The specimens used in this study were all collected from construction sites in Jiangbei New District which were obtained through thin-wall Shelby tube sampling during site investigation drilling. To minimize sample disturbance, the tubes were hydraulically pushed into the soil layer at a constant rate without rotation. After retrieval, each tube was carefully sealed with paraffin wax and plastic film to preserve natural water content and structural integrity. The sealed samples were transported in an upright position and stored at low temperature to prevent desiccation or structural change before laboratory testing. Prior to testing, visual inspection and trimming were conducted to select intact segments for specimen preparation. This ensured that the soil structure remained as close as possible to in-situ conditions throughout the testing process. and are representative of the typical soft clay of the Yangtze River floodplain facies. The undisturbed Yangtze River floodplain facies soft clay appears gray-brown in color, with distinct horizontal bedding and interbedded sandy layers, as shown in Figure 1 . After air-drying, disaggregation, and preliminary sieving, the undisturbed soil becomes a loose granular material. Particle size distribution tests reveal that, apart from a small amount of fine sand, most of the particles are smaller than 0.075 mm after oven-dried sieving. This indicates that the floodplain facies soft clay is mainly composed of clay minerals and fine detritus smaller than silt grade. Figure 1 presents scanning electron microscope (SEM) images of the Yangtze River floodplain facies soft clay. At the microscopic level, the undisturbed clay mainly appears as aggregated flocculent or platy structures, with loosely stacked clay particles often forming lamellar arrangements on their surfaces. In addition to these clay aggregates, numerous angular and irregularly shaped silt particles are observed. As for inter-aggregate connections, these clusters or particles are bound either through direct contact or by cementitious substances, predominantly forming edge-to-face or point-to-face contacts. Due to prolonged fluvial transport during its deposition, this soft clay is highly dispersive and strongly hydrophilic, resulting in high water content and large void ratios. It generally shows high compressibility and sensitivity, along with typical characteristics such as creep and thixotropy. Mineralogical analysis further reveals a relatively simple clay mineral composition, dominated by illite (~70%) and chlorite, with detrital minerals mainly consisting of quartz and feldspar. The overall material composition is relatively homogeneous.

Strain-controlled staged cyclic triaxial tests were conducted using the HCA-300 multifunctional cyclic triaxial apparatus developed by GCTS ( Figure 2 ). This advanced testing system is capable of performing both conventional triaxial tests and torsional shear tests with synchronously coupled bidirectional dynamic loading, allowing simulation of various types of loads such as seismic, traffic, and wave-induced loads. The main technical specifications of the triaxial system used in this study, including controller parameters, sensor ranges, accuracy, and measurement deviations, are summarized in Table 1 . See (Chen et al., 2019) for more details about the HCA-300 system.

According to elastic theory, the shear stress τ and shear strain γ on the 45° plane of the specimen during loading can be calculated using Equation 2 :

In Equation 2 , ν denotes Poisson’s ratio, for the in situ interbedded soil of the Yangtze River floodplain, we take ν = 0.42 (Zhuang et al., 2020). We acknowledge that ν may evolve with increasing strain during cyclic shearing in practical conditions. The assumption of a constant ν was adopted for model simplicity, and it has been widely used in similar studies (Xiao et al., 2023). The calculation methods for G and γ in cyclic triaxial tests are illustrated in Figure 3 . In the equivalent linear viscoelastic constitutive model, the soil is regarded as a viscoelastic material. G is represented by the slope of the line connecting the peak points at both ends of the soil’s hysteresis loop, while λ is related to the energy dissipation and elastic strain energy of the soil.

To investigate the variation characteristics of shear modulus (G) and damping ratio (λ) of interbedded clay-sand soils with respect to consolidation degree (U), a series of strain-controlled cyclic triaxial tests on undisturbed interbedded clay-sand soils were conducted. Undisturbed soft clay samples were selected to preserve the natural microstructure, stratification, and bonding characteristics of the floodplain soil, which play a critical role in its dynamic behavior. By keeping other conditions constant, five test conditions with different U and consolidation ratios (k _c) were designed. k _c was applied under drained conditions to ensure complete dissipation of pore water pressure. Ladd and DeGroot (2004) pointed out that the value of k _c generally ranges from 1.0 to 1.5. The chosen consolidation ratios (k _c = 1.0, 1.2, 1.4) are representative of the stress history and preloading conditions commonly encountered in soft clay foundations in engineering practice, such as surcharge preloading or excavation-induced stress changes. Table 2 presents the basic physical and mechanical properties of the floodplain soft soils from each borehole, as well as the specific test plans. Parameters such as density (ρ), water content (w), void ratio (e), were measured and showed in Table 2 .

For the cyclic triaxial tests under different consolidation degrees, the experimental procedure can be divided into the following four steps: (1) Prepare standard-sized solid cylindrical specimens from undisturbed soft soil samples and fully saturate them; (2) Mount the specimen onto the base of the testing apparatus, connect the top to the displacement sensor and loading system, and seal the pressure chamber; (3) After installation, apply confining pressure and deviator stress to the specimen according to the test conditions to achieve various degrees of consolidation. Consolidation is considered complete once the target degree of consolidation is reached; (4) Subject the specimen to strain-controlled staged cyclic loading, with shear strain amplitude gradually increasing from 1×10−⁵ to 1×10−². This strain range was chosen based on typical working strain levels observed in soft soil foundations in engineering practice (Wong et al., 2022). Each loading stage consists of five cycles at a frequency of 0.1 Hz.

By normalizing the measured consolidation displacement curves of Yangtze River floodplain soft soil specimens under different consolidation conditions (as shown in Figure 4 ), the variation curves of U with time were obtained, as illustrated in Figure 5 . It can be observed that U of the floodplain soft soils exhibits a similar trend over time under different initial static stress conditions. Consequently, U can be expressed as a function of consolidation time t. the relationship between U and t was fitted using an exponential function in the following form:

In Equation 3 , k and b are shape parameters of the curve. The fitting results indicate that ( Equation 3 ) provides a good fit for the floodplain soft soils of the Yangtze River. Therefore, this method is adopted in the present study to control U. Figure 5 presents the reference ranges of consolidation time corresponding to different U. This approach accounts for the potential errors between the fitted curve and the measured data. It can be observed that as the consolidation degree decreases, the time required for specimen consolidation is significantly reduced. The fitted curves do not pass through the origin because of the inherent structural characteristics of the soil.

Figure 6 presents the test results of the dynamic shear modulus (G) and damping ratio (λ) of undisturbed floodplain facies soft clay over a wide strain range under different degrees of consolidation. As shown in the Figure, at a given U, all types of floodplain facies soft clay exhibit a typical trend where G decreases with increasing shear strain amplitude (γ), while the damping ratio λ increases with γ. Furthermore, it can be observed that under the same γ, G increases significantly with increasing U, whereas the λ shows a slight decrease. This indicates that a higher U values correspond to more complete dissipation of excess pore water pressure and further consolidation settlement, which tends to preserve or enhance the existing soil fabric and interparticle contacts in undisturbed samples. Comparisons among Figures 6a-c further reveal that the influence of U on G becomes more pronounced with increasing initial effective confining pressure. This suggests that the effect of U on G of floodplain facies soft clay is correlated with σ’_m. Similarly, by comparing Figures 6b-e , it can be seen that as the consolidation ratio k _c increases, the influence of U on G also becomes more significant. This indicates that G of floodplain facies soft clay is not only affected by the U but also closely related to the k _c.

The maximum G _max is the dynamic shear modulus when the strain percentage is less than 10^-5, in which case the soil is considered to be in a purely elastic state. And so in this study G _max was obtained using the extrapolation method at 0.0001% strain (Hardin and Drnevich, 1972). Figure 7 illustrates the variation trend of G _max of the Yangtze River floodplain soft soil with U. As shown in Figures 4 and 5 , G _max increases with increasing U under different consolidation conditions, and the two exhibit an exponential correlation. This indicates that G _max of the undisturbed Yangtze River floodplain soft soil is influenced not only by the initial effective confining pressure and the consolidation ratio k _c, but also by U.

Figure 7 also reveals that under isotropic consolidation conditions, the variation in σ’_m has a nearly identical effect on the growth rate of G _max with respect to U for the floodplain soft soil. Similarly, under the same σ’_m, the influence of k _c on the growth rate of G _max with increasing U is relatively minor. This indicates that the growth rate of G _max with U is not significantly affected by differences in σ’_m or k _c. Therefore, the relationship between G _max and U for floodplain soft soils under various initial consolidation conditions can be fitted using Equation 4 :

The corresponding fitting parameters, as well as the experimental results, are summarized in the Table 3 below, where A ₁ and k denote the fitting parameters. It can be observed that the values of G _max at U = 1 obtained from the experiments under different σ’_m or k _c conditions are very close to the fitted parameter A ₁ and therefore we approximate that A ₁ is numerically equal to G _max when U = 1. Moreover, the stress index k characterizes the influence of U on the growth rate of G _max. Regression analysis shows that the value of k is approximately 0.5. therefore, we adopted k = 0.5 in our derivation.

To facilitate the empirical estimation of G _max for floodplain soft soils under different U, the value of G _max corresponding to a specific U is denoted as G _max,u, while the value under full consolidation (i.e., U = 100%) is denoted as G _max,100%. Accordingly, ( Equation 5 ) can be rewritten in the following form:

In this equation, μ represents the reduction factor of G _max under partial consolidation. Table 4 provides the reduction factors μ corresponding to different U for floodplain soft soils along the Yangtze River, which can serve as a reference for engineering practice.

To investigate the nonlinear and hysteretic characteristics of floodplain soft soils along the Yangtze River, the G/G _max and λ were fitted using the Martin-Davidenkov model (Martin and Seed, 1983) ( Equation 6 ) and the λ model proposed by (Chen et al., 2006), ( Equation 7 ) respectively.

In the equations, α and β are fitting parameters. The reference shear strain γ ₀ corresponds to the strain value at which G/G _max equals 0.5. λ _min represents the minimum damping ratio of the soil at very small strains, while λ ₀ and β are shape parameters that define the form of λ curve.

As shown in Figure 8 , U has a significant influence on the relationship curves of G/G _max – γ. At the same strain level, the G/G _max values of the Yangtze River floodplain soft soil increase with increasing U, while the λ decreases as U increases. This indicates that as U increases, the dynamic behavior of the soil gradually shifts from nonlinear to linear, accompanied by a reduction in hysteretic behavior. Furthermore, a comparison of Figures 8a-c shows that with increasing σ’_m, the influence of U on the G/G _max – γ and λ – γ curves becomes more pronounced. This suggests that the effect of U on the nonlinear and hysteretic characteristics of the floodplain soft soil is dependent on the σ’_m. Similarly, a comparison of Figures 8b-e reveals that as k _c increases, the influence of U on the G/G _max – γ and λ – γ curves also becomes more evident. This indicates that the effect of U on the nonlinear and hysteretic behavior of the floodplain soft soil is also related to k _c.

This study investigates the influence of U on G and λ of Yangtze River floodplain soft soils under different σ’_m and k _c, based on cyclic triaxial testing. The degradation curve of G/G _max is closely related to the three parameters in the Davidenkov model: α, β, and γ ₀. Table 5 summarizes the values of these parameters under all test conditions. The results show that U has little effect on the parameters α and β. Therefore, when using the three-parameter Davidenkov model to fit the behavior of the floodplain soft soils, α and β can be reasonably taken as 1.0 and 0.47, respectively. In contrast, the reference shear strain γ ₀ exhibits significant variability during nonlinear fitting, which may be associated with the variation in U under different test conditions.

Figure 9 shows the relationship curves between U and γ ₀ under different σ'_m and k _c. It can be observed that when σ'_m and k _c are fixed, γ ₀ increases significantly with increasing U. Moreover, as σ'_m and k _c increase, the influence of U on the rising trend of γ ₀ becomes more pronounced. As previously discussed, the σ'_m and k _c have a notable impact on the fitted parameters for floodplain soft soils. To further quantify the effect of U, the γ ₀ under different initial static stress conditions is normalized. According to ( Equation 8 ), γ ₀ values under varying initial stress conditions can be normalized to γ’ ₀, which corresponds to a confining pressure of 100 kPa and a consolidation ratio k _c of 1.0.

The fitting results of γ’ ₀ under different U are shown in Figure 10 . As illustrated in Figure 10 , γ’ ₀ of various types of floodplain soft soils exhibits an increasing trend with rising U. Based on this observed pattern, an empirical relationship between γ’ ₀ and U can be established as Equation 9 :

In Equation 9 , p and q are fitting parameters, with values of 0.0386 and 0.66, respectively.

To further analyze the nonlinear and hysteretic behavior of Yangtze River floodplain soft soils, G and λ test data for silty clay from the Yangtze River estuary (σ' _m = 50 ~ 200 kPa) (Yang et al., 2019) were collected for fitting analysis. The fitting results for G/G _max and λ of the two clay types were compared with recommended and standard values for cohesive soils. The comparison results are shown in Figure 11 . The recommended values were provided by (Sun et al., 2004). based on the average test data of conventional soils such as clay, silty clay, and silt from various regions across China. As shown in Figure 11a , the G/G _max – γ curves of Yangtze River floodplain soft soils generally fall within the statistical range of recommended and standard values for cohesive soils. Compared to the silty clay from the Yangtze estuary, the floodplain soft soils exhibit slower modulus degradation at large strains and relatively higher G/G _max values, indicating that their nonlinear behavior is weaker. Therefore, the empirical formula proposed in this study can be used to predict G/G _max for Yangtze River floodplain soft soils. As shown in Figure 11b , the λ of the floodplain soft soils shows considerable variability, which aligns with current understanding of damping behavior in cohesive soils. At small strain levels, the λ is relatively high, while at larger strains it approaches the recommended and standard values for cohesive soils, and is higher than the average λ of the estuary silty clay. Overall, the Yangtze River floodplain soft soils tend to exhibit higher λ, reflecting stronger hysteretic behavior.