The authors propose to employ t-z functions for estimating the load-movement response of a pile subjected to a static loading test. Judging by the authors’ Fig. 1, the proposed t-z functions are springslider relations, that is, they model the shaft and toe resistances as bilinear with an elastic initial part followed by a plastic part representing the ultimate resistance (capacity). The authors state that the capacity is mobilized at a pile-head movement of 5% of the pile diameter, which they also apply as the definition for the pile-toe load-movement response. First, the discusser would expect that themovement should be the movement at the pile element considered—a pile does not have to be very long before a substantial portion of the movement at the pile head is attributable to pile axial compression. It is not logical to assume that the length of the initial elastic response decreases with depth, all other factors being equal. Second, applying an elastic-plastic model for the pile-toe response is incorrect. The response of the pile toe—usually denoted as the q-z function to separate it from the t-z function expressing the shaft response—does not show an ultimate resistance but is a gently rising curve showing no kinks or explicit changes in curvature. Third, the pile diameter has nothing to do with the changeover from elastic to plastic response nor, indeed, anything to do with the ultimate shaft resistance. The magnitude of the movement at the point of transition from elastic to plastic response may differ in different soils. However, it is usually also much smaller than the authors’ mentioned range of 10–20 mm. Moreover, it is independent of the pile diameter, be the pile a small-diameter pile, say, 300mm, or a large one, say, 3,000mm, and be the pile shape circular or square or rectangular, such as a barrette, which can have one side about 1 m in length and the other between 3 and 8 m in length. Fourth, the elastic-plastic response is too simplified a model for the shaft resistance. Although it can occur, a strain-hardening response is more common, particularly in sand that includes silt and clay.Other soil types can exhibit strain-softening response, particularly in soft clays. The mathematical expressions for four common t-z functions are given in Eqs. (1)–(4) (Fellenius 2012). Eq. (1) presents the relation for the ratio function, so called because it states that the ratio between two values of unit shaft resistance (or load) is equal to the ratio between the movements produced by the same loads raised to an exponent
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