Probabilities of Low-Strength Events in Concrete

Concrete that does not meet specified tolerances incurs costs. The likelihood of nonconforming concrete tests and associated costs are considered in developing bids and are therefore of concern to the owner, the engineer, the contractor, and the concrete supplier. Knowing the probability of various events is necessary for an informed assessment of risk. American Concrete Institute (ACI) 318-95 requires the minimum average strength of concrete to be high enough that both the probability of the average of any three consecutive tests falling below f' sub c, and the probability of a single individual test falling below f' sub c - 500 psi (3.4 MPa), will not be greater than 1%. Under these conditions, the probability of at least one low-strength event (LSE) for a 4,000 cu yd (3,058 cu m) project could lie between 35% and 70%. Since any LSE will result in a shift in the average strength level, the probabilities for subsequent tests are changed, and accurate estimates of the probability of an LSE cannot be obtained directly. Computer-based simulation was used to estimate the probability of LSEs, explicitly including the effects of process interference with two mutually dependent quality control criteria, with only random variation of strength.