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Mark R. Svinkin, Member, ASCE
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Abstract

The application of dynamic methods to driven piles has advantages in evaluation of the hammer-pile-soil system and in data acquisition during pile driving and restrikes. Therefore during the last twenty five years, dynamic methods have become an integral part of pile capacity prediction and measurement for numerous projects. Dynamic methods use good quality hardware and software, but such great tools cannot themselves solve geotechnical problems of piling without engineering judgment. This paper shows some engineering assessments of determining pile capacity by dynamic formulas, wave equation analysis and dynamic testing.

Introduction

Contemporary dynamic methods are founded on the application of the stress wave theory to piles. There are two different techniques of the use of wave equation analysis for determining pile capacity: computation of pile capacity without dynamic measurements on driven piles and a signal matching technique for computed and measured force and velocity records at the pile head.

Dynamic methods have certain advantages and some uncertainties in their application. The wave equation method is used for prediction of pile capacity during both the design stage and for construction control before restrikes. Unfortunately in most cases, predicted pile capacity differs substantially from results of both static and dynamic load tests. Dynamic measurements of force and velocity at the upper end of the pile during pile driving, followed by a signal matching procedure, is the most common method for dynamic determination of pile capacity. This method is a convenient tool in the pile driving industry. However, though dynamic methods have been used in practice for years, actual accuracy of dynamic methods and understanding the results of dynamic testing are vague.

Also, there is an attempt to breath new life into dynamic formulas and consider a suggested formula as the better alternative to signal matching technique. There are no theoretical and experimental basis for such replacement.

In the medium of geotechnical engineers involved in dynamic testing and analysis, there is a belief that hardware and software themselves can solve geotechnical problems of piling. Indeed, hardware and software are great tools but only tools, and these tools cannot replace engineering judgment. It is known if we put trash in, we will receive trash out. Computer misuse comes in many forms and among them having computer programmers provide services they are unqualified to perform. Formal implementation of the signal matching procedure is a common approach in dynamic pile testing. In spite of a number of excellent engineering assessment of results obtained from static and dynamic tests, it is obvious that the application of dynamic methods to piles lacks engineering judgment.

Misapplication and misuse of the specified computer software are demonstrated. Various problems such as misleading assessment of the accuracy of dynamic formulas, calibration of wave equation programs, the soil consolidation effect in prediction of pile capacity by wave equation analysis, comparison of static and dynamic tests, prediction of pile capacity by dynamic pile testing, overestimated capabilities of signal matching technique and others are discussed. It is shown that dynamic methods have to be used with the proper engineering judgment for prediction and determination of pile capacity.

Dynamic Formulas

Determination of pile capacity by dynamic formulas is the oldest and frequently used method. There is a great number of dynamic formulas available with different degrees of reliability. Dynamic formulas have been criticized in many publications. Unsatisfactory prediction of pile capacity by dynamic formulas is well characterized in FHWA Manual for Design and Construction of Driven Pile Foundations, Hannigan et al.(1996): "Unfortunately, dynamic formulas have fundamental weakness in that they do not adequately model the dynamics of the hammer-pile impact, the influence of axial pile stiffness, or soil response. Dynamic formulas have also proven unreliable in determining pile capacity in many circumstances. Their continued use is not recommended on significant projects".

However, dynamic formulas are traditional dynamic analysis techniques. For example, responses to the questionnaire obtained from 45 state DOTs and 2 FHWA officials showed that Dynamic Formulas usage are 45% ENR (Engineering News Records) and 16% Gates Equation, Paikowsky and Stenersen (2000). Besides, there is an attempt to breathe new life into dynamic formulas. Paikowsky and Chernauskas (1992), Paikowsky et al. (1994) and Paikowsky and Stenersen (2000) have suggested one more energy approach using dynamic measurements for the capacity evaluation of driven piles. Liang and Zhou (1997) have concluded regarding this method: "Although the delivered energy is much more exactly evaluated, this method still suffers similar drawbacks of ENR".

Authors of a new dynamic formula used the ratio, also called index K, of the static load test capacity to the predicted capacity to evaluate performance of the energy approach and dynamic testing. However, such a ratio is irrelevant for verification of dynamic formulas and dynamic testing (DT) results for two reasons: first, dynamic testing methods yield pile capacity only for the time of testing (Rausche et al. 1985), and second, the pile capacity from static load test (SLT) is considered as a constant value which is a major error.

Paikowsky et al. (1994) and Paikowsky and Stenersen (2000) use a false assumption that accuracy of Dynamic Formulas are independent of the time between DT and SLT. However, SLT as well as DT yields the pile capacity at the time of testing (Svinkin 1997). By way of illustration, results of DT and SLT are shown in Figure 1 for two identical cylindrical, 1372 mm x 127 mm, prestressed concrete piles, TP1 and TP2 (Svinkin et al. 1994). These piles were driven at the same site to the depth of penetration of about 24.4 m. Each of the piles TP1 and TP2 was tested 2, 9 and 22 days after the end of initial driving (EOID). The difference was that three restrikes were made for TP1 and three SLTs were made for TP2. Pile capacity from three SLTs was a function of time as well as pile capacity obtained from DT. Tested data in Figure 1 help to explain the causes of unsatisfactory prediction in pile capacity by dynamic formulas. Dynamic formulas using maximum energy, pile set and maximum displacement from DT do not take into account the time between SLT and DT. In the case of a few SLTs made on one pile, like three SLTs performed on pile TP2, what would be the reliability of pile capacity prediction by the energy approach methods? Which SLT should be taken for comparison? Currently, there are no answers to these questions. Nevertheless, Paikowsky and Stenersen (2000) assert that the Energy Approach Formula is ideal for construction and better than Signal Matching technique, e.g. CAPWAP program (GRL and Associates, Inc. 1995). There are no theoretical and experimental confirmation of such conclusions which are wrong and misleading. It is necessary to utilize other appropriate way for comparison of results of the Energy Approach Formula and DT which use the same dynamic measurements. Such comparison was made in the frames of preparation of FHWA-GRL database. The results obtained were very poor and confirmed that the Energy Approach with dynamic measurements cannot yield reliable prediction of pile capacity. Statistical analysis itself cannot reveal good results and replace engineering judgment if comparison of measured pile capacities is incorrect.

Wave Equation Analysis

Limitations in Prediction of Pile Capacity

The main goal in using wave equation analysis is to provide a better prediction of the pile capacity, as a function of pile penetration resistance, than can be obtained from classical dynamic formulas. Today, the most commonly used wave equation programs are either GRLWEAP (GRL and Associates, Inc. 1997) or TNOWAVE (TNO Report 1996).

The wave equation method is used for prediction of pile capacity prior to the beginning of pile driving and before restrikes. However, in most cases, computed pile capacity differs substantially from results of both static and dynamic load tests. Statistical analysis of GRLWEAP results, Hannigan et al. (1996), computed for 99 piles driven into various soils, has demonstrated that GRLWEAP does not have an advantage over the Gates dynamic formula. The mean and coefficient of variation are almost the same for both prediction methods.

Smith (1960) made his model on the basis of existing knowledge of pile driving at the time and he supposed this model could be improved with acquisition of new data. Results obtained by many researchers confirmed that Smith's model is simple and sensible but with some lack of proper presentation of soil properties.

Soil parameters considerably affect solutions of wave equation analysis. Dynamic soil resistance parameters (damping and quake) have to be assigned as constant values for wave equation analysis. These parameters do not reflect the changes of soil properties in the pile-soil interface zone after the completion of pile driving.

There have been attempts to determine values of damping and quake from signal-matching solutions for dynamically tested driven piles or from modified SPT. It could be beneficial for some cases, but, in general, such approaches are not successful in finding proper values of damping and quake. Besides complications with different models in wave equation analysis and signal-matching technique and also with the scale factor effect on the use of SPT results, these approaches yield constant values of soil parameters and cannot be used in prediction of the pile capacity as a function of time after EOID (Svinkin 1996).

Variable Soil Parameters.

Existing dynamic models of the pile-soil system mainly use a velocity-dependent approach for calculation of the dynamic resistance as a damping component of the total resistance during pile driving. There are various linear and nonlinear relationships between the damping component and the velocity. A study of different soil damping models and computed pile capacities has revealed that neither the pile velocity nor the damping constant can reflect time-dependent variation of the pile-soil system after EOID. The existing approach of computing the dynamic resistance does not take into account soil consolidation around the pile after EOID and therefore cannot provide determination of pile capacity as a function of time after pile installation. There is necessity to take into account soil consolidation around a pile after EOID for improvement in accuracy of wave equation analysis, Svinkin (1996).

For the idealized Smith wave equation model, it is important to find an appropriate combination of parameter values, mainly paying attention to soil variables, in order to achieve the accurate prediction of pile capacity. There is a reasonable way to enhancing prediction accuracy of the dynamic resistance with the velocity dependent approach. Variation of the pile-soil system after the completion of driving can be taken into account by a variable damping coefficient which should be considered as a function of time and other parameters characterizing soil consolidation around the pile, Svinkin (1996, 1997). It is assumed that the variable damping coefficient is independent of pile velocity. Inclusion of variable damping is thought to be the next step in the development of Smith's model with the velocity dependent approach for representation of the dynamic resistance.

The damping coefficient as a function of time can be found on the basis of back calculations using the wave equation model of the pile-soil system with known capacity as This procedure is in agreement with Lambe's (1973) equation modified for a general back analysis approach by Leroueil & Tavenas (1981). Since the variable damping coefficient is chosen as only one soil parameter reflecting the field soil consolidation after pile installation, this parameter can be successfully back analyzed.

The results of back analysis has revealed that the shaft damping coefficient in clay is much higher than in unsaturated sand, but upper values of this coefficient in saturated sandy soil (sand with high damping) are close to ones in clay, Svinkin and Woods (1998). Also, a trend of the damping coefficient increase with time after EOID was found for all soil damping models available in GRLWEAP program and this trend is independent of the damping resistances, Svinkin (1996).

The idea of variable damping has been confirmed by results of statistical analysis of damping coefficients from CAPWAP solutions performed by Liang and Zhou (1997) who have found that the damping coefficient is affected by the time. Cho et al. (2000) agree that set-up effects should be accounted for in wave equation analysis for restrikes and suggested constant damping and quake coefficients to computing pile capacity before restrike. This is a partial solution because these coefficients can be used only for one restrike. The variable damping coefficient is a solution for calculation of pile capacity before different restrikes.

Soil damping is the key parameter for adjustment of wave equation solutions with time-dependent soil properties in pre-driving analysis. The use of the variable damping coefficient gives an opportunity to compute the time-dependent pile capacity by the wave equation method.

Software Calibration.

Existing programs for wave equation analysis are not the same. Moreover all programs have a number of versions. Each new version gives usually additional beneficial options to users, but it is not clear how each program version ensures the accuracy of pile capacity calculation. There is confusion what program yields more accurate results. The writer has an experience of pile capacity calculation for the same hammer, pile and soil conditions using two versions of the same program. Variation of obtained capacities was about 20 %. This is an evidence of contradictions available between different program versions.

Obviously, it is necessary to calibrate each program version with some standard data of the hammer-pile-soil system in order to avoid confusion in a choice of the program.

Dynamic Testing

Dynamic testing followed by a signal matching procedure has obvious advantages in determining pile capacity at any time required after pile installation. Since dynamic testing is often used to replace the static loading tests, it is important to ascertain the adequacy of both SLT and DT.

Existing Approach for Comparison of SLT and DT. Static analysis methods predict pile capacity as the long term capacity after soil consolidation around the pile is complete. Independently of the time elapsed between installation of the test pile and the static loading test, the ratio of the predicted ultimate load to the measured ultimate load from static loading test is used for approximate evaluation of the reliability of design methods. For example, Briaud and Tucker (1988) evaluated 13 methods developed to predict the ultimate load capacity of the pile, and they used this ratio for approximate evaluation of the reliability of design methods in calculation of the ultimate pile load although the time elapsed between installation of the test pile and static load test averaged 17 days.

According to the traditional approach, the main criterion for assessment of the pile capacity prediction based on dynamic measurements is the ratio of capacities obtained by dynamic and static tests or vice versa (Figure 2). It is necessary to point out that a ratio of DT/SLT or vice versa, taken for arbitrary time between compared tests, is not a verification of dynamic testing results. It is well-known that dynamic testing methods yield the real static capacity of piles at the time of testing, Rausche et al. (1985). Besides, the static capacity from SLT is considered as a unique standard for assessment of dynamic testing results. Unfortunately, that is a major error. As a matter of fact, pile capacity from Static Loading Tests is a function of time and the so-called actual static capacity from SLT is not a constant value, Svinkin (1997; 1998).

For the general case of assessment of reliability of the DT, the ratio of restrikes to SLT results has been considered for various pile types, soil conditions and times of testing lumped together as shown in Figure 2. Such mixture has no real meaning. It is not a verification of dynamic testing at restrikes and it is not an assessment of real set-up factor because everything is lumped together without taking into account the time between different tests. Such a comparison of the pile capacities from SLT and DT is invalid for piles driven in soils with time-dependent properties because the soil properties at the time of DT do not correspond to the soil properties at the time of SLT i.e. soil consolidation is taken into account for the latter test and not considered for the former test. As a matter of fact, such a comparison uses pile capacity values which are incompatible from the point of DT verification, Svinkin (1997) and Svinkin and Woods (1998).

New Criteria for Comparison of SLT and DT. Criteria should be established for correct comparison of in-situ tests made at different times after EOID. It is important to find how changes of pile capacity between two compared tests may affect the accuracy of determining pile capacity by dynamic testing.

Acceptable time between tests. Pile capacity determined at EOID in various soils changes with time. After the completion of pile driving, soil consolidation, manifested by the dissipation of excess pore pressure at the soil-pile interface zone, is usually accompanied by an increase in pile capacity (soil set-up). In saturated sandy soils, ultimate pile capacity may decrease (soil relaxation) after initial driving due to dissipation of negative pore pressure. Changes of strength in soil after driving and the time required for return of equilibrium conditions are highly variable and depend on soil conditions, and pile type and size. The consequences of soil modification around the pile are essential with respect to changes of pile capacity. Pile capacity as a function of time is displayed, for example, in Figure 1 for piles TP1 and TP2. Comparison of values of the pile capacity obtained from two tests with arbitrary time between them show only a change of pile capacity during a considered period of the time, but it is not verification of DT.

Static Loading Tests and Dynamic Testing present different ways of determining pile capacity at various times after pile installation, but for valid correlations of both tests, static and dynamic testing capacities must be compared at the same time after pile installation in both SLT and DT methods, Svinkin (1997; 2000) and Svinkin and Woods (1998).

The adequacy of SLT and DT have to be confirmed by proper correlation of time. Due to the consolidation phenomenon in soils, comparison of SLT and DT can be made only for tests performed immediately one after another. In practice, it is sometimes difficult to make two immediately successive tests, but nonetheless the time difference between both comparable tests should not exceed 1-2 days during which soil setup changes only slightly.

Rate of pile capacity change. It is important to find quantitative assessment of pile capacity change during 1-2 days. The rate of pile capacity change per day (set-up rate), r_R, between two considered tests can be calculated as

Where R_u1 = pile capacity from test 1; R_u2 = pile capacity from test 2; t₁ and t₂ = elapsed time in days after EOID for test 1 and test 2, respectively.

The set-up rate was calculated for different pile types tested in various soils. Pile capacity from dynamic testings was determined by CAPWAP analysis and the Davisson criterion of failure load was used for static loading tests, Davisson (1972). The obtained results are shown in Table 1-3. Initial data for these tables were taken from Svinkin et al. (1994).

A description of seven prestressed concrete piles is presented in Table 1. The depth of penetration of each pile was approximately 24.4 m. The soil consisted of about 25.6 m of mainly gray clays followed by a bearing layer of silty sand. Water table was at the ground surface. A Delmag D 46-13 hammer was employed for initial driving and restrikes (RSTR). For each pile, 3 to 4 DT and/or SLT were performed after pile installation. The elapsed time after EOID, penetration resistance and the time dependent ultimate capacity of tested piles are shown in Table 1 as well. It can be seen that the set-up rate depends on the elapsed time after pile installation. The set-up rate was about few hundred in 1-2 days after pile installation. Then the rate considerably decreased and became 13-16 %/day for four days after EOID and less than 7-8 %/day for 9-10 days after EOID, Figure 3.

Three piles, two prestressed concrete and one closed ended steel pipe, are presented in Table 2. These piles were tested at different sites but their soil conditions were very close: predominantly unsaturated sandy soils. Soil deposits were mostly fine sands with bare strata of silty sand at site 1 and slightly silty or clayey fine sands at sites 2 and 3. The water table was not encountered during soil boring on each site. For pile 1, a Kobe K-45 hammer was used. Piles 2 and 3 were driven and restruck with a Vulcan 80C and 010 hammers, respectively. For unsaturated sands, the set-up rate was mostly independent of the limited elapsed time of 12-16 days after pile installation and was found in the range of 10-15 %/day.

Five prestressed concrete piles were driven on a site with predominantly silty sands (Table 3). The water table was at a depth of 0.6 m from ground surface. Piles CT1, CT2, CT3, and CT4 were driven and restruck with a Kobe K25 hammer. A Delmag D 62-22 hammer was used for pile CT5. The set-up rate was 7-18 %/day, 4-7 %/day, and less than 1 %/day for 2, 10-11, and 20-23 days after EOID.

Thus, the rate of pile capacity change per day, r_R, decreases with an increase of the elapsed time after EOID and a margin of error about 10-15 %/day would be reasonable for a few days after pile installation.

Comparison of SLT and DT. Thirty nine different piles in various soil conditions were statically and dynamically tested (Table 4). Initial data for these piles were taken from FHWA-GRL database.

Explanation of abbreviations in Table 4 are as follows. Pile number: number in parentheses is from FHWA Database; Pile description: PSC is prestressed concrete, OEP is open ended pipe, CEP is closed ended pipe, HP is H-pile; Soil: HWT is high water table; Time between SLT & DT: minus and plus mean DT was made before or after SLT, respectively; Time after EOID was shown for DT; Signal Matching: reanalyzed results include the "automatic" or "best match" (with asterisk), minus and plus in error mean under or overestimated CAPWAP results.

Static load tests were carried to failure according to the Davisson failure criterion. Dynamic records from restrike testing were available for all piles. A signal matching technique - CAPWAP analysis of the restrike test data was used for pile capacity determination. The "original" CAPWAP capacities were obtained from existing CAPWAP results. For a number of piles, additional CAPWAP analysis was provided because of absence of the "original" CAPWAP capacities or in order to improve signal matching results with "automatic" or "best match" solutions. "Automatic" is an option in the CAPWAP program with automatic search capability which provides a solution using optimal matching of signals with no user interaction. "Best match" is a result of working in a manual operating mode to iteratively seek a best match.

For all considered piles, the time differences between static and dynamic tests were 1-2 days, but time elapsed after EOID was diverse. An acceptable margin of error was determined in accordance with the set-up rate in Tables 1-3. Compared capacities have a good agreement within the acceptable margin of error for 28 piles (1, 3, 4, 5, 6, 8, 9, 11, 13, 15, 16, 17, 19, ,20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, 34, 37, 38, 39). Piles with at least one CAPWAP result within the acceptable limits were included in this group. For example, for pile 11 "original" and "automatic" CAPWAP yielded the pile capacity with an error of -8 % and -40 %, respectively, but even the big error is acceptable in this case because the elapsed time after EOID was only 1 day and DT was made 2 days before SLT. Calculated capacities for five piles (12, 14, 18, 29, 33) have errors from 20 % to 25 %. The worst results were obtained in CAPWAP analysis of six piles (2, 7, 10, 23, 35, and 36) which were analyzed with errors between 30-54 %. First three piles have underestimated results, but piles 23, 35 and 36 have overestimated pile capacity on 31 %, 54 % and 44 %, respectively.

Table 4. Comparison of pile capacities obtained from SLT and DT

Table 4. continued. Comparison of pile capacities obtained from SLT and DT

Table 4. continued. Comparison of pile capacities obtained from SLT and DT

It can be seen the computed capacities for 11 piles exceeded a reasonable margin of error. The Davisson criterion determines a conservative value of pile capacity. Maximum values of pile capacity can be estimated with the Chin method from which results are about 20 % to 40 % greater than from the Davisson limit, Fellenius (2001). Therefore, computed pile capacity exceeding the Davisson limit more than 20 % should be considered as overestimating values. It is not acceptable for pile foundation design. Underestimating pile capacities are good for foundation safety but not acceptable from the economic standpoint. Analysis of 39 cases revealed substantial errors in determination of the pile capacity for 6 piles that is about 15 % of the total number of considered piles. However, it is important to recognize such cases. Besides formal implementation of signal matching procedure, it is necessary to use engineering judgment in assessment of DT results. The main objective of this study is to bring attention of geotechnical engineers to engineering judgment of dynamic testing in order to recognize bad situations in advance.

Effects of various factors on Results of DT. It is important to reveal how various factors affect signal matching results.

Time between compared tests was in the limits of 1-2 days. The time was 48 hours for 8 piles, 24 hours for 26 piles, 12 hours for 1 pile, 5 hours for 3 piles, and 2 hours for 1 pile. Thus, closely time correlated comparisons of SLT and DT have been made.

Time after pile installation affects the rate of pile capacity change. This rate is different for various soils, but a margin of error about 10-15 %/day would be reasonable for a few days after pile installation. For short period after EOID, larger discrepancies are acceptable as was shown for pile 11 and in Figure 3.

Sequence of tests. Four piles (11, 35, 36, and 39) were dynamically tested before SLT. Piles 11 and 39 were tested on the first and the second days, respectively, after EOID when soil consolidation only started and the difference between pile capacities from DT and SLT was acceptable. Piles 35 and 36 were tested on the 14th day. DT destroyed soil consolidation around the pile and during one day soil could not reconsolidate. Perhaps this is the cause of the big discrepancy between compared pile capacities. Therefore, DT should be made after SLT to obtain better results.

Pile type. No correlations was found between pile type and pile capacities computed.

High blow count. No correlations was found between high blow count and pile capacities computed.

Signal matching technique. "Automatic" signal matching improved results computed for 8 piles (2, 6, 13, 18, 22, 26, 31, 39) and made worse calculations for 6 piles (8, 11, 12, 20, 28, 29). "Best match" changed for the worse the pile capacity of only pile 1. It is obvious that "best match" is preferred procedure in signal matching technique. Described results were obtained with CAPWAP program, but similar outputs could be expected from the use of TNODLT program, TNO Report (1996).

Dynamic records should affect computed result. One example was shown in the text. There is a trend to improve wrong records by means of signal matching technique, but it is unknown how record improvement affects computing pile capacity. It seems to be beneficial to prepare a catalog of unacceptable records.

Soil conditions. It is necessary to collect more information in order to reveal effects of soil conditions on computed results.

Prediction of Pile Capacity by DT. Obviously, at EOID and each restrike the pile-soil system has various soil stiffness, damping and soil mass involved in vibration. Therefore, each dynamic testing yields pile capacity corresponding to the properties of the pile-soil system at the time of testing. The pile capacity from a static load test reflects a degree of soil consolidation around a pile at the time of testing as well. Thus, static, dynamic and statnamic tests determine pile capacity only at the time of testing.

In some publications, dynamic testing is used for a capacity prediction without prior knowledge of the static loading test, e.g. Goble (2000) and Holeyman et al. (2000). This is a misleading interpretation of DT which does not have any connection with Class A type prediction defined by Lambe (1973). No in-situ pile test can predict pile capacity as a function of time after pile installation.

Overestimated software capabilities. It is sometimes difficult to activate the pile capacity at restrike and software users calculate the undetermined pile capacity with combined CAPWAP analysis, Stevens (2000). The pile capacity is estimated by compounding resistance distribution from two different DT and using the highest values between the two for each soil element. It seems that such a procedure overestimates capabilities of signal matching technique. It is important to verify similar calculations with SLT or use the special driving technique (Fellenius 1999) which means that one of the nearby piles is driven at EOID shorter so that there is confidence that at restrike the pile will move and its full resistance will be mobilized. The nearby not mobilized piles can be said to have the same shaft resistance and at least as much toe resistance.

Conclusions

The paper's objective is an attempt to emphasize the engineering judgment and eliminate contradictions and/or misunderstanding of determining pile capacity by dynamic methods. The paper demonstrates misapplication and misuse of the specified computer software. It is shown the necessity of consideration of the soil consolidation effect in prediction of long-term pile capacity by wave equation analysis, calibration of wave equation programs, and proper comparison of static and dynamic tests. Also, it is underlined impossibility to predict pile capacity by dynamic pile testing, misleading assessment of the accuracy of dynamic formulas, and paid attention to overestimated capabilities of signal matching technique. Dynamic methods have to be used with the proper engineering judgment for prediction and determination of pile capacity.

Acknowledgement

The writer is grateful to the Federal Highway Administration (FHWA) and GRL and Associates, Inc. for assistance in the use of FHWA-GRL database. Opinions expressed in this paper are those of the writer and not necessarily those of FHWA and GRL and Associates, Inc. The writer wishes to thank the reviewers for their constructive reviews of the paper.

APPENDIX I.REFERENCES

Briaud, J.L. Tucker, L.M. (1988). "Measured and predicted axial response of 98 piles", Journal of Geotechnical Engineering, ASCE, 114(9), 984-1001.

Cho, C.W., Lee, M.W., and Randolph, M.F. (2000). "Set-up considerations in wave equation analysis of pile driving", Proc. Conf. on Application of Stress-Wave Theory to Piles, Sao Paulo, Brazil, Balkema, 41-46.

Davisson, M.T. (1972). "High capacity piles", Proc., lecture Series, Innovations in Foundation Construction, ASCE, Illinois Section.

Fellenius, B.H. (1999). APTLY e-mail archives.

Fellenius, B.H. (2001). "What capacity value to choose from the results of a static loading test", Fulcrum, The Newsletter of the DFI, Winter 2001, 19-22.

Goble, G.G. (2000). "Class A" capacity prediction", GRL + PDI Newsletter 36, February.

GRL and Associates, Inc. (1997). GRLWEAP - Wave Equation Analysis of Pile Driving, Manual, Cleveland, Ohio.

GRL and Associates, Inc. (1995). CAPWAP - CAse Pile Wave Analysis Program, Manual, Cleveland, Ohio.

Hannigan, P.J., Goble, G.G., Thendean, G., Likins, G.E. and Rausche, F. (1996). "Design and construction of driven pile foundations", Workshop manual, Publication No. FHWA-HI-97-014.

Holeyman, A., Maertens, J., Huybrechts, N., and Legrand, C. (2000). "Results of an international pile dynamic testing prediction event," Proc. Conf. on Application of Stress-Wave Theory to Piles, Sao Paulo, Brazil, Balkema, 725-732.

Lambe, T.W. (1973). "Predictions in soil engineering", 13th Rankine Lecture, Geotechnique, 23(2), 149-202.

Leroueil, S. & F. Tavenas (1981). "Pitfalls of back-analysis", Proc. 10th Inter. Conf. on Soil Mechanics and Foundation Engrg., Stockholm, ISSMFE, 1, 185-190.

Liang R.Y. & J. Zhou (1997). "Probability method applied to dynamic pile-driving control", Journal of Geotechnical Engineering, ASCE, 123(2), 137-144.

Rausche, F., G.G. Goble & G. Likins (1985). "Dynamic determination of pile capacity", Journal of Geotechnical Engineering, ASCE, 1985, 111(3), 367-383.

Paikowsky S.G. and Chernauskas L.R. (1992). "Energy approach for capacity evaluation of driven piles", F. Barends (ed.), Proceedings of Fourth International Conference on the Application of Stress-Wave Theory to Piles, The Hague, Balkema, 595-601.

Paikowsky S.G., Regan J.E., and McDonnell J.J. (1994). "A simplified field method for capacity evaluation of driven piles", Publication No. FHWA-RD-94-042.

Paikowsky S.G. and Stenersen, K.L. (2000). "Keynote lecture: The performance of the dynamic methods, their controlling parameters and deep foundation specifications", Proc. Conf. on Application of Stress-Wave Theory to Piles, Sao Paulo, Brazil, Balkema, 281-304.

Smith, E.A.L. (1960). "Pile driving analyses by the wave equation", Journal of the Soil Mechanics and Foundation Division, ASCE, 1960, Vol. 86, 35-61.

Stevens, R.F. (2000). "Pile acceptance based on combined CAPWAP analysis", Proc. Conf. on Application of Stress-Wave Theory to Piles, Sao Paulo, Brazil, Balkema, 17-27.

Svinkin, M.R., C.M. Morgano & M. Morvant (1994). "Pile capacity as a function of time in clayey and sandy soils", Proc. Fifth Inter. Conf. and Exhibition on Piling and Deep Foundations, Bruges, 13-15 June, Rotterdam: Balkema, 1.11.1-1.11.8.

Svinkin, M.R. (1996). "Soil damping in wave equation analysis of pile capacity", In F. Townsend, M. Hussein & M. McVay (eds.), Proc. Fifth Inter. Conf. on the Application of Stress-Wave Theory to Piles, Orlando, 11-13 September, Gainesville, University of Florida, 128-143,

Svinkin, M.R. (1997). "Time-Dependent Capacity of Piles in Clayey Soils by Dynamic Methods", Proc. XIVth Inter. Conf. on Soil Mechanics and Foundation Engineering, Hamburg, 6-12 September, Rotterdam, Balkema, 2, 1045-1048.

Svinkin, M.R. (1998). "Discussion of 'Probability method applied to dynamic pile-driving control' by Liang & Zhou", Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 122(4), 319-321.

Svinkin, M.R. (2000). "Time effect in determining pile capacity by dynamic methods", Proc. Conf. on Application of Stress-Wave Theory to Piles, Sao Paulo, Brazil, Balkema, 35-40.

Svinkin, M.R. & R.D. Woods (1998). "Accuracy of determining pile capacity by dynamic methods", Proc. Seventh Inter. Conf. and Exhibition on Piling and Deep Foundations, Vienna, 15-17 June, Rickmansworth, Westrade Group Ltd, 1.2.1-1.2.8.

TNO Report, (1996). TNOWAVE and TNODLT, User Manual, Delft, TNO Building and Construction Research.

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