## 1 Introduction  
The large deformation, caused by earthquake liquefaction, will endanger the stability of nearby rivers and the environment of formation slopes. Liquefaction caused by earthquakes often leads to the loss of bearing capacity of the foundation and endangers the safety of structures built on the liquefable soil ([PERSON] et al. [1]). Furthermore, liquefaction tends to weaken the saturated sand and produce even greater deformations. According to the post-earthquake survey by [PERSON] [2], Treasure Island had 34 sand boil sites and 28 sites with surface subsidence following the 1989 Loma Prieta earthquake in California, USA. In 1999, the Kocaeli earthquake in Turkey triggered large-scale liquefaction in the Izmit Bay area ([PERSON] et al. [3]), and 20% of the low-rise concrete houses, as well as 56% of the low-rise brick-timber houses in Adapazari were severely damaged or destroyed due to foundation liquefaction ([PERSON] et al. [4]). [PERSON] et al. [5] reported seismic damage to the port structure of Port-Au-Prince during the 2010 Haiti earthquake and pointed out that large-scale liquefaction and lateral spreading of soil near the port caused different degrees of lateral movement of bridge pile foundations and abutments. [PERSON] et al. [6] investigated the damage to pile foundation during the 2011 Christchurch earthquake in New Zealandand found that the lateral spreading of liquefiable soil damaged pile foundation. More recently, [PERSON] et al. [7] studied liquefaction cases in the Wenchuan Earthquake in China in 2008 and reported damage by seismic liquefaction and lateral displacement of pile foundation in Yingxiu Town. The case of the city of Catania, in South-Eastern Sicily (Italy), is subjected to high seismic hazards. In particular, seismic liquefaction phenomena were reported by historical sources following the 1693 (MS =7.0-7.3, Io = X-XI MCS) and 1818 (MS = 6.2, Io = IX MCS) strong earthquakes ([PERSON] and [PERSON] [8]; [PERSON] et al. [9]). Through comparing the damages discussed in the above studies, we noticed that the liquefaction-induced loss of bearing capacity of the foundation, along with the lateral extension of soil, will aggravate the seismic damage to structures. In view of the damage caused by liquefaction of foundation during earthquakes, foundation reinforcement, with gravel piles and anti-liquefaction measures, is an important research direction. In recent years, in order to eliminate liquefaction hazards, a variety of foundation treatment methods have been developed, among which gravel piles in reinforced foundation have the best effect ([PERSON] et al. [10]), and can be used to reinforce weak foundations such as embankments ([PERSON] et al. [11]). Therefore, gravel piles have been widely used in the treatment of weak subgrades such as those in highways, railways, and large petrochemical field stations. A field investigation found that a foundation treated by gravel piles for anti-liquefaction was undamaged during the Loma Prieta earthquake in 1989 ([PERSON] and [PERSON], [12]). Meanwhile, a field investigation, conducted after the Great East Japan Earthquake of 2011, showed that no damage was found in the foundation treated by gravel piles ([PERSON] et al. [13]), even though this earthquake resulted in large-scale liquefaction in the coastal area of Tokyo Bay. Based on 24 case analyses of stone columns reinforcement, [PERSON] et al. [14] pointed out that gravel piles could greatly improve the weak foundation's resistance to liquefaction. In terms of test model research, laboratory tests found that the application of stone columns and granular blankets significantly increased the ultimate bearing capacity of soft foundations ([PERSON] et al. [15]). Shaking table tests, conducted on the four foundations stabilized with stone columns, found that the stone columns had a significant mitigation effect on soil liquefaction during earthquakes ([PERSON] et al. [16]).