Method of determining the length of a pile

A method for determining a length of a pile which includes the steps of affixing a plurality of sound sensors in a vertical array adjacent to the pile, generating an elastic wave adjacent the pile such that the elastic wave propagates through or from the pile, radiating the elastic wave from the pile such that the sound sensors receive the radiated elastic wave, and analyzing the radiated elastic wave so as to determine the length of the pile. The elastic wave can be radiated so as to create upwardly propagating waves and downwardly propagating waves within the pile. The radiated elastic waves can also produce refracted elastic waves along a length of the pile and diffracted elastic waves at a bottom of the pile. The data from the radiated elastic waves is analyzed so as to be determinative of the length of the pile.

TECHNICAL FIELD 
The present invention relates to methods for determining the length of a 
pile used for construction. More particularly, the present invention 
relates to elastic wave methods for determining the length of a pile. 
Furthermore, the present invention relates to elastic wave methods in 
which elastic waves radiating from the pile are analyzed and correlated to 
the length of the pile. 
BACKGROUND ART 
In recent years, it has become increasingly necessary to rehabilitate the 
superstructures of highway bridges. In order to properly rehabilitate the 
superstructures of various constructions, decisions must be made 
concerning the adequacy of the existing foundations. This is particularly 
true for older structures for which as-built records are missing and for 
which foundation deterioration may have occurred. Visual inspection of 
foundations is virtually impossible. As such, a need has developed so as 
to provide procedures for evaluating the capacity of existing foundations. 
In particular, a need has developed to provide a procedure for determining 
the length of a pile in such foundations. A "pile" is defined as a member 
with a small cross-sectional area (in comparison with its length) used to 
provide adequate support for a column or wall resting on soil which is too 
weak or too compressible to support the structure with a spread footer. As 
used herein, the term "bent" includes piers or other structures above the 
foundation. 
There is a serious need to rehabilitate the aging highway system. Within 
the United States, over 35% of the 575,410 bridges in the 1992 National 
Bridge Inventory were classified as needing to be replaced or 
rehabilitated. It has been estimated that over the next 20 years 
approximately $165 billion must be invested to address the tremendous 
rehabilitation backlog and to improve accruing bridge deficiencies. The 
economic value of the foundations for many bridges can be up to 25% of the 
cost of the bridge. This makes foundations a major economic component in 
the rehabilitation/repair effort. Inadequate foundations can, of course, 
jeopardize the entire superstructure of any rehabilitated bridges. 
Bridge safety issues are foremost among the considerations for 
rehabilitation. Foundation failures, or excessive foundation movements, 
mostly from the application of extreme event loads, have occurred too 
frequently in recent years, exposing the public to risks that can be 
reduced by evaluation of the adequacy of existing foundations. Examples of 
major fatal catastrophes are the Sunshine Skyway Bridge in Florida (35 
deaths), the Schoharie Creek Bridge in New York (15 deaths), the collapse 
of the Nimitz Freeway viaduct during the Loma Prieta earthquake (67 
deaths), and a barge impact of a bridge in New Orleans (1 death). Clearly, 
upgrading of structures without appropriate knowledge of the adequacy of 
the foundations increases this vulnerability. 
The traditional approach for evaluating such structures is to examine the 
as-built records. The as-built records include information on number, 
depth and width of the foundation elements, the soil characteristics at 
the bridge site and the recorded observations of the inspector during 
construction (concerning the potential for structural defects in the 
foundations). If necessary, as-built conditions can be confirmed by 
probing the exterior of the foundation and/or coring concrete piles or 
drilled shafts, if appropriate equipment can be positioned for the task. 
Once the loads for the rehabilitated structure are known, the capacity of 
these foundations can be evaluated in light of modern geotechnic design 
methods and the adequacy of the foundation determined. In the event that 
serious difficulties were noted during the installation of one or more 
foundation elements, or if probes and cores reveal defects, judgment must 
be exercised whether to exclude the questionable foundation element from 
consideration as a load-bearing pile or shaft. On occasions where the 
superstructure load can be taken off the foundation during the 
rehabilitation process, representative piles or shafts can be subjected to 
load tests, which is the most definitive way to evaluate the adequacy of 
the foundation. New geometrically identical "sister" piles or shafts can 
be installed immediately adjacent to the foundation of interest and 
subjected to load tests. 
If as-built records are not available, or if they are incomplete, the 
traditional approach is not always appropriate because destructive probing 
and coring necessary to completely identify the foundation must be very 
extensive. In this case, nondestructive testing methods can be employed. 
Appropriate types of nondestructive tests for this purpose include 
pulse-echo and impulse-response testing, steady-state vibration testing, 
ambient vibration surveys, and shear-wave seismic reflection profiling. 
Various other techniques, such as casting sensors, or access tubes for 
sensors, into the pile or shaft, are not practical for evaluating existing 
foundations. 
The pulse-echo and impulse-responsive testing involves the application of 
low-amplitude, impulse-type elastic waves directly to the head of an 
element of the foundation (pile or drilled shaft) with measurement of the 
reflected compression waves (P-waves) or shear waves (S-waves) from the 
bottom of the element or from a significant defect within the element, if 
such a defect exists. The input signal (load time history from an impulse 
source, for example a hammer, that creates the elastic wave in the 
foundation) can be measured along with the reflected signal (velocity or 
acceleration time history on the element near its top), or only the strain 
time history signal at the head of the pile may be measured, and the data 
processed in several ways. If a time history graph of the strain signal is 
displayed, peaks in the signal of a sensor on the element at known times 
can sometimes be interpreted as representing points of reflection if the 
compression or shear wave velocity of the pile material can be estimated. 
This so-called "pulse-echo" method has been applied mostly to piles and 
drilled shafts that are directly accessible (so that instruments can be 
attached directly to the pile or shaft and not to a cap, bent, column, or 
abutment) and has been applied to the investigation of both structural 
integrity and as-built depths of foundations. 
Impulse-response testing (sometimes referred to as transient response 
testing) can be used for the same purpose, although it is somewhat more 
complex. With this method, both the input (elastic impulse source) and 
output (sensor) signals are recorded and processed in the frequency domain 
by a computer to develop a "mobility" function, which varies with 
frequency. In an ideal foundation, the mobility-frequency diagram makes it 
much more straightforward to interpret depths to major defects or 
pile/shaft lengths where defects do not occur. However, the presence of 
multiple defects in the foundation, reverberations from the 
superstructure, and other factors make this method difficult to use in 
evaluating existing foundations. 
A disadvantage of the pulse-echo and impulse-response (mobility function) 
tests are that they appear to require that the sensor be placed on the 
foundation element (pile or shaft) itself, which may be difficult in some 
bridge foundations. 
A well-established method for the characterization of the dynamic behavior 
of a structure is the steady-state vibration test. The superstructure is 
excited by a mechanism that generates a steady sinusoidal force in time. 
After a short period of time, the structure settles into a periodic 
steady-state mode of response at the exciting frequency. The force 
generator can be a small electromagnetic device, a mechanical device with 
a pair of counter-rotating masses, or a large mass driven by a linear 
actuator. The structural response can be monitored by displacement, 
velocity or acceleration sensors. By exciting the structure at several 
frequencies, a frequency response curve is obtained for a given point on 
the structure, from which modal frequencies and damping ratios are 
derived. This method has been rather widely applied to buildings, bridges, 
nuclear power plant structures and dams. When applied to bridges, it is 
mainly used to study the vibration of the superstructure. This forced 
vibration method can conceivably be used to infer foundation performance 
at low strain levels, but it is not likely to be useful in this respect 
because the overall system response of the structure depends very little 
on the foundation contribution. That is, any foundation behavior is 
masked, perhaps totally, by the superstructure behavior and cannot be 
separated from the system response, as the entire 
superstructure-foundation system is responding to the single frequency of 
the exciting force. 
An ambient vibration survey records the vibration of a structure caused by 
ambient forces, such as wind, microtremors, traffic or any other forms of 
excitation that tend to be random and sustained, but small in amplitude. 
This method is most useful for characterizing the overall behavior of the 
structure, and when applied to a bridge, it is again limited in terms of 
characterizing foundation response because the dominant response will be 
from the superstructure. 
Another technique that has been utilized is a technique for imaging 
shear-wave diffractions from pile terminations. This technique was 
described in an article by Ebrom et al. as published in the Society of 
Exploration Geophysics Convention Abstracts, 1994. This method is used to 
determine the subsurface lengths of terminations for a shaft or pile. In 
this method, it is necessary to perform a shear-wave survey in the 
immediate proximity of the pier and to infer the depth from the two-way 
travel time. This survey is aimed at delineating a terminating vertical 
unit, such as the shaft or pile. The goal of this method is to enhance 
diffracted seismic waves from the base of the shaft or pile. These 
diffractions are created when the shear-wave seismic wave field encounters 
the abrupt termination of the shaft or pile. The diffraction event is 
proportional in amplitude to the incident wave and the shear modulus 
contrast between the soil and the shaft or pile. The diffractions from the 
terminus of the shaft or pile possessing large modulus contrasts are 
easily detectable. In a typical highway environment, the shear-wave 
modulus contrast between near-surface soils and concrete are quite large, 
generally far exceeding a factor of 10:1. In this method, a horizontal 
array of sound sensors is provided in an area surrounding the bent or 
pier. A horizontal or vertical hammer blow is applied to the bent or pier. 
The elastic wave sensors will receive the diffracted waves from the bottom 
of the shaft or pile so that calculations can be carried out as to the 
length of the shaft or pile. This method includes a Kirchhoff migration by 
summing together the amplitudes that lie along the diffraction hyperbola 
(as calculated from the velocity field of the medium), and placing the 
summed amplitudes at the apex of the hyperbola. The apex of the 
diffraction hyperbola corresponds geometrically to the position of the 
diffracting point. After migration, diffracting points are imaged as 
high-amplitude events. Unfortunately, this method is often difficult to 
apply in areas in which space is limited. If it is not possible to arrange 
a large horizontal array of sensors in a location adjacent to the bent or 
pier, then this method cannot be effectively used. 
It is an object of the present invention to provide a method which 
effectively determines the length of a shaft or pile. 
It is another object of the present invention to provide a method for 
determining the length of a shaft or pile which is non-destructive. 
It is a further object of the present invention to provide a method for the 
determination of a shaft or pile which is easy to use, easy to implement, 
and relatively inexpensive. 
It is a further object of the present invention to provide a method for the 
determination of the length of a shaft or pile which can be utilized in a 
relatively limited physical area. 
These and other objects and advantages of the present invention will become 
apparent from a reading of the attached specification and appended claims. 
SUMMARY OF THE INVENTION 
The present invention is a method for determining a length of a pile that 
comprises the steps of: (1) affixing a plurality of elastic wave sensors 
in a vertical array adjacent to the pile; (2) generating an elastic wave 
adjacent the pile such that the elastic wave propagates through or from 
the pile; (3) radiating the elastic wave from the pile such that the 
plurality of elastic wave sensors receive the radiated elastic wave; and 
(4) analyzing the radiated elastic wave so as to determine the length of 
the pile. 
One embodiment of the present invention is identified as a transient forced 
vibration survey. In this method, the step of affixing includes affixing 
the plurality of elastic wave sensors directly to a surface of a structure 
connected to and above the pile. In particular, the structure can be a 
bent column and a bent cap located at the above ground portion of the 
bent. Each of the elastic wave sensors is a geophone which is spaced 
equally from an adjacent geophone. The step of generating elastic waves 
includes striking the surface of the structure on a side or top so as to 
generate elastic waves that radiate through the interior of the structure. 
The radiated elastic wave creates upwardly propagating waves and 
downwardly propagating waves within the pier. In this method, the step of 
analyzing includes autocorrelating the data from the upwardly propogating 
waves and the downwardly propagating waves so as to produce a peak 
corresponding to a periodicity relating to a length of the pile. This 
method can further include the step of separating the upwardly propagating 
waves from the downwardly propagating waves, and then autocorrelating the 
upwardly propagating waves and the downwardly propagating waves so as to 
produce a peak corresponding to a periodicity related to a length of the 
pile. The upwardly propagating waves, in this alternative method, are 
filtered from the downwardly propagating waves. The step of 
autocorrelating uses graphical peaks which correspond to a periodicity 
related to the length of the structure and a peak corresponding to a 
periodicity relating to a length of the pile. 
An alternative form of the present invention is identified as a parallel 
seismic survey. In this alternative form of the present invention, the 
step of affixing the sound sensors includes forming a vertical hole 
adjacent to and in generally parallel relationship to the pile, and 
placing a vertical array of the elastic wave sensors in the hole. The 
vertical hole has a length greater than a length of the pile. The vertical 
array has an elastic wave sensor extending so as to be lower than an 
expected bottom of the pile. The step of generating an elastic wave 
includes creating an impulse on or adjacent to a top of the pier so that 
the elastic wave propagates through the pier and pile as a refracted wave. 
The step of reflecting includes refracting the elastic wave through a 
length of the pile and diffracting the elastic wave at a bottom of the 
pile. In this method, the step of analyzing includes determining a point 
along the vertical array in which the refracted wave changes to the 
diffracted wave and correlating the point along the length of the array so 
as to be related to the length of the pile. The step of determining also 
includes migrating the data. A simple method of migrating the data 
includes the steps of: (1) picking a first arrival time of the elastic 
wave to the point; and (2) plotting a circle of radius calculated from a 
velocity of propagation of the elastic wave through the soil between the 
vertical hole and the pile and a departure of the arrival time from a 
linear extrapolation of refraction arrival times so as to establish a 
diffraction center. In this alternative embodiment of the present 
invention, it is preferable that each of the plurality of sensors be a 
hydrophone. At least a portion of the vertical hole is filled with liquid, 
preferably water. Alternatively, it is possible to clamp geophones 
directly to the casing of the hole.

DETAILED DESCRIPTION OF THE INVENTION 
The present invention contemplates the use of a transient forced vibration 
survey and a parallel seismic survey for the determination of the length 
of a pile. In either of these methods, the steps of the present invention 
include the steps of affixing a plurality of sound sensors in a vertical 
array adjacent to the pile so as to be responsive to elastic wave 
radiation passing from the pile. The elastic wave is generated adjacent to 
the pile such that the elastic wave propagates through or from the pile. 
The elastic wave sensors receive the radiated elastic wave from the pile. 
Finally, the radiated elastic wave is analyzed so as to determine a length 
of the pile. In contrast to the prior art, the present invention, in 
either of its embodiments, contemplates a method in which the area 
utilized for the elastic wave sensors is relatively small. In the first 
embodiment of the present invention, the transient forced vibration 
survey, the elastic wave sensors are directly connected to the bent 
structure located above the foundation. In the alternative embodiment of 
the present invention, in the parallel seismic survey, the vertical array 
of elastic wave sensors is positioned in a vertical hole adjacent to the 
pile. In either of the embodiments of the present invention, the term 
"pile" refers to pilings, shafts, foundation structures, and related 
structures that extend vertically into the earth a distance from the earth 
so as to support a structure above the earth. Also, as used herein, in 
either of the embodiments, the phrase "affixing the sound sensors in a 
vertical array" means either placing the sound sensors directly onto a 
structure (such as a bent column and bent cap located at the above ground 
portion of the bent) or in a vertical array spaced from the pile. The term 
"elastic waves" can mean compression waves (P-waves), shear waves 
(S-waves), Raleigh waves, Stoneley waves, reflections, refractions, 
diffractions, head waves, acoustic waves, and the like. 
Transient Forced Vibration Survey 
Referring to FIG. 1, there is shown at 10 the structure for the carrying 
out of the transient forced vibration survey in accordance with the 
preferred embodiment of the present invention. As can be seen in FIG. 1, a 
plurality of geophones 12 are arranged in a vertical array on a surface of 
the bent 14. The bent 14 extends upwardly above the earth 16 from the pile 
cap 18. The pile 20 resides below the pile cap 18 and extends into the 
earth 16. The bent 14 is positioned directly above and is connected (by 
way of the pile cap 18 or by a construction joint) to the pile 20. In the 
preferred form of the present invention, an elastic wave sensor 22 is 
affixed to the pile 20 just below the pile cap 18. However, if, because of 
the nature of the construction it is impossible to attach the sound sensor 
22 to the pile 20, then this step can be avoided. 
In FIG. 1, it can be seen that an elastic wave is generated by creating an 
impulse, such as striking a hammer to the surface 24 of the bent 14 in the 
manner of arrow 26. The elastic wave sensors 12 are attached to the side 
of the bent 14 so as to be spaced approximately an equal distance from 
each other. As shown in FIG. 1, a total of nine sound sensors 12 are 
affixed to the bent 14 and spaced from each other at one foot intervals. 
The elastic wave sensors 12 can be geophones which effectively serve to 
receive radiating elastic waves. The geophones 12 serve to record the 
resulting elastic waves propagating within the bent 14. 
Through the use of the geophones 12, individual elastic waves can be 
recognized that initially propagate upwardly and reflect downwardly with 
reversed polarity from the top of the pier. The geophones 12 can also 
recognize events that initially propagate downwardly and reflect upwardly 
with reversed polarity from the bottom 27 of the pile 20. The individual 
energy arrival times T.sub.1 and T.sub.2 of these events vary 
systematically as the position of the receiving geophone 12 changes. This 
regular variation in arrival time makes it possible to measure the 
velocity in the bent 14 from the first energy arrivals. This measurement 
is illustrated, with particularity, in FIG. 2. FIG. 2 shows a blow-up of 
the early part of the seismic data so as to facilitate the measurement of 
the first energy arrivals accurately. In FIG. 2, the geophones are located 
at one foot intervals and the display time scale is in milliseconds. As 
can be seen in FIG. 2, the measurement of the first energy arrival yields 
a velocity of 6,800 feet per second. In measuring the first energy arrival 
times, it is necessary to take into consideration that the waves are 
dispersive, as shown by the changing phase of the first energy arrivals. 
As such, it is necessary to pick group velocity versus phase velocity. 
This dispersion effect is most pronounced in the early part of the wave 
propagation and becomes less noticeable as the propagation distance 
increases. Beyond the first energy arrivals, the recorded information is 
too complex to uniquely identify individual reflection events from the 
top, bottom, and internal reflecting interfaces. 
The analysis by the method of the present invention is based upon the fact 
that all multiple reflected events pass the geophone array in one 
direction so as to maintain constant time periods .DELTA.T.sub.1 and 
.DELTA.T.sub.2, which are always twice the transit time of the path 
traversed between the effective reflection boundaries. Because the data is 
recorded through an array, it is possible to identify which direction any 
wave is passing the array, either upward or downward. The upward 
propagating waves can be separated from the downward propagating waves by 
appropriate velocity filtering of the array data. Since the time periods 
.DELTA.T.sub.1 and .DELTA.T.sub.2 are fixed by the geometry of the 
structure, multiple reflections within the structure will maintain these 
periodicities. The expected transit time paths for a shear wave 
reverberating within the joined structure is shown in the graphical 
illustration of FIG. 3. 
FIG. 3 shows the paths 30 for initially upward travelling waves and the 
paths 32 for initially downwardly travelling waves. The interior interface 
is shown by vertical line 34. Arrow 36 shows the location of the elastic 
wave energy source. The elastic wave energy source can be located either 
on the top or the side of the cylinder. The waves 30 and 32 show each of 
the wave fronts as hitting the interior interface 34 between cylinder 38 
and cylinder 40. Cylinder 38 will correspond to the bent column 14 and the 
pile cap 18. Cylinder 40 will correspond to the pile 20. The wave fronts 
propagating within the cylinders 38 and 40 are partially reflected and 
partially transmitted at the interfaces at each end of the cylinders. Each 
partial transmission to the lower cylinder 40 is in turn partially 
transmitted and reflected at the interior interface 34. This creates a 
complex pattern of interrelated events that are detected by the geophones 
12. The only commonality is that the periods between the chains of events 
are constant and determined by the transit time in each cylinder. The 
autocorrelation function of the geophone recordings will show their 
inherent periodicity. 
As an example utilizing the present invention, when one examines the 
structure of the individual bent column 14 being tested, the structure 
will appear as two joined columns 38 and 40. Column 38 extends from the 
construction joint joining the column 14 to the pile 20 to the free air 
surface at the top of the bent cap. The column 40 relates to the drilled 
shaft. In an experiment with the present invention, these dimensions, as 
shown from the as-built plans, where, respectively, 14.25 feet and 45 
feet. In this embodiment, .DELTA.T.sub.1 is the round-trip transit time in 
the upper cylinder 38 and .DELTA.T.sub.2 is the round-trip time in the 
lower cylinder 40. 
FIGS. 4A-4C and 5A-5C, respectively, show the seismic record obtained for 
the transient forced vibration survey of the present invention after 
band-pass filtering to pass frequencies between 100 and 1300 hz, followed 
by velocity filtering of .+-.6, 10, and 14.degree. about the measured 
velocity of 6800 feet per second across the geophone array 12 so as to 
isolate the up-going waves (shown in FIGS. 4A-4C) and the down-going waves 
(shown in FIGS. 5A-5C). With reference to these FIGS. 4A-4C and 5A-5C, it 
can be seen that there are many multiple reflected events contained in the 
data. The patterns are far too complex to directly interpret. However, one 
also can recognize that there are major periodicities in these data which 
are also too complex to interpret by visual inspection. However, the pile 
lengths can be determined, in one form of the present invention, by 
correcting the data for spherical spreading and dispersion so as to 
produce gain corrected data to approximate plane wave propagation and then 
by autocorrelating the corrected data. The autocorrelation function will 
show a peak corresponding to a periodicity related to a length of the 
pile. 
Another approach is to autocorrelate the data with both up-going and 
down-going waves. It was found that dividing the record into separately 
up-going and down-going waves by velocity filtering before calculating the 
autocorrelation functions provides much simpler and interpretable 
patterns. The separation into up-going and down-going waves is rather 
straight forward. The up-going waves cross the geophone array 12 with the 
velocity of +6,800 feet per second. The down-going waves cross the array 
with -6,800 feet per second velocity. This velocity was measured from the 
pattern of first energy arrivals as shown in FIG. 2. 
FIGS. 6A-6D show, respectively, the autocorrelation functions of the 
corresponding velocity filters as applied to FIGS. 4A-4C and 5A-5C. The 
effect of broadening the filter aperture is dramatically seen in the 
autocorrelation function. The narrower the aperture, the more oscillatory 
(narrower bandwidth) the filter output. The correlation functions all show 
a consistent, strong correlation peak at 4.3 msec. lag, and another 
slightly weaker correlation peak at 14.3 msec. This is seen on the 
autocorrelation functions from both up-going and down-going waves and the 
summed up-and down-going waves. 
With reference to FIG. 3, these first two peaks should correspond to the 
two predicted periodicities .DELTA.T.sub.1 and .DELTA.T.sub.2. The 
periodicity in the upper cylinder 38 will correspond to the part of the 
bent 14 from the construction joint to the top of the pier cap. The 
periodicity .DELTA.T.sub.2 of the lower cylinder 40 will correspond to the 
bottom 27 of the pile 20 to the construction joint. 
With reference to the experimental data, since the dimension of the two 
parts of the structure are known to be 14.25 and 45 feet, respectively, 
this gives a predicted periodicity of (14.25 ft/6,800 ft/sec).times.2=4.2 
msec and (45 ft/6,800 ft/sec).times.2=13.2 msec. These calculated lag 
times agree acceptably with the measured lag times of 4.3 and 14.3 msec. 
As a result, it can be seen that the autocorrelation function allows the 
identification of the major periodicities in the upper and lower cylinders 
and provides satisfactory accuracy so as to determine the length of pile 
20. 
It should be noted that geophone 22 should ideally be placed on the pile 20 
below the pile cap 18 so as to achieve greater accuracy in the 
determination of the length of the pile 20. It may be necessary to 
excavate sufficiently around the pile cap 18 so as to place the geophone 
22 on the upper end of the pile 20. This placement of the geophone 22 
enables direct measurement of the reverberation in the pile 20 so as to 
verify the identification of the autocorrelation lags with the proper part 
of the total structure. It is expected that the above-ground dimension of 
the structure can be directly measured to assist in the identification of 
the various correlation peaks that are detected. The vertical array of 
geophones 12 on the exposed portion of the bent 14 also provides the data 
required to measure the elastic wave velocity in the structure. 
Parallel Seismic Survey Profile 
FIG. 7 shows an alternative embodiment of the present invention which is a 
parallel seismic survey profile system 40. The system 40 serves to measure 
the length of shaft 42 which is fixed within the earth 44. The bottom 46 
of the shaft 42 extends from the earth 44 a distance which is to be 
measured by the present invention. A vertical hole 48 is drilled into the 
earth 44 for a distance greater than the expected length of the shaft 42. 
A vertical array 50 of hydrophones 52 is positioned within the vertical 
hole 48 so as to extend in the vertical hole 48. At least one of the 
hydrophones 52 should extend below the bottom 46 of the shaft 42. An 
elastic wave generating source 54 is positioned on the surface 44 of the 
earth or on the pier so as to create an elastic wave that passes through 
the shaft 42 and will pass from the shaft 42 as refracted elastic waves. 
The elastic waves generated by the source 54 will pass from the bottom 46 
of the shaft 42 as a diffracted elastic wave. The hydrophones 52 of the 
hydrophone array 50 will serve to receive the elastic wave as refracted 
and diffracted from the shaft 42. 
System 40 serves to conduct a survey by utilizing the theoretical energy 
path propagating down the shaft 42 as a refracted wave. The refracted wave 
radiates energy into the soil 56 between the vertical hole 48 and the 
exterior of the shaft 42. This refracted wave is received by the vertical 
hydrophone array 50. Below the bottom 46 of the shaft 42, the elastic wave 
energy will diffract and be recorded at the hydrophones 58 below the 
bottom 46 of the shaft 42. The vertical array 50 serves to record the 
diffraction, so as to locate the bottom of the shaft 42 by subsequent 
analysis including migration of the data. 
As can be seen in FIG. 7, the seismic data 60 is shown as recorded by the 
vertical array 50. The refracted event propagates down the shaft 42 and is 
readily identified by the linear moveout of the first energy arrivals, 
which fit a P-wave velocity of 15,500 feet per second. This velocity is 
appropriate for concrete. P-waves are generated in this instance since the 
source 54 applies a blow to the top of the shaft 42. The point where the 
refracted wave front changes to a curved diffraction wave front can be 
seen by visual inspection of the seismic data 60. FIG. 8 shows graphically 
the plot of the first energy arrival times from the system 50 of the 
present invention. As can be seen, in FIG. 8, the plot of the first energy 
arrival times shows the change from the linear refraction arrival time 
pattern 64 to the curved diffraction arrival time path 66. It can be seen 
that this change occurs at approximately 16 feet. As such, the shaft 42 
can be easily seen to have a length of approximately 16 feet. The actual 
length of the shaft is 17 feet. 
FIG. 9 shows how this point can be confirmed by picking the first energy 
times and migrating the data. This migration is equivalent to plotting a 
circle of radius calculated from the velocity of propagation of the soil 
56 and the departure of the first energy arrival time from the linear 
extrapolation of the refraction arrival times established by the data from 
the hydrophones 52 above the bottom 46 of the pile 42. FIG. 9 shows the 
circles as calculated from the measured first energy arrival times. The 
circles coalesce in a one foot zone at the known bottom of the shaft. As 
such, the diffraction center is accurately identified as 17 feet (the 
actual length of the pile 42). 
The correct soil velocity is obtained by separately initiating the energy 
source 54 on the earth 44 adjacent to the vertical hole 48 and by 
recording the travel times from the surface 44 to the vertical array of 
hydrophones 52 in the vertical hole 48. The soil velocity is obtained by 
plotting the first energy arrival times as a function of depth, fitting a 
straight line through these measured times, and calculating the velocity 
from the slope of this line. In the experiments shown in FIGS. 7-9, the 
measured velocity is 5,500 feet per second. 
The vertical hole 48 may be filled with a liquid, preferably water. If 
water is not available, it is also possible that clamped geophones can be 
used instead of hydrophones to form the array 50. 
In the system 40, the resolution of the shaft depth to within one foot is 
acceptable for bridge maintenance purposes. The advantages of the system 
40 are that, in contrast to the areal survey, little room is required 
around the bent such that access is much simpler for routine 
investigations. This method does require some second-guessing as to the 
maximum length of the shaft 42, since the test hole must extend far enough 
below the true bottom of the shaft 42 so as to record diffractions. Since 
the typical maximum drilled shaft lengths are generally well known, this 
is a minor problem. The cost of drilling a four inch diameter examination 
hole 48 adjacent to the shaft 42 is relatively minor. 
The foregoing disclosure and description of the invention is illustrative 
and explanatory thereof. Various changes in the steps of the described 
method may be made within the scope of the appended claims without 
departing from the true spirit of the invention. The present invention 
should only be limited by the following claims and their legal 
equivalents.