The Influence of Vibration Frequency and Vibration Duration on the Mechanical Properties of Zhanjiang Formation Structural Clay

Abstract

Vibration frequency and vibration duration are disturbance factors for the structural properties of clay. This study investigates how the vibration frequency and vibration duration from construction disturbances affect the mechanical properties of Zhanjiang Formation structural clay. An electric, frequency-adjustable vibration table applied varying frequencies and durations of vibration to undisturbed soil, creating structural clay samples with different disturbance degrees. Unconfined compressive strength tests and one-dimensional consolidation compression tests were conducted on these samples to obtain disturbance degrees $R{D}_q$ and $R{D}_S$, defined by strength loss values and compression deformation characteristics, respectively. Orthogonal experiments and grey correlation analysis were used to explore the effects of vibration frequency and vibration duration on the mechanical properties of Zhanjiang Formation structural clay. The results indicated that disturbance degrees $R{D}_q$ and $R{D}_S$ increased linearly with increase in vibration frequency and vibration duration. Range analysis was conducted using two-factor three-level orthogonal experiment of disturbance degrees, and a grey relational analysis model was established to determine the primary and secondary effects of vibration duration and vibration frequency on the mechanical properties of Zhanjiang Formation structural clay. The results demonstrated that the findings from orthogonal experiments and grey relational analysis were consistent, showing that vibration duration had a more significant impact than vibration frequency on the mechanical properties of structural clay. The conclusion suggests that vibration disturbance manifests as a “fatigue damage effect”. Continuous vibration disturbance progressively weakens the cementation bonds between soil particles due to “accumulated” energy, leading to gradual fracture and destruction. With constant vibration frequency, longer durations, or with constant duration, higher frequencies intensify the “fatigue damage effect” of vibration disturbance. Furthermore, during vibration disturbance, Zhanjiang Formation structural clay shows a more pronounced “fatigue damage effect” from vibration duration than from vibration frequency, with cementation bonds between soil particles weakening more effectively due to “accumulated” energy. The research findings enhance the understanding of how vibration frequency and vibration duration from disturbance sources impact the mechanical properties of Zhanjiang Formation structural clay, offer theoretical guidance for using construction vibration machinery, and provide a reference for preventing and controlling soil disturbance.

1. Introduction

Capitalizing on strategic Chinese initiatives such as the Beibu Gulf City Cluster, Guangdong–Hong Kong–Macao Greater Bay Area, Hainan Free Trade Zone, and the pivotal position of the Belt and Road initiative, Zhanjiang, China, has experienced significant economic growth in recent years. The city’s expansion and burgeoning population have prompted a surge in large-scale construction projects, including housing and rail transit. Numerous infrastructure and economic projects are founded on the Zhanjiang Formation structural clay. Frequent construction activities, including pile foundations and excavation pits, disturb the surrounding soil to varying degrees. Zhanjiang Formation structural clay, characterized by its strong structure and high sensitivity, is highly susceptible to changes in soil structure and sudden decreases in strength, which can lead to various engineering problems [1,2]. Investigating the patterns and mechanisms of disturbance impacts on Zhanjiang Formation structural clay has emerged as a critical area of research. Zhang Chenghou [3] examined the geotechnical properties of Zhanjiang clay and associated disturbance-related issues, revealing that undisturbed clay with strong structure displays a pronounced structural yield stress exceeding the overlying effective stress. Tang Bin et al. [4] investigated the effect of the disturbance degree on the thixotropic properties of Zhanjiang Formation structural clay. They concluded that the disturbance duration of soil is positively correlated with its disturbance degree. They found that, at a constant disturbance degree, both the extent of strength recovery and the proportion of thixotropic strength recovery increase with rest duration, whereas thixotropy sensitivity diminishes over time. Zang Meng et al. [5] performed experiments to assess the dynamic characteristics of Zhanjiang Formation structural clay under cyclic loads, finding that the clay demonstrates brittle failure under such conditions. While these studies offer essential insights into the engineering consequences of disturbances on Zhanjiang Formation structural clay, they are limited to the effects of disturbance on soil structure.

However, investigating from the characteristics of disturbance sources may enable a more in-depth exploration into the effects of disturbances on the mechanical properties of the Zhanjiang Formation structural clay at the fundamental level, providing theoretical references for disturbance prevention in foundation soils. While Deng Yongfeng [6] and Miao Yonghong et al. [7] have investigated the compression characteristics of soft soil based on vibration duration and vibration frequency, concluding that vibration duration-frequency significantly affects the compression deformation characteristics of soft soil, Liu Juanjuan [8] and Zhang Binghui et al. [9] have established the relationship between vibration duration and the disturbance degree for evaluating soil disturbances. However, these studies have not conducted a comparative analysis of how vibration frequency and vibration duration, as disturbance factors, impact the mechanical properties of structural clay. Indeed, both vibration frequency and vibration duration influence the source of disturbance, with higher frequencies or longer durations resulting in increased energy transfer and greater soil disturbance, thereby significantly altering its mechanical properties. The disturbance degree of soil describes both the state of deterioration and the associated changes in mechanical properties. Therefore, it is necessary to analyze the mechanical properties of the Zhanjiang Formation structural clay based on disturbance degree and study the impact of vibration frequency and vibration duration as disturbance sources on its disturbed mechanical properties.

This paper focuses on Zhanjiang Formation structural clay as the subject of study. An electrically controlled variable frequency vibration table is used to prepare disturbed soil samples at varying vibration frequencies and vibration durations, simulating construction disturbances. Laboratory tests, including unconfined compressive strength and one-dimensional compression, were conducted to investigate the impact of vibration frequency-duration on the disturbance of Zhanjiang Formation structural clay. Additionally, the study employs orthogonal experiments and grey correlation analysis to explore the influence of vibration frequency and duration on the mechanical properties of Zhanjiang Formation structural clay and to elucidate the underlying mechanisms. This research offers theoretical guidance for the use of vibration machinery and informs strategies for mitigating disturbances in Zhanjiang Formation structural clay foundations.

2. Experimental Investigation of Disturbance Effects and Mechanical Properties of Zhanjiang Formation Structural Clay

2.1. Test Soil

The soil samples were collected from the Baosteel Zhanjiang Steel Industrial Park, located on Donghai Island in Zhanjiang City, Guangdong Province, China. The extracted soil samples were cut into cylindrical columns with a diameter of 100 mm and a height of 200 mm using a soil cutter. The soil samples were placed in soil boxes, sealed with wax, and subsequently wrapped with sealing tape and cling film for protection. Following the “Standard for Geotechnical Test Methods”, various physical properties of the undisturbed Zhanjiang Formation structural clay were assessed using laboratory geotechnical testing procedures. The specific properties are detailed in

Table 1. Basic physical properties of Zhanjiang Formation structural clay (Adapted from Ref. [9]).

Water Content ($\mathit{w}/\mathbf{\%}$)	Natural Density $\mathit{\rho }$ ($\mathit{g}/{\mathit{cm}}^3$)	Dry Density $\mathit{\rho }$ ($\mathit{g}/{\mathit{cm}}^3$)	Specific Gravity $\mathit{G}\mathit{s}$	Plasticity Index ${\mathit{I}}_{\mathit{P}}$	Liquid Index ${\mathit{I}}_{\mathit{L}}$	Void Ratio $\mathit{e}$	Sensitivity $\mathit{S}\mathit{r}$
47.22	1.74	1.18	2.72	25.83	0.81	1.29	4.01

.

2.2. Preparation of Vibration Disturbance Samples

Test soil samples were prepared using an electric frequency-modulated vibration table provided by Hebei Tengfei Test Instrument Co., Ltd., Hengshui, China. Vertical vibrations were set to an amplitude of 0.6 mm. According to the related literature [4], similar Zhanjiang Formation structured clay samples reached a 100% disturbance degree after vibrating at 60 Hz for 90 min. To investigate the disturbance process more thoroughly and ensure a uniform distribution of test data, three fixed frequencies of 20, 35, and 50 Hz were selected within the 0–50 Hz range. Vibration durations of 30, 60, and 90 min were chosen. Soil samples were placed in a triaxial cell saturator affixed to the vibration table to undergo vibration, resulting in disturbance samples at various vibration frequencies and vibration durations.

2.3. Evaluation of Soil Disturbance

Numerous scholars domestically and internationally [10,11,12,13,14,15,16] have conducted relevant research on the definition and evaluation of the disturbance degree of soil following sampling. Scholars have introduced a range of approaches to quantify the disturbance degree, utilizing indicators such as variations in pore water pressure, $e-\lg p$ curves, and alterations in soil strength pre- and post-sampling. In this study, the disturbance degree is determined by two aspects: the reduction in unconfined compressive strength and the alterations in compressibility properties.

Disturbance degree is quantified by the reduction in unconfined compressive strength [8], with the following formula:

$${\mathit{RD}}_q={\displaystyle \frac{q_u-{q_u}^{\prime }}{q_u}}$$

(1)

In the formula, $RD$ is the disturbance degree defined by the strength characteristics of the soil, $q_u$ is the unconfined compressive strength of the undisturbed soil, and ${q_u}^{\prime }$ is the unconfined compressive strength of the disturbed soil. The closer the ${\mathit{RD}}_{\mathrm{q}}$ value is to 1, the greater the disturbance degree of the soil sample. Utilizing the compressibility properties to define the disturbance degree, Butterfield [17] analyzed a large amount of consolidation test data and described the consolidation compression curve using a double logarithmic coordinate system of specific volume $v=1+e$ and consolidation pressure $p$. Z. Hong and K. Onitsuka [16] proposed the following calculation formula:

$${\mathit{RD}}_s={\displaystyle \frac{C_{clb}}{C_{clr}}}\times 100\%$$

(2)

where ${\mathit{RD}}_s$ is the disturbance degree defined by the deformation characteristics of the soil, and $C_{clb}$ is the compression index before yielding of the disturbed soil sample, which is the slope of the compression curve of the disturbed soil sample in the pre-yield stage. Meanwhile, $C_{clr}$ is the compression index of the remolded soil sample, which is the slope of the compression curve of the remolded soil sample under the $ln(1+e)-lgp$ coordinates. The closer the ${\mathit{RD}}_{\mathrm{s}}$ value is to 100%, the greater the disturbance degree of the soil sample.

Unconfined compressive strength tests were conducted on the samples. The unconfined compressive strength of the undisturbed soil sample was 241.94 kPa. The results of the unconfined compressive strength test for the disturbed samples are shown in

Table 2. Unconfined compressive strength of disturbed samples.

Vibration Frequency/Hz	Unconfined Compressive Strength (kPa)
	30 min	60 min	90 min
20 Hz	187.57	173.24	174.35
35 Hz	166.79	148.15	137.19
50 Hz	139.89	116.89	101.94

. The relationship between vibration frequency/duration and unconfined compressive strength is illustrated in Figure 1. It can be inferred that higher vibration frequencies correspond to lower sample strength at a fixed duration, and longer vibration durations result in lower strength at a constant frequency. Disturbed soil exhibits lower strength compared to undisturbed soil.

One-dimensional consolidation compression tests were conducted on the samples, with results presented in

Table 3. One-dimensional compression results of samples.

Condition			P/kPa
			12.5	25	50	100	200	400	800	1600	3200
Undisturbed			1.2929	1.294	1.2871	1.2697	1.2409	1.1909	1.1233	0.7539	0.6950
Disturbed	20 Hz	30 min	1.2885	1.2861	1.2827	1.2401	1.1938	1.1287	1.0335	0.7272	0.6707
		60 min	1.2632	1.2605	1.2596	1.2205	1.1502	1.1005	1.0147	0.7081	0.6629
		90 min	1.2545	1.2505	1.2482	1.1812	1.1223	1.0445	0.9443	0.6943	0.6613
	35 Hz	30 min	1.2873	1.2858	1.2812	1.2329	1.1772	1.0913	0.9313	0.7149	0.6703
		60 min	1.2600	1.2565	1.2552	1.2111	1.1497	1.0835	0.9278	0.7011	0.6610
		90 min	1.2524	1.2492	1.2484	1.1862	1.1148	1.0425	0.9160	0.6851	0.6586
	50 Hz	30 min	1.2836	1.2828	1.2772	1.2292	1.1662	1.0877	0.9022	0.7037	0.6640
		60 min	1.2570	1.2541	1.2582	1.2075	1.1229	1.0371	0.8922	0.6832	0.6579
		90 min	1.2512	1.2486	1.2452	1.1790	1.0914	1.0204	0.8835	0.6767	0.6557
Remolded			1.2082	1.1198	1.0506	0.9506	0.89056	0.8105	0.7385	0.6331	0.5768

. The $e-lgp$ curves under different test conditions are depicted in Figure 2a–c. The figures show that the undisturbed sample’s compression curve is positioned above those of disturbed samples under all test conditions, exhibiting the longest linear segment extension. The void ratio of the samples decreases gradually with increasing vertical load. At a vertical load of 50 kPa, the rate of void ratio decrease accelerates; beyond 400 kPa, it declines sharply until reaching 3200 kPa. This suggests that under higher pressures, the sample densifies and disturbances have less impact on its compressive deformation properties. At a void ratio of 0.51 $e_0$, disturbance effects on compressive deformation characteristics become negligible, with all curves intersecting at this point. For disturbed samples, the compression curves move downward with increasing vibration duration at the same vibration frequency. The longer the vibration duration, the lower the position of the compression curve, indicating that the compressibility of the soil sample decreases with the increase of vibration duration at a certain vibration frequency. The main reason is that the longer the vibration duration, the greater the energy transferred to the soil, resulting in greater internal disturbance and a lower void ratio under the same vertical pressure. With equal vibration durations, higher frequency results in a lower compression curve position, signifying decreased soil compressibility with increasing frequency. The primary cause is that the higher vibration frequency leads to more energy absorption and greater internal disturbance, resulting in a lower void ratio under the same vertical pressure [7]. Remolded soil samples exhibit a single-line compression curve, which is located below all the compression curves of the disturbed soil samples. As vertical pressure increases, compression curves of both undisturbed and variously disturbed soil samples gradually converge with that of remolded soil samples.

Figure 2d presents the $ln(1+e)-lgp$ curves for each sample under different conditions, from which the slopes of these compression curves are derived and summarized in

Table 4. Slopes of the compression curves for each sample under different conditions.

Vibration Duration/min	Slope of the Compression Curve
	${\mathit{C}}_{\mathit{clb}}$			${\mathit{C}}_{\mathit{clr}}$
	20 Hz	35 Hz	50 Hz	20 Hz	35 Hz	50 Hz
30	−0.0423	−0.0439	−0.0466	−0.1400
60	−0.0445	−0.0501	−0.0598
90	−0.0466	−0.0562	−0.0714

.

Using Equations (1) and (2), the disturbance degrees, ${\mathit{RD}}_q$ and ${\mathit{RD}}_s$, defined by strength characteristics and deformation characteristics, respectively, are calculated and presented in

Table 5. Disturbance degree $RD$.

Mechanical Properties	Vibration Duration/min	Vibrating Frequency/Hz
		20	35	50
Strength (${\mathit{RD}}_q$) (Reprinted from Ref. [9])	30	0.22	0.31	0.42
	60	0.28	0.39	0.52
	90	0.28	0.43	0.58
Deformation (${\mathit{RD}}_s$)	30	30.2%	31.4%	33.3%
	60	31.8%	35.8%	42.7%
	90	33.3%	40.1%	51%

.

At a vibration frequency of 20 Hz, increasing the vibration duration from 30 min to 90 min, the increases in disturbance degree ${\mathit{RD}}_q$ and ${\mathit{RD}}_s$ are 0.06 and 3.1%, respectively. When the vibration frequency is 50 Hz, extending the vibration duration from 30 min to 90 min, the increases in disturbance degree ${\mathit{RD}}_q$ and ${\mathit{RD}}_s$ are 0.16 and 17.7%, respectively. With a vibration duration of 30 min, increasing the frequency from 20 to 50 Hz, the increases in disturbance degree ${\mathit{RD}}_q$ and ${\mathit{RD}}_s$ are 0.20 and 3.1%, respectively. For a vibration duration of 90 min, an increase in frequency from 20 to 50 Hz, the increases in disturbance degree ${\mathit{RD}}_q$ and ${\mathit{RD}}_s$ are 0.30 and 17.7%, respectively.

Figure 3 and Figure 4 show the variations in disturbance degrees ${\mathit{RD}}_q$ and ${\mathit{RD}}_s$ with respect to vibration duration and vibration frequency, respectively. It can be observed from Figure 3 and Figure 4 that both disturbance degrees ${\mathit{RD}}_q$ and ${\mathit{RD}}_s$ exhibit a linear increasing trend with the increase in vibration duration and vibration frequency. It is apparent that both ${\mathit{RD}}_q$ and ${\mathit{RD}}_s$ can represent the disturbance degree well. Comparing the two, we can see that in terms of parameter acquisition, the disturbance degree ${\mathit{RD}}_q$, defined by strength, is more convenient than ${\mathit{RD}}_s$, defined by deformation, as it can directly utilize the original experimental data. Furthermore, as shown in Table 5, under the same vibration conditions, the disturbance degree ${\mathit{RD}}_q$, defined by strength, is more sensitive than the disturbance degree ${\mathit{RD}}_s$, defined by deformation, with ${\mathit{RD}}_q$ ranging from 0.22 to 0.58, while ${\mathit{RD}}_s$ ranges from 30.2% to 51%. The analysis suggests that the observed changes in the disturbance degree are due to alterations in the soil structure caused by vibration. Prolonged vibration duration transmits more energy into the soil, increasing internal disturbance; likewise, with the vibration duration increases, a higher frequency intensifies energy absorption by the soil, further augmenting internal disturbance. Consequently, increases in both vibration duration and vibration frequency result in elevated soil disturbance degrees. Vibration duration and vibration frequency are important factors in soil vibration disturbance and significantly affect the mechanical properties of structural clay. In practical engineering applications, vibrations can cause disturbance damage to soil, leading to the degradation of the soil’s mechanical properties. Different construction vibration durations and vibration frequencies can cause varying degrees of disturbance damage to the soil, which is detrimental to both construction and maintenance of projects. Therefore, it is possible to select appropriate construction machinery and develop reasonable construction plans based on the vibration duration and vibration frequency corresponding to the disturbance degree of the soil in order to mitigate the harmful effects of vibration on the project. On the other hand, the disturbance degree after vibration can reflect the strength or deformation indicators of the soil, providing a more intuitive guidance for controlling construction vibrations during construction.

3. Orthogonal Experimental Design and Analysis of Disturbance Degree in Zhanjiang Formation Structural Clay

3.1. Experimental Design

Given that vibration duration and frequency can induce structural disturbances in clay, which in turn affect the strength and deformation characteristics of Zhanjiang Formation structural clay, conducting an orthogonal experiment to assess the disturbance degrees ${\mathit{RD}}_q$ and ${\mathit{RD}}_s$ is advantageous. This will allow exploration of how disturbance source characteristics, like vibration frequency and vibration duration from construction machinery, impact the clay. The experimental design evaluates the impacts of vibration duration and frequency on disturbance, employing a two-factor, three-level design as depicted in

Table 6. Experimental factor levels.

Factor Level	Horizontal
	1	2	3
Duration (min)	30	60	90
Frequency (Hz)	20	35	50

.

3.2. Experimental Variance Analysis

The range analysis method is a technique used to analyze experimental data by calculating and comparing the range sizes. The underlying idea is the larger the range, the greater the impact of the factor on thixotropy, and thus the more important it is; the smaller the range, the lesser the impact of the factor on thixotropy [18,19]. Therefore, this analytical method and approach can be employed to examine the effects of soil disturbance.

By comparing the range $R_j$ values from the results of the orthogonal experiment on disturbance degree in

Table 7. Results of the orthogonal experiment on disturbance degree.

Experiment No.		Duration (min)	Frequency (Hz)	Experimental Results
		1 (t)	2 (f)	Disturbance Degree ${\mathit{RD}}_{\mathit{q}}$	Disturbance Degree ${\mathit{RD}}_{\mathit{s}}$ (%)
1		1	1	0.22	30.2
2		1	2	0.28	31.8
3		1	3	0.28	33.3
4		2	1	0.31	31.4
5		2	2	0.39	35.8
6		2	3	0.43	40.1
7		3	1	0.42	33.3
8		3	2	0.52	42.7
9		3	3	0.58	51
Horizontal sum	$k_1$	0.78	0.95	95.3	94.9
	$k_2$	1.13	1.19	107.3	110.3
	$k_3$	1.52	1.29	127	124.4
Horizontal mean	$k_1$	0.26	0.317	31.767	31.633
	$k_2$	0.377	0.397	35.767	36.767
	$k_3$	0.507	0.430	42.333	41.467
Range $R_j$	$R_t$			0.247	10.567
	$R_f$			0.113	9.833

, when the disturbance degree $\mathit{RD}$ is defined by strength, $R_t=0.247$, and $R_f=0.113$; when defined based on deformation, $R_t=10.567$, $R_f=9.833$. Regardless of whether it is disturbance degree ${\mathit{RD}}_q$ or ${\mathit{RD}}_s$, $R_t>R_f$, indicating that the order of significance of the experiment factors on the experiment indicators is vibration duration (min)—vibration frequency (Hz), meaning that vibration duration has a greater impact on disturbance than vibration frequency.

4. Grey Relational Analysis of Disturbance Sources in Zhanjiang Formation Structural Clay

4.1. Analysis Principle

Comparability issues often arise when studying the factors influencing disturbance sources, particularly when the impact of either duration or frequency is considered in isolation, which hampers the ability to draw convincing conclusions. Consequently, it is essential to conduct experimental research that simultaneously investigates the effects of both duration and frequency for comparative analysis to ascertain their influence on disturbances. This approach reveals the impact of vibration duration and frequency on the mechanical properties in Zhanjiang Formation structural clay. Furthermore, grey relational analysis can complement variance analysis of orthogonal experiments for enhanced comparative insights. Grey relational analysis is a comparative method that assesses the similarity or dissimilarity of developmental trends among factors. During this analysis, greater similarity in variation and development trends between two factors indicates higher synchronicity and relational degree. Conversely, less similarity in these trends corresponds to a reduced relational degree [20,21,22,23].

4.2. Grey Relational Analysis

Assume there is a reference sequence $X_0=\{x_0(k), k=1, 2, \cdots n\}$ and a comparative sequence $X_i=\{x_i(k), k=1, 2, \cdots n\}$, then the relational coefficient at point $k$ between sequence $X_0$ and $X_i$ is denoted as ${\xi }_k$.

$${\xi }_k={\displaystyle \frac{{\min }_i{\min }_k\left|x_i(k)-x_0\left.(k)\right|+\rho {\max }_i{\max }_k\left|x_i(k)-x_0\left.(k)\right|\right.\right.}{\left|x_i(k)-x_0\left.(k)\right|+\rho {\max }_i{\max }_k\left|x_i(k)-x_0\left.(k)\right|\right.\right.}}$$

(3)

In the formula, $\rho$ is the resolution coefficient, which lies between 0 and 1, and is typically set at 0.5.

Equation (3) is simplified to Equation (4).

$${\xi }_i(k)={\displaystyle \frac{\Delta (\min )+\rho \Delta (\max )}{{\Delta }_i(k)+\rho \Delta (\max )}}$$

(4)

In the equation, Δ(min) denotes the minimum second-order difference, and Δ(max) signifies the maximum second-order difference.

Since the relational coefficient represents the correlation degree between the comparative sequence and the reference sequence at each moment (i.e., each point on the curve), there is not just a single value, and the information is too dispersed for a holistic comparison. Therefore, we consolidate the relational coefficients at each moment (i.e., each point on the curve) into a single value, namely by calculating their average value. This average value serves as a quantitative representation of the correlation degree between the comparative sequence and the reference sequence, denoted as the correlation degree ${\gamma }_i$.

$${\gamma }_i={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\xi }_i(k)}$$

(5)

For the results of the disturbance degree, grey relational analysis is conducted, taking the disturbance degree as the reference sequence, and the duration of factor A and the frequency of factor B as the comparative sequences. Since the two factors have different physical meanings, resulting in different units of measurement, dimensionless processing is first carried out for ease of comparison. Then, the relational coefficients are calculated using Equation (4), with $\Delta (\min )=0$ and $\Delta (\max )=1.3900$. Finally, the grey relational degrees are calculated using Equation (5) and are denoted as ${\gamma }_1=0.6769$ and ${\gamma }_2=0.6072$, respectively.

Through the calculation of the relational degrees, it is found that both the frequency of factor A and the duration of factor B have a significant impact on the disturbance. According to the principles of grey relational analysis, the larger the relational coefficient, the greater the impact. Therefore, comparing the influencing factors ${\gamma }_1$ (duration) and ${\gamma }_2$ (frequency), the disturbances caused by duration are significantly more pronounced than those caused by frequency. This is consistent with the results analyzed from the previous orthogonal experimental analysis.

5. Analysis of Influence Mechanisms

Firstly, from the physical and mechanical property indices of Zhanjiang Formation structural clay (Table 1), it can be observed that the experimental soil has a relatively high water content of 47.22%, a high void ratio of 1.29, and a high sensitivity ratio ($Sr=4.01$), demonstrating poor physical properties. However, the undisturbed soil possesses a robust unconfined compressive strength (241.94 kPa), reflecting superior mechanical characteristics. Figure 5a reveals that the structure of the undisturbed Zhanjiang Formation structural clay is composed of aggregates that are mutually stacked and interconnected, forming an open honeycomb structure, accompanied by some flocculent structures. Soil particles are spatially connected and arranged to form a soil skeleton, resulting in voids within the framework. Additionally, due to a larger specific surface area and the presence of strong cementation bonds that are resistant to destruction, the soil exhibits a certain degree of structural strength. The Zhanjiang Formation structural clay presents an atypical juxtaposition of weak physical properties and robust mechanical characteristics, typifying a highly sensitive clay with pronounced structural attributes [24,25,26,27]. Although soil cohesion from cementation bonds may resist structural damage, the soil undergoes cumulative damage during the process of cyclic loading with vibrational disturbances., known as “fatigue damage”. Under the combined action of the vertical vibration amplitude and the sustained excitation force, soil samples are subjected to long-term cyclic loading, resulting in the formation of damage defects in the sample structure. As the vibration continues, these damage defects accumulate and expand, causing a gradual deterioration of the mechanical properties of the samples, thereby manifesting a “fatigue damage effect”. Consequently, when the Zhanjiang Formation structural clay is subjected to vibrational disturbances, the continuous accumulation of “weakening energy” from the vibrations gradually diminishes the cementation bonds between the soil particles, leading to their eventual fracture and failure. Subsequently, the clay mineral aggregates disperse, primarily as flakes or large flaky particles (Figure 5b), compromising the soil’s structural integrity.

Secondly, the changes in disturbance degree $RD$ with vibration duration and frequency (Figure 3 and Figure 4) show that when the sample is subjected to low-frequency, short-duration vibrations, both disturbance degrees $R{D}_q$ and $R{D}_s$ are minimal. With increased vibration duration and vibration frequency, the disturbance degree correspondingly escalates. This is likely because the principle of vibration entails the transfer of vibrational energy to the soil sample, causing forced disturbance of the soil particles upon energy reception. Both the frequency and duration of the excitation force from the vibration table influence the degree of disturbance damage to the sample. Longer vibration durations at any given frequency, or higher frequencies for any given duration, intensify the “fatigue damage effect” of the vibrational disturbance. However, the critical vibration duration and vibration frequency needed to disrupt the cementation bonds within the soil’s clay mineral aggregates vary, leading to inconsistent disturbance damage from different vibration durations and frequencies. Integrating the results from orthogonal experiments on disturbance degree with grey relational analysis reveals that duration has a more substantial impact on mechanical properties than frequency due to the “fatigue damage effect” of vibrational disturbance. Continuous vibrational disturbance entails an accumulation of fatigue damage. Prolonged exposure to vibrational disturbance progressively weakens the cementation bonds between soil particles due to “cumulative” energy, resulting in gradual fracture and failure. Although both low-frequency and high-frequency vibrations are likely to destroy the cementation bonds between soil particles, it requires the reinforcement of duration. The “cumulative” weakening energy between the cementation bonds of soil particles is continuously transmitted and accumulates more efficiently, making the “fatigue damage effect” of soil vibration disturbance more pronounced. Consequently, the duration effect of the disturbance source has a more significant impact on the mechanical properties of the structural clay.

6. Conclusions

This study investigates the effects of vibration frequency and vibration duration on the mechanical properties of Zhanjiang Formation structural clay, as well as the mechanisms of action, by conducting vibration disturbance tests on the frequency–duration relationship. The main conclusions are as follows:

1.

Both the disturbance factor ${\mathit{RD}}_q$, defined by strength, and the disturbance factor ${\mathit{RD}}_s$, defined by deformation, exhibit a linear increasing trend with the increase of vibration duration and vibration frequency. As vibration duration and vibration frequency increase, so does the degree of soil disturbance. These two parameters are important factors in the vibrational disturbance of soil.

2.

Vibration duration and vibration frequency both disturb the structural integrity of clay. Through a two-factor, three-level orthogonal experiment assessing disturbance degrees, whether defined by strength as disturbance degree ${\mathit{RD}}_q$ or by deformation as ${\mathit{RD}}_s$, range analysis reveals $R_t>R_f$, indicating a greater impact of vibration duration on disturbance compared to vibration frequency. Grey relational analysis indicates that the relational degrees of the vibration duration and vibration frequency factors are quite close, both significantly impacting disturbance, with the duration having a greater effect than frequency. The grey relational analysis results align with the patterns observed in the orthogonal experiment.

3.

Zhanjiang Formation structural clay, characterized by its strong cementation, is not easily destroyed. However, external vibration can gradually weaken and even destroy the cementation bonds between soil particles. Moreover, vibration disturbance functions as a “fatigue damage effect”, wherein prolonged exposure weakens the cemented bonds between soil particles due to “cumulative” energy, eventually causing fracture and destruction. Both frequent small-scale and large-scale vibrations can destroy the cemented bonds between soil particles, contingent upon sufficient duration.