Figure
1: Schematic of (a ) vacuum and surcharge combined preloading;
(b ) surcharge preloading; and (c ) vacuum preloading
(Mohamedelhassan and Shang 2002)
(Gibson, Schiffman et al. 1989) defined the excess pore water pressure
in the consolidation process in two ways as: excess over the hydrostatic
pressure (the pressure distribution when the pore water is stationary)
and the pore pressure in excess of a steady-state flow condition. These
definitions explain best the two distinct mechanisms which govern in a
combined vacuum and surcharge preloading. Applying surcharge preloading
would increase the excess pore pressure and because of the very low
permeability of clays it can’t be dissipated which is under the first
definition. On the other hand applying vacuum pressure through PVDs
creates a water head between soil and PVD which accelerates the flow in
clay soils and eases the discharge of water which is in accordance with
the second definition. Although the effect of vacuum preloading is
somehow the same as surcharge preloading in the acceleration of the
consolidation process, they shouldn’t be mistaken with each other as
they have two different mechanisms. The vacuum pressure effect is often
demonstrated by negative pore pressure. Care should be taken to not
mistake the negative algebraic term with its real mechanism as it is the
pore pressure in excess of a steady-state flow condition in soil in the
vicinity of PVDs under vacuum preloading. (Lu, Likos et al. 2021) has
discussed in detail the inefficiency of common definition of pore
pressure in soil mechanic and emphasized the necessity for developing
better theories and seeking better engineering solutions for problems in
geotechnical engineering.
To clarify the difference assume that at a given soil depth of z under
combined vacuum and surcharge treatment system (+P) is the quantity of
the excess pore pressure as a result of embankment surcharge and (-P) is
the quantity of the excess pore pressure as a result of the vacuum pump.
Assume the superposition law is valid and as result, there should be no
settlement because of consolidation as the quantity of excess pore
pressure is equal to zero i.e. (+P – P) but in contrast, the
consolidation settlement would occur. Of course, this is not the case
and it is an ideal situation in the real-world where considerable
settlement takes place. It shows the superficial way of using
superposition law. But now the question arises about if the absolute
value of (│-P│) adopted in the analysis would be considering the case of
(2P) a reasonable approach in dealing with such a situation. This
example demonstrates the actual performance of two distinct mechanisms
of surcharge and vacuum preloading. In reality, none of the stated
situations would occur. As it would be seen the superposition law is not
valid and moreover, another phenomena exists which is the interaction
between PVDs and vacuum and surcharge or the hydro-mechanical coupling
(in brief coupling). In coupled consolidation analysis, the excess pore
pressure and deformations would be calculated simultaneously while
considering compressibility of soil particles and pore fluid (Biot 1941)
to observe the stated coupling effect where it can be increasing or
decreasing based on different situations.
(Mohamedelhassan and Shang 2002) reported a minor disagreement between
analytical solutions and consolidation results which might be attributed
to laboratory deficiencies or the coupling effect of vacuum and
surcharge. Refer to formulas (1), (2) ,and (3) and assuming constant
permeability under various preloading (not a valid assumption) the
simplified 1D excess pore pressure might be written as:
\(u\left(z\ ,\ t\ \right)=\ u_{v}\left(z\ ,\ t\ \right)+\ u_{s}\ \left(\ z\ ,\ t\ \right)+\ u_{\text{vs}}(z\ ,\ t)\)(4)
Where uvs is the coefficient of consolidation for
a combined surcharge and vacuum preloading that considers the
hydro-mechanical coupling effect in analytical solutions.
Field case historyModel verification
(Bergado, Chai et al. 1998) has reported the monitoring results of two
trial embankments in Second Bangkok International Airport and
(Indraratna and Rujikiatkamjorn 2006) modeled these two embankments
using FEM modeling in plane-strain condition. The second trial
embankment is used for primary model verification. This case history was
specifically selected because of variable vacuum pressure that was
applied. The related data concerning the history of preloading and
material properties can be accessed through these articles. GEOSTUDIO
2018 SIGMA/W coupled analysis in plane-strain condition was used for
modeling. It should be noted that the effect of well resistance and
clogging were considered in the model by boundary conditions and the
smear effect was considered by the approach proposed by (Indraratna and
Redana 2000). As stated by (Cai 2021) in order to consider nonlinearity
of the consolidation arising from evolving permeability and
compressibility of the soil due to change in void ratio during
consolidation and non-Darcian flow regime for low permeability soil and
large strain elasto-plastic behavior of the soil, a permeability
modifier was applied in FEM analyses (geostudio 2018).
(a)