Civil Insight: A Technical Magazine Volume 2 | Page 24
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TEACHERS’ SECTION
CIVIL INSIGHT 2018
tapered piles by introducing stress-dilatancy relation postulated by Bolton (1986, 1987). In the proposed stress-
dilatancy relationship, the increase in confi ning pressure will increase the relative density along with increase
in angle of internal friction and dilatancy and makes it possible to compute at each segment of pile during
pile penetration (Manandhar, 2010; Manandhar and Yasufuku, 2011, 2013). This drawback is improved and
both properties are considered to evaluate the skin friction at each depth iteratively. The parametric studies
on different types of model tests, prototype tests and real type pile tests are assessed to predict the proposed
model. In the proposed model, this drawback has been improved and the skin friction has been calculated
successfully. The results are verifi ed using parametric study on different types of model tests, prototype tests,
and real type pile tests.
EFFECTS OF STRESS DILATANCY AND CYLINDRICAL CAVITY EXPANSION THEORY
The soil is presumed to be dilated plastically at a constant rate (Davis, 1968). Generally, zero dilatants
angle was considered to compute large strain analyses. In stress-dilatancy relation, secant angle of internal
friction, rate of dilatancy towards critical states and both effective stress and soil density parameters are
interdependent in their strength parameters. In reality, the angle of internal friction and the rate of dilation
towards the critical state is the function of both density and effective stresswhich cannot be avoided in the
computational procedure, however it is more complex during calculation. In addition, density and confi ning
pressure undergo change when tapered piles penetrate with settlement ratios. Confi ning pressure increases
with increasing relative density and angle of internal friction with decreasing dilatancy together with pile
penetration (Manandhar 2010, Manandhar and Yasufuku 2012). For the necessary computations, pile and soil
materials are incorporated from Manandhar and Yasufuku (2012) as shownin Tables 1 and 2. Therefore, it is
important to give closed-form solution to evaluate the skin friction of tapered piles introducing stress-dilatancy
relationship in cylindrical cavity expansion theory.
The stress-dilatancy relation established by Bolton (1986, 1987) has been introduced in Yu and Houlsby’s
(1991) cavity expansion theory to check the bearing behavior of different types of piles. For a plane strain, the
stress-dilatancy relation can be expressed in the following term:
I ᇱ ୫ୟ୶ െ I ᇱ ୡ୴ ൌ ͲǤͺ\ ୫ୟ୶ ൌ ͷ ୖ୭ (1a)
ୖ ൌ ୈ ሺͳͲ െ ᇱ ሻ െ ͳ (1b)
Where,
I ᇱ ୫ୟ୶
,
I ᇱ ୡ୴
, \ ୫ୟ୶ , and
an I ୭ are maximum angle of friction, angle of friction at critical states, maximum
ୖ
dilation angle and relative dilatancy index at plane strain respectively.
The relative dilatancy index IR is a function of relative density ID and mean effective stress p as shown in Eq.
(1b). The mean effective stress can be simply defi ned as the mean radial and hoop stresses explained in the
cavity expansion theory as follows:
ᇱ ൌ
ᇱ
౨ ା ಐ
ଶ
ଵ
ൌ ቈ
(1c)
ଢ଼
ଶ ᇲ ିଵ
൫ಉᇲ షభ൯
ಉᇲ
ି
ଢ଼
ᇲ ିଵ
ᇲ
൫ಉᇲ షభ൯
ಉᇲ
ି
(2a)
Replacing the constant of integration, A, the above equation is simplifi ed into the following form as:
ᇱ
ൌ െ
൫ಉᇲ షభ൯
൫ಉᇲ షభ൯
ି
ಉᇲ
ಉᇲ
(2b)
The general Eq. (2b) can be simplifi ed in the elastic-plastic region (Manandhar 2010, Manandhar and Yasufuku
2013). At the boundary of plastic region, the effective mean stress can be modifi ed into the following structure
as:
ᇱ ൌ െ (3)
Where pc, p 0 , b, r, D and R are described in detail by Manandhar and Yasufuku (2012).