Wave Equation Analysis - Driven Piles.

The penetration resistance in blows/feet (or blows/inch) measured when the pile tip has been driven to the required depth can be used to calculate the ultimate bearing capacity and verify design.  Wave equation analyses can relate  penetration resistance to the static ultimate bearing capacity.

(1)  Computer program GRLWEAP.  A wave equation analysis is recommended, except for the simplest projects when  adequate experience and data already exist, for estimating the behavior of pile driving and confirming pile performance.  This analysis  may be accomplished using program GRLWEAP (Goble et al. 1988), Wave Equation Analysis of Pile Driving, licensed to WES.  Program GRLWEAP and user’s manual with applications are available to offices of the Corps of Engineers. GRLWEAP models the pile driving and soil system by a series of elements supported by linear elastic springs and dashpots with assumed  parameters, Figure 6-1.  Each dashpot and spring represent a pile or soil element.  Information required to use this program includes indentification of the hammer (or ram) and hammer cushion used, description of the pile, and soil input parameters.   Hammer selection is simplified by using the hammer data file that contains all the required information for numerous types of hammers.  A simple guide for selection of soil  input parameters to model the soil resistance force is provided as follows:

(a)  The soil resistance force consists of two components, one depends on pile displacement, and theother depends on pile velocity.  Pile displacement dependent resistance models static soil behavior, and it is assumed to increase linearly up to a  limiting deformation, which is the quake.  Deformation beyond the  quake requires no additional force.  The pile velocity  component models depend on soil damping charactertistics where the relationship between soil resistance and velocity is linear and the slope of such relationship is the damping constant.

Quake and damping constants are required for both skin friction and end-bearing components.  Table 6-2 gives recommended soil parameters, which should be altered depending on local experience.   The distribution of soil resistance between skin friction and end bearing, which depend on the pile and soil
bearing strata, is also required.  End-bearing piles may have all of the soil resistance in end bearing, while friction piles may have all of the soil resistance in skin friction.

(b)  A bearing-capacity graph is commonly determined to relate the  ultimate bearing capacity with the penetration resistance in blow/feet  (or blows/inch).  The penetration resistance measured at the  pile tip is compared with the bearing-capacity graph to determine how close it is to the ultimate bearing capacity.  The contractor  can then determine when the pile has been driven sufficiently to develop the required capacity.

(c)  Wave equation analysis also determines the stresses that develop  in the pile.  These stresses may be plotted versus the penetration  resistance or the ultimate pile capacity to assist the contractor  to optimize pile driving.  The driving force can be adjusted by the contractor to maintain pile tensile and compressive stresses within allowable limits.

(d)  GRLWEAP is a user friendly program and can provide results within a short time if the engineer is familiar with details of the pile driving operation.  The analysis should be performed by Government  personnel using clearly defined data provided by the contractor.

(2)  Analysis pr ior to pile installation.  A wave equation analysis should  be  performed prior to pile driving as a guide to select properly sized driving equipment and piles to ensure that the piles can be driven to final grade without exceeding the allowable  pile driving stresses.

(3) Analysis during pile installation.  Soil, pile, and driving equipment parameters used for design should be checked to closely  correspond  with actual values observed in the field during installation.    Sound judgment and experience are required to estimate the proper input parameters for wave equation analysis.

(a) Hammer efficiencies provided by the manufacturer may overestimate energy actually absorbed by the pile in the field and may lead to an overestimate of the bearing capacity. Significant error in estimating ahmmer efficiency is also possible for driving batter piles.  A bracket analysis is recommended for diesel hammers with variable  strokes.  Results of the PDA and ststic  with variable strokes. Results of the PDA and stat ic load tests described below and proper inspection can be used to make sure that design parameters are realistic and that the driven piles will have adequate capacity.

(b)  Results of wave equation analysis may not be applicable if soil freeze (setup) occurs.  Saturated sensitive clays and loose sands may lose strength during driving which can cause remolding and increasing pore water pressure. Densification of sands during driving contribute to a buildup of pore pressure.  Strength regain is increased with  time, after the soil freeze or setup.  Coral sands may have exceptionally  low penetration resistance during driving, but  a reduction  in pore pressure after driving and cementation that increases with time over a period of several weeks to months can contribute substantially to pile capacity.  Significant cementation may not occur in several weeks.

(c)  Penetration resistance is dense, final submerged sand, inorganic  silts or stiff, fissured, friable shale, or clay stone can dramatically increase during driving, apparently from dilation and reduced  pore water pressure. A “relaxation” (decrease) in penetration  resistance occurs with time after driving.  Driving equipment  and piles shall be selected with sufficient capacity to overcome driving resistance or driving periodically delayed to allow pore water pressures to increse.

(d) The pile shall be driven to a driving resistance that exceeds  the ultimate pile capacity determined from results of wave  equation analysis or penetration resistance when relaxation is not considered.  Driving stresses in the pile shall not exceed allowable stress limits.  Piles driven into soils with freeze
or relaxation effects should be restruck at a later time such as one or  more days after driving to measure a more realistic penetration resistance for design verification.

(e)  Analysis of the bearing capacity and performance of the pile  by wave equation analysis can be contested by the contractor  and resolved at the contractor’s expense through resubmittals performed and sealed by a registered engineer.  The resubmittal should include field verification using driving and load tests, and any other methods approved by the Government design engineer.

Table 6-2 Recommended Soil Parameters for Wave Equation.

Figure 6.1 Schematic of wave equation model.

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