Discussion of “Shaft Resistance of Single Vertical and Batter Piles Driven in Sand” by A. Hanna and T. Q. Nguyen

Abstract

The paper has presented an experimental study on the shaft resistance of driven piles in sand, a topic of interest in foundation design. To better validate the results and analyses, several points are raised here for further clarification. Fig. 6 in the original paper presents the average ratio as a function of pile diameter for different pile length/diameter sdm /fmdave ratios, where dm is the mobilized angle of friction between pile shaft and surrounding soil and fm is the mobilized friction angle of soil. It is indicated that for a specific value of L /D, the ratio sdm /fmdave will increase linearly with the pile diameter; whereas, for a given pile diameter, it will decrease as the ratio L /D increases. The proposed relationships look quite neat; however, care should be exercised in their use because they are established on the basis of limited experimental data that were obtained under different test conditions. The different test conditions may lie in the tested materials, test methods, and, particularly, test scales (i.e., small-scale model tests or prototype field tests). For example, the data point from Vesic’s 1967 work shown in the graph is for a pile having a diameter of 450 mm and a length/diameter ratio of 33.35; whereas, the data points from the authors’ investigation are for piles having a diameter of 76 mm and the length/diameter ratios of 10 and 20, respectively. Only two data points from the authors’ work were included (both for the 76 mm model piles); the test results for the 38 mm model piles were, however, excluded from their Fig. 6. It is noticed from their Fig. 9 (the case of a=0°) that the experimental data for the 38-mm model piles seem not to support the relationships in the authors’ Fig. 6, as shown here in Fig. 1. In deriving the results in the authors’ Tables 3 and 4, the mobilized angle of shearing resistance of the sand fm was assumed to be equal to f, and a specific value f=39° was used in the computation for the 76-mm model piles. In the authors’ Fig. 10, however, f=38.1° was assumed in the computation for the 38 -mm model piles. The justification for choosing these values of friction angle is not clear. It is indicated in the paper that the sand deposit has a relative density of 65.3%; this corresponds to a void ratio of 0.396 if one takes the maximum and minimum void ratios in the authors’ Table 1 as a reference. The values of the friction angle used for the computation, however, imply that the void ratio should be around 0.67 if the triaxial test results in the authors’ Fig. 2 serve as a reference source. Moreover, it is noted that the void ratios covered by Fig. 2 seem to be far beyond the range set by emax=0.52 and emin=0.33, although emax and emin are index void ratios obtained by standard procedures and are not necessarily the absolute maximum and minimum void ratios in reality. In the authors’ Table 3 the average coefficient of earth pressure acting on the pile shaft Kssaved was obtained as 8.04 and 7.28 for L /D=10 and 20, respectively. Following the method of analysis and according to the design charts given in the authors’ Fig. 7, Ksaved should be close to 10 for vertical piles sa=0° d in the sand having the angle of shearing resistance f=39°. It then follows, according to Kssaved=RKsaved, that the reduction factor R takes the