Abstract
In previous published literatures it was stated that superposition law
might be valid for ground improvement techniques consisting of
prefabricated vertical drains (PVDs) along with surcharge and vacuum
preloading. Even some professional geotechnical engineers might think of
this false idea that superposition law might be valid in such ground
improvement techniques. It was shown that the superposition law is not
valid because of the hydro-mechanical coupling interactions which exist
between vacuum and surcharge preloading. A case history was presented
and Finite element modeling (FEM) was used for verification and the
demonstration of coupled consolidation interaction between vacuum and
surcharge preloading. Three main parameters as settlement, lateral
displacement, and excess pore pressure were evaluated for different
scenarios. The results that are based on a macro-element approach can be
used for better comprehension of the working mechanism of combined
treatment systems. Considering the results of this literature, a complex
combined vacuum and surcharge preloading can be broken in simpler cases
that can be used for either deriving analytical or empirical solutions.
Keywords: coupling, superposition, vacuum, finite element modeling,
excess pore pressure, PVD
Vacuum consolidation is a technique that is used along with PVDs and
surcharge preloading to accelerate the process of consolidation of weak
clay or peat soils and meanwhile reduce the issues with ground heaves in
the premier of the embankment. Based on different soil conditions or
project working speculations, different systems or design might be
considered. FEM is a common tool that is used extensively by consultants
to model the soil behavior before, during and after the reclamation
process. The super structures under construction, soil layer
specifications, and machinery availability are the main parameters that
determine the final design parameters including sealing measures (Long,
Nguyen et al. 2015, Anda, Fu et al. 2020), depth (Griffin and O’Kelly
2014, Long, Nguyen et al. 2015)and spacing (Long, Bergado et al. 2013,
Wang, Yu et al. 2020) , and the required preloading pressure (Bhosle and
Deshmukh 2018). (Mesri and Khan 2012) State that there is no difference
in the magnitude and rate of settlement resulting from a vacuum load and
an equivalent fill load. Settlement analysis for vacuum or vacuum plus
fill loading can be carried out using the procedures that are available
for fill loading. (Chai, Carter et al. 2005) Assuming that the
volumetric strain due to vacuum consolidation is the same as for 1D
consolidation with a surcharge load of the same magnitude, proposed an
approximate method for calculating the ground settlement and inward
lateral displacement induced by vacuum preloading. (Chai, Ong et al.
2013) proposed an empirical equation for the estimation of lateral
displacement. In their solution, they proposed that vacuum pressure
induces negative pore pressure while embankment loading induces positive
pore pressure.
(Flessati, Di Prisco et al. 2021) stated that the macro-element approach
nowadays is largely considered to be a successful theoretical tool for
solving soil-structure interaction problems. This approach is based on
the definition of a generalized constitutive law putting in relation a
small number of suitably defined generalized stress/strain variables and
can be used as designing tool according to ultimate limit state and
displacement based approaches. Particularly in the last decades, the
application of the macro-element approach in soil-structure interaction
problems has gained an increased popularity in the practical and
academic implications (Vlahos, Cassidy et al. 2011, Zhang, Cassidy et
al. 2014, Flessati, Di Prisco et al. 2021).
In this literature, the governing equation for combined vacuum and
surcharge preloading is explained and then a case history is introduced
and verified based on existing data and then the model is discretized
and investigated for different conditions and scenarios to illuminate
some misunderstandings or false ideas regarding the combined system of
preloading for ground improvement, especially the explanation of
negative excess pore pressure, superposition law validness, lateral
displacement on surface ground due to the vacuum preloading and the
effect of hydro-mechanical coupling.
Governing equation of combined vacuum and surcharge preloading
in a 1D condition
(Mohamedelhassan and Shang 2002) conducted some laboratory tests on
different clay specimens under surcharge and vacuum preloading. An
analytical solution for the prediction of excess pore pressure was
proposed assuming Terzaghi 1D small strain and also superposition law.
The equations are as follows:
\(\frac{\partial u}{\partial t}=c_{\text{vs\ }}\frac{\partial^{2}u}{\partial z^{2}}\)(0 < z < H, t > 0) (1)
\(\frac{\partial u}{\partial t}=c_{\text{vv\ }}\frac{\partial^{2}u}{\partial z^{2}}\)(0 < z < H, t > 0) (2)
Where t is the time, z is the depth, H is the drainage path,c vs is the coefficient of consolidation for
surcharge preloading, and c vv is the coefficient
of consolidation for vacuum preloading and u is excess pore water
pressure. Assuming the validness of superposition law and stated initial
and boundary conditions the equations were summed as:
\(u\left(z\ ,\ t\ \right)=\ u_{v}\left(z\ ,\ t\ \right)+\ u_{s}\ (\ z\ ,\ t\ )\)(3)
Where uv and us are excess
pore pressure for vacuum and surcharge preloading respectively. Figure 1
shows the schematic of the equations of combined vacuum and surcharge
for a surcharge preloading, q , and a vacuum preloading
pv.