## 1 Introduction  
The stiffened deep cement pile is a composite pile that stiffens a rigid pile into a flexible pile. Using the pile core to bear the load and spreading the load to the soil around the pile through the cement column not only give full play to the advantages of rigid piles and flexible piles but also solve the problems of the high cost of rigid piles and insufficient load-bearing performance of flexible piles [1; 2; 3]. In recent years, some scholars have replaced the traditional rigid pile cores with newly shaped piles and conducted research [4; 5]. The Helix-Stiffened Cement Mixing (HSCM) pile replaces a traditional rigid pile core with a helical pile core. The slurry injection process was used to compensate for the disturbance of the soil by the helix plate while retaining the advantages of the convenient installation of helical piles and improving the installation technology and interface action, further enhancing the construction efficiency and load-bearing performance of the HSCM pile [4]. [PERSON] had earlier verified the feasibility of HSCM pile installation through field tests, which improved the stiffness and load-bearing capacity of the pile foundation through the grouting technology [6]. [PERSON] and [PERSON] tested HSCM piles in sands by using a frustum-confined vessel (FCV). The results showed that the compressive load-bearing capacity of HSCM piles was approximately 1.54-2.2 times that of helical piles with the same parameters [7]. [PERSON] and [PERSON] pointed out that the increased axial bearing capacity of HSCM piles originates from the lateral displacement and extrusion deformation of the sand around the pile during the diffusion of cement slurry, which increased the radial stress and internal friction angle at the pile and soil interface [8]. The factors affected by the load-bearing performance of HSCM piles were various. [PERSON] [9] proposed a parameter optimization method based on the Lagrangian MultiplierMethod programming, capable of proposing diagrams for different design conditions to determine the best regulation and values of design parameters. [PERSON] investigated the effect of the helix number on the axial load-bearing capacity of HSCM piles through field tests. An appropriate helix number could improve the stiffness of the pile, while an excessive helix number could increase the disturbance of the soil [10; 11]. [PERSON] conducted axial loading tests on HSCM piles and found that parameters including helix diameter, helix number, and drilling speed all affected the bearing capacity of HSCM piles, which was due to the change in strength and diameter of the soil-cement column, resulting in changes in skin resistance and end-bearing capacity [12]. [PERSON] investigated the effect of different soil-cement column lengths \(L_{sc}\) on the compressive load-bearing performance of HSCM piles. When \(L_{sc}\) was less than the helical pile length, the load-bearing efficiency increased with \(L_{sc}\)[13]. The material parameters of the cement soil could influence the performance of the structure. [PERSON] [14; 15] investigated the mechanical properties of lightweight expanded perlite and clay ferrocement mixtures using digital image correlation (DIC) and finite element analysis (FEA). The results showed that DIC and FEA were approximate for assessing lightweight expanded perlite and clay ferrocement mixtures. The mean values of the first crack (\(F_{cr}\)) and ultimate loads were higher in the ferrocement mixed with lightweight expanded clay and perlite, respectively. The volumetric content of the lightweight aggregates contributed more to the increase in the Fcr of the ferrocement. For the failure mode of stiffened deep cement mixing (SDCM) piles, [PERSON] proposed the progressive and rapid failure modes based on numerical simulations under axial loading conditions: the former was related to plastic deformation of the soil around the pile, while the latter was due to concrete core cracking [16].