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
Introduction bbbbbbbsfsf
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.