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ABSTRACT: Knowledge of pile capacity over a long period of time after the end of initial driving is important for proper design, construction and estimation of the cost of pile foundations. In this paper, assessment of pile capacity as a function of time has been performed for cohesive soils. On the basis of an existing formula, a new relationship between pile capacity and time after pile installation has been derived. This relationship takes into account pile capacity at the end of driving and an actual time after pile installation. Derived results can be used as a guide for evaluation of long term capacity of piles in cohesive soils.

1 INTRODUCTION

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, remoulding, 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 in cohesive soils, 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). The amount of increase in pile capacity and the time required for return of equilibrium conditions depend on soil properties and pile characteristics. For example, the disturbed zone around a pile is more or less proportional to the soil volume displaced during driving and dissipation of excess pore water pressure occurs faster in friction soils.

The phenomenon of time-dependent strength gain in cohesive soils related to pile driving has been studied and published, for example, Fellenius et al. (1989), Randolph et al. (1979), Skov & Denver (1988), Seed & Reese (1955), Svinkin et al. (1994), Thorburn & Rigden (1980), Tomlinson (1971), Wardle et al. (1992), and others.

Assessment of pile capacity as a function of time is, of course, important in the design and construction of pile foundations. Having knowledge of general tendencies of pile capacity with time after driving would certainly be beneficial in economical standpoint. Such information may be used during construction to reduce the design penetration and pile capacity at the end of initial driving and also to choose relevant time for dynamic testing at restrikes or static loading test. In this paper, an attempt is made to present the relationships between pile capacity and elapsed time after the end of initial driving (EOID) for cohesive soils and to show some benefits for estimation of pile capacity from this approach.

2 EXISTING FORMULA

Skov and Denver (1988) found the following formula for ultimate pile capacity, R_u(t), as a function of relative time between different tests

(1)

Some designations in this formula are different from those given in the original expression. The pile capacity at the first restrike, R_RSTR-1, is the lower limit for appreciable increasing in pile capacity when some time elapsed after initial driving results in developing soil set-up. Quantity, t, is a time elapsed from the end of initial driving and capacity R_RSTR-1 is determined for t=t₁. A factor, A, is dependent on soil conditions.

Consolidation of cohesive soils around the pile after pile installation requires much more time in comparison with other soil types like sand and gravel to regain in soil strength and pile-soil adhesion after EOID. For this reason the existing formula is pertinent for clay and cohesive soils.

Case histories presented by Svinkin et al. (1994) confirmed that formula (1) is a good indicator of the pile capacity versus relative time relationship after pile installation. Besides, it was shown that the factor, A, depends not only on the soil but also on the pile type and size.

The application of formula (1) usually requires to make the first restrike in 1-2 days after pile driving. It might be especially convenient for dynamic testing at construction sites where many piles should be tested by restrike in a short period of time.

Nevertheless, the existing formula yields relative set-up versus relative time for assessment of the pile capacity after the first restrike. This is a contradiction to the set-up approach commonly used in geotechnical practice and inconvenient for certain construction sites to restrike piles on 1-2 days after pile installation.

3 PROPOSED FORMULA

The main goal to derive a new formula for evaluation of the set-up effect of cohesive soils in pile capacity is to take into consideration the pile capacity at EOID and the actual time elapsed after pile installation.

For a soil set-up straight line passing through two points corresponding pile capacity at EOID, R_EOID, and pile capacity at any time after pile installation, R_u(t), a formula with a logarithmic time scale can be written

(2)

Time is calculated in days after pile installation. The time for EOID is taken 0.1 (2.4 hours) that negligibly affects increasing in the pile capacity at EOID but gives an opportunity to use the logarithmic time scale.

After simplification formula (2) becomes

(3)

Formula (3) is similar to formula (1). However, proposed formula (3) has certain advantages. This formula (a) uses the traditional set-up formulation, (b) takes into account the actual time in days passed after pile installation, (c) provides determination of the soil set-up independently of the time of the first restrike.

4 CASE HISTORIES

For verification of formula (3), in the following case histories the existing and proposed expressions were used to calculate the pile capacity as a function of time after EOID.

4.1 Case 1

Three piles were considered in this study from total number of seven prestressed concrete piles tested for a bridge approach (GRL Report 1987, Svinkin et al. 1994). A pile description 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. For each pile, 3 to 4 dynamic testings were performed after pile installation. For piles TP3 and TP4 static loading tests (SLT) were made as well. The elapsed time after EOID, the penetration resistance and the time dependent ultimate capacity of piles tested are shown in Table 1. Pile capacities from dynamic testings were determined by CAPWAP analysis and the Davisson criterion of failure load was used for static loading tests (GRL Manual 1993).

Pile capacity calculation according to formula (1) was made by Svinkin et al. (1994). Quantity, t₁, was equal to 2 days for piles TP1 and 1 day for piles TP3 and TP4. Measured data and results calculated in accordance with the existing formula have been plotted in ordinates R_u(t)/R_RSTR-1 and log₁₀(t/t₁) as broken and straight lines, respectively, in Figure 1. Note that the set-up coefficients from the field tests generally match well to those obtained from the existing formula.

Table 1. Static and Dynamic Data for Prestressed Concrete and Steel Piles in Clayey Soils
Pile		Test	Time after EOID (days)	Penetration Resistance (blows/0.3 m)	Ru (kN)	Factor B	Set-up Measd	Set-up Calcd
No.	Description
TP1	1372 x 127 mm Cylinder Prestressed Concrete	EOID RSTR-1 RSTR-2 RSTR-3	– 2 9 22	38 >240 >240 >240	752 2451 2927 3545	1.60	1 3.26 3.89 4.71	1 3.08 4.13 4.75
TP3	610 x 610 mm (305 mm D. void) Prestressed Concrete	EOID RSTR-1 RSTR-2 RSTR-3 SLT	– 1 10 18 31	10 21 72 144 –	267 912 1530 1672 1841	2.37	1 3.42 5.73 6.26 6.90	1 3.37 5.74 6.35 6.91
TP4	762 x 762 mm (475 mm D. void) Prestressed Concrete	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	3.50	1 4.45 6.50 7.60 8.00 11.37	1 4.45 6.61 7.84 8.90 9.77
B-2	HP 310×94	EOID RSTR-1 RSTR-2 RSTR-3 SLT RSTR-4 RSTR-5	– 2 6 7 15 16 132	12 36 60 72 – 48 >120	489 1201 – 1512 13972002 2291	1.14	1 2.46 – 3.09 2.86 4.09 4.69	1 2.48 – 3.10 3.48 3.50 4.55

EOID – end of initial driving

RSTR – restrike

SLT – static loading test

For piles under consideration, the factor, B, has been found on the basis of back calculations using formula (3). This factor ranges from 1.6 to 3.5 (Table 1). Scattering of the factor, B, is the same for the existing and proposed formulae. The set-up coefficients derived from both the field tests and from formula (3) are given in Table 1 and depicted in ordinates R_u(t)/R_EOID and Time after EOID in days (logarithmic scale) as broken and straight lines, respectively, in Figure 1. Good agreement is found between calculated and measured values of pile capacity as a function of time after EOID.

Figure 1. Pile capacity-time relationship for prestressed concrete and steel piles in clayey soils

4.2 Case 2

Initial data for this case were taken after Fellenius et al. (1989). An H-pile 310×94 (mm, kg/m) with length of 47.2 m was driven and restruck by a Vulcan 010 hammer with a nominal energy of 44 kJ. Restrike No. 4 of this pile was performed by drop hammer with nominal energy of 65 kJ. The soil at the site consisted of about 6.1 m of miscellaneous earth fill followed by about 19.8 m of soft to medium stiff compressible post-glacial silty clay and clayey silt underlain by about 27.4 m of 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.

Five restrikes were made for pile tested. Pile capacities from dynamic testings were determined by CAPWAP analysis (GRL Manual 1993). The static loading test for this pile did not show a plunging behavior. Failure load from the static loading test was 1397 kN (Davisson 1972), 1957 kN (Butler & Hoy 1977), and 2535 kN (Fuller & Hoy 1970). The capacity from the static loading test was evaluated from the Davisson criterion. The results of dynamic and static tests are shown in Table 1.

Pile capacity calculation according to formula (1) was made by Svinkin et al. (1994) and shown in Figure 1. It can be seen the calculated set-up line averages measured values of pile capacity.

Measured soil set-up and calculated set-up in accordance with formula (3) are presented in Table 1 and displayed in Figure 1 as well. For the H-pile, the proposed formula provides better fit to results tested than the existing formula.

5 SUMMARY

The application of the proposed formula shows that the magnitude of gain in pile capacity in cohesive soils depends on soil conditions, pile material and dimensions. However, the same equation with a different factor, B, can be applied for assessment of soil set-up in cohesive soils during relatively long elapsed time after pile installation.

The existing and proposed formulae demonstrate similar tendency of the set-up effect of cohesive soil in pile capacity. However, there are substantial differences between two approaches.

The existing formula yields relative set-up versus relative time for assessment of the pile capacity after the first restrike. This is a contradiction to the set-up approach commonly used in geotechnical practice. Also, it is inconvenient for certain construction sites to restrike piles on 1-2 days after pile installation. Moreover there is no standard time for the first restrike. If this time is different for various piles, the existing formula yields different assessment of soil set-up at the same site and obtained results of increasing in pile capacity cannot be compared.

The proposed formula uses the traditional set-up formulation, calculates the pile capacity at the actual time after EOID, and provides determination of the soil set-up independently of the time of the first restrike.

The proposed formula provides determination of pile capacity as a function of time after pile installation using pile capacity values obtained through dynamic testing at EOID and one restrike or one static loading test. This approach is identical for any construction site. Obtained information would be beneficial to choose sensible pile penetration depth at EOID and search the proper times in days after EOID to verify set-up in cohesive soils with an additional dynamic testing or the static loading test.

6 CONCLUSIONS

Determination of long term pile capacity is important for proper design and construction of pile foundations in cohesive soils.

A new relationship like a linear equation in a logarithmic time scale has been derived to predict an increase in pile capacity with time after pile installation. Soil set-up for several piles in cohesive soils was verified on the basis of the existing and proposed formulae. The latter has certain advantages. Obtained results showed that changes of pile capacity with time in cohesive soil may be predicted well.

Results presented in this paper certainly do not mean that pile capacity will change with time exactly like shown above. However, the demonstrated pile capacity versus time relationships can be used as guide for assessment of pile capacity with respect to time. Presented results give a chance to safe significant amount of time, energy and materials taking into account the gain of pile capacity from soil set-up. Derived relationship can also be useful in choosing representative times for both static loading test and dynamic restrike testing.

REFERENCES

Butler, H.D. & H.E. Hoy 1977. Users manual for the Texas quick-load method for foundation load testing. FHWA, Office of Development, Washington.

Davisson, M.T. 1972. High capacity piles. Proc., Lecture Series, Innovations in Foundation Construction, ASCE, Illinois Section.

Fellenius, B.H., R.E. Riker, A.J. O’Brien, & G.R. Tracy 1989. Dynamic and static testing in soil exhibiting set-up. Journal of Geotechnical Engineering, 115(7): 984-1001.

Fuller, R.M. & H.E. Hoy 1970. Pile load tests including quick -load test method, conventional methods and interpretations. HRB 333: 76-86.

GRL and Associates, Inc. 1993. CAPWAP – Case Pile Wave Analysis Program, Manual, Cleveland, Ohio.

GRL and Associates, Inc. 1987. Dynamic pile tests performed during June and July, 1987, Advance Pile Test Program, Louisiana DOT, Project No. 450-36-06, Cleveland, Ohio.

Randolph, M.F., J.P. Carter & C.P. Wroth 1979. Driven piles in clay – the effect of installation and subsequent consolidation. Geotechnique, 29(4): 361-393.

Skov, R. & H. Denver 1988. Time-dependence of bearing capacity of piles. In B. Fellenius (ed), Proc. Third Inter. Conf. on the Application of Stress-Wave Theory to Piles, Ottawa, 25-27 May: 879-888, Vancouver: BiTech Publisher.

Seed, H.B. & L.C. Reese 1955. The action of soft clay along friction piles. Transactions, ASCE, 122: 731-754.

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: 1.11.1-1.11.8, Rotterdam: Balkema.

Thorburn, S. & W.J. Rigden 1980. A practical study of pile behavior. Proc. 12th Annual Offshore Technology Conf., Houston.

Tomlinson, M.J. 1971. Some effects of pile driving on skin friction behavior of piles. Proc. Institution of Civil Engineers: 107-114, London.

Wardle, I.F., G. Price & T.J. Freeman 1992. Effect of time and maintained load on the ultimate capacity of piles in stiff clay. Piling: European practice and worldwide trends, Proc. Institution of Civil Engineers: 92-99, London: Telford.

This article courtesy of Dr. Mark R. Svinkin, to whom we are deeply grateful. It was originally presented at the 24th Annual Member’s Conference of the Deep Foundations Institute in Dearborn, Michigan, 14-16 October 1999.

Summary: Construction-induced vibrations may be detrimental to adjacent structures and sensitive electronics operating nearby. Construction vibration sources have a wide range of energy and velocity, as a function of time, transmitted on the ground. Analysis of existing methods for predicting ground and structure vibrations shows that empirical equations provide calculations only of amplitudes of vertical soil vibrations with insufficient accuracy. This paper presents the application of the impulse response function concept to solve the geotechnical problem of predicting ground and structure vibrations before installation of vibration sources. Impulse response functions reflect real behaviour of soil and structures without the investigation of soil and structure properties. A procedure is presented to compute predicted ground and structure vibrations. Good agreement is found between predicted and measured records.

1. Introduction

Sources of construction vibration, such as pile driving, dynamic compaction, blasting and operation of heavy construction equipment, may harmfully affect surrounding buildings and its effect ranges from serious disturbances of working conditions for sensitive devices and people to visible structural damage.

Considerable data have been collected, analysed and published with respect to vibrations from construction and industrial sources, e.g. Barkan (1962), Richart et al. (1970), Wiss (1981), Mayne (1985), Massarsch (1992), Svinkin (1993), Dowding (1996), Woods (1997) and others.

Empirical equations employed for assessment of expected soil vibrations from construction and industrial sources usually only allow calculation of a vertical peak amplitude of vibrations and not always with sufficient accuracy. These equations cannot incorporate specific differences of soil conditions at each site because heterogeneity and spatial variation of soil properties strongly affect characteristics of propagated waves in soil from construction and industrial vibration sources.

Svinkin (1996a; 1997) has originated the Impulse Response Function Prediction method (IRFP) for determining complete time domain records on existing soils, structures and equipment prior to installation of construction and industrial vibration sources. The IRFP method has significant advantages in comparison with empirical equations and analytical procedures.

The purpose of this paper is to discuss various approaches and their accuracy to predict and calculate soil and structure vibrations before the beginning of construction activities.

2. Construction Vibrations

2.1. Sources of Vibrations

Impact hammers are common sources of construction vibrations. Maximum rated energy of the most commonly employed piling hammers varies from 5 to 200 kJ per blow. Two kinds of frequencies are observed on the pile acceleration and velocity records. Vibrations with high frequencies of about 300-700 Hz are generated by the hammer-cushion system. Soil vibrations with such frequency content should be taken into account when pile driving occurs in close proximity to a building. Frequencies of natural longitudinal pile oscillations are in the range of 7-50 Hz, with predominance at the lower values. Measured maximum pile velocity and displacement values range from 0.9 to 4.6 m/s and 12 to 35 mm, respectively. Both parameters depend on pile type and hammer transferred energy. Displacement might be affected by soil conditions as well (Svinkin, 1992; 1996b).

Vibratory hammers for driving non-displacement piles usually have low to moderate force amplitudes and operating frequencies above 20 Hz. Displacement piles are driven by vibratory hammers with frequencies of around 10 Hz and commonly along with much higher force amplitudes (Warrington, 1992). The soil resistance to pile penetration and the seismic effect of vibratory driven piles depend substantially on soil conditions, pile type and vibratory hammer model. A coincidence of the operating frequency with the soil layer frequency may generate large ground vibrations of the soil surrounding the pile. The use of vibratory hammers with variable frequency and force amplitude may minimize damage due to accidental ground vibration amplification.

For dynamic compaction of loose sands and granular fills, a large steel or concrete weight of 49.1 to 137.3 kN is usually dropped from a height of 15 to 30 m. Such dynamic impacts generate surface waves with a dominant frequency of 3 to 12 Hz. Thus, dynamic deep compaction is also a source of intensive low frequency ground vibrations (Mayne, 1985).

The dominant frequency of propagating waves from quarry and construction blasting ranges mostly between 10 and 60 Hz. Blasting energy is much larger than energy of other sources of construction vibrations. For example, the energy released by 0.5 kg of TNT is 5400 kJ (Dowding, 1996). Such energy is 50 to 1000 times the energy transferred to piles during driving and 15 to 80 times the energy transferred to the ground during dynamic compaction of soils.

2.2. Ground Vibrations

Sources of construction vibrations generate compression, shear and Rayleigh waves (Barkan, 1992, Richart et al., 1970). Rayleigh waves have the largest practical interest for design engineers because building foundations are placed near the ground surface. In addition, Rayleigh waves contain roughly 70 % of the total vibration energy and become predominant over other wave types at comparatively small distances from the vibration source. For example, pile driving from depths between 4 and 10 m will generate Rayleigh waves within 0.4 to 3 m of the pile, depending on the propagation velocities of Rayleigh and compression waves.

Soil vibrations are mostly vertical near the source of vertical impact loads, but as distance increases, vertical and horizontal soil vibrations become similar in magnitudes, and, for some locations at the ground surface, the amplitude of horizontal vibrations might be up to three times greater than that of vertical vibrations. Waves travel in all directions from the source of vibrations forming a series of fairly harmonic waves with the dominant frequency equal or close to the frequency of the source. Spectra of the radial and transverse components of horizontal soil vibrations may have a few maxima and the one corresponding the frequency of the source is not always the largest. In general, faster attenuation of high frequency components is the primary cause of changes of soil vibrations with distance from the source. However, some records can not be explained by this mechanism and the effect of soil strata heterogeneity and uncertainties of the geologic profile should be taken into account (Svinkin, 1996a).

The proximity of the frequency of horizontal soil vibrations to one of the building’s natural frequencies may generate the conditions of resonance in that building. Moreover, vertical ground vibrations can cause dangerous structural settlements. Considerable data have been collected and published with respect to intolerable vibrations and settlements from construction and industrial sources, e.g. Barkan (1962), Richart et al. (1970), Wiss (1981); Lacy and Gould (1985); Massarsch (1992), Svinkin (1993); Dowding (1996) and others.

To prevent the unacceptable effect of construction vibrations, it is important to accurately predict expected ground and structure vibrations.

3. Empirical Equations

3.1. Golitsin Equation

As early as 1912, Golitsin (1912) suggested the following equation to calculate the amplitude reduction of Rayleigh waves, generated by an earthquake, between two points at distances r₁ and r₂ from the source as

(1)

Where

A₁ = amplitude of vibrations at a distance r₁ from the source
A₂ = amplitude of vibrations at a distance r₂ from the source
γ = attenuation coefficient.

The term (r₁/r₂)^0.5 indicates the radiation or geometric damping and the term exp[-γ(r₂-r₁)] indicates the material damping of wave attenuation between two points.

Equation (1) has been originally derived to estimate the attenuation of low frequency Rayleigh waves with large wavelength for which the coefficient, γ, depends slightly on the soil upper layers properties. For such conditions, the coefficient, γ, changes reasonably in a narrow range in assessment of attenuation properties of soils.

Subsequently, in some studies, by Barkan (1962), Richart et al. (1970), Massarsch (1992), Woods (1997) and others, this equation was used for preliminary computation of ground vibrations from industrial and construction sources. Waves generated in the ground by construction sources have higher frequencies and smaller wavelength in comparison with waves from earthquakes and propagate mostly in the upper soil strata close to the ground surface. It is obvious that the coefficient, γ, is important for the accurate prediction of wave attenuation. Values of γ for various soil types can be found in the referenced publications. An experimental study to quantify of the coefficient, γ, was performed by Woods and Jedele (1985) who investigated soil damping for different construction operations at sites with soils of various stratifications. The observed data were approximated by average curves for frequencies of 5 and 50 Hz.

Nevertheless, there are some other factors that affect the coefficient, γ. Collected experimental data indicates (Svinkin, 1973; 1992) that the coefficient, γ, depends on physical parameters related to the vibration source (pile impedance, length and transferred energy to the pile, for example), frequency, distance from the source and variation of soil stratification at a site. Test data along the ground surface shows that for various pairs of widely separated points on the ground surface, values of γ can differ more than an order of magnitude and even change sign. Thus, the coefficient, γ, acceptable for small distances may be inadequate for long distances. On account of wave refraction and reflection from boundaries of diverse soil layers, an arbitrary arrangement of geophones at a site can yield incoherent results of ground vibration measurements because waveforms measured at arbitrary locations at a site might represent different soil layers. Coherent and consistent results for assessment of surface wave attenuation can be obtained on the basis of measurement of ground vibrations reflected from the same soil layer boundaries. Heisey et al. (1982) indicated certain requirements for a choice of appropriate spacing of the receivers in the application of the spectral analysis surface waves (SASW) method in the evaluation of soil properties.

One more important point. If it is possible to measure an amplitude of ground vibrations at the referenced distance r₁ during construction activities, a ground vibration amplitude at a distance r₂ can be measured as well. Besides, actual structure responses to ground vibrations can be measured without any prediction of expected vibrations. In the correct prediction of ground vibration amplitudes before the beginning of construction operations, the referenced amplitude is usually unknown. So, problems with uncertainty in assignment or determination of the coefficient, γ, and unknown referenced amplitude show that equation (1) cannot be used for predicting ground vibrations and the application of equation (1) to calculate of ground vibrations from construction and industrial sources may yield inaccurate results.

3.2. Scaled-Distance Approach

The scaled-distance approach, ground velocity-distance-energy relationship, was proposed by Attwell and Farmer (1973) to calculate the peak ground velocity at surface distance, D, from a source normalized with energy as

(2)

Where

W_r = energy of source or rated energy of impact hammer
k = value of velocity at one unit of distance.

Wiss (1981) reported an identical equation

(3)

Where the value of ‘n’ yields a slope in a log-log plot between 1.0 and 2.0 with an average value of 1.5. It was an important finding because a slope of amplitude attenuation for all tested soils was in the narrow range of 1 to 2. It turned out that the scaled-distance approach was very useful in the assessment of construction vibrations. Woods and Jedele (1985) and Woods (1997) gathered data from field construction projects at which the source energy was known or could be estimated and developed a scaled distance chart that correlated with ground types. Most of these data correlated with a slope of n=1.525 for soil class II and some of the data presented in that study showed n=1.108 for soil class III.

On the basis of the actual range of energy transferred to piles and the range of the measured peak particle pile velocity at the top of steel, concrete and timber piles, the results of Woods and Jedele (1985) were adapted by Svinkin (1992; 1996b) to calculate the peak ground velocity prior to the beginning of pile driving. The peak vertical ground velocity versus scaled distance from driven piles is depicted in Fig. 1. The reasonable pile velocity range for steel, concrete, and timber piles is 4.6 to 2.4, 2.4 to 0.9 and 4.6 to 1.5 m/s, respectively. The latter is actually the same as for steel piles. Values of 4600, 2400 and 900 mm/s have been marked as extreme left values on the slope lines. There are two areas constructed on the diagram: the upper area for steel and timber piles and the lower one for concrete piles with a slope, n=1.000, which is the upper limit for the peak particle velocity with the lower value for the rate attenuation. Data presented in Fig. 1 provide an opportunity to construct curves of the expected maximum peak ground velocity for various distances from pile driving sources and different magnitudes of transferred energy. The peak particle velocity at the pile head can be calculated in advance as (Svinkin, 1996b)

(4)

where

Z = ES/c is pile impedance
E = modulus of elasticity of pile material
S = pile cross-sectional area
c = velocity of wave propagation in pile
W_r = energy transferred to the pile.

This new development of the scaled-distance approach eliminates the need to know in advance the factor, k, and enhances accuracy of predicted peak ground velocity before pile installation.

3.3. Pile Impedance

Heckman and Hagerty (1978) and Massarsch (1992) pointed out the important effect of the pile impedance on the peak ground velocity and showed that a reduction of the pile impedance from 2000 to 500 kNs/m could increase the peak ground velocity by a factor of 8 (Fig. 2). According to equation (4), the peak particle velocity of the source is inversely proportional to the square root of the pile impedance and, for the referenced impedance range, the expected amplification of the peak pile velocity and the peak ground velocity can only be 2. Equation (4) shows that pile length, velocity of wave propagation in the pile, and transferred energy also can affect the peak ground velocity by means of the wave source velocity.

The analysis of soil vibration records, measured at the same distances from a few piles with different impedances and driven by the same hammer to the same pile penetration into the ground, was conducted. It turned out that a certain range represents the effect of the pile impedance on ground vibration velocity better than a single line (Fig. 2). A lower boundary of this range can be calculated using Equation (4).

3.4. Frequency of Vibration

Frequency and peak particle velocity are basic parameters for assessment of ground vibrations. Dowding (1996) underlying the importance of frequency because structural responses depend on the frequency of ground vibrations. The dominant frequency of expected ground vibrations can be determined prior to the beginning of pile driving (Svinkin, 1992).

4. Predicting Structure Vibrations – IRFP Method

4.1. Proposed Approach

The impulse response function prediction method (IRFP) is based on the utilization of the impulse response function technique for predicting complete vibration records on existing soils, buildings and equipment prior to installation of construction and industrial vibration sources (Svinkin, 1996a; 1997). The impulse response function (IRF) is an output signal of the system based on a single instantaneous impulse input. Impulse response functions are applied in the analysis of any complicated linear dynamic system with unknown internal structure for which its mathematical description is very difficult. 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 of the system is the ground at the place of pile driving, dynamic compaction of soil, or installation of a machine foundation; the output is a location of interest situated on the surface or inside the soil, or any point at a building subjected to vibrations. Outcomes can be obtained, for example, as the vibration records of displacements or velocities at locations of interest.

Impulse response functions of the considered dynamic system are determined by setting up an experiment (Fig. 3). Such an approach (a) does not require routine soil boring, sampling, or testing at the site where waves propagate from the vibration source, (b) eliminates the need to use mathematical models of soil profiles, foundations and structures in practical applications, and (c) provides the flexibility of considering heterogeneity and variety of soil and structural properties. Unlike analytical methods, experimental IRFs reflect real behavior of soil and structures without investigation of the soil and structure properties. Because of that, the proposed method has substantially greater capabilities in comparison with other existing methods.

The following is a general outline of the method for predicting vibrations at a distance from an impact source.

1. At the place in the field for installation of the impact source, impacts of known magnitude are applied on the ground (Fig. 3). The impact can be created using a rigid steel sphere or pear-shaped mass falling from a bridge or mobile crane or a hammer blow on the tested pile. At the moment of impact onto the ground, oscillations are measured and recorded at the points of interest, for example, at the locations of devices sensitive to vibrations. These oscillations are the IRFs of the considered system which automatically take into account complicated soil conditions.
2. Various ways are used to determine the dynamic loads on the ground from different vibration sources. For pile driving, dynamic loads are computed by the wave equation analysis. In the case of the operation of machines on foundations, these loads can be found using existing foundation dynamics theories. For dynamic compaction sites, loads from the source are easily calculated with known falling weights and heights.
3. Duhamel’s integral (Smith and Domney, 1968) is used to compute predicted vibrations which will arise from operating construction impact source.

4.2. Dynamic Loads Onto Ground

Machine Foundations

Dynamic loads at 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 be written as

(5)

with

(6)

where

b = viscous damping coefficient, kN/m/s
k_z = spring constant for the vertical mode of foundation vibrations, kN/cm
P(t) = exciting force, kN
M = mass of foundation and machine, t
f _nz = circular natural frequency of vertical vibrations of foundation, rad/s
= effective damping constant, rad/s.

An expression derived from equation (5) for a dynamic load applied to the soil is

(7)

The dynamic force transmitted from the machine foundation to the soil depends on foundation and machine masses, the damping constant, the natural frequency of vertical foundation vibrations and vertical foundation displacements as a function of time.

Vibration displacements of the machine foundation can be assigned by sampling an arbitrary function or analytically as a damped sinusoid

(8)

with

(9)

where

I_F = impulse force transmitted from machine to foundation, kNs
Φ = modulus of damping, s/rad
k_z¢ = coefficient of vertical subgrade reaction, kN/m^3
f_nd = circular natural frequency of vertical damped vibrations of foundation, rad/s
S₁ = contact area between foundation and soil, m².

The modulus of damping, Φ, ranges in a relatively narrow range and is slightly dependent on soil conditions (Savinov, 1979). For instance, values of Φ range from 0.004 to 0.008 s/rad for the foundation contact area 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 α and k_z¢ .

Pile driving

Equation (7) can be used to determine the dynamic loads transferred from the pile to the surrounding soil. In this case, M is the pile mass. The effective damping constant, α, is chosen from the range of damping constants for foundations with the smallest contact areas. A frequency of the hammer-pile-soil system is calculated by an equation (Svinkin, 1992) which takes into account pile material, the ratio of wave velocity in the pile to pile length and the pile weight to ram weight ratio.

Pile displacements as a function of time are computed by the wave equation analysis, using for example, the GRLWEAP Program (GRL and Associates, 1995). Computed displacement records at the pile top, middle, and bottom are presented in Fig. 4 for a 457 mm x 457 mm prestressed concrete pile with a length of 20.4 m. These three records are very similar and displacements at the pile top can be taken as a function z(t). For comparison, pile displacements at the same points, obtained by dynamic measurement at the pile top and computed with the CAPWAP program (GRL and Associates, 1993) for the pile middle and bottom are shown in Fig. 4. Both sets of curves were derived for the same pile capacity. It can be seen that measured results confirm the reasonableness of the use of the wave equation analysis to compute pile displacements for vibration predicting.

Dynamic Compaction

For dynamic compaction of granular soil, loads from the source are calculated with known falling weights and heights.

4.3. Computation of Predicted Vibrations

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

(10)

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

With substitution of expressions (8) and (9) equation (10) becomes

(11)

Examples of predicted results are shown in Fig. 5, 6 and 7. Measurements and prediction of vertical and horizontal ground surface displacements were made at diverse distances from the foundation under a sizeable drop hammer with a falling weight of 147.2 kN and a maximum drop height of 30.0 m. The soil at the site consisted of about 1.6 m of loose sand followed by about 6.8 m of medium density sand and 1 m of sandy clay underlain by about 10 m of slightly moist sand. The water table was about 6 m below the ground surface. The Rayleigh wave velocity was 270 m/sec. A layout of the machine foundation, the place of impact on the ground and geophones is displayed in Fig. 5.

Predicted and measured vertical and horizontal components of ground surface vibrations at eight locations are shown in Fig. 6. It can be seen that good agreement is matched in time domain vibration records, except for horizontal vibrations at two locations close to the foundation. This can be explained by the different wave paths from the foundation under the operating machine and the place for impact on the ground. The distance between these two sources was 18.7 m. Lack of coincidence of the two dynamic sources slightly affected the predicted ground vibrations at a distance from the machine foundation. Agreement of predicted and measured vibration displacements is quite satisfactory. The differences between the peak predicted and measured vibration amplitudes are less than 30 % at distances larger than 43.0 m from the foundation (Table 1). For some individual points amplitudes actually coincide.

Table 1. Peak Measured and Predicted Vibration Amplitudes

Distance from source (m)	Vertical			Horizontal
	Measured (μm)	Predicted (μm)	Error (%)	Measured (μm)	Predicted (μm)	Error (%)
25	450	330	-27	180	510	+183
33	351	216	-38	227	396	+74
43	270	232	-14	238	252	+6
57	–	–	–	162	144	-11
132	55	60	+9	–	–	–
200	30	30	0	65	59	-9
266	28	36	+30	25	29	+16

Spectrum analysis of predicted and measured time histories revealed that both records have similar frequency domain curves with the same dominant frequency. Moreover, predicted records are slightly dependent on the parameters in equation (7) for determination of the dynamic force transmitted from the source to the soil (Svinkin, 1999).

Predicted vibration curves in Fig. 7 at a distance of 266.0 m from the machine foundation were computed with various values of initial parameters in Eq. (7), Table 2. In spite of the change of the computed natural foundation frequency in the range of 23.8-63.5 rad/s and the damping constant from 8.5 to 60.5 rad/s, the shapes of measured and predicted records are almost the same and their spectra show the same dominant vibration frequency. An increase of the computed natural frequency of foundation vibrations with respect to the measured frequency leads to an increase of the largest amplitude by 10-30 % for both vertical and horizontal predicted soil oscillations. Spectra of these oscillations show a stability of frequency composition for even very long duration soil oscillations. Thus, variations of predicted soil oscillations do not exceed measurement errors even with a 2.7 times increase in the computed natural frequency of the foundation.

TABLE 2. Parameters of Foundation-Soil System

Record No.	kz (kN/m3)	α (rad/s)	Φ (s/rad)	fnz (rad/s)	M t
2	Experimental time domain foundation displacement
3	34433	8.5	0.03	23.8	9614
4	67885	60.5	0.03	63.5	2650
5	39240	35.0	0.03	48.3	2650

5. Conclusions

• Construction operations such as pile driving, dynamic compaction and blasting are wide-spread sources of ground and structure vibrations. These vibration sources have a wide range of energy and velocity, as a function of time, transmitted on the ground. Construction-induced vibrations may harmfully affect surrounding buildings. It is important to accurately predict vibrations of ground, structures, and sensitive devices prior to the beginning of construction activities to avoid the undesirable effect of generated vibrations.
• Empirical equations provide only calculation of a vertical amplitude of ground vibrations and not always with sufficient accuracy. For pile driving, the scaled distance approach with calculated peak particle velocity of the source is probably the most appropriate method for predicting upper limits of the peak particle velocity of ground vibrations. The effect of pile impedance on ground vibrations is exaggerated in some publications. Other parameters of the hammer-pile-soil system like pile length, velocity of wave propagation in the pile, and transferred energy to the pile can affect the peak ground velocity as well.
• The impulse response function prediction method (IRFP) is used to solve a geotechnical problem in predicting time domain ground and structure vibrations prior to the beginning of construction activities or installation of machine foundations.
• The proposed approach uses the impulse response function technique for a considered dynamic system: ground at the place for the source of vibrations – soil medium – output locations of interest on the ground or in any structure receiving vibrations. Experimental impulse response functions reflect real soil behaviour and take into account uncertainty in the geologic environment. Such an approach does not require routine soil boring, sampling, and testing at the site where waves propagate from the vibration source. Different ways were shown to determine dynamic loads onto the ground from machine foundations, pile driving and dynamic compaction of granular soil. An algorithm is presented to compute predicted vibrations, and examples of predicted results are demonstrated for vertical and horizontal ground displacements. There is quite satisfactory agreement between predicted and measured records.
• The proposed approach provides the method for determining and monitoring of ground, structures and sensitive devices vibration levels before the start of construction or industrial vibration activities.

6. Acknowledgement

The writer wishes to thank the reviewers for their constructive reviews of the paper.

7. References

• ATTWELL, P.B. AND FARMER, I.W., 1973. Attenuation of ground vibrations from piles. Ground Engineering, Vol. 6(4), pp. 26-29.
• BARKAN, D.D., 1962. Dynamics of bases and foundations. McGraw Hill Co., New York, 434 p.
• DOWDING, C.H., 1996. Construction Vibrations. Prentice Hall, Upper Saddle River, 610 p.
• GOLITSIN B.B., 1912. On dispersion and attenuation of seismic surface waves. In German, Russian Academy of Science News, Vol. 6, No. 2.
• GRL and ASSOCIATES, INC., 1993. CAPWAP – Case Pile Wave Analysis Program, Continuous Model, Manual, Cleveland, Ohio, USA.
• GRL and ASSOCIATES, INC., 1995. GRLWEAP – Wave Equation Analysis of Pile Driving, Manual, Cleveland, Ohio, USA.
• HECKMAN, W.S. and HAGERTY, D.J., 1978. Vibrations associated with pile driving. American Society of Civil Engineers, ASCE Journal of the Construction Division, Vol. 104, No. CO4, pp. 385-394.
• HEISEY, J.S., STOKOE, K.H.II, and MEYER, A.H., 1982. Moduli of pavement systems from spectral analysis of surface waves. Research Record No. 852, Transportation Research Board, pp. 22-31.
• LACY, H.S. and GOULD, J.P., 1985. Settlement from pile driving in sands. American Society of Civil Engineers, Proceedings of ASCE Symposium on Vibration Problems in Geotechnical Engineering, Detroit, Michigan, G. Gazetas and E.T. Selig, Editors, pp. 152-173.
• MAYNE, P.W., 1985. Ground vibrations during dynamic compaction. American Society of Civil Engineers, Proceedings of ASCE Symposium on Vibration Problems in Geotechnical Engineering, Detroit, Michigan, G. Gazetas and E.T. Selig, Editors, pp. 247-265.
• MASSARSCH, K.R., 1992. Keynote lecture: Static and dynamic soil displacements caused by pile driving. Proceedings of the Fourth International Conference on the Application of Stress-Wave Theory to Piles, F.B.J. Barends, Editor, The Hague, The Netherlands, pp. 15-24.
• RICHART, F.E., HALL, J.R. and WOODS, R.D., 1970. Vibrations of soils and foundations. Prentic-Hall, Inc., Englewood Cliffs, New Jersey, 414 p.
• SAVINOV, O.A., 1979. Modern foundation structures for machines and their calculations. In Russian, Stroiizdat, Leningrad, 200 p.
• SMITH, G.M. and DOWNEY G.L. 1968. Advanced engineering dynamics. International Textbook Company, Scranton, Pennsylvania, 440 p.
• SVINKIN, M.R., 1973. To the calculation of soil vibrations by the empirical formulas. In Russian, Computation of building structures, Proceedings of Kharkov Scientific-Research and Design Institute for Industrial Construction, Stroiizdat, Moscow, pp. 223-230.
• SVINKIN, M.R., 1992. Pile driving induced vibrations as a source of industrial seismology. Proceedings of the 4th International Conference on the Application of Stress-Wave Theory to Piles, The Hague, The Netherlands, F.B.J. Barends, Editor, A.A. Balkema Publishers, pp. 167-174.
• SVINKIN, M.R., 1993. Analyzing man-made vibrations, diagnostics and monitoring. Proceedings of the 3rd International Conference on Case Histories in Geotechnical Engineering, S. Prakash, Editor, Rolla, Missouri, Vol. 1, pp. 663-670.
• SVINKIN, M.R., 1996a. Overcoming soil uncertainty in prediction of construction and industrial vibrations. American Society of Civil Engineers, ASCE, Proceedings of Uncertainty in the Geologic Environment: From theory to Practice, Geotechnical Special Publications No. 58, C.D. Shackelford, P. Nelson, and M.J.S. Roth, Editors, Vol. 2, pp. 1178-1194.
• SVINKIN M.R., 1996b. Velocity-impedance-energy relationships for driven piles. Proceedings of the Fifth International Conference on the Application of Stress-Wave Theory to Piles, Orlando, F. Townsend, M. Hussein and M. McVay, Editors, pp. 870-890.
• SVINKIN, M.R., 1997. Numerical methods with experimental soil response in predicting vibrations from dynamic sources. Proceedings of the Ninth International Conference of International Association for Computer Methods and Advances in Geomechanics, Wuhan, China, J.-X. Yuan, Editor, A.A. Balkema Publishers, Vol. 3, pp. 2263-2268.
• SVINKIN, M.R., 1999. A novel approach for estimating natural frequencies of foundation vibrations. Proceedings of 17th International Modal Analysis Conference, SEM, Kissimmee, Florida, pp. 1633-1639.
• WARRINGTON, D.C., 1992. Vibratory and impact-vibration pile driving equipment. Pile Buck, Inc., Second October Issue, pp. 2A-28A.
• WISS, J.F., 1981. Construction vibrations: State-of-the-Art. American Society of Civil Engineers, ASCE Journal of Geotechnical Engineering, Vol. 107, No. GT2, pp. 167-181.
• WOODS R.D., 1997. Dynamic effects of pile installations on adjacent structures. Synthesis Report, National Cooperative Highway Research Program NCHRP Synthesis 253, Washington, D.C., 86 p.
• WOODS, R.D. and JEDELE, L.P., 1985. Energy-attenuation relationships from construction vibrations. American Society of Civil Engineers, Proceedings of ASCE Symposium on Vibration Problems in Geotechnical Engineering, Detroit, Michigan, G. Gazetas and E.T. Selig, Editors, pp. 229-246.

ABSTRACT: Elastic properties of cushion materials are used to determine elastic properties of composite hammer cushions. Equivalent stiffness of the composite hammer cushion depends mostly on the characteristics of soft cushion material and only the thickness of a soft material, not the total cushion thickness, should be taken for calculations. Equivalent modulus of elasticity of the composite hammer cushion depends on the modulus of elasticity of a soft material and a ratio of stiff to soft layers thicknesses. A change of soft and stiff layers thicknesses and their ratio may be used as a tool to increase force transmitted to the pile.

1 INTRODUCTION

Hammer cushion is installed in a well on a top of the drive cap (helmet) under the anvil which is struck by the hammer ram. The drive cap is employed to hold the pile head in position under hammer and to transfer impact energy to the pile.

The hammer cushion is used for two opposite purposes. On the one hand the hammer cushion must transfer the hammer energy to the pile without excessive energy losses, but on the other hand the hammer cushion has to prevent pile and hammer damage from driving.

Various materials such as wood, rope, polymers, fibers, aluminum and others are placed in the hammer cushion well. Combination of materials, like aluminium with Conbest or micarta, are frequently used for hammer cushions (Practical guidelines 1984; GRL Manual 1997; SPS 1999; Penn State Fabricators 1999).

Laminated materials such as aluminium and Conbest or aluminium and micarta have a relatively constant elasticity during relatively long life, consistent and predictable energy transfer and more uniform driving results.

The transfer of hammer energy to the pile and protection of pile and hammer from possible damage during pile driving depend on the moduli of elasticity and the stiffness of the materials used to composite hammer cushions.

The purpose of this paper is to show how moduli of elasticity and stiffness of different laminated cushion materials effect equivalent modulus of elasticity and equivalent stiffness of the composite hammer cushions.

2 TWO CUSHION MATERIALS

A composite hammer cushion has alternate layers of soft materials like Conbest or micarta and layers of stiff materials like aluminium or steel.

Stiffness of a soft layer, k_soft, and a stiff layer, k_stf, may be written

(1)

where

• E_soft = modulus of elasticity of soft material;
• E_stf = modulus of elasticity of stiff material;
• A = cross-section of cushion materials;
• t_soft = thickness of soft material layer;
• t_stf = thickness of stiff material layer.

It is common that E_stf is considerably greater than E_soft and t_stf is equal or less than t_soft.

2.1 Equal number of layers

Soft and stiff material layers are in series. Therefore equivalent stiffness of the composite hammer cushion, k_eq, is

(2)

where

• n = number of layers of each material;
• remaining parameters are the same as defined previously.

Equation (2) may be rewritten as

(3)

Relationship between equivalent stiffness and equivalent modulus of elasticity is

(4)

Equating the right pars of equations (3) and (4), we obtain

(5)

Equation (3) can be simplified to analyze a contribution of each cushion material to elastic properties of the composite hammer cushion. Since term t_softE_stf in the denominator of equation (3) is 30-100 times greater than term t_stfE_soft, the latter term can be neglected. After simplification, equation (3) becomes

(6)

According to equation (6), equivalent stiffness of the composite hammer cushion depends on the modulus of elasticity, the layer thickness, and the cross-section of a soft material.

After analogous simplification, equation (5) takes the form

(7)

where

• a = t_stf/t_soft

It can be seen that equivalent modulus of elasticity of the composite hammer cushion depends on the modulus of elasticity of a soft material and a ratio of stiff to soft layers thicknesses.

Calculation of the equivalent stiffness and the equivalent modulus of elasticity using simplified equations (6) and (7) has an error margin about 3 % in comparison with results of equations (3) and (5).

2.2 Unequal numbers of layers

A stiff material has usually one additional layer in a combination of Conbest or micarta with aluminium. Equivalent stiffness of the composite hammer cushion, k_eq, can be expressed

(8)

where all parameter are as defined previously.

After transformation and simplification, equation (8) becomes equal to equation (6).

3 THREE CUSHION MATERIALS

Composite cushions of three materials like aluminium, micarta and steel rope are sometimes used. Such cushions consist of two soft and one stiff materials connected in series. Assume that each cushion material has one layer and two soft layers have the same thickness, t_soft. Also, assume a ratio of the materials moduli of elasticity as E_stf>>E_soft>E_softest, where E_softest is modulus of elasticity of the softest material.

Equivalent stiffness of the composite hammer cushion, k_eq, may be written

After transformation and simplification, equation (9) takes the form

(10)

According to equation (10), equivalent stiffness of the composite hammer cushion filled with three materials depends on the modulus of elasticity of two soft materials, the thickness of a soft material layer and the cross-section of cushion materials.

Relationship between equivalent stiffness and equivalent modulus of elasticity is

(11)

Equating the right parts of equations (10) and (11), and, assume E_soft=2E_softest for simplicity, we obtain

(12)

For assumptions taken, equivalent modulus of elasticity depends on the modulus of elasticity of the softest material and the ratio of stiff to soft layers thicknesses.

4. DISCUSSION OF RESULTS

4.1 Two cushion materials

Equivalent modulus of elasticity and equivalent stiffness of the composite hammer cushion are used in wave equation analysis of pile drivability and pile capacity. It is common that the total thickness of hammer cushion is taken for wave equation analysis.

Equation (6) shows that only the soft material effects the equivalent stiffness and only the thickness of a soft material should be used in calculations. Decreasing the total thickness of the composite hammer cushion to the actual thickness of a soft material increases force transmitted to the pile and provides more realistic consideration of hammer cushion properties in wave equation analysis of pile drivability and capacity.

According to equation (7), the ratio of stiff to soft layers thicknesses effects the equivalent modulus of elasticity. Values of E_eq are increased with increasing the aluminium or steel thickness and keeping the same Conbest or micarta thickness. For example, an enlargement of the aluminium layer thickness from 1 to 3 inches with the same Conbest thickness of 1 inch increases two times the value of E_eq.

Thus, equivalent stiffness depends on the thickness of soft cushion layers and equivalent modulus of elasticity depends on the ratio of stiff to soft layers thicknesses. Therefore a change of layers thicknesses provides certain flexibility to regulate elastic properties of the composite hammer cushions and, under certain drivability conditions, gives an opportunity to increase force transmitted to the pile for account of the layers thicknesses change instead of switching to more powerful hammer. Such a hammer will increase force transmitted down the pile in limits allowable by the pile impedance. It is reasonable to change the thickness of soft and stiff layers of the composite hammer cushion as the first step in increasing dynamic force applied to the pile.

4.2 Three cushion materials

Equivalent stiffness of the composite hammer cushion in equation (10) depends on the moduli of elasticity, the thicknesses, and the cross-section of the softest and soft material layers. According to equation (12), equivalent modulus of elasticity depends to a lesser degree on the ratio of stiff to soft layers in comparison with two cushion materials.

5 CONCLUSIONS

Proper determination of elastic properties of composite hammer cushions is important for the application of the wave equation method to piles.

Equivalent stiffness of the composite hammer cushion depends mostly on elastic properties of a soft cushion material: the modulus of elasticity, the layer thickness and the cross-section.

The total thickness of composite hammer cushion is usually taken into account for wave equation analysis of pile drivability and pile capacity. Since a soft material mostly effects the equivalent stiffness, only the thickness of a soft material should be used in calculations.

Equivalent modulus of elasticity of the composite hammer cushion depends on the modulus of elasticity of soft material and the ratio of stiff to soft layers thicknesses.

A change of soft and stiff layers thicknesses and their ratio may be used as a tool to increase force transmitted to the pile. This may improve pile drivability without switching to more powerful hammer for certain driving conditions.

REFERENCES

• GRL and Associates, Inc. 1997. GRLWEAP – Wave Equation Analysis of Pile Driving, Manual, Cleveland, Ohio.
• Penn State Fabricators. 1999. Conbest cushion blocks – Information, New York.
• Practical guidelines for the selection, design and installation of piles. 1984. Committee on Deep Foundations, ASCE.
• Specialty Piling Systems, Inc. 1999. Hammer cushion materials – Information, Slidell, Louisiana.

Mark R. Svinkin

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

Abstract

Uncertainty in geological stratification can strongly affect the prediction of ground and structure vibrations from construction and industrial sources. This paper presents the application of the deterministic impulse response function concept to solve the geotechnical problem of prediction of ground and structure vibrations before installation of a vibration source. This approach employs experimental impulse response functions for the considered dynamic system. These functions reflect real behaviour of soil and structures without the investigation of soil and structure properties. Ways for determining dynamic loads applied to the ground from different dynamic sources are also shown. A procedure is presented to compute predicted ground and structure vibrations. Good correlation is found between predicted and measured records.

1. Introduction

Construction operations and vibrations of foundations under machines with dynamic loads generate elastic waves in soil which may adversely affect surrounding buildings. Their effects range from serious disturbance of working conditions for sensitive devices and people, to visible structural damage. The most prevalent powerful sources of construction and industrial vibrations are pile driving activities, dynamic compaction of granular soil, and vibrations of foundations for impact machines. These sources transmit predominantly vertical dynamic forces to the ground.

Analysis of experimental data (Barkan, 1962; Richart et al., 1970; Attewell and Farmer, 1973; Svinkin, 1976a; Mallard and Bastow, 1979; Woods and Jedele, 1985; Mayne, 1985) reveals that soil vibrations are mostly vertical near the sources of vertical impact loads, but at a certain distance vertical and horizontal soil vibrations become similar. For some locations on the ground surface, amplitudes of horizontal vibrations might be 2-3 times greater than vertical ones. Waves travel in all directions from the source of vibrations forming a series of fairly harmonic waves with the predominant frequency equal or close to the frequency of the source. In various soils, the basic frequency of vertical soil vibrations may either increase or decrease with distance from the source by 30-50 %. Spectra of the radial components of horizontal soil vibrations have a few maxima and the one corresponding the frequency of the source is not always the largest. The tangential components of horizontal soil vibrations have a higher frequency content as compared with radial ones. Spectra maxima of the tangential components are 2-2.5 times higher in frequency than the natural frequencies of source vibrations. In general, faster attenuation of high frequency components is the primary cause of changes of soil vibrations with distance from the source. However, some records can not be explained by this mechanism. Typical records and spectra of hammer foundation and soil vibrations from an operating forge hammer with a falling mass of 7.25 tonnes are shown on Figure 1.

Actually, a real soil medium displays some degree of elastic anisotropy and wave propagation has to be assumed to be anisotropic unless it has been shown to be effectively isotropic (Helbig, 1993). Moreover, uncertainties about the geologic profile cannot be accurately characterized, even by thorough and extensive investigations. The inherent spatial variations in the ground are not always readily identifiable by routine boring, sampling, and testing (Thorburn, 1994). For instance, Hammond (1959) reported a case history of the influence of the soil strata upon frequencies of soil vibrations and amplitudes of building vibrations at the site where a foundation was installed for a forge hammer with a falling mass of 8.0 tonnes. The main frequency of propagated waves was 22.0 Hz to the west of the hammer foundation and, at the same time, in opposite direction to the east of the source, this frequency was 10.0 Hz. Soil vibrations with the higher frequency excited resonant building oscillations.

The proximity of the frequency of horizontal soil vibrations to one of a building’s natural frequencies may generate the conditions of resonance in that building. Moreover, vertical ground vibrations can cause dangerous structural settlements. Considerable data have been collected and published with respect to intolerable vibrations and settlements from construction and industrial sources, e.g. Barkan (1962), Richart et al. (1970), Wiss (1981); Lacy and Gould (1985), Svinkin (1993); Dowding (1994) and others. To estimate the undesirable effect of generated vibrations, it is important to predict accurately and reliably vibrations of the ground, building structures and equipment.

Empirical equations are used for practical assessment of expected soil vibrations from industrial and construction sources. However, they usually allow calculation of only a vertical amplitude of the peak part of vibration records, and not always with the required accuracy. These equations cannot reflect specific differences of soil conditions at each site, even though heterogeneity and spatial variation of soil properties strongly affect characteristics of propagated waves in soil from construction and industrial vibration sources.

Complicated analytical methods (e.g. Broers and Dieterman, 1992; Hanazato and Kishida, 1992) give accurate results for certain cases, but actually these methods are mostly powerful tools for cases where quality investigations have been performed at a site. Indeed, for the prediction of expected vibrations it is necessary to have actual information about the soil deposit and to choose a proper soil model to compute vibrations. Half-space or layered media are used for idealization of existing soil conditions. Computed results contain valuable data about general tendencies of wave propagation at a site, but cannot present accurate and complete soil vibration records at any point of interest. For the use of computational methods, it is necessary to know some soil properties as, for example, shear wave velocity. Similar information is often missing for sites with a real source of vibrations. Leroueil and Tavenas (1981) demonstrated that the assumptions in analytical methods should be adequate to achieve good computed results. Besides, Thorburn (1994) underlined that “although soil variability can be expressed in terms of probability, the reliability of the theoretical models used in predictive calculations cannot be determined by probability theory”.

From the deterministic perspective, this paper deals with the application of the impulse response function concept to predict ground and structure vibrations before the beginning of construction activities or installation of machine foundations. This approach employs experimental impulse response functions reflecting real behavior of soil and structures without the investigation of soil and structure properties. It also provides an opportunity for proper determination of vibration levels and aids in monitoring of ground, structure and device vibrations prior to start of construction and industrial activities.

2. Suggested Approach

The suggested deterministic approach is founded on utilization of the impulse response function technique for predicting complete vibration records on existing soils, buildings and equipment prior to installation of construction and industrial vibration sources (Svinkin 1973a, 1991). The impulse response function (IRF) is an output signal of the system based on a single instantaneous impulse input (Mayhan, 1984; Bendat and Piersol, 1993). Impulse response functions are applied for analysis of any complicated linear dynamic system with unknown internal structure for which mathematical description is very difficult. 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 of the system is the ground at the place of pile driving, dynamic compaction of soil, or installation of a machine foundation; the output is a location of interest situated on the surface or inside the soil, or any point at a building receiving vibrations. Output can be obtained, for example, as the vibration records of displacements at locations of interest.

Impulse response functions of the considered dynamic system are determined by setting up an experiment (Figure 2). Such an approach (a) does not require routine soil boring, sampling, or testing at the site where waves propagate from the vibration source, (b) eliminates the need to use mathematical models of soil bases and structures in practical applications, and (c) provides the flexibility of considering heterogeneity and variety of soil and structural properties. Unlike analytical methods, experimental IRFs reflect real behaviour of soil and structures without investigation of the soil and structure properties. Because of that, the suggested method has substantially greater capabilities in comparison with other existing methods.

The following is a general outline of the method for predicting vibrations at a distance from an impact source.

1. At the place in the field for installation of the impact source, impacts of known magnitude are applied onto the ground (Figure 2). The impact can be created using a rigid steel sphere or pear-shaped mass falling from a bridge or mobile crane. At the moment of the impact onto the ground, oscillations are measured and recorded at the points of interest, for example, at the locations of devices sensitive to vibrations. These oscillations are the IRFs of the treated system which automatically take into account complicated soil conditions.
2. Various ways are used to determine the dynamic loads on the ground from different vibration sources. For pile driving, dynamic loads are computed by wave equation analysis. In the case of operation of machines on foundations, these loads can be found using existing foundation dynamics theories. For dynamic compaction sites, loads from the source are easily calculated with known falling weights and heights.
3. Duhamel’s integral (Smith and Downey, 1968) is used to compute predicted vibrations, which will arise after impact of the source.

3. Linearity of Soil Vibrations

A basic assumption of the suggested method is linearity of the soil medium where waves propagate from vibration sources. Considerable data related to linearity of the foundation-soil system have been published, for example, Barkan (1962), Bibanov et al. (1964), Sliwa (1964), Lysmer and Richart (1966), Svinkin (1973b) and others.

It is important to show that the linear technique can be used for a soil medium to predict ground vibrations at some distance from the source. For this goal, records of ground vibrations were measured at various distances from vibration sources-foundations for impact machines. Vibration records were analyzed with respect to the magnitude of excited forces applied to machine foundations. Linearity of soil medium was investigated by direct verification of the requirements of linear systems (Mayhan, 1984). Suppose, there are two records of soil displacements as functions of force z₁=f(F₁) and z₂=f(F₂). The system is linear if and only if both the property of homogeneity is satisfied

(1)

and the property of additivity is satisfied

(2)

Actually, for any linear system it is always correct to separate the excitation into an arbitrary number of parts, find the response of each separately, and add the results. This superposition technique is demonstrated in Figure 3. In this typical example, measured records of ground vibration displacements were obtained from an operating drop hammer with a falling mass of 10.0 tonnes. Velocities at the moment of impact were 6.3 and 18.8 m/s. Then, records of vibrations were redrawn in proportional scales corresponding to values of operating impulse loadings. A good correlation of compared records can be seen for each of two locations at different distances from the source. Similar results were obtained in other case histories.

Analysis of experimental studies has shown that shapes of records depend slightly on intensity of impulse loading and maxima of vibration displacements are actually proportional to values of impulse loading. These results support the application of the linear theory to describe ground vibrations excited by construction and industrial sources.

4. Impulse Response Functions

The effect of soil properties on expected vibrations at locations of interest is completely reflected in the records of IRFs obtained at the moment of impact onto the ground at the place of the vibration source. Stability of the IRFs is very important for reliable prediction of ground and structure vibrations. At the moment of impact, an inelastic collision occurs at the contact area between the falling mass and the ground. For that reason, in-situ experiments were made to investigate the effect of plastic soil deformations at the moment of impact under a falling rigid mass on ground surface vibrations (Svinkin, 1976b). Both small and large falling masses were used.

The small falling steel weight had a cylindrical shape with a 20 cm diameter and 100 kg mass. Drop heights were 0.5 and 2 m. Impacts were made by the dropping the steel mass on the same spot for various conditions at the contact area between the ground and the mass. First, impacts were applied to the ground surface. Then an excavation was dug with dimensions 0.7 x 0.7 m in a plan and 0.3 m deep. Impacts were applied to the bottom of the excavation, then onto a steel plate with spikes pressed in the soil at the bottom of the excavation, and after that, onto the sand and gravel which were used in lifts to fill the excavation. Accelerations of the falling mass and vibration displacements of the ground surface at distances of 1.5, 4.3 and 10.8 m from the contact area were measured in the experiments.

The ground vibration measurement system consisted of VAGIK or K-001 seismographs and a H-004 oscillograph with GB galvanometers. The frequency range of this system for velocity and displacement measurements was from 1.0 to 100.0 Hz. For the same values of impacts, records and spectra of ground vibrations at 1.5, 4.3, and 10.8 m from the centre of the contact area are depicted in Figure 4.

Soil conditions at the contact area influenced the duration of impacts. Acceleration impulses were close to a bell shape for impacts onto the ground surface, bottom of the excavation, gravel and steel plate. The minimum contact time of 0.025 sec was observed for an impact onto the steel plate. In the rest of the three cases, duration of contact did not exceed 0.035 sec. For an impact onto sand, contact time increased to 0.06 sec and the impulse shape was close to a shifted half-sine with its greater steepness in the leading phase. Changing the drop height from 0.5 to 2.0 m did not affect the contact time.

Shapes of records measured at each location were approximately the same for different conditions at the contact area. The predominant frequency of ground vibrations, approximately 160.0 rad/sec, turned out to be independent of conditions at the contact area. In fact, an increase of duration of the bell-shaped impulse from 0.025 to 0.035 sec did not significantly change the amplitudes of ground vibrations. Thus, at distances of 4.3 and 10.8 m these amplitudes differed by only 5-8 % (Fig. 4, records 1-4). Enhancement of low-frequency components of the half-sine shaped acceleration impulse had only a weak effect on the frequency content of ground vibrations (Fig. 4, record 5). In the proximity of the contact area (r=1.5 m), an increase of impulse duration to 0.06 sec diminished the amplitudes of ground vibrations to 50-70 % as compared with other conditions at the contact area. However, moving further from the place of impact, this difference decreased to 20-35 % and 10-25 % for r=4.3 and 10.8 m, respectively. The distances of 4.3 and 10.8 m were 40-100 times greater than the radius of the contact area between the falling weight and the ground. Thus, at the locations in the proximity of the place of impact, amplitudes of ground vibrations decreased with an increase in impulse duration, but these changes decreased with distance from the contact area.

The effect of large plastic soil deformations at the contact area under a falling mass on ground vibrations was studied with a falling mass of 15.0 tonnes at a site where soil deposits were mostly fine moist sands. The drop height ranged from 10 to 15 m. Many impacts were performed at the same spot; consequently, large plastic soil deformations occurred at the point of impact. Records of ground vibration displacements at various distances from the place of impact onto the ground are depicted in Figure 5.

Comparison was made for records obtained for two equal impacts with different degrees of plastic soil deformations at the contact area. In particular, vibrations were measured at distance of 43 m for the first and ninth impacts, and at a distance of 57 m for the first and seventeenth impacts. For the first impact, the falling mass dropped onto a flat ground surface, but for the seventeenth impact, it dropped into a pit deeper than 1 m. In spite of considerable soil deformations at the contact area, each pair of ground surface vibrations are similar at locations of measurements. The results demonstrate that at any location on the ground, except probably a zone at close proximity to the source, soil vibration displacements measured simultaneously with impact onto the ground are stable, have well-defined shapes, are independent from the intensity of soil deformations at the contact area. The differences between displacement amplitudes measured during various impacts are within the limits of error of the measurement system. This confirms the reliability of using a deterministic perspective for prediction of construction and industrial vibrations.

Based on the experimental program described above, it has been shown that impacts directly onto the soil can be used for deriving impulse response functions of the considered dynamic system: the base under the source of vibrations – soil medium – ground or structure at some distance from the source.

5. Dynamic Loads Onto Ground

5.1 Machine Foundations

Dynamic loads at 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 be written as

(3)

with

(4)

where 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; /_nz = natural frequency of vertical vibrations of foundation; a = effective damping constant.

An expression derived from equation (3) for a dynamic load applied to the soil is

(5)

The dynamic force transmitted from the machine foundation to the soil base 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.

Vibration displacements of the machine foundation can be assigned digitally by using an arbitrary shape or analytically as a damped sinusoid

(6)

with

(7)

where I_F = impulse force transmitted from machine to foundation; F = modulus of damping; k_zN = coefficient of vertical subgrade reaction; /_nd = natural frequency of vertical damped vibrations of foundation; A = contact area between foundation and soil.

As suggested by Pavliuk and Kondin (1936), the modulus of damping, F, ranges in a relatively narrow range and is slightly dependent on soil conditions. For instance, values of F ranges from 0.004 to 0.008 sec for foundations with contact areas less than 10.0 m². Coefficient, k_zN is determined according to Barkan (1962). Also, it is possible to use other approaches for determining values of a and k_zN.

5.2 Pile driving

Equation (5) can be used for determination of the dynamic loads transferred from the pile to the surrounding soil. In this case, M is the pile mass. The effective damping constant, a, is chosen from the range of damping constants for foundations with the smallest contact areas. A frequency of the hammer-pile-soil system is calculated by an equation (Svinkin, 1992) which takes into account pile material, the ratio of wave velocity in the pile to pile length and the pile weight to ram weight ratio.

Pile displacements as a function of time are computed by wave equation analysis, using for example, GRLWEAP Program (GRL and Associates, 1995). Computed displacement records at the pile top, middle, and bottom are presented in Figure 6 for a 457 x 457 mm prestressed concrete pile with length of 20.4 m. These three records are very similar and displacements at the pile top can be taken as a function z(t). For comparison, pile displacements at the same points, obtained by dynamic measurement at the pile top and by Case Pile Wave Analysis Program (CAPWAP) for the pile middle and bottom are shown in Figure 6. Both sets of curves were derived for the same pile capacity. It can be seen that measured results confirm the reasonableness of the use of wave equation analysis to compute pile displacements for vibration prediction.

5.3 Dynamic Compaction

For dynamic compaction of granular soil, loads from the source are calculated with known falling weights and heights.

6. Computation of Predicted Vibrations

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

(8)

where F(t) = the 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.

With substitution of expression (5) and (6) equation (8) becomes

(9)

An example of predicted results is shown in Figure 7. Vertical and horizontal ground displacements were predicted at a distance of 266.0 m from the foundation under a powerful drop hammer at a site with the Rayleigh-wave velocity of 270 m/sec. The falling mass was 15.0 tonnes and the maximum drop height was 30.0 m. For both vertical and horizontal displacement components, three records are depicted: IRF, predicted, and measured curves. It can be seen that the IRFs make a substantial contribution to the actual vibrations, reflecting a very close record shapes to the measured ones. Correlation of predicted and measured vibration displacements is quite satisfactory. The differences between the highest calculated and measured amplitudes of oscillations are 16 and 30 % for horizontal and vertical components, respectively.

In current practice, the amplitude reduction of Rayleigh waves between two points at distances r₁ and r₂ from the source is calculated as (r₁/r₂)^0.5 with a factor exp[-a(r₂-r₁)], where a is the coefficient of attenuation. The coefficient, a, depends on soil properties, on parameters of the source, on frequency and distance from the source. Test data along the ground surface show that for various pairs of widely separated points on the ground surface, values of a differ more than an order magnitude and even change a sign. Calculated maximum response is in the range of -100 to 330 %.

Unlike current practice, the suggested method predicts complete 3-D waveforms, vertical and two horizontal, with reasonable accuracy actual performance (an example demonstrates vertical and one horizontal waveforms). The best index of the reliability of the method is the comparison of computed and measured records. It was successfully done using the IRF concept.

7. Conclusions

The impulse response function concept is used to solve a geotechnical problem to predict ground and structure vibrations prior to the beginning of construction activities or installation of machine foundations.

The suggested deterministic approach uses the impulse response function technique for a considered dynamic system: ground at the place for the source of vibrations – soil medium – output locations of interest on ground or in any structure receiving vibrations. Experimental impulse response functions reflect real soil behavior and take into account uncertainty in the geologic environment. Such an approach does not require routine soil boring, sampling, and testing at the site where waves propagate from the vibration source. On the basis of experiments it was proved that impacts directly onto the soil can be used for deriving impulse response functions for the considered dynamic system.

Different ways were shown to determine dynamic loads onto the ground from machine foundations, pile driving and dynamic compaction of granular soil. An algorithm is presented to compute predicted vibrations, and an example of predicted results are demonstrated for vertical and horizontal ground displacements. There is quite satisfactory correlation between predicted and measured records.

The suggested approach provides the method for determining and monitoring of ground, structures and sensitive devices vibration level before the start of construction or industrial vibration activities.

Acknowledgements

The writer is grateful to Professor Richard D. Woods for many valuable comments and suggestions for the manuscript. The writer wishes to thank the reviewers for their constructive reviews of the manuscript.

APPENDIX. REFERENCES

• Attewell, P.B. and Farmer, I.W. (1973). “Attenuation of ground vibrations from piles.” Ground Engrg., 6(4), 26-29.
• Barkan, D.D. (1962). Dynamics of bases and foundations. McGraw Hill Co., New York, 434.
• Bendat, J.S and Piersol, A.G. (1993). Engineering applications of correlation and spectral analysis. John Wiley & Sons, Inc., 458.
• Bibanov, V.I., Goncharov, L.A., Konstantinov, B.B., Krasnikov, N.D., and Tishenko, V.G. (1964). “Experimental investigations of vibrations of massive concrete blocks on sandy base” (in Russian). Questions of Engrg. Seismology, Proc. of Institute of Earth Physics, Vol. 9, “Nauka”, Moscow.
• Broers, H. and Dieterman H.A. (1992). “Environmental impact of pile-driving.” Proc., 4th Intern. Conf. on Application of Stress Wave Theory to Piles, F.B.J. Barends, ed., A.A. Balkema, The Hague, The Netherlands, 61-68.
• Dowding, C.H. (1994). “Vibration induced settlement from blast densification and pile driving.” Proc., ASCE Settlement ’94, Vertical and Horizontal Deformations of Foundations and Embankments, Vol. 2, 1672-1688.
• GRL and Associates, Inc. (1993). CAPWAP- Case Pile Wave Analysis Program, Continuous Model, Manual. Cleveland, Ohio, USA.
• GRL and Associates, Inc. (1995). GRLWEAP- Wave Equation Analysis of Pile Driving, Manual. Cleveland, Ohio, USA.
• Hammond, R.E.R. (1959). “Vibration-controlled foundations at Salten.” Iron and Steel, Vol. 32, No. 3.
• Hanazato, T. and Kishida, H. (1992). Analysis of ground vibrations generated by pile driving – Application of pile driving analysis to environmental problem.” Proc., 4th Intern. Conf. on Application of Stress Wave Theory to Piles, F.B.J. Barends, ed., A.A. Balkema, The Hague, The Netherlands, 105-110.
• Helbig, K. (1993). “Simultaneous observation of seismic waves of different polarization indicates subsurface anisotropy and might help to unravel its cause.” J. Applied Geophysics, Vol. 30, 1-24.
• Lacy, H.S. and Gould, J.P. (1985). “Settlement from pile driving in sands.” Proc., ASCE Symposium on Vibration Problems in Geotech. Engrg., Detroit, Michigan, 152-173.
• Leroueil, S. and Tavenas, F. (1981). “Pitfalls of back-analysis.” 10th Inter. Conf. on Soil Mechanics and Foundation Engrg., Stockholm, Vol. 1, 185-190.
• Lysmer, J and Richart F.E. Jr. (1966). “Dynamic response of footings to vertical loading.” J. Soil Mech. and Found. Div., ASCE, 92, No. SM 1, 65-91.
• Mallard, D.J. and Bastow, P. (1979). “Some observations on the vibrations caused by pile driving.” Proc., Conf. on Recent Developments in the Design and Construction of Piles, ICE, Thomas Telford Ltd, London, 261-284.
• Mayhan, R.J. (1984). Discrete-time and continuous-time linear systems. Addison-Wesley Publishing Co., 644.
• Mayne, P.W. (1985). “Ground vibrations during dynamic compaction.” Proc., ASCE Symposium on Vibration Problems in Geotech. Engrg., Detroit, Michigan, 247-265.
• Pavliuk, N.P. and Kondin, A.D. (1936). “Damping of vibrations of foundations under machinery” (in Russian). Proekt i Standart, No. 11.
• Richart, F.E., Hall, J.R. and Woods, R.D. (1970). Vibrations of soils and foundations. Prentic-Hall, Inc., Englewood Cliffs, NJ, 414.
• Sliwa, G. (1964). “Some dynamic problems of foundations under drop hammers” (in Polish). Zesk. Nauk. Politechn, Slaskiej, No. 107.
• Smith, G.M. and Downey G.L. (1968). Advanced engineering dynamics. International Textbook Company, Scranton, Pennsylvania, 440.
• Svinkin, M.R. (1973a). “Prediction of soil oscillations from machine foundation vibrations” (in Russian). Dynamics of structures, Proc., Kharkov Scientific-Research and Design Inst. for Industrial Constr., Budivelnic, Kiev, 53-65.
• Svinkin, M.R. (1973b). “On linearity of soil bases and machine foundations” (in Russian). Dynamics of structures, Proc., Kharkov Scientific-Research and Design Inst. for Industrial Constr., Budivelnic, Kiev, 44-52.
• Svinkin, M.R. (1976a). “Some features of soil vibrations due to effect of operating machines producing impact loads” (in Russian). Dynamic of Building Structures, Proc. Leningrad Design Institute for Industrial Construction, Leningrad, 57-66.
• Svinkin, M.R. (1976b). “Experimental investigations of soil vibrations under impulse force” (in Russian). Dynamics of Structures, Proc. of the Kharkov Scientific-Research and Design Institute for Industrial Construction, Budivelnic, Kiev, 15-23.
• Svinkin, M.R. (1991). “Predicting vibrations of soil and buildings excited by machine foundations under dynamic loads.” Proc., 2nd Inter. Conf. on Recent Advances in Geotechn. Engrg. and Soil Dynamics, University of Missouri-Rolla, Rolla, Mo., Vol. 2, 1435-1441.
• Svinkin, M.R. (1992). “Pile driving induced vibrations as a source of industrial seismology.” Proc. 4th Inter. Conf. on the Application of Stress-Wave Theory to Piles, F.B.J. Barends, ed., A.A. Balkema, The Hague, The Netherlands, 167-174.
• Svinkin, M.R. (1993). “Analyzing man-made vibrations, diagnostics and monitoring.” Proc., 3rd Inter. Conf. on Case Histories in Geotechn. Engrg., University of Missouri-Rolla, Rolla, Mo., Vol. 1, 663-670.
• Thorburn, S. (1994). “Uncertainty and judgement in geotechnical engineering.” Ground Engrg., Vol. 27, No.3, 18-22.
• Wiss, J.F. (1981). “Construction vibrations: State-of-the-Art.” J. Geotech. Engrg., ASCE,Vol. 107, No. GT2, 167-181.
• Woods, R.D. and Jedele, L.P. (1985). “Energy-attenuation relationships from construction vibrations.” Proc., ASCE Symposium on Vibration Problems in Geotech. Engrg., Detroit, Michigan, 229-246.

FIG. 1. Displacement Records and Spectra of (1) Forge Hammer Foundation and (2-9) Ground Vibrations: 1-5 – Vertical Component, 6 – Horizontal Tangential Component, 7-9 – Horizontal Radial Component

FIG. 2. Experimental Determination of Impulse Response Functions

FIG. 3. Linearity of Vertical Ground Vibrations at Distances of (a) 6.0 m and (b) 53.0 m from Source for Different Impact Velocity of Hammer Falling Mass

FIG. 4. Displacement Records and Spectra of Vertical Ground Vibrations for Various Conditions at Contact Area: 1 – Ground Surface, 2 – Bottom of Excavation, 3 – Gravel, 4 – Steel Plate, 5 – Sand

FIG. 5. Comparison of Two Different Displacement Records of Ground Vibrations in Fine Sands for Identical Impacts onto Ground by Falling Mass of 15.0 tonnes

FIG. 6. Displacements at Pile Top, Middle and Bottom during Driving: a – Computed by GRLWEAP, b – Measured at Pile Top and Obtained by CAPWAP Analysis at Pile Middle and Bottom

FIG. 7. Displacement Records of (a) Vertical and (b) Horizontal Ground Vibrations at Distance of 266.0 m from the Drop Hammer Foundation (m = 15 tonnes, h = 30 m): 1 – Impulse Response Function, 2 – Predicted Record, 3 – Measured Record

Webmaster’s note: This letter is reproduced at the request of Dr. Mark Svinkin, and does not necessarily reflect the views of the webmaster, vulcanhammer.net or The Wave Equation Page for Piling.

June 25, 2001

Dr. Michael Holloway
Chair
DFI Committee on Deep Foundations Testing and Implementation

Dear Mike:

You wrote in Fulcrum magazine that “The committee’s objective is to demystify testing methods and their applications in foundation design and construction practice“. In the frame of this objective, I am sending you my opinion regarding the project on application of dynamic testing results for rewriting AASHTO Deep Foundation Specifications for the year 2001, the NCHRP Project 24-17, “LRFD Deep Foundation Design”. The basic ideas of the project are presented in Paikowsky and Stenersen (2000).

A LRFD was originated in the USSR in 1920s with peak usage in 1960s. As any other method, the LRFD has its advantages and disadvantages. The LRFD is applicable to calculations of steel and concrete structures. Due to tolerance of plastic deformations, the LRFD provides more economical design solutions of certain types of structures. For example, plastic design is ideally suited to continuous beams and frames, and is not normally used with single-span beams. While the LRFD allows for cracks in concrete structures, such approach is not acceptable for some concrete structures. That was one of the reasons why the LRFD was not used for foundations design in the Soviet Union.

There is no doubt that learning Russian experience with the LRFD would be very beneficial for the Project. According to Paikowsky and Stenersen (2000), there are references only to Russian initial publication on the subject. So, Russian experience was not actually learned.

Applicability of the LRFD to bridge structures does not mean that this method is appropriate for calculation of bridge foundations. Nevertheless, there are different opinions regarding the LRFD concept. This approach may be accepted or not, but without doubt, good quality data would have to be used for consideration of the application of LRFD concept to foundations. It is important to reveal true resistance factors for deep foundation design. However, the resistance factors obtained in the Project are founded on wrong databases. These databases use comparison of pile capacity values that are incompatible from the point of verification of pile dynamic testing and analysis.

The Project is founded on PD/LT 2000 Database made for comparison of pile capacities obtained with dynamic methods and static loading tests. The principles, and the major part of this Database, were created for the Research Project, Paikowsky et al. (1994), where one more dynamic formula was suggested for determination of pile capacity. There are problems with PD/LT 2000 Database in evaluation of accuracy of Dynamic Formulas and Dynamic Testing.

Determination of pile capacity by dynamic formulas is the oldest and most 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 in 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, 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 or vise versa 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 an 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 et al. 1994; Svinkin 1997, 1998; Svinkin and Woods, 1998). In mentioned papers, by way of illustration, results of DT and SLT are shown for two identical cylindrical, 1372 mm x 127 mm, prestressed concrete piles, TP1 and TP2. 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 well as pile capacity obtained from DT. These tested data 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. There is no theoretical and experimental confirmation of such conclusions. It is necessary to utilize other appropriate way for comparison of results of the Energy Approach Formula and DT which use data from the same dynamic measurements. Such comparison was made in the frames of preparation of FHWA-GRL Database. The results obtained were very poor and confirmed that the Energy Approach with dynamic measurements cannot yield reliable prediction of pile capacity. Statistical analysis itself cannot reveal good results and replace engineering judgment if comparison of measured pile capacities is incorrect.

Dynamic testing followed by a signal matching procedure has obvious advantages in determining pile capacity at any time 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. Paikowsky et al. (1994) and Paikowsky and Stenersen (2000) use a wrong approach for comparison of DT and SLT.

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 to the measured ultimate load from static loading test is used for approximate evaluation of the reliability of design methods, Briaud and Tucker (1988). 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.

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). This is not a predicted value. Moreover, 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. As it was shown before, 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, Svinkin (2000, 2001). 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.

Static Loading Tests and Dynamic Testing present different ways of determining pile capacity at various times after pile installation. 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.

Also, it is necessary to point out that assertion about independence of soil damping of soil type is incorrect. The damping coefficient in sandy soil is substantially less than the damping coefficient in clayey soils, but the latter is close to the damping coefficient in saturated sandy soils, Svinkin (1995a, 1995b, 1996a, 1996b, 1997).

So, PD/LT 2000 Database in the Project has no common and engineering sense and its conclusions are misleading. It is clear that an AASHTO mandatory document based on false assumptions and misleading results would be a disaster for geotechnical community. I believe that situation with the Project “LRFD Deep Foundation Design” should be considered by the Special Committee of Congress.

My opinion has received support from participants of prestigious conferences, papers reviewers, authors of discussion papers, Journal of Geotechnical and Geoenvironmental Engineering, and Ground Engineering Magazine. Some of my publications regarding determination of pile capacity by dynamic methods you can find by clicking here.

Best regards,

Mark Svinkin

References

• Briaud, J.L. and L.M. Tucker 1988. Measured and predicted axial response of 98 piles. Journal of Geotechnical Engineering, ASCE, 114(9): 984-1001.
• 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.
• 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, A.A. Balkema, The Hague, 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, A. A. Balkema: 281-304.
• 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: 1.11.1-1.11.8. Rotterdam: Balkema.
• Svinkin, M.R. 1995a. Pile-soil dynamic system with variable damping. Proc. 13th International Modal Analysis Conference, IMAC-XIII, Beyond the Modal Analysis, Nashville, 13-16 February, 1: 240-247, Bethel, Connecticut: SEM.
• Svinkin, M.R. 1995b. Soil damping in saturated sandy soils for determining capacity of piles by wave equation analysis. Proc. DFI Annual Member’s Conference, Charleston, South Carolina, 16-18 October: 199-216, Englewood Cliffs: DFI.
• Svinkin, M.R. 1996a. Discussion of ‘Setup and relaxation in glacial sand’ by York et al., Journal of Geotechnical Engineering, ASCE, 122(4): 319-321.
• Svinkin, M.R. 1996b. 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: 128-143, Gainesville: University of Florida.
• 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, 2: 1045-1048, Rotterdam: Balkema.
• 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: 1.2.1-1.2.8, Rickmansworth: Westrade Group Ltd.
• 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, A. A. Balkema: 35-40.
• Svinkin, M.R. 2001. Pitfalls in wave equation analysis of pile capacity. Proc. Inter. Conf. on Computer Methods and Advances in Geomechanics, A.A. Balkema, V. 2, pp. 1495-1499.