## 1 Introduction  
Urban issues such as land resource scarcity and traffic congestion resulting from rapid city expansion are a significant threat to the sustainable development of coastal cities. The development of high-quality underground spaces is an effective way to address this issue [1]. Due to the complex engineering properties of soil, foundation pit excavation in coastal areas has resulted in fatal accidents [2]. Foundation excavations conducted without adequate safeguards also result in significant deformation or even structural damage to adjacent underground structures, including shield tunnels and metro stations [3; 4; 5]. When evaluating the safety and environmental impact of foundation engineering, the mechanical properties and parameters of soil are typically determined through loading tests, which include conventional triaxial and pressure-meter tests [6; 7]. The excavation of foundation pits is a common unloading problem, and extensive research demonstrates that the mechanical properties of soil are intercirably linked to the stress path [8; 9]. As a result, the difference in soil properties between loading and unloading stress paths may result in unpredictable calculation errors in foundation engineering. It is thus critical to have a thorough understanding of the stress and deformation characteristics of coastal soil during unloading. Numerous experimental studies on the mechanical properties of soils subjected to unloading paths have confirmed that the unloading process has a significant effect on the strength and stiffness properties of the soil. Unloading ratio \(R\) is frequently used to represent various unloading stress paths. It is defined as the ratio of the absolute value of vertical stress unloading (\(\left\lvert\Delta\sigma_{1}\,\right\rvert\)) to the absolute value of horizontal stress unloading (\(\left\lvert\,\Delta\sigma_{3}\,\right\rvert\)). \(R\) is zero for axial unloading and tends to infinity for lateral unloading. Triaxial compression tests on soft soils demonstrate that, in comparison to axial loading, soil samples subjected to unloading stress paths exhibit decreased shear strength and a smaller initial tangent modulus [10; 11]. [PERSON] et al. [12] investigated the mechanical properties of marine sedimentary soft soils in relation to pore pressure and unloading ratio. Results indicate that increased pore pressure significantly reduces unloading strength, particularly cohesion. [PERSON] et al. [13; 14] conducted a series of triaxial CU and CD tests on marine silty clay subjected to unloading stress paths. Total shear strength under drained and unloaded conditions was greater than that in conventional triaxial tests, but effective shear strength was not significantly different. Under undrained and unloaded conditions, the initial tangent modulus was directly proportional to the initial confining pressure. [PERSON] et al. [15] conducted unloading stress path drainage tests on silty clay under \(K_{0}\) consolidation. The stress-strain relationship was quite different under various unloading stress paths. [PERSON] et al. [16] investigated the deformation properties of silty clay during unloading and loading in Guangzhou. The results of tests conducted on silty clay and mucky soil under axial and lateral unloading stress paths indicated that the failure modes of axial and lateral unloading samples are distinct, and that the stress-strain relationship is highly dependent on consolidation stress, plastic index, and confining pressure. However, because foundations are typically excavated layer by layer, the soil unloading process occurs in stages, resulting in a significantly different unloading intensity levels. It is unknown how unloading intensity affects the mechanical properties of coastal soil. Over the last few decades, the nonlinear effect of strain on soil stiffness has been extensively investigated.