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ABSTRACT: Numerical methods are presented to predict complete vibration response of the soil, buildings or sensitive instruments caused by anticipated, future vibration sources such as construction or heave industry. The suggested methods make use of either Duhamel’s integral or Fourier transforms and experimental soil response.

1 INTRODUCTION

Construction and industrial dynamic sources, such as pile driving and foundations for impact machines, generate elastic waves in soil which may adversely affect surrounding buildings and sensitive instruments (Targets). The effects of these waves range from visible structural damage to serious disturbance of working conditions for sensitive devices and people. Therefore, legitimate concerns frequently arise about possible ground and structure vibrations before the start of construction activities or installation of machine foundations.

Analytical methods (Miller and Pursey, 1954; Broers and Dieterman, 1992; Hanazato and Kishida, 1992; Wolf, 1994) already exist which give accurate results for certain limited cases, but these methods are applicable only to well defined and simple sites like a half-space or horizontally layered media. Indeed, for the prediction of expected vibrations, it is necessary to have information about the actual soil deposit and to choose a proper soil model to compute vibrations. Computed results from the simple models contain valuable data about general tendencies of wave propagation at a site, but cannot take into account spatial variations of soil properties and produce accurate and complete soil vibration records at any point of interest.

This paper presents numerical methods coupled with experimental soil response measurements to predict ground and structure vibrations before the beginning of construction activities or installation of machine foundations. This approach employs experimental impulse response functions containing real behaviour of soil and structures without the investigation of soil and structure properties. It also provides an opportunity for accurate determination of vibration levels and aids in monitoring of ground, structure and device vibrations prior to start of construction and industrial activities.

2 DEFINITION OF METHODS

The suggested methods for predicting soil and building vibrations are founded on utilization of the impulse response functions technique for predicting complete vibration records on existing soils, buildings and equipment prior to installation of construction and industrial dynamic sources (Svinkin 1973, 1996). The impulse response function is an output signal of the system based on a single instantaneous impulse input (Bendat and Piersol 1993). These functions are applied for studies of complicated linear dynamic systems with unknown internal structures for which mathematical description is difficult or impossible. In the case under consideration, the dynamic system is the soil medium through which waves propagate outward from sources of construction and industrial vibrations. The input signal of the system is the impulse response of the ground at the place of pile driving, dynamic compaction of soil, or installation of a machine foundation; the output signal is the vibratory response of a location of interest situated on the surface or within the soil stratum, or any point at a building receiving vibrations. Output can be obtained, for example, as the vibration traces for displacements at locations of interest. Actually, these records are experimental Green’s functions.

Impulse response functions for the dynamic system being considered are determined by setting up an experiment. Such an approach does not require routine soil boring, sampling, or testing at the site where waves propagate from the vibration source, eliminates the need to use mathematical models of soil bases and structures in practical applications, and provides the flexibility of considering heterogeneity and variety of soil and structural properties. Unlike analytical methods, experimental impulse response functions reflect real behavior of soil and structures without direct investigation of the soil and structure properties. Because of that, the suggested methods have substantially greater capabilities in comparison with other existing methods.

The following is a general outline of the methods for predicting vibrations at a distance from an impact source. It is assumed that the dynamic loads transmitted onto the soil are known or can be found using existing theories. At the place in the field for installation of the wave source, impacts of known magnitude are applied onto the soil. The impact is often created using a rigid steel sphere or pear-shaped mass falling from a mobile or bridge crane. The oscillations resulting from the impact on the soil are measured and recorded at the points of interest (target points), for example, at the locations of instruments sensitive to vibration, communication lines and other devices, etc. These oscillations are the impulse response functions (Green’s functions) of the treated dynamic system which automatically take into account complicated soil conditions. Predicted vibrations are computed using Duhamel’s integral or a Fourier transform.

3 APPLICATION OF DUHAMEL’S INTEGRAL

For each single output point, the considered input – soil medium – output system is a one degree of freedom system and predicted displacements can be written as follows

(1)

where

• F(t) = resultant dynamic force transmitted to the ground;
• x,y = coordinates of the output point under consideration at ground or structure;
• h_z(x,y,t-t) = impulse response function at the output point under consideration;
• t = variable of integration.

Dynamic loads on a machine foundation can be found using existing foundation dynamics theories, for example Barkan (1962) and Richart et al. (1970). It is known that the equation of vertical damped vibrations of foundations for machines with dynamic loads can is given by

(2)

with initial conditions z = z₀ and t = t₀ for t = 0. In Equation (2),

• c = viscous damping coefficient;
• k_z = spring constant for the vertical mode of foundation vibrations;
• P(t) = exciting force;
• M = mass of foundation and machine.

Parameters of the foundation-soil system M, c and k_z are considered known in predicting vibrations.

Figure 1 Dynamic Forces on machine foundations and soil base

Equation (2) can be converted into another form as

(3)

with

(4)

where

• f _nz = natural frequency of vertical vibrations of foundation;
• a = effective damping constant.

An expression derived from Equations (3) and (4) for a dynamic load applied to the soil can be written as

(5)

The dynamic force transmitted from the machine foundation to the soil base (Figure 1) depends on the foundation and machine mass, the damping constant, natural frequency of vertical foundation vibrations and vertical foundation displacements as a function of time.

Substitution of Equation (5) to Equation (1) gives

(6)

For an arbitrary dynamic load, P(t), the total foundation displacement is

(7)

where f_nd = damped natural frequency of vertical vibrations of the foundation and

(8)

The general solution for determining dynamic displacements of points on the soil or in structures is obtained substituting Equation (7) to Equation (6)

(9)

3.1 Source with impact loads

Impact loads are transmitted to foundations from moulding machines, forge and drop hammers, and many construction operations like pile driving.

Vibration displacements of the source machine foundation can be assigned analytically as a damped sinusoid

(10)

with

(11)

where

• I_F = impulse force transmitted from machine to foundation;
• f = modulus of damping;
• k_z = coefficient of vertical subgrade reaction;
• A = contact area between foundation and soil.

According to Savinov (1979), the modulus of damping, f, ranges in a relatively narrow range and is slightly dependent on soil conditions. For instance, f values range from 0.004 to 0.008 sec for foundations with contact areas less than 10.0 m². Coefficient, k_z¢ is determined according to Barkan (1962). Also, it is possible to use other approaches for determining values of f and k_z .

After substitution of Equation (10) to Equation (6), vibration displacement at a target point is

(12)

3.2 Source with steady state vibration loads

A harmonic dynamic load applied to the foundation can be written as

(13)

where

• P₀ = load amplitude;
• w = angular frequency.

Such loads are transmitted to foundations under various machines. The most prevalent powerful sources of steady state vibrations are compressors and crushing equipment.

The solution of Equation (3) with the right side of expression (13) is

(14)

with

(15)

After substitution of Equation (14) to Equation (6), vibration displacement in a target point is

(16)

Integration limits were taken (-¥ , t) because steady state vibrations are considered.

3.3 Source with transient state vibration loads

Dynamic transient loads are transferred to a foundation from a vibro-isolated block for a forge hammer. These dynamic loads can be represented as

(17)

with

(18)

where

• z₁ = dynamic displacement of the vibro-isolated block;
• z^.₁ = dynamic velocity of the vibro-isolated block;
• λ = natural frequency of vertical vibrations of the vibro-isolated block;
• k_b = spring constant for the vertical mode of the vibro-isolated block;
• M_b = mass of the vibro-isolated block and machine;
• c_b = viscous damping coefficient of vibro-isolation;
• β = damping constant of vibro-isolation.

Parameters M_b, c_b and k_b are considered known.

Vibration displacements of the vibro-isolated block can be assigned as

(19)

with

(20)

where I_b = impulse applied to the vibro-isolated block; λ₁ = damped natural frequency of the vibro-isolated block.

Substitution of Equation (19) to Equation (17) gives

(21)

The duration of transient state vibrations is commensurate with the time of attenuation of foundation natural vibrations. For that reason determining dynamic loads transmitted to the soil, F(t), it is necessary to take into account natural foundation vibrations.

Next consider determination of the function F(t) in detail. A general integral of a linear nonhomogeneous Equation (3) with the right side equal to expression (21) is

(22)

where a partial integral will be found in a form

(23)

because the vibro-isolated block parameter range eliminates the coincidence of β+iλ with roots of characteristic equation equal α+if_nd. The use of the method of indeterminate coefficients gives

(24)

(25)

Differentiation of Equation (22) gives

(26)

Substituting initial conditions to Equation (22) and (26), we obtain arbitrary constants c₁ and c₂. After substitution these constants to Equation (22) and using expression (23), a general solution of Equation (3) is

(27)

The first term of the right side of Equation (27) presents the initial free displacement of a point under consideration determined by initial conditions and independent of the exciting force, the second term is excited free vibrations determined by the exciting force and independent of initial conditions, and third term is forced vibrations.

For zero initial conditions at the time of vibro-isolated hammer operations, Equation (27) becomes

(28)

Equation (28) can be transformed as

(29)

with

(30)

(31)

Substituting expression (29) into Equation (6), we obtain vertical or, similarly, horizontal displacements of soil and structures as

(32)

The first integral represents the displacements of a point under consideration excited by free foundation vibrations, and the second one by forced foundation vibrations.

Coefficients in equation (32) are defined as follows

(33)

It is necessary to point out that displacements at target points depends only on parameters observed in experiments.

Duhamel’s integral was applied to compute ground surface vibrations at distance of 8.4 and 14.0 m from the foundation with an area of 80.0 m² under a forge hammer at a site with clay soils. A falling weight of 7.25 tonnes produced the vibration records in Figure 2. The prediction was performed using various frequencies of natural vertical foundation vibrations obtained according to different theoretical approaches. Changes of this frequency affect predicted records only slightly. It can be seen in Figure 2 that measured and predicted records have very close shapes and the difference between maximum amplitudes is 9-25 % and 2-10 % at distances 8.4 and 14.0 m, respectively.

Figure 2 Measured (1) and Predicted (2-5) records of vertical soil vibrations excited by operating large forge hammer with falling mass of 7.25 tonnes

4 APPLICATION OF FOURIER TRANSFORM

Application of the direct Fourier transform to an impulse response function h_z(x,y,t-τ) gives

(34)

For a real physical system, records can be measured only over some finite time interval T, so that S_x,y(iω) is estimated by computing the finite Fourier transform

(35)

The complex Fourier transform can be presented as

(36)

where

S(x,y,ω) = magnitude spectrum and

θx,y(ω) = phase spectrum.

Figure 3 Vertical and horizontal amplitudes of soil vibrations at distances 16.6 and 23.3 m from the machine foundation: 1 – Measured vibrations; 2 – Predicted vibrations

In fact, the magnitude spectrum is the transfer function of the considered dynamic system: ground at the place of the dynamic source – soil medium through which waves propagate outward from the source – target point at any location of interest at the soil or in buildings. If the impact applied onto the soil is not instantaneous, the transfer function of the considered dynamic system can be obtained as a ratio of spectrum magnitudes of output to input.

A magnitude spectrum of the dynamic source, P_s, transmitted from the foundation onto the soil is

(37)

where

Pf(ω) = magnitude spectrum of the dynamic load onto foundation,

μ = amplification factor of the foundation-soil system.

A predicted magnitude displacement spectrum in the target point with coordinates x and y is

(38)

Predicted vertical or, similarly, horizontal displacements of soil and structures as a function of time at the location under consideration may be derived using the inverse Fourier transform of S_p(x,y,ω)

(39)

For a source with steady state vibration loads, it is very easy to predict vibration amplitudes in target points. Predicting amplitude Z_x,y at target point can be find as

(40)

where

P0 = amplitude of the source dynamic load;

μ0 = ordinate of the amplification factor corresponding the source angular frequency ω0.

Figure 3 demonstrates examples of predicting amplitudes of soil vibrations from a steady state vibration source. The machine foundation with contact area of 15.1 m² was installed at the site with type-I slump-prone soils (Svinkin & Zhuchkova 1972). The predicted amplitudes of soil vibrations matched well the measured vibration amplitudes excited by the vibration machine installed on the foundation. Comparison was performed at distances 16.6 and 23.2 m from the machine foundation in frequency range of 400-800 rpm. Error margins were within 5-20%.

Comparison of the suggested numerical predicting methods shows a preference for Duhamel’s integral for sources with impact and transient state vibration loads because there are some difficulties in calculation of the inverse Fourier transform for expression with an unknown load function phase spectrum. Besides, Duhamel’s integral is almost insensitive to small changes of original curves.

5 CONCLUSIONS

Numerical methods coupled with experimental soil response measurements are used to predict soil and building vibrations before the installation of construction and industrial vibration sources. Such an approach does not require routine soil boring, sampling, or testing at the site where waves propagate from the vibration source.

Experimental Green’s functions reflect real soil and structure behavior and take into account spatial variations of soil properties. Because of that, the suggested methods have substantially greater capabilities in comparison with other existing methods.

ACKNOWLEDGEMENT

The writer is pleased to acknowledge special contributions to the paper made by Dr. Richard D. Woods, professor of civil engineering at the University of Michigan at Ann Arbor, USA.

REFERENCES

Barkan, D.D. 1962. Dynamics of bases and foundations. New York: McGraw Hill Co.

Bendat, J.S and Piersol, A.G. 1993. Engineering applications of correlation and spectral analysis. New York: John Wiley & Sons, Inc.

Broers, H. and Dieterman H.A. 1992. Environmental impact of pile-driving. In F. Barends (ed.), Proc., 4th Intern. Conf. on Application of Stress Wave Theory to Piles: 61-68, The Hague: Balkema.

Hanazato, T. and Kishida, H. 1992. Analysis of ground vibrations generated by pile driving – Application of pile driving analysis to environmental problem. In F. Barends (ed.), Proc., 4th Intern. Conf. on Application of Stress Wave Theory to Piles: 105-110, The Hague: Balkema.

Miller, G.F. & Pursey, H. 1954. The field and radiation impedance of mechanical radiators on the free surface of a semi-infinite isotropic solid. Proc. Royal Society, A 223: 521-541.

Richart, F.E., Hall, J.R. and Woods, R.D. 1970. Vibrations of soils and foundations. Englewood Cliffs: Prentice-Hall, Inc.

Savinov, O.A. 1979. Modern construction of machine foundations and their calculations. Second Ed. Stroiizdat, Leningrag.

Svinkin, M.R. & Zhuchkova, A.Y. 1972. Dynamic tests of foundations on type-I slump-prone soils. Soil Mech. and Found. Engrg., 9(1): 33-36.

Svinkin, M.R. 1973. Prediction of soil oscillations from machine foundation vibrations (in Russian). Dynamics of structures, Proc., Kharkov Scientific-Research and Design Inst. for Industrial Constr.: 53-65, Kiev: Budivelnic.

Svinkin, M.R. 1996. Overcoming soil uncertainty in prediction of construction and industrial vibrations. Proc. Uncertainty in the Geologic Environment: From theory to Practice, Geotech. Special Publication No. 58, 2:1178-1194, Madison: ASCE.

Wolf, J.P. 1994. Foundation vibration analysis using simple physical models. Englewood Cliffs: PTR Prentice Hall.

Mark R. Svinkin, Member, ASCE
VibraConsult
13821 Cedar Road, #205
Cleveland, OH 44118-2376
PH 216-397-9625
FAX 216-397-1175
msvinkin@vulcanhammer.net

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 judgement. 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 judgement. 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 judgement.

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 judgement 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 non-linear 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 analysed.

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 set-up 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.

Table 1. Static and Dynamic Data for Prestressed Concrete Piles in Clay over Silty Sand
Pile		Test	Time after EOID (days)	Penetration Resistance (blows/0.3 m)	Ru (kN)	Set-up Measuredd	Set-up Rate (%/day)
No.	Description
TP1	1372 mm x 127 mm Cylinder	EOID RSTR-1 RSTR-2 RSTR-3	– 2 9 22	38 >240 >240 >240	752 2451 2927 3545	1 3.26 3.89 4.71	– 113 3 2
TP2	1372 mm x 127 mm Cylinder	EOID SLT-1 SLT-2 SLT-3	– 2 9 22	48 – – –	712 1913 2789 3189	1 2.69 3.92 4.48	– 84 7 1
TP3	610 mm x 610 mm (305 mm D. void)	EOID RSTR-1 RSTR-2 RSTR-3 SLT	– 1 10 18 31	10 21 72 144 –	267 912 1530 1672 1841	1 3.42 5.73 6.26 6.90	– 242 8 1 <1
TP4	762 mm x 762 mm (475 mm D. void)	EOID RSTR-1 RSTR-2 RSTR-3 RSTR-4 SLT	– 1 4 9 18 32	14 23 60 >240 168 –	200 890 1299 1517 1601 2273	1 4.45 6.50 7.60 8.00 11.37	– 345 15 3 <1 3
TP5	762 mm x 762 mm (475 mm D. void)	EOID RSTR-1 RSTR-2 RSTR-3 RSTR-4 SLT	– 1 4 11 20 34	23 59 96 91 >240 –	262 952 1401 1588 1748 2473	1 3.63 5.37 6.06 6.67 9.44	– 263 16 2 1 3
TP6	914 mm x 127 mm Cylinder	EOID RSTR-1 RSTR-2 RSTR-3 RSTR-4 SLT	– 1 4 11 21 35	15 34 64 162 113 –	400 885 1241 1766 2300 2406	1 2.21 3.10 4.42 5.75 6.02	– 121 13 6 3 <1
TP7	914 mm x 127 mm Cylinder (spliced)	EOID RSTR-1 RSTR-2 RSTR-3 RSTR-4 SLT	– 1 4 10 20 35	32 32 102 168 186 –	454 876 1285 1890 2260 2406	1 1.93 2.83 4.16 4.98 5.30	– 93 16 8 2 <1

Table 2. Static and Dynamic Data for Piles in Unsaturated Sandy Soils
Pile			Test	Time after EOID (days)	Penetration Resistance (blows/0.3 m)	Ru (kN)	Set-up Measured	Set-up Rate (%/day)
No.	Description	Embedment (m)
1	Prestressed concrete 508 mm x 508 mm (38 mm D. void)	38.0	EOID RSTR-1 SLT	– 3 12	110 1114 –	2487 3243 6450	1 1.30 2.59	– 10 11
2	Prestressed concrete 356 mm x 356 mm	27.4	EOID RSTR-1 SLT	– 7 16	68 78 –	1134 2309 3736	1 2.03 3.29	– 15 7
3	324 mm O.D. by 6 mm thick closed end steel pipe	25.3	EOID RSTR-1 SLT	– 7 14	27 48 –	681 1232 2224	1 1.81 3.26	– 12 12

Table 3. Static and Dynamic Data for Prestressed Concrete Piles in Saturated Sandy Soils
Pile			Test	Time after EOID (days)	Penetration Resistance (blows/0.3 m)	Ru (kN)	Set-up Measured	Set-up Rate (%/day)
No.	Description	Embedment (m)
CT1	457 mm x 457 mm	19.7	EOID RSTR-1 RSTR-2 SLT	– 2 11 21	18 84 84 –	913 1145 1702 1666	1 1.25 1.86 1.85	– 13 5 -<1
CT2	457 mm x 457 mm	22.9	EOID RSTR-1 RSTR-2 SLT	– 2 11 21	42 84 60 –	1907 2176 2668 2540	1 1.14 1.40 1.34	– 7 4 -<1
CT3	610 mm x 610 mm (267 mm D. void, solid ends)	19.5	EOID RSTR-1 RSTR-2 SLT	– 1 10 22	34 72 108 –	1513 – 2615 2869	1 – 1.73 1.90	– – 7 <1
CT4	610 mm x 610 mm (267 mm D. void, solid ends)	22.9	EOID RSTR-1 RSTR-2 SLT	– 2 11 23	77 96 216 –	1986 2691 3617 3724	1 1.35 1.82 1.90	– 18 4 <1
CT5	915 mm x 915 mm (570 mm D. void, solid ends)	22.3	EOID RSTR-1 SLT	– 6 20	92 60 –	2949 4210 4900	1 1.43 1.66	– 7 1

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

Pile			Soil	SLT	Time between	Dynamic Testing			Signal Matching
No.	Description	Length (m)		(kN)	SLT & DT (hours)	Time a/EOID (days)	Test	Blow Count (bl/0.3 m)	Original (kN)	Error (%)	Reanalzd (kN)	Error (%)
1(1)	610 mm PSC 305 mm void D.	28.42	Sand HWT	4228	+24	13	RSTR-2	360	4116	-2.6	3498*	-17
2(3)	610 mm PSC 305 mm void D.	20.20	Sand & Clay HWT	3160	+24	12	RSTR-2	240	2011	-36	2216	-30
3(5)	610 mm PSC 305 mm void D.	24.54	Sand & Clay HWT	3560	+24	24	RSRT-2	288	3573	+0.4	–	–
4(6)	610 mm PSC 305 mm void D.	37.69	Clay & Sand HWT	3560	+24	24	RSTR-2	720	3467	-2.6	4041*	+14
5(7)	610 mm PSC 305 mm void D.	37.03	Sand & Clay HWT	4361	+24	29	RSTR-2	576	3386	-22	4236*	-3
6(46)	610 mm PSC	25.58	Sand, HWT	2216	+24	13	RSTR-2	120	2114	-4.6	2123	-4.2
7(48)	762 mm PSC 457 mm void D.	31.10	Sand HWT	6635	+48	31	RSTR-2	432	3039	-54	3836*	-42
8(49)	762 mm PSC 457 mm void D.	30.80	Sand & Clay HWT	2812	+24	10	RSTR-2	144	2523	-10	2376	-16
9(50)	762 mm PSC 457 mm void D.	31.57	Sand & Clay HWT	4005	+24	33	RSTR-2	312	–	–	3435*	-14
10(51)	762 mm PSC 457 mm void D.	30.02	Sand, HWT	6439	+24	26	RSTR-2	264	–	–	3751*	-42
11(56)	610 mm PSC 76 mm void D.	19.60	Sand with Silt & Clay, HWT	3524	-48	1	RSTR-1	72	3253	-8	2100	-40
12(62)	610 mm PSC	58.52	Sand, Clay HWT	2893	+24	8	RSTR-2	80	2382	-17	2203	-24
13(68)	610 mm PSC 102 mm void D.	27.43	Clay & Sand HWT	4717	+48	21	RSTR-1	1000	4517	-4.2	4632	-1.8

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

Pile			Soil	SLT	Time between	Dynamic Testing			Signal Matching
No.	Description	Length (m)		(kN)	SLT & DT (hours)	Time a/EOID (days)	Test	Blow Count (bl/0.3 m)	Original (kN)	Error (%)	Reanalzd (kN)	Error (%)
14(69)	406 mm PSC 102 mm void D.	24.38	Clay & Sand HWT	2626	+48	15	RSTR-1	180	3204	+22	–	–
15(70)	HP 346×109	27.43	Clay, HWT	2750	+48	34	RSTR-1	1000	2799	+1.7	–	–
16(71)	HP 346×109	27.43	Sand & Clay HWT	1393	+24	10	RSRT-1	96	–	–	1517*	+8.9
17(72)	610 mm x 13 mm OEP	25.91	–	2670	+24	10	RSTR-1	150	–	–	2652*	-0.7
18(73)	610 mm PSC Octagonal	25.91	Sand & Clay HWT	4873	+24	10	RSTR-1	1000	3783	-22	3814	-22
19(74)	305 mm PSC	27.74	Sand, Clay & Silt, HWT	1602	+48	22	RSTR-3	208	–	–	1687*	+5
20(75)	610 mm PSC	24.84	Sand & Clay HWT	2238	+24	3	RSTR-1	24	2448	+9	2617	+17
21(76)	610 mm PSC	20.27	Sand & Clay HWT	4650	+24	3	RSTR-1	60	–	–	5006*	+7.6
22(92)	244 mm x 14 mm CEP	44.20	Sand & Clay	2924	+48	52	RSTR-2	602	2559	-12.4	2051	-43
23(102)	HP 299×79	22.86	–	1664	+5	1	RSTR-2	192	2185	+31	–	–
24(103)	HP 299×79	12.19	–	2318	+5	1	RSTR-1	360	2323	+0.2	–	–
25(104)	HP 299×79	24.38	–	1682	+5	1	RSTR-1	240	1918	+14	–	–
26(121)	406 mm x 6 mm CEP	12.10	Sand & Silt	1161	+24	10	RSTR-1	107	1077	-7	1068	-8

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

Pile			Soil	SLT	Time between	Dynamic Testing			Signal Matching
No.	Description	Length (m)		(kN)	SLT & DT (hours)	Time a/EOID (days)	Test	Blow Count (bl/0.3 m)	Original (kN)	Error (%)	Reanalzd (kN)	Error (%)
27(122)	800 mm PSC 560 mm void D.	18.00	Clay & Sand HWT	659	+24	10	RSTR-1	46	–	–	699*	+9
28(129)	387 mm/140 mm Timber	10.67	Clay, Loam, Till	757	+2	<1	RSTR-1	60	659	-13	636	-16
29(130)	324 mm x 6 mm CEP	24.99	Silt	970	+24	16	RSRT-1	120	797	-18	774	-20
30(133)	(356 mm x 5 mm) (318 mm x 6 mm) (279 mm x 6 mm) CEP	24.08	Silt & Clay	1197	+24	26	RSTR-1	600	1046	-13	–	–
31(154)	457 mm PSC	13.72	Sand, HWT	1041	+48	6	RSTR-1	42	730	-30	948	-9
32(155)	457 mm PSC	10.67	Sand	757	+24	4	RSTR-1	34	–	–	730*	-3.5
33(165)	324 mm x 13 mm CEP	27.43	Clay & Silt HWT	2496	+12	17	RSTR-1	96	3115	+25	–	–
34(166)	324 mm x 13 mm CEP	27.43	Clay & Silt HWT	2211	+24	17	RSTR-1	72	2390	+8	–	–
35(169)	324 mm x 13 mm CEP	21.00	–	788	-24	14	RSTR-1	48	1504	+54	–	–
36(170)	324 mm x 13 mm CEP	17.00	–	712	-24	14	RSTR-1	24	1148	+44	–	–
37(183)	305 mm PSC	26.52	Sand & Silt	1691	+24	12	RSTR-3	Refusal	1927	+14	–	–
38(184)	305 mm PSC	24.08	Sand & Silt	1090	+24	16	RSTR-3	120	1144	+5	–	–
39(185)	244 mm x 19 mm OEP	43.61	Clay with Silt & Sand	1896	-24	2	RSTR-1	60	1900	0	1878	<1

Comments about the worst obtained results. Pile 2 was tested at the same site with piles 1, 3, 4, and 5, but only pile 2 has a big error. “Automatic” analysis decreased an error from -36 % to -30 %. Perhaps the quality of the velocity record is the reason of unsatisfactory solution. Dynamic testing records of piles 2 and 4 (for comparison) are depicted in Figure 4. For pile 7, “automatic” analysis decreased an error in calculation of pile capacity from -54 % to -42 %. The time between SLT and DT was 2 days, but an elapsed time after EOID was 31 days. For such period of time the difference between compared tests should be minimal. There is no obvious explanation of the underestimating pile capacity for pile 7. An error in the computed capacity of pile 10 was -42 % in spite of the “best match” solution. Relaxation of pile capacity is possible in saturated sand, but 42 % of decreasing pile capacity on the 26th day after EOID and 1 day after SLT is very strange. For pile 23, the computed pile capacity with an error of +31 % is acceptable because the elapsed time after EOID was 1 day. Overestimating capacities for piles 35 and 36 were computed with big errors of +54 % and +44 %, respectively. These results may be explained with implementation of DT on one day before SLT.

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

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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.

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This article courtesy of Dr. Mark R. Svinkin, to whom we are deeply grateful. Figures supplied by the authors can be viewed at the bottom of the page.

SYNOPSIS

Reliability of dynamic methods for determination of pile capacity is particularly important for piles driven in soils with time-dependent properties. This paper shows the advantages of the dynamic capacity methods and points out the necessity of considering the time effect for correct assessment of the accuracy of dynamic methods. The prediction of pile capacity in pre-driving wave equation analysis can be improved by the use of variable damping as a function of time. Pile capacity obtained from a static loading test cannot be accepted as a unique standard because the static loading test yields the pile capacity at the time of test only, due to the consolidation phenomenon. Dynamic capacity testing has this same limitation. Any comparison of static and dynamic tests has to be made for tests performed within a short duration.

INTRODUCTION

Pile foundations are widely used in highway construction, buildings and other structures. Accurate and reliable determination of pile capacity is very important for proper design, construction and estimation of the cost of these foundations. It is common in design practice to predict pile capacity by static analysis in advance of pile driving based on the results of in-situ and/or laboratory soil and rock tests. Traditionally, the static loading test is used to determine ultimate capacity of the pile-soil system or the value of a service load to be supported by a pile. In recent decades, because of advances in data acquisition during pile driving and restrikes, dynamic testing has become an integral part of pile capacity prediction and measurement.

Dynamic methods have certain advantages and some uncertainties in their application. Wave equation analysis of driven piles is a prevalent method of pile driving stress calculations. Besides driveability analysis, the wave equation method is used for determination and prediction of pile capacity during both the design stage and for construction control during pile installation. Unfortunately in most cases, computed pile capacity differs substantially from results of both static and dynamic load tests. Errors in determination of pile capacity will create insufficiencies in pile foundation selection and will decrease foundation reliability.

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 reliability of dynamic methods is vague because their comparison with static loading tests is made incorrectly in most cases.

This paper considers some aspects of the verification of dynamic capacity formulas and dynamic testing methods. It also considers the improvement of pile capacity prediction by wave equation analysis.

DYNAMIC METHODS DEVELOPMENT

Determination of pile capacity by dynamic formulas is the oldest and most frequently used method. All such formulas assume that the hammer kinetic energy is to be equal to the driving resistance and the soil resistance is equal to pile capacity under static loading. There are a great number of dynamic formulas available with different degrees of reliability. The derivation of most of these formulas and details of some of the parameters required are available in Whitaker (53) and Chellis (3).

The main goal in using the wave equation method 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. The first solution of longitudinal wave propagation in elastic rods with impact was given by St. Venant almost a century ago, Timoshenko and Goodier (49). In the 1930s, Isaacs (21), Fox (8) and Granville et al. (13) pointed out that the one-dimensional wave equation can be used to analyze pile driving. However, the first step in the practical use of wave equation analysis was pioneered by Smith (36,37) when he developed a mathematical model of the hammer-pile-soil system in the late 1950s. This model is the numerical idealization of load-deformation characteristics of the soil, taking into account accumulated experience of that time of the actual behavior of driven piles and surrounding soil.

The first computer program for pile driving analysis was developed by Smith. Although some modifications and improvements of Smith’s model were subsequently necessary, results obtained by many researchers confirmed the soundness of the basic approach. Today, the most commonly used wave equation programs are based on either WEAP – Goble and Rausche (10), TTI – Hirsch et al. (17) or TNOWAVE -TNO Reports (50).

The second step was made in the middle of 1960s when Dr. G.G. Goble and associates developed pile capacity calculations from measured force and velocity at the upper end of the pile. They have suggested a simplified close form solution: The Case Method, which yields straight forward real time results. Other simple procedures such as Impedance Method and TNO Method were produced later by Beringen et al. (1) and Foeken et al. (7), respectively. In 1970, Rausche (31) has originated the signal matching technique for measured and computed pile responses in his CAPWAP program which was the next step in improvement of dynamic methods. Today, there are similar programs like TAPWAP – Wiseman and Zeitlen (54), TNOWAVE-SM – TNO Reports (50), and ADIG – Meunier et al. (26). These more accurate methods utilize a numerical solution of more rigorous mathematical models of the multi-parameter hammer-pile-soil system and provide evaluation the pile and soil boundary conditions through an iterative process of signal matching. The interpretation of measured data with the signal matching technique methods is much more reliable than those with the simple methods. Dynamic testing methods are described in Holloway et al. (19), Goble et al.(11), Rausche et al. (32), Hannigan (15) and Holeyman (18).

Dynamic pile testing (DT) has become widely used as a replacement for or supplement to static loading tests (SLT) because of its inherent savings in cost and time. These dynamic methods allow monitoring pile driving and restrikes, and also provide a method of identifying problems during driving for many kinds of piles. To obtain reliable ultimate resistance, it is necessary that the long term pile capacity be fully mobilized. Dynamic testing methods can determine static capacity at the time of testing, in other words either at the end of driving or at restrikes. This is a substantial advantage because dynamic tests can be easily repeated and, consequently, there is an opportunity to obtain pile capacity as a function of time as well as pile embedment.

PILE CAPACITY VARIATIONS WITH TIME

Piles have to withstand design loads for a long period of time. Therefore, the consequences of soil modification around the pile are essential with respect to changes of pile capacity. During pile installation, the soil around the pile experiences plastic deformations, remolding, and pore pressure changes. Excess pore water pressure developed during driving reduces the effective soil shear strength and ultimate pile capacity. After the completion of pile driving, soil reconsolidation, manifested by the dissipation of excess pore pressure at the soil-pile interface zone, is usually accompanied by an increase in pile capacity (soil setup). The amount of increase in pile capacity depends on soil properties and pile characteristics. 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 type, and pile size and type.

The phenomenon of time-dependent strength gain and loss in soils related to pile driving has been studied and published, for example Davie and Bell (4), Fellenius et al. (6), Randolph et al. (30), Rice and Cody (34), Skov and Denver (35), Svinkin (42), Tavenas and Audy (46), Thompson and Thompson (48), Tomlinson (51), Wardle et al. (52), Yang (55), York et al. (56) and others.

Pile capacity as a function of time is shown, for example, in Figure 1. Initial data for this case were taken from Fellenius et al., (6). A H-pile 310×94 (mm, kg/m) with length of 47.2 m was driven and five times restruck by a Vulcan 010 hammer. The soil at the site consisted of about 6.1 m miscellaneous earth fill followed by about 19.8 m soft to medium stiff compressible post-glacial silty clay and clayey silt underlain by about 27.4 m glacial material deposited on dolomite bedrock. The water table was about 2.5 m below grade. The H-pile was founded in the glacial material. This example demonstrates obvious advantage of DT to determine pile capacity at any time after pile installation.

SLT as well as DT yields the pile capacity at the time of testing, Svinkin (45). By way of illustration, results of DT and SLT are shown in Figure 2 for two identical cylindrical, 1372 mm x 127 mm, prestressed concrete piles, TP1 and TP2, Svinkin et al. (39). 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. The water table was at the ground surface. A Delmag D 46-13 hammer was employed for initial driving and restrikes. Each of the piles TP1 and TP2 was tested 2, 9 and 22 days after the end of initial driving. 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 was the pile capacity obtained from DT, Figure 2.

ACCURACY OF DYNAMIC FORMULAS

The well-known dynamic formulas have been criticized in many publications. Unsatisfactory prediction in pile capacity by dynamic formulas is well characterized in the recent published Manual for Design and Construction of Driven Pile Foundations, Hannigan et al.(16), in which it was concluded: “Whether simple or more comprehensive dynamic formulas are used, pile capacities determined from dynamic formulas have shown poor correlations and wide scatter when statistically compared with static load test result. Therefore, except where well supported empirical correlations under a given set of physical and geological conditions are available, dynamic formulas should not be used.”

There are two attempts to breathe new life into dynamic formulas. First, Paikowsky and Chernauskas (27) and Paikowsky et al. (28) have suggested one more simplified energy approach using dynamic measurements for the capacity evaluation of driven piles. Liang and Zhou (23) have concluded regarding this method: “Although the delivered energy is much more exactly evaluated, this method still suffers similar drawbacks of ENR“. In a second, criticizing the simplified energy approach, Liang and Zhou (23) have developed a probabilistic energy approach as an alternative to the signal matching technique for effective pile-driving control in the field.

Both attempts to improve dynamic formulas, comparison of pile capacity determined by the simplified and probabilistic energy methods with results of SLT, are incorrect. Dynamic formulas, including their two new representations, 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 (Figure 2), 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.

ACCURACY OF WAVE EQUATION ANALYSIS

The wave equation method (WEAP) was originally suggested by Smith (37) to compute the pile capacity at the end of driving (EOID). WEAP is also used for prediction of pile capacity at restrike (RSTR) performed at any time after EOID. By adjusting WEAP input with results of dynamic measurements, some researchers, for example, Hunt and Baker (20), York et al. (56) have obtained good correlation between computed and observed pile capacities. However, in most other cases, computed pile capacity differs substantially from results of static or dynamic tests. Results obtained from wave equation correlation studies made by Rausche et al. (33) and Thendean et al. (47) did not clarify the question regarding reliability of pile capacity prediction because in these studies the pile capacity was taken from SLT and blow count per 0.3 m was taken from RSTR. However, the time between compared tests was not taken into account. Also soil properties around a pile were considered the same for both EOID and RSTR. This inconsistent and illogical procedure serves only to confuse the reliability of pile capacity prediction by WEAP.

The pile-soil system changes with time after the completion of driving, but the pile velocity is only a pile property and remains in the same range for EOID and RSTRs. The largest values of pile velocity measured at the upper end of the pile and calculated along a pile shaft depend only on pile parameters and energy transferred to the pile and cannot reflect regain in soil strength and pile-soil adhesion after EOID. This is the first cause of unsatisfactory prediction of pile capacity with time after EOID.

One of the major points of criticism of the Smith soil model is that soil constants cannot be determined from standard geotechnical laboratory or in-situ tests. There are numerous experimental investigations of Smith soil parameters for driveability analysis. However, successful in-situ or laboratory determination of soil parameters does not necessarily guarantee the prediction of accurate and reliable pile capacity. The basic disadvantage of many models is the attempt to select the model parameters directly from actual soil properties. This can yield acceptable results for some cases, but in general this approach is not successful in finding good correlation between predicted and actual pile capacity after EOID.

The use of the constant damping coefficients for calculation of the dynamic resistance is the second cause of unsatisfactory prediction of pile capacity with time after EOID. Neither the pile velocity nor the damping constant can reflect time-dependent variation of the pile-soil system after EOID, Svinkin (44).

Although wave equation analysis is an excellent tool for driveability calculations, this method apparently cannot predict reliable pile capacity for various elapsed times after EOID because existing programs, for example, GRLWEAP, TTI and TNOWAVE, do not take into account changes of soil properties after pile installation. The most recent GRLWEAP (12) version of April 1997 recommends a setup factor with maximum value of 2.5 for clays and does not require wave equation analysis at restrikes for determining pile capacity. This simple approach is similar to calculation of pile capacity by dynamic formulas and does not demonstrate the good GRLWEAP capabilities.

Statistical analysis of GRLWEAP results, Hannigan et al. (16), computed for 99 piles driven into various soils, has demonstrated that WEAP does not have an advantage over the Gates dynamic formula. The mean and coefficient of variation are almost the same for both prediction methods.

For the idealized Smith wave equation model, it is desirable to find an appropriate combination of parameter values, mainly paying attention to soil variables, in order to achieve the reliable prediction of pile capacity. Paikowsky and Chernauskas (29) have suggested to include soil inertia in calculation of dynamic resistance. Apparently, at EOID and RSTR the pile-soil system has various soil deformations, stiffness, damping and soil mass participating in vibration. However, a physically based soil inertia model is an unrealistic approach because even for the simpler machine foundation-soil system, in which vibrations reflect only elastic soil deformations, the question about the soil mass involved in vibrations is not resolved. Probably, there is only one direction to enhance 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. For example, the soil shear modulus or the frequency of the fundamental mode of the pile-soil system could be considered, Svinkin (43). 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. The five soil damping options, available in GRLWEAP program, were investigated: Standard Smith Damping, Viscous Smith Damping, Case Damping, Coyle-Gibson Damping, and Coyle-Gibson/GRL Damping, Svinkin (43). A trend of the damping coefficient increase with time after EOID was found for all the considered dynamic soil models and this trend is independent of the damping resistances, Figures 3. Standard Smith damping as a function of time for various soil types is shown in Figures 4 and 5. It can be seen 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 Teferra (38), Svinkin (40,41).

Soil damping is the key parameter for adjustment of wave equation solutions with time-dependable soil properties in pre-driving analysis. In order to improve the prediction of pile capacity by wave equation analysis, in addition to energy and force adjustment, it is also necessary to make adjustment of WEAP input data with variable damping.

The idea of variable damping has been confirmed by results of statistical analysis performed by Liang and Zhou (23) who have found that the damping coefficient is affected by the time. Obviously, the effect of soil type on the damping coefficient could also be found if dynamic testing results obtained in unsaturated and saturated sands would be separately analyzed. It is necessary to point out that statistical analysis was provided for the outcome of the signal matching procedure where the damping coefficient is arbitrarily modified, together with other soil parameters, to obtain the best match of compared curves. For 611 pile cases the damping factor was in the range of 1.4-1.8 times for RSTRs than for EOID in spite of the effects of other soil parameters. These results confirm the necessity of using a variable damping coefficient to compute pile capacity at restrikes.

ACCURACY OF DYNAMIC TESTING AND ANALYSIS

Since dynamic testing is often used to replace the static loading tests, it is important to ascertain the adequacy of both SLT and DT. Design methods predict pile capacity as the long term capacity after soil consolidation around the pile is complete. Independently of the time elapsed between the driving of the test pile and the static loading test, the ratio of the predicted ultimate load over the measured ultimate load from static loading test is used for approximate evaluation of the reliability of design methods, Briaud and Tucker (2). 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. A number of papers, for example, Goble et all. (9), Goble et al. (11), Rausche et al. (32), Denver and Skov (5), Hannigan (15), Liu et al. (25) present pictures which show good agreement between dynamic and static tests in spite of ignoring the time between compared tests. These are strange correlation results. Other papers, for example, Hannigan and Webster (14), Paikowsky et al. (28), Lee et al. (22), Liang and Zhou (23) reveal substantial over and under prediction of pile capacity obtained by dynamic testing. Paikowsky et al. (28) made comparison of DT and SLT for 204 pile-cases in various types of soil. The computed pile capacity from DT ranged from under prediction of about 0.4 to maximum over prediction of about 1.7. These correlation results look as more realistic.

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. (32). This is not a predicted value. Moreover, the papers referenced above consider the static capacity from SLT 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. As it was shown in Figure 2, SLT, as well as DT, yields a different pile capacity depending on the time of testing, as measured after pile installation.

For a few separate piles, it is possible to find published information regarding the time between static and dynamic tests. However, 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 in the papers referenced above. What is the real meaning of such mixture? Nobody knows. It is not a verification of dynamic testing at restrikes and it is not assessment of real setup 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 restrikes using the DT but is not in the SLT. A statistical approach for assessment of the time between comparable SLT and DT, Paikowsky et al. (28), Likins et al. (24), Rausche et al. (33), is also unacceptable for piles in soils with time-dependent properties because this approach demonstrates correlation of setup factors rather than correlation of dynamic methods.

Static Loading Tests and Dynamic Testing present different ways of determining pile capacity at various times after pile installation, but for valid correlations two principal conditions have to be the same for both kinds of tests. 1) static and dynamic capacities must be compared at the same time after pile installation in both SLT and DT methods, and 2) the ultimate pile capacity is obtained in the SLT only if it provides the fully mobilized pile capacity (long term capacity), similar to the DT, Svinkin (45).

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 only be made 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. Closely time correlated comparisons of SLT and DT have to be made in order to clarify the reliability of pile capacity by dynamic testing in soils with time-dependent properties.

CONCLUSIONS

It is imperative to consider time effects for accurate determination of pile capacity by both static and dynamic methods.

The prediction of pile capacity in pre-driving wave equation analysis can be improved by the use of variable damping as a function of time. Variable damping is the key parameter to enhance accuracy of wave equation solutions because this damping takes into consideration soil consolidation after pile installation.

The main criterion for accurate assessment of pile capacity prediction based on dynamic measurements of force and velocity at the upper end of the pile during driving is the ratio of capacities obtained by dynamic and static tests. Such a ratio, taken for arbitrary time between compared tests, in not a verification of dynamic testing results.

Dynamic testing and analysis yield the real, not predicted, static capacity of piles at the time of testing. The static capacity from a static loading test is not a unique standard for assessment of dynamic testing results. Both static loading test and dynamic testing yields the pile capacity at the time of testing.

In soils with time-dependent properties, comparison of static loading test and dynamic testing must be made only for tests performed immediately, in short succession.

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Fig. 1 Pile capacity versus time for HP 310×94 in clayey soil

Fig. 2 Pile capacity versus time for prestressed concrete piles in clayey soil

Fig. 3 Shaft damping coefficient as a function of time after pile installation

Fig. 4 Variable Smith damping in clay and unsaturated sand, after Svinkin (40)

Fig. 5 Variable Smith damping in saturated sand, after Svinkin (41)