Revisiting Hvorslev's intake factors using the finite element method

A constant-head pumping test method using direct-push equipment for in situ hydraulic conductivity measurements T. KOBAYASHI, N. ONOUE, S. OBA, N. YASUFUKU and K. OMINE (2012). Géotechnique 62, No. 3, 253–262, http:dx.doi.org/10.1680/geot.9.P.150

“…In this case, as the length of the test interval approaches zero so must the flow. The Ratnam et al (2001) regression equation (4) proposed for the M1 geometry matches this expected result. By contrast, the regression equation proposed by Kobayashi et al (2012) predicts that as the aspect ratio L/D approaches zero, the shape factor approaches a value F/D ¼ 1 .…”

“…18 shows the ratio of the intake factors of equation (5) and those proposed by other researchers (Hvorslev, 1951;Wilkinson, 1968;Brand & Premchitt, 1980;Chapuis, 1989;Ratnam et al, 2001) to equation (6). This figure indicates that equation (7) by Ratnam et al (2001) gives a slightly smaller F compared to equation (6) and that the difference is within a range of 10% throughout the full range of aspect ratio, whereas the differences between equation (6) and the other solutions become significant when L/D is less than 1. The disparity seems to be attributable to the difference in the boundary conditions of the intake screen; equations (6) and (7) assume a closed-end cylindrical model (M1 geometry), while the other solutions assume an open-ended cylindrical model (using a screen with a permeable bottom).…”

“…The authors performed the finite-element calculations under axisymmetric conditions, as did Ratnam et al (2001), and therefore, both the solutions should coincide if Ratnam et al (2001) used the same seepage governing equation. It appears that possible factors causing the difference between equations (6) and (7) techniques, including the finite-element domain size and numerical resolution.…”

“…15, along with the regression equation of Ratnam et al (2001) and the results from the numerical modelling of AlDhahir & Morgenstern (1969) and Tavenas et al (1990). There are subtle differences between the shape factors; these differences are more evident in the expanded view shown in Fig.…”

“…For the technique of Kobayashi et al (2012), the appropriate idealisation appears to be the M1 geometry of Ratnam et al (2001), reproduced in Fig. 14. With the M1 geometry, there is neither flow out of the bottom of the test interval, nor is there flow back into the borehole some distance above and below the test interval.…”