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Pile Dynamics This document downloaded from vulcanhammer.net vulcanhammer.info Chet Aero Marine Don’t forget to visit our companion site http://www.vulcanhammer.org Use subject to the terms and conditions of the respective websites. ENCEENCE 46104610 FoundationFoundation AnalysisAnalysis andand DesignDesign Lecture 16 Pile Dynamics OverviewOverview ofof PilePile DynamicsDynamics z Background and the Dynamic Formulae z Development of the Wave Equation z Application of the Wave Equation to Piles z Use of the Wave Equation in field monitoring z Statnamic Testing PilePile BlowBlow CountsCounts DynamicDynamic FormulaeFormulae • The original method of estimating the relationship between the blow count of the hammer and the "capacity" of the pile • Use Newtonian impact mechanics EngineeringEngineering NewsNews FormulaFormula 2 E z Variables r z E = Rated striking Pa= r s+ 0.1 energy of the hammer, ft-kips z Developed by z s = set of the hammer A.M. Wellington in per blow, in. 1888 z P = allowable pile z The most common a capacity, kips dynamic formula z Assumes a factor of safety of 6 OtherOther DynamicDynamic FormulaeFormulae (after(after Parola,Parola, 1970)1970) WeaknessesWeaknesses ofof DynamicDynamic FormulaeFormulae z Does not take into consideration the elasticity of the pile, which is distributed with the mass z No really accurate model of the cushion and cap system between the hammer and the pile z Newtonian impact mechanics not applicable since the pile is in constant contact with the soil z No ability to estimate or calculate tensile stresses in the pile The Wave Equation z When applied to piling, must z Variables be expanded to include z u = displacement, m dampening and spring of shaft resistance z x = distance along the length of the rod, m z Closed form solution possible z t = time, seconds but limited in application z Hyperbolic, second order differential z Solved numerically for real piling problems equation SemiSemi--InfiniteInfinite PilePile TheoryTheory • From this, • Assumes pile: o Has no resistance of any kind along pile shaft • This relates pile particle o Starts at x = 0 and goes to velocity to pile infinity displacement o Has no reflections back to the pile head • Define pile impedance: • For semi-infinite piles, ModelingModeling thethe PilePile HammerHammer • With semi-infinite pile theory, pile is modeled as a dashpot • Ram and pile top motion solved using methods from dynamics and vibrations • For cushionless ram: ClosedClosed FormForm SolutionSolution FiniteFinite UndampedUndamped PilePile • Simple hammer-pile-soil KHammer Cushion system mPile Cap • We will use this to analyze the effect of the variation of the pile toe • Pile toe spring stiffness can vary from zero (free end) to infinite (fixed end) and an K Pile Toe Spring p intermediate condition Pile Period: FixedFixed EndEnd ResultsResults IntermediateIntermediate CaseCase ResultsResults FreeFree EndEnd ResultsResults NumericalNumerical SolutionsSolutions z Subsequent z First developed at Solutions Raymond z TTI (Texas Concrete Pile by Transportation E.A.L. Smith (1960) Institute) – late 1960's z Very similar to Smith's z Solution was first solution done manually, z GRL/Case – 1970's then computers and 1980's were involved z Added adequate modelling of diesel z One of the first hammers applications of z Added convenience features computers to civil z TNO engineering NecessityNecessity forfor NumericalNumerical SolutionSolution • Non-uniformity of the pile cross • Existence of dampening, both at the section along the length of the toe, along the shaft, and in all of the pile, and in some cases the pile physical components of the system. In theory, inclusion of distributed spring changes materials. constant and dampening along the • Slack conditions in the pile. These shaft could be simulated using the are created by splices in the pile Telegrapher’s wave equation, but and also pile defects. other factors make this impractical • With diesel hammers, the force- also. time characteristics during • Non-linear force-displacements along the toe and shaft, and in the cushion combustion are difficult to simulate material. Exceeding the “elastic limit” in closed form. (It actually took of the soil is in fact one of the central around fifteen years, until the first objects of pile driving. version of WEAP was released, to • Non-uniformity of soils along the pile do a proper job numerically.) shaft, both in type of soil and in the • Unusual driving conditions, such as intensity of the resistance. driving from the bottom of the pile • Inextensibililty of many of the interfaces or use of a long follower between of the system, including all interfaces of the hammer and the pile head. the hammer-cushion-pile system and the pile toe itself. WaveWave EquationEquation forfor PilesPiles inin PracticalPractical SolutionSolution ““BearingBearing GraphGraph”” ResultResult ofof WaveWave EquationEquation AllowableAllowable AxialAxial StressesStresses inin DrivenDriven PilesPiles TAMWAVE • Originally developed in 2005; • Uses method presented earlier recently extensively revised to estimate static capacity • With simple soil and pile input, • Uses ALP method for axial capable of the following for load-deflection analysis single piles: • Uses CLM 2 method for lateral – Axial load-deflection analysis load-deflection analysis – Lateral load-deflection analysis • Hammer database (in ascending – Wave Equation Drivability energy order) and initial Analysis hammer selection estimate available • Includes estimate of soil set-up in clays 16” Concrete Pile Example 16” Concrete Pile Example 16” Concrete Pile Example 900 3 800 2.5 700 600 2 k p 500 1.5 SRD, ki SRD, 400 Stress, 300 1 200 0.5 100 0 0 0 20 40 60 80 100 120 140 160 180 200 Blows per Foot of Penetration Soil Resistance, kips Maximum Compressive Stress, ksi Maximum Tensile Stress, ksi BasicBasic StepsSteps inin WaveWave EquationEquation AnalysisAnalysis • Gather information • Construct Analysis o Run static capacity analysis on o Hammer type, ram weight, pile as pile driving resistance cushion data, etc. o Apply setup factor (if necessary) o Suggested trial energy shown on static capacity in chart below (included in o Input data for hammer, pile and program) soil resistance profile into wave equation analysis o Pile data, including length, material, etc. • Run program o Soil data; layers, soil types, o Run wave equation analysis for properties different soil resistances (factoring original static analysis) and (for some wave equation programs) different depths of driving • Analyse Results o Blow counts, tension and compression stresses, driving time SoilSoil ResistanceResistance toto DrivingDriving PilePile SetupSetup inin ClaysClays soil setup factor: the failure load from a static load test divided by the end-of-drive wave equation capacity PilePile ResistanceResistance ExampleExample DynamicDynamic PilePile TestingTesting strain gage FF(t)(t) vv(t)(t) accelerometer Load is measured by Load is applied strain transducers by impacting ram Motion is measured by accelerometers TheThe PilePile DrivingDriving AnalyserAnalyser z For Dynamic Pile z For Dynamic Load Monitoring: Test: z Stresses z Bearing Capacity z Hammer Performance at time of testing z Pile Integrity z Separating Dynamic from Total (Static + Dynamic) Soil Resistance z Case Method z CAPWAP-C DynamicDynamic PilePile TestingTesting Isolation of the static pile resistance from the total pile response is the key challenge in the interpretation of dynamic pile testing methods. 1. CASE METHOD Simple closed-form solution which can be computed in real time on site, but needs a damping factor to be estimated. 2. WAVE EQUATION ANALYSIS The mechanics of the pile and soil behavior is modelled. The model is adjusted to match the measured and computed responses. CAPWAPCAPWAP ModelingModeling ofof PilePile ResponseResponse andand CapacityCapacity CaseCase MethodMethod forfor PilePile AnalysisAnalysis • Simple Method for Estimating Pile Capacity from Dynamic Results • Assumptions: o The pile resistance is concentrated at the pile toe, as was the case with the closed form solutions above. o The static toe resistance is completely plastic, as opposed to the purely elastic resistance modelled above. (Both the wave equation numerical analysis and CAPWAP assume an elasto-plastic model for the static component of the resistance. CaseCase MethodMethod ExampleExample • Find • Given o Case Method ultimate o Pile with impedance of 381 kN- capacity for the RSP and RMX sec/m methods. o Force-time history as shown at the left • FT1 = 1486 kN • FT2 = 819 kN • VT1 = 3.93 m/sec (Z·VT1 = (381)(3.93) = 1497.33 kN) • VT2 = 1.07 m/sec (Z·VT2 = (381)(1.07) = 407.67 kN) NotesNotes AboutAbout CaseCase MethodMethod ExampleExample RSPRSP SolutionSolution • There are two curves, both at the • Case Method results can be pile top. The first “F” curve (solid interpreted in several ways. line) is the force-time history of the The method shown in the impact blow. The “V” curve (dashed line) is the velocity-time graph is the RSP method, best history. Generally speaking, the used for piles with low velocity history is multiplied by the displacements and high shaft pile impedance, as is the case resistances. The t1 for the RSP here. This is not only to make the method is the first peak point in two quantities scale properly on the force-time curve; the time one graph; as noted earlier, if the t2 is time 2L/c after that. The pile were semi-infinite, the two time t1 is not the same as the curves would be identical. This is in time t = 0 in the closed form fact the case in the early portion of the impact; neither pile movement solution, or the very beginning relative to the soil nor reflections of impact. from the shaft are a factor until • A Case damping constant J = later. 0.4 is assumed. CaseCase MethodMethod ExampleExample RMXRMX SolutionSolution • The time t1 is now the peak initial force plus a time shift, generally 30 msec with the RMX method (Fellenius (2009).) The time t2 is still t1 + 2L/c. This time shift is to account for the delay caused by the elasticity of the soil.
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