u l a rf o u n d a t i o n s fo rL I B < 10 can beo b t a i n e db y

i n t e r p o l a t i o n . The d e p t h s at w h i c h the m a x i m u m /z o c c u r s may be c a l c u l a t e d as f o l l o w sFig 13.10),

13.28)

w h e r e p Q = e f f e c t i v e o v e r b u r d e n p r e s s u r e a t d e p t h s B /2 a n d B f o r s q u a r e a n d s t r i pf o u n d a t i o n s r e s p e c t i v e l y.F u r t h e r ,/ is e q u a lto0.1at the baseand zeroat d e p t h2Bb e l o w the b a s efor s q u a r e f o o t i n g ;

w h e r e a s f o r a s t r i p f o u n d a t i o n i t i s 0 .2 a t t h e b a s e a n d z e r o a t d e p t h 4B .V a l u e s o fE5g i v e n i n E q s . 1 3 .2 6 ) a n d 1 3 .2 7 ) a r e su g g e s t e d b y S c h m e r t m a n n 1 9 78 ). L u n n ea n d C h r i s t o f f e r s e n 1985)p r o p o s e d t h e u s e o f t h et a n g e n t m o d u l u so n t h eb a s i so f ac o m p r e h e n s iv e

r e v i e w o f f i e l d a n d l a b o r a t o r y t e s t s a s f o l l o w s :F o r n o r m a l l y c o n s o l i d a t e d s a n d s ,

13.29)5= 44cfor9c< 10E s = (2q c + 20 for\050 13.32b)

w h e r e E s a n dqc a r e e x p r e s s e d i n M P a .T h e c o n e r e s i s t a n c e d i a g r a m i s d i v i d e d i n t o la y e r s o f a p p r o x i m a t e l y c o n s t a n t v a l u e s o fqca n dthes t ra i n i n f l u e n c e f a c t o r d i a g r a misp l a c e dalongsidet h i s d i a g r a mbeneaththe fo u n d a t i o n w h i c his


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Shallow Foundation II: Safe Bearing Pressure andSettlementCalculation 57drawnto thesamescale.Th e settlementso feach layer resultingfromthe netcontact pressureqnar ethencalculated using the v alues ofE s an d/zappropriate to each layer. The sum of the settleme nts ineach layer is then corrected for the depth and creep factors us ingEqs. 13.24) and 13.25)respectively.x mple 13 8Estimate the immediate settlement of a concrete footing 1.5 x 1.5 m in size founded at a depth of1m insiltysoil whose mo dulu s of elasticity is 90kg/cm2.The footing is expected to transm it auni tpressure of 200 kN/m2.SolutionUse Eq. 13.20a)

Immediate settlement,

Assumen=0.35 / = 0.82for arigid footing .Given: q= 200kN/m2,B=1.5 m,E s=90 kg/cm29000kN/m2.B ysu bst i tut ing the known values , we have

1-0352S =200xl.5xx0.82=0.024m=2.4cm9000x mple 13 9A square footing of size 8 x 8 m is founded at a depth of 2 m below the ground surface inloosetomedium dense sand withqn=1 20kN/m2.Standard p enetration tests conducted at the site gave thefollowing corrected N6Q values.

Depth below G.L. m )2468

or881212

Depth below G.L.1012141618

Ncor16181720

The water table is at the base of thefoun dation. Above thewater table y =16.5kN/m3 ,an dsubmerged y =8.5kN/m3.Compute th e elastic settlement by Eq. 13.20a). Use the equation Es =250 N co r +15) forcomputing the moduluso felasticityof thesand. Assume ] =0.3 an d the depthof the compressiblelayer= B= 16 m =//)SolutionFor com pu ting the elastic settlement, it is essential to determine the weigh ted average v alue o fN co r.The dep th of the compressible layer below the base of the founda tion is taken as equal to16 m =H ). This depth may be divided into three layers in such a way thatN co r is approximatelyconstant in each layer as given below.


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572 Chapter 3

Layer No.123

Depth m)From To

2 55 1111 18

Thickness m )367

or

91217

The weighted average9 x 3 + 1 2 x 6 + 1 7 x 7

^13.6 or say 14I DFrom equat ionE s =25 0 Nco r +15) we haveE s =250 1 4+ 15)=7250kN/m 2

The total sett lement of the center of the footing of size 8 x 8 m is equal to four t imes thesett lement of a corner of a footing of size 4 x 4 m.In the Eq. 13.20a),B =4 m ,qn= 1 20kN/m 2,p = 0.3.Now from Fig. 13.7,fo r H IB = 16/4 = 4,LIB =1

F 2 =0.03 fo r = 0.5Now f romEq . 13.20 b) T ^ f o r /*= 0.3 is

q- -2I // 1 0.32

From Eq. 13.20a)we have sett lement of a corner of a footing of size 4 x 4 m as= B 7, 7 72 5W ith the correction factor, the f inal elastic sett lement from Eq. 13.21)i ss e f c rd fse

where Cr= rigidity factor = 1 for flexible footin gd , = depth factorFrom Fig. 13.8 forD f 2 L 4= 0.5, = =1w e havedr=0.85 r A s 11U.VW L rV 4 x 4 B 4 f

N ow 5^= 1 x0.85 x 2.53 = 2.15 cmThe total elastic sett lement of the center of the footing isSe =4x2.15 = 8.6 cm = 8 6 mmPer Table 13 . l a , the maximum permissible se t t lement for a raft foundat ion in sand is62.5 mm. Since the calculated value is higher, the contact pressure qnhas to be reduced.


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Shallow Foundation II: Safe Bear ing Pressure an d ettlement Calculation 57

Example 1 3 1 0It is proposed to construct an overhead tank at a site on a raft foundat ion of s ize 8 x 12 m w ith thefooting at a depth of 2 m below gro und level. The soil investigation conducted at the site indicatesthat the soil to a depth of 20 m is norm ally consolidated insensitive inorganic clay with the watertable 2 m below ground level. Static cone penetration tests were conducted at the site using amechanical cone penetrometer. The average value of cone penetration resistance qc w as found tobe 1540 kN/m 2 and the average saturated unit weight of the soil =18 k N / m 3. Determine theimmediate settlement of the foundat ion using Eq. (13.22). The contact pressure qn = 100 kN/m 2(= 0.1 M Pa). Assume that the s t ratum below 20 m is incompress ib le.SolutionCom putat ion of the modu lus of elas t ici ty

Use Eq. (13. 19) wi th A = 500

wherecu= the undra ined shear stren gth of the soilFrom Eq. (9.14)

where qc = average static cone penetration resistance = 1540 kN/m 2po = average total overburden pressure =10x18= 1 80 k N / m 2N k = 20 (assumed)

Therefore c = 54~ 8 = 68 kN/m 220E s = 500 x 68 = 34 000kN/m 2 = 34 MPaE q . ( 1 3 . 2 2 ) f o r S e i s

_

From Fig. 13.9 f or Dj E = 2/8 = 0.25, 0= 0.95, fo r HIB = 16/8 = 2 and U B = 12/8 = 1 .5,= 0.6.Substituting. 0 . 9 5 x 0 . 6 x 0 . 1 x 8S e (average)==0.0134m=13.4 mmFrom Fig. 13.8 for D f< B L = 2 / V 8 x l 2 = 0.2, L B = 1.5 the dep th fa ctor d f= 0.94The corrected settlementSef is

S = 0 . 9 4 x 1 3.4 = 12.6 m m

Example 13 11Refer to Example 13.9. Estimate the elastic settlement by Schmer tmann s method by m aking use ofthe relationship qc = 4 N co r kg /cm 2 where qc = s tatic cone penetration value in kg /cm 2 .Assumesettlement is required at the end of a period of 3 years.


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7 Chap te r 35xL= 8 x 8 m

y= 16.5k N / m 3

Sand

0 0.1 0.2 0.3 0.4 0.5St ra in in f luence f a c to r ,/,Figure Ex 13 11

0.6 0.7

SolutionThe ave r age va l ue o f f o r N cor each l ayer g iven in Ex. 13.9 i s g iven below

Laye rNo Aver ageN

Aver age qckg/cm2 MPa

91217

364868

3.64.86.8

T h e v e r t i c a l st r a i n i n f l u e n c e f a c t o r / w i t h r e s pe c t t o d e p t h i s c a l c u l a t e d b y m a k i n g u s e o fFig. 13.10.

At thebaseo f t h e fo u n d a t i o n7 = 0 . 1

At dep th B /2 , 7; =-50'\Hr

wher e qn = 120 kpap g e f fec t ive ave r age ove rbu r de n p r essu r e a t dep th = 2 + B /2) = 6m be l ow g r oun d l eve l .

= 2 x 16.5 4x8 .5=67k N / m 2 .


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Shallow Foundation II : Safe Bearing Pressure and Sett lement Calculat ion 7

I z max)= 0.5 +0.1J=0.63/z =0a t z=/ f= 16m below base level of thefounda t ion.T he distribution of Iz is giveni n

Fig. Ex. 13.11. The equation for settlement is2B I

^ zo s

where C ,=1-0.5 =1-0.5 =0.86qn 120C2 =l +0.21og^- =l +0.21og^- =1.3

where t =3years.The elas t ic modulus Es for norm ally consolidated sands may be calculated by Eq. 13.29).E s = qc forqc < 1 0 M P a

where qc is the average fo r each layer.Layer 2 isdivided into sublayers 2a and 2b for comput ing / . The average of theinf luencefactorsfor each of the layers given inFig.Ex. 13.11are tabulated along with the other calculations

Layer N o.1

2a2b3

Substituting

A z cm )30 0100500700

qc MPa) Es3.64.84.86.8

;in theequationfo r settlement5, we5 =0.86x1.3x0.12x26.82= 3.6 cm = 36 mm

MPa)14.419.219.227.2

have

Iz av )0.3

0.560.500.18Total

^T6.252.9213.024.6326.82

13 13 ESTIMATION OF CONS OLID TION SETTLEMENT BYUSING OEDOMETER TEST D TEquations forComputing SettlementSettlement calculation from e-logp curves

A general equation for computing oedometer consol idat ion set t lement may be wri t ten asfollows.Norm ally consolidated claysr ,_/?0APsc =//-log 13.33)P o


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576 Chapter 3Overconsolidated clays

fo r pQ A p


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Shallow FoundationII Safe Bearing Pressure andSettlement alculation 77The valueo f Adependson thetypeo fclay,thestress levels and the stress system.Fig. 13.1la presents theloading conditionat apointin aclay layer below thecentral lineof

circular footing.Figs. 13.11 b), (c) and (d)show thecondition before loading, immediately afterloading an dafter consolidation respectively.

By theone-dimensional method, consolidation settlement S isexpressed as

13.38)Bythe Skempton-Bejerrum method, consolidation settlementisexpressedas

or S A C T ,Asettlement coefficient 3 i sused, such thatSc= (3 SoThe expression for (3 is

T Acr3+- 1-A) < f e

13.39)

13.40)

H^ f h *

/ i//

ii

s

o\7 1i\^u

Ar r.

*

t1

q n73Wo

K 0

, ,a - a\K>

b )

a 0+ Aa3

a 0 + Aa,-Lo 0+Aa3- A M _ La ; r A a l o

(a)

(a) Physical plane (b)Initial conditions(c) I mmediately after loading (d)After consolidationigur 13 11 Insitu effective stresses


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578 Chapter 13

CircleStripNormal ly consolidated~ I ~

Verysensi tivec lays

0. 2 0.4 0.6 0.8Pore pressure coefficient A 1.0 1.2Figure 13 12 Se t t lement coef f ic ient versus pore-pressure coef f ic ient fo r c i rculara ndstripfootings A f t e r SkemptonandBjerrum 1957)

Table 13 5 V a lu es o f se t t l e me n t coef f ic ientType o f c lay

Very s ens i t ive c lays (soft a l lu v ia l and m a r i n e c l a ys )N o r m a l l y conso l ida ted c laysOverconsol ida ted c laysHeavi ly Overconsol ida ted c lays

1.0 to 1.20.7 to 1.00.5 to 0.70.2 to 0.5

Sc ftSoc (13 .41)where ft is called th e settlement coefficientIf i t can be assumed that m v and A are constan t wi th depth (sublayers can be used in theanalysis), then ft can be expressed as

(13.42)

where adz

(13.43)

Taking P oisson s ra t io J i as 0.5 for a sa tura ted c lay during loading under undrainedconditions, the value of 3 depends only on the shape of the loaded area and the thickness o f the claylayer in relation to the dimensions of the loaded area and thus ft can be es t imated from e las t ictheory.

The value of initial excess pore water pressure A w ) should, in general , correspond to the insitu s t ress con di t ions. The use of a va lue of pore pressure coeff ic ien t A obta ined from the resul ts of


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Shallow oundation II: Safe Bear ing Pressure andSettlementCalculat ion 79a triaxial test on a cylindrical clay specimen is strictly applicable only for the condition of axialsymmetry, i e., for the caseo fset t lement und erthecentero f acircular footing. However, th evalueof A so obtained will serve as agood approximat ion for thecase ofset t lement unde rthecentero f asquare foot ing us ing th ec i rcular foot ingof the same area).

U n d e rastrip footing plane strain condition s prevail. Scott 1963)h asshown thatthevalueof Mapprop ria tein thecaseof astripfooting can beobtainedbyus ingapore pressure coefficient A sasA s =0 .866A+0.211 13.44)T he coefficient AS replaces A th e coefficient for the condi t ion of axial symmetry) inEq. 13.42)for thecaseof astrip footing, th e expression fo ra be ing unchanged .Values of the settlement coefficient /3for circularan d strip footings, in termsof A and ratios

H/B are given in Fig 13.12.Typical valueso f /3aregiveni n Table 13.5 fo r various types of clay soils.

Example 1 3 1 2For the problem given in Ex. 13.10 compute the consolidation settlement by the Skempton-Bjerrum method. The com press ible layer of depth 1 6 mbelow the base of the founda tion is dividedinto four layers and the soil properties of each layer are given in Fig. Ex. 13.12. The net contactpressure q n= 100 kN/m2 .olut onFrom Eq. 13.33), the oedometer settlement for the entire clay layer system m ay be expressed as

C p +A p

From Eq. 13.41), th e consolidation settlement as per Skempton-Bjerrum may be expressedas

fiSoewhere /3 = se ttlement coefficient wh ich can be obtained from Fig. 13.12 for various valuesof A and H /B .

p o = effective overburden pressureat the middle ofeach layer Fig. Ex. 13.12)C c = compression index of each layer// = thicknessof i thlayereo initial void ratioofeach layerAp = the excess pressure at the middle of each layer obtained from elastic theory Chapter 6)

The average pore pressure coefficient is 0.9 + 0.75 + 0.70 + 0.45 _ _A= = 0.74

The details of the calculations are tabulated below.


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58 Chapter 13

G.L.

- Layer1

Layer2aQ 1

12

14

16

18

Layer3

Layer4

f l x L = 8 x 1 2 m L

m o i s tu n i tweigh ty m = 1 7 k N / m 3

Cc= 0 .16A = 0.9

Submergedu n i t we ightyb isyb= 17.00- 9.81)=7.19kN/m 3

e = 0 84

Cc= 0.14A 0.75

=7.69kN/m 3

C =0.11y f = 8 . 19 kN /m 3A =0.70

e = 0 73

C c=0.09A =0.45

yb=8.69kN/m 3

Figure Ex 13 12

LayerNo.1234

H cm)400400300500

po k N / m ^ )48.478.1105.8139.8

A /? k N / m z75432214

0.160.140.110.09

o

0.930.840.760.73

ltj

0.4070.1910.0820.041Total

4 cm)13.505.811.541.07

21.92PorH/B =16/8= 2 A =0.7, from Fig. 13.12wehave0=0.8.Theconsolidation settlement5Ci s5 = 0.8 x21.92=17.536cm =175.36mm

3 5 PROBLEMS13.1 A plate load test w asconducted in amedium dense sand a t adepth of 5 f tbelow ground

level in atest pit.Th esizeof theplate usedwas 12 x 12in. Thedata obtained f rom th etestare plotted in Fig. Prob. 13.1as aload-settlement curve. Determine from th ecurve the netsafe bearing pressure fo r footings o f size a) 10 x 10 ft , and b) 15 x 15 ft . Assume th epermissible settlement for the f ou n d a t i on i s 2 5 m m .


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ShallowFoundationII: Safe Bearing PressureandSettlementCalculation 58Plate bearing pressure, lb/f t2 6 8 x l 0 3

0 5

1.0

1.5Figure Prob 13 1

13.2 R e f e r to Prob. 13.1.Determine the set t lements of the foot ing s given in Prob 13.1.A s s u m ethe set t lement of the p late as equal to 0.5 in. What i s the net bear ing pressure f romFig. Prob. 13.1 for the computed set t lements of thef o u n d a t io n s ?13.3 For Prob lem 13.2, determ ine the safe bear ing pressure of the foot ings i f the set t lement i s

l imi ted to 2 in .13.4 Ref er to Prob. 13.1.If the curve given in Fig. Prob. 13.1appl ies to a p late test of 1 2 x 12 in.

conducted in a clay stratum, determine the safe bearing pressuresof the foot ings for ase t t l e m e n to f 2 i n .13.5 Two plate load tests were conducted in ac 0 soil as given below.

Size of p lates m)0.3 x 0.30.6 x 0.6

Load kN40100

Set t lement mm)3030

Determine the requi red size of a foot ing to carry a load of1250kN for the same se t t lementof 30 mm.13.6 Ar ec t angu l a r f o o t i ngo fsize4 x 8 m isf o u nd eda t adeptho f 2 mbelow th eg ro u n d su r f acein d ense sand and the water table is at the base of the f o u nd a t i o n . N Q T = 30 Fig. Prob. 13.6) . Compute the safe bear ing pressureq usin g the char t given in Fig. 13.5.

5 x L = 4 x 8 m

IDf= m

DensesandN co r av ) =30F igure P rob 13 6


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8 Chapter 313.7 Refe r to Prob. 13.6. Com puteqsby using modified (a) Teng's form ula, and (b) Meyerhof sformula.13.8 Refer to Prob. 13.6. Determine the safe bearing pressure based on the static cone

penetration test value basedon the relationship givenin Eq. (13.7b)forq 120 kN/m2.13.9 Refe r to Prob. 13.6. Estim ate the immedia te settlemen t of the footing by usin gEq.(13.20a). The additional data available are:

H =0.30, If 0.82 for rigid footing andEs = 11,000 kN/m2. Assumeqn=qs as obtainedfrom Prob. 13.6.13.10 Referto Prob13.6. Comp utetheimmediate settlementfor a flexible footing, given = 0.30

andEs 11,000 kN/m2. Assumeqn qs13.11 If the foo ting given in Prob. 13.6 rests on norm ally consolidated saturated clay, com pute

the immediate settlement using Eq. (13.22). Use the following relationships.qc 120kN/m2

E s 600ctt kN/m2Given:ysat 18.5 kN/m 3,^ = 150 kN/m2. Assume that the incompressible stratum liesat at depth of 10 m below the base of the foundation.

13.12 A footing of size 6 x 6 m rests in med ium dense sand at a depth of 1.5 below ground level.The contact pressureqn 175 kN /m 2.The compressible stratum belowthe foundation baseis divided into three layers. The corrected Ncor values for each layer is given inFig. Prob. 13.12 with other data . Compute the immediate settlement using Eq. (13.23).Use the relationshipqc 400Ncor kN/m 2 .

0 11e

2

4

6

8

10-

10

//A>7sat=

10

15

c o r o x o mU 2U * qn=175 kN/m2 G.L.V19/kN/m3 1 1 1 1 1 : i ^ 5 r n

Layer 1 dense sand

Layer2 dense sandysa t= 19.5kN/m3

20 Layer3 dense sand

Figure Prob 13 12


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Shallow Foundation II: Safe ear ing PressureandSettlementCalculation 58313.13 It is proposed to construct a n overhead tank o n a raft foundation o f size 8 x 16 m with the

foundation at a depth of 2 m below ground level. The subsoil at the site is a stiffhomogeneous clay with the w ater table at the base of the founda tion. The subsoil is dividedinto 3 layers and the properties of each layer are given in Fig. Prob. 13.13. Estimate theconsolidation settlement by the Skempton-Bjerrum M ethod.

G.L.

e sJSa

ym=18.5kN/m3

5 x L = 8 x16mqn= 150kN/m 2 G.L.

Df=2m

Layer 1 e = 0.85ysat= 18.5 kN/m 3Cc= 0.18A =0.74

Layer2 ysat= 19.3 kN/m 3Cc=0.16A = 0.83

Layer3 e =0.68ysat=20.3 kN/m 3Cc= 0.13A= 0.58

Figure Prob 13 1313.14 A footing o f size 10 x 10 m is founded at a depth of 2.5 m below ground level on a sand

deposit. The water table is at the base of the foundation. The saturated un it weight of soilfrom ground level to a depth of 22.5 m is 20 kN/m 3. The compressible stratum of 20 mbelow th e f oundatio n base is divided into three layers with corrected SP T values (/V) an dCPT values qc} constant i n each layer as given below.

Layer No Depth from m)foundation level

From To q av ) MPa

23

05

11.05

11.020.0

202530

8.010.012.0

Com pute the settlements by Schmertm ann s method.Assume the net contact pressure at the base of the foundation is equal to 70 kPa, and 10 years


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584 Chapter1313.15 A square r igid footingof size 10 x 10 m isf ounded at adepthof 2.0 m below ground level .

The type of strata met at the site isD e p t h b e l o w G . L . m)

O t o 55 to 7m

Below 7m

Type o f so i lSandClaySand

The water table is a t the base level of the foundation. The saturated uni t weight of soi labove th e f ounda t ionbase is 20kN/ m 3.T he coef f ic iento f volume compress ibi l i ty ofc lay,mv is 0 0001m 2/kN,and thecoef f ic iento fconsolidat ioncv is 1 m2 /year . The total contactpressure q =100 kN/m 2 . Water table is a t the base level of foun dation .Com pute p r imary consol ida t ion se t t lement .

13.16 A c ircular tanko fd iamete r3 m is f oundeda t adepthof 1 m below ground sur faceon a 6 mthick normally consolidated clay. The water table is at the base of the f ounda t ion . Thesaturated unit weighto fsoil is 19.5kN/m 3 , and thein situvoid ratio eQ is 1.08. Laboratorytests on r epr esen ta tive u ndis turbe d samples of the c lay gave a va lue of 0.6 for the porepressure coefficient A and a va lue of 0.2 for the compress ion index Cf Compute th econsolidat ion set t lement of the f ounda t ion for a total contact pressure of 95 KPa. Use 2 :1method fo rc o m p u t i n g Ap.

13.17 A raft foun datio n of s ize 10 x 40 m is founded at a depth of 3 m below groun d sur face andis un i form ly loaded wi tha net pressure of 50 kN /m 2. The subsoil is normally consolidatedsaturated clay to a depth of 20 m below th e base of the foundation with var iable elas t icmoduli with respect to dep th .For thepurpose ofana lys i s ,the s tra tum i sdivided into threelayer s w i th cons tan t mo dulus as g iven be low:

Layer No

123

DepthFrom

38

18

below ground m )To81823

Elastic ModulusE s MPa)

2253

Com pute the imme diate set t lements by us ing Eqs 13.20a) . Assum e the footing is f lexible .

bearing capacity based on settlement

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