## 1 Introduction  
In the past few decades, large destructive earthquakes, such as the 1964 Niigata earthquake in Japan, the 1964 Alaskan earthquake, the 1985 Michoacan earthquake in Mexico, the 1995 Hyogoken-Nambu earthquake in Kobe, Japan, the 2008 Wenchuan earthquake in China, the 2010 Chile earthquake, and the 2011 Great East Japan earthquake, have resulted in various geological hazards in which liquefaction was particularly remarkable [1; 2; 3; 4; 5; 6]. The 1976 Tangshan earthquake in China induced serious liquefaction in a vast area of 24,000 square meters. In the liquefaction area, the ground suffered a rapid and dramatic loss of soil strength, and the bearing capacity suddenly disappeared due to the motion of the earthquake, leading to the significant settlement or collapse of massive buildings. Liquefaction is a kind of natural hazard that usually occurs in loose, saturated sand during an earthquake. Under the effect of a vibrating load, sand particles deviate from their original location, separating from each other and becoming suspended in the pore water. Both dead seismic loads can only act on the pore water under this circumstance, and the lateral movement of intact soil blocks over shallow liquefied deposits is typically induced. Some sloping areas in mountainous regions and those along the waterfront are more susceptible to lateral movement compared with the flat terrain. Therefore, the infrastructure in these areas is presented with a great risk from lateral spreading due to liquefaction [7]. Liquefaction-induced lateral spreading and ground failure will bring great damage to the upper parts of structures, which is a costly natural phenomenon. For example, a major part of the billion-dollar damage in the 1964 Niigata earthquake can be attributed to the lateral movement triggered by liquefaction. Besides, liquefaction also caused billions of dollars of damage to port facilities during the 1995 Kobe event [8,9]. To increase liquefaction resistance and limit the potential deformations of ground soil, one of the most popular soil improvement techniques is densification. Dynamic compaction, vibro-compaction, and explosive compaction have been extensively adopted to densify soil to mitigate liquefaction risk. Pioneering works, conducted by [PERSON] et al. (1954), [PERSON] (1975), [PERSON] et al. (1984), and [PERSON] (1986), have facilitated the development and implementation of these densification techniques [10, 11, 12, 13]. However, these reinforcement measures can only be adopted in undeveloped sites, given the fact that the buildings and structures are sensitive to vibration and dynamic compaction. At constrained and developed sites, underpinning and grouting seems to be the most feasible technique [7]. With underpinning, foundation is extended in depth or breadth so that it can either rest on a more supportive soil stratum or distribute its load across a broader area. The stress states of the existing structural elements are significantly improved in order to mitigate liquefaction. Nevertheless, this method targets specific structures rather than the entire ground. In the case of grouting, permeation grout can be classified into two categories, namely, cement suspension and chemically based solutions [14]. Both grouting materials are of high viscosity, so that they are often adopted to form grout columns rather than a uniform distribution across the entire ground beneath the structure [7,15]. In addition, most typical chemical solutions, such as acrylate and epoxy, are toxic and likely to create pollution to the local underground water. Especially in the case of cement, where the mean particle size of Portland cement ranges from 10-30 \(\upmu\)m, allowing it to permeate through voids with a size greater than 0.2-0.3 mm. As a consequence, only on the condition that the soil stratum is mainly composed of medium to coarse sand can Portland cement be adopted as a grouting material.