# Study on Stiffness Parameters of the Hardening Soil Model in Sandy Gravel Stratum
## 1 Introduction  
The sandy gravel stratum, characterized by a high concentration of coarse particles, presents challenges in obtaining accurate mechanical parameters through laboratory testing, thereby hindering the efficacy of numerical simulation in analyzing projects within these strata [1; 2; 3]. It is crucial to identify practical and reasonable parameters for engineering projects in the sandy gravel stratum. The results of a large-scale cyclic triaxial study conducted by [PERSON] and [PERSON] on sandy soils with varying coarse grain contents demonstrated a correlation between the increase in shear modulus and the increase in coarse grain content [4]. [PERSON] et al. [5] found that the modulus normalization curve shifted progressively upward as the surrounding pressure increased. Particle size, permeability, direct shear, and compressive strength of coarse-grained soils were investigated by [PERSON] et al. [6]. [PERSON] et al. [7] used a large triaxial test on sand and gravel soil, focusing on the effect of the volume fraction of gravel, particle size, particle gradation, and initial stress state on the mechanical properties of gravel soil. [PERSON] et al. [8] explained the stress-strain characteristics of different granular materials of the same gradation in the elasto-plastic range, especially the effect of the static soil pressure coefficient on the static soil pressure in the compacted state.  
In 1970, [PERSON] et al. [9] established a currently widely used incremental model of elasticity based on the hyperbolic stress-strain relationship proposed by [PERSON], namely the D-C principal model, which is also the most representative nonlinear elastic model.  
[PERSON] et al. [10] introduced plasticity theory into the D-C model in 1998, and proposed a soil hardening model considering both shear hardening and compression hardening. The HS model is an advanced constitutive model for soils which belongs to the isotropic hardening elastic-plastic model [11; 12; 13; 14]. It can accurately reflect the mechanical behavior of soil under loading and unloading [15]. The HS model has obvious advantages, as it can accurately describe the soil properties by inputting three [PERSON]'s moduli: triaxial loading \(E_{50}\), oedometric loading \(E_{\text{oed}}\), and unloading-reloading \(E_{\text{ur}}\)[16; 17; 18].  
\(E_{\text{s1-2}}\) is the compression modulus of soil commonly used in the geological report and is obtained from a 100 to 200 kPa loading test. Usually, \(E_{\text{s1-2}}\) equals \(E_{\text{oed}}\)[19; 20]. However, the \(E_{50}\) and \(E_{\text{ur}}\) required for the HS model cannot be calculated. Therefore, establishing a geometric relationship between \(E_{\text{s1-2}}\) and the stiffness modulus of the HS model can simplify the value selection process of numerical simulation. These three parameters can usually be determined by laboratory tests. Many experts and scholars have studied the HS model parameters of clay and sand [21; 22], as shown in Table 1.  
Research on the HS model key stiffness relationship mainly focused on sandy soil, silty clay, and residual granite soil, with little research on coarse particles of soil like sandy gravel. One of the most important reasons is that the particle of sandy gravel has a large volume and high strength. It is difficult to directly obtain its soil constitutive parameters through conventional lab tests. This paper conducts large-scale mechanical experiments, including the triaxial drained shear test, the loading-unloading test, and the standard consolidation test on large-scale sandy gravel specimens. The objective of the experiment is to test the Young's modulus under triaxial loading (\(E_{50}\)), oedometric loading (\(E_{\text{oed}}\)), and unloading-reloading (\(E_{\text{ur}}\)), and analyze the proportional relationship of these parameters in the HS model. The results of the experiments are then utilized in a numerical simulation of a foundation pit project and compared with engineering monitoring data to validate the accuracy of the test outcomes.