Mark R. Svinkin, Cleveland, USA

Richard D. Woods, University of Michigan at Ann Arbor, USA

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)

I just wanted to thank you for the very informative article about pile design and it’s capacity. It was really interesting to learn more about this, and how the prediction of pile capacity in the design and even construction phase could affect how they are installed. After reading this, I’m really curious to see this in action in real life. It would be cool to be able to put words into a visual image.

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