esa-sceva/satcom-chunk-collection huggingface dataset:
# Improving the Performance of Turbo-Coded Systems under Suzuki Fading Channels
## 2 System Model  
The system model of Figure 1 was considered in the analysis of this paper. The binary generated data are encoded, with a 1/3- and 1/2-rate turbo encoder with a codeword length of 4096 bits. Binary codewords were converted to equivalent symbols and modulated with M-quadrature amplitude modulation (M-QAM) to be transmitted via a Suzuki faded channel. The data were received in the presence of AWGN, such that  
\[\mathbf{y}=\mathbf{h}\mathbf{x}+\mathbf{w}, \tag{1}\]  
where \(\mathbf{y}\in\mathbb{C}^{1\times N}\) and \(\mathbf{x}\in\mathbb{C}^{1\times N}\) are the received and transmitted vectors with length \(N\), while \(\mathbf{h}\in\mathbb{C}^{1\times N}\) and \(\mathbf{w}\in\mathbb{C}^{1\times N}\) are the channel and the AWGN parameters, respectively. The received signal was equalized utilizing the ZFE, such that  
\[\mathbf{\hat{x}}=\mathbf{x}+\mathbf{\hat{w}}, \tag{2}\]  
where \(\mathbf{\hat{x}}=\mathbf{x}/\mathbf{h}\) and \(\mathbf{\hat{w}}=\mathbf{w}/\mathbf{h}\) are the equalized received signal and noise, respectively. The LLRs were calculated based on the noise PDF that is proposed in this work utilizing ratio distribution \(\mathbf{w}/\mathbf{h}\), which we describe in Section 3. Finally, the turbo decoder generates the binary data using these LLRs. It is worth mentioning that the channel parameters were assumed to be known at the receiver side.
# Seismic Wave Amplification Characteristics in Slope Sections of Various Inclined Model Grounds
## 3 Analysis of 1 g Shaking Table Experiment Results
### Comparative Analysis of Acceleration Amplification
#### 3.1.1 Slope Section PGA  
Figure 4 shows the Peak Ground Acceleration (PGA) measured by the accelerometers (AS11, 12, 13) in the slope section of the four model grounds. It can be observed that in all four model grounds, the PGA increases towards the upper part of the slope, with Case 3 showing less amplification compared to the other models with slopes. Figure 4d,e compare the input motion with the PGA at the measurement points to evaluate the amplification of seismic PGA. In the lower part of the slope, Case 3 showed a 13% amplification, while Case 2 showed about a 16% amplification, resulting in a difference of approximately 3%. However, in the upper part, Case 3, which had the smallest amplification, showed a 22% increase, while Case 2, with the largest amplification, showed a 31% increase. The largest amplification was observed in Case 1, which had the lowest relative density. Amplification was observed in the following order: Case 4, where the lower and upper parts had different relative densities, Case 2, with the highest relative density, and Case 3, the flat model ground.
# A Survey of Analog-to-Digital Converters for Operation under Radiation Environments
## 5 Design Guidelines
### Step 3--Selection of the ADC Architecture  
Usually, after analyzing the radenv-ADC requirements in Step 1, no more than two possible architectures are considered. Traditionally, the preferred choice has been a PIP architecture, since it offers a good trade-off between electrical performance and radiation robustness (cf. Section 4.5). In fact, PIP achieves higher resolutions than F or FIF, and is easier to harden against SET than \(\Delta\Sigma\) or SAR. However, PIP cannot reach the ENOB that \(\Delta\Sigma\) does, or be as power efficient as modern SAR. In short, the architecture choice is highly dependent on the particular radenv-ADC requirements. As a rule of thumb, it is advisable to use \(\Delta\Sigma\) architecture for low-frequencies high-resolution applications, SAR for low/medium-frequencies medium/high-resolution, PIP for medium/high-frequencies moderate-resolution, and FIF for high-frequencies low-resolution.  
Once the basic ADC architecture is chosen, the need of additional hardening blocks against SEFI (current alarms, watch-dogs, etc.) is evaluated with system-level simulation. Additionally, test structures (test buses, built-in self tests, etc.) to be included are also assessed.
# Closed-Form Analytical Solutions for the Deflection of Elastic Beams in a Peridynamic Framework
## 2 Peridynamic Beam Theory  
### Classical Equations and Assumptions  
Let \(x\) be the coordinate for a point of the centerline of the initially straight beam, and \(z\) is the transverse coordinate of cross-section points with the origin at the centroid of the cross-section. The corresponding Cartesian base vectors will be specified by \(\mathbf{e}_{x}\) and \(\mathbf{e}_{z}\), respectively. In what follows, let us analyze the plane-bending of the beam. In this case, the deformed centerline belongs to the \(x-z\) plane. In the case of small cross-sectional rotations, the displacement vector \(\mathbf{u}\) can be represented as follows:  
\[\mathbf{u}(x,z)=w(x)\mathbf{e}_{z}+\theta(x)z\mathbf{e}_{x}, \tag{1}\]  
where \(w\) is the deflection and \(\theta\) is the small angle of cross-sectional rotation.  
Assuming small strains, the linear strain tensor \(\boldsymbol{\varepsilon}\) is related to the displacement field according to the following equation:  
\[\boldsymbol{\varepsilon}=\frac{1}{2}\Big{(}\boldsymbol{\
abla}\mathbf{u}+( \boldsymbol{\
abla}\mathbf{u})^{\mathrm{T}}\Big{)},\quad\boldsymbol{\
abla}( \ldots)=\mathbf{e}_{x}\frac{\partial(\ldots)}{\partial x}+\mathbf{e}_{z} \frac{\partial(\ldots)}{\partial z}. \tag{2}\]  
With Equation (1) inserted into Equation (2), the strain tensor is computed as follows:  
\[\boldsymbol{\varepsilon}=\epsilon\mathbf{e}_{x}\otimes\mathbf{e}_{x}+\frac{1 }{2}\gamma(\mathbf{e}_{x}\otimes\mathbf{e}_{z}+\mathbf{e}_{z}\otimes\mathbf{e }_{x}), \tag{3}\]  
with the following expressions for normal strain \(\varepsilon\) and the transverse shear strain \(\gamma\):  
\[\varepsilon=z\frac{\mathrm{d}\theta}{\mathrm{d}x},\quad\gamma=\theta+\frac{ \mathrm{d}w}{\mathrm{d}x}. \tag{4}\]  
For the shear rigid beams, \(\gamma=0\) is assumed, resulting in  
\[\theta=-\frac{\mathrm{d}w}{\mathrm{d}x},\quad\epsilon=-z\frac{\mathrm{d}^{2}w }{\mathrm{d}x^{2}}. \tag{5}\]  
For the linear-elastic material behavior, the strain energy per unit length is defined as follows:  
\[\mathcal{U}=\frac{1}{2}\int\limits_{A}E\varepsilon^{2}\mathrm{d}A, \tag{6}\]  
where \(E\) is the Young's modulus, and \(A\) is the cross-sectional area. With Equation (5), the strain energy density (6) takes the following form:  
\[\mathcal{U}=\frac{EI}{2}\kappa^{2},\quad\kappa=-\frac{\mathrm{d}^{2}w}{\mathrm{ d}x^{2}} \tag{7}\]  
where \(I\) is the second area moment of the beam cross-section.
###### Abstract  
Knowing the importance of assuring their reliability and availability, prognosis and remaining useful life calculation (RUL) concepts are highly suggested to be applied in critical applications such as hybrid electric vehicles (HEV). In the electrical propulsion system of HEVs, the electrical machine is one of the most critical elements considering its cost and function. Most electrical machines used in HEVs are permanent magnet machines (PMM). Most severe faults in PMM that affect its normal operation are the result of demagnetization. However, applying prognosis to a real prototype to detect the presence of mechanical defects such as cracks in the magnet of PMM and calculating the RUL of this defective element are challenging. In this paper, we are going to take advantage of a finite element model already built for the PMM in the healthy state and the state where cracks of different depths are integrated into the magnet. After that, relevant vital parameters that are affected when this type of fault persists in the machine are collected. Then, prognosis is applied to detect the presence of the crack in one piece of magnet in the electrical machine. Following this, the RUL calculation is performed to predict the remaining time before the crack propagates and a total fracture occurs in the magnet. The method used to execute the prognosis is the hidden Markov model (HMM). The RUL calculation will be performed using Paris equation, being the most important equation that models the growth and propagation of cracks  
hybrid electric vehicle; permanent magnet machine; demagnetization; remaining useful life calculation; Paris equation; hidden Markova model
# Optimal Configuration of Integrated Energy System Based on Energy-Conversion Interface
## 3 Optimal Configuration Model of Energy-Conversion Interface
### Objective Function  
#### 3.1.1 Economic Performance  
As shown in Equations (9)-(14), aiming at minimizing the cost of the ECI, including energy purchase cost \(C_{1}(t)\), device-installation cost \(C_{2}\), device-maintenance cost \(C_{3}(t)\), environmental costs \(C_{4}(t)\), and electricity sales revenue \(C_{5}(t)\), the following variables were optimized, including the type of installed energy-conversion device in the system, the corresponding installed capacity, and the energy-flow ratio at each moment.  
Device-installation cost is calculated by the equivalent annual cost, which is the converted annual input cost considering life- and time-related market factors.  
Device-maintenance cost is related to the working status and output level in each period.  
Environmental cost is calculated by the environmental value converted from the pollutants discharged by the device during system operation [13].  
\[C=\min(\sum C_{1}(t)+C_{2}+\sum C_{3}(t)+\sum C_{4}(t)+\sum C_{5}(t)) \tag{9}\]  
\[C_{1}(t)=\sum P_{i}(t)\lambda_{i} \tag{10}\]  
Figure 6: Optimal energy-conversion-interface configuration system.  
\[C_{2}=\sum\sigma_{i}\cdot N_{i}\cdot\frac{r(1+r)^{\tau_{i}}}{(1+r)^{\tau_{i}}-1} \tag{11}\]  
\[C_{3}(t)=\sum\delta_{i}\cdot P_{i}(t) \tag{12}\]  
\[C_{4}(t)=\sum P_{ij}(t)\lambda_{ij}\gamma_{ij} \tag{13}\]  
\[C_{5}(t)=P_{s}(t)\cdot c_{s} \tag{14}\]  
Equation (10) is the energy purchase cost, which is obtained by multiplying the energy-consumption amount by the corresponding energy price. \(\lambda_{i}\) is the unit price of the \(i\)-th energy.  
Equation (11) is the device-installation cost, expressed by the equivalent annual cost. \(\sigma_{i}\), \(IC_{i}\), \(\tau_{i}\) represent the unit installed price, quantity, and service life of the \(i\)-th device, respectively. \(r\) is the discount rate.  
Equation (12) is the device-maintenance cost, where \(\delta_{i}\) is the maintenance cost corresponding to the unit energy output of the \(i\)-th device.  
Equation (13) is the environmental cost. \(\lambda_{ij}\left(\mathbb{F}/\text{kg}\right)\) is the environmental value of the \(j\)-th pollutant produced by the \(i\)-th device. \(\gamma_{ij}\) (kg/kWh) is the intensity of the \(j\)-th class pollutant corresponding to the output unit energy of the device.  
Equation (14) is the electricity sale revenue, \(P_{s}(t)\) is the sale power, and \(c_{s}\) is the sale price.
## 3 Preliminaries
### Queueing Model  
For this work, we assumed that time is discrete and that time slots are normalized to unit time. We considered a fluid flow queuing system with an infinite size buffer. Given the time interval \([s,t)\) such that \(0\leq s\leq t\), we denote \(A(s,t)\) the cumulative arrival to a store forward node system, shown in Figure 1. Similarly, \(D(s,t)\) denotes the cumulative departures from the system. \(S(s,t)\) defines the service offered by the system.  
We assumed that, along with the non-decreasing (in \(t\)) bivariate processes, \(A(s,t),D(s,t)\), and \(S(s,t)\) are also stationary non-negative random processes with \(A(t,t)=D(t,t)=S(t,t)=0\) for all \(t\geq 0\). The cumulative arrival and service processes for all \(0\leq s\leq t\) are given as follows:  
\[A(s,t) =\sum_{i=0}^{t-1}a_{i}, \tag{1}\] \[S(s,t) =\sum_{i=0}^{t-1}s_{i}, \tag{2}\]  
where \(a_{i}\) and \(s_{i}\) are instantaneous values during the \(i^{th}\) time slot.  
\(W(t)\) denotes the virtual delay of the system at time \(t\). The (min, +) algebra is the basis of network calculus, for which convolution and deconvolution play a crucial role in determining bounds on the system performance. For non-decreasing and strictly positive bivariate processes \(X(s,t)\) and \(Y(s,t)\), the (min, +) convolution and deconvolution are, respectively, defined as,  
\[(X\otimes Y)(s,t) \stackrel{{\Delta}}{{=}}inf\{X(s,\tau)+Y(\tau,t)\} \ \text{where,}\ (s\leq\tau\leq t), \tag{3}\] \[(X\oslash Y)(s,t) \stackrel{{\Delta}}{{=}}sup\{X(\tau,t)-Y(\tau,s)\} \ \text{where,}\ (0\leq\tau\leq s). \tag{4}\]  
In the queueing system, we characterize time-varying systems using a dynamic server that relates the departures of a system to its arrivals as \(D(0,t)\geq(A\otimes S)(0,t)\) for all \(t\geq 0\), which holds with strict equality when the system is linear [10]. An example of a system that satisfies the definition of a dynamic server is a lossless, work-conserving server with a time-varying capacity. Based on this server model, the end-to-end delay and PDV, which are critical performance measures in system evaluation, can be analyzed using network calculus [11].  
For a given queueing system with cumulative arrival \(A(0,t)\) and departure \(D(0,t)\) and for \(t\geq 0\), the virtual delay \(W(t)\) is defined as the time it takes for the last bit received  
Figure 1: Queuing model of a store forward node.  
by time \(t\) to leave the system under a first-come-first-serve (FCFS) scheduling scheme [12]. Therefore,  
\[W(t)\triangleq inf\{w\geq 0:A(0,t)\geq D(0,t+w)\geq 0\}. \tag{5}\]  
Substituting \(D(0,t)\geq(A\otimes S)(0,t)\) and using (min, +) convolution and the deconvolution definitions in (5), we can obtain the following bounds on \(W(t)\)[13] as  
\[W(t)\leq inf\{w\geq 0:(A\odot D)(t+w,t)\geq 0\}. \tag{6}\]
# Antimicrobial Volatiles of the Insect Pathogen _Metarhizium brunneum_
## 1 Introduction  
The rhizosphere is a highly competitive environment in which microbes exhibit different strategies for survival. Entomopathogenice fungi (EPF) are commonly found in the rhizosphere, using root exudates as a source of nutrition but switching to insects when the opportunity arises [1, 2, 3, 4, 5]. EPF form symbiotic relationships with plants, leading to improved plant growth and productivity [1, 6]. Plants treated with EPF species, such as _M. brunneum_ and _Beauveria basisana_, usually have more extensive root systems (lateral roots, root hairs), greater biomass (roots, shoots) and higher crop yields than untreated plants [7, 8, 9]. Besides stimulating plant growth and increasing nitrogen uptake, EPF antagonise plant pathogenicfungi, stimulate plant defences and increase plant tolerance to stress [6; 10; 11]. Exactly how EPF compete with antagonistic microbes in the rhizosphere is unclear.  
Most rhizosphere microbes produce antimicrobial compounds, which include secretory products, as well as low-molecular-weight volatile organic compounds (VOCs), which differ in their specificity and mode of action [12; 13; 14; 15]. VOCs were also reported to promote or inhibit plant growth, trigger plant resistance and attract other micro- and macro-organisms [14; 16; 17; 18; 19; 20; 21]. Although EPF are known to produce VOCs, very few have been identified and characterised. Some of the VOCs have semiochemical properties while others are toxic to invertebrates, including crop pest species like plant-parasitic nematodes and molluscs [22; 23; 24; 25; 26; 27]. VOCs allow [PERSON] to locate _Metahizium anisopliae_ conidia to feed on [28; 29] and ants and termites to discriminate between pathogenic and non-pathogenic strains of _M. anisopliae_[30; 31]. The current study presented the first evidence that _Metahizium_ VOCs have antimicrobial properties that inhibit a wide range of soil microbes. The significance of these compounds to _Metahizium_ survival in the rhizosphere and protection of plants against plant pathogenic microbes is discussed. An understanding of EPF survival strategies in the rhizosphere could help to not only improve plant productivity but also make more efficacious use of these natural biopesticides in pest management programmes.
## 3 Data and Methods
### Burn Severity Classification Using Vegetation Indices  
Burn severity was calculated from the three VIs as the difference between the VI value prior to and following the fire (\(\Delta\)VI = VI\({}_{\text{before}}-\text{VI}_{\text{after}}\)) [23]. A larger (positive) \(\Delta\)VI would correspond to a higher level of burn severity and vice versa. The image that best represented the woody vegetation status before the fire was chosen as VI\({}_{\text{before}}\), instead of taking the image with the closest date prior to the fire (Figure 2). We then compared the field-based burn severity level map (from Section 3.4) with the \(\Delta\)VI map using Two-way ANOVA with Tukey HSD separation procedure to test for significant differences between averaged \(\Delta\)VI in the areas classified in the field as low, moderate, and severe classes.
## 2 Regional Geological Setting  
### Topography and Geomorphology  
Situated in the southern region of the Loess Plateau of Longdong, in Lingtai County, Pingliang City, Gansu Province (Figure 1), the study area is a typical loess hilly-gully landform with a total area of 2039 km\({}^{2}\) and geographic coordinates ranging from 107\({}^{\circ}\)00\({}^{\prime}\) to 107\({}^{\circ}\)57\({}^{\prime}\) east longitude and 34\({}^{\circ}\)02\({}^{\prime}\) to 34\({}^{\circ}\)23\({}^{\prime}\) north latitude. The topography of the region is dominated by loess beam-pebble hills and erosion-accumulation valley plains. It has loess beams and a pebble hills base for the Cretaceous sandstone and gravel, the surface layer is covered with Malan loess, the formation of beams and pebbles interlace terrain, elevation is 910 to 1020 m, the gully is a V-shaped cut, depth is 20 to 150 m, a valley slope gradient of 15 to 40 degrees, and development of the gully and the intensive local collapse landslide. Erosion-accumulation of the river valley plains is distributed in the valley of the Daxi River and its tributaries, the development of river beds, river rambling beach, and multi-level terrace. The first and second terraces are flat and broad, while the third and fourth terraces are sporadically distributed and are base terraces, with a difference of 20 to 40 m in height between the terrace surfaces. Micro-geomorphology in the area is dominated by waterfall holes and gullies, with waterfall holes of 0.2-1.5 m in diameter, which are concentrated in the upper and middle slopes due to precipitation or irrigation seepage, and gullies have proliferated due to the frequency of torrential rains in recent years, aggravating the erosion and damage of slopes.
## 3 Results and Discussion
### The Protein Fraction of MI Silages
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multirow{2}{*}{**Treatments**} & \multicolumn{4}{c}{**Ensiling Days**} & \multirow{2}{*}{**SEM**} & \multicolumn{4}{c}{\(p\)**-Value**} \\ \cline{3-10}  & & **3** & **7** & **14** & **30** & & **D** & **T** & **D**\(\times\)**T** \\ \hline Crude protein & CK & 134 \({}^{\text{A,b}}\) & 147 \({}^{\text{A,a}}\) & 154 \({}^{\text{A,a}}\) & 153 \({}^{\text{A,a}}\) & & & & \\ (g/kg DM) & CA1 & 136 \({}^{\text{A,a}}\) & 138 \({}^{\text{A,B,a}}\) & 137 \({}^{\text{B,a}}\) & 146 \({}^{\text{A,B,a}}\) & 8.57 & 0.000 & 0.000 & 0.011 \\  & CA2 & 133 \({}^{\text{A,b,c}}\) & 130 \({}^{\text{B,c}}\) & 143 \({}^{\text{B,a}}\) & 139 \({}^{\text{B,a,b}}\) & & & & \\ True protein & CK & 878 \({}^{\text{A,a}}\) & 792 \({}^{\text{A,b}}\) & 679 \({}^{\text{B,c}}\) & 620 \({}^{\text{B,d}}\) & & & & \\ (g/kg TN) & CA1 & 816 \({}^{\text{B,a}}\) & 748 \({}^{\text{B,b}}\) & 752 \({}^{\text{A,b}}\) & 625 \({}^{\text{A,b}}\) & 80.1 & 0.000 & 0.679 & 0.000 \\  & CA2 & 808 \({}^{\text{B,a}}\) & 764 \({}^{\text{A,B,b}}\) & 678 \({}^{\text{B,c}}\) & 690 \({}^{\text{A,c}}\) & & & & \\ Non-protein & CK & 122 \({}^{\text{A,b}}\) & 208 \({}^{\text{B,c}}\) & 321 \({}^{\text{A,b}}\) & 380 \({}^{\text{A,a}}\) & & & & \\ nitrogen & CA1 & 184 \({}^{\text{A,c}}\) & 252 \({}^{\text{A,b}}\) & 248 \({}^{\text{B,b}}\) & 375 \({}^{\text{A,B,a}}\) & 80.1 & 0.000 & 0.679 & 0.000 \\ (g/kg TN) & CA2 & 196 \({}^{\text{A,c}}\) & 236 \({}^{\text{A,b}}\) & 322 \({}^{\text{A,a}}\) & 310 \({}^{\text{B,a}}\) & & & & \\ Ammonia-N & CK & 4.40 \({}^{\text{A}}\) & 7.38 \({}^{\text{A}}\) & 14.6 \({}^{\text{A}}\) & 18.9 \({}^{\text{A}}\) & & & & \\ (g/kg TN) & CA1 & 3.71 \({}^{\text{B}}\) & 4.57 \({}^{\text{B}}\) & 7.58 \({}^{\text{B}}\) & 10.8 \({}^{\text{B}}\) & 5.15 & 0.000 & 0.000 & 0.000 \\  & CA2 & 1.76 \({}^{\text{B}}\) & 2.45 \({}^{\text{C}}\) & 3.95 \({}^{\text{C}}\) & 6.07 \({}^{\text{C}}\) & & & & \\ \hline \hline \end{tabular} D, ensiling days; T, treatments; D \(\times\) T, the interaction of ensiling days and treatments; DM, dry matter; CK, the control; CA1, 1% citric acid; CA2, 2% citric acid; TN, total nitrogen. Different lowercase letters \({}^{(\text{A,c})}\) in the same row indicate significant differences at \(p<0.05\); different uppercase letters \({}^{(\text{A,b})}\) in the same column indicate significant differences at \(p<0.05\).  
\end{table} 
Table 2: The protein fractions of mulberry leaf silages. silages treated with 2% CA showed the lowest ammonia-N content during the ensiling process. The above results indicate that CA improved the silage quality of ML.
# Multiport Energy Management System Design for a 150 kW Range-Extended Towing Vessel
## 2 EMS Model for RETV
### ESS Model  
#### 2.2.1 Lithium Battery Model  
The charging and discharging process of the lithium battery involves complex electrochemical reactions [32]. This study adopted the equivalent circuit model to describe the battery's characteristics [33; 34]. It used an internal resistance model to explain the battery's charge and discharge processes.  
Discharge (\(i>0\)):  
\[f_{1}(it,\,i^{*},\,i\,,\,Exp)=E_{0}-K\cdot\frac{Q}{Q-it}\cdot i^{*}-K\cdot\frac {Q}{Q-it}\cdot it+Laplace^{-1}\bigg{(}\frac{Exp(s)}{Sel(s)}\cdot 0\bigg{)} \tag{1}\]  
Figure 1: The proposed EMS for a 150 kW RETV.  
Figure 2: Circuit topology of a three-phase controlled bridge-type rectifier.  
Charge (\(i<0\)):  
\[f_{2}(it,\,i^{*},\,i,\,Exp)=E_{0}-K\cdot\frac{Q}{Q-it}\,i^{*}-K\cdot\frac{Q}{Q-it} \cdot it+Laplace^{-1}\bigg{(}\frac{Exp(s)}{Sel(s)}.\frac{1}{s}\bigg{)} \tag{2}\]  
where  
\(E_{0}\) is the battery's constant voltage;  
\(Exp(s)\) is the battery's exponential area characteristic;  
\(K\) is the battery's polarity constant;  
\(i^{*}\) is the battery's low-frequency current characteristics;  
\(it\) is the battery's extraction capacity;  
\(Q\) is the battery's maximum battery capacity.
## 3 Experimental Study
### Experimental Design
#### 3.1.3 Design of Test Conditions  
To effectively and quantitatively analyze the influence of roughness on grouting diffusion, a triangular saw-tooth model was used to simulate the fracture roughness in this test. The cross profile of saw-tooth strips is an isosceles right-angled triangle with a height of 2 mm and a width of 4 mm. The saw-tooth strips are equally spaced on the lower surface of the fracture. The density of the saw-tooth distribution varies in different test conditions. To clearly observe the grouting diffusion process, the upper surface was kept smooth. The saw teeth were glued to the lower surface with a distribution density of one per 100 mm, one per 50 mm, and one per 25 mm. The different test conditions were defined as R1, R2, and R3, which are shown in Figure 9. During the experiment, the grouting pressure was maintained at 0.05 MPa, and the original fracture openness was 5 mm.