theory and practice_of_foundation_design_readable

1.THEORY AND PRACTICE OFN.N. SOM S.C. DAS

,.., Pies0FlO. 4.11 Pl'le foundollon.U..J...H1T> Plies Hard SOilFig. 4.12 Piled raft.Piers IUld caiseou These arc large diameter piles, in effect. which are used to suppon heavy structural load from bridges or very tall multistoreyed buildings. A pier or a well is a shaft drilled into the soil which is then filled with concrete, gravel, and so on. The bottom of the shaft may be undercut or belled out. either by hand or machine as depicted in Fig. 4.13 to afford a large bearing area. Wells are rigid structural elements and can take large lateral forces while piles are slender and liable to bend under flexural stress. Cais.Cions are large diameter wells which are installed by special construction technique.f9 HFLRmr bedI CaissonWell fourdatlonFig. 4.13 caisson and well foundation.Copyrighted material 88. 70 Theory and Practice of FoundaJiorr De.sign4 .2.3 Choice of Foundation Type The main criteria governing the choice of foundation for a struc.ture comprise (a) (b) (c) (d)Function of the building-residential, commercial, bridge. dam. and so on. Loads, the foundation will be rc, = (q.,,l. + rD1(4.1)where yD1 is the total overburden pressure at the foundation level (ybeing the unit weight of the soil ond D , the depth of foundation) as in Fig. 4. 14. 1Copyrighted material 89. Foundalio11s: Types curd Design Criteria 71FJg. .14 Gross and net ultimate bearing capacity.Allowablebearl.aC capecltyThe allowable bearing capacity of a foundation is the muimum allowable net pressure on the foundation deccrmined from considerations or shear failure of the ground. This is obtained by dividing the net ultimate bearing capacity by a suitable factor of safety. that is,qau- (q,ul, F where. F = factor of safety. The determination of allowable bearing capacity of a foundation from shear failure consideration involves a bearing capacity analysis of the foundation with the relevant soil propenies and the choice of an appropriate safety factor. A factor of safery is applied on the ultimate bearing capacity of a foundation to safeguard against: (i) natural variation in the shear strength of the soil. (ii) uncertainties in the accuracy of test results to detennine shear strength. (iii) uncenainties in the reliability of theoretical and empirical methods of determining bearing capacity. (iv) excessive yielding of the foundation when the soil apprOOches shear failure.Of the above. narural variation in subsoil propenies and uncenainty about the accuracy of test results are the primary reasons for requiring an adequate factor of safety in determining the allowable bearing capacity of a foundation. Subsoil propeniesa1a site by their verynature, are heterogeneous and there is usually wide variation of rest resultS. Therefore. a high degree of judgement is required in selecting the shear strength parameters for design. Any general guidance in thjs regard is neither possible nor always desirable. but a safety faclOr of 2.5- 3.0 may be adopted to guard against the variations and uncertainties listed above. Lower factor of safety, say, 2.0 may be adopted for a temporary construction or on sites where subsoil condition is well known and uniform. Lowering the factor of safery even funhet may lead to locaJ yielding and excessive shear deformation of the soil. The first step in a foundation design is to determine the net allowable bearing capacity, as described above. It would, then be required to estimate the selllement of the foundation for a bearing pressure equal to the net allowable bearing capacity and then to see if the estimated seulemcnr is within the permissible Umirs. lf not, lhe foundation is to be redesigned.4 .3 .2The Settlement CriteriaLet us consider the columns in a building frame which were originally at the same level but have settled differentially after application of the building load, illustrated in Fig. 4.15. The different settlement criteria c:Jn then be stated as:Copyrighted material 90. 72 + Titeory and Practice of Foundation Design (a) MaJ long before there is structural damage in beams and columns and consequently a stn>Ctural damage is almost invariably accompanied by architectural damage. VlsiUII efful: Even before there is any architectural or structural damage. excessive differen1ial settlement or tilt which can he recognised by naked eye cannot he accepted either psychologically or aesthetically. Allowableeettlemeat The allowable settlement of a building can he determined from an integrated analysis of the building frame for given magnitudes of settlement. This is, however, laborious and time consuming and has to he done separately for each building. Therefore. attempu have been made to estimate the allowable settlement from statistical correlation between damage and settlement criteria. The allowable settlement of buildings depends upon the type of con$11Uction, the type of foundation, and the natwe of soil (sand or clay). The angular distortion appears to he the more useful criterion for establishing the allowable limits. Terzaghi (1938) studied the settlement pattern of a number of brick walls in Vienna. He found that the walls reached their ultimate strength when the angular distortion was 1128S and concluded that an average settlement of S-7.5 em woold be considered normal. Skempton and McDonald (19SS) derived a statistical correlation between damage and settlement of 98 buildings from different partS of the world and coocluded that an angular distortion of 11300 should be considered the allowable limit for conventional buildings. Jappeli (1965) obsaved the damages to a three-storeyed building on clay due to differential settlement and confirmed that an angular distortion of greater than 11300 would lead to severe damages in walls of ordinary buildings. Whitman and Lambe (1964), on the other hand, studied the settlement pattern of buildings in MIT Campus and observed that an angular distortion of as little as 11800 was sufficient to cause cracks in bricks and masonry elements. Mackinley (1964) made a study of more than fifteen structures damaged by settlement. He observed that there was no simple rule to define the tolerance of structures to settlement. A cement silo had collapsed in New York after ortly 5 em of differential settlement whereas some public buildings in Mexico City had been in u.c;e even after differential settlement of more than 10 em. Rethatl (1961) carried out an investigation of twelve buildings on fill. This time. the rigidity or the structure as represented by the number of storeys was also considered. While the critical angular distortion of 11300 agreed well with those proposed by Skempton and McDonald, it was found that 91% of the buildings that suffered structural damage were two storeys or lower. Hence, the author concluded, the critical angular distonion should he related to the rigidity of the building. Some funher studies on allowable settlement have been made by Feld ( 1964) and Grant et al. (1974). While much work still remains to he done on the subject to recommend some readily acceptable values of allowable settlement. it seems there is a common agreement that an angular dis tortion of more than 11300 may lead to damages in conventional load hearing wall and framed construction. There is, as yet, no agreed guideline as regards the allowable maximum settlement of a building. Skempton and McDonald (1955) have proposed some tentative damage limits which are shown in Table 4.1.Copyrighted material 92. 74 111eory and Practice of Foundation Design Tab~Damage limilS for load bowing walls in tr.ldilional cype framed buildings4.1IsoJa1~d formdationRaft fotmdalionS emS-1.5 em 1~12.5 emSand Clay7.5 emIndian Standard Code of Practice (IS 1904-1986) recommends the following (Table 4.2) permissible total settlement for RCC framed buildings on different types of foundat ion. Tablt 4.2 Pcnnissible ~ulcment (IS 1904-1986) lsoJlg, Das (1997). Copyrighted material 107. Stress Distribution in Soils 895 .7STRESS AT ANY POINT BELOW RECTANGULAR LOADThe principle of superposition allows determination of vertical stres:s at any point below a rectangular looded area. For point A, for example, Fig. 5.13. the loaded area may be: divided into four s maller rectangles keeping the point A at the comer of each rectangle. The n,(5.27)I II :A--- - rB2 tan!l Let 2Ppc + Be lall1=BeN,(6.7)2P,, = BqN, 2P,,- 4I y8 tant 2I 2= 8 yBN7Eq. (6.7) can now be written as qd= eN, + qN,AO.SyBN7(6.8)Eq. (6.8) is lhe Tenaghi's bearing capacity equation for a strip footing correspor>ding 10 gcneFIII shear failure. N., N., and N7 are dimensionless bearing capacity factors which depend on 9 only. The values of Terzaghi's bearing capacity factors for general shear failure given in Table 6. 1. Table 6.1 Tenaghi's bearing capocity fact s., and sr are empirical s hape faclors. d,. d,. and d 7 are empirical depth factors. i,.. ;,, and iy are empirical inclination factors. The recommendations of Hansen for Nr and N, are identicaJ 10 those of Meyerhof. and are the result of those of Prandll (1921) and Reissner (1924). These are : N, = (N - l)cot 9 N = (e"'")tan 2 (45+ ~12) N7:(6.14)I.S(N - I) tan 96 .2 .6 VesJc's method l'be failure surface considered by Vcsic is similar to that of Tcrzaghi's with the exception that the zone I below the footing is in active Rankine state. with inclined faces of the wedge at (45 + 4JI2) to the horizonml. The bearing capacity equation is the same as Eq, (6.13). The factors N, and N are identical to those of Meycrhof and Hansen. N.,. given by Vesic, is a simplified form of that given by Caq1 ll and Kerisal (1948), N 7 = 2(N + l )tan~(6.15)For shape, depth and inclination factors, the reader may refer to Vesic ( 1973). 1.$. 6403-(1981 ) incorporates the results of Hansen, Vesic, and Meyerhofs analyses and gives the same fonn of equation as Eq. (6.13). The corresponding shape factors, depth fac1ors, and inclinmion facrors are dealt wilh in Chapter 8 (see Seetion 8.2).6.3 LOCAL SHEAR FAILURE Local shenr failure may develop for foocings on loose sand or soft cohesive soil, where lo..rge senJemem is required for mobilization of full shearing resis.1ance of soil. Wi1bin permissible limil of se1d cment, lhe shear strength parameters mobilized along the failure surface are c,., and 4J,,. Terzaghi proposed thai for local shear failure. and "' s hould be used in thec,,Copyrighted material 145. Staring Capacity of Shallow Foundntions 127 bearing capacity equation and factors N; . N,j, and instead of ; . Terzaghi empirically suggested lhatNT shouJd be detennined on the basis of,..; ., : (213)1 and c., = (2/3)c Thus, lhe bearing capacity equation for local shear fail ure becomes, q4 = (213)cN; + qNq + O .SyBN;where N,.'. Nq' and Fig. 6.9.N are Ybearing c.apacity factors for local shear failure depicted in40' 'Nq...30N, -.....120,N..'' ' 'IN'/'N'r~~ ','f N,.-= ....N,=260 =..o N,= 180 ..~10 0 70(6.16)~60!5040302010I0 5.7 1.0Fig. U204060llO100NrToaaglll's beaotng cac>adl)' falute tor geno B. take D1 = B. W~ and = correction factors for water table.=wy3. Staticcon~ t~st:IS:6403-1981 gives a method of determining net ultimate bearing capacity of strip footings on cohesionless soil using static cone resistance. q". The chart is presented in fig. 6. 14. q~ values at different depth are obtained for selecred locations at the site. The fie ld values are com:cted for the dead weight of the sounding rod. Then the average q, value is obtained for each of the locations by averaging the values between the base of the footing and depth below the base 1..5-2 limt$ the width of the footing. The smallest of the average values is used in Fig. 6. I I to find bearing cal"'city factors N, and N,. which may be used for computing the bearing cai"'City.0~--~~--~~--~--~ 0 100 200 300B(em)Fig. 6.14 Bearing copacfty 11om static cone Int.Example 6.1 A square footing of width 2 m re.~ts at a depth of 1 m at a site where the subsoil consists of soft to medium clay down a depth of 8 m below ground level, which is underlain by a dense coarse sand deposit. The water table is at l.S m below G.L. The clay has c. = 30 kNim1. 9 = 0 and = 19 kN/rn 3. Determine the net load the footing can safely carry with a factor of safety of 3 against shear failure. Vhat will be the safe load if the wotcr table rises to the ground surface?rSolulion Since the thickness of clay layer beneath the level of footing base is more than the width of the footing. the bearing capacity will be governed by upper layer of clay.Copyrighted material 152. 134 + Theory and Practice of Foundation Design According co Skempton's fonnula(q,.),.. = c.N,N, = 6( 1 + 0.2D 1B) 1Here,= 30 x 6.6 kN/m2= 6.6 (q .,,,),..=30 X 6.6 2.5= 2.5)(Fs= 80kN/m2 Net safe canying copocity of the footing = 80 x 2 x 2= 320 kNSince this is a total stress analysis, there will be no change in the safe load if the water table rises to the ground surfoce, unless there is a change in strength of the clay. Example 6.2 The subsoil at a building site consists of medium sand with y = 18 kN/ml. c' = 0, ~ = 32 and water wble at the ground surface. A 2.5 m square footi ng is to be placed at 1.5 m below ground surface. Compute the safe bearing capacity of the footing. What wouJd be safe bearing pressure if the water wble goes down to 3 m below G.L?Solunon Since ,. lies between 28 and35~the bearing capacity factors are obtained by interpolationbetween local and general shear failure conditions. Refening to Fig. 6.7, for 9' = 32, Nq = 28. N', = 10, N1 = 30. Ni= 6= 10 + [18;~ 2-- 2 ; 8)] = 20.3we get.N,andNr = 6 + [24i;2-2~8)) = 19.7Cas. I (water lJible at G.L.) Using Eq. (6.27) modified for square footing, ultimote gross bearing capac ity (q,,.)1..,, = y'D1N, + 0.4y'BN1 : 8.0 X 1.5 X 20.3 + 0 .4X8.0X2,5X19.7= 243.6 + 157.6 =401.2 kN/m2 and ultimate net bearing capaciry. (q,"),,.. = (q,,.>...,.-= 40 1.2 - 18rDt X1.5 = 384.2 kN/m2Copyrighted material 153. Baring Capacity of Shallow Foundations 135 Safe net bearing capacity. (q.,1,).., = 384.212.5 = 152 kN/m2(Fs = 2.5)and gross bearing capacity, (q..rJ.,...= 152 +18 x 1.5= 179 kN/m2Case II (Water table at 3m below G.L., that is, at a depth greater lhan width footing)(q.,J.,....: 18X1.5X20.3 + 0.4{14X2.5)19.7= 548.1 + 275.8 = 823.9 kN/m2 (q.1 ,),.. = 823.9 - 18 x 1.5 = 796.9 kN/m2 safe net bearing capacity. (q..rJ... = 796.912.5 = 319 "320 kN/m2 and safe gross bearing capacity, (q..rJ..- = 320 + 18 x 1.5 = 347 =350 kN/m2 (This problem may also be solved using water table correction factors W~ and W' with 1 marginal change in the result Also Fig. 6.10 may be used for obtaining relevant N 9 and N 1 values.) Example 6.3A rectangular footing, with a plan area of 1.4 m x 2 m is to be placed at a depth of 2m below the ground surface. The footing would be subjected to a load inclined at 10" to the venical. The subsoil is clayey, sandy silt with saturated unit weight of 18 kN/m3, and c' = 10 kN/m2 and ~ = 30. Assuming the rate of loading i.s such that drained condition prevails, compute the magnitude of load the footing can carry if the water table is at the base of the footing. Use IS: 640>-1981 recommendations and take Fs = 3. Equation (6.13) gives, q_, = cN.s, d, i, + q(Nq - l)sdi + O.Sy8N1 s 1 d1 i 1 W'Here c = c' = 10 kNim'. ; = ; = 30 N = (e",.. 0 )tan 2(45 + ;12) N, = (N. - l)cot;= 18.38= 17.38cot30=30.10N1 = 2(Nq + I) tan;= 22.37s, = I + 0.28/L = 1.14 sq= I + 0.28/L = 1.14s1 = I - 0.48/L = 0 .72If. =1 + 0 .2Dtf8tan (45 +;n> = 1 + 0.2 x 2/1.4 x 1.732 = 1.5 Copyrighted material 154. 136t11reory a11d Practice of Fomulntio, Dtm'g11 d, = d 1 = 1 + 0.1D1 tan (45 + frl) = 1 + 0.35/1.4 = 1.25i,= ;, = (1- a/90)1 = 0.79iy = 0.44W' = 0.5 Hem:e.q..,: ( 1030.J X J.l4 0.79) + (0.5 X 18 XX XJ.5 1.40.79) + (18 X 2 X (18.38 - 1) X J.l4 22.37 X 0.72 X 1.25 X 0A4 X 0.5)X XXJ.25X= 406.6 + 704.4 + 55.8 =1166.8 kN. (q..J..t. = 1166.813 = 388.92!380 kN/mlHence, safe load = 380 x 1.4 x 2 = 10642!1060 kNEsample 6.4 Wbat will be lbe safe load in Example 6.3 if undrained condition prevails? Take c. = 30 kN/m2, 0, N, 5.14, N, =I, and N1 : 0.;,. ==St>iuJU>II: 30X5.14X1.14X1.5X0.79= 208.3 kN/m2 kN!m 2(q ..J..r, = 208.313 = 69.42! 70Safe load : 70= 196 kNX1.4X22! 200 kNBrinch Hansen. 1. (1961). A General FomJUla For Bearing Capacity, Danish Geotechnical Institute, Bulle.tin No. 11 . Copenhage.n. Brinch Hansen. 1. (1970). A Revised and Extended Fomru/a for Bearing Copaciry. Danish Geotechnical Institute, Bulletin No. 28, Copenhagen. Davis and Brooker (1973), The Effect of Increasing Strength with Depth on the Bearing Capacity of Clays, Geottchnique, Vol. 23. pp. 551-.563. D'Appolonia. D.J. and T.W. Lambe (1970). Method of Predicting Initial Settlement, Journal Soil Mechanics and Foundarwn Division. ASCE. Vol. 96. pp. 523-544. IS 6403 ( 1981). Codt of Practice for Dettnninarion of Bearing Capaciry of Shallow Foundations. Bureau of Indian Standards, New Delhi. Meyerhof. G.G. ( 1951), The Ultimate Bearing Capacity of Foundations. Geottchnique, Vol. 2. pp. 301- 332.Copyrighted material 155. Btaring Capacity of Shallow Foundations 137 Peck, R.B., W.E. Hansen, and W.H. Thombum (1962). Foundation Engineering, 2nd Edition. John Wiley & Sons. New York. Prandtl, L (1921). Uber die Endvingungs Festingkite von Schneiden, 'kirsclrrift fur Angebandrt Mathtmatik and Mechanik, Vol. I, No. I , pp. 15-22. Reissner (1924). Zuns Erdd,.,ck-problem. Proc. Fint Int. Congress on Applied Mechanics. Dept. pp. 295-311. Skempton. A.W. (1951), The Btaring Capacity of Clays. Building Research Congress, England. Terzaghi. K. (1951),7l~eoreticalSoil Mtchanics. John Wiley, New York.Vesic, A.S. (1973). Analysis of Ultimate Loads of Shallow Foundations, Journal of Soil Mtchanics and Foundation Division ASCE, Vol. 99, No. S M I, pp. 45-73. Vesic, A.S. (1975), Bearing Capacity of Shallow Foundations. Chapter 3 of Foundation Englnetrlng Handbook. Van Nootrand Reinhold Co., New York.Copyrighted material 156. Settlement Analysis7.1INTRODUCTIONFoundacions on soft clay are liable to undergo excessive settlement and prediction of this settlement is an imponant aspect of foundi, to give the final senlemenr. p1 of the foundation. Therefore.Pt=P; + p,(7.1)7 . 1.2 Me thods of Settlement Analysis The principle of effective stress :md Tenaghi's theory of onellod .............. 164. 146 Tlreory and Practice of Foundatiotl Design Method I, described by Skempton and McDonald (1955) as the conventional method, was first proposed by Tcrzaghi (1929) and later used by Taylor (1948). It a.,gumes that all settlement occurs from one-dimensional compression and that the excess pore-pressure is equal to lhe increase in verticaJ sttess. Therefore. the corresponding stress-path is ~Method 2 recognizes that the soil undergoes shear deformation during undrained loading (path AB). and this causes the immediate seulement, but still assumes that the excess pore-pressure, which should be a function of the induced shear stress~ is equal to the vertical stress increment. Consolidation settlement. therefore. occurs along the stress- path AF. This inconsistency in Method 2 has been overcome by Skempton and Bjerrum (1957) in Method 3. Here. the immediare settlement is a function of the stress- path AB whiJe the consolidation settlement occurs along the path EF. The latter. therefore. is only a part of the total strain along the path AF depending on the magnitude of the excess pore-pressure set up during loading. While the method of $kempton and Bjerrum introduces for the first time, the concept of strcss,.path in settJement analysis, the as."umption ls still implicit that during consolidation all strain is one-dimensional which requires the horizontal stresses to adjust accordingly. Therefore, there is a discrepancy between the field stress-path 80 and the path EF used in the analysis. The condition of no lateral strain may be approximately true in cases like that of a loaded area which is very large compared to the thickness of the clay layer. But in the majority of field problems. this condition may be far from ltue. Moreover. while computing the immediate settlement. Method 3 obviously accepts that the clay undergoes lateral dcfonnation during loading (with constant volume, there would he no set~ement otherwise) but th.is is neglected in estimating the consolidation seulement. Consequently, of course. the effect of the horizontal stress is completely ignored except in determining the e xcess pore-water pressure.7 .2.1 Stresses During Loading and Consolidation in the Field It is evident that during load application in the field. most of the defonnation takes place under condition of no volume change, implying a value of Poisson's ratio of the soil equal to 0.5. As the excess pore-pressures dissipate. Poisson' s ratio also decreases and finally drops to its fully drained value. It is known that for an isotropic homogeneous e lastic medium. the venicaJ stresses are independent of the elastic parameters and are. therefore. unlikely to be significantly affected by this decrease in Poisson's ratio. On che other hand. Poisson's ratio has a cons-iderable influence on the horizontal stresses even for the Boussinesq case beneath the centte of a uniform circular load. Therefore, it is clear that the problem of consolidation in the field is very much interlinked with the problem of stress distribution, whose rigorous analytical treatment is extremely complex. An approximate analysis may he made on the assumption that the horiwntal stress at the e nd of consolidation will be the same as the Boussinesq stresses for the appropriate value of Poisson's ratio. If we consider an element of clay at a certain depth where. during load appliealion, 60'., and 60'111 are rhe increase in vertical and horizontal stre.'.Ses respectively lhen, at the end Or consolidation. the venica1 stress will still remain unchanged but lhe horizontal stres.~ will have decreased to the new vaJue 6a111 due to the reduction of Poisson's ratio.Copyrighted material 165. S~ttl~m~nlAnalysis 147So. the changes in effective stress during consolidation an: given as[6u,l, =Horizontal:11.u-6(7 .11 )Vertkal:where6 = 6u, 1 - 6a.,.The ratiO of the effective stress changes during consolidation, K' is then given by K'=[Au,J.: I - .!.._[Aa,l,(7.12)6uNow. for the Boussinesq problem, the general expressions for stresses beneath the centre of a uniform circular load (dlameter 2b and load intensity. q) are (Wu 1966), u _' - q[I _(tlb)3 ](I + t 2/b2 ) 311 (7.13) 3a = !l.[(l + 2v) _ 2(1 + v)(tlb) + (t/1>) ] ' 2 (I+ z2 /l?) (I + z3/b3 ) 311which can be more conveniently written as,u, = q(l - '1')u, = ~((I + 2v)- 2(1 +V)'l+ '1'1(7. 14)where. (7.15) Using these expressions,Aa, = (u, ),. 111 = q(l - 11'>6a,, = (u,),. 112 = ~ [2- 3'1 + 11'1(7.16)6u., = (u,), . .. = ~[(I+ 2v') ~ 2(1 + v') '1 + 11'1 Combining Eqs. (7.13) to (7. 16). we haveK' _ I _ [ I - 2v ] I + IJ{l + 1J)(3A - I)(7 .17)Eq. (7 .17) can then be used co determine the mt.io of the s tress increase during consolidation at any depth beneath the centre or a uniform circular load.Copyrighted material 166. 148 Theory and Practice of Foundat;o,7.2.2Desig~tIn1luence of Stress-path on the Drained Deformation of ClayIt has been shown in the foregoing that the stress changes thai occur in the field during consolidation are primarily dependent on the drained Poisson's ratio and the pore pressure parameter A of the soil. Therefore. it is of considerable practical significance to study the influence of scress-path, such as BD (sec Fig. 7.5) on che axial and volumetric strain during consolidation. Expcriment J investigation with undisturbed London clay (Som. 1968). a normally consolidaced KaoliniiC (Das and Som e1 al., 1975) and undisturbed Calcuna clay (Guha, 1979) show lhol lhe stress incrcmcnc mtio during consolidation has importanl effccc on the deformation characteristks of the soil. Two things need to be considered here: (a) the influence of stress incremenl mtio on lhe volumetric strain of the soil and (b) the influence of stress increment ratio on the strain ratio (that is, axial strain/ volumetric Slnlin) of the soil. There is conflicting evidence on the effect of s tress ratio on the volumetric compressibility of clay. Some investigators have found that the volumetric compressibility is independent of the stress increment ratio and can be expressed as function of vertical effective stress only (Som. 1968). This means !hat !he results of one-dimensional consolidation ccsts would be applicable irrespective of the changes in lateral pressure during consolidation. Others hove found that the volumetric compressibility is not independent of the lateral pressure and can be$1 be expressed as functions of mean effective stress during consolidation (Dos, 1975). It seems chat the appropriate relationship has to be determined for the particular soil under investigation. The major effect of lateral stresses during consolidation is, however. manifested in the axial strain associated with volumetric defonnation. Figure 7.7 shows some typical results of stress-path controlled triaxial tests on different clays. The results are plotted as relationships between the stress increment ratio. K' and the strain ratio, A during consolidation or drained deformation. It is to be noted that one~dimensional consolidation implies a strain ratio, A= L.O nnd that occurs at a pank,ular stress increment ratio only. For any other. stress ratio. the strain ratio would also the difference and assumption of one...cJimensional strain (i.e. 11., :: 1.0) would lead to significant error in settlement analysis. 4.03.22.4 1.61 Undistu'bed Calcufta day 2 Sedimented bolinite3 UndisiUrbed London clay Observed- - - - Theoretical (""Isotropic elastcity}"z~0.8"~ ~ --.0.00.4 0.8 0.8 1.0 K' = Aa'.,IIJ.a ' 1 Fig. 7.7 Strain ratio, .t versus stress increment ratio. K for draln~~~~!iq'Xf 0.00.2material 167. Seulemem Analysis 149 The relationships shown in Fig. 7.7 can best be determined from stress controlled triaxiaJ tests. However, Som (1968), Simons and Som (1969) have demonstrated that this relat.ions hip can also be established cheoreHcally from considerarion of aniso1ropic elas1icicy as:e,I - 2~/,K' , = (I - 2v)) + 21)(1 - vj - Vz)K'(7.18)where. v '1 = effect of one horizontal strain in the othe- horizontal scrain; r v'2 = effect of horizontal strain on vertic.al strain; v'1 = effect of vertical strain on horizontal strain; Jf = ratio of venical drained dcformatjon modulus to the horizontal drained defoTITUition modulus. Equation (7.18) can also be expressed as I - 2~V,K' , = (I - 2v))[K'/K0 - 1)- 2~V,K' 1(7.19)The parameters v'3 and rJVi can be detennined from two tests with different values of K' and measuring 1/e., in each case. The most convenient values ofK' to choose are u and 1.0. that is, !hose from lhe standard drained compression test and lhe isotropic consolidation test.7 .2 .3Settlement Analyala by Stre..-path MethodThe methods of settlement analysis in current use have been described earlier. These methods have given satisfactory results in many field problems, particularly where lhe condition of zero lateral strain is satisfied. However, more often !han not appreciable lateral deformation occurs in lhe field and lhe currently used methods of settlement analysis become inadequate to predict lhe seulemenL A method of settlement prediction by the stress-path method has, therefore. been introduced for lhe case of axi-symmetric loading (Simons and Som, 1969. Som et al., 1975).Immediate oettlemeat The common practice in estimating lhe immediate (elastic) settlement of foundat ion on clay is to assume the soil to be a homogeneous, isotropic. clastic medium. thus, permitting the application of Boussincsq analysis. However, in practice, the elastic modulus~ E of tt:e soil varies with depth as a consequence not only of the inherent nonhomogeneity of the soil but also of varying applied stress levels at different depths. Stress- strain relationship of soft clay is essentially non-linear and the deformation modulus varies considerably with the stress level. While it is possible to make theoretical analysis of undrained deformation using the finite clement technique and taking the non-linear stress versus strain behaviour of the soil into consideration, they are nor yet available in readily usable form. A ~il"ple expression for immediate settlement following the stress-path method may be given as,Copyrighted material 168. 150 Theory and Pmctice of Foundation Design_ 'JAa, - aa.p, -(1.20)e(z)0where C.a. and La11 are the increase in toral vertical and horizontal stresses at any depth re.pectively and E{z) is the corresponding deforrru~tion modulus, taking due account of the vertical and horizontal effective stresses prior to and at the end of loading. It has been shown by many investigators that the stresses in the subsoil due to a foundation loadjng are not significantly dependent upon the variation of E (Huang 1968. Som 1968). Therefore. in the absence of more rigorous analysis. the Boussinesq stresses may be used in evaluating the settlement by Eq. (7.21), the integration being done numerically by dividing the compressible stratum into a number of layers and taking the appropriate value of E for the layer into account.Conaolldatlon aetUement In the conventional method. the consolidation settlement is given by,p,J=(m,), a a, dz(7.21)0where (m,) 1 is the coefficient of volume compressibility determined from standard consolidation test and C.a: is the increase of vertical pressure at the centre of layer. Following the Skempton and Bjerrum (1957) method, the settlement is,p, = J.1'J ) !!.a, dz (m, 1(7.22)0where J.1, the pore-pressure corTOCtion factor, is a function of the soil type and tbe geometry of the foundation, (refer Fig. 7.4). For the stress-path method. the settlement is given by,p; =J).(m,)3 l!.udz(7.23)0= ).p, where, tJ.u= increase of pore-water pressure under undrained loading which dissipatesduring the consolidation. (m,h = coefficient of volume compressibility for three-dimensional strain. A = the ratio of venicaJ strain to volumetric strain which is a function of the stress increment ratio during consolidation. If Eq. (7.23) is to be applied in seulement analysis, K' during consolidation needs to be known in order to determine the value of A. Ac-eurate determination of K' for actual foundation may be difficult becau,s e it depends on many factors such as Poisson' s ratio,Copyrighted material 169. Seltlement Analysis + 151 pore pressure parameter A. stress-strain relationshjp of the soil. and so on. As an approximation, however, its value can be determined from Eq. (7.17), for a footing of diameter 2a. According to Eq. (7. 17),K _ I _[ I - 2v ] I + IJ(l + q)(JA - I) where,)-t/2' 1]= -< ( 1 + Qa'v = Poisson's ratio A = Skempton's pore-pressure parameter Knowing the value of K', A. can be obtained from experimental relationships as shown in Fig. 7.7. The value of (m,):, should, of cour>e, be obtained from appropriate stress-path test, bu~ for practieal purposes, can be determined from properly conducted oedometer test. Then, (m.)) may be taken as approximately equal to (m,) 1, the oedometer compressibility in terms of venical effective stress. It may be noted here that evaluation of the K versus A relationship for any problem requires determination of Poisson's ratio and pore-pressure parameter, A of the soil. But for most soils, Poisson's ratio varies between 0.1 and 0.3 and pore-pressure parameter, A between 0 and I. Accordingly, K varies within a narrow range of 0.6-0.9 and A in the range 0 ..5-0.8. It would, therefore, be convenient to select a value of l within this range for most practical problems (Som, 1968).7 .SRATE OF SETTLEMENTThe rate of settlement of foundations on clay is generally determined from Tenaghi's theory of one-dimensional consolidation although tield..:onsolidation is often three-dimensional (See O!apter I. Section 1.9.5). According to this, the excess pore-pressure at any point at depth t within a soil mass after a time from load application, is governed by the equationC lflu = 8u'8:' where~8t(7.24)u is the excess porepressure andC" coefficient of consolidation. The degree of consolidation at any time, 1 (defined as the percentage dissipation of pore-pressure) may be obraincd by solving Eq. (7.24) for appropriate boundary conditions. Table 7.2 gives the relationship between time factor, T, = C,JIH 2 and degree of consoHdation, U for different boundary conditions.Copyrighted material 170. 1S2 Tlr~oryand Practice of Foundalion Design Tablt' 7.2U versus T~ relationship (T~ C~t!H 1)U%(u,Ju,) 0o.s1.0s.oT,0 20 400 0.01 Cl.llo.os0.0490.640 0.014 0.081 0.19S 0.4600 0.010.17 0.3 1 0.580 0.031 0.1 26 0.237 0.567600.3980 100"'"'"'"'"'0O ISS . 0.420For double drainage (any distribution of pressure, that is, u 11u: :;:; any value). take H = 112 times thickness of cJay and T,. values fo r (u 1/ui) = I.7 .4FOUNDATION ON SANDFoundations on sand do not present the !>arne degree of problem with regard to settlement as foundations on c;:lay. Firstly, except for loose sand. settleme- t is usually small and secondly. n because of high permcabilily the settlement is usually over during the period of construction. In this case. there is no time dependent settlement similar to the consolidation settlement in clayey soils. although large foundations may undergo minor settlement caused by fluctuations of load due to wind, machinery vibrations. and storage loads. a Prediction of settlement of foundations on sand is, by and lange. empiric- l although elastic theory has sometimes been used. The common methods used for this purpose are:7 .4 . 1Elastic TheoryThe problem is similar to calculation of immediate settlement of foundations on clay as given in Eq . (7.3). For a homogeneous. isotropic, e lastic medium6 = q.B (I - v) 2 /E(7.25)Pwhere the different terms have the same meaning as in Eq. (7 .3). However. it is to beconsidered thac because of volume change during load application, Poisson's rutio. v can no longer be taken as 0.5. The value of E and v should be determined from tbe laboratory triaxial tests for the appropriate relative dens icy and confining pressure- The Poisson's ratio normally . varies between 0. 15 for coarse sand to 0.3 for fine to silty sand. The value of E can also be determined from the standard penetration resistance or the soil (refer Otaptcr 2. Table 2.7). Elastic theory. however, gives only a very approximate estimate of settlement, because the assumption of homogeneity would be far from renlity.7 .4 .2Semi-empirical Method ()3ulsman, 1948)Buisman (1 948) has given on empirical method or es timating the senlement of foundations on sand by numerical integration of the strains occ urring in different strata. as s hown in fig. 7.8. Accordingly.Copyrighted material 171. Settlemtntlog 10Pu + l!.p dz p.,r l l ! ~)'OfLa)'llf2E,z,E,z,E,z,"'Po dl>~Layer 4(7 .26)l ! ! layer 3 153Net foundation pressure, q,~1llrr 2 ' 5(b) Immediate settlementq. = 11 2.5 kN/m2 B=2mv = 0.5 IP.oH log p., + flp PoTwo layers (I and If) are involved in the pressure influence zone.AtA: Po = 19 x 1.0 + 9 x 1.0 = 28 kN/m ' flp [for Z/8 = 1.6/2.5AtB: Po= 19 x1.0 + 9 x 2.0 + 8 x 1.5flp (for Z18...~= 0.4] = 0.85 x 65 = 55.2 kN/m '= 004 .=49 kN/m2= 3.512.5 = 1.4) = 0.42 x 65 = 27.3 kN/m 2 x21og28 + SS.2D0 IS+ .x21 49 + 27.3 49= O.Q38 + 0.058 m = 0.096 m Depth correction= 0. 95Rigidity correction = 0.8 (lnrerconnected strip provides rigidity to the foundation)Pore-pressure correction. J1 = 0.75(Major contribution to settlement comes from strata I and II. Hence. J1 correction for N.C. clay is considered.) ..(p,)""' = 0.95 x 0.8 x 0.75 x 0.096 = 0.055 m = 55 mm..Total setdement. p1= 17 + SS = 72mm < 75 mmExample 8.3 A column carrying a superimposed load of 1500 kN is to be founded in a medium sand asshown in Fig. 8.22. Design a suitable isolated footing.Copyrighted material 208. 188 Theory and Practice of Foundation Design 1SOO kNN {Biow>/30 em)Depth (m)o--------~ ~~~----~~~~r;18kNim32 --,.-,,..-----,,. . ."' .I-i-5mFig. 8.22 Example 8.3.Nu., = 15Average N value,f =34 (Eq. (2.5))N, = 30 N1 = 41Q... = 1500 lcN/m2Assume footing size = 2.5 m 2.5 m.qftll!f.="1500 _ _ = 240 kN/m' 2 5 25Solution (a) Bearing capaciry = 1.2; s, =0.8; dq =d, = 1.15; ;, = ;, = 1.0q,.(n) = q(N, - l)sqd,i, + 0 .5yBN1s1 d1 i1= (J8K2(30- I)K1.2K1.15K1.0) + (0.5X9X2.5X41X0,8X1.15X1.0)= 1440 + 424 2 = 1864 kN/mFs =1864 = 7.8 > 2.5 240(b) SettlementConsidering single layer of 5 m depthS=2~fl log Pn + l!.pPoCopyrighted material 209. Footings ami Rafi Design 189p. = 18 l!.pEX2 + 9X2.5 = 58.5 kN/m2= (for 718 = 1.0) = 0.35 x 240 = 84 kN/m2 = 39 + 4.5 x IS = 1065 kg/cm 2 = 10,650 kN/m2 (refer Eq. (2.6))6 =2.3 X 58.5 I 58.5 + 84 x 5 og 58.5 10,650=0 .024 m = 24 mm EXample 8.4 Three columns in a building frame spaced 4 m apart carry vertical superimposed loads of 500 kN, 720 kN and 600 kN. Design suitable isolated footings for the columns for equal settlement. Subsoil condition is shown in Fig. 8.23. Depth (m)o --------~RI ~-------,-.~t77 s k~Nhn~,------- - ~----------------------I Medium day r 18 kNim, c;. = 40 kNhn'm~ = 0.0005 m'lkN-s----------~-----------11 SUff Clay r=19 kNim1c;.. 90 """"' 0.0003 m21kN-1 0----------=....::;=:.:.::..=-----m.. Fig. 8.23 Subsoil condition (&ample 8. .4).Solution Approximate q.,,(n) of slr.ltum I= cll/Nt: = 40 X 6.0 = 240 kN/m2 qo~,(n). = 240 25,= 96 kN/m- (for Fs = 2.5)Choosing approximate fOOting size accordingly and carrying out detailed analysis. Column A Take footing size = 2.2 m x 2.2 m Area= 4.84m2500 2 q..,. = = 103.3 kN/m 4. 84Copyrighted material 210. 190 Titeory and Practice of Foundation Design (n) Bearing copaciryFailure surface in layer 1: Take c. = 40 I 2.5 103 3Fs = (b) Immediate senlemelllq. = 103.3 ItOGOTime after driving (days) Fig.. i.4Gain in load carrying capacity with time of driven piles in soft clay (Tomlinson. 1994).High porcprcssure is developed in the c lay due to pile driving fo rces. This porepressure often takes time to dissipate. When reconsolidation of the clay occurs, the soft clayCopyrighted material 225. Hidden page 226. 206 Theory and Pracll'celeat pile groups.Tripfe row for a wallCopyrighted material 247. Hidden page 248. 228tTiteory and Practice of Foundation Design p= M rCI11Lx;s!':!.Jz. Z.uOn the other side or CG. the reaction is upward, that is, P1 is negative.P _ Ma x, _ Mu Thus.where" -L,x; -Z.uP11 = maximum reaction due to moment M11 and x1 ;::; maximum distance of pile from YY axis.Similarly, maximum pile reaction due to the moment. MD is given by P~, =where.Thus,MuYJ ~2~ y"=Mu t yyP_. 1 = maximum reaction due 10 moment Mu and x1 = maximum distance of pile from XX axis.I I.load V " 1 M,.y1 pile =P= NMyy.'rversus UD (K, =coefficient of passive earth pressure and r= unit weight of soil) are presented. The curves for long piles in cohesive soil are given in Fig. 9.30. The normalized ultimate lateral resistance, H Jc..D 1 is ploued against normali:z.ed yield moment, M,;.,Jc.,D'. Figure 9.31 shows corresponding curves for cohesionless soil. where normalized ulcimate lateral resistance. H./K,!Yr has been ploued against normali:z.ed yield moment, M,..1JK,rD'...Copyrighted material 255. Q,.(g)11"Pile Foundatioru 235--pileEmbedment qth. uoFig. 1.21 Oulgn chafls for short pleo in coho5Ne ooll (llroms 19M).Lenglll, LIDFig. 8.21 Design charts fot Short plies In coheslonleas 8041 (Stems, 19&4).Copyrighted material 256. ~ Theory tmd Pro1670 kN. (Marginal overloading on one pile may be accepted.)DL + U + SL Co11dition:!:V = 6478 + 657 = 7135 kN M., = 123.5 kNm, MTI = 115.2 + 985 = 1100.2.H,= 380 kN., 125 Load perp1e, p - -7135 123.5 ... 45 ... 110 .2 - 1845 kN (r (1/2(5 1 X IS + S X 5 1))= 1600 kNQ = 7rl4 (1) 2(8 x IS X 43) = 3950 kN , Q. = 1600 + 3950 = 5950 QoJJ =5950 2.5 51 Nim' -1 o- 20 ' - - - . . . J= 2380 kN "' 2300 kNExample 9.7If !he pile in Example 9.6 is laken down to 28 m below cutoff, what will be safe capacity? SolutionQ. = Q,+Q, Q/ =1r X1.0X(5 1X15 + 51X10 + 0.5X100X3)= 3270 kN Qp = Jr/4(1 )2X9X100= 700 kN Q. = 3270 + 700 = 3970 kN 3970 = 1590 kN ., 1600 kN 2.5Q. 11 = -[Note that increasing the pile length increases frictional resistance but there i.s major reduction end bearing also.) Example 9.8 A foot bridge having !he main trestle consisting of steel columns (refer Fig. 9.51(a)) is to be founded in the subsoil shown in Fig. 9.5l(b). Design a suitable pile group for the trestle foundation.Copyrighted material 282. 260 Theory and Practlce of FouudaHon Design Depth (m)0Top sol: Rubbish/day/Brickbats and so on.140kNN6 4' I6.55N6 Btownish grey sandy silt v.ilh ctay binder. N I I I II,3 ,64mPile$I I IN N 0.5f8Y Clayey silt with tine sand y= 18 kN/ms, Cu = 35 kNfm2Bt~ishGtey/dal1t grey silty day with decompomsed wood. r= 17 kNim3 C11 = 25 kN.ffn2silty day Ytflh kankar. 12 Bluish grey 3 r 19 kNim c;, 65 kN!m216Monied brown silty day. r = 19 kNim3, tv = 10 kN!m222 N4.0....Yellowish/greyish brown silty day with kanlcar and occasional sand ten- of End5.0= 25borehole(a)(b)Fig. 1.51 (a) Main mile COI..,.,s and (b) subsoilIYPt tor~9.8.SoiMtionPile copaciryPile djameter = SOO mm Depth ~ 18 m/24 mCutOff level~I m below ground levelPile tip at 18 m below ground levelQ... per pile ~ L.A1J, + A,q, ~~Uplift per pile0.5/t (J4Q + 200 + 136 + 84) + (0.2~Q,1 per pile 10.5lr(4 X 35 X 1.0 + 8 + lr/4(0.5)2 (9 X 70) 879 + 126 ~ 1005 kN 1005= 3 (FS) =333 kN ~879 T~293 kN~X25X1.0 + 3 XX65X0.7 + 2X70X0.6)630),. 300 kN 250 kNCopyrighted material 283. Hidden page 284. 262 + 111eory and Practice of Foundation De. ign s~ St1uness f actor,T ---.{El K! K~l2X106-4;r/64(0.5) 60X= ~ 102.2 = 2.52 m Slorm Impact 1404Rigid cap1504 =n.skN ---- ~ -"""'!'~------- +c;,= 35 ltN!m2 Pile 0.5 m diaAs pile deplh= 18 m > 4T. Hence, it !:!,__ = c,B'is a long elastic pile and we use Brom's method.35 = 4.0 35 x (0.5)2Considering restrained pile.. -M, C11 8 3= 5, whichM. = 5X35Xgives (O.S)'= 21.8 kNmBerczantzev. V.G.. V. Khristoforov. and V. Golubkov (1961 ). Load Bearing Capacily and Deformation of Piled Fou11dations, Proc. Slh Int. Conf. on SMFE, Vol. 2, pp. 11- 15. Birmingham, P. and M. James (1989), An Innovative Approach to Load Testing of Higlr Capacily Piles, Proceedings of the International Conference on Piling and Deep Foundations, London, Balkema, Roterdam, 1989. Bishop. A.W. (I 966). Sixth Rankine Lecture: The Suength of Soils as Engineering Materials, Georec/mique, Vol. 16, pp. 89-1 30. Bowles, J.E. (1968), Formdcaio" Jbialysis and Design, McGrnw-Hill [nc., New York.Copyrighted material 285. Pile Foundations U3 Bowles, J.E. (1974), Analytical and Complllu Methods in Foundation Engineering. McGraw-Hill, New York. Broms, B.B. and J.O. Silbenn.an (1964), Skin Friction Resistance for PUes in Cohesionless Soils, Sols-Soils, pp. 10-33.Broms, B.B. ( 1966), Methods of Calculating the Ultimate Bearing Capacity of Piles- sunurwry. Sols-Soiis, pp. 18-19: 21-32. Broms. B.B. and L. Hill (1973), Pile Foundatioru for Kuwait Towus, Proc. 8th Int. Conf. on SMFE. Moscow, Vol. 2-1, pp. 33-,;18. Burland, J.B. (1973), Shaft Friction of Piles in Cia~ simple .fundamental approach, Ground Engineering, Vol. 6, No. 3, pp. 30-42. Cooke, R.W. and G. Price (1973), Strains and Displacements Around Friction Piles, 8th Int. Conf. on SMFE. Moscow, Vol. 2-1, pp. 53-l.ProcDas, B.M. (1998), Principles of Foundation Englnuring, PWS Publishing, California, USA. Davisson, M.T. and H.L. Gill (1963), Laterally Loaded Piles in a Layered Soil System, Jou.m al of tht Soil Muhanics and Foundtl.tion~ Division, American Society of Civil Engineers, Vol. 89, No. SM3, pp. 63-94. De Beer, E.E. (1970). Experimental Detennination of the Shape Factors and Bearing Capacity Factors of Sand, Geotechnkple, Vol. 20. No. 4, pp. 387-411. Aaate, K. (1972), Effects of Pile Driving in Clays, Canadian Geotechnical Journal, Vol. 9. No. I. Hanna, T.H. and R.H.S. Tan (1973), The Behavior of Long Piles Under Compressive Loads in Sand, Canadian Geotechnical Joumat Vol. 10, No. 3: pp. 311-340. Janbu, N. (1953), An Energy Analysis of Pile Driving with the Use of Dimensionless Parameters, Norwegian Qe()(echnical Institute, Oslo, Publication No. 3. IS 2911 (1979)--Code of Practice for Design of Pile Foundations. Bureau of Indian Standards, New Delhi. Kerisel, 1. (1961), Foundations Profondes en Milieu Sableux, Proc. 5th Int. Conf. oo SMFE, Vol. 2: pp. 73-83. Marsland, A. (1971), Shear Stwogth of Fissured Clay. StressStroin Behavior of Soils, T.G. Foulis, pp. 59~8. McClelland, B. (1974), Design of Deep Penetnltion Piles for Ocean Structures. Journal of the Geotechnical Engineering Division, American Society of Civil En.gineers. Vol. 100, No. GT7, pp. 709-747. Meyerhof, G.G. (1959), Compaction of Sands and Bearing Capacity of Piles, ASCE, Journal of Soil Mechanics and Foundation Division, SM6, pp. 1-29. Meyerhof.G.G. and L.J. Murdock (1953), An lnvestigation of the Bearing Capacity of Some Bored and Driven Piles in London Clay, Geottchniqut, Vol. 3: p. 267. Meyerhof, G.G. ( 1976), Bearing Capacity and Settlement of Pile Foundations, Journal, Geotechnical Engineering Division. ASCE, Vol. 88, SM4: pp. 32-67.Copyrighted material 286. 264 Theory and Practice of Foundation DesignNordlund, R.L. ( 1969). Bearing Capacity of Piles in Cohesionless Soil, Journal of Soil Mechanics and Foundation, ASCE. Vol. S9, No. SM3, pp. 1-35. Poulos, H.G. and E.H. Davis (1980), Pile Foundatior1.1 Analysis and Design, John Wiley and Sons. New Yorlc. Radhakrishnan, H.S . and 1.1. Adams (1973), Long-term Uplift Capacity of Augured Footings in Fissured Clays, Canadian Geottchnical Journal, Vol. 10, No. 4, pp. 647-652. Rees, L.C. and H. Matlock ( 1956), Non-dimensional Solutions for Laterally Loaded Pil.s with Soil Modulus AJsumed Proportional to Depth, Sib Texa.< Conf. on SMFE, Special Publication No. 29, University of Texas. ' Schultze, E. and G. Sherif (I 973), Prediction of Selllment from Evaluated Selllement Observatwns for Sand, Proc. Sib Int. Conf. on SMFE, Moscow, Vol. I, p. 225. Sltempton, A.W. (194S), The f 2 o Analysis of Stability and its Theoretical Basi.r, Proc. 2nd Int. Conf. on SMFE. Rotterdam, Vol. 2. Skempton, A.W. (195 1), The Bearing Capacity of Clays, Building Research Congress, England. Sltempton, A.W. (1959), Cast in-situ Bored Piles in London Clay, Geotechniqu, Vol. 9, No. 4, pp. I 53-173. Skempton, A.W. and P. La Rochelle (1955), The Bradwell Ship: A shon term failure: in London Clay, Geotechnique, Vol. 15, No. 3. Skempton, A.W. and R.D. Nonliey (1952), The Sensitivity of Clays, Geotechnique, Vol. 3. No. I , pp. 40-5 I. Smith, E.A.L. (1960), Pile Driving Analysis by the Wave Equation, Journal on Soil Mechanics and Foundation Division, ASCE, Vol. 86, SM4: pp. 35-61. Sliwinski, Z. and W.G.K. A eming ( 1974), Practical Consideratio11s Affecting the Performance of Diaphragm Walls, Proc. Conference on diaphragm walls and anchors, ICE. London, pp. 1-10. Tenaghi, K. ( 1942), Discussion on the Progress Repon of rite Committee on the Beanirg Value of Pile Foundations, Proc. ASCE, Vol. 68: pp. 311-323. Terz.agbi, K. (1943). Theoretical Soil Mechanics, John Wiley and Sons Lid., p. 510. Terz.agbi, K. (1955), Evaluation of Coefficient of Subgrade Reaction, Geotechnique, Vol. 5: p. 297. Terz.aghi, K. and R.B. Peck (1967), Soil Mechanics in Enginuring Practice, 2nd ed., John Wiley and Sons, New York. Thorburn, S. and R.S.L. Mac Vicar ( 1970), Dis.:ussion, Conf. on Behaviour of Piles, ICE, London, p. 54. Tomlinson, M.J. (1965), Foundation Design and Construction, 2nd ed., Pitman, London. Tomlinson, MJ. (1977), Pile Design and Construction Practices, lst ed., Viewpoint Publications, London.Copyrighted material 287. Pile Fmmdallons 265Tomlinson, M.J. (1981). Pile Design and Constmction Pmctices, 4th ed.. E ond F N Spon, London.Touma. F.T. and L.C. Reese (.1974), Behaviour of Bored Piles in Sond. Joumal on Geoteclmicnl Enginuring Division, ASCE. Vol. 100. No. GT7: pp. 749-761. Vargas, M. ( 1948), Building SJmb-bell -~00 (t) Double octagonal with c:ircula.r dredge hotesAg. 10.2 Typical(d) Blad nedu!Jnent pier Well cap r--'-__.+-o ' V" !,WI, 300 lntermeclateffop plug Staining.......... .... .. .... .. :r.. . . . ... .. . ...... ', , . . . !.~ .. ."e~.... :.:.:0~800B ard rutting edge.Copyrighted material 291. Well Fmmdarions 26910.4.1 Steining The well steim'ng is lhe main body of the well which transfers load 10 the subsoil. It also acts as a coffer dam during sinking, and provides !he weight for sinking. In addition to the usual design forces at service condition. the steining is likely to be subjected to certain additional loading during instaJiation. The thickness and reinforcement of well steining are generally detennined as per recommendations of IRC 7&-1983. The thickness of well steining should not be less lhan SOO mm and should satisfy lhe following relatjons.hip" = kd.fi. where(10.1)h = minimum thickness of stcining (in m), d = external djameter of circular/dumb-beiJ shaped well or smaller dimension in plan for twin D wells (in m), L = depth of well (in m) below LWL or ground level whichever is higher, and k = a consmnt varying from 0.030 to 0.068 depending on shape of well and type of soil strata.10.4.2 Well Curb The wedge shaped pan of the well steining at the lower end is called well curb. It facilitates the process of sinking. To satisfy the requirement of minimum resistance during sin1dng and the strength to transmit superimposed load from ste- ning 1 bonom plug, the shape and i 0 outline dimensions may be as per Fig. 10.3. The concrete grnde s hould not be lower lllan M20 and minimum reinforcement of 72 kg/cu m should be provided.10.4.3Cutting EdgeThe lower moSl portion of the well curb is the cutti11g edge. This should be strong enough to facilitate sinking through the type of soil strata expecled to be encountered during sinking and should be properly anchored to well curbs. Cutting edge should be fabricated from steel angles and plates weighing not less than 40 kg/m length of the cuuing edge. Heavier section (80 kglm) is required for hard and booldery soil Slfatl.10.4.4Bottom PlugAfter the well is sunk to the required depth, the base of the well is plugged with concrete. This is called bouom plug which transmits the load to the subsoil. The top of the bouom plug should not be less than 300 mm above the top of well curb. A suitable sump below the level of the culling edge should be made and cleaned thoroughly before concreting. The concrete mix used in bouom plug should not be leaner than I :2:4. with minimum cement content of 330 kglm3. and should be placed by tremie or skip boxes under water.Copyrighted material 292. 270 Theory and Practice of Foundation Design10.4 .5Dredge HoleThe well is sunk by excavating soil from within the well. The hole so formed is called dredge hole which is later filled fully or partly by sand or excavated soil. The extent of filling is decided by the function it is required to do. Filling is used to increase the stability of 1he well against overturning. Where it is not possible lO attain a positive sump for bottom plug (specially in sandy strata), complete filling of well is desirnble. In case of so!Vnormally consolidated clay. the allowable bearing pressure can be considerably increased by keeping the well emply.10.4.6 Intermediate/ Top Plug lnlennediale plugs over the fill should be of thickness 500 mm of 1:3:6 concrete. When the well is filled upto the lOp, a top plug of lhickness 300 mm of I :3:6 concrele is generally provided. The top plug provides contact between the well cap and lhe sand filling. and helps in lransferring the load through tl1e sand fill ing.10.4 .7Well CapWells are provided wilh a properly designed RCC well cap, with iiS bottom surface preferably al LWL.10.5SINKING OF WELLSWells are sunk 10 the desired depth by excavating lhe soil from the dredge hole by means of manual labour. mechanical winch and grab. Divers help and/or pneumatic sinking may be adop1ed in difficult situations. As far as possible, the wells shall be sunk plumb without any tilt and shift However, a tilt of I in 80 and a shifl of ISO mm is considered allowable and the s.ame has to be considered in the design of well fou ndations.10.6 PHYSICAL CHARACTERISTICS-DEPTH The depth of a well foundation must be such that the foHow ing requirements are met: In erodable soil, there is a minimum grip length of one third the maximum anticipated depth of scour below high flood level (HFL),ln non-crodablc strata. there is adequate seating and embedment on sound rock soil. and The base pressure is within permissible limits.10.6.1Scour DepthFor natural streams in c.ohcsionlcss soil. the scour depth may be determined from Lacey's formula. Accordingly.Copyrighted material 293. Well Foundations 271the normal depth of scour, d (in metres), below the highest flood level is given byd = 1.34 where2)"3 (7(10.2)q = discharge (in m3/s) through width of the channel obtained by dividing the design discharge by linear waterway between abutments/guidebanks and f = Laceys sih fac.tor which is related to the mean diameter of soil grains forming the bed. by the empirical formula, f = 1.76 J;. Here, m is the weighted mean diameter in mm. The value off generally varies from 0.6 to I .50. The method of determination of m is described in IRC S-1998.For preliminary design, the normal depth of scour below HFL may be obtained from d= 0.473l )tt3(~( 10.3)where Q = maximum flood discharge in mJ/s. The maximum depth of scour below the highest flood level (HFL) is given by,D,... = 2d in the vicinity of piers= 1.27d(scour restrained)}near abutment= 2d(scour all round)If the river bed is not readily sus H=Step 4 mM1=I x 48,680_ 972 45=so; r, (Kp- K.l = 9.2 xwith seismic. 1.25r'(Kp - K.) Step= 1.25 x64.77.035 = 64.7= 80.88' > 50s W - f./pMB A 21 : 13,790 - 0.364 24.42 = 465.8 137.7X6641 :1: 48,680 X 5.5 2 X 972.45= 603.5. 328.1 kN/m2 < 800 kN/m2 Hence, it is acceptable. Method based on IRC: 45 (Uitilllllte)Copyrighted material 312. Hidden page 313. Well Foundations 291Applied moment = 2439.6(24.603 - 0.2 x 12.678) (Point of rotation 0.20 above base) = 53.830 kNm < 68,500 kNm. Therefore. accepted. Example 10.4 For the bridge considered in Example 10.3. check the adequacy of the abutment well whose elevation and nature of earth pressure diagrams have been shown in Fig. 10.12,.ll,J: f 28 2~3013--23 < iS> 3S 2S-41 IS-28 > 10 ISProboblr uponsion (~)> 30 2Q-30 IQ-20 < 10Dtgru of uponsit.M.euVery high HiahMediumLowU .S EFFECT OF SWELLING ON BUILDING FOUNDATIONS In tropical countries, the soil near the ground surface dries up during the summer as a consequence of intense heat and recession of ground water table. The soil becomes stiff and cracks and fissures open up. When rains come. the soil gelS wet by the precipitation and with time, the ground water table also rises. This causes increase in water content of the soil and hence, swelling of the soil. The structure built on the soil protects the soil from the heat but nonetheless water tends to accumulate from the surrounding areas and contributes to swelling. The depth over which such variation in water content occurs depends on the nature of soil and cliii'Uitic conditions but an active zone of 35-4 m has generally been observed. The movement of the foundation with swelling and shrinkage of the soil causes the floor slabs of buildings to lift up and develop a dome shaped deformation pattern. This leads to cracks in the floor and external walls. The diffen:ntjal movement also cause$ diagonalCopyrighted material 320. 298 Theory and Prac tice of Foundati011 Design cracks in the walls and at the corner of doors and windows. as shown in Fig. ll.2 Utilities buried in the soil get damaged and the leakage of water into the soil results in funher swelling. The effect is more pronounced in the one or two storey buildings where the foundation pressure is often Jess than the swelling pressure. For Ulll structu res, foundation pressure generally exceeds rhe sw~ll::tg press ure and the swelling potential reduces.Roof sl&bFlOOr stabheavedt t t ExpansionFi g. 11.2 Oi$tress In buildings dueto swelling.11.4 FOUNDATION DESIGN IN EXPANSIVE SOD.. Foundation design in expansive soil needs a different approach as compared to that in non-swelling soil. II must be realized that limiting the snfe bearing pressure to a low value does not help to counteract the swelling pressure. Rather. design should be done with a high enough bearing pressure and following the criteria of beaiing capacity failure and pennissible of settlement. so that chances of swelling are minimized. Foundation design in expansive soil c:an be done in the following ways:l. lsol:uing the foundation from the swelling soil, 2. Taking measures to prevent the swelling. and 3. Employing measures to make the structure withstand the movement.11.4.1Isolating the Foundation from the Swelling Zone: Under-reamed PilesA common method of building fou ndation in expansive soil is to provide under-reamed piles below the foundation. Here. the structural load is transferred to the soil beneath the zone of Outtuation of water content. The piles are taken to depths of 5- 6 m, that is. well beyond the expansive zone. These piles are bored cast-in-situ piles with the lower end e nlarged to fonn under-reamed bulbs with the help of special tools. Fig. 11 .3. The piles generally have shaftCopyrighted material 321. Fouudotlmu on Expo11Jive Soils 299 diameter of 300 mm and bulb diameter of 750 mm. as depicted in Fig. 11.4. The piles are fixed at the top to RCC plinth beams. A gap of 75- 100 mm is kep~ between the-plinth beam and the soil which is filled with granular material 10 pe- nit swelling of the undetlying soil n without straining the plinth beam-s. The piles are adequately reinforced 10 take care of the uplift forces caused by the swelling ac1ion of the soil. Kellycaslng(3)aouom hingeFlg. 11.3 TOOls(b) T01> hingetor bulb fotmatlonin under-teamedd~=Mles.(anor Tomlinson. 1994)d!LA'AT :/nd on its inclined faces during boring and till the concreting is done. For this. sufficient cohesion should be available. Clayey soil provides this cohesion without much difficuhy. But the fonnation of bulb i n granular soil is not free from uncertainties. Field experiments have shown that the sand tends to disintegmte during the stand up time and no bulb is really formed. It should also be noted that the under-reamed piles should penetrate well into the firm gromld to give sufficient end bearing at lhe level of the under-retlms. Presence of soft clay benenth the expansive soil would preclude the use of under-reamed piles. Indiscriminate use of under-reamed piles simply because the soil at ground surface is expansive in narure., ofren serves no useful purpose.11.4.2 Controlling Swelling Impervioua apron Swelling of soil near the ground surface can be controlled by providing an impervious apron around the s tructure as illustrated in Fig. L1.5. This prevents surfac-e precipilation from penetrating inro the soil but the sea..o;onal rise of ground water .table is not controlled. The impervious apron is generally made of bituminous concrere but it should be sufficiently flexible to prevent c racking and distress due to soil movement caused by swelling. It is necessary fo r the apron to penetrate sufficiently into the foundation to prevent ingress of water into the soil during inundation.Copyrighted material 323. Foundations on E.rpans;ve Soils 301 Brick waJIAIsarocompactiOn.Copyrighted material 352. Hidden page 353. Hidden page 354. Ground Improvement Techniques + 333 has to be approached on a trial and error basis with past experiences serving as useful guide. A suitable approach may be to (a) carry out detailed soil exploration by conducting standard penetration tests or cone penetration tests within the influence zone below the proposed foundations. (b) determine the extent of improvement required in terms of increased Nor Nr value from appropriate foundation analysis. (c) choose the method of ground improvement, say, dynamic consolidation, vibrocompaction. or compaction piles depe,nding on availability of facilities. (d) select a representative area close to the consttuction site and carry out trial ground improvement wortc varying the construction control parameters, such as weight of hammer, height of fall, number of blows, spacing of compaction piles. and so on. In genernl, the weight of hammer and height of fall are predetermined as per equipment capacity. Before s"'Jting the trial ground improvement scheme, make sure that predensification propenies of the soil, namely SPT, CPT da"', and so forth are determined. (e) carry out field tests to determine the post densification parnmeters after completion of trial ground improvement work and determine the extent of improvement as a function of spacing of compaction piles. (0 choose the spacing of compaction piles on the basis of pre and post densification data. (g) carry out field tests to check the efficacy of compaction at different locations.A trial ground improvement work has recently been done for the proposed construction ofa 120 m high temple obout 75 km from Kolka"'. The subsoil consists of a thin layer of firm silty clay/clayey silt followed by a deep deposit of loose to medium silty fine sand to 25 m below GL. Thereafter, a thin lyer of stiff clay is found and the same is followed by dense to very dense sand. 1be soil condition at the temple site is shown in Fig. 12.36. In view of the high foundation loading anticipated from the temple structure. the ' sandy soil immediately beneath the top silty clay 12- 14 m below GL required improvement. Depth (m)o ----~-=nm 7---.-.-.;~ da~d.---~~~~------------, A ~ ~~ ~~~~~~ 7. N 10s------------------------------------------------II Loose to me 60Fig,. 12.36 Soil condition at temple site.Copy~ightedmaterial 355. Hidden page 356. Ground01002lmprov~memTuhnlqw~s 335N (biOws/30 em) 20 3()~~ 1'----.. ' .... .... /............... IPool....--- Pro 10''12;Pile Spacing mx2n~ample 12.1),Sol.au"' (a) Net foundation pressun:. considering 45 disper>ion of water load (140 kN/m2) through compacted sand pad. 222 = 140 x 2 + (I.S x 20) (sand pad) q, (22 + 3)= 108 + 30 = 138 kN/m2 Average c. of Strata I andn = ""'-' ;;.:; (30__2)-::+:--"'( --=5)-" 1.:.5 7 = 19.3 kN/m2 q,,(n) = c.,N,= 19.3 x 6 = 116 kN/m2 < 138 kN/m2 Copyrighted material 358. Hidden page 359. I338 + Theory and Practice of FoundatWn Design Stratum II lip= l!.c.~38 " 29.551x 0.9 = 24.6 kNtm',= 0.3 x 24.6 = 7.4 kN/mHence, strao. 1969 lallipan. Muico. 1959 Alaska. 1964GI"Qirt-~iuMognitud' of ttJffhqr.aU 7.5 7.4 6.9D10 (mm)O.Q?- 0.25 0.0$-0.25 O .Ot-O. tO o.ot-o. tDntent IS%) with SPT blow count of 10 blows/ 30 em. Determine the tone of liquefaction (Take = 18 kN/m 3 and water table at ground surface).rSol..,ion (a) Average shear stress in the soilT,; = 0.6s(a~ )("~)r, Cfoga(JThe calculations giveCopyrighted material 389. 368 Theory a11d Practice of Fo1mdorion Design l'able 13.7 Calculation of cyclk suess ratio a_tga.,(kNim2)a;(kNfml)0.1/kpth (m)54 108 162 216 270 324 37824 483 6 9 12 15 18 21'fla~' 0.98 0.96 0.94 0.85 0.74 0.64 0.607295 120 1441680.1430.140 0.137 0.124 0.108 0.094 0.088(b) Shear stress ratio causing liquefaction (see Fig. 13.10) For N = 10 nnd 15% finesT ': a.= 0.15with FS = 1.2 .15 (.!..)"' = 01.2 = 0.124 a:, The da1a are plotted in Fig. 13.22. It is seen that liquefaction potenlial exists in the top 12 m of 1he deposil. 0.090.10.110. 120.133I6g------ -- . . -- -----/15 18//91120. 150.140/v. ./.':/ -----------.21Fig. 13.22 Zont; of liQuefaction.Copyrighted material 390. &nhquake R1I II11:111 ,II ..3td Strut 2.1SMB6001I I~1I t1~ ____ , I I, ____ .,1l1 N cBo"::'a.rt levet~ Fig. 14.2 BtaOt required. However, if heterogeneous fill exists near the ground surface. sjde protection with timber planks and small suuts should be sufficient. Deep excavation for two or three basements (excavation depth: ~10 m) would require adequate lateral support with diaphragm walls or contiguous bored piles and struts. Because of large excavation width, it may not be feasible to have horizontal struts which would tend to deflect under their own weight. In such cases. inclined props supported between the diaphragm wall and the already cast base raft at the centre may be adopted. Otherwise, a number of Hpiles may be driven at close intervals and the struts be made to span among them to reduce the effective length. Figure 14.3 depicts inclined props to support diaphragm wall and Fig. 14.4 shows struts in wide cuts.lAgend: 1. Dlap!Vagm wall 2. Exc8Yation a b c d 3. C..StbaiO slab 4. Put Inclined strutse5. E>o:IVollon up to ~ ...,u 6. cast balance base slab 7. Erect wal lhrough ' " " 'Fig. 1"-3 Inclined propo to -Strut 1- - 'clophracJn ..,.._Slrut2 ~Strut 31950Fig. 1ol.4Struts In wfde cuts.Copyrighted material 395. 374 + Theory and Practice of Foundation Design14.3 . 1Design of Braced CutaThe design of braced excavation involves two distincl yet intemlated features~ namely ' (a) stability of the excavation, ground movement. control of water into the excavatjon, effect on adjoining structures, and so on and (b) design of structural elements, lhat is, diaphragm wall or sheet pile, struts or anchors and so forth..Although the overall s tabillry of braced cuts in soft ground does not depend to any great extent on the number and spacing of struts or anchors~ lhey very much influence lbe pattern of ground movement expected in a given situation. The depth of diaphragm walV sheet pile determines both the slllbility of the system and the ground movement associated with it. Depending on the subsoil stratification, one may get adequate Slllbllity against bottom heave by having the diaphragm wall exteruled to a stiffer layer existing no more than a few metres below the cur depth. However. this may not give adequate fixity to the diaphragm waH to minimize ground settlement. The essential featur"s of the design of braced cut in soft ground are discussed in the subsequent subsections in details.Depth of dlapbnpl wall There is no established procedure for determining the depth of diaphragm wall below the excavation. In homogeneous clay. not much is gained by !liking the diaphragm wall below a critical depth. which is given by N'- YHc.(14.1)where,r-=unit weight of soil, c. = undrained shear strength of soil below the cut. and N, = slllbility number (" 6). The depth of sheet pile/diaphragm wall is often determined by balancing the moment at the bottom strut leveJ due to active and passive earth pressure on either side of the wall. This gives rise to extended depth of wall, particularly if tbere is no appreciable improvement of shear strength within the depth of wall. On the other hand, it may be adequate to determine the depth of diaphragm wall from consideration of bottom heave alone. If, in particular, the shear strength of the soil improves within shallow depth below the bottom of the cut, it may just be sufficient to take the diaphragm wall to the stiffer stratum. For the Calcutta metro construction, 10-14 m deep cuts have been made with 600 mm diaphragm walls !liken to only 4-6 m below the bouom of the cut to rest in a stratum of stiff clay or medium/dense sand. as shown in Fig. 14.5 (Som. 1998). Where the diophragm wall terminates in c lay. factor of safety against bottom heave may be determined from Eq. (1 4.2). taking into consideration the fOntribu&ion of shearing resistance al the soil-waH interface. shown in Fig. 14.6. A facto[ o f safety of 2.0 would normally suffice. Needless ro say, presence of struts. whntever the number, does not contribute to safety against bottom heave.Copyrighted material 396. Construction ProbhmsF=y,D, + r.D, +c N, +L:C. -1.!:1mSligo Illtmeuw-13.2m ;-.-13.5 mSer.tum Ill Bluiolo ~ ..ly dayof WI f.. ~ -17.5. .Yri1h kankar - 17.2m Stntum IVYellowjsh brown sandy dayfry siltFig. 1U 8noced cu1 for Calwaa me1ro conSlruclion.G.l..c,., )I! Hc..ItI " !- o f cui IIIVI Iy,III ' ' ,_--/g''/'o,!Fig. 14.1 Slalllllly agoml bOliOm ,...,. In stratified soil.Number llDd IIJMICIDC of 8tnlteStruts are required to prevent failure of the diaphragm waiJ in flexure and to mmmuze la~ral deflection or the wall. The diaphragm wall and the soruos make up a rigid structural system which prevent excessive ground movement. Obviously. greater the number of struts,Copyrighted material 397. Hidden page 398. Hidden page 399. 378 Tlreory a11d Practice of Foundation Des;gn variation of ground settlement for the final cut level may be obtained from Peck's normalized plot for braced cut with sheet pile suppons in different types of soil. as depicted in Fig. 14..9. Differe

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