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Propagation Laws of Ultrasonic Continuous Signals at the Transmitting Transducer–Soil Interface

Agriculture

August 2024
14(9):1470

DOI:10.3390/agriculture14091470

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CC BY 4.0

Authors:

Caiyun Lu

China Agricultural University

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Ultrasonic detection is one of the main methods for information detection and has advantages in soil detection. Ultrasonic signals attenuate in soil, resulting in unique propagation laws. This paper studies the propagation laws of ultrasound in soil, focusing on the propagation characteristics of ultrasonic continuous signals at the transducer–soil interface. This study uses excitation frequency and amplitude as experimental factors and employs the discrete element simulation method to analyze the vibration characteristics of soil particles. It reveals the relationship between changes in soil pressure at the interface and the movement of the transducer. The results show that the motion curve of the transmitting transducer lags behind the soil pressure changes, and the energy of the ultrasonic signal increases with higher excitation frequency and amplitude. Specifically, the peak value of the first wave |H0| at 40 kHz and 60 kHz is 210% and 263% of that at 20 kHz, respectively. When the excitation amplitude increases from 0.005 mm to 0.015 mm, the value of the peak value of other waves |H| increases by 323%. This paper preliminarily reveals the propagation laws of ultrasonic continuous signals at the transducer–soil interface, providing theoretical support for the development of ultrasonic soil property detection instruments.

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Citation: Wang, Z.; Lu, C.; Li, H.;

Wang, C.; Wang, L.; Yang, H.

Propagation Laws of Ultrasonic

Continuous Signals at the

Transmitting Transducer–Soil

Interface. Agriculture 2024,14, 1470.

https://doi.org/10.3390/

agriculture14091470

Academic Editor: Hailong He

Received: 19 July 2024

Revised: 21 August 2024

Accepted: 27 August 2024

Published: 28 August 2024

Licensee MDPI, Basel, Switzerland.

This article is an open access article

distributed under the terms and

conditions of the Creative Commons

Attribution (CC BY) license (https://

creativecommons.org/licenses/by/

4.0/).

agriculture

Article

Propagation Laws of Ultrasonic Continuous Signals at the

Transmitting Transducer–Soil Interface

Zhinan Wang 1,2 , Caiyun Lu 1,2,* , Hongwen Li 1,2, Chao Wang 1,2, Longbao Wang 1,2 and Hanyu Yang 1,2

College of Engineering, China Agricultural University, Beijing 100083, China; zhinan.wang@cau.edu.cn (Z.W.)

2Scientiﬁc Observing and Experiment Station of Arable Land Conservation (North Hebei), Ministry of

Agricultural and Rural Affairs, Beijing 100083, China

*Correspondence: lucaiyun@cau.edu.cn; Tel.: +86-135-8172-2037

Abstract: Ultrasonic detection is one of the main methods for information detection and has advan-

tages in soil detection. Ultrasonic signals attenuate in soil, resulting in unique propagation laws. This

paper studies the propagation laws of ultrasound in soil, focusing on the propagation characteristics

of ultrasonic continuous signals at the transducer–soil interface. This study uses excitation frequency

and amplitude as experimental factors and employs the discrete element simulation method to

analyze the vibration characteristics of soil particles. It reveals the relationship between changes in

soil pressure at the interface and the movement of the transducer. The results show that the motion

curve of the transmitting transducer lags behind the soil pressure changes, and the energy of the

ultrasonic signal increases with higher excitation frequency and amplitude. Speciﬁcally, the peak

value of the ﬁrst wave |H

| at 40 kHz and 60 kHz is 210% and 263% of that at 20 kHz, respectively.

When the excitation amplitude increases from 0.005 mm to 0.015 mm, the value of the peak value

of other waves |H| increases by 323%. This paper preliminarily reveals the propagation laws of

ultrasonic continuous signals at the transducer–soil interface, providing theoretical support for the

development of ultrasonic soil property detection instruments.

Keywords: ultrasonic detection; continuous signal; transducer–soil interface; discrete element

method; propagation law

1. Introduction

Ultrasonic detection is a key method for information gathering and has been widely

used in various ﬁelds, including metal ﬂaw detection [

], parameter measurement [

], civil

engineering safety assessments [

], and damage evaluation of ancient buildings [

]. This

technique boasts several advantages, such as safety [

], environmental friendliness, low

energy consumption, the lack of need for external additives, and ease of use. Additionally,

ultrasound can propagate through opaque materials and has non-destructive properties [

Consequently, the application of ultrasound across different domains has emerged as a

signiﬁcant research focus in recent years [8].

The ultrasonic method also has many applications in agriculture, such as the use of

ultrasound to judge the hollow and disease of potatoes [

], to identify corn stalks [

], to

pollinate strawberries [

], and to determine the maturity of fruits [

]. Soil information,

including soil temperature, moisture, and soil compaction, is one of the main components

of agricultural information [

–

]. Soil information can be obtained by the ultrasonic

method. Baskota et al. [

] studied a single-chip GHz ultrasonic micro-imager for imaging

soil temperature, morphology, moisture, and pests. Zhang et al. [

] measured the freezing

state of soil by the ultrasonic method. The study of Zhang et al. [

] shows that with

the increase in pore equivalent diameter, the ultrasonic pulse velocity decreases slightly

at ﬁrst, and then rises greatly. The results of Zhao et al. [

] show that it is feasible to

use the ultrasonic pulse velocity test to detect the hard foreign object embedded in the

Agriculture 2024,14, 1470. https://doi.org/10.3390/agriculture14091470 https://www.mdpi.com/journal/agriculture

Agriculture 2024,14, 1470 2 of 21

farmland layer according to the variation in the ultrasonic wave propagation velocity and

the amplitude of the sound wave in the soil medium. Compared to existing soil detection

methods that require digging up soil or bringing it back to the laboratory for detecting,

the ultrasonic method supports in situ detection, is easy to operate [

], and is one of the

important means of efﬁcient detection.

This paper aims to provide foundational research for various ultrasonic soil detection

technologies. When using ultrasonic methods to detect soil properties, it is necessary for

the ultrasonic signal to propagate through the soil, but this presents certain challenges.

Soil is a porous medium composed of minerals, organic matter, water, and air, making

it a complex and randomly varying dispersive mixture. Compared to continuous media,

the looseness of the soil and the ﬂuids in its pores lead to greater energy loss of ultrasonic

signals, resulting in signiﬁcant attenuation [23]. The interface, being the junction between

two substances, is a key location where attenuation occurs [

]. As the ﬁrst stage in the

propagation of ultrasonic signals in soil, the interface is where the signal transitions from

the motion of the ultrasonic transducer to the vibration of the soil. The quality of the

signal at the interface directly affects subsequent propagation into the soil, necessitating a

dedicated study of the propagation characteristics at the interface. To address the issue of

ultrasonic energy loss in soil media, using ultrasonic continuous signals offers advantages.

Ultrasonic continuous signals are vibration signals generated by the continuous drive of

the transmitting transducer on the soil, forcing soil particles to vibrate persistently under

the steady and uniﬁed force direction of the transducer. Moreover, because the transmitting

time of ultrasonic continuous signals is longer, they carry stronger energy, resulting in

greater anti-interference capability as they propagate through the soil medium. The signal

shape becomes easier to control, and the receiving end can receive more stable signals,

facilitating their reception, processing, and analysis. Additionally, parameters carrying

important information in continuous signals are easier to identify after post-processing [

Therefore, when the medium is soil, ultrasonic continuous signals may be more suitable

for detection. However, there is currently no research on the attenuation laws of continu-

ous signals at soil interfaces. This paper introduces ultrasonic continuous signals as the

transmitting signal and studies their propagation characteristics at the interface between

the transmitting transducer and the soil to alleviate the problem of energy attenuation.

The interaction between ultrasonic waves and the medium is a microscopic process.

To study the laws of vibration propagation among medium particles, it is essential to obtain

microscopic data. Currently, many researchers utilize numerical simulation methods to

investigate these microscopic processes. This approach allows for the acquisition of process

data through computer-aided calculations, facilitating the analysis of localized physical

quantities during the interaction. Cho et al. [

] employed the ﬁnite element method to

predict motor vibration. Shen et al. [

] explored the relationships among P-wave velocity,

pre-existing cracks, and conﬁning pressure using the discrete element method (DEM). In soil

detection environments, discrete element simulation technology is particularly applicable,

enabling the modeling of soil particles and the application of forces or motion to them. This

technology has been extensively used by researchers in the agricultural engineering ﬁeld to

examine the interaction mechanisms between working components and soil [

]. Xu

et al. [

] analyzed the interaction between soil and subsoiling shovel, aiming to clarify

the drag reduction mechanism of a bionic subsoiling shovel by through EDEM software.

Yang et al. [

] used EDEM software to simulate the spread of commonly used agricultural

fertilizers by a fertilizer applicator. Zhou et al. [

] designed a high-efﬁciency drag-reducing

bionic soil-loosening shovel based on EDEM technology. We are studying the propagation

characteristics at the ultrasonic incident interface, which is a local aspect of the overall

process of ultrasonic wave propagation in soil. Given current technological conditions, it is

not feasible to observe this local aspect through practical experiments. Additionally, we

need to investigate the microscopic mechanisms and laws of ultrasonic attenuation, which

are also challenging to achieve through experiments. Therefore, using simulation methods

for research is necessary. The essence of ultrasonic propagation lies in the vibration of the

Agriculture 2024,14, 1470 3 of 21

medium, which involves the transmission of forces and the movement of the medium itself.

In order to fully analyze the propagation process of sound wave in soil medium and study

the vibration of soil particles, this paper employs discrete element simulation software

(EDEM 2018) to simulate the propagation process and results of ultrasonic waves within

the soil. By tracking designated particles and extracting their target data, we can observe

the microscopic phenomena associated with vibration propagation.

In conclusion, the ultrasonic method offers signiﬁcant advantages for soil detection.

To minimize the energy attenuation of ultrasonic signals in soil, this paper studies the

propagation laws of ultrasonic continuous signals at the transducer–soil interface. Addi-

tionally, EDEM 2018 software is utilized to simulate the propagation process of ultrasound

in soil, aiming to explore the microscopic mechanisms underlying ultrasonic propagation.

As this is a preliminary study on the propagation of continuous signals in soil, the effects

of various factors in actual ﬁeld environments on propagation characteristics remain un-

clear. It is necessary to start by investigating the impact of each individual factor and

then consider the complex effects of multiple factors. This paper mainly focuses on the

attenuation of ultrasonic continuous signals at the soil interface and the vibration laws of

the soil under varying frequencies and amplitudes. In future research, we will continue to

explore the inﬂuence of environmental factors in ﬁeld soil, improve detection accuracy, and

provide theoretical support for the development of instruments for ultrasonic detection of

soil properties.

2. Materials and Methods

2.1. The Ultrasound–Soil Interaction Model

The ultrasound–soil interaction model primarily comprises three components: the

geometric model of the experimental device, the soil particle model, and the continuous

ultrasonic signal. The geometric model of the experimental device acts as the platform

for the experiment, and the generation and propagation of ultrasonic signals occur in

this model. The soil particle model constitutes the propagation medium of ultrasonic

signals, and characterizes the propagation law of ultrasonic signals through the dynamic

characteristics of soil particles, which is the research object of this study’s experiments.

2.1.1. The Geometric Model

The geometric model of the experimental device, which includes the container and

ultrasonic transducers, is created using 3D modeling software (SolidWorks 2018), as illus-

trated in Figure 1. The container is designed to hold soil and securely mount the ultrasonic

transducers (comprising both the transmitting transducer and the receiving transducer),

which are employed to simulate vibrations in order to generate ultrasonic signals.

Agriculture 2024, 14, x FOR PEER REVIEW 3 of 22

through practical experiments. Additionally, we need to investigate the microscopic

mechanisms and laws of ultrasonic aenuation, which are also challenging to achieve

through experiments. Therefore, using simulation methods for research is necessary. The

essence of ultrasonic propagation lies in the vibration of the medium, which involves the

transmission of forces and the movement of the medium itself. In order to fully analyze

the propagation process of sound wave in soil medium and study the vibration of soil

particles, this paper employs discrete element simulation software (EDEM 2018) to simu-

late the propagation process and results of ultrasonic waves within the soil. By tracking

designated particles and extracting their target data, we can observe the microscopic phe-

nomena associated with vibration propagation.

In conclusion, the ultrasonic method oﬀers signiﬁcant advantages for soil detection.

To minimize the energy aenuation of ultrasonic signals in soil, this paper studies the

propagation laws of ultrasonic continuous signals at the transducer–soil interface. Addi-

tionally, EDEM 2018 software is utilized to simulate the propagation process of ultra-

sound in soil, aiming to explore the microscopic mechanisms underlying ultrasonic prop-

agation. As this is a preliminary study on the propagation of continuous signals in soil,

the eﬀects of various factors in actual ﬁeld environments on propagation characteristics

remain unclear. It is necessary to start by investigating the impact of each individual factor

and then consider the complex eﬀects of multiple factors. This paper mainly focuses on

the aenuation of ultrasonic continuous signals at the soil interface and the vibration laws

of the soil under varying frequencies and amplitudes. In future research, we will continue

to explore the inﬂuence of environmental factors in ﬁeld soil, improve detection accuracy,

and provide theoretical support for the development of instruments for ultrasonic detec-

tion of soil properties.

2. Materials and Methods

2.1. The Ultrasound–Soil Interaction Model

The ultrasound–soil interaction model primarily comprises three components: the

geometric model of the experimental device, the soil particle model, and the continuous

ultrasonic signal. The geometric model of the experimental device acts as the platform for

the experiment, and the generation and propagation of ultrasonic signals occur in this

model. The soil particle model constitutes the propagation medium of ultrasonic signals,

and characterizes the propagation law of ultrasonic signals through the dynamic charac-

teristics of soil particles, which is the research object of this study’s experiments.

2.1.1. The Geometric Model

The geometric model of the experimental device, which includes the container and

ultrasonic transducers, is created using 3D modeling software (SolidWorks 2018), as illus-

trated in Figure 1. The container is designed to hold soil and securely mount the ultrasonic

transducers (comprising both the transmiing transducer and the receiving transducer),

which are employed to simulate vibrations in order to generate ultrasonic signals.

Figure 1. The geometric model of the experimental device, including the container and ultrasonic

transducers. The dimensions of the container are as follows: length (l) = 100 mm, height (h) = 130

Figure 1. The geometric model of the experimental device, including the container and ultrasonic

transducers. The dimensions of the container are as follows: length (l) = 100 mm, height

(h) = 130 mm

and width (d) = 40 mm. The container body and the pressure plate are made of steel plates with a

thickness (s) of 10 mm. The container is designed to hold soil and secure the ultrasonic transducers

(including both the the transmitting and receiving transducers), which are utilized for simulating

vibrations to generate ultrasonic signals. A total of 600,000 soil particles are allowed to free-fall into

Agriculture 2024,14, 1470 4 of 21

the container under the inﬂuence of gravity (g= 9.8 m/s

), using the Hertz–Mindlin model with

an expanded particle size of 2 mm. The upper pressure plate is pressed down h

along the inner

wall of the container to achieve a set soil compression rate of 12%. The ﬁxed time step is set to

1.0

−7

s (2% of the Rayleigh time step), and the grid unit size is set to 2 mm (twice the minimum

particle radius).

The container consists of a container body and a pressure plate. Except for the pressure

plate, which can slide up and down along the inner wall of the container body, all other

components are ﬁxed in place. An ultrasonic transmitting transducer and a receiving

transducer are arranged on opposite sides of the container and positioned coaxially. To

simulate soil compaction, we establish a soil compression rate by adding a pressure plate to

the top of the container, ensuring that the lower plane of the pressure plate is coplanar with

the upper plane of the container body in its initial position. During the experiment, we

adjust the sliding distance of the pressure plate according to the required soil compression

rate, thereby applying varying degrees of compression to the soil.

The dimensions of the container are as follows: length (l) = 100 mm, height

(h) = 130 mm

and width (d) = 40 mm. Both the container body and the pressure plate are constructed from

steel plates with a thickness (s) of 10 mm. The height (h

) from the lower plane of the pressure

plate to the upper edge of the container body represents the sliding distance of the pressure

plate. The soil compression rate is calculated using Equation (1).

α=h1/h(1)

where

is the soil compression rate, %. h

is the height from the lower plane of the pressure

plate to the upper edge of the container body, mm. his the hight of the container, mm.

2.1.2. The Soil Particle Model and Parameters

To investigate propagation laws of ultrasound among soil particles, this article focuses

on pure soil as the research object, excluding other substances and moisture. The Hertz–

Mindlin model is chosen for modeling due to the relatively weak binding force between

dry soil particles. Soil particles are represented as circular particles, and a particle factory

is positioned above the container to generate this type of particle. Under the inﬂuence of

gravity (g= 9.8 m/s

), soil particles fall freely, with a total of 600,000 particles ﬁlling the

container. To enhance computational efﬁciency, the particle size of soil particles is scaled

up to 2 mm. The material parameters for the model are set as shown in Table 1, and the

material contact parameters are speciﬁed in Table 2. The particles are dropped into the

container to simulate the soil conditions. In order to create optimal ultrasonic propagation

conditions, the compression ratio is set to 12%, corresponding to h

= 15.60 mm. The

ﬁxed time step is set to 1.0

−7

s (2% of the Rayleigh time step), and the grid unit size

is established at 2 mm (twice the minimum particle radius). The soil model parameters

primarily include physical and contact parameters of soil particles, with the settings for

these parameters mainly referring to the research conducted by Ucgul et al. [33–35].

Table 1. Model material parameters.

Object Soil Steel Pzt

Poisson’s Ratio 0.30 0.25 0.32

Density (kg/m3)2650 7860 7900

Shear Modulus (Pa) 1.2 ×1097.9 ×1010 7.5 ×1010

Note: Pzt is the piezoelectric material of the ultrasonic transducer, which represents the surface of the transmitting

transducer in contact with the soil in Tables 1and 2.

Table 2. Contact parameters.

Object Soil-Soil Soil-Steel Soil-Pzt

Coefﬁcient of Restitution 0.6 0.5 0.5

Agriculture 2024,14, 1470 5 of 21

Table 2. Cont.

Object Soil-Soil Soil-Steel Soil-Pzt

Coefﬁcient of Static Friction 0.5 0.5 0.4

Coefﬁcient of Rolling Friction 0.16 0.05 0.04

2.1.3. Generation of Ultrasonic Continuous Signals

Sound waves are fundamentally vibrations of the medium through which they propa-

gate, while ultrasonic waves are sound waves with vibration frequencies exceeding 20 kHz.

In experiments, ultrasonic continuous signals can be generated using a signal generator,

while in simulation, vibration is modeled by applying periodic reciprocating motion to

the “transmission transducer model”. The frequency and amplitude of this reciprocating

motion correspond to the frequency and amplitude of the simulated vibration.

In this experiment, the motion mode of the transmitting transducer is set to sinusoidal

translation. Figure 2illustrates a schematic diagram of the transmitting transducer motion.

When the signal is transmitted, the transmitting transducer begins at its original position

and moves in the positive direction of the Y-axis (Figure 2a). Upon reaching the maximum

movement distance, the distance from the transmitting transducer to the original position

is referred to as the amplitude (Figure 2b). It then starts moving in the negative direction

of the Y-axis, and after reaching the farthest point, it reverses direction again to move in

the positive direction of the Y-axis (Figure 2c). When it returns to its original position,

a complete movement cycle is accomplished (Figure 2d). While transmitting ultrasonic

continuous signals, the transmitting transducer does not stop moving as it passes passing

through the original position; instead, it continues to repeat the aforementioned motion

process according to the set motion frequency within the deﬁned time (Figure 2a–d).

Agriculture 2024, 14, x FOR PEER REVIEW 5 of 22

Tab l e 2 . Contact parameters.

Object Soil-Soil Soil-Steel Soil-Pzt

Coefficient of Restitution 0.6 0.5 0.5

Coefficient of Static Friction 0.5 0.5 0.4

Coefficient of Rolling Friction 0.16 0.05 0.04

2.1.3. Generation of Ultrasonic Continuous Signals

Sound waves are fundamentally vibrations of the medium through which they prop-

agate, while ultrasonic waves are sound waves with vibration frequencies exceeding 20

kHz. In experiments, ultrasonic continuous signals can be generated using a signal gener-

ator, while in simulation, vibration is modeled by applying periodic reciprocating motion

to the “transmission transducer model”. The frequency and amplitude of this reciprocat-

ing motion correspond to the frequency and amplitude of the simulated vibration.

In this experiment, the motion mode of the transmiing transducer is set to sinusoi-

dal translation. Figure 2 illustrates a schematic diagram of the transmiing transducer

motion. When the signal is transmied, the transmiing transducer begins at its original

position and moves in the positive direction of the Y-axis (Figure 2a). Upon reaching the

maximum movement distance, the distance from the transmiing transducer to the orig-

inal position is referred to as the amplitude (Figure 2b). It then starts moving in the nega-

tive direction of the Y-axis, and after reaching the farthest point, it reverses direction again

to move in the positive direction of the Y-axis (Figure 2c). When it returns to its original

position, a complete movement cycle is accomplished (Figure 2d). While transmiing ul-

trasonic continuous signals, the transmiing transducer does not stop moving as it passes

passing through the original position; instead, it continues to repeat the aforementioned

motion process according to the set motion frequency within the deﬁned time (Figure 2a–

d).

Figure 2. Schematic diagram of the transmiing transducer motion. The motion mode of the trans-

miing transducer is set to sinusoidal translation. When transmiing an ultrasonic signal, the trans-

miing transducer actively translates along the Y axis, while the receiving transducer remains sta-

tionary. When the signal is transmied, the transmiing transducer starts from its original position

and moves in the positive direction of the Y-axis (a). Upon reaching the maximum movement dis-

tance, the distance from the transmiing transducer to its original position is deﬁned as the ampli-

tude (b). It then begins to move in the negative direction of the Y-axis, and after reaching the farthest

position, it reverses direction again to move in the positive direction of the Y-axis (c). When it returns

to its original position, it completes a full movement cycle (d). During the transmission of ultrasonic

continuous signals, the transmiing transducer does not stop moving when passing through the

Figure 2. Schematic diagram of the transmitting transducer motion. The motion mode of the

transmitting transducer is set to sinusoidal translation. When transmitting an ultrasonic signal, the

transmitting transducer actively translates along the Yaxis, while the receiving transducer remains

stationary. When the signal is transmitted, the transmitting transducer starts from its original position

and moves in the positive direction of the Y-axis (a). Upon reaching the maximum movement

distance, the distance from the transmitting transducer to its original position is deﬁned as the

amplitude (b). It then begins to move in the negative direction of the Y-axis, and after reaching the

farthest position, it reverses direction again to move in the positive direction of the Y-axis (c). When

it returns to its original position, it completes a full movement cycle (d). During the transmission

of ultrasonic continuous signals, the transmitting transducer does not stop moving when passing

through the original position, but continues to repeat the above motion process according to the set

motion frequency within the deﬁned time (a–d).

Agriculture 2024,14, 1470 6 of 21

2.2. Characterization of Ultrasonic Signals

2.2.1. Characterization Method before Entering Interface

Before entering the transmitting transducer–soil interface (Figure 1), the generation

and transmission process of ultrasonic signals occurs, which exclusively involves the

movement of the transmitting transducer itself and does not involve the movement of the

soil. Therefore, the movement of the transmitting transducer is utilized to characterize the

ultrasonic signal. The methods for generating and transmitting ultrasonic signals have

been described in Section 2.1.3.

2.2.2. Characterization after Passing through the Interface

The transmitting transducer is designed to make close contact with the soil in the

experimental device. When the transducer begins to reciprocate, the interaction between

the transducer and the soil particles facilitates the propagation of ultrasonic signals into

the soil particles. Since the interaction between the transmitting transducer and the soil

is characterized by “force and reaction force”, this paper studies the force exerted by the

transmitting transducer to examine the mechanical characteristics of soil particles at the

interface. Considering that the end face area of the transmitting transducer is equivalent

to the stress area (S) of the soil at the interface, the pressure (p) is used for convenience

instead of the force (F). The conversion formula between pressure and force is provided in

Equation (2). In summary, ultrasonic signals are characterized by the pressure applied to

the soil particles at the interface.

p=F/S(2)

where pis the pressure applied to the transmitting transducer, Pa. Fis the force applied

to the transmitting transducer, N. Sis the stress area of the transmitting transducer–soil

interface, m2.

Because of the weight of soil and the compression of pressure plate, an initial pressure

) exists between the soil and the transducer at the start of the experiment. Assuming

that when the ultrasonic signal generated by the transducer vibration acts on the soil, the

measured pressure is P

, and the interaction pressure |P| between the ultrasonic signal

and the soil is given by:

|P|=|P1−P0|(3)

where |P| is the interaction pressure between the ultrasonic signal and the soil, Pa. P

the measured pressure when the ultrasonic signal generated by the transducer vibration

acts on the soil, Pa. P

is the pressure between soil and transducer at the initial time of

experiment, Pa.

2.3. Experiment Factors and Levels

Excitation frequency and excitation amplitude of ultrasonic signal are two important

parameters in ultrasonic detection. The attenuation characteristics of ultrasound waves

at different frequencies vary across different materials. Low-frequency signals, although

having low axial resolution, are suitable for high-attenuation materials due to relatively

weaker attenuation and better penetration capability. In contrast, high-frequency signals

offer greater axial resolution and higher detection accuracy but experience more severe

attenuation, making them more suitable for low-attenuation materials. Considering that

soil is a porous medium with strong attenuation characteristics, the ultrasonic frequency

range typically used for detection it is relatively low, generally between 1 kHz and a few

tens of kHz. To study the inﬂuence of different excitation frequencies on the propagation

of ultrasonic continuous signals, the excitation frequency is set as one of the experimental

factors. Based on the aforementioned principles and by referencing previous studies, we

have set the levels at 20 kHz, 40 kHz, and 60 kHz [

–

]. The larger the amplitude of

ultrasonic excitation, the greater the energy carried by the signal. A larger excitation

amplitude facilitates the distinction of the received signal from noise and other interference

signals, making it easier to identify and analyze the received signal. In order to study the

Agriculture 2024,14, 1470 7 of 21

inﬂuence of different excitation amplitude on the propagation of ultrasonic continuous

signals, the excitation amplitude is taken as the second experimental factor, with three

levels set at 0.005 mm, 0.010 mm and 0.015 mm. A total of 9 experiments are conducted

using a full-factorial design. Detailed parameter settings are presented in Table 3.

Table 3. Experiment factors and levels.

Factor Level 1 Level 2 Level 3

Frequency (kHz) 20 40 60

Amplitude (mm) 0.005 0.010 0.015

2.4. Data Acquisition

The peak value and trough value of ultrasonic signal represent the maximum and

minimum values of the interface soil pressure, respectively, indicating the inﬂuence range of

ultrasonic signal on soil medium and serving as important parameters for ultrasonic signal

analysis. It has been observed that the soil pressure itself changes regularly during the

transmission of ultrasonic continuous signals. As the excitation frequency and excitation

amplitude vary, the peak value and trough values of pressure correlate with these changes.

In order to reveal the variation law of soil pressure at the interface under the inﬂuence of

continuous signals, we select three parameters: the peak value of the ﬁrst wave (|H

|),

the peak value of other waves (|H|) and the trough value (|L|). We analyze their relative

values and their variation with excitation frequency and excitation amplitude in detail. In

Figure 3, we use the interface soil pressure image with an excitation frequency of 40 kHz

and excitation amplitude of 0.010 mm as an example, labeling the key wave bands and

important points. We analyze only the wave bands where the signal has been transmitted

(“Early wave”, “Wave in the process” and “Late wave”). The “Wave after the transmitting

transducer stops moving” is only labeled in Figure 3and is not analyzed.

Agriculture 2024, 14, x FOR PEER REVIEW 7 of 22

factors. Based on the aforementioned principles and by referencing previous studies, we

have set the levels at 20 kHz, 40 kHz, and 60 kHz [36–38]. The larger the amplitude of

ultrasonic excitation, the greater the energy carried by the signal. A larger excitation am-

plitude facilitates the distinction of the received signal from noise and other interference

signals, making it easier to identify and analyze the received signal. In order to study the

inﬂuence of diﬀerent excitation amplitude on the propagation of ultrasonic continuous

signals, the excitation amplitude is taken as the second experimental factor, with three

levels set at 0.005 mm, 0.010 mm and 0.015 mm. A total of 9 experiments are conducted

using a full-factorial design. Detailed parameter seings are presented in Table 3.

Tab l e 3 . Experiment factors and levels.

Factor Level 1 Level 2 Level 3

Frequency (kHz) 20 40 60

Amplitude (mm) 0.005 0.010 0.015

2.4. Data Acquisition

The peak value and trough value of ultrasonic signal represent the maximum and

minimum values of the interface soil pressure, respectively, indicating the inﬂuence range

of ultrasonic signal on soil medium and serving as important parameters for ultrasonic

signal analysis. It has been observed that the soil pressure itself changes regularly during

the transmission of ultrasonic continuous signals. As the excitation frequency and excita-

tion amplitude vary, the peak value and trough values of pressure correlate with these

changes. In order to reveal the variation law of soil pressure at the interface under the

inﬂuence of continuous signals, we select three parameters: the peak value of the ﬁrst

wave (|H0|), the peak value of other waves (|H|) and the trough value (|L|). We analyze

their relative values and their variation with excitation frequency and excitation ampli-

tude in detail. In Figure 3, we use the interface soil pressure image with an excitation fre-

quency of 40 kHz and excitation amplitude of 0.010 mm as an example, labeling the key

wave bands and important points. We analyze only the wave bands where the signal has

been transmied (“Early wave”, “Wave in the process” and “Late wave”). The “Wave after

the transmiing transducer stops moving” is only labeled in Figure 3 and is not analyzed.

Figure 3. Interface soil pressure waveform at an excitation frequency of 40 kHz and an excitation

amplitude of 0.010 mm. The signal is received at 0 s, and the soil pressure changes in the time period

of 0–5 × 10−4 s are observed, including the 10-cycle ultrasonic signal when the transmiing trans-

ducer is moving and the soil pressure change after the transmiing transducer stops moving. Based

on the characteristics of the waveform, the entire waveform is divided into four bands: “Early

wave”, “Wave in the process”, “Late wave” and “Wave after the transmiing transducer stops mov-

ing”. In the subsequent analysis, only the bands in the transmission process (“First wave”, “Wave

in the process”, “Late wave”) are analyzed, while the bands after the transmission stops is only

Figure 3. Interface soil pressure waveform at an excitation frequency of 40 kHz and an excitation

amplitude of 0.010 mm. The signal is received at 0 s, and the soil pressure changes in the time period of

0–5

−4

s are observed, including the 10-cycle ultrasonic signal when the transmitting transducer

is moving and the soil pressure change after the transmitting transducer stops moving. Based on the

characteristics of the waveform, the entire waveform is divided into four bands: “Early wave”, “Wave

in the process”, “Late wave” and “Wave after the transmitting transducer stops moving”. In the

subsequent analysis, only the bands in the transmission process (“First wave”, “Wave in the process”,

“Late wave”) are analyzed, while the bands after the transmission stops is only labeled and not

analyzed. H

–H

represent the peak positions of the ﬁrst six cycles, and L

–L

represent the trough

positions of the ﬁrst ﬁve cycles. |H1|–|H5| represent the peak value of the wave corresponding to

–H

(calculated by Equation (3)), and |L

|–|L

| represent the trough values corresponding to

–L

(calculated by Equation (3)). |H

| represents the peak value of the ﬁrst wave (calculated by

Equation (3)), |H| represents the average peak value of other waves (calculated by Equation (4)),

and |L| represents the average of the trough values (calculated by Equation (5)). In Equation (3), to

Agriculture 2024,14, 1470 8 of 21

distinguish between the peak value and the trough value, when referring to the peak value,

|P| = |H| or |P| = |H

| (x= 0, 1, 2, 3, 4, 5); when referring to the trough value, |P| = |L|

or |P|=|Lx| (x= 0, 1, 2, 3, 4, 5).

Under each detection condition, we extract |H

| and calculate |H| and |L|. We plot

images of |H

|, |H| and |L| with respect to frequency and amplitude, and analyze the

peak and trough values in relation to frequency and amplitude. The correlation coefﬁcient R

between soil pressure and excitation amplitude is calculated using Excel. We also calculate

the difference Jbetween the peak values of all waves except for the ﬁrst wave and trough

values under various experimental conditions, and analyze the reasons for its variations as

well as the inﬂuence of frequency and amplitude.

2.4.1. The Peak Value of the First Wave |H0|

After the continuous ultrasonic signal is transmitted, the waveform formed by the

ﬁrst vibration period is referred to as the ﬁrst wave. Preliminary experiments have found

that the peak value of the ﬁrst wave (|H

|) is consistently smaller than the peak value

of other waves (|H|), and there is a signiﬁcant difference compared to the peak values

of other waves. Therefore, the peak value of the ﬁrst wave (|H

|) (Figure 3) under each

experimental condition is extracted and analyzed separately.

2.4.2. The Peak Value of Other Waves |H|

In order to make the data more generalizable, the peak values of other waves, exclud-

ing the ﬁrst wave, from ﬁve cycles starting from the second cycle are selected, and their

average values represent the peak values of other waves under this detection condition.

|H| is calculated using Equation (4).

|H|=|(H1+H2+H3+H4+H5)/5|(4)

where |H| is the peak values of other waves, Pa. H

–H

are the peak values of other waves

except the ﬁrst wave in 5 cycles from the second cycle, Pa.

2.4.3. The Trough Value |L|

Since there is no signiﬁcant difference between the ﬁrst trough and other troughs

excluding the ﬁrst wave, we select the trough values |L

|–|L

| (Figure 3) from the ﬁrst

cycle for ﬁve consecutive cycles, and their average value represents the trough value of the

curve under this detection condition. |L| is calculated using Equation (5).

|L|=|(L1+L2+L3+L4+L5)/5|(5)

where |L| is the trough value, Pa. L

–L

are the troughs of 5 consecutive cycles from the

trough of the ﬁrst cycle, Pa.

2.4.4. The Difference Jbetween |H| and |L|

The difference between the peak value of other waves |H| and the trough value |L|

is represented by J.Jis calculated using Equation (6). The Jvalue is calculated at different

excitation frequencies and amplitudes, and an image is plotted showing how the Jvalue

changes with the excitation frequency and amplitude.

J=|H|−|L|(6)

where Jis the difference between |H| and |L|, Pa. |H| is the peak value of other waves,

Pa. |L| is the trough value, Pa.

Agriculture 2024,14, 1470 9 of 21

3. Results and Analysis

3.1. Analysis of Continuous Ultrasonic Signal Transmitting Process

In order to illustrate the change in soil pressure at the interface from the beginning to

the end of the signal transmission (Figure 4), as well as the variation in soil particle pressure

near the interface under the continuous action of transmitting transducer (Figure 5), this

paper analyzes the key steps during the time period of 0–2.68

−4

s. The pressure curves

of soil and particles at the interface exhibit similar characteristics across each experimental

group. Therefore, using an excitation frequency of 40 kHz and an excitation amplitude

of 0.010 mm as an example, the transmitting process of ultrasonic continuous signal is

analyzed, with the initial signal transmitting time of transmitting transducer set as 0 s.

Agriculture 2024, 14, x FOR PEER REVIEW 9 of 22

where J is the diﬀerence between |H| and |L|, Pa. |H| is the peak value of other waves,

Pa. |L| is the trough value, Pa.

3. Results and Analysis

3.1. Analysis of Continuous Ultrasonic Signal Transmiing Process

In order to illustrate the change in soil pressure at the interface from the beginning

to the end of the signal transmission (Figure 4), as well as the variation in soil particle

pressure near the interface under the continuous action of transmiing transducer (Figure

5), this paper analyzes the key steps during the time period of 0–2.68 × 10−4 s. The pressure

curves of soil and particles at the interface exhibit similar characteristics across each ex-

perimental group. Therefore, using an excitation frequency of 40 kHz and an excitation

amplitude of 0.010 mm as an example, the transmiing process of ultrasonic continuous

signal is analyzed, with the initial signal transmiing time of transmiing transducer set

as 0 s.

As shown in Figure 4a, the ultrasonic signal transmission process in the interface soil

mainly includes three forms: I, II and III, which correspond to the initial stage of signal

transmission, the stabilization of the signal transmission, and the moment just before the

signal transmission stops, respectively. Within a continuous section of signal, form I and

form III appear only once, while form II appears cyclically between form I and III. The

number of occurrences of form II depends on the number of transmission periods set.

Figure 4. Ultrasonic continuous signal transmiing process (40 kHz-0.010 mm). (a) The complete

waveform of the ultrasonic continuous signal at the transmiing transducer–soil interface is labeled

with three typical paerns of the ultrasonic transmiing process: I, II, III. Ⅰ represents the waveform

Figure 4. Ultrasonic continuous signal transmitting process (40 kHz-0.010 mm). (a) The complete

waveform of the ultrasonic continuous signal at the transmitting transducer–soil interface is labeled

with three typical patterns of the ultrasonic transmitting process: I, II, III. I represents the waveform at

the initial stage of signal transmission (b(i)), marking the inﬂection point of the soil pressure change

–G

). II is the waveform of the signal transmission process (c(i)), marking the inﬂection point

of the soil pressure change (A

–G

). III is the waveform at the end of the signal transmission (d(i)),

which marks the inﬂection point of the soil pressure change (A

–G

). b(ii), c(ii) and d(ii) show the

color changes in soil particles near the interface at the initial stage of signal transmission, during

signal transmission process, and at the end of the signal transmission, respectively. The red color of

the interface soil particles indicates that the interface soil is compressed, and the soil pressure is in

the positive direction of the Y-axis; the blue color of the particles indicates that the interface soil is

gradually loosening, and the soil pressure changes to the negative direction of the Y-axis. The same

symbol labels in the diagram represent the same meaning or stage.

Agriculture 2024,14, 1470 10 of 21

As shown in Figure 4a, the ultrasonic signal transmission process in the interface soil

mainly includes three forms: I, II and III, which correspond to the initial stage of signal

transmission, the stabilization of the signal transmission, and the moment just before the

signal transmission stops, respectively. Within a continuous section of signal, form I and

form III appear only once, while form II appears cyclically between form I and III. The

number of occurrences of form II depends on the number of transmission periods set.

3.1.1. The Initial Stage of Signal Transmission

In the initial stage of signal transmission, the soil is stationary (Figure 4(b(i)) A

), while

the transmitting transducer has an initial velocity in the positive direction of the Y-axis

(Figure 5b,c A

). The interface soil is compressed and the stress gradually increases. The

soil particles at the interface are red (Figure 4(b(ii)) A

–B

) and begin to move forward

towards the Y-axis.

Agriculture 2024, 14, x FOR PEER REVIEW 11 of 22

Figure 5. The correspondence between the change in interface soil pressure and the motion of the

transmiing transducer. (c) The local enlargement of (a(i)). The motion curve of the transmiing

transducer lags behind the soil pressure curve. The change in soil pressure and the motion of the

transmiing transducer are divided into three phases: “The beginning” (a(i)), “Cyclical changes”

(a(ii)), and “The end” (a(iii)). The blue curve indicates the change in soil pressure, while the red

curve indicates the motion trajectory of the transmiing transducer. A4–D4 represent the position of

the transmiing transducer when the soil pressure reaches its peak and trough (a(i)), and A5–E5

represent the inﬂection points where the magnitude and direction of the transmiing transducer’s

velocity change (c). (b) shows the changes in the magnitude and direction of the transmiing trans-

ducer’s velocity during “The beginning” and “Cyclical changes”, with the meanings of A4–D4, and

A5–E5 corresponding to those in (a(i),c). (d) illustrates the motion state during “The end” and after

the transmiing transducer stops moving. The length of the arrow indicates the magnitude of the

velocity value (b,d). The graph only expresses the correspondence between the soil pressure curve

and the motion curve of the transmiing transducer on the time axis, and the magnitude of the curve

shape does not represent the actual values.

3.1.2. The Stage of Signal Transmission Process

The transmiing transducer starts the movement of the second cycle after completing

the ﬁrst cycle, and the interaction process between the transmiing transducer and the

interface soil is the same as in the ﬁrst cycle. When the acceleration of the transmiing

transducer toward the Y-axis matches that of the soil (Figure 5(a(i),b) C4), the soil pressure

reaches its maximum value (Figure 4(b(i)) E1), after which the soil pressure begins to de-

crease. When the velocity of the interface soil equals that of the transmiing transducer

(Figure 5(a(i),b) D4), the pressure on the interface soil reaches a minimum (Figure 4(b(i))

F1).

Observing the stress curve of soil at the interface (Figure 4a), it can be seen that the

peak value of other waves |H| are larger than the peak value of the ﬁrst wave |H0|. This

Figure 5. The correspondence between the change in interface soil pressure and the motion of the

transmitting transducer. (c) The local enlargement of (a(i)). The motion curve of the transmitting

transducer lags behind the soil pressure curve. The change in soil pressure and the motion of the

transmitting transducer are divided into three phases: “The beginning” (a(i)), “Cyclical changes”

(a(ii)), and “The end” (a(iii)). The blue curve indicates the change in soil pressure, while the red curve

indicates the motion trajectory of the transmitting transducer. A

–D

represent the position of the

transmitting transducer when the soil pressure reaches its peak and trough (a(i)), and A

–E

represent

the inﬂection points where the magnitude and direction of the transmitting transducer’s velocity

change (c). (b) shows the changes in the magnitude and direction of the transmitting transducer’s

velocity during “The beginning” and “Cyclical changes”, with the meanings of A

–D

, and A

–E

corresponding to those in (a(i),c). (d) illustrates the motion state during “The end” and after the

transmitting transducer stops moving. The length of the arrow indicates the magnitude of the velocity

value (b,d). The graph only expresses the correspondence between the soil pressure curve and the

motion curve of the transmitting transducer on the time axis, and the magnitude of the curve shape

does not represent the actual values.

Agriculture 2024,14, 1470 11 of 21

After the transmission begins, the transmitting transducer decelerates gradually

(Figure 5b,c A

–B

), and the soil also decelerates due to internal resistance until the acceler-

ation of the transmitting transducer matches that of the soil (Figure 5(a(i),b) A

), at which

point the soil pressure reaches its maximum value (Figure 4(b(i)) B1).

Since then, both the transmitting transducer and the soil continue to move forward to

the Yaxis, but because the velocity of the transmitting transducer is lower than that of the

soil, the transmitting transducer gradually separates from the soil, causing the interface

soil pressure to begin decreasing. After that, the forward velocity of the transmitting

transducer decreases to 0 (Figure 5b,c B

) and starts to accelerate in the reverse direction

(Figure 5b,c B5–C5)

. During this process, the degree of separation between the transmitting

transducer and the interface soil increases, the pressure on the interface soil decreases,

and the soil becomes loose gradually. At this point, the soil pressure shifts to the negative

direction of Yaxis, and the particles turn blue (Figure 4(b(ii)) B

–C

). The soil begins to

move in the opposite direction when the velocity decreases to 0.

The transmitting transducer starts to decelerate when it passes through the initial

position (Figure 5b,c C

), while the soil accelerates to the negative direction of the Y

axis. When the velocity of the interface soil matches that of the transmitting transducer

(Figure 5(a(i),b) B4)

, the interface soil pressure reaches its minimum value

(Figure 4(b(i)) C1)

After that, the contact degree between the transmitting transducer and the interface

soil increases, causing the interface soil to be compressed again, which leads to an increase

in the interface soil pressure. When the velocity of transmitting transducer decreases to

0 (Figure 5b,c D

), it accelerates to Y-axis again (Figure 5b,c D

–E

), and the pressure

on soil particles increases continuously. At this time, the interface soil particles are red

(Figure 4(b(ii)) C1–E1).

3.1.2. The Stage of Signal Transmission Process

The transmitting transducer starts the movement of the second cycle after completing

the ﬁrst cycle, and the interaction process between the transmitting transducer and the

interface soil is the same as in the ﬁrst cycle. When the acceleration of the transmitting

transducer toward the Y-axis matches that of the soil (Figure 5(a(i),b) C

), the soil pressure

reaches its maximum value (Figure 4(b(i)) E

), after which the soil pressure begins to

decrease. When the velocity of the interface soil equals that of the transmitting transducer

(Figure 5(a(i),b) D

), the pressure on the interface soil reaches a minimum

(Figure 4(b(i)) F1)

Observing the stress curve of soil at the interface (Figure 4a), it can be seen that the

peak value of other waves |H| are larger than the peak value of the ﬁrst wave |H

This may be because the motion of the transmitting transducer has not completed a full

cycle when the interface soil pressure curve forms a cycle (Figure 4(b(i)) D

, G

). When

the transducer completes a full cycle and returns to the initial position again (Figure 5b,c

), the interface soil pressure value exceeds the initial pressure value. Therefore, when

the transmitting transducer moves from the initial position for the second time, the peak

value (Figure 4(b(i)) E

) of the interface soil pressure is larger than that of the ﬁrst time

(Figure 4(b(i)) B

). From the second period of transducer movement, the stress process of

the soil interface is the same as that of the second period, so only the peak value of the ﬁrst

wave |H0| is smaller than that of other waves |H|.

Due to the inertia of soil particles, early soil pressure will transmit into the interior of

the soil. Therefore, during the signal transmission process, radial red and blue alternating

bands (Figure 4(b(ii)) G1) can be observed diffusing into the soil.

During the signal transmission process, the transmitting transducer continuously

cycles back and forth. The pressure on the interface soil varies with the movement of the

transmitting transducer (Figure 5(a(ii))), showing a consistent variation law in each cycle

(Figure 4(c(i)) A

–D

, D

–G

), similar to that in the second cycle of signal transmission

(Figure 4(b(i)) D

–G

). In each cycle, the peak value and trough values of the interface soil

stress waveform remain consistent.

Agriculture 2024,14, 1470 12 of 21

Jis always positive under all detection conditions (the minimum value of Joccurs at an

excitation frequency of 20 kHz and an excitation amplitude of 0.005 mm, which is 6674.6 Pa,

also positive). This may be due to the fact that when the transmitting transducer moves

forward toward the Y-axis, the compression degree of the interface soil increases, the range

of soil particles to move decreases, and the rate of pressure change is large. However, when

the transmitting transducer moves negatively toward Y-axis, the soil becomes loose, the soil

rebound speed decreases, and the rate of pressure change decreases. Therefore, the interface

soil pressure increases more when the transmitting transducer moves positively toward the

Y-axis, and decreases less when it moves negatively toward the Y-axis, which results in an

increase in J.

During the signal transmission process, the soil at the interface is continuously subjected

to alternating pressure from the transmitting transducer [

]. At this stage, the magnitude

and direction of the interface soil pressure are constantly changing, and are continuously

transmitted to the interior of the soil, causing the color of particles at the interface and within

the soil to alternate between red and blue at each time moment (Figure 4(c(ii)) A2–G2).

3.1.3. The End Stage of Signal Transmission

At the end stage of signal transmission, the transmitting transducer stops at the initial

position after completing the last complete movement cycle (Figure 5(a(iii)) E

), after which

the transmitting transducer does not move any more (Figure 5d E

). Before the transmitting

transducer stops, the pressure curve of the interface soil (Figure 4(d(i)) A

–E

) and the color

change in the soil particle pressure (Figure 4(d(ii)) A

–E

) are consistent with the stage of

signal transmission process. At the moment the transmitting transducer stops, the interface

soil still has a positive velocity towards the Y-axis. At this time, the interface soil gradually

separates from the transmitting transducer, the pressure drops sharply, the pressure curve

shows a sharp peak (Figure 4d(i) E

), while the color of the interface soil particles is red

(Figure 4(d(ii)) E

). The interface soil oscillates several times along the positive and negative

directions of Y-axis in situ, and then gradually comes to rest. At this point, the pressure on the

interface soil (Figure 4(d(i)) F3–G3) fluctuates several times around the initial value and then

returns to the initial value. The color of the interface soil particles begins to trend towards a

chaotic state of mixing red and blue (Figure 4(d(i)) G

), and the changes in pressure on the

interface soil are no longer regular.

After the transducer stops moving, the red and blue pressure waves generated in the

early stage continue to diffuse into the soil (Figure 4(d(ii)) G

), but no new red or blue

bands are produced at the interface, marking the end of the signal transmission process.

3.2. The Effect of the Excitation Frequency on the Waveform

In order to explore the inﬂuence of the excitation frequency on the peak and trough

values of the ultrasonic continuous signal, we plot the change curves (Figure 6b) of soil

pressure at different excitation frequencies (20 kHz, 40 kHz, and 60 kHz) when the excitation

amplitude is 0.010 mm. The |H

curves are extracted separately for comparative analysis, and the results are as follows.

Agriculture 2024, 14, x FOR PEER REVIEW 13 of 22

3.2. The Eﬀect of the Excitation Frequency on the Waveform

In order to explore the inﬂuence of the excitation frequency on the peak and trough

values of the ultrasonic continuous signal, we plot the change curves (Figure 6b) of soil

pressure at diﬀerent excitation frequencies (20 kHz, 40 kHz, and 60 kHz) when the exci-

tation amplitude is 0.010 mm. The |H0| (Figure 6a), |H| (Figure 6c) and |L| (Figure 6d)

of the curves are extracted separately for comparative analysis, and the results are as fol-

lows.

Figure 6. The change curves of soil pressure at diﬀerent excitation frequencies (20 kHz,40 kHz, and

60 kHz) when the excitation amplitude is 0.010 mm (b). (a) |H0|, (c) |H| and (d) |L| of the curves

are extracted separately for comparative analysis, showing that the |H0|, |H| and |L| increase with

the increase in excitation frequency. In (d), L’ is the original value of the trough, which is negative,

and it is analyzed in the text according to Equation (5) to become an absolute value |L|.

3.2.1. The Peak Value of the First Wave |H0| and the Peak Value of Other Waves |H|

Observing the pressure waveforms of the interface soil at diﬀerent excitation frequen-

cies (Figure 6b), it can be seen that |H0| increases with the increase in the excitation fre-

quency. When the excitation frequency is 40 kHz and 60 kHz, |H0| is 158% and 191% of

that at 20 kHz, respectively (Figure 6a). |H| also increases with the increase in the excita-

tion frequency. When the excitation frequency is 40 kHz and 60 kHz, |H0| is 210% and

263% of that at 20 kHz, respectively (Figure 6c).

Both |H0| and |H| increase with increasing excitation frequency, likely because a

higher frequency results in greater acceleration of the transmiing transducer compared

to the soil, allowing the transmiing transducer to exert pressure on the soil for a longer

duration. At this time the transmiing transducer is separated from the soil more to the

right (Figure 5b A4), leading to a greater peak in interface soil pressure. The study of Yang,

Wang, Zhang and Wang [39] also showed that increasing the vibration frequency increases

the pressure exerted on the particles, which is consistent with the ﬁndings of this paper.

3.2.2. The Trough Value |L|

|L| increases with increasing excitation frequency. When the excitation frequency is

40 kHz and 60 kHz, |L| is 167% and 192% of that at 20 kHz, respectively (Figure 6d). This

may be due to the fact that when the excitation frequency increases, the motion velocity

of the transmiing transducer increases, leading to a greater separation from the soil.

When the separation degree of the transmiing transducer from the interface soil is max-

imized, the distance of separation is larger and the value of pressure is smaller than when

the excitation frequency is low, thus making |L| larger. The study of Gheibi and Hedayat

[40] also shows that the transmission amplitude is dependent on the true contact area be-

tween the particles. An increase in the contact area between particles leads to an increase

in the ultrasonic transmission amplitude. Similarly, when the degree of detachment be-

tween the particles increases, their contact area decreases, leading to a decrease in ampli-

tude.

Figure 6. The change curves of soil pressure at different excitation frequencies (20 kHz, 40 kHz, and

60 kHz) when the excitation amplitude is 0.010 mm (b). (a) |H

|, (c) |H| and (d) |L| of the curves

Agriculture 2024,14, 1470 13 of 21

are extracted separately for comparative analysis, showing that the |H

|, |H| and |L| increase with

the increase in excitation frequency. In (d), ‘L’ is the original value of the trough, which is negative,

and it is analyzed in the text according to Equation (5) to become an absolute value |L|.

3.2.1. The Peak Value of the First Wave |H0| and the Peak Value of Other Waves |H|

Observing the pressure waveforms of the interface soil at different excitation frequen-

cies (Figure 6b), it can be seen that |H

| increases with the increase in the excitation

frequency. When the excitation frequency is 40 kHz and 60 kHz, |H

| is 158% and 191%

of that at 20 kHz, respectively (Figure 6a). |H| also increases with the increase in the

excitation frequency. When the excitation frequency is 40 kHz and 60 kHz, |H

| is 210%

and 263% of that at 20 kHz, respectively (Figure 6c).

Both |H

| and |H| increase with increasing excitation frequency, likely because a

higher frequency results in greater acceleration of the transmitting transducer compared

to the soil, allowing the transmitting transducer to exert pressure on the soil for a longer

duration. At this time the transmitting transducer is separated from the soil more to the

right (Figure 5b A

), leading to a greater peak in interface soil pressure. The study of Yang,

Wang, Zhang and Wang [

] also showed that increasing the vibration frequency increases

the pressure exerted on the particles, which is consistent with the ﬁndings of this paper.

3.2.2. The Trough Value |L|

|L| increases with increasing excitation frequency. When the excitation frequency is

40 kHz and 60 kHz, |L| is 167% and 192% of that at 20 kHz, respectively (Figure 6d). This

may be due to the fact that when the excitation frequency increases, the motion velocity of

the transmitting transducer increases, leading to a greater separation from the soil. When

the separation degree of the transmitting transducer from the interface soil is maximized,

the distance of separation is larger and the value of pressure is smaller than when the

excitation frequency is low, thus making |L| larger. The study of Gheibi and Hedayat [

]

also shows that the transmission amplitude is dependent on the true contact area between

the particles. An increase in the contact area between particles leads to an increase in the

ultrasonic transmission amplitude. Similarly, when the degree of detachment between the

particles increases, their contact area decreases, leading to a decrease in amplitude.

3.2.3. The Difference Jbetween |H| and |L|

Jincreases with the increase in excitation frequency. When the excitation frequency

is 40 kHz and 60 kHz, Jis 598% and 900% of that at 20 kHz, respectively (Figure 7). This

may be due to the fact that when the transmitting transducer moves positively toward the

Y-axis, the squeezing degree of the soil increases, resulting in higher internal stress within

the soil. The pressure change becomes more pronounced for the squeezing velocity, i.e.,

the pressure is more sensitive to the change in squeezing velocity. Therefore, when the

interface soil pressure increases, the higher excitation frequency leads to a larger increment

in interface soil pressure. When the transmitting transducer moves negatively toward the

Y-axis, the extrusion degree of the soil decreases, the soil becomes loose, the soil internal

stress decreases, and the sensitivity of the soil pressure to the extrusion velocity decreases.

Therefore, when the excitation frequency increases, the decrease in soil pressure |L| (when

the soil is squeezed to a lesser extent) is less than the increase in soil pressure |H| (when

the soil is squeezed to a greater extent), resulting in an increase in J.

Agriculture 2024,14, 1470 14 of 21

Agriculture 2024, 14, x FOR PEER REVIEW 14 of 22

3.2.3. The Diﬀerence J between |H| and |L|

J increases with the increase in excitation frequency. When the excitation frequency

is 40 kHz and 60 kHz, J is 598% and 900% of that at 20 kHz, respectively (Figure 7). This

may be due to the fact that when the transmiing transducer moves positively toward the

Y-axis, the squeezing degree of the soil increases, resulting in higher internal stress within

the soil. The pressure change becomes more pronounced for the squeezing velocity, i.e.,

the pressure is more sensitive to the change in squeezing velocity. Therefore, when the

interface soil pressure increases, the higher excitation frequency leads to a larger incre-

ment in interface soil pressure. When the transmiing transducer moves negatively to-

ward the Y-axis, the extrusion degree of the soil decreases, the soil becomes loose, the soil

internal stress decreases, and the sensitivity of the soil pressure to the extrusion velocity

decreases. Therefore, when the excitation frequency increases, the decrease in soil pres-

sure |L| (when the soil is squeezed to a lesser extent) is less than the increase in soil pres-

sure |H| (when the soil is squeezed to a greater extent), resulting in an increase in J.

Figure 7. The variation in J with diﬀerent excitation frequencies (20 kHz, 40 kHz, and 60 kHz) at an

excitation amplitude of 0.010 mm, showing that J increases with the increase in the excitation fre-

quency.

3.3. The Eﬀect of the Excitation Amplitude on the Waveform

In order to explore the inﬂuence of the excitation amplitude on the peak and trough

values of the ultrasonic continuous signal, we plot the change curves (Figure 8b) of soil

pressure at diﬀerent excitation amplitudes (0.005 mm,0.010 mm, and 0.015 mm) when the

excitation frequency is 40 kHz. The |H0| (Figure 8a), |H| (Figure 8c) and |L| (Figure 8d)

of the curves are extracted separately for comparative analysis, and the results are as fol-

lows.

Figure 7. The variation in Jwith different excitation frequencies (20 kHz, 40 kHz, and 60 kHz) at an

excitation amplitude of 0.010 mm, showing that Jincreases with the increase in the excitation frequency.

3.3. The Effect of the Excitation Amplitude on the Waveform

In order to explore the inﬂuence of the excitation amplitude on the peak and trough

values of the ultrasonic continuous signal, we plot the change curves (Figure 8b) of soil

pressure at different excitation amplitudes (0.005 mm, 0.010 mm, and 0.015 mm) when the

excitation frequency is 40 kHz. The |H

the curves are extracted separately for comparative analysis, and the results are as follows.