Nondestructive testing of drilled shaft foundations.pdf

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1、Application: Nondestructive Testing of Drilled Shaft FoundationsNondestructive tests offer a rapid, economical means of evaluating the characteristics ofdeep foundations (i.e. drilled shafts, piles, auger-cast piles). There are two broadapplications:quality control testing of new foundations anddete

2、rmining the type and depth of unknown foundations.For the first application, nondestructive tests are used to check for defects in cast-in-placefoundations such as drilled shafts. The figures on the next page illustrate two methods ofconstructing cast-in-place foundations. Defects in the constructed

3、 foundation may arisefrom one of the following problems that could adversely affect the performance of theshaft (ONeill 1992).drilling,casing,slurry, orconcreting problems.Nondestructive tests are ideally suited to use as a construction quality control tool todetect the presence or absence of a void

4、 arising from one or more of these problems.Sonic EchoConceptually, the sonic echo method is very simple. The end of the shaft and any defectsthat exist along its length cause reflections of the seismic waves as they propagatedownward through the shaft. By observing the time required for these refle

5、ctions to returnto the top of the shaft, the depth to the reflector can be determined:zt =V2b(1)where z is the depth to a reflector (a defect or the bottom of the shaft), Vb is thelongitudinal wave velocity in concrete, and t is the travel time of the reflected wave.Since t is a two-way travel time,

6、 the numerator in Eq. 1 must be divided by two.The acceleration time history recorded at the top of a drilled shaft is shown in Figure 1.There is a clearly identified reflection that occurs 9.47 msec after the initial impact. Thelongitudinal wave velocity of the concrete measured on 15-cm by 30-cm (

7、6-in. by 12-in.)test cylinders was equal to 3700 m/sec (12,130 ft/sec). Using the observed travel time andcompression wave velocity, the depth to the reflector is calculated to be 17.5 m (57.4 ft).The depth agrees well with the design length of 16.9 m (55.5 ft). No other reflections canbe identified

8、 in the acceleration record.0481216-0.4-0.3-0.2-0.10.00.10.20.30.4Time (msec)Acceleration (g)Figure 1Sonic Echo Test ResultsIn the absence of a measured value of Vb, it is common to assume the velocity of theconcrete using the guidelines shown in Table 1.Table 1 Suggested Compression Wave Velocity R

9、atings for Concrete QualityCompression Wave Velocity(ft/sec)General Concrete ConditionAbove 13,500Excellent10,800 to 13,500Good9,000 to 10,800Questionable6,300 to 9,000PoorBelow 6,300Very PoorSonic MobilityTheoryWave propagation in a long, slender foundation can be reasonably modelled using the one-

10、dimensional wave equation. Recall that the one-dimensional wave equation is:2222utEux=(2a)or22222utVuxb=(2b)Consider a rod of finite length L with a free-fixed boundary conditions. This correspondsto a drilled shaft foundation end bearing into rock.Consider a solution to the wave equation of the for

11、m:u x tU x ei t( , )( )=(3)with U(x) of the form:U xAxVBxVbb( )cossin=+(4)At x = 0 (the fixed end), U = 0 and at x = L, Ux= 0. The first boundary condition impliesA = 0. The second results in:BVLVcccos= 0(5)This equation is satisfied only if:nbLVn=+2 for n = 0, 1, 2, .(6)()fVnLnb=+214(7)To determine

12、 the length of the shaft (or possibly the depth to a significant defect), we canrearrange Eq. 7 as follows:()LVnffixedbn=+214(8)where Lfixed denotes the length of the drilled shaft with a fixed end condition. We canderive similar expressions for other boundary conditions. For example, suppose that t

13、hedrilled shaft is floating and relies primarily on side friction for resistance. In this case, thedrilled shaft is more accurately modeled as a free end. The corresponding equation forthis condition is:LV nffreebn=2(9)Clearly, the length is not only a function of the natural frequency of the drille

14、d shaft inlongitudinal vibration (and the longitudinal velocity), but also of the end condition. Thisraises an important practical question because the end (bottom) of the shaft is not perfectlyfixed or free and, in fact, may not be known.To solve this practical problem, consider the difference betw

15、een any two adjacent naturalfrequencies. For the fixed end condition:()()fffVLnnVLnnbb=+=+ 14211212(10)After rearranging, we obtain:LVfb=2(11)For the free end condition:()fffVLnnVLnnbb=+=+ 1212(12)which is the same result we obtained for the fixed end. Thus, although the naturalfrequencies differ fo

16、r various boundary conditions, the difference between adjacent naturalfrequencies is the same for different boundary conditions. We can take advantage of thisfact to determine the length of a drilled shaft without having to assume or know theboundary conditions at the bottom of the shaft.Testing Pro

17、cedureIn the sonic mobility method, the force and acceleration time histories are transformed tothe frequency domain using the FFT analyzer. The results are the spectra, P(f) and A(f), ofthe force and acceleration, respectively. The mobility is a frequency response functiondefined as the particle ve

18、locity observed at the top of the shaft normalized by the force:Mobility V(f)P(f) = A(f)i P(f)(13)where V(f) is the particle velocity spectrum, = 2f is the circular frequency, and i is -1.The particle velocity spectrum is obtained by integrating the particle acceleration spectrumin the frequency dom

19、ain as shown in the right-hand term of Eq. 13. The mobility is acomplex quantity, but typically only the magnitude is plotted. The figure below shows themobility curve measured for a drilled shaft. The shaft length and depth to defects, averagediameter, and stiffness are determined from the curve us

20、ing the following interpretiveprocedures.020040060080010000.0E+01.0E-42.0E-43.0E-4Frequency (Hz)Mobility (mm/sec/N)fThe length of the shaft and the depth to any defects are determined from the spacingbetween peaks, f:LVfb=2(11 again)In the figure, the spacing between adjacent peaks is 107.5 Hz. This

21、 corresponds to a shaftlength of 17.2 m (56.4 ft) which also agrees well with the design length of 16.9 m (55.5ft). Defects in the shaft would appear as more widely spaced peaks with larger amplitudes.No other peaks are evident in the figure, indicating that the shaft has no major defects.The averag

22、e impedance of the shaft can be determined using the average value of themobility at higher frequencies:NAVcb=1(14)where N is the average value of the mobility at high frequencies, c is the mass density ofconcrete, and A is the average cross-sectional area of the concrete. In the figure theaverage v

23、alue of the mobility from 200 to 1000 Hz is approximately 1.5 x 10-4 mm/sec/N.Using the measured Vb and a measured unit weight of 23.5 kN/m3 (150 pcf), the averagediameter of the shaft is 979 mm (38.5 in.).The low-strain stiffness is calculated from the slope of the initial portion of the mobilitypl

24、ot:Kmob = 2 fMV fP fM( )( )(15)where Kmob is the low-strain stiffness, fM is the frequency of a point on the initial slope ofthe curve, and term in the denominator of Eq. 15 is the magnitude of the mobility at thatfrequency. The low-strain stiffness varies depending on the frequency used in Eq. 15.

25、Forthis example, the stiffness varies from 2.0 MN/mm to 2.7 MN/mm (11,421 kips/in. to15,420 kips/in.) when frequencies from 25 to 50 Hz are used in Eq. 15.The low-strain stiffness is often several times larger than the working load stiffnessbecause of the difference in strain levels. For this reason, the low-strain stiffness is oftenused as a relative measurement. Once a typical value is established for the shafts at a site,shafts that have stiffnesses that differ significantly from the typical value can be identifiedas suspect.