WITHDRAWN: An experimental study on the effects of moisture content and confining pressure on the damping ratio of silty clay

doi:10.21203/rs.3.rs-4886675/v1

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WITHDRAWN: An experimental study on the effects of moisture content and confining pressure on the damping ratio of silty clay

https://doi.org/10.21203/rs.3.rs-4886675/v1

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The damping ratio is a crucial dynamic parameter in soil. In order to study the damping ratio characteristics of silty clay, dynamic triaxial tests were conducted. Two influencing factors, moisture content and confining pressure, were considered, and the specific effects and sensitivities of changes in these factors on the damping ratio were discussed in detail. The research results indicate that an increase in moisture content leads to an increase in the damping ratio of silty clay, while an increase in confining pressure results in a decrease in the damping ratio. The relationship curve between the damping ratio and dynamic shear strain (λ–γ_d) demonstrates distinct phase characteristics. Furthermore, the sensitivity of the damping ratio to moisture content is generally higher than its sensitivity to confining pressure, with significant differences in sensitivity observed across different phases. This study uncovers the complex influence of moisture content and confining pressure on the mechanical properties of silty clay, providing an important reference for a deeper understanding of its behavior in various conditions.

Physical sciences/Engineering/Civil engineering

Earth and environmental sciences/Solid earth sciences

Silty clay

Damping ratio

Moisture content

Confining pressure

Dynamic triaxial test

In the field of civil engineering, silty clay is widely used in foundation construction, slope stability analysis, and road engineering. However, the mechanical properties of silty clay are complex and variable, especially under the influence of external dynamic loads, making changes in its damping ratio particularly significant. The damping ratio, a key parameter for measuring the soil's energy dissipation capacity during vibration, is crucial for evaluating soil stability and seismic performance. The shear strength parameters of silty clay under dynamic loading significantly increase as temperature decreases, while the damping ratio decreases, reducing the soil's ability to absorb seismic waves (Guo et al., 2023). The dynamic elastic modulus ratio and reference dynamic strain amplitude increase as confining pressure and soil temperature decrease, while soil moisture content and loading frequency increase, indicating that dynamic behavior is most sensitive to soil temperature (Zhang et al., 2023). Additives can effectively enhance the mechanical properties of soil; for example, the MgO content significantly affects the mechanical properties of silty clay. At the same confining pressure, the maximum shear modulus of soil with 22% moisture content is lower than that of soil with 16% moisture content, and the shear modulus increases linearly with the increase in nano–MgO content (Gao et al., 2020). Adding cement and fly ash to silty clay can alter its dynamic characteristics; the micro-aggregate effect and hollow structure of fly ash particles help increase the G value and enhance the energy dissipation capacity of silty clay (Lang et al., 2020). Zhang et al. studied factors such as cyclic stress ratio (CSR), static deviator stress ratio (SDR), and overconsolidation ratio (OCR) on the resilient modulus and dynamic damping ratio of silty clay (Zhang et al., 2020). Freeze–thaw cycles cause changes in the mechanical properties of silty clay, with both the maximum dynamic shear modulus and maximum damping ratio decreasing as the number of freeze-thaw cycles increases (Jing et al., 2019; Zhang et al., 2018; Xu et al., 2019). Shen et al. examined the changes in dynamic parameters of silty clay under different confining pressures and established empirical formulas for the variation of these parameters with confining pressure (Shen et al., 2013; Lee et al., 2007). In frozen saline silty clay, salinity and confining pressure significantly affect cumulative axial strain and dynamic shear modulus (Zhao et al., 2024; Zhao et al., 2020). The migration characteristics of fine particles in silty clay are influenced by the duration and amplitude of cyclic loading. With increasing loading time, the mass of migrating fine particles increases nonlinearly, and the rate of increase gradually decreases. The maximum mass of migrating fine particles increases with increasing cyclic loading amplitude and decreases with the initial dry density of subgrade soil (Ding et al., 2023). The principal stress direction significantly affects the deformation characteristics of frozen silty clay; when the principal stress angle is less than 15°, the main strain in the sample is axial. When the angle is between 15° and 45°, the rate of increase in circumferential torsional strain is greater than that of axial strain. When the angle exceeds 45°, the axial strain manifests as tensile deformation (Liu et al., 2022; Li et al., 2018). The cyclic characteristics and post-cyclic characteristics of silty clay stabilize after a certain number of reconsolidation cycles and remain unchanged with further cycling (Lei et al., 2022). Zhao et al. proposed a criterion for the dynamic strength of frozen sulfate saline silty clay under cyclic loading (Zhao et al., 2020). Wang et al. found that the post-cyclic shear strength of remolded marine silty clay increases with complete reconsolidation and decreases in the absence of reconsolidation (Wang et al., 2019). Remolded silty clay exhibits phase change behavior under cyclic loading, characterized by initial contraction, temporary phase change, and subsequent expansion stages (Qian et al., 2019).

Moisture content and confining pressure are important factors affecting the damping ratio of silty clay. Previous studies have shown that an increase in moisture content usually leads to an increase in the soil damping ratio, but the specific mechanisms and patterns of this influence under different dynamic loading conditions remain unclear. Additionally, the impact of confining pressure on the soil damping ratio is also significant, yet systematic studies on the impact of increased confining pressure on the damping ratio are relatively scarce. This paper analyzes the characteristics of damping ratio changes in silty clay under different moisture content and confining pressure conditions through a series of systematic experiments. We not only examine the influence of individual factors on the damping ratio but also conduct a comparative analysis of the sensitivity of the damping ratio under the combined effects of moisture content and confining pressure. This paper aims to reveal the influence patterns of moisture content and confining pressure on the damping ratio of silty clay, providing a scientific basis for the reasonable prediction and control of soil damping performance in engineering practice.

2.1. Sample preparation

The soil samples for the experiment were collected from the entrance of the Dashiban Tunnel in Ya'an, Sichuan Province. The particle size distribution curve of the soil samples is illustrated in Fig. 1. Laboratory tests determined that the plastic limit moisture content of the soil samples was 16.6%, the liquid limit moisture content was 27.4%, and the plasticity index was 10.8. Based on the data for the plastic limit moisture content and liquid limit moisture content, as well as a careful observation and analysis of the samples, the soil was classified as silty clay.

Before preparing the test soil samples, the soil collected from the field was dried and crushed. The crushed soil was then sieved, and only particles with a diameter of ≤ 1mm were used. The dry soil samples were weighed using an electronic scale accurate to 0.01g. Distilled water was then added to prepare soil samples with moisture contents of 8%, 12%, and 16%. The soil samples with added distilled water were thoroughly mixed and sealed with plastic wrap for 24 hours to ensure uniform moisture content.

The specimens were cylindrical, with a height of 100mm and a diameter of 50mm (Fig. 2). They were prepared by compacting the soil in layers using a three–part mold to reach a dry density of 2.4g/cm³. After preparation, the specimens were sealed with plastic wrap and placed in a constant temperature and humidity chamber for 14 days to cure.

2.2. Experimental scheme

This study employs a GDS dynamic triaxial apparatus, which includes an axial drive device, pressure chamber, and DCS digital control system. The loading waveform used is a sine wave with a loading frequency of 1 Hz. Figure 3 shows the GDS dynamic triaxial loading system.

Table 1 presents the cyclic loading test scheme. Two variables, moisture content and confining pressure, were set for this experiment. The study investigates the effects of moisture content and confining pressure on the damping ratio of silty clay while controlling other variables constant during the tests.

Table 1. Test programme.

Sample number	Moisture content	Confining pressure (kPa)	CSR
1	8%	50	0.3
2	12%
3	16%
4	12%	100
5	12%	200

2.3. Data processing

The axial dynamic stress and axial dynamic strain collected by the test system are converted to dynamic shear stress and dynamic shear strain using the following equations:

$${\tau _{\text{d}}}=\frac{{{\sigma _{\text{d}}}}}{2}$$

$${\gamma _{\text{d}}}=\left( {1+\mu } \right){\varepsilon _{\text{d}}}$$

where τ_d is the dynamic shear stress, σ_d is the dynamic stress, γ_d is the dynamic shear strain, ε_d is the dynamic strain, and µ is Poisson ratio.

$${\tau _{\text{d}}}=\frac{{{\gamma _{\text{d}}}}}{{a+b{\gamma _{\text{d}}}}}$$

$${G_{\text{d}}}=\frac{{{\tau _{\text{d}}}}}{{{\gamma _{\text{d}}}}}=\frac{1}{{a+b{\gamma _{\text{d}}}}}$$

The dynamic shear modulus G_d and the hyperbolic model fitting parameters a and b for the sample's dynamic nonlinear characteristics are obtained from the experimental data. The maximum dynamic shear modulus G_dmax=1/a, the ultimate dynamic shear stress τ_dmax = 1/b, and the reference shear strain γ_r = a/b. The dynamic shear modulus ratio G_d/G_dmax can be expressed by Eq. (5):

$$\frac{{{G_{\text{d}}}}}{{{G_{{\text{dmax}}}}}}=\frac{a}{{a+b{\gamma _{\text{d}}}}}=\frac{1}{{1+{\gamma _{\text{d}}}/{\gamma _{\text{r}}}}}=\frac{{{\gamma _{\text{r}}}}}{{{\gamma _{\text{r}}}+{\gamma _{\text{d}}}}}$$

Figure 4 shows the hysteresis loops plotted from the dynamic shear stress and dynamic shear strain data collected by the test system.

The damping ratio λ is calculated using Eq. (6) (Sutter et al.,2000):

$$\lambda =\frac{{{S_{{\text{Delayed Curve}}}}}}{{4\pi {S_{\Delta AOB}}}}$$

where S_{Delayed curve} is the area of the hysteresis loop of dynamic shear stress and dynamic shear strain, numerically representing the energy dissipated due to the damping force in one cycle of dynamic loading; S_ΔAOB is the area of the triangle formed by the amplitudes of dynamic shear stress and dynamic shear strain, representing the maximum energy stored by the dynamic load.

The relationship between the damping ratio and dynamic shear strain can be expressed by Eq. (7) (Ding et al.,2019):

$$\lambda ={\lambda _{\hbox{max} }}{\left( {\frac{{{\gamma _{\text{d}}}}}{{{\gamma _{\text{r}}}+{\gamma _{\text{d}}}}}} \right)^n}$$

where γ_d is the dynamic shear strain, λ_max is the maximum damping ratio, n is the shape coefficient of the λ–γ_d relationship curve, and γ_r is the reference shear strain. λ_max and n are obtained by fitting the damping ratio and dynamic shear strain data.

3.1. Effect of moisture content on damping ratio

Figure 5 presents the λ–γ_d relationship curves for varying moisture contents. As illustrated in the figure, moisture content significantly impacts the damping ratio of silty clay near the Dashiban Tunnel in Ya'an, Sichuan Province. As the moisture content of the silty clay increases, the λ–γ_d relationship curves shift upward, with the λ value for the same γ_d consistently increasing. The overall slope of the λ–γ_d relationship curves also rises, transitioning from a gentle to a steep slope. The rate at which the damping ratio λ increases with dynamic shear strain γ_d also intensifies.

The λ–γ_d relationship curves in Fig. 5 exhibit distinct phase characteristics, categorized into four stages: stable stage (I), up slow stage (II), up fast stage (III), and convergent stage (IV). During the stable stage (I), the curve is horizontal, indicating minimal change in the damping ratio λ with dynamic shear strain γ_d. During the up slow stage (II), the curve begins to exhibit a slow upward trend, transitioning from horizontal to slightly upward, with a slightly concave shape, indicating a gradual increase in the growth rate of the damping ratio λ. In the up fast stage (III), the curve rises rapidly, with a significantly increased slope and a distinctly concave shape, indicating a rapid increase in the growth rate of the damping ratio λ. In the convergent stage (IV), the curve transitions from a concave to a convex shape, indicating a decrease in the growth rate of the damping ratio λ, and the curve demonstrates a convergent nature.

The λ–γ_d relationship curves for varying moisture contents exhibit distinct behaviors across different stages. During the stable stage (I), the curves for moisture contents of 8% and 12% show almost no difference, with a maximum damping ratio difference of only 0.0001. However, the curve for a moisture content of 16% differs significantly from the other two, with a maximum damping ratio four times that of the other two moisture contents. In the up slow stage (II), the curves for moisture contents of 8% and 12% still show little difference, but towards the end of this stage, the two curves begin to diverge, with the 16% moisture content curve being significantly higher than the other two, having a maximum damping ratio twice that of the other two moisture contents. In the up fast stage (III), the curves for the three different moisture contents exhibit clear differences, with higher moisture content resulting in a steeper slope, indicating a faster change in the damping ratio λ with dynamic shear strain γ_d. During the convergent stage (IV), the differences between the curves for different moisture contents further increase as the curves enter a convergent state.

During the stable stage (I) and up slow stage (II), the curves for moisture contents of 8% and 12% are very similar, indicating that within the range of 8–12%, the impact of moisture content on the damping ratio of silty clay is minimal. However, when the moisture content exceeds 12%, its impact becomes more significant. During the up fast stage (III) and convergent stage (IV), significant differences emerge between the curves for moisture contents of 8% and 12%, indicating that when the dynamic shear strain γ_d exceeds 10⁻⁴, the effect of different moisture contents on the damping ratio becomes significantly more pronounced.

Figure 6 shows the variation curves of the maximum damping ratio λ_max with moisture content at different stages. As illustrated in the figure, λ_max continuously increases with increasing moisture content. The growth rates vary significantly across different stages: in the stable stage (Ⅰ) and up slow stage (Ⅱ), the growth rates of λ_max are notably lower than in the up fast stage (Ⅲ) and convergent stage (Ⅳ). During the increase of moisture content from 8–16%, the change in λ_max in the stable stage (Ⅰ) is minimal, remaining essentially stable with a horizontal curve. In the up slow stage (Ⅱ), the change in λ_max is slightly larger than in the stable stage (Ⅰ), with a slight increase observed after the moisture content exceeds 12%. In the up fast stage (Ⅲ) and convergent stage (Ⅳ), λ_max increases significantly with increasing moisture content, showing similar trends and consistent slopes in both stages, demonstrating a strong linear relationship between the maximum damping ratio λ_max and moisture content.

In the stable stage (Ⅰ), the change in maximum damping ratio λ_max is very small, with a difference of only 0.0001 between moisture contents of 8% and 12%, and the curve remains generally horizontal, indicating that the impact of moisture content on the maximum damping ratio λ_max of silty clay is very weak in this stage. In the up slow stage (Ⅱ), the maximum damping ratio λ_max shows a slight increase when the moisture content rises from 12–16%, with a change of 0.0137, yet the curve remains approximately horizontal overall, indicating that the impact of moisture content on the maximum damping ratio λ_max remains low. In the up fast stage (Ⅲ) and convergent stage (Ⅳ), the curves show a linear upward trend, with the impact of moisture content on the maximum damping ratio λ_max significantly increasing. For every 4% increase in moisture content, the maximum damping ratio λ_max correspondingly increases by 0.04.

In summary, moisture content significantly impacts the damping ratio of silty clay. As moisture content increases, the thickness of the bound water around clay particles and the volume of free water in the pores both increase. The increase in bound water thickness leads to a reduction in effective contact between soil particles and an increase in viscosity, resulting in a greater propagation distance of shear waves within the soil, increased refraction and reflection, and faster attenuation of vibrational energy, which increases the soil's damping ratio. The increase in free water volume in the pores leads to a significant reduction in the soil's cohesion and internal friction angle, enhancing the soil's degradation effect, thereby affecting the damping characteristics of the soil.

3.2. Effect of confining pressure on damping ratio

Figure 7 illustrates the λ–γ_d relationship curves at various confining pressures. Increasing the confining pressure results in a continuous decrease in the damping ratio λ with dynamic shear strain γ_d. The λ–γ_d relationship curves exhibit decreasing overall slopes as confining pressure increases, transitioning from steep to gentler curves. Additionally, the rate of λ's increase with dynamic shear strain γ_d decreases.

These curves manifest in four stages: stable stage (Ⅰ), up slow stage (Ⅱ), up fast stage (Ⅲ), and convergent stage (Ⅳ), each displaying distinct curve shapes. During stable stage (Ⅰ), the damping ratio λ remains low, showing minimal variation with dynamic shear strain γ_d and presenting a horizontal curve. In up slow stage (Ⅱ), λ significantly increases, exhibiting a slight concave shape, indicating an accelerated rate of increase. In up fast stage (Ⅲ), the curve displays a significant increase with a pronounced concave feature, and the rate of λ's increase with dynamic shear strain γ_d continuously rises. The curve in convergent stage (Ⅳ) shows an outward convex shape, indicating a decreasing rate of λ's increase, gradually converging.

The λ–γ_d relationship curves under different confining pressures exhibit varying states across stages. During stable stage (Ⅰ), differences among curves at three confining pressures are minimal. In up slow stage (Ⅱ), significant differences emerge among curves at three confining pressures, with the curve at 200 kPa confining pressure being horizontal; as confining pressure decreases, the slope of the curve gradually increases, and the maximum damping ratio at 50 kPa confining pressure is six times that at 200 kPa.

In up fast stage (Ⅲ), the rate of λ's increase at low confining pressures significantly accelerates. In convergent stage (Ⅳ), curves at low confining pressures clearly converge.

During stable stage (Ⅰ), dynamic shear strain γ_d ranges from 0 to 3 × 10^− 6, with confining pressure exerting a relatively weak influence on λ; however, beyond 3 × 10^− 6, this influence becomes significant. In up slow stage (Ⅱ), dynamic shear strain γ_d ranges from 3 × 10^− 6 to 2.9 × 10^− 5, with the influence of confining pressure gradually increasing and peaking at this stage's end. In up fast stage (Ⅲ), dynamic shear strain γ_d ranges from 2.9 × 10^− 5 to 3.2 × 10^− 3; beyond 3.2 × 10^− 3, the influence of confining pressure on λ gradually diminishes. Therefore, during the cyclic loading process, the influence of confining pressure on λ is gradual.

Figure 7 also shows that λ initially increases nonlinearly and stabilizes gradually with the increase in dynamic shear strain γ_d. This trend correlates closely with changes in the pore structure of silty clay under vibration loading. Initially, due to low dynamic stress, the internal microstructure of the soil remains relatively undisturbed, resulting in lower energy consumption during stress propagation. With increased dynamic stress, the soil undergoes plastic deformation, gradually deteriorating the initial microstructure of silty clay. This increases frictional effects between particles and energy consumption under vibration loading, thereby indicating a gradual increase in the damping ratio of silty clay.

Figure 8 depicts the variation of the maximum damping ratio λ_max with confining pressure across different stages. λ_max exhibits a continuous decreasing trend with increasing confining pressure. The rates of decrease in λ_max vary across different stages: In the stable stage (Ⅰ), owing to the minor influence of confining pressure on the damping ratio, the curve remains horizontal. Within the up slow stage (Ⅱ), as the confining pressure increases from 50 kPa to 100 kPa, λ_max decreases by 41%; with a further increase to 200 kPa, λ_max decreases by 73%. The rate of decrease in λ_max in the up fast stage (Ⅲ) and the convergent stage (Ⅳ) is higher than that in the first two stages.

In summary, increasing confining pressure effectively reduces the damping ratio of silty clay. Research indicates that the soil damping ratio is primarily influenced by particle friction and soil compression deformation (Sutter et al., 2000). Higher confining pressure results in tighter particle contact in silty clay, thereby reducing energy losses due to friction. Additionally, the reduction in internal porosity of silty clay increases the propagation path of vibration waves, accelerating their speed and consequently lowering the damping ratio of silty clay (Ding et al., 2019).

4.1. Sensitivity analysis of damping ratio to moisture content

Based on Fig. 9, it is evident that the impact of moisture content on the damping ratio varies across different stages, indicating that the sensitivity of silty clay to moisture content changes with the duration of dynamic loading. In the stable stage (Ⅰ), an increase in moisture content from 8–12% results in a maximum damping ratio increase of 0.0001, and when the moisture content further increases to 16%, the maximum damping ratio increases by 0.0045. In the up slow stage (Ⅱ), an increase in moisture content from 8–12% results in a maximum damping ratio increase of 0.0047, and with the moisture content rising to 16%, the maximum damping ratio increases by 0.0184, indicating a greater impact of moisture content on the damping ratio of silty clay. In the up fast stage (Ⅲ), the impact of moisture content on the damping ratio of silty clay further intensifies; as moisture content rises from 8–12%, the maximum damping ratio increases by 0.0343, and when moisture content rises to 16%, the maximum damping ratio increases by 0.0783. In the convergent stage (Ⅳ), the impact of moisture content on the damping ratio of silty clay peaks; as moisture content rises from 8–12%, the maximum damping ratio increases by 0.0428, and when moisture content reaches 16%, the maximum damping ratio increases by 0.0839.

From the above analysis, it is evident that in the stable stage (Ⅰ) and the up slow stage (Ⅱ), the change in damping ratio remains relatively low when the moisture content increases from 8–12%. However, once the moisture content exceeds 12%, there is a significant increase in the damping ratio, indicating that the threshold value for the influence of moisture content on the damping ratio is 12%. In the up fast stage (Ⅲ) and convergent stage (Ⅳ), changes in all three levels of moisture content lead to significant variations in the damping ratio, suggesting that the effect of moisture content on the damping ratio intensifies with prolonged dynamic loading.

The sensitivity of the damping ratio of silty clay to moisture content varies over time. In the initial stages of dynamic loading, the variation in the damping ratio due to changes in moisture content is minimal. As the stable stage (Ⅰ) transitions to the up slow stage (Ⅱ), the damping ratio increases by a factor of 4.7 to 6.5. As the up slow stage (Ⅱ) transitions to the up fast stage (Ⅲ), the damping ratio increases by a factor of 5.9 to 8.9. As the up fast stage (Ⅲ) transitions to the convergent stage (Ⅳ), the damping ratio increases by a factor of 1.2 to 1.4.

In summary, the sensitivity of the damping ratio of silty clay to moisture content is influenced by both the moisture content value and the duration of dynamic loading. When the moisture content exceeds 12%, the damping ratio of silty clay increases significantly, particularly in the stable stage (Ⅰ) and the up slow stage (Ⅱ). This pattern arises because, in the early stages of the experiment, the dynamic loading duration on silty clay is relatively short, and its internal structure remains largely intact. Consequently, the increase in moisture content has a limited effect on the mechanical properties of silty clay, resulting in minimal changes in the damping ratio. As the duration of dynamic loading increases, the internal structure of silty clay begins to deteriorate, and the lubricating effect of water further accelerates structural damage. At this stage, the increase in moisture content significantly impacts the mechanical properties of silty clay, resulting in a noticeable increase in the damping ratio.

4.2. Sensitivity analysis of damping ratio to confining pressure

Figure 10 illustrates that the influence of confining pressure on the damping ratio varies across different stages. In the stable stage (Ⅰ), reducing the confining pressure from 200 kPa to 100 kPa results in an increase in the maximum damping ratio by 0.0013, and further reducing the confining pressure to 50 kPa results in an increase in the maximum damping ratio by 0.0025. At this stage, the effect of confining pressure on the damping ratio is relatively minor. In the up slow stage (Ⅱ), decreasing the confining pressure from 200 kPa to 100 kPa results in an increase in the maximum damping ratio by 0.0124, and further reducing the confining pressure to 50 kPa results in an increase in the maximum damping ratio by 0.0255, indicating a significant rise in the effect of confining pressure on the damping ratio. In the up fast stage (Ⅲ), reducing the confining pressure from 200 kPa to 100 kPa results in an increase in the maximum damping ratio by 0.0299, and further reducing the confining pressure to 50 kPa results in an increase in the maximum damping ratio by 0.0536. In the convergent stage (Ⅳ), decreasing the confining pressure from 200 kPa to 100 kPa results in an increase in the maximum damping ratio by 0.0190, and reducing the confining pressure to 50 kPa results in an increase in the maximum damping ratio by 0.0390. The effect of confining pressure on the damping ratio reaches its peak in the up fast stage (Ⅲ) and begins to decline in the convergent stage (Ⅳ).

From the above analysis, it is evident that in the stable stage (Ⅰ), changes in confining pressure have a minimal impact on the damping ratio. In the up slow stage (Ⅱ), the effect of confining pressure on the damping ratio gradually increases. In the later part of the up fast stage (Ⅲ), the effect of confining pressure on the damping ratio reaches its maximum, and in the subsequent convergent stage (Ⅳ), the impact begins to decrease. Thus, throughout the experiment, the effect of confining pressure on the damping ratio exhibits a trend of initially increasing and then decreasing.

The sensitivity of the damping ratio of silty clay to confining pressure demonstrates temporal variation. When transitioning from the stable stage (Ⅰ) to the up slow stage (Ⅱ), the damping ratio increases by a factor of 3.0 to 7.4. When moving from the up slow stage (Ⅱ) to the up fast stage (Ⅲ), the damping ratio increases by a factor of 6.4 to 29.0. When transitioning from the up fast stage (Ⅲ) to the convergent stage (Ⅳ), the damping ratio increases by a factor of 1.2 to 1.4.

4.3. Comparative analysis of damping ratio sensitivity to moisture content and confining pressure

Based on the above analysis, it can be concluded that changes in moisture content and confining pressure both affect the damping ratio of silty clay, but the sensitivity of the damping ratio to these two factors differs. Table 2 presents a comparative analysis of the sensitivity of the damping ratio to moisture content and confining pressure. The comparative results indicate that in the stable stage (Ⅰ), up slow stage (Ⅱ), up fast stage (Ⅲ), and convergent stage (Ⅳ), when both moisture content and confining pressure increase by 100%, the change in λ_max caused by the increase in moisture content is 3 times, 1.4 times, 2.6 times, and 4.6 times that caused by the increase in confining pressure, respectively. When confining pressure increases by 400%, the change in λ_max is 0.5 times, 1.4 times, 0.7 times, and 0.5 times that caused by a 100% increase in moisture content, respectively. When both moisture content and confining pressure increase by 100%, the change in λ_max caused by moisture content is always higher than that caused by confining pressure, showing a trend of initially decreasing and then increasing. Comparing the change in λ_max caused by a 400% increase in confining pressure with that caused by a 100% increase in moisture content, only in the up slow stage (Ⅱ) is the change caused by confining pressure higher than that caused by moisture content; in all other stages, the change caused by confining pressure is lower, exhibiting a trend of initially increasing and then decreasing.

In summary, the sensitivity of the damping ratio of silty clay to moisture content is higher than to confining pressure, with significant variations across different stages. The greatest difference is observed in the convergent stage (Ⅳ), where the sensitivity of the damping ratio to moisture content is 4.6 times that to confining pressure. The smallest difference is in the up slow stage (Ⅱ), where the sensitivity to moisture content is 1.4 times that to confining pressure.

Table 2

Comparative analysis of the sensitivity of damping ratio to moisture content and confining pressure.
Stage	Variables		Change in maximum damping ratio (λ_max)	Comparative analysis
Stable stage(Ⅰ)	Moisture content	8%→12% (50%)	0.0001	When both moisture content and confining pressure increase by 100%, the change in λ_max caused by moisture content is 3 times that caused by confining pressure. When confining pressure increases by 400%, the change in λ_max is 0.5 times that caused by a 100% increase in moisture content.
		12%→16% (33.3%)	0.0044
		8%→16% (100%)	0.0045
	Confining pressure	50 kPa→100 kPa (100%)	0.0013
		100 kPa→200 kPa (200%)	0.0012
		50 kPa→200 kPa (400%)	0.0025
Up slow stage(Ⅱ)	Moisture content	8%→12% (50%)	0.0047	When both moisture content and confining pressure increase by 100%, the change in λ_max caused by moisture content is 1.4 times that caused by confining pressure. When confining pressure increases by 400%, the change in λ_max is 1.4 times that caused by a 100% increase in moisture content.
		12%→16% (33.3%)	0.0137
		8%→16% (100%)	0.0184
	Confining pressure	50 kPa→100 kPa (100%)	0.0124
		100 kPa→200 kPa (200%)	0.0131
		50 kPa→200 kPa (400%)	0.0255
Up fast stage(Ⅲ)	Moisture content	8%→12% (50%)	0.0343	When both moisture content and confining pressure increase by 100%, the change in λ_max caused by moisture content is 2.6 times that caused by confining pressure. When confining pressure increases by 400%, the change in λ_max is 0.7 times that caused by a 100% increase in moisture content.
		12%→16% (33.3%)	0.0440
		8%→16% (100%)	0.0783
	Confining pressure	50 kPa→100 kPa (100%)	0.0299
		100 kPa→200 kPa (200%)	0.0237
		50 kPa→200 kPa (400%)	0.0536
Convergent stage(Ⅳ)	Moisture content	8%→12% (50%)	0.0428	When both moisture content and confining pressure increase by 100%, the change in λ_max caused by moisture content is 4.6 times that caused by confining pressure. When confining pressure increases by 400%, the change in λ_max is 0.5 times that caused by a 100% increase in moisture content.
		12%→16% (33.3%)	0.0411
		8%→16% (100%)	0.0839
	Confining pressure	50 kPa→100 kPa (100%)	0.0184
		100 kPa→200 kPa (200%)	0.0206
		50 kPa→200 kPa (400%)	0.0390

This study investigates the effects of moisture content and confining pressure on the damping ratio of silty clay and compares the sensitivity of the damping ratio to these two factors, yielding the following findings:

(1) The λ–γ_d relationship curves for different moisture contents and confining pressures exhibit significant stage–specific characteristics: the higher the moisture content, the steeper the slope of the λ–γ_d curve in each stage; conversely, the higher the confining pressure, the gentler the slope of the λ–γ_d curve in each stage.

(2) An increase in moisture content leads to an increase in the damping ratio of silty clay, whereas an increase in confining pressure results in a decrease in the damping ratio.

(3) When both moisture content and confining pressure are increased by 100%, the change in λ_max due to moisture content is 3 times, 1.4 times, 2.6 times, and 4.6 times that due to confining pressure in the respective stages, showing a trend of initially increasing and then decreasing.

(4) The sensitivity of the damping ratio to moisture content and confining pressure varies, with the damping ratio being more sensitive to moisture content than to confining pressure. This sensitivity difference is most pronounced in the convergent stage (Ⅳ), where it is 4.6 times, and least in the up slow stage (Ⅱ), where it is 1.4 times.

Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Correspondence and requests for materials should be addressed to Y.P.

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Author Contribution

J.S.C: conceptualization, investigation, writing and preparing the original draft; G.Q.C: methodology, formal analysis, resource, funding acquisition, supervision; Y.G.P: writing, reviewing and editing; Y.C.Z: supervision, writing, reviewing and editing; H.J.Z: resource, funding acquisition, supervision; S.Y.S: writing, reviewing and editing; F.L: writing, reviewing and editing.

Acknowledgements

This research was supported by the authors appreciate the financial support of the National Natural Science Foundation of China (Grant No.: 52078431).

Data Availability

The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

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No competing interests reported.

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WITHDRAWN: An experimental study on the effects of moisture content and confining pressure on the damping ratio of silty clay

Status:

Version 1

Editorial Note

Abstract

Figures

1. Introduction

2. Sample preparation and experimental scheme

2.1. Sample preparation

2.2. Experimental scheme

2.3. Data processing

3.Results

3.1. Effect of moisture content on damping ratio

3.2. Effect of confining pressure on damping ratio

4.Discussion

4.1. Sensitivity analysis of damping ratio to moisture content

4.2. Sensitivity analysis of damping ratio to confining pressure

4.3. Comparative analysis of damping ratio sensitivity to moisture content and confining pressure

5. Conclusions

Declarations

Competing interests

Additional information

Author Contribution

Acknowledgements

Data Availability

References

Additional Declarations

Status:

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