application of iterative technique (it) using spt n-values

7/30/2019 Application of Iterative Technique (IT) Using SPT N-Values

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Pertanika J. Sci. & Techno!. Supplement 9(1): 11 - 21 (2001)ISSN: 0128-7680

Universiti Putra Malaysia Press

Application of Iterative Technique ( IT ) Usi ng SPT N-Valuesand Correlations for Analysis of Tip and Shaft Capacity

for an Axially Loaded Pile in Sand

Rosely Ab.Malik l & Jasmin Ambrose%IDepartment of Civil Engineering, Universiti Putra Malaysia2Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor

ABSTRACf

This is a theoret ical method on how to analyze th e axial capacity (tip and shaft) of asingle p ile using iterative technique on SPT-N values an d SPT-N correlation. Thistechnique allows the engineer who conducts th e analyses to control th e i npu t and outputinformation of th e analyses in a systematic an d organized fashion. This method is also

very helpful especially fo r the development of pile capacity prediction using reliabilitymethod. Research on th e subject is being carried ou t at Universiti Putra Malaysia (UPM).

Keywords: SP T N-values, iterative technique (IT), axial pile capacity

INTRODUCTION

Th e Standard Penetration Test (SPT), developed around 1927 (Bowles 1996), is still oneof t he mo st popular an d economica l means to obtain subsurface information of soil. Ithas been used in correlation to determine uni t weight, (y), relative density, (D,), angleof internal friction, (


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Rosely Ab. Malik & Jasmin Ambrose

calculated using " T h i s step requires at least two complete i terations, i .e. seconditeration of LOOP 1 (2 nd LOOP 1) .STEP

3. Meyerhof (1959) relates th e effective angle of shearing resistance (4)') and th erelative density, (D), in equation 3. This equation is rearranged to obtain(D) as afunction of (4)') in Eqn. 4. Where:

4>' = 28 + 0.15 Dr (3 )

(4)

Even though Eqn. (4), can give a rough approximation of Dr' th e expression in Eqn. 3was not derived fo r t he purpose of evaluating relative densi ty from effective angle ofinternal friction, 4>'. In other words, Dr = f (4)') is not a correct function representation.

STEP 4. Now the relative density ca n be applied in Eqn. 5 to fm d the probable uni tweight, gn' of sand.

D = ( y ~-Y:Oin) x (Y;"ax)r (Y;"ax - Y :run ) X (y ~ ) (5)

Where Yrn= and Ymin ar e arbitrarily chosen values considering medium an d dense sand asa preset limit fo r normal sand condi tion . Preset values chosen ar e Yrn= = 20 k N / m ~(D =0.65) fo r dense sand and Y . = 17 k N / m ~(D =0.35) for medium dense sand (relatived e ~ s i t yfor most soil is in b e ~ e n0.35-0.65). The simplification of this formula is asshown in Eqn. 6:

340Yn = 20 -3D

r(6)

Eqns. 4, 5 an d 6 a re app li ed to find Dr an d yn ', this will b e i dent ifi ed as route A. Toobtain effective unit weight, Yn"Yw (9.8 k N / m ~) is subtracted from th e unit weight inEqn. 6 (for submerged cases).

(7)

STEP 3 an d STEP 4 ar e highly debatable because of th e assumptions used to derive Drand Yn. One met ho d t ha t could overcome this problem is by using empirical values fo r4>', Dr' and Yn of granular soils based on the N-Values at about 6m depth fo r normallyconsolidated sand derived by Shioi an d Fukui (1982) to replace Eqns. (4) an d (6). Thesedata were fit ted using a spreadsheet program and th e formula for f ine, medium an dcourse sand is as below :

D = 0.074>' - 1.92Dr = 0.054>' - 1. 54Dr = 0.034>' - 1.00ynr= -0.0164>'2 + 1.644>'- 20.4

Yn= -0.0194>'2 + 1.904>'- 24.7Yn= -0.0464>'2 + 3.754>'1- 54.3

}fine sand}medium sand}coarse sand}fine sand}medium sand}coarse sand

12 PertanikaJ. Sci. & Techno\. Supplement Vo\. 9 No.1, 2001


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Iterative Technique for Ti p an d Shaft Capacity Analysis in Axially Loaded Pile i n Sand

The alternative equation introduced above will be identified as route B. A comparisonof results obtained using route A an d B will be discussed in th e results an d discussionsection later in th e paper.

STEP 5. I t is known from basic soil mechanics theory that th e effective overburden stress,0 : , can be dete rmined as long as th e unit weight an d t he dep th of th e soil element canbe determined accurately. Therefore, overburden stress, 0 : , can be represented as:

Oy ' = ~ [ yn 'z] (8)

STEP 6. The final l ink for thi s procedure is completed using a correction factor similarlyused by Wolff (1989) an d Ab. Malik (1992). Liao an d Whitman (1986) introduced thiscorrection factor fo r effective overburden stress.

IN"= ' [95.76/o y ' ] 2 ; ( 0 : is inkPa) (9)

However, th e correlat ion in Eqn. 9 causes a very rapid increase in N-Values especially fo rlower overburden stress values (shallow depth). Therefore, the au thors have suggestedanother correlation proposed by Heydinger in 1984, (Coyle et at. 1981):

" = N'0.77*[log(1915.2/0:)]

Eqn. 10 will be used in all th e analyses of data as presented in Table 1.

(10)

STEP 7. Now a loop has been created where the corrected SPT-N value N" can be used

to obtain ',Dr an d Yn' by continuous i teration. This loop as shown be low is namedLOOP 1. This is done simply fo r ident if icat ion purposes. Not ice that th e wholeprocedure only uses on e data input, N-Value.

Yo'

Olnl ' lJT( L O O P 1 ~

~ '

- - - . OLil1'liTDr -------.. (LOOI'2)

/

)N'

N ~ " - - -N"IN r nAL INPUT

(J ,

/ \ " ' - . OlITPlrr(Ll.XW2)

Fig. 1: LOOP 1

Similar IT were used by Fleming et at. (1992), to obt ai n t he ultimate t ip capacity insand. Fleming used overburden stress, 0 : , and relative density, Dr' as hi s ini ti al input .This method will be explained in detai l in th e next section, but th e initial input will beorig ina ted f rom LOOP 1. This means that LOOP 1 an d 2 (as discussed in the nextsection) are linked.

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TIP CAPACIlY IN SAND

Randolph (1994) an d Fleming et al. (1992), applied cavity expansion theorem to further

develop this method of axial pile capacity analysis. However, Randolph 's method o fanalysis was more refined an d found be tter agreement with numerical solutions comparedto fleming'S. Tip capacity in sand was derived using th e analogy between spherical cavityexpansion and bearing fai lure by Randolph in 1994 (Gibson 1950). This l eads to therelationship between end-bearing pressure, qb' and limit pressure, Plim' (Eqn. 11).

{ , ("cv)b = P lim 1 + tancpcv ta n (45 + - 2 - ) } (11)Limit pressure, p lim, solut ions can be very long and confusing. However, Yu &

Houlsby (1991) have published analytical solutions that comply with numerical solutions.Parameters needed to solve the l imit pressure equations (Eqns. (11), (28) an d (29are E, G, v, c, cp', 'ljI', Po an d m ar e as explained below:

i. Stress-strain Modulus, E in kPa, Bazaraa, in 1982 (D'Appolonia 1970) is:

Saturated sand,N.C sand,O.C sand,

E = 250(N + 15 )E = 500(N + 15 )E = 40,000+1050N

(12)(13)(14)

ii. Shear modulus, G, in kPa (Randolph 1994) is:

G = 40,000*exp(O.7D.)*(p'/100)o.5 (15)

(16)

Eiii. Poisson 's rat io , n , is a dimensionless factor. From the original expression G = 2(1 + v ) '

an d using th e solut ion for E and G (Eqns. (12)-(15 above:

Ev = -:-=--::::::---..,..

(2G) - 1

Notice t ha t t he p ro po se d formulas for parameters E, G and v ar e all derived fromN-Values using correlations.

IV. Initial mean effective stress Po' Simple explanation (Briaud 1992) an d detailedexplanation (Baguelin et al. 1978) on cavity expansion can be obtained from variousreferences. (A slight se t back is that these references can be used for generalunderstanding of th e cavity expansion theorem bu t canno t be used directly for pilecapacity analysis because only radial st ress is considered, i.e. pressuremeter analysis,and not axial). However, to avoid confusion, it must be made clear that the initialmean effective stress, Po' is related to the p' - q' plot (Baguelin et al. 1978) an d is notsimilar to overburden stress 0v ' Atkinson & Bransby (1982) defined mean effectivestress p' as:

(17)

v. Factor i dent ifyi ng cavity type, m, for spheri ca l expansion solutions is equal to2(m = 2) .

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Iterative Technique fo r Ti p an d Shaft Capacity Analysis in Axially Loaded Pile in S and

vi. Two important parameter ar e still lef t unsolved, effect ive angle of friction anddilation, 4>' and 'i", respectively. To solve these we will use input from LOOP 1. Wewill require the input of overburden stress, 0 , ' , bearing capacity factor, q' an drelative density, D" to find th e suitable 4>'cv (Fleming et al. 1992 ; Bolton 1986).

Solution for ' an d 1JJ'

Following th e work of Bolton (1986,1987), rigidity index, I" is related to relative density,D" an d mean effective stress, p' , Eqns. (18-19).

I, = D, [5.4 - In(p'jl00)]-1 fo r p ' < 150kPa (18)

I, = 5D,- 1 for p' ~ 150kPa (19)

Fleming suggested t ha t t he mean effective stress at failure p' , be approximated using

Eqn. (20)

(20)

Fig. 2: LOOP 2

Rigidity index, I" is obta ined for its respective mean effective stress p' an d D, usingEqns. (18)-(19. Effective friction and dilation angles, 4>' an d 'i", a re deduced , whichleads to effective friction an d dilation angles fo r cavity expansion solutions as in Eqns.(21) and (22).

4> = 4>' + 1.51'i" =1.8751, '

(21)(22)

Thi s ang le of friction, 4> an d angle of dilation, 'i', is th e final input into th e limitpressure equation (Eqns. ( 11) , (28) an d (29 required fo r solving th e l imit pressure,plim, equation. Simplified formula fo r input into th e plim solution is given by Eqns. (28)an d (29). The critical state angle of friction, 4>cv'relates to conditions where soil shearswith zero dilat ion (Le. a t constan t volume).

A logical question that should arise is that, why no t apply relative density, D" straightinto Eqns. (18 )-(19 ) to find the corresponding 4> and 'i' for analysis? This is simplybecause relative density, D" in this analysis mus t b e a function of critical state angle offriction, 4>cv' How many iterations should be conducted before a good solution is

PertanikaJ. Sci. & Technol. Supplement Vol. 9 0.1,2001 15


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achieved? (i.e. Fleming et al. (1992) used three iterations to f ind th e corrected bearingcapacity factor, q' for t ip capacity analysis) . Parameters Dr and


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Iterative Technique for Tip an d Shaft Capacity Analysis in Axially Loaded Pile in Sand

WhA I-sin' A .

ere, p . ... K a = . , ;1"max as m equauon.nu n 1 + sm

an d Kmax

as in Eqn. (25). Therefore;

(24)

"t ,

( J ~tanO= _ * [_ (L-Z\](z ) K mi n +(K max K mi n ) exp u \ d } (27)

Where I.l is th e rate of exponential ( O.025


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RESULTS

For each dep th , Tab le 1, th e first iteration (1st LOOP fo r each depth) is represented by

th e first row, an d th e second iteration by th e second row.

DISCUSSION AND CONCLUSION

Th e resul t in Table 1 shows that th e number of iteration required to achieve satisfactoryresults is 2 iterations (2nd LOOP 1) . These a re results of data analysed using IT, for th eorthwestern pile prediction symposium and th e results comply with th e results obtained

by Heydinger (1984) in th e symposium. Compared with the other 24 predictors,Heydinger obtained a predicted to measured pile capacity ratio of more t ha n 90% .However, th e application of LOOP 2 in non-homogenus or residual soil (Le. Malaysiansoil) is still being experimented with.

Suggested Correlation for Further ApplicationBazaraa (1967) suggested these correlations:

N' = N; for fine to coarse sandN' = 0.6N; fo r very fine or silty sand

D' Appolonia et al. (1970) and Gibbs et al. (1957):

, = 4N/(1+4p') fo r p' s 0.7Skg/cm 2

, = 4N/(3 .2S+p ' ) fo r p ' 2: 0.7Skg/cm 2

Thomburn et al. (1971) & Meyerhof (1976).

"t . = /SOtons"t = 4N tons

1

"t . = /60tons"t = 2.SN tons

1

} Driven pile in sand

} Driven pile in silt

Limit Pressure, Plim, Solutions

Fo r spherical cavity expansion in th e associated Mohr-Coulomb mater ia l (Le. m=2 an d~ = a) is E, v, c, lj>,'ljJ, Po'

(m+a)(a-1)PumR oc= - - - , - - - - , - - ~ " " " ' -a ( l + m) (a - l )po

( ~ + m ) l;( 2 1 ) ( l - b ) - ~ -= *[Roc(n-

y) -1]y n!(n - y )

(28)

(29)

Solving Eqns. (28)-(29) will produce th e value of Plim' And this PUm should be replacedin Eqn. (11) to give th e tip capacity, qb' Where symbols are:

l+sinlj>'a = 1-sinlj>'

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Iterative Technique for Ti p an d Shaft Capacity Analysis in Axially Loaded Pile in Sand

1+ simp~ = - -

1- sin'ljJ

a ( ~+m )y = - -

m ( a - 1 ) ~

( ~+ m) (1 - 2v) *[(a -1 ) Po] *[1 + (2 - m )v]1]=

E (a - l ) ~

j1-V2(2-m)]*(1+m)& [ m v ( a + ~ ) ] )

~ = * a ~+m(1- 2v) + 2v - ----( l - v ) * ( a - 1 ) ~ 1-v(2-m)

Appendix:1 0 0 0 + - - - + - - - 1 -500

/ .--/200 + - - ~ - - - t - - - < : : - : : . ?... ' f1 0 0 - + - - - - - - t - - - . I - v--::.,.. . - t - - - - t -60

30

- + - - - t - - - - + - - - - t - - -.25 30 3 5 10 45

Chart 1. Berzavantez et aL 1961

ACKNOWLEDGEMENT

This paper was made possible under th e financial assistance of University Putra Malaysia,an d t he const an t guidance p rovided by GeoEnTech Sdn Bhd., with col laboration ofth e Ministry of Science, Technology & Environment. Th e authors would also like toacknowledge th e constructive comment s made by th e reviewers of t he p ap er pr ior topublication.

NOTATION

mNN'

soil cohesionrelative densityYoung's modulus of soilshear modulus of soilrigidity indexactive earth pressure coefficientmaximum ratio of radial effective stress at pile surface to in situ ver tical effect ivestressfactor identifying cavity typeSPT -ValuesSPT blow count after initial correction ( fo r 1st LOOP 1)SPT blow count after cor rect ing for overburden stress (for 2nd LOOP 1)

q bearing capacity factor

c

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Plim limit pressure for spherical cavity expansionPo initial total stressqb tip bearing capacity (kN)qu unconfined compressive strength (kN/m 2 )S, ratio of radial effective stress to end bearing pressure in vicinity of th e pile~ m a x m a x i m u mratio of shaft friction to effective overburden stress~ m i nminimum ratio of shaft friction to effective overburden stress$' effective angle of shearing resistance$'cv critical state friction angleYo' effective unit weight of soil (kN/m B)Yo total unit weight of soil (kN/m B)Yw unit weight of water (kN/m B)v Poisson's ratio of soilo 'h effective horizontal stress

o' v effective overburden stress'tmax

uni t peak shaft capacity (kN/m 2 )'t unit shaft friction capacity(kN/m 2 )'t: unit t ip capacity (kN/m 2 )\jJ' dilation angle of soilN"A, N"B as in Table 1; superscript indicates th e me thod o r route (A or B) used to derive

go' an d D,

REFERENCES

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BAGUEUN, F., J.F. JEZEQUEL and D.H. SHIELDS. 1978. Th e Pressure meter an d Foundation Engineering.Trans Teeh Publication. Ed. A.R. Bazaraa, W. Germany, Clausthal-Zellerfeld. (1982). StandardPenetration Test, in Foundation Eng., Vol 1, Soil properties - Foundation Design &Construction, Ponts et Chaussees.

BOLTON, M.D. 1986. Th e strength an d dilatancy of sands. Ceoteehnique 36, No.1, U.K.,: 65-78.

BOLTON, M.D. 1987. Discussion on th e strength an d dilatancy of sands. Ceoteehnique 37(2): 219-226.

CoYLE,H.M. an d R R COSfELLO. 1981. New design correlations fo r piles in sand.]. Ceot. Eng. (ASCE)July 107(17).

D'A!'POLONIA, DJ., E.D' A!'poLONIA and RF. BRlSETrE. 1970. Discussion on settlement of spreadfootings on sand. Jour. Soil. Meeh. & Found. Div. ASCE.

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GIBSON, RE . 1950.]. Inst. Civ. Engrs 34: 382-383.

HEEREMA, E.P. 1980. Predicting pile drivability: heather as an illustration of th e friction fatiguetheory. Ground Eng., Apr. 13.

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Iterative Technique f or Tip an d Shaft Capacity Analysis in Axially Loaded Pi le in Sand

LEHANE, B.M., RJ. JARDINE, AJ . BOND an d R FRANK. 1993. Mechanisms of shaft friction in sand frominstrumented pile tests. J. Ceo. Eng. Div. ASCE 119, No. 1.

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application of iterative technique (it) using spt n-values

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