Civil Insight: A Technical Magazine Volume 2 | Page 27
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TEACHERS’ SECTION
CIVIL INSIGHT 2018
27
For small tapering angles, the increase in radial stress for radial expansion may be calculated from cylindrical
cavity expansion theory. When the pile-ground is continuously
yielding, the vertical shear stress x acting on the pile wall can be expressed as:
ɒ ୶ ൌ ሺɐ ȟɐሻ൫I ୧ Ƚ൯ ୧ᇱ
Where, ୧ᇱ ൌ
ୡ ୱୣୡ మ
൫ଵି୲ୟ୬ ୲ୟ୬ I ൯
(7)
(7a)
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In Eq. (6), the ground deformation u g may be related to shear stress W x . Using this approximation, the
W x -u p relationship for this phase can be written as:
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ɒ ୶ ൌ
୲ୟ୬ ୲ୟ୬൫I ା൯୳ ౦ ା బ ୲ୟ୬൫I ା൯ାୡ ᇲ
ే ]౨
ଵା ౣ ୲ୟ୬ ୲ୟ୬൫I ା൯
(8)
ృ
When (u p > (u p ) Y ) or V>V Y , it indicates a plastic zone adjacent to pile wall. In this case it will explain the infl uence
of plastic zone which will extend further with more pile deformation. The corresponding vertical shear stress,
W x can be expressed in terms of tangent gradient (K p ) as
୴
ɒ ୶ ൌ ൫ɐ ଢ଼ ୴ଢ଼ ୮ ൯ ൫I ୧ Ƚ൯ ୧ᇱ (9)
PARAMETRIC STUDIES
In order to determine the skin friction in closed form, the variables were iteratively determined using a load
transfer method. The results of small-scale model test, prototype test together with full scale test have been
validated through the results from the calculation in parametric study.
Two different types of sands Toyoura sand (TO) at high relative density (80%) and K-7 sand at medium relative
density (60%) have been considered for the analyses. The chromium plated steel model piles, one straight (S)
and two taper-shaped (T1 and T2), with equal lengths of 500 mm and same tip diameters of 25 mm were
used for pile penetration. Parameters of Fanshawe brick sand and pile materials have been adapted from Sakr
et al. (2004, 2005 and 2007) as a prototype. The cylindrical fi ber-reinforced polymer (FRP) FC pile and another
three tapered FRP composite tapered piles have been considered for analyses (Tables 1 and 2).
Similarly, a real type pile material has been taken for analyses. For this, the pile used by Rybnikov (1990) was
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accomplished.
The top and bottom radii of the piles were 200 mm and 100 mm (1.2º tapering angle), one
tapered pile with corresponding radii of 250 mm and 100 mm (2º tapering angle) and for last two tapered
piles had radii of 300 mm and 100 mm (2.4º tapering angle) respectively. For this pile, soil parameters of
Toyoura Sand are considered due to lack of information in the literature (Table 2).
Angle of tapering and normalized ratios of average vertical shear stress at 0.1 settlement ratio for all soils have
been studied as the main effective key variables (Manandhar and Yasufuku 2013).
Figure 3 shows the effect of tapering angle in four types of soil by taking the ratios of average vertical shear
stress divided by average vertical shear stress of straight pile. In the fi gure, with the increase in the tapering
angle of the pile, average vertical shear stress increases. The parametric study shows that the most tapered
angle shows 236% increase in Fanshawe brick sand, 331% in K-7 sand, 287% in TO sand and 295% increase
by Rybnikov pile on sandy ground respectively. Similarly, the total skin friction of tapered pile divided by
straight pile for all types of soils at settlement ratios of 0.1 was shown in Figure 4. The total skin friction of
maximum tapered pile of Fanshawe brick sand was about 6.5 times to more than 10 times in Rybnikov type
full scale pile loading test at maximum tapering angle when compared with conventional straight piles
CONCLUSIONS
Among different key variables, effects of tapering angle have been put in this paper as the parametric study
on average vertical shear stress and total skin friction at 0.1 settlement ratios of pile penetration. It has been
shown that the proposed model support strongly the general behavior of tapered piles to evaluate the skin
friction. New proposed and extended form of cavity expansion theory on non-associated fl ow rule introducing
Bolton’s stress-dilatancy
relationship can successively evaluate the skin friction of tapered piles without altering
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the basic formula of the cavity expansion theory. It has the ability to introduce the interdependent functions
of confi ning pressure and relative density in angle of internal friction and dilation angle.