Grouted soil nails are often used to strengthen soil slopes against stability failure. However, full grouting along the entire length of the nail is generally not achieved in certain cases. On given project, an engineer estimates the average fraction of length grouted to be within 0.75 to 0.95 with 95% confidence, based on his previous experiences with the particular geologic formation and construction crew. To improve his estimate, the engineer tested a sample of four soil nails for the given job. The average grouted length measured is 0.89, while standard deviation of measured grouted length is 0.06.

a) Determine the updated mean and c.o.v. of the average grouted length of soil nails for the site. State any assumptions used. b) Final approval of the construction job requires inspection and testing by the regulatory agency. Suppose a sample of two nails will be selected and tested by the agency. Acceptance requires that each of the following two conditions be satisfied.

i. The sample average grouted length must be at least 0.85.

ii. The minimum grouted lengths of nails tested should not be lower than 0.83.

Which condition does the engineer think is more stringent (less likely) to be met for this site?