7 Design of Piled Foundation

Chapter 7 Design of Piled Foundations

7.0 NOT A TION

a Deflection due to slenderness of a circular pile av Distance of shear plane fro m nearest support ax Deflection due to slenderness producing additional moment about x-axis ay Deflection due to slenderness producing additional moment about y-axis A c Net area of concrete in a p ile cross-section Ap Cross-sectional area of pile (m2) A s Surface area of pile in contact with soil Av Total area of link bars perpendicular to longitudinal bars Asc Total area of steel reinforcement in a pile A51 Area of tensile reinforcement in pile cap Asv Area of steel effective in resisting shear in a pile A sx Area of tensile steel in a pile section resisting moment about b-axis A sy Area of tensile steel in a pile section resisting moment about h-axis b Width of reinforced concrete section b Overall dimension of rectangular pile section b' Effective depth of tensile reinforcement in b direction B Width or diameter of pile B Overall width of a group of piles c Soil cohesion for a stratum (kN/m2) CH Horizontal load-carrying capacity of a single pile Cv Vertical load-carrying capacity of a single pile d Effective depth to tensile re inforcement in a concrete section D Depth of a group of piles below ground Dr Relative density ex Eccentricity of combined unfactored vertical load on pile cap in x-direction ey Eccentricity of combined unfactored vertical load on pile cap in y-direction e11x Eccentricity in x-direction of combined unfactored horizontal load Hy ehy Eccentricity in y-direction of combined unfactored horizontal load Hx Er Stress-strain modulus of pile material {kN/m2) Es Stress-strain modulus of soil (kN/m2) fc Stress in concrete due to prestress aJone f s Skin resistance at soil/pile interface f1 Maximum design principal tensile stress in concrete /y Characteristic yield strength of steel reinforcement /ci Cube strength of concrete at transfer of prestress

293

294 Reinforced Concrete

[cp Average concrete stress in a prestressed concrete section after losses feu Characteristic cube strength of concrete at 28 days [pc Average tensile stress in steel tendons after all losses [pu Characteristic ultimate strength of steel tendons [yv Characteristic yield strength of shear reinforcement h Overall depth of pile cap h Overall dimension of a rectangular pile h Overall diameter of a circular pile h' Effective depth of tensile reinforcement in a rectangular pile in h-direction H Unfactored horizontal load on a single circular pile H x Unfactored combined horizontal loads on pile cap in x-direction H.v Unfactored combined horizontal loads on pile cap in y-direction Hpx Unfactored horizontal load on a single pile in x-direction Hpy Unfactored horizontal load on a single pile in y-direction H.m Ultimate horizontal load on pile cap in x-direction H_.u Ultimate horizontal load on pile cap in y-direction Hpxu Ultimate horizontal load on a single pile in x-direction H pyu Ultimate horizontal load on a single pile in y-direction lr Moment of inertia of pile (m4) 1: Polar moment of inertia of a group of piles about z-axis through CG fx x Moment of inertia of a group of piles about x-x axis through CG of group f.v.v Moment of inertia of a group of piles about y-y axis through CG of group k, Modulus of subgrade reaction of soil (kN/m3) K, Coefficient of friction K, Factor used to determine transmission length of prestressing wires or

strand lc Effective length of pile for calculation of slenderness ratio 10 Unsupported length of pile / 1 Transmission length of prestressing wires or strands L Depth of penetration of pile L Overall length of a group of piles Lb Average depth of pile in ground m Modular ratio Esl Ec mv Coefficient of volume compressibility (m2 /kN) M Factored bending moment in a circular pile section M0 Moment to produce zero stress at tension fibre of a prestressed section

with 0.8/cp (average uniform prestress) Mp Unfactored bending moment in a single circular pile M x Unfactored combined moment on pile cap about x-axis M .v Unfactored combined moment on pile cap about y-axis

M~ Modified bending moment about x-axis to account for biaxial bending M.~ Modified bending moment about y-axis to account for biaxial bending M; Unfactored moment about x-axis due to eccentric surcharge on pile cap

M.~ Unfactored moment about y-axis due to eccentric surcharge on pile cap Mpx Unfactored bending moment in a single pile about x-axis due to Hpy Mp.v Unfactored bending moment in a single pile about y-axis due to Hpx Mxx Unfactored combined moment on pile group about x-axis M yy Unfactored combined moment on pile group about y-axis

Mp.ru Mpyu Madd.x

Madd _v n

N N Nq Nu Ny N~ N~ Nu, Nbal p Px

p Pa Pu Ppu P si

ii qc qu qcs R R;H R;v s

Sv T Ta Tu u v

Design of Piled Foundations 295

Ultimate bending moment in pile about x-axis Ultimate bending moment in pile about y-axis Additional bending moment in pile about x-axis due to slenderness Additional bending moment in pile about y-axis due to slenderness Slenderness ratio in a prestressed pile Statistical average of SPT number for a soil stratum Combined vertical load on pile cap - unfactored Soil bearing capacity coefficient as per Terzaghi Ultimate vertical load on a circular pile Soil bearing capacity coefficient as per Terzaghi Adjusted bearing capacity factor for cohesion Adjusted bearing capacity factor for Ll 8 > 1 Design ultimate capacity of a concrete section subjected to axial load only Design axial load capacity of a balanced section ( = 0.25 fcubd) Percentage of tensile reinforcement in a circular pile Percentage of tensile reinforcement in a pile section to resist bending about x-axis Percentage of tensile reinforcement in a pile section to resist bending about y-axis Total vertical load on a group of piles Allowable unfactored vertical load on pile Ultimate axial compressive load on pile End-bearing resistance of pile Skin friction resistance of pile Effective vertical stress at pile point Statistical average of cone resistance of soil in a stratum (kN/m2) Unconfined compressive strength (kN/m2) Side friction resistance in a cone penetrometer Number of piles in a group Initial estimate of number of piles based on total horizontal load Initial estimate of number of piles based on total vertical load Spacing of nodes in pile for finite element analysis Spacing of links used as shear reinforcement Unfactored torsion on a group of piles Allowable unfactored tension load on pile Ultimate axial tensile load on pile Perimeter at punching shear plane in a pile cap Shear stress in concrete in pile cap Design concrete shear stress in concrete Shear stress in concrete for shear due to bending about x-axis Shear stress in concrete for shear due to bending about y-axis Modified design shear stress to take into account axial compression Design shear stress in concrete for shear due to bending about x-axis Design shear stress in concrete for shear due to bending about y-axis Ultimate shear force in a circular pile section Shear resistance of a concrete section Shear resistance of uncrackcd prestressed section Shear resistance of cracked prestressed section


W Weight of pile (kN) z Depth of lever arm

a Coefficient for calculation of skin resistance of a pile f3 Factor for computation of effective length of a pile j3 Factor for conversion of biaxial bending moment into uniaxial bending y Unit weight of soil (kN/m3) 0 Angle of friction between soil and concrete J.l. Poisson's ratio Angle of internal friction Nominal diameter of tendon in prestressed concrete section

7.1 VERTICAL LOAD - SINGLE PILE CAPACITY

Ft. = Applioo load

1 . t Psi 11 tPsi

1 . tSkin friction 1 t

Ppu= End b~aring SK 711 Single pile capacity.

P u = P pu + "LPs; - W Tu = 'LPs; + W

where Pu = ultimate compressive load on pile Tu = ultimate tensile load on pile

'LP,; = skin friction resistance P pu = end-bearing resistance

W = weight of pile

First method for point resistance

(see Reference 6, page 602)

where Ap = cross-sectional area of pile (m2) N = statistical average of the SPT number in a zone of about 88

above to 38 below the pile point


B = width or diameter of pile Lb = average depth of pile in the ground

Second metlwd for poinJ resistance Ppu = Apqc (see Reference 6, page 602) where Ap = cross-sectional area of pile (m2)

qc = statistical average of cone point resistance in a zone of about 88 above to 38 below pile point (kN/m2)

Third metlwd for poinJ resistance (see Reference 6, page 598)

where Ap = cross-sectional area of pile (m2) c = cohesion or undrained shear strength Su = qu/2 kN/m2

qu = unconfined compressive strength q = effective vertical stress at pile point N~ = adjusted bearing capacity factor for cohesion (see Fig. 7.2) N~ = bearing capacity factor adjusted for Ll b > 1 dependent on

initial angle of shearing resistance (see Fig. 7.2). (See Reference 8. page 600.)

L = depth of penetration B = width or diameter of pile

Ll B should be greater than Lei B as obtained from Fig. 7.2 for the value of .

Note: Find point resistance by more than one method if soil test data allow and take the lowest for a conservative estimate.

Determination of skin resistance LPs; = LAsfs

where As == pile perimeter x pile length over which Is acts (m2) Is = skin resistance (kN/m2)

First method of skin resistance Is= 2N kN/m2 Is= N kN/m2

for large volume displacement piles for small volume displacement piles

where N = statistical average blow count in stratum for S.fYf.

Second metlwd of skin resistDnce Is= 0.005qckN/m2

where Qc = cone penetration resistance (kN/m2).

Third method of skin resistance for small volume displacement piles


fs = l.5qc5 to 2.0qcs for large volume displacement piles where qcs = side friction resistance in cone penetrometer.

Fourth nutlwd of skin resisllmce fs = ac + 0.5 ij K5 tano (see Reference 8, page 603) where c = average cohesion or Su of stratum (kN/m2)

ij = effective vertical stress (kN/m2) () = angle of friction between soil and pile

Ks = coefficient of friction Dr = relative density of sand.

Table 7.1 Values of K, (Reference 8, page 603).

Pile type K5 for low Dr K5 for high Dr

Steel Concrete Wood

20 0.754> 0.674>

(See Reference 7, page 136.)

0.5 1.0 1.5

Table 7.2 Values of a (Reference 7, page 126) .

Soil condition

1.0 2.0 4.0

Values of oc

DIB c =50 c = 100 c= 150 c =200 c= 250

Sands or sandy gravel 40 0.9 0.65 0.4 0.4 0.4 Soft clays or silts 10 0.35 0.30 0.25 0.2 0.2 overlying stiff to very > 20 0.75 0.70 0.63 0.55 0.5 stiff cohesive soil

Stiff to very stiff 10 0.9 0.7 0.3 0.2 0.2 cohesive soils without >40 1.0 0.9 0.3 0.3 0.3 overlying strata

The units of c are kN/m2

Note: Find skin resistance by more than one method if soil test data allow and take an average.

p = Pu a 2.5

Tu T =-a 2.5

where P8 = allowable pile load in compression T3 = allowable pile load in tension

- --- - --- -- ..


7.2 HORIZONTAL LOAD- SINGLE PILE CAPACITY

Method I Cohesive soils

k sB = 1.3(EsB4)fi (~) Etlr 1 - f.L

as per Vesic, 1961 (see Reference 6). where k5 = modulus of subgrade reaction (kN/m3)

B = width or diameter of pile (m) E5 = stress- strain modulus of soil (kN/m2) Er = stress-strain modulus of pile material (kN/m2) Ir = moment of inertia of pile (m4) !l = Poisson's ratio of soil

Es may be obtained by the following methods:

(1) Triaxial tests. (2) Borehole pressuremeter tests. (3) Es = 650N (kN/m2)

N = SPT number of blows. ( 4) Es = 3 (1 - 2!!)/ mv where mv = coefficient of volume compress-

ibility (m2/kN).

Method 2 Cohesive soils

k s = 240qu kN/m3

where qu = unconfined compression strength (kN/m2).

Cohesionkss soils

ks = 80 fC2qNq + C, (0.5 y BNy)] kN/m3 as per Vesic (see Reference 8, page 631 and page 323, equation 9-8). where c, = c2 = 1.0 for square piJes

C1 = 1.3 to 1. 7 for circular piles c2 = 2.0 to 4.4 for circular piles q = effective stress (kN/m2) y = unit weight of soil B = width or diameter of pile

N,1 and Ny may be obtained from the following table (Hansen equations) - see Reference 8, page 137, Table 4- 4:

Finite ekment model of vertical pik Spring stiffness = SBk5 kN/m

where S = node spacing not greater than B B = width or diameter of pile (m) k, = modulus of subgrade reaction (kN/m3)


Table 7.3 Values of N4 and Ny (Reference 8, page 137).

Rotation about X Z axis

Translations about x and y axis

Translations

......._Rotation about a-

(degrees)

0 5

lO 15 20 25 30 35 40 45 50

Nq

l.O 1.6 2.5 3.9 6.4

10.7 18.4 33.3 64.2

134.9 319.0

Ny

0 0.1 0.4 1.2 2.9 6.8

15.1 33.9 79.5

200.8 568.5

SK 7/2 Two-dimensional model of pile in soil (degrees of freedom -top and bottom of pile).

Note: For horizontal loads which are not constant and are reversible or repetitive, the top 1.58 of pile may be assumed unsupported by soil.

Boundary conditions (I) Free head pile Translations x, y Rotation z Translations y Rotation z (2) Fixed head pile Translations x, y Rotation z Translations y Rotation z

Material type

Free at top Free at top Restrained :at bottom Free at bottom

Free at top Rigid at top Restrained at bottom Free at bottom

For sustained horizontal load due to dead load, water pressure, earth


pressure, etc., use short-term Young's modulus of concrete for bending moment computations but long-term Young's modulus of concrete for pile head deformation.

For short-term horizontal loads due to wind, earthquake, crane surge, etc., use short-term Young's modulus of concrete for bending moment and deflection computations.

Software Use any fully validated software which has a suite for analysis of 2-D plane frame with sprung boundaries.

Member type For rectangular pile usc minimum width Bin all computations involving B. A cracked section moment of inertia may be used for reinforced concrete piles based on Section 2 .1.

7.3 PILE GROUP EFFECTS

7.3.1 Spacing of piles

S?:. 2B S?:. 3B

for end-bearing piles for friction piles

where S = spacing of piles B = least width or diameter of pile.

Note: Piles carrying horizontal load should not be spaced at less than 3B.

7 .3.2 Pile group capacity

Ultimate group capacity :::;; group friction capacity + group end-bearing capacity

Ultimate group friction capacity = 2D( B + L )c~

SK 7/3 Group of piles - plan of overall dimensions of group.


0 ~.,.,... I Frict1on

where c = average cohesion of clay = average Su = average qu/2

SK 714 Elevation of group of piles showing group capacity.

CY = coefficient (from Section 7.1, Table 7.2) D = depth of pile group below ground B = overall width of group L = overall length of group.

Ultimate group end-bearing capacity= BL (N~ + qN~) where c = cohesion or undrained shear strength Su = quf2 at bottom of

pile group qu = unconfined compressive strength q = effective stress at bottom of pile group N~ = bearing capacity factor (see Fig. 7.2) N; = bearing capacity factor (see Fig. 7.2)

Note: Total vertical load on a group of piles should not exceed the group capacity. Individual pile loads inside the group will be limited by the single pile capacity. Piles carrying horizontal load and spaced at 38 or more need not be checked for group effects due to horizontal load.

ultimate group capacity + ultimate group end-bearing capacity Allowable group capacity =-------~"----'--"------

2.5

7.4 ANALYSIS OF PILE LOADS AND PILE CAPS

7.4.1 Rigid pile cap

N = combined vertical load on pile cap - unfactored Mx = combined moment about x-x - unfactored My= combined moment about y - y - unfactored


SK 7/5 Loads and eccentricity on pile cap.

SK 7/6 Plan view of loads and eccentricity on pile cap.

X

y e.

Hx . M. -.~. 1 Hy! e~uc

. .

y

"'In - 0

ey

X

Hx = combined horizontal load on pile cap- unfactored in x- x direction Hy = combined horizontal load on pile cap- unfactored in y - y direction ex= eccentricity of N from CG of pile group in x- x direction ey = eccentricity of N from CG of pile group in y-y direction

ehx = eccentricity of Hy from CG of pile group in x-x direction eh.v = eccentricity of Hx from CG of pile group in y-y direction

h = depth of pile cap.

Loads on pile group

P = vertical load on pile group = N + weight of pile cap + weight of backfill on pile cap + surcharge

on backfill Mxx = moment about x-x on pile group

= Mx + Ney + Hyh + M: Myy = moment about y-y on pile group

= My + Nex + Hxh + M:


X

y !JC.G. of pile goop

----

:-- ---+ f~ ,__ .

v y, . .

X 1---,: 1"---~ f-- X y

y' '

x' xr ' x2 Xl X4 i

y

-~ i ! xs

~ Y,

R:Total - ~x' x= Ff

number of piles

- ~ y = R x: andy' arc orthogonal dtstanccs of each pile from corner pile

SK 717 Typical pile foundation showing CG of group and co-ordinates of piles.

SK 7/8 Group of piles subject to horizontal loads and torsion.

where M: and M; are moments with respect to CG of pile group due to eccentric surcharge on backfill or pile cap.

T = torsion on pile group = H,ehy + H_.ehx

fxx = l:y2 about x-x axis passing through CG of pile group lyy = U about y-y axis passing through CG of pile group

f l = f xx + f yy

R = number of piles in group.

Vertical load on a pile = (!_) ( M xxY) ( M,vyx) R fxx l yy


(H2 + H 2)! T(x2 + y 2)f Horizontal load on any pile = resultant of x Y and - ----

R f z

Sign convention Vertical loads: Torsion on pile group:

Moments on pile group:

downwards positive clockwise positive

clockwise positive

+ve M xx produces compression in piles which have +ve y ordinates.

+ve M.v.v produces compression in piles which have +ve X ordinates.

Hx is positive in direction of increasing x in positive direction.

Hy is positive in direction of increasing y in positive direction.

Eccentricities arc +ve for +vex and +ve for +ve y.

Bending moments in pile cap

SK 7/9 Critical sections for bending moment in a pile cap.

Take sections X- X or Y- Y through pile cap at faces of columns or base plates. Find pile reactions due to combined and load factored basic load cases. Consider all upward and downward loadings across sections X-X and Y- Y. Find bending mo ments across section . Find horizontal load on each pile by using the following expressions:

H = Hxu pxu R

Hyu Hpyu = R where R is number of piles in pile cap. Find bending moments in pile Mpxu corresponding to Hpyu and M pyu corresponding to Hpxu assuming an end fixity to pile cap following the method in Section 7.2. Hxu and Hyu are combined factored ultimate horizontal loads.


HPIW i Hpxu i Hpllu i Hpxu Hpxu

SK 7/10 Additional bending moment in pile cap due to pile fixity.

AlgebraicaUy add the bending moments in pile cap due to vertical load and pile fixity moments due to horizontal load to find design bending moments in pile cap.

7 .4.2 Flexible pile cap

Large pile caps including piled raft foundations should be modelled as flexible . The modelling will normally be carried out using either a grillage suite of a computer program or a general-purpose finite element program. The piles should be modelled as springs in the vertical direction. The vertical spring stiffness should be obtained from test results on site. A parametric study can be carried out using minimum and maximum stiffness of the pile if there is a large variation.

Grillage model

(1) Divide pile cap into an orthogonal grillage network of beams. Ensure that piles are located at crossing of orthogonal beams. Each grillage beam represents a certain width of pile cap.

(2) Use short-term Young's modulus for concrete material properties. (3) Full section concrete stiffness properties may be used for hypothetical

grillage beams (hypothetical width X depth of pile cap). (4) Piles will be modelled as sprung supports vertically. (5) Vertical loads on pile cap may be dispersed at 45 up to central depth

of pile cap. (6) Apply at each node with a pile, the moments given by the following

formulae:

about x-axis


SK 7/tt Plan of raft on piles showing idealised grillage elements - flexible analysis.

Column load may spread onto grill~ ~l~ment

Pil~ Cap/ Raft

SK 7/12 Part section through raft showing details of grillage idealisation.

M = Hxh Y R abow y-axis

(7) Find horizontal load on each pile by using the following expressions:

where R is total number of piles in group.


(8) Find bending moments in pile, Mpx corresponding to Hv.v and Mp.v corresponding to Hpx assuming an end fixity to pile cap following method in Section 7 .2. Apply these moments to pile cap grillage model as nodal loads. The pile head to pile cap connection may be assumed a'i hinged and then Mv:c and Mp_v will be zero.

(9) Find bending moments in pi1e cap by grillage analysis. Divide bending moments by width of hypothetical strips of pile cap representing grillage beams and obtain Mx, M_. and Mx.v in pile cap per metre width. Apply load factors and combine basic load cases. Modify these combined moments by Wood- Armer method to find design bending moments. [11.121

(10) Combine basic load cases at serviceability limit state to find reactions at pile nodes. Compare maximum reaction with pile capacity.

Finite-element model

SK 7/13 Typical finite element modelling of a circular raft on piles.

(1) Create a finite element model of pile cap using either 4-noded or 8-noded plate bending elements. The elements may only have three degrees of freedom at each node viz z. ex and Ely. The piles will be represented by vertical springs.

Piles will come at nodes in finite element model. Between two piles' nodes there should be a minimum of one plate node without pile.

(2) Use short-term Young's modulus for concrete material properties. (3) Full section concrete section properties may be used in the analysis. (4) Vertical loads on pile cap may be dispersed at 45 up to central depth

of pile cap. These loads may be applied as nodal loads or uniformly distributed loads on plate elements depending on software used.

(5) Apply at each node with a pile, the moments given by the following formulae.

M = Hxh .v R

about x-axis

about y-axis


(6) Find horizontal load on each pile by using the following expressions: Hx H.,

Hpx = R and Hp_v = R where R is total number of piles in group.

(7) Find bending moments in pile, Mpx corresponding to Hp_v a nd Mpy corresponding to Hpx , assuming an e nd fixity to pile cap following method in Section 7.2. Apply these moments as nodal loads in finite e lement model at nodes with piles. These moments will be zero in the case of a hinged connection of pile to pile cap.

(8) Carry out analysis using a validated general-purpose finite e lement software . Apply load factors to combine basic load cases. Modify the combined Mx, M., and Mxv using the Wood - Armer method to find design bending moments.lll.l2]

(9) Combine basic load cases at serviceability limit state to find reactions at pile nodes. Compare maximum reaction with rated pile capacity.

7.5 LOAD COMBINATIONS

Applied loads on pile cap will be combined using the following principles.

7 .5.1 Pile load calculations

LCI: l.ODL + 1.0/L + l.OEP + l.OCL v + l.OCLH LC2 : l.ODL + l .OEP + l.OCLV + 1.0CLH + l.OWL (or l.OEL) LC3: l.ODL + 1.0/L + l.OEP + l.OWL (or l.OEL) LC4 : l.OL + l.OWL (or l.OEL) where DL = dead load

I L = imposed load EP = earth pressure and water pressure

CL V = crane vertical loads CLH = crane horizo ntal loads

WL = wind load EL = earthquake load.

7 .5.2 Bending moment and shear calculations in pile cap or piles

LC5 : 1.4DL + 1.6/L + 1.4EP LC6: 1.2DL + 1.2/L + l.2EP + 1.2WL (or 1.2EL) LC1 : 1.4DL + 1.4WL (or 1.4EL) + 1.4EP LC8 : l.ODL + 1.4WL (or 1.4EL) + 1.4EP (if adverse) LC9: 1.4DL + 1.4CLV + 1.4CLH + 1.4EP LC10: 1.4DL + 1.6CL V + 1.4EP LC11 : l.4DL + 1.6CLH + 1.4EP LC12: 1.2DL + 1.2CLV + 1.2CLH + 1.2EP + 1.2WL (or 1.2EL)


7.6 STEP-BY-STEP DESIGN PROCEDURE FOR PILED FOUNDATIONS

Step 1 Select type of pile The type of pile will depend on the following principal factors:

Environmental issues like noise, vibration. Location of structure. Type of structure. Ground conditions. Durability requirements. Programme duration. Cost.

The commonly available types of piles can be broadly classified as below.

Large-displacement piles (driven)

Precast concrete. Prestressed concrete. Steel tube with closed end. Steel tube tiJied with concrete.

S11Ulll-displacement piles (driven)

Precast concrete tube with open end. Prestressed concrete tube with open end. Steel H-section. Screw pile.

Non-disphlcement piles

Bored and cast-in-situ concrete pile. Steel tube in bored hole tilled with concrete. Steel or precast section in drilled hole.

Step 2 Determine vertical capacity of single pile Follow Section 7 .1.

Step 3 Determine horizontal capacity of single pile Follow Section 7 .2.

Nou: Horizontal capacity of a single pile is limited by maximum deflection of pile cap that structure can accommodate and also by pile structural capacity.

Step 4 Deurmine approxi11Ulle number of piles and spacing p

R;v = Cv

H R;H = CH


R; = R;v or R;H, whichever is greater

where R; :;: approximate number of piles P = total vertical load on pile cap - unfactored

Cv = rated working load capacity of pile - vertical load CH = rated working load capacity of pile - horizontal load H = total horizontal load on pile cap - unfactored

= (H; + H;)4 Spacing of piles should be according to Section 7.3. To minimise the cost of pile cap , the spacing should be kept close to minimum allowed. Larger spacing increases the pile group capacity and pile group moment capacity .

SK 7/14 Determination of approximate number of piles.

X

(1} Select a group of piles with approximate number of piles= R;. (2) Find CG of pile group and locate orthogonal axes x- x and y-y

through the CG. (3) Find CG of group of piles on left of axis y - y and right of axis y-y. (4) Find the x-axis distance between these two CGs and call it Sx (5) Similarly, find Sv about y-axis. (6) Find M .. IP = ey and MyfP = ex, where Mx and My are total combined

applied moments on pile cap about x- x and y - y respectively. (7) Find exiSx and e_) S_v (8) Find Ex and E.v from Fig. 7.1.

1.1 R;v (9) R = -- ~ RiH ExEv

where R = number of piles in group for checking pile load.

Not$: The factor 1.1 is introduced to cater for additional vertical loads from self-weight of pile cap, surcharge on pile caps, backfilHng, etc.

Revise the number of piles in group from R; toR.


Step 5 Determine size of pile cap Allow 1.58 from centre of pile to edge of pile cap . Depth of pile cap is governed by the following:

Shrinking and swelling of clay. Frost attacks. Holding down bolt assemblies for columns. Water table and soluble sulphates. Pile anchorage. Punching shear capacity of pile cap .

Step 6 Carry out load combination Follow Section 7.5.

Step 7 Check pile group effects Follow Section 7 .3.

Step 8 Carry out analysis of pile cap Follow Section 7 .4.

Step 9 Determine cover to reinforcement From the soils investigations report , find the concentration of sulphates expressed as so). Find, from Table 17 of BS8004: 1986121, the appropriate type of concrete.

Table 7.4 Minimum cover to reinforcement for class of exposure.

Class of Total S03 Minimum cover Minimum cover exposure percentage on blinding (mm) elsewhere (mm)

I < 0.2 35 75 2 0.2 to 0.5 40 80 3 0.5 to l.O 50 90 4 1.0 to 2.0 60 100 5 > 2.0 60 100

Note: Concrete in 'class of exposure 5' needs protective membrane, or coating. The uneven heads of piles normally necessitate a minimum 75 mm cover over blinding for pile caps. The concrete piles will have minimum cover as specified elsewhere.

Step 10 Calculate area of reinforcement in pile cap M = bending moment as found in Step 8 at ultimate limit state

M K = --2 s 0.156 fcubd where feu = concrete characte ristic cube strength at 28 days


b = width of section over which moment acts d = effective depth to tension reinforcement.

If K is greater than 0.156, increase depth of pile cap.

M Ast = - - -

0.87/yz

z = d[ 0.5 + J ( 0.25 - 0~9) J ~ 0.95d Distribute this area of reinforcement uniformly across the section.

Note: The effective depth to tension reinforcement will be different in the two orthogonal directions.

Step 11 Check shear stress in pile cap

SK 7/15 Critical section for checking shear stress in pile cap.

cap (~ffective depth = d)

Enhanc~mmt of shear stress is allowed i f ay:ralSd

The critical section for checking shear stress in a pile cap is cjl/5 into the pile. All piles with centres outside this line should be considered for calculating shear across this section in pile cap. For shear enhancement, av is from face of column to t his critical section. No enhancement of shear stress is allowed if av is greater than 1.5d. Where pile spacing is more than 3cjl then enhancement of shear should be applied only on strips of width 3cjl. The rest of the section will be limited to uncnhanced shear stress.

IP V=-~ v Bd c or enhanced vc1 if applicable

where IP = sum of all pile reactions at ultimate loading on left of section

8 = width of pile cap at critical section


Pil~ with dia!Tl4Zter

d = average effective depth at critical section

Vel = Vc (~) ::; 0.8y feu or 5 N/mm2 For rectangular piles the critical section may be considered at face of pile.

"-----+-Vc ~-4~ --GT--~~~J-.~2d a;

a-+----1- Vc

SK 7116 Diagram showing zones of enhanced shear stress on critical section.

The value of ve1 can be found from Figs 11.2 to 11.5 depending on percentage of tensile reinforcement and feu

Shear capacity of section should be greater than or equal to applied shear. Ultimate limit state analysis results should be used for checking shear capacity.

Step 12 Check punching shear stress in pile cap

M II

No check necessary if. pile spacing is less than 3 +

Pllnching shear perimeter around loaded area ' Check V


When the spacing of piles is greater than 3 times the diameter of a pile then the punching shear plane for column should be considered . For rectanguJar piles the plane can be considered at face of pile. The stress on this punching shear plane should not exceed vc depending on the percentage of tensile reinforcement in pile cap.

Check of punching shear stress is also requjred at perimeter at face of column or pile. This shear stress should not exceed 0.8\/ feu or 5 N/mm2

Punching perimeter

SK 7118 Further perimeters for punching shear checks in a pile cap.

The punching shear planes for piles will depend on location of pile with respect to edge of pile cap . Find the perimeter U at punching shear plane.

p v=-:sv Ud c

where P = ultimate vertical column load or ultimate vertical pile reaction vc =design concrete shear stress obtained from Figs 11.2 to 11.5.

Percentage area of tensiJe reinforcement for computation of design concrete shear stress will be average percentage across punching shear planes.

Step 13 Check area of reinforcement in pik Effective length of pile, lc = ~10 where 10 = unsupported length of pile (piles which are not subjected to

horizontal load may be assumed fully supported by ground from ground level; piles subjected to horizontal load may be assumed supported by ground at a depth of l .5b below ground level where b is width of pile or diameter of pile)


h t_

~ = 1.2 = 1.6

Rectangular piles

-pM y y ..

. -+--f-

for piles with head fixed to pile cap for piles with head free to rotate.

L.-~- ._. Asc_/2 I. y .I SK 7119 Typical section through a rectangular pile.

(A) If lelb ~ 10, then treat piles as a short column. (i) Pile with no moment

N = 0.4/cubh + 0. 75AsJy Check N ~ applied direct load on pile. (ii) Pile subjected to uniaxial moment Find e = MIN and then elh. Find N I bh and select appropriate table from Tables 11.8 to 11 .17 depending on feu and k = dlh. From appropriate table find p which satisfies value of Nlbh for given elh. Find A sc = pbhl l OO. Put A scl2 on each face of pile equidistant from axis of moment.

Note: The moment M in pile is due to horizontal load as obtained in Step 3 following Section 7.2. (iii) Pile subjected to biaxial moment Assuming diameter of reinforcement and finding cover from Step 9, find h' and b' . Find Mxl h ' and M_.lb' . If Mxlh ' > Mylb', then

M~ = Mx + ~Mv (h') . b'

If M . .fb' > Mxlh', then

M~ = M., + ~Mx (b') . . h'


Find Nlfcubh. The values of~ are given in the table below.

Table 7.5 Values of~ for biaxial bending of pile.

0 1.00

0.1 0.88

0.2 0.77

0.3 0.65

0.4 0.53

0.5 0.42

~0.6 0.30

Design as uniaxial bending with N and M~ or M~ whichever is more promi-nent. Find Asc in manner described in (ii) for pile subjected to uniaxial moment.

(B) If lelb > 10, then treat pile as a slender column.

1 (/ )2 ax= 2000 ~ hK

ay = 2~ (iYbK Select A sc

N - N K = uz s 1 Nuz- Nbal

Nuz = 0.45fcuAc + 0.87/yAsc Nbal = 0.25fcubh A c = bh- A sc

Maddx = Nax M addy= Nay

Combine these additional moments with moments obtained from analysis as in Step 3 following Section 7.2. Design pile subjected to biaxial bending as described previously.

Circular piles

SK 7120 Typical section through a circular pile.

h Usc m inimum six bars


X

(A) If lclh ::: 10, then treat pile as a short column. (i) Pile with no moment Assume size of reinforcement and at least six bars.

Ac = 0.25rrh2 - Asc

N = 0.4/cuAc + 0.75Asc/y Check N ~ applied vertical load o n pile. (ii) Pile with moment Find e = MIN and the e!R, where 2R =h. Find N/11 2 and select appropriate table from Tables 11.18 to 11.27 corresponding to feu and k = h51 h. Find p from appropriate table which satisfies N/h 2 for given value of e!R . Find Asc = p1tR21100. Use at least six bars.

(B) If lclh > 10, then treat pile as a slender column . [2

a = 2~11 K (assume K = 1 conservatively) M add = Na

Combine this additional moment with moment obtained by analysis in Step 3 following Section 7 .2. Design pile with moment as described in (ii) above.

Step 14 Check stresses in prestressed concrete piles

X

v

y

+ X y

y X SK 7/21 Typical section of a prctcnsioned prestressed pile.

Stresses may be checked at the serviceability limit state only as per BS8110: Part 1, Section 4.1 11

Permissible maximum compressive fibre stress in concrete = 0.4/cu

Assume pile as Class 3 member with a limiting crack width of 0.1 mm.


Hypothetical flexural tensile stress in concrete = 4.1 N/mm2 for Grade 40

= 4.8 N/mm2 for Grade 50 and above

Depth factors to modify tensile stress are shown in the following table.

Depth (mm)

Up to 400 500 600

N = direct service load on pile

Factor

1.0 0.95 0.9

M:rx = bending moment as obtained from Step 3 about axis x-x M yy = bending moment as obtained from Step 3 about axis y-y.

Assume the pile section is uncraeked.

Find A~ = area of concrete I= = moment of inertia about x- x axis fyy = moment of inertia about y-y axis P = residual prestress after all losses.

Maximum compressive stress in concrete = (~) + (MxY) A c lxx + (~:)

( P A+c: N\ _ (M/~) Maximum tensile stress in concrete = - ) ~ - (~:)

m = modular ratio fs = strand stress prior to release fc = stress in concrete due to prestress alone.

( ) . . (lOOmfc:) 1 Loss due to elastiC shortenmg = --- % Is

(2) Loss due to relaxation of steel - refer to strand manufacturer's brochure.

(3) Loss due to creep of concrete - follow clause 4.8.5 of BS 8110: Part 1.(1 ]

(4) Loss due to shrinkage o f concrete - follow clause 4.8.4 of BS8110: Part L l1l

Note: Prestressed piles designed as fixed to pile cap must extend into pile cap by


a minimum distance equal to transmission length given by the following equation:

K, 11 == Y/cu (mm) where feu = concrete cube strength at 28 days

K1 = 600 for plain or indented wire == 400 for crimped wire = 240 for 7-wire standard or super strand = 360 for 7-wire drawn strand

0.6h and/or MpyuiNu > 0.6b Find Vx = Hpyufbh' and Vy = Hpxulhb' Find Px = lOOAsxlbh' and P.v = lOOAs_vfhb' Find Vex and Vcy corresponding to Px and P.v from Figs 11.2 to 11.5.


If this check fails, provide shear reinforcement in the form of links.

I

Nu

Enhancement of design

Enhancement of design concrete shear stress

=0-6 NuHxub/MyuAc Hxub/Myu~ 10 concrete stress= 06 N"u Hyu h/ MxuAc

Hyuh/ Mxu~ 10 SK 7124 Shear stress enhancement due to presence of axial load. SK 7/23 Shear stress enhancement due to

presence of axial load.

Note: v,. ... and vc_v may be enhancecl by using the following formulae due to presence of an axial load Nu:

HpyuhiMpxu and Hpxub!Mpyu should be less than or equal to 1.0.

Shear reinforcement bSv( V - v~) Asv = -~-____:~

0.87/yv

where A sv = total area of legs in direction of shear b = width of section perpendicular to direction of shear

Sv = spacing of links {yv s 460N/mm2 for links.

Circular piles

Nu = ultimate vertical load with Hpu Hpu = combined ultimate horizontal load Mpu = moment in pile due to Hpu


A_ 2:: bxSv(Vx -Vex> ""'SVX - 087 Jyv

Asvy ~ by5v(Vy-Vty) 087Jyv

Asv(aYUof link)

Sv

Sv

No shear check is necessary if"

SK 7/25 Shear reinforcement in a rectangular pile.

SK 7/26 Shear reinforcement in a circular pile.

Mpu1Nu s 0.60h and Hpu/0.75Acs0.8Vfc:uS5N/mm2

where A c: = 0.25nh2

Shear check is necessary if' M pu/ Nu > 0.60h

Shear stress, v = Hpuf0.75Ac

p = 100A5/ 1.5Ac assuming 50% of bars effectively in tension

where A s = total area of steel in pile.


Find vc corresponding top from Figs 11.2 to 11.5. The shear stress vc may be enhanced by using the following formula due to presence of an axial load Nu:

0.6NuHpuh , 1 2 v~ = Vc + ::5 0.8 vfcu ::5 SN/mm AcMpu

H puhl M pu should be less than or equal to 1.0.

If v > v~. then use shear reinforcement.

where Av = total area of link bars perpendicular to longitudinal bars, i.e. the two legs of hoop reinforcement

fY" = characteristic yield strength of link reinforcement S = spacing of links.

Find z/ R from appropriate table from Tables 11.18 to 11.27 corresponding to feu hsfh, p , NIR2 and e/R. Check H pu ::5 V5 + Vc

The total shear resistance for inclined links = Vs = l0.87 f yA sv (cos~+ sin ~cot~) (z/S)] where Asv = total area of link bars i.e. the two legs of hoop reinforcement.

~ may be taken as 45 when ~ is angle of inclination of link.

Step 16 Check shear capacity of prestressed pile

b

h d Spiral link .r~in~ccment

Aps to find Vc

SECTION

SK 7127 Typical section and elevation of a prestressed concrete pile.

Vco = 0.67bh(f~ + 0.8fcpft)! ( 0.55fpe) M 0 V Vcr = 1 - -- vcbd + -- ~ O.lbdVfcu fpu M

j r

ELEVATION

Spiral link

Vc = V co or Vcr as the case may be (kN) resistance

design ultimate shear


h

Vco = shear resistance of section uncracked (kN) Vcr = shear resistance of section cracked (kN)

f, = maximum design principal stress at the centroidal axis = 0.24'1/ feu fcp = design compressive stress at centroidal axis of concrete section due

to prestress alone

fpe = design effective prestress in tendons after all losses~ 0.6fpu fpu = characteristic ultimate strength of tendons

vc = design concrete shear strength from Figs 11.2 to 11.5 where percent-age of steel reinforcement should include tendons plus any ordinary untensioned longitudinal steel reinforcement in tensile zone of section

d = effective depth to centroid of reinforcing steel in tension zone where reinforcing steel should include tendons and any untensioned reinforcement

feu = characteristic cube concrete strength at 28 days M 0 = moment to produce zero stress at tension fibre with 0.8fcp on

section.

b

.I ~t~ssmg strands

l.Jc.1tformly. prestr~sed t.hiform Prest~ss ptle sectton :OSfcp

+

-1, Stress due to M0 M0 = ZJc = 08Zfcp

SK 7/18 Stress diagram for a symmetrical rectangular prestressed pile due to M,,.

If Hpu < 0.5 Vc, no shear reinforcement is required. If Hpu;::: 0.5Vc, then provide shear reinforcement as follows. Shear reinforcement If horizontal shear on pile , Hpu is less than or equal to ( Vc + 0.4bd) then, A,v 0.4b -=---

Sv 0.87fyv

lf horizontal shear on pile, Hpu is more than ( Vc + 0.4bd) then,


Note: For biaxial bending and shear, check requirement for shear reinforcement for each direction of bending separately, but allow for contribution of concrete shear resistance V< in one direction of loading only for calculation of shear reinforcement. (See Step 7 of Section 4.3.1.)

Step 17 Check minimum reinforcenuml in RC pile For rectangular and circular piles, lOOAsciAc ~ 0.4.

Step 18 Check minimum prestress in prestressed pile

Find slenderness ratio of pile = n = ~ where b = minimum width of pile

l = total length of prestressed pile at commencement of driving.

Minimum prestress after losses = 60n psi or = 0.4n N/mm2

If diesel hammer is used,

minimum prestress in concrete= 5 N/mm2

Step 19 Maximum reinforcement in pile lOOA scl Ac :s 6

Step 20 Containment of reinforcement in pile Minimum dia . of links = 0.25 x largest bar ~ 6 mm Maximum spacing of links = 12 x smallest dia. of bar

Step 21 Links in. prestressed piles At top and bottom 38 length of pile , provide 0.6% of volume of pile in volume of link.

Step 22 Minimum tension reinforcement in pile cap As~ 0.0013bh in both directions

Step 23 Curtailment of bars in pile cap A minimum anchorage of 12 times diameter of bar should be provided at ends by bending bar up vertically. Additionally check that full tension anchorage bond length is provided from cri tical section for bending in a pile cap where design for flexure and requirement for flexural steel in tension is determined. In finding anchorage bond length beyond that section, actual area of steel provided may be taken into account.

Step 24 Spacing of bars in pile cap Clear spacing of bars should not exceed 3d or 750 mrn.


h

L = Tension Anchorage Bond Length

Percentage of reinforcement, IOOAsfbd (%)

1 or over 0.75 0.5 0.3

Les~ than 0.3

SK 7/29 Typical section through a pile cap.

Maximum clear spacing of bars in pile cap (mm)

160 210 320 530

3d or 750

Note: This will deem to satisfy a crack width limitation of 0.3 mm.

Step 25 Early thermal cracking See Chapter 3.

Step 26 Assessment of crack width in flexure See Chapter 3.

Step 27 Connections See Chapter 10 for connection of pile to pile cap and column to pile cap.

7.7 WORKED EXAMPLE

Example 7.1 Pile cap for an internal column of a building Size of column = 800 mm x 800 mm Spacing of column = 8 m x 8 m on plan


Unfactored column loads

Dead Imposed Wind

Vertical load, N (kN) Horizontal shear, Hx (kN) Horizontal shear, Hy ( kN) Moment, Mx (kNm) Moment, My (kNm)

1610 28

112

Geotechnical information (see SK 7130) Stratum 1 Average thickness of layer= 1.5 m

1480 18

72

156 112 448 624

Classification: very loose yellow brown to brownish grey sandy silt.

Average N = 3 (SPT) c = 11.3 kN/m2 = 40 y = 26kN/m3

Stratum 2 Average thickness of layer= 9 m Classification: soft to medium bluish-grey clayey silt.

Average N = 5 (SPT) c = 20.2 kN/m2 = so y = 24kN/m3

Ysat = 27 kN/m3

Stratum 3 Average thickness of layer = 2 m

Classification : stiff to very stiff bluish-grey silty clay.

Average N = 14 (SPT} c = 60kN/m2 = 60

Ysat = 26 kN/m3

Stratum 4 Average thickness of layer = 7 m

Classification: dense to very dense mottled brown sandy silt.

Average N = 24 (SPT) c = 13.8 kN/m2 = 31

Ysat = 27kN/m3

3~ Reinforced Concrete

~ -----------------------------::::> ~ "'

VERY LOOSE YELLOW BROWN SANOY SILT N=3 ~ ------------------------------

SOFT TO MED IUM BLUiSH-GREY CLAYEY SILT N=S AVERAGE

~ STIFF TO VEQY STIFF BLUISH-GREY ~ SILTY CLAY N-14 ~VERAGE "' ::;;----------------------------

_,

::E: ::::> JENSE TO VERY OENSE MOTTLED BROWN ~ SANOY SILT N 24 AVERAGE .....

VI

VERY S"IFF TO HARO S:LTY CLAY N=31 AVERAGE

:r ....

0. w O CJ'I

a: I.Ul!J 0>- u. < O

0 0 0 01

0 0 0

""

0 0 0

~

SK 7/30 Average ground condition soil strata.


Stratum 5 Average thickness of layer= 15m

Classification: very stiff to hard silty clay.

Average N = 31 (SPT) c = 71.5 KN/m2 =S"

Ysat = 28kN/m3

Water table at 3.0m below ground level.

Step 1 Select type of pile Considering all the factors as described in Step 1 of Section 7.6 it 1s decided to use a non-displacement pile. Choose 600mm diameter bored and cast-in-situ concrete pile.

Step 2 Determine vertical capacity of pile Follow Section 7.1.

First method of point resistance

Assume pile to go into Stratum 5 and stop at 8.0 m within Strlllum 5.

Lb = average length of pile = (1.5 + 9 + 2 + 7 + 8) m = 27.5 m 0.62

Ap = cross-sectional area of pile = 1t x 4 = 0.283 m2

B = 0.60 m N = statistical average of SPT in a zone of about 88 above to 38 below

pile point = 31

27.5 P pu = 0.283 X 38 X 31 X 0.6 = 15280 kN

~ 380N(Ap) = 380 X 31.0 X 0.283 = 3334 kN

Second method of point resistance Ppu = Ap(N~c + qN;,) Ap = 0.283m2

c = 71.5 kN/m2

Yw = 10kN/m3

q = effective vertical stress at pile point = 1.5 X 26 + 1.5 X 24 + 7.5 X 27 + 2 X 26 + 7 X 27 + 8 X 27

- (27.5 - 3) X 10 = 489.5 kN/m2


0 0 "' !'-

"'

STRATUM 1

Water Table ..

STRATUM 2

STRATUM 3

STRATUM 4

STRATUM 5

-

-

-

-

-

6=26KN/m

~=24KN/m

~ a50 t=27KN/m' !'-

6sot =26KN/m

0 8 650 t=27KN/m' !'-

0 8 650 t=27KN/m' (X)

L = 27.5m B = 0.6011l"

L/8 = 46 =SO From Fig. 7.2,

N~ = 3 N~ = 15 and LJB = 3.5 L Lc - >>-B B

SK 7/31 The pile penetrating different strata.

Ppu = 0.283 ((15 X 71.5) + (3 X 489.5)) = 719kN

SK 7132 Condition at bottom of pile.

Determination of skin resismnce '1:P5; = kAJ s


0 IDO ([) ID

....

0 0 0


Stratum 4

A s4 =it X 0.60 X 7 = 13.2m2

/s4 = 24 kN/m2

P si4 = 13.2 X 24 = 316.8 kN

Stratum 5

A ss= :It X 0.60 X 8 = 15.1m2

Iss = 31 kN/m2

Psi5 = 15.1 X 31 X 468.1 kN

'1:P8; = 931.6 kN

Fourth method of skin resistance /s =


q = effective vertical stress at middle of layer = 1.5 X 26 + 1.5 X 24 + 7.5 X 27 + 2 X 26 + 3.5 X 27 - {16- 3) X 10 = 294kN/m2

Is = ~c + 0.5ij Ks tan 0 P si4 = 13.2 [2 X 13.8) + (0.5 X 294 X 2 X 0.43)] = 2033 kN The fourth method of skin resistance is giving much higher values than the first method and may be ignored from the point of view of conservatism.

Pu = P pu + P su = 719 + 932 = 1651 kN

Allowable working load on pile = 1651 = 660 kN 2.5

Designed pile is 600 mm diameter bored and cast in-situ concrete pile with an average length of 27.5 rn to carry a working load of 660 kN. This is a conservative theoretical estimate of single pile vertical load capacity and must be verified by actual pile tests on site.

Step 3 Determine horizontal capacity of singk pile See Section 7.2. Assume cohesive soil.

Mellwd 1

Es = 650N where N = SPT No. Es of Stratum 1 = 650 X 3 = 1950 kN/m2 5 of Stratum 2 = 650 x 5 = 3250 kN/m2 5 of Stratum 3 = 650 x 14 = 9100kN/m2 Es of Stratum 4 = 650 X 24 = 15 600 kN/m2 5 of Stratum 5 = 650 X 31 = 20150 kN/m2

ksB = t.3(s84)ft (~) Erlr 1 - ~

Er = 28 x 106 kN/m2 for pile concrete

k8 ,B = 1672kN/m2 k52B = 2909 kN/m2 k53B = 8875kN/m2 k54B = 15914 kN/m2 ks58 = 20999 kN/m2

X 0.604 = 6.36 X 10-3 m4

k s l = 2787kN/m3 k s2 = 4848 kN/m3 ks3 = 14 792 kN/m3 ks4 = 26 523 kN/m3 k55 = 34998kN/m3


g 0>

:.:: ~ UJ

e

8 0 10 ..

"' z 0 ... (.) lJ.J 111

0 ...,

1

2 r-~

4 1--~ 6 ~ 1--6

1--~ 10

1-11

1--12

1-13 ~ 1--15

~ 17 18 -

19 -

20 -

21 1-22 ----23 -24 -~ 26 tn 1-26

~ 30 ~

Method 2

k5 = 240qu kN/m2 = 480ckN/m2

k5 , = 480 X 11.3 = 5424 kN/m3 ks2 = 480 X 20.2 = 9696kN/m3 ks3 = 480 X 60 = 28800kN/m3 k54 = 480 X 13.8 = 6624 kN/m3 kss = 480 X 71.5 = 34320kN/m3

The values given by Method 1 are smaller or softer which will produce larger deflection and bending moments in pile. For the sake of conservatism use values given by Method 1.

S = node spacing for finite element analysis = 0.60 m 8 = 0.60m spring stiffness = SBks kN/m

-

~ ~ :;;

.....

X :::>

~ ex ...

VI

!i tc ex :;;

-7

X :::>

'C ex ...

"'

SK 7/33 Finite element model of pile.


Ignore top l.SB of pile for lateral support from soil. The whole length of pile need not be modelled.

Stratum 1 Spring stiffness = 0.60 x 0.60 x 27'07

= 1003kN/m

Stratum 2 Spring stiffness = 0.60 x 0.60 x 4848

= 174SkN/m

Stratum 3 Spring stiffness = 0.60 X 0.60 x 14 792

= 5325 kN/m

Stratum 4 Spring stiffness = 0.60 x 0.6 x 26523 = 9548 kN/m

Assume full fixity of pile with pile cap. Apply unit load at top of pile and find pile stiffness and bending moment and shear in pile using a two-dimensional computer program.

A = 0.283 m2 I = 6.36 x w-3 m4

ResuUs of computer run Maximum moment = 2.481cNm/kN

Pile top deflection = 0.12 mm/kN

Single pile horizontal stiffness = ~~ = 8333 kN/m Step 4 Determine approximate number of piles and spacing

Maximum vertical load on pile cap = 1610 + 1480 = 3090 kN = P p 3090

R;v = Cv = 660 == 4.7

Assume maximum allowable horizontal displacement of pile cap is 10 mm.

Maximum horizontal load = 28 + 18 + 156 = 202 kN = H

Maximum horizontal load on pile to limit deflection to lOmm = 8333 X 0.010 = 83 kN per pile

H 202 R;H = Cu = 83 = 2.4 R; = greater of R;v and R;H = 4.7

l.lR; == 4.7 X 1.1 = 5.17

Use 6 no. piles.


8

10

11

12

13

14

15

16

11

19

20

21

22

23

24

25

2.48

1. 05

.058

0.21

-O.OB

-0.28

-0.42

- 0.51

-0.56

- 0.57

-0.57

-0. 56

-0.52

- 0.48

-0.43

-0.37

-0.31

-0.25

-0. 19

-0.1 4

-0. 11

-0.09

-0.05

-0.02

0

Step 5 Determine size of pile cap B = diameter of pile = 0.6 m

1.58 = 1.5 X 0.6 = 0.9 m

SK 7/34 Bending moment (kNm) due to 1 kN horizontal load at top of pile.

Allow 0.9 m from centre of pile to edge of pile cap. Assume 0. 9 m depth of pile cap.

SK 7/35 Layout of piles under pile cap.

Spacing of piles:::::: 38 2: 3 x 0.6 = l.R rn


Size of pile cap assumed is 5.4 rn x 3.6 m x 0.9 m.

Step 6 Carry out load combination

Estimation of load on pile LCI = l.ODL + 1.0/L

N = L610 + 1480 = 3090 kN

Hx = 28 + 18 = 46kN H_.., = OkN

MA = OkNm M_. = 112 + 72 = 184kNm

LC3 = l.ODL + 1.0/L + l.OWL

N = 3090kN

Wind in x-x direction

H X = 46 + 156 = 202 kN H_. = OkN

M , = OkNm M,. = 184 + 624 = 808kNm

Wind in y-y direction

H_. = 46kN H . = ll2kN

M .. - = 448kNm Mv = 184kNm

LC4 = l.ODL + l.OWL


N = l 610kN

Wind in x - x direction

H,. = 2H + 156 = 184kN H_. = OkN

M_, = OkNm Mv = 112 + 624 = 736 kNm

Wind in y - y direction

II,. = 28kN lfv = 112kN

M.r = 448kNm M_. = 112 kNm

Estimation of loads on piles .for bending moment and sliear calculations in pile cap

LC5 = 1.4DL + 1.6/L

N = 1.4 X 1610 + l4RO x 1.6 = 4622 kN

H,. = 1.4 X 28 + 1.6 X 18 = 68 kN Hv = OkN

Mx = OkNm M_. = l .4 X 112 + 1.6 X 72 = 272 kNm

LC6 = 1.2DL + 1.2/L + 1.2WL

N = 1.2 X 1610 + 1.2 X 1480 = ::\708 kN


H,. = l.2 x (28 + 18 + 156) = 242.4 kN H_v = OkN

M_. = OkNm Mv = 1.2 X (112 + 72 + 624) = 969.6kNm Wind in y - y direction

H, = 1.2 X (28 + 18) = 55.2 kN II,, = 1.2 X 112 = 134.4 kN

M, = 1.2 X 448 = 537.6kNm M_,. = 1.2 x (112 + 72) = 220.8 kNm

LC1 = 1.4DL + 1.4WL

N = 1.4 X 1610 = 2254kN

Wind in x-x direction

H, = l.4 (28 + 156) = 257.6 kN H_. = OkN

II T031985 0011425 bTT II

SK 7/35 Layout of piles under pile cap.

..


1800 1800

~7- $ g _y __ - '--=r~-+-m

~ -4- ---4+--f-t: 0 m

Spacing of piles~ 3B ~ 3 x 0.6 = 1.8 m

Size of pile cap assumed is 5.4 m x3.6 m x0.9m.

Step 6 Carry out load combination

Estimation of load on pile LC1 = l.ODL + 1.0/L

N = 1610 + 1480 = 3090 kN Hx = 28 + 18 = 46kN H.v = OkN

Mx = OkNm My = 112 + 72 = 184kNm

LC3 = l.ODL + 1.0/L + l.OWL

N = 3090kN


Hx = 46 + 156 = 202kN H.v = OkN

Mx = OkNm M,v = 184 + 624 = 808 kNm

Wind in y-y direction

Hx = 46kN H.v = 112kN

Mx = 448kNm My = 184kNm

LC4 = l.ODL + l.OWL


c = 71.5 kN/m2 at bottom of group

q = effective stress at bottom of group = 489.5 kN/m2 (see Step 2) N'= 3} N! = 15 for = 8" Group end-bearing capacity = 1 .8 x 3.6 x (15 x 71.5 + 489.5 x 3)

= 16465 kN

Ultimate group capacity = 7996 + 16465 = 24461 kN

24461 Allowable group capacity = -- = 9784 kN

2.5

Allowable group capacity based on single pile capacity 3960kN

Design basis is single pile capacity.

Step 8 Carry out analysis of pile cap

6X660=

Assume that pile cap is rigid. Assume SOO mm backfill on top of pile cap. Assume a surcharge of 5 kN/m2 on backfill with no eccentricity. It is always advisable to use the table as presented.

W = weight of pile cap + weight of backfill on pile cap + weight of surcharge on backfill

= ).4m X 3.6m X U.Y m X 24kN/m3 + 5.4 X 3.6 X 0.5 m X 20 kN/m3 + 5.4 X 3.6 X 5 kN/m2

= 712kN

Maximum service load on pile without wind = 665 kN

Maximum service load on pile with wind = 771 kN

X y

X

T--'1/--f-;-- - --, - - --r- ~-+--x

4-- ~~- -8- -y

SK 7/37 Calculations of pile group stiffness.

Analysis of loads on pile cap.

Load case N Mx My Hx Hy ex e,. ehx eh,- h P or Pu M: M* y Mxx Myy T

LC1 3090 0 184 46 0 0 0 0 0 0.9 3802 0 0 0 225.4 0 LC3 3090 0 808 202 0 0 0 0 0 0.9 3802 0 0 0 989.8 0 LC3 3090 448 184 46 112 0 0 0 0 0.9 3802 0 0 548.8 225.4 0 LC4 1610 0 736 184 0 0 0 0 0 0.9 2322 0 0 0 901.6 0 LC4 1610 448 112 28 112 0 0 0 0 0.9 2322 0 0 548.8 137.2 0 LCs 4622 0 272 68 0 0 0 0 0 0.9 5619 0 0 0 333.2 0 LCt. 3708 0 969.6 242.4 0 0 0 0 0 0.9 4562 0 0 0 1187.6 0 LCt. 3708 537.6 220.8 55.2 134.4 0 0 0 0 0.9 4562 0 0 658.6 270.5 0 LC1 2254 0 1030.4 257.6 0 0 0 0 0 0.9 3251 0 0 0 1262.2 0 LC1 2254 627.2 156.8 39.2 156.8 0 0 0 0 0.9 3251 0 0 768.3 192.1 0 I~ (I) 60' Mxx = Mx + Ne1 + Hyh + M: Myy = My + Nex + Hxh + Mi I ~ T = Hxehy + Hyeh.< P =N+W Pu = N + 1.4W (or l.2W)

~ 0 Q..

6' c :::3 Q.. I .... s :::3 Cll

~ .....

Loads on pile.

Load case Por Pu Hx Hy M.u Myy T

LCI 3802 46 225.4 -LC3 3802 202 989.8 -LC3 3802 46 112 548.8 225.4 -LC4 2322 184 901.6 -LC4 2322 28 112 548.8 137.2 -LC5 5619 68 333.2 -LC6 4562 242.4 1187.6 -LC6 4562 55.2 134.4 658.6 270.5 -LC1 3251 257.6 1262.2 -LC7 3251 39.2 156.8 768.3 192.1 -

fxx = ~y2 = 4.86 m2 l yy = u 2 = 12.96m2 l u = lxx + l yy = 17.82m2 P MxxY MyyX Q --+ --+--

max - R lxx f yy P MxxY MyyX

Qmin = R - fxx - l yy H = y(H; + H;)

R R = no. of piles = 6

Mr = bending moment in pile = 2.48H (see Step 3) x = 1.8m y = 0.9m b = horizontal displacement at top of pile = 0.12H mm (see Step 3)

~ ~ ~. ::I 0' ..,

@ 0.. ('} 0 = (') ...

Cb

Qmax Qmin H or 0

Mp or Mpu b (mm) Hpu

665 602 7.67 19.0 0.9 771 496 33.67 83.5 4.0 767 501 20.18 50.0 2.4 512 262 30.67 76.1 3.7 508 266 19.24 47.7 2.3 983 890 11.33 28.1 1.4 925 595 40.40 100.2 4.8 920 601 24.21 60.0 2.9 717 367 42.93 106.5 5.2 711 373 26.94 66.8 3.2


SK 7138 General arrangement of pile cap and piles. y

SURCHARGE ON BACKFILL

0 0 U'l

0 0 en

Allowable service load on pile without wind = 660 kN OK

Allowable service load on pile with wind = 660 x 1.25 = 825 kN OK

Bending monunJ and shear force in pile cap

SK 7/39 Critical sections for calculation of bending moment in pile cap.

2


Sections 1-1 and 2- 2 are taken at the face of column. Assume column size = 800 mm x 800 mm Dead load of pile cap+ surcharge+ backfill = 0.9 x 24 + 0.5 x 20 + 5 = 36.6kN/m2

Applying load factors for different load cases:

1.4 X 36.6 = 51.2 kN/m2 1.2 X 36.6 = 43.9 kN/m2

Ml 1 = bending moment due to dead load of pile cap etc. on section 1-1 3.6 X 51.2 X 2.32

48 2

= 7.5kNm

3.6 X 43.9 X 2.32 =

2 = 418.0 kNm or

Mn = Bending moment due to dead load of pile cap etc. on section 2-2 5.4 X 51.2 X 1.42 O

2 = 271. kNm

5.4 X 43.9 X 1.42 =

2 = 232.3 kNm or

SK 7/40 Critical sections for shear.

Step 9 Determine cover to reinforcement From soil test reports, the total S03 is 0.75%. This means it is Class 3 exposure (see table in Step 9 of Section 7.6). Minimum cover on blinding concrete= 50 mm Minimum cover elsewhere = 90 mm

Assume 90 mrn cover for pile cap everywhere.

Step 10 Calculate area of reinforcement in pile cap M = bending moment in pile cap as found in Step 8.

Mll = 2264.9kNm from table in Step 8.

Bending moments and shear in pile cap.

Load case Qt Q2 Q;~ Q4 M)t Mh Mit Mh M11 M22 V' 3.' V44

LC5 890 937 983 983 -487.5 -271.0 2752.4 1405 2264.9 1134.0 - 199.1 -298.6 LC6 595 760 925 925 - 418.0 - 232.3 2590.0 1140 2172.0 907.7 - 170.7 -256.0 LC, 844 882 920 676 - 418.0 -232.3 2234.4 1323 1816.4 1090.7 -170.7 -256.0 LC1 367 542 717 717 -487.5 - 271.0 2007.6 813 1520.1 542.0 - 199. 1 -298.6 LC1 657 684 711 427 - 487.5 - 271.0 1593.2 1026 1105.7 755.0 -199.1 - 298.6

Q ., Q2, Q;~ and Q4 are pile reactions Mit = 1.4 (Q;~ + Q4) M22 =0.5 (Qt + Q2 + Q;~) M11 = M]t +Mit

\13:~ = Q;~ + Q4 V44 = Qt + Q2 + Q;~ V33 = V:b + Vj;~ Mit. Mh, V;\3 and V44 are bending moments and shears in pile cap due to dead load of pile cap+ surcharge Mil> Mh, V~3 and V44 are bending moments and shears in pile cap due to pile reaction M 11 , M22, V;~3 and V44 are combined bending mome nts and shears in pile cap /5 = 120 mm


I ,, II

I I I ,, ,, It It

I I SK 7/41 Moments in pile and pile cap due to pile fixity.

For this load case, pile fixity moment = 19.0 kNm per pile.

Pile fixity moment on pile cap is opposite in sign to moment M 11 and may be ignored. Assume 20 mm diameter reinforcement.

dx = 900 - 90 (cover) - 10 (half bar dia.) = 800 mm feu = 30 N/mm2 for concrete in pile cap

K = ~ = 2264.9 X l ~Ji = 0.033 /cubd2 30 X 3600 X 8002

z = d[ 0.5 + J ( 0.25 - 0~9) J = 0.96d =:; 0.95d = 760mm

M 11 2264.9 X lW 2 A = -- = = 7447 mm st 0.87 [yZ 0.87 X 460 X 7fiJ

Assume /y = 460 N/mm2 for HT reinforcement

b = 3.6 m

Area of 20mm dia. bar = 314 mm2 24 x 314 = 7536 mm2

Use 24 no. 20mm diameter bars equally spaced (approximate spacing 150 mm) in the x-x direction. Mzz = 1134kNm from table in Step 8.

Ignore the effect of pile fixity moments. Assume 12 mm diameter reinforcement.

dy = 900 - 90(cover - 20(bar d ia.) - 6(half bar) = 784 mm


K = M 12 = 1134 X l(f = O.Oll fcubd2 30 X 5400 X 7842

z = 0.95d by inspection = 0.95 X 784 = 745 mm

k = Mn = 1134 x 1


1.5dx = 1.5 X 800 = 1200 mm

hence no enhancement of shear stress is allowed

V 1766.9 X 103 v =- = = 061N/mm2 bd 3600 X 800 .

p = lOOAs = 100 X 7536 = 0.26% bd 3600 X 800

Vc = 0.425 N/mm2 < 0.61 N/mm2 from Fig. 11.3

400 1200 1100 Ov

SK 7143 Critical shear plane in pile cap.

The cheapest alternative is to bring the outer piles in towards the centre of pile cap by 20mm in the x-x direction only. This has very little effect on pile reactions.

av = 1200mm 1.5dx = 1200 mm 2d 2 X 800 av 1200 1.333

Increase grade of concrete from feu= 30N/mm2 to feu= 40N/mm2 in pile cap.

Vet = 0.47N/mm2 from Figs 11.2 to 11.5

Vc2 = Vc~e~) = 0.47 x 1.333 = 0.63N/mm2 > 0.61N/mm2 OK

V 44 = shear on critical section 4-4 = 2511.4 kN (see table in Step 8).

av = 1800 - 1200 + 120 - 400 (half column) = 320 mm 1.5dy = 1.5 X 784 = 1176mm > av


2dv 2 X 784 -a-: = 320 = 4'9

= lOOAsc = 100 X 3482 = O OS'Y< p bd 5400 X 784 . 0

(See Step 22 for minimum percentage of reinforcement.) Vet = 0.40N/mm2 for feu = 40N/mm2 vc2 = 0.40 x 4.9 = 1.96N/mm2

V 2511 X toJ Vc = bd = 5400 X 784

= 0.59N/mm2 < 1.96N/mm2 OK

Step 12 Check punching shear stress in pile cap

0 oo (DOl

SK 7144 Critical planes for punching shear of piles in pile cap. CRITICAL PL ANE FOR PUNCHING SHEAR

U 1 = perimeter of column = 2 (800 + 800) = 3200 mm Since pile spacing is not greater ~han 3 times diameter of pile, then punching shear stress at critical perimeter for column need not be checked.

u2 = perimeter on punching shear critical plane for pile load = 2300 + 2256 = 4556 mm

Ultimate maximum column load, N = 4622 kN

Ultimate maximum pile load, Q = 983 kN from table in Step 8.


N 4622 X 103 Column punching shear stress = U

1d = 3200 x 0_5 X (800 + 784)

= 1.82 N/mm2 < 0.8'-/ leu or 5 N/mm2 OK

P . h . f .1 983 X loJ unchmg s ear stress at pen meter o pt e = 600 800 ;tX X

= 0.65 N/mm2 < 0.8'-/ leu OK . . Q 983 X loJ

Ptle punchmg shear stress = U2d = 4556 x 0_5 (SOO + 784)

= 0.27 N/mm2

Minimum ve for Grade 40 N/mm2 concrete = 0 .40 N/mm2 OK

Step 13 Check area of reinforcemenJ in pile Unsupported length of pile, /0 , is assumed negligible. Assume lclh < 10. The pile is treated as a short column . From tables in Step 8,

Qmax = 983 kN Qmin = 367 kN

with M = 28.1 kNm with M = 106.5 kNm

Max. shear , Vmax = 42.93kN

Assume minimum cover is 75 mm.

h 600

SK 7/45 Pile reinforcement .

Allowing for links and bar diamete r, assume hs = 420mm.

hs 420 h = 600 = 0.70 = k

leu = 30 N/mm2

~ = 0.029 = 0.095 R 0.3

M 28.1 e = - = - = 0.029 m

N 983

_Q_ma_x = 983 X 103 = 2.73 N/mm2 h 2 600 X 600


From Table 11.19, it is observed that minimum reinforcement may be used. Use minimum reinforcement. For the second load case,

Qmin = 367 X 1oJ = 1 N/mm2 h2 600 X 600

e -= 1 R

Again use minimum reinforcement.

Step 14 Check stresses in prestressed concrete piles Not required.

Step 15 Check shear capacity of RC pile No shear check is necessary if MpuiNu ~0.60h. Mpu 106.5 X 106 -= =290mm Nu 367 X 1oJ

0.60h = 0.60 x 600 = 360 mm No shear check is necessary.

Hpu 42.93 X toJ 0.75Ac = 0.75 X 1t X t/Xf/4

= 0.20N/mm2 < 0.8Yfcu OK

Step 16 Check shear capacity of prestressed pile Not required.

Step 17 Check minimum reinforcement in RC pile lOOAsc -- ~ 0.4

A c

Ac X 0.4 A sc = .....:;__100--

Tt X 30Q2 X 0.4 = 100 = 1131mm2

Use 6 no. 16 mm dia. HT bars (1206 mm2).

Step 18 Check minimum prestress in prestressed pile Not required.

Step 19 Maximum reinforcement in pile Not required.


-

-

Step 20 ConlllinnumJ of reinforcement in pik Minimum dia. of links= 0.25 x bar dia. = 4mm :::: 6mm

Maximum spacing of links = 12 x smallest dia. of bar = 12 x 16 192mm

Use 6 mm dia. links at 175 mm centres.

Step 21 Links in prestressed piks Not required.

Step 22 Minimum Unsion reinforcement in pile cap

I I

-- $ -I

I ~ - ~ -'r

I I

A s ;:: 0.0013bh in both directions

Minimum reinforcement in the x-x direction = 0.0013 x 3600 x 900 = 4212mm2

Provided 7536mm2 (see Step 10). Minimum reinforcement in the y-y direction = 0.0013 x 5400 x 900 = 6318mm2

Area of 16 mm dia. bar = 201 mm2 32 X 201 = 6432mm2

Area required = 3842 mm2 from Step 10

Use 32 no. 16mm dia. bars equally spaced (approximate spacing 170 mm) in the y-y direction.

I I

1f -{-(l-

I I

24 - 20

I I

$-I

I rv-I I

32 - 1 6

f--

-

SK 7/4(, Pile cap reinforcement revised to suit minimum reinforcement.

Step 23 Curtailment of bars in pile cap Minimum anchorage at ends of bars is 12 X dia. of bar.

12 x 20 = 240mm 12 x 16 = 192mm

Provide a minimum 250 mm bent up length of pile bottom reinforcement. Check full anchorage bond length of the main tension bars.


feu = 40N/mm2

Reinforcement used is Type 2 deformed bars. From Table 3.29 of BS8110: Part 1: 1985,1ll

tension anchorage length = 32 = 32 X 20 = 640 mm

More than 640 mm length of bar is available beyond section 1- 1 in Step 8.

Step 24 Spacing of bars in pile cap . . lOOA. Maxtmum percentage of retnforcement = p = ----;;;{

_ 100 X 7536 _ 0

- 3600 X 800 - 026 Yo

Maximum allowed clear spacing for p less 0.3% is 3d or 750 mm, whichever is less. Spacing of bars adopted is 150 mm.

Step 25 Early thermal cracking If it is felt necessary to limit early thermal cracking of concrete in pile cap then minimum reinforcement on sides and top of pile cap should be provided based on method of calculation shown in Chapter 2.

Step 26 Assessment of crack width in flexure Normally the calculations in Step 24 will deem to satisfy the crock width limitations of BS8110: Part 1: 198s.tJ

If calculations are necessary to prove the limitations of crack width due to flexure in pile cap then methods shown in Chapter 3 should be followed.

Step 27 Connection of pile to pile cap From Step 17, 16mm HT Type 2 deformed bars arc used. From Table 3.29 of BS8110,

full anchorage bond length = 32; 32 x 16 = 512 mm

The bars from the pile will project 600 mm into pile cap. (Sec general recommendations for design of connections in Chapter 10.)


7.8 FIGURES FOR CHAPTER 7

l O

0 9

0 8

E 07

06

0-5

~ I""~

' '-.... ........ ~

......

!'"-r-.. k. 01 02 0 3 04 05 0 '6 07 08 0 ~ 10

e s

1000 8

6

4

l

. o-700 I

v I [// v v v ~ v /

./

/ /

I ,, 16 11

~-4 0 r

/. lO 1 0 8 .s:! ~ 6

-iiQ:) 4

l

1 lO 30 40 B,deg

7 Design of Piled Foundation

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