Re-evaluation of the method to determine pile damage using the Beta Method Verbeek, G. E. H. VMS, USA

Goble, G. Goble Pile Test, USA

Keywords: pile damage, concrete piles, Beta method, MPI method

ABSTRACT: In 1979, a paper was published by Rausche and Goble describing a method to determine damage in driven piles using the Beta Method. Over the years this method has become the standard for pile damage assessment in many parts of the world, often without an understanding of that method by those that apply it. Instead the numerical outcome was seen as a reliable indicator of damage in driven piles. Recently developed technologies have begun to shed a different light on the reliability of this method, suggesting that a thorough assessment of the method derivation would be appropriate. In this paper the Beta method will be re-evaluated to assess whether it is a reliable indicator of pile damage. This re-evaluation will cover both the theory behind the method as well as the review of Pile Driving Analysis data collected from a large number of concrete piles. Taken together the results of this re-evaluation clearly demonstrate that this widely applied method cannot be considered a reliable indicator and should therefore be used with extreme care. 1 INTRODUCTION

When driving concrete foundation piles the objective is to have a sound deep foundation element in place at the end of pile driving. To achieve this objective it is essential that pile damage is minimized during pile driving as invariably some damage will occur (if only due to the fact that the small cracks present in the concrete before the start of pile driving will grow as a result of the pile driving stresses), but this damage should not affect the integrity of the foundation, which the pile will be part of.

To ensure that this is the case, a pile can be load tested (either by a Static Load Test, a High Strain Dynamic Test or a Rapid Load Test) to demonstrate that the pile shaft is able to transfer the top loads to the bearing layers. If the pile passes the test, the issue of potential pile damage is in the short term no longer relevant: the pile’s capacity has been demonstrated and therefore it can be considered an acceptable deep foundation element. An alternate, albeit less conclusive method, is a Low Strain Impact Integrity Test of the pile. Here the top of the pile is hit with a hand held hammer and reflected stress waves are recorded and subsequently analyzed to detect changes in pile impedance which could be the result of dimensional changes or cracks in the pile.

It should be noted that since this test does not detect all defects and also does not provide any information regarding the pile’s bearing capacity, a positive test result does not automatically qualify the pile as an acceptable deep foundation element.

However, the drawback of both approaches is that the damage assessment is done when the pile is already in place. To provide a real-time pile damage assessment capability, Rausche and Goble introduced a method in 1979 to “detect discontinuities or reductions in the cross section of the pile” and “to reach quantitative conclusions regarding the degree of section reduction at the discontinuity”. This method uses measurements at the pile top during pile driving, the same measurements that are used for pile driving analysis (PDA). Over the years this method, known as the Beta method, has become a standard tool, especially in the USA, even though its validity was never independently assessed (as the authors note in their paper).

More recently an alternative to pile driving analysis, the EDC Method was developed by embedding data collectors (strain gauges and accelerometers) into the concrete at both ends of pre-stressed pile. This approach, which has been studied extensively by the University of Florida and the Florida Department of Transportation (FDOT) and applied in numerous FDOT projects

247

in recent years, allows for direct monitoring of the pile toe condition, instead of assessing the situation at the buried pile toe by interpreting the recorded stress waves at the top of the pile. It also provides for an alternate damage assessment method, the Measured Pile Integrity (MPI) method introduced by Smart Structures as part of their SmartPile EDC system (Hecht, 2010).

As the number of driven piles with an EDC system increased, the reliability of the Beta Method has become suspect, suggesting that a thorough assessment of the method derivation would be appropriate (Verbeek and Middendorp, 2011). In this paper the Beta method will be re-evaluated to assess whether it is a reliable indicator of damage. This re-evaluation will cover both the theory behind the method as well as the review of Pile Driving Analysis data collected from a large number of concrete piles.

2 BETA METHOD

When an axial load is applied on the pile top a stress wave is generated in the pile that will propagate along the pile to the toe. As it travels downwards, upward acting stress waves are generated by changes in pile impedance, by the soil resistance along the pile shaft, and finally by the pile toe. The Beta Method is based on a signal analysis technique of the upward wave signal involving a search for abruptly occurring waveforms during the time that the stress wave travels from the top of the pile to the toe and back up to the top (i.e. during the interval 0 ≤T ≤ 2L/c, with L the length of the pile and c the wave speed). The magnitude of any detected anomalies is appropriately weighted and the impedance ratio Beta is reported as a percentage:

β = Znew / Zold (1)

where Znew is the impedance of the pile with the anomaly and Zold the original pile impedance.

Assuming that the pile originally had a uniform cross section over the entire length, this Beta is then assumed to reflect damage that has occurred in the concrete pile and in their paper Rausche and Goble even provided a damage classification scale (see Table 1), which is widely used in the industry, despite the fact that (as mentioned before) the authors clearly stated in their paper in 1979 that “there is no experimental proof available justifying the (…) classification”.

Over the years several equations have been published for Beta, but the basic equation has always been:

(2)

where α is is defined by Rausche and Goble in their original paper as

(3)

where μΔ is the relative increase of the proportional velocity at the point of damage, Fi the impact force, and RΔ the resistance force when the relative velocity increase due to the defect becomes noticeable.

Equation (2) clearly implies that the Beta has a specific value, which can easily be determined based on the measurements at the top of the pile during pile driving. Appendix 1 contains an example of a force and velocity measurement in a broken pile that was included in the original paper that illustrates this approach. Table 1. Beta Method Damage Classification.

B (%) Severity of damage

100 Undamaged

80 – 99 Slight damage

60 – 79 Damage

< 60 Broken

3 MPI METHOD

As mentioned before, by embedding data collectors (strain gauges and accelerometers) into the concrete at both ends of a pre-stressed pile the EDC system provides for an alternate damage assessment method, the Measured Pile Integrity (MPI) method introduced by Smart Structures as part of their SmartPile EDC system (Hecht, 2010).

One element of this method takes into account changes in the pre-load stresses in the concrete pile, especially near the pile toe where the pile is subject to the greatest compressive stresses, shear stresses, and stress gradients within the foundation element during installation.

The original pre-stress levels in a pre-tensioned pre-stressed concrete pile are established when two directly opposing forces reach equilibrium: the tensile stress in the steel strands multiplied by the total cross sectional area of these strands, and the compressive stress in the concrete multiplied by the total cross sectional area of the concrete. Once this equilibrium condition and corresponding pre-stress level are established, any change in either force will upset this balance and result in a new

248

equilibrium (and therefore new pre-stress level). For example, a vertically oriented crack extending up from the pile toe is very likely to upset this balance. When viewed looking into the pile end (see Figure 1), separate concrete sections will result, with the resulting pre-stress level in each section determined by the section’s cross sectional area and the number of steel strands in that section. Therefore any vertical crack resulting in non-symmetric volumes will cause a change in pre-stress levels, with a complete loss of pre-stress potentially indicating the complete loss of bonding between the steel and the concrete from the pile toe up to the location of the strain gauge.

Figure 1. Orientation of vertical cracking indicated by the dashed line in black.

From practical experience with the EDC system, if the recorded change in pre‐stress level (the “Pre-Load Delta”) drops the equivalent of more than 50 microstrain for 10 consecutive blows, it can safely be assumed that pile damage has occurred. In all other cases, it should be assumed that the pile is intact. It should be noted that with this method no attempt is made to classify the extent of the damage. Instead it is suggested to seek a qualified professional assessment of the pile in question. Obviously this damage assessment approach only applies to those parts of piles where a strain gauge has been placed, which is normally at the top and toe of a pile, and it will only detect pile damage that results in a change in pre-stress level, which excludes tension cracks.

In Figure 2 the change in pre-stress reading at the top and the toe of the pile are shown (left vertical axis in microstrain) as well as the compressive stresses (CSB) at the pile toe (right vertical axis in ksi), all as a function of the blow number (horizontal axis).

Around blow 1500 the pile penetrates a hard soil layer, causing the compressive stresses measured at a point in the toe core to increase to approximately 1.6 ksi (11 MPa) (red arrow in Figure 2). At the same time the static toe strain (pre-stress) begins to fall and eventually drops some 50 microstrain (black arrow in Figure 2), indicating likely damage to the pile toe. It should be noted that this damage was detected some 900 blows before pile driving was finally stopped.

Figure 2. Measured CSB (magenta) plotted with top (green) and toe (blue) pre-load deltas. Note the loss of pre-stress occurring right after punching through a hard layer (~ 1.55 ksi or 10.7 MPa) resulting in an eventual pre-stress relaxation of approximately 50 microstrains.

0.00.20.40.60.81.01.21.41.61.82.0

-100

-80

-60

-40

-20

0

20

40

60

80

100

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800

Com

pres

sive

Str

ess

Pile

Toe

(ksI

)

Prel

oad

Del

ta (u

e )

Blow Number

Project Name Removed Pre-load Delta & Compressive Toe Stresses

249

4 BETA METHOD - THEORETICAL REVIEW

From the Stress Wave Equation theory and as illustrated in Figure 3, it is clear that when F and F are the upward and downward travelling force respectively, v and v the velocity of the upward and downward travelling wave respectively, Z the pile impedance, with the subscript 1 and 2 indicating the pile segment, and assuming that there is no friction

F = Zv (4)

F = Zv (5)

F1+ F1 = F2+ F2 (6)

v1+ v1 = v2+ v2 (7)

Assuming that there is no upward wave F2, equations (6) and (7) will become:

F1+ F1 = F2 (8)

v1+ v1 = v2 (9)

Inserting (4) and (5) into (7) results in

F1/Z1 - F1/Z1 = F2/Z2 (10)

And Z2/Z1 = (F1+ F1) / (F1- F1) (11)

Or to use Beta Method approach:

Z2/Z1 = (1 – α) / (1 + α) (12)

where α = - F1 / F1. It should be noted, however, that both F1 and

F1 contain a soil interaction component (represented by W):

F1 = Fmeasured +W (13)

F1 = Fmeasured - W (14)

Consequently, while both Fmeasured and Fmeasured can be determined based on the force or acceleration measurements at the top of the pile during pile driving, the soil interaction component is not known and therefore the value of α (and thus Beta) cannot be derived from these measurements, irrespective of the equations published for α.

Figure 3. Wave theory.

As an aside, if the value of α could be determined solely based on the force and acceleration measurements at the top of the pile during pile driving, the soil interaction component would be known. In turn this would mean that the analysis of the dynamic load testing data would not require any signal matching (to determine the soil model that will generate the soil interaction component that allows the best match between the calculated signals and those measured at the pile top during the test). Since this is not the case, the fallacy of simply calculating the value for Beta for any part of the pile where there is a soil interaction component should be obvious.

5 BETA METHOD – PRACTICAL REVIEW

As the number of driven piles with an EDC system increased, many of the test piles on which PDA was applied as well, more than 400 data sets for piles driven in Florida are now available to perform a comparison of the Beta method with the MPI method. The results of this comparison were consistent and clearly showed that the pre-stress approach indicated pile damage well before a change in pile impedance occurred, if at all. Two typical examples will be discussed in this section.

A 60 ft (18 m) long 30 in x 30 in (0.75 m x 0.75 m) square concrete pile (with sensors in the pile top and pile toe) was placed in a 20 ft (6 m) deep pre-drilled hole, after which the pile was driven further into the ground using a diesel hammer. Initially pile driving was uneventful (with just 11 blows required to drive it 1 ft (0.3 m) further into the ground). However, around blow 85 the pre-load delta at the pile toe began to increase, and right around blow 100 the pre-load delta exceeded 50 microstrain. It was decided to continue, in part because the Beta value indicated no damage whatsoever (value was still at 100 %) until the pile had been driven to refusal less than 6 ft (1.8 m) from the start of driving. As the pile had not been driven to the required depth, the contractor decided to pull the pile (which was seemingly undamaged

250

based on the Beta value of 100 %) to pre-drill the hole further so the pile could be installed as specified. When the pile was pulled the pile damage indicated by the pre-load delta became apparent: vertical cracks extended 10 ft (3 m) up from the pile toe as noted by the visible ends of the tape measure (see Figure 5). It should be noted that the toe instrumentation, located in a segmented mass within the pile core, remained operational, even after the pile was pulled.

Table 2: Blow count.

Penetration (ft) Blow count

20-21 11

21-22 120

22-23 105

23-24 63

24-25 130

25-26 264 (refusal)

A second example deals with a 101 ft (31 m)

long 24 in x 24 in (0.61 m x 0.61 m) square concrete pile (with sensors in the pile top and pile toe). This pile was subjected to 3544 blows and throughout this process the Beta value remained at 100 %. However, around blow 1500 the pre-load delta exceeded 50 microstrain indicating pile damage. When the pile driving was finally halted and the pile was pulled the damage was obvious.

While the results shown above are obviously not typical for the more than 400 data sets (simply because for the vast majority of the data sets

neither the pre-load delta nor the Beta Method show any pile damage), the data clearly indicated that a significant number of these piles are damaged near the toe during pile driving, despite the fact that Beta Method does not show any pile damage. In those cases where the piles were pulled (more than 15 instances), the damage indicated by the pre-load delta (by dropping below –50 microstrain) was confirmed in every case, clearly supporting the proposition that the Beta Method is not a reliable indicator for pile toe damage.

It should be noted that these practical reviews are based on a relatively small number of piles, all driven in one state in the USA and mostly test piles. Because of the latter one can and should expect a greater occurrence of pile damage and for that reason this paper does not provide any specific number for piles that are damaged. It should also be remembered that at this time we cannot quantify the extent of the damage on the basis of the pre-load delta values, and that the damage shown in Figure 5 was obviously aggravated due to the 600 additional blows after the initial damage occurred. Nevertheless, even without the results of the theoretical review, the data available at this time clearly shows that the Beta Method should not be relied upon to protect against pile toe damage.

Figure 4. Condition of the 30 inch square concrete pile after it had been pulled.

Figure 5. Measured pre-load delta and Beta values in the 60 ft long 30 inch square concrete pile during pile driving.

-400-350-300-250-200-150-100

-500

50100150

0 100 200 300 400 500 600Blow Number

Pre-load Delta and Beta

pre-load delta,microstrain

Beta value,percent

251

Figure 6. Measured pre-load delta values in the 101 ft long 24 inch square concrete pile during pile driving.

Figure 7. Condition of the 24 inch square concrete pile after it had been pulled.

6 CONCLUSION

The development of the EDC system for driven concrete piles has not only provided an alternative method to assess driving damage in a concrete pile near the pile toe, it has also allowed to independently evaluate the accuracy of the Beta Method to assess the integrity near the pile toe. The data obtained from this evaluation generated sufficient grounds to carefully re-evaluate the Beta Method to assess pile damage.

The theoretical review of the method showed clearly that the Beta Method cannot be a reliable

indicator of pile toe damage, and a practical review using more than 400 data sets for piles driven in Florida showed independently that the Beta Method is not a reliable indicator. Taken together it is clear that the Beta method should not be used to protect against pile toe damage.

This conclusion is still justified despite the fact that the practical review is based on a relatively small number of piles, all driven in one state in the USA and mostly test piles

REFERENCES

Hecht, K. (2010). Interpretation of SmartPile™ EDC Measured Pile Integrity (MPI) Results, http://www.smart-structures-inc.com/smartpile-edc-measured-pile-integrity-mpi-2010-paper.

Herrera, R., Jones, L. E. and Lai, P. (2009). "Driven concrete pile foundation monitoring with embedded datac collector", Proceedings of the International Foundation Congress & Equipment Expo, 2009: Orlando, FL, pp. 621-628.

Rausche, F. and Goble, G. G. (1979). "Determination of pile damage by top measurements", American Society for Testing an Materials, 1979: Philadelphia, PA, pp. 500-506.

Rausche, F., Likins, G. E. an, Ren-Kung, S. (1992). "Pile integrity testing and analysis". Proceedings of the Fourth International Conference on the Application of Stress-Wave Theory to Piles, The Netherlands, pp. 613-617.

Verbeek, G. and Middendorp, P. (2011). "Determination of Pile Damage in concrete piles", DFI Journal, Vol. 5 (2), pp. 23-29.

-150.00

-130.00

-110.00

-90.00

-70.00

-50.00

-30.00

-10.00

10.00

30.00

50.00

0 500 1000 1500 2000 2500 3000 3500 4000

Blow Number

Pre-Load Delta (microstrain)

252

APPENDIX 1

In their 1979 paper Rausche and Goble included the following example of a broken concrete pile (see Figure 8)

The early force and velocity behavior shows the typical force-velocity proportionality. At the time 8.6 ms after impact, the velocity shows an increase relative to the force. This increase can only be explained by a small pile mass and stiffness approx. 54 ft (16.5 m) below the pile top [x = ½ c tx = 54 ft]. Before the relative velocity increase became noticeable, the proportional velocity had already dropped by an amount of RΔ = 208 kips (925 kN) relative to the force. The relative increase at the point of damage effect was uΔ = 304 kips (1352 kN) and the impact force was Fi = 518 kips (2304 kN). Therefore

Figure 8. Force and velocity signals damage assessment example.

253