5 - Piles

The University of Queensland

CIVL3210 – Geotechnical Engineering – Piled footings

Piled footings References Poulos and Davis; Tomlinson; AS2159 SAA Piling Code; BHP Steel Piling Booklet; http://sbe.napier.ac.uk/projects/piledesign

Extension of Funchai airport in Maderia. 3m diameter columns (80 000kN) are supported by eight 1.5m diameter bored piles up to 50 m long. (Ground Engineering, 31, 6, 1988)

Scope • • • • • •

Pile types and uses Axial load capacity o Settlement of piles Lateral capacity of piles o deflection of piles under lateral load Pile group effects Load testing o static o dynamic Piling code AS2159

Function •

• • •

Transmit structural loads through soil strata of low bearing capacity (and/or stiffness) to deeper soil or rock having high bearing capacity (and/or stiffness) Resist uplift forces. eg due to wind or wave loading Resist horizontal loads. eg wharfs, oil platforms Structures on reactive soils

© Dr Robert Day, The University of Queensland, 2009



Pile types (ref. Tomlinson, Simons and Menzies) •

Displacement piles - Driven: o Driven Large displacement - Timber, steel tube, concrete Small displacement - Steel H section o Screw pile o Jacked pile • Replacement pile - Drilled shaft: o Bored and cast in place o Cased - temporary or permanent o Uncased (with bentonite support) o Non-rotar - eg. Percussive, clamshell grab • Driven & cast in place. eg Franki, Western pedestal, Wests shell pile.

Behaviour of piles under Vertical load




Distribution of loads between shaft and end bearing At all stages of loading the total pile load = sum of shaft friction and end bearing components End bearing pile - Founded in hard strong layer. Large end bearing component, small shaft friction. Friction pile (floating pile) - No distinctly different layer at base of pile. (End bearing component and significant shaft friction).




Mobilisation of full shaft resistance at settlement = 0.5% shaft diameter (5 - 15 mm) Mobilisation of full base resistance (and hence ultimate capacity) at settlement = 10% of base diameter (about 120 mm) Typically if a structure can tolerate say 15mm settlement then full shaft resistance is mobilised but only about 50% of the base resistance.

Load Capacity of vertically loaded piles - SINGLE piles Three ways to estimate ultimate load capacity of a single pile • Static analysis • Dynamic analysis and testing • Test loading

Static analysis Pult = Ps + Pb Pult = ultimate load capacity of pile Ps = ultimate shaft resistance (or skin friction) of pile Pb = ultimate resistance of soil at pile base Shaft resistance Ps = A s .q s As is the surface area of shaft in contact with soil is the average skin friction resistance / unit area at full slip Base resistance (bearing capacity) Pb = Ab.qb = Ab.(Nc.c + Nq.p + ½.B.γ.Nγ) - Remember the bearing capacity formula? Ab is the gross area of the pile base qb is the ultimate bearing capacity (pressure) of the soil at the base of the pile Total stress analysis - ie φ = 0 • immediate undrained capacity • rapid loading • short term capacity For piles in clay the undrained capacity is usually less than the drained capacity except for HIGHLY overconsolidated material. The undrained capacity is usually used for design. Base: Nc = 9 for deep footings (L/d > 4) - use smaller value for short piles Nq = 1, Nγ = 0, p = γL Pb = Ab (Nc.cu + p)




Shaft: The skin friction usually varies with depth, z, due to increasing strength. qs(z) = α . cu(z) α depends on: soil type • type of pile • cu of soil - α decreases with increasing cu • time • nature of soil overlying the clay Great variability of α for piles in stiff clay - fissures In absence of better data use chart on handout, textbooks or AS2159 L

1 q s = ∫ α . c u dz L0

We have, Pcapacity + W = Ab.Nc.cu + Ab.p + As. q s , W is the weight of pile, W is approx = Ab.p Pcapacity is the maximum net load that can be put on the top of the pile. so, Pcapacity = Ab.Nc.cu + As. q s , Effective stress analysis - ie φ' ≠ 0, c' ≠ 0 • • •

drained analysis slow loading long term analysis

Base: Nc,c' & ½.B.γ.Nγ terms are small compared to the other term (c' and B are small). Usually neglect these. Hence, qb = Nq.p, where p = σ'vb is the effective vertical stress at the base of the pile but in sands this leads to and overestimate in the capacity of long piles. The maximum value of σ'vb is therefore limited to the value of the effective vertical stress (σ'v) at the critical depth zl ( see figure). The limiting depth is about 6d in loose sand and 15d in dense sand (where d is the pile diameter).




Shaft: L 1 q s = ∫ K σ′v tan δ dz L0 where, δ is the friction angle between the pile and the soil K is the earth pressure coefficient (ratio of horizontal stress / vertical stress) Kp, Ko, or Ka ??? but again in sands this leads to an overestimate in the capacity of long piles. The maximum value of σ'v is therefore limited to the value at the critical depth zl ( see figure). so, Pult = Ab.Nq.σ'vb + As. q s Beta method (Burland; Poulos and Davis) qs = Κ . σ'v tan δ qs = β . σ'v In stiff clay it appears that β is fairly constant (0.24 - 0.29 for values of φ' between 20 and 30)

Design - common practice, Factors of safety Working load method: • Overall factor of safety about 2 to 2.5 • Separate factors on shaft and base resistance (shaft resistance factor 1.0 to 1.5, base factor usually about 3.0)




ie. the maximum working load capacity, Pdesign, of a pile is the lesser of: •

Pdesign + W ≤ Pult / (2.0 to 2.5) = (Ps+Pb) / (2 to 2.5)

•

Pdesign + W ≤ Ps / (1.0 to 1.5) + Pb / 3.0

where Ps is the shaft resistance capacity and Pb is the base resistance capacity

Limit state method - AS2159: Strength and serviceability limit states must be checked For strength - Ultimate design pile capacity, P* = φ Pultimate Need to look at both the Geotechnical and Structural capacity. ie: • Design geotechnical capacity, Pg* = φg.Pult = φg (Ps + Pb) • Design structural capacity, Ps* = φs.Nu • The design pile capacity P* is therefore the smaller of these two values • φs is usually given in the structural design standard • φg is given in the piling standard (about 0.45 to 0.6) As usual in the limit state methods P* ≥ S* (S* is the ultimate load which includes the weight) For serviceability need to check settlement (of deflection) against tolerance of structure.

Negative skin friction In general friction between pile shaft and the ground tends to increase the load carrying capacity of piles. In special circumstances - eg. piles driven through a soft consolidating soil - a drag force on the pile shaft will act downwards adding to total pile load. Such a force is known as negative skin friction or down drag. Negative skin friction is a SERVICEABILITY load only. It cannot cause ultimate failure. Downward forces: • P - load on top of pile • W - weight of pile • Psd - Negative skin friction Resistance forces: • Pb - Base resistance • Psr - upwards skin resistance How this force is considered depends on the design methodology:




Working stress design: P + W + Psd ≤ (Psr + Pb) / 2.5 P + W ≤ (Psr + Pb - Psd ) / 2.5 P + W ≤ Psr / 1.5 + Pb / 3.0 - Psd Limit state design: Strength P* = φg (Psr + Pb) S* does NOT INCLUDE the load Psd because negative skin friction is a serviceability load, and does not occur at the strength limit state. Serviceability Psd must be included as an adverse load when calculating settlement.

Settlement of vertically loaded piles Settlement is mostly due to deformation in shear of surrounding soil (not volume change) • Clay soils - most settlement is immediate (undrained) Typically for L/d = 25 immediate settlement is about 75%, consolidation settlement is about 25% • Sandy soils - final settlement occurs almost immediately on application of load. Estimates of settlement • Pile load test on prototype pile - Most accurate • Using elastic theory (Poulos and Davis) or empirical equations • Back analysis of load tests to give elastic parameters for above • From dynamic stress wave analysis • Advanced numerical analysis such as finite or boundary element analysis. It is very difficult to get sufficient data of appropriate quality to obtain worthwhile results. Elastic theory Use published solutions to the elastic problem. The pile head settlement, s, is given by: a) Friction pile in deep uniform layer ⎛ P ⎞ ⎟⎟I s = ⎜⎜ ⎝ L.E s ⎠ Ep K= RA ES

; where I is a function of L/d and K. ; is called the relative stiffness or pile stiffness factor.




Pile displacement factors 100.0

P

L

Settlement Influence Factor, I

d

10.0

200 100 70 50 30 20 15 10 7 5

1.0

3

0.1 10

100

1000

Pile stiffness factor, K


10000



I is an influence factor (from tables or chart) P is the load on the pile L is the pile embedded length Es is the Young's modulus of the soil Ep is the Young's modulus of the pile RA is the area ratio of the pile = area of section / gross pile area (eg for a solid pile RA = 1) b) End bearing pile on rigid stratum ⎛ P.L ⎞ ⎟M s=⎜ ⎜ E .A ⎟ R ⎝ p p⎠

Ap is the cross sectional area of the pile MR is the movement ratio (from tables) The term in brackets is the axial shortening of a free standing column in compression. MR is the interaction effect of the pile and the soil It is not simple to determine a suitable value of the soil modulus Es (table in code gives estimates for various types of soil which may be used for preliminary calculations). •

•

Triaxial values are not reliable for pile settlement o sample disturbance o loading conditions o small strain stiffness not measured in triaxial test Back-calculate Es from test pile results for reliable calculations

Pile groups Pile group effects Groups of piles typically spaced at 2d to 4d (d = diameter of pile) • Connected by a rigid pile cap - uniform settlement for all piles • All piles in the group do not necessarily carry equal load (edge piles carry more load) • The ultimate load of a group is less than the total of the individual piles. The group efficiency factor is typically about 0.7 • Settlement of group > settlement of single pile with same average load average group settlement • Rs = settlement of a single pile with the same average load per pile as in the group

is the settlement ratio. Load capacity of pile groups The ultimate capacity of a group Pu is the lesser of:




•

Pu = n . Pu1 Where n is the no. of piles in the group. Pu1 is the ultimate capacity of a single pile in the group.

•

Pu = the ultimate capacity of an equivalent block, containing the piles and the soil between the piles. The capacity of the block is calculated using the previous theory for single piles and treating the block as if it were a large short pile.

Settlement of pile groups Interaction between piles increases the deflection of a pile group.

With a rigid pile cap all piles settle by the same amount. Sg = s Rs where, Sg is the settlement of the pile group s is the settlement of a single pile at the same average load as a pile in the group Rs is the settlement ratio for the group - obtained from tables based on elastic solutions.

Laterally loaded piles Typical situations where lateral load is significant: • Marine Structures - ship impact, berthing loads, wave action • Bridge piers - water flow, traffic load, curved bridges • Transmission line tower foundations • Pile supported retaining walls • Structures in seismic areas Design requires: • Adequate factor of safety against ultimate failure • Adequate deflection at working load Horizontal load capacity • Statics of problem are complex o Soil resistance force depends on interaction of soil and pile movement o The load deflection relationship is nonlinear • Design methods are based on o semi-theoretical (Broms) o empirical (pressuremeter) o p-y method o finite element or boundary element analysis - (quality of data) • Room for improvement and more research • Most exact method method is well planned and executed in-situ load test

The ultimate lateral load capacity Hu depends on: • Soil type - failure may occur by failure of the ground. Short stubby piles. • Pile type - failure fails in bending. Long slender piles.



•


Boundary conditions at pile head - Restrained or free to rotate. Capacity of a pile with restrained pile head > pile with free head.

Method of Broms • assumed pressure distributions and magnitudes of earth pressure at failure. • considered short / long and free / restrained cases. • derived solutions from simple static equilibrium. • produced dimensionless design charts for ultimate lateral resistance (Theory and eqns presented in Poulos and Davis) • must calculate capacity using BOTH short and long assumptions and choose the lesser. This will also indicate the mode of failure. • for cohesionless soil the value ok Kp used in the charts is the RANKINE value. p-y method • models the pile as a beam (vertical) supported by springs (horizontal) • spring constant is obtained from the coefficient of subgrade reaction • load deflection curve specified for each spring (p-y curve) - nonlinear • need to limit spring force to a maximum value (three times the Rankine value?) Ultimate lateral load capacity of pile groups Lesser of : • n x the ultimate lateral resistance of a single pile • ultimate lateral capacity of a block containing piles and soil between them, but with the "dead zone" near the top of the pile equal to the lesser of 1.5 d and 0.1 L Deflection and rotation of laterally loaded piles: Use published solutions based on elastic calculations. These are usually in the nondimensional form. Free headed pile: ⎛ M ⎞ ⎛ H ⎞ ⎟I ⎟⎟ I ρH + ⎜⎜ translation, ρ = ⎜⎜ 2 ⎟ ρM E . L E . L s ⎠ ⎝ ⎝ s ⎠

⎛ H ⎞ ⎛ M ⎞ ⎟ I + ⎜⎜ ⎟I rotation, θ = ⎜⎜ 2 ⎟ θH 3 ⎟ θM ⎝ E s .L ⎠ ⎝ E s .L ⎠ fixed headed pile – no rotation, translation only: ⎛ H ⎞ ⎟⎟ I ρF ρ = ⎜⎜ ⎝ E s .L ⎠

Where the terms, IρH, IθM, etc are influence factors, determined from charts. They are a function of the flexibility factor: E p .I pile KR = E s .L4 When using published results and tables ensure the notation, meaning and definitions of all terms is clearly understood.




Pile testing and test loading Static test loading • • • • • • •

Expensive procedure. Load pile and measure settlement. o pre-contract: to confirm design parameters. o during construction: to check quality control and design. Usually 1 to 3 weeks between construction and testing (to allow for pore pore pressure dissipation). Usually load to about 2 times the "allowable load". Sometimes load to failure. Refer to ASTM D-1143 1974 and also AS2159 for procedures. Usually apply a slow maintained load. European method is constant rate of penetration (0.5mm / minute).

Methods of load application • Load with kentledge • Jack against kentledge • Jack against tension piles

Pile test arrangement for 1.5m diameter pile (Ground Engineering, 31, 6, 1988)

Dynamic testing and analysis • •

Analysis during driving – Hiley formula and stress wave analysis Testing after installation (driven, cast in place) – Stress wave analysis

Pile driving formula – Hiley formula • traditional method of assessing load capacity of driven piles • pile driven until acceptably small displacement (set) per hammer blow is achieved



•

•


the required set is calculated from considerations of the dynamics of bodies under impact. ie Newtonian impact dynamics. The application of this theory is fundamentally invalid !!. Two invalid assumptions are made: o Dynamic resistance of pile to driving can be estimated from the kinetic energy of the hammer at the point of impact and distance penetrated under the hammer blow o Ultimate static resistance of soil is equal to the dynamic resistance of pile to driving However formula have been developed and used on this basis.

Hiley formula: n.W.h Pu = c s+ 2 where, Pu is the average resistance to penetration = ultimate static pile load n is a hammer efficiency factor - depends on mass on pile and hammer and coefficient of restitution W is the weight of the hammer h is the hammer drop distance s is the set per hammer blow c is an energy loss term (compression of packing, pile and ground)

Wave equation analysis

Wave equation analysis is better and more widely used - test after installation

Dynamic Pile Load Testing (Chapman and Seidel, in Williams, 1989) • • • • •

• • •

Dynamic pile load testing commenced in Australia in the early 1980's in Australia (in the early 1970's worldwide). Dynamic pile load testing involves recording the force (via strain gauges) and velocity (via accelerometers) in the top of a pile, as it is subjected to one or more hammer blows. The measured responses are analysed for pile integrity and the estimation of pile load capacity. Dynamic pile load testing is rapid and cheap. The main criticism of the use of dynamic pile load testing to estimate pile load capacity is that the displacement of the pile under a hammer blow is very small. This may restrict the mobilisation of shaft resistance, but will almost certainly severely limit the mobilisation of end bearing. In uniform clays, in which the majority of the pile load capacity will come from the shaft, this limitation is of little importance. In sands or end bearing situations, the end bearing capacity will be underestimated by dynamic pile load testing. Dynamic pile load capacities are far more reliable than the results of simplistic Hiley pile driving formula, but should be calibrated against static pile load testing taken to failure.




Wave behaviour in piles • A hammer blow sends a compressive wave down the pile. • A free end (floating pile) or crack in the pile will reflect a tensile wave • A crack will transmit a compressive wave • A rigid base of a pile will reflect a compressive wave • An increase in pile section will reflect a compressive wave and transmit a tensile wave • Coinciding waves in the pile superimpose. • The compressive wave delivered by a hammer blow causes compressive stress and velocity in the pile to rise together. As the wave meets shaft resistance a compressive wave will be reflected and a tensile wave transmitted, raising the force and lowering the velocity recorded at the top of the pile. The separation of the stress and velocity curves is a measure of the shaft resistance. • When the wave reaches the toe, it will • Almost totally reflect as a tensile wave if there is essentially no end bearing. This can have significant implications for concrete piles with limited tensile capacity. Prestress and/or limited hammer weight and drop will accommodate this. • Almost totally reflect as a compressive wave if the base is essentially rigid. This can have significant implications for the integrity of the pile where the reflected compressive wave and a subsequent compressive wave meet. • In most cases, the behaviour is between these two extremes. Analysis of data • Shaft resistance – separation of stress and velocity curves. • Soil shaft resistance can only produce compressive reflection. • Any tensile reflection arriving at the gauge location (near the top of the pile) is due to: o Reflection from base o Reflection from change in cross section of the pile o Damage The first two are expected – the time of arrival of the tensile wave is known. If the tensile wave does not correspond to the first two than damage is likely. • By comparing the size of the tensile reflection with that of the incident compressive wave, corrected for the shaft resistance above the point, a β or integrity factor can be calculated.

β

PILE CONDITION

1.0

Undamaged

0.8-1.0

Slight damage

0.6-0.8

Severe damage

< 0.6

Pile broken

Wave equation



•

•

• • •


The basic differential equation governing the propagation of a wave in a pile is given by Stress-Wave Equation: ∂ 2u 1 ∂ 2u = ∂x 2 c 2 ∂t 2 where u is the pile displacement x is the longitudinal co-ordinate c is the wave velocity t is time The solution to the stress-wave equation is u(x, t) = f(x - c.t) + g (x + c.t) The two functions f and g correspond to two stress waves propagating at the same velocity in opposite directions. The pile and hammer are approximated by lumped masses connected by elastic linear springs, with dashpots and springs representing the soil resistance. Smith (1960) Using this model Goble developed the Case Method of calculating pile capacity and the CAPWAP model for matching force and velocity responses. The Case Method Capacity (called the RSP) is a closed-form solution of the 1D wave equation Assumes: rigid plastic soil model, all damping occurs at the toe and uniform pile section.

CAPWAP: (a refinement of the RSP closed form solution) • The CAse Pile Wave Analysis Program (CAPWAP) separates the pile into a series of discrete elements, usually 1m long, allowing piles of non-constant impedance to be analysed. • A soil model is attached to each or every second pile (shaft) element and to the pile toe. In its simplest form it comprises a viscous damper to model dynamic resistance and an elastic spring with a slip element to model elasto-plastic static resistance. • A distribution of shaft resistance and a toe resistance and damping factors are first assumed. • The program applies the measured pile velocity to the pile top, and calculates the stress at the measuring point. This is compared with the measured stress. The assumed parameters are then varied until the computed force is in agreement with the measured values. • Although the match obtained is not unique, independent CAPWAP analyses on particular data show very good agreement on predicted total capacity, and good agreement on predicted distributions.


5 - Piles

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