## 1 Introduction  
Floodplain soils formed by unstable sedimentary environments are widespread in rivers, lakes, coasts, and other landforms. Foundations of bridges, offshore projects, and sub-sea tunnels will inevitably pass through this type of soil. However, under the reciprocal influence of the water flow or wave, the floodplain soils exhibit distinctive horizontal stratification and depositional rhythm. They are characterized by a high water content, large porosity ratio, high compressibility, and an evident over-consolidation state. The floodplain soils are susceptible to residual deformation or strength damage caused by waves and earthquakes, essential to soil subsidence and building instability. \(G_{\text{max}}\) (defined as the dynamic shear modulus \(G\) when the shear strain level is less than \(10^{-5}\), with the soil deformation belonging to the elastic range) is a fundamental parameter for describing the dynamic properties of soils, and it plays a vital role in geotechnical problems such as soil deformation prediction, potential liquefaction evaluation, seismic site response analysis, and dynamic foundation design parameters [1; 2; 3; 4]. Therefore, conducting a systematic study on the \(G_{\text{max}}\) of overconsolidated floodplain soft soils is necessary. Extensive studies have been conducted to investigate the \(G_{\text{max}}\) of soils using resonant column (RC) and bender element (BE) tests [5; 6; 7]. The level of densification (void ratio \(e\) or relative density \(D_{\text{r}}\)) and the initial effective confining pressure \(\sigma_{\text{3c}}\)\({}^{\prime}\) is surely the most fundamental effects on \(G_{\text{max}}\)[8; 9; 10]. However, the effect of frequency \(f\) on \(G_{\text{max}}\) is controversial. [PERSON] and [PERSON] [11] proposed that an increase in \(f\) will lead to an increase in \(G\) of clay soils in the range 0.001 Hz \(<\)\(f\) \(<\) 200 Hz, while [PERSON] [12] insisted that the \(f\) range of 10-100 Hz did not have a significant effect on \(G\). In this paper, the effect of \(e\) and \(\sigma_{\text{3c}}\)\({}^{\prime}\) was considered instead of \(f\). For sandy soils, [PERSON] and [PERSON] [13] indicated, based on a large number of RC tests, that \(G_{\text{max}}\) rises as \(\sigma_{\text{3c}}\)\({}^{\prime}\) increases and decreases as \(e\) improves. [PERSON] and [PERSON] [14] confirmed the effect of \(\sigma_{3\epsilon}\), \(e\), and other factors on \(G_{\rm max}\). [PERSON] and [PERSON] [15] and [PERSON] et al. [16] demonstrated that stress anisotropy and the particle shape of soils can still affect \(G_{\rm max}\). [PERSON] et al. [17] conducted a series of combined cyclic triaxial and bender element tests regarding clayey soils. They revealed that cyclic stress and strain history lead to a decrease in \(G_{\rm max}\), while the reduction in \(G_{\rm max}\) in the strain-controlled tests is less than that in the stress-controlled tests. [PERSON] and Yoshida [18] reported that factors such as stress history (OCR) and plasticity index (\(I_{\rm p}\)) also have some influence on the \(G_{\rm max}\). [PERSON] and [PERSON] [19] exhibited that \(G_{\rm max}\) does not change with \(I_{\rm p}\) for normally consolidated clays (OCR = 1), and for overconsolidated clays (OCR > 1), \(G_{\rm max}\) increases with \(I_{\rm p}\). [PERSON] et al. [20] also explored the effect of the initial consolidation path on the \(G_{\rm max}\) of Boston blue clay. [PERSON] et al. [21] examined the impact of moisture content (\(w\)) and consolidation time (\(T\)) on the \(G_{\rm max}\) of Texas-expanded clay and established an empirical equation considering these two factors. [PERSON] et al. [22] investigated the influence of montmorillonite to kaolinite (M-K) ratio and \(T\) on the \(G_{\rm max}\) of clay soils. [PERSON] et al. [23] discovered that the \(G_{\rm max}\) initially decreases as clay content increases from 0 to 20% and then rises slightly as clay content ranges from 20 to 30%.