###### Abstract  
Collapsible loess is a kind of soil with special properties, and is widely distributed in China. When it is not wetted by water, its strength is generally high and its compressibility is low. However, when collapsible loess is wetted by water under a certain pressure, the soil structure will be rapidly destroyed, resulting in large additional subsidence. Therefore, when engineering constructions on collapsible loess sites are carried out, appropriate foundation treatment measures must be taken to eliminate foundation collapsibility. Because of their advantages, static pressure plain soil compaction (SP\(-\)PSC) piles are widely used for collapsible loess foundation treatments in China. However, at present, there is still a lack of accurate understanding of the distribution of compaction coefficient of soil among SP\(-\)PSC pile groups on collapsible loess foundations. The present study systematically investigated the distribution of the soil compaction coefficient among SP\(-\)PSC pile groups based on SP\(-\)PSC pile group tests and finite element analyses. The effect of different factors on soil compaction coefficient was analyzed and explored, including the pile diameter and length of SP\(-\)PSC piles, the soil moisture content, the pile spacing within the SP\(-\)PSC pile group, and the depth to ground. Finally, the simplified calculation models of the compaction coefficient of the soil at the center of pile group and at the midpoints of adjacent piles were analytically formulated. These models established a theoretical basis for the design and construction of SP\(-\)PSC pile groups on collapsible loess foundations. collapsible loess foundation; SP\(-\)PSC pile group; compaction coefficient; soil stress; influence factors +
Footnote †: journal: Applied Sciences  
the penetration process of jacked-in piles on sandy soil foundations [7; 8], and the pile-soil interaction and the foundation stress change were examined. There are also some studies on the penetration process of different compaction piles using various numerical methods, such as the finite element method and discrete element method [9; 10; 11; 12]. In the theoretical analysis of foundation pile penetration, the most effective method is still considered to be the Cavity Expansion Method (CEM) [13; 14], which provides theoretical support for the analysis of the change in mechanical properties of soil around piles. However, regarding penetration compaction piles in collapsible loess sites, the experimental, numerical, and theoretical studies are currently inadequate. In addition, there are still no reasonable calculation models of the compaction coefficient of soil within pile groups. To improve the material properties of collapsible soils, some scholars have carried out a series of studies on the influence of different admixtures (such as nanomaterials or industrial wastes) on the properties of collapsible loess [15; 16]. The results show that collapsible soils are very sensitive to the addition of different admixtures. The amount and type of admixtures added to the collapsible soils could have both positive and negative impacts on the desired properties. The relationship between the collapse potential of soils and the type and proportion of admixtures under different conditions has also been established. Therefore, in order to achieve the optimal performance improvement in collapsible soils, the most appropriate admixture type and percentage should be used. Unfortunately, the research results of the admixture improvement methods cannot be applied to the compaction pile improvement method. In a part of jacked-in pile composite foundations, the reamed pile is not pulled out after penetration, and is used as a part of the composite foundation. This situation leads to a significant increase in the cost of foundation treatment.