## 1 Introduction  
The geotechnical engineering field confronts significant challenges as traditional soil improvement techniques face increasingly stringent environmental requirements and urban development constraints [1, 2]. Conventional soil improvement methods primarily fall into two categories: physical reinforcement and chemical treatment [3, 4]. While physical reinforcement techniques (e.g., compaction, grouting, installation of inclusions) demonstrate notable effectiveness, they frequently entail high energy consumption, construction noise, and disturbance to surrounding ground structures [5], which limit their applicability in densely built environments. On the other hand, chemical treatment methods, though relatively mature, often involve the use of synthetic additives such as cement or lime, which pose concerns regarding carbon emissions and potential environmental contamination [6, 7]. Against this backdrop, there is a growing demand for sustainable, low-impact, and in situ soil improvement technologies, particularly in the context of large-scale infrastructure expansion and urban redevelopment. Weak granular soils, especially poorly to moderately graded sands, are commonly encountered in various geotechnical applications such as foundation support, embankments, road subgrades, retaining structures, and coastal land reclamation. These soils often suffer from insufficient shear strength and low bearing capacity, making them unsuitable for direct engineering use without reinforcement [4]. Therefore, the development of advanced soil treatment techniques that can enhance the mechanical performance of these problematic sands in an environmentally compatible manner is of critical importance for modern geotechnical practice [8; 9]. Against this backdrop, microbially induced carbonate precipitation (MICP) technology has emerged as an innovative soil improvement method based on biomineralisation processes. With its distinctive advantages of environmental friendliness, in situ treatment capability, sustainability, and cost-effectiveness, MICP is gradually becoming a research focus and technological frontier in the geotechnical engineering field [4; 10]. MICP technology utilises the enzymatic catalysis of specific microorganisms (primarily urease-producing bacteria) to induce in situ generation of calcium carbonate crystals within soil pores, forming natural cementation materials that improve soil mechanical properties [11; 12]. Compared to traditional chemical reinforcement methods, MICP technology offers significant technical advantages. First, this technology utilises urease-producing microbial strains such as _Sporosarcina pasteurii_, cultivated under controlled laboratory conditions, along with inorganic salt solutions as treatment materials, reducing the use of toxic synthetic chemicals and demonstrating superior environmental compatibility compared to conventional methods. Second, the generated calcium carbonate cement exhibits compositional consistency with natural carbonate rock minerals, enabling MICP-treated geotechnical materials to demonstrate excellent stability and durability [13; 14]. However, MICP faces substantial challenges in practical engineering applications, particularly the difficulty in accurately evaluating treatment effectiveness [6]. This technology involves multi-phase coupling processes encompassing biological, chemical, and physical interactions, with treatment outcomes influenced by multiple factors including soil particle characteristics, microbial activity, and site environmental conditions [15; 16]. These influencing factors typically demonstrate nonlinear and coupled relationships, making traditional empirical formulas and simplified theoretical models inadequate for accurately describing the variation patterns of MICP-treated sand strength characteristics [6]. Unconfined compressive strength (UCS) serves as a critical indicator for evaluating MICP treatment effectiveness, with research and determination primarily conducted through laboratory-based experimental methods [17].