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OCR for page 41
41 5 0.25 4.5 0.225 4 0.2 3.5 log-normal distribution 0.175 mlnx = -0.357 lnx = 0.479 Number of Pile-Cases 3 Relative Frequency 0.15 2.5 0.125 2 normal distribution 0.1 1.5 0.075 mx = 0.783 1 0.05 0.5 0.025 x = 0.395 0 0 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the Design Method Figure 23. Histogram and frequency distributions of Ksx for 19 cases of H piles in sand. for driven piles and FHWA for drilled shafts) introduces certain number of production piles are tested to ensure that variability. Analyses reported in sections 2.3.2 and 2.3.4 the piles, as constructed, are satisfactory, in a way that is sim- suggest that this COV due to the failure criterion alone is ilar to quality assurance testing in manufacturing. about 0.10. Adding this to the COV for the natural within- For specifying a quality assurance testing plan, the number site variability yields COVs of 0.18, 0.27, and 0.36 for low, of piles to be dynamically tested and the criterion for accept- medium, and high variability sites, respectively. ing a set of piles need to be determined. Two concerns are at The reduction in COV on the mean pile capacity at the issue: the chance that poor quality (i.e., under capacity) piles site should decrease in proportion to 1/n, where n is the are incorrectly accepted as being good, and the chance that number of pile tests (Benjamin and Cornell, 1970). This good quality piles are incorrectly rejected as being poor (see leads to the results presented in Table 24, which describes Figure 42). For a given level of sampling effort or cost, reduc- the resistance factors as a function of the site variability, ing the chance of one kind of error invariably increases the number of piles tested, and target reliability. The recom- chance of the other, and thus the two must be balanced. mended factors assigned are presented in section 3.45. The definition of "poor quality" piles was taken to be that the average pile capacity is less than the design capacity, that is, less than the reciprocal of the factor of safety. The proba- 3.3.3 Numbers of Dynamic Tests Performed bility chosen as a reasonable chance that such a set of poor on Production Piles quality piles be incorrectly accepted as good was equilibrated to a reliability index of three, or a probability of about 0.001. Dynamic pile testing is carried out for quality control, tar- This is sometimes called the "buyer's risk" or the "owner's get capacity, integrity, and driving system performance. A risk" as demonstrated in Figures 42 and 43. The definition of
OCR for page 42
42 22 0.14 20 18 0.12 16 0.1 14 Number of Pile-Cases Relative Frequency 12 0.08 x = 0.387 normal distribution 10 log-normal distribution 0.06 8 mlnx = -0.293 lnx = 0.494 6 0.04 4 mx = 0.835 0.02 2 0 0 0 0.5 1 1.5 2 2.5 3 KSX = Ratio of Static Load Test Results over the Pile Capacity Prediction using the -API/Nordlund/Thurman design method Figure 24. Histogram and frequency distributions of Ksx for 146 cases of all pile types (concrete, pipe, H) in mixed soil. "good quality" piles was taken to be nominal capacity. The is, if f = n/N = 1, then there is no variance in the sample aver- probability chosen as a reasonable chance that such a set of age since all the piles have been accounted for. good quality piles be incorrectly rejected as poor was taken An assumption, consistent with that projected in section to be 0.10. This is sometimes called the "seller's risk" or the 3.3.2, is made to categorize sites as having low, medium, or "contractor's risk." high variability and to assign COVs of 0.15, 0.25, and 0.35 Given a large total number of piles, N, relative to the num- to these three cases, respectively. In addition, the dynamic ber tested, n, the variance of the sample mean, x ¯ , is (Benjamin test method also introduces variability. For that, two meth- and Cornell, 1970), ods are considered based on the results presented in sections 3.1.2 and 3.2.4, Energy Approach (EA) to be used for capac- N - n i =1 xi n Var ( x ) ity evaluation at the EOD and signal matching (CAPWAP) N -1 n -1 (34) to be used during BOR. Setting the owner's and contractor's risks on the one hand, For sampling fractions, f = n/N, greater than about 10%, the and the definitions of "good" and "poor" piles on the other, as "finite population correction factor," (N - n)/(N - 1), comes defined above, and noting that the sampling variance of the into play. This reduces the sampling variance, because the average pile capacity of the tested piles decreases in propor- assumption of sampling without replacement is no longer tion to 1 n, where n is the number of pile tests, values for the reasonable. For example, if 100% of the piles are tested, that number of piles to be tested can be estimated. The obtained