PERFORMANCE OF OPEN-ENDED PIPE PILES IN CRETACEOUS SOILS Sanjeev Malhotra, P.E., G.E., M.ASCE Supervising Geotechnical Engineer, Parsons Brinckerhoff Quade & Douglas, One Penn Plaza, New York 10119, USA, Tel: (212) 465-5231, E-mail: [email protected]ABSTRACT This paper presents the results of a pile installation monitoring and performance assessment program for pile foundations supporting 14 piers and 2 abutments of the 1700-ft long bridge crossing over a river in Baltimore, Maryland. Dynamic measurements were conducted during installation and restrike of 16 test piles, one at each support location. The foundation piles were 30-inch diameter, 0.75 inch thick pipe piles at the piers and 24-inch diameter, 0.5 inch thick at the abutments. The piles at the piers were approximately 100 ft long and were designed to carry 260 kips service load with a factor of safety of 2.25. The piles were driven open ended into a variable site stratigraphy containing recent deposits of organic clayey silts near the mud line followed by loose to medium dense sand, with some silt, and then by soil deposits from the Cretaceous period consisting primarily of dense to very dense, poorly- to well graded sands and gravels and cobbles, with occasional seams of very hard to very stiff, low to moderate plasticity silts and clays. This paper presents the approach taken to evaluate the driven index piles and to develop criteria for driving production piles, and provides the Engineer with some data on pile driveability in Cretaceous soils in the Baltimore area, soil set-up effect, and an estimate of pile capacity. INTRODUCTION The typical approach to pile foundation design and construction should include an indicator pile program with dynamic measurements and a static load test program. However, very often paucity of funds and schedule constraints cause an owner to not perform conventional static load testing which can take $25,000 to $100,000 and several weeks per test. This paper examines an alternate (though not equivalent) truncated approach to foundation assessment and presents a case history where this approach was implemented. Dynamic measurements were conducted during pile installation for the 14 piers and two abutments of the new 1700-ft long bridge over a river in Baltimore, Maryland. Strain transducers and accelerometers were attached to the pile top during initial driving and restrike of 16 pipe piles. The foundation piles consisted of 30-inch outside diameter, 0.75-inch thick pipe piles at the piers and 24-inch outside diameter, 0.5 inch thick at the abutments. A total of 230 piles were installed. The piles were driven open ended at a site with variable GSP 158 Contemporary Issues in Deep Foundations Copyright ASCE 2007 Geo-Denver 2007: New Peaks in Geotechnics Contemporary Issues In Deep Foundations Downloaded from ascelibrary.org by MISSOURI, UNIV OF/COLUMBIA on 04/12/13. Copyright ASCE. For personal use only; all rights reserved.
Transcript
PERFORMANCE OF OPEN-ENDED PIPE PILES IN CRETACEOUS SOILS
Sanjeev Malhotra, P.E., G.E., M.ASCE
Supervising Geotechnical Engineer, Parsons Brinckerhoff Quade & Douglas, One PennPlaza, New York 10119, USA, Tel: (212) 465-5231, E-mail: [email protected]
ABSTRACT
This paper presents the results of a pile installation monitoring and performance assessmentprogram for pile foundations supporting 14 piers and 2 abutments of the 1700-ft long bridgecrossing over a river in Baltimore, Maryland. Dynamic measurements were conductedduring installation and restrike of 16 test piles, one at each support location. The foundationpiles were 30-inch diameter, 0.75 inch thick pipe piles at the piers and 24-inch diameter, 0.5inch thick at the abutments. The piles at the piers were approximately 100 ft long and weredesigned to carry 260 kips service load with a factor of safety of 2.25. The piles were drivenopen ended into a variable site stratigraphy containing recent deposits of organic clayey siltsnear the mud line followed by loose to medium dense sand, with some silt, and then by soildeposits from the Cretaceous period consisting primarily of dense to very dense, poorly- towell graded sands and gravels and cobbles, with occasional seams of very hard to very stiff,low to moderate plasticity silts and clays. This paper presents the approach taken to evaluatethe driven index piles and to develop criteria for driving production piles, and provides theEngineer with some data on pile driveability in Cretaceous soils in the Baltimore area, soilset-up effect, and an estimate of pile capacity.
INTRODUCTION
The typical approach to pile foundation design and construction should include an indicatorpile program with dynamic measurements and a static load test program. However, veryoften paucity of funds and schedule constraints cause an owner to not perform conventionalstatic load testing which can take $25,000 to $100,000 and several weeks per test. This paperexamines an alternate (though not equivalent) truncated approach to foundation assessmentand presents a case history where this approach was implemented.
Dynamic measurements were conducted during pile installation for the 14 piers and twoabutments of the new 1700-ft long bridge over a river in Baltimore, Maryland. Straintransducers and accelerometers were attached to the pile top during initial driving and restrikeof 16 pipe piles. The foundation piles consisted of 30-inch outside diameter, 0.75-inch thickpipe piles at the piers and 24-inch outside diameter, 0.5 inch thick at the abutments. A totalof 230 piles were installed. The piles were driven open ended at a site with variable
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subsurface conditions. A site specific subsurface investigation including a soil boringprogram and a soil testing program in the laboratory was implemented during the preliminarydesign of the bridge foundations. The soil boring program consisted of a total 23 hollow-stem auger borings designated as B-1 through B-23, ranging in depth from 63 ft to 130 ft, andspaced approximately 70 to 120 ft. The locations of these borings are shown in Figure 1.The laboratory testing program included soil classification and index property tests, gradationanalyses, triaxial strength tests and compressibility tests.
The approach taken to assess the foundation performance included 1) a pre-field waveequation driveability analyses, 2) field pile driving measurements, 3) post-field Case PileWave Equation Analyses (CAPWAP), and, 4) revised wave equation analyses based on fieldand CAPWAP data. The following sections describe in greater detail each of the steps takento assess foundation performance and the results obtained.
GEOLOGY AND SUBSURFACE CONDITIONS
The bridge site lies within the Coastal Plain Physiographic Province. The Coastal PlainProvince is characterized by a gently rolling topography with shallow, open valleys of gravel,sand, and clay deposits of the Pleistocene terrace plains, over older Cretaceous deposits.Cretaceous deposits of coastal eastern North America underlie broad areas of the continentalmargin as eastward tilted layers of gravel, sand, silt, and clay, which overlap rocks of theeastern Piedmont. Figure 2 presents a generalized subsurface profile for the bridge alignmentbased on the data obtained from the borings drilled for this investigation. The soil boringsindicate that the project site is underlain by four principal soil strata.
Stratum 1 consists of fill material composed primarily of brown to gray, loose to mediumdense, coarse to fine sand, with some silt and clay, and trace of gravel.
Stratum 2, which covers the entire project area, consists of recent deposits of low to highplasticity, organic clayey silts. This stratum is highly compressible. The thickness of thisstratum varies along the bridge alignment from approximately 18 ft to 66 ft between PierNos. 2 and 7.
Stratum 3 consists of Pleistocene era deposits of medium dense, poorly to well graded sand,with trace to some silt, and occasional beddings of poorly- to well-graded gravels and lowplasticity silts. The thickness of this stratum varies along the bridge alignment as well aslaterally and ranges from 26 to 43 ft.
Stratum 4 represents soil deposits from the Cretaceous period and consists primarily ofdense to very dense, poorly to well graded sands and gravels, with trace to some silt andclayey silt. It also contains zones of very stiff, low to moderate plasticity silts and clays.Fairly thick zones (>25 ft) of very stiff clay and silts were encountered between Piers 9 and12. The N-values for this stratum are generally greater than 50 blows per foot (bpf). Theelevation of the top of this stratum varies both longitudinally and laterally, and is deepest atthe location of the existing river channel.
Two groundwater observation wells installed near the abutments indicated groundwaterlevels between El. +3.35 and +3.75 with reference to the City datum. The mean high waterlevel in the river is El. +1.4 ft
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Figure 1: Bridge Layout and Locations of Borings
Figure 2: Generalized Subsurface Profile
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DESIGN SOIL PARAMETERS
A summary of the design parameters recommended for the four soil strata described aboveare presented in Table 1.
*ratio of undrained shear strength to the effective overburden stress
RIVERBED SCOUR
A scour study for the river at the location of the bridge indicated scour depths below existingmudline in the main channel (Piers 3 through 7) as deep as 32 ft and 37 ft for the 100-year and500-year floods, respectively. Scour depths of about 14 ft and 18.5 ft are estimated for the leftoverbank (Piers 1 and 2) and, 11 ft and 15 ft are estimated for the right overbank (Piers 9through 14) for the 100-year and 500-year floods, respectively. Scour is not expected to occurat the abutments. The 500 year scour level is shown on Figure 2. The significance of thescour study is that the lateral and axial pile design would have to account for loss of soilsupport from scour. However, given the low shear strength of Stratum 1 soils, the loss of soilsupport has relatively minor impact on foundation design.
AXIAL PILE CAPACITY ANALYSES
For the piers, the pile lengths were estimated for a service level load of 260 kips with a factorof safety of 2.25 based on a post-scour soil profile. The static pile capacity calculations wereperformed using the conventional procedures outlined in NAVFAC DM 7.02 and API-RP2Aguidelines which recommend limiting values of skin friction and end resistance. Since thepiles were expected to be driven open-ended, the tip capacity was simply taken as the capacityin end bearing of the annular rim of the open-ended pile. However, the total capacity isincreased by the lesser of the total internal shaft friction and the end bearing of the plug(Malhotra, 2000). Since there was uncertainty with regards to the occurrence of plugging, forpurposes of comparison, axial capacity of a fully plugged pile was also computed. The tipcapacity for plugged open-ended pipe piles is equal to that of a closed-ended pile of an equaldiameter. Graphical plots of predicted pile capacity versus pile penetration for three locationsare presented in Figures 3 a, b and c. It is evident from Figures 3a, b and c that the piles atPier 2 are unlikely to plug, the piles at Pier 7 might form a temporary plug near El. -87 ft, andthe piles at Pier 11 are quite likely to plug below El. -52 ft.
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Figure 3a: Measured and Predicted AxialPile Capacity for Test Pile at Pier 2.
Figure 3 b: Measured and Predicted AxialPile Capacity for Test Pile at Pier 7.
Figure 3 c: Measured and Predicted AxialPile Capacity for Test Pile at Pier 11.
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Figure 4: Approach for Performance Assessment of Piles
PILE INSTALLATION MONITORING APPROACH
The approach taken to assess the foundation performance is shown schematically in a ProcessFlow Diagram, Figure 4. It includes: 1) a preliminary wave equation driveability analyses, 2)field pile driving measurements, 3) post-field CAPWAP analyses, and, 4) revised wave equationanalyses based on field and CAPWAP data.
Preliminary Wave Equation Analyses: One-dimensional wave equation analyses have beenwidely used to evaluate pile driveability and hammer performance. The purpose of the waveequation analyses is to predict the behavior of the pile during installation for specific siteconditions and driving equipment. The study estimates driving resistances at various depthsduring driving (End of Initial Drive, EOID). Estimates of driving resistances for varioushammer efficiencies are also obtained. The results are used to evaluate the suitability of theselected hammer in driving the selected pile to the design depth and capacity.
Field Dynamic Measurements: Dynamic measurements provide data for assessing thehammer and cushion system, measure the energy transferred to the pile top, and can identifylocalized stresses that might occur in the pile during driving. Moreover, estimates of pilecapacity are obtained from these measurements. Information on set-up is also obtained bycomparing dynamic measurements from EOID with those obtained at the beginning of restriketests.
Post-field Assessment: These analyses use the actual measured transferred energy and stresswave in the pile. First the CAPWAP program integrates the measured acceleration, with time toobtain velocity. It then applies the velocity time history to a lumped mass model of the pile andcomputes a predicted force-time history from the change in momentum of each lumped mass.The CAPWAP user compares the measured and predicted force time histories. The match of thecomputed and measured force time histories is obtained by trial and error by changing the soilresistance and associated parameters. The soil model parameters that result in a reasonablematch between the computed and predicted force time histories are considered to be the mostappropriate values. The results of the CAPWAP analyses include the magnitude anddistribution along the pile of dynamic resistance forces and a best estimate of the pile capacity.
Revised Wave Equation Analyses: Wave Equation analyses calibrated to the actualperformance of the test piles are performed to develop pile driving criteria for production piles.
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PRELIMINARY PILE DRIVEABILITY STUDY
The computer program GRLWEAP developed by Goble, Rausche and Likens (GRL) (1997)was selected for the pre-field wave equation analyses performed to 1) estimate the feasibility ofdriving the piles to design depth with the selected hammer, 2) evaluate pile tensile andcompressive stresses and pile driving resistances for the selected range in hammer energies, and,3) develop preliminary driving criteria.
Since the piles were to be driven in the pre-scour soil profile, the design called for a minimumpenetration and a required ultimate capacity (Ru). For the piers Ru, taken as the sum of theservice load times 2.25 and the shaft resistance anticipated within the upper organic clays andsilts, was about 630 kips. Extensive parametric studies have been performed by others (Doveret al, 1982) to investigate the sensitivity of predicted capacity to variation in hammer efficiency,cushion stiffness, damping, quakes, and skin friction resistances. It has been found that sidedamping is a particularly important parameter. For this study, damping and quakesrecommended by GRLWEAP were used.
In clays the dynamic soil resistances encountered during driving differ from static soilresistances for several reasons. These include phenomenon such as sensitivity of cohesive soils,cyclic mobility, and Poisson’s effect. For those piles to be driven primarily in sandy soilprofiles, the dynamic soil resistance was taken as the same skin friction and end bearing as thosecomputed for static pile capacity using the method recommended by API (1993). For the pilesto be driven primarily in clay soil profiles the shaft resistance between the pile and the clayeysilts and clays of Stratum 2 and 3 was assumed to be 50 percent of the static shaft resistance.
A Delmag hammer Model D30-32 with a rated energy of 74 kip-ft was selected by theContractor for the preliminary pile driveability study. The hammer manufacturer recommends a4-inch thick Micarta/Aluminum hammer cushion and reports an efficiency of 0.8 for thehammer. These values were used in the analyses. The driveability study predicted the stressesand driving resistances that will be encountered during pile driving at Piers 2, 7 and 11 (Figures5a, 6a and 7a). The results of the wave equation analyses indicated that with the Delmag D30-32 hammer, the piles could be driven to the required design depth (80 to 90 ft below mudline)with a reasonable range of driving resistance (60 to 100 bpf). Moreover, the maximumpredicted driving stresses, both compressive and tensile, were below the allowable limit of (0.9fy) = 31.5 ksi (AASHTO, 1992). For the various piers, the driving resistance required toachieve the required ultimate capacity (Ru) for a range of strokes was developed from thepreliminary wave equation analyses for the Delmag D 30-32 hammer.
DYNAMIC TESTING DURING PILE DRIVING
Dynamic pile testing using the Pile Driving Analyzer (PDA) was performed on the 16 indexpiles. Instrumentation for dynamic measurement of the pile included two strain gages and twoaccelerometers mounted near the top of the pile and connected through a coaxial cable to thePDA equipment which includes a data recorder.
Initial Drive Monitoring: One pile at each of the 16 foundation locations was instrumentedand monitored during initial driving. These piles have a final penetration of about 80 to 90 ftbelow the mudline. The measurements for initial driving were conducted immediately after thepiles penetrated under their own weight by about 40 ft below the mudline and continuallythereafter until final penetration. Measured strains and accelerations were recorded on the PDA.Pile capacity obtained from dynamic measurements during initial driving are also presented inFigures 5b through 7b.
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(a) (b)Figure 5: Measured and Predicted Soil Resistances at Pier 2.
(a) (b)Figure 6: Measured and Predicted Soil Resistances at Pier 7.
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(a) (b)Figure 7: Measured and Predicted Soil Resistances at Pier 11.
Restrike Monitoring: Restrike on each pile was performed using the same drivingequipment, cushioning material and thickness, stroke and fuel setting as used at the end ofinitial driving. The hammer was warmed up before the restrike test. The warm-upprocedure consisted of a minimum of 20 blows of the hammer at full stroke on a pile that wasat least 25 ft from the pile to be restruck. The restrike test consisted of driving the pile adistance of 6 inches, or to a total of 50 blows, whichever occurred first. The number ofhammer blows was recorded for each 1 inch or less of pile penetration. With a fewexceptions the restrike test was conducted 5 days after initial driving. The ratio of PDAresistances from the beginning of restrike (BOR) to the end-of-initial driving (EOID) for eachtest pile is presented in Figure 8.
Figure 8: Estimates of Set-up (after 5-days)
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Soil setup is an increase in pile capacity resulting from increase in soil shear strength due todissipation of excess pore pressure generated during pile driving. Increases in drivingresistance were observed during restrike indicating that soil setup on the order of 5 percent toas much as 40 percent occurred at the site. The higher values of setup occurred at Piers 9, 11,12 and the South abutment. Borings at these locations indicated that the bearing stratum,Stratum 4, consisted of stiff to hard silty clay. Increases of 40 percent in capacity within ashort period of 5 days might not be entirely explained by dissipation of pore pressure in thisclayey material. It is conceivable that much of the increase in capacity could have occurredbecause of plug formation. Any setup that occurred in the upper cohesive soils could not becounted upon since these soils were above the design scour level and would be eroded in thefuture.
FORMATION OF SOIL PLUG
Sometimes, open-ended pipe piles get plugged during driving. Plugging occurs mainly dueto the mobilization of friction between the soil core and the internal walls of the pile. Bydefinition, full plugging is said to have occurred when there is no relative movement betweenthe soil plug inside the pile and the pile itself. Fully plugged piles behave as closed-ended,full-displacement piles, which are known to have a higher unit skin friction. Thus an open-ended pile that gets plugged during the course of driving would have a unit skin frictionbetween that of a fully unplugged pile and a closed-ended full-displacement pile. Pluggingalso has an effect on the ultimate bearing capacity of the piles. It also has an effect on thetime-dependent capacity of piles and more so in pile groups, where the dissipation of excesspore pressures takes longer. The excess pore pressure inside the pile may take much longerto dissipate, compared to pore pressure outside, thus making matters more complex. Theoccurrence of plugging also changes the dynamic characteristics of piles, leading to situationswhere the selected hammer may not be suitable to drive a pile to the design depth. There canbe wasteful expenditures involved in obtaining a heavier hammer or jetting the pile to thedesign depth, leading to uncertainty in the actual capacity. To add to the uncertainty, apreviously plugged pile may become unplugged during further driving (Randolph, 1990).This slip may occur due to the development of high pore pressures in the soil inside the pileor from “Poisson’s Effect.” Poisson’s effect can occur, when a stress wave from hammerimpact travels down the pile causing the pile to expand and subsequently slip relative to theinner soil. At present the prediction of plugging has not been established. Currently availableplug prediction methods are mostly based on laboratory model tests (Randolph, 1985,Paikowsky, 1990). However, comparison of total internal shaft friction with plug end bearingcan be used as an indicator of whether plugging will occur. To ascertain whether a pile isplugged or unplugged during driving, soil plug measurements should be taken just before andafter restriking the pile. However, often field constraints such as lack of accessibility orschedule driven constraints, prevent measuring soil plug heights, which was the case at thesubject site.
HAMMER PERFORMANCE
Hammer energy was monitored for various test pile installations. Energy transmitted fromthe fully warmed up hammer towards the end of driving the test pile at Pier 2 is shown inFigure 9a. Also shown is the energy transmitted from the same hammer while redriving thesame pile the following day. The energy transmitted shown is from the hammer blows withinone foot of pile penetration. Moreover, the measured soil resistances did not vary much, thusallowing us to make this comparison. It was found that hammer energy output slowly
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becomes uniform as the hammer progressively warms up during the driving operation. Thewarmed up hammer indicates a more consistent energy output. It can be shown that erratichammer energy leads to an unreliable estimate of pile capacity if one bases the prediction onblow counts alone.
(a) (b)Figure 9: Hammer Performance Before and After a) Warmup, and b) Maintenance
Efficiency of a diesel hammer can vary considerably (33% to 80%) because it depends notonly on the make and model of the hammer but also on the level of maintenance. Therefore,an accurate estimate of energy transmitted into the pile is important. Moreover, duringproduction driving, sometimes the characteristics of the pile driving system may change,consequently invalidating the driving criteria. Sometimes, a simple maintenance of thehammer can change the driving energy substantially. For example, after driving the first testpile at Pier 2, the contractor dismantled the open ended diesel hammer, inspected thecompression rings and replaced the fuel pipe which increased the energy from the hammer byas much as 50 percent (Figure 9b). In view of the above reasons, to ascertain hammerperformance during production pile driving and to validate the driving criteria, PDA testing isoften recommended for about 5 percent of the production piles.
POST-FIELD FOUNDATION ASSESSMENT
Case Pile Wave Equation AnalysesProgram (CAPWAP) analyses wereperformed for each of the 16 tested piles.The CAPWAP analyses, provided anestimate of ultimate pile capacity, thedistribution of soil resistance along thelength of the pile, and the various soilparameters (such as damping and quakevalues) required for a revised Wave EquationAnalyses. The hammer blow that wasselected for analysis was either from near thedesign penetration depth or near the designcapacity based on field PDA data and withrepresentative hammer transferred energy. Aplot of PDA versus CAPWAP capacities forboth EOID and BOR is shown in Figure 10.
0
10
20
30
40
50
60
5 6 7 8 9 10 11
Stroke (ft)
Post Maintenance
Pre-Maintenance
Transm ittedEnergy (kip-ft)
Figure 10: PDA versus CAPWAPCapacities for EOID and BOR.
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For restrike the earliest representative blow of a warmed-up hammer was selected forCAPWAP. The CAPWAP BOR capacities are also shown on Figure 4. The assessed BORpile capacities by the CAPWAP are in general agreement with the computed static pilecapacities.
Figure 11: Damping Constants (Smith) and Quakes derived from CAPWAP analyses
The CAPWAP-generated damping and quake values for each test pile are presented in Figure11. These data indicate that the damping and quake values vary across the site, with highervalues of shaft damping occurring at Pier 5 and between Piers 9 and 12. It has been shown thatSmith damping constants slightly decrease for both skin and toe as the soil grain size increases(Likins et al., 1996). Therefore, the variation exhibited across the site might be explained bygradation analyses and index test data which indicate the presence of more fine-grainedcohesive soils near Pier 5 and between Piers 9 and 12. For this project site, the quakes anddamping values were generally higher than those recommended in the GRLWEAP manual.Consistent with previous experience, it was observed that damping constants during restrikeare generally higher than those during the end-of-driving. Toe quakes during restrikes werelower than those at the end-of-driving.
PRODUCTION PILE DRIVING CRITERIA
Based on the results of dynamic piletesting at each pier, additional waveequation analyses were performed todevelop pile driving and restrikecriteria for production piles at eachpier. Production pile driving criteriafor typical piers (Pier 2 and Pier 11) arepresented in Figure 12. The piledriving equipment used by thecontractor along with the soil damping
Figure 12: Pre- and Post- Field TestingCriteria for Piers 2 and 11.
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and quakes obtained from CAPWAP analyses and measured transferred energies by PDA wereused in the wave equation analyses model. These criteria when compared with driving criteriaobtained from the pre-field wave equation analyses are less stringent at some locations (Pier2), and more stringent at others (Pier 11).
CONCLUSIONS
Typical results of a pile installation monitoring and assessment program implemented duringthe construction of a new bridge in Baltimore are presented. The approach taken to assess thepile foundations, involved 1) preliminary wave equation analyses, using site specific soilinformation and hammer data, 2) pile driving measurements, 3) post-field CAPWAP analyses,and 4) revised wave equation analyses based on field data and CAPWAP analyses. The staticpile capacities predicted using the conventional procedures compared favorably with the fieldmeasured EOID capacities and were less than BOR capacities. The field measured blowcounts compared favorably with those predicted using wave equation analyses. Set-up factorsfor the Cretaceous soils at the site in Baltimore were variable and ranged between 1.0 and 1.4.The higher values of setup occurred at locations underlain by stiff clay. Given the variablenature of setup behavior of these soils, recommending a single value is not prudent. Sitespecific testing is therefore, essential to determining setup. Plugging did not appear to occurduring pile driving for test piles at Pier 2 and 7. It may have occurred during restrike at Piers11 and 12 as was predicted by static computations and evidenced by increase in BOR capacity.Performance of the hammer was also evaluated. It was found that sometimes the hammerperformed erratically and needed some adjustment. Hammer performance can changesignificantly with time. To ascertain hammer performance during production pile driving andto assure the validity of driving criteria, additional PDA testing should be recommended forthe production piles. Production pile driving criteria established from the test pile programresulted in reduced uncertainty and a more reliable foundation.
ACKNOWLEDGEMENTS
The author expresses his gratitude to Raymond Castelli and John Wisniewski, PBQD, fortheir guidance during the field program. Dynamic measurements were taken by William Fungof D.W. Kozera, Inc. The opinions expressed in this paper are solely of the writer and are notnecessarily consistent with the policy or opinions of Parsons Brinckerhoff.
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APPENDIX: CONVERSION TO SI UNITS
Feet (ft) × 0.305 = meter (m)Kip × 0.45359 = metric tonKip × 4.44822 = kNPounds per cubic foot (pcf) × 0.157 = kilonewton on per cubic meter (kN/m3)Pounds per square foot (psf) × 0.04788 = kilopascal (kPa)
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